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/tags/1.0/install.csh
0,0 → 1,193
# ----- Load modules --------------------------
 
module load netcdf/4.2.1-pgf90
module list
 
# ---- set some directories and other stuff ---
 
set mode = $1
set svnpath=https://svn.iac.ethz.ch/pub/pvinversion.ecmwf/
set bdir = ${PWD}
 
# ----- Set libraries and includes ------------
 
set libs = "-L ${bdir}/lib"
set libs = "${libs} -lcdfio"
set libs = "${libs} -lcdfplus"
set libs = "${libs} -lipo"
set libs = "${libs} -lgm2em"
 
set ncdf_incs = `nc-config --fflags`
set ncdf_libs = `nc-config --flibs`
 
# ----- Create a new SVN tag ------------------
tag:
 
if ( "${mode}" == "tag" ) then
svn info
if ( "${#argv}" != 2 ) then
echo "Usage: install.csh tag id <id=tag number>"
else
set tagnr = $2
endif
svn copy ${svnpath}/trunk ${svnpath}/tags/${tagnr} -m "Release ${tagnr}"
exit 0
endif
 
 
if ( "${mode}" != "clean" ) goto compile
# ----- Make clean ----------------------------
clean:
 
if ( "${mode}" != "clean" ) goto compile
 
cd ${bdir}/lib
foreach lib ( libcdfio libcdfplus libipo libgm2em )
\rm -f ${lib}.o
end
 
cd ${bdir}/diag/
foreach tool ( calc_qgpv check_boundcon difference hydrostatic qvec_analysis )
\rm -f ${tool}.o
\rm -f ${tool}
end
 
cd ${bdir}/post/
foreach tool ( add2p rotate_lalo )
\rm -f ${tool}.o
\rm -f ${tool}
end
 
cd ${bdir}/prep/
foreach tool ( coastline cutnetcdf def_anomaly p2z ref_profile rotate_grid z2s )
\rm -f ${tool}.o
\rm -f ${tool}
end
 
cd ${bdir}/pvin/
foreach tool ( inv_cart prep_iteration pv_to_qgpv z2s )
\rm -f ${tool}.o
\rm -f ${tool}
end
 
cd ${bdir}/spec/
foreach tool ( modify_anomaly )
\rm -f ${tool}.o
\rm -f ${tool}
end
 
# ----- Compile -------------------------------
compile:
 
if ( "${mode}" != "compile" ) goto done
 
cd ${bdir}/lib
 
foreach lib ( libcdfio libcdfplus libipo libgm2em )
 
\rm -f ${lib}.o
 
echo "pgf90 -c ${lib}.f ${ncdf_incs}"
pgf90 -c ${lib}.f ${ncdf_incs}
 
end
 
cd ${bdir}/diag/
 
foreach tool ( calc_qgpv check_boundcon difference hydrostatic qvec_analysis )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${bdir}/post/
 
foreach tool ( add2p rotate_lalo )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${bdir}/prep/
 
foreach tool ( coastline cutnetcdf def_anomaly p2z ref_profile rotate_grid z2s )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${bdir}/pvin/
 
foreach tool ( inv_cart prep_iteration pv_to_qgpv z2s )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${bdir}/spec/
 
foreach tool ( modify_anomaly )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
# ----- Done ----------------------------------
done:
 
exit 0
Property changes:
Added: svn:executable
/tags/1.0/diag/calc_qgpv.f
0,0 → 1,819
PROGRAM main_calc_qgpv
 
c ********************************************************************************
c * CALCULATE QUASI-GEOSTROPHIC PV ACCORDING TO ITS DEFINITION *
c * Michael Sprenger / Summer, Autumn 2006 *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Declaration of variables, parameters, externals and common blocks
c --------------------------------------------------------------------------------
 
implicit none
 
c Input and output file
character*80 diagfile
character*80 referfile
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real deltax,deltay,deltaz
real mdv
real, allocatable,dimension (:,:) :: coriol
 
c Reference state
real, allocatable,dimension (:) :: nsqref
real, allocatable,dimension (:) :: thetaref
real, allocatable,dimension (:) :: rhoref
real, allocatable,dimension (:) :: pressref
real, allocatable,dimension (:) :: zref
 
c 3d fields for calculation of qgPV
real,allocatable,dimension (:,:,:) :: qgpv,th,uu,vv
 
c Auxiliary variables
integer i,j,k
integer stat
character*80 varname
 
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* CALC_QGPV *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) diagfile
read(10,*) referfile
close(10)
print*
print*,trim(diagfile)
print*,trim(referfile)
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> diagfile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for Coriolis parameters
allocate(coriol(0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating coriol'
 
c Allocate memory for reference profile
allocate(rhoref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rhoref'
allocate(pressref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pressref'
allocate(thetaref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating thetaref'
allocate(nsqref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsqref'
allocate(zref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating zref'
c Allocate memory for 3d fields
allocate(qgpv(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating qgpv'
allocate(uu(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating uu'
allocate(vv(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating vv'
allocate(th(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating th'
 
c --------------------------------------------------------------------------------
c Calculate the qgPV from definition and put it onto file
c --------------------------------------------------------------------------------
 
c Read data from file
varname='U'
call read_inp (uu,varname,diagfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='V'
call read_inp (vv,varname,diagfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='TH'
call read_inp (th,varname,diagfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read reference profile and grid parameters
call read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> referfile)
deltax=1000.*deltax
deltay=1000.*deltay
print*,'Deltax,deltay,deltaz =',deltax,deltay,deltaz
 
c Calculate qgPV
print*,'C qgPV'
call calc_qgpv (qgpv,uu,vv,th,
> rhoref,pressref,nsqref,thetaref,coriol,
> nx,ny,nz,deltax,deltay,deltaz,mdv)
 
c Write result to netcdf file
varname='QGPV_DIA'
call write_inp (qgpv,varname,diagfile,nx,ny,nz)
 
end
 
c ********************************************************************************
c * NETCDF OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Write input field to netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE write_inp (field,fieldname,pvsrcfile,nx,ny,nz)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field (0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(0:nx,0:ny,0:nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Get grid parameters from THETA
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Save variables (write definition, if necessary)
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
endif
call putdat(cdfid,varname,time(1),0,field,stat)
print*,'W ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
return
 
c Exception handling
998 print*,'Write_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Read input fields
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters from theta
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*, 'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Read refernece profile from netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> pvsrcfile)
 
c Read the reference profile from file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nx,nny,nz : Grid dimension in x,y,z direction
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
c coriol : Coriolis parameter (s^-1)
c pvsrcfile : Input file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
real deltax,deltay,deltaz
real coriol (0:nx,0:ny)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real x(0:nx,0:ny),y(0:nx,0:ny)
real mean,count
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
 
c Read data from netcdf file
isok=0
varname='NSQREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='RHOREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
isok=0
varname='THETAREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='PREREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ZREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='CORIOL'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,coriol,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='X'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,x,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='Y'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,y,stat)
if (stat.ne.0) goto 997
 
c Close netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Determine the grid spacings <deltax, deltay, deltaz>
mean=0.
count=0.
do i=1,nx
do j=0,ny
mean=mean+abs(x(i,j)-x(i-1,j))
count=count+1.
enddo
enddo
deltax=mean/count
 
mean=0.
count=0.
do j=1,ny
do i=0,nx
mean=mean+abs(y(i,j)-y(i,j-1))
count=count+1.
enddo
enddo
deltay=mean/count
 
mean=0.
count=0.
do k=1,nz-1
mean=mean+abs(zref(k+1)-zref(k-1))
count=count+1.
enddo
deltaz=mean/count
 
return
 
c Exception handling
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
 
c --------------------------------------------------------------------------------
c Calculate qgPV from wind and theta
c --------------------------------------------------------------------------------
 
subroutine calc_qgpv (qgpv,uu,vv,th,
> rhoref,pressref,nsqref,thetaref,coriol,
> nx,ny,nz,deltax,deltay,deltaz,mdv)
 
c Calculate qgPV from wind and potential temperature according to
c equation 2.9 p 16 Thesis Rene Fehlmann. Note a cartesian grid with
c equidistant grid spacings <deltax,deltay,deltaz> is assumend. No
c 'correction' is made for spherical geoemtry.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real qgpv(0:nx,0:ny,0:nz)
real uu(0:nx,0:ny,0:nz)
real vv(0:nx,0:ny,0:nz)
real th(0:nx,0:ny,0:nz)
real rhoref(0:2*nz)
real nsqref(0:2*nz)
real thetaref(0:2*nz)
real pressref(0:2*nz)
real deltax,deltay,deltaz
real mdv
real coriol(0:nx,0:ny)
 
c Numerical epsilon and physical constants
real g
parameter (g=9.81)
real eps
parameter (eps=0.01)
real scale
parameter (scale=1e6)
 
c Auxiliary variables
integer i,j,k
integer kk,jj
real dvdx(0:nx,0:ny,0:nz)
real dudy(0:nx,0:ny,0:nz)
real dtdz(0:nx,0:ny,0:nz)
real t1,t2
c Calculate horizontal derivatives dudy and dvdx of velocity
do k=0,nz
do j=0,ny
do i=0,nx
c Calculate dudy
if (j.eq.0) then
if ( (abs(uu(i,1,k)-mdv).gt.eps).and.
> (abs(uu(i,0,k)-mdv).gt.eps)) then
dudy(i,0,k)=(uu(i,1,k)-uu(i,0,k))/deltay
else
dudy(i,0,k)=mdv
endif
elseif (j.eq.ny) then
if ( (abs(uu(i,ny, k)-mdv).gt.eps).and.
> (abs(uu(i,ny-1,k)-mdv).gt.eps)) then
dudy(i,ny,k)=(uu(i,ny,k)-uu(i,ny-1,k))/deltay
else
dudy(i,ny,k)=mdv
endif
else
if ( (abs(uu(i,j+1,k)-mdv).gt.eps).and.
> (abs(uu(i,j-1,k)-mdv).gt.eps)) then
dudy(i,j,k)=(uu(i,j+1,k)-uu(i,j-1,k))/(2.*deltay)
else
dudy(i,j,k)=mdv
endif
endif
 
c Calculate dvdx
if (i.eq.0) then
if ((abs(vv(1,j,k)-mdv).gt.eps).and.
> (abs(vv(0,j,k)-mdv).gt.eps)) then
dvdx(0,j,k)=(vv(1,j,k)-vv(0,j,k))/deltax
else
dvdx(0,j,k)=mdv
endif
elseif (i.eq.nx) then
if ((abs(vv(nx, j,k)-mdv).gt.eps).and.
> (abs(vv(nx-1,j,k)-mdv).gt.eps)) then
dvdx(nx,j,k)=(vv(nx,j,k)-vv(nx-1,j,k))/deltax
else
dvdx(nx,j,k)=mdv
endif
else
if ((abs(vv(i+1,j,k)-mdv).gt.eps).and.
> (abs(vv(i-1,j,k)-mdv).gt.eps)) then
dvdx(i,j,k)=(vv(i+1,j,k)-vv(i-1,j,k))/(2.*deltax)
else
dvdx(i,j,k)=mdv
endif
endif
 
enddo
enddo
enddo
 
c Calculate vertical derivative of potential temperature
do i=0,nx
do j=0,ny
do k=0,nz
 
if (k.eq.0) then
if ((abs(th(i,j,2)-mdv).gt.eps).and.
> (abs(th(i,j,1)-mdv).gt.eps)) then
t1=rhoref(2)*th(i,j,1)/thetaref(2)/nsqref(2)*g
t2=rhoref(0)*th(i,j,0)/thetaref(0)/nsqref(0)*g
dtdz(i,j,0)=(t1-t2)/deltaz
else
dtdz(i,j,0)=mdv
endif
else if (k.eq.nz) then
if ((abs(th(i,j,nz )-mdv).gt.eps).and.
> (abs(th(i,j,nz-1)-mdv).gt.eps)) then
kk=2*nz
t1=rhoref(kk )*th(i,j,nz )/
> thetaref(kk)/nsqref(kk)*g
t2=rhoref(kk-2)*th(i,j,nz-1)/
> thetaref(kk-2)/nsqref(kk-2)*9.8
dtdz(i,j,nz)=(t1-t2)/deltaz
else
dtdz(i,j,nz)=mdv
endif
else
if ((abs(th(i,j,k+1)-mdv).gt.eps).and.
> (abs(th(i,j,k )-mdv).gt.eps).and.
> (abs(th(i,j,k-1)-mdv).gt.eps)) then
kk=2*k
t1=rhoref(kk+1)*(th(i,j,k)+th(i,j,k+1))/2.
> /thetaref(kk+1)/nsqref(kk+1)*g
t2=rhoref(kk-1)*(th(i,j,k)+th(i,j,k-1))/2.
> /thetaref(kk-1)/nsqref(kk-1)*g
dtdz(i,j,k)=(t1-t2)/deltaz
else
dtdz(i,j,k)=mdv
endif
endif
enddo
enddo
enddo
c Calculate qgPV
do i=0,nx
do j=0,ny
do k=0,nz
kk=2*k
 
if ((abs(dudy(i,j,k)-mdv).gt.eps).and.
> (abs(dvdx(i,j,k)-mdv).gt.eps).and.
> (abs(dtdz(i,j,k)-mdv).gt.eps)) then
qgpv(i,j,k)=-dudy(i,j,k)+dvdx(i,j,k)+
> coriol(i,j)*dtdz(i,j,k)/rhoref(kk)
else
qgpv(i,j,k)=mdv
endif
enddo
enddo
enddo
 
end
 
Property changes:
Added: svn:executable
/tags/1.0/diag/check_boundcon.f
0,0 → 1,871
 
PROGRAM set_boundcon
 
c ************************************************************************
c * Set boundary conditions for inversion; lower and upper boundary *
c * conditions for potential temperature; lateral boundary conditions *
c * for zonal and meridional wind; in particular, missing data values *
c * are removed. *
c * *
c * Michael Sprenger / Summer 2006 *
c ************************************************************************
 
c --------------------------------------------------------------------------------
c Declaration of variables, parameters, externals and common blocks
c --------------------------------------------------------------------------------
 
implicit none
 
c Input and output file
character*80 anomafile
character*80 referfile
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real mdv
real deltax,deltay,deltaz
real, allocatable,dimension (:,:) :: coriol
 
c Reference state
real, allocatable,dimension (:) :: nsqref
real, allocatable,dimension (:) :: thetaref
real, allocatable,dimension (:) :: rhoref
real, allocatable,dimension (:) :: pressref
real, allocatable,dimension (:) :: zref
 
C Boundary conditions
real, allocatable,dimension (:,:) :: thetatop
real, allocatable,dimension (:,:) :: thetabot
real, allocatable,dimension (:,:) :: ua
real, allocatable,dimension (:,:) :: ub
real, allocatable,dimension (:,:) :: va
real, allocatable,dimension (:,:) :: vb
 
c 3d arrays
real,allocatable,dimension (:,:,:) :: th_anom,pv_anom
real,allocatable,dimension (:,:,:) :: uu_anom,vv_anom
 
c Auxiliary variables
integer i,j,k,kk
integer stat
character*80 varname
integer n1,n2
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* CHECK_BOUNDCON *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) anomafile
read(10,*) referfile
close(10)
print*
print*,trim(anomafile)
print*,trim(referfile)
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> anomafile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for 3d arrays
allocate(pv_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv_anom'
allocate(th_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating th_anom'
allocate(uu_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating uu_anom'
allocate(vv_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating vv_anom'
 
c Allocate memory for reference profile
allocate(rhoref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rhoref'
allocate(pressref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pressref'
allocate(thetaref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating thetaref'
allocate(nsqref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsqref'
allocate(zref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating zref'
 
c Allocate memory for Coriolis parameter
allocate(coriol(0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating f'
 
c Allocate memory for boundary conditions
allocate(thetatop(0:nx,0:ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array thetatop ***'
allocate(thetabot(0:nx,0:ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array thetabot ***'
allocate(ua(0:nx,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ua ***'
allocate(ub(0:nx,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ub ***'
allocate(va(0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array va ***'
allocate(vb(0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array vb ***'
 
c Read reference profile and ngrid parameters
call read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> referfile)
deltax=1000.*deltax
deltay=1000.*deltay
print*,'Deltax,deltay,deltaz =',deltax,deltay,deltaz
c Read data from MOD file
varname='QGPV'
call read_inp (pv_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='TH'
call read_inp (th_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='U'
call read_inp (uu_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='V'
call read_inp (vv_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
 
c --------------------------------------------------------------------------------
c Consistency check for boundary conditions and adaptions
c --------------------------------------------------------------------------------
 
c Copy 3d to boundary conditions
do i=0,nx
do j=0,ny
thetatop(i,j)=th_anom(i,j,nz)
thetabot(i,j)=th_anom(i,j,0)
enddo
enddo
do i=0,nx
do k=0,nz
ua(i,k)=uu_anom(i, 0,k)
ub(i,k)=uu_anom(i,ny,k)
enddo
enddo
do j=0,ny
do k=0,nz
va(j,k)=vv_anom( 0,j,k)
vb(j,k)=vv_anom(nx,j,k)
enddo
enddo
 
c Check the lower and upper boundary condition for consistency check
print*
call combouncon(pv_anom,nsqref,rhoref,thetatop,
> thetabot,thetaref,coriol,ua,ub,va,vb,
> nx,ny,nz,deltax,deltay,deltaz)
print*
 
 
end
 
 
c ********************************************************************************
c * NETCDF INPUT AND OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Read input fields for reference profile
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters from theta
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*, 'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='QGPV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read refernece profile from netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> pvsrcfile)
 
c Read the reference profile from file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nx,nny,nz : Grid dimension in x,y,z direction
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
c coriol : Coriolis parameter (s^-1)
c pvsrcfile : Input file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
real deltax,deltay,deltaz
real coriol (0:nx,0:ny)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real x(0:nx,0:ny),y(0:nx,0:ny)
real mean,count
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
 
c Read data from netcdf file
isok=0
varname='NSQREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='RHOREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
isok=0
varname='THETAREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='PREREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ZREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='CORIOL'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,coriol,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='X'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,x,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='Y'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,y,stat)
if (stat.ne.0) goto 997
 
c Close netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Determine the grid spacings <deltax, deltay, deltaz>
mean=0.
count=0.
do i=1,nx
do j=0,ny
mean=mean+abs(x(i,j)-x(i-1,j))
count=count+1.
enddo
enddo
deltax=mean/count
 
mean=0.
count=0.
do j=1,ny
do i=0,nx
mean=mean+abs(y(i,j)-y(i,j-1))
count=count+1.
enddo
enddo
deltay=mean/count
 
mean=0.
count=0.
do k=1,nz-1
mean=mean+abs(zref(k+1)-zref(k-1))
count=count+1.
enddo
deltaz=mean/count
 
return
 
c Exception handling
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
stop
 
end
 
 
c ********************************************************************************
c * BOUNDARY CONDITIONS - CONSISTENCY CHECK AND ADAPTIONS *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Boundary condition
c --------------------------------------------------------------------------------
 
subroutine combouncon(pv,nsq,rhoref,thetatop,
> thetabot,thetaref,coriol,
> ua,ub,va,vb,nx,ny,nz,dx,dy,dz)
 
c Evaluate the consistency integrals A.7 from Rene's dissertation. This inegral
c is a necessary condition that the von Neumann problem has a unique solution.
c Adjust the upper and lower boundary conditions on <thetabot> and <thetatop>, so
c that the consitency check is ok.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real dx,dy,dz
real pv(0:nx,0:ny,0:nz)
real nsq(0:2*nz)
real rhoref(0:2*nz)
real thetatop(0:nx,0:ny)
real thetabot(0:nx,0:ny)
real thetaref(0:2*nz)
real coriol(0:nx,0:ny)
real ua(0:nx,0:nz)
real ub(0:nx,0:nz)
real va(0:ny,0:nz)
real vb(0:ny,0:nz)
 
c Numerical and physical parameters
real g
parameter (g=9.81)
 
c Auxiliary variables
integer i,j,k
real dxy,dxz,dyz,dxyz
real integr,denombot,denomtop,denom
real shifttop,shiftbot
 
c Set the area and volume infinitesimals for integration
dxy =dx*dy
dxz =dx*dz
dyz =dy*dz
dxyz=dx*dy*dz
 
c Init integration variables
integr=0.
 
c Inner
do k=1,nz-1
do i=1,nx-1
do j=1,ny-1
integr=integr+dxyz*rhoref(2*k)*pv(i,j,k)
enddo
enddo
enddo
 
c ZY plane
do k=1,nz-1
do j=1,ny-1
integr=integr+dyz*
> rhoref(2*k)*(dx*pv(0, j,k)+va(j,k))
c
integr=integr+dyz*
> rhoref(2*k)*(dx*pv(nx,j,k)-vb(j,k))
enddo
enddo
 
c ZX plane
do k=1,nz-1
do i=1,nx-1
integr=integr+dxz*
> rhoref(2*k)*(dy*pv(i,0,k)-ua(i,k))
c
integr=integr+dxz*
> rhoref(2*k)*(dy*pv(i,ny,k)+ub(i,k))
enddo
enddo
 
c XY plane
do i=1,nx-1
do j=1,ny-1
integr=integr+dxy*rhoref(0)*(
> dz*pv(i,j,0)+coriol(i,j)*g*thetabot(i,j)/
> (nsq(0)*thetaref(0)))
c
integr=integr+dxy*rhoref(2*nz)*(
> dz*pv(i,j,nz)-coriol(i,j)*g*thetatop(i,j)/
> (nsq(2*nz)*thetaref(2*nz)))
c
enddo
enddo
 
c X edges
do i=1,nx-1
integr=integr+dx*
> rhoref(0)*(dyz*pv(i,0,0)-
> dz*ua(i,0)+dy*coriol(i,0)*g*thetabot(i,0)/
> (nsq(0)*thetaref(0)))
c
integr=integr+dx*
> rhoref(0)*(dyz*pv(i,ny,0)+
> dz*ub(i,0)+dy*coriol(i,ny)*g*thetabot(i,ny)/
> (nsq(0)*thetaref(0)))
c
integr=integr+dx*
> rhoref(2*nz)*(dyz*pv(i,0,nz)-
> dz*ua(i,nz)-dy*coriol(i,0)*g*thetatop(i,0)/
> (nsq(2*nz)*thetaref(2*nz)))
 
integr=integr+dx*
> rhoref(2*nz)*(dyz*pv(i,ny,nz)+
> dz*ub(i,nz)-dy*coriol(i,ny)*g*thetatop(i,ny)/
> (nsq(2*nz)*thetaref(2*nz)))
c
enddo
 
c Y edges
do j=1,ny-1
integr=integr+dy*
> rhoref(0)*(dxz*pv(0,j,0)+
> dz*va(j,0)+dx*coriol(0,j)*g*thetabot(0,j)/
> (nsq(0)*thetaref(0)))
c
integr=integr+dy*
> rhoref(0)*(dxz*pv(nx,j,0)-
> dz*vb(j,0)+dx*coriol(nx,j)*g*thetabot(nx,j)/
> (nsq(0)*thetaref(0)))
c
integr=integr+dy*
> rhoref(2*nz)*(dxz*pv(0,j,nz)+
> dz*va(j,nz)-dx*coriol(0,j)*g*thetatop(0,j)/
> (nsq(2*nz)*thetaref(2*nz)))
c
integr=integr+dy*
> rhoref(2*nz)*(dxz*pv(nx,j,nz)-
> dz*vb(j,nz)-dx*coriol(nx,j)*g*thetatop(nx,j)/
> (nsq(2*nz)*thetaref(2*nz)))
c
enddo
 
c Z edges
do k=1,nz-1
integr=integr+dz*
> rhoref(2*k)*(dxy*pv(0,0,k)+
> dy*va(0,k)-dx*ua(0,k))
c
integr=integr+dz*
> rhoref(2*k)*(dxy*pv(nx,0,k)-
> dy*vb(0,k)-dx*ua(nx,k))
c
integr=integr+dz*
> rhoref(2*k)*(dxy*pv(0,ny,k)+
> dy*va(ny,k)+dx*ub(0,k))
c
integr=integr+dz*
> rhoref(2*k)*(dxy*pv(nx,ny,k)-
> dy*vb(ny,k)+dx*ub(nx,k))
enddo
 
c Points
integr=integr+rhoref(0)*(dxyz*pv(0,0,0)+
> dyz*va(0,0)-dxz*ua(0,0)+
> dxy*coriol(0,0)*g*thetabot(0,0)/
> (nsq(0)*thetaref(0)))
c
integr=integr+rhoref(0)*(dxyz*pv(nx,0,0)-
> dyz*vb(0,0)-dxz*ua(nx,0)+
> dxy*coriol(nx,0)*g*thetabot(nx,0)/
> (nsq(0)*thetaref(0)))
c
integr=integr+rhoref(0)*(dxyz*pv(0,ny,0)+
> dyz*va(ny,0)+dxz*ub(0,0)+
> dxy*coriol(0,ny)*g*thetabot(0,ny)/
> (nsq(0)*thetaref(0)))
c
integr=integr+rhoref(0)*(dxyz*pv(nx,ny,0)-
> dyz*vb(ny,0)+dxz*ub(nx,0)+
> dxy*coriol(nx,ny)*g*thetabot(nx,ny)/
> (nsq(0)*thetaref(0)))
c
integr=integr+rhoref(2*nz)*(dxyz*pv(0,0,nz)+
> dyz*va(0,nz)-dxz*ua(0,nz)-
> dxy*coriol(0,0)*g*thetatop(0,0)/
> (nsq(2*nz)*thetaref(2*nz)))
c
integr=integr+rhoref(2*nz)*(dxyz*pv(nx,0,nz)-
> dyz*vb(0,nz)-dxz*ua(nx,nz)-
> dxy*coriol(nx,0)*g*thetatop(nx,0)/
> (nsq(2*nz)*thetaref(2*nz)))
c
integr=integr+rhoref(2*nz)*(dxyz*pv(0,ny,nz)+
> dyz*va(ny,nz)+dxz*ub(0,nz)-
> dxy*coriol(0,ny)*g*thetatop(0,ny)/
> (nsq(2*nz)*thetaref(2*nz)))
c
integr=integr+rhoref(2*nz)*(dxyz*pv(nx,ny,nz)-
> dyz*vb(ny,nz)+dxz*ub(nx,nz)-
> dxy*coriol(nx,ny)*g*thetatop(nx,ny)/
> (nsq(2*nz)*thetaref(2*nz)))
c
 
c Get the integrals from the reference state at bottom and top
denombot=0.
denomtop=0.
do i=0,nx
do j=0,ny
denombot=denombot+dxy*
> rhoref(0)*coriol(i,j)*g/
> (nsq(0)*thetaref(0))
c
denomtop=denomtop+dxy*
> rhoref(2*nz)*coriol(i,j)*g/
> (nsq(2*nz)*thetaref(2*nz))
enddo
enddo
denom=denomtop-denombot
c Determine the deviation of potential temperature from reference profile
shiftbot=0.
shifttop=0.
do i=0,nx
do j=0,ny
shifttop=shifttop+thetatop(i,j)
shiftbot=shiftbot+thetabot(i,j)
enddo
enddo
shifttop=shifttop/real((nx+1)*(ny+1))
shiftbot=shiftbot/real((nx+1)*(ny+1))
 
c Write some information about the consitency integrals
print*,'Consistency Check for boundary'
print*,' integ = ', integr
print*,' denombot = ', denombot
print*,' denomtop = ', denomtop
print*,' denom = ', denom
print*,' theta adjustment = ', integr/denom
print*,' theta shift @ top = ', shifttop,
> thetaref(2*nz)
print*,' theta shift @ bot = ', shiftbot,
> thetaref(0)
 
end
Property changes:
Added: svn:executable
/tags/1.0/diag/check_boundcon.m
0,0 → 1,267
% -------------------------------------------------------------------------
% Load files
% -------------------------------------------------------------------------
 
% Base directory and filename
base = '/net/rossby/lhome/sprenger/PV_Inversion_Tool/';
folder = base;
filename = 'Z1_20060115_18';
disp([folder filename])
 
% First image (otherwise first image is not correctly written)
figname = [base '/test.eps'];
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% Load variables from file (on model levels)
z_th = cdf_loadV(folder,filename,'TH');
z_uu = cdf_loadV(folder,filename,'U');
z_vv = cdf_loadV(folder,filename,'V');
 
% -------------------------------------------------------------------------
% Lower boundary condition for potential temperature
% -------------------------------------------------------------------------
 
ilev=1;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set projection
load coast
h=axesm('MapProjection','eqdcylin');
setm(gca,'FLatLimit',[z_th.latmin z_th.latmax],'FLonLimit',[z_th.lonmin z_th.lonmax]);
h=plotm(lat,long);
gridm;
 
% Scale the plotting field for color map
fld=squeeze(z_th.var(ilev,:,:));
c_map = scale_col(230:5:310,fld);
 
% Plot TH
lat=z_th.ymin + (0:z_th.ny-1) * z_th.dy;
lon=z_th.xmin + (0:z_th.nx-1) * z_th.dx;
[C,h]=contourfm(lat,lon,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Lower Boundary Condition : Potential Temperature @' num2str(z_th.aklay(ilev)) ' m ASL' ]);
 
% Save figure
figname = [ base '/bound_lower_th_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% -------------------------------------------------------------------------
% Upper boundary condition for potential temperature
% -------------------------------------------------------------------------
 
ilev=z_th.nz;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set projection
load coast
h=axesm('MapProjection','eqdcylin');
setm(gca,'FLatLimit',[z_th.latmin z_th.latmax],'FLonLimit',[z_th.lonmin z_th.lonmax]);
h=plotm(lat,long);
gridm;
 
% Scale the plotting field for color map
fld=squeeze(z_th.var(ilev,:,:));
c_map = scale_col(450:10:550,fld);
 
% Plot TH
lat=z_th.ymin + (0:z_th.ny-1) * z_th.dy;
lon=z_th.xmin + (0:z_th.nx-1) * z_th.dx;
[C,h]=contourfm(lat,lon,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Upper Boundary Condition : Potential Temperature @ ' num2str(z_th.aklay(ilev)) ' m ASL' ]);
 
% Save figure
figname = [ base '/bound_upper_th_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
 
% -------------------------------------------------------------------------
% Southern lateral boundary condition for zonal wind
% -------------------------------------------------------------------------
 
ilev=1;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(z_uu.var(:,ilev,:));
c_map = scale_col(-50:10:50,fld);
 
% Plot
lev=z_uu.aklev/10000;
lon=z_uu.xmin + (0:z_uu.nx-1) * z_uu.dx;
[C,h]=contourf(lon,lev,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Southern lateral Boundary Condition : Zonal Wind @ ' num2str(z_uu.ymin) '^\circ N' ]);
xlabel('Longitude');
ylabel('Height [km]');
 
% Save figure
figname = [ base '/bound_south_uu_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
 
% -------------------------------------------------------------------------
% Northern lateral boundary condition for zonal wind
% -------------------------------------------------------------------------
 
ilev=z_uu.ny;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(z_uu.var(:,ilev,:));
c_map = scale_col(-50:10:50,fld);
 
% Plot
lev=z_uu.aklev/10000;
lon=z_uu.xmin + (0:z_uu.nx-1) * z_uu.dx;
[C,h]=contourf(lon,lev,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Northern lateral Boundary Condition : Zonal Wind @ ' num2str(z_uu.ymax) '^\circ N' ]);
xlabel('Longitude');
ylabel('Height [km]');
 
% Save figure
figname = [ base '/bound_north_uu_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% -------------------------------------------------------------------------
% Western lateral boundary condition for meridional wind
% -------------------------------------------------------------------------
 
ilev=1;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(z_vv.var(:,:,ilev));
c_map = scale_col(-50:10:50,fld);
 
% Plot
lev=z_vv.aklev/10000;
lat=z_vv.ymin + (0:z_vv.ny-1) * z_vv.dy;
[C,h]=contourf(lat,lev,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Western lateral Boundary Condition : Meridional Wind @ ' num2str(z_vv.xmin) '^\circ E' ]);
xlabel('Latitude');
ylabel('Height [km]');
 
% Save figure
figname = [ base '/bound_west_vv_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% -------------------------------------------------------------------------
% Eastern lateral boundary condition for meridional wind
% -------------------------------------------------------------------------
 
ilev=z_vv.nx;
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(z_vv.var(:,:,ilev));
c_map = scale_col(-50:10:50,fld);
 
% Plot
lev=z_vv.aklev/10000;
lat=z_vv.ymin + (0:z_vv.ny-1) * z_vv.dy;
[C,h]=contourf(lat,lev,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,2);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Eastern lateral Boundary Condition : Meridional Wind @ ' num2str(z_vv.xmax) '^\circ E' ]);
xlabel('Latitude');
ylabel('Height [km]');
 
% Save figure
figname = [ base '/bound_east_vv_' filename '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
Property changes:
Added: svn:executable
/tags/1.0/diag/difference.f
0,0 → 1,241
PROGRAM difference
 
c **************************************************************************
c * Get the difference between two runs *
c * Michael Sprenger / Autumn 2006 *
c **************************************************************************
 
implicit none
 
c --------------------------------------------------------------------------
c Declaration of subroutine parameters
c --------------------------------------------------------------------------
 
c Physical and numerical parameters
real eps
parameter (eps=0.01)
integer nmax
parameter (nmax=300*300*200)
 
c Variables for input file 1
character*80 i1_filename
real i1_varmin(4),i1_varmax(4),i1_stag(4)
integer i1_vardim(4)
real i1_mdv
integer i1_ndim
integer i1_nx,i1_ny,i1_nz
real i1_time
integer i1_nvars
character*80 i1_vnam(100)
real i1_field(nmax)
 
c Variables for input file 2
character*80 i2_filename
real i2_varmin(4),i2_varmax(4),i2_stag(4)
integer i2_vardim(4)
real i2_mdv
integer i2_ndim
integer i2_nx,i2_ny,i2_nz
real i2_time
integer i2_nvars
character*80 i2_vnam(100)
real i2_field(nmax)
 
c Variables for output file
character*80 o_filename
real o_varmin(4),o_varmax(4),o_stag(4)
integer o_vardim(4)
real o_mdv
integer o_ndim
integer o_nx,o_ny,o_nz
real o_time
real o_field(nmax)
 
c Auxiliary variables
integer i,j,k
integer cdfid,ierr
integer isok
character*80 cfn,varname
 
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* DIFFERENCE *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) i1_filename
read(10,*) i2_filename
read(10,*) o_filename
close(10)
print*
print*,trim(i1_filename)
print*,trim(i2_filename)
print*,trim(o_filename)
print*
 
c Get a list of all variables on the two input files
call cdfopn(i1_filename,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,i1_nvars,i1_vnam,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,i1_vnam(i1_nvars),i1_ndim,i1_mdv,i1_vardim,
> i1_varmin,i1_varmax,i1_stag,ierr)
call clscdf(cdfid,ierr)
print*,(trim(i1_vnam(i))//' ',i=1,i1_nvars)
 
call cdfopn(i2_filename,cdfid,ierr)
if (ierr.ne.0) goto 997
call getvars(cdfid,i2_nvars,i2_vnam,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
print*,(trim(i2_vnam(i))//' ',i=1,i2_nvars)
print*
 
c Create the output file
o_ndim=i1_ndim
do i=1,i1_ndim
o_varmin(i)=i1_varmin(i)
o_varmax(i)=i1_varmax(i)
enddo
cfn=trim(o_filename)//'_cst'
call crecdf(trim(o_filename),cdfid,o_varmin,o_varmax,
> o_ndim,trim(cfn),ierr)
if (ierr.ne.0) goto 996
call clscdf(cdfid,ierr)
 
c --------------------------------------------------------------------------------
c Loop through all variables
c --------------------------------------------------------------------------------
 
do i=1,i1_nvars
 
c Check wether the variable is available on both files
varname=i1_vnam(i)
if (varname.eq.'time') goto 100
isok=0
call check_varok (isok,varname,i2_vnam,i2_nvars)
if (isok.eq.0) goto 100
 
c Read first input file
call cdfopn(i1_filename,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,i1_ndim,i1_mdv,i1_vardim,
> i1_varmin,i1_varmax,i1_stag,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,0.,0,i1_field,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
c Read second input file
call cdfopn(i2_filename,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,i2_ndim,i2_mdv,i2_vardim,
> i2_varmin,i2_varmax,i2_stag,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,0.,0,i2_field,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Consistency check
if (i1_ndim.ne.i2_ndim) then
print*,'Inconsistent input files... Stop',i1_ndim,i2_ndim
stop
endif
do j=1,3
if ( (i1_vardim(j).ne.i2_vardim(j)).or.
> (abs(i1_varmin(j)-i2_varmin(j)).gt.eps).or.
> (abs(i1_varmax(j)-i2_varmax(j)).gt.eps).or.
> (abs(i1_stag(j)-i2_stag(j)).gt.eps)) then
print*,'Inconsistent input files... Stop'
print*,j,i1_varmin(j),i2_varmin(j)
print*,j,i1_varmax(j),i2_varmax(j)
print*,j,i1_vardim(j),i2_vardim(j)
print*,j,i1_stag(j), i2_stag(j)
stop
endif
enddo
c Get the difference
do j=1,i1_vardim(1)*i1_vardim(2)*i1_vardim(3)
if ( (abs(i1_field(j)-i1_mdv).gt.eps).and.
> (abs(i2_field(j)-i2_mdv).gt.eps) ) then
o_field(j)=i1_field(j)-i2_field(j)
else
o_field(j)=i1_mdv
endif
enddo
 
c Write to output file
o_ndim=i1_ndim
o_mdv =i1_mdv
do j=1,i1_ndim
o_vardim(j)=i1_vardim(j)
o_varmin(j)=i1_varmin(j)
o_varmax(j)=i1_varmax(j)
o_stag(j) =i1_stag(j)
enddo
call cdfwopn(o_filename,cdfid,ierr)
if (ierr.ne.0) goto 996
call putdef(cdfid,varname,o_ndim,o_mdv,o_vardim,
> o_varmin,o_varmax,o_stag,ierr)
if (ierr.ne.0) goto 996
call putdat(cdfid,varname,0.,0,o_field,ierr)
if (ierr.ne.0) goto 996
print*,'W ',trim(varname),' ',trim(o_filename)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 996
 
c Next
100 continue
 
enddo
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Problems with input file 1 ',trim(i1_filename)
stop
 
997 print*,'Problems with input file 2 ',trim(i2_filename)
stop
 
996 print*,'Problems with output file ',trim(o_filename)
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
Property changes:
Added: svn:executable
/tags/1.0/diag/hydrostatic.f
0,0 → 1,542
PROGRAM hydrostatic
 
c Calculate the geopotential and add it to the P file
c Michael Sprenger / Spring 2006
 
implicit none
 
c ---------------------------------------------------------------
c Declaration of variables
c ---------------------------------------------------------------
 
c Variables for input P file : model level
character*80 ml_pfn
real ml_varmin(4),ml_varmax(4),ml_stag(4)
integer ml_vardim(4)
real ml_mdv
integer ml_ndim
integer ml_nx,ml_ny,ml_nz
real ml_xmin,ml_xmax,ml_ymin,ml_ymax,ml_dx,ml_dy
integer ml_ntimes
real ml_aklev(500),ml_bklev(500)
real ml_aklay(500),ml_bklay(500)
real ml_time
real ml_pollon,ml_pollat
integer ml_nvars
character*80 ml_vnam(100)
integer ml_idate(5)
real,allocatable, dimension (:,:) :: ml_ps,ml_zb
real,allocatable, dimension (:,:,:) :: ml_t3,ml_q3,ml_p3,ml_tv3
real,allocatable, dimension (:,:,:) :: ml_zlay3
 
c Variables for input Z file : pressure level
character*80 pl_zfn
real pl_varmin(4),pl_varmax(4),pl_stag(4)
integer pl_vardim(4)
real pl_mdv
integer pl_ndim
integer pl_nx,pl_ny,pl_nz
real pl_xmin,pl_xmax,pl_ymin,pl_ymax,pl_dx,pl_dy
integer pl_ntimes
real pl_aklev(500),pl_bklev(500)
real pl_aklay(500),pl_bklay(500)
real pl_time
real pl_pollon,pl_pollat
integer pl_nvars
character*80 pl_vnam(100)
integer pl_idate(5)
real,allocatable, dimension (:,:,:) :: pl_z3,pl_p3
 
c Physical and numerical parameters
real g
parameter (g=9.80665)
real eps
parameter (eps=0.01)
real tzero
parameter (tzero=273.15)
real kappa
parameter (kappa=0.6078)
real zerodiv
parameter (zerodiv=0.0000000001)
real dpmin
parameter (dpmin=10.)
real rdg
parameter (rdg=29.271)
 
c Auxiliary variables
integer ierr
integer cdfid,cstid
character*80 cfn
integer stat
real time
real tv1(1000),z1(1000),p1(1000),f1(1000)
real spline_tv1(1000),spline_f1(1000),spline_z1(1000)
real pu,po,zu,zo,p,z,dp,p0,tvu,tvo,ff
integer i,j,k,l
integer lmin,n
character*80 varname,cdfname
integer isok
integer mode
 
c -----------------------------------------------------------------
c Read input fields
c -----------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* hydrostatic *'
print*,'*********************************************************'
 
c Read in the parameter file
open(10,file='fort.10')
read(10,*) ml_pfn
read(10,*) pl_zfn
close(10)
 
c Decide which mode is used (1: reference from Z, 2: reference from ORO/PS)
if ( trim(ml_pfn).ne.trim(pl_zfn) ) then
mode=1
print*,'Taking reference from Z ',trim(pl_zfn)
else
mode=2
print*,'Taking reference from ORO/PS ',trim(pl_zfn)
endif
 
print*,trim(ml_pfn)
print*,trim(pl_zfn)
c Get grid description for P file : model level
call cdfopn(ml_pfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,ml_nvars,ml_vnam,ierr)
varname='T'
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 998
ml_nx =ml_vardim(1)
ml_ny =ml_vardim(2)
ml_nz =ml_vardim(3)
ml_xmin=ml_varmin(1)
ml_ymin=ml_varmin(2)
call getlevs(cstid,ml_nz,ml_aklev,ml_bklev,ml_aklay,ml_bklay,ierr)
call getgrid(cstid,ml_dx,ml_dy,ierr)
ml_xmax=ml_xmin+real(ml_nx-1)*ml_dx
ml_ymax=ml_ymin+real(ml_ny-1)*ml_dy
call gettimes(cdfid,ml_time,ml_ntimes,ierr)
call getstart(cstid,ml_idate,ierr)
call getpole(cstid,ml_pollon,ml_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Get grid description reference: either ORO(P) or Z(Z)
call cdfopn(pl_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,pl_nvars,pl_vnam,ierr)
if (mode.eq.1) then
varname='Z'
isok=0
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,pl_ndim,pl_mdv,pl_vardim,
> pl_varmin,pl_varmax,pl_stag,ierr)
if (ierr.ne.0) goto 998
call getlevs(cstid,pl_nz,pl_aklev,pl_bklev,
> pl_aklay,pl_bklay,ierr)
call getgrid(cstid,pl_dx,pl_dy,ierr)
call gettimes(cdfid,pl_time,pl_ntimes,ierr)
call getstart(cstid,pl_idate,ierr)
call getpole(cstid,pl_pollon,pl_pollat,ierr)
 
else if (mode.eq.2) then
varname='ORO'
isok=0
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,pl_ndim,pl_mdv,pl_vardim,
> pl_varmin,pl_varmax,pl_stag,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,pl_dx,pl_dy,ierr)
call gettimes(cdfid,pl_time,pl_ntimes,ierr)
call getstart(cstid,pl_idate,ierr)
call getpole(cstid,pl_pollon,pl_pollat,ierr)
endif
pl_nx =pl_vardim(1)
pl_ny =pl_vardim(2)
pl_nz =pl_vardim(3)
pl_xmin=pl_varmin(1)
pl_ymin=pl_varmin(2)
pl_xmax=pl_xmin+real(pl_nx-1)*pl_dx
pl_ymax=pl_ymin+real(pl_ny-1)*pl_dy
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Consitency check for the grids
if ( (ml_nx.ne.pl_nx).or.
> (ml_ny.ne.pl_ny).or.
> (abs(ml_xmin-pl_xmin ).gt.eps).or.
> (abs(ml_ymin-pl_ymin ).gt.eps).or.
> (abs(ml_xmax-pl_xmax ).gt.eps).or.
> (abs(ml_ymax-pl_ymax ).gt.eps).or.
> (abs(ml_dx -pl_dx ).gt.eps).or.
> (abs(ml_dy -pl_dy ).gt.eps).or.
> (abs(ml_time-pl_time ).gt.eps).or.
> (abs(ml_pollon-pl_pollon).gt.eps).or.
> (abs(ml_pollat-pl_pollat).gt.eps)) then
print*,'Input P and Z grids are not consistent... Stop'
print*,'Xmin ',ml_xmin ,pl_xmin
print*,'Ymin ',ml_ymin ,pl_ymin
print*,'Xmax ',ml_xmax ,pl_xmax
print*,'Ymax ',ml_ymax ,pl_ymax
print*,'Dx ',ml_dx ,pl_dx
print*,'Dy ',ml_dy ,pl_dy
print*,'Pollon ',ml_pollon ,pl_pollon
print*,'Pollat ',ml_pollat ,pl_pollat
print*,'Time ',ml_time ,pl_time
stop
endif
 
c Allocate memory for all fields
allocate(ml_ps(ml_nx,ml_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_ps ***'
allocate(ml_zb(ml_nx,ml_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_zb ***'
allocate(ml_p3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_p3 ***'
allocate(ml_t3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_t3 ***'
allocate(ml_q3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_q3 ***'
allocate(ml_tv3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_tv3 ***'
allocate(ml_zlay3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_zlay3 ***'
 
allocate(pl_z3(pl_nx,pl_ny,pl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pl_z3 ***'
allocate(pl_p3(pl_nx,pl_ny,pl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pl_p3 ***'
 
c Read T, Q, PS from P file
call cdfopn(ml_pfn,cdfid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='T'
call check_varok (isok,varname, ml_vnam,ml_nvars)
varname='Q'
call check_varok (isok,varname, ml_vnam,ml_nvars)
varname='PS'
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.ne.3) goto 998
print*,'R T ',trim(ml_pfn)
call getdat(cdfid,'T',ml_time,0,ml_t3,ierr)
print*,'R Q ',trim(ml_pfn)
call getdat(cdfid,'Q',ml_time,0,ml_q3,ierr)
print*,'R PS ',trim(ml_pfn)
call getdat(cdfid,'PS',ml_time,1,ml_ps,ierr)
call clscdf(cdfid,ierr)
 
c Read ORO from P or Z from Z file
call cdfopn(pl_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
if (mode.eq.1) then
isok=0
varname='Z'
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
print*,'R Z ',trim(pl_zfn)
call getdat(cdfid,varname,pl_time,0,pl_z3,ierr)
else if (mode.eq.2) then
isok=0
varname='ORO'
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
print*,'R ORO ',trim(pl_zfn)
call getdat(cdfid,varname,pl_time,1,pl_z3,ierr)
endif
call clscdf(cdfid,ierr)
 
c Set the values for the pressure on the pressure levels
do i=1,pl_nx
do j=1,pl_ny
do k=1,pl_nz
if (mode.eq.1) then
pl_p3(i,j,k)=pl_aklay(k)
else if (mode.eq.2) then
pl_p3(i,j,k)=ml_ps(i,j)
endif
enddo
enddo
enddo
 
c Calculate 3d pressure field
print*,'C P'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
ml_p3(i,j,k)=ml_aklay(k)+ml_bklay(k)*ml_ps(i,j)
enddo
enddo
enddo
 
c Calculate 3d virtual temperature
print*,'C TV'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
ml_tv3(i,j,k) = (ml_t3(i,j,k)+tzero)*
> (1.+kappa*ml_q3(i,j,k))
enddo
enddo
enddo
 
c -----------------------------------------------------------------
c Calculate geopotential
c -----------------------------------------------------------------
 
c Integrate hydrostatic equation towards layers
print*,'C HYDROSTATIC EQUATION (LAYERS)'
do i=1,ml_nx
do j=1,ml_ny
 
c Make the virtual temperature profile available
do k=1,ml_nz
p1 (ml_nz-k+1)=ml_p3 (i,j,k)
tv1(ml_nz-k+1)=ml_tv3(i,j,k)
enddo
call spline (p1,tv1,ml_nz,1.e30,1.e30,spline_tv1)
 
c Loop over all model levels
do k=1,ml_nz
 
c Get pressure at the grid point
p = ml_aklay(k)+ml_bklay(k)*ml_ps(i,j)
 
c Find nearest pressure level which is above topography
if (mode.eq.1) then
lmin=pl_nz
do l=1,pl_nz
if ((abs(p-pl_p3(i,j,l))).lt.
> (abs(p-pl_p3(i,j,lmin)))
> .and.
> (pl_p3(i,j,l).lt.ml_ps(i,j)) ) then
lmin=l
endif
enddo
else if (mode.eq.2) then
lmin=1
endif
 
c Integrate hydrostatic equation from this level to the grid point
p0 = pl_p3(i,j,lmin)
n = nint(abs(p-p0)/dpmin)
if (n.lt.1) n=1
dp = (p-p0)/real(n)
 
pu = p0
z = pl_z3(i,j,lmin)
call splint(p1,tv1,spline_tv1,ml_nz,pu,tvu)
do l=1,n
po = pu+dp
call splint(p1,tv1,spline_tv1,ml_nz,po,tvo)
z = z + rdg*0.5*(tvu+tvo)*alog(pu/po)
tvu = tvo
pu = po
enddo
c Set the geopotential at the grid point
ml_zlay3(i,j,k) = z
enddo
 
enddo
 
enddo
 
c -----------------------------------------------------------------
c Calculate height of topography
c -----------------------------------------------------------------
 
if (mode.eq.1) then
print*,'C TOPOGRAPHY'
do i=1,ml_nx
do j=1,ml_ny
c Make the z/p profile available
do k=1,ml_nz
p1(ml_nz-k+1)=ml_p3(i,j,k)
z1(ml_nz-k+1)=ml_zlay3(i,j,k)
enddo
 
c Cubic spline interpolation
call spline (p1,z1,ml_nz,1.e30,1.e30,spline_z1)
call splint (p1,z1,spline_z1,ml_nz,ml_ps(i,j),ml_zb(i,j))
enddo
enddo
endif
 
c -----------------------------------------------------------------
c Write the topography and geopotential to P file
c -----------------------------------------------------------------
 
c Open P file
call cdfwopn(trim(ml_pfn),cdfid,ierr)
 
c Write orography (levels)
if (mode.eq.1) then
varname='ORO'
print*,'W ',trim(varname),' ',trim(ml_pfn)
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_vardim(3)=1
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
ml_vardim(3)=ml_nz
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,ml_time,1,ml_zb,ierr)
if (ierr.ne.0) goto 997
endif
 
c Write geopotential on layers
varname='Z_DIA'
print*,'W ',trim(varname),' ',trim(ml_pfn)
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_stag(3)=-0.5
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,ml_time,0,ml_zlay3,ierr)
if (ierr.ne.0) goto 997
 
c Close P file
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Z: Problems with input from m level'
stop
 
997 print*,'Z: Problems with output on m level'
stop
 
996 print*,'F: Problems with input from m level'
stop
 
995 print*,'F: Problems with output on z level'
stop
 
 
end
 
c -------------------------------------------------------------
c Natural cubic spline
c -------------------------------------------------------------
 
SUBROUTINE spline(x,y,n,yp1,ypn,y2)
INTEGER n,NMAX
REAL yp1,ypn,x(n),y(n),y2(n)
PARAMETER (NMAX=500)
INTEGER i,k
REAL p,qn,sig,un,u(NMAX)
if (yp1.gt..99e30) then
y2(1)=0.
u(1)=0.
else
y2(1)=-0.5
u(1)=(3./(x(2)-x(1)))*((y(2)-y(1))/(x(2)-x(1))-yp1)
endif
do 11 i=2,n-1
sig=(x(i)-x(i-1))/(x(i+1)-x(i-1))
p=sig*y2(i-1)+2.
y2(i)=(sig-1.)/p
u(i)=(6.*((y(i+1)-y(i))/(x(i+
*1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*
*u(i-1))/p
11 continue
if (ypn.gt..99e30) then
qn=0.
un=0.
else
qn=0.5
un=(3./(x(n)-x(n-1)))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1)))
endif
y2(n)=(un-qn*u(n-1))/(qn*y2(n-1)+1.)
do 12 k=n-1,1,-1
y2(k)=y2(k)*y2(k+1)+u(k)
12 continue
return
END
 
 
SUBROUTINE splint(xa,ya,y2a,n,x,y)
INTEGER n
REAL x,y,xa(n),y2a(n),ya(n)
INTEGER k,khi,klo
REAL a,b,h
klo=1
khi=n
1 if (khi-klo.gt.1) then
k=(khi+klo)/2
if(xa(k).gt.x)then
khi=k
else
klo=k
endif
goto 1
endif
h=xa(khi)-xa(klo)
if (h.eq.0.) pause 'bad xa input in splint'
a=(xa(khi)-x)/h
b=(x-xa(klo))/h
y=a*ya(klo)+b*ya(khi)+((a**3-a)*y2a(klo)+(b**3-b)*y2a(khi))*(h**
*2)/6.
return
END
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
Property changes:
Added: svn:executable
/tags/1.0/diag/qvec_analysis.f
0,0 → 1,1468
PROGRAM z2s
 
c Calculate secondary fields on z levels
c Michael Sprenger / Summer 2006
 
implicit none
 
c ---------------------------------------------------------------
c Declaration of parameters
c ---------------------------------------------------------------
 
real tzero
parameter (tzero=273.15)
real kappa
parameter (kappa=0.6078)
real rd
parameter (rd=287.)
 
c ---------------------------------------------------------------
c Declaration of variables
c ---------------------------------------------------------------
 
c Variables for output Z file : height level
character*80 cfn
real varmin(4),varmax(4),stag(4)
integer vardim(4)
real mdv
integer ndim
integer nx,ny,nz
real xmin,xmax,ymin,ymax,dx,dy
integer ntimes
real aklev(1000),bklev(1000)
real aklay(1000),bklay(1000)
real time
real pollon,pollat
integer idate(5)
integer nfields
character*80 field_nam(100)
real,allocatable, dimension (:,:,:,:) :: field_dat
real,allocatable, dimension (:,:,:) :: z3
real,allocatable, dimension (:,:) :: x2,y2,f2,oro
real,allocatable, dimension (:,:,:) :: out1,out2
real,allocatable, dimension (:,:,:) :: inp
real,allocatable,dimension (:) :: nsqref
real,allocatable,dimension (:) :: thetaref
real,allocatable,dimension (:) :: tref
real,allocatable,dimension (:) :: rhoref
real,allocatable,dimension (:) :: pressref
real,allocatable,dimension (:) :: zref
real deltax,deltay,deltaz
integer nvars
character*80 vnam(100),varname
integer isok
integer cdfid,cstid
character*3 mode
 
c Parameter file
character*80 fieldname
integer nfilt
character*80 ofn,gri
 
c Auxiliary variables
integer ierr,stat
integer i,j,k,n
real,allocatable, dimension (:,:) :: tmp
character*80 vnam2(100)
integer nvars2
 
c ---------------------------------------------------------------
c Preparations
c ---------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* qvec_analysis *'
print*,'*********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) fieldname
read(10,*) ofn
read(10,*) gri
read(10,*) nfilt
close(10)
 
c Decide whether to enter ANO or MOD/ORG mode
mode = ofn(1:3)
if ( (mode.ne.'ANO').and.
> (mode.ne.'MOD').and.
> (mode.ne.'ORG') )
>then
print*,'Unsupported mode ',trim(mode)
stop
endif
 
c Get grid description for Z file : height level
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,'T',ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
nx =vardim(1)
ny =vardim(2)
nz =vardim(3)
xmin=varmin(1)
ymin=varmin(2)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
call gettimes(cdfid,time,ntimes,ierr)
if (ierr.ne.0) goto 998
call getstart(cstid,idate,ierr)
if (ierr.ne.0) goto 998
call getpole(cstid,pollon,pollat,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Get a list of all variables on the GRID file
if (trim(gri).ne.trim(ofn)) then
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars2,vnam2,ierr)
if (ierr.ne.0) goto 998
do i=1,nvars2
vnam(nvars+i)=vnam2(i)
enddo
nvars=nvars+nvars2
endif
 
c Check whether calculation of <fieldname> is supported
if ( (fieldname.ne.'GEO' ).and.
> (fieldname.ne.'AGEO' ).and.
> (fieldname.ne.'DIV_UV' ).and.
> (fieldname.ne.'QVEC' ).and.
> (fieldname.ne.'DIV_Q' ) ) then
print*,'Variable not supported ',trim(fieldname)
stop
endif
c Set dependencies
if (fieldname.eq.'GEO') then
nfields=2
field_nam(1)='T'
field_nam(2)='P'
elseif (fieldname.eq.'AGEO') then
nfields=4
field_nam(1)='U'
field_nam(2)='UG'
field_nam(3)='V'
field_nam(4)='VG'
else if (fieldname.eq.'DIV_UV') then
nfields=2
field_nam(1)='U'
field_nam(2)='V'
else if (fieldname.eq.'QVEC') then
nfields=3
field_nam(1)='UG'
field_nam(2)='VG'
field_nam(3)='TH'
else if (fieldname.eq.'DIV_Q') then
nfields=2
field_nam(1)='QX'
field_nam(2)='QY'
endif
 
c Allocate memory
allocate(field_dat(nfields,nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating field_dat'
allocate(out1(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating out1'
allocate(out2(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating out2'
allocate(inp(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating inp'
allocate(z3(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating z3'
allocate(x2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating x2'
allocate(y2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating y2'
allocate(f2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating f2'
allocate(oro(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating oro'
 
C Allocate memory for reference profile
allocate(rhoref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rhoref'
allocate(pressref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pressref'
allocate(thetaref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating thetaref'
allocate(nsqref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsqref'
allocate(zref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating zref'
allocate(tref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating tref'
 
c Allocate auxiliary fields
allocate(tmp(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating tmp'
c Read reference profile and grid parameters
call read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,f2,oro,gri)
 
c Read X grid
varname='X'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,x2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Read Y grid
varname='Y'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,y2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Calculate reference profile of temperature
print*,'C T_ref = TH_ref * ( P_ref/1000)^kappa'
do i=0,2*nz
tref(i) = thetaref(i) * ( pressref(i)/1000. ) ** kappa
enddo
 
c Init height levels
do i=1,nx
do j=1,ny
do k=1,nz
z3(i,j,k)=zref(2*k-1)
enddo
enddo
enddo
 
c Load needed variables
do n=1,nfields
 
c Check whether variable is available on file
varname=field_nam(n)
isok=0
call check_varok (isok,varname,vnam,nvars)
 
c Variable is available on file
if (isok.eq.1) then
 
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,inp,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(ofn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=inp(i,j,k)
enddo
enddo
enddo
else
print*,'Variable missing : ',trim(varname)
stop
endif
 
enddo
 
c Add reference profile if ANO file is provided
if ( mode.eq.'ANO' ) then
 
print*,'C T -> T_ano + T_ref'
n=0
do i=1,nfields
if (field_nam(i).eq.'T') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k) = field_dat(n,i,j,k) + tref(2*k-1)
enddo
enddo
enddo
endif
 
print*,'C TH -> TH_ano + TH_ref'
n=0
do i=1,nfields
if (field_nam(i).eq.'TH') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k) = field_dat(n,i,j,k)+thetaref(2*k-1)
enddo
enddo
enddo
endif
 
print*,'C P -> P_ano + P_ref'
n=0
do i=1,nfields
if (field_nam(i).eq.'P') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k) = field_dat(n,i,j,k)+pressref(2*k-1)
enddo
enddo
enddo
endif
 
endif
 
c Change units: P (hPa -> Pa), T(K -> degC)
n=0
do i=1,nfields
if (field_nam(i).eq.'P') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=100.*field_dat(n,i,j,k)
enddo
enddo
enddo
endif
 
n=0
do i=1,nfields
if (field_nam(i).eq.'T') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
if ( field_dat(n,i,j,1).gt.100. ) then
field_dat(n,i,j,k)=field_dat(n,i,j,k) - tzero
endif
enddo
enddo
enddo
endif
 
c ----------------------------------------------------------------
c Calculations
c ----------------------------------------------------------------
 
c Geostrophic wind (GEO)
if (fieldname.eq.'GEO') then
 
print*,'C ',trim(fieldname)
field_nam(1)='RHO'
do i=1,nx
do j=1,ny
do k=1,nz
if ( mode.eq.'ANO' ) then
field_dat(1,i,j,k)=rhoref(2*k-1)
else
field_dat(1,i,j,k)=
> 1./rd*field_dat(2,i,j,k)/(field_dat(1,i,j,k)+tzero)
endif
enddo
enddo
enddo
call calc_geo (out1,out2, ! (Ug,Vg)
> field_dat(1,:,:,:), ! RHO
> field_dat(2,:,:,:), ! P
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
c Ageostrophic wind (AGEO)
elseif (fieldname.eq.'AGEO') then
 
print*,'C ',trim(fieldname)
call calc_ageo (out1,out2, ! (Ua,Va)
> field_dat(1,:,:,:), ! U
> field_dat(2,:,:,:), ! UG
> field_dat(3,:,:,:), ! V
> field_dat(4,:,:,:), ! VG
> nx,ny,nz,mdv)
 
c Divergence of wind (DIV_UV)
else if (fieldname.eq.'DIV_UV') then
 
print*,'C ',trim(fieldname)
call calc_div_uv (out1, ! Div(U,V))
> field_dat(1,:,:,:), ! U
> field_dat(2,:,:,:), ! V
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
c Q vector (QVEC)
else if (fieldname.eq.'QVEC') then
 
print*,'C ',trim(fieldname)
call calc_qvec (out1,out2, ! (Qx,Qy)
> field_dat(1,:,:,:), ! UG
> field_dat(2,:,:,:), ! VG
> field_dat(3,:,:,:), ! TH
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
c Divergence of Q vector (DIV_Q)
else if (fieldname.eq.'DIV_Q') then
print*,'C ',trim(fieldname)
call calc_div_q (out1, ! Div(U,V))
> field_dat(1,:,:,:), ! QX
> field_dat(2,:,:,:), ! QY
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
endif
 
c Horizontal filtering of the resulting fields
print*,'F ',trim(fieldname)
do k=1,nz
do i=1,nx
do j=1,ny
tmp(i,j)=out1(i,j,k)
enddo
enddo
do n=1,nfilt
call filt2d (tmp,tmp,nx,ny,1.,mdv,0,0,0,0)
enddo
do i=1,nx
do j=1,ny
out1(i,j,k)=tmp(i,j)
enddo
enddo
 
do i=1,nx
do j=1,ny
tmp(i,j)=out2(i,j,k)
enddo
enddo
do n=1,nfilt
call filt2d (tmp,tmp,nx,ny,1.,mdv,0,0,0,0)
enddo
do i=1,nx
do j=1,ny
out2(i,j,k)=tmp(i,j)
enddo
enddo
enddo
 
c ----------------------------------------------------------------
c Save result onto netcdf file
c ----------------------------------------------------------------
 
c Open output file
call cdfwopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Save geostrophic wind
if (fieldname.eq.'GEO') then
isok=0
varname='UG'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out1,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
isok=0
varname='VG'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out2,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
 
c Save ageostrophic wind
elseif (fieldname.eq.'AGEO') then
isok=0
varname='UA'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out1,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
isok=0
varname='VA'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out2,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
 
c Save divergence of wind field
else if (fieldname.eq.'DIV_UV') then
isok=0
varname='DIV_UV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out1,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
 
c Save components of Q vector
else if (fieldname.eq.'QVEC') then
isok=0
varname='QX'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out1,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
isok=0
varname='QY'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out2,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
 
c Save divergence of wind field
else if (fieldname.eq.'DIV_Q') then
isok=0
varname='DIV_Q'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out1,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
 
endif
 
c Close output file
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
 
c ----------------------------------------------------------------
c Exception handling
c ----------------------------------------------------------------
stop
 
998 print*,'Problem with netcdf file'
stop
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: AUXILIARY ROUTINES *
c ****************************************************************
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: CALCULATE SECONDARY FIELDS *
c ****************************************************************
 
c ----------------------------------------------------------------
c Calculate geostrophic wind components
c ----------------------------------------------------------------
 
subroutine calc_geo (ug,vg,rho,p,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate the geostrophic wind components (ug,vg) if the temperature
c (t) and the pressure (p) are given. The grid and the missing data
c value are specified by (z3,x2,y2,f2,nx,ny,nz,mdv)
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real ug (nx,ny,nz)
real vg (nx,ny,nz)
real rho(nx,ny,nz)
real p (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
real mdv
 
c Physical parameters and numerical constants
real eps
parameter (eps=0.01)
real g
parameter (g=9.80616)
 
 
c Auxiliray variables
integer i,j,k
real dpdx(nx,ny,nz)
real dpdy(nx,ny,nz)
 
c Calculate horizontal derivatives of pressure
call deriv(dpdx,p,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv(dpdy,p,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
 
if ((abs(rho (i,j,k)-mdv).gt.eps).and.
> (abs(dpdx(i,j,k)-mdv).gt.eps).and.
> (abs(dpdy(i,j,k)-mdv).gt.eps)) then
 
ug(i,j,k)=-1./(rho(i,j,k)*f2(i,j))*dpdy(i,j,k)
vg(i,j,k)= 1./(rho(i,j,k)*f2(i,j))*dpdx(i,j,k)
endif
 
enddo
enddo
enddo
 
end
 
c ----------------------------------------------------------------
c Calculate ageostrophic wind components
c ----------------------------------------------------------------
 
subroutine calc_ageo (ua,va,u,ug,v,vg,nx,ny,nz,mdv)
 
c Calculate the geostrophic wind components (ug,vg) if the temperature
c (t) and the pressure (p) are given. The grid and the missing data
c value are specified by (z3,x2,y2,f2,nx,ny,nz,mdv)
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real ua (nx,ny,nz)
real va (nx,ny,nz)
real u (nx,ny,nz)
real ug (nx,ny,nz)
real v (nx,ny,nz)
real vg (nx,ny,nz)
real mdv
 
c Parameters
real eps
parameter (eps=0.01)
 
c Auxiliray variables
integer i,j,k
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
 
if ((abs(u (i,j,k)-mdv).gt.eps).and.
> (abs(ug(i,j,k)-mdv).gt.eps).and.
> (abs(v (i,j,k)-mdv).gt.eps).and.
> (abs(vg(i,j,k)-mdv).gt.eps)) then
 
ua(i,j,k)=u(i,j,k) - ug(i,j,k)
va(i,j,k)=v(i,j,k) - vg(i,j,k)
 
endif
 
enddo
enddo
enddo
 
end
 
c ----------------------------------------------------------------
c Calculate divergence of wind field
c ----------------------------------------------------------------
 
subroutine calc_div_uv (div_uv,u,v,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate the divergence (div_uv) of the horizontal wind field if+
c the wind components (u,v) are given. The grid and the missing data
c value are specified by (z3,x2,y2,f2,nx,ny,nz,mdv)
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real div_uv(nx,ny,nz)
real u (nx,ny,nz)
real v (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
real mdv
 
c Physical parameters and numerical constants
real eps
parameter (eps=0.01)
 
c Auxiliray variables
integer i,j,k
real rho
real dudx(nx,ny,nz)
real dvdy(nx,ny,nz)
 
c Calculate horizontal derivatives of pressure
call deriv(dudx,u,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv(dvdy,v,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
 
if ((abs(dudx(i,j,k)-mdv).gt.eps).and.
> (abs(dvdy(i,j,k)-mdv).gt.eps)) then
 
div_uv(i,j,k)=dudx(i,j,k)+dvdy(i,j,k)
endif
 
enddo
enddo
enddo
 
end
 
c ----------------------------------------------------------------
c Calculate Q vector
c ----------------------------------------------------------------
 
subroutine calc_qvec (qx3,qy3,
> th3,u3,v3,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate teh Q vector components <qx3> and <qy3>, as well as the divergence
c of the Q vector <divq3> on the model grid. The grid is specified in the horizontal
c by <xmin,ymin,dx,dy,nx,ny>. The number of vertical levels is <nz>. The input field
c are: potential temperature <th3>, horizontal wind <u3> and <v3>, pressure <p3>.
c The calculation follows the one described in "Weather Analysis, Dusan Djuric"
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real qx3(nx,ny,nz)
real qy3(nx,ny,nz)
real th3(nx,ny,nz)
real u3 (nx,ny,nz)
real v3 (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
real mdv
 
c Physical and numerical parameters
real scale1,scale2
parameter (scale1=1.E10,scale2=1.E14)
real eps
parameter (eps=0.01)
real g
parameter (g=9.80616)
real tzero
parameter (tzero=273.16)
 
c Auxiliary variables
real dudx(nx,ny,nz)
real dudy(nx,ny,nz)
real dvdx(nx,ny,nz)
real dvdy(nx,ny,nz)
real dtdx(nx,ny,nz)
real dtdy(nx,ny,nz)
integer i,j,k
 
c Needed derivatives
call deriv (dudx, u3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dudy, u3,'y',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdx, v3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdy, v3,'y',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdx,th3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdy,th3,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate vector components of the Q vector
do i=1,nx
do j=1,ny
do k=1,nz
 
c Evaluate Q vector formula with missing data check
if ((abs(dudx(i,j,k)-mdv).gt.eps).and.
> (abs(dudy(i,j,k)-mdv).gt.eps).and.
> (abs(dvdx(i,j,k)-mdv).gt.eps).and.
> (abs(dvdy(i,j,k)-mdv).gt.eps).and.
> (abs(dtdx(i,j,k)-mdv).gt.eps).and.
> (abs(dtdy(i,j,k)-mdv).gt.eps)) then
 
qx3(i,j,k) = -g/tzero * (dudx(i,j,k)*dtdx(i,j,k)
> +dvdx(i,j,k)*dtdy(i,j,k))
qy3(i,j,k) = -g/tzero * (dudy(i,j,k)*dtdx(i,j,k)
> +dvdy(i,j,k)*dtdy(i,j,k))
 
else
qx3(i,j,k)=mdv
qy3(i,j,k)=mdv
endif
 
enddo
enddo
enddo
 
c Scale the output
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(qx3(i,j,k)-mdv).gt.eps) then
qx3(i,j,k)=scale1*qx3(i,j,k)
endif
if (abs(qy3(i,j,k)-mdv).gt.eps) then
qy3(i,j,k)=scale1*qy3(i,j,k)
endif
enddo
enddo
enddo
 
end
 
c ----------------------------------------------------------------
c Calculate divergence of wind field
c ----------------------------------------------------------------
 
subroutine calc_div_q (div_q,qx,qy,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate the divergence (div_q) of the Q vector field if
c the components (qx,qy) are given. The grid and the missing data
c value are specified by (z3,x2,y2,f2,nx,ny,nz,mdv)
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real div_q(nx,ny,nz)
real qx (nx,ny,nz)
real qy (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
real mdv
 
c Physical parameters and numerical constants
real eps
parameter (eps=0.01)
 
c Auxiliray variables
integer i,j,k
real rho
real dqxdx(nx,ny,nz)
real dqydy(nx,ny,nz)
 
c Calculate horizontal derivatives of pressure
call deriv(dqxdx,qx,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv(dqydy,qy,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
 
if ((abs(dqxdx(i,j,k)-mdv).gt.eps).and.
> (abs(dqydy(i,j,k)-mdv).gt.eps)) then
 
div_q(i,j,k)=dqxdx(i,j,k)+dqydy(i,j,k)
endif
 
enddo
enddo
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: GRID HANDLING *
c ****************************************************************
 
c -----------------------------------------------------------------
c Horizontal and vertical derivatives for 3d fields
c -----------------------------------------------------------------
 
subroutine deriv (df,f,direction,
> z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate horizontal and vertical derivatives of the 3d field <f>.
c The direction of the derivative is specified in <direction>
c 'x','y' : Horizontal derivative in x and y direction
c 'p','z','t','m' : Vertical derivative (pressure, height, theta, model)
c The 3d field <z3> specifies the isosurfaces along which the horizontal
c derivatives are calculated or the levels for the vertical derivatives.
 
implicit none
 
c Input and output parameters
integer nx,ny,nz
real df (nx,ny,nz)
real f (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
character direction
real mdv
c Numerical and physical parameters
real pi180
parameter (pi180=3.141592654/180.)
real deltay
parameter (deltay=111.1775E3)
real zerodiv
parameter (zerodiv=0.00000001)
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
real vmin,vmax
real scale,lat
real vu,vl,vuvl,vlvu
integer o,u,w,e,n,s
 
c Vertical derivative
if ((direction.eq.'z').or.
> (direction.eq.'th').or.
> (direction.eq.'p').or.
> (direction.eq.'m').and.
> (nz.gt.1)) then
 
do i=1,nx
do j=1,ny
do k=1,nz
o=k+1
if (o.gt.nz) o=nz
u=k-1
if (u.lt.1) u=1
 
if ((abs(f(i,j,o)-mdv).gt.eps).and.
> (abs(f(i,j,u)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps)) then
 
vu = z3(i,j,k)-z3(i,j,o)
vl = z3(i,j,u)-z3(i,j,k)
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
 
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,j,u)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,j,o)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Horizontal derivative in the y direction: 3d
elseif (direction.eq.'y') then
do i=1,nx
do j=1,ny
do k=1,nz
s=j-1
if (s.lt.1) s=1
n=j+1
if (n.gt.ny) n=ny
 
if ((abs(f(i,n,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(i,s,k)-mdv).gt.eps)) then
vu = 1000.*(y2(i,j)-y2(i,n))
vl = 1000.*(y2(i,s)-y2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,s,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,n,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
 
c Horizontal derivative in the x direction: 3d
elseif (direction.eq.'x') then
 
do i=1,nx
do j=1,ny
do k=1,nz
w=i-1
if (w.lt.1) w=1
e=i+1
if (e.gt.nx) e=nx
 
if ((abs(f(w,j,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(e,j,k)-mdv).gt.eps)) then
vu = 1000.*(x2(i,j)-x2(e,j))
vl = 1000.*(x2(w,j)-x2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
 
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(w,j,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(e,j,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Undefined direction for derivative
else
print*,'Invalid direction of derivative... Stop'
stop
endif
 
end
 
c -----------------------------------------------------------------
c Horizontal filter
c -----------------------------------------------------------------
 
subroutine filt2d (a,af,nx,ny,fil,misdat,
& iperx,ipery,ispol,inpol)
 
c Apply a conservative diffusion operator onto the 2d field a,
c with full missing data checking.
c
c a real inp array to be filtered, dimensioned (nx,ny)
c af real out filtered array, dimensioned (nx,ny), can be
c equivalenced with array a in the calling routine
c f1 real workarray, dimensioned (nx+1,ny)
c f2 real workarray, dimensioned (nx,ny+1)
c fil real inp filter-coeff., 0<afil<=1. Maximum filtering with afil=1
c corresponds to one application of the linear filter.
c misdat real inp missing-data value, a(i,j)=misdat indicates that
c the corresponding value is not available. The
c misdat-checking can be switched off with with misdat=0.
c iperx int inp periodic boundaries in the x-direction (1=yes,0=no)
c ipery int inp periodic boundaries in the y-direction (1=yes,0=no)
c inpol int inp northpole at j=ny (1=yes,0=no)
c ispol int inp southpole at j=1 (1=yes,0=no)
c
c Christoph Schaer, 1993
 
c argument declaration
integer nx,ny
real a(nx,ny),af(nx,ny),fil,misdat
integer iperx,ipery,inpol,ispol
 
c local variable declaration
integer i,j,is
real fh
real f1(nx+1,ny),f2(nx,ny+1)
 
c compute constant fh
fh=0.125*fil
 
c compute fluxes in x-direction
if (misdat.eq.0.) then
do j=1,ny
do i=2,nx
f1(i,j)=a(i-1,j)-a(i,j)
enddo
enddo
else
do j=1,ny
do i=2,nx
if ((a(i,j).eq.misdat).or.(a(i-1,j).eq.misdat)) then
f1(i,j)=0.
else
f1(i,j)=a(i-1,j)-a(i,j)
endif
enddo
enddo
endif
if (iperx.eq.1) then
c do periodic boundaries in the x-direction
do j=1,ny
f1(1,j)=f1(nx,j)
f1(nx+1,j)=f1(2,j)
enddo
else
c set boundary-fluxes to zero
do j=1,ny
f1(1,j)=0.
f1(nx+1,j)=0.
enddo
endif
 
c compute fluxes in y-direction
if (misdat.eq.0.) then
do j=2,ny
do i=1,nx
f2(i,j)=a(i,j-1)-a(i,j)
enddo
enddo
else
do j=2,ny
do i=1,nx
if ((a(i,j).eq.misdat).or.(a(i,j-1).eq.misdat)) then
f2(i,j)=0.
else
f2(i,j)=a(i,j-1)-a(i,j)
endif
enddo
enddo
endif
c set boundary-fluxes to zero
do i=1,nx
f2(i,1)=0.
f2(i,ny+1)=0.
enddo
if (ipery.eq.1) then
c do periodic boundaries in the x-direction
do i=1,nx
f2(i,1)=f2(i,ny)
f2(i,ny+1)=f2(i,2)
enddo
endif
if (iperx.eq.1) then
if (ispol.eq.1) then
c do south-pole
is=(nx-1)/2
do i=1,nx
f2(i,1)=-f2(mod(i-1+is,nx)+1,2)
enddo
endif
if (inpol.eq.1) then
c do north-pole
is=(nx-1)/2
do i=1,nx
f2(i,ny+1)=-f2(mod(i-1+is,nx)+1,ny)
enddo
endif
endif
 
c compute flux-convergence -> filter
if (misdat.eq.0.) then
do j=1,ny
do i=1,nx
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
enddo
enddo
else
do j=1,ny
do i=1,nx
if (a(i,j).eq.misdat) then
af(i,j)=misdat
else
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
endif
enddo
enddo
endif
end
 
c --------------------------------------------------------------------------------
c Read refernece profile from netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,oro,
> pvsrcfile)
 
c Read the reference profile from file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nx,nny,nz : Grid dimension in x,y,z direction
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
c coriol : Coriolis parameter (s^-1)
c oro : Height of orography (m)
c pvsrcfile : Input file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
real deltax,deltay,deltaz
real coriol (0:nx,0:ny)
real oro (0:nx,0:ny)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real x(0:nx,0:ny),y(0:nx,0:ny)
real mean,count
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
 
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
 
c Read data from netcdf file
isok=0
varname='NSQREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='RHOREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='THETAREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='PREREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ZREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='CORIOL'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,coriol,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ORO'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,oro,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='X'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,x,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='Y'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,y,stat)
if (stat.ne.0) goto 997
 
c Close netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Determine the grid spacings <deltax, deltay, deltaz>
mean=0.
count=0.
do i=1,nx
do j=0,ny
mean=mean+abs(x(i)-x(i-1))
count=count+1.
enddo
enddo
deltax=mean/count
 
mean=0.
count=0.
do j=1,ny
do i=0,nx
mean=mean+abs(y(j)-y(j-1))
count=count+1.
enddo
enddo
deltay=mean/count
 
mean=0.
count=0.
do k=1,nz-1
mean=mean+abs(zref(k+1)-zref(k-1))
count=count+1.
enddo
deltaz=mean/count
 
return
 
c Exception handling
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
stop
 
end
Property changes:
Added: svn:executable
/tags/1.0/docu/BoxedEPS.tex
0,0 → 1,803
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%% BoxedEPS.tex FOR FIGURE INSERTS OF EPSF NORM %%%%%
%%%%% (EPSF = Encapsulated PostScript File)
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%% AUTHOR: Laurent Siebenmann
%% lcs@matups.matups.fr
%%
%%% VERSIONS: Feb 1991 -- October, 1992
%%
%%% SOMMAIRE: BoxedEPS.tex d\'efinit des macro-commandes
%% qui permettent d'int\'egrer dans un document TeX des
%% objets graphiques d\'ecrits par fichier de norme EPSF,
%% tout en accordant a chacun le statut d'une bo\^ite TeX ayant
%% les bonnes dimensions. La (seule!) contribution unique
%% de ce fichier est de faire cela d'une fa{\c}con universelle.
%% C'est a dire de fa{\c}con \`a pouvoir commod\'ement
%% servir avec tout pilote d'imprimante de norme
%% PostScript --- malgr\'e l'absence d'une norme
%% pour \special.
%%
%%% POSTINGS: anonymous ftp
%% --- ftp 130.84.128.100 (alias rsovax.circe.fr);
%% login: anonymous; password: <anything>; directory
%% [anonymous.siebenmann]. This is the master copy in 1992.
%%
%% --- ftp 129.69.1.12 (alias rusinfo.rus.uni-stuttgart.de);
%% login: anonymous; password: <anything>;
%% directory hints .../tex/graphics/...
%%
%%%% DOCUMENTATION:
%% --- see BoxedEPS.doc
%%
%%%% ACTIVATION:
%% by a driver-by-driver protocol
%% see \SetTexturesEPSFSpecial
%% and its companions below.
%%
 
\ifx\MYUNDEFINED\BoxedEPSF
\let\temp\relax
\else
\message{}
\message{ !!! BoxedEPS %
or BoxedArt macros already defined !!!}
\let\temp\endinput
\fi
\temp
\chardef\EPSFCatAt\the\catcode`\@
\catcode`\@=11
 
\chardef\C@tColon\the\catcode`\:
\chardef\C@tSemicolon\the\catcode`\;
\chardef\C@tQmark\the\catcode`\?
\chardef\C@tEmark\the\catcode`\!
\chardef\C@tDqt\the\catcode`\"
 
\def\PunctOther@{\catcode`\:=12
\catcode`\;=12 \catcode`\?=12 \catcode`\!=12 \catcode`\"=12}
\PunctOther@
 
%%temporarily suppress Plain's logging of allocations
\let\wlog@ld\wlog
\def\wlog#1{\relax}
 
%% New for TOOLS
\newif\ifIN@
\newdimen\XShift@ \newdimen\YShift@
\newtoks\Realtoks
%%% New for Boxed EPSF
%
\newdimen\Wd@ \newdimen\Ht@
\newdimen\Wd@@ \newdimen\Ht@@
%
\newdimen\TT@
\newdimen\LT@
\newdimen\BT@
\newdimen\RT@
%
\newdimen\XSlide@ \newdimen\YSlide@
%
\newdimen\TheScale %% secretly scale in mils: 1pt= 1mil
\newdimen\FigScale %% secretly scale in mils: 1pt= 1mil
%
\newdimen\ForcedDim@@
 
\newtoks\EPSFDirectorytoks@
\newtoks\EPSFNametoks@
\newtoks\BdBoxtoks@
\newtoks\LLXtoks@ %% useful info for Oz
\newtoks\LLYtoks@
 
\newif\ifNotIn@
\newif\ifForcedDim@
\newif\ifForceOn@
\newif\ifForcedHeight@
\newif\ifPSOrigin
 
\newread\EPSFile@
%%%% MESSAGES (separate macro needed for Europe)
%%
\def\ms@g{\immediate\write16}
 
%%%% WORD-PROCESSING MACROS
%%
%%% \IN@0#1@#2@ : Is 1st exp of #1 in 1st exp of #2 ??
%% Answer in \ifIN@
\newif\ifIN@\def\IN@{\expandafter\INN@\expandafter}
\long\def\INN@0#1@#2@{\long\def\NI@##1#1##2##3\ENDNI@
{\ifx\m@rker##2\IN@false\else\IN@true\fi}%
\expandafter\NI@#2@@#1\m@rker\ENDNI@}
\def\m@rker{\m@@rker}
 
%%% \SPLIT@0#1@#2@ : Split 1st exp of #2 at 1st exp of #1
%% \Initialtoks@ , \Terminaltoks@ will contain pieces
\newtoks\Initialtoks@ \newtoks\Terminaltoks@
\def\SPLIT@{\expandafter\SPLITT@\expandafter}
\def\SPLITT@0#1@#2@{\def\TTILPS@##1#1##2@{%
\Initialtoks@{##1}\Terminaltoks@{##2}}\expandafter\TTILPS@#2@}
 
%%%% MACROS TO TRIM \ForeTrim@0#1@ and \Trim@0#1@
%% result appears in \Trimtoks@
%% LIMITATION: assume no multiple spaces to trim
 
\newtoks\Trimtoks@
 
%%% \ForeTrim@0#1@ trims initial space of first erpansion of #1
%% #1 of form \the\toks0 or \mymacro
\def\ForeTrim@{\expandafter\ForeTrim@@\expandafter}
\def\ForePrim@0 #1@{\Trimtoks@{#1}}
\def\ForeTrim@@0#1@{\IN@0\m@rker. @\m@rker.#1@%
\ifIN@\ForePrim@0#1@%
\else\Trimtoks@\expandafter{#1}\fi}
%%\m@rker expands here to \m@@rker since spot initial,
%% so no confusuion with \m@rker
 
%%% \Trim@0#1@ trims init and terminal spaces
%% Same syntax.
%% Warns if internal spaces found.
%%
\def\Trim@0#1@{%
\ForeTrim@0#1@%
\IN@0 @\the\Trimtoks@ @%
\ifIN@
\SPLIT@0 @\the\Trimtoks@ @\Trimtoks@\Initialtoks@
\IN@0\the\Terminaltoks@ @ @%
\ifIN@
\else \Trimtoks@ {FigNameWithSpace}%
\fi
\fi
}
 
 
%%%% MATH MACROS (provisional)
%% use dimen registers for reals; unit 1pt
%% (numerical dimension arguments OK unless contrary noted)
 
%%%% One needs the point token seq (pt with cat 12) USES dimen 0
\newtoks\pt@ks
\def \getpt@ks 0.0#1@{\pt@ks{#1}}
\dimen0=0pt\relax\expandafter\getpt@ks\the\dimen0@
 
%%% Convert dimen to "decimal multiplier"% USES dimens 0,2
\newtoks\Realtoks% the output!
\def\Real#1{%
\dimen2=#1%
\SPLIT@0\the\pt@ks @\the\dimen2@%% lop off the points
\Realtoks=\Initialtoks@%\showthe\Realtoks
}
 
%%% Multiplication
% USES dimens 0,2,4,6; preserves args; output \Product
\newdimen\Product
\def\Mult#1#2{%
\dimen4=#1\relax
\dimen6=#2%
\Real{\dimen4}%
\Product=\the\Realtoks\dimen6%
}
 
%%% Inverse
% USES dimens 0; preserves arg; output \Inverse
\newdimen\Inverse
\newdimen\hmxdim@ \hmxdim@=8192pt%halfmaxdimen
\def\Invert#1{%
\Inverse=\hmxdim@
\dimen0=#1%
\divide\Inverse \dimen0%
\multiply\Inverse 8}
 
%%% \Rescale#1#2#3 % USES dimens 0,2,4,6
%% alters dimen register #1 by ratio #2/#3
%% where #2,#3 can be raw dimensions OR dimen registers
\def\Rescale#1#2#3{% Adequate accuracy. Can improve.
\divide #1 by 100\relax
\dimen2=#3\divide\dimen2 by 100 \Invert{\dimen2}%
\Mult{#1}{#2}%
\Mult\Product\Inverse
#1=\Product}
 
%%% \Scale#1 scales dimen register #1
% by dimen register real \TheScale; USES dimens 0
\def\Scale#1{\dimen0=\TheScale %
\divide #1 by 1280 %% 1280*5120*10=1000*2^16
\divide \dimen0 by 5120 %
\multiply#1 by \dimen0
\divide#1 by 10 %% max size of #1 about 32000/10 pt
}
%%% SCRUNCHING BOXES AND SHIFTING CONTENTS
%% TeX has to do this in general
%% since some drivers do not let
%% one do it readily using Postscript
 
\newbox\scrunchbox
 
%%% \Scrunched#1 puts #1 in an hbox
%% then in effect zeros the dimensions of this box
\def\Scrunched#1{{\setbox\scrunchbox\hbox{#1}%
\wd\scrunchbox=0pt
\ht\scrunchbox=0pt
\dp\scrunchbox=0pt
\box\scrunchbox}}
 
%%% \Shifted@#1 puts #1 in \hbox
%% then locates basepoint to bottom left corner
%% then translates ink only by \XShift@,\YShift@
%% with Postscript convention
%% For simplicity use only on scrunched boxes
%\newdimen\XShift@
%\newdimen\YShift@
\def\Shifted@#1{%
\vbox {\kern-\YShift@
\hbox {\kern\XShift@\hbox{#1}\kern-\XShift@}%
\kern\YShift@}}
 
%%% \cBoxedEPSF#1 the main macro
%% component macros are explained in order below
 
\def\cBoxedEPSF#1{{\leavevmode
%% double brace for amstex \allign, \alligned, ...
\ReadNameAndScale@{#1}%
\SetEPSFSpec@
\ReadEPSFile@ \ReadBdB@x
%% Calculations
\TrimFigDims@
\CalculateFigScale@
\ScaleFigDims@
\SetInkShift@
\hbox{$\mathsurround=0pt\relax
\vcenter{\hbox{%
\FrameSpider{\hskip-.4pt\vrule}%
\vbox to \Ht@{\offinterlineskip\parindent=\z@%
\FrameSpider{\vskip-.4pt\hrule}\vfil
\hbox to \Wd@{\hfil}%
\vfil
\InkShift@{\EPSFSpecial{\EPSFSpec@}{\FigSc@leReal}}%
\FrameSpider{\hrule\vskip-.4pt}}%
\FrameSpider{\vrule\hskip-.4pt}}}%
$}%
\CleanRegisters@
\ms@g{ *** Box composed for the %
EPSF file \the\EPSFNametoks@}%
}}
\def\tBoxedEPSF#1{\setbox4\hbox{\cBoxedEPSF{#1}}%
\setbox4\hbox{\raise -\ht4 \hbox{\box4}}%
\box4
}
 
\def\bBoxedEPSF#1{\setbox4\hbox{\cBoxedEPSF{#1}}%
\setbox4\hbox{\raise \dp4 \hbox{\box4}}%
\box4
}
 
\let\BoxedEPSF\cBoxedEPSF% default setting
 
%% Some compatibility with BoxedArt.tex
%
\let\BoxedArt\BoxedEPSF
 
%% Some compatibility with Sweet-teX
%
\def\gLinefigure[#1scaled#2]_#3{%
\BoxedEPSF{#3 scaled #2}}
%% Some compatibility with Rokicki's dvips
%
\let\EPSFbox\bBoxedEPSF \let\EPSFfile\bBoxedEPSF
\def\EPSFxsize{\afterassignment\ForceW@\ForcedDim@@}
\def\ForceW@{\ForcedDim@true\ForcedHeight@false}
\def\EPSFysize{\afterassignment\ForceH@\ForcedDim@@}
\def\ForceH@{\ForcedDim@true\ForcedHeight@true}
 
\def\EmulateRokicki{%
\let\epsfbox\bBoxedEPSF \let\epsffile\bBoxedEPSF
\let\epsfxsize\EPSFxsize \let\epsfysize\EPSFysize}
%%% \ReadNameAndScale@#1
%
\def\ReadNameAndScale@#1{\IN@0 scaled@#1@% DOUBLE BARRELED
\ifIN@\ReadNameAndScale@@0#1@%
\else \ReadNameAndScale@@0#1 scaled\DefaultMilScale @%
\fi}
\def\ReadNameAndScale@@0#1scaled#2@{% HELPER MACRO
\let\OldBackslash@\\%
\def\\{\OtherB@ckslash}%
\edef\temp@{#1}%
\Trim@0\temp@ @%
\EPSFNametoks@\expandafter{\the\Trimtoks@ }%
\FigScale=#2 pt%
\let\\\OldBackslash@
}
\def\SetDefaultEPSFScale#1{%
\global\def\DefaultMilScale{#1}}
 
\SetDefaultEPSFScale{1000}
 
 
%%% \ReadEPSFile@
%
\def \SetBogusBbox@{%
\global\BdBoxtoks@{ BoundingBox:0 0 100 100 }%
\global\def\BdBoxLine@{ BoundingBox:0 0 100 100 }%
\ms@g{ !!! Will use placeholder !!!}%
}
 
{\catcode`\%=12\gdef\P@S@{%!}} %% %! min sign of PS file
 
\def\ReadEPSFile@{%\show\EPSFSpec@%
\openin\EPSFile@\EPSFSpec@
\relax %necessary to prevent precocious expansion of \ifeof
\ifeof\EPSFile@
\ms@g{}%
\ms@g{ !!! EPS FILE \the\EPSFDirectorytoks@
\the\EPSFNametoks@\space WAS NOT FOUND !!!}%
\SetBogusBbox@
\else%\fi
\begingroup%%
\catcode`\%=12\catcode`\:=12\catcode`\!=12
\catcode`\G=14\catcode`\\=14\relax% 14 is comment
\global\read\EPSFile@ to \BdBoxLine@%\show\BdBoxLine@
\IN@0\P@S@ @\BdBoxLine@ @%
\ifIN@ %% %! accepted as %!PS so do BdBox search!!
\NotIn@true
\loop
\ifeof\EPSFile@\NotIn@false
\ms@g{}%
\ms@g{ !!! BoundingBox NOT FOUND IN %
\the\EPSFDirectorytoks@\the\EPSFNametoks@\space!!! }%
\SetBogusBbox@
\else\global\read\EPSFile@ to \BdBoxLine@
%\show\BdBoxLine@
\fi
\global\BdBoxtoks@\expandafter{\BdBoxLine@}%
\IN@0BoundingBox:@\the\BdBoxtoks@ @%
\ifIN@\NotIn@false\fi%
\ifNotIn@\repeat
\else
\ms@g{}%
\ms@g{ !!! \the\EPSFNametoks@\space not PS!\space !!!}%
\SetBogusBbox@
\fi
\endgroup\relax
\fi
\closein\EPSFile@
}
 
 
%%% \ReadBdB@x
% Rmk For simplicity 0 not used in syntax
% of \ReadBdB@x@, \ReadBdB@x@@
\def\ReadBdB@x{% PART 0
\expandafter\ReadBdB@x@\the\BdBoxtoks@ @}
\def\ReadBdB@x@#1BoundingBox:#2@{% PART 1
\ForeTrim@0#2@%
\IN@0atend@\the\Trimtoks@ @%
\ifIN@\Trimtoks@={0 0 100 100 }%
\ms@g{}%
\ms@g{ !!! BoundingBox not found in %
\the\EPSFDirectorytoks@\the\EPSFNametoks@\space !!!}%
\ms@g{ !!! It must not be at end of EPSF !!!}%
\ms@g{ !!! Will use placeholder !!!}%
\fi%% cf \SetBogusBbox@
\expandafter\ReadBdB@x@@\the\Trimtoks@ @%
}
\def\ReadBdB@x@@#1 #2 #3 #4@{% PART 2
\Wd@=#3bp\advance\Wd@ by -#1bp%
\Ht@=#4bp\advance\Ht@ by-#2bp%
\Wd@@=\Wd@ \Ht@@=\Ht@ %% useful info for Clark
\LLXtoks@={#1}\LLYtoks@={#2}%% useful info for Oz
\ifPSOrigin\XShift@=-#1bp\YShift@=-#2bp\fi
}
 
%%% \SetEPSFDirectory
%
\def\G@bbl@#1{}
\bgroup
\global\edef\OtherB@ckslash{\expandafter\G@bbl@\string\\}
\egroup
 
\def\SetEPSFDirectory{% Part 1
\bgroup\PunctOther@\relax
\let\\\OtherB@ckslash
\SetEPSFDirectory@}
 
\def\SetEPSFDirectory@#1{% Part 2
\edef\temp@{#1}%
\Trim@0\temp@ @% result in \Trimtoks@
\global\toks1\expandafter{\the\Trimtoks@ }\relax
\egroup
\EPSFDirectorytoks@=\toks1
}
 
%%% \SetEPSFSpec@
\def\SetEPSFSpec@{%
\bgroup
\let\\=\OtherB@ckslash
\global\edef\EPSFSpec@{%
\the\EPSFDirectorytoks@\the\EPSFNametoks@}%
\global\edef\EPSFSpec@{\EPSFSpec@}%
\egroup}
 
%%% \TrimFigDims@
%
\def\TrimTop#1{\advance\TT@ by #1}
\def\TrimLeft#1{\advance\LT@ by #1}
\def\TrimBottom#1{\advance\BT@ by #1}
\def\TrimRight#1{\advance\RT@ by #1}
 
\def\TrimBoundingBox#1{%
\TrimTop{#1}%
\TrimLeft{#1}%
\TrimBottom{#1}%
\TrimRight{#1}%
}
 
\def\TrimFigDims@{%
\advance\Wd@ by -\LT@
\advance\Wd@ by -\RT@ \RT@=\z@
\advance\Ht@ by -\TT@ \TT@=\z@
\advance\Ht@ by -\BT@
}
 
 
%%% \CalculateFigScale@
%
\def\ForceWidth#1{\ForcedDim@true
\ForcedDim@@#1\ForcedHeight@false}
\def\ForceHeight#1{\ForcedDim@true
\ForcedDim@@=#1\ForcedHeight@true}
 
\def\ForceOn{\ForceOn@true}
\def\ForceOff{\ForceOn@false\ForcedDim@false}
\def\CalculateFigScale@{%
%Have default \FigScale or read \FigScale
\ifForcedDim@\FigScale=1000pt% %% start afresh
\ifForcedHeight@
\Rescale\FigScale\ForcedDim@@\Ht@
\else
\Rescale\FigScale\ForcedDim@@\Wd@
\fi
\fi
\Real{\FigScale}%
\edef\FigSc@leReal{\the\Realtoks}%
}
\def\ScaleFigDims@{\TheScale=\FigScale
\ifForcedDim@
\ifForcedHeight@ \Ht@=\ForcedDim@@ \Scale\Wd@
\else \Wd@=\ForcedDim@@ \Scale\Ht@
\fi
\else \Scale\Wd@\Scale\Ht@
\fi
\ifForceOn@\relax\else\global\ForcedDim@false\fi
\Scale\LT@\Scale\BT@ %%%\Scale\Wd@\Scale\Ht@
\Scale\XShift@\Scale\YShift@
}
%%% \ShowReservedBoxes
%% shows (prints) corrected scaled and positioned
%% bounding boxes; for diagnostics
%%% \HideReservedBoxes makes them invisible again
%%
\def\HideReservedBoxes{\global\def\FrameSpider##1{\null}}
\def\ShowReservedBoxes{\global\def\FrameSpider##1{##1}}
\let\HideDisplacementBoxes\HideReservedBoxes %% some synonyms
\let\ShowDisplacementBoxes\ShowReservedBoxes
\let\HideFigureFrames\HideReservedBoxes
\let\ShowFigureFrames\ShowReservedBoxes
\ShowDisplacementBoxes
%%% \hSlide#1, \vSlide#1
%%
\def\hSlide#1{\advance\XSlide@ by #1}
\def\vSlide#1{\advance\YSlide@ by #1}
%%% \SetInkShift@, \InkShift@#1
%%
\def\SetInkShift@{%
\advance\XShift@ by -\LT@
\advance\XShift@ by \XSlide@
\advance\YShift@ by -\BT@
\advance\YShift@ by -\YSlide@
}
%
\def\InkShift@#1{\Shifted@{\Scrunched{#1}}}
%%% \CleanRegisters@
%
\def\CleanRegisters@{%
\globaldefs=1\relax
\XShift@=\z@\YShift@=\z@\XSlide@=\z@\YSlide@=\z@
\TT@=\z@\LT@=\z@\BT@=\z@\RT@=\z@
\globaldefs=0\relax}
 
%%% Special syntax for several drivers. The macros
%% \SetTexturesEPSFSpecial %% Textures
%% \SetUnixCoopEPSFSpecial %% dvi2ps early unix
%% \SetBechtolsheimDVI2PSEPSFSpecial and
%% \SetBechtolsheimDVITPSEPSFSpecial %% by S.P.Bechtolsheim
%% \SetLisEPSFSpecial %% dvi2ps by Tony Lis
%% \SetRokickiEPSFSpecial %% dvips by Tom Rokicki
%% --- also for DVIReader, in DirectTeX by W. Ricken
%% \SetOzTeXEPSFSpecial %% OzTeX (>=1.42) by Andrew Trevorrow
%% \SetPSprintEPSFSpecial %% PSprint by Andrew Trevorrow
%% --- also for OzTeX versions <= 1.41 !!
%% \SetArborEPSFSpecial %% ArborTeX DVILASER/PS
%% \SetClarkEPSFSpecial %% dvitops by James Clark
%% \SetDVIPSoneEPSFSpecial %% DVIPSONE of Y&Y
%% \SetBeebeEPSFSpecial %% DVIALW by N. Beebe
%% \SetNorthlakeEPSFSpecial %% Northlake Software
%% \SetStandardEPSFSpecial %% Nonexistant: Placebo below
%% Many drivers supported roughly
%% by (re-)defining the macro \EPSFSpecial#1#2, where
%% #1 = EPS file pathname (use \\ for the letter backslash)
%% #2 = scale in mils
%% Be wary of using strange characters in pathnames!
%% Textures, Blue Sky Research, Barry Smith
\def\SetTexturesEPSFSpecial{\PSOriginfalse%\PSOrigintrue
\gdef\EPSFSpecial##1##2{\relax
\edef\specialthis{##2}%
\SPLIT@0.@\specialthis.@\relax
\special{illustration ##1 scaled
\the\Initialtoks@}}}
%% Unix : dvi2ps by: Mark Senn, Stephan Bechtolsheim,
% Bob Brown, Richard, Furuta, James Schaad, Robert Wells,
% Norm Hutchinson, Neal Holt, Scott Jones, Howard Trickey.
% Introduced by B. Horn <bkph@ai.mit.edu>
\def\SetUnixCoopEPSFSpecial{\PSOrigintrue % Please test!
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4}%dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%
%%convert dimen to real
\special{psfile=##1\space
hscale=\Aux@\space
vscale=\Aux@}}}
 
%% dvi2ps and dvitps by S.P. Bechtolsheim,
% Introduced by B. Horn <bkph@ai.mit.edu> and Carl.M.Jones,
% testing by R. Evans <Robert@cm.cardiff.ac.uk>
% Note that a prolog file psfig.pro
% specific to the driver should be available.
\def\SetBechtolsheimEPSFSpecial@{%% tool macro only
\PSOrigintrue
\special{\DriverTag@ Include0 "psfig.pro"}%
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt %% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4} %% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%% convert dimen to real
\special{\DriverTag@ Literal "10 10 0 0 10 10 startTexFig
\the\mag\space 1000 div 3.25 neg mul
\the\mag\space 1000 div .25 neg mul translate %% correction
\the\mag\space 1000 div \Aux@\space mul
\the\mag\space 1000 div \Aux@\space mul scale "}%
\special{\DriverTag@ Include1 "##1"}%
\special{\DriverTag@ Literal "endTexFig "}%
}}
 
%% dvi2ps and dvitps by S.P. Bechtolsheim,
% Introduced by B. Horn <bkph@ai.mit.edu> and Carl.M.Jones,
% testing by R. Evans <Robert@cm.cardiff.ac.uk>
% Note that a prolog file psfig.pro
% specific to the driver should be available.
\def\SetBechtolsheimEPSFSpecial@{%% tool macro only
\PSOrigintrue
\special{\DriverTag@ Include0 "psfig.pro"}%
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt %% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4} %% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%% convert dimen to real
\special{\DriverTag@ Literal "10 10 0 0 10 10 startTexFig
\the\mag\space 1000 div
dup 3.25 neg mul 2 index .25 neg mul translate %% correction line
\Aux@\space mul dup scale "}%
\special{\DriverTag@ Include1 "##1"}%
\special{\DriverTag@ Literal "endTexFig "}%
}}
 
\def\SetBechtolsheimDVITPSEPSFSpecial{\def\DriverTag@{dvitps: }%
\SetBechtolsheimEPSFSpecial@}
 
\def\SetBechtolsheimDVI2PSEPSFSSpecial{\def\DriverTag@{DVI2PS: }%
\SetBechtolsheimEPSFSpecial@}
 
%% dvi2ps by Tony Lis,
% implantations? ; dates?; availability?
% Introduced by B. Horn <bkph@ai.mit.edu>
\def\SetLisEPSFSpecial{\PSOrigintrue
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4}% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%
%%convert dimen to real
\special{pstext="10 10 0 0 10 10 startTexFig\space
\the\mag\space 1000 div \Aux@\space mul
\the\mag\space 1000 div \Aux@\space mul scale"}%
\special{psfile=##1}%
\special{pstext=endTexFig}%
}}
 
%% dvips by Tom Rokicki; free driver in portable C
% Introduced by W.D. Neumann <neumann@mps.ohio-state.edu>
\def\SetRokickiEPSFSpecial{\PSOrigintrue
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt% convert real to dimen
\divide\dimen4 by 10\relax
\Real{\dimen4}% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%
%%convert dimen to real
\special{psfile="##1"\space
hscale=\Aux@\space
vscale=\Aux@}}}
 
\def\SetInlineRokickiEPSFSpecial{\PSOrigintrue
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4}% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%
%%convert dimen to real
\special{ps::[begin] 10 10 0 0 10 10 startTexFig\space
\the\mag\space 1000 div \Aux@\space mul
\the\mag\space 1000 div \Aux@\space mul scale}%
\special{ps: plotfile ##1}%
\special{ps::[end] endTexFig}%
}}
 
%%% OzTeX (versions 1.42 and later), by Andrew Trevorrow
%%% (for earlier versions see PSprint below!!)
%% complete public domain TeX for Macintosh
%% Send 10 UNFORMATTED 800K disks
%% with return postage to
%% Peter Abbott, Computing Service,
%% Aston University, Aston Triangle, Birmingham B4 7ET
%% Posting: ftp midway.uchicago.edu
%% Nota: Version 1.42 may give
%% spurious "offpage" error notices on printing.
%% Nota: Support for MacPaint files not here yet.
\def\SetOzTeXEPSFSpecial{\PSOrigintrue
\gdef\EPSFSpecial##1##2{%
\dimen4=##2pt%% convert real to dimen
\divide\dimen4 by 1000\relax
\Real{\dimen4}%% dimens 0,2 used here
\edef\Aux@{\the\Realtoks}%% convert dimen to real
\special{epsf=\string"##1\string"\space scale=\Aux@}%
}}
 
%% PSprint, by AndrewTrevorrow for VaX VMS
%% and OzTeX versions <= 1.41
% tested 2-91 by Max Calviani <ISICA@ASTRPD.infn.it>
\def\SetPSprintEPSFSpecial{\PSOriginFALSE % artifice; see below
\gdef\EPSFSpecial##1##2{%note order
\special{##1\space
##2 1000 div \the\mag\space 1000 div mul
##2 1000 div \the\mag\space 1000 div mul scale
\the\LLXtoks@\space neg \the\LLYtoks@\space neg translate
}}}
 
%% DVILASER/PS driver originally written by David Fuchs
% marketed and supported by ArborTeXt 535 W. William St.
% Suite 300, Ann Arbor, MI 48103, U.S.A
% (313) 996-3566 (313) 996-3573
% help@arbortext.com, Andrew Dobrowolski
\def\SetArborEPSFSpecial{\PSOriginfalse % check!
\gdef\EPSFSpecial##1##2{%
\edef\specialthis{##2}%
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%% dvitops, (c) James Clark <jjc@jclark.uucp>
% public domain; distributed by UK TeX Archive
% computers: unix, msdos, vms, primos and vm/cms,
% introduced by S. Ratz <spqr@uk.ac.southampton.ecs>
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%% DVIPSONE, for PC compatibles
% Y&Y, 106 Indian Hill, Carlisle MA 01741, USA
% (508) 371-3286
% (introduced by B. Horn <bkph@ai.mit.edu>)
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%% DVIALW by N. Beebe, public domain
% DVI Driver Distribution, Center for Scientific Computing,
% Department of Mathematics, 220 South Physics Building,
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literal "##2 1000 div ##2 1000 div scale",
position = "bottom left",
include "##1"}}}
\let\SetDVIALWEPSFSpecial\SetBeebeEPSFSpecial
 
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\def\SetStandardEPSFSpecial{%
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\ms@g{}
\ms@g{%
!!! Sorry! There is still no standard for \string%
\special\space EPSF integration !!!}%
\ms@g{%
--- So you will have to identify your driver using a command}%
\ms@g{%
--- of the form \string\Set...EPSFSpecial, in order to get}%
\ms@g{%
--- your graphics to print. See BoxedEPS.doc.}%
\ms@g{}
\gdef\EPSFSpecial####1####2{}
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0,0 → 1,4320
\documentclass[12pt]{article}
 
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\pagenumbering{Roman}
 
% ----------------------------------------------------------------------------------------------
% Title page
% ----------------------------------------------------------------------------------------------
 
\thispagestyle{empty}
 
\vspace{0.7cm}
 
\begin{center}
 
{\Large\bf Numerical Piecewise Potential Vorticity Inversion \\[2mm]
A user guide for real-case experiments}
 
\vspace{1cm}
\begin{center}
\begin{minipage}[t]{10cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{Fig05_pv_320K.eps}
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\end{center}
 
 
\vspace{1cm}
Michael Sprenger, Ph.\,D.$^{1}$ \\
\vspace{0.3cm}
{\sl Institute for Atmospheric and Climate Science, ETH Z\"urich, Switzerland}\\
\vspace{1.8cm}
\today \\
{Diploma Thesis for the Postgraduate Course in Computer Science, FHSS Schweiz,\\
under the supervision of Lars Kruse, Ph.\,D.}
\end{center}
\vspace{2cm}
 
\noindent
{\sl $^1$Corresponding author and his address:}\\[1mm]
Michael Sprenger\\
Institute for Climate and Atmospheric Science, {\it IAC}ETH \\
ETH Zurich \\
CH-8092 Zurich, Switzerland \\
e-mail: michael.sprenger@env.ethz.ch
 
 
\newpage
\vspace{20cm}
\noindent
{\bf Title figure:} Ertel's potential vorticity at 320\,K.
 
% ----------------------------------------------------------------------------------------------
% Abstract
% ----------------------------------------------------------------------------------------------
 
\newpage
 
\begin{center}
{\large \bf Abstract}
\end{center}
 
\noindent
Potential vorticity (PV) is a key quantity in atmospheric dynamics. Its value is based upon several
points: (a) PV is conserved in purely adiabatic flows, i.e. if radiative and condensational heating and other
diabatic processes can be neglected; (b) under suitable balance conditions the specification of PV
in the interior of a domain and with boundary values for potential temperature completely determines
the flow field, in particular horizontal wind and temperature can be derived; (c) in many respects
the atmosphere can be partitioned into several distinct PV features, which then interact and allow
the dynamics to be interpreted as the interaction of these PV elements. Points (b) and (c) are known
as the invertibility and partitioning principle, respectively.\\
 
\noindent
In this thesis, a program package is presented which allows to isolate PV elements and then to
study their impact on the atmospheric flow field and on the temperature distribution. Technically,
this is done with a so-called PV inversion, which in turn comprises several different steps, as for
example transformation into suitable co-ordinate systems and numerical solution of a poisson equation. With PV inversion, two major problems arise: Firstly, a suitable balance condition must
be formulated, secondly the inversion problem for Ertel's PV is nonlinear, and therefore poses a significant challenge. The program presented in this thesis is based upon the so-called
quasi-geostrophic balance condition. More specifically, the linear quasi-geostrophic PV equation is
solved. Since quasi-geostrophic and Ertel's PV do not exactly coincide, an iterative technique
is adopted to approach the nonlinear Ertel-PV inversion by means of successively quasi-geostrophic
inversions.\\
 
\noindent
The aim of this work is to present an in-depth discussion of all steps which are needed for a PV inversion.
Special focus was given to a clear and user-friendly program package, where all steps are
well documented and hence are attractive for further development. In this respect, the complete
inversion is controlled by one single Linux Shell script.
The new user needs only to adjust some few paths in this script. The
main parameters for the inversion itself are specified in a separate parameter file.
 
\newpage
 
\begin{center}
{\large \bf Zusammenfassung}
\end{center}
 
\noindent
Die potentielle Vortizit\"at (PV) ist eine Kerngr\"osse der dynamischen Meteorologie. Ihre Bedeutung basiert auf mehreren Eigenschaften: (a) In einer adiabatischen Str\"omung, dh. wenn Strahlung,
die Freisetzung von latenter W\"arme und andere diabatische Prozesse vernachl\"assigt werden
k\"onnen, ist PV eine lagrange'sche Erhaltungsgr\"osse; (b) unter geeigneten Balancebedingungen bestimmt die Verteilung der PV im Innern und der potentiellen Temperatur am Rand eines Gebietes
vollst\"andig den Zustand der Atmosph\"are, insbesondere die horizontalen Windfelder und das
Temperaturfeld; (c) h\"aufig l\"asst sich die Atmosph\"are in mehrere, klar voneinander getrennte PV-Elemente unterteilen, die dann die Dynamik der Atmosph\"are durch ihre Wechselwirkung bestimmen.
Die Eigenschaften (b) und (c) sind in der Literatur bekannt als das Invertibilit\"atsprinzip und
Partitionierungsprinzip.\\
 
\noindent
In dieser Arbeit wird ein Programmpaket vorgestellt, mit dessen Hilfe sich einzelne PV-Elemente
isolieren und ihr Einfluss auf die atmosph\"arischen Windfelder und Temperaturen studieren
lassen. Programmtechnisch besteht diese sogenannte PV-Inversion aus mehreren Schritten. So muss
zum Beispiel eine Koordinatentransformation durchgef\"uhrt werden und eine Poisson-Gleichung
numerisch gel\"ost werden. Damit die PV-Inversion sinnvoll ist, m\"ussen zwei Probleme gel\"ost
werden. Zun\"achst muss eine geeignete Balancebedingung vorgegegeben sein. Ausserdem handelt es
sich bei der Inversion um einen nichtlinearen Prozess, der numerisch einige Herausforderungen
stellt. In dem Programmpaket dieser Arbeit wird die sogenannte quasi-geostrophische Balance
verwendet, dh. der mathematische/numerische Inversionsprozess besteht in der L\"osung der
linearen quasi-geostrophischen PV-Gleichung. Das Problem der Nichtlinearit\"at wird dadurch gel\"ost, dass
die Berechnung des genannten linearen Inversionsproblems mehrmals wiederholt wird. Iterativ
ergibt sich somit eine L\"osung des nichtlinearen Problems.\\
 
\noindent
Ziel dieser Arbeit ist eine detailierte Darstellung aller Schritte, die bei einer PV-Inversion
n\"otig sind. Besonderes Augenmerk wurde bei der Entwicklung des Programmpakets auf die klare
Strukturierung und Anwenderfreundlichkeit gelegt. Dadurch kann das Paket einerseits als Black-Box
verwendet werden, zugleich erlaubt es erfahrenen Benutzern eine leichte Einarbeitung in die
Programme und damit die M\"oglichkeit zu deren Erweiterung. Die ganze Inversion wird von einem einzigen
Linux Shell Skript kontrolliert, in dem lediglich einige wenige Pfade angepasst werden m\"ussen. Die
meisten Parameter, welche das gestellte Problem der PV-Inversion beschreiben, sind in einer
separaten Parameterdatei eingetragen.
 
 
 
 
% ----------------------------------------------------------------------------------------------
% Inhalt
% ----------------------------------------------------------------------------------------------
 
\newpage
\section*{Contents}
 
\vspace{0.5cm}
\renewcommand{\contentsname}{}
\contentsline{section}{\hspace{0.5cm} Abstract}{III}
\contentsline{section}{\hspace{0.5cm} Zusammenfassung}{IV}
\contentsline{section}{\hspace{0.5cm} Abbreviations}{VII}
\contentsline{section}{\hspace{0.5cm} List of Figures}{VIII}
\vspace{-1.5cm}
\tableofcontents
 
 
 
% ----------------------------------------------------------------------------------------------
% Abkürzungen
% ----------------------------------------------------------------------------------------------
 
\newpage
\section*{Abbreviations}
 
\vspace{0.5cm}
\begin{tabular}{rll}
{\bf [1]} & {\bf DWD} & Deutscher Wetterdienst (German weather service)\\[2mm]
{\bf [2]} & {\bf ECMWF} & European Centre for Medium Range Weather Forecasts\\[2mm]
{\bf [3]} & {\bf ERA-40} & Re-analysis of the ECMWF for the periods 1958-2001\\[2mm]
{\bf [4]} & {\bf ERA-15} & Re-analysis of the ECMWF for the periods 1979-1993\\[2mm]
{\bf [5]} & {\bf ETH} & Eidgen\"ossische Technische Hochschule\\[2mm]
{\bf [6]} & {\bf f} & Coriolis parameter (in $s^{-1}$)\\[2mm]
{\bf [7]} & {\bf IACETH} & Institute for Atmospheric and Climate Science at ETH Zurich\\[2mm]
{\bf [8]} & {\bf METEOSAT} & European geostationary weather satellite\\[2mm]
{\bf [9]} & {\bf MeteoSwiss} & Swiss weather service\\[2mm]
{\bf [10]} & {\bf NaN } & Not a Number (missing data flag)\\[2mm]
{\bf [11]} & {\bf netcdf } & Compact and random-access file format\\[2mm]
{\bf [12]} & {\bf NWP } & Numerical weather prediction\\[2mm]
{\bf [13]} & {\bf $N^2$ } & Squared Brunt-Vais\"al\"a frequency (in $s^-2$)\\[2mm]
{\bf [14]} & {\bf PV} & Potential vorticity (if not otherwise stated Ertel's potential vorticity)\\[2mm]
{\bf [15]} & {\bf pvu} & Potential vorticity unit\\[2mm]
{\bf [16]} & {\bf PDE} & Partial differential equation\\[2mm]
{\bf [17]} & {\bf SOR} & Successive over-relaxation\\[2mm]
{\bf [18]} & {\bf T} & Temperature (in $^\circ$C)\\[2mm]
{\bf [19]} & {\bf $T_v$} & Virtual temperature (in $^\circ$C)\\[2mm]
{\bf [20]} & {\bf U} & Zonal velocity component (in west/east direction)\\[2mm]
{\bf [21]} & {\bf V} & Meridional velocity component (in south/north direction)\\[2mm]
{\bf [22]} & {\bf $\omega$} & Vertical velocity component (in Pa/s)\\[2mm]
{\bf [23]} & {\bf q} & Specific humidity (in kg/kg)\\[2mm]
{\bf [24]} & {\bf $\theta$} & Potential temperature (in K)\\[2mm]
{\bf [25]} & {\bf $\rho$} & Air density (in kg/m$^3$)\\[2mm]
{\bf [26]} & {\bf R$_d$} & Gas constant for dry air (in kg/m$^3$)\\[2mm]
{\bf [27]} & {\bf $\epsilon$} & Ratio of gas constants for dry air and water vapour\\[2mm]
{\bf [28]} & {\bf g} & Earth's gravity (in kg m/s$^2)$\\
\end{tabular}
 
\newpage
\listoffigures
 
% ----------------------------------------------------------------------------------------------
% Introduction and Motivation
% ----------------------------------------------------------------------------------------------
 
\newpage
\clearpage
\pagenumbering{arabic}
 
\section{Introduction and Motivation}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{sat_wv.ps}
\end{minipage}
\\
\caption{\it Water vapour satellite imagery (in gray shading) and isolines of Ertel's potential vorticity (PV)
at 350\,hPa and for 3 May 1998, 12\,UTC. Dark regions indicate a dry upper troposphere, whereas bright and white regions are
indicative for a lot of moisture in the upper troposphere. Note that high-PV regions are coincident with
dry regions. }
\label{satwv}
\end{center}
\end{figure}
 
There are different ways how the state of the atmosphere can be described. Traditionally this is done by specification of temperature, horizontal and vertical wind components and of either pressure, if geometrical height is used as the vertical co-ordinate, or geopotential height, if pressure is used as the vertical co-ordinate. This traditional approach has its main advantage in its simplicity. On the other hand, theoretical physics has often experienced the case that new insight can be gained if abstract, but physically more fundamental quantities were introduced. Consider for example the introduction of action and its primary physical parameter, the Planck constant. Similarly, geophysical fluid dynamics and hence atmospheric dynamics made some transitions away from the simple traditional meteorological fields toward more abstract ones.\\
 
\noindent
A long existing concept of engineering fluid dynamics is the concept of vorticity, which mathematically is defined as the curl of the wind vector field. Vorticity is treated in nearly every text book on fluid dynamics, for instance in Acheson (1990). Vorticity is a scalar quantity, but nevertheless, in a divergent-free and two-dimensional flow its specification is sufficient to deduce the complete velocity field. We could call this the invertibility principle for vorticity in such a non-divergent and two-dimensional flow. Moreover, an interesting conservation law hold for vorticity under these assumptions: Following the fluid motion, vorticity is conserved, i.e. its lagrangian derivative with respect to time is zero. Probably, in its most elegant way this conservation principle is expressed in Kelvin's circulation theorem (Acheson, 1990). These concepts of barotropic flow and of conservation of vorticity were indeed the basis for the first numerical weather predictions by Charney in 1950 (for an interesting history of numerical weather prediction, consult either Lynch, 2006, or Nebeker, 1995).\\
 
\noindent
Of course, the atmosphere cannot be treated in an exact way as a barotropic fluid. It constitutes a
stratified fluid where density and pressure decreases with increasing height. Therefore, a suitable
generalisation of the barotropic-vorticity equation for the real atmosphere is by far not trivial, but would be highly desirable.
Potential vorticity goes into this direction. The fundamental work by Rossby (1940) and Ertel (1942)
showed that potential vorticity is conserved in adiabatic (no latent heat release, no radiative heating
or cooling) and frictionless flow. The generalisation of the "invertibility principle for vorticity"
in two-dimensional flow was first stated in a rough way by Kleinschmidt (1950). He was able to attribute
some low-level flow features to an upper-level PV anomaly, in his words to a "Zyklonenk\"orper". Figure\,1
is a nice illustration of an upper-level PV anomaly. It shows some isolines of Ertel's PV on 350\,hPa,
which form an elongated and narrow filament of high PV extending from Scandinavia south to the north-western
edge of Spain. Remarkably, this anomaly of high PV is also discernible as a dark band in the water vapour
imagery of the geostationary METEOSAT weather satellite. Hence, the high PV band is associated with a very dry upper troposphere. \\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{Fig11_PVInv_tropo1.ps}
\end{minipage}
\\
\caption{\it Section across the circularly symmetric structure induced by an isolated, circularly symmetric, cyclonic potential vorticity anomaly near the model tropopause across which the Rossby-Ertel potential vorticity has a strong discontinuity, by a factor of 6. The bold line is the tropopause, the horizontal
thin lines are potential temperature, plotted at 5\,K intervals, and the circular/elliptical lines denote tangential velocity, at 3\,m/s intervals. The structure is typical for middle latitudes; the Coriolis parameter is $10^{-4}s^{-1}$ (as at geographical latitude $43.3^\circ$N). The domain shown has a radius of 2500\,km (taken from McIntyre,
1997).}
\label{inversion}
\end{center}
\end{figure}
 
\noindent
A very influential set of equations was introduced by Charney by means of a scale analysis of the dynamical equations (1948). These so called quasi-geostrophic equations are well suitable to describe synoptic and planetary-scale
processes, whilst neglecting smaller-scale features. Although these equations nowadays are considered no
longer of sufficient accuracy for numerical weather prediction, they nevertheless still are of great importance in
theoretical dynamic meteorology due to their simplicity and elegance (Holton, 1992).
Along with this set of equations came a new version of potential vorticity. This quasi-geostrophic
potential vorticity is linearly "linked" to the flow and temperature field, and -particularly interesting for
this study- an invertibility principle can be formulated. Indeed, the linear relationship between quasi-geostrophic potential vorticity and the flow field makes it very interesting since sophisticated
numerical techniques exist for the solution of this kind of problem. An example of such an inversion is shown in Fig.\,\ref{inversion} where
a cyclonic potential-vorticity anomaly near a model tropopause is shown. The potential vorticity is high
in the stratosphere and low in the troposphere. Therefore, the downward excursion of the tropopause is
associated locally with anomalously high potential vorticity. This anomaly is marked in the figure with
stippling. The "horizontal" lines correspond to the potential temperature, the "circular/elliptical" contours to the tangential velocity. Note that the isolines of potential temperature (the so-called isentropes) are
pulled upwards below the PV anomaly, and pulled downward within the PV anomaly. An interesting aspect of
the upward pulling of the isentropes is the associated reduction in atmospheric stability. Due to the reduced
vertical gradient of potential temperature, the atmosphere is more prone to convective instability. In fact,
in a recent study Martius et al. (2006) showed that many heavy precipitation events in the south of the Alps are
associated with such upper-level distortions of the tropopause, and hence with a PV anomaly. Moreover, note
that the upper-level PV anomaly is not only associated with a deformation of the isentropes, but is
also linked with a wind field. The induced wind field in this idealised setting reaches 21\,m/s at its maximum and
is cyclonically (anti-clockwise) oriented. The wind field is strongest at the tropopause level, but is even discernible at
the surface far below the anomaly. In this respect, the PV field exhibits a far-field effect, and this in turn
is the basic idea behind the invertibility principle. If this principle is taken together with the partitioning
principle, its explaining power becomes particularly attractive. This latter principles states that the atmospheric state can
be expressed as the interaction of isolated PV elements. This immediately invokes a research strategy, which is: to
enter, modify or remove some of these PV elements, and to see how the flow evolves in the thus
changed state. A very influential review article on PV and PV thinking was presented by Hoskins et al. (1985).
Here the key elements of PV thinking are discussed and applied to many atmospheric dynamical problems. \\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\vspace{-2cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{streamer.eps}
\end{minipage}
\\[-2cm]
\caption{\it Stratospheric PV streamer and positions with stratosphere-troposphere mass exchange. The section is
for 1 January 1986, 06\,UTC and on the 320\,K isentrope. It is taken from the ERA-15 data set of the ECMWF. In color Ertel's potential vorticity is shown in pvu. Mass exchange from the stratosphere to the troposphere is
marked with stars, transport in the opposite direction by open circles (taken from Sprenger et al., 2007)}
\label{streamer}
\end{center}
\end{figure}
 
 
\noindent
Many studies relate to this PV thinking perspective. For instance, Davis and Emanuel (1991) looked at the
potential vorticity diagnostics of cyclogenesis; Fehlmann and Davies (1997) investigated the impact of PV
structures on precipitation events over Europe. In addition to this methodology, PV has gained a lot of
interest in recent years as a diagnostic tool. Indeed, from a dynamicist's point of view it is highly
attractive to use potential vorticity as the defining component of the extra-tropical tropopause (Stohl et al. 2003). Typically,
this value is set to 2\,pvu, and every air parcel with larger PV is treated as stratospheric and
every air parcel with lower PV as tropospheric. This definition allows to discuss the dynamics of the extra-tropical tropopause, as it would not be feasible with the more common thermal (or lapse-rate) definition of the tropopause. In Fig.\,\ref{streamer} a prominent feature of the extra-tropical tropopause is shown: a stratospheric
PV streamer. It corresponds to a pronounced excursion of stratospheric (high-PV) air towards the south. These
features are quite common in the extra-tropics and are important for the mass exchange between the stratosphere
and the troposphere, amongst other impacts (for example they are often related to cyclogenesis). The positions where stratospheric mass (and chemical constituents, as for example ozone) crosses the tropopause are marked in the figure by stars. They are predominantly found on the upstream
(western) side of the streamer. Crossing in the opposite direction, i.e. from the troposphere to the stratosphere,
on the other hand occurs on the downstream (eastern) side of the streamer. Interesting questions emerge from the
inspection of a such a figure: If the intensity, or the southward excursion of the PV streamer was reduced, would there still be a significant mass flux across the tropopause? These, and similar questions are at the heart of
the PV inversion, which is introduced in this study.\\
 
 
\noindent
The study is organised in the following way: In chapter 2 the mathematical problem of PV inversion is
formulated and some essential aspects of the numerical algorithm are discussed. Chapter~3 introduces some
key aspects for the re-structuring of the program package.
Then, in chapter 4 a detailed
example of PV inversion is discussed. This part is intended to be a practical user guide for PV inversion,
and therefore rather detailed technical aspects are presented. Chapter 5 follows with some helpful
diagnostic tools which allow to quality and impact of the PV inversion. Finally, chapter 6 concludes
with some general remarks and wishes regarding the PV inversion tool.
 
 
 
 
\newpage
 
\section{Mathematical Framework and Numerical Aspects}
 
In this study we use the quasi-geostrophic approximation for the real-case
inversion problem. In this limit the relative (quasi-geostrophic) potential vorticity
$q$ is given by:\\[-2mm]
 
\[
q = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} ( \frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z})
\]
 
\vspace{0.3cm}
\noindent
with the boundary values of potential temperature at the upper and lower lid and
of zonal and meridional wind components at the lateral boundaries:\\[-2mm]
 
\[
g \cdot \frac{\theta^*}{\theta_0} = f \cdot \frac{\partial \psi}{\partial z}
\quad \quad
u = -\frac{\partial \psi}{\partial y}
\quad \quad
v = -\frac{\partial \psi}{\partial x}
\]
 
\vspace{0.3cm}
\noindent
Here $N_0^2$, $\rho_0$ and $\theta_0$ denote the squared Brunt-V\"as\"ala frequency, the density and the
potential temperature of a reference state depending only on the vertical co-ordinate $z$. $\psi$ is the
streamfunction from which the horizontal wind components can be derived. Finally, $f$ is the Coriolis parameter
which measures the Earth's rotation rate (typically $10^{-4}s^{-1}$ in the mid-latitudes and 0 at the equator),
and $g$ is the Earth's gravity.\\
 
 
 
\noindent
The above equations constitute a so-called von Neumann boundary problem for the elliptic
differential equation relating the potential vorticity $q$ to the streamfunction $\psi$. Hence,
the elliptic partial differential equation (PDE) can be transformed into the general form:\\[-2mm]
 
\[
\frac{\partial}{\partial x}(\alpha \cdot \frac{\partial \psi}{\partial x}) +
\frac{\partial}{\partial y}(\beta \cdot \frac{\partial \psi}{\partial y}) +
\frac{\partial}{\partial z}(\gamma \cdot \frac{\partial \psi}{\partial z}) +
\sigma = 0
\]
 
\vspace{0.3cm}
\noindent
where the coefficients $\alpha$, $\beta$, $\gamma$ and $\sigma$ are easily expressed in terms of
the density $\rho_0$, the Coriolis parameter $f$ and the squared Brunt-Vais\"al\"a frequency $N^2$:\\[-2mm]
 
\[
\alpha = \rho_0(z) \quad \quad
\beta = \rho_0(z) \quad \quad
\gamma = \frac{f^2(y) \cdot \rho_0(z)}{N_0^2(z)} \quad \quad
\sigma = - \rho_0(z) \cdot q(x,y,z)
\]
 
\vspace{0.3cm}
\noindent
The next step is to discretise the above PDE by means of finite differences. We assume that all
fields (quasi-geostrophic PV $q$, streamfunction $\psi$,...) are defined on a three-dimensional grid, whose
grid points can be addressed by the three indices $i$, $j$, and $k$ in the x-, y- and z-direction (see Fig.\,ref{grid}). With this
convention, the discretised PDE can be written as:\\[-2mm]
 
\[
\Delta_x(A \cdot \Delta_x \psi) +
\Delta_y(B \cdot \Delta_y \psi) +
\Delta_z(C \cdot \Delta_z \psi) +
S = 0
\]
 
\vspace{0.3cm}
\noindent
Here the operators $\Delta_x(A \cdot \Delta_x\psi)$, $\Delta_y(B \cdot \Delta_y\psi)$ and
$\Delta_z(C \cdot \Delta_z\psi)$ at the grid position $i,j,k$ are defined by:
 
\begin{eqnarray*}
\Delta_x(A \cdot \Delta_x\psi)_{i,j,k} & = &
A_{i+1/2,j,k} \cdot (\psi_{i+1,j,k}-\psi_{i,j,k}) -
A_{i-1/2,j,k} \cdot (\psi_{i,j,k}-\psi_{i-1,j,k}) \\[0.2cm]
\Delta_y(B \cdot \Delta_y\psi)_{i,j,k} & = &
B_{i,j+1/2,k} \cdot (\psi_{i,j+1,k}-\psi_{i,j,k}) -
B_{i,j-1/2,k} \cdot (\psi_{i,j,k}-\psi_{i,j-1,k}) \\[0.2cm]
\Delta_z(C \cdot \Delta_z\psi)_{i,j,k} & = &
C_{i,j,k+1/2} \cdot (\psi_{i,j,k+1}-\psi_{i,j,k}) -
C_{i,j,k-1/2} \cdot (\psi_{i,j,k}-\psi_{i,j,k-1})
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
Some simple algebra yields the following expressions for $A$, $B$ and $C$:
 
\begin{eqnarray*}
A_{i,j,k} & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \alpha_{i,j,k}\\[0.2cm]
B_{i,j,k} & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \beta_{i,j,k}\\[0.2cm]
C_{i,j,k} & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \gamma_{i,j,k}
\end{eqnarray*}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{numericalgrid.eps}
\end{minipage}
\\
\caption{\it The numerical grid for the PV inversion in an xz cross-section. The horizontal grid spacing is $\Delta x$
in the x-direction (and correspondingly $\Delta y$ in the y-direction), the vertical grid spacing $\Delta z$. Note that in the vertical, a staggered grid at half-levels is also needed (taken from Fehlmann, 1997).}
\label{grid}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\noindent
Finally, the additive operator $S$ is expressed as:
 
\[
S_{i,j,k} = \Delta x \cdot \Delta y \cdot \Delta z \cdot \sigma_{i,j,k}
\]
 
\vspace{0.3cm}
\noindent
It turns out to be advantageous to have the coefficients $\alpha$, $\beta$, $\gamma$ and $\sigma$
not only on the 3d grid where the quasi-geostrophic PV and the streamfunction are defined, but to
have them also on intermediate points. These leads to the grid structure which is shown in Fig.\,\ref{grid}.
On the left side the indices for the $\psi$-grid is shown, i.e. for the grid where the
quasi-geostrophic PV and the streamfunction is defined. The right side gives the indices for the
coefficients $\alpha$, $\beta$, $\gamma$ and $\sigma$, i.e. for the intermediate layers.\\
 
\noindent
Let $\rho(k) = \rho_{k/2}$ and $N^2(k)=N^2_{k/2}$, hence expressing the vertical grid with intermediate layers. With these definitions the coefficients $A$, $B$ and $C$ for the inversion problem are readily obtained (note that these coefficients are dependent only on the vertical index z):
 
\begin{eqnarray*}
A_k & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \rho(2k) \quad (k=0,...,nz)\\[0.2cm]
B_k & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \rho(2k) \quad (k=0,...,nz)\\[0.2cm]
C_k & = & \frac{\Delta y \cdot \Delta z}{\Delta x} \cdot \frac{\rho(k) \cdot f^2}{N^2(k)} \quad (k=0,...2\cdot nz)
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
The additive operator $S$ depends on all three grid indices. In its discretised form it is:
 
\[
S_{i,j,k} = - \Delta x \cdot \Delta y \cdot \Delta z \cdot \rho(2k) \cdot q_{i,j,k}
\quad (i=0,...,nx, j=0,...,ny, k=0,...,nz)
\]
 
\vspace{0.3cm}
\noindent
It is convenient to additionally define the coefficients $C_{-1}=C_0$ and $C_{2nz+1}=C_{2nz}$. With
all these definitions the fully discretised quasi-geostrophic PV equation can be written as:
 
\begin{eqnarray*}
S_{i,j,k} & = &
\quad \quad (\psi_{i-1,j,k}-2\psi_{i,j,k}+\psi_{i+1,j,k}) \cdot A_k \\[0.2cm]
& & + \quad (\psi_{i,j-1,k}-2\psi_{i,j,k}+\psi_{i,j+1,k}) \cdot B_k \\[0.2cm]
& & + \quad (\psi_{i,j,k-1} - \psi_{i,j,k}) \cdot C_{2k-1} \\[0.2cm]
& & + \quad (\psi_{i,j,k+1} - \psi_{i,j,k}) \cdot C_{2k+1}
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
with the indices ranges as follows: $i=0, ... nx$ and $k=0, ... nz$. In addition to this discretised
PV equation, additional equations must be specified for terms like $\psi_{-1,j,k}$. These discretised
von Neumann boundary conditions are:
 
\begin{eqnarray*}
A_k \cdot (\psi_{0,j,k} - \psi_{-1,j,k}) & = & {\Delta y} \cdot {\Delta z} \cdot \rho(2k) \cdot v_a(j,k)\\[0.2cm]
A_k \cdot (\psi_{nx+1,j,k} - \psi_{nx,j,k}) & = & {\Delta y} \cdot {\Delta z} \cdot \rho(2k) \cdot v_b(j,k)\\[0.2cm]
B_k \cdot (\psi_{i,0,k} - \psi_{i,-1,k}) & = & -{\Delta x} \cdot {\Delta z} \cdot \rho(2k) \cdot u_a(i,k)\\[0.2cm]
B_k \cdot (\psi_{i,ny+1,k} - \psi_{i,ny,k}) & = & -{\Delta x} \cdot {\Delta z} \cdot \rho(2k) \cdot u_b(i,k)
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
where $u_a,u_b$ denote the velocity components in x direction at the left (western) and right (eastern) lateral boundary, and
correspondingly $v_a,v_b$ denote the velocity components in y direction at the front (southern) and back (northern) lateral boundary. Additional boundary values are specified at the lower and upper lid of the domain:
 
\begin{eqnarray*}
C_{-1} \cdot (\psi_{i,j,0} - \psi_{i,j,-1}) & = & {\Delta x} \cdot {\Delta z} \cdot
\frac{f \cdot g \cdot \rho(0) \cdot \theta_{bot}(i,j)}{N^2(0) \cdot \theta_0(0)}\\[0.2cm]
C_{2 nz + 1} \cdot (\psi_{i,j,nz+1} - \psi_{i,j,nz}) & = & {\Delta x} \cdot {\Delta z} \cdot
\frac{f \cdot g \cdot \rho(2 nz) \cdot \theta_{top}(i,j)}{N^2(2 nz) \cdot \theta_0(2 nz)}
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
Here, $\theta_{bot}$ and $\theta_{top}$ denote the boundary conditions for potential temperature at the
lower and upper lid of the domain.\\
 
\noindent
This is a system of linear equations which can be expressed as\\[-2mm]
 
\[
B\psi = b
\]
 
\vspace{0.3cm}
\noindent
where $B$ is a $m \times m$ matrix with in total $m=(nx+1) \cdot (ny+1) \cdot (nz+1)$ elements (not to be
confused with the above coefficients $B_k$). This linear
system has a solution if the following condition is fulfilled:
 
\[
\sum_{i,j,k} b_{i,j,k} = 0
\]
 
\vspace{0.3cm}
\noindent
This is exactly the discrete version of the compatibility condition in section~5.1. The derivation of the
condition starts with the observation that the null space, i.e. the kernel of the system is at least
one-dimensional because the non-trivial vector $\psi_{i,j,k}=1 \forall i,j,k$ is element of this kernel. Physically, this expresses the fact that the streamfunction is determined only up to an additive constant. Since the kernel of the linear system is at least one-dimensional, the image of the operator $B$ is
at most (m-1) dimensional. Moreover, the operator $B$ is normal, and therefore the image is orthogonal to the
kernel. Because $b$ is in the image of the operator $B$ and $\psi_{i,j,k}=1$ is in the kernel, the two vectors
are orthogonal. This leads immediately to the necessary consistency condition $\sum_{i,j,k} b_{i,j,k} = 0$.
Note that this expresses a complicated relationship which must be fulfilled by the interior PV distribution and the boundary values of potential temperature and horizontal wind components, because $b$ includes all these
forcing terms.\\
 
\noindent
The consistency condition is not met if vanishing boundary values are specified. This automatically
leads to an inconsistency in the numerical solution of the equation. In practice, the fulfillment
of the consistency condition can be enforced if a potential temperature "correction" is added at the
lower and upper lid, this correction being uniform and of opposite sign on the two boundaries. For
reasonable PV and temperature distributions this additive temperature shift remains smaller than about 2\,K.\\
 
\noindent
There exist several techniques how to solve linear systems of equations. Here we adopt the successive
over-relaxation (SOR) method: Let $A$ be a linear operator which is represented by an $m \times m$ matrix, and
let $\omega$ be a real number (the relaxation parameter) such that $|1-\omega (1+A)|< 1$. Then a solution
of the equation can be obtained iteratively, starting with an arbitrary first guess $\psi_i^{(0)}$. The iterations
 
\[
\psi_i^{(n+1)} = \omega \cdot (b_i - \sum_{j=1}^{i-1} A_{i,j} \cdot \psi_j^{(n+1)}
- \sum_{j=i}^{m} A_{i,j} \cdot \psi_j^{(n)})
+ (1-\omega) \cdot \psi_i^{(n)}
\]
 
\vspace{0.3cm}
\noindent
converge toward the solution of the system $A\psi + \psi =b$. If we choose $A=B-1$, the iterations converge toward a solution of the quasi-geostrophic PV equation. \\
 
\noindent
Note that the above outlined algorithm allows to overwrite the variable $\psi_i^{(n)}$ with the updated
variable $\psi_i^{(n+1)}$, and therefore needs a minimum of computational memory. In the Fortran program
{\em inv\-cart.f} the number of iterations and the SOR parameter $\omega$ are specified. The are set to 500 iterations and 1.81, respectively.
 
% ----------------------------------------------------------------------------------------------
% Program philosophy
% ----------------------------------------------------------------------------------------------
 
\newpage
\section{Re-Structuring of the Code}
 
In this section some key concepts of the program package are described. In fact, an earlier version of the package already existed (developed originally by Rene Fehlmann and later modified by Sebastien Dirren) and the present work is based upon this pre-existing package. So, the question arises what added value this re-development and re-structuring of the code is associated with. The basic
idea is to provide a code which fulfills the following three requirements:
 
\begin{center}
\begin{minipage}[t]{10cm}
\begin{itemize}
\item[a)] {\bf Transparency and Modularity}\\[-3mm]
\item[b)] {\bf Universality and Model Independence}\\[-3mm]
\item[c)] {\bf User friendliness}
\end{itemize}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
In the following parts, a detailed discussion is intended to illustrate how this requirements were missing in the existing code
and how they could be incorporated into the new version. Before doing so, it is worthwhile to consider why the original code was lacking these requirements. A short review of the relevant literature
illustrates that the situation is actually quite common. Any software which is really used has to be adapted to the changing demands. It must be maintained. Unfortunately this maintenance often leads
to a degeneration of the code. The changes introduced into the code then make necessary some further
adaptions, and so on. Finally, in the end the code becomes so "distorted" and "chaotic" that often
a complete re-coding is easier to be done than a re-structuring of the existing version. The
remedy against this code degeneration is a continuous re-structuring. Hence, if changes in the code
are obligatory due to new user demands, it is important not only to introduce the needed changes
short-sightedly. The overall structure of the program should be kept in mind, and if possible
long-term perspectives in code maintenance should be allowed, although such a long-term perspective
momentarily leads to an additional effort. \\
 
\noindent
Computer science, in particular software engineering, has defined the term "re-structuring" (or
"re-factoring" for object-oriented programming languages) for the process how code should be
maintained in order to avoid severe degeneration. Fowler defines the term re-factoring in the
following way (taken from URL {\em www.refactoring.com}):\\
 
\begin{center}
\parbox{14cm}{"Refactoring is a disciplined technique for restructuring an existing body of code, altering its internal structure without changing its external behavior. Its heart is a series of small behavior preserving transformations. Each transformation (called a 'refactoring') does little, but a sequence of transformations can produce a significant restructuring. Since each refactoring is small, it's less likely to go wrong. The system is also kept fully working after each small refactoring, reducing the chances that a system can get seriously broken during the restructuring."}
\end{center}
 
\vspace{0.6cm}
\noindent
Hence, the key aspect of re-structuring is to continuously maintain the code, not only in
its performance, but also in its readability, documentation and adaptabilty to needed
changes.\\
 
\vspace{0.3cm}
\noindent
Scientific programming in particular is very prone to code degeneration. This is certainly due
to the fact that cutting-edge science is, by "definition", investigating what is not known.
Therefore, if for instance a computer program is written to numerically simulate a physical
process, it might well turn out during the development of the code that complete new aspects
must be included. This naturally leads to chaotically structured code. In the present case, i.e.
for the PV inversion program, this certainly explains to a large part why the code became
so un-organised. Several works have been done with the program, several researchers included
into the code what they needed for their specific task, without considering that other users might have no use of their changes. The results was a program package which, in principle, was still
working, but the knowledge of how to apply it went lost.\\
\noindent
A first rough inspection immediately made
clear that major changes were necessary to make the code available to a broader community again.
Would it have been possible to only re-organise the code and write a new user guide? In a first
try, this was in fact considered. But then the advantages of a more or less complete
re-coding turned out to be more suitable. Hence, the original software package joined the
sad fate of so many degenerated codes: a complete re-coding. On the other hand, such a re-coding
must be seen as a great chance. It allows to improve the code in such a way, as it would never be
possible if only "slight" changes at the existing code were made.\\
\noindent
In the following three
subsections, some key aspects of this re-coding will be presented. They are by no means
exhausting, but should give an impression of the new "philosophy". Hopefully, they also motivate
future users of the program package to "successfully" maintain it.
 
\subsection{Transparency and Modularity}
 
What makes a computer program readable? Probably one of the most important points is "modularity".
The problem to be solved numerically can and should be split into several distinct steps. For instance,
for the PV inversion a classic three step splitting is appropriate: pre-processing, PV inversion, and post-processing. Moreover, each of these three primary steps can further be split into several secondary sub-steps.
In the existing code, the splitting of the problem into distinct sub-problems was not clearly discernible. Indeed, the main Fortran program included not only the numerical inversion of the quasi-geostrophic PV equation, but also some of the
preparatory steps and some of the post-processing steps. \\
 
\noindent
A major improvement was gained by a very strict separation of the distinct primary steps. So, pre-processing, inversion and post-processing are done by three completely separated program packages. This strict
separation is supported by the fact that three separated directories are used: There is one directory where pre-processing is done, on directory where inversion is done, and finally one directory where post-processing is done. A flow of data between the three directories is allowed only at well-defined
steps within the whole process. At the end of pre-processing the relevant files, and only those, are moved to the inversion (or run) directory. Similarly, at the end of the inversion, the relevant files
are moved from the run directory to the post-processing directory.\\
 
\noindent
Additional improvement resulted from a very clear separation of the sub-processes in the three main-processes (pre-processing, inversion, post-processing). In fact, it was not tried to incorporate
all preparatory steps into one large Fortran program, but instead each well-defined task (as for example transformation into a new co-ordinate system) constitutes a separate Fortran program. This
modularity is very similar to the "philosophy" of the Linux operating system: Keep flexibility and
clarity by offering not one program which handles everything (and thereby becomes a "monstrosity"), but offer many flexible and simple tools which the user only has to combine in order to perform complex tasks.\\
 
\noindent
What else except for modularity can be done to improve the readability of computer programs? It is obvious, and probably the most neglected aspect of good computer code generation: in-code documentation. Every
small sub-section of a computer program should be documented. It should be possible to gain
insight into an algorithm only by looking at the in-code documentation. It is definitely not
sufficient only to document for every subroutine what its aim is and what its interface is, although
quite often even this most basic principle is not fulfilled. Hence, in the re-coding of the
PV inversion focus was led to good documentation: Where are files opened, where variables initialised, what is a subroutine call meaning? \\
 
\noindent
Finally a remark concerning the used programming language. A complete re-coding of a software package might also be
a chance to switch to a "better" programming language. In the present case, the original code was written in
Fortran 77, and this language was also used for the re-coding. Fortran, and in particular its older version
Fortran 77, is by far not a modern language. Comparing its vocabulary and its structural elements to languages like C++ or Java, its power is very limited. Moreover, Fortran includes jump statements like {\em Goto} which could easily make
any code un-readable. So why do so many research codes still rely on Fortran? In fact, most numerical
weather prediction models are written in Fortran. There are two reasons why the PV inversion was written in Fortran: Firstly, the small vocabulary and the intuitive naming of the inherent Fortran commands
makes it quite easy to read a code. Many researches never had a profound introduction into programming. Nevertheless they should be able to implement algorithms for their daily work. This is easily done with Fortran, and certainly much easier done than using object-oriented concepts offered by C++ and other modern languages. The PV inversion should be available
to a research community which has excellent algorithmic thinking, but only a "weak" background in computer languages. Fortran is an optimal choice in this respect. The second reason why the re-coding was done in Fortran is its high performance. In fact, PV inversion is very resource demanding, and compilers must create fast-running codes in order
the PV inversion tool to be helpful.\\
 
\noindent
Regarding the "unholy" {\em Goto} statements, it can be immediately said that good programming style is not restricted to languages which do not offer a {\em Goto} statement. A well-structured and carefully developed Fortran program is
certainly preferable to a "bad" algorithm in a "good" computer language, "good" meaning that this language offers many
controlling structures. Probably, a key concept of well-written computer code is a good balance between the "power" of a (Fortran)
subroutine and its length (expressed in the number of code lines). Two extreme examples might illustrate this point: If no subroutines at all are used, i.e. if the program consists only in one single main program, the algorithm might get
"lost" in two many "technical" details. On the other hand, if every single and minor step is a separate subroutine, the
code lacks clarity due to the large number of subroutines. In the present re-coding of the PV inversion, focus was given
to a good balance of functionality (power) of a subroutine and its length.
 
 
\subsection{Universality and Model Independence}
 
Universality was another aspect which was important in re-coding the PV inversion. In the present
example universality might be better named "model independence". Model in this respect refers either to different numerical weather prediction (NWP) models or to idealised experiments. In the former case,
the variety of NWP models is very large. The PV inversion tool was originally written for the Europa
model (EM) of the German weather service (DWD). Later it was applied to the higher-resolution
model (HRM and CHRM) which was run by the DWD and the Swiss weather service (MeteoSwiss). In recent years, the
non-hydrostatic local model (LM) developed by the DWD replaced the HRM in regional
weather forecasting. So, an adaption of the existing PV inversion code would have been necessary.
Moreover, PV inversion is particularly attractive for global-scale data sets. So, the method and the
programs were adapted to conform with the global model of the European Centre for Medium Range Forecasts (ECMWF). To make things worse, idealised experiments should also be performed. What actually
makes the situation so difficult is that each model has its own horizontal grid structure and its own vertical grid structure. For instance, ECMWF uses a terrain-following co-ordinate system which in higher levels becomes a pressure-level co-ordinate system, quite in contrast what is used by the regional LM model (a variant of geometrical height). \\
 
\noindent
Model independence cannot completely avoided. It is a fact which has to be adopted and cleverly
dealt with. In the re-coding, model aspects were removed in the first two preparatory steps (out of
eight different steps, see section~4.4) and the way back to the model is done in the last post-processing steps.
Essentially the preparatory steps interpolate the needed meteorological fields onto a stack of height levels and
transforms the fields into a local quasi-cartesian co-ordinate system. After completing these steps, the other preparatory steps and the PV inversion itself is completely independent of the model from which the input data is retrieved. As a particular example consider the PV inversion of a structure over the North Pole. In the existing code such an inversion would not have been feasible due to the convergence of the
longitude circles at the North Pole. The new code, on the other hand, elegantly circumvents this
problem by introducing a new quasi-cartesian co-ordinate system centered over the North Pole. In this
respect the North Pole is not different from any other region on the globe.\\
\noindent
With respect to idealised experiments, the following strategy was adopted. This kind of experiments
is generally so different from what is needed for real-case studies that a complete separation
is preferable. So, in contrast to the existing code, this type of experiments is now handled by
a completely separated program package. Of course, many programs "overlap" or are even identical, but it nevertheless makes sense to treat the two kind of experiments (real-case versus idealised) separately.
 
 
 
 
 
\subsection{User Friendliness}
 
Computer programs are not written for a computer's joy, but because they should solve a problem
which cannot be solved analytically by any person. So, computer programs are tools which should
make "life" easier for their users, or at least they should make some problems tractable. If the
user-interface of a computer program is chaotic and badly structured, the computer does not complain.
The user, on the other hand, might give up using the tool simply because it needs too much effort to understand how the program must be handled. Scientific programs are especially in danger of
having bad user-interfaces because these kind of programs are always "in the flow". This in turn
means that often it is not worthwhile to develop a graphical user-interface, as it is an absolute
must for commercial software. \\
 
\noindent
In the existing code for the PV inversion the user-interface was highly "chaotic". It consisted of
several hundred lines of Linux Shell scripts which were difficult to read -partly due to lack of documentation, partly due to the unnecessarily complex structure. The behaviour of the inversion
was controlled by many variables set in the beginning of the Linux Shell script, set without
knowing exactly where and when these variables are used. This gave the user a "bad feeling" about
his experiments, simply because it was not always clear what changing parameters really meant.\\
 
\noindent
Although a graphical user-interface is not provided for the new version, an attractive command-based
interface is now available. This interface essentially consists of two parts. Firstly, a Linux Shell script
is provided which handles all calls to the computing Fortran programs. For instance, {\em inversion.sh prep} runs through all preparatory steps. User friendliness is reached by the fact the the user needs to make no changes to this Linux Shell script, although its limited size and documentation would make it quite simple.
Probably the best user-interface is provided by a parameter file. Such a file is provided in the new
version, and all parameters describing the inversion problem can be entered into this file. In fact,
this kind of user-interface was motivated by sophisticated numerical weather prediction (NWP) models. There too,
the specifications characterising a model run are passed to the NWP model by means of a parameter
file.\\
 
 
\noindent
What else made the existing user-interface chaotic? A close inspection revealed that the flow of data and information was absolutely non-transparent. Meteorological fields were moved from one file to
another, only to be renamed there and subsequently being moved again to another file. For a part-time user it would have been impossible to keep track of the flow of information. In the new code the flow of information is very strictly controlled (see also the above subsection~3.1). In fact, there are many different files involved in the PV inversion:
input files, several intermediate files and finally the output files. It is not the number of files which makes a
process difficult to understand. If the flow of information is well controlled, it remains tractable. For the case of
the PV inversion, this information flow can be kept clear, and this was indeed an important aspect of the re-coding.
 
 
% ----------------------------------------------------------------------------------------------
% PV Inversion for Real Cases
% ----------------------------------------------------------------------------------------------
 
\newpage
 
\section{Inversion of an Extra-tropical PV Streamer}
 
\subsection{Scientific question}
 
The PV inversion starts with the selection of a distinct PV anomaly which should be
removed or added to the original PV distribution. It is then the aim to analyse
and compare the meteorological fields of horizontal wind and potential temperature
associated with the modified PV distribution with the corresponding fields associated with
the original PV distribution.\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_20060114_18_315K.eps}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_20060115_18_315K.eps}
\end{minipage}
\\
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_20060116_18_315K.eps}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_20060117_18_315K.eps}
\end{minipage}
\\
\begin{minipage}[t]{11cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_colorbar.eps}
\end{minipage}
\\
\caption{\it Time evolution of Ertel's potential vorticity (PV) on the 315\,K isentropic surface. The four
plots are for 14, 15, 16 and 17 January 2006, 18\,UTC. The PV inversion will be exemplified in this user guide for 16 January 2006, 18\,UTC.}
\label{question}
\end{center}
\end{figure}
 
\noindent
The time evolution of potential vorticity (PV) on the 315\,K isentropic surface shows a distinct feature over the Eastern United States (Fig.\,\ref{question}). This so-called stratospheric PV streamer is indicative for
a deep intrusion of stratospheric air towards the equator. In the course of the four days shown, the
PV streamer moves towards the east, and in the later stages exhibits an cyclonic rolling-up. An eminent
question is how this stratospheric PV streamer influences the atmospheric flow in its neighbourhood. From theoretical
considerations, it can be expected that the impact on the horizontal velocity and on the static stability
is quite large (see introduction, Fig.\,2). By means of the so-called quasi-geostrophic omega equation (Holton, 1992), it is also expected that pronounced
vertical motions are directly associated with the passage of the PV streamer. It is the aim of this study -and of PV inversion in general- to surmount the qualitative argumentation, and to
quantitatively assess the impact of such a structure on the atmospheric flow. \\
 
\noindent
In the following chapters, all steps are discussed which are needed to quantify this impact. Here, we
exemplarily consider the date of 16 January 2006, 18\,UTC, and determine explicitly for this date
the atmospheric response the upper-level (near tropopause level) PV structure.
 
 
 
\subsection{Necessary input files}
 
\begin{figure}[t]
\vspace{-2cm}
\begin{center}
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{q_20060116_18_500hPa.eps}
\end{minipage}
\hspace{-0.6cm}
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{t_20060116_18_500hPa.eps}
\end{minipage}
\\[-3cm]
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{uv_20060116_18_500hPa.eps}
\end{minipage}
\hspace{-0.6cm}
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{ps_20060116_18_500hPa.eps}
\end{minipage}
\\[-2cm]
\caption{\it Specific humidity (g/kg), temperature (in $^\circ$C), wind vectors
at 500\,hPa and surface pressure for 16 January 2006, 18\,UTC. These field are needed
as input for the PV inversion, and are available on the so-called P file.}
\label{inpp}
\end{center}
\end{figure}
Several preparatory steps are necessary before the PV inversion itself can be
performed. Here each of these steps is described in detail and -where possible-
illustrated with suitable figures. Starting point of the analysis is the P and
Z file of the ECMWF (re-)analysis:
 
\begin{itemize}
\item {\bf P20060116\_18} with temperature T (in $^\circ$C), horizontal wind components U,V (in m/s) in
zonal and meridional direction, respectively,
specific humidity Q (in kg/kg) and surface pressure PS (in hPa).
\item {\bf Z20060116\_18} with geopotential height Z (in m) on a stack of pressure
levels (for instance on 850, 500 and 250\,hPa).
\end{itemize}
 
\begin{figure}[t]
\vspace{-2cm}
\begin{center}
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{z_20060116_18_250hPa.eps}
\end{minipage}
\hspace{-0.6cm}
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{z_20060116_18_500hPa.eps}
\end{minipage}
\\[-3.5cm]
\begin{minipage}[t]{8.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{z_20060116_18_850hPa.eps}
\end{minipage}
\\[-1.5cm]
\caption{\it Geopotential height (in m) on 250, 500 and 850\,hPa for 16 January 2006, 18\,UTC. These field are needed
as input for the PV inversion, and are available on the Z file.}
\label{inpz}
\end{center}
\end{figure}
 
\noindent
Figure\,\ref{inpp} shows temperature T, specific humidity Q and wind vectors (U,V) at 500\,hPa and the surface pressure for 16 January 2006, 18\,UTC. A narrow band of high specific humidity is discernible on the downstream
side (to the east) of the PV streamer (upper-left panel). Most probably, this extended band is directly associated with
the southerly winds which prevail to the east of the PV streamer, and which are able to transport moist
air from the warm subtropics to the north. In the temperature field (upper-right panel), the PV streamer's impact is also discernible. It is associated -at this level- by a local warm anomaly. On theoretical grounds, we would expect a local cold anomaly below the streamer and a local warm anomaly within and above the streamer (see introduction, Fig.\,2). The present signal indicates that the streamer reaches far down into the troposphere, and enforces a local warm anomaly at the low level of 500\,hPa. As already mentioned before, and explicitly shown by the wind vectors (lower-left panel), the PV streamer is also associated with a cyclonic flow. Besides the impact on the temperature field, this PV induced flow field is the most eminent impact of a PV streamer. Indeed, it is the wind field where the far-field effect of a PV streamer becomes most evident, because the streamer's impact on temperature and stratification is essentially confined to the
regions just below or above.
Finally, the P file contains the surface pressure PS (lower-right panel), which of course to the largest extent simply reflects the surface topography. So for instance,
the high topography of the Rocky Mountains or of the Greenland ice shield, is associated with low
surface pressure, 700\,hPa corresponding to about 3\,km height above sea level.\\
 
\noindent
In addition to the P file, a so-called Z file must be provided as input for the PV inversion. This file contains the geopotential height on a distinct set of pressure levels. Typically, these levels are
850, 500 and 250\,hPa. A plot of these levels is shown in Fig.\,\ref{inpz}. The need for this reference levels
will become evident in a subsequent section. In short: They are needed to integrate the hydrostatic equation and thereby to transform from pressure to geometrical height as vertical co-ordinate.
Note how the PV streamer over the west Atlantic is discernible in the geopotential as a deep trough.
 
 
 
\subsection{An overview of the inversion}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{6cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{threesteps.eps}
\end{minipage}
\\
\caption{\it Data flow diagram for the three steps of the PV inversion. The preparatory steps are
essentially performed in the input directory, the inversion in the run directory and the output is
finally written to the output directory.}
\label{threesteps}
\end{center}
\end{figure}
 
The PV inversion can be split into three well-separated steps. The first step is associated with
preparations, in particular with the definition of the modified Ertel-PV field. In addition, some
preparatory steps have to be performed in order to adapt the ECMWF grid to the cartesian grid which is
assumed in the inversion algorithm. In the second step the atmospheric state is iteratively adjusted to
the modified PV field, as it was specified in the previous preparatory step. This second part comprises the "core" of the algorithm, i.e. the numerical inversion of the quasi-geostrophic potential
vorticity equation by means of a successive over-relaxation (SOR) technique. Finally, in the third step
the modified atmospheric state is brought back from the cartesian grid of the inversion to the
original latitude/longitude grid of the ECMWF, including its hybrid vertical co-ordinate. After this
step a direct comparison between input and output fields is feasible due to the equivalent
grid structure of input and output fields. The basic three steps are shown in Fig.\,\ref{threesteps}, and will subsequently be described in greater detail in the following sections. Before doing so, a note has to be made on the user-interface for the PV inversion.\\
 
 
\noindent
The inversion is controlled by one master Linux Shell script (inversion.sh), which calls the performing Fortran programs
(for a complete listing of the Linux Shell script consider Appendix~9.2).
A major aim of this work was to make the
application of the inversion as easy as possible. Therefore, the typical user is not forced to study
the master script itself, but can provide all needed parameters by means of a so-called "parameter file"
(inversion.param).
The contents of this file is parsed by a Perl script, which extracts all needed information. In the
description of the subsequent steps, the relevant parts of this parameter file will be reproduced and
described. A complete listing of the parameter file can be found in Appendix~9.3.\\
 
 
\noindent
Nevertheless, it will be necessary for an advanced usage of the inversion package to go into
some greater details. For instance, if particular PV structures should be removed or added, the
implemented simple filtering approach (to be discussed in section~4.4.4) might not be sufficient.
In this case, the advanced user is encouraged to modify the Fortran code in order to fulfill his particular
tasks.\\
 
 
\noindent
In a first step some directories must be specified. This is done in the parameter file {\em inversion.param} in the section DATA. For the example of this study this section looks like:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\begin{verbatim}
BEGIN DATA
DATE = 20060116_18;
INP_DIR = /lhome/sprenger/PV_Inversion_Tool/real/inp;
RUN_DIR = /lhome/sprenger/PV_Inversion_Tool/real/run;
OUT_DIR = /lhome/sprenger/PV_Inversion_Tool/real/out;
END DATA
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The first argument (DATE) gives the date of the case. Then the following three entries specify the input (INP\_DIR), the run (RUN\_DIR) and the output (OUT\_DIR) directory, respectively. These directories can be created by the call
\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\begin{verbatim}
inversion.sh inst
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
For test reasons a set of sample files is provided. These sample P20060115\_18 and Z20060115\_18 files can be copied to the input directory with the call
\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\begin{verbatim}
inversion.sh sample
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The fields available on the two files are:
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Q & Specific humidity ($kg/kg$) & P20060116\_18 \\
U & Zonal velocity ($m/s$) & P20060116\_18 \\
V & Meridional velocity ($m/s$) & P20060116\_18 \\
T & Temperature ($^\circ C$) & P20060116\_18 \\
OMEGA & Vertical velocity ($Pa/s$) & P20060116\_18 \\
PS & Surface pressure ($hPa$) & P20060116\_18 \\
\hline
Z & Geopotential height ($m$) on 850, 500 and 250\,hPa & Z20060115\_18 \\
\hline
\end{tabular}
\end{center}
 
 
\vspace{0.5cm}
\noindent
With these preparatory steps, the inversion can be performed. The following sections discuss the three basic step, i.e. the preparation of the input files for the inversion, the inversion itself and the post processing of the output files.
 
 
 
\subsection{Pre-processing: Defining the inversion problem [prep]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{12cm}
\vspace{2.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{preparation.eps}
\end{minipage}
\\
\caption{\it Flowchart of preparatory steps. Additionally, to the left of the single steps the
essential flow of information is shown. For instance, H $\rightarrow$ R means that the input is taken from
the file with prefix H and the output is then written to the file with prefix R.}
\label{preparation}
\end{center}
\end{figure}
 
Firstly, the vertical co-ordinate
has to be changed from pressure to geometrical height (section~4.4.1) and the fields have to be
transformed from the geographical latitude/longitude grid to a cartesian grid (section~4.4.2). Then additional meteorological
fields have to be computed on this new cartesian grid (section~4.4.3). With these two preparations the
Ertel-PV anomaly can be defined (section~4.4.4), and the input files for the quasi-geostrophic PV inversion be written
(section~4.4.5). Some additional steps are then: definition of a reference profile (in section~4.4.6) and
the transformation of the coastlines into the cartesian grid (section~4.4.6).\\
 
\noindent
These single steps have to be done once for every inversion problem. A complete flowchart of
the preparatory steps is shown in Fig.\,\ref{preparation}. In the following description every single step will
be launched and discussed individually. If desired, the call
\\[0.0cm]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\begin{verbatim}
inversion.sh prep
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.6cm}
\noindent
will run through all steps without waiting for intermediate check. This is particularly practical if all
settings remain essentially unchanged, and therefore a detailed check after each step is not necessary.
 
 
\subsubsection{Transformation to height levels [prep1]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{10cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{sigma_level.eps}
\end{minipage}
\\
\caption{\it Illustration of the terrain-following hybrid co-ordinate system of the ECMWF grid.
Here it is shown with 15 levels, recent versions of the ECMWF model contain 60 hybrid levels for the ERA-40 re-analysis and 91 levels for the operational analysis and deterministic 10\,day forecast [illustration taken
from "An Introduction to dynamic meteorology" by Holton, 1992].}
\label{sigma}
\end{center}
\end{figure}
 
The input data are available on a latitude/longitude grid
in the horizontal and on a so-called hybrid $\sigma$-grid on the vertical. Whereas the former is
well known, the latter needs some explanation. The basic idea is illustrated in Fig.\,\ref{sigma}. The
model levels are terrain-following, and the pressure p(i,j,k) at a specific grid point (with grid indices i,j,k) is given by the expression:
\[
p(i,j,k) = ak(k) + bk(k)*ps(i,j)
\]
 
\vspace{0.3cm}
\noindent
where $ps(i,j)$ is the pressure at the surface at the specified grid position. The two one-dimensional
arrays $ak$ and $bk$ are part of the P file, more specifically of the constants file associated with the P file. The main advantage of this hybrid grid is its non-intersection with the ground, which
facilitates many numerical calculations.\\
 
\noindent
The ECMWF fields are easily plotted on pressure surfaces since the vertical co-ordinate of the
underlying data set is essentially based upon pressure. On the other hand, the inversion program
assumes a cartesian grid with geometrical height (in m) as vertical co-ordinate. Therefore, all needed fields from the
original P file must be interpolated onto a stack of height levels. This transformation is easily
done by means of the hydrostatic equation:
\[
\frac{\partial p}{\partial z} = - \rho \cdot g
\]
 
\vspace{0.3cm}
\noindent
where $\rho$ denotes the density of moist air and $g$ is the Earth's gravity. Note that this
equation can be re-formulated to one including temperature if the ideal gas equation
\[
p = \rho \cdot R_d \cdot T_v
\]
is used and $\rho$ replaced. Here $R_d$ is the ideal gas constant of dry air and $T_v$ is the virtual temperature,
i.e. the temperature corrected for the water vapour contents of the air. The definition of
virtual temperature takes into account the specific humidity of an air parcel and its (sensible)
temperature (see for instance Wallace and Hobbs, 1977):\\
\[
T_v = T \cdot \{ 1 - \frac{q}{\epsilon} \cdot (1 - \epsilon) \}^{-1} \approx
T \cdot ( 1 + \epsilon \cdot q )
\]
 
\vspace{0.3cm}
\noindent
where $T$ is the temperature (in K), $q$ the specific humidity (in kg/kg), $\epsilon=R_d/R_v$ is the ratio of the gas constant for dry ($R_d$) air and water vapour ($R_v$). \\
 
\noindent
With the previous definitions, the hydrostatic equation can be integrated vertically to get
the height as a function of the pressure p:
 
\[
z(p) = z_{ref} - \frac{R_d}{g} \cdot \int_{\log(p_{ref})}^{\log(p)} T_v \cdot d\log(p)
\]
 
\vspace{0.3cm}
\noindent
where $z_{ref}$ and $p_{ref}$ denote the reference level. If several reference levels are given
(for example at 850, 500 and 250\,hPa, see Fig.\,7) the integration can be performed from the nearest
reference level to the specified pressure level. Note that at least one reference level
must be given, i.e. at one pressure level the geometrical height must be known.
Typically, this correspondence is known for the 500\,hPa level (see Fig.\,\ref{hydro}). As a result
of the integration, the geometrical height is given as a function of the pressure at all points
of the model grid.\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pro_t_70w40n_20060115_18.eps}
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pro_q_70w40n_20060115_18.eps}
\end{minipage}
\\
\caption{\it Left: Vertical profile of temperature (in $^\circ$C) in dependence of pressure at 70$^\circ$W
and 40$^\circ$ for 15 January 2006, 18\,UTC. Additionally the reference pressure levels are included with
the corresponding geopotential height (in m). Right: Vertical profile of specific humidity (in g/kg).}
\label{hydro}
\end{center}
\end{figure}
 
\noindent
In addition to the geometrical height at each grid point, the hydrostatic equation can be integrated
downward to obtain a consistent estimate of topography height. In fact, if the surface pressure
$p_s$ is given, the height of the topography is readily determined by\\
 
\[
z(p_s) = z_{ref} - \frac{R_d}{g} \cdot \int_{\log(p_{ref})}^{\log(p_s)} T_v \cdot d\log(p)
\]
 
\vspace{0.3cm}
\noindent
The advantage of the thus determined topography (instead of using the ECMWF topography) is its
consistency.\\
 
\noindent
Having determined the geometrical height $z(i,j,k)$ at each grid point $i,j,k$ in addition to the already known
pressure $p(i,j,k)$, it is straightforward to interpolate a field (temperature, velocity,...) onto an arbitrary height level.
The method adopted here is to lie a natural cubic spline through the grid points along a vertical
profile and then to evaluate the spline at the pre-specified height levels. In detail: The cubic spline at a horizontal grid position $i,j$ is based upon the values $[x_k=z(i,j,k),y_k=T(i,j,k)]$ if temperature $T$ is to be interpolated onto
a stack of height levels. Having determined the associated cubic spline $T_{sp}$, temperature at an arbitrary height $z$
can be calculated by evaluating the cubic spline at this level: $T_{sp}(z)$. The algorithm for the cubic spline is taken from Press et al. (1992).
\\
 
 
\noindent
The interpolation onto height levels is done with the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep1
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
which numerically
integrates the hydrostatic equation and therefore attributes to each grid point not only its
pressure (in hPa) but also its geometrical height (in m). The relevant numerical parameters are taken from the
parameter file {\em inversion.param}, where the following section is essential:\\
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN GRID
GEO_ZMIN = 0.;
GEO_NZ = 125 ;
GEO_DZ = 200.;
END GRID
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The three parameters describe the new vertical co-ordinate. The lowest levels is assumed to be at ground
(GEO\_ZMIN), the number of vertical levels is 125 (GEO\_NZ) and the vertical resolution is equidistantly
200\,m (GEO\_DZ). Hence, the new vertical grid spans the range from ground up to 25\,km.\\
 
\noindent
The output file H20060115\_18 is a new netcdf file which has now geometrical height as vertical co-ordinate
and the variables ({U,V,T,Q}) interpolated onto the height levels from surface up to 25\,km. Note that the height of the topography ({ORO}) is also
determined. If a model level is below the topography, all field values are set to missing data. The following table gives all the variables which are available on the new H file:\\
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Q & Specific humidity ($kg/kg$) & H20060116\_18 \\
U & Zonal velocity ($m/s$) & H20060116\_18 \\
V & Meridional velocity ($m/s$) & H20060116\_18 \\
T & Temperature ($^\circ C$) & H20060116\_18 \\
P & Pressure ($hPa$) & H20060116\_18 \\
ORO & Height of topography ($m$) & H20060116\_18 \\
\hline
\end{tabular}
\end{center}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{14cm}
\vspace{-1cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{latlon_nh.eps}
\end{minipage}
\\[-0.5cm]
\caption{\it Latitude/longitude grid of the ECMWF P and Z files. For clarity, the grid spacing was reduced to 5 degrees, instead of the 1 degree in the files. Meteorological fields -as for instance
temperature, wind vectors, pressure and geopotential- are given at the intersection of the latitude and
longitude circles. Note how this grid becomes singular toward the north pole.}
\label{latlon}
\end{center}
\end{figure}
 
 
\subsubsection{Rotating to a quasi-cartesian co-ordinate system [prep2]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{local_cart_grid.eps}
\end{minipage}
\\
\caption{\it Local cartesian grid which is centered at the PV streamer's position and which
shows much less distortion due to the sphericity of the Earth. The center of the new grid
corresponds to the rotated latitude and longitude (0,0). The boundaries are at $-31^\circ$ and
$+31^\circ$ rotated longitude, and at $-31^\circ$ and $+31^\circ$ rotated latitude.}
\label{localcart}
\end{center}
\end{figure}
 
The input fields are given on a latitude/longitude grid, with -after the previous step- the fields
on an equi-distant grid of height levels. The inversion itself assumes a cartesian grid, hence a
uniform grid spacing is also assumed in the horizontal directions. This is clearly not the case for the
latitude/longitude grid, as illustrated in Fig.\,\ref{latlon}.
Due to the sphericity of the Earth, the zonal
grid spacing decreases with increasing geographical latitude. As a remedy to this singularity, all
input fields are transformed to a "quasi-cartesian" grid with its center on the PV structure of
interest. The transformation between the two grids is illustrated in Fig.\,\ref{localcart}. It becomes evident
that the grid distortion is significantly reduced by this step. The formula which relates the two
grids is based upon the co-ordinate transformation given in the Appendix~A (Fortran subroutines {\em lmstolm} and
{\em phstoph}). The geographical latitude/longitude corresponding to a grid point in the rotated (quasi-cartesian) co-ordinate system is obtained in the following way. Firstly, the rotated latitude/longitude $\phi_{rot},\lambda_{rot}$ is transformed into
 
\begin{eqnarray*}
\lambda'_{rot} & = & 90+lmstolm(\phi_{rot},\lambda_{rot}-90,90+\alpha,-180) \\[0.2cm]
\phi'_{rot} & = & phstoph(\phi_{rot},\lambda_{rot}-90,90+\alpha,-180)
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
where $\alpha$ is the rotation angle given in the parameter file (CROT, see below). These two
values are then, in a second rotation, transformed into geographical latitude and longitude:
 
\begin{eqnarray*}
\lambda_{geo} & = & lmstolm(\phi'_{rot},\lambda'_{rot},90-\phi_{cen},\lambda_{cen}-180) \\[0.2cm]
\phi_{geo} & = & phstoph(\phi'_{rot},\lambda'_{rot},90-\phi_{cen},\lambda_{cen}-180))
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
where the centre of the PV anomaly (the centre of the quasi-cartesian co-ordinate system in geogrpahical
latitude/longitude co-ordinates) is given by $\phi_{cen}$ and $\lambda_{cen}$ (CLAT and CLON in the
parameter file, see below).\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{latlon_grid.eps}
\end{minipage}
\hspace{-0.5cm}
\begin{minipage}[t]{8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{xy_grid.eps}
\end{minipage}
\\
\caption{\it Quasi-cartesian grid which is centered at the PV streamer's position and which
shows much less distortion due to the sphericity of the Earth. On the left panel the latitude and
longitude on the Earth surface is shown, on the right panel the x and y co-ordinates in the new
co-ordinate system. Note how the distortion is considerably reduced with the new x,y co-ordinates (right), as compared with the original latitude/longitude co-ordinates (left). Additionally, the topography (in m above sea level) is shown
in color: Clearly discernible is Greenland and the east coast of North America.}
\label{xylatlon}
\end{center}
\end{figure}
\noindent
The transformation looks quite complicated, but has an easy geometrical interpretation. In fact, we create a new
latitude/longitude grid, but now longitude and latitude are defined not relative to the Earth's north
pole, but relative to a rotated imaginary "north pole". Therefore, we call the new latitudes/longitudes rotated co-ordinates. The link between the geographical latitude/longitude and
the rotated ones is shown in Fig.\,\ref{xylatlon} for the case study. Here, the left panel gives the latitude and longitude at the grid positions of the quasi-cartesian grid. The right panel gives the quasi-cartesian co-ordinates x and y, which correspond to the grand-circle distance on the Earth surface.
While the transformation of a scalar quantity (like for instance temperature, pressure, wind speed) is straightforward with the above formulas, the transformation of a vector field is much more
complicated. This is easily illustrated with the following example: Consider a perfectly zonal flow
in the geographical grid, i.e. there is only a wind component along the geographical latitude circles, but none along the geographical longitude circles (hence, in the left panel of Fig.\,14 the velocity vector is parallel to the latitude
circles). In the rotated grid -the quasi-cartesian grid- this
pure zonal velocity is transformed into a wind vector which has components both along the rotated
longitude and latitude circles (i.e. in Fig.\,14 the vector has a component along the horizontal and the
vertical axis).
In principle, a complicated formula could be derived which gives an explicit expression how the
individual velocity components transform. Here, we adopt a more pragmatic approach: We numerically
determine the local rotation angle between the two orthogonal co-ordinate systems, and subsequently
use these angles to get the transformed velocity components. \\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{10cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{coriol_grid.eps}
\end{minipage}
\\
\caption{\it Coriolis parameter (in $10^{-4}s^{-1}$) in the quasi-cartesian co-ordinate frame.
The Coriolis parameter is a local measure for the Earth's rotation. It is constant along
latitude circles. Note that $f$ becomes maximal at the pole and vanishes at the equator. No
PV inversion can be performed if the cartesian grid crosses the equator and hence crosses the
zero isoline of the Coriolis parameter.}
\label{coriol}
\end{center}
\end{figure}
 
\noindent
Of course, the Coriolis parameter must be kept in the transformation to the quasi-cartesian
co-ordinate frame. Tis parameter is given by:
 
\[
f = 2 \cdot \Omega \cdot sin(\phi)
\]
 
\vspace{0.3cm}
\noindent
where $\Omega$ is the angular velocity of the Earth rotation and $\phi$ is the geographical latitude.
From the definition it is clear that the Coriolis parameter is constant along latitude circles. Furthermore,
it takes its maximum value at the pole and vanishes at the equator. A typical value for the mid-latitudes
is $f=10^{-4}s^{-1}$. For the case study the Coriolis parameter is shown in Fig.\,\ref{coriol}.\\
 
 
 
\noindent
Numerically, the rotation of the fields to the quasi-cartesian co-ordinate frame is done with the
call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep2
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The program needs some information from the parameter file. The relevant section is:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN GRID
ROT_NX = 250 ;
ROT_NY = 250 ;
ROT_DX = 0.25;
ROT_DY = 0.25;
CLON = -65.;
CLAT = 45.;
CROT = 0.;
END GRID
\end{verbatim}
\end{minipage}
\end{center}
\vspace{0.3cm}
\noindent
The first two parameters (ROT\_NX and ROT\_NY) give the number of grid points in the horizontal directions for
the rotated co-ordinate system. Here it is assumed that the grid has 250 grid points in x and in y direction. Note
that the number of grid points in the z direction needs not to be specified because this information is
already available on the file H20060115\_18. The new horizontal resolution of the rotated grid is given by the
next two values. They give the resolution in x (ROT\_DX) and in y (ROT\_DY) direction. In the present case these
resolutions are 0.25 degrees, which corresponds to approximately 28\,km, according to the formula\\
 
\[
0.25 \cdot \frac{2\pi}{360} \cdot R_E \quad \quad \mbox{with the Earth's radius} \quad R_E=6370\,km
\]
 
\vspace{0.3cm}
\noindent
Note that the resolution of the rotated grid is higher than the resolution of the input grid, where a value of
1\,degree is given. Finally, the last three parameters specify where the new co-ordinate system is centered on the
globe. Here, this position is at 65\,W (CLON) and 45\,N (CLAT), i.e. approximately in the centre of the PV streamer
shown in Fig.\,\ref{question}. The last parameter (CROT) allows the new grid to be rotated. At the end of this step, the following fields are available on the R20060115\_18 file:\\[0.2cm]
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Q & Specific humidity ($kg/kg$) & R20060116\_18 \\
U & (Rotated) Zonal velocity ($m/s$) & R20060116\_18 \\
V & (Rotated) Meridional velocity ($m/s$) & R20060116\_18 \\
T & Temperature ($^\circ C$) & R20060116\_18 \\
P & Pressure ($hPa$) & R20060116\_18 \\
ORO & Height of topography ($m$) & R20060116\_18 \\
LAT & Geographical latitude & R20060116\_18 \\
LON & Geographical longitude & R20060116\_18 \\
CORIOL & Coriolis parameter ($1/s$) & R20060116\_18 \\
X & Cartesian distance from centre along x axis ($km$) & R20060116\_18 \\
Y & Cartesian distance from centre along x axis ($km$) & R20060116\_18 \\
\hline
\end{tabular}
\end{center}
 
 
 
\subsubsection{Calculating secondary fields [prep3]}
 
 
Several additional fields are needed for the PV inversion, the most prominent of course being Ertel's PV itself.
This field can easily derived from the horizontal wind components, the potential temperature and
the density. Firstly, the potential temperature $\theta$ is calculated from pressure $p$ (in hPa) and
temperature $T$ (in K) according to its definition:
 
\[
\theta = T \cdot (\frac{p_0}{p})^\kappa
\]
where the reference pressure is fixed as 1000\,hPa and $\kappa=R/C_p$ is the ratio of the gas constant
for dry air ($R$) and the specific heat at constant pressure ($c_p$). Numerically, this value
is in good approximation: $\kappa=0.286$.
Note that an inherent property of the atmosphere is its stability. This is expressed physically by
a potential temperature which increases with height. Regions where potential temperature decreases
with height are hydrostatically unstable and the pre-requisites for a PV inversion are not fulfilled
there. \\
 
 
\noindent
The density $\rho$ (in kg/m$^3$) of the air is determined by the ideal gas equation for air.\\[-0.3cm]
 
\[
\rho = \frac{p}{R_D \cdot T}
\]
 
\vspace{0.3cm}
\noindent
where $R_d$ is the gas constant for dry air and p and T are the pressure (in Pa) and temperature
(in K), respectively.\\
 
\noindent
With this definition of potential temperature and density, Ertel's PV is readily calculated according to:
 
\[
PV = -\frac{1}{\rho} \cdot ( \vec{\xi} + f \cdot \hat{k} ) \cdot \vec{\nabla}{\theta}
\]
 
\vspace{0.3cm}
\noindent
Here, $\hat{k}$ is a unit vector pointing in the vertical direction, $f$ is the planetary vorticity
(typically $10^{-4} s^{-1}$ in the extra-tropics),
i.e. the vorticity due to the Earth's rotation, and $\vec{\xi}$ is the curl $\vec{\nabla} \times \vec{u}$
of the wind vector $\vec{u}$. In large-scale dynamics vertical wind components can be neglected in the
above formula. The final expression for Ertel's PV then reduces to:
 
\[
PV = -\frac{1}{\rho} \cdot [ ( \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} + f )
\cdot \frac{\partial \theta}{\partial z}
+ \frac{\partial u}{\partial z} \cdot \frac{\partial \theta}{\partial y}
- \frac{\partial v}{\partial z} \cdot \frac{\partial \theta}{\partial x}]
\]
 
\vspace{0.3cm}
\noindent
In many cases the latter two terms (involving vertical derivatives of horizontal velocity) can
also be neglected. Here, we keep these terms in order to have a higher-order approximation to Ertel's
PV. Note that the first term on the right side includes the aforementioned vertical
derivative of potential temperature. The stability criterion forces this derivative to be positive.
The theory of atmospheric turbulence leads to a still stronger constraint. Indeed, the whole PV
must be positive (on the northern hemisphere), since otherwise symmetric instability will set in and
turbulently adjust the atmosphere to a state where PV is non-negative.\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{zus_pv_k40.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{zus_th_k40.eps}
\end{minipage}
\\[0cm]
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{zus_nsq_k40.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{zus_rho_k40.eps}
\end{minipage}
\\[0cm]
\caption{\it Secondary fields:
Ertel's potential vorticity (upper-left, in $pvu$), potential temperature (upper-right, in K),
squared Brunt-V\"ais\"al\"a frequency (lower-left, in $10^{-4} s^{-2}$) and density (lower-right,
in $kg m^{-3}$). The stratification is a measure of the vertical stratification of the atmosphere.
High values correspond
to strong stratification and suppression of vertical motions. Note how the stratospheric PV streamer is
associated with enhanced stratification. The density, on the other hand, is slightly decreased within the
streamer's region. All
fields are plotted on model level 40, corresponding to a geometrical height of approximately 8\,km.
}
\label{secfield}
\end{center}
\end{figure}
 
\noindent
The last field which is needed for the PV inversion is strongly related to the vertical derivative
of potential temperature. It is the so-called squared Brunt-V\"as\"ala frequency (or stratification),
defined by
 
\[
N^2 = \frac{g}{\theta} \cdot \frac{\partial \theta}{\partial z}
\]
 
\vspace{0.3cm}
\noindent
where $g$ is the Earth's gravity. Following the above discussion, a necessary condition for
atmospheric stability is that $N^2$ is non-negative. Note that strong stratifications counteract
vertical motions. Particularly strong stratifications are typically found in the stratosphere,
($N^2 \approx 10^{-4} s^{-2}$) whereas the troposphere is considerably weaker stratified
($N^2 \approx 10^{-4} s^{-2}$).\\
 
\noindent
All these secondary fields are calculated with the call to \\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep3
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
After this step, four additional variables are available on the file R20060116\_18. They are listed in the following table and are shown in Fig.\,\ref{secfield}:\\
 
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
TH & Potential temperature ($K$) & R20060116\_18 \\
PV & Ertel's potential vorticity ($pvu$) & R20060116\_18 \\
NSQ & Squared Brunt-Vai\"al\"a frequency ($1/s^2$) & R20060116\_18 \\
RHO & Air density ($kg/m^3$) & R20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
\subsubsection{Identification of a PV anomaly [prep4]}
 
 
Having calculated Ertel's PV on height levels, it is now time to specify the modified PV distribution
which should be obtained by the PV inversion. In short, a PV anomaly has to be identified from the original
PV field and then the effect of this anomaly on the potential temperature and velocity has to be determined.\\
 
\noindent
There is no unique and fool-proof method how to specify an anomaly. Indeed, this step strongly depends on
the features which should be studied. In the present example, we look at a so-called stratospheric PV streamer and the aim
is to remove this streamer from the PV field and thereby to quantify its influence on the stability and wind
fields in the middle and lower troposphere. Figure\,ref{box} shows the PV in a horizontal cross-section at 8\,km
height. The PV streamer is clearly discernible as a
southward intrusion of high-PV, i.e. stratospheric air toward the south. In the vertical the streamer reaches
down to levels of 6\,km (not shown).\\
 
\noindent
The extraction of the streamer is performed by filtering the original PV field. This filtering is done
by the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep4
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
Essentially, the program performs
the following two steps: Choose a grid point within the filtering box (see Fig\,ref{box}), and
replace the PV value at this grid point by the zonal mean of all PV values. Formally this might be
written as:
 
\[
PV \quad \rightarrow \quad <PV>
\]
 
\vspace{0.3cm}
\noindent
where $<>$ denotes the filtering operator which applies only within the filtering box.
The anomaly could now be determined as the difference of the original and filtered PV:
It turns out that this simple difference $AN=PV-<PV>$ would produce not only the desired positive anomaly associated
with the streamer, but also surrounding negative PV anomalies. We neglect all these negative anomalies
by simply setting them to zero. \\[-0.2cm]
 
\[
AN = PV - <PV> \quad \mbox{and} \quad AN \rightarrow AN^+.
\]
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{13cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{box.eps}
\end{minipage}
\\
\caption{\it Ertel's PV on level $k=40$ (corresponding to a height of 8\,km). Additionally the horizontal
grid is shown, and the filtering box is marked with the bold black lines.}
\label{box}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\noindent
The outcome $AN^+$ is a "well-behaved" PV anomaly, which in turn is used to finally define the modified $PV^M$, i.e.
the PV field which should be obtained by the inversion:\\
 
\[
PV^M = PV - AN^+
\]
 
\vspace{0.3cm}
\noindent
The original $PV$, modified $PV^M$ and the anomaly $AN^+$ is shown in Fig.\,\ref{ano} at several model levels. Note how the PV streamer of Fig.\,\ref{question} is well captured by the PV anomaly
 
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_org_k20.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_mod_k20.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_ano_k20.eps}
\end{minipage}
\\
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_org_k30.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_mod_k30.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_ano_k30.eps}
\end{minipage}
\\
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_org_k40.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_mod_k40.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_ano_k40.eps}
\end{minipage}
\\
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_org_k50.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_mod_k50.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_ano_k50.eps}
\end{minipage}
\\
\caption{\it Original (left), modified (middle) and anomaly (right) Ertel's PV for 16 January 2006, 18\,UTC. The different rows correspond to the levels (from top to bottom) 20, 30 40 50 corresponding to the heights 4, 6, 8 and 10\,km.}
\label{ano}
\end{center}
\end{figure}
 
\noindent
The filtering
is characterised by the values in six lines of the parameter file. \\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN ANOMALY
BOX_XMIN = -1200.;
BOX_XMAX = 1200.;
BOX_YMIN = -1200.;
BOX_YMAX = 1200.;
BOX_ZMIN = 2000.;
BOX_ZMAX = 10000.;
NFILTER = 5 ;
BOUND_XY = 500.;
BOUND_Z = 500.;
END ANOMALY
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.6cm}
\noindent
The lines specify the filtering box in the west-east direction (from -1200\,km to
1200\,km, from BOX\_XMIN to BOX\_XMAX), in the south-north direction (from -1200\,km to 1200\,km, from BOX\_YMIN to BOX\_YMAX), and in the vertical
(from 2000\,m to 10000\,m, from BOX\_ZMIN to BOX\_ZMAX). The filtering is not only applied once, but
(as given by NFILTER) $n=5$ times.
Finally the last two parameters describe the handling at the boundaries of the filtering box. In fact,
it is advantageous to force the anomaly PV to zero at the boundaries of the box. This is accomplished
by multiplying the PV anomaly with a function f$_{\partial F}$ which is 0 without the box, then monotonically increases
to 1 within a boundary zone, and then is constant 1 in the interior of the box. The width of the boundary
zone is given as 500\,km in the horizontal direction (BOUND\_XY) and 500\,m in the vertical direction (BOUND\_Z).\\
 
\noindent
The modified PV field and the anomaly are written to the R20060116\_18 file.
Additionally the boundary values are written. The velocity fields must be specified on the lateral
boundaries, whereas the potential temperature anomaly must be specified on the lower and upper boundary. In
the present settings, all boundary values are zero. The following table lists all fields which are additionally
written to the R file.
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
PV\_FILT & Modified Ertel's PV ($pvu$) & R20060116\_18 \\
PV\_ANOM & Anomaly in Ertel' PV ($pvu$) & R20060116\_18 \\
UU\_ANOM & Lateral boundary condition of zonal wind($m/s$) & R20060116\_18 \\
VV\_ANOM & Lateral boundary condition of meridional wind ($m/s$) & R20060116\_18 \\
TH\_ANOM & Upper and lower boundary of potential temperature ($K$) & R20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
 
\subsubsection{Splitting into different files [prep5]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{11.5cm}
\hspace{-2.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{splitting.eps}
\end{minipage}
\\
\caption{\it Splitting of the initial R20060116\_18 file into four different files with
prefix ORG, MOD, ANO and REF. }
\label{split}
\end{center}
\end{figure}
 
\noindent
So far, all new fields are written to the R20060116\_18 file. In the further steps it is
advantageous to split this file into several files. One file should get all original
fields, one only the modified fields and one only anomaly fields. Additionally, some
"static" fields, such as orography and Coriolis parameter, should be written to a special
file, from here on called the reference file.\\
 
\noindent
The splitting is done with the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{15cm}
\begin{verbatim}
inversion.sh prep4
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The result of this step is a set of new netcdf files with prefix ORG, MOD, ANO and REF. The following table
(and Fig.\,\ref{split}) illustrates which variables are written to which file. Note that some variables are renamed in this process.
\\
 
\begin{center}
\begin{tabular}{|r|r|r|r|}
\hline
Old variable name & New variable name & Source file & Destination file \\
\hline
PV & PV & R20060115\_18 & ORG\_20060116\_18 \\
U & U & R20060115\_18 & ORG\_20060116\_18 \\
V & V & R20060115\_18 & ORG\_20060116\_18 \\
TH & TH & R20060115\_18 & ORG\_20060116\_18 \\
Q & Q & R20060115\_18 & ORG\_20060116\_18 \\
P & P & R20060115\_18 & ORG\_20060116\_18 \\
T & T & R20060115\_18 & ORG\_20060116\_18 \\
\hline
PV\_FILT & PV\_AIM & R20060115\_18 & MOD\_20060116\_18 \\
U & U & R20060115\_18 & MOD\_20060116\_18 \\
V & V & R20060115\_18 & MOD\_20060116\_18 \\
Q & Q & R20060115\_18 & MOD\_20060116\_18 \\
P & P & R20060115\_18 & MOD\_20060116\_18 \\
T & T & R20060115\_18 & MOD\_20060116\_18 \\
NSQ & NSQ & R20060115\_18 & MOD\_20060116\_18 \\
RHO & RHO & R20060115\_18 & MOD\_20060116\_18 \\
TH & TH & R20060115\_18 & MOD\_20060116\_18 \\
\hline
\end{tabular}
\begin{tabular}{|r|r|r|r|}
\hline
Old variable name & New variable name & Source file & Destination file \\
\hline
PV\_ANOM & PV & R20060115\_18 & ANO\_20060115\_18 \\
TH\_ANOM & TH & R20060115\_18 & ANO\_20060115\_18 \\
UU\_ANOM & U & R20060115\_18 & ANO\_20060115\_18 \\
VV\_ANOM & V & R20060115\_18 & ANO\_20060115\_18 \\
\hline
ORO & ORO & R20060115\_18 & REF\_20060115\_18 \\
X & X & R20060115\_18 & REF\_20060115\_18 \\
Y & Y & R20060115\_18 & REF\_20060115\_18 \\
LAT & LAT & R20060115\_18 & REF\_20060115\_18 \\
LON & LON & R20060115\_18 & REF\_20060115\_18 \\
CORIOL & CORIOL & R20060115\_18 & REF\_20060115\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
 
 
\subsubsection{Specifying the reference profile [prep6]}
 
 
A reference vertical profile must be
defined for the PV inversion. The profile should be as near as possible to the real profile. Any quantity is defined in
the inversion as a deviation from this profile. Hence if the profile is well chosen only small
deviations can be expected and the assumed linearisation (see later) is better. Physically we determine
a good reference profile by taking the area mean over the subdomain, i.e at every model level the
mean over potential temperature $\theta$, squared Brunt Vais\"al\"a frequency $N^2$ and density $\rho$
is calculated. The resulting profiles are shown in Fig.\,\ref{reference} as a function of height, and additionally
as a function of pressure.\\
 
\noindent
Note how the density of the reference profile exponentially decreases
decreases with increasing height. If pressure is used as vertical co-ordinate, the decrease in density
is essentially linear with decreasing pressure. The profile of potential temperature increases with
increasing height: This is a necessary condition for the convective stability of the air column. In fact,
any region where potential temperature decreases with increasing height is unstable and characterised by high levels
of turbulence. The stability expressed by this potential temperature increase with height is numerically
determined by the so-called (squared) Brunt-Vais\"al\"a frequency, shown in the left panels. Since this
field directly goes into the solution of the quasi-geostrophic PV equation (see section~3.5), it must
be guaranteed that it always remains positive.\\
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{reference.eps}
\end{minipage}
\\
\caption{\it Reference profiles of potential temperature $\theta$, squared Brunt Vais\"al\"a frequency $N^2$ and density $\rho$ as a function of height (upper panels) and pressure (lower panels). The
reference profiles correspond to the area-averaged values over the inversion subdomain. }
\label{reference}
\end{center}
\end{figure}
 
\noindent
The reference profile is calculated with the call to \\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep5
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
After his step some additional variables are available on the REF file. These are:\\
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
NSQREF & Reference squared Brunt-Vais\"al\"a frequency ($1/s^2$) & MOD\_20060116\_18 \\
RHOREF & Reference air density ($kg/m^3$) & MOD\_20060116\_18 \\
PREREF & Reference pressure ($hPa$) & MOD\_20060115\_18 \\
THETAREF & Reference potential temperature ($K$) & MOD\_20060116\_18 \\
ZREF & Reference geopotential height ($m$) & MOD\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
\subsubsection{Adding the coastlines [prep7]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{coast1.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{coast2.eps}
\end{minipage}
\\
\caption{\it Coastlines transformed into the quasi-cartesian co-ordinate system. In the left panel, the
coastlines are shown in a system with rotated longitude and latitude as axes, in the right panel they
are shown in a x/y co-ordinate system.}
\label{coastline}
\end{center}
\end{figure}
 
At this stage it is not possible to plot the continental coastlines in the quasi-cartesian co-ordinate frame.
In fact, this becomes only feasible if the geographical coastlines (as given in latitude/longitude co-ordinates) are transformed into the new quasi-cartesian co-ordinate system. This is done
with the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep7
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
In Fig.\,\ref{coastline} the transformed co-ordinates are shown. On the left panel, the co-ordinate axis are the rotated longitude and latitude and on the left panel they are given by the distance (in km) from the co-ordinate's center (see Fig.\,14).
In this step the following additional fields are written to the REF\_20060116\_18 file:
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
COAST\_LON & Longitude of coastline & REF\_20060115\_18 \\
COAST\_LAT & Latitude of coastline & REF\_20060115\_18 \\
COAST\_RLON & Rotated longitude of coastline & REF\_20060115\_18 \\
COAST\_RLAT & Rotated latitude of coastline & REF\_20060115\_18 \\
COAST\_X & X co-ordinate of coastline & REF\_20060115\_18 \\
COAST\_Y & Y co-ordinate of coastline & REF\_20060115\_18 \\
\hline
\end{tabular}
\end{center}
 
\vspace{0.3cm}
\noindent
The coastline in geographical co-ordinates is taken from a global data set which can be retrieved from
the National Geophysical Data Center
(rimmer.ngdc.noaa.gov/coast/). Only, the part of the coastlines inside the rotated co-ordinate system are specified. This allows
an efficient plotting of the coastlines. If Matlab is used as a visualisation tool, the plotting can be
done with the following few lines, depending whether rotated longitude/latitude or X/Y is used as co-ordinate
axes.\\[0.0cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
%Read input file
inp = ncget('REF_20060116_18');
 
% Plot continental boundaries (rotated latitude/longitude)
figure;
plot(inp.COAST_RLON.data,inp.COAST_RLAT.data,'k');
 
% Plot continental boundaries (x/y)
figure;
plot(inp.COAST_X.data,inp.COAST_Y.data,'k');
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.6cm}
\noindent
The first command reads the reference file. All variables and parameters are then available in the Matlab structure inp. The COAST subfields of this structure can then immediately be plotted. Sometimes it turns
out to be better to set all co-ordinates outside the plotting domain to NaN.
 
 
\subsubsection{Moving the files to the run directory [prep8]}
 
At this stage, all essential preparatory steps for the PV inversion are done: The modified PV field is defined, the
boundary conditions are written and the reference profile is available. In this last step, the files are moved from the
input directory to the run directory, where all iterations of the PV inversions are performed. The moving of the
files is done with\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh prep8
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The ORG, MOD, ANO and REF files are now available in the run directory (see Fig.\,8). No further processes are
run in the input directory.
 
 
 
\subsection{Inversion - Iterative steps toward modified PV field [pvin]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{14cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{iterations.eps}
\end{minipage}
\\
\caption{\it Flowchart of the different inversion steps. Additionally, to the right of the different blocks, the
"flow" of information is illustrated. For instance, MOD $\rightarrow$ ANO means that the input information
is taken from the MOD file and then written to the ANO file. }
\label{iterations}
\end{center}
\end{figure}
 
The following steps build the core of the PV inversion. An interior anomaly of Ertel's PV
and the boundary values for the inversion were specified in the previous preparatory steps.
Now the flow anomalies (wind vectors, temperature, pressure and potential temperature) associated
with this PV anomaly has to be determined. This is the aim of the inversion. More specifically
the process must be split again into several distinct steps. These different steps are shown as a flowchart in
Fig.\,\ref{iterations}.
 
 
 
 
\subsubsection{Calculation of secondary fields [pvin1]}
 
Secondary fields have to be calculated. These fields are potential temperature, potential vorticity
density and squared Brunt-Vais\"al\"a frequency. The details of these calculations were already presented
in section~4.4.3, and are not repeated here. All the secondary fields are calculated with the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin1
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The call subsequently calculates potential temperature, squared Brunt-V\"as\"ala frequency, density and Ertel's PV. Where the height levels are below topography,
missing data values are written. The following table lists the new fields which are written to the MOD file:
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
TH & Potential temperature ($K$) & MOD\_20060116\_18 \\
PV & Ertel's potential vorticity ($pvu$) & MOD\_20060116\_18 \\
NSQ & Squared Brunt-Vai\"al\"a frequency ($1/s^2$) & MOD\_20060116\_18 \\
RHO & Air density ($kg/m^3$) & MOD\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
\subsubsection{Transforming Ertel's PV to quasi-geostrophic PV [pvin2]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{14.0cm}
\hspace{-1.0cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{pv_to_qgpv.eps}
\end{minipage}
\\
\caption{\it Determination of Ertel's PV anomaly and its transformation into
an anomaly of quasi-geostrophic PV. The calculated Ertel's PV is subtracted from
Ertel's PV which should be reached, and then this difference is transformed into
an approximate quasi-geostrophic PV. The input is taken from the MOD file, and the
output is written to the ANO file.}
\label{pvtoqg}
\end{center}
\end{figure}
 
So far only Ertel's PV was used. On the other hand, the inverson problem is formulated for the
quasi-geostrophic PV. Therefore a conversion between the two has to be done. In a first approximation
Ertels's PV is given by (for clarity it is denoted as EPV in this section):\\[-0.2cm]
 
\[
EPV = \frac{1}{\rho} \cdot ( \xi + f ) \cdot \frac{\partial \theta}{\partial z}
\]
 
\vspace{0.3cm}
\noindent
where $\rho$ is the density, $\xi$ the relative vorticity, $f$ the Coriolis parameter and $\theta$ the potential temperature.
Ertel's PV can be expressed in terms of the reference profile and deviation thereof. If we set
$\theta=\theta_0 + \theta^*$ and $\rho=\rho_0 + \rho^*$, consider the definition
of the reference stratification $N^2_0=g/\theta_0 \cdot \partial {\theta_0}/{\partial z}$ and furthermore
apply the quasi-geostrophic assumption $\xi \ll f$, the following approximate
expression hold in first order (we have neglected the density perturbation $\rho^*$ in the denominator):\\[-2mm]
 
\[
EPV = \frac{\theta_0 N_0^2}{g \rho_0} \cdot (\xi + \frac{f g}{\theta_0 N_0^2} \cdot \frac{\partial \theta^*}{\partial z})
\]
 
\vspace{0.3cm}
\noindent
On the other hand, the quasi-geostrophic PV (denoted by qgPV in this section) is defined by the streamfunction $\psi$\\[-0.2cm]
 
\[
qgPV = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} (\frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z} )
\]
 
\vspace{0.3cm}
\noindent
where $\rho_0$ and $N_0^2$ denotes a reference profile of density and stratification (as defined in the
preparatory steps and written to the REF file). The following relationship between the streamfunction and the meteorological fields persists:\\[-2mm]
 
\[
g \cdot \frac{\theta^*}{\theta_0} = f \cdot \frac{\partial \psi}{\partial z}
\quad \quad
u = -\frac{\partial \psi}{\partial y}
\quad \quad
v = -\frac{\partial \psi}{\partial x}
\]
 
\vspace{0.3cm}
\noindent
If these expressions are inserted into the above equation for $q$, one gets:\\[-2mm]
 
\[
qgPV = \xi + \frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z}
(\frac{\rho_0 g}{N_0^2 f \theta_0} \cdot \theta^* )
\]
 
\vspace{0.3cm}
\noindent
In a first approximation, we treat the reference profile and the Coriolis parameter as constant. Then,
this last expression is further simplified to:\\[-2mm]
 
\[
qgPV = \xi + \frac{f g}{N_0^2 \theta_0} \cdot \frac{\partial \theta^*}{\partial z}
\]
 
 
\vspace{0.3cm}
\noindent
With this form, it is easy to see that the following approximate relationship between Ertel's and the
quasi-geostrophic PV holds. \\[-2mm]
 
\[
qgPV \approx \frac{\rho_0 g}{\theta_0 N_0^2} \cdot EPV - f
\]
 
\vspace{0.3cm}
\noindent
Note that according to the previous derivation, this equation does not hold exactly. It is based upon
an assumption of linearisation and on approximate forms of Ertel's PV. Nevertheless, we can expect it
to be a good first-order approximation. In the PV inversion tool, use is made of this relationship,
but since it is only approximate, an iterative technique has to be applied. Finally note that this
formula can be easily applied to PV anomalies. Indeed, if $\Delta PV$ refers to a anomaly in Ertel's
PV, the corresponding anomaly in quasi-geostrophic PV is given by:\\[-2mm]
 
\[
\Delta(qgPV) \approx \frac{\rho_0 g}{\theta_0 N_0^2} \cdot \Delta(EPV)
\]
 
 
\vspace{0.3cm}
\noindent
It is in this latter form that the program call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin2
\end{verbatim}
\end{minipage}
\end{center}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{8.1cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{qgpv_ano_ew.eps}
\end{minipage}
\hspace{-0.5cm}
\begin{minipage}[t]{8.1cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{qgpv_ano_ns.eps}
\end{minipage}
\\
\caption{\it Quasi-geostrophic PV anomaly in an east/west (left) and an north/south (right)
vertical cross-section for 16 January 2006, 18\,UTC. }
\label{qgano}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\noindent
makes the conversion. It takes the Ertel-PV from the MOD file, and subtracts it from the PV\_AIM which is also
available on the MOD file. The difference between the two PV is the new anomaly in Ertel's PV which has to
be inverted in this iterative step. The approximate relationship between quasi-geostrophic PV and Ertel's
PV is then used to get a corresponding anomaly of the former one (see Fig.\,ref{pvtoqg}).
Note that this program handles also missing data values. If at some grid point Ertel's PV is not defined,
i.e. the missing data flag is set, the corresponding value of quasi-geostrophic PV is set to zero. It is not
set to the missing data value since no check will be done by the PV inversion program. Therefore, it is
best to treat every missing value as a vanishing anomaly of quasi-geostrophic PV. A vertical cross-section
of the anomaly in quasi-geostrophic PV is shown in Fig.\,\ref{qgano}.
The additional or changed fields on the file ANO\_20060116\_18 are given in the following table:\\
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
PV & Ertel's PV anomaly ($pvu$) & ANO\_20060116\_18 \\
QGPV & Anomaly in quasi-geostrophic PV ($s^{-1}$) & ANO\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
 
 
 
 
 
\subsubsection{Inversion of the quasi-geostrophic PV [pvin3]}
 
At this stage the interior distribution of quasi-geostrophic PV and the boundary values
are given, and therefore the inversion can be performed in order to get the streamfunction.
Numerical aspects of the inversion were already presented in section~2. Here, we focus on the
practical aspects. The numerical problem solved in this step is expressed in the following
boundary value problem: \\[-0.3cm]
 
\[
q = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} ( \frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z})
\]
 
\vspace{0.3cm}
\noindent
with the pre-described values\\[-0.3cm]
 
\[
g \cdot \frac{\theta^*}{\theta_0} = f \cdot \frac{\partial \psi}{\partial z}
\quad \quad
u = -\frac{\partial \psi}{\partial y}
\quad \quad
v = -\frac{\partial \psi}{\partial x}
\]
 
\vspace{0.3cm}
\noindent
on the upper and lower boundaries (for $\theta^*$) and on the lateral boundaries (for $u$ and $v$). The inversion program is called by\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin3
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
Note that the inversion affects only the file ANO\_20060116\_18 because the inversion is
performed for an anomaly of quasi-geostrophic PV.
The final aim of this step is to calculate the wind, temperature, pressure and potential temperature
perturbations which are associated with the specified anomaly of quasi-geostrophic PV.
The call to the program yields some information about the ongoing iterative steps. First of all,
the spectral width in the x-, y- and z-direction is written to screen. In the present example this
is:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{small}
\begin{verbatim}
Spectrum of the matrix in each direction
Spectrum = 1.028528 0.9136161 1.231250
\end{verbatim}
\end{small}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The spectral widths $\lambda_x,\lambda_y, \lambda_z$ (in the same order as in the above program output) are important to decide whether the inversion can be reasonably be performed. The
criterion is based upon the matrix elements defining the inversion problem. For a reasonable setting
the following inequalities should be fulfilled:
 
\[
\lambda_x > 1/2 \cdot \lambda_y \quad \quad \mbox{and} \quad \quad \lambda_x > 1/2 \cdot \lambda_z
\]
\[
\lambda_y > 1/2 \cdot \lambda_x \quad \quad \mbox{and} \quad \quad \lambda_y > 1/2 \cdot \lambda_z
\]
\[
\lambda_z > 1/2 \cdot \lambda_x \quad \quad \mbox{and} \quad \quad \lambda_z > 1/2 \cdot \lambda_y
\]
 
\vspace{0.3cm}
\noindent
which is evidently fulfilled in our case study (otherwise the program would abort with the error
message that the grid dimensions are not large enough). Then some run-time statistics is provided for the
iterative solution of the elliptical partial differential equation. As described in section~2 the
solution of the quasi-geostrophic PV equation is found by means of an successive over-relaxation (SOR)
technique. Starting from an initial estimate of the streamfunction $\psi$ several hundred iterations of
 
 
\[
\psi_i^{(n+1)} = \omega \cdot (b_i - \sum_{j=1}^{i-1} A_{i,j} \cdot \psi_j^{(n+1)}
- \sum_{j=i}^{m} A_{i,j} \cdot \psi_j^{(n)})
+ (1-\omega) \cdot \psi_i^{(n)}
\]
 
\vspace{0.3cm}
\noindent
are performed (see section~2 for details). Essentially two statistical measures are provided: The first one $\psi_{gauge}$
measures the amplitude of the streamfunction which is produced in the course of the iteration,
the second one is a direct check whether the iteration solution converges. In fact, after several iterations the so-far
reached streamfunction is used to calculate the quasi-geostrophic $PV^{c}$ according to the formula:\\[-0.3cm]
 
\[
PV^c = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} ( \frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z})
\]
 
\vspace{0.3cm}
\noindent
This value can then be compared to the quasi-geostrophic
$PV^{i}$ distribution which was given as input to the inversion algorithm. The following norm $\Delta^2$ is then
calculated as a measure of the convergence:\\[-0.3cm]
\[
\Delta^2 = \sum_{i,j,k} (\psi^{i}_{i,j,k}-\psi^{c}_{i,j,k})^2
\]
 
\vspace{0.3cm}
\noindent
Some sample output is reproduced below for the case study, the first column corresponding to $\psi_{gauge}$ and the
second one to $\Delta^2$:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
psigauge = 0.000E+00 deltasq = 0.850E-09
psigauge = 0.000E+00 deltasq = 0.112E-09
psigauge = -0.681E+03 deltasq = 0.643E-10
psigauge = -0.681E+03 deltasq = 0.466E-10
psigauge = -0.806E+03 deltasq = 0.367E-10
psigauge = -0.806E+03 deltasq = 0.303E-10
psigauge = -0.547E+03 deltasq = 0.259E-10
psigauge = -0.547E+03 deltasq = 0.228E-10
psigauge = -0.398E+03 deltasq = 0.206E-10
psigauge = -0.398E+03 deltasq = 0.191E-10
psigauge = -0.309E+03 deltasq = 0.180E-10
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.6cm}
\noindent
Note that the gauge streamfunction reaches a value of order -3000 (corresponding to a substantial anomaly of wind
and temperature), and that the convergence measure $\Delta^2$ decreases
by an order of magnitude from the beginning to the end. At the end of this step, the streamfunction associated with the quasi-geostrophic PV anomaly is determined. It is shown in Fig.\,\ref{stream} at three horizontal cross-sections. The
minimum of the streamfunction is found in the interior of the domain, in agreement with the cyclonic flow around the
positive anomaly of quasi-geostrophic PV. \\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{psi_ano_k01.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{psi_ano_k20.eps}
\end{minipage}
\hspace{0.0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{psi_ano_k40.eps}
\end{minipage}
\\
\caption{\it Streamfunction associated with the quasi-geostrophic PV anomaly shown in Fig.\,ref{qgano}. The three panels show horizontal cross-sections at 0, 4\,km and 8\,km above ground.}
\label{stream}
\end{center}
\end{figure}
 
\noindent
Now, additional perturbation fields can be computed from this streamfunction: Potential temperature,
wind components in x and y direction, pressure, and temperature. The corresponding formula are:\\[-0.5cm]
 
\begin{eqnarray*}
\theta^* & = & \frac{f}{g} \cdot \theta_0 \cdot \frac{\partial \psi}{\partial z}\\[0.2cm]
u & = & - \frac{\partial \psi}{\partial y}\\
\end{eqnarray*}
\begin{eqnarray*}
v & = & \frac{\partial \psi}{\partial x}\\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
The anomaly of potential temperature $\theta^*$ and the two horizontal wind components $u$ and $v$ can directly determined from the
streamfunction. Moreover, the pressure anomaly is directly proportional to the streamfunction, which is only
determined up to an additive constant. In order to obtain a vanishing pressure at the boundary of the
inversion domain, we firstly calculate such a constant $\psi_0$ (essentially the average over the domain boundary) and then set the pressure to:\\[-0.2cm]
 
\[
p^* = \rho_0 \cdot f \cdot (\psi - \psi_0)
\]
 
\vspace{0.3cm}
\noindent
The temperature anomaly is now easily calculated from pressure and potential temperature according the relationship
$\theta = T \cdot (p_ref/p)^\kappa$, where $T$ is the temperature in Kelvin, $p_ref$ is the reference pressure level (1000\,hPa) and $\kappa$ is the ratio between the gas constant for dry air ($R_d$) and the specific heat at constant pressure ($c_p$). Consistent with previous approximations we set:\\[-0.2cm]
 
\[
T^* = (\frac{p_0}{p_ref})^\kappa \cdot (\theta^* + \kappa \cdot \theta_0 \cdot \frac{p^*}{p_0} )
\]
 
\vspace{0.3cm}
\noindent
Figure\,\ref{anofield} shows some of these perturbation fields. The positive anomaly of quasi-geostrophic PV is
associated with a cyclonic (anti-clockwise) flow field, which reaches down to surface levels. Furthermore, we know from theoretical studies that a positive PV anomaly goes along with an increase of potential temperature above the anomaly, and correspondingly a decrease of
potential temperature below. This is nicely confirmed in the perturbation field of the calculation.
Finally, the cyclonic flow must be associated with a local pressure minimum, according to the
geostrophic wind equation. This is also fulfilled in our calculation. The following table gives all anomaly fields on the ANO\_10060116\_18 file which are calculated:
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{ano_00_k35_pr.eps}
\end{minipage}
\hspace{-0.6cm}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{ano_00_k35_tt.eps}
\end{minipage}
\\[-0.3cm]
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{ano_00_k35_uv.eps}
\end{minipage}
\hspace{-0.6cm}
\begin{minipage}[t]{7.5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{ano_00_k35_psi.eps}
\end{minipage}
\\
\caption{\it Pressure, temperature, wind vectors and streamfunction (from upper-left to lower-right)
associated with the quasi-geostrophic PV anomaly. The horizontal cross-section is at level 7\,km. For clarity,
some isolines of quasi-geostrophic PV are also shown.}
\label{anofield}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
STREAM & Streamfunction ($m^2/s$) & ANO\_20060116\_18 \\
THETA & Potential temperature ($K$) & ANO\_20060116\_18 \\
U & Velocity component in X direction ($m/s$) & ANO\_20060116\_18 \\
V & Velocity in Y direction ($m/s$) & ANO\_20060116\_18 \\
T & Temperature ($^\circ C$) & ANO\_20060116\_18 \\
P & Pressure ($hPa$) & ANO\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
 
\vspace{0.3cm}
\noindent
Finally, the question emerges whether the convergence of the algorithm was sufficient. In order to assess the
quality of convergence a diagnostic tool is presented in section~5.2, which allows to calculate the
quasi-geostrophic PV according to its definition and then to compare it with the anomaly given at
the beginning of the PV inversion.
 
 
\subsubsection{Preparing the next step for iteration [pvin4]}
 
 
\noindent
At this point, the quasi-geostrophic PV anomaly is inverted and the associated streamfunction and
other flow fields have been determined. But the inversion problem is not yet solved. In fact,
we specified an anomaly of Ertel's PV, but in the previous step a anomaly of quasi-geostrophic PV
was inverted. By the above reasoning, we expect the two anomalies to be closely linked. However,
inversion of the quasi-geostrophic PV equation is a linear problem, whereas the inversion of Ertel's
PV is inherently non-linear. That is why some further iteration must be performed.\\
 
\noindent
In a first step, we take the basic flow fields (temperature, velocity, pressure) from the anomaly (ANO)
file and subtract it from the MOD file (Fig.\,\ref{prepiter}). This is done by call to\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin3
\end{verbatim}
\end{minipage}
\end{center}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{10cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{prepiter.eps}
\end{minipage}
\\
\caption{\it Preparation for the next iteration: The fields (pressure, temperature, velocity, potential
temperature) from iteration n and the anomalies of iteration n are combined to give the fields at iteration
n+1.}
\label{prepiter}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\noindent
There is one external parameter involved in this step. It is found in the NUMERICS section of the
parameter file and is called ALPHA. This value determines which fraction of the perturbation has to
be subtracted from the MOD fields. Formally, we do the following transformation (see also Fig.\,\ref{prepiter}):
 
\begin{eqnarray*}
u^{n+1}_{MOD} & \leftarrow & u^n_{MOD} - \alpha \cdot u^n_{ANO}\\[0.2cm]
v^{n+1}_{MOD} & \leftarrow & v^n_{MOD} - \alpha \cdot v^n_{ANO}\\[0.2cm]
T^{n+1}_{MOD} & \leftarrow & T^n_{MOD} - \alpha \cdot T^n_{ANO}\\[0.2cm]
p^{n+1}_{MOD} & \leftarrow & p^n_{MOD} - \alpha \cdot p^n_{ANO}
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
A value $\alpha < 1$ slows down the convergence because only part of the inversion result is used. On the other hand, it was found that the stability of the algorithm is enhanced by values $\alpha < 1$. In
the case study a value of 0.5 was used, and good convergence reached, whereas a value of 1 resulted in unrealistic small-scale perturbations which diverge with continuing iterative steps.\\
 
\noindent
The variables which are adjusted in the MOD\_20060116\_18 file are given in the following table and an example
for the adjustment is shown in Fig.\,\ref{prepsub}:
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
THETA & Potential temperature & MOD\_20060115\_18 \\
U & Velocity component in X direction ($m/s$) & MOD\_20060115\_18 \\
V & Velocity in Y direction ($m/s$) & MOD\_20060115\_18 \\
T & Temperature ($^\circ C$) & MOD\_20060115\_18 \\
P & Pressure ($hPa$) & MOD\_20060115\_18 \\
\hline
\end{tabular}
\end{center}
 
\vspace{0.5cm}
\noindent
It might be valuable to study the convergence of the inversion in greater detail. To this aim, the
master script allows the call:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin5
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
which makes a copy of the momentarily reached MOD and ANO file. For this save option to work, the
SAVEITER flag in the NUMERICS section of the parameter file must be set to "yes".
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN NUMERICS
SAVEITER = yes;
END NUMERICS
\end{verbatim}
\end{minipage}
\end{center}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{prep_k35_org_ano.eps}
\end{minipage}
\hspace{-1cm}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{prep_k35_mod.eps}
\end{minipage}
\\
\caption{\it Left: Temperature in the modified MOD file (in color) and in the anomaly ANO file (with contour lines)
at the end of the quasi-geostrophic PV inversion. The temperature anomaly in ANO is subtracted from the initial temperature in MOD. Right: New modified temperature in the MOD file after the subtraction.
This new modified field gives the next entry for the PV inversion. }
\label{prepsub}
\end{center}
\end{figure}
 
 
\subsubsection{Convergence after several iterations [pvin5]}
 
At this stage, the next iterative steps can be performed. The MOD file has been adjusted according to
the outcome of the quasi-geostrophic PV inversion. The modified wind and temperature fields can be used to calculate a new Ertel-PV field, which in turn can be compared with the pre-specified aim-PV field.
Hopefully, after several iterative steps, the re-currently calculated PV of the MOD file converges
toward the aim-PV. If so, the non-linear inversion problem for Ertel's PV is solved. Figure\,\ref{convergence}
illustrates the convergence for the case study. Note that the iterative steps need not be
launched by hand, but can be run automatically with call to\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh pvin
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The script will run through all inversion steps and will loop through the number of iterations specified in NOFITER in the NUMERICS section of the parameter file.
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN NUMERICS
NOFITER = 6;
END NUMERICS
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The panels of Fig.\,\ref{convergence} show the streamfunction at three consecutive iterative steps.
Note that the amplitiude of the streamfunction clearly decreases, indicating that the iteration
process converges.
Generally, after six steps good convergence is reached. This is further supported by
the standard output during the quasi-geostrophic inversion (see listing on page~38). The final line of this output
is shown below for several consecutive iterations (the first one corresponding to the line on page~38):
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{con_01_k35_psi.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{con_02_k35_psi.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{5cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{con_03_k35_psi.eps}
\end{minipage}
\\
\caption{\it streamfunction for three iterative steps. Note the different contour intervals
for the three sub panels. The decrease of the amplitude clearly indicates a convergence of the
PV inversion.}
\label{convergence}
\end{center}
\end{figure}
 
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
psigauge = -0.309E+03 deltasq = 0.180E-10
psigauge = -0.128E+03 deltasq = 0.548E-11
psigauge = -0.570E+02 deltasq = 0.233E-11
psigauge = -0.265E+02 deltasq = 0.117E-11
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
Note that with each iterative step "less" streamfunction is produced. Since the basic perturbation
fields (temperature, pressure, horizontal wind, potential temperature) are directly proportional
to the streamfunction, the corrections to the flow fields also
become smaller and smaller.
 
\subsection{Post processing - Changing the P file [post]}
 
The PV inversion was completed in the previous step and the modified temperature, pressure and wind field is available in the run files. It is the aim of the post processing steps to bring these modified
fields back to the format of the input fields. The steps are summarised in Fig.\,\ref{postproc}.\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{12cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{postproc.eps}
\end{minipage}
\\
\caption{\it Different steps of post processing. Additionally, to the left of the different
blocks the main flow of information is indicated. For instance, MOD $\rightarrow$ GEO means
that the input is taken from the MOD file and the output written to the GEO file. }
\label{postproc}
\end{center}
\end{figure}
 
\noindent
But at first the input field and the link to the modified output field must be made available with a call to:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh post1
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The P file is copied from the input directory to the output directory and a symbolic link is set to the
MOD file in the run directory.
 
 
 
 
\subsubsection{Rotating to the geographical latitude/longitude grid [post2]}
 
Figure~\ref{backrot} illustrates the step which is necessary to transform the meteorological fields to a geographical co-ordinate system. The left panel shows the temperature at 2000\,m above sea level in the local-cartesian co-ordinate system, the right panel is the same field, but projected back to a geographical grid. Note that in this latter frame only a small section is filled by temperature values, whereas most are
undefined.\\
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{rot_k35_rot_t.eps}
\end{minipage}
\hspace{-1.2cm}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{rot_k35_geo_t.eps}
\end{minipage}
\\
\caption{\it Modified temperature field at 7\,km above ground in the rotated co-ordinate system (left) and transformed back into the geographical latitude/longitude grid (right). Additionally
the wind vectors are shown in both co-ordinate systems. Note that the transformation of the vectorial
wind is much more complicated than the transformation of the scalar temperature.}
\label{backrot}
\end{center}
\end{figure}
 
\noindent
The rotation itself is the reverse transformation performed in the preparatory steps (section~4.4.2). It is called by (and its effect shown in Fig.\,\ref{backrot})\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh post2
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
and its behaviour is controlled by the following entries in the parameter file:
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
BEGIN GRID
GEO_XMIN = -180.;
GEO_NX = 361 ;
GEO_DX = 1.;
GEO_YMIN = 0.;
GEO_NY = 91 ;
GEO_DY = 1.;
CLON = -65.;
CLAT = 45.;
CROT = 0.;
END GRID
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The first six parameters define the geographical grid of the input files. More specifically the left grid boundary is at $180^\circ$\,W (GEO\_XMIN), the number of grid points in the zonal (west-to-east) direction is 361 (GEO\_NX) and
the grid resolution in zonal direction is $1^\circ$\,longitude (GEO\_DX). Analogously, the parameters of the
grid in meridional (south-to-north) direction are given: Lowest latitude $0^\circ$\,N (GEO\_YMIN), number of grid
points 91 (GEO\_NY) and grid resolution $1^\circ$\,latitude (GEO\_DY). The rotation itself is described by
the last three entries (CLON, CLAT and CROT), which have the exactly same meaning as given in section~4.4.2\\
 
\noindent
Note again, that the transformation of a scalar quantity is considerably easier than the transformation of a vectorial quantity. In the latter case, the specific transformation
of the vectorial components must be correctly handled. The transformation algorithm for a scalar quantity is based
upon the transformation rules given in Appendix~9.1 (Fortran subroutines {\em lmtolms} and {\em phtophs}). Essentially, the
steps are the reverse of the ones presented in section~4.4.2.
The rotated (quasi-cartesian) latitude/longitude corresponding to a grid point in the geographical co-ordinate system is obtained in the following way. Firstly, the geographical latitude/longitude $\phi_{geo},\lambda_{geo}$ is transformed into
 
\begin{eqnarray*}
\lambda'_{rot} & = & lmtolms(\phi_{geo},\lambda_{geo},90-\phi_{cen},\lambda_{cen}-180) \\[0.2cm]
\phi'_{rot} & = & phtophs(\phi_{geo},\lambda_{geo},90-\phi_{cen},\lambda_{cen}-180))
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
where the centre of the PV anomaly (the centre of the quasi-cartesian co-ordinate system in geographical
latitude/longitude co-ordinates) is given by $\phi_{cen}$ and $\lambda_{cen}$ (CLAT and CLON in the
parameter file, see above).
These two
values are then, in a second rotation, transformed into rotated latitude and longitude:
 
\begin{eqnarray*}
\lambda_{rot} & = & 90+lmtolms(\phi'_{rot},\lambda'_{rot}-90,90+\alpha,-180) \\[0.2cm]
\phi_{rot} & = & phtophs(\phi'_{rot},\lambda'_{rot}-90,90+\alpha,-180)
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
where $\alpha$ is the rotation angle given in the parameter file (CROT, see below). With the correspondence
$(\lambda_{geo},\phi_{geo}) \leftrightarrow (\lambda_{rot},\phi_{rot})$ it is straightforward to perform
the transformation of a scalar field. In the program package this is done by means of linear interpolation.\\
\noindent
The fields which are written to GEO\_20060116\_18 are given in the following table:\\
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
U & Zonal velocity ($m/s$) & GEO\_20060116\_18 \\
V & Meridional velocity ($m/s$) & GEO\_20060116\_18 \\
T & Temperature ($^\circ C$) & GEO\_20060116\_18 \\
P & Pressure ($hPa$) & GEO\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.5cm}
 
\begin{figure}[t]
\vspace{-3cm}
\begin{center}
\begin{minipage}[t]{16cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{weight1.eps}
\end{minipage}
\\[-4.2cm]
\caption{\it Weighting function (in color) for the insertion of the modified fields into the original
P file. Additionally, the distance from the boundary of insertion region is plotted as contour lines (positive
inside the region, negative outside region). The zero contour line of the distance corresponds to the
boundary of the insertion domain.}
\label{comparep}
\end{center}
\end{figure}
 
 
\subsubsection{Transformation from height to hybrid ECMWF co-ordinates [post3]}
 
\begin{figure}[t]
\vspace{-1cm}
\begin{center}
\begin{minipage}[t]{8.2cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{inp_tt_k38.eps}
\end{minipage}
\hspace{-0.7cm}
\begin{minipage}[t]{8.2cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{out_tt_k38.eps}
\end{minipage}
\\[-2.8cm]
\begin{minipage}[t]{8.2cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{inp_uv_k38.eps}
\end{minipage}
\hspace{-0.7cm}
\begin{minipage}[t]{8.2cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{out_uv_k38.eps}
\end{minipage}
\\[-1.5cm]
\caption{\it Comparison of original (with PV streamer, left) and modified (without PV streamer, right)
temperature (top panels) and velocity/wind vectors bottom panels) at model level 38 of the ECMWF grid.}
\label{comparep2}
\end{center}
\end{figure}
 
\noindent
The vertical co-ordinate in the back-rotated field is still geometrical height, whereas the input
fields are given on the hybrid ECMWF grid. In this step the transformation to the hybrid vertical co-ordinate is performed. The call is:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh post3
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The transformation is based upon a cubic spline interpolation. The fields which are overwritten
in the P20060116\_18 file are:\\
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
U & Velocity component in zonal direction ($m/s$) & P20060115\_18 \\
V & Velocity in meridional direction ($m/s$) & P20060115\_18 \\
T & Temperature ($^\circ C$) & P20060115\_18 \\
PS & Surface pressure ($hPa$) & P20060115\_18 \\
\hline
\end{tabular}
\end{center}
 
\vspace{0.3cm}
\noindent
An impression of the modified flow field is given in Fig.\,\ref{comparep2}.
 
 
\subsubsection{Calculating secondary fields [post4]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{inp_pv.th_45n.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{out_pv.th_45n.eps}
\end{minipage}
\\[-1.5cm]
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{inp_pv_350hPa.eps}
\end{minipage}
\hspace{0cm}
\begin{minipage}[t]{7.8cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{out_pv_350hPa.eps}
\end{minipage}
\\[-1.5cm]
\caption{\it Comparison of original (with PV streamer, left) and modified (without PV streamer, right)
potential temperature and PV in a west/east cross section along the $45^\circ$\,N latitude circle (top panels)
and PV at 350\,hPa (bottom panels)}
\label{compares}
\end{center}
\end{figure}
 
In this last step, Ertel's PV and potential temperature are calculated on the ECMWF grid. This allows
to directly check whether the PV anomaly was removed and to investigate how the corresponding potential temperature is
changed in the absence of the PV anomaly. The call to this step is:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh post4
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The program creates the S file and writes the following two fields onto it:\\[-0.3cm]
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
TH & Potential temperature ($K$) & S20060116\_18 \\
PV & Ertel's PV ($pvu$) & S20060116\_18 \\
\hline
\end{tabular}
\end{center}
 
\vspace{0.3cm}
\noindent
Figure~\ref{compares} shows a direct comparison of the input and of the output Ertel-PV and potential temperature.
It can clearly be seen that the stratospheric PV streamer is essentially removed from the output
file. Moreover, the potential temperature is considerably changed. Whereas in the presence of the
PV streamer the isolines of potential temperature are pulled upwards, they are much more horizontally
aligned in its absence. This "vacuum cleaner" effect of upper-level PV structures is well documented
and predicted by theoretical considerations (see also Fig.\,2 in section~1).
 
 
% ----------------------------------------------------------------------------------------------
% PV Inversion for Idealised Cases
% ----------------------------------------------------------------------------------------------
 
\newpage
 
 
\section{Diagnostic Tools}
 
\subsection{A consistency check for the boundary condition [diag1]}
 
The problem posed by the inversion equations constitutes a von Neumann boundary value problem.
It has only a solution if some additional conditions are fulfilled between the interior PV distribution and the values of potential temperature on the upper and lower boundaries and the values of horizontal wind components on the lateral sides of the inversion domain. What follows is a
detailed description of these additional requirements. The discussion very closely follows the one given
in Fehlmann (1997).\\
 
\noindent
To facilitate the derivation, let's define a new vertical co-ordinate such theta the quasi-geostrophic PV q can be expressed as the divergence of a vector field $\vec{E}$. Let\\[-0.2cm]
 
\[
\eta(z) = - \frac{p_0(z)}{g f^2} \quad \quad \mbox{and} \quad \quad
\Delta_h = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}
\]
 
\vspace{0.3cm}
\noindent
where $p_o(z)$ is the reference profile of pressure, $f$ is the Coriolis parameter and $g$ is the Earth's gravity. Note that $\eta$ is a scaled pressure co-ordinate. If we use the hydrostatic assumption $\partial{\eta}/{\partial z} = \rho_0/f^2$, the following expression for the quasi-geostrophic PV q results:
 
\[
q = \Delta_h\psi + \frac{\partial}{\partial \eta} ( \frac{\rho_0^2}{f^2 N_0^2}
\cdot \frac{\partial \psi}{\partial \eta} )
\]
 
\vspace{0.3cm}
\noindent
Here, $\rho_o(z)$ and $N_o^2(z)$ are the reference profiles of density and squared Brunt-Vais\"al\"a frequency,
respectively, and $\psi$ is the streamfunction. Hence, q is now expressed as the divergence of a vector field ${\vec E}$, and Gauss' theorem can be
applied:
 
\[
\int_G q(x,y,\eta) dx dy d\eta = \int_{\partial G} \vec{E}(x,y,\eta) \vec{d\sigma} \quad \quad
\mbox{with} \quad \quad
\vec{E} = ( \frac{\partial \psi}{\partial x}, \frac{\partial \psi}{\partial y},
\frac{\rho_0^2}{f^2 N_0^2} \cdot \frac{\partial \psi}{\partial \eta} )
\]
 
\vspace{0.3cm}
\noindent
Note that this integration has to be carried out in the co-ordinate system (x,y,$\eta$). If we now specify
the inversion domain B as a two-dimensional domain in the (x,y)-plane and $[z_a,z_b]$ be the vertical domain, then $G=B \times [z_a,z_b]$ in the Cartesian space. This compatibility condition can be
transformed back into the Cartesian co-ordinate system and the integration be split over the boundary of
the domain G into an integration over the surface, the lid and the lateral boundaries of the domain. It then
follows that
 
\begin{eqnarray*}
\int_G \rho_0(z) q(x,y,z) dx dy dz & = &
\int _{z_a}^{z_b} (\int_{\partial B} \vec{v}(x,y,z) \cdot \vec{dr} ) \rho_0(z) dz\\[4mm]
& - & \int_B \frac{\rho_0(z_a) g f \theta^*(x,y,z_a)}{\theta_0(z_a) N_0^2(z_a)} dx dy \\[4mm]
& + & \int_B \frac{\rho_0(z_b) g f \theta^*(x,y,z_b)}{\theta_0(z_b) N_0^2(z_b)} dx dy \\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
Only if this condition is fulfilled, does there exist a unique solution (up to a constant). This means
that not every formulation of the inversion problem needs to have a solution.\\
 
\noindent
The inversion program has to check whether the just discussed integral constraint is fulfilled to
satisfactory accuracy. In order to estimate, how big these inconsistencies really are, we ask for a constant perturbation potential temperature $\theta^*$ which is needed in order to fulfill the integral
constraint. If readily follows from the above discussion that this value is:
 
\begin{eqnarray*}
\theta^* & = &
( \int_G \rho_0(z) q(x,y,z) dx dy dz -
\int _{z_a}^{z_b} (\int_{\partial B} \vec{v}(x,y,z) \cdot \vec{dr} ) \rho_0(z) dz )\\[4mm]
& &
(
- \int_B \frac{\rho_0(z_a) g f}{\theta_0(z_a) N_0^2(z_a)} dx dy
+ \int_B \frac{\rho_0(z_b) g f}{\theta_0(z_b) N_0^2(z_b)} dx dy )^{-1}\\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
If this quantity is calculated for the present example, $\theta^*=$-2.8\,K results. This value seems
sufficiently small that problem can be solved despite the inconsistency. But note that the problems due
to the ill-posedness of the problem are not well understood (see references in Fehlmann, 1997).\\
 
\noindent
The program handling the consistency check related to the boundary values is:\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh diag1
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The output from this program is given in the following table (the labels A,B,C and D are entered for easier
reference in the text):\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
A integ = 1.7558686E+12
B denombot = 5.6644076E+11
C denomtop = 5.9614413E+09
D denom = -5.6047934E+11
theta adjustment = -3.132798
theta shift @ top = 0.000000 613.2715
theta shift @ bot = 0.000000 271.9355
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
The first line is the integral which includes the quasi-geostrophic PV in the interior, the
velocity integrals on the laterals boundaries and the potential temperature integrals at the
lower and upper boundary:
 
\begin{eqnarray*}
A & = & \int_G \rho_0(z) q(x,y,z) dx dy dz -
\int _{z_a}^{z_b} (\int_{\partial B} \vec{v}(x,y,z) \cdot \vec{dr} ) \rho_0(z) dz\\[6mm]
& & + \int_B \frac{\rho_0(z_a) g f \theta^*(x,y,z_a)}{\theta_0(z_a) N_0^2(z_a)} dx dy
- \int_B \frac{\rho_0(z_b) g f \theta^*(x,y,z_b)}{\theta_0(z_b) N_0^2(z_b)} dx dy \\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
In exact fulfillment of the integral constraint, this term A would vanish, i.e. $A=0$.
The second and third line give the integrals over the upper and lower boundary only:
 
\begin{eqnarray*}
B & = & \int_B \frac{\rho_0(z_a) g f \theta^*(x,y,z_a)}{\theta_0(z_a) N_0^2(z_a)} dx dy\\[6mm]
C & = & \int_B \frac{\rho_0(z_b) g f \theta^*(x,y,z_b)}{\theta_0(z_b) N_0^2(z_b)} dx dy\\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
The difference between these two lines is the contents of the next line:
 
\begin{eqnarray*}
D & = & \int_B \frac{\rho_0(z_a) g f \theta^*(x,y,z_a)}{\theta_0(z_a) N_0^2(z_a)} dx dy
- \int_B \frac{\rho_0(z_b) g f \theta^*(x,y,z_b)}{\theta_0(z_b) N_0^2(z_b)} dx dy\\
\end{eqnarray*}
 
\noindent
Note that this term D corresponds to the last two terms in expression~A.
With these expressions an estimate can be made for the correction which would eliminate the inconsistency
of the boundary conditions with respect to the interior distribution of quasi-geostrophic PV. This adjustment
of potential temperature is the next line
 
\begin{eqnarray*}
\theta^* & = & A / D
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
and corresponds with the aforementioned expression for $\theta^*$.
Finally, in the last two lines the shift in potential temperature at the upper and at the
lower boundary is given, together with the mean potential temperatures at these two boundaries.
At the moment, no shift (value 0 in the output lines) is performed, i.e. the inconsistency in the boundary conditions
is not "solved".
 
 
\subsection{Convergence of the quasi-geostrophic inversion [diag2]}
 
The key numerical algorithm is the inversion of the quasi-geostrophic PV equation (see section~4.5.3).
It relates the PV to the streamfunction by\\[-0.3cm]
 
\[
q_a = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} ( \frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z}
\]
 
\vspace{0.3cm}
\noindent
with the boundary conditions of potential temperature at the lower and upper lid, and of horizontal wind
components at the lateral sides of the inversion domain:\\[-0.3cm]
 
\[
g \cdot \frac{\theta^*}{\theta_0} = f \cdot \frac{\partial \psi}{\partial z}
\quad \quad
u = -\frac{\partial \psi}{\partial y}
\quad \quad
v = \frac{\partial \psi}{\partial x}
\]
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{qgpv_k35_calc.eps}
\end{minipage}
\hspace{-1cm}
\begin{minipage}[t]{8.3cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{qgpv_k35_spec.eps}
\end{minipage}
\\
\caption{\it Comparison of calculated (left) and pre-described (right) quasi-geostrophic PV. }
\label{compqg}
\end{center}
\end{figure}
 
\vspace{0.3cm}
\noindent
The numerical solution by means of the successive over-relaxation (SOR) technique
then completely determines the perturbations of potential temperature and of horizontal wind. These meteorological fields can be expressed
in the following way by the streamfunction (see also section~2):
 
\begin{eqnarray*}
\theta^* & = & \frac{f}{g} \cdot \theta_0 \cdot \frac{\partial \psi}{\partial z}\\
u & = & - \frac{\partial \psi}{\partial y}\\
v & = & \frac{\partial \psi}{\partial x}\\
\end{eqnarray*}
 
\vspace{0.3cm}
\noindent
This allows a simple test whether the inversion of the quasi-geostrophic equation was successful. Indeed, the
quasi-geostrophic PV can be calculated from the perturbation fields:
 
\[
q_c = \frac{\partial^2\psi}{\partial x^2} + \frac{\partial^2\psi}{\partial y^2} +
\frac{f^2}{\rho_0} \cdot \frac{\partial}{\partial z} ( \frac{\rho_0}{N_0^2}
\cdot \frac{\partial \psi}{\partial z})
\]
 
\vspace{0.3cm}
\noindent
If the inversion was successful, this calculated quasi-geostrophic PV ($q_c$) must coincide with the
pre-described PV ($q_a$). For the present case study, the validation is shown in Fig.\,\ref{compqg} for the first step
of the iteration. The two panels show the calculated and the pre-described PV, respectively, and it becomes
immediately clear that a reasonable degree of convergence was reached.\\
 
 
\noindent
The calculation of the quasi-geostrophic PV is accomplished with the call\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
inversion.sh diag2 ANO
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
where the second argument (ANO) specifies that the ANO\_20060116\_18 file is taken for the
calculation. It is implictely assumed that the reference file is available on the corresponding REF file. The output of the calculation is then written to the same ANO\_20060116\_18 file,
with the name QGPV\_DIAG. Hence the table of modified fields and files is:
 
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
QGPV\_DIAG & Calculated quasi-geostrophic PV ($1/s$) & ANO\_20060116\_18 \\
\hline
\end{tabular}
\end{center}
\vspace{0.3cm}
 
\subsection{Difference between two files [diag3]}
 
\begin{figure}[t]
\begin{center}
\begin{minipage}[t]{16cm}
\vspace{-1cm}
\ForceWidth{1.0\textwidth}
\BoxedEPSF{difference.eps}
\end{minipage}
\\[-0.5cm]
\caption{\it Difference between the ORG and the MOD file in a vertical cross section. In color, the difference of the meridional
wind velocity is shown. The difference of potential temperature is given by the thin lines (black:positive,
blue:negative). The bold black line is the 2.5 isoline of the difference of Ertel's PV. }
\label{diff}
\end{center}
\end{figure}
 
The impact of a PV anomaly is most easily determined if the meteorological fields (temperature, velocity,
pressure,...) in the presence of the anomaly is subtracted from the corresponding fields in the absence
of the anomaly. The change in the meteorological fields can then be attributed to the PV anomaly. In order
to facilitate this with/without comparison, a diagnostic tool is provide which calculates the difference.
For instance, the call to
\begin{center}
\begin{minipage}[t]{11cm}
\begin{verbatim}
inversion.sh diag3 ORG MOD
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
takes the ORG and MOD file in the run directory and calculates the difference of all fields which
are available on both input files. The difference fields are then written to a new file with prefix DIA.
An example is shown in Fig.\,\ref{diff}.
 
% ---------------------------------------------------------------------------------------------
% Final Remarks
% ---------------------------------------------------------------------------------------------
 
\newpage
 
\section{Final Remarks and Outlook}
 
Several additional extensions are possible for the PV inversion tool introduced in this study. Most of them will attract a lot of interest in the research and education community. Some extensions which are and will be undertaken recently in our institute are:
 
\begin{itemize}
\item [a] The PV inversion is not only of interest in real-case studies, as was described in this work. Considerable insight can also be gained by looking at highly idealised experiments. Such experiments enforce the existence of a tool which allows to set set up them. In the course of this diploma thesis, such a tool was developed. However, it was considered to be preferable to limit
the thesis's documentation itself to the real-case experiments.\\
\item [b] Removing and adding, or more generally modifying the initial PV distribution, is particularly interesting if the modified state of the atmosphere is used as the input -initial
and boundary values- for a regional weather prediction model. This kind of experiments allows to
assess in a quantitative way how the PV field influences the future weather development. In parallel to this thesis a program package has been developed at the Institute for Atmospheric and Climate Science at ETH Zurich (IACETH) which allows to transform
the (modified) P files of the PV inversion directly into the input and boundary files for the
Climate HRM model. It is the aim that some case studies will be undertaken in this way by a
diploma student at our institute.\\
\item [c] From the quasi-geostrophic omega equation it is well known that PV structures are able to
enforce vertical motions. These are particularly interesting because vertical motion leads to
condensation or convective instability, if the vertical temperature and humidity profile are suitable. Therefore,
it would be of great interest to see how the modified PV distribution is associated with different
vertical motions. Technically this means that an additional equation, the aforementioned
quasi-geostrophic omega equation, has to be solved. In the coming summer semester, a student with focus on scientific
programming will attack this problem.\\
\item [d] Teaching atmospheric dynamics at the graduate level involves several challenges. One
particular challenge is associated with the abstract concept of potential vorticity. An easy-to-use
PV inversion tool might be of great relieve to the teacher since he can easily illustrate and
apply the concepts to real and idealised cases. It is quite certain that such a visualisation help
would be much appreciated by graduate students in atmospheric dynamics. It is one aim of the
dynamic's group at {\it IAC}ETHto improve teaching in this respect, while keeping the mathematical and physical
level of the taught contents.
\end{itemize}
 
 
\newpage
\section{Acknowledgment}
 
 
There are many persons which need to be mentioned in this acknowledgment. Perhaps, most crucially is
a heartily thanks to Rene Fehlmann who initially developed the inversion tool. I had the joy to start my atmospheric research under Rene's supervision, and his enthusiasm for mathematics, numerics and atmosphere
always was and still is very inspiring for me. \\
 
\noindent
Recently I read that success in science cannot be attributed solely to one's own intelligence an
"superiority". And with my long experience in science, I fully agree with that statement. Success needs
luck, and last but not least it needs excellent teachers, supervisors and colleagues. I had the great pleasure
to work together and get help from excellent scientists and teachers: Christoph Sch\"ar, Heini Wernli and Huw Davies. I appreciated very much their scientific qualities, but probably still more their warmth and
friendliness as colleagues.\\
 
\noindent
Many research colleagues were indirectly important in the development of this PV inversion tool. Conny Schwierz, Olivia Martius, Mischa Croci-Maspoli, Sarah Kew. Certainly, thanks should also go to Linda Schlemmer who
accepted a diploma thesis based on this tool, and is now testing all aspects of it.\\
 
\noindent
Finally, this work was done in the frame of the postgraduate course in Computer Science at the Fernfachhochschule Schweiz. Thanks goes to all teachers, and in particular to Lars Kruse who accepted to supervise this diploma thesis and discussed with me the different steps. Although we had some
different views what should be included into this thesis ("Why do you want to send this part to the appendix? This is a diploma thesis,...") I enjoyed working with him, particularly because of his interest in the atmospheric sciences.
 
 
\newpage
\section{References}
 
\noindent
{\bf [1]} Acheson, D.\,J., 1990:
Elementary Fluid Dynamics.
{\sl Oxford Applied Mathematics and Computing Science Series,}, Oxford UP, 395pp.\\
 
\noindent
{\bf [2]} Appenzeller, C., H.~C.~Davies, and W.~A.~Norton, 1996:
Fragmentation of stratospheric intrusions.
{\sl J.~Geophys.~Res.,} {\bf 101,} 1435-1456.\\
 
\noindent
{\bf [3]} Hoskins, B.\,J., M.\,E.\,McIntyre, and A.\,W.\,Robertson, 1985:
On the use and significance of isentropic potential vorticity maps. Quart.\,J.\,Roy.\,Meteor.\,Soc.,{\bf 111}, 877-946.\\
 
\noindent
{\bf [4]} Bluestein,\,H.\,B., 1993:
Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of Weather Systems, Oxford University Press, {594 pp}.\\
 
\noindent
{\bf [5]} Charney, J.\,B., 1993:
On the scale of atmospheric motions. Geofysisk.\,Publ.,{\bf 17}, No.\,2.\\
 
\noindent
{\bf [6]} Davis, C.\,A., 1992:
Piecewise potential vorticity inversion. J.\,Atmos.\,Sci., {\bf 49}, 1397-1411.\\
 
\noindent
{\bf [7]} Davis, C.\,A., and K.\,A.\,Emanuel, 1992:
Potential vorticity diagnostic of cyclogenesis. Mon.\,Wea.\,Rev., {\bf 119}, 1929-1953.\\
 
\noindent
{\bf [8]} Ertel, H., 1942:
Ein neuer hydrodynamischer Wirbelsatz. Meteor.\,Z., {\bf 59}, 277-281.\\
 
\noindent
{\bf [9]} Fehlmann, R., 1997:
Dynamics of seminal PV elements.
PhD thesis No. 12229, ETH Z\"urich, 143 pp.\\
 
\noindent
{\bf [10]} Fehlmann, R. and H.\,C.\,Davies, 1997:
Misforecasts of synoptic systems: Diagnosis via PV retrodiction. Mon.\,Wea.\,Rev., {\bf 125}, 2247-2264.\\
 
 
\noindent
{\bf [11]} Holton, J.\,R., 1992:
An Introduction to Dynamic Meteorology. Third Edition.
Academic Press, San Diego, California, 511pp.\\
 
\noindent
{\bf [12]} Kleinschmidt, E., 1950:
\"Uber Aufbau und Entstehung von Zyklonen. Teil 1. Meteor.\,Rundsch., {\bf 3}, 1-6.\\
 
\noindent
{\bf [13]} Martius, O., E.\,Zenklusen, C. Schwierz, and H.\,C.\,Davies 2006:
Episodes of alpine heavy precipitation with an overlying elongated stratospheric intrusion: a climatology. Intl.\,J.\,Climatology., {\bf Vol. 96, Issue 9}, 1149-1164.\\
 
\noindent
{\bf [14]} McIntyre, M., 1997:
GEFD (Geophysical and Environmental Fluid Dynamics) Summer School, DAMPTP University of Cambridge.\\
 
\noindent
{\bf [15]} Lynch, P., 2006:
The Emergence of Numerical Weather Prediction. Richardson's Dream.
Cambridge UP, Cambridge, UK. 279pp.\\
 
\noindent
{\bf [16]} Nebeker, F., 1995:
Calculating the Weather. Meteorology in the 20th Century..
Academic Press, San Diego, California, 255pp.\\
 
\noindent
{\bf [17]} Press, W.\,H., Flannery, B.\,P., Teukolsky, S.\,A., and Vetterling, W.\,T., 1992:
Numerical Recipes in FORTRAN: The Art of Scientific Computing.
Cambridge University Press, Cambridge, UK, 1447pp.\\
 
 
\noindent
{\bf [18]} Sprenger, M.~and H.~Wernli, 2003:
A northern hemispheric climatology of cross-tropopause exchange for the ERA15
time period (1979-1993).
{\sl J.~Geophys.~Res.,} {\bf 108}(D12), 8521, doi:10.1029/2002JD002636.\\
 
\noindent
{\bf [19]} Stohl, A., P. Bonasoni, P. Cristofanelli, W. Collins, J. Feichter,
A. Frank, C. Forster, E. Gerasopoulos, H. G\"uggeler, P. James,
T. Kentarchos, H. Kromp-Kolb, B. Kr\"uger, C. Land, J. Meloen,
A. Papayannis, A. Priller, P. Seibert, M. Sprenger, G. J. Roelofs,
H. E. Scheel, C. Schnabel, P. Siegmund, L. Tobler, T. Trickl,
H. Wernli, V. Wirth, P. Zanis, and C. Zerefos: 2003.
Stratosphere-troposphere exchange: A review, and what we have learned from STACCATO.
J.\,Geophys.\,Res.,{\bf Vol. 108}, No. D12, 8516, doi:10.1029/2002JD002490.\\
 
 
\noindent
{\bf [20]} Wallace, J.\,M. and P.\,V.\,Hobbs, R., 1977:
Atmospheric Science. An Introductory Survey.
Academic Press, San Diego, California, 467pp.\\
 
 
 
\newpage
\section{Appendix}
 
\subsection{Scalar co-ordinate transformation}
 
Four real function are needed for the transformation between the geographical latitude/-longitude grid
used by ECMWF and the quasi-cartesian grid used by the PV inversion. Physically the new quasi-cartesian
co-ordinate system is obtained by introducing a new latitude/longitude grid, but now the two co-ordinates
being defined relative to a rotated north pole. Therefore, the new longitude and latitude are referred to as rotated co-ordinates. The position (in geographical latitude and longitude) of the new north pole is given as parameters POLPHI and POLLAM. Then, the functions\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
LAM = REAL FUNCTION LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
PHI = REAL FUNCTION PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
relate the rotated latitude (PHIS) and longitude (LAMS) to corresponding latitude (PHI) and
longitude (LAM) in the geographical system. Correspondingly, the following two functions give
the reverse transformation, i.e. to every position in geographical latitude/longitude a rotated
pair of co-ordinates is attributed. Again, the pole position (in the geographical grid) must be
passed as parameters (POLPHI and POLLAT).\\[-0.3cm]
\begin{center}
\begin{minipage}[t]{13cm}
\begin{verbatim}
LAMS = REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
PHIS = REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
\end{verbatim}
\end{minipage}
\end{center}
 
\vspace{0.3cm}
\noindent
Here, the geographical co-ordinates (PHI, LAM) are transformed into rotated co-ordinates (PHIS, LAMS).
If the corresponding pair of coordinates are given, any scalar field can easily be transformed. The following
Fortran functions are taken from the source code from the numerical weather prediction model of the German/Swiss weather service.
 
 
\begin{small}
\begin{verbatim}
C -------------------------------------------------------------------------
REAL FUNCTION LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C -------------------------------------------------------------------------
C
C**** LMSTOLM - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C** IM ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ZARG1 = SIN(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) -
2 COS(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
ZARG2 = COS(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) +
2 SIN(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMSTOLM = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMSTOLAM = 90.0
ELSE
LMSTOLAM = -90.0
ENDIF
ELSE
LMSTOLM = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
C -------------------------------------------------------------------------
REAL FUNCTION PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C -------------------------------------------------------------------------
C
C**** PHSTOPH - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C**** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE BREITE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
SINPOL = SIN(ZPIR18*POLPHI)
COSPOL = COS(ZPIR18*POLPHI)
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ARG = COSPOL*COS(ZPHIS)*COS(ZLAMS) + SINPOL*SIN(ZPHIS)
PHSTOPH = ZRPI18*ASIN(ARG)
RETURN
END
C -------------------------------------------------------------------------
REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C -------------------------------------------------------------------------
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** LMTOLMS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG1 = - SIN(ZLAM-ZLAMPOL)*COS(ZPHI)
ZARG2 = - ZSINPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL)+ZCOSPOL*SIN(ZPHI)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMTOLMS = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMTOLMS = 90.0
ELSE
LMTOLMS = -90.0
ENDIF
ELSE
LMTOLMS = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
 
C -------------------------------------------------------------------------
REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C -------------------------------------------------------------------------
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** PHTOPHS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: ROTIERTE BREITE PHIS ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG = ZCOSPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL) + ZSINPOL*SIN(ZPHI)
PHTOPHS = ZRPI18*ASIN(ZARG)
RETURN
END
\end{verbatim}
\end{small}
 
\newpage
\subsection{Controlling Linux Shell Script}
 
In this appendix the controlling Linux Shell script of the PV inversion is reproduced. This script
offers a user-friendly interface to the inversion. It is essentially split into five
different section: (1) installation and parameter settings, (2) preparatory steps, (3)
iterative solution of the PV inversion problem, (4) post-processing, and (5) diagnostic
tools.\\
\begin{small}
\begin{verbatim}
#!/bin/csh
 
# Master Linux script for PV inversion
# Michael Sprenger / Winter 2006,2007
 
# -------------------------------------------------------------------
# Set some variables and paths
# -------------------------------------------------------------------
 
# Handling of input parameters
set step="help"
if ( $#argv == 1 ) then
set step=$1
endif
if ( $#argv == 2 ) then
set step=$1
set file1=$2
endif
if ( $#argv == 3 ) then
set step=$1
set file1=$2
set file2=$3
endif
 
# Set base directory for programmes
set bdir=/home/sprenger/PV_Inversion_Tool/real/
 
# Set name of the parameter file, the coastline file and the sample files
set parafile="${PWD}/inversion.param"
set coastfile="${bdir}/prep/coastline.dat"
set sampledir="/net/rossby/lhome/sprenger/PV_Inversion_Tool/real/inp/"
 
# Extract parameters from parameter file
set progex=${bdir}/inversion.perl
set date=`${progex} ${parafile} date | awk '{ print $2}'`
set nofiter=`${progex} ${parafile} n_of_iteration | awk '{ print $2}'`
set save=`${progex} ${parafile} save_iteration | awk '{ print $2}'`
set idir=`${progex} ${parafile} inp_dir | awk '{ print $2}'`
set rdir=`${progex} ${parafile} run_dir | awk '{ print $2}'`
set odir=`${progex} ${parafile} out_dir | awk '{ print $2}'`
 
# ---------------------------------------------------------------------------
# Installation, help and sample
# ---------------------------------------------------------------------------
 
# Create the needed directories
if ( ${step} == "inst" ) then
if ( ! -d ${idir} ) mkdir ${idir}
if ( ! -d ${rdir} ) mkdir ${rdir}
if ( ! -d ${odir} ) mkdir ${odir}
endif
 
# Create the needed directories
if ( ${step} == "help" ) then
echo
echo "Installation"
echo " inst: Creates the input, run and output directory"
echo
echo "Sample case study"
echo " sample: Copy all files for a sample case study"
echo
echo "Preparing input files [prep]"
echo " prep0: Calculate S file with PV and TH"
echo " prep1: Interpolate onto height levels"
echo " prep2: Rotate into local cartesian co-ordinate system"
echo " prep3: Add TH,PV,NSQ and RHO to the data file"
echo " prep4: Define modified and anomaly PV field and boundary values"
echo " prep5: Reduce the domain size and split the input files"
echo " prep6: Add the reference profile"
echo " prep7: Add coastlines to REF file"
echo " prep8: Move the files to the run directory"
echo
echo "Perform the PV inversion [pvin]"
echo " pvin1: Add NSQ, TH, RHO, and PV"
echo " pvin2: Change Ertel's PV anomaly into one of quasi-geostrophic PV"
echo " pvin3: Inversion of quasi-geostrophic PV anomaly"
echo " pvin4: Subtract anomaly from MOD file"
echo " pvin5: Keep iterative steps if save flag is set"
echo
echo "Postprocessing [post]"
echo " post1: Copy needed files from input and run directory"
echo " post2: Rotate from quasi-cartesian co-ordinate frame to lat/lon system"
echo " post3: Bring modified fields back to P file"
echo " post4: Calculate S file with PV and TH"
echo " post5: Make clean"
echo
echo "Diagnostic Tools"
echo " diag1: Check the consistency of the boundary conditions"
echo " diag2: Calculate the quasi-geostrophic PV"
echo " diag3: Get the difference between two files"'
echo
endif
 
 
# Copy sample files (if specified)
if ( ${step} == "sample" ) then
\cp ${sampledir}/P20060116_18 ${idir}
\cp ${sampledir}/ml_cst ${idir}
\cp ${sampledir}/Z20060116_18 ${idir}
\cp ${sampledir}/pl_cst ${idir}
endif
 
# ---------------------------------------------------------------------------
# Preparatory steps
# ---------------------------------------------------------------------------
 
# Change to data directory
cd ${idir}
 
# Step 0: Calculate S file with PV and TH (not in prep mode)
if ( ${step} == "prep0" ) then
\rm -f S${date}
p2s P${date} TH PV
endif
 
# Step 1: Interpolate onto height levels
if ( ${step} == "prep1" | ${step} == "prep" ) then
echo "P${date}" >! fort.10
echo "Z${date}" >> fort.10
echo "H${date}" >> fort.10
${bdir}/inversion.perl ${parafile} p2z >> fort.10
echo "U U P${date}" >> fort.10
echo "V V P${date}" >> fort.10
echo "T T P${date}" >> fort.10
echo "Q Q P${date}" >> fort.10
${bdir}/prep/p2z
\mv H${date}_cst zl_cst
changecst H${date} zl_cst
#\rm -f fort.10
endif
 
# Step 2: Rotate into local cartesian co-ordinate system
if ( ${step} == "prep2" | ${step} == "prep" ) then
echo "H${date}" >! fort.10
echo "R${date}" >> fort.10
${bdir}/inversion.perl ${parafile} rotate_grid >> fort.10
echo "5" >> fort.10
echo "ORO" >> fort.10
echo "U.V" >> fort.10
echo "P" >> fort.10
echo "T" >> fort.10
echo "Q" >> fort.10
${bdir}/prep/rotate_grid
\mv R${date}_cst ro_cst
changecst R${date} ro_cst
\rm -f fort.10
endif
 
# Step 3: Add TH,PV,NSQ and RHO to the data file
if ( ${step} == "prep3" | ${step} == "prep" ) then
echo "TH" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "PV" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "NSQ" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "RHO" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
\rm -f fort.10
endif
 
# Step 4: Set the modified PV field and boundary values
if ( ${step} == "prep4" | ${step} == "prep" ) then
echo "R${date}" >! fort.10
${bdir}/inversion.perl ${parafile} def_anomaly >> fort.10
${bdir}/prep/def_anomaly
\rm -f fort.10
endif
 
# Step 5: Reduce the domain size and split the input files
if ( ${step} == "prep5" | ${step} == "prep" ) then
echo "PV PV R${date} ORG_${date}" >! fort.10
echo "U U R${date} ORG_${date}" >> fort.10
echo "V V R${date} ORG_${date}" >> fort.10
echo "TH TH R${date} ORG_${date}" >> fort.10
echo "Q Q R${date} ORG_${date}" >> fort.10
echo "P P R${date} ORG_${date}" >> fort.10
echo "T T R${date} ORG_${date}" >> fort.10
echo "PV_FILT PV_AIM R${date} MOD_${date}" >> fort.10
echo "U U R${date} MOD_${date}" >> fort.10
echo "V V R${date} MOD_${date}" >> fort.10
echo "Q Q R${date} MOD_${date}" >> fort.10
echo "P P R${date} MOD_${date}" >> fort.10
echo "T T R${date} MOD_${date}" >> fort.10
echo "NSQ NSQ R${date} MOD_${date}" >> fort.10
echo "RHO RHO R${date} MOD_${date}" >> fort.10
echo "TH TH R${date} MOD_${date}" >> fort.10
echo "PV_ANOM PV R${date} ANO_${date}" >> fort.10
echo "TH_ANOM TH R${date} ANO_${date}" >> fort.10
echo "UU_ANOM U R${date} ANO_${date}" >> fort.10
echo "VV_ANOM V R${date} ANO_${date}" >> fort.10
echo "ORO ORO R${date} REF_${date}" >> fort.10
echo "X X R${date} REF_${date}" >> fort.10
echo "Y Y R${date} REF_${date}" >> fort.10
echo "LAT LAT R${date} REF_${date}" >> fort.10
echo "LON LON R${date} REF_${date}" >> fort.10
echo "CORIOL CORIOL R${date} REF_${date}" >> fort.10
${bdir}/prep/cutnetcdf
\rm -f fort.10
endif
 
# Step 6: Add the reference profile
if ( ${step} == "prep6" | ${step} == "prep" ) then
\rm -f fort.10
echo "MOD_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/prep/ref_profile
\rm -f fort.10
endif
 
# Step 7: Add coastlines to REF file
if ( ${step} == "prep7" | ${step} == "prep" ) then
\rm -f fort.10
echo \"REF_${date}\" >! fort.10
echo \"${coastfile}\" >> fort.10
${bdir}/inversion.perl ${parafile} coastline >> fort.10
${bdir}/prep/coastline
\rm -f fort.10
endif
 
# Step 8: Move the files to the run directory
if ( ${step} == "prep8" | ${step} == "prep" ) then
\mv MOD_${date} MOD_${date}_cst ${rdir}
\mv ORG_${date} ORG_${date}_cst ${rdir}
\mv ANO_${date} ANO_${date}_cst ${rdir}
\mv REF_${date} REF_${date}_cst ${rdir}
\rm -f fort.10
endif
 
# ---------------------------------------------------------------------------
# Inversion
# ---------------------------------------------------------------------------
 
# Change to data directory
cd ${rdir}
 
# Start loop
set count=0
loop:
 
# Step 1: Add NSQ, TH, RHO, and PV to MOD file, take grid from REF file
if ( ${step} == "pvin1" | ${step} == "pvin" ) then
echo "NSQ" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "RHO" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "TH" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "PV" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
\rm -f fort.10
endif
 
# Step 2: Change Ertel's PV anomaly into an anomaly of quasi-geostrophic PV
if ( ${step} == "pvin2" | ${step} == "pvin" ) then
echo "MOD_${date}" >! fort.10
echo "REF_${date}" >> fort.10
echo "ANO_${date}" >> fort.10
${bdir}/pvin/pv_to_qgpv
\rm -f fort.10
endif
 
# Step 3: Inversion of quasi-geostrophic PV anomaly with Neumann boundary
if ( ${step} == "pvin3" | ${step} == "pvin" ) then
echo "ANO_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/pvin/inv_cart
\rm -f fort.10
endif
 
# Step 4: Prepare the output of the inversion for next iteration step
if ( ${step} == "pvin4" | ${step} == "pvin" ) then
\rm -f fort.10
echo "MOD_${date}" >! fort.10
echo "ANO_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} prep_iteration >> fort.10
${bdir}/pvin/prep_iteration
\rm -f fort.10
endif
 
# Step 5: Keep iterative steps if save flag is set
if ( ${step} == "pvin5" | ${step} == "pvin" ) then
if ( "${save}" == "yes" ) then
set pre=''
if ( ${count} < 10 ) then
set pre='0'
endif
\cp MOD_${date} MOD_${date}_${pre}${count}
\cp ANO_${date} ANO_${date}_${pre}${count}
endif
endif
 
# End loop for iterations
if ( ${step} == "pvin" ) then
@ count = ${count} + 1
if ( ${count} < ${nofiter} ) goto loop
endif
 
# ---------------------------------------------------------------------------
# Postprocessing
# ---------------------------------------------------------------------------
 
# Change to data directory
cd ${odir}
 
# Step 1: Copy needed files from input and run directory
if ( ${step} == "post1" | ${step} == "post" ) then
ln -sf ${rdir}/MOD_${date} ${rdir}/MOD_${date}_cst .
\cp ${idir}/P${date} ${idir}/ml_cst .
endif
 
# Step 2: Rotate from quasi-cartesian co-ordinate frame to lat/lon system
if ( ${step} == "post2" | ${step} == "post" ) then
echo "MOD_${date}" >! fort.10
echo "GEO_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} rotate_lalo >> fort.10
echo "3" >> fort.10
echo "T" >> fort.10
echo "U.V" >> fort.10
echo "P" >> fort.10
${bdir}/post/rotate_lalo
\rm -f fort.10
endif
 
# Step 3: Bring modified fields back to P file
if ( ${step} == "post3" | ${step} == "post" ) then
\rm -f fort.10
echo "P${date}" >! fort.10
echo "GEO_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} add2p >> fort.10
${bdir}/post/add2p
\rm -f fort.10
endif
 
# Step 4: Calculate S file with PV and TH
if ( ${step} == "post4" | ${step} == "post" ) then
\rm -f S${date}
p2s P${date} TH PV
endif
 
# Step 5: Make clean
if ( ${step} == "post5" | ${step} == "post" ) then
\rm -f MOD_${date} MOD_${date}_cst
\rm -f GEO_${date} GEO_${date}_cst
endif
 
# ---------------------------------------------------------------------------
# Diagnostic Tools
# ---------------------------------------------------------------------------
 
# Change to run directory
cd ${rdir}
 
# Step 1: Check the consistency of the boundary conditions (diag1)
if ( ${step} == "diag1" ) then
\rm -f fort.10
echo "ANO_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/diag/check_boundcon
\rm -f fort.10
endif
 
# Step 2: Calculate the quasi-geostrophic PV (diag2 [ORG|MOD|ANO]
if ( ${step} == "diag2" ) then
\rm -f fort.10
echo "${file1}_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/diag/calc_qgpv
\rm -f fort.10
endif
 
# Step 3: Get difference between two files (diag3 [ORG|MOD|ANO] - [ORG|MOD|ANO])
if ( ${step} == "diag3" ) then
\rm -f fort.10
echo "${file1}_${date}" >! fort.10
echo "${file2}_${date}" >> fort.10
echo "DIA_${date}" >> fort.10
${bdir}/diag/difference
\rm -f fort.10
endif
\end{verbatim}
\end{small}
 
\newpage
\subsection{Controlling Parameter File}
 
The inversion problem is specified in a parameter file. This file is set as a parameter in the
controlling Linux Shell script (see Appendix~9.2) and is often the only file which has to be adapted.
 
\begin{small}
\begin{verbatim}
BEGIN DATA
DATE = 20060116_18; ! Date for case study
INP_DIR = /lhome/sprenger/PV_Inversion_Tool/real/inp; ! Input directory
RUN_DIR = /lhome/sprenger/PV_Inversion_Tool/real/run; ! Run directory
OUT_DIR = /lhome/sprenger/PV_Inversion_Tool/real/out; ! Output directory
END DATA
 
BEGIN GRID
GEO_XMIN = -180.; ! Geographical grid in zonal direction
GEO_NX = 361 ;
GEO_DX = 1.;
GEO_YMIN = 0.; ! Geographical grid in meridional direction
GEO_NY = 91 ;
GEO_DY = 1.;
GEO_ZMIN = 0.; ! Vertical levels ( ZMIN and DZ in [m] )
GEO_NZ = 125 ;
GEO_DZ = 200.;
ROT_NX = 250 ; ! Rotated grid ( DX and DY in [deg] )
ROT_NY = 250 ;
ROT_DX = 0.25;
ROT_DY = 0.25;
CLON = -65.; ! Longitude, latitude [deg] and angle of rotated grid
CLAT = 45.;
CROT = 0.;
END GRID
 
BEGIN ANOMALY
BOX_XMIN = -1200.; ! Box where to apply the digital filter
BOX_XMAX = 1200.;
BOX_YMIN = -1200.;
BOX_YMAX = 1200.;
BOX_ZMIN = 2000.;
BOX_ZMAX = 10000.;
NFILTER = 5 ; ! Number of filter iterations;
BOUND_XY = 500.; ! Transition zone for horizontal boundaries ( in [km] )
BOUND_Z = 500.; ! Transition zone for vertical boundaries ( in [m] )
END ANOMALY
 
BEGIN NUMERICS
ALPHA = 0.5; ! Adjustment factor after one iteration step
NOFITER = 6; ! Number of "external" iterations
SAVEITER = no; ! Flag whether to save iteration steps
END NUMERICS
\end{verbatim}
\end{small}
 
\newpage
\subsection{List of Fortran, Perl and Linux programs}
 
The main tasks of the PV inversion are handled by Fortran programs. The following table contains a complete list
of these programs with some details. The first column gives the name of the program, the second column the section
(pre-processing, inversion, post-processing, diagnostics) where this program is needed, the third column the authors (in
order of their contribution), and the fourth column is a short description of the code. In the table, Fortran programs
are marked with the appendix ".f", Perl programs with the appendix ".perl", and Linux Shell scripts with the appendix ".sh".
 
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
{\bf Name of program} & {\bf Section} & {\bf Author} & {\bf Short description} \\[2mm]
\hline
{\bf p2z.f} & prep & Michael Sprenger & Interpolation onto height levels\\[2mm]
\hline
{\bf rotate\_grid.f} & prep & Michael Sprenger & Rotation to quâsi-cartesian system\\[2mm]
\hline
{\bf z2s.f} & prep, pvin & Michael Sprenger & Calculation of secondary fields\\[2mm]
\hline
{\bf def\_anomaly.f} & prep & Michael Sprenger & Definition of modified Ertel's PV\\[2mm]
\hline
{\bf cutnetcdf.f } & prep & Michael Sprenger & Splitting of netcdf files\\
& & Heini Wernli & \\[2mm]
\hline
{\bf ref\_profile.f} & prep & Michael Sprenger & Definition of reference profile\\
& & Olivia Martius & \\[2mm]
\hline
{\bf coastline.f} & prep & Michael Sprenger & Add coastlines to reference file\\[2mm]
\hline
{\bf pv\_to\_qgpv.f} & pvin & Michael Sprenger & Calculate quasi-geostrophic PV\\[2mm]
\hline
{\bf inv\_cart.f} & pvin & Rene Fehlmann & Inversion of quasi-geostrophic PV\\
& & Michael Sprenger & \\[2mm]
\hline
{\bf prep\_iteration.f} & pvin & Michael Sprenger & Prepare next iteration step\\
& & Rene Fehlmann & \\[2mm]
\hline
{\bf rotate\_lalo.f} & post & Michael Sprenger & Rotate to geographical grid\\[2mm]
\hline
{\bf add2p.f} & post & Michael Sprenger & Interpolation to hybrid grid\\[2mm]
\hline
{\bf p2s.f} & prep, post & Heini Wernli & Secondary fields on hybrid grid\\[2mm]
\hline
{\bf check\_boundcon.f} & diag & Rene Fehlmann & Consistency check for boundaries\\
& & Michael Sprenger & \\[2mm]
\hline
{\bf calc\_qgpv.f} & diag & Sebastien Dirren & Convergence check for inversion\\
& & Michael Sprenger & \\[2mm]
\hline
{\bf difference.f} & diag & Michael Sprenger & Difference of two netcdf files\\[2mm]
\hline
{\bf inversion.sh} & & Michael Sprenger & Master Linux Shell script\\[2mm]
\hline
{\bf inversion.perl} & & Michael Sprenger & Extraction of parameters\\[2mm]
\hline
\end{tabular}
\end{center}
 
 
\end{document}
Property changes:
Added: svn:executable
/tags/1.0/inversion.docu
0,0 → 1,0
okular ${DYN_TOOLS}/inversion/docu/userguide.pdf
Property changes:
Added: svn:executable
/tags/1.0/inversion.install
0,0 → 1,123
# ----- Load modules --------------------------
 
module load netcdf/4.2.1-pgf90
module list
 
# ----- Set libraries and includes ------------
 
set libs = "-L ${DYN_TOOLS}/lib"
set libs = "${libs} -lcdfio"
set libs = "${libs} -lcdfplus"
set libs = "${libs} -lipo"
set libs = "${libs} -lgm2em"
 
set ncdf_incs = `nc-config --fflags`
set ncdf_libs = `nc-config --flibs`
 
# ----- Compile --------------------- ----------
 
cd ${DYN_TOOLS}/inversion/diag/
 
foreach tool ( calc_qgpv check_boundcon difference hydrostatic qvec_analysis )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${DYN_TOOLS}/inversion/post/
 
foreach tool ( add2p rotate_lalo )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
cd ${DYN_TOOLS}/inversion/prep/
 
foreach tool ( coastline cutnetcdf def_anomaly p2z ref_profile rotate_grid z2s )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
 
cd ${DYN_TOOLS}/inversion/pvin/
 
foreach tool ( inv_cart prep_iteration pv_to_qgpv z2s )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
 
cd ${DYN_TOOLS}/inversion/spec/
 
foreach tool ( modify_anomaly )
 
\rm -f ${tool}.o
\rm -f ${tool}
 
echo "pgf90 -c ${tool}.f ${ncdf_incs}"
pgf90 -c ${tool}.f ${ncdf_incs}
echo "pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}"
pgf90 -o ${tool} ${tool}.o ${libs} ${ncdf_libs}
 
if ( ! -f ${tool} ) then
echo "ERROR: compilation of <tool> failed... exit"
exit 1
endif
 
end
 
 
# ----- Set <bin> --------------------------------
 
ln -svf ${DYN_TOOLS}/inversion/inversion.sh ${DYN_TOOLS}/bin/inversion
 
chmod og+rx ${DYN_TOOLS}/bin/inversion
 
exit 0
Property changes:
Added: svn:executable
/tags/1.0/inversion.param
0,0 → 1,46
BEGIN DATA
DATE = 20060116_18; ! Date for case study
INP_DIR = /lhome/sprenger/PV_Inversion_Tool/real/inp; ! Input directory
RUN_DIR = /lhome/sprenger/PV_Inversion_Tool/real/run; ! Run directory
OUT_DIR = /lhome/sprenger/PV_Inversion_Tool/real/out; ! Output directory
END DATA
 
BEGIN GRID
GEO_XMIN = -180.; ! Geographical grid in zonal direction
GEO_NX = 361 ;
GEO_DX = 1.;
GEO_YMIN = 0.; ! Geographical grid in meridional direction
GEO_NY = 91 ;
GEO_DY = 1.;
GEO_ZMIN = 0.; ! Vertical levels ( ZMIN and DZ in [m] )
GEO_NZ = 125 ;
GEO_DZ = 200.;
ROT_NX = 250 ; ! Rotated grid ( DX and DY in [deg] )
ROT_NY = 250 ;
ROT_DX = 0.25;
ROT_DY = 0.25;
CLON = -65.; ! Longitude, latitude [deg] and angle of rotated grid
CLAT = 45.;
CROT = 0.;
REF_R = 500.; ! Radius for reference radius; -1 if whole domain)
END GRID
 
BEGIN ANOMALY
BOX_XMIN = -1200.; ! Box where to apply the digital filter
BOX_XMAX = 1200.;
BOX_YMIN = -1200.;
BOX_YMAX = 1200.;
BOX_ZMIN = 2000.;
BOX_ZMAX = 10000.;
NFILTER = 5 ; ! Number of filter iterations;
BOUND_XY = 500.; ! Transition zone for horizontal boundaries ( in [km] )
BOUND_Z = 500.; ! Transition zone for vertical boundaries ( in [m] )
END ANOMALY
 
BEGIN NUMERICS
ALPHA = 0.5; ! Adjustment factor after one iteration step
NOFITER = 6; ! Number of "external" iterations
SAVEITER = no; ! Flag whether to save iteration steps
TRANS_XY = 500.; ! Smooth transition zone (in km) for back-insertion into P file
PS_CHANGE = 0.0; ! Allow (1.0), do not allow (0.0), or fractionally allow (0<x<1) changes in surface pressure
END NUMERICS
Property changes:
Added: svn:executable
/tags/1.0/inversion.perl
0,0 → 1,129
#!/usr/bin/perl
 
# Get input arguments
$paramfile=$ARGV[0];
$parammode=$ARGV[1];
 
# Define the extraction tables for the inversion programmes
if ( "$parammode" eq "p2z" )
{ @list = ('GRID.GEO_ZMIN',
'GRID.GEO_NZ',
'GRID.GEO_DZ'); }
if ( "$parammode" eq "ref" )
{ @list = ('GRID.REF_R'); }
 
if ( "$parammode" eq "def_anomaly" )
{ @list = ('ANOMALY.BOX_XMIN',
'ANOMALY.BOX_XMAX',
'ANOMALY.BOX_YMIN',
'ANOMALY.BOX_YMAX',
'ANOMALY.BOX_ZMIN',
'ANOMALY.BOX_ZMAX',
'ANOMALY.NFILTER',
'ANOMALY.BOUND_XY',
'ANOMALY.BOUND_Z'); }
 
if ( "$parammode" eq "rotate_grid" )
{ @list = ('GRID.ROT_NX',
'GRID.ROT_NY',
'GRID.ROT_DX',
'GRID.ROT_DY',
'GRID.CLON',
'GRID.CLAT',
'GRID.CROT'); }
 
if ( "$parammode" eq "rotate_lalo" )
{ @list = ('GRID.GEO_NX',
'GRID.GEO_NY',
'GRID.GEO_DX',
'GRID.GEO_DY',
'GRID.GEO_XMIN',
'GRID.GEO_YMIN',
'GRID.CLON',
'GRID.CLAT',
'GRID.CROT'); }
 
if ( "$parammode" eq "add2p" )
{ @list = ('NUMERICS.TRANS_XY',
'NUMERICS.PS_CHANGE' ); }
 
if ( "$parammode" eq "coastline" )
{ @list = ('GRID.CLON',
'GRID.CLAT',
'GRID.CROT'); }
 
if ( "$parammode" eq "prep_iteration" )
{ @list = ('NUMERICS.ALPHA'); }
 
if ( "$parammode" eq "inp_dir" )
{ @list = ('DATA.INP_DIR'); };
 
if ( "$parammode" eq "run_dir" )
{ @list = ('DATA.RUN_DIR'); };
 
if ( "$parammode" eq "out_dir" )
{ @list = ('DATA.OUT_DIR'); };
 
if ( "$parammode" eq "n_of_iteration" )
{ @list = ('NUMERICS.NOFITER'); };
 
if ( "$parammode" eq "save_iteration" )
{ @list = ('NUMERICS.SAVEITER'); };
 
if ( "$parammode" eq "date" )
{ @list = ('DATA.DATE'); };
 
# Read the parameter file
@zeilen = `more $paramfile`;
 
# Set the first parameter which should be retrieved
foreach $listentry (@list)
{
# Get section and name of the parameter
@param = split /\./, "$listentry";
$found=0;
 
# Loop over all variables
foreach $zeile ( @zeilen )
{
# -------------- BEGIN ------------------------------------
if ( $zeile =~ 'BEGIN' )
{
@field = split / /, "$zeile";
$_=$field[1];s/\s+//g;$bmode=$_;
}
 
# -------------- ASSIGNMENT -------------------------------
if ( ($zeile =~ '=') && ($zeile =~ ';') )
{
@field1 = split /=/, "$zeile";
@field2 = split /;/, "$field1[1]";
$_=$field1[0];s/\s+//g;$field1[0]=$_;
$_=$field2[0];s/\s+//g;$field2[0]=$_;
@field = ( $field1[0], $field2[0] );
if ( ("$bmode" eq "$param[0]") && ("$field[0]" eq "$param[1]" ) )
{
$found=1;
print "$field[0] $field[1] \n";
}
}
 
# -------------- END --------------------------------------
if ( $zeile =~ 'END' )
{
@field = split / /, "$zeile";
$_=$field[1];s/\s+//g;$emode=$_;
if ( "$bmode" ne "$emode" )
{
die "Invalid structure of parameter file... $bmode\n";
}
}
}
if ( $found == 0 )
{
die("Parameter $listentry not found... Stop");
}
}
Property changes:
Added: svn:executable
/tags/1.0/inversion.sh
0,0 → 1,550
#!/bin/csh
 
# -------------------------------------------------------------------
# Set some variables and paths
# -------------------------------------------------------------------
 
# Jump to specified step
set step="help"
set param1=
set param2=
set param3=
 
if ( $#argv == 1 ) then
set step=$1
endif
if ( $#argv == 2 ) then
set step=$1
set param1=$2
endif
if ( $#argv == 3 ) then
set step=$1
set param1=$2
set param2=$3
endif
if ( $#argv == 4 ) then
set step=$1
set param1=$2
set param2=$3
set param3=$4
endif
 
set file1=${param1}
set file2=${param2}
 
# Set base directory for programmes
set bdir=${DYN_TOOLS}/inversion/
 
# Set name of the parameter file, coastline file and sample directory
set parafile="${PWD}/inversion.param"
set coastfile="${bdir}/prep/coastline.dat"
set sampledir="/net/bio/atmosdyn/erainterim/cdf/2006/01/"
 
# ---------------------------------------------------------------------------
# Installation, help and sample
# ---------------------------------------------------------------------------
 
# Get parameter file, if not yet available
if ( ! -f ${parafile} ) then
cp ${bdir}/inversion.param .
endif
 
# Extract parameters from parameter file
set progex=${bdir}/inversion.perl
set date=`${progex} ${parafile} date | awk '{ print $2}'`
set nofiter=`${progex} ${parafile} n_of_iteration | awk '{ print $2}'`
set save=`${progex} ${parafile} save_iteration | awk '{ print $2}'`
set idir=`${progex} ${parafile} inp_dir | awk '{ print $2}'`
set rdir=`${progex} ${parafile} run_dir | awk '{ print $2}'`
set odir=`${progex} ${parafile} out_dir | awk '{ print $2}'`
 
# Create the needed directories
if ( ${step} == "inst" ) then
if ( ! -d ${idir} ) mkdir ${idir}
if ( ! -d ${rdir} ) mkdir ${rdir}
if ( ! -d ${odir} ) mkdir ${odir}
endif
 
# Create the needed directories
if ( ${step} == "help" ) then
echo
echo "Installation"
echo " inst: Creates the input, run and output directory; copy template parameter file"
echo
echo "Sample case study"
echo " sample: Copy all files for a sample case study"
echo
echo "Preparing input files [prep]"
echo " prep0: Calculate S file with PV and TH [ P -> S ]"
echo " prep1: Interpolate onto height levels [ P,Z -> H ]"
echo " prep2: Rotate into local cartesian coordinate system [ H -> R ]"
echo " prep3: Add TH,PV,NSQ and RHO to the data file [ -> R ]"
echo " prep4: Define modified and anomaly PV field and boundary values [ -> R ]"
echo " prep5: Reduce the domain size and split the input files [ R -> ORG,MOD,ANO,REF]"
echo " prep6: Add the reference profile [MOD -> REF]"
echo " prep7: Add coastlines to REF file [-> REF]"
echo " prep8: Move the files to the run directory [ORG,MOD,ANO,REF -> ]"
echo
echo "Perform the PV inversion [pvin]"
echo " pvin1: Add NSQ, TH, RHO, and PV [ -> MOD]"
echo " pvin2: Change Ertel's PV anomaly into one of quasi-geostrophic PV [MOD -> ANO]"
echo " pvin3: Inversion of quasi-geostrophic PV anomaly [ANO -> ANO]"
echo " pvin4: Subtract anomaly from MOD file [MOD-ANO -> MOD]"
echo " pvin5: Keep iterative steps if save flag is set"
echo
echo "Postprocessing [post]"
echo " post1: Copy needed files from input and run directory [P,MOD -> ]"
echo " post2: Rotate from quasi-cartesian coordinate frame to lat/lon system [ MOD -> GEO ]"
echo " post3: Bring modified fields back to P file [ P+GEO -> P ]"
echo " post4: Calculate S file with PV and TH [ P -> S ]"
echo " post5: Make clean"
echo " post6: Calculate difference to original P and S file"
echo
echo "Diagnostic Tools"
echo " diag1: Check the consitency of the boundary conditions"
echo " diag2: Calculate the quasi-geostrophic PV (diag2 [ORG|MOD|ANO])"
echo " diag3: Get the difference between two files (diag3 [ORG|MOD|ANO] [ORG|MOD|ANO])"
echo " diag4: Calculate geopotential with hydrostatic equation (diag4 [P|ORG|MOD|ANO])"
echo " diag5: Q vector analysis; geostrophic wind balance [ORG|MOD|ANO] [GEO|DIV_UV|QVEC|DIV_Q]"
echo
echo "Modifying Pv anomalies"
echo " mod1: Stretching and amplitude changes for anomalies [MOD]"
endif
 
 
# Copy sample files (if specified)
if ( ${step} == "sample" ) then
\cp ${sampledir}/P20060116_18 ${idir}
\cp ${sampledir}/eraint_cst ${idir}
\cp ${sampledir}/Z20060116_18 ${idir}
\cp ${sampledir}/pressure_cst ${idir}
endif
 
# ---------------------------------------------------------------------------
# Preparatory steps
# ---------------------------------------------------------------------------
 
# Change to data directory
cd ${idir}
 
# Step 0: Calculate S file with PV and TH (not in prep mode)
if ( ${step} == "prep0" ) then
\rm -f S${date}
p2s P${date} TH PV
endif
 
# Step 1: Interpolate onto height levels
if ( ${step} == "prep1" | ${step} == "prep" ) then
echo "P${date}" >! fort.10
echo "Z${date}" >> fort.10
echo "H${date}" >> fort.10
${bdir}/inversion.perl ${parafile} p2z >> fort.10
echo "U U P${date}" >> fort.10
echo "V V P${date}" >> fort.10
echo "T T P${date}" >> fort.10
echo "Q Q P${date}" >> fort.10
${bdir}/prep/p2z
\rm -f fort.10
endif
 
# Step 2: Rotate into local cartesian coordinate system
if ( ${step} == "prep2" | ${step} == "prep" ) then
echo "H${date}" >! fort.10
echo "R${date}" >> fort.10
${bdir}/inversion.perl ${parafile} rotate_grid >> fort.10
echo "5" >> fort.10
echo "ORO" >> fort.10
echo "U.V" >> fort.10
echo "P" >> fort.10
echo "T" >> fort.10
echo "Q" >> fort.10
${bdir}/prep/rotate_grid
\rm -f fort.10
endif
 
# Step 3: Add TH,PV,NSQ and RHO to the data file
if ( ${step} == "prep3" | ${step} == "prep" ) then
echo "TH" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "PV" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "NSQ" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
echo "RHO" >! fort.10
echo "R${date}" >> fort.10
echo "R${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/prep/z2s
\rm -f fort.10
endif
 
# Step 4: Set the modified PV field and boundary values
if ( ${step} == "prep4" | ${step} == "prep" ) then
echo "R${date}" >! fort.10
${bdir}/inversion.perl ${parafile} def_anomaly >> fort.10
${bdir}/prep/def_anomaly
\rm -f fort.10
endif
 
# Step 5: Reduce the domain size and split the input files
if ( ${step} == "prep5" | ${step} == "prep" ) then
echo "PV PV R${date} ORG_${date}" >! fort.10
echo "U U R${date} ORG_${date}" >> fort.10
echo "V V R${date} ORG_${date}" >> fort.10
echo "TH TH R${date} ORG_${date}" >> fort.10
echo "Q Q R${date} ORG_${date}" >> fort.10
echo "P P R${date} ORG_${date}" >> fort.10
echo "T T R${date} ORG_${date}" >> fort.10
echo "PV_FILT PV_AIM R${date} MOD_${date}" >> fort.10
echo "U U R${date} MOD_${date}" >> fort.10
echo "V V R${date} MOD_${date}" >> fort.10
echo "Q Q R${date} MOD_${date}" >> fort.10
echo "P P R${date} MOD_${date}" >> fort.10
echo "T T R${date} MOD_${date}" >> fort.10
echo "NSQ NSQ R${date} MOD_${date}" >> fort.10
echo "RHO RHO R${date} MOD_${date}" >> fort.10
echo "TH TH R${date} MOD_${date}" >> fort.10
echo "PV_ANOM PV R${date} ANO_${date}" >> fort.10
echo "TH_ANOM TH R${date} ANO_${date}" >> fort.10
echo "UU_ANOM U R${date} ANO_${date}" >> fort.10
echo "VV_ANOM V R${date} ANO_${date}" >> fort.10
echo "ORO ORO R${date} REF_${date}" >> fort.10
echo "X X R${date} REF_${date}" >> fort.10
echo "Y Y R${date} REF_${date}" >> fort.10
echo "LAT LAT R${date} REF_${date}" >> fort.10
echo "LON LON R${date} REF_${date}" >> fort.10
echo "CORIOL CORIOL R${date} REF_${date}" >> fort.10
${bdir}/prep/cutnetcdf
\rm -f fort.10
endif
 
# Step 6: Add the reference profile
if ( ${step} == "prep6" | ${step} == "prep" ) then
\rm -f fort.10
echo "MOD_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} ref >> fort.10
${bdir}/prep/ref_profile
\rm -f fort.10
endif
 
# Step 7: Add coastlines to REF file
if ( ${step} == "prep7" | ${step} == "prep" ) then
\rm -f fort.10
echo \"REF_${date}\" >! fort.10
echo \"${coastfile}\" >> fort.10
${bdir}/inversion.perl ${parafile} coastline >> fort.10
${bdir}/prep/coastline
\rm -f fort.10
endif
 
# Step 8: Move the files to the run directory
if ( ${step} == "prep8" | ${step} == "prep" ) then
\mv MOD_${date} MOD_${date}_cst ${rdir}
\mv ORG_${date} ORG_${date}_cst ${rdir}
\mv ANO_${date} ANO_${date}_cst ${rdir}
\mv REF_${date} REF_${date}_cst ${rdir}
\rm -f fort.10
endif
 
# ---------------------------------------------------------------------------
# Inversion
# ---------------------------------------------------------------------------
 
# Change to data directory
cd ${rdir}
 
# Start loop
set count=0
loop:
 
# Step 1: Add NSQ, TH, RHO, and PV to MOD file, take grid from REF file
if ( ${step} == "pvin1" | ${step} == "pvin" ) then
echo "NSQ" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "RHO" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "TH" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
echo "PV" >! fort.10
echo "MOD_${date}" >> fort.10
echo "REF_${date}" >> fort.10
echo "5 " >> fort.10
${bdir}/pvin/z2s
\rm -f fort.10
endif
 
# Step 2: Change Ertel's PV anomaly into an anomaly of quasi-geostrophic PV
if ( ${step} == "pvin2" | ${step} == "pvin" ) then
echo "MOD_${date}" >! fort.10
echo "REF_${date}" >> fort.10
echo "ANO_${date}" >> fort.10
${bdir}/pvin/pv_to_qgpv
\rm -f fort.10
endif
 
# Step 3: Inversion of quasi-geostrophic PV anomaly with Neumann boundary
if ( ${step} == "pvin3" | ${step} == "pvin" ) then
echo "ANO_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/pvin/inv_cart
\rm -f fort.10
endif
 
# Step 4: Prepare the output of the inversion for next iteration step
if ( ${step} == "pvin4" | ${step} == "pvin" ) then
\rm -f fort.10
echo "MOD_${date}" >! fort.10
echo "ANO_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} prep_iteration >> fort.10
${bdir}/pvin/prep_iteration
\rm -f fort.10
endif
 
# Step 5: Keep iterative steps if save flag is set
if ( ${step} == "pvin5" | ${step} == "pvin" ) then
if ( "${save}" == "yes" ) then
set pre=''
if ( ${count} < 10 ) then
set pre='0'
endif
\cp MOD_${date} MOD_${date}_${pre}${count}
\cp ANO_${date} ANO_${date}_${pre}${count}
endif
endif
 
# End loop for iterations
if ( ${step} == "pvin" ) then
@ count = ${count} + 1
if ( ${count} < ${nofiter} ) goto loop
endif
 
# ---------------------------------------------------------------------------
# Postprocessing
# ---------------------------------------------------------------------------
 
# Change to output directory
cd ${odir}
 
# Step 1: Copy needed files from input and run directory
if ( ${step} == "post1" | ${step} == "post" ) then
ln -sf ${rdir}/MOD_${date} .
ln -sf ${rdir}/MOD_${date}_cst .
ln -sf ${rdir}/ORG_${date} .
ln -sf ${rdir}/ORG_${date}_cst .
\cp ${idir}/P${date} .
set cfn = `getcfn P${date}`
\cp ${idir}/${cfn} .
endif
 
# Step 2: Rotate from quasi-cartesian coordinate frame to lat/lon system
if ( ${step} == "post2" | ${step} == "post" ) then
echo "MOD_${date}" >! fort.10
echo "GEO.MOD_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} rotate_lalo >> fort.10
echo "3" >> fort.10
echo "T" >> fort.10
echo "U.V" >> fort.10
echo "P" >> fort.10
${bdir}/post/rotate_lalo
\rm -f fort.10
echo "ORG_${date}" >! fort.10
echo "GEO.ORG_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} rotate_lalo >> fort.10
echo "3" >> fort.10
echo "T" >> fort.10
echo "U.V" >> fort.10
echo "P" >> fort.10
${bdir}/post/rotate_lalo
\rm -f fort.10
endif
 
# Step 3: Bring modified fields back to P file
if ( ${step} == "post3" | ${step} == "post" ) then
\rm -f fort.10
echo "P${date}" >! fort.10
echo "GEO.MOD_${date}" >> fort.10
echo "GEO.ORG_${date}" >> fort.10
${bdir}/inversion.perl ${parafile} add2p >> fort.10
${bdir}/post/add2p
\rm -f fort.10
endif
 
# Step 4: Calculate S file with PV and TH
if ( ${step} == "post4" | ${step} == "post" ) then
\rm -f S${date}
p2s P${date} TH PV
endif
 
# Step 5: Make clean
if ( ${step} == "post5" | ${step} == "post" ) then
\rm -f MOD_${date} MOD_${date}_cst
\rm -f GEO_${date} GEO_${date}_cst
endif
 
# Step 6: Get difference of original and modified P,S files
if ( ${step} == "post6" | ${step} == "post" ) then
\rm -f levs
echo "950." >! levs
echo "925." >> levs
echo "900." >> levs
echo "875." >> levs
echo "850." >> levs
echo "825." >> levs
echo "800." >> levs
echo "775." >> levs
echo "750." >> levs
echo "725." >> levs
echo "700." >> levs
echo "675." >> levs
echo "650." >> levs
echo "625." >> levs
echo "600." >> levs
echo "575." >> levs
echo "550." >> levs
echo "525." >> levs
echo "500." >> levs
echo "475." >> levs
echo "450." >> levs
echo "425." >> levs
echo "400." >> levs
echo "375." >> levs
echo "350." >> levs
echo "325." >> levs
echo "300." >> levs
echo "275." >> levs
echo "250." >> levs
echo "225." >> levs
echo "200." >> levs
echo "175," >> levs
echo "150." >> levs
echo "125." >> levs
echo "100." >> levs
echo " 75." >> levs
echo " 50." >> levs
 
\rm -f vars
echo "U P" >! vars
echo "V P" >> vars
echo "T P" >> vars
echo "Z P" >> vars
echo "TH S" >> vars
echo "PV S" >> vars
 
nput2p ${date} pr_cst levs vars
ncks -A -v PS P${date} L${date}
\mv -f L${date} L${date}.1
 
\cp levs vars ${idir}/
cd ${idir}
nput2p ${date} pr_cst levs vars
ncks -A -v PS P${date} L${date}
\rm levs
\rm vars
\mv L${date} ${odir}/L${date}.0
cd ${odir}
 
ncdiff L${date}.1 L${date}.0 L${date}
\rm -f L${date}.1
\rm -f L${date}.0
 
endif
 
 
# ---------------------------------------------------------------------------
# Diagnotic Tools
# ---------------------------------------------------------------------------
 
# Step 1: Check the consistency of the boundary conditions (diag1)
if ( ${step} == "diag1" ) then
cd ${rdir}
\rm -f fort.10
echo "ANO_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/diag/check_boundcon
\rm -f fort.10
endif
 
# Step 2: Calculate the quasi-geostrophic PV (diag2 [ORG|MOD|ANO]
if ( ${step} == "diag2" ) then
cd ${rdir}
\rm -f fort.10
echo "${file1}_${date}" >! fort.10
echo "REF_${date}" >> fort.10
${bdir}/diag/calc_qgpv
\rm -f fort.10
endif
 
# Step 3: Get difference between two files (diag3 [ORG|MOD|ANO] - [ORG|MOD|ANO])
if ( ${step} == "diag3" ) then
cd ${rdir}
\rm -f fort.10
echo "${file1}_${date}" >! fort.10
echo "${file2}_${date}" >> fort.10
echo "DIA_${date}" >> fort.10
${bdir}/diag/difference
\rm -f fort.10
endif
 
# Step 4: Calculate geopotential with hydrostatic equation (diag4)
if ( ${step} == "diag4" ) then
cd ${odir}
\rm -f fort.10
echo "P${date}" >! fort.10
echo "P${date}" >> fort.10
${bdir}/diag/hydrostatic
\rm -f fort.10
endif
 
# Step 5: Q vector analysis / geostrophic balance check
if ( ${step} == "diag5" ) then
cd ${rdir}
\rm -f fort.10
echo "${param3}" >! fort.10
echo "${file1}" >> fort.10
echo "${file2}" >> fort.10
echo 1 >> fort.10
${bdir}/diag/qvec_analysis
\rm -f fort.10
endif
 
 
# ---------------------------------------------------------------------------
# Modifying tools
# ---------------------------------------------------------------------------
 
if ( ${step} == "mod1" ) then
cd ${idir}
\rm -f fort.10
set commandstr=$2
echo "R${date}" >! fort.10
echo \"${commandstr}\" >> fort.10
${bdir}/spec/modify_anomaly
\rm -f fort.10
endif
 
 
 
 
 
 
 
 
Property changes:
Added: svn:executable
/tags/1.0/inversion.summary
0,0 → 1,0
piecewise potential vorticity inversion for ECMWF data; qg- and Ertel-PV
/tags/1.0/lib/libcdfio.f
0,0 → 1,1648
subroutine clscdf (cdfid, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine closes an open netCDF file.
c Aguments :
c cdfid int input the id of the file to be closed.
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer cdfid, error
 
c Local variable declarations.
integer ncopts
 
c Get current value of error options.
call ncgopt (ncopts)
 
c Make sure netCDF errors do not abort execution.
call ncpopt (NCVERBOS)
 
c Close requested file.
call ncclos (cdfid, error)
 
c Reset error options.
call ncpopt (ncopts)
 
end
 
 
subroutine cdfwopn(filnam,cdfid,ierr)
C------------------------------------------------------------------------
 
C Opens the NetCDF file 'filnam' and returns its identifier cdfid.
 
C filnam char input name of NetCDF file to open
C cdfid int output identifier of NetCDF file
C ierr int output error flag
C------------------------------------------------------------------------
 
include 'netcdf.inc'
 
integer cdfid,ierr
character*(*) filnam
 
integer strend
 
call ncpopt(NCVERBOS)
cdfid=ncopn(filnam(1:strend(filnam)),NCWRITE,ierr)
 
return
end
 
 
subroutine cdfopn(filnam,cdfid,ierr)
C------------------------------------------------------------------------
 
C Opens the NetCDF file 'filnam' and returns its identifier cdfid.
 
C filnam char input name of NetCDF file to open
C cdfid int output identifier of NetCDF file
C ierr int output error flag
C------------------------------------------------------------------------
 
include 'netcdf.inc'
 
integer cdfid,ierr
character*(*) filnam
 
integer strend
 
call ncpopt(NCVERBOS)
cdfid=ncopn(filnam(1:strend(filnam)),NCNOWRIT,ierr)
 
return
end
 
 
subroutine crecdf (filnam, cdfid, phymin, phymax, ndim, cfn,
& error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to create a netCDF file for use with
c the UWGAP plotting package.
c Any netCDF file written to must be closed with the call
c 'call clscdf(cdfid,error)', where cdfid and error are
c as in the argumentlist below.
c Arguments:
c filnam char input the user-supplied netCDF file name.
c cdfid int output the file-identifier
c phymin real input the minimum physical dimension of the
c entire physical domain along each axis.
c phymin is dimensioned (ndim)
c phymax real input the maximum physical dimension of the
c entire physical domain along each axis.
c phymax is dimensioned (ndim)
c ndim int input the number of dimensions in the file
c (i.e. number of elements in phymin,
c phymax)
c cfn char input constants file name
c ('0' = no constants file).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created cr3df.
c Jan. 92 CS UW Created crecdf.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
integer ndim, error
character *(*) filnam,cfn
real phymin(*), phymax(*)
 
c Local variable declarations.
character *(20) attnam
character *(1) chrid(MAXDIM)
integer cdfid, k, ibeg, iend, lenfil, ncopts
data chrid/'x','y','z','a'/
 
c Get current value of error options, and make sure netCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c create the netCDF file
cdfid = nccre (trim(filnam), NCCLOB, error)
if (error.ne.0) go to 920
 
c define global attributes
do k=1,ndim
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='min'
attnam=attnam(1:7)
call ncapt(cdfid,NCGLOBAL,attnam,NCFLOAT,1,phymin(k),error)
if (error.gt.0) goto 920
 
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='max'
attnam=attnam(1:7)
call ncapt(cdfid,NCGLOBAL,attnam,NCFLOAT,1,phymax(k),error)
if (error.gt.0) goto 920
enddo
 
c define constants file name
if (cfn.ne.'0') then
call ncaptc (cdfid, NCGLOBAL, 'constants_file_name',
c & NCCHAR, len_trim(cfn)+1, cfn // char(0) , error)
& NCCHAR, len_trim(cfn), cfn , error)
if (error.gt.0) goto 920
endif
 
c End variable definitions.
call ncendf (cdfid, error)
if (error.gt.0) goto 920
 
c normal exit
call ncpopt (ncopts)
return
 
c error exit
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'create the data file in subroutine crecdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
end
 
subroutine opncdf(filnam, cdfid,
& phymin, phymax, ndim, varnam, nvar, cfn, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to open a netCDF file for read and write
c with the UWGAP plotting package.
c Arguments:
c filnam char input the user-supplied netCDF file name.
c cdfid int output the file-identifier
c phymin real output the minimum physical dimension of the
c entire physical domain along each axis.
c phymin is dimensioned (ndim)
c phymax real output the maximum physical dimension of the
c entire physical domain along each axis.
c phymax is dimensioned (ndim)
c ndim int output the number of dimensions in the file
c (i.e. number of elements in phymin,
c phymax)
c varnam char output an array containing the variable names.
c varnam is dimensioned (nvar).
c nvar int output the number of variables in the file
c cfn char output constants file name
c ('0'=no constants file).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created cr3df.
c Jan. 92 CS UW Created opncdf.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
integer ndim, nvar, error
character *(*) filnam, varnam(*),cfn
real phymin(*), phymax(*)
 
c Local variable declarations.
character *(20) attnam,vnam
character *(1) chrid(MAXDIM)
integer cdfid, i,k
integer ncopts, ndims,ngatts,recdim
integer nvdims,vartyp,nvatts,vardim(MAXDIM)
real attval
integer lenstr
data chrid/'x','y','z','a'/
data lenstr/80/
 
c Get current value of error options and make sure netCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c open the netCDF file for write
cdfid = ncopn (trim(filnam), NCWRITE, error)
if (error.ne.0) then
c try to open the netCDF file for read
cdfid = ncopn (trim(filnam), NCNOWRIT, error)
if (error.ne.0) go to 920
endif
 
c inquire for number of variables
call ncinq(cdfid,ndims,nvar,ngatts,recdim,error)
if (error.eq.1) goto 920
 
c read the variables
do i=1,nvar
call ncvinq(cdfid,i,varnam(i),vartyp,nvdims,vardim,
& nvatts,error)
if (vartyp.ne.NCFLOAT) error=1
if (error.gt.0) goto 920
enddo
 
c get global attributes
k=0
100 continue
k=k+1
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='min'
attnam=attnam(1:7)
 
c switch off error message
call ncpopt(0)
 
c check whether dimension k is present
call ncagt(cdfid,NCGLOBAL,attnam,attval,error)
if (error.gt.0) goto 110
phymin(k)=attval
 
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='max'
attnam=attnam(1:7)
call ncagt(cdfid,NCGLOBAL,attnam,attval,error)
if (error.gt.0) goto 920
phymax(k)=attval
if (k.lt.3) goto 100
k=k+1
 
c define ndim-parameter
110 continue
ndim=k-1
error=0
 
c switch on error messages
call ncpopt(NCVERBOS)
 
c get constants file name
c call ncagt(cdfid,NCGLOBAL,'constants_file_name',cfn,error)
c ! chrigel
call ncagtc(cdfid,NCGLOBAL,'constants_file_name',cfn,lenstr,error)
if (error.gt.0) cfn='0'
 
c normal exit
call ncpopt (ncopts)
return
 
c error exit
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'read the data file in subroutine opncdf.'
call ncclos (cdfid, error)
call ncpopt (ncopts)
end
 
 
subroutine readcdf(filnam, cdfid,
& phymin, phymax, ndim, varnam, nvar, cfn, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to open a netCDF file for read
c with the UWGAP plotting package.
c Arguments:
c filnam char input the user-supplied netCDF file name.
c cdfid int output the file-identifier
c phymin real output the minimum physical dimension of the
c entire physical domain along each axis.
c phymin is dimensioned (ndim)
c phymax real output the maximum physical dimension of the
c entire physical domain along each axis.
c phymax is dimensioned (ndim)
c ndim int output the number of dimensions in the file
c (i.e. number of elements in phymin,
c phymax)
c varnam char output an array containing the variable names.
c varnam is dimensioned (nvar).
c nvar int output the number of variables in the file
c cfn char output constants file name
c ('0'=no constants file).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created cr3df.
c Jan. 92 CS UW Created opncdf.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
integer ndim, nvar, error
character *(*) filnam, varnam(*),cfn
real phymin(*), phymax(*)
 
 
c Local variable declarations.
character *(20) attnam
character *(1) chrid(MAXDIM)
integer cdfid, i,k
integer ncopts, ndims,ngatts,recdim
integer nvdims,vartyp,nvatts,vardim(MAXDIM)
real attval
integer lenstr
data chrid/'x','y','z','a'/
data lenstr/80/
 
c Get current value of error options.
call ncgopt (ncopts)
 
c make sure netCDF-errors do not abort execution
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c open the netCDF file for read
cdfid = ncopn (trim(filnam), NCNOWRIT, error)
if (error.ne.0) go to 920
 
c inquire for number of variables
call ncinq(cdfid,ndims,nvar,ngatts,recdim,error)
if (error.eq.1) goto 920
 
c read the variables
do i=1,nvar
call ncvinq(cdfid,i,varnam(i),vartyp,nvdims,vardim,
& nvatts,error)
if (vartyp.ne.NCFLOAT) error=1
c print *,varnam(i),nvdims,nvatts
if (error.gt.0) goto 920
enddo
 
c get global attributes
k=0
100 continue
k=k+1
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='min'
attnam=attnam(1:7)
 
c switch off error message
call ncpopt(0)
 
c check whether dimension k is present
call ncagt(cdfid,NCGLOBAL,attnam,attval,error)
if (error.gt.0) goto 110
phymin(k)=attval
 
attnam(1:3)='dom'
attnam(4:4)=chrid(k)
attnam(5:7)='max'
attnam=attnam(1:7)
call ncagt(cdfid,NCGLOBAL,attnam,attval,error)
if (error.gt.0) goto 920
phymax(k)=attval
if (k.lt.4) goto 100
k=k+1
 
c define ndim-parameter
110 continue
ndim=k-1
error=0
 
c switch on error messages
call ncpopt(NCVERBOS)
 
c get constants file name
c call ncagt(cdfid,NCGLOBAL,'constants_file_name',cfn,error)
c ! chrigel
call ncagtc(cdfid,NCGLOBAL,'constants_file_name',cfn,lenstr,error)
if (error.gt.0) cfn='0'
c print *,cfn
 
c normal exit
call ncpopt (ncopts)
return
 
c error exit
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'read the data file in subroutine opncdf.'
call ncclos (cdfid, error)
call ncpopt (ncopts)
end
 
 
 
subroutine getcdf (cdfid, varnam, ndim, misdat,
& vardim, varmin, varmax, stag, dat, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to get a variable and its attributes
c from a netCDF file for use with the UWGAP plotting package.
c It is assumed that the data is floating-point data. Prior to
c calling this routine, the file must be opened with a call to
c opncdf.
c Arguments:
c cdfid int input file-identifier
c (can be obtained by calling routine
c opncdf)
c varnam char input the user-supplied variable name.
c (can be obtained by calling routine
c opncdf)
c ndim int output the number of dimensions (ndim<=4)
c misdat real output missing data value for the variable.
c vardim int output the dimensions of the variable.
c is dimensioned at least (ndim).
c varmin real output the location in physical space of the
c origin of each variable.
c is dimensioned at least Min(ndim,3).
c varmax real output the extent of each variable in physical
c space.
c is dimensioned at least Min(ndim,3).
c stag real output the grid staggering for each variable.
c is dimensioned at least Min(ndim,3).
c dat real output data-array dimensioned suffiecently
c large, at least
c vardim(1)* ... vardim(ndim)
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created cr3df.
c Jan. 92 CS UW Created getcdf.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
character *(*) varnam
integer vardim(*), ndim, error, cdfid
real misdat, stag(*), varmin(*), varmax(*), dat(*)
 
c Local variable declarations.
character *(20) dimnam(100),attnam
character *(1) chrid(MAXDIM)
integer id,i,k,corner(MAXDIM)
integer ndims,nvars,ngatts,recdim,dimsiz(100)
integer vartyp,nvatts, ncopts
data chrid/'x','y','z','a'/
data corner/1,1,1,1/
 
c Get current value of error options, and make sure netCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c inquire for number of dimensions
call ncinq(cdfid,ndims,nvars,ngatts,recdim,error)
if (error.eq.1) goto 920
 
c read dimension-table
do i=1,ndims
call ncdinq(cdfid,i,dimnam(i),dimsiz(i),error)
if (error.gt.0) goto 920
enddo
 
c get id of the variable
id=ncvid(cdfid,varnam,error)
if (error.eq.1) goto 910
 
c inquire about variable
call ncvinq(cdfid,id,varnam,vartyp,ndim,vardim,nvatts,error)
if (vartyp.ne.NCFLOAT) error=1
if (error.gt.0) goto 920
 
c Make sure ndim <= MAXDIM.
if (ndim.gt.MAXDIM) then
error = 1
go to 900
endif
 
c get dimensions from dimension-table
do k=1,ndim
vardim(k)=dimsiz(vardim(k))
enddo
 
c get attributes
do k=1,min0(ndim,3)
c get staggering
attnam(1:1)=chrid(k)
attnam(2:5)='stag'
attnam=attnam(1:5)
call ncagt(cdfid,id,attnam,stag(k),error)
if (error.gt.0) goto 920
c get min postion
attnam(1:1)=chrid(k)
attnam(2:4)='min'
attnam=attnam(1:4)
call ncagt(cdfid,id,attnam,varmin(k),error)
if (error.gt.0) goto 920
c get max position
attnam(1:1)=chrid(k)
attnam(2:4)='max'
attnam=attnam(1:4)
call ncagt(cdfid,id,attnam,varmax(k),error)
if (error.gt.0) goto 920
enddo
 
c get missing data value
call ncagt(cdfid,id,'missing_data',misdat,error)
if (error.gt.0) goto 920
 
c get data
call ncvgt(cdfid,id,corner,vardim,dat,error)
if (error.gt.0) goto 920
 
c normal exit
call ncpopt (ncopts)
return
 
 
c Error exits.
900 write (6, *) 'ERROR: When calling getcdf, the number of ',
& 'variable dimensions must be less or equal 4.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
910 write (6, *) 'ERROR: The selected variable could not be found ',
& 'in the file by getcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'read the data file in subroutine getcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
end
 
 
subroutine putcdf (cdfid, varnam, ndim, misdat,
& vardim, varmin, varmax, stag, dat, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to put a variable and its attributes
c onto a netCDF file for use with the UWGAP plotting package.
c It is assumed that the data is floating-point data. Prior to
c calling this routine, the file must be created (crecdf) or
c opened (opncdf).
c Any netCDF file written to must be closed with the call
c call ncclos(cdfid,error), where cdfid and error are
c as in the argumentlist below.
c Arguments:
c cdfid int input file-identifier
c (can be obtained by calling routine
c opncdf)
c varnam char input the user-supplied variable name.
c (can be obtained by calling routine
c opncdf)
c ndim int input the number of dimensions (ndim<=4)
c misdat real input missing data value for the variable.
c vardim int input the dimensions of the variable.
c is dimensioned at least (ndim).
c varmin real input the location in physical space of the
c origin of each variable.
c is dimensioned at least Min(ndim,3).
c varmax real input the extent of each variable in physical
c space.
c is dimensioned at least Min(ndim,3).
c stag real input the grid staggering for each variable.
c is dimensioned at least Min(ndim,3).
c dat real input data-array dimensioned suffiecently
c large, at least
c vardim(1)* ... vardim(ndim)
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 error detected.
c History:
c Nov. 91 PPM UW Created cr3df, wr3df.
c Jan. 92 CS UW Created putcdf.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
character *(*) varnam
integer vardim(*), ndim, error, cdfid
real misdat, stag(*), varmin(*), varmax(*), dat(*)
 
c Local variable declarations.
character *(20) dimnam,attnam,dimchk
character *(1) chrid(MAXDIM)
character *(20) dimnams(MAXNCDIM)
integer dimvals(MAXNCDIM)
integer numdims,numvars,numgats,dimulim
integer id,did(MAXDIM),i,k,corner(MAXDIM)
integer ncopts
integer ibeg,iend
data chrid/'x','y','z','t'/
data corner/1,1,1,1/
 
c Get current value of error options.
call ncgopt (ncopts)
 
c make sure netCDF-errors do not abort execution
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c Make sure ndim <= MAXDIM.
if (ndim.gt.MAXDIM) then
error = 1
go to 900
endif
 
c Read existing dimensions-declarations from the file
call ncinq(cdfid,numdims,numvars,numgats,dimulim,error)
if (error.ne.0) numdims=0
if (numdims.gt.0) then
do i=1,numdims
call ncdinq(cdfid,i,dimnams(i),dimvals(i),error)
c print *,dimnams(i),dimvals(i)
enddo
endif
 
c put file into define mode
call ncredf(cdfid,error)
if (error.ne.0) goto 920
 
c define the dimension
do k=1,ndim
c define the dimension-name
dimnam(1:3)='dim'
dimnam(4:4)=chrid(k)
dimnam(5:5)='_'
dimnam(6:5+len_trim(varnam))=trim(varnam)
dimnam=dimnam(1:5+len_trim(varnam))
did(k)=-1
if (numdims.gt.0) then
c check if an existing dimension-declaration can be used
c instead of defining a nuw dimension
do i=1,numdims
dimchk=dimnams(i)
if ((vardim(k).eq.dimvals(i)).and.
& (dimnam(1:4).eq.dimchk(1:4))) then
did(k)=i
goto 100
endif
enddo
100 continue
endif
if (did(k).lt.0) then
c define the dimension
did(k)=ncddef(cdfid,dimnam,vardim(k),error)
if (error.ne.0) goto 920
endif
enddo
 
c define variable
id=ncvdef(cdfid,varnam,NCFLOAT,ndim,did,error)
if (error.ne.0) goto 920
 
c define attributes
do k=1,min0(ndim,3)
c staggering
attnam(1:1)=chrid(k)
attnam(2:5)='stag'
attnam=attnam(1:5)
call ncapt(cdfid,id,attnam,NCFLOAT,1,stag(k),error)
if (error.gt.0) goto 920
c min postion
attnam(1:1)=chrid(k)
attnam(2:4)='min'
attnam=attnam(1:4)
call ncapt(cdfid,id,attnam,NCFLOAT,1,varmin(k),error)
if (error.gt.0) goto 920
c max position
attnam(1:1)=chrid(k)
attnam(2:4)='max'
attnam=attnam(1:4)
call ncapt(cdfid,id,attnam,NCFLOAT,1,varmax(k),error)
if (error.gt.0) goto 920
enddo
 
c define missing data value
call ncapt(cdfid,id,'missing_data',NCFLOAT,1,misdat,error)
if (error.gt.0) goto 920
 
c leave define mode
call ncendf(cdfid,error)
if (error.gt.0) goto 920
 
c define data
call ncvpt(cdfid,id,corner,vardim,dat,error)
if (error.gt.0) goto 920
 
c synchronyse output to disk and exit
call ncsnc (cdfid,error)
call ncpopt (ncopts)
return
 
c Error exits.
900 write (6, *) 'ERROR: When calling putcdf, the number of ',
& 'variable dimensions must be less or equal 4.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'write the data file in subroutine putcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
end
c
c
subroutine getdef (cdfid, varnam, ndim, misdat,
& vardim, varmin, varmax, stag, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to get the dimensions and attributes of
c a variable from an IVE-NetCDF file for use with the IVE plotting
c package. Prior to calling this routine, the file must be opened
c with a call to opncdf.
c Arguments:
c cdfid int input file-identifier
c (can be obtained by calling routine
c opncdf)
c varnam char input the user-supplied variable name.
c (can be obtained by calling routine
c opncdf)
c ndim int output the number of dimensions (ndim<=4)
c misdat real output missing data value for the variable.
c vardim int output the dimensions of the variable.
c Is dimensioned at least (ndim).
c varmin real output the location in physical space of the
c origin of each variable.
c Is dimensioned at least Min(3,ndim).
c varmax real output the extend of each variable in physical
c space.
c Is dimensioned at least Min(3,ndim).
c stag real output the grid staggering for each variable.
c Is dimensioned at least Min(3,ndim).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 the variable is not on the file.
c error =10 other errors.
c History:
c Apr. 93 Christoph Schaer (ETHZ) Created.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
character *(*) varnam
integer vardim(*), ndim, error, cdfid
real misdat, stag(*), varmin(*), varmax(*)
 
c Local variable declarations.
character *(20) dimnam(MAXNCDIM),attnam,vnam
character *(1) chrid(MAXDIM)
integer id,i,k
integer ndims,nvars,ngatts,recdim,dimsiz(MAXNCDIM)
integer vartyp,nvatts, ncopts
data chrid/'x','y','z','t'/
 
c Get current value of error options.
call ncgopt (ncopts)
 
c make sure NetCDF-errors do not abort execution
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c inquire for number of dimensions
call ncinq(cdfid,ndims,nvars,ngatts,recdim,error)
if (error.eq.1) goto 920
 
c read dimension-table
do i=1,ndims
call ncdinq(cdfid,i,dimnam(i),dimsiz(i),error)
if (error.gt.0) goto 920
enddo
 
c get id of the variable
id=ncvid(cdfid,varnam,error)
if (error.eq.1) goto 910
 
c inquire about variable
call ncvinq(cdfid,id,vnam,vartyp,ndim,vardim,nvatts,error)
if (vartyp.ne.NCFLOAT) error=1
if (error.gt.0) goto 920
 
c Make sure ndim <= MAXDIM.
if (ndim.gt.MAXDIM) then
error = 1
go to 900
endif
 
c get dimensions from dimension-table
do k=1,ndim
vardim(k)=dimsiz(vardim(k))
enddo
 
c get attributes
do k=1,min0(3,ndim)
c get min postion
attnam(1:1)=chrid(k)
attnam(2:4)='min'
attnam=attnam(1:4)
call ncagt(cdfid,id,attnam,varmin(k),error)
if (error.gt.0) goto 920
c get max position
attnam(1:1)=chrid(k)
attnam(2:4)='max'
attnam=attnam(1:4)
call ncagt(cdfid,id,attnam,varmax(k),error)
if (error.gt.0) goto 920
c get staggering
attnam(1:1)=chrid(k)
attnam(2:5)='stag'
attnam=attnam(1:5)
call ncagt(cdfid,id,attnam,stag(k),error)
if (error.gt.0) goto 920
enddo
 
c get missing data value
call ncagt(cdfid,id,'missing_data',misdat,error)
if (error.gt.0) goto 920
 
c normal exit
call ncpopt (ncopts)
return
 
c Error exits.
900 write (6, *) '*ERROR*: When calling getcdf, the number of ',
& 'variable dimensions must be less or equal 4.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
910 write (6, *) '*ERROR*: The selected variable could not be found ',
& 'in the file by getcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
920 write (6, *) '*ERROR*: An error occurred while attempting to ',
& 'read the data file in subroutine getcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
end
 
 
 
subroutine getdat(cdfid, varnam, time, level, dat, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to read the data of a variable
c from an IVE-NetCDF file for use with the IVE plotting package.
c Prior to calling this routine, the file must be opened with
c a call to opncdf (for extension) or crecdf (for creation) or
c readcdf (for readonly).
c Arguments:
c cdfid int input file-identifier
c (must be obtained by calling routine
c opncdf,readcdf or crecdf)
c varnam char input the user-supplied variable name (must
c previously be defined with a call to
c putdef)
c time real input the user-supplied time-level of the
c data to be read from the file (the time-
c levels stored in the file can be obtained
c with a call to gettimes).
c level int input the horizontal level(s) to be read
c to the NetCDF file. Suppose that the
c variable is defined as (nx,ny,nz,nt).
c level>0: the call reads the subdomain
c (1:nx,1:ny,level,itimes)
c level=0: the call reads the subdomain
c (1:nx,1:ny,1:nz,itimes)
c Here itimes is the time-index corresponding
c to the value of 'time'.
c dat real output data-array dimensioned sufficiently
c large. The dimensions (nx,ny,nz)
c of the variable must previously be defined
c with a call to putdef. No previous
c definition of the time-dimension is
c required.
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 the variable is not present on
c the file.
c error = 2 the value of 'time' is not
c known.to the file.
c error = 3 inconsistent value of level
c error =10 another error.
c History:
c March 93 Heini Wernli (ETHZ) Created wr2cdf.
c April 93 Bettina Messmer (ETHZ) Created putdat.
c June 93 Christoph Schaer (ETHZ) Created getdat
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
C Declaration of local variables
character*(*) varnam
character*(20) chars
integer cdfid
 
real dat(*)
real misdat,varmin(4),varmax(4),stag(4)
real time, timeval
 
integer corner(4),edgeln(4),didtim,vardim(4),ndims
integer error, ierr
integer level,ntime
integer idtime,idvar,iflag
integer i
 
call ncpopt(NCVERBOS)
 
c access the variable
call getdef (cdfid, trim(varnam), ndims, misdat,
& vardim, varmin, varmax, stag, ierr)
if (ierr.ne.0) then
print *,'*ERROR* in getdef in getdat'
error=1
return
endif
idvar=ncvid(cdfid,trim(varnam),ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncvid in getdat'
error=1
return
endif
 
C Get times-array
didtim=ncdid(cdfid,'time',ierr)
if (ierr.ne.0) then
print *,'*ERROR* didtim in getdat'
error=10
return
endif
call ncdinq(cdfid,didtim,chars,ntime,ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncdinq in getdat'
error=10
return
endif
idtime=ncvid(cdfid,'time',ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncvid for time in getdat'
error=10
return
endif
c find appropriate time-index
iflag=0
do i=1,ntime
call ncvgt1(cdfid,idtime,i,timeval,ierr)
if (ierr.ne.0) print *,'*ERROR* in ncvgt1 in getdat'
if (time.eq.timeval) iflag=i
enddo
if (iflag.eq.0) then
error=2
print *,'Error: Unknown time in getdat'
return
endif
 
C Define data volume to be written (index space)
corner(1)=1
corner(2)=1
edgeln(1)=vardim(1)
edgeln(2)=vardim(2)
if (level.eq.0) then
corner(3)=1
edgeln(3)=vardim(3)
else if ((level.le.vardim(3)).and.(level.ge.1)) then
corner(3)=level
edgeln(3)=1
else
error=3
return
endif
corner(4)=iflag
edgeln(4)=1
 
C Read data from NetCDF file
c print *,'getdat vor Aufruf ncvgt'
c print *,'cdfid ',cdfid
c print *,'idvar ',idvar
c print *,'corner ',corner
c print *,'edgeln ',edgeln
 
call ncvgt(cdfid,idvar,corner,edgeln,dat,error)
if (error.ne.0) then
print *, '*ERROR* in ncvgt in getdat'
error=10
endif
end
 
 
 
subroutine putdat(cdfid, varnam, time, level, dat, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to write the data of a variable
c to an IVE-NetCDF file for use with the IVE plotting package.
c Prior to calling this routine, the file must be opened with
c a call to opncdf (for extension) or crecdf (for creation), the
c variable must be defined with a call to putdef.
c Arguments:
c cdfid int input file-identifier
c (must be obtained by calling routine
c opncdf or crecdf)
c varnam char input the user-supplied variable name (must
c previously be defined with a call to
c putdef)
c time real input the user-supplied time-level of the
c data to be written to the file (the time-
c levels stored in the file can be obtained
c with a call to gettimes). If 'time' is not
c yet known to the file, a knew time-level is
c allocated and appended to the times-array.
c level int input the horizontal level(s) to be written
c to the NetCDF file. Suppose that the
c variable is defined as (nx,ny,nz,nt).
c level>0: the call writes the subdomain
c (1:nx,1:ny,level,itimes)
c level=0: the call writes the subdomain
c (1:nx,1:ny,1:nz,itimes)
c Here itimes is the time-index corresponding
c to the value of 'time'.
c dat real output data-array dimensioned sufficiently
c large. The dimensions (nx,ny,nz)
c of the variable must previously be defined
c with a call to putdef. No previous
c definition of the time-dimension is
c required.
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 the variable is not present on
c the file.
c error = 2 the value of 'time' is new, but
c appending it would yield a non
c ascending times-array.
c error = 3 inconsistent value of level
c error =10 another error.
c History:
c March 93 Heini Wernli (ETHZ) Created wr2cdf.
c April 93 Bettina Messmer (ETHZ) Created putdat.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
C Declaration of local variables
 
character*(*) varnam
character*(20) chars
integer cdfid
 
 
real dat(*)
real misdat,varmin(4),varmax(4),stag(4)
real time, timeval
data stag/0.,0.,0.,0./
 
integer corner(4),edgeln(4),did(4),vardim(4),ndims
integer error, ierr
integer level,ntime
integer idtime,idvar,iflag
integer i
 
call ncpopt(NCVERBOS)
 
c get definitions of data
call getdef (cdfid, trim(varnam), ndims, misdat,
& vardim, varmin, varmax, stag, ierr)
if (ierr.ne.0) print *,'*ERROR* in getdef in putdat'
 
c get id of variable
idvar=ncvid(cdfid,trim(varnam),ierr)
if (ierr.ne.0) print *,'*ERROR* in ncvid in putdat'
 
c get times-array
did(4)=ncdid(cdfid,'time',ierr)
if (ierr.ne.0) print *,'*ERROR* did(4) in putdat'
call ncdinq(cdfid,did(4),chars,ntime,ierr)
if (ierr.ne.0) print *,'*ERROR* in ncdinq in putdat'
idtime=ncvid(cdfid,'time',ierr)
if (ierr.ne.0) print *,'*ERROR* in ncvid in putdat'
C Check if a new time step is starting
iflag=0
do i=1,ntime
call ncvgt1(cdfid,idtime,i,timeval,ierr)
if (ierr.ne.0) print *,'*ERROR* in ncvgt1 in putdat'
if (time.eq.timeval) iflag=i
enddo
if (iflag.eq.0) then ! new time step
ntime=ntime+1
iflag=ntime
idtime=ncvid(cdfid,'time',ierr)
if (ierr.ne.0) print *, '*ERROR* in ncvid in putdat'
call ncvpt1(cdfid,idtime,ntime,time,ierr)
if (ierr.ne.0) print *, '*ERROR* in ncvpt1 in putdat'
endif
 
C Define data volume to write on the NetCDF file in index space
corner(1)=1 ! starting corner of data volume
corner(2)=1
edgeln(1)=vardim(1) ! edge lengthes of data volume
edgeln(2)=vardim(2)
if (level.eq.0) then
corner(3)=1
edgeln(3)=vardim(3)
else
corner(3)=level
edgeln(3)=1
endif
corner(4)=iflag
edgeln(4)=1
C Put data on NetCDF file
 
c print *,'vor Aufruf ncvpt d.h. Daten schreiben in putdat '
c print *,'cdfid ',cdfid
c print *,'idvar ',idvar
c print *,'corner ',corner
c print *,'edgeln ',edgeln
 
call ncvpt(cdfid,idvar,corner,edgeln,dat,error)
if (error.ne.0) then
print *, '*ERROR* in ncvpt in putdat - Put data on NetCDF file'
endif
 
C Synchronize output to disk and close the files
 
call ncsnc(cdfid,ierr)
if (ierr.ne.0) print *, '*ERROR* in ncsnc in putdat'
end
 
 
 
 
 
 
subroutine putdef (cdfid, varnam, ndim, misdat,
& vardim, varmin, varmax, stag, error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to define the dimensions and the
c attributes of a variable on an IVE-NetCDF file for use with the
c IVE plotting package. Prior to calling this routine, the file must
c be opened with a call to opncdf (extend an existing file) or
c crecdf (create a new file).
c Arguments:
c cdfid int input file-identifier
c (can be obtained by calling routine
c opncdf)
c varnam char input the user-supplied variable name.
c ndim int input the number of dimensions (ndim<=4).
c Upon ndim=4, the fourth dimension of the
c variable is specified as 'unlimited'
c on the file (time-dimension). It can
c later be extended to arbitrary length.
c misdat real input missing data value for the variable.
c vardim int input the dimensions of the variable.
c Is dimensioned at least Min(3,ndim).
c varmin real input the location in physical space of the
c origin of each variable.
c Is dimensioned at least Min(3,ndim).
c varmax real input the extent of each variable in physical
c space.
c Is dimensioned at least Min(ndim).
c stag real input the grid staggering for each variable.
c Is dimensioned at least Min(3,ndim).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error =10 other errors detected.
c History:
c Apr. 93 Christoph Schaer (ETHZ) Created.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
integer MAXDIM
parameter (MAXDIM=4)
character *(*) varnam
integer vardim(*), ndim, error, cdfid
real misdat, stag(*), varmin(*), varmax(*)
 
c Local variable declarations.
character *(20) dimnam,attnam,dimchk
character *(1) chrid(MAXDIM)
character *(20) dimnams(MAXNCDIM)
integer dimvals(MAXNCDIM)
integer numdims,numvars,numgats,dimulim
integer id,did(MAXDIM),idtime,i,k,ierr
integer ncopts
integer ibeg,iend
data chrid/'x','y','z','t'/
 
c Get current value of error options.
call ncgopt (ncopts)
 
c make sure NetCDF-errors do not abort execution
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c Make sure ndim <= MAXDIM.
if (ndim.gt.MAXDIM) then
error = 10
go to 900
endif
 
c Read existing dimensions-declarations from the file
call ncinq(cdfid,numdims,numvars,numgats,dimulim,error)
if (numdims.gt.0) then
do i=1,numdims
call ncdinq(cdfid,i,dimnams(i),dimvals(i),error)
c print *,dimnams(i),dimvals(i)
enddo
endif
 
c put file into define mode
call ncredf(cdfid,error)
if (error.ne.0) goto 920
 
c define spatial dimensions
do k=1,min0(3,ndim)
c define the default dimension-name
dimnam(1:3)='dim'
dimnam(4:4)=chrid(k)
dimnam(5:5)='_'
dimnam(6:5+len_trim(varnam))=trim(varnam)
dimnam=dimnam(1:5+len_trim(varnam))
did(k)=-1
if (numdims.gt.0) then
c check if an existing dimension-declaration can be used
c instead of defining a new dimension
do i=1,numdims
dimchk=dimnams(i)
if ((vardim(k).eq.dimvals(i)).and.
& (dimnam(1:4).eq.dimchk(1:4))) then
did(k)=i
goto 100
endif
enddo
100 continue
endif
if (did(k).lt.0) then
c define the dimension
did(k)=ncddef(cdfid,dimnam,vardim(k),error)
if (error.ne.0) goto 920
endif
enddo
 
c define the times-array
if (ndim.eq.4) then
c define dimension and variable 'time'
if (numdims.ge.4) then
did(4)=ncdid(cdfid,'time',ierr)
idtime=ncvid(cdfid,'time',ierr)
else
c this dimension must first be defined
did(4) = ncddef (cdfid,'time',NCUNLIM,ierr)
idtime = ncvdef (cdfid,'time',NCFLOAT,1,did(4),ierr)
endif
endif
 
c define variable
id=ncvdef(cdfid,varnam,NCFLOAT,ndim,did,error)
if (error.ne.0) goto 920
 
c define attributes
do k=1,min0(ndim,3)
c min postion
attnam(1:1)=chrid(k)
attnam(2:4)='min'
attnam=attnam(1:4)
call ncapt(cdfid,id,attnam,NCFLOAT,1,varmin(k),error)
if (error.gt.0) goto 920
c max position
attnam(1:1)=chrid(k)
attnam(2:4)='max'
attnam=attnam(1:4)
call ncapt(cdfid,id,attnam,NCFLOAT,1,varmax(k),error)
if (error.gt.0) goto 920
c staggering
attnam(1:1)=chrid(k)
attnam(2:5)='stag'
attnam=attnam(1:5)
call ncapt(cdfid,id,attnam,NCFLOAT,1,stag(k),error)
if (error.gt.0) goto 920
enddo
 
c define missing data value
call ncapt(cdfid,id,'missing_data',NCFLOAT,1,misdat,error)
if (error.gt.0) goto 920
 
c leave define mode
call ncendf(cdfid,error)
if (error.gt.0) goto 920
 
c synchronyse output to disk and exit
call ncsnc (cdfid,error)
call ncpopt (ncopts)
return
 
c Error exits.
900 write (6, *) '*ERROR*: When calling putcdf, the number of ',
& 'variable dimensions must be less or equal 4.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
920 write (6, *) '*ERROR*: An error occurred while attempting to ',
& 'write the data file in subroutine putcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
end
 
 
subroutine gettimes(cdfid,times,ntimes,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get all times on the specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C times real output array contains all time values on the file,
C dimensioned at least times(ntimes)
C ntimes int output number of times on the file
C error int output errorflag
C History:
C Heini Wernli, ETHZ
C------------------------------------------------------------------------
 
include "netcdf.inc"
 
integer ierr,i
real times(*)
integer didtim,ntimes
 
integer cdfid,idtime
integer ncopts
character*(20) dimnam
 
c Get current value of error options, and make sure netCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt(NCVERBOS)
 
didtim=ncdid(cdfid,'time',ierr) ! inquire id for time dimension
if (ierr.ne.0) goto 900
idtime=ncvid(cdfid,'time',ierr) ! inquire id for time array
if (ierr.ne.0) goto 900
call ncdinq(cdfid,didtim,dimnam,ntimes,ierr) ! inquire # of times
if (ierr.ne.0) goto 900
do 10 i=1,ntimes
call ncvgt1(cdfid,idtime,i,times(i),ierr) ! get times
if (ierr.ne.0) goto 900
10 continue
c normal exit
call ncpopt (ncopts)
return
 
c error exit
900 ntimes=1
times(1)=0.
call ncpopt (ncopts)
end
 
 
subroutine puttimes(cdfid,times,ntimes,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get all times on the specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C times real input array contains all time values on the file,
C dimensioned at least times(ntimes)
C ntimes int input number of times on the file
C error int output errorflag
C History:
C Heini Wernli, ETHZ
C Christoph Schaer, ETHZ
C Note:
C This preliminary version does not define the times-array, but only
C overwrites or extends an existing times-array.
C------------------------------------------------------------------------
 
integer ierr,i
real times(*)
integer didtim,ntimes
 
integer cdfid,idtime,nfiltim
integer ncdid,ncvid
 
idtime=ncvid(cdfid,'time',ierr) ! inquire id for time array
if (ierr.ne.0) return
didtim=ncdid(cdfid,'time',ierr) ! inquire id for time dimension
if (ierr.ne.0) return
 
call ncdinq(cdfid,didtim,'time',nfiltim,ierr) ! inquire # of times
if (ierr.ne.0) return
if (nfiltim.lt.ntimes) then
print *,'Warning: puttimes is extending times-array'
else if (nfiltim.gt.ntimes) then
print *,'Warning: puttimes does not cover range of times-array'
endif
 
do 10 i=1,ntimes
call ncvpt1(cdfid,idtime,i,times(i),ierr)
if (ierr.ne.0) return
10 continue
end
 
 
 
subroutine cpp_crecdf(filnam,filnam_len,cdfid,phymin,phymax,ndim,
& cfn,cfn_len,error)
C------------------------------------------------------------------------
C Purpose:
C allows to call crecdf from c++
C Arguments:
C see crecdf
C additionally: fname_len and cfn_len, the length of the
C strings
C
C
C History:
C 981221 Mark A. Liniger ETHZ
C
C Note:
C
C
C------------------------------------------------------------------------
integer filnam_len,ndim,cfn_len,error,cdfid
character *(*) filnam,cfn
real phymin(*),phymax(*)
 
call crecdf (filnam(1:filnam_len),cdfid,phymin,phymax,ndim,
& cfn(1:cfn_len),error)
 
end
 
 
subroutine cpp_putdef(cdfid,varnam,varnam_len,ndim,misdat,
& vardim,varmin,varmax,stag,error)
C------------------------------------------------------------------------
C Purpose:
C allows to call putdef from c++
C Arguments:
C see crecdf
C additionally: varnam_len, the length of the
C strings
C
C
C History:
C 981221 Mark A. Liniger ETHZ
C
C Note:
C
C
C------------------------------------------------------------------------
integer varnam_len,ndim,error,vardim(*),cdfid
character *(*) varnam
real misdat,stag(*),varmin(*),varmax(*)
 
call putdef (cdfid, varnam(1:varnam_len), ndim, misdat,
& vardim, varmin, varmax, stag, error)
 
end
 
 
subroutine cpp_putdat(cdfid, varnam,varnam_len,
& time, level, dat, error)
C------------------------------------------------------------------------
C Purpose:
C allows to call putdef from c++
C Arguments:
C see crecdf
C additionally: varnam_len, the length of the
C strings
C
C
C History:
C 981221 Mark A. Liniger ETHZ
C
C Note:
C
C
C------------------------------------------------------------------------
integer varnam_len,cdfid,error,level
character *(*) varnam
real dat(*)
real time
 
call putdat(cdfid, varnam(1:varnam_len), time, level, dat, error)
 
 
 
end
 
FUNCTION strbeg (string)
c-----------------------------------------------------------------------
c Purpose:
c This function returns the position of the first nonblank
c character in the input string. Returns 0 if the entire
c string is blank.
c Arguments:
c string char input string to be examined.
c History:
c-----------------------------------------------------------------------
IMPLICIT NONE
c Function declaration
INTEGER strbeg
 
c Argument declarations
CHARACTER*(*) string
 
c Local variable declarations.
INTEGER i
 
c External function declarations.
INTEGER len
 
DO i = 1, len(string)
strbeg = i
IF (string(i:i) .NE. ' ' .AND. string(i:i) .NE. char(0)) THEN
RETURN
ENDIF
ENDDO
strbeg = 0
END
 
FUNCTION strend (string)
c-----------------------------------------------------------------------
c Purpose:
c This function returns the position of the last nonblank
c character in the input string. Returns 0 if the entire
c string is blank.
c Arguments:
c string char input string to be examined.
c History:
c-----------------------------------------------------------------------
IMPLICIT NONE
c Function declaration
INTEGER strend
 
c Argument declarations
CHARACTER*(*) string
 
c Local variable declarations.
INTEGER i
 
c External function declarations.
INTEGER len
 
DO i = len(string), 1, -1
strend = i
IF (string(i:i) .NE. ' ' .AND. string(i:i) .NE. char(0)) THEN
RETURN
ENDIF
ENDDO
strend = 0
END
/tags/1.0/lib/libcdfplus.f
0,0 → 1,1128
subroutine wricst(cstnam,datar,aklev,bklev,aklay,bklay,stdate)
C------------------------------------------------------------------------
 
C Creates the constants file for NetCDF files containing ECMWF
C data. The constants file is compatible with the one created
C for EM data (with subroutine writecst).
C
C Input parameters:
C
C cstnam name of constants file
C datar array contains all required parameters to write file
C datar(1): number of points along x
C datar(2): number of points along y
C datar(3): maximum latitude of data region (ymax)
C datar(4): minimum longitude of data region (xmin)
C datar(5): minimum latitude of data region (ymin)
C datar(6): maximum longitude of data region (xmax)
C datar(7): grid increment along x
C datar(8): grid increment along y
C datar(9): number of levels
C datar(10): data type (forecast or analysis)
C datar(11): data version
C datar(12): constants file version
C datar(13): longitude of pole of coordinate system
C datar(14): latitude of pole of coordinate system
C aklev array contains the aklev values
C bklev array contains the bklev values
C aklay array contains the aklay values
C bklay array contains the bklay values
C stdate array contains date (year,month,day,time,step) of first
C field on file (start-date), dimensionised as stdate(5)
C------------------------------------------------------------------------
 
 
include "netcdf.inc"
 
integer nchar,maxlev
 
parameter (nchar=20,maxlev=32)
real aklev(maxlev),bklev(maxlev)
real aklay(maxlev),bklay(maxlev)
real pollat,latmin,latmax
integer datar(14)
integer stdate(5)
character*80 cstnam
 
C declarations for constants-variables
 
integer nz
integer dattyp, datver, cstver
 
C further declarations
 
integer ierr ! error flag
integer cdfid ! NetCDF id
integer xid,yid,zid ! dimension ids
integer pollonid, pollatid, ! variable ids
> aklevid, bklevid, aklayid, bklayid,
> lonminid, lonmaxid, latminid, latmaxid,
> dellonid, dellatid,
> startyid, startmid, startdid, starthid, startsid,
> dattypid, datverid, cstverid
 
nz=datar(9) ! number of levels
 
C Set data-type and -version, version of cst-file-format
 
dattyp=datar(10)
datver=datar(11)
cstver=datar(12)
 
C Initially set error to false
 
ierr=0
 
C Create constants file
 
cdfid=nccre(trim(cstnam),NCCLOB,ierr)
 
C Define the dimensions
 
xid = ncddef (cdfid,'nx',datar(1),ierr)
yid = ncddef (cdfid,'ny',datar(2),ierr)
zid = ncddef (cdfid,'nz',datar(9),ierr)
 
C Define integer constants
 
pollonid = ncvdef(cdfid,'pollon', NCFLOAT,0,0,ierr)
pollatid = ncvdef(cdfid,'pollat', NCFLOAT,0,0,ierr)
 
aklevid = ncvdef (cdfid, 'aklev', NCFLOAT, 1, zid, ierr)
bklevid = ncvdef (cdfid, 'bklev', NCFLOAT, 1, zid, ierr)
aklayid = ncvdef (cdfid, 'aklay', NCFLOAT, 1, zid, ierr)
bklayid = ncvdef (cdfid, 'bklay', NCFLOAT, 1, zid, ierr)
 
lonminid = ncvdef (cdfid, 'lonmin', NCFLOAT, 0, 0, ierr)
lonmaxid = ncvdef (cdfid, 'lonmax', NCFLOAT, 0, 0, ierr)
latminid = ncvdef (cdfid, 'latmin', NCFLOAT, 0, 0, ierr)
latmaxid = ncvdef (cdfid, 'latmax', NCFLOAT, 0, 0, ierr)
dellonid = ncvdef (cdfid, 'dellon', NCFLOAT, 0, 0, ierr)
dellatid = ncvdef (cdfid, 'dellat', NCFLOAT, 0, 0, ierr)
startyid = ncvdef (cdfid, 'starty', NCLONG, 0, 0, ierr)
startmid = ncvdef (cdfid, 'startm', NCLONG, 0, 0, ierr)
startdid = ncvdef (cdfid, 'startd', NCLONG, 0, 0, ierr)
starthid = ncvdef (cdfid, 'starth', NCLONG, 0, 0, ierr)
startsid = ncvdef (cdfid, 'starts', NCLONG, 0, 0, ierr)
dattypid = ncvdef (cdfid, 'dattyp', NCLONG, 0, 0, ierr)
datverid = ncvdef (cdfid, 'datver', NCLONG, 0, 0, ierr)
cstverid = ncvdef (cdfid, 'cstver', NCLONG, 0, 0, ierr)
 
C Leave define mode
 
call ncendf(cdfid,ierr)
 
C Store levels
call ncvpt(cdfid, aklevid, 1, nz, aklev, ierr)
call ncvpt(cdfid, bklevid, 1, nz, bklev, ierr)
call ncvpt(cdfid, aklayid, 1, nz, aklay, ierr)
call ncvpt(cdfid, bklayid, 1, nz, bklay, ierr)
 
C Store position of pole (trivial for ECMWF data)
call ncvpt1(cdfid, pollonid, 1, real(datar(13))/1000., ierr)
if (datar(14).gt.0) then
pollat=min(real(datar(14))/1000.,90.)
else
pollat=max(real(datar(14))/1000.,-90.)
endif
call ncvpt1(cdfid, pollatid, 1, pollat, ierr)
 
C Store horizontal data borders and grid increments
call ncvpt1(cdfid, lonminid, 1, real(datar(4))/1000., ierr)
call ncvpt1(cdfid, lonmaxid, 1, real(datar(6))/1000., ierr)
latmin=max(real(datar(5))/1000.,-90.)
latmax=min(real(datar(3))/1000.,90.)
call ncvpt1(cdfid, latminid, 1, latmin, ierr)
call ncvpt1(cdfid, latmaxid, 1, latmax, ierr)
call ncvpt1(cdfid, dellonid, 1, real(datar(7))/1000., ierr)
call ncvpt1(cdfid, dellatid, 1, real(datar(8))/1000., ierr)
 
C Store date of first field on file (start-date)
call ncvpt1(cdfid, startyid, 1, stdate(1), ierr)
call ncvpt1(cdfid, startmid, 1, stdate(2), ierr)
call ncvpt1(cdfid, startdid, 1, stdate(3), ierr)
call ncvpt1(cdfid, starthid, 1, stdate(4), ierr)
call ncvpt1(cdfid, startsid, 1, stdate(5), ierr)
 
C Store datatype and version
call ncvpt1(cdfid, dattypid, 1, dattyp, ierr)
call ncvpt1(cdfid, datverid, 1, datver, ierr)
 
C Store version of the constants file format
call ncvpt1(cdfid, cstverid, 1, cstver, ierr)
 
C Store strings
 
call ncclos(cdfid,ierr)
return
 
end
subroutine writelmcst(cdfid,nx,ny,nz,pollon,pollat,lonmin,
&lonmax,latmin,latmax,dellon,dellat,dattyp,datver,cstver,
&psref,tstar,tbeta,pintf,p0top,idate)
c ------------------------------------------------------------------
 
implicit none
 
integer cdfid
 
c deklarationen der constants-variablen
real pollon,pollat
real lonmin,lonmax,latmin,latmax,dellon,dellat
integer idate(5)
integer nx,ny,nz
integer dattyp, datver, cstver
real psref, tstar, tbeta, pintf, p0top
 
include 'netcdf.inc'
 
* netcdf declaration
integer iret, k
* dimension ids
integer nxdim, nydim, nzdim
* variable ids
integer startyid, startmid, startdid, starthid
* variable shapes, corners and edge lengths
integer dims(1), corner(1), edges(1)
 
* enter define mode
call ncredf(cdfid, iret)
 
startyid = ncvdef (cdfid, 'starty', NCLONG, 0, 0, iret)
startmid = ncvdef (cdfid, 'startm', NCLONG, 0, 0, iret)
startdid = ncvdef (cdfid, 'startd', NCLONG, 0, 0, iret)
starthid = ncvdef (cdfid, 'starth', NCLONG, 0, 0, iret)
 
* store the rest as global attributes
* store nx,ny,nz
call ncapt(cdfid,NCGLOBAL,'nx',NCLONG,1,nx,iret)
call ncapt(cdfid,NCGLOBAL,'ny',NCLONG,1,ny,iret)
call ncapt(cdfid,NCGLOBAL,'nz',NCLONG,1,nz,iret)
 
* store pollon, pollat
call ncapt(cdfid,NCGLOBAL,'pollon',NCFLOAT,1,pollon,iret)
call ncapt(cdfid,NCGLOBAL,'pollat',NCFLOAT,1,pollat,iret)
 
* store lonmin, etc
call ncapt(cdfid,NCGLOBAL,'lonmin',NCFLOAT,1,lonmin,iret)
call ncapt(cdfid,NCGLOBAL,'lonmax',NCFLOAT,1,lonmax,iret)
call ncapt(cdfid,NCGLOBAL,'latmin',NCFLOAT,1,latmin,iret)
call ncapt(cdfid,NCGLOBAL,'latmax',NCFLOAT,1,latmax,iret)
call ncapt(cdfid,NCGLOBAL,'dellon',NCFLOAT,1,dellon,iret)
call ncapt(cdfid,NCGLOBAL,'dellat',NCFLOAT,1,dellat,iret)
 
* store data type and version
call ncapt(cdfid,NCGLOBAL,'dattyp',NCLONG,1,dattyp,iret)
call ncapt(cdfid,NCGLOBAL,'datver',NCLONG,1,datver,iret)
call ncapt(cdfid,NCGLOBAL,'cstver',NCLONG,1,cstver,iret)
 
* store information of lm model vertical grid
call ncapt(cdfid,NCGLOBAL,'psref',NCFLOAT,1,psref,iret)
call ncapt(cdfid,NCGLOBAL,'tstar',NCFLOAT,1,tstar,iret)
call ncapt(cdfid,NCGLOBAL,'tbeta',NCFLOAT,1,tbeta,iret)
call ncapt(cdfid,NCGLOBAL,'pintf',NCFLOAT,1,pintf,iret)
call ncapt(cdfid,NCGLOBAL,'p0top',NCFLOAT,1,p0top,iret)
 
* leave define mode
call ncendf(cdfid, iret)
 
* store starty, etc
corner(1) = 1
edges(1) = 1
call ncvpt(cdfid, startyid, corner, edges, idate(1), iret)
call ncvpt(cdfid, startmid, corner, edges, idate(2), iret)
call ncvpt(cdfid, startdid, corner, edges, idate(3), iret)
call ncvpt(cdfid, starthid, corner, edges, idate(4), iret)
 
end
subroutine globcst(cdfnam,datar,aklev,bklev,aklay,bklay,stdate)
C------------------------------------------------------------------------
C+
C NAME:
C subroutine globcst
C
C PURPOSE:
C instead of writing a constants-file (*_cst), the information
C is added to the netCDF file as global variables
C the data format is compatible with the one requested by
C the IVE ETH/MIT version, contact author about details
C
C CATEGORY:
C model,netCDF
C
C CALLING SEQUENCE:
C subroutine globcst(cdfnam,datar,aklev,bklev,aklay,bklay,stdate)
C
C INPUTS:
C cdfnam name of netCDF file
C The file needs to exist, otherwise an ERROR occurs,
C i.e. nothing is done
C datar array contains all required parameters to write file
C datar(1): number of points along x
C datar(2): number of points along y
C datar(3): maximum latitude of data region (ymax)
C datar(4): minimum longitude of data region (xmin)
C datar(5): minimum latitude of data region (ymin)
C datar(6): maximum longitude of data region (xmax)
C datar(7): grid increment along x
C datar(8): grid increment along y
C datar(9): number of levels
C datar(10): data type (forecast or analysis)
C datar(11): data version
C datar(12): constants file version
C datar(13): longitude of pole of coordinate system
C datar(14): latitude of pole of coordinate system
C aklev array contains the aklev values
C bklev array contains the bklev values
C aklay array contains the aklay values
C bklay array contains the bklay values
C stdate array contains date (year,month,day,time,step) of first
C field on file (start-date), dimensionised as stdate(5)
C list the griblist-ASCII-file
C varno the GRIB code number
C
C OUTPUTS:
C Adds cdf-information to EXISTING netCDF-file
C
C MODIFICATION HISTORY:
C
C June 93 Christoph Schaer (ETHZ) created
C Nov 93 Heini Wernli (ETHZ) wricst
C Nov 98 David N. Bresch (MIT) wricst to globcst
C-
C Sun include statement.
include "netcdf.inc"
integer nchar,maxlev
parameter (nchar=20,maxlev=32)
real aklev(maxlev),bklev(maxlev)
real aklay(maxlev),bklay(maxlev)
integer datar(14)
integer stdate(5)
character*80 cdfnam
C declarations for constants-variables
integer nz
integer dattyp, datver, cstver
C further declarations
integer ierr ! error flag
integer cdfid ! NetCDF id
integer xid,yid,zid ! dimension ids
integer pollonid, pollatid, ! variable ids
> aklevid, bklevid, aklayid, bklayid,
> lonminid, lonmaxid, latminid, latmaxid,
> dellonid, dellatid,
> startyid, startmid, startdid, starthid, startsid,
> dattypid, datverid, cstverid
nz=datar(9) ! number of levels
C Set data-type and -version, version of cst-file-format
dattyp=datar(10)
datver=datar(11)
cstver=datar(12)
C Initially set error to false
ierr=0
C open the netCDF-file:
call cdfwopn(cdfnam,cdfid,ierr)
if (ierr.ne.0) then
print*,'ERROR opening netCDF-file ',cdfnam
return
endif
C Put file into define mode
call ncredf(cdfid,ierr)
if (ierr.ne.0) then
print*,'ERROR switching to netCDF redefine mode'
return
endif
C Define the dimensions
xid = ncddef (cdfid,'nx',datar(1),ierr)
yid = ncddef (cdfid,'ny',datar(2),ierr)
zid = ncddef (cdfid,'nz',datar(9),ierr)
C Define integer constants
pollonid = ncvdef(cdfid,'pollon', NCFLOAT,0,0,ierr)
pollatid = ncvdef(cdfid,'pollat', NCFLOAT,0,0,ierr)
aklevid = ncvdef (cdfid, 'aklev', NCFLOAT, 1, zid, ierr)
bklevid = ncvdef (cdfid, 'bklev', NCFLOAT, 1, zid, ierr)
aklayid = ncvdef (cdfid, 'aklay', NCFLOAT, 1, zid, ierr)
bklayid = ncvdef (cdfid, 'bklay', NCFLOAT, 1, zid, ierr)
lonminid = ncvdef (cdfid, 'lonmin', NCFLOAT, 0, 0, ierr)
lonmaxid = ncvdef (cdfid, 'lonmax', NCFLOAT, 0, 0, ierr)
latminid = ncvdef (cdfid, 'latmin', NCFLOAT, 0, 0, ierr)
latmaxid = ncvdef (cdfid, 'latmax', NCFLOAT, 0, 0, ierr)
dellonid = ncvdef (cdfid, 'dellon', NCFLOAT, 0, 0, ierr)
dellatid = ncvdef (cdfid, 'dellat', NCFLOAT, 0, 0, ierr)
startyid = ncvdef (cdfid, 'starty', NCLONG, 0, 0, ierr)
startmid = ncvdef (cdfid, 'startm', NCLONG, 0, 0, ierr)
startdid = ncvdef (cdfid, 'startd', NCLONG, 0, 0, ierr)
starthid = ncvdef (cdfid, 'starth', NCLONG, 0, 0, ierr)
startsid = ncvdef (cdfid, 'starts', NCLONG, 0, 0, ierr)
dattypid = ncvdef (cdfid, 'dattyp', NCLONG, 0, 0, ierr)
datverid = ncvdef (cdfid, 'datver', NCLONG, 0, 0, ierr)
cstverid = ncvdef (cdfid, 'cstver', NCLONG, 0, 0, ierr)
C Leave define mode
call ncendf(cdfid,ierr)
if (ierr.ne.0) then
print*,'ERROR exiting define mode'
return
endif
C Store levels
call ncvpt(cdfid, aklevid, 1, nz, aklev, ierr)
call ncvpt(cdfid, bklevid, 1, nz, bklev, ierr)
call ncvpt(cdfid, aklayid, 1, nz, aklay, ierr)
call ncvpt(cdfid, bklayid, 1, nz, bklay, ierr)
C Store position of pole (trivial for ECMWF data)
call ncvpt1(cdfid, pollonid, 1, real(datar(13))/1000., ierr)
call ncvpt1(cdfid, pollatid, 1, real(datar(14))/1000., ierr)
C Store horizontal data borders and grid increments
call ncvpt1(cdfid, lonminid, 1, real(datar(4))/1000., ierr)
call ncvpt1(cdfid, lonmaxid, 1, real(datar(6))/1000., ierr)
call ncvpt1(cdfid, latminid, 1, real(datar(5))/1000., ierr)
call ncvpt1(cdfid, latmaxid, 1, real(datar(3))/1000., ierr)
call ncvpt1(cdfid, dellonid, 1, real(datar(7))/1000., ierr)
call ncvpt1(cdfid, dellatid, 1, real(datar(8))/1000., ierr)
C Store date of first field on file (start-date)
call ncvpt1(cdfid, startyid, 1, stdate(1), ierr)
call ncvpt1(cdfid, startmid, 1, stdate(2), ierr)
call ncvpt1(cdfid, startdid, 1, stdate(3), ierr)
call ncvpt1(cdfid, starthid, 1, stdate(4), ierr)
call ncvpt1(cdfid, startsid, 1, stdate(5), ierr)
C Store datatype and version
call ncvpt1(cdfid, dattypid, 1, dattyp, ierr)
call ncvpt1(cdfid, datverid, 1, datver, ierr)
C Store version of the constants file format
call ncvpt1(cdfid, cstverid, 1, cstver, ierr)
if (ierr.ne.0) then
print*,'ERROR adding cst-date as global variables'
return
endif
C Store strings
call ncclos(cdfid,ierr)
if (ierr.ne.0) then
print*,'ERROR closing netCDF file'
endif
return
end
 
subroutine getsdat(cdfid,varnam,time,ix,iy,iz,sx,sy,sz,dat,error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to read the data within a selected
c domain of a variable from an IVE-NetCDF file.
c Prior to calling this routine, the file must be opened with
c a call to opncdf (for extension) or crecdf (for creation) or
c readcdf (for readonly).
c Arguments:
c cdfid int input file-identifier
c (must be obtained by calling routine
c opncdf,readcdf or crecdf)
c varnam char input the user-supplied variable name
c time real input the user-supplied time-level of the
c data to be read from the file (the time-
c levels stored in the file can be obtained
c with a call to gettimes).
c ix/y/z int input indices of lower left corner of selected
c data volume.
c sx/y/z int input size of selected data volume
c dat real output data-array with dimensions (sx,sy,sz).
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 the variable is not present on
c the file.
c error = 2 the value of 'time' is not
c known.to the file.
c error = 6,7,8 data volume too large
c error =10 another error.
c History:
c June 93 Christoph Schaer (ETHZ) Created getdat
c Nov 93 Heini Wernli (ETHZ) Created getsdat
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
C Declaration of local variables
character*(*) varnam
character*(20) chars
integer cdfid
 
integer ix,iy,iz,sx,sy,sz
real dat(sx,sy,sz)
real misdat,varmin(4),varmax(4),stag(4)
real time, timeval
 
integer corner(4),edgeln(4),didtim,vardim(4),ndims
integer error, ierr
integer ntime
integer idtime,idvar,iflag
integer i
 
call ncpopt(NCVERBOS)
 
c access the variable
call getdef (cdfid, trim(varnam), ndims, misdat,
& vardim, varmin, varmax, stag, ierr)
if (ierr.ne.0) then
print *,'*ERROR* in getdef in getdat'
error=1
return
endif
idvar=ncvid(cdfid,trim(varnam),ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncvid in getsdat'
error=1
return
endif
 
C Get times-array
didtim=ncdid(cdfid,'time',ierr)
if (ierr.ne.0) then
print *,'*ERROR* didtim in getsdat'
error=10
return
endif
call ncdinq(cdfid,didtim,chars,ntime,ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncdinq in getsdat'
error=10
return
endif
idtime=ncvid(cdfid,'time',ierr)
if (ierr.ne.0) then
print *,'*ERROR* in ncvid for time in getsdat'
error=10
return
endif
c find appropriate time-index
iflag=0
do i=1,ntime
call ncvgt1(cdfid,idtime,i,timeval,ierr)
if (ierr.ne.0) print *,'*ERROR* in ncvgt1 in getsdat'
if (time.eq.timeval) iflag=i
enddo
if (iflag.eq.0) then
error=2
print *,'Error: Unknown time in getsdat'
print *,time,timeval
return
endif
 
C Define data volume to be written (index space)
corner(1)=ix
corner(2)=iy
corner(3)=iz
corner(4)=iflag
edgeln(1)=sx
edgeln(2)=sy
edgeln(3)=sz
edgeln(4)=1
 
C Check if data volume is within data domain
 
if (ix+sx-1.gt.vardim(1)) then
error=7
print *,'Error: data volume too large in x-direction'
print *,ix,sx,vardim(1)
return
endif
if (iy+sy-1.gt.vardim(2)) then
error=8
print *,'Error: data volume too large in y-direction'
return
endif
if (iz+sz-1.gt.vardim(3)) then
error=9
print *,'Error: data volume too large in z-direction'
return
endif
 
C Read data from NetCDF file
 
call ncvgt(cdfid,idvar,corner,edgeln,dat,error)
if (error.ne.0) then
print *, 'corner ',corner(1),corner(2),corner(3)
print *, 'edgeln ',edgeln(1),edgeln(2),edgeln(3)
print *, '*ERROR* in ncvgt in getsdat'
error=10
endif
end
subroutine getlevs(cstid,nlev,aklev,bklev,aklay,bklay,error)
c-----------------------------------------------------------------------
c Purpose:
c This routine is called to get the level arrays aklev and
c bklev from a NetCDF constants file.
c Arguments:
c cstid int input identifier for NetCDF constants file
c nlev int input number of levels
c aklev real output array contains all aklev values
c bklev real output array contains all bklev values
c aklay real output array contains all aklay values
c bklay real output array contains all bklay values
c error int output error flag
c error = 0 no errors detected
c error = 1 error detected
c History:
c Aug. 93 Heini Wernli Created.
c-----------------------------------------------------------------------
 
integer error
 
integer cstid
integer ncdid,ncvid ! NetCDF functions
integer didz,idak,idbk,idaky,idbky
integer nlev
real aklev(nlev),bklev(nlev),aklay(nlev),bklay(nlev)
character*(20) dimnam
integer i
 
didz =ncdid(cstid,'nz',error)
if (error.ne.0) goto 920
idak =ncvid(cstid,'aklev',error)
if (error.ne.0) goto 920
idbk =ncvid(cstid,'bklev',error)
if (error.ne.0) goto 920
idaky =ncvid(cstid,'aklay',error)
if (error.ne.0) goto 920
idbky =ncvid(cstid,'bklay',error)
if (error.ne.0) goto 920
 
call ncdinq(cstid,didz,dimnam,nlev,error) ! read number of levels
if (error.ne.0) goto 920
 
do 10 i=1,nlev
call ncvgt1(cstid,idak,i,aklev(i),error) ! get aklev
call ncvgt1(cstid,idbk,i,bklev(i),error) ! get bklev
call ncvgt1(cstid,idaky,i,aklay(i),error) ! get aklay
call ncvgt1(cstid,idbky,i,bklay(i),error) ! get bklay
if (error.ne.0) goto 920
10 continue
 
return
 
c Error exits.
920 write(*,*)'*ERROR*: An error occured in subroutine getlevs'
return
 
end
subroutine getntim(cdfid,ntimes,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get number of times on the specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C ntimes int output number of times on the file
C error int output errorflag
C History:
C Heini Wernli, ETHZ
C------------------------------------------------------------------------
include "netcdf.inc"
integer ierr
integer didtim,ntimes
integer cdfid,idtime
integer ncopts
character*(20) dimnam
c Get current value of error options, and make sure netCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt(NCVERBOS)
didtim=ncdid(cdfid,'time',ierr) ! inquire id for time dimension
if (ierr.ne.0) goto 900
idtime=ncvid(cdfid,'time',ierr) ! inquire id for time array
if (ierr.ne.0) goto 900
call ncdinq(cdfid,didtim,dimnam,ntimes,ierr) ! inquire # of times
if (ierr.ne.0) goto 900
c normal exit
call ncpopt (ncopts)
return
c error exit
900 ntimes=1
call ncpopt (ncopts)
end
subroutine getstart(cdfid,idate,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get start date for fields on specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C idate int output array contains date (year,month,day,time,step)
C dimensioned as idate(5)
C ierr int output error flag
C------------------------------------------------------------------------
 
include "netcdf.inc"
 
c variable declarations
integer ierr
integer idate(5)
integer cdfid,ncopts,idvar,nvars
integer ndims,ngatts,recdim,i,vartyp,nvatts,vardim(4)
character*20 vnam(100)
 
c Get current value of error options, and make sure NetCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt (NCVERBOS)
 
idvar=ncvid(cdfid,'starty',ierr)
if (ierr.ne.0) goto 930
call ncvgt1(cdfid,idvar,1,idate(1),ierr)
if (ierr.ne.0) goto 920
 
idvar=ncvid(cdfid,'startm',ierr)
if (ierr.ne.0) goto 920
call ncvgt1(cdfid,idvar,1,idate(2),ierr)
if (ierr.ne.0) goto 920
 
idvar=ncvid(cdfid,'startd',ierr)
if (ierr.ne.0) goto920
call ncvgt1(cdfid,idvar,1,idate(3),ierr)
if (ierr.ne.0) goto 920
 
idvar=ncvid(cdfid,'starth',ierr)
if (ierr.ne.0) goto 920
call ncvgt1(cdfid,idvar,1,idate(4),ierr)
if (ierr.ne.0) goto 920
 
C Starts is not defined on all files
C Only ask for it if it exists
C Inquire number of dimensions, variables and attributes
idate(5)=0
call ncinq(cdfid,ndims,nvars,ngatts,recdim,ierr)
do i=1,nvars
call ncvinq(cdfid,i,vnam(i),vartyp,ndims,vardim,nvatts,ierr)
if (vnam(i).eq.'starts') then
idvar=ncvid(cdfid,'starts',ierr)
call ncvgt1(cdfid,idvar,1,idate(5),ierr)
if (ierr.ne.0) goto 920
endif
enddo
 
c normal exit
call ncpopt (ncopts)
return
 
c error exit
920 continue
write (6, *) 'ERROR: An error occurred while attempting to ',
& 'read the starting-time in subroutine putstart.'
930 continue
call ncpopt (ncopts)
 
end
subroutine putstart(cdfid,idate,ierr)
C----------------------------------------------------------------------
C Purpose:
C Puts the 'starting-time' on the specified NetCDF file.
C Arguments:
C cdfid int input identifier for NetCDF file
C idate int input array contains date (year,month,day,time,step)
C dimensioned as idate(5)
C ierr int output error flag
C------------------------------------------------------------------------
 
include "netcdf.inc"
 
c variable declarations
integer ierr,idate(5),startid(5),cdfid,ncopts,i
 
c Get current value of error options, and make sure NetCDF-errors do
c not abort execution
call ncgopt (ncopts)
call ncpopt (NCVERBOS)
 
c define variables
call ncredf(cdfid,ierr)
if (ierr.ne.0) goto 920
startid(1) = ncvdef (cdfid, 'starty', NCLONG, 0, 0, ierr)
if (ierr.ne.0) goto 920
startid(2) = ncvdef (cdfid, 'startm', NCLONG, 0, 0, ierr)
if (ierr.ne.0) goto 920
startid(3) = ncvdef (cdfid, 'startd', NCLONG, 0, 0, ierr)
if (ierr.ne.0) goto 920
startid(4) = ncvdef (cdfid, 'starth', NCLONG, 0, 0, ierr)
if (ierr.ne.0) goto 920
startid(5) = ncvdef (cdfid, 'starts', NCLONG, 0, 0, ierr)
if (ierr.ne.0) goto 920
call ncendf(cdfid, ierr)
if (ierr.ne.0) goto 920
 
c store variables
do i=1,5
call ncvpt1(cdfid,startid(i),1,idate(i),ierr)
if (ierr.ne.0) goto 920
enddo
 
c synchronyse output to disk, revert to previous error-mode, and exit
call ncsnc (cdfid,ierr)
call ncpopt (ncopts)
return
 
c error exit
920 write (6, *) 'ERROR: An error occurred while attempting to ',
& 'write the starting-time in subroutine putstart.'
call ncpopt (ncopts)
call ncclos (cdfid, ierr)
 
end
subroutine getgrid(cdfid,dx,dy,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get grid increments for fields on specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C dx real output grid increment along latitude
C dy real output grid increment along longitude
C ierr int output error flag
C------------------------------------------------------------------------
 
integer ierr
 
integer cdfid
integer ncvid
 
integer idilon,idilat
real dx,dy
 
idilon =ncvid(cdfid,'dellon',ierr)
if (ierr.ne.0) return
idilat =ncvid(cdfid,'dellat',ierr)
if (ierr.ne.0) return
 
call ncvgt1(cdfid,idilon,1,dx,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idilat,1,dy,ierr)
if (ierr.ne.0) return
 
end
subroutine getdattyp(cdfid,typ,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get data type for specified NetCDF file
C Arguments:
C cdfid int input identifier for NetCDF file
C typ int output data type: 1 (52) for pressure (theta) coord
C ierr int output error flag
C------------------------------------------------------------------------
integer ierr
integer cdfid
integer ncvid
integer idtyp,typ
idtyp =ncvid(cdfid,'dattyp',ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idtyp,1,typ,ierr)
if (ierr.ne.0) return
end
subroutine getpole(cdfid,pollon,pollat,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get physical coordinates of pole of coordinate system
C Arguments:
C cdfid int input identifier for NetCDF file
C pollon real output longitude of pole
C pollat real output latitude of pole
C ierr int output error flag
C------------------------------------------------------------------------
 
integer ierr
 
integer cdfid
integer ncvid
 
integer idplon,idplat
real pollon,pollat
 
idplon =ncvid(cdfid,'pollon',ierr)
if (ierr.ne.0) return
idplat =ncvid(cdfid,'pollat',ierr)
if (ierr.ne.0) return
 
call ncvgt1(cdfid,idplon,1,pollon,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idplat,1,pollat,ierr)
if (ierr.ne.0) return
 
end
subroutine getmc2grid(cdfid,polx,poly,delx,shem,phi0,lam0,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get physical coordinates of pole of coordinate system
C Arguments:
C cdfid int input identifier for NetCDF file
C ierr int output error flag
C------------------------------------------------------------------------
integer ierr
integer cdfid
integer ncvid
integer idpolx,idpoly,iddelx,idshem,idphi0,idlam0
real polx,poly,delx,shem,phi0,lam0
idpolx =ncvid(cdfid,'polx',ierr)
if (ierr.ne.0) return
idpoly =ncvid(cdfid,'poly',ierr)
if (ierr.ne.0) return
iddelx =ncvid(cdfid,'delx',ierr)
if (ierr.ne.0) return
idshem =ncvid(cdfid,'shem',ierr)
if (ierr.ne.0) return
idphi0 =ncvid(cdfid,'phi0',ierr)
if (ierr.ne.0) return
idlam0 =ncvid(cdfid,'lam0',ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idpolx,1,polx,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idpoly,1,poly,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,iddelx,1,delx,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idshem,1,shem,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idphi0,1,phi0,ierr)
if (ierr.ne.0) return
call ncvgt1(cdfid,idlam0,1,lam0,ierr)
if (ierr.ne.0) return
end
 
 
subroutine getcfn(cdfid,cfn,ierr)
C------------------------------------------------------------------------
C Purpose:
C Get name of constants file
C Arguments:
C cdfid int input identifier for NetCDF file
C cfn char output name of constants file
C ierr int output error flag
C------------------------------------------------------------------------
 
include 'netcdf.inc'
 
integer ierr
integer cdfid,lenstr
character*80 cfn
 
lenstr=80
call ncagtc(cdfid,NCGLOBAL,"constants_file_name",cfn,lenstr,ierr)
if (ierr.ne.0) write(*,*)'error in SR getcfn'
 
end
 
 
subroutine getdim (cdfid, varnam, nx, ny, nz, error)
c-------------------------------------------------------------------------
c Purpose:
c This routine is called to get the dimensions of
c a variable from an IVE-NetCDF file for use with the IVE plotting
c package. Prior to calling this routine, the file must be opened
c with a call to opncdf.
c Arguments:
c cdfid int input file-identifier
c (can be obtained by calling routine
c opncdf)
c varnam char input the user-supplied variable name.
c (can be obtained by calling routine
c opncdf)
c nx int output the zonal dimension of the variable.
c ny int output the meridional dimension of the variable.
c nz int output the vertical dimension of the variable.
c
c error int output indicates possible errors found in this
c routine.
c error = 0 no errors detected.
c error = 1 the variable is not on the file.
c error =10 other errors.
c History:
c March 2000 Heini Wernli (ETHZ) Created.
c-----------------------------------------------------------------------
 
include "netcdf.inc"
 
c Argument declarations.
character *(*) varnam
integer vardim(4), ndim, error, cdfid
integer nx,ny,nz
 
c Local variable declarations.
character *(20) dimnam(MAXNCDIM),vnam
integer id,i,k
integer ndims,nvars,ngatts,recdim,dimsiz(MAXNCDIM)
integer vartyp,nvatts, ncopts
 
c Get current value of error options.
call ncgopt (ncopts)
 
c make sure NetCDF-errors do not abort execution
call ncpopt(NCVERBOS)
 
c Initially set error to indicate no errors.
error = 0
 
c inquire for number of dimensions
call ncinq(cdfid,ndims,nvars,ngatts,recdim,error)
if (error.eq.1) goto 920
 
c read dimension-table
do i=1,ndims
call ncdinq(cdfid,i,dimnam(i),dimsiz(i),error)
if (error.gt.0) goto 920
enddo
 
c get id of the variable
id=ncvid(cdfid,varnam,error)
if (error.eq.1) goto 910
 
c inquire about variable
call ncvinq(cdfid,id,vnam,vartyp,ndim,vardim,nvatts,error)
if (vartyp.ne.NCFLOAT) error=1
if (error.gt.0) goto 920
 
c get dimensions from dimension-table
do k=1,ndim
vardim(k)=dimsiz(vardim(k))
enddo
 
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
 
c normal exit
call ncpopt (ncopts)
return
 
c Error exits.
910 write (6, *) '*ERROR*: The selected variable could not be found ',
& 'in the file by getdim.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
return
 
920 write (6, *) '*ERROR*: An error occurred while attempting to ',
& 'read the data file in subroutine getcdf.'
call ncpopt (ncopts)
call ncclos (cdfid, error)
end
 
 
subroutine new_gettra(cdfid,varnam,ix,ntimes,array,ierr)
C------------------------------------------------------------------------
C
C Reads the time-evolution for one grid-point of the variable
C indicated by varnam.
C
C cdfid int input identifier for NetCDF file
C varnam char input name of variable
C ix int input index for trajectory to read
C ntimes int input number of time-indices to read
C array real output array contains the readed values
C ierr int output error flag
C------------------------------------------------------------------------
C Declaration of attributes
integer cdfid
character*(*) varnam
integer ix
integer ntimes
real array(ntimes)
C Declaration of local variables
integer corner(4),edgeln(4)
integer idvar,ierr
integer ncvid
integer strend
corner(1)=ix
corner(2)=1
corner(3)=1
corner(4)=1
edgeln(1)=1
edgeln(2)=1
edgeln(3)=1
edgeln(4)=ntimes
idvar =ncvid(cdfid,varnam(1:strend(varnam)),ierr)
call ncvgt(cdfid,idvar,corner,edgeln,array,ierr)
if (ierr.ne.0) goto 991
return
991 stop 'Variable not found on NetCDF file in SR new_gettra'
end
subroutine getvars(cdfid,nvars,vnam,ierr)
C------------------------------------------------------------------------
C Opens the NetCDF file 'filnam' and returns its identifier cdfid.
C filnam char input name of NetCDF file to open
C nvars int output number of variables on file
C vnam char output array with variable names
C ierr int output error flag
C------------------------------------------------------------------------
 
include 'netcdf.inc'
integer cdfid,ierr,nvars
character*(*) vnam(*)
 
integer ndims,ngatts,recdim,i,vartyp,nvatts,vardim(4)
call ncpopt(NCVERBOS)
 
C Inquire number of dimensions, variables and attributes
call ncinq(cdfid,ndims,nvars,ngatts,recdim,ierr)
C Inquire variable names from NetCDF file
do i=1,nvars
call ncvinq(cdfid,i,vnam(i),vartyp,ndims,vardim,nvatts,ierr)
enddo
return
end
/tags/1.0/lib/libgm2em.f
0,0 → 1,229
REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** PHTOPHS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: ROTIERTE BREITE PHIS ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG = ZCOSPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL) + ZSINPOL*SIN(ZPHI)
PHTOPHS = ZRPI18*ASIN(ZARG)
RETURN
END
REAL FUNCTION PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** PHSTOPH - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C**** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE BREITE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
SINPOL = SIN(ZPIR18*POLPHI)
COSPOL = COS(ZPIR18*POLPHI)
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ARG = COSPOL*COS(ZPHIS)*COS(ZLAMS) + SINPOL*SIN(ZPHIS)
PHSTOPH = ZRPI18*ASIN(ARG)
RETURN
END
REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** LMTOLMS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG1 = - SIN(ZLAM-ZLAMPOL)*COS(ZPHI)
ZARG2 = - ZSINPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL)+ZCOSPOL*SIN(ZPHI)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMTOLMS = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMTOLMS = 90.0
ELSE
LMTOLMS = -90.0
ENDIF
ELSE
LMTOLMS = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
REAL FUNCTION LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** LMSTOLM - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C** IM ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ZARG1 = SIN(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) -
2 COS(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
ZARG2 = COS(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) +
2 SIN(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMSTOLM = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMSTOLAM = 90.0
ELSE
LMSTOLAM = -90.0
ENDIF
ELSE
LMSTOLM = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
/tags/1.0/lib/libipo.f
0,0 → 1,1368
real function int2d(ar,n1,n2,rid,rjd)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 2d-array to an arbitrary
c location within the grid.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2)
c n1,n2 int input dimensions of ar
c ri,rj real input grid location to be interpolated to
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2
real ar(n1,n2), rid,rjd
 
c local declarations
integer i,j,ip1,jp1,ih,jh
real frac0i,frac0j,frac1i,frac1j,ri,rj
 
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
ih=nint(ri)
jh=nint(rj)
 
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
 
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
 
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int2d=ar(i,j)
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int2d = ar(i ,j ) * frac1i * frac1j
& + ar(i ,jp1) * frac1i * frac0j
& + ar(ip1,j ) * frac0i * frac1j
& + ar(ip1,jp1) * frac0i * frac0j
endif
end
real function int2dm(ar,n1,n2,rid,rjd,misdat)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 2d-array to an arbitrary
c location within the grid. The interpolation includes the
c testing of the missing data flag 'misdat'.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2)
c n1,n2 int input dimensions of ar
c ri,rj real input grid location to be interpolated to
c misdat real input missing data flag (on if misdat<>0)
c Warning:
c This routine has not yet been seriously tested
c History:
c-----------------------------------------------------------------------
c argument declarations
integer n1,n2
real ar(n1,n2), rid,rjd, misdat
c local declarations
integer i,j,ip1,jp1,ih,jh
real frac0i,frac0j,frac1i,frac1j,ri,rj,int2d
c check if routine without missing data checking can be called instead
if (misdat.eq.0.) then
int2dm=int2d(ar,n1,n2,rid,rjd)
return
endif
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
ih=nint(ri)
jh=nint(rj)
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int2dm=ar(i,j)
else
if ((misdat.eq.ar(i ,j )).or.
& (misdat.eq.ar(i ,jp1)).or.
& (misdat.eq.ar(ip1,j )).or.
& (misdat.eq.ar(ip1,jp1))) then
int2dm=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int2dm = ar(i ,j ) * frac1i * frac1j
& + ar(i ,jp1) * frac1i * frac0j
& + ar(ip1,j ) * frac0i * frac1j
& + ar(ip1,jp1) * frac0i * frac0j
endif
endif
end
real function int2dp(ar,n1,n2,rid,rjd)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 2d-array to an arbitrary
c location within the grid. The 2d-array is periodic in the
c i-direction: ar(0,.)=ar(n1,.) and ar(1,.)=ar(n1+1,.).
c Therefore rid can take values in the range 0,...,n1+1
c Arguments:
c ar real input surface pressure, define as ar(n1,n2)
c n1,n2 int input dimensions of ar
c ri,rj real input grid location to be interpolated to
c History:
c-----------------------------------------------------------------------
c argument declarations
integer n1,n2
real ar(0:n1+1,n2), rid,rjd
c local declarations
integer i,j,ip1,jp1,ih,jh
real frac0i,frac0j,frac1i,frac1j,ri,rj
c do linear interpolation
ri=amax1(0.,amin1(float(n1+1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
ih=nint(ri)
jh=nint(rj)
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-5) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-5) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int2dp=ar(i,j)
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int2dp = ar(i ,j ) * frac1i * frac1j
& + ar(i ,jp1) * frac1i * frac0j
& + ar(ip1,j ) * frac0i * frac1j
& + ar(ip1,jp1) * frac0i * frac0j
endif
end
real function cint2d(ar,n1,n2,n3,rid,rjd,ikd)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location in the horizontal. ikd specifies the level (must
c be an integer). A bicubic method is applied (following
c the Numerical Recipes).
c Arguments:
c ar real input field, define as ar(n1,n2,n3)
c n1,n2 int input dimensions of ar
c rid,rjd real input grid location to be interpolated to
c ikd int input level for interpolation
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3,ikd
real ar(n1,n2,n3), rid,rjd
 
c local declarations
integer i,j,k
real y(4),y1(4),y2(4),y12(4)
 
c indices of lower left corner of interpolation grid
 
i=int(rid)
j=int(rjd)
k=ikd
 
c do not interpolate if i or j are at the boundaries
 
if ((i.eq.1).or.(j.eq.1).or.(i.eq.n1).or.(j.eq.n2)) then
cint2d=ar(i,j,k)
return
endif
 
c define the arrays y,y1,y2,y12 necessary for the bicubic
c interpolation (following the Numerical Recipes).
 
y(1)=ar(i,j,k)
y(2)=ar(i+1,j,k)
y(3)=ar(i+1,j+1,k)
y(4)=ar(i,j+1,k)
 
y1(1)=-(ar(i-1,j,k)-ar(i+1,j,k))/2.
y1(2)=-(ar(i,j,k)-ar(i+2,j,k))/2.
y1(3)=-(ar(i,j+1,k)-ar(i+2,j+1,k))/2.
y1(4)=-(ar(i-1,j+1,k)-ar(i+1,j+1,k))/2.
 
y2(1)=-(ar(i,j-1,k)-ar(i,j+1,k))/2.
y2(2)=-(ar(i+1,j-1,k)-ar(i+1,j+1,k))/2.
y2(3)=-(ar(i+1,j,k)-ar(i+1,j+2,k))/2.
y2(4)=-(ar(i,j,k)-ar(i,j+2,k))/2.
 
y12(1)=(ar(i+1,j+1,k)-ar(i+1,j-1,k)-ar(i-1,j+1,k)+ar(i-1,j-1,k))/4.
y12(2)=(ar(i+2,j+1,k)-ar(i+2,j-1,k)-ar(i,j+1,k)+ar(i,j-1,k))/4.
y12(3)=(ar(i+2,j+2,k)-ar(i+2,j,k)-ar(i,j+2,k)+ar(i,j,k))/4.
y12(4)=(ar(i+1,j+2,k)-ar(i+1,j,k)-ar(i-1,j+2,k)+ar(i-1,j,k))/4.
 
call bcuint(y,y1,y2,y12,i,j,rid,rjd,cint2d)
return
end
real function int3d(ar,n1,n2,n3,rid,rjd,rkd)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location within the grid.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,n2,n3 int input dimensions of ar
c ri,rj,rk real input grid location to be interpolated to
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3
real ar(n1,n2,n3), rid,rjd,rkd
 
c local declarations
integer i,j,k,ip1,jp1,kp1,ih,jh,kh
real frac0i,frac0j,frac0k,frac1i,frac1j,frac1k,ri,rj,rk
 
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
rk=amax1(1.,amin1(float(n3),rkd))
ih=nint(ri)
jh=nint(rj)
kh=nint(rk)
 
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
 
c Check for interpolation in j
if (abs(float(jh)-rj).lt.1.e-3) then
j =jh
jp1=jh
else
j =min0(int(rj),n2-1)
jp1=j+1
endif
 
c Check for interpolation in k
* if (abs(float(kh)-rk).lt.1.e-3) then
* k =kh
* kp1=kh
* else
k =min0(int(rk),n3-1)
kp1=k+1
* endif
 
if (k.eq.kp1) then
c no interpolation in k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int3d=ar(i,j,k)
c print *,'int3d 00: ',rid,rjd,rkd,int3d
else
c horizontal interpolation only
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3d = ar(i ,j ,k ) * frac1i * frac1j
& + ar(i ,jp1,k ) * frac1i * frac0j
& + ar(ip1,j ,k ) * frac0i * frac1j
& + ar(ip1,jp1,k ) * frac0i * frac0j
c print *,'int3d 10: ',rid,rjd,rkd,int3d
endif
else
frac0k=rk-float(k)
frac1k=1.-frac0k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c vertical interpolation only
int3d = ar(i ,j ,k ) * frac1k
& + ar(i ,j ,kp1) * frac0k
c print *,'int3d 01: ',rid,rjd,rkd,int3d
else
c full 3d interpolation
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3d = ar(i ,j ,k ) * frac1i * frac1j * frac1k
& + ar(i ,jp1,k ) * frac1i * frac0j * frac1k
& + ar(ip1,j ,k ) * frac0i * frac1j * frac1k
& + ar(ip1,jp1,k ) * frac0i * frac0j * frac1k
& + ar(i ,j ,kp1) * frac1i * frac1j * frac0k
& + ar(i ,jp1,kp1) * frac1i * frac0j * frac0k
& + ar(ip1,j ,kp1) * frac0i * frac1j * frac0k
& + ar(ip1,jp1,kp1) * frac0i * frac0j * frac0k
c print *,'int3d 11: ',rid,rjd,rkd,int3d
endif
endif
end
real function int3dm(ar,n1,n2,n3,rid,rjd,rkd,misdat)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location within the grid. The interpolation includes the
c testing of the missing data flag 'misdat'.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,n2,n3 int input dimensions of ar
c ri,rj,rk real input grid location to be interpolated to
c misdat real input missing data flag (on if misdat<>0)
c Warning:
c This routine has not yet been seriously tested
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3
real ar(n1,n2,n3), rid,rjd,rkd, misdat
 
c local declarations
integer i,j,k,ip1,jp1,kp1,ih,jh,kh
real frac0i,frac0j,frac0k,frac1i,frac1j,frac1k,ri,rj,rk,int3d
 
c check if routine without missing data checking can be called instead
if (misdat.eq.0.) then
int3dm=int3d(ar,n1,n2,n3,rid,rjd,rkd)
return
endif
 
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
rk=amax1(1.,amin1(float(n3),rkd))
ih=nint(ri)
jh=nint(rj)
kh=nint(rk)
 
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
 
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
 
c Check for interpolation in k
* if (abs(float(kh)-rk).lt.1.e-3) then
* k =kh
* kp1=kh
* else
k =min0(int(rk),n3-1)
kp1=k+1
* endif
 
if (k.eq.kp1) then
c no interpolation in k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
if (misdat.eq.ar(i,j,k)) then
int3dm=misdat
else
int3dm=ar(i,j,k)
endif
c print *,'int3dm 00: ',rid,rjd,rkd,int3dm
else
c horizontal interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k ))) then
int3dm=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dm = ar(i ,j ,k ) * frac1i * frac1j
& + ar(i ,jp1,k ) * frac1i * frac0j
& + ar(ip1,j ,k ) * frac0i * frac1j
& + ar(ip1,jp1,k ) * frac0i * frac0j
c print *,'int3dm 10: ',rid,rjd,rkd,int3dm
endif
endif
else
frac0k=rk-float(k)
frac1k=1.-frac0k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c vertical interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,j ,kp1))) then
int3dm=misdat
else
int3dm = ar(i ,j ,k ) * frac1k
& + ar(i ,j ,kp1) * frac0k
c print *,'int3dm 01: ',rid,rjd,rkd,int3dm
endif
else
c full 3d interpolation
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k )).or.
& (misdat.eq.ar(i ,j ,kp1)).or.
& (misdat.eq.ar(i ,jp1,kp1)).or.
& (misdat.eq.ar(ip1,j ,kp1)).or.
& (misdat.eq.ar(ip1,jp1,kp1))) then
int3dm=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dm = ar(i ,j ,k ) * frac1i * frac1j * frac1k
& + ar(i ,jp1,k ) * frac1i * frac0j * frac1k
& + ar(ip1,j ,k ) * frac0i * frac1j * frac1k
& + ar(ip1,jp1,k ) * frac0i * frac0j * frac1k
& + ar(i ,j ,kp1) * frac1i * frac1j * frac0k
& + ar(i ,jp1,kp1) * frac1i * frac0j * frac0k
& + ar(ip1,j ,kp1) * frac0i * frac1j * frac0k
& + ar(ip1,jp1,kp1) * frac0i * frac0j * frac0k
c print *,'int3dm 11: ',rid,rjd,rkd,int3dm
endif
endif
endif
end
real function int3dmlog(ar,n1,n2,n3,rid,rjd,rkd,misdat)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location within the grid. The interpolation includes the
c testing of the missing data flag 'misdat'.
c Prior to vertical interpolations the log is taken from the array.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,n2,n3 int input dimensions of ar
c ri,rj,rk real input grid location to be interpolated to
c misdat real input missing data flag (on if misdat<>0)
c Warning:
c This routine has not yet been seriously tested
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3
real ar(n1,n2,n3), rid,rjd,rkd, misdat
 
c local declarations
integer i,j,k,ip1,jp1,kp1,ih,jh,kh
real frac0i,frac0j,frac0k,frac1i,frac1j,frac1k,ri,rj,rk,int3d
 
c print*,'hallo in SR int3dmlog'
c check if routine without missing data checking can be called instead
if (misdat.eq.0.) then
int3dmlog=int3d(ar,n1,n2,n3,rid,rjd,rkd)
return
endif
 
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
rk=amax1(1.,amin1(float(n3),rkd))
ih=nint(ri)
jh=nint(rj)
kh=nint(rk)
 
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
 
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
 
c Check for interpolation in k
* if (abs(float(kh)-rk).lt.1.e-3) then
* k =kh
* kp1=kh
* else
k =min0(int(rk),n3-1)
kp1=k+1
* endif
 
if (k.eq.kp1) then
c no interpolation in k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
if (misdat.eq.ar(i,j,k)) then
int3dmlog=misdat
else
int3dmlog=ar(i,j,k)
endif
c print *,'int3dmlog 00: ',rid,rjd,rkd,int3dmlog
else
c horizontal interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k ))) then
int3dmlog=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dmlog = ar(i ,j ,k ) * frac1i * frac1j
& + ar(i ,jp1,k ) * frac1i * frac0j
& + ar(ip1,j ,k ) * frac0i * frac1j
& + ar(ip1,jp1,k ) * frac0i * frac0j
c print *,'int3dmlog 10: ',rid,rjd,rkd,int3dmlog
endif
endif
else
frac0k=rk-float(k)
frac1k=1.-frac0k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c vertical interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,j ,kp1))) then
int3dmlog=misdat
else
int3dmlog = log(ar(i ,j ,k )) * frac1k
& + log(ar(i ,j ,kp1)) * frac0k
int3dmlog = exp(int3dmlog)
c print *,'int3dmlog 01: ',rid,rjd,rkd,int3dmlog
endif
else
c full 3d interpolation
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k )).or.
& (misdat.eq.ar(i ,j ,kp1)).or.
& (misdat.eq.ar(i ,jp1,kp1)).or.
& (misdat.eq.ar(ip1,j ,kp1)).or.
& (misdat.eq.ar(ip1,jp1,kp1))) then
int3dmlog=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dmlog = log(ar(i ,j ,k )) * frac1i * frac1j * frac1k
& + log(ar(i ,jp1,k )) * frac1i * frac0j * frac1k
& + log(ar(ip1,j ,k )) * frac0i * frac1j * frac1k
& + log(ar(ip1,jp1,k )) * frac0i * frac0j * frac1k
& + log(ar(i ,j ,kp1)) * frac1i * frac1j * frac0k
& + log(ar(i ,jp1,kp1)) * frac1i * frac0j * frac0k
& + log(ar(ip1,j ,kp1)) * frac0i * frac1j * frac0k
& + log(ar(ip1,jp1,kp1)) * frac0i * frac0j * frac0k
int3dmlog = exp(int3dmlog)
c print *,'int3dmlog 11: ',rid,rjd,rkd,int3dmlog
endif
endif
endif
end
 
real function int3dmvc(ar,n1,n2,n3,rid,rjd,rkd,misdat)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location within the grid. The interpolation includes the
c testing of the missing data flag 'misdat'.
c In the vertical a Lagrangian cubic interpolation is
c performed.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,n2,n3 int input dimensions of ar
c ri,rj,rk real input grid location to be interpolated to
c misdat real input missing data flag (on if misdat<>0)
c Warning:
c This routine has not yet been seriously tested
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3
real ar(n1,n2,n3), rid,rjd,rkd, misdat
c local declarations
integer i,j,k,ip1,jp1,kp1,ih,jh,kh,klow,n
real frac0i,frac0j,frac1i,frac1j,ri,rj,rk
real int2d(4)
 
real int3dm
 
c if n3 < 4 then do call linear interpolation in the vertical
if (n3.lt.4) then
int3dmvc=int3dm(ar,n1,n2,n3,rid,rjd,rkd,misdat)
return
endif
c do linear interpolation in the horizontal
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
rk=amax1(1.,amin1(float(n3),rkd))
ih=nint(ri)
jh=nint(rj)
kh=nint(rk)
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
c Check for interpolation in k
* if (abs(float(kh)-rk).lt.1.e-3) then
* k =kh
* kp1=kh
* else
k =min0(int(rk),n3-1)
kp1=k+1
* endif
if (k.eq.kp1) then
c no interpolation in k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int3dmvc=ar(i,j,k)
c print *,'int3dmvc 00: ',rid,rjd,rkd,int3dmvc
else
c horizontal interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k ))) then
int3dmvc=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dmvc = ar(i ,j ,k ) * frac1i * frac1j
& + ar(i ,jp1,k ) * frac1i * frac0j
& + ar(ip1,j ,k ) * frac0i * frac1j
& + ar(ip1,jp1,k ) * frac0i * frac0j
c print *,'int3dmvc 10: ',rid,rjd,rkd,int3dmvc
endif
endif
else
if ((i.eq.ip1).and.(j.eq.jp1)) then
c vertical interpolation only
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,j ,kp1))) then
int3dmvc=misdat
else
if (k-1.lt.1) then
klow=1
else if (k+2.gt.n3) then
klow=n3-3
else
klow=k-1
endif
call cubint(ar(i,j,klow),ar(i,j,klow+1),ar(i,j,klow+2),
& ar(i,j,klow+3),klow,rk,int3dmvc)
endif
else
c full 3d interpolation
if ((misdat.eq.ar(i ,j ,k )).or.
& (misdat.eq.ar(i ,jp1,k )).or.
& (misdat.eq.ar(ip1,j ,k )).or.
& (misdat.eq.ar(ip1,jp1,k )).or.
& (misdat.eq.ar(i ,j ,kp1)).or.
& (misdat.eq.ar(i ,jp1,kp1)).or.
& (misdat.eq.ar(ip1,j ,kp1)).or.
& (misdat.eq.ar(ip1,jp1,kp1))) then
int3dmvc=misdat
else
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
if (k-1.lt.1) then
klow=1
else if (k+2.gt.n3) then
klow=n3-3
else
klow=k-1
endif
do n=1,4
int2d(n) = ar(i ,j ,klow-1+n ) * frac1i * frac1j
& + ar(i ,jp1,klow-1+n ) * frac1i * frac0j
& + ar(ip1,j ,klow-1+n ) * frac0i * frac1j
& + ar(ip1,jp1,klow-1+n ) * frac0i * frac0j
enddo
call cubint(int2d(1),int2d(2),int2d(3),int2d(4),
& klow,rk,int3dmvc)
endif
endif
endif
end
real function int4d(ar,n1,n2,n3,n4,rid,rjd,rkd,rld)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 4d-array to an arbitrary
c location within the grid.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,..,n4 int input dimensions of ar
c ri,..,rl real input grid location to be interpolated to
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3,n4
real ar(n1,n2,n3,n4), rid,rjd,rkd,rld
 
c local declarations
integer l,lp1,lh
real frac0l,frac1l,rl,int3d
 
c do linear interpolation in l-direction
rl=amax1(1.,amin1(float(n4),rld))
lh=nint(rl)
 
c Check for interpolation in l
* if (abs(float(lh)-rl).lt.1.e-3) then
* l =lh
* lp1=lh
* else
l =min0(int(rl),n4-1)
lp1=l+1
* endif
 
if (l.eq.lp1) then
c no interpolation in l
int4d=int3d(ar(1,1,1,l),n1,n2,n3,rid,rjd,rkd)
else
c interpolation in l
frac0l=rl-float(l)
frac1l=1.-frac0l
int4d = int3d(ar(1,1,1,l ),n1,n2,n3,rid,rjd,rkd) * frac1l
& + int3d(ar(1,1,1,lp1),n1,n2,n3,rid,rjd,rkd) * frac0l
endif
end
real function int4dm(ar,n1,n2,n3,n4,rid,rjd,rkd,rld,misdat)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 4d-array to an arbitrary
c location within the grid. The interpolation includes the
c testing of the missing data flag 'misdat'.
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,..,n4 int input dimensions of ar
c ri,..,rl real input grid location to be interpolated to
c misdat real input missing data flag (on if misdat<>0)
c Warning:
c This routine has not yet been seriously tested.
c History:
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3,n4
real ar(n1,n2,n3,n4), rid,rjd,rkd,rld, misdat
 
c local declarations
integer l,lp1,lh
real frac0l,frac1l,rl,rint0,rint1,int4d,int3dm
 
c check whether missing data checking is required
if (misdat.eq.0.) then
int4dm=int4d(ar,n1,n2,n3,n4,rid,rjd,rkd,rld)
return
endif
 
c do linear interpolation in l-direction
rl=amax1(1.,amin1(float(n4),rld))
lh=nint(rl)
 
c Check for interpolation in l
* if (abs(float(lh)-rl).lt.1.e-3) then
* l =lh
* lp1=lh
* else
l =min0(int(rl),n4-1)
lp1=l+1
* endif
 
if (l.eq.lp1) then
c no interpolation in l
int4dm = int3dm(ar(1,1,1,l),n1,n2,n3,rid,rjd,rkd,misdat)
else
c interpolation in l
frac0l=rl-float(l)
frac1l=1.-frac0l
rint0 = int3dm(ar(1,1,1,l ),n1,n2,n3,rid,rjd,rkd,misdat)
rint1 = int3dm(ar(1,1,1,lp1),n1,n2,n3,rid,rjd,rkd,misdat)
if ((rint0.eq.misdat).or.(rint1.eq.misdat)) then
int4dm = misdat
else
int4dm = rint0*frac1l + rint1*frac0l
endif
endif
end
real function int3dl(ar,n1,n2,n3,levels,rid,rjd,rkd)
c-----------------------------------------------------------------------
c Purpose:
c This subroutine interpolates a 3d-array to an arbitrary
c location within the grid. The vertical interpolation is linear
c in log(pressure).
c Arguments:
c ar real input surface pressure, define as ar(n1,n2,n3)
c n1,n2,n3 int input dimensions of ar
c levels real input array contains pressure levels for ar
c ri,rj,rk real input grid location to be interpolated to
c History:
c Based on int3d July 93
c-----------------------------------------------------------------------
 
c argument declarations
integer n1,n2,n3
real ar(n1,n2,n3), rid,rjd,rkd
real levels(n3)
 
c local declarations
real pval
integer i,j,k,ip1,jp1,kp1,ih,jh,kh
real frac0i,frac0j,frac0k,frac1i,frac1j,frac1k,ri,rj,rk
 
c do linear interpolation
ri=amax1(1.,amin1(float(n1),rid))
rj=amax1(1.,amin1(float(n2),rjd))
rk=amax1(1.,amin1(float(n3),rkd))
ih=nint(ri)
jh=nint(rj)
kh=nint(rk)
 
c Check for interpolation in i
* if (abs(float(ih)-ri).lt.1.e-3) then
* i =ih
* ip1=ih
* else
i =min0(int(ri),n1-1)
ip1=i+1
* endif
 
c Check for interpolation in j
* if (abs(float(jh)-rj).lt.1.e-3) then
* j =jh
* jp1=jh
* else
j =min0(int(rj),n2-1)
jp1=j+1
* endif
 
c Check for interpolation in k
* if (abs(float(kh)-rk).lt.1.e-3) then
* k =kh
* kp1=kh
* else
k =min0(int(rk),n3-1)
kp1=k+1
* endif
 
if (k.eq.kp1) then
c no interpolation in k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c no interpolation at all
int3dl=ar(i,j,k)
c print *,'int3dl 00: ',rid,rjd,rkd,int3dl
else
c horizontal interpolation only
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dl = ar(i ,j ,k ) * frac1i * frac1j
& + ar(i ,jp1,k ) * frac1i * frac0j
& + ar(ip1,j ,k ) * frac0i * frac1j
& + ar(ip1,jp1,k ) * frac0i * frac0j
c print *,'int3dl 10: ',rid,rjd,rkd,int3dl
endif
else
* frac0k=rk-float(k)
c calculate the pressure value to be interpolated to
pval=levels(int(rk))
> -(rk-aint(rk))*(levels(int(rk))-levels(int(rk)+1))
frac0k=log(levels(int(rk))/pval)
& /log(levels(int(rk))/levels(int(rk)+1))
frac1k=1.-frac0k
if ((i.eq.ip1).and.(j.eq.jp1)) then
c vertical interpolation only
int3dl = ar(i ,j ,k ) * frac1k
& + ar(i ,j ,kp1) * frac0k
c print *,'int3dl 01: ',rid,rjd,rkd,int3dl
else
c full 3d interpolation
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
int3dl = ar(i ,j ,k ) * frac1i * frac1j * frac1k
& + ar(i ,jp1,k ) * frac1i * frac0j * frac1k
& + ar(ip1,j ,k ) * frac0i * frac1j * frac1k
& + ar(ip1,jp1,k ) * frac0i * frac0j * frac1k
& + ar(i ,j ,kp1) * frac1i * frac1j * frac0k
& + ar(i ,jp1,kp1) * frac1i * frac0j * frac0k
& + ar(ip1,j ,kp1) * frac0i * frac1j * frac0k
& + ar(ip1,jp1,kp1) * frac0i * frac0j * frac0k
c print *,'int3dl 11: ',rid,rjd,rkd,int3dl
endif
endif
end
subroutine bcucof(y,y1,y2,y12,c)
c-----------------------------------------------------------------------
c Given arrays y,y1,y2 and y12, each of length 4, containing the
c function, gradients, and cross derivative at the four grid points
c of a rectangular grid cell (numbered counterclockwise from the
c lower left), and given d1 and d2, the length of the grid cell in
c the 1- and 2-directions, this routine returns the table c that is
c used by routine bcuint for biqubic interpolation.
c Source: Numerical Recipes, Fortran Version, p.99
c-----------------------------------------------------------------------
real c(4,4),y(4),y1(4),y2(4),y12(4),cl(16),x(16)
integer wt(16,16)
 
data wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,
> 8*0,3,0,-9,6,-2,0,6,-4,
> 10*0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,
> 4*0,1,0,-3,2,-2,0,6,-4,1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,
> 10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0,-6,4,2*0,3,-2,
> 0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2,
> 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,
> 5*0,1,-2,1,0,-2,4,-2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,
> 10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0,2,-2,2*0,-1,1/
 
real xx
integer i,j,k,l
 
do i=1,4 ! pack a temporary vector x
x(i)=y(i)
x(i+4)=y1(i)
x(i+8)=y2(i)
x(i+12)=y12(i)
enddo
 
do i=1,16 ! matrix multiply by the stored table
xx=0.
do k=1,16
xx=xx+wt(i,k)*x(k)
enddo
cl(i)=xx
enddo
 
l=0
do i=1,4 ! unpack the result into the output table
do j=1,4
l=l+1
c(i,j)=cl(l)
enddo
enddo
 
return
end
subroutine bcuint(y,y1,y2,y12,x1l,x2l,x1,x2,ansy)
c-----------------------------------------------------------------------
c Bicubic interpolation within a grid square. Input quantities are
c y,y1,y2,y12 (as described in bcucof); x1l and x1u, the lower and
c upper coordinates of the grid square in the 1-direction; x2l and
c x2u likewise for the 2-direction; and x1,x2, the coordinates of
c the desired point for the interpolation. The interplated function
c value is returned as ansy. This routine calls bcucof.
c Source: Numerical Recipes, Fortran Version, p.99/100
c !!! changed the proposed code !!!
c-----------------------------------------------------------------------
 
real y(4),y1(4),y2(4),y12(4),c(4,4)
real ansy,x1,x2,t,u
integer i,x1l,x2l
 
call bcucof(y,y1,y2,y12,c)
 
t=x1-real(x1l)
u=x2-real(x2l)
 
ansy=0.
 
do i=4,1,-1
ansy=t*ansy+((c(i,4)*u+c(i,3))*u+c(i,2))*u+c(i,1)
enddo
 
return
end
subroutine cubint(ya1,ya2,ya3,ya4,k,x,y)
c-----------------------------------------------------------------------
c Interface routine for SR polint for special case of cubic
c interpolation in index space, with xa=k,k+1,k+2,k+3
c-----------------------------------------------------------------------
integer k
real ya1,ya2,ya3,ya4,x,y
 
integer n
real xa(4),ya(4),dy
 
do n=1,4
xa(1)=real(k)
xa(2)=real(k+1)
xa(3)=real(k+2)
xa(4)=real(k+3)
ya(1)=ya1
ya(2)=ya2
ya(3)=ya3
ya(4)=ya4
enddo
 
call polint(xa,ya,4,x,y,dy)
 
return
end
subroutine polint(xa,ya,n,x,y,dy)
c-----------------------------------------------------------------------
c Given arrays xa and ya, each of length n, and given a value x, this
c routine returns a value y, and an error estimate dy. If P(x) is the
c polynomial of degree n-1 such that p(xa(i))=ya(i),i=1,...,n, then
c the returned value y=p(x)
c Source: Numerical Recipes, Fortran Version, p.82
c-----------------------------------------------------------------------
 
integer nmax,n
parameter(nmax=10)
real xa(n),ya(n),x,y,dy
integer i,m,ns
real c(nmax),d(nmax),den,dif,dift,ho,hp,w
 
ns=1
dif=abs(x-xa(1))
 
do i=1,n
dift=abs(x-xa(i))
if (dift.lt.dif) then
ns=i
dif=dift
endif
c(i)=ya(i)
d(i)=ya(i)
enddo
 
y=ya(ns)
ns=ns-1
do m=1,n-1
do i=1,n-m
ho=xa(i)-x
hp=xa(i+m)-x
w=c(i+1)-d(i)
den=ho-hp
den=w/den
d(i)=hp*den
c(i)=ho*den
enddo
if (2*ns.lt.n-m) then
dy=c(ns+1)
else
dy=d(ns)
ns=ns-1
endif
y=y+dy
enddo
 
return
end
subroutine filt2d (a,af,f1,f2,nx,ny,fil,misdat,
& iperx,ipery,ispol,inpol)
c =============================================================
c Apply a conservative diffusion operator onto the 2d field a,
c with full missing data checking.
c
c a real inp array to be filtered, dimensioned (nx,ny)
c af real out filtered array, dimensioned (nx,ny), can be
c equivalenced with array a in the calling routine
c f1 real workarray, dimensioned (nx+1,ny)
c f2 real workarray, dimensioned (nx,ny+1)
c fil real inp filter-coeff., 0<afil<=1. Maximum filtering with afil=1
c corresponds to one application of the linear filter.
c misdat real inp missing-data value, a(i,j)=misdat indicates that
c the corresponding value is not available. The
c misdat-checking can be switched off with with misdat=0.
c iperx int inp periodic boundaries in the x-direction (1=yes,0=no)
c ipery int inp periodic boundaries in the y-direction (1=yes,0=no)
c inpol int inp northpole at j=ny (1=yes,0=no)
c ispol int inp southpole at j=1 (1=yes,0=no)
c
c Christoph Schaer, 1993
c argument declaration
integer nx,ny
real a(nx,ny),af(nx,ny),f1(nx+1,ny),f2(nx,ny+1),fil,misdat
integer iperx,ipery,inpol,ispol
c local variable declaration
integer i,j,is
real fh
c compute constant fh
fh=0.125*fil
c compute fluxes in x-direction
if (misdat.eq.0.) then
do j=1,ny
do i=2,nx
f1(i,j)=a(i-1,j)-a(i,j)
enddo
enddo
else
do j=1,ny
do i=2,nx
if ((a(i,j).eq.misdat).or.(a(i-1,j).eq.misdat)) then
f1(i,j)=0.
else
f1(i,j)=a(i-1,j)-a(i,j)
endif
enddo
enddo
endif
if (iperx.eq.1) then
c do periodic boundaries in the x-direction
do j=1,ny
f1(1,j)=f1(nx,j)
f1(nx+1,j)=f1(2,j)
enddo
else
c set boundary-fluxes to zero
do j=1,ny
f1(1,j)=0.
f1(nx+1,j)=0.
enddo
endif
c compute fluxes in y-direction
if (misdat.eq.0.) then
do j=2,ny
do i=1,nx
f2(i,j)=a(i,j-1)-a(i,j)
enddo
enddo
else
do j=2,ny
do i=1,nx
if ((a(i,j).eq.misdat).or.(a(i,j-1).eq.misdat)) then
f2(i,j)=0.
else
f2(i,j)=a(i,j-1)-a(i,j)
endif
enddo
enddo
endif
c set boundary-fluxes to zero
do i=1,nx
f2(i,1)=0.
f2(i,ny+1)=0.
enddo
if (ipery.eq.1) then
c do periodic boundaries in the x-direction
do i=1,nx
f2(i,1)=f2(i,ny)
f2(i,ny+1)=f2(i,2)
enddo
endif
if (iperx.eq.1) then
if (ispol.eq.1) then
c do south-pole
is=(nx-1)/2
do i=1,nx
f2(i,1)=-f2(mod(i-1+is,nx)+1,2)
enddo
endif
if (inpol.eq.1) then
c do north-pole
is=(nx-1)/2
do i=1,nx
f2(i,ny+1)=-f2(mod(i-1+is,nx)+1,ny)
enddo
endif
endif
c compute flux-convergence -> filter
if (misdat.eq.0.) then
do j=1,ny
do i=1,nx
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
enddo
enddo
else
do j=1,ny
do i=1,nx
if (a(i,j).eq.misdat) then
af(i,j)=misdat
else
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
endif
enddo
enddo
endif
end
 
subroutine pipo(var3d,p3d,lev,var,nx,ny,nz,mdv,mode)
C ====================================================
 
C Interpolates the 3d variable var3d on the pressure surface
C defined by lev. The interpolated field is returned as var.
C p3d denotes the 3d pressure array.
C mode determines the way of vertical interpolation:
C mode=0 is for linear interpolation
C mode=1 is for logarithmic interpolation
 
integer nx,ny,nz,mode
real lev,mdv
real var3d(nx,ny,nz),p3d(nx,ny,nz),var(nx,ny)
 
integer i,j,k
real kind
real int3dm
 
do i=1,nx
do j=1,ny
 
kind=0.
do k=1,nz-1
if ((p3d(i,j,k).ge.lev).and.(p3d(i,j,k+1).le.lev)) then
kind=float(k)+(p3d(i,j,k)-lev)/
> (p3d(i,j,k)-p3d(i,j,k+1))
goto 100
endif
enddo
100 continue
 
if (kind.eq.0.) then
var(i,j)=mdv
else
var(i,j)=int3dm(var3d,nx,ny,nz,float(i),float(j),kind,mdv)
endif
 
enddo
enddo
 
return
end
 
subroutine thipo(var3d,th3d,lev,var,nx,ny,nz,mdv,mode)
C ======================================================
 
C Interpolates the 3d variable var3d on the isentropic surface
C defined by lev. The interpolated field is returned as var.
C th3d denotes the 3d theta array.
C mode determines the way of vertical interpolation:
C mode=0 is for linear interpolation
C mode=1 is for logarithmic interpolation
 
integer nx,ny,nz,mode
real lev,mdv
real var3d(nx,ny,nz),th3d(nx,ny,nz),var(nx,ny)
 
integer i,j,k
real kind
real int3dm
 
do i=1,nx
do j=1,ny
 
kind=0
do k=1,nz-1
if ((th3d(i,j,k).le.lev).and.(th3d(i,j,k+1).ge.lev)) then
kind=float(k)+(th3d(i,j,k)-lev)/
> (th3d(i,j,k)-th3d(i,j,k+1))
goto 100
endif
enddo
100 continue
 
if (kind.eq.0) then
var(i,j)=mdv
else
var(i,j)=int3dm(var3d,nx,ny,nz,float(i),float(j),kind,mdv)
endif
 
enddo
enddo
 
return
end
/tags/1.0/post/add2p.f
0,0 → 1,1567
PROGRAM add2p
 
c *********************************************************************
c * Add output from the PV inversion to the original P file *
c * Zonal wind (U), meridional wind (V) and temperature (T) are *
c * modified. All other fields are not affected by the programme *
c * *
c * Michael Sprenger / Summer, Autumn 2006
c *********************************************************************
 
implicit none
 
c ---------------------------------------------------------------------
c Declaration of parameters and variables
c ---------------------------------------------------------------------
 
c Input parameters
character*80 ml_fn
character*80 zm_fn
character*80 or_fn
real transxy
 
c Variables for input P file : model level
real ml_varmin(4),ml_varmax(4),ml_stag(4)
integer ml_vardim(4)
real ml_mdv
integer ml_ndim
integer ml_nx,ml_ny,ml_nz
real ml_xmin,ml_xmax,ml_ymin,ml_ymax,ml_dx,ml_dy
integer ml_ntimes
real ml_aklev(500),ml_bklev(500)
real ml_aklay(500),ml_bklay(500)
real ml_time
real ml_pollon,ml_pollat
integer ml_idate(5)
integer ml_nvars
character*80 ml_vnam(80)
real,allocatable, dimension (:,:) :: ml_ps,ml_oro
real,allocatable, dimension (:,:,:) :: ml_t3,ml_u3,ml_v3,ml_z3
real,allocatable, dimension (:,:,:) :: ml_p3,ml_tv3,ml_q3,ml_p0
integer,allocatable, dimension (:,:,:) :: flag_ml
 
c Variables for GEO.MOD
real zm_varmin(4),zm_varmax(4),zm_stag(4)
integer zm_vardim(4)
real zm_mdv
integer zm_ndim
integer zm_nx,zm_ny,zm_nz
real zm_xmin,zm_xmax,zm_ymin,zm_ymax,zm_dx,zm_dy
integer zm_ntimes
real zm_aklev(500),zm_bklev(500)
real zm_aklay(500),zm_bklay(500)
real zm_time
real zm_pollon,zm_pollat
integer zm_idate(5)
integer zm_nvars
character*80 zm_vnam(80)
real,allocatable, dimension (:,:,:) :: zm_u3,zm_v3,zm_t3,zm_z3
real,allocatable, dimension (:,:,:) :: zm_p3
real,allocatable, dimension (:,:) :: zm_rlat,zm_rlon
integer,allocatable, dimension (:,:,:) :: flag_zm
 
c Variables for GEO.ORG
real or_varmin(4),or_varmax(4),or_stag(4)
integer or_vardim(4)
real or_mdv
integer or_ndim
integer or_nx,or_ny,or_nz
real or_xmin,or_xmax,or_ymin,or_ymax,or_dx,or_dy
integer or_ntimes
real or_time
real or_pollon,or_pollat
integer or_idate(5)
integer or_nvars
character*80 or_vnam(80)
real,allocatable, dimension (:,:,:) :: or_p3
real,allocatable, dimension (:,:,:) :: or_u3,or_v3,or_t3
 
c Anomalies
real,allocatable, dimension (:,:,:) :: an_p3,an_u3,an_v3,an_t3
 
c Array with the weighting function
real,allocatable, dimension (:,:) :: weight,dist
 
c Flag for test mode
integer test
parameter (test=1)
 
c Flag for Poisson filling
integer poisson
parameter (poisson=1)
 
c Physical and numerical parameters
real eps ! Numerical epsilon
parameter (eps=0.001)
real dpextra ! Allowed range for extrapolation (% of pressure)
parameter (dpextra=0.1)
real g ! Earth's gravity
parameter (g=9.80665)
real tzero ! Conversion Celius/Kelvin
parameter (tzero=273.15)
real kappa ! Kappa (Definition of potential temperature)
parameter (kappa=0.6078)
real zerodiv ! Zero division handling
parameter (zerodiv=0.0000000001)
real dpmin ! Pressure step for hydrostatic equation
parameter (dpmin=10.)
real rdg ! Ratio gas constant / Earth's gravity
parameter (rdg=29.271)
c Auxiliray variables
integer i,j,k,l
character*80 varname
integer isok
integer stat
integer cdfid,ierr,cstid
character*80 cfn
real p1(1000),z1(1000),f1(1000),tv1(1000)
real spline_f1(1000),spline_tv1(1000)
integer n1
real hh
real pmin,pmax
real boundlat(100000),boundlon(1000000)
integer nbound
integer il,ir,ju,jd,im,jm
real lat,lon
real distmin,distpos
character*80 name
real pu,po,zu,zo,p,z,dp,p0,tvu,tvo,ff
integer lmin,n
real mean,nmean
real psfc
integer count0,count1
 
c Externals
real sdis,kink
external sdis,kink
 
 
c -----------------------------------------------------------------
c Read input fields
c -----------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* add2p *'
print*,'*********************************************************'
print*
 
c Read in the parameter file
open(10,file='fort.10')
read(10,*) ml_fn
read(10,*) zm_fn
read(10,*) or_fn
read(10,*) name,transxy
if ( trim(name).ne.'TRANS_XY' ) stop
read(10,*) name,psfc
if ( trim(name).ne.'PS_CHANGE' ) stop
close(10)
print*,trim(ml_fn)
print*,trim(zm_fn)
print*,trim(or_fn)
print*
c Get grid description for P file : model level
call cdfopn(ml_fn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,ml_nvars,ml_vnam,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='T'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 998
ml_nx =ml_vardim(1)
ml_ny =ml_vardim(2)
ml_nz =ml_vardim(3)
ml_xmin=ml_varmin(1)
ml_ymin=ml_varmin(2)
call getlevs(cstid,ml_nz,ml_aklev,ml_bklev,ml_aklay,ml_bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,ml_dx,ml_dy,ierr)
ml_xmax=ml_xmin+real(ml_nx-1)*ml_dx
ml_ymax=ml_ymin+real(ml_ny-1)*ml_dy
if (ierr.ne.0) goto 998
call gettimes(cdfid,ml_time,ml_ntimes,ierr)
if (ierr.ne.0) goto 998
call getstart(cstid,ml_idate,ierr)
if (ierr.ne.0) goto 998
call getpole(cstid,ml_pollon,ml_pollat,ierr)
if (ierr.ne.0) goto 998
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Get grid description for MOD file
call cdfopn(zm_fn,cdfid,ierr)
if (ierr.ne.0) goto 997
call getvars(cdfid,zm_nvars,zm_vnam,ierr)
if (ierr.ne.0) goto 997
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 997
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 997
isok=0
varname='T'
call check_varok(isok,varname,zm_vnam,zm_nvars)
if (isok.ne.1) goto 997
call getdef(cdfid,varname,zm_ndim,zm_mdv,zm_vardim,
> zm_varmin,zm_varmax,zm_stag,ierr)
if (ierr.ne.0) goto 997
zm_nx =zm_vardim(1)
zm_ny =zm_vardim(2)
zm_nz =zm_vardim(3)
zm_xmin=zm_varmin(1)
zm_ymin=zm_varmin(2)
call getlevs(cstid,zm_nz,zm_aklev,zm_bklev,zm_aklay,zm_bklay,ierr)
if (ierr.ne.0) goto 997
call getgrid(cstid,zm_dx,zm_dy,ierr)
if (ierr.ne.0) goto 997
zm_xmax=zm_xmin+real(zm_nx-1)*zm_dx
zm_ymax=zm_ymin+real(zm_ny-1)*zm_dy
call gettimes(cdfid,zm_time,zm_ntimes,ierr)
if (ierr.ne.0) goto 997
call getstart(cstid,zm_idate,ierr)
if (ierr.ne.0) goto 997
call getpole(cstid,zm_pollon,zm_pollat,ierr)
if (ierr.ne.0) goto 997
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Get grid description for ORG file
call cdfopn(or_fn,cdfid,ierr)
if (ierr.ne.0) goto 997
call getvars(cdfid,or_nvars,or_vnam,ierr)
if (ierr.ne.0) goto 997
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 997
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 997
isok=0
varname='P'
call check_varok(isok,varname,or_vnam,or_nvars)
if (isok.ne.1) goto 997
call getdef(cdfid,varname,or_ndim,or_mdv,or_vardim,
> or_varmin,or_varmax,or_stag,ierr)
if (ierr.ne.0) goto 997
or_nx =or_vardim(1)
or_ny =or_vardim(2)
or_nz =or_vardim(3)
or_xmin=or_varmin(1)
or_ymin=or_varmin(2)
call getgrid(cstid,or_dx,or_dy,ierr)
if (ierr.ne.0) goto 997
or_xmax=or_xmin+real(or_nx-1)*or_dx
or_ymax=or_ymin+real(or_ny-1)*or_dy
call gettimes(cdfid,or_time,or_ntimes,ierr)
if (ierr.ne.0) goto 997
call getstart(cstid,or_idate,ierr)
if (ierr.ne.0) goto 997
call getpole(cstid,or_pollon,or_pollat,ierr)
if (ierr.ne.0) goto 997
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Consistency check for the grids
if ( (abs(ml_xmin-zm_xmin).gt.eps).or.
> (abs(ml_xmax-zm_xmax).gt.eps).or.
> (abs(ml_ymin-zm_ymin).gt.eps).or.
> (abs(ml_ymax-zm_ymax).gt.eps).or.
> (abs(ml_dx -zm_dx ).gt.eps).or.
> (abs(ml_dy -zm_dy ).gt.eps).or.
> (abs(ml_time-zm_time).gt.eps).or.
> (abs(ml_xmin-or_xmin).gt.eps).or.
> (abs(ml_xmax-or_xmax).gt.eps).or.
> (abs(ml_ymin-or_ymin).gt.eps).or.
> (abs(ml_ymax-or_ymax).gt.eps).or.
> (abs(ml_dx -or_dx ).gt.eps).or.
> (abs(ml_dy -or_dy ).gt.eps) )
>then
print*,'P, GEO.MOD, GEO.ORG grids not consistent... Stop'
print*,ml_xmin,zm_xmin,or_xmin
print*,ml_ymin,zm_ymin,or_ymin
print*,ml_dx, zm_dx ,or_dx
print*,ml_dy, zm_dy ,or_dy
print*,ml_time,zm_time,or_time
stop
endif
 
c Allocate memory for input and output P file
allocate(ml_p3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_p3'
allocate(ml_u3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_u3'
allocate(ml_v3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_v3'
allocate(ml_t3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_t3'
allocate(ml_tv3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_tv3'
allocate(ml_z3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_z3'
allocate(ml_q3 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_q3'
allocate(ml_ps (ml_nx,ml_ny ),stat=stat)
if (stat.ne.0) print*,'error allocating ml_ps'
allocate(ml_oro (ml_nx,ml_ny ),stat=stat)
if (stat.ne.0) print*,'error allocating ml_oro'
allocate(ml_p0 (ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'error allocating ml_p0'
 
c Allocate memory for input GEO.MOD file
allocate(zm_p3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_p3'
allocate(zm_u3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_u3'
allocate(zm_v3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_v3'
allocate(zm_t3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_t3'
allocate(zm_z3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_z3'
allocate(zm_rlat(zm_nx,zm_ny),stat=stat)
if (stat.ne.0) print*,'error allocating zm_rlat'
allocate(zm_rlon(zm_nx,zm_ny),stat=stat)
if (stat.ne.0) print*,'error allocating zm_rlon'
 
c Allocate memory for input GEO.ORG file
allocate(or_p3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_p3'
allocate(or_t3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_t3'
allocate(or_u3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_u3'
allocate(or_v3(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating zm_v3'
 
c Allocate memory for weighting function, flag and anomalies
allocate(weight(zm_nx,zm_ny),stat=stat)
if (stat.ne.0) print*,'error allocating weight'
allocate(dist (zm_nx,zm_ny),stat=stat)
if (stat.ne.0) print*,'error allocating dist'
allocate(flag_zm(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating flag'
allocate(flag_ml(zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating flag'
allocate(an_p3 (zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating an_p3'
allocate(an_t3 (zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating an_t3'
allocate(an_u3 (zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating an_u3'
allocate(an_v3 (zm_nx,zm_ny,zm_nz),stat=stat)
if (stat.ne.0) print*,'error allocating an_v3'
 
c Read variables from P file : model levels
call cdfopn(ml_fn,cdfid,ierr)
if (ierr.ne.0) goto 998
varname='T'
call getdat(cdfid,varname,ml_time,0,ml_t3,ierr)
if (ierr.ne.0) goto 998
print*,'R T ',trim(ml_fn)
varname='U'
call getdat(cdfid,varname,ml_time,0,ml_u3,ierr)
if (ierr.ne.0) goto 998
print*,'R U ',trim(ml_fn)
varname='V'
call getdat(cdfid,varname,ml_time,0,ml_v3,ierr)
if (ierr.ne.0) goto 998
print*,'R V ',trim(ml_fn)
varname='Z'
call getdat(cdfid,varname,ml_time,0,ml_z3,ierr)
if (ierr.ne.0) goto 998
print*,'R Z ',trim(ml_fn)
varname='Q'
call getdat(cdfid,varname,ml_time,0,ml_q3,ierr)
if (ierr.ne.0) goto 998
print*,'R Q ',trim(ml_fn)
varname='PS'
call getdat(cdfid,varname,ml_time,0,ml_ps,ierr)
if (ierr.ne.0) goto 998
print*,'R PS ',trim(ml_fn)
varname='ORO'
call getdat(cdfid,varname,ml_time,0,ml_oro,ierr)
if (ierr.ne.0) goto 998
print*,'R ORO ',trim(ml_fn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Read variables from GEO.MOD
call cdfopn(zm_fn,cdfid,ierr)
if (ierr.ne.0) goto 997
 
varname='T'
call getdat(cdfid,varname,zm_time,0,zm_t3,ierr)
if (ierr.ne.0) goto 997
print*,'R T ',trim(zm_fn)
varname='U'
call getdat(cdfid,varname,zm_time,0,zm_u3,ierr)
if (ierr.ne.0) goto 997
print*,'R U ',trim(zm_fn)
varname='V'
call getdat(cdfid,varname,zm_time,0,zm_v3,ierr)
if (ierr.ne.0) goto 997
print*,'R V ',trim(zm_fn)
varname='P'
call getdat(cdfid,varname,zm_time,0,zm_p3,ierr)
if (ierr.ne.0) goto 997
print*,'R P ',trim(zm_fn)
varname='RLAT'
call getdat(cdfid,varname,zm_time,0,zm_rlat,ierr)
if (ierr.ne.0) goto 997
print*,'R RLAT ',trim(zm_fn)
varname='RLON'
call getdat(cdfid,varname,zm_time,0,zm_rlon,ierr)
if (ierr.ne.0) goto 997
print*,'R RLON ',trim(zm_fn)
 
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Read variables from GEO.ORG
call cdfopn(or_fn,cdfid,ierr)
if (ierr.ne.0) goto 998
varname='P'
call getdat(cdfid,varname,or_time,0,or_p3,ierr)
if (ierr.ne.0) goto 998
print*,'R P ',trim(or_fn)
varname='U'
call getdat(cdfid,varname,or_time,0,or_u3,ierr)
if (ierr.ne.0) goto 998
print*,'R U ',trim(or_fn)
varname='V'
call getdat(cdfid,varname,or_time,0,or_v3,ierr)
if (ierr.ne.0) goto 998
print*,'R V ',trim(or_fn)
varname='T'
call getdat(cdfid,varname,or_time,0,or_t3,ierr)
if (ierr.ne.0) goto 998
print*,'R T ',trim(or_fn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Initialize the height levels of the Z file
do i=1,zm_nx
do j=1,zm_ny
do k=1,zm_nz
zm_z3(i,j,k)=zm_aklay(k)
enddo
enddo
enddo
 
c Calculate 3d pressure field on model levels
print*,'C P (ORIGINAL)'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
if (abs(ml_stag(3)+0.5).lt.eps) then
ml_p0(i,j,k)=ml_aklay(k)+ml_bklay(k)*ml_ps(i,j)
else
ml_p0(i,j,k)=ml_aklev(k)+ml_bklev(k)*ml_ps(i,j)
endif
enddo
enddo
enddo
 
c Calculate 3d anomalies due to inversion
print*,'C DP (MODIFIED-ORIGINAL)'
print*,'C DU (MODIFIED-ORIGINAL)'
print*,'C DV (MODIFIED-ORIGINAL)'
print*,'C DT (MODIFIED-ORIGINAL)'
do k=1,zm_nz
do i=1,zm_nx
do j=1,zm_ny
 
c P
if ( ( abs(zm_p3(i,j,k)-zm_mdv).gt.eps).and.
> ( abs(or_p3(i,j,k)-or_mdv).gt.eps) )
> then
an_p3(i,j,k) = zm_p3(i,j,k) - or_p3(i,j,k)
elseif ( poisson.eq.1 ) then
an_p3(i,j,k) = zm_mdv
else
an_p3(i,j,k) = 0.
endif
 
c T
if ( ( abs(zm_t3(i,j,k)-zm_mdv).gt.eps).and.
> ( abs(or_t3(i,j,k)-or_mdv).gt.eps) )
> then
an_t3(i,j,k) = zm_t3(i,j,k) - or_t3(i,j,k)
elseif ( poisson.eq.1 ) then
an_t3(i,j,k) = zm_mdv
else
an_t3(i,j,k) = 0.
endif
 
c U
if ( ( abs(zm_u3(i,j,k)-zm_mdv).gt.eps).and.
> ( abs(or_u3(i,j,k)-or_mdv).gt.eps) )
> then
an_u3(i,j,k) = zm_u3(i,j,k) - or_u3(i,j,k)
elseif ( poisson.eq.1 ) then
an_u3(i,j,k) = zm_mdv
else
an_u3(i,j,k) = 0.
endif
 
c V
if ( ( abs(zm_v3(i,j,k)-zm_mdv).gt.eps).and.
> ( abs(or_v3(i,j,k)-or_mdv).gt.eps) )
> then
an_v3(i,j,k) = zm_v3(i,j,k) - or_v3(i,j,k)
elseif ( poisson.eq.1 ) then
an_v3(i,j,k) = zm_mdv
else
an_v3(i,j,k) = 0.
endif
 
enddo
enddo
enddo
 
c ----------------------------------------------------------------
c Get the weight function for the inset (from 1 inside to 0 outside)
c ----------------------------------------------------------------
 
print*,'C BOUNDARY FILTER'
 
c Init the weight function (1 inside, 0 outside)
do i=1,ml_nx
do j=1,ml_ny
if ( (zm_rlat(i,j).lt. -90.).or.
> (zm_rlat(i,j).gt. 90.).or.
> (zm_rlon(i,j).lt.-180.).or.
> (zm_rlon(i,j).gt. 180.) ) then
weight(i,j)=0.
else
weight(i,j)=1.
endif
 
enddo
enddo
 
c Get a list of all boundary points
nbound=0
do i=1,ml_nx
do j=1,ml_ny
 
c Get neighbouring points
ir=i+1
if (ir.gt.ml_nx) ir=ml_nx
il=i-1
if (il.lt. 1) il=1
ju=j+1
if (ju.gt.ml_ny) ju=ml_ny
jd=j-1
if (jd.lt. 1) jd=1
 
c A boundary point has a 0/1 switch
if (abs(weight(i,j)-0.).lt.eps) then
if ( (abs(weight(ir, j)-1.).lt.eps).or.
> (abs(weight(il, j)-1.).lt.eps).or.
> (abs(weight(i ,ju)-1.).lt.eps).or.
> (abs(weight(i ,jd)-1.).lt.eps).or.
> (abs(weight(ir,ju)-1.).lt.eps).or.
> (abs(weight(ir,jd)-1.).lt.eps).or.
> (abs(weight(il,ju)-1.).lt.eps).or.
> (abs(weight(il,jd)-1.).lt.eps).or.
> (abs(weight(ir,ju)-1.).lt.eps).or.
> (abs(weight(il,ju)-1.).lt.eps).or.
> (abs(weight(ir,jd)-1.).lt.eps).or.
> (abs(weight(il,jd)-1.).lt.eps) ) then
 
nbound=nbound+1
boundlon(nbound)=ml_xmin+real(i-1)*ml_dx
boundlat(nbound)=ml_ymin+real(j-1)*ml_dy
endif
endif
enddo
enddo
 
c Get the distance from the subdomain
do i=1,ml_nx
do j=1,ml_ny
lon=ml_xmin+real(i-1)*ml_dx
lat=ml_ymin+real(j-1)*ml_dy
distmin=sdis(lon,lat,boundlon(1),boundlat(1))
do k=2,nbound
distpos=sdis(lon,lat,boundlon(k),boundlat(k))
if (distpos.lt.distmin) distmin=distpos
enddo
if ( abs(weight(i,j)-1.).lt.eps) then
dist(i,j)=distmin
else
dist(i,j)=-distmin
endif
enddo
enddo
 
c Set the new weights
do i=1,ml_nx
do j=1,ml_ny
if (weight(i,j).gt.0.) then
weight(i,j)=kink(dist(i,j),transxy)
endif
enddo
enddo
 
c ----------------------------------------------------------------
c Remove MDV regions in input field
c ----------------------------------------------------------------
 
if ( poisson.ne.1 ) goto 120
 
c Define region for mdv filling
do i=1,zm_nx
do j=1,zm_ny
do k=1,zm_nz
 
c Get neighbour of grid point
il = i-1
if (il.lt.1) il=1
ir = i+1
if ( ir.gt.zm_nx ) ir=zm_nx
jd = j-1
if (jd.lt.1) jd=1
ju = j+1
if ( ju.gt.zm_ny ) ju=zm_ny
 
c Set flag 2 for boundary and exterior points
if ( (abs(zm_rlat(il, j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir, j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i , j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(il,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i ,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(il,jd)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir,jd)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i ,jd)-zm_mdv).lt.eps) )
> then
flag_zm(i,j,k) = 2
an_p3(i,j,k) = 0.
an_u3(i,j,k) = 0.
an_v3(i,j,k) = 0.
an_t3(i,j,k) = 0.
 
c Set flag 1 for interior MDV points
elseif ( abs(an_p3(i,j,k)-zm_mdv).le.eps ) then
flag_zm(i,j,k) = 1
 
c Set flag 0 for interior valid points
else
flag_zm(i,j,k) = 0
endif
 
enddo
enddo
enddo
 
c Apply mdv filling
print*,'C DP (POISSON FILLING)'
call mdvfill(an_p3,an_p3,flag_zm,zm_nx,zm_ny,zm_nz,100)
print*,'C DT (POISSON FILLING)'
call mdvfill(an_t3,an_t3,flag_zm,zm_nx,zm_ny,zm_nz,100)
print*,'C DU (POISSON FILLING)'
call mdvfill(an_u3,an_u3,flag_zm,zm_nx,zm_ny,zm_nz,100)
print*,'C DV (POISSON FILLING)'
call mdvfill(an_v3,an_v3,flag_zm,zm_nx,zm_ny,zm_nz,100)
 
c Special treatment: if the number of missing values surpasses 50%
c on a level, then the anomaly is imported from the level above
do k=zm_nz-1,1,-1
 
count1 = 0
count0 = 0
do i=1,zm_nx
do j= 1,zm_ny
if ( flag_zm(i,j,k).eq.1 ) count1 = count1 + 1
if ( flag_zm(i,j,k).eq.0 ) count0 = count0 + 1
enddo
enddo
 
if ( count1.gt.count0 ) then
print*,'C P (IMPORTING FROM LEVEL ABOVE)',k
do i=1,zm_nx
do j= 1,zm_ny
an_p3(i,j,k) = an_p3(i,j,k+1)
flag_zm(i,j,k) = flag_zm(i,j,k+1)
enddo
enddo
print*,'C U (IMPORTING FROM LEVEL ABOVE)',k
do i=1,zm_nx
do j= 1,zm_ny
an_u3(i,j,k) = an_u3(i,j,k+1)
flag_zm(i,j,k) = flag_zm(i,j,k+1)
enddo
enddo
 
print*,'C V (IMPORTING FROM LEVEL ABOVE)',k
do i=1,zm_nx
do j= 1,zm_ny
an_v3(i,j,k) = an_v3(i,j,k+1)
flag_zm(i,j,k) = flag_zm(i,j,k+1)
enddo
enddo
 
print*,'C T (IMPORTING FROM LEVEL ABOVE)',k
do i=1,zm_nx
do j= 1,zm_ny
an_t3(i,j,k) = an_t3(i,j,k+1)
flag_zm(i,j,k) = flag_zm(i,j,k+1)
enddo
enddo
 
endif
 
enddo
 
c Write new fields for tests
if ( test.eq.1 ) then
 
call cdfwopn(zm_fn,cdfid,ierr)
if (ierr.ne.0) goto 994
 
isok=0
varname='P_ANO'
call check_varok(isok,varname,zm_vnam,zm_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,zm_ndim,zm_mdv,zm_vardim,
> zm_varmin,zm_varmax,zm_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,zm_time,0,an_p3,ierr)
if (ierr.ne.0) goto 994
print*,'W P_ANO ',trim(zm_fn)
 
isok=0
varname='T_ANO'
call check_varok(isok,varname,zm_vnam,zm_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,zm_ndim,zm_mdv,zm_vardim,
> zm_varmin,zm_varmax,zm_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,zm_time,0,an_t3,ierr)
if (ierr.ne.0) goto 994
print*,'W T_ANO ',trim(zm_fn)
 
isok=0
varname='U_ANO'
call check_varok(isok,varname,zm_vnam,zm_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,zm_ndim,zm_mdv,zm_vardim,
> zm_varmin,zm_varmax,zm_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,zm_time,0,an_u3,ierr)
if (ierr.ne.0) goto 994
print*,'W U_ANO ',trim(zm_fn)
 
isok=0
varname='V_ANO'
call check_varok(isok,varname,zm_vnam,zm_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,zm_ndim,zm_mdv,zm_vardim,
> zm_varmin,zm_varmax,zm_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,zm_time,0,an_v3,ierr)
if (ierr.ne.0) goto 994
print*,'W V_ANO ',trim(zm_fn)
 
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 994
 
endif
 
c Exit point for SOR solver
120 continue
 
c ----------------------------------------------------------------
c Change surface pressure and get 3d presure field
c ----------------------------------------------------------------
 
print*,'C PS'
 
c Change surface pressure: based on PV inversion on GEO
do i=1,ml_nx
do j=1,ml_ny
c Make vertical profile of pressure available
n1=0
do k=1,zm_nz
n1=n1+1
p1(n1)=an_p3(i,j,k)
z1(n1)=zm_z3(i,j,k)
enddo
 
if ( n1.ne.0 ) then
 
c Keep the original surface pressure (psfc=0)
if ( abs(psfc).lt.eps ) then
ml_ps(i,j) = ml_ps(i,j)
 
c Take the full change of surface pressure (psfc=1);
c Interpolation/extrapolation with a natural cubic spline
elseif ( abs(psfc-1.).lt.eps ) then
call spline (z1,p1,n1,1.e30,1.e30,spline_f1)
call splint (z1,p1,spline_f1,n1,ml_oro(i,j),hh)
ml_ps(i,j)=ml_ps(i,j) + hh*weight(i,j)
 
c Only take a fractional change of surface pressure
c Interpolation/extrapolation with a natural cubic spline
else
call spline (z1,p1,n1,1.e30,1.e30,spline_f1)
call splint (z1,p1,spline_f1,n1,ml_oro(i,j),hh)
ml_ps(i,j)=ml_ps(i,j) + hh*psfc*weight(i,j)
 
endif
 
endif
 
enddo
enddo
 
c Calculate 3d pressure field on model levels
print*,'C P'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
if (abs(ml_stag(3)+0.5).lt.eps) then
ml_p3(i,j,k)=ml_aklay(k)+ml_bklay(k)*ml_ps(i,j)
else
ml_p3(i,j,k)=ml_aklev(k)+ml_bklev(k)*ml_ps(i,j)
endif
enddo
enddo
enddo
 
c ----------------------------------------------------------------
c Get T,U,V at the new pressure levels, based on the original P file
c ----------------------------------------------------------------
 
c Interpolate T from original P file to new pressure levels
print*,'C T (ORIGINAL)'
do i=1,ml_nx
do j=1,ml_ny
 
n1=0
do k=ml_nz,1,-1
n1=n1+1
f1(n1)=ml_t3(i,j,k)
p1(n1)=ml_p0(i,j,k)
enddo
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_t3(i,j,k)=hh
enddo
 
enddo
enddo
 
c Interpolate U from original P file to new pressure levels
print*,'C U (ORIGINAL)'
do i=1,ml_nx
do j=1,ml_ny
 
n1=0
do k=ml_nz,1,-1
n1=n1+1
f1(n1)=ml_u3(i,j,k)
p1(n1)=ml_p0(i,j,k)
enddo
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_u3(i,j,k)=hh
enddo
 
enddo
enddo
 
c Interpolate V from original P file to new pressure levels
print*,'C V (ORIGINAL)'
do i=1,ml_nx
do j=1,ml_ny
 
n1=0
do k=ml_nz,1,-1
n1=n1+1
f1(n1)=ml_v3(i,j,k)
p1(n1)=ml_p0(i,j,k)
enddo
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_v3(i,j,k)=hh
enddo
 
enddo
enddo
 
c ----------------------------------------------------------------
c Add T,U,V anomalies at the new pressure levels
c ----------------------------------------------------------------
 
c Change temperature field
print*,'C T (ANOMALY)'
do i=1,ml_nx
do j=1,ml_ny
 
c Make vertical profile of temperature available
n1=0
pmax=-100.
pmin=2000.
do k=zm_nz,1,-1
if ((abs(an_t3(i,j,k)-zm_mdv).gt.eps).and.
> (zm_z3(i,j,k).gt.ml_oro(i,j)).and.
> (abs(zm_p3(i,j,k)-zm_mdv).gt.eps)) then
n1=n1+1
f1(n1)=an_t3(i,j,k)
p1(n1)=zm_p3(i,j,k)
if (p1(n1).lt.pmin) pmin=p1(n1)
if (p1(n1).gt.pmax) pmax=p1(n1)
endif
enddo
pmin=pmin-dpextra*pmin
pmax=pmax+dpextra+pmax
 
c Cubic spline interpolation
if (n1.gt.0) then
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
if ( (ml_p3(i,j,k).gt.pmin).and.
> (ml_p3(i,j,k).lt.pmax) ) then
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_t3(i,j,k)=ml_t3(i,j,k) + hh*weight(i,j)
endif
enddo
endif
 
enddo
enddo
 
c Change zonal velocity field
print*,'C U'
do i=1,ml_nx
do j=1,ml_ny
 
c Make vertical profile of zonal velocity available
n1=0
pmax=-100.
pmin=2000.
do k=zm_nz,1,-1
if ((abs(an_u3(i,j,k)-zm_mdv).gt.eps).and.
> (zm_z3(i,j,k).gt.ml_oro(i,j)).and.
> (abs(zm_p3(i,j,k)-zm_mdv).gt.eps)) then
n1=n1+1
f1(n1)=an_u3(i,j,k)
p1(n1)=zm_p3(i,j,k)
if (p1(n1).lt.pmin) pmin=p1(n1)
if (p1(n1).gt.pmax) pmax=p1(n1)
endif
enddo
pmin=pmin-dpextra*pmin
pmax=pmax+dpextra*pmax
 
c Cubic spline interpolation
if (n1.gt.0) then
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
if ( (ml_p3(i,j,k).gt.pmin).and.
> (ml_p3(i,j,k).lt.pmax) ) then
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_u3(i,j,k)=ml_u3(i,j,k) + hh*weight(i,j)
endif
enddo
endif
 
enddo
enddo
 
c Change meridional velocity field
print*,'C V'
do i=1,ml_nx
do j=1,ml_ny
 
c Make vertical profile of zonal velocity available
n1=0
pmax=-100.
pmin=2000.
do k=zm_nz,1,-1
if ((abs(an_v3(i,j,k)-zm_mdv).gt.eps).and.
> (zm_z3(i,j,k).gt.ml_oro(i,j)).and.
> (abs(zm_p3(i,j,k)-zm_mdv).gt.eps)) then
n1=n1+1
f1(n1)=an_v3(i,j,k)
p1(n1)=zm_p3(i,j,k)
if (p1(n1).lt.pmin) pmin=p1(n1)
if (p1(n1).gt.pmax) pmax=p1(n1)
endif
enddo
pmin=pmin-dpextra*pmin
pmax=pmax+dpextra*pmax
 
c Cubic spline interpolation
if (n1.gt.0) then
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
if ( (ml_p3(i,j,k).gt.pmin).and.
> (ml_p3(i,j,k).lt.pmax) ) then
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_v3(i,j,k)=ml_v3(i,j,k) + hh*weight(i,j)
endif
enddo
endif
 
enddo
enddo
 
c ---------------------------------------------------------------------
c Change geopotential height
c ---------------------------------------------------------------------
 
c Interpolate Z from original P file to new pressure levels
print*,'C Z (ORIGINAL)'
do i=1,ml_nx
do j=1,ml_ny
 
n1=0
do k=ml_nz,1,-1
n1=n1+1
f1(n1)=ml_z3(i,j,k)
p1(n1)=ml_p0(i,j,k)
enddo
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
ml_z3(i,j,k)=hh
enddo
 
enddo
enddo
 
c Calculate 3d virtual temperature
print*,'C TV'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
ml_tv3(i,j,k) = (ml_t3(i,j,k)+tzero)*
> (1.+kappa*ml_q3(i,j,k))
enddo
enddo
enddo
 
c Add geopotential height anomaly: first, the pressure anomaly is
c interpolated to the new position, then it is transformed into
c a correction of geopotential height with the hydrostatic equation
print*,'C DZ (MODIFIED -ORIGINAL)'
do i=1,ml_nx
do j=1,ml_ny
 
c Make vertical profile of pressure available
n1=0
pmax=-100.
pmin=2000.
do k=zm_nz,1,-1
if ((abs(an_p3(i,j,k)-zm_mdv).gt.eps).and.
> (zm_z3(i,j,k).gt.ml_oro(i,j)).and.
> (abs(zm_p3(i,j,k)-zm_mdv).gt.eps)) then
n1=n1+1
f1(n1)=an_p3(i,j,k)
p1(n1)=zm_p3(i,j,k)
if (p1(n1).lt.pmin) pmin=p1(n1)
if (p1(n1).gt.pmax) pmax=p1(n1)
endif
enddo
pmin=pmin-dpextra*pmin
pmax=pmax+dpextra*pmax
 
c Cubic spline interpolation and conversion dp -> dz
if (n1.gt.0) then
call spline (p1,f1,n1,1.e30,1.e30,spline_f1)
do k=1,ml_nz
if ( (ml_p3(i,j,k).gt.pmin).and.
> (ml_p3(i,j,k).lt.pmax) ) then
call splint (p1,f1,spline_f1,n1,ml_p3(i,j,k),hh)
hh = -rdg * ml_tv3(i,j,k) * hh/ml_p3(i,j,k)
ml_z3(i,j,k)=ml_z3(i,j,k) + hh*weight(i,j)
endif
enddo
endif
 
enddo
enddo
 
c ----------------------------------------------------------------
c Remove unrealistic values from final fields
c ----------------------------------------------------------------
 
if ( poisson.ne.1 ) goto 120
 
c Define region for mdv filling
count1 = 0
 
do i=1,ml_nx
do j=1,ml_ny
do k=1,ml_nz
 
c Get neighbour of grid point
il = i-1
if (il.lt.1) il=1
ir = i+1
if ( ir.gt.ml_nx ) ir=ml_nx
jd = j-1
if (jd.lt.1) jd=1
ju = j+1
if ( ju.gt.ml_ny ) ju=ml_ny
 
c Set flag 2 for boundary and exterior points
if ( (abs(zm_rlat(il, j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir, j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i , j)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(il,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i ,ju)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(il,jd)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(ir,jd)-zm_mdv).lt.eps).or.
> (abs(zm_rlat(i ,jd)-zm_mdv).lt.eps) )
> then
flag_ml(i,j,k) = 2
 
c Set flag 1 for interior unphysical points
elseif ( ( abs(ml_t3(i,j,k)).gt.500. ).or.
> ( abs(ml_u3(i,j,k)).gt.500. ).or.
> ( abs(ml_v3(i,j,k)).gt.500. ) )
> then
flag_ml(i,j,k) = 1
count1 = count1 + 1
 
c Set flag 0 for interior valid points
else
flag_ml(i,j,k) = 0
endif
 
enddo
enddo
enddo
 
print*,'C MASK UNREALISTIC VALUES FOR T,U,V',count1
 
c Apply mdv filling
print*,'C T (POISSON FILLING)'
call mdvfill(ml_t3,ml_t3,flag_ml,ml_nx,ml_ny,ml_nz,10)
print*,'C U (POISSON FILLING)'
call mdvfill(ml_u3,ml_u3,flag_ml,ml_nx,ml_ny,ml_nz,10)
print*,'C V (POISSON FILLING)'
call mdvfill(ml_v3,ml_v3,flag_ml,ml_nx,ml_ny,ml_nz,10)
 
c ----------------------------------------------------------------
c Write modified fields to P file
c ----------------------------------------------------------------
 
c Open output file
call cdfwopn(ml_fn,cdfid,ierr)
if (ierr.ne.0) goto 994
 
c Write surface pressure
isok=0
varname='PS'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_vardim(3)=3
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
ml_vardim(3)=4
endif
call putdat(cdfid,varname,ml_time,0,ml_ps,ierr)
if (ierr.ne.0) goto 994
print*,'W PS ',trim(ml_fn)
 
c Write temperature
isok=0
varname='T'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,0,ml_t3,ierr)
if (ierr.ne.0) goto 994
print*,'W T ',trim(ml_fn)
 
c Write zonal wind
isok=0
varname='U'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,0,ml_u3,ierr)
if (ierr.ne.0) goto 994
print*,'W U ',trim(ml_fn)
 
c Write meridional wind
isok=0
varname='V'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,0,ml_v3,ierr)
if (ierr.ne.0) goto 994
print*,'W V ',trim(ml_fn)
 
c Write geopotential height
isok=0
varname='Z'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,0,ml_z3,ierr)
if (ierr.ne.0) goto 994
print*,'W Z ',trim(ml_fn)
 
c Filter matrix (only in test mode)
if (test.eq.1) then
isok=0
varname='DIST'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_vardim(3)=1
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,1,dist,ierr)
if (ierr.ne.0) goto 994
print*,'W DIST ',trim(ml_fn)
 
isok=0
varname='WEIGHT'
call check_varok(isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_vardim(3)=1
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 994
endif
call putdat(cdfid,varname,ml_time,1,weight,ierr)
if (ierr.ne.0) goto 994
print*,'W WEIGHT ',trim(ml_fn)
 
endif
 
c Close output file
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 994
 
c ----------------------------------------------------------------
c Exception handling
c ----------------------------------------------------------------
 
stop
 
998 print*,'Problem with input netcdf file ',trim(ml_fn)
stop
 
997 print*,'Problem with input netcdf file ',trim(zm_fn)
stop
 
994 print*,'Problem with output netcdf file ',trim(ml_fn)
stop
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: AUXILIARY ROUTINES *
c ****************************************************************
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c -------------------------------------------------------------
c Natural cubic spline /from Numerical Recipes)
c -------------------------------------------------------------
 
SUBROUTINE spline(x,y,n,yp1,ypn,y2)
INTEGER n,NMAX
REAL yp1,ypn,x(n),y(n),y2(n)
PARAMETER (NMAX=500)
INTEGER i,k
REAL p,qn,sig,un,u(NMAX)
if (yp1.gt..99e30) then
y2(1)=0.
u(1)=0.
else
y2(1)=-0.5
u(1)=(3./(x(2)-x(1)))*((y(2)-y(1))/(x(2)-x(1))-yp1)
endif
do 11 i=2,n-1
sig=(x(i)-x(i-1))/(x(i+1)-x(i-1))
p=sig*y2(i-1)+2.
y2(i)=(sig-1.)/p
u(i)=(6.*((y(i+1)-y(i))/(x(i+
*1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*
*u(i-1))/p
11 continue
if (ypn.gt..99e30) then
qn=0.
un=0.
else
qn=0.5
un=(3./(x(n)-x(n-1)))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1)))
endif
y2(n)=(un-qn*u(n-1))/(qn*y2(n-1)+1.)
do 12 k=n-1,1,-1
y2(k)=y2(k)*y2(k+1)+u(k)
12 continue
return
END
 
 
SUBROUTINE splint(xa,ya,y2a,n,x,y)
INTEGER n
REAL x,y,xa(n),y2a(n),ya(n)
INTEGER k,khi,klo
REAL a,b,h
klo=1
khi=n
1 if (khi-klo.gt.1) then
k=(khi+klo)/2
if(xa(k).gt.x)then
khi=k
else
klo=k
endif
goto 1
endif
h=xa(khi)-xa(klo)
if (h.eq.0.) pause 'bad xa input in splint'
a=(xa(khi)-x)/h
b=(x-xa(klo))/h
y=a*ya(klo)+b*ya(khi)+((a**3-a)*y2a(klo)+(b**3-b)*y2a(khi))*(h**
*2)/6.
return
END
 
 
c ---------------------------------------------------------
c Spherical distance between two lat/lon points
c ---------------------------------------------------------
 
real function sdis(xp,yp,xq,yq)
c
c calculates spherical distance (in km) between two points given
c by their spherical coordinates (xp,yp) and (xq,yq), respectively.
c
real re
parameter (re=6370.)
real xp,yp,xq,yq,arg
arg=sind(yp)*sind(yq)+cosd(yp)*cosd(yq)*cosd(xp-xq)
if (arg.lt.-1.) arg=-1.
if (arg.gt.1.) arg=1.
sdis=re*acos(arg)
end
 
C -----------------------------------------------------------------
c Rene's KINK function (for smoothing at bounadries)
C -----------------------------------------------------------------
 
real function kink (x,a)
 
implicit none
 
c declaration of parameters
real x,a
 
c parameters
real pi
parameter (pi=3.1415926535)
 
if (x.lt.0.) then
kink=0.
elseif (x.gt.a) then
kink=1.
else
kink=(1.+cos(pi*(x-a)/a))/2.
endif
return
end
 
C -----------------------------------------------------------------
c Rene's KINK function (for smoothing at bounadries)
C -----------------------------------------------------------------
 
subroutine mdvfill (out,inp,flag,nx,ny,nz,maxiter)
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real inp (nx,ny,nz)
real out (nx,ny,nz)
integer flag(nx,ny,nz)
integer maxiter
 
c Parameters
real omega ! Omega fopr SOR
parameter (omega=1.5)
 
c Auxiliary variables
integer i,j,k
integer iter
real tmp0(nx,ny,nz)
real tmp1(nx,ny,nz)
integer il,ir,ju,jd
integer count
real mean(nz)
 
c Calculate mean of variable for all levels
do k=1,nz
mean(k) = 0.
count = 0
do i=1,nx
do j=1,ny
if ( flag(i,j,k).eq.0 ) then
count = count + 1
mean(k) = mean(k) + inp(i,j,k)
endif
enddo
enddo
if ( count.ne.0 ) then
mean(k) = mean(k)/real(count)
else
mean(k) = 0.
endif
enddo
 
c Create first guess
do k=1,nz
do i=1,nx
do j=1,ny
if ( flag(i,j,k).eq.0 ) then
tmp0(i,j,k) = inp(i,j,k)
else
tmp0(i,j,k) = mean(k)
endif
enddo
enddo
enddo
 
c SOR iterations
iter = 0
122 continue
 
c Loop over all points
do k=1,nz
do i=1,nx
do j=1,ny
 
c Apply the updating only for specified points
if ( flag(i,j,k).ne.1 ) goto 121
 
c Get neighbouring points - no handling of periodic domains!
il = i-1
if (il.lt.1) il=1
ir = i+1
if ( ir.gt.nx ) ir=nx
jd = j-1
if (jd.lt.1) jd=1
ju = j+1
if ( ju.gt.ny ) ju=ny
 
c Update field
tmp1(i,j,k) = 0.25 * ( tmp0(il,j,k) + tmp0(ir,j,k) +
> tmp0(i,ju,k) + tmp0(i,jd,k) )
 
tmp0(i,j,k) = omega * tmp1(i,j,k) +
> (1. - omega) * tmp1(i,j,k)
 
c Exit point for loop
121 continue
 
enddo
enddo
enddo
 
c Decide whether further iterations are needed
iter = iter + 1
if ( iter.lt.maxiter) goto 122
 
c Save output
do i=1,nx
do j=1,ny
do k=1,nz
if ( flag(i,j,k).eq.1 ) then
out(i,j,k) = tmp0(i,j,k)
endif
enddo
enddo
enddo
 
end
 
c
Property changes:
Added: svn:executable
/tags/1.0/post/rotate_lalo.f
0,0 → 1,1154
PROGRAM rotate_lalo
 
c *******************************************************************
c * Rotate to a geographical latitude/longitude grid *
c * Michael Sprenger / Autumn 2006 *
c *******************************************************************
 
implicit none
 
c -------------------------------------------------------------------
c Declaration of parameters and variables
c -------------------------------------------------------------------
 
c Specification of input parameters
real clon,clat,rotation
integer nx,ny
real dx,dy,xmin,ymin
integer nfield
character*80 fieldname(100)
 
c Numerical and physical parameters
real degrad
parameter (degrad=0.0174532925)
real omegaerd
parameter (omegaerd=7.292e-5 )
real eps
parameter (eps=0.001)
 
c Variables for input Z file : height level
character*80 in_cfn
real in_varmin(4),in_varmax(4),in_stag(4)
integer in_vardim(4)
real in_mdv
integer in_ndim
integer in_nx,in_ny,in_nz
real in_xmin,in_xmax,in_ymin,in_ymax,in_dx,in_dy
integer in_ntimes
real in_aklev(500),in_bklev(500)
real in_aklay(500),in_bklay(500)
real in_time
real in_pollon,in_pollat
integer in_nvars
character*80 in_vnam(100)
integer in_idate(5)
real,allocatable, dimension (:,:,:) :: in_field3
real,allocatable, dimension (:,:,:) :: in_vect1
real,allocatable, dimension (:,:,:) :: in_vect2
 
c Variables for output Z file : height level
character*80 out_cfn
real out_varmin(4),out_varmax(4),out_stag(4)
integer out_vardim(4)
real out_mdv
integer out_ndim
integer out_nx,out_ny,out_nz
real out_xmin,out_xmax,out_ymin,out_ymax,out_dx,out_dy
integer out_ntimes
real out_aklev(500),out_bklev(500)
real out_aklay(500),out_bklay(500)
real out_time
real out_pollon,out_pollat
integer out_idate(5)
real,allocatable, dimension (:,:,:) :: out_field3
real,allocatable, dimension (:,:,:) :: out_vect1
real,allocatable, dimension (:,:,:) :: out_vect2
real,allocatable, dimension (:,:) :: out_lat,out_lon
real,allocatable, dimension (:,:) :: out_x,out_y
real,allocatable, dimension (:,:) :: out_coriol
 
c Auxiliary variables
integer ifield
integer i,j,k
integer cdfid,cstid
character*80 cfn
integer stat,ierr,isok
real time
character*80 varname,cdfname,varname1,varname2
integer idate(5),stdate(5),datar(14)
integer rotmode
integer i1,i2,i3,i4
integer isvector
real lat
character*80 name
 
c Externals
real sdis
external sdis
 
c -------------------------------------------------------------------
c Preparations
c -------------------------------------------------------------------
print*,'*********************************************************'
print*,'* rotate_lalo *'
print*,'*********************************************************'
 
c Read parameter file
open(10,file='fort.10')
 
read(10,*) in_cfn
read(10,*) out_cfn
 
read(10,*) name,nx
if ( trim(name).ne.'GEO_NX' ) stop
read(10,*) name,ny
if ( trim(name).ne.'GEO_NY' ) stop
read(10,*) name,dx
if ( trim(name).ne.'GEO_DX' ) stop
read(10,*) name,dy
if ( trim(name).ne.'GEO_DY' ) stop
read(10,*) name,xmin
if ( trim(name).ne.'GEO_XMIN') stop
read(10,*) name,ymin
if ( trim(name).ne.'GEO_YMIN') stop
read(10,*) name,clon
if ( trim(name).ne.'CLON' ) stop
read(10,*) name,clat
if ( trim(name).ne.'CLAT' ) stop
read(10,*) name,rotation
if ( trim(name).ne.'CROT' ) stop
read(10,*) nfield
do i=1,nfield
read(10,*) fieldname(i)
enddo
close(10)
print*,clon,clat,rotation
print*,nx,ny,dx,dy,xmin,ymin
print*,trim(in_cfn),' -> ',trim(out_cfn)
 
c Get grid description for input Z file : height level
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,in_nvars,in_vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname=fieldname(1)
call check_varok (isok,varname,in_vnam,in_nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 998
in_nx =in_vardim(1)
in_ny =in_vardim(2)
in_xmin=in_varmin(1)
in_ymin=in_varmin(2)
call getlevs(cstid,in_nz,in_aklev,in_bklev,in_aklay,in_bklay,ierr)
call getgrid(cstid,in_dx,in_dy,ierr)
in_xmax=in_xmin+real(in_nx-1)*in_dx
in_ymax=in_ymin+real(in_ny-1)*in_dy
call gettimes(cdfid,in_time,in_ntimes,ierr)
call getstart(cstid,in_idate,ierr)
call getpole(cstid,in_pollon,in_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Set grid description for output file : height level
out_vardim(1) = nx
out_vardim(2) = ny
out_vardim(3) = in_nz
out_varmin(1) = xmin
out_varmin(2) = ymin
out_varmin(3) = in_varmin(3)
out_varmax(1) = xmin+real(nx-1)*dx
out_varmax(2) = ymin+real(ny-1)*dy
out_varmax(3) = in_varmax(3)
do i=1,in_nz
out_aklay(i) = in_aklay(i)
out_bklay(i) = in_bklay(i)
out_aklev(i) = in_aklev(i)
out_bklev(i) = in_bklev(i)
enddo
out_dx = dx
out_dy = dy
out_time = in_time
out_ntimes = in_ntimes
out_ndim = 4
out_mdv = in_mdv
out_nx = out_vardim(1)
out_ny = out_vardim(2)
out_nz = out_vardim(3)
out_xmin = out_varmin(1)
out_ymin = out_varmin(2)
out_pollon = 0.
out_pollat = 90.
do i=1,5
out_idate(i) = in_idate(i)
enddo
 
c Allocate memory for all fields
allocate(in_field3(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_field3 ***'
allocate(in_vect1(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_vect1 ***'
allocate(in_vect2(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_vect2 ***'
allocate(out_field3(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_field3 ***'
allocate(out_vect1(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_vect1 ***'
allocate(out_vect2(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_vect2 ***'
allocate(out_lat(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_lat ***'
allocate(out_lon(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_lon ***'
allocate(out_x(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_x ***'
allocate(out_y(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_y ***'
allocate(out_coriol(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_coriol ***'
 
c Create constants file and output file (if requested)
datar(1)=out_nx
datar(2)=out_ny
datar(3)=int(1000.*out_varmax(2))
datar(4)=int(1000.*out_varmin(1))
datar(5)=int(1000.*out_varmin(2))
datar(6)=int(1000.*out_varmax(1))
datar(7)=int(1000.*out_dx)
datar(8)=int(1000.*out_dy)
datar(9)=out_nz
datar(10)=1
datar(11)=1
datar(12)=0
datar(13)=int(1000.*out_pollon)
datar(14)=int(1000.*out_pollat)
cfn=trim(out_cfn)//'_cst'
call wricst(cfn,datar,out_aklev,out_bklev,
> out_aklay,out_bklay,out_idate)
call crecdf(trim(out_cfn),cdfid,out_varmin,out_varmax,
> out_ndim,trim(cfn),ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Loop through all fields - rotate to new grid
c -----------------------------------------------------------------
 
do ifield=1,nfield
 
c Check if scalar or vectorial field (X for scalar, U.V for vector)
varname=fieldname(ifield)
i1=1
i2=1
i3=0
i4=0
100 if (varname(i1:i1).eq.' ') then
i1=i1+1
goto 100
endif
i2=i1
101 if ((varname(i2:i2).ne.' ').and.(varname(i2:i2).ne.'.')) then
i2=i2+1
goto 101
endif
if (varname(i2:i2).eq.'.') then
i3=i2+1
102 if (varname(i3:i3).eq.' ') then
i3=i3+1
goto 102
endif
i4=i3
104 if (varname(i4:i4).ne.' ') then
i4=i4+1
goto 104
endif
endif
if ((i3.ne.0).and.(i4.ne.0)) then
isvector=1
i2=i2-1
varname1=varname(i1:i2)
i4=i4-1
varname2=varname(i3:i4)
print*,'Rotating vector : ',
> trim(varname1),' / ',trim(varname2)
else
isvector=0
i2=i2-1
varname=varname(i1:i2)
print*,'Rotating scalar : ',trim(varname)
endif
c Rotate a scalar field
if (isvector.eq.0) then
 
c Read input field
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,in_time,0,in_field3,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Rotate to new coordinate system
out_nz=in_nz
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
 
c Write output scalar field
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
out_vardim(3)=out_nz
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_field3,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
c Rotate vector field
else if (isvector.eq.1) then
c Read input vector field
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname1,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname1,in_time,0,in_vect1,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname2,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname2,in_time,0,in_vect2,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Get new vector component in x direction
out_nz=in_nz
call getenvir (clon,clat,rotation,1,
> in_vect1,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
out_vect1(i,j,k)=out_field3(i,j,k)
enddo
enddo
enddo
call getenvir (clon,clat,rotation,2,
> in_vect2,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
if ( (abs(out_vect1 (i,j,k)-out_mdv).gt.eps).and.
> (abs(out_field3(i,j,k)-out_mdv).gt.eps) ) then
out_vect1(i,j,k)=out_vect1(i,j,k)-
> out_field3(i,j,k)
endif
enddo
enddo
enddo
 
c Get new vector component in y direction
out_nz=in_nz
call getenvir (clon,clat,rotation,2,
> in_vect1,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
out_vect2(i,j,k)=out_field3(i,j,k)
enddo
enddo
enddo
call getenvir (clon,clat,rotation,1,
> in_vect2,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
if ( (abs(out_vect2 (i,j,k)-out_mdv).gt.eps).and.
> (abs(out_field3(i,j,k)-out_mdv).gt.eps) ) then
out_vect2(i,j,k)=out_vect2(i,j,k)+
> out_field3(i,j,k)
endif
enddo
enddo
enddo
 
c Write output vector field
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
out_vardim(3)=out_nz
call putdef(cdfid,varname1,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname1,out_time,0,out_vect1,ierr)
if (ierr.ne.0) goto 997
call putdef(cdfid,varname2,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname2,out_time,0,out_vect2,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
endif
 
enddo
 
c -----------------------------------------------------------------
c Write additional fields: latitude, longitude, Coriolis parameter
c -----------------------------------------------------------------
 
c Open the output file
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Geographical latitude
varname='RLAT'
print*,'Rotating scalar : ',trim(varname)
do i=1,in_nx
do j=1,in_ny
in_field3(i,j,1)=in_ymin+real(j-1)*in_dy
enddo
enddo
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,1,in_mdv,
> out_lat,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,1)
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_lat,ierr)
if (ierr.ne.0) goto 997
 
c Geographical longitude
varname='RLON'
print*,'Rotating scalar : ',trim(varname)
do i=1,in_nx
do j=1,in_ny
in_field3(i,j,1)=in_xmin+real(i-1)*in_dx
enddo
enddo
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,1,in_mdv,
> out_lon,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,1)
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_lon,ierr)
if (ierr.ne.0) goto 997
 
 
 
c Close output file
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Z: Problems with input rotated grid'
stop
 
997 print*,'Z: Problems with output to lat/lon grid'
stop
 
end
 
 
c ********************************************************************************
c * SUBROUTINE: ROTATION TO LATITUDE/LONGITUDE COORDINATE SYSTEM *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Subroutine to get environment of strcof
c --------------------------------------------------------------------------------
 
SUBROUTINE getenvir (clon,clat,rotation,rotmode,
> inar, rdx,rdy,rxmin,rymin,rnx,rny,rnz,mdv,
> outar, dx, dy, xmin, ymin, nx, ny, nz)
 
c Rotate from a local quasi-cartesian coordiante system into lat/lon coordinate
c system.
 
implicit none
 
c Declaration of input parameters
integer rnx,rny,rnz
real rdx,rdy,rxmin,rymin
real inar(rnx,rny,rnz)
real clon,clat,rotation
real mdv
integer rotmode
 
c Declaration of output parameters
integer nx,ny,nz
real dx,dy,xmin,ymin
real outar(nx,ny,nz)
 
c Set numerical and physical constants
real g2r
parameter (g2r=0.0174533)
real pi180
parameter (pi180=3.14159265359/180.)
real eps
parameter (eps=0.0001)
 
 
c Flag for test mode
integer test
parameter (test=0)
character*80 testfile
parameter (testfile='ROTGRID')
 
c Auxiliary variables
real pollon,pollat
integer i,j,k,l
real rlon(nx,ny),rlat(nx,ny)
real rlon1(nx,ny),rlat1(nx,ny)
real lon(nx,ny),lat(nx,ny)
real rotangle1(nx,ny),rotangle2(nx,ny)
real rotangle(nx,ny)
real sinoutar(nx,ny,nz),cosoutar(nx,ny,nz)
real rxmax,rymax
real xind,yind,pind
real outval
integer ix,iy
real ax,ay,az,bx,by,bz,zx,zy,zz
real clon1,clat1,clon2,clat2
real rindx,rindy
integer indx,indy,indr,indu
real frac0i,frac0j,frac1i,frac1j
character*80 cdfname,varname,cstname
real vx1,vx2,vy1,vy2,angle,vx2min
integer s
 
c Externals
real lmtolms,phtophs
external lmtolms,phtophs
 
c Get geographical coordinates
do i=1,nx
do j=1,ny
lon(i,j)=xmin+real(i-1)*dx
lat(i,j)=ymin+real(j-1)*dy
enddo
enddo
 
c First rotation
pollon=clon-180.
if (pollon.lt.-180.) pollon=pollon+360.
pollat=90.-clat
do i=1,nx
do j=1,ny
rlon1(i,j)=lmtolms(lat(i,j),lon(i,j),pollat,pollon)
rlat1(i,j)=phtophs(lat(i,j),lon(i,j),pollat,pollon)
enddo
enddo
 
c Second coordinate transformation
pollon=-180.
pollat=90.+rotation
do i=1,nx
do j=1,ny
rlon(i,j)=90.+lmtolms(rlat1(i,j),rlon1(i,j)-90.,pollat,pollon)
rlat(i,j)=phtophs(rlat1(i,j),rlon1(i,j)-90.,pollat,pollon)
enddo
enddo
 
c Get the angle between the rotated and non-rotated coordinate frame
if ((rotmode.eq.1).or.(rotmode.eq.2)) then
do i=2,nx-1
do j=2,ny-1
c Angle between latitude circles
vx1=1.
vy1=0.
vx2min=(rlon(i+1,j)-rlon(i-1,j))*cos(pi180*rlat(i,j))
do s=-1,1,2
vx2=(rlon(i+1,j)-rlon(i-1,j)+real(s)*360.)*
> cos(pi180*rlat(i,j))
if (abs(vx2).lt.abs(vx2min)) vx2min=vx2
enddo
vx2=vx2min
vy2=rlat(i+1,j)-rlat(i-1,j)
call getangle(vx1,vy1,vx2,vy2,angle)
rotangle1(i,j)=angle
 
c Angle between longitude circles
vx1=0.
vy1=1.
vx2min=(rlon(i,j+1)-rlon(i,j-1))*cos(pi180*rlat(i,j))
do s=-1,1,2
vx2=(rlon(i+1,j)-rlon(i-1,j)+real(s)*360.)*
> cos(pi180*rlat(i,j))
if (abs(vx2).lt.abs(vx2min)) vx2min=vx2
enddo
vx2=vx2min
vy2=rlat(i,j+1)-rlat(i,j-1)
call getangle(vx1,vy1,vx2,vy2,angle)
rotangle2(i,j)=angle
enddo
enddo
 
c Set the angle at the boundaries
do i=1,nx
rotangle1(i,ny)=2.0*rotangle1(i,ny-1)-rotangle1(i,ny-2)
rotangle1(i,1) =2.0*rotangle1(i,2)-rotangle1(i,3)
rotangle2(i,ny)=2.0*rotangle2(i,ny-1)-rotangle2(i,ny-2)
rotangle2(i,1) =2.0*rotangle2(i,2)-rotangle2(i,3)
enddo
do j=1,ny
rotangle1(nx,j)=2.0*rotangle1(nx-1,j)-rotangle1(nx-2,j)
rotangle1(1,j) =2.0*rotangle1(2,j)-rotangle1(3,j)
rotangle2(nx,j)=2.0*rotangle2(nx-1,j)-rotangle2(nx-2,j)
rotangle2(1,j) =2.0*rotangle2(2,j)-rotangle2(3,j)
enddo
c Set the final rotation angle
do i=1,nx
do j=1,ny
rotangle(i,j)=0.5*(rotangle1(i,j)+rotangle2(i,j))
enddo
enddo
 
endif
 
c Bring longitude into domain of geographical grid (shift by 360 deg)
do i=1,nx
do j=1,ny
100 if (rlon(i,j).lt.rxmin) then
rlon(i,j)=rlon(i,j)+360.
goto 100
endif
102 if (rlon(i,j).gt.(rxmin+real(rnx-1)*rdx)) then
rlon(i,j)=rlon(i,j)-360.
goto 102
endif
enddo
enddo
 
c Rotate the scalar or the vector component
do i=1,nx
do j=1,ny
do k=1,nz
 
c Get index
rindx=(rlon(i,j)-rxmin)/rdx+1.
rindy=(rlat(i,j)-rymin)/rdy+1.
indx=int(rindx)
indy=int(rindy)
if ((indx.lt.1).or.(indx.gt.rnx).or.
> (indy.lt.1).or.(indy.gt.rny)) then
outar(i,j,k)=mdv
goto 103
endif
 
c Get inidices of left and upper neighbours
indr=indx+1
if (indr.gt.rnx) indr=1
indu=indy+1
if (indu.gt.rny) indu=ny
c Do linear interpolation
if ( ( abs(inar(indx ,indy, k)-mdv).gt.eps ).and.
& ( abs(inar(indx ,indu, k)-mdv).gt.eps ).and.
& ( abs(inar(indr ,indy, k)-mdv).gt.eps ).and.
& ( abs(inar(indr ,indu, k)-mdv).gt.eps ) ) then
frac0i=rindx-float(indx)
frac0j=rindy-float(indy)
frac1i=1.-frac0i
frac1j=1.-frac0j
outval = inar(indx ,indy, k ) * frac1i * frac1j
& + inar(indx ,indu, k ) * frac1i * frac0j
& + inar(indr ,indy, k ) * frac0i * frac1j
& + inar(indr ,indu, k ) * frac0i * frac0j
else
outval=mdv
endif
 
c Update output array
outar(i,j,k)=outval
 
c Next
103 continue
 
enddo
enddo
enddo
 
c Get components for tests
if (test.eq.1) then
do i=1,nx
do j=1,ny
do k=1,nz
cosoutar(i,j,k)=outar(i,j,k)*cos(pi180*rotangle(i,j))
sinoutar(i,j,k)=-outar(i,j,k)*sin(pi180*rotangle(i,j))
enddo
enddo
enddo
endif
 
c Get correct component of rotated field
do i=1,nx
do j=1,ny
do k=1,nz
if ( abs(outar(i,j,k)-mdv).gt.eps ) then
if (rotmode.eq.1) then
outar(i,j,k)= outar(i,j,k)*cos(pi180*rotangle(i,j))
else if (rotmode.eq.2) then
outar(i,j,k)=-outar(i,j,k)*sin(pi180*rotangle(i,j))
else if (rotmode.eq.0) then
outar(i,j,k)=outar(i,j,k)
endif
endif
enddo
enddo
enddo
 
c Test mode: Write grids to cdf file
if (test.eq.1) then
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLON1'
call writecdf2D(cdfname,cstname,
> varname,rlon1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 1,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLON'
call writecdf2D(cdfname,cstname,
> varname,rlon,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='LON'
call writecdf2D(cdfname,cstname,
> varname,lon,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLAT1'
call writecdf2D(cdfname,cstname,
> varname,rlat1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLAT'
call writecdf2D(cdfname,cstname,
> varname,rlat,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='LAT'
call writecdf2D(cdfname,cstname,
> varname,lat,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='ANGLE1'
call writecdf2D(cdfname,cstname,
> varname,rotangle1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='ANGLE2'
call writecdf2D(cdfname,cstname,
> varname,rotangle2,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='U'
call writecdf2D(cdfname,cstname,
> varname,cosoutar,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='V'
call writecdf2D(cdfname,cstname,
> varname,sinoutar,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
 
endif
 
END
 
 
c --------------------------------------------------------------------------------
c Auxiliary routines: angle between two vectors
c --------------------------------------------------------------------------------
 
SUBROUTINE getangle (vx1,vy1,vx2,vy2,angle)
 
c Given two vectors <vx1,vy1> and <vx2,vy2>, determine the angle (in deg)
c between the two vectors.
 
implicit none
 
c Declaration of subroutine parameters
real vx1,vy1
real vx2,vy2
real angle
 
c Auxiliary variables and parameters
real len1,len2,len3
real val1,val2,val3
real pi
parameter (pi=3.14159265359)
 
len1=sqrt(vx1*vx1+vy1*vy1)
len2=sqrt(vx2*vx2+vy2*vy2)
 
if ((len1.gt.0.).and.(len2.gt.0.)) then
vx1=vx1/len1
vy1=vy1/len1
vx2=vx2/len2
vy2=vy2/len2
 
val1=vx1*vx2+vy1*vy2
val2=-vy1*vx2+vx1*vy2
 
len3=sqrt(val1*val1+val2*val2)
 
if ( (val1.ge.0.).and.(val2.ge.0.) ) then
val3=acos(val1/len3)
else if ( (val1.lt.0.).and.(val2.ge.0.) ) then
val3=pi-acos(abs(val1)/len3)
else if ( (val1.ge.0.).and.(val2.le.0.) ) then
val3=-acos(val1/len3)
else if ( (val1.lt.0.).and.(val2.le.0.) ) then
val3=-pi+acos(abs(val1)/len3)
endif
else
val3=0.
endif
 
angle=180./pi*val3
 
END
 
c --------------------------------------------------------------------------------
c Transformation routine: LMSTOLM and PHSTOPH from library gm2em
c --------------------------------------------------------------------------------
 
REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** LMTOLMS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG1 = - SIN(ZLAM-ZLAMPOL)*COS(ZPHI)
ZARG2 = - ZSINPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL)+ZCOSPOL*SIN(ZPHI)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMTOLMS = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMTOLMS = 90.0
ELSE
LMTOLMS = -90.0
ENDIF
ELSE
LMTOLMS = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
 
 
REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** PHTOPHS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: ROTIERTE BREITE PHIS ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG = ZCOSPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL) + ZSINPOL*SIN(ZPHI)
PHTOPHS = ZRPI18*ASIN(ZARG)
RETURN
END
 
 
c ---------------------------------------------------------
c Spherical distance between two lat/lon points
c ---------------------------------------------------------
 
real function sdis(xp,yp,xq,yq)
c
c calculates spherical distance (in km) between two points given
c by their spherical coordinates (xp,yp) and (xq,yq), respectively.
c
real re
parameter (re=6370.)
real xp,yp,xq,yq,arg
arg=sind(yp)*sind(yq)+cosd(yp)*cosd(yq)*cosd(xp-xq)
if (arg.lt.-1.) arg=-1.
if (arg.gt.1.) arg=1.
sdis=re*acos(arg)
end
 
 
c ********************************************************************************
c * NETCDF INPUT/OUTPUT *
c ********************************************************************************
 
c ---------------------------------------------------------
c Subroutines to write the netcdf output file
c ---------------------------------------------------------
 
subroutine writecdf2D(cdfname,cstname,
> varname,arr,ctime,
> dx,dy,xmin,ymin,nx,ny,
> crefile,crevar)
 
c Create and write to the netcdf file <cdfname>. The variable
c with name <varname> and with time <time> is written. The data
c are in the two-dimensional array <arr>. The list <dx,dy,xmin,
c ymin,nx,ny> specifies the output grid. The flags <crefile> and
c <crevar> determine whether the file and/or the variable should
c be created. 1: create / 0: not created
 
IMPLICIT NONE
 
c Declaration of input parameters
character*80 cdfname,cstname,varname
integer nx,ny
real arr(nx,ny)
real dx,dy,xmin,ymin
integer ctime
integer crefile,crevar
 
c Further variables
real varmin(4),varmax(4),stag(4)
integer ierr,cdfid,ndim,vardim(4)
real mdv
integer datar(14),stdate(5)
integer i
real time
C Definitions
varmin(1)=xmin
varmin(2)=ymin
varmin(3)=1050.
varmax(1)=xmin+real(nx-1)*dx
varmax(2)=ymin+real(ny-1)*dy
varmax(3)=1050.
ndim=4
vardim(1)=nx
vardim(2)=ny
vardim(3)=1
stag(1)=0.
stag(2)=0.
stag(3)=0.
mdv=-999.98999
time=real(ctime)
 
C Create the file
if (crefile.eq.0) then
call cdfwopn(cdfname,cdfid,ierr)
if (ierr.ne.0) goto 906
else if (crefile.eq.1) then
call crecdf(cdfname,cdfid,
> varmin,varmax,ndim,cstname,ierr)
if (ierr.ne.0) goto 903
 
C Write the constants file
datar(1)=vardim(1)
datar(2)=vardim(2)
datar(3)=int(1000.*varmax(2))
datar(4)=int(1000.*varmin(1))
datar(5)=int(1000.*varmin(2))
datar(6)=int(1000.*varmax(1))
datar(7)=int(1000.*dx)
datar(8)=int(1000.*dy)
datar(9)=1
datar(10)=1
datar(11)=0 ! data version
datar(12)=0 ! cstfile version
datar(13)=0 ! longitude of pole
datar(14)=90000 ! latitude of pole
do i=1,5
stdate(i)=0
enddo
call wricst(cstname,datar,0.,0.,0.,0.,stdate)
endif
 
c Write the data to the netcdf file, and close the file
if (crevar.eq.1) then
call putdef(cdfid,varname,ndim,mdv,
> vardim,varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 904
endif
call putdat(cdfid,varname,time,0,arr,ierr)
if (ierr.ne.0) goto 905
call clscdf(cdfid,ierr)
 
return
c Error handling
903 print*,'*** Problem to create netcdf file ***'
stop
904 print*,'*** Problem to write definition ***'
stop
905 print*,'*** Problem to write data ***'
stop
906 print*,'*** Problem to open netcdf file ***'
stop
 
END
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/coastline.dat
0,0 → 1,61632
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
-91.383413 0.147851
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-999. -999.
-91.526570 -0.051630
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-999. -999.
-157.343561 2.013585
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-999. -999.
-162.079475 5.937493
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-999. -999.
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-999. -999.
170.884800 8.861649
170.950511 8.849915
170.950511 8.828794
170.962245 8.807672
171.006835 8.795938
171.072547 8.763082
171.117137 8.718493
171.171114 8.643394
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171.060813 8.500237
170.995101 8.554214
170.938777 8.587070
170.894187 8.652781
170.861332 8.718493
170.840210 8.763082
170.840210 8.817060
170.828476 8.849915
170.851944 8.861649
170.884800 8.861649
-999. -999.
172.860835 1.891549
172.881957 1.879815
172.881957 1.868081
172.926546 1.835225
172.959402 1.724924
172.959402 1.602888
172.971136 1.501974
173.015726 1.415142
173.048582 1.325962
173.048582 1.281372
172.959402 1.269638
172.905425 1.358818
172.905425 1.447997
172.905425 1.534830
172.905425 1.635744
172.881957 1.769514
172.860835 1.868081
172.860835 1.891549
-999. -999.
163.112082 5.364865
163.133203 5.353131
163.133203 5.332009
163.058105 5.308541
163.001781 5.296807
162.990047 5.341397
163.013515 5.364865
163.067492 5.364865
163.112082 5.364865
-999. -999.
166.909261 9.288773
166.942117 9.309895
166.953851 9.277039
167.031297 9.277039
167.087621 9.265305
167.162719 9.265305
167.240165 9.255918
167.317611 9.309895
167.395056 9.333363
167.439646 9.300508
167.505357 9.169085
167.582803 9.070518
167.639127 8.993072
167.660248 8.894505
167.671983 8.784204
167.627393 8.697371
167.561681 8.741961
167.538213 8.849915
167.505357 8.939095
167.463114 8.993072
167.362200 9.079905
167.240165 9.157351
167.141598 9.157351
167.087621 9.169085
166.998441 9.190206
166.899874 9.255918
166.888140 9.300508
166.909261 9.288773
-999. -999.
169.549451 5.993817
169.537717 6.003204
169.493127 5.993817
169.493127 6.014938
169.549451 5.993817
169.549451 5.993817
-999. -999.
152.126547 7.115604
152.171137 7.139072
152.150015 7.127338
152.138281 7.115604
152.126547 7.115604
-999. -999.
153.661377 5.606589
153.640255 5.651179
153.684845 5.639445
153.717701 5.606589
153.705967 5.585468
153.673111 5.585468
153.661377 5.606589
-999. -999.
158.286989 7.005303
158.331579 6.995916
158.387903 6.939591
158.397290 6.873880
158.387903 6.841024
158.343313 6.841024
158.277602 6.873880
158.254133 6.939591
158.265867 6.984181
158.286989 7.005303
-999. -999.
134.729458 7.664764
134.738845 7.699966
134.738845 7.622520
134.738845 7.512219
134.705990 7.390184
134.628544 7.357328
134.595688 7.455895
134.607422 7.577931
134.628544 7.610786
134.694255 7.655376
134.729458 7.664764
-999. -999.
138.240323 9.584475
138.240323 9.572740
138.273179 9.572740
138.282566 9.528151
138.240323 9.507029
138.216855 9.539885
138.240323 9.584475
-999. -999.
123.368429 10.215773
123.246394 9.988130
123.192416 9.844973
123.180682 9.725285
123.168948 9.605596
123.192416 9.462439
123.237006 9.342751
123.225272 9.136229
123.058647 9.037662
122.903756 9.190206
122.793454 9.354485
122.673766 9.408462
122.539996 9.528151
122.429695 9.704163
122.486019 9.943540
122.563465 9.964662
-999. -999.
125.687102 10.161796
125.698836 9.997518
125.719958 9.856708
125.687102 9.812118
125.654246 9.943540
-999. -999.
126.018006 9.997518
126.071983 9.901297
126.107186 9.868442
126.116573 9.790996
126.071983 9.812118
126.006272 9.889563
126.018006 9.997518
-999. -999.
123.699333 10.020986
123.633621 9.889563
123.544442 9.692429
123.490464 9.518763
123.413019 9.462439
123.368429 9.659573
123.368429 9.856708
-999. -999.
123.833102 9.844973
123.833102 9.868442
123.887080 9.877829
123.985647 9.955275
-999. -999.
124.572355 10.020986
124.572355 9.901297
124.539500 9.844973
124.548887 9.737019
124.504297 9.671308
124.393996 9.638452
124.250839 9.593862
124.107682 9.605596
123.976259 9.617330
123.908201 9.683042
123.854224 9.779262
123.833102 9.844973
-999. -999.
125.421910 9.713551
125.410176 9.746406
125.454765 9.746406
125.499355 9.746406
125.597922 9.737019
125.654246 9.638452
125.719958 9.561006
125.851381 9.495295
125.928826 9.396728
126.029740 9.277039
126.128307 9.265305
126.205753 9.124495
126.316054 8.894505
126.327788 8.795938
126.238608 8.697371
126.161163 8.587070
126.194019 8.554214
126.337175 8.479115
126.348910 8.258513
126.426355 8.181067
126.438089 7.995667
126.447477 7.852510
126.515535 7.721088
126.581246 7.491098
126.581246 7.324472
126.569512 7.148460
126.482679 7.017037
126.370031 6.963060
126.283198 6.819903
126.271464 6.587566
126.271464 6.366964
126.149429 6.477265
126.083717 6.709602
126.071983 6.995916
125.973416 7.139072
125.895970 7.315085
125.818525 7.357328
125.731692 7.270495
125.675368 7.193050
125.576801 7.038159
125.466500 6.852759
125.421910 6.611035
125.543945 6.488999
125.642512 6.301252
125.708224 6.080650
125.698836 5.970349
125.565067 5.761480
125.475887 5.594855
125.344464 5.672301
125.288140 5.892903
125.278753 6.014938
125.123862 5.904637
124.936115 5.871781
124.769490 5.916371
124.572355 6.014938
124.372874 6.125240
124.229718 6.289518
124.131150 6.444409
124.107682 6.632156
124.053705 6.787047
124.009115 7.017037
124.086561 7.106217
124.217983 7.303351
124.217983 7.446508
124.074826 7.622520
123.865958 7.786799
123.699333 7.852510
123.567910 7.840776
123.511586 7.721088
123.424753 7.566196
123.413019 7.467629
123.389551 7.467629
123.290983 7.533341
123.192416 7.533341
123.192416 7.664764
123.082115 7.566196
122.948346 7.446508
122.927224 7.390184
122.915490 7.336207
122.849778 7.500485
122.805189 7.709353
122.662032 7.709353
122.528262 7.566196
122.450817 7.479364
122.385105 7.303351
122.319394 7.160194
122.230214 6.939591
122.119913 6.906736
122.009612 6.930204
121.943900 7.127338
122.000224 7.282229
122.077670 7.533341
122.110525 7.688232
122.152768 7.840776
122.331128 8.040257
122.518875 8.082500
122.673766 8.127090
122.903756 8.192801
122.960080 8.357080
123.091503 8.488503
123.279249 8.587070
123.389551 8.709105
123.478730 8.676249
123.743923 8.577682
123.833102 8.345346
123.743923 8.061379
123.732188 8.016789
123.908201 8.094234
124.131150 8.192801
124.274307 8.488503
124.462054 8.587070
124.593477 8.533093
124.692044 8.652781
124.727247 8.849915
124.814079 8.960217
124.936115 8.927361
125.025295 8.882771
125.112128 8.939095
125.245897 9.004806
125.377320 8.948482
125.466500 9.025928
125.487621 9.169085
125.487621 9.277039
125.475887 9.333363
125.454765 9.462439
125.421910 9.605596
125.421910 9.671308
125.421910 9.713551
-999. -999.
121.833599 6.632156
121.932166 6.709602
122.065936 6.709602
122.253682 6.643890
122.307660 6.587566
122.176237 6.456143
122.000224 6.432675
121.899310 6.533589
121.833599 6.632156
-999. -999.
120.951189 5.871781
120.951189 5.937493
120.984045 6.003204
121.106080 6.036060
121.204647 6.014938
121.347804 5.970349
121.425250 5.949227
121.347804 5.815457
121.183526 5.892903
121.049756 5.860047
120.951189 5.871781
-999. -999.
119.967865 5.186506
120.089900 5.254564
120.221323 5.221708
120.254179 5.144263
120.134490 5.099673
-999. -999.
121.115467 1.325962
121.204647 1.314228
121.314948 1.314228
121.446371 1.302493
121.481574 1.203926
121.601262 1.103013
121.735032 1.081891
121.899310 1.114747
122.009612 1.114747
122.152768 1.103013
122.263070 1.070157
122.417961 1.070157
122.584586 1.025567
122.662032 0.948121
122.748865 0.927000
122.861513 0.882410
122.960080 0.894144
123.091503 0.959856
123.246394 0.980977
123.457609 0.948121
123.621887 0.927000
123.788513 0.903532
123.908201 0.894144
124.164006 0.959856
124.274307 1.058423
124.405730 1.213314
124.548887 1.347083
124.692044 1.436263
124.837548 1.624010
125.025295 1.724924
125.135596 1.713190
125.177839 1.656866
125.213041 1.513709
125.189573 1.370552
125.102740 1.203926
124.957236 1.037301
124.804692 0.882410
124.626333 0.638339
124.450320 0.483448
124.262573 0.361413
124.020849 0.361413
123.797900 0.316823
123.556176 0.305089
123.389551 0.305089
123.192416 0.438858
122.903756 0.492835
122.760599 0.504570
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122.152768 0.459980
121.922779 0.415390
121.767887 0.492835
121.624731 0.504570
121.547285 0.459980
121.368926 0.516304
121.282093 0.504570
121.127202 0.415390
120.906599 0.427124
120.697731 0.459980
120.498250 0.459980
120.331624 0.272233
120.188467 0.028162
-999. -999.
119.956131 0.471714
120.057045 0.682929
120.134490 0.760375
120.265913 0.903532
120.343359 0.903532
120.474781 0.793230
120.608551 0.816699
120.772829 1.004445
120.817419 1.236782
120.927721 1.302493
121.049756 1.325962
121.115467 1.325962
-999. -999.
125.433644 3.717387
125.454765 3.717387
125.520477 3.661063
125.576801 3.541374
125.597922 3.473316
125.642512 3.353627
125.543945 3.541374
125.466500 3.639941
125.433644 3.717387
-999. -999.
126.768993 4.536432
126.834705 4.536432
126.867560 4.447253
126.867560 4.348685
126.891029 4.247772
126.879294 4.071759
126.822970 4.027169
126.813583 4.203182
126.780727 4.402663
126.768993 4.536432
-999. -999.
128.557282 2.654271
128.590137 2.588559
128.644114 2.522848
128.667583 2.433668
128.655849 2.299898
128.655849 2.299898
128.611259 2.201331
128.524426 2.055828
128.336679 2.055828
128.303823 2.189597
128.280355 2.311633
128.292089 2.445402
128.381269 2.555703
128.500957 2.654271
-999. -999.
127.937717 2.222453
127.961185 2.234187
128.015163 2.213066
128.026897 2.112152
127.949451 1.978382
127.872006 1.912671
127.862618 1.846959
127.937717 1.778901
128.005775 1.570033
128.026897 1.415142
128.005775 1.269638
127.949451 1.192192
127.785173 1.025567
127.639669 0.927000
127.651403 0.882410
127.794560 0.849554
127.904861 0.971590
128.059752 1.081891
128.148932 1.248516
128.238112 1.415142
128.402390 1.513709
128.601871 1.525443
128.655849 1.480853
128.723907 1.325962
128.723907 1.093625
128.601871 0.992711
128.446980 0.882410
128.324945 0.804964
128.324945 0.736906
128.512692 0.614871
128.634727 0.549159
128.667583 0.415390
128.723907 0.337944
128.834208 0.260499
128.667583 0.251111
128.500957 0.349678
128.226378 0.406002
128.038631 0.471714
127.949451 0.361413
127.928330 0.061018
-999. -999.
127.749970 -0.269886
127.717115 0.093873
127.695993 0.293354
127.597426 0.537425
127.597426 0.760375
127.552836 0.927000
127.475391 0.992711
127.376823 1.147602
127.397945 1.335349
127.419066 1.347083
127.463656 1.513709
127.552836 1.778901
127.651403 1.957260
127.827416 2.133273
127.937717 2.222453
-999. -999.
109.965654 1.835225
110.108811 1.778901
110.219112 1.757780
110.329413 1.769514
110.451449 1.790635
110.540628 1.757780
110.660317 1.680334
110.815208 1.635744
110.916122 1.635744
111.080400 1.602888
111.124990 1.602888
111.136724 1.614623
111.157846 1.736658
111.214170 1.856347
111.223557 1.924405
111.223557 1.957260
111.247026 2.034706
111.291615 2.133273
111.268147 2.245921
111.247026 2.323367
111.333859 2.389078
111.455894 2.356222
111.479362 2.323367
111.479362 2.532235
111.479362 2.588559
111.512218 2.666005
111.577929 2.764572
111.643641 2.842017
111.721086 2.898341
111.831388 2.910076
111.920567 2.919463
112.019134 2.919463
112.096580 2.954665
112.084846 2.964053
112.084846 2.964053
112.117701 2.975787
112.185760 2.987521
112.251471 2.987521
112.373506 2.987521
112.526051 3.020377
112.648086 3.020377
112.770122 3.032111
112.868689 3.086088
112.990724 3.208124
113.068170 3.285569
113.145615 3.395870
113.199592 3.463929
113.267651 3.529640
113.321628 3.595351
113.377952 3.705653
113.443663 3.806567
113.509375 3.884012
113.586820 3.949724
113.640797 3.982579
113.729977 4.060025
113.807423 4.137470
113.863747 4.238384
113.905990 4.280627
113.941192 4.348685
113.962314 4.426131
113.974048 4.480108
113.983435 4.545820
113.983435 4.569288
114.006904 4.590410
-999. -999.
114.006904 4.590410
114.018638 4.613878
114.039759 4.623265
114.105471 4.634999
114.204038 4.679589
114.293218 4.679589
114.382397 4.691323
114.469230 4.712445
114.603000 4.789890
114.725035 4.888458
114.811868 4.965903
114.901048 5.031615
114.955025 5.076204
114.978493 5.022227
114.999615 4.944782
115.055939 4.933047
115.088795 4.933047
115.133385 4.944782
115.175628 4.944782
115.220217 4.933047
115.243686 4.933047
-999. -999.
115.243686 4.933047
115.276542 4.933047
115.353987 4.944782
115.440820 5.010493
115.530000 5.144263
115.562855 5.186506
115.464288 5.242830
115.419698 5.353131
115.497144 5.475166
115.583977 5.508022
115.661422 5.496288
115.771724 5.508022
115.884372 5.639445
116.004060 5.782602
116.060384 5.904637
116.104974 5.993817
116.114362 6.092384
116.215276 6.214419
116.292721 6.289518
116.367820 6.390432
116.435878 6.444409
116.513324 6.521855
116.567301 6.599300
116.633012 6.718989
116.665868 6.841024
116.743313 6.951326
116.787903 6.939591
116.799638 6.895002
116.799638 6.829290
116.799638 6.697867
116.766782 6.599300
116.766782 6.542976
116.844227 6.632156
116.909939 6.709602
116.963916 6.787047
117.031974 6.930204
117.163397 6.930204
117.207987 6.873880
117.252577 6.754192
117.297167 6.620422
117.351144 6.575832
117.416855 6.542976
117.494301 6.599300
117.571746 6.533589
117.637458 6.477265
117.672660 6.444409
117.705516 6.324721
117.714903 6.235541
117.660926 6.158095
117.660926 6.026673
117.672660 5.916371
117.705516 5.892903
117.771227 5.925759
117.836939 5.916371
117.935506 5.970349
118.036420 5.970349
118.090397 5.883516
118.081010 5.782602
118.003564 5.716890
118.045807 5.672301
118.134987 5.672301
118.245288 5.773214
118.343855 5.749746
118.465890 5.695769
118.609047 5.585468
118.754551 5.484554
118.907095 5.430576
119.019744 5.409455
119.139432 5.374252
119.249733 5.296807
119.273202 5.209974
119.228612 5.120794
119.052599 5.055083
118.930564 4.977637
118.742817 4.900192
118.641903 4.888458
118.543336 4.867336
118.400179 4.944782
118.268756 4.879070
118.245288 4.757035
118.257022 4.700711
118.289878 4.646734
118.400179 4.545820
118.477625 4.524698
118.576192 4.458987
118.599660 4.390929
118.489359 4.369807
118.355589 4.348685
118.245288 4.292361
118.146721 4.271240
118.045807 4.226650
117.926118 4.238384
117.836939 4.271240
117.726637 4.348685
117.705516 4.336951
117.672660 4.247772
117.660926 4.193794
-999. -999.
117.660926 4.193794
117.660926 4.160939
117.637458 4.125736
117.550625 4.071759
117.449711 4.048291
117.595215 3.982579
117.693782 3.884012
117.825204 3.851156
117.825204 3.696265
117.726637 3.639941
117.595215 3.672797
117.562359 3.618820
117.473179 3.607086
117.318288 3.607086
117.240843 3.541374
117.297167 3.452194
117.383999 3.353627
117.461445 3.309038
117.473179 3.240979
117.407468 3.187002
117.449711 3.109557
117.571746 3.020377
117.649192 2.919463
117.714903 2.788040
117.815817 2.633149
117.958974 2.412547
118.045807 2.278777
117.991830 2.189597
117.970708 2.112152
117.926118 2.067562
117.914384 1.990116
117.947240 1.891549
118.113865 1.746045
118.278144 1.591154
118.477625 1.424529
118.677106 1.257904
118.864852 1.103013
118.975154 0.992711
118.975154 0.903532
118.808528 0.849554
118.587926 0.837820
118.465890 0.826086
118.310999 0.870676
118.191311 0.894144
118.102131 1.013833
118.045807 1.070157
118.003564 0.980977
118.069275 0.837820
118.045807 0.793230
117.848673 0.704051
117.714903 0.528038
117.628070 0.370800
117.583480 0.215909
117.583480 0.007041
-999. -999.
119.130045 10.009252
118.951685 9.943540
118.820263 9.856708
118.754551 9.593862
118.543336 9.363872
118.343855 9.211328
118.146721 9.037662
117.926118 8.807672
117.759493 8.676249
117.604602 8.643394
117.494301 8.511971
117.374612 8.411057
117.240843 8.434525
117.297167 8.664515
117.428589 8.894505
117.562359 9.025928
117.825204 9.223062
117.935506 9.244184
118.102131 9.420196
118.268756 9.605596
118.510480 9.844973
-999. -999.
119.878685 4.989371
119.845830 5.031615
119.902154 5.132528
119.967865 5.186506
-999. -999.
120.134490 5.099673
119.979599 5.043349
119.878685 4.989371
-999. -999.
119.791852 -0.049284
119.913888 0.150197
119.913888 0.260499
119.956131 0.471714
-999. -999.
104.049282 1.436263
104.049282 1.525443
104.049282 1.525443
104.037548 1.525443
104.037548 1.546564
104.025814 1.546564
104.016427 1.546564
104.016427 1.558299
103.938981 1.558299
103.816946 1.501974
103.751234 1.370552
103.751234 1.335349
103.870923 1.325962
103.992958 1.358818
104.049282 1.436263
-999. -999.
100.207513 6.444409
100.073744 6.676746
-999. -999.
102.216404 6.190951
102.437007 6.202685
102.559042 6.059528
102.678731 5.925759
102.789032 5.838926
102.922801 5.738012
103.087080 5.618323
103.241971 5.409455
103.385128 5.186506
103.495429 4.977637
103.528285 4.745301
103.528285 4.414397
103.507163 4.193794
103.474308 3.970845
103.495429 3.684531
103.507163 3.496784
103.518898 3.231592
103.629199 2.886607
103.760622 2.799774
103.938981 2.654271
104.037548 2.400812
104.213561 2.055828
104.323862 1.868081
104.279272 1.579420
104.201827 1.447997
104.082138 1.513709
103.938981 1.579420
103.805211 1.647478
103.694910 1.579420
103.650320 1.469119
103.572875 1.403407
103.518898 1.436263
103.673789 1.391673
103.650320 1.391673
103.584609 1.403407
103.518898 1.480853
103.507163 1.501974
103.441452 1.457385
103.230237 1.656866
102.988513 1.802369
102.812500 1.879815
102.547308 2.091030
102.293850 2.189597
102.138958 2.323367
101.906622 2.522848
101.608574 2.731716
101.441948 2.910076
101.409093 3.142412
101.298792 3.374749
101.134513 3.562496
100.946766 3.818301
100.803609 4.006048
100.780141 4.137470
100.669840 4.336951
100.693308 4.602144
100.681574 4.822746
100.538417 4.933047
100.470359 5.120794
100.449237 5.418842
100.437503 5.705156
100.371792 5.949227
100.327202 6.268397
100.249756 6.432675
100.207513 6.444409
-999. -999.
99.909465 9.244184
100.008032 9.058784
100.040888 8.763082
100.130068 8.500237
100.294346 8.324224
100.404647 8.148212
100.470359 7.819655
100.526683 7.512219
100.615862 7.324472
100.625250 7.315085
100.714430 7.258761
100.946766 6.984181
101.265936 6.930204
101.575718 6.895002
101.840910 6.686133
102.061513 6.432675
102.216404 6.190951
-999. -999.
106.630801 10.086697
106.609679 9.988130
-999. -999.
106.499378 10.009252
106.443054 9.910685
106.543968 9.725285
106.478257 9.572740
106.299897 9.638452
106.145006 9.823852
106.013583 9.943540
106.013583 9.737019
106.135619 9.561006
106.145006 9.429584
106.102763 9.375606
106.079295 9.354485
105.903282 9.288773
105.694414 9.201941
105.527788 9.037662
105.340042 8.784204
105.086583 8.598804
104.919958 8.587070
104.887102 8.676249
104.976282 8.751348
104.887102 8.971951
104.842513 9.190206
104.833125 9.396728
104.842513 9.561006
104.865981 9.692429
104.997404 9.868442
-999. -999.
99.885997 3.130678
100.052622 2.942931
100.106599 2.755184
100.228635 2.731716
100.350670 2.698860
100.460971 2.478258
100.604128 2.323367
100.714430 2.213066
100.824731 2.133273
100.923298 2.091030
100.935032 2.168476
100.979622 2.255309
101.155635 2.255309
101.277670 2.168476
101.364503 2.013585
101.399705 1.912671
101.441948 1.823491
101.477151 1.769514
101.519394 1.736658
101.608574 1.692068
101.697753 1.656866
101.796321 1.647478
101.862032 1.614623
102.005189 1.525443
102.094369 1.492587
102.171814 1.403407
102.216404 1.325962
102.282115 1.203926
102.359561 1.159337
102.371295 1.293106
102.371295 1.358818
102.446394 1.314228
102.535574 1.180458
102.669343 1.081891
102.821888 1.093625
103.021368 1.103013
103.164525 1.025567
103.209115 0.971590
103.187994 0.927000
103.176260 0.870676
103.122282 0.804964
103.042490 0.804964
103.065958 0.682929
103.098814 0.605483
103.110548 0.605483
103.131670 0.560894
103.131670 0.438858
103.009634 0.361413
102.911067 0.305089
102.889946 0.260499
102.922801 0.239377
103.042490 0.293354
103.164525 0.349678
103.286561 0.438858
103.408596 0.492835
103.507163 0.528038
103.596343 0.471714
103.739500 0.328557
103.816946 0.173666
103.838067 0.072752
-999. -999.
101.817442 1.790635
101.730609 1.802369
101.730609 1.802369
101.697753 1.835225
101.641429 1.856347
101.596840 1.912671
101.552250 1.968995
101.542862 2.022972
101.552250 2.067562
101.620308 2.067562
101.697753 2.112152
101.784586 2.133273
101.840910 2.079296
101.894888 2.046440
101.894888 1.945526
101.894888 1.879815
101.873766 1.823491
101.840910 1.802369
101.817442 1.790635
-999. -999.
102.160080 1.668600
102.160080 1.668600
102.204670 1.668600
102.303237 1.624010
102.371295 1.635744
102.458128 1.624010
102.523839 1.614623
102.580163 1.447997
102.601285 1.370552
102.580163 1.347083
102.547308 1.391673
102.469862 1.447997
102.371295 1.480853
102.270381 1.534830
102.192936 1.614623
102.160080 1.668600
-999. -999.
104.666500 1.171071
104.743945 1.114747
104.765067 1.004445
104.732211 0.894144
104.645378 0.882410
104.600789 0.992711
104.544464 1.070157
104.457632 1.070157
104.424776 1.180458
104.445897 1.213314
104.535077 1.225048
104.621910 1.203926
104.666500 1.171071
-999. -999.
109.623016 2.055828
109.679340 2.100417
109.723930 2.123886
109.745051 2.055828
109.777907 1.957260
109.843618 1.879815
109.965654 1.835225
-999. -999.
109.202932 -0.082139
109.193545 0.138463
109.092631 0.316823
109.026920 0.382534
109.005798 0.483448
108.994064 0.638339
108.994064 0.816699
109.005798 0.927000
109.017532 1.058423
109.059775 1.225048
109.127833 1.415142
109.202932 1.579420
109.336702 1.724924
109.458737 1.945526
109.557304 2.001850
109.623016 2.055828
-999. -999.
100.073744 6.676746
99.930587 6.819903
99.787430 6.972447
99.686516 7.225905
99.477647 7.413652
99.313369 7.655376
99.212455 7.807920
99.102154 7.864245
98.926141 8.040257
98.738394 8.258513
98.550648 8.246779
98.384022 8.225657
98.330045 8.389936
98.330045 8.664515
98.362901 8.981338
98.440346 9.255918
98.527179 9.551619
98.616359 9.812118
98.639827 9.964662
-999. -999.
99.191334 10.009252
99.224189 9.704163
99.268779 9.396728
99.322756 9.244184
99.501116 9.201941
99.731106 9.288773
99.909465 9.244184
-999. -999.
98.384022 8.115356
98.339432 8.105969
98.339432 7.939343
98.384022 7.840776
98.484936 7.929956
98.494324 8.049644
98.419225 8.148212
98.384022 8.115356
-999. -999.
93.847590 7.282229
93.758410 7.303351
93.680965 7.204784
93.680965 7.028771
93.749023 6.829290
93.859324 6.951326
93.892180 7.181315
93.859324 7.315085
93.758410 7.303351
-999. -999.
95.326096 5.606589
95.326096 5.594855
95.370686 5.606589
95.436397 5.606589
95.492721 5.630057
95.504456 5.630057
95.525577 5.630057
95.537311 5.630057
95.546699 5.630057
95.614757 5.630057
95.725058 5.630057
95.835359 5.606589
95.933926 5.552612
96.011372 5.442311
96.077083 5.341397
96.210853 5.332009
96.321154 5.320275
96.431455 5.263951
96.562878 5.263951
96.661445 5.254564
96.816336 5.275685
96.982962 5.287420
97.137853 5.275685
97.313865 5.186506
97.534468 5.198240
97.689359 5.165384
97.820782 5.055083
97.975673 4.933047
98.053119 4.801625
98.064853 4.691323
98.130564 4.590410
98.264334 4.512964
98.362901 4.348685
98.395756 4.292361
98.440346 4.170326
98.527179 4.092880
98.672683 3.982579
98.759516 3.872278
98.881551 3.750243
99.090420 3.661063
99.289901 3.562496
99.510503 3.463929
99.644273 3.330159
99.885997 3.130678
-999. -999.
99.963442 -0.147851
99.864875 0.028162
99.721718 0.138463
99.543359 0.251111
99.411936 0.251111
99.379080 0.260499
99.355612 0.293354
99.301635 0.483448
99.268779 0.671195
99.212455 0.849554
99.146744 1.070157
99.057564 1.281372
98.937875 1.501974
98.937875 1.692068
98.792372 1.868081
98.604625 2.046440
98.419225 2.145007
98.252600 2.234187
98.076587 2.299898
97.855984 2.332754
97.799660 2.522848
97.755070 2.710595
97.701093 2.898341
97.567324 2.942931
97.557936 2.987521
97.513346 3.053233
97.424167 3.142412
97.334987 3.297303
97.215298 3.473316
97.027552 3.651675
96.884395 3.740855
96.696648 3.740855
96.508901 3.916868
96.354010 4.104615
96.231974 4.214916
96.065349 4.315830
95.901071 4.491842
95.790769 4.613878
95.647613 4.768769
95.546699 4.900192
95.459866 5.066817
95.382420 5.231096
95.370686 5.332009
95.370686 5.418842
95.358952 5.552612
95.326096 5.606589
-999. -999.
95.868215 2.809162
95.844747 2.865486
95.879949 2.877220
95.922192 2.919463
96.055962 2.832630
96.199119 2.731716
96.342276 2.644883
96.476045 2.543969
96.530023 2.445402
96.551144 2.377344
96.530023 2.367957
96.407987 2.478258
96.231974 2.532235
96.077083 2.621415
95.945661 2.698860
95.868215 2.809162
-999. -999.
97.302131 1.403407
97.292744 1.457385
97.334987 1.480853
97.424167 1.513709
97.501612 1.546564
97.644769 1.415142
97.755070 1.257904
97.855984 1.171071
98.031997 1.025567
98.041384 0.971590
98.041384 0.870676
98.053119 0.760375
98.053119 0.694663
98.008529 0.614871
97.909962 0.614871
97.820782 0.793230
97.743336 0.903532
97.644769 0.980977
97.534468 1.081891
97.424167 1.248516
97.370189 1.314228
97.334987 1.370552
97.302131 1.403407
-999. -999.
80.024731 9.812118
80.024731 9.812118
-999. -999.
79.926164 9.746406
80.048199 9.650186
80.203091 9.584475
80.278189 9.462439
80.191356 9.474173
80.081055 9.354485
80.048199 9.112761
-999. -999.
79.893308 6.510121
80.048199 6.202685
80.212478 6.014938
80.510526 5.958614
80.754597 5.958614
80.951731 6.059528
81.240392 6.223807
81.526706 6.423288
81.735574 6.718989
81.791898 7.160194
81.813019 7.533341
81.780164 7.688232
81.658128 7.732822
81.571295 7.951077
81.482116 8.225657
81.371814 8.455647
81.240392 8.565948
81.195802 8.676249
81.195802 8.697371
81.130090 8.807672
81.106622 8.817060
81.040911 8.894505
80.918875 9.004806
80.853164 9.190206
80.665417 9.408462
80.501139 9.584475
80.334513 9.737019
80.179622 9.802730
80.024731 9.812118
-999. -999.
79.186911 10.096085
79.154055 9.964662
79.032020 9.802730
78.900597 9.617330
78.877129 9.441318
78.888863 9.321629
78.900597 9.265305
78.787949 9.244184
78.590815 9.223062
78.391334 9.136229
78.182465 9.025928
78.149610 8.960217
78.126141 8.849915
78.048696 8.652781
78.072164 8.577682
78.027574 8.479115
77.917273 8.368814
77.839828 8.324224
77.795238 8.303103
77.795238 8.258513
77.640347 8.115356
77.330564 8.105969
77.100574 8.303103
76.835382 8.631660
76.603045 8.981338
76.481010 9.232449
76.337853 9.746406
-999. -999.
80.024731 9.812118
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-155.752407 20.044319
-155.665574 19.980954
-155.564660 19.980954
-155.477827 19.950445
-155.344058 19.898815
-155.233756 19.856572
-155.189167 19.826063
-155.135189 19.762699
-155.090599 19.689947
-155.069478 19.659438
-155.024888 19.638316
-154.980298 19.617195
-154.923974 19.544443
-154.881731 19.481078
-154.813673 19.429448
-154.780817 19.323840
-154.792551 19.283944
-154.869997 19.136094
-154.959177 19.157215
-155.123455 19.168949
-155.257225 19.136094
-155.376913 19.051608
-155.388648 19.042220
-155.487215 18.927225
-155.520070 18.842739
-155.609250 18.769987
-155.743020 18.842739
-155.818118 18.978856
-155.853321 19.126706
-155.886177 19.356696
-155.940154 19.492813
-155.951888 19.617195
-155.841587 19.804942
-155.829853 19.919937
-999. -999.
166.489178 19.366083
166.489178 19.356696
166.500912 19.344962
166.500912 19.323840
166.489178 19.344962
166.489178 19.366083
166.500912 19.323840
166.489178 19.344962
166.489178 19.366083
-999. -999.
166.888140 11.415006
166.920995 11.436128
166.953851 11.436128
167.019562 11.447862
167.064152 11.403272
167.031297 11.370416
166.965585 11.316439
166.920995 11.217872
166.855284 11.142773
166.754370 11.154507
166.700393 11.208485
166.700393 11.295317
166.721514 11.361029
166.787226 11.415006
166.843550 11.415006
166.888140 11.415006
-999. -999.
145.360621 20.013810
145.348887 19.971567
145.316031 19.950445
145.292563 19.992688
-999. -999.
145.888659 18.138689
145.923861 18.171544
145.933249 18.159810
145.900393 18.087058
145.867537 18.075324
145.855803 18.087058
145.855803 18.096446
145.855803 18.108180
145.879272 18.117567
145.879272 18.129301
145.888659 18.129301
145.888659 18.138689
-999. -999.
145.790092 15.017398
145.822948 15.050254
145.822948 14.996276
145.768970 14.975155
145.724380 14.975155
145.712646 15.017398
145.757236 15.050254
145.790092 15.038520
145.790092 15.017398
-999. -999.
144.952272 13.513077
145.006249 13.513077
144.985127 13.449712
144.907682 13.405122
144.895948 13.374613
144.884214 13.287780
144.806768 13.254925
144.752791 13.330024
144.764525 13.374613
144.818502 13.437978
144.874826 13.470834
144.928803 13.513077
144.952272 13.513077
-999. -999.
119.946743 11.891414
120.000721 11.858558
120.057045 11.795193
120.045311 11.741216
120.000721 11.696626
-999. -999.
119.967865 12.227011
120.045311 12.163646
120.101635 12.151912
120.176733 12.163646
120.244791 12.076814
120.254179 12.032224
120.200202 12.032224
120.111022 12.022836
120.012455 12.086201
-999. -999.
120.376214 13.416856
120.355093 13.470834
120.420804 13.480221
120.542840 13.480221
120.697731 13.470834
120.850275 13.470834
120.927721 13.480221
121.028634 13.459099
121.192913 13.416856
121.347804 13.287780
121.425250 13.179826
121.490961 13.168092
121.514429 12.963917
121.502695 12.780864
121.535551 12.682297
121.556672 12.574343
121.490961 12.508631
121.481574 12.367821
121.392394 12.292722
121.225769 12.184768
121.148323 12.325578
121.005166 12.445267
120.927721 12.607198
120.817419 12.823107
120.796298 13.039016
120.697731 13.189213
120.575695 13.254925
120.519371 13.395735
120.432538 13.428591
120.376214 13.416856
-999. -999.
122.253682 18.422656
122.319394 18.371025
122.331128 18.307661
122.263070 18.213787
122.187971 18.011960
122.152768 17.833600
122.152768 17.622385
122.164503 17.441679
122.253682 17.326684
122.340515 17.284441
122.385105 17.188220
122.474285 17.082613
122.474285 16.913641
122.385105 16.690691
122.274804 16.479476
122.230214 16.298770
122.131647 16.106329
122.033080 16.031231
122.009612 16.073474
121.845333 15.977254
121.711563 15.871646
121.612996 15.712061
121.601262 15.552476
121.523817 15.369423
121.404128 15.296671
121.425250 15.134740
121.502695 14.954033
121.591875 14.792102
121.678708 14.695882
121.624731 14.611396
121.634118 14.416608
121.711563 14.266411
121.735032 14.116213
121.845333 14.019993
122.000224 13.890917
122.098791 13.879183
122.241948 13.933160
122.209093 14.008259
122.230214 14.181925
122.286538 14.149069
122.441429 14.287532
122.629176 14.266411
122.716009 14.332122
122.849778 14.287532
122.971814 14.170191
123.058647 13.977750
123.082115 13.804084
123.168948 13.728986
123.279249 13.836940
123.258128 14.029380
123.356695 13.998872
123.413019 13.954282
123.577297 13.912039
123.711067 13.846327
123.842490 13.794697
123.887080 13.707864
123.732188 13.686742
123.589032 13.567054
123.621887 13.428591
123.743923 13.330024
123.854224 13.297168
123.797900 13.158705
123.821368 13.092993
123.908201 13.092993
123.908201 13.081259
123.919935 13.081259
123.931669 13.039016
124.030237 13.017894
124.107682 12.942796
124.107682 12.790251
124.107682 12.607198
124.020849 12.508631
123.887080 12.628320
123.833102 12.769130
123.908201 12.823107
123.964525 12.865350
123.887080 12.888819
123.666477 12.877084
123.478730 13.017894
123.344961 13.060137
123.279249 13.266659
123.168948 13.416856
122.971814 13.513077
122.870900 13.611644
122.838044 13.675008
122.673766 13.836940
122.486019 13.890917
122.507141 13.663274
122.605708 13.459099
122.694887 13.266659
122.694887 13.200948
122.596320 13.212682
122.486019 13.416856
122.319394 13.545932
122.176237 13.696130
122.077670 13.794697
121.922779 13.879183
121.800743 13.912039
121.591875 13.890917
121.490961 13.707864
121.347804 13.621031
121.183526 13.611644
121.094346 13.707864
120.960576 13.740720
120.829153 13.846327
120.730586 13.782963
120.662528 13.944894
120.641407 14.127947
120.697731 14.266411
120.829153 14.395487
120.927721 14.536297
120.918333 14.653639
120.808032 14.738125
120.629672 14.749859
120.608551 14.491707
120.563961 14.407221
120.420804 14.566806
120.322237 14.749859
120.200202 14.759246
120.101635 15.050254
120.057045 15.306059
-999. -999.
119.967865 16.211937
120.134490 16.042965
120.355093 16.106329
120.343359 16.392643
120.322237 16.636714
120.355093 16.901907
120.432538 17.157712
120.432538 17.462800
120.409070 17.676362
120.432538 17.906352
120.474781 18.117567
120.498250 18.295927
120.596817 18.464899
120.718852 18.601015
120.829153 18.579894
121.038022 18.579894
121.270358 18.528263
121.481574 18.401534
121.666974 18.307661
121.878189 18.295927
122.009612 18.338170
122.042467 18.528263
122.176237 18.537651
122.230214 18.476633
122.253682 18.422656
-999. -999.
121.889923 14.996276
121.899310 15.071375
122.000224 15.038520
122.009612 14.921178
122.021346 14.749859
122.021346 14.684147
121.932166 14.663026
121.911044 14.813223
121.889923 14.930565
121.889923 14.996276
122.000224 15.038520
-999. -999.
121.866455 13.320636
121.821865 13.362879
121.821865 13.384001
121.833599 13.503689
121.932166 13.503689
122.021346 13.524811
122.087057 13.470834
122.119913 13.374613
122.098791 13.266659
122.077670 13.200948
121.965022 13.200948
121.889923 13.287780
121.866455 13.320636
-999. -999.
121.988490 12.445267
122.000224 12.508631
122.009612 12.607198
122.098791 12.607198
122.098791 12.412411
122.077670 12.205890
122.021346 12.130791
121.976756 12.238745
121.988490 12.445267
-999. -999.
122.441429 12.445267
122.450817 12.478122
122.474285 12.478122
122.551730 12.466388
122.629176 12.412411
122.662032 12.358434
122.662032 12.304457
122.563465 12.337312
122.450817 12.358434
122.441429 12.445267
-999. -999.
123.004670 13.114115
123.037525 13.135236
123.058647 13.071872
123.103237 13.027282
123.168948 12.942796
123.258128 12.898206
123.290983 12.855963
123.323839 12.801986
123.335573 12.736274
123.302718 12.780864
123.225272 12.790251
123.136092 12.909940
123.058647 12.996773
123.004670 13.060137
123.004670 13.114115
-999. -999.
123.654743 12.628320
123.678211 12.661176
123.699333 12.618932
123.743923 12.508631
123.743923 12.424145
123.722801 12.412411
123.678211 12.520365
123.654743 12.628320
-999. -999.
123.258128 12.562608
123.323839 12.532100
123.344961 12.487510
123.389551 12.466388
123.478730 12.466388
123.589032 12.367821
123.743923 12.250479
123.865958 12.151912
123.985647 12.043958
124.030237 11.924269
124.041971 11.849171
124.041971 11.762338
123.985647 11.783459
123.865958 11.816315
123.711067 11.924269
123.600766 12.109669
123.523320 12.163646
123.389551 12.086201
123.269862 11.968859
123.213538 12.001715
123.246394 12.163646
123.258128 12.238745
123.246394 12.346700
123.258128 12.433533
123.246394 12.508631
123.258128 12.553221
123.258128 12.562608
-999. -999.
124.318897 12.520365
124.318897 12.532100
124.340019 12.532100
124.372874 12.532100
124.483176 12.520365
124.527766 12.508631
124.593477 12.508631
124.781224 12.499244
124.903259 12.553221
125.001826 12.586077
125.112128 12.562608
125.255284 12.478122
125.323343 12.337312
125.475887 12.217624
125.475887 12.151912
125.487621 12.022836
125.466500 11.750603
125.487621 11.567550
125.553333 11.415006
125.597922 11.295317
125.630778 11.208485
125.731692 11.055940
125.630778 11.067674
125.454765 11.055940
125.255284 11.109918
125.177839 11.295317
125.067538 11.337561
124.947849 11.447862
124.936115 11.534695
124.990092 11.675505
124.957236 11.729482
124.804692 11.891414
124.670923 12.011102
124.548887 12.065079
124.429199 12.217624
124.351753 12.391289
124.318897 12.478122
124.318897 12.520365
-999. -999.
121.932166 11.870292
121.976756 11.891414
122.042467 11.870292
122.143381 11.849171
122.230214 11.795193
122.375718 11.684892
122.417961 11.576938
122.528262 11.555816
122.706622 11.544082
122.826310 11.544082
122.861513 11.480717
123.025791 11.522960
123.091503 11.511226
123.103237 11.295317
123.037525 11.088796
122.894368 11.001963
122.748865 10.816563
122.605708 10.708609
122.518875 10.664019
122.363984 10.642897
122.143381 10.556064
122.009612 10.391786
121.955634 10.598307
121.955634 10.828297
122.009612 11.067674
122.033080 11.316439
122.054201 11.567550
122.033080 11.675505
121.932166 11.771725
121.932166 11.870292
-999. -999.
122.650298 10.664019
122.694887 10.642897
122.694887 10.565452
122.683153 10.490353
122.605708 10.434029
122.551730 10.434029
122.551730 10.556064
122.584586 10.631163
122.650298 10.664019
-999. -999.
122.960080 10.828297
123.025791 10.882274
123.147827 10.957373
123.213538 10.924518
123.323839 10.915130
123.499852 10.870540
123.511586 10.717996
123.478730 10.499740
123.389551 10.424642
123.368429 10.215773
-999. -999.
122.563465 9.964662
122.760599 10.042108
122.826310 10.194652
122.826310 10.499740
122.894368 10.664019
122.927224 10.783707
122.960080 10.828297
-999. -999.
124.405730 11.654383
124.417464 11.717748
124.471442 11.684892
124.527766 11.654383
124.548887 11.576938
124.581743 11.534695
124.516031 11.490105
124.483176 11.490105
124.438586 11.576938
124.405730 11.654383
-999. -999.
124.318897 11.490105
124.318897 11.501839
124.361140 11.403272
124.429199 11.337561
124.516031 11.382150
124.605211 11.328173
124.748368 11.349295
124.858669 11.349295
124.990092 11.163895
125.001826 10.957373
125.001826 10.717996
125.091006 10.556064
125.177839 10.337809
125.245897 10.239242
125.123862 10.185264
125.013560 10.227507
124.990092 10.030373
124.858669 10.074963
124.769490 10.260363
124.760102 10.490353
124.769490 10.717996
124.670923 10.924518
124.548887 10.882274
124.471442 10.870540
124.417464 11.077062
124.384609 11.304705
124.340019 11.382150
124.318897 11.480717
124.318897 11.490105
-999. -999.
125.553333 10.161796
125.543945 10.185264
125.543945 10.304953
125.621391 10.466885
125.675368 10.380052
125.687102 10.161796
-999. -999.
125.654246 9.943540
125.586188 10.042108
125.553333 10.161796
-999. -999.
123.997381 11.217872
124.041971 11.241340
124.053705 11.163895
124.030237 11.055940
124.041971 10.849419
124.041971 10.642897
124.020849 10.391786
123.943404 10.314340
123.797900 10.206386
123.699333 10.020986
-999. -999.
123.368429 9.856708
123.434140 10.042108
123.499852 10.206386
123.589032 10.337809
123.687599 10.511475
123.776778 10.717996
123.833102 10.858806
123.887080 11.011350
123.931669 11.163895
123.997381 11.217872
-999. -999.
123.985647 9.955275
124.074826 10.074963
124.206249 10.161796
124.307163 10.119553
124.429199 10.074963
124.572355 10.119553
124.572355 10.020986
-999. -999.
110.883266 20.034931
110.948978 19.814329
110.958365 19.680559
110.782352 19.523321
110.650929 19.283944
110.550016 19.105585
110.496038 18.915491
110.451449 18.800496
110.308292 18.697235
110.141666 18.537651
110.064221 18.455511
-999. -999.
119.449214 11.337561
119.503192 11.382150
119.526660 11.349295
119.526660 11.217872
119.538394 11.109918
119.571250 11.044206
119.514926 10.947986
119.526660 10.804829
119.571250 10.664019
119.604106 10.544330
119.559516 10.424642
119.392890 10.314340
119.282589 10.152409
119.130045 10.009252
-999. -999.
118.510480 9.844973
118.665371 10.030373
118.763939 10.086697
118.874240 10.260363
119.019744 10.370664
119.151166 10.424642
119.216878 10.532596
119.282589 10.664019
119.273202 10.771973
119.273202 10.849419
119.317792 10.762586
119.383503 10.816563
119.360035 10.882274
119.282589 10.947986
119.327179 11.001963
119.383503 11.142773
119.404625 11.295317
119.449214 11.337561
-999. -999.
119.878685 11.924269
119.890419 11.924269
119.946743 11.891414
-999. -999.
120.000721 11.696626
119.946743 11.741216
119.913888 11.816315
119.878685 11.882026
119.878685 11.924269
-999. -999.
119.913888 12.292722
119.890419 12.283335
119.967865 12.227011
-999. -999.
120.012455 12.086201
119.946743 12.250479
119.913888 12.292722
-999. -999.
120.057045 15.306059
119.988986 15.465643
119.923275 15.712061
119.857564 15.892767
119.803586 16.202550
119.812974 16.265914
119.967865 16.211937
-999. -999.
102.988513 11.642649
102.833622 11.717748
102.779644 11.828049
102.690465 12.065079
102.601285 12.119057
102.568429 12.076814
102.469862 12.151912
102.336093 12.205890
102.216404 12.367821
102.082634 12.466388
101.894888 12.640054
101.707141 12.682297
101.531128 12.649441
101.343381 12.670563
101.101657 12.682297
101.000743 12.670563
101.057067 12.607198
100.979622 12.618932
100.923298 12.748008
100.935032 12.985039
100.946766 13.179826
100.967888 13.384001
100.913911 13.480221
100.714430 13.534198
100.526683 13.557667
100.350670 13.534198
100.240369 13.534198
100.008032 13.449712
100.052622 13.243191
100.073744 13.039016
100.029154 12.769130
-999. -999.
104.490487 10.466885
104.389573 10.490353
104.335596 10.544330
104.237029 10.598307
104.091525 10.610042
103.927247 10.631163
103.784090 10.556064
103.605730 10.565452
103.605730 10.762586
103.694910 10.882274
103.662054 11.055940
103.551753 11.121652
103.462573 11.077062
103.375741 10.924518
103.209115 10.891662
103.131670 11.109918
103.054224 11.349295
103.054224 11.403272
103.122282 11.337561
103.110548 11.424393
103.033103 11.534695
102.955657 11.609793
102.955657 11.675505
102.955657 11.663771
102.988513 11.642649
-999. -999.
107.050884 17.030983
107.128330 16.967618
107.262100 16.796299
107.426378 16.681304
107.581269 16.542841
107.712692 16.350400
107.912173 16.308157
108.022474 16.298770
108.099920 16.190816
108.123388 16.148573
108.123388 16.115717
108.132775 16.064086
108.243077 16.073474
108.243077 16.139185
108.254811 16.139185
108.254811 16.085208
108.287667 15.892767
108.397968 15.721449
108.564593 15.573598
108.684282 15.456256
108.806317 15.327180
108.872028 15.092497
108.961208 14.857813
109.038654 14.632517
109.104365 14.407221
109.137221 14.149069
109.170077 13.900304
109.202932 13.836940
109.202932 13.815818
109.202932 13.663274
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109.226401 13.437978
109.226401 13.320636
109.247522 13.179826
109.247522 13.039016
109.315580 12.996773
109.336702 12.834841
109.348436 12.682297
109.348436 12.640054
109.348436 12.703419
109.270990 12.726887
109.202932 12.628320
109.214666 12.499244
109.214666 12.424145
109.148955 12.478122
109.127833 12.412411
109.170077 12.227011
109.202932 12.001715
109.202932 11.914882
109.160689 11.924269
109.127833 11.858558
109.181811 11.795193
109.170077 11.684892
109.116099 11.654383
109.059775 11.598059
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108.827439 11.316439
108.707750 11.196750
108.573980 11.142773
108.275932 11.001963
108.144510 10.936252
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107.745548 10.664019
107.569535 10.565452
107.438112 10.478619
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107.172920 10.412907
107.050884 10.466885
106.895993 10.434029
106.797426 10.401173
106.741102 10.281485
106.675391 10.227507
106.698859 10.074963
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-999. -999.
106.609679 9.988130
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-999. -999.
104.997404 9.868442
105.063115 10.030373
104.952814 10.140675
104.809657 10.194652
104.621910 10.260363
104.490487 10.466885
-999. -999.
106.168474 20.053706
105.968993 19.877694
105.858692 19.647704
105.760125 19.417714
105.727269 19.199458
105.659211 19.032833
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105.727269 18.579894
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106.091029 18.234909
106.299897 18.108180
106.400811 17.854722
106.433667 17.634119
106.642535 17.474534
106.797426 17.284441
106.961705 17.167099
107.050884 17.030983
-999. -999.
110.064221 18.455511
109.855352 18.401534
109.756785 18.265418
109.712195 18.192666
109.613628 18.213787
109.524449 18.274805
109.369558 18.317048
109.160689 18.380413
108.839173 18.464899
108.684282 18.676114
108.663160 18.957734
108.651426 19.126706
108.651426 19.302719
108.761727 19.387205
108.994064 19.617195
109.170077 19.741577
109.193545 19.804942
109.315580 19.887081
109.536183 19.980954
109.723930 19.992688
109.932798 19.992688
-999. -999.
104.004692 10.445763
104.091525 10.347196
104.103259 10.206386
104.082138 10.107819
103.981224 10.215773
103.927247 10.326075
103.927247 10.391786
104.004692 10.445763
-999. -999.
98.571769 10.173530
98.538913 10.314340
98.562382 10.544330
98.628093 10.783707
98.804106 11.217872
98.804106 11.415006
98.848696 11.576938
98.869817 11.729482
98.792372 11.771725
98.672683 11.837436
98.538913 11.936003
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98.682070 12.217624
98.717273 12.466388
98.682070 12.694031
98.639827 12.942796
98.571769 13.092993
98.428612 13.416856
98.351167 13.750107
98.273721 13.686742
98.229131 13.611644
98.142298 13.890917
98.053119 14.308654
97.942817 14.587927
97.844250 14.954033
97.766805 15.390545
97.733949 15.754304
97.701093 16.064086
97.710481 16.211937
97.710481 16.413765
97.701093 16.413765
97.710481 16.425499
97.710481 16.509985
97.579058 16.542841
97.358455 16.648448
97.182443 16.796299
97.036939 16.955884
96.917250 16.901907
96.828071 17.242198
96.738891 17.432291
96.738891 17.094347
96.652058 16.702426
96.398600 16.552228
96.121673 16.425499
95.922192 16.254180
95.725058 16.127451
95.546699 15.977254
95.358952 15.766038
95.272119 15.838790
95.150083 15.829403
95.060904 15.925623
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94.488276 15.977254
94.553987 16.127451
94.377975 16.010109
94.267673 16.052352
94.267673 16.073474
94.267673 16.031231
94.288795 16.169694
94.312263 16.362135
94.387362 16.606205
94.443686 16.892519
94.553987 17.178833
94.553987 17.537899
94.500010 17.803091
94.464808 18.065937
94.387362 18.202053
94.377975 18.328782
94.267673 18.537651
94.145638 18.727744
94.002481 18.936613
93.936770 19.126706
93.880446 18.906104
93.680965 19.011711
93.561276 19.241701
93.615253 19.387205
93.824122 19.302719
93.791266 19.398939
93.648109 19.492813
93.704433 19.596073
93.680965 19.701681
93.472096 19.804942
-999. -999.
98.639827 9.964662
98.571769 10.173530
-999. -999.
100.029154 12.769130
99.984564 12.454654
99.963442 12.163646
99.808551 11.914882
99.677128 11.654383
99.576215 11.349295
99.522237 11.175629
99.522237 10.978495
99.433058 10.795442
99.346225 10.717996
99.322756 10.532596
99.224189 10.370664
99.191334 10.260363
99.191334 10.009252
-999. -999.
98.527179 11.804581
98.550648 11.771725
98.484936 11.828049
98.339432 11.588672
98.494324 11.555816
98.571769 11.576938
98.595237 11.717748
98.527179 11.804581
-999. -999.
98.339432 11.762338
98.306577 11.741216
98.285455 11.588672
98.273721 11.490105
98.339432 11.588672
98.374635 11.771725
98.339432 11.762338
-999. -999.
98.374635 12.670563
98.362901 12.628320
98.362901 12.424145
98.384022 12.358434
98.461468 12.424145
98.374635 12.670563
-999. -999.
92.929977 13.524811
92.965180 13.567054
92.897122 13.470834
92.843145 13.287780
92.786820 13.081259
92.721109 12.682297
92.699988 12.487510
92.709375 12.337312
92.709375 12.227011
92.667132 12.097935
92.610808 11.978246
92.556831 11.891414
92.566218 11.708360
92.577952 11.642649
92.667132 11.534695
92.753965 11.567550
92.721109 11.684892
92.753965 11.914882
92.777433 12.076814
92.843145 12.259867
92.843145 12.379555
92.897122 12.541487
92.941712 12.790251
92.897122 12.909940
92.897122 13.027282
92.986301 13.092993
92.998036 13.254925
93.007423 13.362879
93.007423 13.524811
92.929977 13.524811
-999. -999.
86.572401 20.199210
86.274353 19.941058
86.042016 19.847185
85.732234 19.762699
85.457654 19.617195
85.168994 19.459957
84.939004 19.283944
84.694933 19.011711
84.497799 18.769987
84.298318 18.528263
84.110571 18.359291
84.065981 18.349904
84.021391 18.286539
83.821910 18.171544
83.559065 17.981451
83.326728 17.727993
83.005212 17.516777
82.564007 17.167099
82.322283 17.009861
82.211981 16.838542
82.211981 16.636714
82.101680 16.500598
81.747308 16.371522
81.669862 16.341013
81.428138 16.308157
81.195802 16.244793
81.162946 16.223671
81.073766 16.010109
80.942344 15.787160
80.799187 15.721449
80.620827 15.817669
80.456549 15.808281
80.278189 15.712061
80.125645 15.465643
-999. -999.
79.980141 14.888322
80.015344 14.674760
80.036465 14.632517
80.069321 14.587927
80.081055 14.587927
80.092789 14.545684
80.092789 14.374365
80.048199 14.257023
80.036465 14.181925
80.069321 14.019993
80.113911 13.869796
80.146766 13.717251
80.167888 13.621031
80.113911 13.686742
80.057587 13.621031
80.113911 13.578788
80.135032 13.491955
80.235946 13.405122
80.268802 13.233803
80.268802 13.158705
80.245334 13.017894
80.224212 12.963917
80.167888 12.757396
80.102177 12.532100
80.003610 12.271601
-999. -999.
73.577975 15.754304
73.512264 15.871646
73.446552 15.935011
73.411350 16.031231
73.401962 16.127451
73.345638 16.169694
73.247071 16.362135
73.202481 16.509985
73.181360 16.732934
73.169626 16.880785
73.148504 17.030983
73.103914 17.145977
73.103914 17.314950
73.047590 17.432291
72.981879 17.634119
72.916167 17.824213
72.904433 17.885231
72.883312 17.885231
72.859843 18.033081
72.850456 18.192666
72.859843 18.253684
72.826988 18.286539
72.761276 18.401534
72.761276 18.497754
72.794132 18.748866
72.826988 18.842739
72.826988 18.906104
72.859843 18.969468
72.850456 19.084463
72.815254 19.147828
72.749542 19.105585
72.695565 19.042220
72.695565 19.105585
72.695565 19.199458
72.683831 19.323840
72.639241 19.398939
72.627507 19.513934
72.594651 19.617195
72.585264 19.701681
72.585264 19.887081
72.594651 19.950445
-999. -999.
73.610831 15.744917
73.643686 15.712061
73.676542 15.573598
73.709398 15.486765
73.753988 15.456256
73.810312 15.510233
73.899491 15.498499
73.887757 15.465643
73.831433 15.402279
73.819699 15.317793
73.864289 15.209838
73.887757 15.092497
73.920613 15.005664
73.941734 14.954033
-999. -999.
80.125645 15.465643
79.980141 15.284937
79.970754 15.146474
79.980141 14.888322
-999. -999.
80.003610 12.271601
79.914430 12.086201
79.794741 11.828049
79.750151 11.630915
79.738417 11.403272
79.738417 11.109918
79.750151 10.957373
79.759539 10.771973
79.783007 10.586573
79.783007 10.466885
79.783007 10.347196
79.783007 10.337809
79.783007 10.272097
79.726683 10.272097
79.595260 10.272097
79.529549 10.337809
79.473225 10.337809
79.285478 10.293219
79.186911 10.096085
-999. -999.
76.337853 9.746406
76.117251 10.260363
75.941238 10.685140
75.819203 11.142773
75.697167 11.490105
75.631456 11.567550
75.377998 11.882026
75.190251 12.043958
75.047094 12.283335
75.035360 12.292722
75.035360 12.379555
74.969648 12.553221
74.814757 13.050750
74.737312 13.395735
74.704456 13.588175
74.594155 13.846327
74.460385 14.019993
74.406408 14.278145
74.317228 14.470585
74.230395 14.663026
74.096626 14.728737
73.941734 14.954033
-999. -999.
49.905449 11.497145
50.137786 11.539388
50.325533 11.682545
50.480424 11.931310
50.623581 11.898454
50.656436 11.964165
50.665824 11.964165
50.799593 11.910188
50.921629 11.898454
50.975606 11.877333
51.097641 11.823355
51.151618 11.659077
51.053051 11.530001
51.008462 11.302358
51.031930 11.192057
51.085907 11.018391
51.085907 10.769626
51.085907 10.593614
51.064786 10.485659
51.175087 10.495047
51.261920 10.398826
51.118763 10.387092
50.931016 10.333115
50.832449 10.159449
-999. -999.
54.404332 12.569649
54.514633 12.560262
54.493512 12.503938
54.359742 12.374862
54.195464 12.342006
54.007717 12.255173
53.819970 12.288029
53.587633 12.332619
53.411621 12.461695
53.479679 12.656482
53.587633 12.689338
53.688547 12.602505
53.730790 12.569649
53.775380 12.569649
53.885681 12.569649
54.040573 12.635360
54.216585 12.602505
54.404332 12.569649
-999. -999.
57.689901 20.070134
57.701635 19.945752
57.689901 19.830757
57.668780 19.736883
57.668780 19.621889
57.668780 19.570258
57.678167 19.518628
57.689901 19.403633
57.734491 19.319147
57.788468 19.140787
57.722757 19.037527
57.579600 18.995284
57.448177 18.995284
57.227575 18.953041
57.117273 18.983549
57.051562 18.901410
56.896671 18.859167
56.720658 18.732438
56.619744 18.532957
56.598623 18.375719
56.544646 18.185625
56.389754 17.995532
56.234863 17.922780
56.070585 17.932167
55.882838 17.901658
55.716213 17.871150
55.540200 17.838294
55.451020 17.744420
55.364188 17.638813
55.253886 17.542593
55.242152 17.448719
55.265620 17.310256
55.131851 17.108428
54.976960 17.002821
54.922983 16.939456
54.791560 16.951190
54.646056 16.993433
54.470043 17.023942
54.294031 17.014555
54.096897 17.002821
53.942005 16.887826
53.697935 16.791605
53.489066 16.770484
53.223874 16.685998
53.003271 16.610899
52.806137 16.526413
52.618390 16.430193
52.442378 16.312851
52.308608 16.165000
52.242897 15.984294
52.198307 15.909195
52.254631 15.770732
52.275752 15.632269
52.177185 15.568904
52.034028 15.590026
51.923727 15.536049
51.768836 15.493806
51.649148 15.460950
51.494256 15.280244
51.240798 15.193411
51.020196 15.172289
50.787859 15.108925
50.600112 15.012704
50.391244 14.958727
50.226965 14.883628
50.048606 14.820264
-999. -999.
39.994764 15.301365
40.093331 15.097190
40.215367 15.000970
40.379645 15.000970
40.567392 14.946993
40.677693 14.862507
40.701162 14.766287
40.865440 14.724044
41.086043 14.658332
41.262055 14.552725
41.395825 14.369671
41.494392 14.228861
41.592959 14.090398
41.726729 13.928466
41.935597 13.799391
42.067020 13.691436
42.165587 13.606950
42.275888 13.498996
42.386189 13.325330
42.487103 13.229110
42.630260 13.130543
42.740561 12.980345
42.806273 12.851269
43.038609 12.806679
-999. -999.
43.038609 12.806679
43.059731 12.797292
43.125442 12.698725
43.224009 12.527406
43.334311 12.386596
43.411756 12.180074
43.402369 12.060386
43.181766 11.898454
43.003407 11.769378
42.818007 11.682545
42.740561 11.605100
42.630260 11.539388
42.630260 11.443168
42.782804 11.485411
42.970551 11.530001
43.104321 11.539388
43.224009 11.452555
-999. -999.
43.224009 11.452555
43.202888 11.497145
43.235744 11.452555
43.390635 11.356335
43.545526 11.182669
43.665214 10.985535
43.831840 10.769626
44.040708 10.551371
44.294166 10.419948
44.690781 10.333115
44.955974 10.365971
45.242288 10.539637
45.462890 10.671059
45.627169 10.779014
45.760938 10.856459
46.014396 10.779014
46.288976 10.692181
46.697325 10.680447
46.941396 10.877581
47.237097 11.149814
47.415457 11.248381
47.722892 11.149814
48.032675 11.116958
48.208687 11.126345
48.208687 10.779014
48.551325 11.269502
48.736725 11.236647
49.001917 11.248381
49.267110 11.290624
49.443122 11.377457
49.708315 11.464290
49.905449 11.497145
-999. -999.
42.684237 16.409071
42.672503 16.463048
42.639647 16.526413
42.639647 16.622633
42.639647 16.695385
42.585670 16.779871
42.541080 16.854970
42.508225 16.918334
42.463635 17.002821
42.419045 17.066185
42.353334 17.108428
42.308744 17.174139
42.275888 17.216383
42.266501 17.237504
42.266501 17.258626
42.233645 17.385355
42.198442 17.521471
42.144465 17.584836
42.034164 17.669322
41.869886 17.828906
41.714994 17.901658
41.625815 17.995532
41.506126 18.155117
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41.428681 18.270111
41.384091 18.375719
41.294911 18.544691
41.229200 18.659686
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41.151754 18.711316
41.118898 18.762947
41.107164 18.838046
41.097777 18.859167
41.064921 18.962428
41.053187 19.161909
40.987476 19.319147
40.919417 19.413020
40.877174 19.497506
40.820850 19.549137
40.743405 19.612501
40.689427 19.725149
40.611982 19.788514
40.546271 19.882387
40.457091 19.997382
-999. -999.
43.468080 12.698725
43.456346 12.764436
43.444612 12.839535
43.411756 12.905246
43.402369 12.947489
43.390635 12.959224
43.346045 13.001467
43.292068 13.088300
43.214622 13.175132
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43.214622 13.337064
43.214622 13.520117
43.214622 13.649193
43.191154 13.811125
43.092587 13.907345
43.038609 14.036421
43.003407 14.198353
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42.961164 14.444770
42.949430 14.529256
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42.937696 14.658332
42.928308 14.700575
42.883718 14.799142
42.827394 14.883628
42.827394 14.979849
42.827394 15.033826
42.782804 15.097190
42.740561 15.162902
42.672503 15.247388
42.618526 15.289631
42.663116 15.334221
42.707706 15.322487
42.707706 15.385851
42.672503 15.460950
42.672503 15.620535
42.639647 15.716755
42.663116 15.749611
42.749949 15.812975
42.773417 15.888074
42.773417 16.014803
42.749949 16.174388
42.717093 16.366828
42.684237 16.409071
-999. -999.
50.048606 14.820264
49.917183 14.799142
49.752905 14.775674
49.598014 14.754552
49.365677 14.648945
49.189664 14.583233
49.067629 14.498747
49.001917 14.369671
48.903350 14.240596
48.760193 14.090398
48.560712 13.940201
48.396434 13.940201
48.220421 13.961322
48.020940 13.949588
47.844928 13.940201
47.668915 13.832246
47.600857 13.790003
47.568001 13.712558
47.457700 13.628072
47.260566 13.520117
47.072819 13.475527
46.896806 13.433284
46.687938 13.369920
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-999. -999.
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-999. -999.
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92.223580 20.863364
92.092157 21.154372
92.026446 21.391402
91.960735 21.649554
91.937266 21.895972
91.871555 22.233916
91.737785 22.449825
91.561773 22.693896
91.439737 22.776035
91.242603 22.715017
91.010266 22.693896
90.867109 22.766648
90.766195 22.940313
90.691097 22.898070
90.623039 22.724405
90.491616 22.632878
90.536206 22.419316
90.545593 22.276159
90.545593 22.233916
90.458760 22.111881
90.280401 21.917093
90.193568 21.802098
90.116122 21.844341
-999. -999.
93.472096 19.804942
92.953446 20.053706
92.941712 20.241453
92.786820 20.271962
92.676519 20.417466
92.643664 20.365835
92.521628 20.471443
92.444183 20.635721
92.345615 20.760104
92.268170 20.884486
-999. -999.
90.613651 22.684508
90.613651 22.614103
90.623039 22.489721
90.623039 22.327789
90.766195 22.285546
90.855375 22.407582
90.855375 22.541351
90.766195 22.715017
90.691097 22.745526
90.613651 22.684508
-999. -999.
88.891074 21.628433
88.780773 21.597924
88.747917 21.586190
88.691593 21.649554
88.637616 21.813833
88.593026 21.741081
88.581292 21.607311
88.503846 21.628433
88.405279 21.555681
88.262122 21.534559
88.194064 21.668329
88.140087 21.689450
88.095497 21.680063
88.083763 21.710572
88.083763 21.823220
88.083763 21.865463
88.083763 21.926481
88.107231 22.029741
88.116619 22.081372
88.116619 22.090759
88.116619 22.111881
88.116619 22.121268
88.062641 22.133002
87.964074 22.018007
87.928872 21.917093
87.842039 21.771589
87.720003 21.689450
87.543991 21.628433
87.123907 21.443033
86.959629 21.360893
86.846981 21.091007
86.924426 20.832855
86.959629 20.677964
86.771882 20.490218
86.727292 20.377569
86.572401 20.199210
-999. -999.
90.116122 21.844341
89.940109 22.060250
89.850930 21.947602
89.818074 21.853729
89.707773 21.783324
89.642061 21.719959
89.585737 21.844341
89.487170 21.762202
89.376869 21.771589
89.287689 21.783324
89.275955 21.701184
89.210244 21.731693
89.144532 21.719959
89.088208 21.637820
89.013110 21.597924
88.891074 21.628433
-999. -999.
72.594651 19.950445
72.627507 20.086562
72.672097 20.189823
72.728421 20.356448
72.728421 20.511339
72.704952 20.708473
72.627507 20.914995
72.606385 20.978359
72.594651 20.987747
72.585264 21.029990
72.561795 21.102741
72.561795 21.154372
72.496084 21.154372
72.484350 21.206002
72.484350 21.297529
72.496084 21.400790
72.540674 21.525172
72.594651 21.628433
72.484350 21.680063
72.439760 21.731693
72.451494 21.802098
72.463228 21.895972
72.474962 21.926481
72.418638 21.947602
72.430373 21.987498
72.474962 22.090759
72.496084 22.163511
72.573530 22.163511
72.695565 22.163511
72.737808 22.212794
72.794132 22.264425
72.782398 22.294934
72.650975 22.306668
72.507818 22.306668
72.385783 22.306668
72.254360 22.306668
72.186302 22.337177
72.141712 22.407582
72.141712 22.388807
72.132325 22.306668
72.108856 22.142389
72.076000 22.039129
72.054879 21.935868
72.054879 21.823220
72.043145 21.628433
72.031411 21.482929
71.944578 21.309263
71.834276 21.154372
71.679385 21.072233
71.524494 20.978359
71.414193 20.966625
71.357869 20.936116
71.271036 20.884486
71.238180 20.863364
71.226446 20.853977
71.116145 20.823468
70.916664 20.781225
70.686674 20.802347
70.585760 20.802347
70.442603 20.802347
70.344036 20.823468
70.278325 20.884486
70.266591 20.884486
70.132821 20.987747
-999. -999.
69.825386 22.428703
70.013132 22.553086
70.200879 22.705630
70.266591 22.879296
70.344036 23.052961
70.287712 23.144488
70.200879 23.113979
70.132821 22.980210
70.013132 22.940313
-999. -999.
68.025363 23.773440
68.079340 23.764053
67.992507 23.752318
67.858738 23.803949
67.760171 23.834458
67.694459 23.843845
67.551302 23.843845
67.494978 23.895475
67.462123 23.996389
67.340087 24.127812
67.253254 24.320252
67.185196 24.500959
67.140606 24.611260
67.131219 24.712174
67.053773 24.712174
66.866026 24.773192
66.732257 24.843597
66.699401 24.975019
66.678280 25.125217
66.666546 25.183888
66.612568 25.263680
66.478799 25.355207
66.356763 25.413878
66.180751 25.444386
65.993004 25.404490
65.805257 25.373981
65.563533 25.364594
65.429763 25.373981
65.298341 25.334085
65.155184 25.275414
65.000293 25.315311
-999. -999.
70.132821 20.987747
69.945074 21.142638
69.715084 21.391402
69.262145 21.813833
69.172965 21.874850
68.964097 22.081372
68.919507 22.346564
68.996953 22.428703
69.083786 22.377073
69.151844 22.316055
69.262145 22.346564
69.360712 22.367686
69.503869 22.388807
69.604783 22.388807
69.825386 22.428703
-999. -999.
70.013132 22.940313
69.968543 22.919192
69.945074 22.919192
69.679882 22.848787
69.426424 22.818278
69.283267 22.818278
69.128376 22.827665
68.919507 22.858174
68.752882 22.940313
68.565135 23.123367
68.433712 23.266523
68.299943 23.428455
68.234231 23.571612
68.189642 23.571612
68.135664 23.571612
68.102809 23.580999
68.091074 23.651404
68.079340 23.724156
68.025363 23.773440
-999. -999.
61.616156 25.158073
61.571566 25.167460
61.437797 25.118176
61.174951 25.136951
60.942615 25.188581
60.632832 25.277761
60.501410 25.409184
60.379374 25.317657
60.015615 25.338779
-999. -999.
65.000293 25.315311
64.824280 25.338779
64.723366 25.348166
64.591943 25.148685
64.502764 25.247252
64.282161 25.247252
64.117883 25.366941
63.864424 25.338779
63.622700 25.366941
63.479543 25.237865
63.235473 25.207356
62.970280 25.247252
62.716822 25.268374
62.519688 25.258986
62.364797 25.188581
62.242761 25.136951
62.111339 25.207356
61.968182 25.097055
61.825025 25.087668
61.726458 25.038384
61.681868 25.136951
61.616156 25.158073
-999. -999.
49.938305 26.810245
50.027484 26.711677
50.015750 26.662394
50.006363 26.533318
50.072074 26.444138
50.149520 26.345571
50.158907 26.176599
50.137786 26.115581
50.060340 26.047523
50.083808 25.848042
50.203497 25.676723
50.358388 25.547647
50.480424 25.418571
50.513279 25.197969
50.623581 25.167460
50.743269 25.467855
50.853570 25.587543
50.931016 25.768250
50.975606 25.995893
51.074173 26.124969
51.175087 26.195374
51.273654 26.075685
51.362834 25.946609
51.461401 25.817533
51.470788 25.667336
51.461401 25.507751
51.470788 25.366941
51.527112 25.298883
51.538846 25.007875
51.482522 24.885840
51.416811 24.726255
51.318244 24.625341
51.327631 24.554936
51.405077 24.524427
51.351099 24.463409
51.318244 24.303825
51.482522 24.334333
51.571702 24.273316
51.658535 24.313212
51.703125 24.132506
51.726593 24.120771
51.768836 24.071488
51.968317 24.031592
52.221775 24.010470
52.364932 24.031592
52.463499 24.132506
52.606656 24.221685
52.850727 24.212298
53.047861 24.202911
53.181631 24.141893
53.334175 24.141893
53.467945 24.090263
53.676813 24.101997
53.897416 24.111384
54.073428 24.212298
54.118018 24.282703
54.183729 24.303825
54.261175 24.282703
54.371476 24.353108
54.359742 24.564323
54.514633 24.735642
54.735236 24.885840
55.000428 25.097055
55.209296 25.308270
55.408777 25.498364
55.561322 25.636827
55.749068 25.737741
55.948549 25.937222
56.035382 26.136703
56.145684 26.254045
56.202008 26.254045
56.300575 26.315062
56.378020 26.275166
56.366286 26.195374
56.312309 26.155478
56.300575 26.085072
56.345165 26.047523
56.345165 25.887938
56.246598 25.737741
56.223129 25.667336
56.267719 25.596931
56.267719 25.418571
56.255985 25.167460
56.279453 24.906961
56.366286 24.695746
56.565767 24.515040
56.720658 24.362495
56.819225 24.221685
56.929527 24.191177
57.072683 24.111384
57.161863 24.040979
57.039828 24.120771
57.028094 24.120771
57.060949 24.080875
57.182985 24.019858
57.326142 23.949452
57.502154 23.888435
57.591334 23.857926
57.713369 23.818030
57.889382 23.787521
58.053661 23.787521
58.196818 23.717116
58.307119 23.656098
58.440888 23.665485
58.605167 23.604468
58.659144 23.543450
58.769445 23.433149
58.814035 23.351010
58.914949 23.259483
58.957192 23.137448
59.058106 23.045921
59.144939 22.994291
59.177795 22.832359
59.266974 22.759607
59.365541 22.677468
59.499311 22.646959
59.586144 22.646959
59.619000 22.597675
59.684711 22.546045
59.762157 22.463906
59.719914 22.330136
59.651855 22.177592
59.630734 22.043822
59.487577 21.797405
59.344420 21.612005
59.210650 21.417217
59.079228 21.313957
58.914949 21.198962
58.769445 20.992440
58.715468 20.837549
58.638023 20.764797
58.539455 20.567663
58.417420 20.422159
58.297731 20.443281
58.229673 20.494911
58.187430 20.619293
58.098250 20.579397
57.955094 20.403385
57.767347 20.152273
57.689901 20.070134
-999. -999.
50.555522 26.235270
50.480424 26.254045
50.424100 26.284553
50.424100 26.106194
50.456955 25.967731
50.546135 26.007627
50.555522 26.235270
-999. -999.
60.015615 25.338779
59.752769 25.348166
59.421865 25.409184
59.210650 25.477242
59.123817 25.449080
59.090962 25.378675
58.870359 25.507751
58.626288 25.578156
58.307119 25.587543
57.931625 25.627440
57.734491 25.688457
57.415321 25.707232
57.260430 25.927835
57.117273 26.235270
57.051562 26.512196
57.028094 26.641272
57.016359 26.641272
56.983504 26.711677
56.896671 26.908812
56.619744 27.066050
56.443732 27.124720
56.300575 27.134108
56.169152 27.084824
55.925081 26.997991
55.727947 26.948708
55.573056 26.899424
55.462755 26.770348
55.307863 26.699943
55.131851 26.690556
54.833803 26.533318
54.624934 26.493422
54.359742 26.552093
54.240053 26.650660
53.963127 26.699943
53.709669 26.662394
53.587633 26.662394
53.411621 26.838407
53.479679 26.810245
53.467945 26.887690
53.334175 26.958095
53.026740 27.056662
52.749813 27.134108
52.597269 27.331242
52.597269 27.401647
52.430644 27.558885
52.165451 27.685614
51.923727 27.753672
51.625679 27.772447
51.461401 27.852239
51.327631 27.997743
51.306510 28.009477
51.261920 28.096310
51.175087 28.368543
51.008462 28.652510
50.942750 28.884847
50.755003 29.018616
50.578991 29.154733
50.501545 29.387069
50.424100 29.541961
50.269208 29.617059
50.170641 29.753176
50.072074 29.868171
50.048606 29.983166
-999. -999.
56.169152 26.927586
56.091706 26.948708
55.925081 26.927586
55.760803 26.918199
55.683357 26.779736
55.474489 26.662394
55.253886 26.582602
55.275008 26.512196
55.540200 26.573214
55.760803 26.631885
56.035382 26.829019
56.169152 26.927586
-999. -999.
40.457091 19.997382
40.346790 20.091256
40.281078 20.121764
40.182511 20.203904
40.083944 20.267268
-999. -999.
48.495001 28.300485
48.506735 28.300485
48.539591 28.204265
48.584181 28.086923
48.649892 27.988356
48.727338 27.871014
48.879882 27.821730
48.980796 27.636330
49.112219 27.558885
49.234254 27.500214
49.267110 27.450931
49.201398 27.411034
49.255376 27.342976
49.288231 27.183391
49.389145 27.134108
49.443122 27.145842
49.520568 27.084824
49.675459 26.997991
49.806882 26.927586
49.938305 26.810245
-999. -999.
48.262664 28.807401
48.274399 28.748730
48.295520 28.671285
48.318988 28.572718
48.405821 28.495272
48.473880 28.368543
48.495001 28.300485
-999. -999.
48.372966 29.955004
48.372966 29.924495
-999. -999.
48.065530 30.079386
47.966963 29.992553
48.009206 29.924495
48.208687 29.809500
48.274399 29.694505
48.152363 29.598285
47.910639 29.551348
47.746361 29.464515
47.690037 29.337786
47.767482 29.337786
47.889518 29.337786
48.042062 29.281462
48.098386 29.117183
48.142976 28.952905
48.220421 28.816789
-999. -999.
48.551325 30.098161
48.473880 29.973778
-999. -999.
49.663725 30.069999
49.532302 29.945616
49.487712 29.992553
-999. -999.
32.365203 30.163872
32.386325 29.983166
32.386325 29.886945
32.353469 29.722667
32.365203 29.588897
32.419180 29.434006
32.529482 29.173507
32.630396 28.952905
32.696107 28.798014
32.794674 28.631389
32.916710 28.436601
33.092722 28.253548
33.292203 28.056414
33.411892 27.960194
33.456482 27.950806
33.477603 27.880401
33.477603 27.772447
33.489337 27.626943
33.522193 27.518989
33.655963 27.342976
33.787385 27.223287
33.853097 26.997991
33.909421 26.800857
33.951664 26.582602
34.085433 26.324450
34.216856 26.124969
34.327157 25.866817
34.493783 25.667336
34.592350 25.467855
34.702651 25.207356
34.812952 25.017262
34.923254 24.876452
35.045289 24.625341
35.120388 24.484531
35.242423 24.343721
35.373846 24.233420
35.561593 24.080875
35.716484 23.958840
35.728218 23.928331
35.728218 23.909556
35.716484 23.879047
35.716484 23.869660
35.662507 23.909556
35.484147 23.949452
35.418436 23.857926
35.474760 23.726503
35.474760 23.543450
35.495881 23.320501
35.552205 23.189078
-999. -999.
36.831231 22.001579
36.852352 21.867810
36.852352 21.724653
36.896942 21.518131
37.040099 21.344465
37.159787 21.220083
37.204377 21.107435
37.150400 21.116822
37.159787 20.776531
37.183256 20.422159
37.183256 20.152273
-999. -999.
35.552205 23.189078
35.573327 23.106939
35.662507 22.975516
35.793929 22.790116
36.059122 22.698589
36.256256 22.585941
36.467471 22.360645
36.631750 22.278506
36.831231 22.001579
-999. -999.
34.890398 29.492677
34.934988 29.387069
34.911519 29.445740
34.801218 29.368295
34.756628 29.272075
34.735507 29.250953
34.735507 29.232178
34.679183 29.107796
34.646327 28.981067
34.592350 28.826176
34.547760 28.652510
34.482049 28.485885
34.392869 28.309872
34.383481 28.164368
34.392869 28.028252
34.360013 27.929685
34.294302 27.880401
34.139411 27.793568
33.942276 27.842852
33.820241 27.969581
33.632494 28.173756
33.477603 28.330994
33.379036 28.436601
33.224145 28.622001
33.191289 28.875459
33.104456 29.039738
32.893241 29.250953
32.827530 29.377682
32.705494 29.520839
32.672639 29.656956
32.663251 29.753176
32.651517 29.771950
32.630396 29.840009
32.574072 29.915107
32.552950 29.992553
-999. -999.
37.910775 24.172402
37.877919 24.212298
37.854451 24.212298
37.821595 24.221685
37.800473 24.273316
37.734762 24.303825
37.657316 24.343721
37.547015 24.343721
37.481304 24.322599
37.403858 24.353108
37.371003 24.475144
37.281823 24.606566
37.159787 24.735642
37.159787 24.897574
37.183256 24.928083
37.126932 25.078280
37.072955 25.258986
37.007243 25.418571
36.906329 25.547647
36.786641 25.756516
36.631750 25.817533
36.577772 25.887938
36.542570 26.007627
36.422881 26.146090
36.333701 26.244657
36.256256 26.423017
36.169423 26.641272
36.059122 26.770348
35.925352 26.859528
35.772808 27.026153
35.695362 27.134108
35.671894 27.223287
35.617917 27.281958
35.540471 27.371138
35.517003 27.429809
35.474760 27.518989
35.409048 27.636330
35.319869 27.772447
35.254157 27.892136
35.197833 27.969581
35.155590 28.056414
35.054676 28.124472
34.899785 28.124472
34.747241 28.145594
34.714385 28.164368
34.625205 28.145594
34.580616 28.065801
34.604084 28.136206
34.702651 28.321606
34.789484 28.535168
34.801218 28.739343
34.801218 28.884847
34.834074 29.018616
34.857542 29.058513
34.911519 29.185242
34.890398 29.492677
-999. -999.
40.083944 20.267268
39.973643 20.318899
39.938440 20.340020
39.938440 20.328286
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130.545051 30.353966
-999. -999.
130.897076 37.539975
130.843099 37.495385
130.843099 37.478957
130.885342 37.453142
130.974522 37.504772
130.897076 37.539975
-999. -999.
130.035788 33.416585
129.970076 33.470563
129.859775 33.397811
129.770595 33.306284
129.660294 33.174861
129.770595 33.092722
129.838654 33.055173
129.880897 33.008236
129.948955 32.935484
129.958342 32.813449
129.871509 32.963646
129.749474 32.973034
129.782329 32.766512
129.815185 32.562337
129.916099 32.656211
-999. -999.
128.855330 32.721922
128.712173 32.665598
128.712173 32.534175
128.867064 32.581112
128.855330 32.721922
-999. -999.
129.219089 32.954259
129.197968 33.027011
129.132256 33.027011
129.054811 32.888547
129.097054 32.794674
129.219089 32.888547
129.219089 32.954259
-999. -999.
129.749474 33.839016
129.728352 33.766264
129.749474 33.702899
129.815185 33.756876
129.749474 33.839016
-999. -999.
129.284800 34.289608
129.197968 34.151145
129.230823 34.069006
129.320003 34.134717
129.284800 34.289608
-999. -999.
129.406836 34.636940
129.484281 34.571228
129.484281 34.498476
129.484281 34.425725
129.463160 34.334198
129.439692 34.298995
129.385714 34.390522
129.373980 34.545413
129.406836 34.636940
-999. -999.
128.435246 38.506871
128.512692 38.438813
128.655849 38.220557
128.810740 37.995261
128.986752 37.863838
129.165112 37.671397
129.308269 37.460182
129.430304 37.187949
129.496016 36.871127
129.484281 36.612975
129.472547 36.338395
129.505403 36.033307
129.618051 36.026266
129.549993 35.854947
129.463160 35.578021
129.329390 35.352724
129.132256 35.188446
128.942162 35.080492
128.756763 35.108654
128.601871 35.153243
128.557282 35.089879
128.536160 35.071104
128.491570 34.988965
128.491570 34.981924
128.479836 34.953762
128.425859 34.890398
128.346066 34.808259
128.280355 34.918560
128.181788 34.918560
128.071487 34.953762
127.994041 34.998352
127.895474 34.981924
127.773439 34.934988
127.674872 34.899785
127.749970 34.808259
127.707727 34.709692
127.606813 34.653368
127.541102 34.763669
127.463656 34.817646
127.451922 34.726119
127.451922 34.571228
127.341621 34.507864
127.254788 34.498476
127.198464 34.564188
127.332234 34.653368
127.341621 34.735507
127.231320 34.709692
127.078775 34.627552
126.989596 34.526638
126.945006 34.489089
126.933272 34.489089
126.900416 34.453887
126.834705 34.453887
126.790115 34.554800
126.724403 34.479702
126.548391 34.343585
126.524922 34.472661
126.360644 34.435112
126.294932 34.308383
126.238608 34.371747
126.316054 34.489089
126.348910 34.643980
126.447477 34.627552
126.536656 34.590003
126.524922 34.690917
126.581246 34.798871
126.492067 34.852848
126.393500 34.754281
126.337175 34.881011
126.393500 35.007740
126.438089 35.080492
126.438089 35.225995
126.524922 35.413742
126.625836 35.540471
126.569512 35.594448
126.736137 35.702403
126.780727 35.810357
126.712669 35.899537
126.712669 35.988717
126.592981 36.080243
126.569512 36.265643
126.515535 36.436962
126.492067 36.631750
126.381765 36.676339
126.426355 36.497980
126.337175 36.453390
126.238608 36.596547
126.140041 36.596547
126.161163 36.737357
126.294932 36.852352
126.447477 36.861739
126.569512 36.906329
126.691548 36.932144
126.855826 36.826537
126.923884 36.807762
126.834705 36.950919
126.834705 37.072955
126.768993 37.143360
126.790115 37.232539
126.834705 37.267742
126.736137 37.338147
126.679813 37.328760
126.602368 37.417939
126.592981 37.478957
126.646958 37.488344
126.614102 37.530587
126.536656 37.584565
126.503801 37.671397
126.503801 37.751190
126.503801 37.767618
-999. -999.
126.327788 33.360261
126.226874 33.259347
126.238608 33.167821
126.426355 33.149046
126.691548 33.174861
126.933272 33.350874
126.900416 33.463522
126.614102 33.463522
126.327788 33.360261
-999. -999.
128.005775 40.022926
127.928330 39.903238
127.749970 39.825792
127.552836 39.776509
127.541102 39.682635
127.552836 39.598149
127.564570 39.417443
127.541102 39.316529
127.529368 39.436218
127.451922 39.264899
127.496512 39.171025
127.728849 39.100620
127.928330 38.922261
128.181788 38.774410
128.381269 38.635947
128.435246 38.506871
-999. -999.
126.569512 37.723028
126.426355 37.838023
126.238608 37.784046
126.161163 37.723028
126.039127 37.802820
125.907705 37.838023
125.785669 37.960058
125.663634 37.976486
125.719958 37.915468
125.654246 37.777005
125.543945 37.741803
125.466500 37.662010
125.332730 37.662010
125.288140 37.671397
125.234163 37.828635
125.112128 37.812208
125.091006 37.899040
125.189573 37.899040
125.255284 37.985873
125.267019 38.056278
125.091006 38.021076
124.870404 38.021076
124.804692 38.030463
124.947849 38.211170
125.034682 38.445853
125.156717 38.497483
125.177839 38.558501
125.344464 38.610132
125.454765 38.661762
125.311609 38.661762
125.267019 38.765023
125.377320 39.093580
125.443031 39.365812
125.511090 39.504276
125.410176 39.553559
125.245897 39.562947
125.135596 39.579374
124.903259 39.647433
124.727247 39.572334
124.670923 39.546519
124.593477 39.689676
124.462054 39.776509
124.361140 39.835179
124.393996 39.903238
-999. -999.
121.568407 29.980819
121.514429 30.077039
121.514429 30.077039
121.347804 30.201421
121.192913 30.238971
121.016900 30.173259
120.817419 30.095814
120.608551 30.182647
120.387948 30.238971
120.211936 30.123976
120.364480 30.307029
120.563961 30.335191
120.850275 30.335191
121.061490 30.450186
121.127202 30.534672
121.148323 30.544059
121.270358 30.612117
121.469839 30.668441
121.657586 30.830373
121.922779 30.839760
121.932166 30.914859
121.800743 31.123727
121.645852 31.285659
121.392394 31.407695
121.204647 31.597788
120.972310 31.729211
120.772829 31.747986
120.718852 31.870021
120.629672 31.926345
120.409070 31.879408
120.155612 31.841859
120.155612 31.935732
120.409070 31.982669
120.641407 32.020218
120.873743 31.954507
121.106080 31.823084
121.314948 31.813697
121.568407 31.747986
121.767887 31.672887
121.911044 31.616563
121.922779 31.663500
121.833599 31.785535
121.711563 31.945120
121.634118 31.992056
121.514429 32.095317
121.392394 32.198578
121.368926 32.358163
121.127202 32.449689
120.960576 32.656211
120.883131 32.916710
120.763442 33.139659
120.707118 33.325059
120.653141 33.526887
120.596817 33.738102
120.465394 33.885952
120.376214 34.134717
120.254179 34.280221
120.078166 34.362360
-999. -999.
119.845830 35.578021
120.045311 35.667200
120.176733 35.800970
120.254179 35.927699
120.111022 36.052081
120.244791 36.185851
120.420804 36.185851
120.474781 36.026266
120.662528 36.042694
120.796298 36.293805
120.883131 36.373598
120.939455 36.373598
120.906599 36.516755
120.894865 36.561344
121.106080 36.561344
121.326682 36.657565
121.601262 36.683380
121.723298 36.702155
121.845333 36.835924
121.976756 36.922757
122.087057 36.887555
122.197358 36.950919
122.241948 36.871127
122.263070 36.800722
122.340515 36.756132
122.518875 36.932144
122.507141 36.995509
122.605708 37.126932
122.638563 37.232539
122.650298 37.321719
122.584586 37.347534
122.352249 37.373349
122.176237 37.434367
122.119913 37.460182
121.965022 37.389777
121.744419 37.363962
121.591875 37.373349
121.458105 37.495385
121.270358 37.514160
121.106080 37.591605
120.995779 37.680785
120.906599 37.758230
120.772829 37.741803
120.542840 37.654970
120.364480 37.584565
120.233057 37.434367
120.024189 37.312332
-999. -999.
119.803586 39.870382
120.012455 39.980683
-999. -999.
121.955634 40.046395
121.756153 39.825792
121.556672 39.724878
121.523817 39.553559
121.347804 39.478461
121.469839 39.452645
121.624731 39.358772
121.756153 39.316529
121.702176 39.152250
121.624731 38.997359
121.359538 38.938688
121.192913 38.765023
121.303214 38.696964
121.645852 38.835428
121.756153 38.922261
121.922779 38.922261
121.976756 38.955116
122.119913 39.041949
122.241948 39.213268
122.408573 39.342344
122.739477 39.443258
123.046913 39.546519
123.323839 39.689676
123.401285 39.757734
123.511586 39.666207
123.654743 39.708450
123.908201 39.757734
124.107682 39.767121
124.250839 39.802324
124.372874 39.860995
124.393996 39.903238
-999. -999.
120.078166 34.362360
119.890419 34.435112
119.648695 34.526638
119.482070 34.643980
119.282589 34.690917
119.249733 34.817646
119.392890 35.052329
119.547781 35.233036
119.615840 35.315175
119.726141 35.514656
119.845830 35.578021
-999. -999.
120.024189 37.312332
119.935009 37.206724
119.812974 37.072955
119.559516 37.047139
119.327179 37.117544
119.061987 37.197337
118.918830 37.363962
118.907095 37.504772
118.874240 37.619767
118.796794 37.767618
118.599660 37.899040
118.444769 37.899040
118.355589 38.002301
118.224166 38.002301
118.069275 38.063319
117.991830 38.185354
117.825204 38.316777
117.672660 38.464628
117.726637 38.706352
117.836939 38.990319
118.012951 39.126435
118.233554 39.110007
118.355589 39.048990
118.555070 39.058377
118.763939 39.110007
119.019744 39.135823
119.195756 39.229696
119.350647 39.358772
119.404625 39.553559
119.526660 39.741306
119.681551 39.792936
119.803586 39.870382
-999. -999.
49.973507 37.464876
50.170641 37.455489
50.304411 37.375696
50.435834 37.148053
50.689292 36.988468
51.041317 36.819496
51.372221 36.723276
51.682003 36.652871
51.902606 36.634096
52.045763 36.678686
52.210041 36.704501
52.430644 36.758479
52.674714 36.819496
52.916438 36.892248
53.235608 36.927451
53.489066 36.979081
53.655692 37.007243
53.578246 36.943879
53.334175 36.899289
53.479679 36.882861
53.655692 36.873474
53.885681 36.908676
54.073428 36.934491
54.061694 37.209071
53.951393 37.436714
53.918537 37.516506
-999. -999.
53.918537 37.516506
53.930271 37.577524
53.885681 37.823942
53.819970 38.161886
53.798848 38.535033
53.876294 38.854202
54.040573 39.060724
53.841092 39.112354
53.655692 39.241430
53.521922 39.386934
53.378765 39.412749
53.378765 39.454992
53.554778 39.523050
53.754259 39.581721
53.876294 39.649780
53.676813 39.701410
53.533656 39.762428
53.390499 39.853954
53.587633 39.999458
53.709669 39.922012
53.885681 39.863341
-999. -999.
53.092451 40.083944
52.961028 39.957215
52.850727 39.957215
-999. -999.
48.879882 38.570235
48.891616 38.380142
48.924472 38.145458
49.001917 37.866185
49.100485 37.673744
49.321087 37.535281
49.520568 37.507119
49.708315 37.446101
49.973507 37.464876
-999. -999.
49.508834 40.067516
49.475978 39.947828
49.443122 39.694369
49.332821 39.471420
49.278844 39.215615
49.255376 39.112354
49.112219 39.215615
49.023039 39.300101
48.980796 39.274286
48.891616 39.225002
48.847026 39.102967
48.837639 38.802572
48.858761 38.673496
48.879882 38.570235
-999. -999.
48.372966 29.924495
48.253277 30.001940
48.065530 30.079386
-999. -999.
48.560712 30.116935
48.551325 30.098161
-999. -999.
50.048606 29.983166
49.982895 30.088773
49.884327 30.145097
49.663725 30.069999
-999. -999.
49.487712 29.992553
49.389145 30.020715
49.332821 30.098161
49.201398 30.175606
49.112219 30.307029
49.091097 30.461920
49.001917 30.537019
48.847026 30.565181
48.760193 30.518244
48.804783 30.412636
48.760193 30.328150
48.769581 30.213155
48.626424 30.213155
48.593568 30.079386
-999. -999.
29.861130 31.257497
30.093467 31.353717
30.236624 31.456978
30.457226 31.466365
30.677829 31.522689
30.710684 31.494527
30.468960 31.410041
30.412636 31.334943
30.468960 31.325555
30.612117 31.353717
30.809252 31.381879
30.931287 31.466365
30.987611 31.503915
30.975877 31.541464
31.208214 31.494527
31.548505 31.485140
31.813697 31.466365
31.935732 31.344330
32.100011 31.288006
32.111745 31.288006
-999. -999.
31.724517 31.541464
31.724517 31.494527
31.747986 31.428816
31.715130 31.372492
31.682274 31.266884
31.614216 31.182398
31.682274 31.182398
31.759720 31.182398
31.780841 31.126074
31.780841 31.032201
31.935732 30.994652
32.022565 30.926593
32.088277 30.860882
32.144601 30.642626
32.177456 30.499469
32.198578 30.452533
32.198578 30.440798
32.189191 30.403249
32.198578 30.328150
32.287758 30.260092
32.365203 30.163872
-999. -999.
35.937086 35.815051
35.948821 35.958208
35.991064 36.101365
35.915965 36.296152
35.991064 36.537876
36.169423 36.624709
36.246869 36.758479
36.080243 36.882861
35.981676 36.838271
35.761074 36.777253
35.728218 36.624709
35.585061 36.580119
35.340990 36.608281
35.155590 36.732663
34.934988 36.793681
34.801218 36.819496
34.690917 36.838271
34.944375 36.803068
34.756628 36.828884
34.547760 36.758479
34.404603 36.634096
34.216856 36.500327
34.139411 36.368904
33.951664 36.340742
33.808507 36.242175
33.721674 36.216360
33.623107 36.181157
33.423626 36.197585
33.235879 36.152995
33.071601 36.127180
32.904975 36.063815
32.740697 36.101365
32.562337 36.152995
32.386325 36.305539
32.308879 36.420534
32.198578 36.500327
32.022565 36.589506
31.870021 36.652871
31.682274 36.723276
31.560239 36.767866
31.494527 36.812456
31.339636 36.882861
31.173011 36.899289
31.029854 36.918063
30.853841 36.892248
30.698950 36.892248
30.644973 36.767866
30.644973 36.580119
30.579262 36.519101
30.555793 36.350129
30.403249 36.324314
30.192034 36.279724
-999. -999.
34.040844 35.472413
34.094821 35.481800
34.282568 35.552205
34.404603 35.634345
34.580616 35.707096
34.658061 35.714137
34.604084 35.589755
34.449193 35.453638
34.315423 35.409048
34.216856 35.282319
34.118289 35.155590
34.151145 35.066410
34.040844 34.949069
33.820241 34.911519
33.611373 34.749588
33.325059 34.702651
33.137312 34.594697
33.027011 34.594697
32.815796 34.620512
32.585806 34.712038
32.442649 34.866930
32.353469 35.028861
32.430915 35.047636
32.585806 35.092226
32.750084 35.164978
32.926097 35.183752
33.048132 35.218955
33.059866 35.336297
33.071601 35.355071
33.137312 35.326909
33.235879 35.326909
33.357915 35.336297
33.501071 35.345684
33.688818 35.390274
33.853097 35.437210
34.040844 35.472413
-999. -999.
35.991064 34.740200
35.948821 34.902132
36.002798 35.092226
35.991064 35.364459
35.904231 35.561593
35.847907 35.615570
35.883109 35.669547
35.937086 35.815051
-999. -999.
35.474760 33.970438
35.474760 33.961051
35.474760 33.951664
35.474760 33.923502
35.463026 33.923502
35.441904 33.914114
35.385580 33.850750
35.340990 33.777998
35.298747 33.693512
35.287013 33.639535
35.254157 33.592598
35.188446 33.510459
35.164978 33.454135
35.132122 33.407198
35.111000 33.353221
35.087532 33.306284
35.066410 33.268735
35.045289 33.233532
35.000699 33.186596
34.988965 33.139659
34.977231 33.120884
35.474760 33.970438
35.578021 34.000947
35.660160 34.237978
35.721177 34.374094
35.843213 34.484395
36.026266 34.585309
35.991064 34.740200
-999. -999.
32.144601 31.278619
32.177456 31.248110
32.231434 31.248110
32.332348 31.201173
32.376937 31.144849
32.419180 31.088525
32.496626 31.022814
32.728963 31.013426
32.872120 31.032201
32.937831 31.088525
33.015277 31.107300
33.080988 31.032201
33.104456 31.013426
33.214758 31.022814
33.357915 31.041588
33.522193 31.060363
33.688818 31.116687
33.853097 31.182398
34.029109 31.297393
34.130023 31.372492
34.130023 31.381879
34.162879 31.391267
34.261446 31.456978
34.360013 31.541464
34.437459 31.625950
34.493783 31.691662
34.514904 31.738598
34.514904 31.750332
-999. -999.
34.514904 31.750332
34.559494 31.872368
34.580616 31.947467
34.604084 32.003791
34.636940 32.078889
34.646327 32.144601
34.679183 32.245515
34.702651 32.311226
34.723773 32.395712
34.747241 32.470811
34.780097 32.545910
34.780097 32.602234
34.801218 32.665598
34.857542 32.759472
34.899785 32.825183
34.934988 32.890894
34.944375 32.982421
34.944375 33.048132
34.956109 33.066907
-999. -999.
32.552950 29.992553
32.520094 30.020715
32.475505 30.060611
32.463770 30.060611
32.430915 30.079386
32.409793 30.154485
32.341735 30.260092
32.308879 30.297642
32.222046 30.440798
32.198578 30.633239
32.198578 30.736500
32.189191 30.851495
32.189191 31.004039
32.189191 31.116687
32.189191 31.173011
32.165722 31.229335
-999. -999.
25.364594 39.922012
25.308270 39.795283
25.331738 39.922012
25.320004 39.983030
25.209703 39.990071
25.066546 39.964255
25.021956 39.830486
25.087668 39.795283
25.143992 39.846914
25.188581 39.837526
25.275414 39.804671
25.298883 39.830486
25.364594 39.922012
-999. -999.
26.533318 39.079499
26.643619 39.060724
26.554439 39.225002
26.455872 39.361119
26.366693 39.454992
26.223536 39.393974
26.080379 39.351731
25.916100 39.293061
25.871510 39.163985
25.991199 39.147557
26.136703 39.206228
26.247004 39.215615
26.157824 39.070111
26.312715 39.009094
26.465260 39.079499
26.465260 39.128782
26.533318 39.079499
-999. -999.
25.970078 38.241678
26.047523 38.267494
26.092113 38.302696
26.124969 38.448200
26.136703 38.560848
26.092113 38.621866
25.880898 38.638294
25.880898 38.527992
25.991199 38.415344
25.904366 38.319124
25.904366 38.248719
25.970078 38.241678
-999. -999.
28.098657 36.073203
28.176103 36.101365
28.197224 36.181157
28.274670 36.286765
28.319259 36.458084
28.218346 36.429922
28.054067 36.368904
27.866320 36.235134
27.788875 36.181157
27.767753 36.101365
27.779487 35.930046
27.922644 35.984023
28.098657 36.073203
-999. -999.
25.066546 35.373846
24.923389 35.418436
24.747376 35.399661
24.569017 35.373846
24.371883 35.345684
24.249847 35.427823
24.151280 35.437210
24.195870 35.526390
24.118425 35.599142
24.008123 35.517003
23.808642 35.606183
23.742931 35.615570
23.698341 35.500575
23.599774 35.526390
23.578653 35.383233
23.545797 35.193140
23.644364 35.211914
23.799255 35.202527
23.975268 35.218955
24.195870 35.211914
24.348414 35.183752
24.470450 35.155590
24.569017 35.092226
24.723908 35.047636
24.813088 34.892745
25.111136 34.911519
25.298883 34.965497
25.463161 34.956109
25.606318 34.984271
25.805799 34.993659
25.970078 35.028861
26.157824 34.956109
26.322103 35.183752
26.289247 35.256504
26.169559 35.202527
26.068645 35.193140
25.937222 35.148550
25.782331 35.193140
25.695498 35.310481
25.496017 35.291707
25.373981 35.301094
25.188581 35.301094
25.066546 35.326909
25.066546 35.373846
-999. -999.
24.944511 37.657316
25.000835 37.708947
25.000835 37.814554
24.967979 37.875572
24.845944 37.945977
24.712174 37.971792
24.702787 37.901387
24.789619 37.823942
24.845944 37.734762
24.890533 37.666704
24.944511 37.657316
-999. -999.
25.430305 36.918063
25.552341 36.927451
25.573462 37.068261
25.585197 37.155094
25.517138 37.155094
25.474895 37.138666
25.385716 37.058874
25.385716 36.934491
25.430305 36.918063
-999. -999.
22.034435 38.309737
21.912400 38.302696
21.792711 38.283921
21.527519 38.145458
21.384362 38.190048
21.173147 37.917815
21.130904 37.788739
21.250592 37.596299
21.527519 37.490691
21.658941 37.305291
21.572109 37.068261
21.614352 36.873474
21.715265 36.784294
21.858422 36.739704
21.903012 36.899289
22.022701 37.023671
22.100146 36.918063
22.243303 36.819496
22.332483 36.580119
22.353605 36.420534
22.442784 36.411147
22.475640 36.500327
22.520230 36.704501
22.684508 36.767866
22.794810 36.617669
22.937967 36.509714
23.092858 36.439309
23.069389 36.669299
23.060002 36.767866
23.015412 36.918063
22.926232 37.199684
22.794810 37.359268
22.740832 37.535281
22.815931 37.507119
22.937967 37.446101
23.069389 37.368656
23.104592 37.279476
23.191425 37.295904
23.313460 37.385084
23.468351 37.401511
23.435496 37.507119
23.334582 37.551709
23.214893 37.622114
23.137448 37.760577
23.081123 37.840370
23.092858 37.953018
22.926232 38.023423
22.475640 38.145458
22.255038 38.197089
22.156470 38.197089
22.088412 38.267494
22.034435 38.309737
-999. -999.
20.731942 38.068013
20.776531 38.190048
20.645109 38.267494
20.600519 38.405957
20.501952 38.361367
20.370529 38.267494
20.358795 38.248719
20.445628 38.190048
20.501952 38.129030
20.633374 38.110256
20.731942 38.068013
-999. -999.
24.569017 38.075053
24.613607 38.032810
24.604219 38.154846
24.416473 38.190048
24.315559 38.222904
24.205258 38.431772
24.205258 38.553807
24.106690 38.638294
23.832111 38.682883
23.644364 38.750942
23.477739 38.863590
23.358050 38.966850
23.325194 39.025521
23.214893 39.025521
23.036534 38.915220
22.961435 38.837775
23.003678 38.828387
23.146835 38.837775
23.268870 38.750942
23.358050 38.682883
23.534063 38.579623
23.566918 38.466975
23.721809 38.396570
23.930678 38.380142
23.996389 38.335552
24.127812 38.258106
24.195870 38.171273
24.238113 38.039851
24.339027 37.971792
24.449328 37.953018
24.536161 37.945977
24.569017 37.945977
24.569017 37.978833
24.569017 38.075053
-999. -999.
20.049013 39.393974
20.060747 39.454992
-999. -999.
19.938711 39.386934
20.049013 39.393974
-999. -999.
23.942412 40.142615
23.963534 39.964255
-999. -999.
23.501207 40.100372
23.665485 39.999458
23.566918 39.940787
-999. -999.
22.607063 40.152002
22.639918 39.973643
22.761954 39.872729
22.839399 39.659167
23.027146 39.532438
23.158569 39.419790
23.247749 39.274286
23.289992 39.163985
23.203159 39.121742
23.125713 39.138169
23.158569 39.232043
23.081123 39.318876
22.916845 39.335304
22.872255 39.215615
22.949701 39.070111
22.970822 39.018481
22.916845 38.976238
22.827665 38.957463
22.717364 38.966850
22.541351 38.941035
22.618797 38.847162
22.827665 38.769716
22.994291 38.734514
23.125713 38.673496
23.289992 38.664109
23.379172 38.499830
23.501207 38.499830
23.632630 38.387182
23.775787 38.302696
23.874354 38.293309
24.008123 38.222904
24.017511 38.084440
24.017511 37.927203
24.017511 37.779352
24.029245 37.683132
23.787521 37.805167
23.599774 37.988220
23.358050 37.953018
23.092858 37.953018
22.926232 38.023423
23.113979 38.068013
23.146835 38.180661
22.937967 38.206476
22.806544 38.293309
22.684508 38.396570
22.574207 38.319124
22.398194 38.370754
22.165858 38.344939
21.945255 38.380142
21.626086 38.344939
21.372628 38.422385
21.306916 38.422385
21.274060 38.370754
21.163759 38.344939
21.086314 38.441159
20.987747 38.621866
20.877445 38.750942
20.755410 38.889405
20.943157 38.872977
21.119169 38.898792
21.053458 39.018481
20.788266 39.102967
20.743676 38.976238
20.645109 39.102967
20.469096 39.335304
20.293083 39.438564
20.260228 39.539478
20.215638 39.668554
20.182782 39.701410
20.159314 39.701410
-999. -999.
20.081868 39.684982
20.081868 39.684982
-999. -999.
19.938711 32.172763
20.072481 32.301839
20.215638 32.414487
20.379916 32.527135
20.555929 32.646823
20.853977 32.778246
21.152025 32.815796
21.372628 32.890894
21.647207 32.900282
21.935868 32.900282
22.165858 32.834570
22.463906 32.750084
22.595329 32.693760
22.740832 32.684373
22.916845 32.602234
22.926232 32.452036
22.905111 32.423874
22.860521 32.433261
22.893377 32.320613
23.069389 32.198578
23.158569 32.172763
23.247749 32.189191
23.510594 32.151641
23.754665 32.097664
23.864966 32.050727
24.017511 31.994403
24.315559 31.956854
24.559630 31.956854
24.768498 31.938079
24.923389 31.862981
25.000835 31.663500
25.021956 31.672887
-999. -999.
25.066546 31.560239
25.188581 31.522689
25.507751 31.588401
25.782331 31.607176
26.014667 31.569626
26.223536 31.532077
26.488728 31.513302
26.763308 31.475753
27.127067 31.372492
27.359404 31.238722
27.624596 31.201173
27.788875 31.163624
27.932032 31.069750
28.230080 31.069750
28.462416 31.013426
28.727609 30.935981
28.913009 30.842107
29.201670 30.898431
29.487983 31.032201
29.652262 31.144849
29.861130 31.257497
-999. -999.
30.192034 36.279724
29.938576 36.197585
29.729707 36.197585
29.553695 36.235134
29.377682 36.314927
29.222791 36.448696
29.178201 36.589506
29.157080 36.662258
29.157080 36.723276
29.023310 36.777253
28.981067 36.713889
28.990454 36.662258
28.924743 36.662258
28.769852 36.739704
28.671285 36.847658
28.626695 36.857046
28.474151 36.847658
28.352115 36.828884
28.307525 36.749091
28.131513 36.652871
28.086923 36.652871
28.152634 36.758479
28.119779 36.812456
27.899176 36.758479
27.678574 36.704501
27.502561 36.669299
27.601128 36.784294
27.779487 36.864086
28.021211 36.864086
28.143247 36.918063
28.176103 36.953266
28.328647 37.014284
28.384971 37.094076
28.241814 37.103463
28.032946 37.068261
27.866320 37.033058
27.669186 37.033058
27.436849 37.033058
27.392260 37.112851
27.490827 37.173868
27.612862 37.270089
27.547151 37.314679
27.481439 37.385084
27.413381 37.420286
27.314814 37.436714
27.338282 37.551709
27.436849 37.603339
27.469705 37.673744
27.347670 37.666704
27.270224 37.631501
27.216247 37.622114
27.127067 37.727722
27.249103 37.788739
27.281958 37.910775
27.195125 38.049238
27.084824 38.110256
26.929933 38.129030
26.840753 38.154846
26.709331 38.241678
26.620151 38.215863
26.542705 38.206476
26.455872 38.248719
26.354958 38.328511
26.345571 38.380142
26.465260 38.415344
26.488728 38.544420
26.465260 38.621866
26.509850 38.708699
26.575561 38.682883
26.685862 38.457587
26.796164 38.431772
26.951055 38.457587
27.117680 38.457587
27.171657 38.457587
27.127067 38.499830
26.929933 38.560848
26.840753 38.692271
26.873609 38.795532
27.016766 38.889405
26.974523 38.976238
26.873609 39.060724
26.873609 39.147557
26.763308 39.257858
26.786776 39.412749
26.951055 39.539478
26.906465 39.600496
26.742186 39.574681
26.620151 39.548866
26.432404 39.548866
26.289247 39.539478
26.178946 39.548866
26.169559 39.616924
26.190680 39.743653
26.223536 39.905585
-999. -999.
20.060747 39.454992
19.971567 39.574681
19.894121 39.710797
19.786167 39.778855
19.652397 39.743653
19.750964 39.591109
19.819023 39.487848
19.938711 39.386934
-999. -999.
20.081868 39.684982
19.995035 39.762428
19.962180 39.914972
-999. -999.
15.331874 40.100372
15.418707 39.999458
-999. -999.
15.683899 40.025273
15.728489 39.964255
15.737876 39.872729
15.803588 39.684982
15.904502 39.539478
16.003069 39.412749
16.035924 39.309488
16.080514 39.154597
16.134492 39.060724
16.179081 38.931648
16.223671 38.854202
15.970213 38.760329
15.827056 38.682883
15.892767 38.527992
15.770732 38.380142
15.695633 38.232291
15.705021 38.058625
15.749611 37.953018
15.770732 37.978833
15.761345 37.945977
15.892767 37.936590
16.035924 37.953018
16.092248 37.988220
16.134492 38.075053
16.179081 38.145458
16.235405 38.232291
16.289383 38.293309
16.411418 38.380142
16.533453 38.405957
16.575697 38.492790
16.587431 38.664109
16.587431 38.760329
16.587431 38.811959
16.643755 38.880018
16.786912 38.915220
16.974658 38.992666
17.061491 38.992666
17.094347 39.051337
17.084960 39.128782
17.094347 39.250818
17.073226 39.309488
17.073226 39.445605
17.061491 39.464380
16.984046 39.532438
16.808033 39.607536
16.718853 39.701410
16.599165 39.743653
16.521719 39.769468
16.533453 39.914972
-999. -999.
17.997879 40.126187
18.131648 39.964255
18.307661 39.896197
18.328782 39.879769
18.328782 39.914972
-999. -999.
15.618188 38.319124
15.552476 38.302696
15.561864 38.293309
15.540742 38.136071
15.430441 37.988220
15.287284 37.823942
15.165249 37.596299
15.099537 37.446101
15.087803 37.368656
15.165249 37.305291
15.176983 37.234886
15.221573 37.129279
15.263816 37.058874
15.209838 36.962653
15.153514 36.819496
15.132393 36.713889
15.010357 36.704501
14.857813 36.713889
14.646598 36.758479
14.449464 36.882861
14.294573 37.042446
14.041115 37.112851
13.874489 37.119891
13.731332 37.183256
13.599910 37.288863
13.391041 37.368656
13.170439 37.500079
12.949836 37.577524
12.783211 37.603339
12.640054 37.631501
12.541487 37.734762
12.485163 37.936590
12.518019 38.058625
12.553221 38.110256
12.595464 38.171273
12.672910 38.197089
12.738621 38.171273
12.839535 38.100868
12.949836 38.110256
13.081259 38.180661
13.247884 38.241678
13.325330 38.206476
13.412163 38.171273
13.489608 38.145458
13.621031 38.100868
13.698477 37.997608
13.832246 38.006995
13.951935 38.039851
14.139682 38.058625
14.294573 38.068013
14.381406 38.075053
14.393140 38.075053
14.515175 38.084440
14.658332 38.119643
14.822611 38.190048
15.076069 38.190048
15.153514 38.190048
15.263816 38.267494
15.308406 38.258106
15.475031 38.274534
15.618188 38.319124
-999. -999.
14.372018 35.948821
14.372018 35.993410
14.416608 35.974636
14.491707 35.939433
14.515175 35.885456
14.580887 35.850253
14.559765 35.815051
14.449464 35.831479
14.372018 35.913618
14.372018 35.948821
-999. -999.
9.873135 37.331106
10.028027 37.288863
10.192305 37.244273
10.171183 37.209071
10.225161 37.112851
10.302606 36.997856
10.281485 36.892248
10.281485 36.838271
10.469232 36.777253
10.546677 36.838271
10.678100 36.873474
10.788401 36.953266
10.886968 37.068261
11.020738 37.068261
11.119305 36.892248
11.020738 36.749091
10.910437 36.554304
10.689834 36.483899
10.546677 36.385332
10.490353 36.181157
10.556064 35.958208
10.645244 35.850253
10.832991 35.822091
10.886968 35.714137
11.030125 35.634345
11.053593 35.526390
11.074715 35.399661
11.131039 35.265891
11.053593 35.139162
10.964414 34.949069
10.854112 34.784790
10.722690 34.667449
10.612388 34.585309
10.490353 34.503170
10.391786 34.465621
10.281485 34.374094
10.126594 34.329504
10.093738 34.219203
10.082004 34.137064
10.082004 34.092474
-999. -999.
9.929459 33.794426
10.028027 33.749836
10.126594 33.684125
10.236895 33.648922
10.347196 33.648922
10.445763 33.674737
10.502087 33.583211
10.579533 33.510459
10.743811 33.592598
10.832991 33.592598
10.898702 33.472909
10.964414 33.315671
10.964414 33.261694
11.030125 33.195983
11.152161 33.195983
11.217872 33.214758
11.316439 33.158434
-999. -999.
10.776667 33.878912
10.743811 33.904727
10.788401 33.850750
10.821257 33.794426
10.821257 33.702899
10.732077 33.693512
10.612388 33.702899
10.588920 33.831975
10.633510 33.869525
10.710956 33.904727
10.776667 33.878912
-999. -999.
11.316439 33.158434
11.515920 33.111497
11.748257 33.001196
12.046305 32.900282
12.243439 32.825183
12.628320 32.806408
12.994426 32.890894
13.269006 32.872120
13.477874 32.787634
13.721945 32.778246
14.029380 32.693760
14.184272 32.611621
14.569152 32.461424
14.801489 32.414487
15.043213 32.330001
15.153514 32.245515
15.221573 32.050727
15.230960 31.853593
15.406973 31.616563
15.683899 31.363105
16.080514 31.229335
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132.366195 43.033916
132.399051 43.137177
132.399051 43.242784
132.288749 43.209928
132.068147 43.090240
132.002435 43.146564
132.089268 43.282680
131.934377 43.299108
131.913256 43.418797
131.847544 43.292068
131.781833 43.106668
131.648063 42.984632
131.558884 42.928308
131.504906 42.822701
131.382871 42.740561
131.284304 42.611485
131.073089 42.611485
130.908810 42.620873
130.753919 42.595058
130.810243 42.529346
130.843099 42.423739
130.622496 42.562202
-999. -999.
140.028612 42.120997
139.883108 42.212523
139.894842 42.334559
139.927698 42.522306
-999. -999.
130.699942 42.374455
130.732798 42.278235
130.610762 42.301703
130.476993 42.268848
130.324448 42.130384
130.103846 41.956718
-999. -999.
130.103846 41.956718
129.981810 41.851111
129.904365 41.736116
129.749474 41.562450
129.704884 41.412253
129.770595 41.287870
129.761208 41.071962
129.749474 40.888908
129.639173 40.813810
129.373980 40.712896
129.230823 40.579126
129.064198 40.452397
128.834208 40.335055
128.712173 40.257610
128.655849 40.173124
128.435246 40.055782
128.170054 40.029967
128.005775 40.022926
-999. -999.
120.012455 39.980683
120.265913 40.072210
120.474781 40.140268
120.552227 40.215367
120.662528 40.384339
120.772829 40.478212
120.883131 40.595554
121.038022 40.703508
121.183526 40.830238
121.347804 40.879521
121.547285 40.879521
121.779622 40.895949
121.866455 40.987476
121.965022 40.895949
122.033080 40.729324
122.152768 40.602595
122.187971 40.579126
122.241948 40.536883
122.286538 40.426582
122.152768 40.241182
121.955634 40.046395
-999. -999.
74.903937 46.833442
74.979036 46.809973
75.178517 46.748956
75.443709 46.786505
75.730023 46.817014
76.072661 46.779465
76.415299 46.704366
76.725081 46.687938
77.023129 46.612839
77.255466 46.598758
77.541779 46.657429
77.851562 46.673857
78.072164 46.589371
78.203587 46.521313
78.391334 46.650389
78.579081 46.772424
78.787949 46.809973
78.987430 46.809973
79.085997 46.748956
79.097731 46.558862
78.888863 46.399277
78.701116 46.392237
78.522757 46.453255
78.325622 46.385196
77.950129 46.347647
77.640347 46.439174
77.386888 46.490804
77.044250 46.460295
76.713347 46.490804
76.403564 46.507232
76.117251 46.544781
75.875527 46.544781
75.586866 46.507232
75.399119 46.544781
75.366263 46.619880
75.288818 46.657429
75.255962 46.507232
75.178517 46.446214
74.979036 46.429786
74.803023 46.324179
74.648132 46.148166
74.450998 46.056639
74.239782 46.002662
74.174071 45.817262
74.129481 45.641250
74.052036 45.493399
74.063770 45.230553
74.141215 45.002910
74.328962 44.815164
74.096626 44.838632
73.920613 45.082703
73.709398 45.338508
73.488795 45.462890
73.401962 45.678799
73.434818 45.918176
73.545119 46.124698
73.765722 46.162247
73.899491 46.324179
74.084891 46.460295
74.340696 46.598758
74.549565 46.734875
74.716190 46.817014
74.903937 46.833442
-999. -999.
59.973372 43.597156
60.170506 43.653480
60.423964 43.693376
60.489675 43.813065
60.611711 43.885817
60.710278 44.115807
60.853435 44.195599
60.998939 44.336409
61.041182 44.486607
61.174951 44.683741
61.482387 44.747105
61.637278 44.817510
61.735845 45.028726
61.649012 45.122599
61.559832 45.317386
61.461265 45.472277
61.350964 45.563804
61.163217 45.648290
61.052916 45.833690
61.008326 46.127044
61.085772 46.195103
61.261784 46.432133
61.449531 46.575290
61.604422 46.734875
61.616156 46.809973
61.461265 46.788852
61.240663 46.690285
61.064650 46.568249
60.888637 46.500191
60.778336 46.741915
60.656301 46.727834
60.578855 46.612839
60.567121 46.561209
60.456820 46.523660
60.379374 46.605799
60.280807 46.673857
60.149384 46.462642
60.161119 46.354687
60.269073 46.310098
60.468554 46.286629
60.632832 46.303057
60.799458 46.310098
60.820579 46.195103
60.545999 46.117657
60.480288 46.178675
60.304275 46.256120
60.193974 46.202143
-999. -999.
53.885681 39.863341
53.775380 40.032314
53.402233 40.126187
53.092451 40.083944
-999. -999.
52.850727 39.957215
52.785016 40.184858
52.728692 40.379645
52.761547 40.588514
52.895317 40.741058
52.904704 40.799729
52.895317 40.940539
52.883583 41.048493
52.871849 41.123592
52.904704 41.064921
52.970416 40.914724
53.059595 40.806769
53.280198 40.799729
53.444476 40.806769
53.622836 40.764526
53.808236 40.715243
53.995983 40.731670
54.282297 40.673000
54.448922 40.741058
54.272909 40.764526
54.249441 40.839625
54.526367 40.891255
54.756357 41.140020
54.350355 41.372356
54.052307 41.621121
53.942005 41.860498
53.754259 42.050592
53.721403 42.074060
53.500800 42.099875
53.169897 42.024777
52.895317 41.902741
52.728692 41.745503
52.728692 41.621121
52.817871 41.588265
52.817871 41.372356
52.827259 41.231546
52.785016 41.264402
52.540945 41.614081
52.463499 41.909782
52.463499 42.090488
52.454112 42.393230
52.618390 42.541080
52.651246 42.808620
52.442378 42.871984
52.221775 42.888412
51.858016 43.010447
51.682003 43.188807
51.538846 43.179420
51.318244 43.205235
51.285388 43.444612
51.261920 43.716845
51.053051 43.979690
50.909894 44.059483
50.766738 44.258964
50.358388 44.376305
50.149520 44.589867
50.280943 44.676700
50.611846 44.683741
50.931016 44.620376
51.107029 44.557012
51.252532 44.596908
51.505991 44.573440
51.416811 44.676700
51.351099 44.817510
51.306510 45.052194
51.405077 45.200045
51.581089 45.270450
51.581089 45.176576
51.780570 45.160148
51.989439 45.207085
52.034028 45.331467
52.210041 45.439422
52.529211 45.448809
52.817871 45.331467
53.104185 45.254022
53.390499 45.293918
53.554778 45.361976
53.578246 45.385445
53.643957 45.371364
53.730790 45.317386
54.061694 45.237594
54.282297 45.160148
54.470043 45.183617
54.702380 45.153108
54.756357 45.254022
54.624934 45.401872
54.812681 45.401872
54.681259 45.573191
54.470043 45.742163
54.294031 45.826650
54.207198 45.965113
54.007717 45.972153
53.798848 46.188062
53.697935 46.483763
53.566512 46.629267
53.512535 46.554168
53.378765 46.758343
53.280198 46.758343
53.247342 46.908541
52.993884 47.058738
52.895317 47.112715
52.684102 47.126796
52.684102 47.201895
52.442378 47.218323
52.242897 47.157305
52.066884 47.143224
51.869750 47.075166
51.813426 47.201895
51.682003 47.208935
51.548234 47.201895
51.461401 47.232404
51.217330 47.269953
50.963872 47.276994
50.644702 47.082206
50.337267 46.870991
-999. -999.
49.950039 40.698815
50.083808 40.621369
50.194110 40.588514
50.280943 40.471172
50.337267 40.344443
50.137786 40.471172
-999. -999.
59.973372 43.597156
59.973372 43.597156
-999. -999.
60.193974 46.202143
59.982759 46.157553
59.917048 46.310098
59.830215 46.385196
59.684711 46.324179
59.651855 46.178675
59.642468 46.042558
59.541554 45.904095
59.344420 45.857158
59.344420 45.981541
59.365541 46.033171
59.123817 45.981541
58.837504 45.887667
58.715468 45.648290
58.527721 45.317386
58.220286 45.035766
58.196818 44.801083
58.241407 44.683741
58.220286 44.503035
58.285997 44.359878
58.351709 44.099379
58.372830 43.909285
58.408033 43.749700
58.539455 43.700417
58.638023 43.766128
58.703734 43.766128
58.858625 43.796637
58.990048 43.749700
59.144939 43.700417
59.266974 43.796637
59.421865 43.806025
59.619000 43.740313
59.696445 43.669908
59.785625 43.606544
59.895926 43.597156
59.973372 43.597156
-999. -999.
41.506126 41.646936
41.592959 41.679792
41.703260 41.771318
41.736116 41.959065
41.714994 42.116303
41.571837 42.245379
41.538982 42.393230
41.506126 42.548121
41.438068 42.726480
41.318379 42.864944
41.130632 42.961164
41.020331 43.050344
40.910030 43.116055
40.799729 43.139523
40.644838 43.172379
40.480559 43.195847
40.292812 43.268599
40.149655 43.397675
-999. -999.
39.994764 41.025025
40.379645 41.041453
40.799729 41.257362
41.118898 41.423987
41.449802 41.571837
41.506126 41.646936
-999. -999.
50.337267 46.870991
49.973507 46.847523
49.508834 46.751303
49.034773 46.697325
48.617037 46.622227
48.760193 46.554168
49.034773 46.432133
48.715604 46.347647
48.605302 46.303057
48.462145 46.063680
48.372966 45.934604
48.295520 45.934604
48.196953 45.904095
48.053796 45.911136
47.966963 46.087148
47.866049 46.232652
47.877783 46.324179
47.690037 46.333566
47.469434 46.378156
47.645447 46.178675
47.624325 46.026131
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47.403723 45.803181
47.347399 45.603700
47.293422 45.347895
47.117409 45.237594
47.084553 45.113212
47.051697 45.082703
46.995373 45.082703
46.852217 44.948933
46.831095 44.801083
46.676204 44.620376
46.753649 44.432629
46.950784 44.439670
47.171386 44.209680
47.347399 43.989078
47.391989 43.756741
47.448313 43.676949
47.612591 43.956222
47.657181 43.782556
47.525758 43.428184
47.525758 43.139523
47.591470 42.961164
47.755748 42.799232
47.898905 42.604445
48.086652 42.376802
48.241543 42.139772
48.318988 42.001308
48.527857 41.909782
48.736725 41.719688
48.957328 41.506126
49.100485 41.280830
49.267110 41.041453
49.431388 40.832584
49.574545 40.689427
49.720049 40.630757
49.950039 40.698815
-999. -999.
50.137786 40.471172
49.872593 40.464131
49.684847 40.360871
49.541690 40.217714
49.508834 40.067516
-999. -999.
40.149655 43.397675
39.994764 43.477468
39.863341 43.580728
39.675595 43.700417
39.532438 43.733273
39.410402 43.836533
39.276633 43.996118
39.058377 44.115807
38.814306 44.266004
38.527992 44.369265
38.274534 44.446711
38.032810 44.519462
37.910775 44.603948
37.767618 44.683741
37.669051 44.770574
37.591605 44.714250
37.403858 44.730678
37.227846 44.871488
37.126932 45.052194
36.906329 45.176576
36.676339 45.254022
36.852352 45.307999
36.852352 45.385445
36.918063 45.448809
37.194990 45.425341
37.436714 45.432381
37.612727 45.664718
37.788739 45.826650
37.999954 46.056639
38.110256 46.042558
38.229944 46.178675
38.474015 46.127044
38.527992 46.148166
38.340246 46.272548
38.175967 46.432133
38.075053 46.462642
37.943630 46.493151
37.779352 46.591718
37.821595 46.720794
38.009342 46.734875
38.286268 46.765384
38.474015 46.727834
38.560848 46.758343
38.483402 46.826401
38.474015 46.887419
38.682883 46.939049
38.980931 47.058738
39.189800 47.112715
39.365812 47.119756
39.398668 47.171386
39.344691 47.208935
39.255511 47.208935
39.210921 47.225363
39.201534 47.232404
39.189800 47.300462
39.079499 47.328624
38.924607 47.307503
38.826040 47.291075
38.694618 47.232404
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38.429425 47.232404
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38.032810 47.171386
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37.138666 46.939049
36.950919 46.894460
36.896942 46.751303
36.774906 46.802933
36.676339 46.840482
36.500327 46.779465
36.390026 46.741915
36.267990 46.697325
36.211666 46.643348
36.190545 46.704366
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35.728218 46.584677
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35.254157 46.188062
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33.841363 46.256120
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-999. -999.
29.929188 41.172876
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30.391515 41.182263
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30.710684 41.090736
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31.548505 41.339501
31.769107 41.423987
31.980322 41.564797
32.231434 41.630508
32.419180 41.752544
32.651517 41.853458
32.860385 41.919169
33.125578 42.001308
33.435360 42.034164
33.731061 42.041204
34.139411 42.008349
34.493783 42.017736
34.812952 42.017736
35.033555 42.099875
35.164978 42.116303
35.265891 42.083448
35.265891 41.975493
35.409048 41.820602
35.662507 41.719688
35.892496 41.719688
36.136567 41.761931
36.256256 41.604693
36.399413 41.323073
36.676339 41.316032
36.896942 41.290217
37.040099 41.224506
37.314679 41.116551
37.535281 41.015638
37.645582 41.074308
37.755884 41.107164
38.131377 40.966354
38.527992 40.989822
38.826040 41.074308
39.091233 41.100124
39.365812 41.132979
39.696716 41.074308
39.994764 41.025025
-999. -999.
29.640528 45.385445
29.696852 45.331467
29.685118 45.254022
29.685118 45.106171
29.652262 44.965361
29.509105 44.824551
29.321358 44.794042
29.133611 44.700169
28.990454 44.566399
28.859032 44.479566
28.814442 44.557012
28.936477 44.653232
29.046778 44.817510
29.035044 44.887916
29.046778 44.995870
28.903621 44.995870
28.870766 44.864447
28.837910 44.700169
28.748730 44.533543
28.715875 44.392733
28.659551 44.282432
28.659551 44.195599
28.659551 44.043055
28.638429 43.939794
28.659551 43.789597
-999. -999.
28.659551 43.789597
28.617308 43.580728
28.516394 43.428184
28.176103 43.364820
27.955500 43.172379
27.943766 42.994020
27.943766 42.775764
27.788875 42.735868
27.734898 42.663116
27.657452 42.604445
27.535417 42.531693
27.591741 42.475369
27.678574 42.449554
27.756019 42.360374
27.821730 42.221911
27.899176 42.132731
28.021211 42.024777
28.032946 41.935597
-999. -999.
28.032946 41.935597
28.009477 41.827643
28.065801 41.679792
28.197224 41.555410
28.340381 41.473270
28.593839 41.381744
28.903621 41.299605
29.079634 41.290217
29.091368 41.165835
28.981067 41.048493
28.715875 40.989822
28.572718 41.041453
28.319259 41.057881
28.032946 41.048493
27.833465 41.015638
27.612862 41.008597
27.457971 40.865440
27.127067 40.656572
26.885343 40.539230
26.664741 40.421888
26.488728 40.311587
26.366693 40.159043
26.223536 40.109759
26.223536 40.311587
26.247004 40.403114
26.444138 40.496987
26.709331 40.572086
26.840753 40.673000
26.631885 40.656572
26.354958 40.630757
26.235270 40.621369
26.101500 40.673000
26.059257 40.731670
-999. -999.
26.354958 41.811215
26.399548 41.729075
26.566174 41.621121
26.542705 41.463883
26.345571 41.348888
26.312715 41.140020
26.247004 40.931151
26.059257 40.731670
-999. -999.
24.712174 40.614329
24.813088 40.647184
24.768498 40.682387
24.756764 40.780954
24.669931 40.806769
24.515040 40.689427
24.526774 40.630757
24.637075 40.588514
24.712174 40.614329
-999. -999.
26.059257 40.731670
25.892632 40.839625
25.606318 40.898296
25.331738 40.956967
25.197969 40.973395
25.033690 41.008597
24.857678 40.924111
24.756764 40.898296
24.625341 40.898296
24.425860 40.956967
24.238113 40.806769
23.942412 40.757486
23.665485 40.621369
23.820377 40.504027
23.942412 40.471172
24.085569 40.428929
24.184136 40.353830
24.261582 40.278731
24.306171 40.201286
24.228726 40.243529
24.106690 40.328015
23.930678 40.370258
23.820377 40.379645
23.742931 40.252916
23.942412 40.142615
-999. -999.
23.963534 39.964255
23.820377 40.083944
23.710075 40.217714
23.534063 40.269344
23.456617 40.252916
23.501207 40.100372
-999. -999.
23.566918 39.940787
23.379172 40.083944
23.280604 40.259957
23.092858 40.360871
22.860521 40.471172
22.851134 40.522802
22.905111 40.621369
22.815931 40.588514
22.651653 40.555658
22.607063 40.353830
22.607063 40.152002
-999. -999.
30.105201 45.864199
29.971431 45.864199
29.929188 45.803181
29.818887 45.765632
29.807153 45.671758
29.717973 45.702267
29.696852 45.826650
29.663996 45.880627
29.663996 45.758591
29.663996 45.634209
29.675730 45.519214
29.696852 45.439422
29.640528 45.385445
-999. -999.
26.411283 40.067516
26.533318 40.210673
26.676475 40.311587
26.807898 40.438316
26.929933 40.428929
27.040234 40.428929
27.138801 40.454744
27.314814 40.496987
27.413381 40.421888
27.624596 40.370258
27.833465 40.379645
27.788875 40.496987
27.767753 40.572086
27.922644 40.555658
28.032946 40.513415
28.021211 40.438316
28.143247 40.428929
28.384971 40.464131
28.605573 40.454744
28.880153 40.445357
29.112490 40.471172
29.091368 40.565045
28.936477 40.588514
28.913009 40.640144
29.091368 40.698815
29.333092 40.705855
29.520839 40.722283
29.708586 40.731670
29.896333 40.741058
29.884599 40.806769
29.741442 40.832584
29.631140 40.806769
29.464515 40.816157
29.387069 40.823197
29.333092 40.881868
29.255647 40.898296
29.222791 40.982782
29.112490 41.032065
29.157080 41.123592
29.234525 41.231546
29.267381 41.273789
29.288502 41.224506
29.455128 41.224506
29.685118 41.165835
29.929188 41.172876
-999. -999.
26.223536 39.905585
26.312715 40.041701
26.322103 40.041701
26.411283 40.067516
-999. -999.
19.962180 39.914972
19.840144 40.048741
19.520975 40.142615
19.354349 40.344443
19.276904 40.471172
19.410673 40.454744
19.410673 40.572086
19.344962 40.764526
19.410673 40.940539
19.443529 40.973395
19.431795 41.107164
19.464651 41.224506
19.387205 41.372356
19.410673 41.456843
19.443529 41.529594
19.476385 41.604693
19.553830 41.794787
19.464651 41.869886
19.309759 41.893354
-999. -999.
19.309759 41.893354
19.211192 41.952025
19.100891 42.132731
18.946000 42.212523
18.737132 42.360374
18.626830 42.419045
18.549385 42.465982
18.396841 42.541080
18.230215 42.637301
18.054203 42.735868
17.887577 42.825047
17.723299 42.832088
17.591876 42.857903
17.303215 42.986979
17.073226 43.026875
17.138937 43.083199
17.338418 43.050344
17.436985 42.961164
17.535552 42.954123
17.514431 43.017488
17.359539 43.099627
17.127203 43.285027
16.864357 43.428184
16.542841 43.524404
16.322238 43.540832
16.068780 43.524404
15.991335 43.533792
15.958479 43.630012
15.881033 43.749700
15.683899 43.820106
15.561864 43.909285
15.374117 43.996118
15.176983 44.186212
15.165249 44.258964
15.221573 44.312941
15.406973 44.345797
15.209838 44.463138
15.033826 44.557012
14.890669 44.770574
14.890669 44.958321
14.834345 45.089743
14.756899 45.169536
14.702922 45.169536
14.658332 45.207085
14.548031 45.293918
14.327428 45.347895
14.205393 45.113212
14.106826 44.981789
14.008259 44.855060
13.909692 44.840979
13.820512 44.887916
13.665621 45.113212
13.578788 45.230553
13.534198 45.418300
13.510730 45.502786
13.653887 45.580232
13.698477 45.695227
13.632765 45.556764
-999. -999.
14.503441 45.237594
14.515175 45.237594
14.526909 45.207085
14.536297 45.176576
14.559765 45.113212
14.625477 45.082703
14.691188 45.042807
14.712309 45.005257
14.712309 44.988829
14.658332 45.005257
14.580887 45.035766
14.470585 45.042807
14.416608 45.075662
14.437730 45.146067
14.458851 45.200045
14.503441 45.237594
-999. -999.
14.282839 45.160148
14.271104 45.183617
14.306307 45.193004
14.315694 45.183617
14.339163 45.146067
14.339163 45.129640
14.339163 45.099131
14.339163 45.059234
14.360284 45.021685
14.372018 44.974748
14.372018 44.948933
14.372018 44.887916
14.372018 44.848019
14.393140 44.794042
14.425996 44.714250
14.437730 44.683741
14.416608 44.700169
14.315694 44.824551
14.261717 44.887916
14.261717 44.911384
14.282839 44.918424
14.339163 44.974748
14.339163 45.035766
14.306307 45.089743
14.282839 45.146067
14.282839 45.160148
-999. -999.
16.390297 43.414103
16.411418 43.428184
16.423152 43.428184
16.432540 43.428184
16.477129 43.421144
16.533453 43.414103
16.599165 43.404716
16.664876 43.397675
16.742322 43.364820
16.808033 43.357779
16.829155 43.331964
16.819767 43.324923
16.808033 43.317883
16.786912 43.317883
16.730588 43.317883
16.620286 43.301455
16.533453 43.301455
16.432540 43.317883
16.399684 43.364820
16.390297 43.414103
-999. -999.
16.643755 42.977592
16.676610 43.010447
16.730588 43.010447
16.819767 43.010447
16.930069 43.010447
17.007514 43.010447
17.073226 42.994020
17.094347 42.944736
17.040370 42.944736
16.984046 42.944736
16.906600 42.937696
16.796299 42.937696
16.685998 42.937696
16.653142 42.937696
16.643755 42.961164
16.643755 42.977592
-999. -999.
9.861401 44.082951
10.171183 43.989078
10.225161 43.925713
10.258016 43.766128
10.358930 43.557260
10.502087 43.308495
10.556064 43.155951
10.546677 43.059731
10.600654 43.010447
10.800135 42.871984
10.919824 42.782804
11.095836 42.620873
11.131039 42.524653
11.163895 42.419045
11.307052 42.458941
11.438474 42.458941
11.605100 42.360374
11.736522 42.205483
11.858558 42.083448
12.034571 42.067020
12.133138 41.959065
12.365474 41.736116
12.595464 41.555410
12.860657 41.407559
13.048403 41.280830
13.146970 41.306645
13.456753 41.299605
13.632765 41.290217
13.743067 41.264402
13.874489 41.156448
14.008259 41.032065
14.085704 40.891255
14.249983 40.839625
14.381406 40.799729
14.404874 40.757486
14.381406 40.647184
14.559765 40.673000
14.724044 40.689427
14.822611 40.673000
14.900056 40.588514
14.968114 40.438316
14.956380 40.379645
14.932912 40.337402
15.022092 40.236488
15.230960 40.168430
15.331874 40.100372
-999. -999.
15.418707 39.999458
15.507887 40.126187
15.606454 40.126187
15.627575 40.083944
15.683899 40.025273
-999. -999.
16.533453 39.914972
16.587431 40.067516
16.620286 40.184858
16.775178 40.353830
16.984046 40.529843
17.183527 40.555658
17.282094 40.487600
17.481575 40.386686
17.735033 40.337402
17.932167 40.252916
17.997879 40.126187
-999. -999.
18.328782 39.914972
18.385106 40.006498
18.471939 40.133228
18.417962 40.236488
18.307661 40.360871
18.131648 40.504027
18.021347 40.656572
17.932167 40.764526
17.744420 40.806769
17.481575 40.891255
17.282094 40.949926
17.138937 41.074308
16.918334 41.165835
16.697732 41.231546
16.488864 41.299605
16.268261 41.372356
16.125104 41.440415
16.014803 41.473270
15.937357 41.473270
15.881033 41.529594
15.881033 41.604693
15.991335 41.696220
16.125104 41.761931
16.146226 41.886313
16.092248 41.926210
16.024190 42.001308
15.925623 42.001308
15.838790 41.984880
15.761345 41.952025
15.904502 41.984880
15.770732 41.952025
15.606454 41.942637
15.430441 41.952025
15.209838 41.952025
15.198104 41.926210
15.198104 41.919169
15.198104 41.844070
14.968114 42.024777
14.890669 42.067020
14.780368 42.123344
14.724044 42.139772
14.691188 42.132731
14.646598 42.238339
14.569152 42.238339
14.515175 42.287622
14.327428 42.419045
14.196006 42.508225
14.095092 42.620873
13.963669 42.808620
13.897958 42.930655
13.853368 43.050344
13.787656 43.116055
13.731332 43.292068
13.677355 43.428184
13.611644 43.510323
13.534198 43.630012
13.456753 43.669908
13.346451 43.669908
13.325330 43.686336
13.313596 43.716845
13.236150 43.749700
13.146970 43.796637
13.060137 43.845921
12.938102 43.932754
12.794945 43.972650
12.640054 44.028974
12.553221 44.068870
12.442920 44.162743
12.342006 44.282432
12.288029 44.399774
12.288029 44.542931
12.288029 44.636804
12.299763 44.770574
12.320884 44.855060
12.431186 44.918424
12.452307 45.005257
12.398330 45.089743
12.266907 45.122599
12.243439 45.207085
12.222317 45.317386
12.255173 45.408913
12.342006 45.448809
12.452307 45.519214
12.518019 45.519214
12.541487 45.495746
12.628320 45.509827
12.816067 45.580232
13.092993 45.671758
13.224416 45.735123
13.391041 45.702267
13.555320 45.765632
13.689089 45.749204
13.698477 45.671758
13.665621 45.617781
13.632765 45.580232
13.689089 45.725736
-999. -999.
5.132528 43.383594
5.120794 43.383594
5.066817 43.392982
4.965903 43.392982
4.933047 43.343698
4.780503 43.336657
4.625612 43.376554
4.581022 43.423490
4.524698 43.449306
4.393275 43.465733
4.250118 43.479814
4.184407 43.529098
4.085840 43.529098
3.919215 43.465733
3.820648 43.392982
3.764324 43.367166
3.621167 43.296761
3.489744 43.247478
3.269141 43.184113
3.158840 43.038609
3.114250 42.843822
3.137719 42.820354
3.179962 42.787498
3.224551 42.395577
-999. -999.
3.224551 42.395577
3.358321 42.355680
3.358321 42.332212
3.391177 42.257113
3.236286 42.200789
3.257407 42.069367
3.323119 41.947331
3.158840 41.790093
2.827936 41.625815
2.464177 41.468577
2.222453 41.292564
1.900936 41.210425
1.504321 41.093083
1.140562 40.994516
0.919959 40.785648
0.919959 40.694121
0.767415 40.574433
0.546813 40.365564
0.403656 40.180164
-999. -999.
4.306442 40.027620
4.327564 40.027620
-999. -999.
4.085840 39.910278
3.952070 40.011192
4.029516 40.069863
4.196141 40.079250
4.261853 40.062822
4.306442 40.027620
-999. -999.
-0.105608 49.292925
0.049284 49.314047
0.237030 49.400879
0.457633 49.414960
0.612524 49.429041
0.645380 49.466591
0.535078 49.487712
0.269886 49.494753
0.258152 49.558117
0.380187 49.708315
0.657114 49.823310
0.919959 49.872593
1.239129 49.942998
-999. -999.
7.547422 43.836533
7.523953 43.813065
7.425386 43.773169
7.293964 43.726232
7.183662 43.686336
7.160194 43.630012
7.049893 43.580728
6.951326 43.510323
6.841024 43.437571
6.730723 43.374207
6.676746 43.348392
6.665012 43.268599
6.620422 43.228703
6.488999 43.188807
6.355230 43.148911
6.256662 43.123095
6.190951 43.090240
6.167483 43.099627
6.036060 43.106668
5.904637 43.106668
5.848313 43.148911
5.794336 43.172379
5.738012 43.219316
5.618323 43.219316
5.529144 43.228703
5.463432 43.252171
5.430576 43.317883
5.320275 43.348392
5.186506 43.357779
5.099673 43.388288
5.043349 43.421144
5.132528 43.383594
-999. -999.
7.547422 43.836533
7.699966 43.829493
7.866591 43.845921
8.066072 43.899898
8.152905 43.939794
8.185761 44.036014
8.263206 44.115807
8.352386 44.209680
8.439219 44.242536
8.472075 44.322328
8.561255 44.352837
8.626966 44.376305
8.793591 44.423242
8.946136 44.423242
9.124495 44.392733
9.309895 44.322328
9.652533 44.169784
9.861401 44.082951
-999. -999.
9.133882 41.316032
9.199594 41.306645
9.211328 41.299605
9.267652 41.273789
9.342751 41.257362
9.377953 41.215119
9.431930 41.191650
9.476520 41.156448
9.497642 41.123592
9.530497 41.074308
9.563353 41.008597
9.598556 40.907683
9.673654 40.722283
9.708857 40.522802
9.708857 40.464131
9.697123 40.344443
9.664267 40.227101
9.673654 40.142615
-999. -999.
8.495543 39.973643
8.462687 40.100372
8.483809 40.210673
8.472075 40.353830
8.439219 40.464131
8.385242 40.572086
8.352386 40.588514
8.263206 40.588514
8.209229 40.673000
8.209229 40.741058
8.209229 40.832584
8.218617 40.898296
8.209229 40.966354
8.218617 40.982782
8.296062 40.914724
8.385242 40.865440
8.561255 40.891255
8.683290 40.982782
8.802979 41.074308
8.925014 41.156448
9.035315 41.191650
9.089292 41.257362
9.133882 41.316032
-999. -999.
9.342751 43.033916
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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18.328782 59.384316
18.429696 59.400744
18.450818 59.356154
18.340517 59.311564
18.340517 59.255240
18.218481 59.255240
18.131648 59.299830
18.152770 59.248200
18.185625 59.180141
17.922780 59.067493
17.789010 58.947805
17.624732 58.931377
17.568408 58.936071
17.568408 59.051066
17.425251 59.074534
17.425251 58.959539
17.326684 58.891481
17.228117 58.828116
17.117815 58.783526
16.984046 58.788220
16.873745 58.776486
16.840889 58.692000
16.709466 58.656797
16.477129 58.696693
16.068780 58.675572
16.035924 58.645063
16.068780 58.645063
16.125104 58.640369
16.301117 58.633329
16.399684 58.623942
16.542841 58.605167
16.599165 58.581698
16.718853 58.525374
16.676610 58.478438
16.500598 58.466704
16.333972 58.497212
16.289383 58.485478
16.465395 58.438542
16.608552 58.375177
16.632021 58.328240
16.608552 58.229673
16.587431 58.166309
16.599165 58.119372
16.542841 58.060701
16.533453 58.020805
16.587431 57.955094
16.500598 57.950400
16.390297 57.978562
16.366828 57.938666
16.390297 57.884688
16.477129 57.821324
16.509985 57.732144
16.399684 57.633577
16.477129 57.567866
16.488864 57.462258
16.390297 57.361344
16.312851 57.241656
16.333972 57.103192
16.256527 56.971770
16.235405 56.765248
16.068780 56.596276
15.904502 56.366286
15.815322 56.169152
15.606454 56.169152
15.385851 56.206701
15.186370 56.176192
15.022092 56.211395
14.756899 56.218436
14.569152 56.150377
14.491707 56.047117
14.315694 56.077625
14.205393 55.960284
14.118560 55.817127
14.172537 55.598871
14.095092 55.455714
14.008259 55.413471
13.820512 55.462755
13.510730 55.455714
13.179826 55.387656
12.970958 55.425205
12.738621 55.418165
12.762089 55.469795
12.816067 55.481529
12.839535 55.537853
12.839535 55.598871
12.893512 55.655195
12.827801 55.756109
12.684644 55.873451
12.562608 56.021301
12.496897 56.119868
12.398330 56.225476
12.410064 56.291187
12.529753 56.255985
12.672910 56.248944
12.640054 56.286494
12.595464 56.347511
12.541487 56.413223
12.574343 56.450772
12.705765 56.439038
12.816067 56.474241
12.816067 56.554033
12.684644 56.657294
12.475776 56.737086
12.374862 56.852081
12.177727 56.952995
12.067426 57.133701
12.022836 57.253390
11.936003 57.384813
11.858558 57.396547
11.781112 57.389506
11.802234 57.502154
11.769378 57.567866
11.748257 57.650005
11.867945 57.732144
11.825702 57.851833
11.626221 57.828364
11.659077 57.915197
11.682545 57.985602
11.626221 58.079476
11.471330 58.107638
11.339907 58.138147
11.471330 58.236714
11.560510 58.271916
11.515920 58.293038
11.438474 58.288344
11.450209 58.304772
11.494798 58.379871
11.417353 58.422114
11.384497 58.351709
11.328173 58.316506
11.274196 58.283650
11.295317 58.316506
11.283583 58.391605
11.250728 58.433848
11.163895 58.445582
11.131039 58.497212
11.119305 58.581698
11.107571 58.623942
11.074715 58.727202
11.062981 58.795260
11.030125 58.886787
11.030125 58.983007
11.107571 59.074534
11.107571 59.107390
-999. -999.
13.808778 58.851585
13.820512 58.926683
13.853368 59.022903
13.963669 59.095655
13.886223 59.142592
13.897958 59.259934
13.897958 59.339726
13.721945 59.372582
13.621031 59.396050
13.567054 59.412478
13.433284 59.412478
13.313596 59.377276
13.215029 59.384316
13.114115 59.367888
13.027282 59.344420
12.982692 59.266974
12.994426 59.163714
13.060137 59.046372
13.081259 58.987701
13.104727 58.926683
12.926368 59.062800
12.783211 59.107390
12.684644 59.095655
12.586077 59.011169
12.553221 58.943111
12.464041 58.823423
12.442920 58.736590
12.508631 58.675572
12.419452 58.525374
12.288029 58.450276
12.243439 58.410380
12.353740 58.454969
12.452307 58.403339
12.553221 58.462010
12.738621 58.548843
12.905246 58.623942
12.982692 58.537109
13.125849 58.577005
13.191560 58.652104
13.477874 58.696693
13.632765 58.720162
13.698477 58.771792
13.743067 58.816382
13.787656 58.839850
-999. -999.
16.244793 56.279453
16.279995 56.305268
16.390297 56.378020
16.465395 56.493015
16.533453 56.669028
16.643755 56.852081
16.730588 56.983504
16.808033 57.152476
16.864357 57.288592
16.918334 57.335529
16.930069 57.377772
16.840889 57.330835
16.775178 57.258083
16.730588 57.168904
16.599165 56.934220
16.500598 56.852081
16.345707 56.669028
16.289383 56.523524
16.268261 56.427304
16.244793 56.328737
16.244793 56.279453
-999. -999.
18.021347 56.964729
18.143382 57.006972
18.230215 57.084418
18.295927 57.164210
18.462552 57.241656
18.572853 57.307367
18.572853 57.347263
18.671420 57.389506
18.769987 57.431749
18.727744 57.520929
18.716010 57.727450
18.760600 57.767347
18.793456 57.767347
18.870901 57.802549
18.870901 57.856526
18.880289 57.922238
18.781722 57.943359
18.671420 57.884688
18.528263 57.922238
18.406228 57.844792
18.164504 57.685207
18.065937 57.579600
18.033081 57.478686
18.042468 57.396547
17.997879 57.300327
17.997879 57.234615
18.054203 57.187678
18.042468 57.110233
18.075324 57.114927
18.143382 57.114927
18.119914 57.056256
18.054203 57.002278
18.021347 56.964729
-999. -999.
14.977502 55.021550
14.977502 55.047365
14.923525 55.181134
14.768633 55.256233
14.637211 55.286742
14.602008 55.185828
14.580887 55.110729
14.670066 55.054405
14.789755 55.028590
14.911790 55.028590
14.977502 55.021550
-999. -999.
9.861401 57.560825
10.072616 57.614802
10.258016 57.668780
10.380052 57.720410
10.412907 57.696942
10.358930 57.633577
10.326075 57.537357
10.368318 57.462258
10.424642 57.342570
10.424642 57.258083
10.302606 57.152476
10.236895 57.072683
10.204039 57.002278
10.171183 56.934220
10.182918 56.863815
10.182918 56.814532
10.159449 56.802797
10.171183 56.814532
10.150062 56.718311
10.004558 56.687803
10.004558 56.638519
10.171183 56.669028
10.204039 56.645560
10.082004 56.572808
10.072616 56.511790
10.114859 56.462506
10.192305 56.530565
10.314340 56.530565
10.391786 56.469547
10.523209 56.500056
10.699221 56.511790
10.788401 56.488322
10.821257 56.413223
10.809523 56.305268
10.633510 56.206701
10.546677 56.169152
10.523209 56.206701
10.412907 56.126909
10.347196 56.194967
10.347196 56.241904
10.248629 56.225476
10.171183 56.101094
10.215773 55.972018
10.126594 55.903960
-999. -999.
9.995171 54.385557
10.093738 54.385557
10.171183 54.448922
10.391786 54.397291
10.469232 54.326886
10.588920 54.326886
10.776667 54.359742
10.886968 54.390251
10.964414 54.352702
10.964414 54.256481
10.865847 54.186076
10.732077 54.127405
10.666366 54.028838
10.699221 53.977208
-999. -999.
10.699221 53.977208
10.743811 53.913843
10.832991 53.958433
10.997269 54.010064
11.107571 53.984248
11.217872 53.972514
11.384497 53.972514
11.328173 54.028838
11.372763 54.042919
11.438474 54.082816
11.605100 54.164955
11.802234 54.197810
11.957125 54.216585
11.957125 54.146180
12.034571 54.179036
12.112016 54.282297
12.231705 54.359742
12.365474 54.455962
12.518019 54.474737
12.640054 54.460656
12.464041 54.397291
12.365474 54.338621
12.320884 54.282297
12.442920 54.333927
12.586077 54.364436
12.738621 54.390251
12.872391 54.397291
12.970958 54.326886
13.114115 54.275256
13.158705 54.197810
13.215029 54.190770
13.325330 54.134446
13.456753 54.139140
13.501342 54.146180
13.588175 54.075775
13.653887 53.998329
13.677355 53.925578
13.698477 53.855173
13.832246 53.822317
13.963669 53.796502
14.106826 53.775380
14.196006 53.770686
14.282839 53.730790
14.404874 53.690894
14.458851 53.756605
14.458851 53.841092
14.306307 53.880988
14.217127 53.888028
-999. -999.
13.510730 54.467697
13.510730 54.448922
13.522464 54.404332
13.578788 54.345661
13.567054 54.301071
13.477874 54.338621
13.367573 54.319846
13.313596 54.289337
13.158705 54.308112
13.048403 54.364436
13.092993 54.411372
13.104727 54.460656
13.060137 54.545142
13.137583 54.556876
13.269006 54.512286
13.367573 54.493512
13.334717 54.545142
13.224416 54.589732
13.158705 54.641362
13.203294 54.678912
13.301862 54.667177
13.325330 54.615547
13.468487 54.608507
13.555320 54.582691
13.534198 54.519327
13.501342 54.474737
-999. -999.
14.217127 53.888028
14.372018 53.951393
14.548031 53.991289
14.569152 53.951393
14.670066 54.010064
14.780368 54.082816
15.022092 54.160261
15.352995 54.197810
15.573598 54.237707
15.737876 54.268216
15.937357 54.301071
16.146226 54.397291
16.345707 54.507593
16.533453 54.596772
16.786912 54.646056
17.007514 54.723502
17.204648 54.775132
17.490962 54.805641
17.744420 54.845537
17.988491 54.871352
18.241949 54.871352
18.450818 54.838496
18.605709 54.793907
18.737132 54.711767
18.716010 54.641362
18.582241 54.685952
18.483673 54.730542
18.385106 54.761051
18.406228 54.692993
18.495408 54.552183
18.582241 54.437188
18.638565 54.345661
18.760600 54.312805
18.781722 54.352702
18.859167 54.390251
19.124359 54.397291
19.377818 54.430147
19.553830 54.486471
-999. -999.
19.553830 54.486471
19.586686 54.519327
19.685253 54.563917
19.762699 54.601466
19.819023 54.653096
19.840144 54.697686
19.861266 54.716461
19.905856 54.805641
19.917590 54.934717
-999. -999.
-0.037549 50.801940
0.171319 50.769084
0.380187 50.797246
0.699357 50.858264
0.919959 50.893467
1.053729 50.928669
1.074850 50.970912
1.295453 51.060092
1.471466 51.151618
1.516055 51.276001
1.471466 51.322937
1.218007 51.329978
1.020873 51.315897
0.800271 51.329978
0.788537 51.433239
0.699357 51.503644
0.767415 51.515378
0.887104 51.543540
0.919959 51.604558
1.009139 51.667922
0.964549 51.700778
0.865982 51.728940
0.976283 51.775877
1.095972 51.804039
1.185152 51.768836
1.328309 51.796998
1.361164 51.865056
1.340043 51.904953
1.328309 51.968317
1.417488 51.961277
1.548911 52.001173
1.692068 52.109127
1.790635 52.346158
1.814104 52.515130
1.757780 52.695836
1.593501 52.836646
1.417488 52.909398
1.274331 52.942254
1.030261 52.949294
0.800271 52.916438
0.633645 52.902357
0.535078 52.808484
0.445899 52.749813
0.368453 52.796750
0.237030 52.815525
0.138463 52.822565
0.114995 52.822565
0.114995 52.829606
0.183053 52.928173
0.281620 52.989190
0.326210 53.022046
0.403656 53.087757
0.445899 53.155816
0.445899 53.261423
0.380187 53.327135
0.269886 53.404580
0.159585 53.465598
0.105608 53.524269
0.004694 53.557124
-999. -999.
-0.061018 53.655692
0.028162 53.615795
0.037549 53.615795
0.061018 53.615795
0.147851 53.601714
0.258152 53.594674
0.269886 53.601714
0.225296 53.773033
0.093873 53.836398
-999. -999.
5.010493 53.214487
5.076204 53.254383
5.076204 53.240302
4.989371 53.141735
4.834480 53.029087
4.780503 52.935213
4.923660 52.996231
4.989371 53.101838
5.010493 53.214487
-999. -999.
3.534334 51.351099
3.578924 51.372221
3.710346 51.379261
3.841769 51.315897
3.898093 51.301816
4.062372 51.358140
4.261853 51.372221
4.339298 51.365180
4.282974 51.398036
4.151551 51.412117
3.975539 51.398036
3.874625 51.419158
3.942683 51.508337
4.062372 51.522418
4.315830 51.564661
4.503577 51.625679
4.822746 51.674963
4.933047 51.714859
4.855602 51.754755
4.712445 51.714859
4.634999 51.700778
4.470721 51.707818
4.327564 51.743021
4.217263 51.804039
4.217263 51.904953
4.228997 51.947196
4.238384 51.968317
4.250118 51.968317
4.282974 51.994132
4.294708 51.994132
4.348685 52.041069
4.414397 52.083312
4.491842 52.144330
4.634999 52.259325
4.691323 52.447071
4.768769 52.674714
4.879070 52.862461
5.043349 52.902357
5.099673 52.916438
5.001106 52.946947
-999. -999.
4.062372 51.761796
4.017782 51.789958
4.029516 51.789958
4.151551 51.796998
4.238384 51.743021
4.315830 51.700778
4.339298 51.667922
4.306442 51.667922
4.184407 51.714859
4.062372 51.761796
-999. -999.
3.832382 51.693737
3.865237 51.714859
3.930949 51.721899
4.008394 51.700778
4.095227 51.674963
4.106961 51.639760
4.041250 51.646801
3.919215 51.686697
3.832382 51.693737
-999. -999.
3.665756 51.536499
3.644635 51.461401
3.644635 51.433239
3.698612 51.433239
3.754936 51.468441
3.754936 51.508337
3.665756 51.536499
-999. -999.
2.806815 51.095294
2.806815 51.137537
3.003949 51.205596
3.224551 51.287735
3.400564 51.337018
3.510865 51.351099
3.534334 51.351099
-999. -999.
1.239129 49.942998
1.483200 50.057993
1.715536 50.205844
1.736658 50.283289
1.659212 50.332573
1.692068 50.508586
1.724924 50.684598
1.846959 50.900507
2.079296 50.963872
2.321020 51.010808
2.508767 51.024889
2.663658 51.053051
2.717635 51.060092
2.806815 51.095294
-999. -999.
10.004558 59.015863
9.751100 59.015863
9.521110 59.083921
9.563353 59.006476
9.399075 58.907909
9.267652 58.839850
9.223062 58.783526
9.101027 58.731896
9.047049 58.628635
8.826447 58.569964
8.659822 58.462010
8.462687 58.311812
8.098928 58.182737
7.965158 58.288344
7.878326 58.161615
7.657723 58.060701
7.437121 58.013764
7.139072 58.072435
7.270495 58.154574
6.995916 58.166309
6.930204 58.079476
6.754192 58.131106
6.643890 58.084169
6.686133 58.206205
6.686133 58.375177
6.554711 58.253142
6.334108 58.271916
6.080650 58.358749
5.695769 58.537109
5.463432 58.696693
5.540878 58.875053
5.594855 58.999435
5.660566 58.999435
5.728625 58.931377
5.738012 58.931377
5.815457 58.947805
5.914025 58.943111
5.914025 58.966579
5.925759 58.983007
5.904637 59.051066
6.014938 59.107390
6.057181 59.170754
6.167483 59.255240
6.167483 59.288096
6.167483 59.349114
6.057181 59.344420
6.125240 59.389010
6.312986 59.506352
6.235541 59.541554
6.134627 59.480536
5.871781 59.405438
5.738012 59.445334
5.761480 59.389010
5.728625 59.339726
5.594855 59.332686
5.550265 59.417172
5.484554 59.332686
5.320275 59.316258
5.296807 59.356154
5.231096 59.384316
5.231096 59.461762
5.308541 59.546248
5.484554 59.658896
5.585468 59.630734
5.672301 59.658896
5.848313 59.651855
5.871781 59.691752
5.970349 59.748076
6.125240 59.780931
6.334108 59.825521
6.301252 59.858377
6.202685 59.813787
6.125240 59.818481
5.848313 59.809093
5.716890 59.851336
5.782602 59.902967
5.949227 59.989800
-999. -999.
5.794336 60.083673
5.684035 59.980412
5.496288 59.919395
5.407108 59.956944
-999. -999.
5.439964 59.741035
5.451698 59.780931
5.451698 59.841949
5.451698 59.891232
5.407108 59.912354
5.364865 59.952250
5.296807 59.947557
5.287420 59.886539
5.275685 59.834908
5.287420 59.797359
5.353131 59.769197
5.397721 59.752769
-999. -999.
5.263951 59.159020
5.263951 59.215344
5.263951 59.276362
5.254564 59.327992
5.221708 59.356154
5.177118 59.327992
5.177118 59.266974
5.165384 59.175448
5.165384 59.163714
5.177118 59.159020
5.198240 59.163714
-999. -999.
8.659822 54.908902
8.626966 55.009815
8.626966 55.122464
8.626966 55.230418
8.626966 55.350107
8.540133 55.451020
8.418098 55.526119
8.242085 55.587137
8.176374 55.563669
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155.083559 60.398149
154.919281 60.316010
154.851222 60.287848
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154.663475 60.086020
-999. -999.
70.320568 66.640730
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70.865034 66.741644
71.062168 66.805009
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70.785241 66.499920
70.630350 66.504614
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70.320568 66.640730
-999. -999.
72.526593 70.006092
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72.592304 69.914565
72.592304 69.884056
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70.189145 66.753378
-999. -999.
69.780796 66.697054
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70.024867 66.460024
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-999. -999.
60.020308 70.050682
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60.517837 69.815998
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60.517837 69.729165
60.414577 69.663454
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60.151731 69.703350
60.062551 69.675188
-999. -999.
59.888886 68.691864
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60.447432 68.710639
60.592936 68.778697
60.771296 68.853796
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60.592936 69.353672
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60.602324 69.656413
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61.146789 69.825386
61.320455 69.806611
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63.118131 69.642332
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68.027710 68.438406
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66.990409 69.522644
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66.858986 69.764368
66.858986 69.888750
-999. -999.
66.912963 70.036601
67.025611 69.975583
67.213358 69.975583
-999. -999.
70.189145 66.753378
69.968543 66.809702
69.780796 66.779194
69.780796 66.697054
-999. -999.
49.842084 68.008935
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54.197810 68.933588
54.286990 68.945322
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54.451269 68.966444
54.516980 68.973484
-999. -999.
49.896062 69.259798
50.018097 69.170619
50.093196 69.161231
50.093196 69.278573
50.182376 69.184700
50.313798 69.083786
50.280943 68.996953
50.238700 69.039196
50.158907 69.090826
-999. -999.
58.806995 69.963849
58.764752 69.968543
-999. -999.
60.064898 69.675188
59.867764 69.672841
59.637774 69.733859
59.689405 69.790183
59.515739 69.834773
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59.248200 69.771408
59.205957 69.729165
59.041678 69.846507
58.886787 69.938034
58.806995 69.963849
-999. -999.
54.516980 68.973484
54.629628 68.985219
54.596772 68.968791
54.498205 68.950016
54.376170 68.926548
54.221279 68.917160
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59.778584 68.360960
59.989800 68.466568
59.966331 68.529933
59.877151 68.595644
59.891232 68.691864
-999. -999.
39.914972 68.079340
40.018233 68.046485
40.083944 67.987814
40.205979 67.938530
40.304547 67.886900
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40.614329 66.488186
40.435969 66.399006
40.271691 66.354416
40.224754 66.333295
40.093331 66.274624
-999. -999.
39.950174 64.608371
40.156696 64.573169
40.344443 64.545007
40.475865 64.526232
40.574433 64.540313
40.729324 64.502764
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40.752792 64.601331
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40.565045 64.810199
40.466478 64.915806
40.335055 65.028455
40.133228 65.141103
40.034660 65.213855
-999. -999.
39.860995 65.617510
40.081597 65.648019
40.302200 65.720771
40.508721 65.802910
40.630757 65.915558
40.851359 65.976576
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-999. -999.
48.661626 69.445198
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-999. -999.
50.161254 69.090826
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48.419902 69.313776
48.541938 69.391221
48.663973 69.445198
-999. -999.
29.978472 69.703350
30.001940 69.684575
30.067652 69.642332
30.100507 69.656413
30.100507 69.736206
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30.476001 69.785489
30.588649 69.783143
30.687216 69.759674
30.842107 69.754981
30.893738 69.754981
-999. -999.
30.893738 69.754981
30.907819 69.754981
30.931287 69.764368
31.104953 69.729165
31.292700 69.705697
31.391267 69.675188
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31.658806 69.632945
31.733905 69.675188
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33.024664 69.736206
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32.320613 69.546112
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32.339388 69.414689
32.395712 69.414689
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32.813449 69.445198
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32.926097 69.348978
32.893241 69.295001
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33.268735 69.332550
33.245266 69.295001
33.310978 69.273879
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33.334446 69.259798
33.367302 69.241024
33.386077 69.208168
33.522193 69.248064
33.686471 69.248064
33.827282 69.259798
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34.169919 69.259798
34.381135 69.243370
34.592350 69.219902
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34.963150 69.182353
35.118041 69.149497
35.216608 69.149497
35.287013 69.182353
35.230689 69.217555
35.441904 69.189393
35.681281 69.172965
35.859641 69.165925
35.958208 69.130722
36.080243 69.107254
36.333701 69.060317
36.577772 69.008687
36.727970 68.938282
36.850005 68.905426
36.972041 68.870224
37.192643 68.823287
37.324066 68.762269
37.493038 68.710639
37.633848 68.675436
37.798127 68.607378
37.999954 68.541667
38.098521 68.499424
38.197089 68.471262
38.328511 68.400857
38.361367 68.349226
38.492790 68.276474
38.516258 68.281168
38.680537 68.248312
38.891752 68.234231
38.746248 68.353920
38.835428 68.304636
38.980931 68.250659
39.046643 68.166173
39.112354 68.128624
39.145210 68.184948
39.309488 68.116890
39.440911 68.074647
39.609883 68.041791
39.717838 68.006588
39.863341 68.025363
39.783549 68.116890
39.914972 68.079340
-999. -999.
40.093331 66.274624
39.807017 66.227687
39.544172 66.178404
39.290714 66.129120
39.070111 66.115039
38.835428 66.070449
38.713392 66.075143
38.483402 66.084530
38.262800 66.089224
37.967099 66.093918
37.830982 66.107999
37.633848 66.129120
37.788739 66.107999
37.723028 66.115039
37.600992 66.124427
37.446101 66.194832
37.248967 66.222994
36.981428 66.272277
36.709195 66.288705
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35.901884 66.373191
35.606183 66.403700
35.460679 66.474105
35.230689 66.474105
35.118041 66.544510
34.888051 66.575019
34.789484 66.584406
34.512557 66.539816
34.437459 66.626649
34.390522 66.722870
34.282568 66.736951
34.193388 66.687667
34.104208 66.711135
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33.827282 66.713482
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33.423626 66.774500
33.212411 66.830824
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32.860385 66.973981
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31.987363 67.056120
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32.405099 66.936432
32.484892 66.823783
32.761818 66.713482
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32.804061 66.631343
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33.066907 66.518695
33.254654 66.455330
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33.606679 66.403700
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33.573823 66.288705
33.874218 66.239422
34.071352 66.234728
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34.521945 66.079837
34.658061 65.927292
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34.780097 65.594042
34.733160 65.507209
34.709692 65.425070
34.456233 65.392214
34.381135 65.333543
34.559494 65.195080
34.709692 65.051923
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34.780097 64.920500
34.888051 64.871217
34.855195 64.739794
34.897438 64.582556
34.723773 64.507457
34.676836 64.441746
34.920907 64.498070
35.033555 64.399503
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36.113099 64.164819
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36.596547 63.981766
36.906329 63.904321
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37.600992 63.768204
37.600992 63.798713
37.666704 63.857384
37.798127 63.904321
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38.164233 63.904321
38.262800 63.880852
38.164233 63.944217
38.107909 64.087374
38.051585 64.202369
38.018729 64.317364
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37.061220 64.474601
36.948572 64.573169
36.864086 64.660001
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38.140765 64.861829
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39.013787 64.730407
39.342344 64.622452
39.478461 64.591943
39.699063 64.554394
39.929053 64.535619
39.971296 64.563781
39.952521 64.608371
-999. -999.
40.037007 65.213855
39.914972 65.319462
39.882116 65.453232
39.863341 65.521290
39.863341 65.617510
-999. -999.
30.215502 59.963984
30.182647 60.001534
30.048877 60.013268
-999. -999.
30.931287 61.681868
30.954755 61.693602
31.020467 61.677174
31.142502 61.672480
31.231682 61.646665
31.339636 61.613809
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32.341735 61.207807
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32.508360 61.069344
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32.806408 60.689156
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32.552950 60.330091
32.376937 60.189281
32.222046 60.177546
32.111745 60.222136
31.980322 60.243258
31.780841 60.231524
31.571973 60.182240
31.449938 60.083673
-999. -999.
30.987611 59.940516
30.964143 60.055511
30.975877 60.182240
30.910165 60.304275
30.886697 60.423964
30.788130 60.553040
30.633239 60.646913
30.480695 60.722012
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30.501816 60.839354
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30.292948 61.031794
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30.126323 61.472999
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30.281214 61.604422
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30.375087 61.672480
30.407943 61.672480
30.450186 61.667787
30.501816 61.688908
30.511204 61.735845
-999. -999.
19.987995 69.806611
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20.185129 69.895791
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20.340020 69.785489
20.307164 69.672841
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21.011215 69.783143
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21.166106 69.825386
21.222430 69.893444
21.320997 69.888750
-999. -999.
21.255286 70.013132
21.386709 69.970889
21.541600 69.914565
21.705878 69.839467
21.884238 69.736206
22.006273 69.698656
22.006273 69.790183
21.926481 69.858241
21.926481 69.930993
21.973417 69.989664
-999. -999.
22.987250 70.048335
22.987250 69.989664
23.085817 69.952115
23.226627 69.956808
-999. -999.
29.173507 70.001398
29.403497 69.956808
29.516145 69.919259
29.450434 69.884056
29.825928 69.895791
29.910414 69.855894
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29.624100 69.729165
29.549001 69.649373
29.746135 69.691616
29.891639 69.693963
29.933882 69.703350
29.976125 69.703350
-999. -999.
19.865959 63.650862
20.006769 63.704840
20.142886 63.681371
20.217985 63.721267
20.340020 63.744736
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23.911903 65.765361
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24.066794 65.847500
24.024551 65.936680
-999. -999.
24.024551 65.936680
24.090263 65.910865
24.099650 65.910865
24.132506 65.892090
24.165361 65.878009
24.254541 65.866275
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24.653503 65.701996
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25.080627 65.551799
25.146338 65.516596
25.258986 65.443844
25.324698 65.378133
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-999. -999.
27.624596 60.585896
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27.457971 60.522531
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23.578653 60.006227
-999. -999.
23.346316 59.980412
23.358050 60.067245
23.313460 60.090713
-999. -999.
23.069389 59.989800
23.015412 60.001534
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21.351506 62.977321
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21.346812 63.021911
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-999. -999.
19.983301 60.025002
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-999. -999.
19.983301 60.222136
20.039625 60.280807
20.049013 60.325397
20.016157 60.346519
-999. -999.
21.769243 60.210402
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21.614352 60.243258
21.581496 60.182240
21.658941 60.139997
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21.802098 60.156425
-999. -999.
22.553086 60.050817
22.618797 60.083673
22.672774 60.172853
22.696243 60.264379
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22.639918 60.271420
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22.553086 60.050817
-999. -999.
29.002189 59.947557
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29.255647 60.006227
-999. -999.
30.048877 60.013268
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28.495272 60.731399
28.384971 60.700891
28.262935 60.663341
28.152634 60.602324
28.065801 60.553040
27.866320 60.560081
27.767753 60.569468
27.624596 60.585896
-999. -999.
9.941194 63.411485
10.105472 63.397404
10.185264 63.411485
10.138328 63.465462
10.194652 63.495971
10.382399 63.495971
10.579533 63.519440
10.701568 63.549948
10.715649 63.578110
10.668712 63.603926
10.612388 63.636781
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10.649938 63.704840
10.471578 63.650862
10.340156 63.603926
10.161796 63.554642
10.039761 63.578110
-999. -999.
9.962315 63.754123
10.004558 63.798713
-999. -999.
9.929459 63.923095
10.117206 63.977072
10.117206 64.005234
10.051495 64.087374
10.103125 64.136657
10.182918 64.183594
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10.412907 64.336138
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13.017894 65.981270
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-999. -999.
18.234909 63.000789
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-999. -999.
15.632269 68.926548
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15.519621 68.774003
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15.599413 68.910120
15.632269 68.926548
-999. -999.
14.451811 68.680130
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14.428342 68.663702
14.451811 68.680130
-999. -999.
15.775426 69.194087
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15.888074 69.252758
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-999. -999.
14.925871 67.795373
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14.860160 67.828229
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14.939952 67.774252
14.925871 67.795373
-999. -999.
16.944150 69.194087
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16.822114 69.229289
16.944150 69.219902
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-999. -999.
18.244296 69.693963
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18.244296 69.693963
-999. -999.
18.863861 70.020173
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-999. -999.
19.150175 70.031907
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-999. -999.
19.347309 70.006092
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-999. -999.
18.087058 63.012523
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-999. -999.
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-999. -999.
20.049013 60.090713
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-999. -999.
20.016157 60.346519
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19.962180 60.391108
-999. -999.
7.547422 63.010176
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-999. -999.
10.039761 63.578110
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-999. -999.
10.006905 63.798713
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-999. -999.
8.450953 63.568723
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8.493196 63.524133
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-999. -999.
4.933047 61.130361
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
140.028612 73.362066
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139.704748 73.416043
139.653118 73.437165
139.784541 73.472367
-999. -999.
137.038744 71.613674
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137.193635 71.566737
137.301589 71.564390
137.367301 71.587859
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136.785285 71.571431
136.907321 71.573778
136.949564 71.599593
137.015275 71.608980
137.038744 71.613674
-999. -999.
138.043189 71.526841
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138.249711 71.578471
138.348278 71.578471
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138.029108 71.508066
138.029108 71.515107
138.029108 71.536228
138.043189 71.526841
-999. -999.
139.972288 72.472616
139.972288 72.472616
-999. -999.
140.138913 72.237932
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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-999. -999.
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95.260385 76.143066
95.260385 76.126638
95.354258 76.110210
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95.476294 76.089089
95.476294 76.037458
95.532618 76.013990
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95.626491 76.096129
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95.654653 76.182962
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95.194673 76.431726
95.166511 76.445807
95.161818 76.464582
-999. -999.
98.804106 76.464582
98.888592 76.469276
98.935529 76.464582
99.001240 76.459888
99.104501 76.450501
99.245311 76.441114
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99.714678 76.422339
99.817939 76.438767
99.874263 76.441114
99.883650 76.441114
99.958749 76.450501
-999. -999.
96.321154 76.274489
96.321154 76.272142
96.283605 76.248673
96.283605 76.215818
96.330542 76.185309
96.311767 76.159494
96.321154 76.128985
96.189731 76.133678
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95.757914 76.147759
95.645266 76.171228
95.504456 76.175921
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95.326096 76.211124
95.288547 76.239286
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95.354258 76.265101
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95.457519 76.215818
95.513843 76.248673
95.607716 76.255714
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95.776688 76.274489
95.917499 76.267448
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96.030147 76.236939
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96.584000 76.225205
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96.555838 76.157147
96.508901 76.185309
96.490126 76.236939
96.396253 76.262754
96.321154 76.274489
-999. -999.
96.300033 77.004354
96.300033 76.987926
96.196772 76.964458
96.084124 76.931602
95.999638 76.898747
95.868215 76.889359
95.736792 76.861197
95.671081 76.868238
95.671081 76.894053
95.755567 76.896400
95.877602 76.933949
95.868215 76.952724
95.736792 76.926909
95.577207 76.910481
95.436397 76.912828
95.239263 76.896400
95.173552 76.915175
95.333137 76.948030
95.483334 76.997314
95.633532 77.004354
95.868215 77.046597
96.027800 77.067719
96.121673 77.095881
96.271871 77.140471
96.337582 77.117002
96.393906 77.088840
96.393906 77.048944
96.365744 77.009048
96.337582 76.994967
96.328195 76.990273
96.300033 77.004354
-999. -999.
80.341554 73.164932
80.454202 73.183707
80.562156 73.209522
80.585625 73.261152
80.519913 73.272886
80.407265 73.270540
80.341554 73.315129
80.407265 73.352679
80.463589 73.345638
80.552769 73.329210
80.552769 73.364413
80.651336 73.385534
80.782759 73.418390
80.829696 73.458286
80.740516 73.465327
80.707660 73.437165
80.641949 73.430124
80.576237 73.477061
80.552769 73.526345
80.627868 73.540426
80.740516 73.549813
80.839083 73.547466
80.871939 73.568588
81.036217 73.592056
81.148865 73.568588
81.247432 73.561547
81.303756 73.573281
81.303756 73.596750
81.402323 73.606137
81.491503 73.610831
81.599457 73.620218
81.712106 73.629605
81.843528 73.641340
81.965564 73.657767
82.054743 73.657767
82.172085 73.655421
82.294121 73.641340
82.449012 73.653074
82.636759 73.660114
82.716551 73.648380
82.801037 73.634299
82.932460 73.638993
83.176531 73.646033
83.373665 73.648380
83.664672 73.660114
83.918131 73.676542
84.068328 73.702357
84.171589 73.704704
84.368723 73.714091
84.547082 73.723479
84.753604 73.753988
84.819315 73.751641
84.852171 73.716438
84.983594 73.704704
85.194809 73.695317
85.429492 73.751641
85.481123 73.793884
85.626627 73.812658
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85.847229 73.805618
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86.443325 74.458038
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86.509037 74.523750
86.584135 74.540177
86.509037 74.547218
86.462100 74.561299
86.344758 74.573033
86.232110 74.605889
86.020895 74.608236
85.833148 74.610582
85.692338 74.624663
85.668870 74.650479
85.748662 74.662213
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85.814373 74.723231
85.889472 74.730271
85.969264 74.749046
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85.870697 74.812410
85.889472 74.819451
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86.002120 74.805370
86.086606 74.795982
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86.232110 74.732618
86.330677 74.716190
86.476181 74.697415
86.518424 74.671600
86.584135 74.643438
86.649847 74.619970
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86.663928 74.688028
86.715558 74.737312
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86.884530 74.767820
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87.048809 74.854653
87.091052 74.880468
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87.170844 74.967301
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87.292879 74.948527
87.400834 74.934446
87.588581 74.976689
87.654292 75.007198
87.522869 75.011891
87.358591 75.021279
87.260024 75.016585
87.114520 75.042400
86.950242 75.054134
86.828206 75.079949
86.917386 75.101071
87.072277 75.126886
87.245943 75.124539
87.490014 75.115152
87.644905 75.108111
87.701229 75.082296
87.734084 75.068215
87.776327 75.072909
87.898363 75.094030
87.987543 75.096377
88.039173 75.115152
88.020398 75.145661
88.039173 75.166782
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88.325487 75.237187
88.395892 75.267696
88.438135 75.293511
88.503846 75.302899
88.616494 75.307592
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88.790160 75.347489
88.968520 75.368610
88.921583 75.394425
88.823016 75.394425
88.846484 75.415547
88.968520 75.417894
89.067087 75.427281
89.189122 75.469524
89.278302 75.441362
89.376869 75.417894
89.475436 75.403813
89.606859 75.436668
89.728894 75.462484
89.916641 75.462484
-999. -999.
90.003474 75.488299
89.890826 75.502380
89.834502 75.523501
89.980006 75.551663
-999. -999.
89.496558 77.304749
89.468396 77.302402
89.468396 77.285974
89.440234 77.260159
89.505945 77.243731
89.515332 77.208529
89.590431 77.199142
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89.487170 77.131083
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89.196163 77.135777
89.139839 77.208529
89.196163 77.250772
89.261874 77.271893
89.365135 77.293015
89.449621 77.304749
89.496558 77.304749
-999. -999.
82.188513 75.413200
82.254224 75.401466
82.272999 75.342795
82.230756 75.340448
82.108721 75.356876
82.043009 75.298205
82.052397 75.232494
82.043009 75.192598
81.944442 75.248922
81.920974 75.352182
81.831794 75.328714
81.723840 75.368610
81.611192 75.382691
81.601804 75.321673
81.658128 75.251268
81.690984 75.201985
81.625273 75.244228
81.545480 75.319327
81.493850 75.370957
81.503237 75.427281
81.658128 75.464830
81.681597 75.424934
81.766083 75.403813
81.855262 75.434322
81.888118 75.460137
81.986685 75.497686
81.822407 75.483605
81.855262 75.509420
82.075865 75.516461
82.240143 75.488299
82.155657 75.457790
82.188513 75.413200
-999. -999.
82.319936 70.398013
82.319936 70.423829
82.352792 70.470765
82.441971 70.515355
82.564007 70.517702
82.639105 70.451991
82.714204 70.379239
82.770528 70.308834
82.817465 70.240775
82.747060 70.214960
82.648493 70.158636
82.517070 70.189145
82.427890 70.231388
82.385647 70.273631
82.352792 70.315874
82.319936 70.360464
82.319936 70.398013
-999. -999.
79.961367 72.198036
80.181969 72.144059
80.379103 72.099469
80.590318 72.068960
80.843777 72.031411
80.843777 71.984474
80.918875 71.937537
81.153559 71.850704
81.294369 71.766218
81.327225 71.780299
81.416404 71.745097
81.538440 71.714588
81.669862 71.702854
81.834141 71.669998
81.989032 71.679385
82.167392 71.681732
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82.575741 71.702854
82.716551 71.723975
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83.073270 71.475211
83.059189 71.407152
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82.674308 71.306239
82.430237 71.249915
82.298814 71.174816
82.331670 71.113798
82.355138 71.015231
82.298814 70.933092
82.312895 70.846259
82.322283 70.759426
82.387994 70.719530
82.298814 70.623310
82.242490 70.543517
82.233103 70.456684
82.233103 70.386279
82.242490 70.329955
82.242490 70.257203
82.289427 70.182105
82.387994 70.137515
82.477174 70.114046
82.632065 70.111699
82.796343 70.102312
82.951234 70.081191
83.092045 70.064763
83.246936 70.048335
83.303260 70.099965
83.237548 70.151596
83.148369 70.226694
83.181224 70.273631
83.312647 70.252510
83.523862 70.273631
83.598961 70.297099
83.720996 70.360464
83.800789 70.444950
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83.767933 70.646778
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83.622429 70.846259
83.589574 70.928398
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83.303260 71.062168
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83.270404 71.228793
83.401827 71.313279
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83.688141 71.583165
83.702222 71.637142
83.655285 71.674692
83.547331 71.745097
83.481619 71.829583
83.425295 71.789687
83.270404 71.829583
83.082657 71.848357
82.894910 71.864785
82.716551 71.899988
82.585128 71.991514
82.477174 72.029064
82.275346 72.047838
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82.430237 72.139365
82.322283 72.230892
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82.054743 72.254360
81.913933 72.294256
81.716799 72.308337
81.482116 72.308337
81.228657 72.334152
81.106622 72.381089
80.975199 72.423332
80.900101 72.482003
80.886020 72.533633
80.900101 72.580570
80.810921 72.620466
80.787452 72.700259
80.834389 72.763623
80.867245 72.791785
80.942344 72.824641
80.951731 72.864537
81.022136 72.892699
80.918875 72.927902
80.867245 72.979532
80.843777 73.024122
80.820308 73.045243
80.754597 73.038203
80.646642 73.064018
80.665417 73.089833
80.580931 73.110955
80.510526 73.127383
80.458896 73.136770
80.444815 73.136770
80.341554 73.164932
-999. -999.
70.243122 73.014735
70.144555 73.021775
70.177411 73.054631
70.275978 73.134423
70.285365 73.204828
70.233735 73.279927
70.341689 73.343291
70.473112 73.434818
70.806363 73.462980
71.092677 73.432471
71.214712 73.378494
71.158388 73.331557
71.083289 73.249418
71.181856 73.242378
71.346135 73.242378
71.524494 73.235337
71.599593 73.176666
71.336747 73.150851
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70.862687 73.099221
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70.454337 73.120342
70.374545 73.071059
70.341689 73.040550
70.318221 73.014735
70.243122 73.014735
-999. -999.
74.202233 73.019428
74.258557 73.066365
74.413448 73.085140
74.634051 73.064018
74.854653 73.038203
74.878122 73.019428
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74.657519 72.906780
74.657519 72.841069
74.469772 72.902086
74.225701 72.967798
74.202233 73.019428
-999. -999.
79.276091 73.012388
79.266703 72.960757
79.379351 72.927902
79.496693 72.892699
79.529549 72.780051
79.529549 72.700259
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79.055488 72.704952
78.834886 72.756583
78.703463 72.812907
78.816111 72.890352
78.971002 72.944329
79.078957 73.005347
79.177524 73.047590
79.243235 73.040550
79.308946 73.021775
79.276091 73.012388
-999. -999.
77.368114 72.500778
77.466681 72.514859
77.490149 72.524246
77.588716 72.575876
77.720139 72.568836
77.931354 72.543021
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78.316235 72.474962
78.269298 72.402211
78.086245 72.364661
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77.025476 72.233238
76.969152 72.291909
77.081800 72.378742
77.222610 72.444454
77.368114 72.500778
-999. -999.
69.947421 72.871578
70.144555 72.871578
70.365158 72.871578
70.473112 72.876271
70.792282 72.859843
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71.289811 72.883312
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71.829583 72.824641
72.106509 72.782398
72.383436 72.749542
72.505471 72.740155
72.589957 72.723727
-999. -999.
72.592304 72.723727
72.629854 72.723727
72.629854 72.716686
72.550061 72.683831
72.629854 72.653322
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72.409251 70.257203
72.442107 70.177411
72.559449 70.132821
72.573530 70.095272
72.526593 70.006092
-999. -999.
73.641340 69.942727
73.763375 70.006092
73.749294 70.114046
73.796231 70.196186
74.059076 70.308834
74.082545 70.355770
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-999. -999.
52.310955 71.287464
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-999. -999.
58.764752 69.968543
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58.577005 70.144555
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-999. -999.
47.624325 80.005956
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-999. -999.
29.957350 70.705449
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-999. -999.
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-999. -999.
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-999. -999.
22.888683 78.281033
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-999. -999.
28.976373 78.839579
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64.749181 80.972852
64.852442 80.975199
64.927541 80.972852
65.012027 80.970506
65.030801 80.961118
65.058963 80.949384
65.105900 80.954078
65.199774 80.963465
65.256098 80.961118
65.312422 80.958771
65.378133 80.958771
65.425070 80.963465
65.490781 80.958771
65.509556 80.965812
65.443844 80.975199
65.378133 80.998668
65.312422 81.015095
65.199774 81.024483
65.143450 81.043258
65.143450 81.062032
65.134062 81.080807
65.134062 81.099582
65.049576 81.099582
64.965090 81.101928
64.946315 81.123050
64.871217 81.130090
64.833667 81.146518
64.824280 81.148865
64.814893 81.158252
64.749181 81.172333
64.777343 81.191108
64.814893 81.209883
64.889991 81.223964
64.918153 81.238045
64.918153 81.256820
64.899379 81.277941
64.899379 81.292022
64.899379 81.303756
64.946315 81.322531
64.965090 81.336612
64.918153 81.348346
64.871217 81.362427
64.805505 81.369468
64.702245 81.362427
64.674082 81.378855
64.617758 81.385895
64.505110 81.385895
64.392462 81.378855
64.307976 81.378855
64.232877 81.385895
64.139004 81.378855
64.063905 81.357733
63.913708 81.334265
63.801060 81.320184
63.688412 81.301409
63.622700 81.289675
63.566376 81.284982
63.528827 81.287328
-999. -999.
63.538214 81.693331
63.613313 81.695678
63.632088 81.681597
63.669637 81.665169
63.688412 81.651088
63.632088 81.632313
63.556989 81.615885
63.406792 81.625273
63.256594 81.611192
63.162721 81.615885
63.125171 81.634660
62.974974 81.637007
62.852938 81.658128
62.806002 81.676903
62.712128 81.676903
62.599480 81.665169
62.524382 81.667516
62.458670 81.667516
62.411733 81.672209
62.421121 81.686290
62.421121 81.690984
62.392959 81.700371
62.411733 81.712106
62.421121 81.721493
62.468057 81.721493
62.552544 81.728533
62.599480 81.712106
62.627642 81.700371
62.674579 81.695678
62.730903 81.707412
62.777840 81.726187
62.843551 81.721493
62.909262 81.716799
62.937424 81.730880
62.974974 81.744961
63.059460 81.754349
63.162721 81.749655
63.200270 81.735574
63.265981 81.735574
63.359855 81.744961
63.406792 81.735574
63.444341 81.721493
63.500665 81.709759
63.538214 81.693331
-999. -999.
50.844183 80.871939
50.834796 80.871939
50.769084 80.864898
50.693986 80.839083
50.374816 80.822655
50.252781 80.820308
50.299717 80.843777
50.393591 80.862551
50.393591 80.878979
50.374816 80.890713
50.337267 80.869592
50.299717 80.864898
50.243393 80.860204
50.224619 80.869592
50.149520 80.857858
50.065034 80.853164
-999. -999.
49.996976 80.853164
50.006363 80.864898
-999. -999.
49.928917 80.806227
50.013403 80.787452
50.069727 80.771025
50.097889 80.759290
50.050953 80.752250
50.032178 80.731128
-999. -999.
49.964120 80.318085
50.039219 80.313392
50.114317 80.320432
50.057993 80.339207
50.067381 80.339207
50.161254 80.329820
50.217578 80.346247
50.245740 80.357982
50.226965 80.374409
50.255127 80.379103
50.292677 80.388491
50.283289 80.407265
50.283289 80.426040
50.180029 80.421346
50.076768 80.437774
-999. -999.
49.964120 80.484711
50.067381 80.496445
50.067381 80.505832
50.142479 80.508179
50.264515 80.510526
50.283289 80.526954
50.292677 80.529301
50.377163 80.526954
50.480424 80.522260
50.583684 80.512873
50.696332 80.505832
50.743269 80.517566
50.818368 80.512873
50.884079 80.498792
50.987340 80.496445
51.043664 80.496445
51.043664 80.515220
51.109375 80.526954
51.231411 80.545728
51.306510 80.531647
51.362834 80.531647
51.372221 80.548075
51.400383 80.562156
51.494256 80.576237
51.513031 80.599706
51.513031 80.616134
51.569355 80.630215
51.578742 80.648989
51.578742 80.663070
51.578742 80.681845
51.531806 80.691232
51.466094 80.681845
51.419158 80.691232
51.390996 80.714701
51.362834 80.726435
51.297122 80.733475
51.231411 80.733475
51.165699 80.719394
51.062439 80.724088
50.959178 80.726435
50.893467 80.717047
50.837143 80.710007
50.790206 80.698273
50.696332 80.698273
50.564910 80.684192
50.452262 80.674804
50.349001 80.674804
50.292677 80.686539
50.283289 80.702966
50.302064 80.714701
50.311451 80.738169
50.349001 80.759290
50.424100 80.761637
50.555522 80.763984
50.640008 80.787452
50.705720 80.789799
50.818368 80.785106
50.893467 80.803880
50.884079 80.822655
50.884079 80.836736
50.931016 80.853164
50.959178 80.867245
50.977953 80.874285
50.959178 80.883673
50.959178 80.886020
50.884079 80.886020
50.865305 80.876632
50.837143 80.871939
-999. -999.
53.029087 80.353288
53.066636 80.357982
53.085411 80.365022
53.104185 80.348594
53.113573 80.339207
53.226221 80.334513
53.357643 80.332166
53.376418 80.308698
53.470292 80.285230
53.573552 80.264108
53.573552 80.245334
53.639264 80.240640
53.714362 80.224212
53.676813 80.196050
53.658038 80.165541
53.611102 80.165541
53.554778 80.172582
53.460904 80.170235
53.385806 80.160847
53.460904 80.142073
53.460904 80.113911
53.413968 80.116258
53.357643 80.130339
53.273157 80.127992
53.169897 80.113911
53.132347 80.111564
53.076023 80.116258
53.038474 80.132685
52.963375 80.135032
52.944601 80.123298
52.953988 80.104523
52.897664 80.113911
52.831952 80.120951
52.775628 80.120951
52.691142 80.116258
52.653593 80.125645
52.672368 80.146766
52.634818 80.139726
52.540945 80.142073
52.503396 80.163194
52.437684 80.174929
52.381360 80.186663
52.371973 80.198397
52.343811 80.205437
52.353198 80.212478
52.465846 80.207784
52.559720 80.228906
52.653593 80.235946
52.794403 80.245334
52.813178 80.261761
52.850727 80.287577
52.850727 80.296964
52.785016 80.296964
52.785016 80.306351
52.831952 80.318085
52.831952 80.329820
52.822565 80.339207
52.878889 80.341554
52.935213 80.332166
52.972763 80.336860
52.982150 80.350941
53.029087 80.353288
-999. -999.
56.767595 80.327473
56.758208 80.336860
56.739433 80.329820
56.579848 80.329820
56.598623 80.306351
56.636172 80.292270
56.626785 80.289923
56.532911 80.280536
56.476587 80.287577
56.410876 80.294617
56.298228 80.287577
56.204355 80.282883
56.157418 80.289923
56.072932 80.289923
55.988446 80.287577
55.922734 80.282883
55.866410 80.275842
55.857023 80.254721
55.913347 80.235946
55.913347 80.207784
55.932122 80.196050
55.922734 80.181969
55.885185 80.174929
55.857023 80.160847
55.866410 80.123298
55.866410 80.111564
55.810086 80.092789
55.781924 80.074015
55.800699 80.059934
55.875798 80.064627
55.941509 80.066974
55.997833 80.071668
56.044770 80.057587
56.138643 80.052893
56.194967 80.062280
56.260679 80.071668
56.298228 80.064627
56.326390 80.045853
56.420263 80.038812
56.495362 80.038812
56.551686 80.050546
56.579848 80.055240
56.598623 80.055240
56.626785 80.036465
56.711271 80.034118
56.786370 80.041159
56.889630 80.036465
56.936567 80.038812
56.955342 80.055240
56.917792 80.069321
56.870856 80.095136
56.861468 80.116258
56.805144 80.127992
56.880243 80.132685
56.917792 80.146766
56.936567 80.174929
56.983504 80.189010
57.002278 80.205437
56.992891 80.214825
57.011666 80.217172
57.067990 80.219518
57.058602 80.240640
57.105539 80.261761
57.105539 80.278189
57.077377 80.296964
57.049215 80.304004
56.936567 80.311045
56.880243 80.327473
56.833306 80.334513
56.805144 80.332166
56.767595 80.327473
-999. -999.
58.102944 80.456549
58.084169 80.465936
58.027845 80.442468
57.962134 80.437774
57.924585 80.449508
57.868261 80.454202
57.811937 80.433080
57.765000 80.426040
57.671126 80.428387
57.558478 80.430734
57.445830 80.428387
57.370732 80.426040
57.351957 80.433080
57.351957 80.449508
57.286245 80.451855
57.220534 80.449508
57.173597 80.454202
57.107886 80.449508
57.098499 80.435427
57.098499 80.426040
57.126661 80.409612
57.201759 80.390837
57.220534 80.379103
57.201759 80.372063
57.201759 80.357982
57.220534 80.350941
57.267471 80.336860
57.314408 80.325126
57.314408 80.304004
57.305020 80.278189
57.258083 80.261761
57.258083 80.238293
57.229921 80.233599
57.220534 80.221865
57.258083 80.198397
57.239309 80.179622
57.220534 80.170235
57.136048 80.170235
57.117273 80.151460
57.107886 80.137379
57.145435 80.132685
57.248696 80.123298
57.267471 80.102177
57.323795 80.097483
57.408281 80.088096
57.408281 80.057587
57.483380 80.055240
57.567866 80.057587
57.671126 80.050546
57.736838 80.052893
57.793162 80.059934
57.765000 80.074015
57.755613 80.102177
57.708676 80.109217
57.671126 80.135032
57.671126 80.151460
57.614802 80.181969
57.689901 80.186663
57.811937 80.191356
57.962134 80.207784
58.027845 80.224212
58.168656 80.235946
58.206205 80.254721
58.271916 80.273496
58.375177 80.280536
58.459663 80.282883
58.553536 80.287577
58.609861 80.282883
58.694347 80.285230
58.778833 80.285230
58.872706 80.285230
58.910255 80.278189
58.947805 80.266455
59.004129 80.280536
59.079228 80.285230
59.116777 80.296964
59.116777 80.308698
59.098002 80.322779
58.975967 80.334513
58.910255 80.348594
58.806995 80.348594
58.675572 80.353288
58.581698 80.374409
58.459663 80.383797
58.337628 80.395531
58.318853 80.414306
58.243754 80.428387
58.149881 80.447161
58.121719 80.454202
58.102944 80.456549
-999. -999.
59.227078 80.045853
59.217691 80.045853
59.189529 80.045853
59.142592 80.024731
59.076881 80.029425
58.954845 80.020037
58.804648 80.001263
-999. -999.
59.656549 79.996569
59.590838 80.005956
59.496964 80.012997
59.412478 80.031772
59.337379 80.038812
59.262281 80.043506
59.224731 80.045853
-999. -999.
60.097754 80.806227
60.003881 80.806227
59.938169 80.817961
59.816134 80.803880
59.712873 80.789799
59.665936 80.775718
59.684711 80.761637
59.665936 80.752250
59.637774 80.740516
59.590838 80.728782
59.590838 80.710007
59.600225 80.679498
59.543901 80.660723
59.478190 80.639602
59.384316 80.620827
59.356154 80.599706
59.290443 80.569197
59.271668 80.533994
59.252893 80.522260
59.318605 80.505832
59.337379 80.468283
59.346767 80.458896
59.356154 80.437774
59.384316 80.416653
59.496964 80.414306
59.534514 80.407265
59.525126 80.393184
59.534514 80.381450
59.590838 80.367369
59.665936 80.357982
59.759810 80.362675
59.825521 80.360328
59.881845 80.374409
59.938169 80.376756
-999. -999.
58.422114 81.787204
58.422114 81.791898
58.403339 81.791898
58.365790 81.782511
58.309466 81.782511
58.253142 81.798938
58.168656 81.803632
58.112331 81.791898
58.009071 81.787204
57.924585 81.770776
57.933972 81.754349
57.933972 81.740268
57.887035 81.723840
57.933972 81.714452
57.896423 81.700371
57.877648 81.681597
57.980909 81.672209
58.027845 81.646394
58.149881 81.632313
58.271916 81.641700
58.384564 81.653435
58.469050 81.651088
58.525374 81.644047
58.609861 81.641700
58.656797 81.655781
58.750671 81.655781
58.825769 81.660475
58.891481 81.683943
58.966579 81.702718
58.966579 81.716799
58.966579 81.735574
58.994741 81.749655
58.957192 81.768430
58.872706 81.798938
58.760058 81.801285
58.703734 81.784857
58.628635 81.782511
58.515987 81.787204
58.422114 81.787204
-999. -999.
57.671126 81.531399
57.586640 81.531399
57.558478 81.529052
57.455218 81.536093
57.408281 81.524359
57.380119 81.522012
57.239309 81.524359
57.126661 81.514971
57.098499 81.500890
56.985851 81.498544
56.873203 81.486809
56.854428 81.472728
56.798104 81.463341
56.704230 81.458647
56.723005 81.439873
56.704230 81.425792
56.694843 81.414057
56.779329 81.411711
56.910752 81.416404
56.985851 81.411711
57.051562 81.392936
57.117273 81.385895
57.145435 81.390589
57.192372 81.399976
57.248696 81.395283
57.295633 81.383549
57.370732 81.378855
57.473992 81.376508
57.539704 81.378855
57.539704 81.371814
57.539704 81.360080
57.605415 81.362427
57.699288 81.357733
57.755613 81.348346
57.765000 81.336612
57.877648 81.350693
57.980909 81.360080
58.056007 81.360080
58.140493 81.369468
58.187430 81.385895
58.234367 81.388242
58.271916 81.395283
58.318853 81.397630
58.365790 81.411711
58.384564 81.423445
58.337628 81.437526
58.206205 81.432832
58.178043 81.449260
58.112331 81.463341
58.046620 81.486809
57.933972 81.498544
57.877648 81.514971
57.811937 81.524359
57.793162 81.536093
57.671126 81.531399
-999. -999.
56.535258 81.369468
56.535258 81.374161
56.422610 81.376508
56.366286 81.367121
56.366286 81.348346
56.356899 81.341306
56.356899 81.331918
56.422610 81.324878
56.450772 81.313144
56.413223 81.303756
56.403835 81.282635
56.431998 81.282635
56.507096 81.273247
56.469547 81.266207
56.403835 81.266207
56.403835 81.247432
56.413223 81.231004
56.413223 81.216923
56.356899 81.216923
56.300575 81.214576
56.281800 81.235698
56.225476 81.242738
56.178539 81.233351
56.131603 81.226311
56.065891 81.235698
56.009567 81.242738
55.981405 81.235698
55.896919 81.231004
55.859370 81.233351
55.849982 81.238045
55.849982 81.249779
55.812433 81.254473
55.746722 81.268554
55.671623 81.270901
55.615299 81.268554
55.549588 81.259166
55.427552 81.259166
55.408777 81.245085
55.418165 81.226311
55.436939 81.207536
55.521425 81.193455
55.605912 81.184068
55.681010 81.179374
55.727947 81.158252
55.803046 81.153559
55.925081 81.160599
56.009567 81.160599
56.065891 81.169987
56.169152 81.177027
56.197314 81.174680
56.197314 81.148865
56.234863 81.148865
56.375673 81.155906
56.488322 81.160599
56.535258 81.160599
56.544646 81.165293
56.488322 81.177027
56.525871 81.191108
56.638519 81.195802
56.732392 81.200495
56.873203 81.209883
56.948301 81.219270
56.948301 81.207536
57.060949 81.209883
57.192372 81.214576
57.295633 81.219270
57.380119 81.233351
57.455218 81.238045
57.502154 81.256820
57.567866 81.259166
57.633577 81.270901
57.671126 81.266207
57.680514 81.259166
57.727450 81.261513
57.793162 81.263860
57.793162 81.275594
57.774387 81.294369
57.727450 81.306103
57.624190 81.310797
57.558478 81.317837
57.520929 81.303756
57.502154 81.294369
57.427056 81.303756
57.305020 81.301409
57.229921 81.310797
57.229921 81.324878
57.098499 81.329571
56.948301 81.336612
56.873203 81.362427
56.798104 81.376508
56.685456 81.374161
56.535258 81.369468
-999. -999.
58.708428 80.853164
58.727202 80.860204
58.727202 80.855511
58.745977 80.841430
58.708428 80.825002
58.774139 80.808574
58.774139 80.782759
58.745977 80.771025
58.661491 80.754597
58.558230 80.728782
58.445582 80.712354
58.361096 80.710007
58.342321 80.726435
58.276610 80.731128
58.210899 80.733475
58.117025 80.726435
58.060701 80.740516
57.985602 80.752250
57.863567 80.754597
57.769694 80.756944
57.760306 80.768678
57.854180 80.782759
57.948053 80.794493
58.060701 80.808574
58.088863 80.822655
58.182737 80.825002
58.257835 80.825002
58.285997 80.841430
58.323547 80.846123
58.408033 80.846123
58.492519 80.853164
58.548843 80.855511
58.614554 80.855511
58.680266 80.855511
58.708428 80.853164
-999. -999.
56.105787 80.719394
56.068238 80.719394
56.030689 80.717047
55.983752 80.702966
55.908653 80.712354
55.796005 80.717047
55.730294 80.705313
55.711519 80.688885
55.608258 80.681845
55.476836 80.677151
55.401737 80.670111
55.429899 80.663070
55.533160 80.663070
55.589484 80.656030
55.504998 80.651336
55.495610 80.637255
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-999. -999.
50.062687 80.853164
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-999. -999.
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-999. -999.
50.029831 80.731128
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-999. -999.
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31.323208 80.071668
31.370145 80.076361
31.445244 80.083402
31.510955 80.097483
31.557892 80.092789
31.661153 80.095136
31.745639 80.109217
31.820738 80.106870
31.933386 80.109217
32.064808 80.132685
32.092970 80.125645
32.177456 80.127992
32.261943 80.142073
32.337041 80.151460
32.374591 80.156154
32.430915 80.158501
32.468464 80.163194
32.534175 80.167888
32.637436 80.170235
32.703148 80.167888
32.759472 80.170235
32.797021 80.186663
32.815796 80.189010
32.881507 80.191356
32.947218 80.205437
32.956606 80.221865
32.975380 80.224212
33.059866 80.217172
33.106803 80.217172
33.172515 80.224212
33.238226 80.217172
33.322712 80.214825
33.416585 80.217172
33.454135 80.217172
33.463522 80.207784
-999. -999.
22.778382 80.512873
22.759607 80.515220
22.759607 80.512873
22.806544 80.498792
22.825318 80.482364
22.909805 80.468283
23.031840 80.472977
23.106939 80.465936
23.182037 80.465936
23.219587 80.454202
23.228974 80.440121
23.200812 80.421346
23.200812 80.407265
23.182037 80.393184
23.078777 80.388491
23.069389 80.381450
23.116326 80.369716
23.135101 80.353288
23.163263 80.343901
23.200812 80.334513
23.238361 80.322779
23.200812 80.306351
23.182037 80.287577
23.172650 80.273496
23.163263 80.254721
23.097551 80.242987
23.041227 80.233599
23.031840 80.217172
23.031840 80.200744
23.003678 80.189010
22.966129 80.174929
22.947354 80.163194
22.928579 80.153807
22.919192 80.139726
22.937967 80.125645
22.975516 80.109217
23.013065 80.102177
23.060002 80.102177
23.069389 80.102177
23.069389 80.102177
23.106939 80.104523
23.153875 80.120951
23.153875 80.132685
23.153875 80.142073
23.182037 80.139726
23.238361 80.142073
23.247749 80.160847
23.257136 80.167888
23.285298 80.163194
23.285298 80.149113
23.294685 80.132685
23.313460 80.132685
23.360397 80.132685
23.379172 80.158501
23.379172 80.177275
23.407334 80.177275
23.435496 80.163194
23.473045 80.142073
23.482432 80.132685
23.482432 80.125645
23.473045 80.113911
23.501207 80.102177
23.557531 80.099830
23.604468 80.116258
23.585693 80.123298
23.576306 80.132685
23.642017 80.132685
23.698341 80.132685
23.726503 80.144420
23.707728 80.153807
23.679566 80.163194
23.660792 80.170235
23.698341 80.172582
23.754665 80.170235
23.810989 80.181969
23.810989 80.191356
23.764053 80.205437
23.726503 80.217172
23.726503 80.233599
23.764053 80.231253
23.820377 80.228906
23.857926 80.233599
23.848539 80.245334
23.773440 80.252374
23.735890 80.257068
23.735890 80.271149
23.773440 80.268802
23.820377 80.254721
23.876701 80.245334
23.951799 80.245334
24.017511 80.245334
24.026898 80.252374
24.026898 80.264108
23.989349 80.273496
23.979961 80.280536
23.998736 80.278189
24.064447 80.261761
24.120771 80.252374
24.186483 80.242987
24.205258 80.242987
24.205258 80.261761
24.148933 80.273496
24.120771 80.280536
24.130159 80.287577
24.177095 80.280536
24.214645 80.271149
24.299131 80.264108
24.374230 80.257068
24.421166 80.240640
24.468103 80.240640
24.524427 80.245334
24.571364 80.245334
24.590138 80.264108
24.646463 80.266455
24.693399 80.259415
24.730949 80.266455
24.768498 80.294617
24.806047 80.315739
24.815435 80.329820
24.815435 80.332166
24.834209 80.334513
24.881146 80.336860
24.890533 80.322779
24.890533 80.301658
24.881146 80.289923
24.862371 80.273496
24.862371 80.257068
24.862371 80.235946
24.862371 80.224212
24.777885 80.217172
24.730949 80.207784
24.655850 80.200744
24.618301 80.191356
24.618301 80.179622
24.618301 80.163194
24.590138 80.151460
24.552589 80.142073
24.524427 80.132685
24.486878 80.113911
24.486878 80.116258
24.524427 80.127992
24.608913 80.137379
24.693399 80.153807
24.730949 80.170235
24.759111 80.186663
24.796660 80.198397
24.834209 80.200744
24.899921 80.207784
24.928083 80.200744
24.946857 80.196050
25.012569 80.193703
25.068893 80.198397
25.087668 80.217172
25.115830 80.228906
25.172154 80.235946
25.284802 80.242987
25.350513 80.242987
25.388062 80.238293
25.369288 80.233599
25.303576 80.233599
25.247252 80.219518
25.219090 80.207784
25.256640 80.200744
25.312964 80.200744
25.341126 80.186663
25.350513 80.170235
25.425612 80.170235
25.444386 80.181969
25.444386 80.198397
25.453774 80.207784
25.510098 80.203091
25.528873 80.186663
25.538260 80.174929
25.566422 80.163194
25.613359 80.165541
25.660295 80.181969
25.697845 80.196050
25.726007 80.191356
25.763556 80.184316
25.782331 80.179622
25.791718 80.179622
25.819880 80.172582
25.810493 80.172582
25.810493 80.170235
25.810493 80.151460
25.782331 80.144420
25.782331 80.139726
25.848042 80.139726
25.894979 80.142073
25.932528 80.146766
25.970078 80.160847
26.017014 80.160847
26.026402 80.151460
26.167212 80.151460
26.270472 80.151460
26.354958 80.151460
26.458219 80.153807
26.533318 80.151460
26.599029 80.139726
26.645966 80.132685
26.664741 80.132685
26.730452 80.139726
26.796164 80.132685
26.843100 80.123298
26.824326 80.102177
26.824326 80.095136
26.880650 80.085749
26.908812 80.074015
26.955748 80.074015
26.955748 80.062280
26.955748 80.055240
26.974523 80.055240
27.040234 80.059934
27.105946 80.062280
27.115333 80.055240
27.134108 80.055240
27.134108 80.038812
27.115333 80.017691
27.105946 80.005956
-999. -999.
19.955139 80.402572
20.030238 80.388491
20.133499 80.409612
20.217985 80.418999
20.302471 80.409612
20.302471 80.390837
20.321245 80.374409
20.358795 80.362675
20.433893 80.346247
20.452668 80.329820
20.424506 80.322779
20.433893 80.299311
20.462055 80.280536
20.555929 80.271149
20.649802 80.280536
20.734288 80.289923
20.743676 80.273496
20.734288 80.252374
20.734288 80.245334
20.781225 80.231253
20.781225 80.219518
20.781225 80.210131
20.781225 80.212478
20.781225 80.207784
20.846936 80.198397
20.959585 80.196050
21.053458 80.196050
21.109782 80.196050
21.222430 80.214825
21.241205 80.217172
21.288141 80.231253
21.306916 80.219518
21.372628 80.212478
21.457114 80.228906
21.494663 80.240640
21.579149 80.233599
21.644860 80.207784
21.748121 80.207784
21.757508 80.228906
21.757508 80.252374
21.785671 80.254721
21.860769 80.266455
21.907706 80.250027
21.898319 80.221865
21.917093 80.198397
21.917093 80.196050
21.841995 80.172582
21.738734 80.151460
21.710572 80.130339
21.541600 80.095136
21.588536 80.099830
21.682410 80.116258
21.795058 80.127992
21.841995 80.130339
21.907706 80.109217
22.001579 80.076361
22.039129 80.038812
22.123615 80.010650
-999. -999.
22.435744 79.991875
22.445131 80.010650
22.370032 80.024731
22.323096 80.034118
22.407582 80.041159
22.426356 80.057587
22.379420 80.074015
22.370032 80.092789
22.351258 80.123298
22.360645 80.149113
22.379420 80.198397
22.407582 80.217172
22.426356 80.247680
22.426356 80.261761
22.445131 80.280536
22.445131 80.292270
22.445131 80.306351
22.416969 80.315739
22.323096 80.318085
22.323096 80.339207
22.351258 80.355635
22.379420 80.381450
22.379420 80.400225
22.379420 80.402572
22.435744 80.400225
22.501455 80.407265
22.539005 80.407265
22.548392 80.367369
22.614103 80.346247
22.632878 80.322779
22.717364 80.329820
22.792463 80.334513
22.792463 80.346247
22.801850 80.357982
22.783075 80.362675
22.792463 80.397878
22.820625 80.421346
22.811237 80.428387
22.792463 80.458896
22.792463 80.475323
22.764301 80.494098
22.764301 80.505832
22.754913 80.505832
22.764301 80.512873
22.783075 80.512873
-999. -999.
15.996028 79.998916
16.099289 80.012997
16.183775 80.050546
16.305810 80.062280
16.409071 80.036465
16.512332 80.031772
16.559269 80.017691
16.559269 80.010650
-999. -999.
18.730091 79.989529
18.814577 80.003610
18.870901 80.017691
18.880289 80.029425
18.823965 80.024731
18.720704 80.017691
18.645605 80.012997
18.561119 80.012997
18.504795 80.012997
18.495408 80.024731
18.457858 80.027078
18.429696 80.034118
18.392147 80.034118
18.382760 80.020037
18.345210 80.015344
18.317048 80.015344
18.279499 80.022384
18.204400 80.024731
18.157463 80.045853
18.091752 80.045853
18.063590 80.066974
18.082365 80.074015
18.138689 80.076361
18.138689 80.090442
18.063590 80.102177
18.035428 80.123298
18.016653 80.132685
17.950942 80.142073
17.904005 80.132685
17.847681 80.137379
17.810132 80.139726
17.781970 80.139726
17.763195 80.142073
17.650547 80.132685
17.547286 80.125645
17.547286 80.142073
17.622385 80.160847
17.753808 80.189010
17.828906 80.193703
17.913393 80.179622
18.035428 80.181969
18.091752 80.181969
18.101139 80.174929
18.119914 80.160847
18.204400 80.160847
18.317048 80.167888
18.410922 80.160847
18.476633 80.170235
18.561119 80.144420
18.654992 80.142073
18.701929 80.170235
18.720704 80.186663
18.786415 80.179622
18.852127 80.172582
18.908451 80.163194
18.908451 80.139726
18.908451 80.123298
18.983549 80.118604
19.086810 80.106870
19.096197 80.085749
19.161909 80.066974
19.161909 80.048199
19.274557 80.015344
19.359043 80.001263
19.424754 80.012997
19.424754 80.024731
19.405980 80.052893
19.405980 80.069321
19.359043 80.088096
19.387205 80.081055
19.452916 80.074015
19.509240 80.083402
19.462304 80.095136
19.452916 80.104523
19.424754 80.111564
19.387205 80.132685
19.415367 80.132685
19.490466 80.125645
19.565564 80.116258
19.603114 80.123298
19.603114 80.135032
19.565564 80.146766
19.509240 80.158501
19.405980 80.160847
19.330881 80.163194
19.283944 80.179622
19.171296 80.172582
19.133747 80.198397
19.124359 80.205437
19.068035 80.221865
19.039873 80.228906
19.039873 80.242987
19.096197 80.252374
19.096197 80.271149
19.096197 80.282883
19.086810 80.299311
19.086810 80.313392
19.077423 80.336860
19.077423 80.350941
19.124359 80.332166
19.190071 80.315739
19.255782 80.292270
19.340268 80.275842
19.387205 80.247680
19.415367 80.224212
19.481078 80.210131
19.528015 80.214825
19.574952 80.214825
19.659438 80.207784
19.725149 80.189010
19.781473 80.167888
19.828410 80.177275
19.837797 80.189010
19.856572 80.198397
19.856572 80.200744
19.856572 80.214825
19.828410 80.224212
19.828410 80.221865
19.762699 80.228906
19.734537 80.247680
19.734537 80.252374
19.800248 80.259415
19.800248 80.280536
19.828410 80.301658
19.800248 80.306351
19.772086 80.327473
19.828410 80.325126
19.847185 80.325126
19.847185 80.327473
19.790861 80.327473
19.743924 80.334513
19.734537 80.341554
19.762699 80.348594
19.847185 80.362675
19.884734 80.374409
19.865959 80.383797
19.781473 80.374409
19.725149 80.374409
19.715762 80.393184
19.715762 80.402572
19.678213 80.404918
19.640663 80.383797
19.612501 80.365022
19.584339 80.367369
19.574952 80.383797
19.546790 80.388491
19.509240 80.386144
19.490466 80.393184
19.443529 80.407265
19.443529 80.426040
19.490466 80.454202
19.518628 80.468283
19.565564 80.475323
19.603114 80.451855
19.668825 80.442468
19.678213 80.465936
19.668825 80.487058
19.668825 80.501139
19.706375 80.515220
19.743924 80.515220
19.762699 80.491751
19.800248 80.465936
19.959833 80.465936
19.987995 80.449508
19.950445 80.416653
19.959833 80.402572
Property changes:
Added: svn:executable
/tags/1.0/prep/coastline.f
0,0 → 1,528
PROGRAM coastline
c *********************************************************************
c * Add the coastline and land sea mask to the REF file *
c * Michael Sprenger / Winter 2006,07 *
c *********************************************************************
 
implicit none
 
c --------------------------------------------------------------------
c Declaration of parameters and variables
c --------------------------------------------------------------------
 
c Input parameters
character*80 coastfile
character*80 reffile
real clon,clat,crot
c Output arrays
integer nmax
parameter (nmax=100000)
real,allocatable, dimension (:,:) :: landsea
real,allocatable, dimension (:,:) :: xcor,ycor
real xpos(nmax),ypos(nmax)
real lon(nmax), lat(nmax)
real rlon(nmax),rlat(nmax)
integer ncoast
integer rnx,rny
real rxmin,rymin,rxmax,rymax
real rdx,rdy
 
c Auxiliary variables
integer i,j
character*80 name
integer cdfid,cstid
character*80 cfn
integer ierr,stat
character*80 varname
real varmin(4),varmax(4),stag(4)
integer vardim(4),ndim
real mdv
integer isok
integer nvars
integer ntimes
real time
character*80 vnam(100)
 
c --------------------------------------------------------------------
c Preparations
c --------------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* coastline *'
print*,'*********************************************************'
 
 
c Read parameter file
open(10,file='fort.10')
read(10,*) reffile
read(10,*) coastfile
read(10,*) name,clon
if ( trim(name).ne.'CLON' ) stop
read(10,*) name,clat
if ( trim(name).ne.'CLAT' ) stop
read(10,*) name,crot
if ( trim(name).ne.'CROT' ) stop
close(10)
 
print*
print*,trim(reffile)
print*,trim(coastfile)
print*,clon,clat,crot
 
c Read grid parameters
call cdfopn(reffile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
varname='X'
call getdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
call gettimes(cdfid,time,ntimes,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
rnx=vardim(1)
rny=vardim(2)
rxmin=varmin(1)
rymin=varmin(2)
rxmax=varmax(1)
rymax=varmax(2)
rdx=(rxmax-rxmin)/real(rnx-1)
rdy=(rymax-rymin)/real(rny-1)
 
c Allocate memory
allocate(landsea(rnx,rny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array landsea ***'
allocate(xcor(rnx,rny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array xcor ***'
allocate(ycor(rnx,rny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ycor ***'
 
c Read data
call cdfopn(reffile,cdfid,ierr)
if (ierr.ne.0) goto 998
varname='X'
call getdat(cdfid,varname,time,1,xcor,ierr)
if (ierr.ne.0) goto 998
varname='Y'
call getdat(cdfid,varname,time,1,ycor,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Read the coastfile
open(10,file=coastfile)
ncoast=1
100 read(10,*,end=200) lon(ncoast),lat(ncoast)
ncoast=ncoast+1
goto 100
 
200 close(10)
ncoast=ncoast-1
 
c Handle missing data values
mdv=-100000.
do i=ncoast,nmax
lon(i)=mdv
lat(i)=mdv
enddo
 
c --------------------------------------------------------------------
c Transform coast(lat/lon) to coast(x/y)
c --------------------------------------------------------------------
call getenvir (clon,clat,crot,
> xcor,ycor,rnx,rny,rxmin,rymin,rdx,rdy,mdv,
> lon,lat,rlon,rlat,xpos,ypos,nmax)
 
c --------------------------------------------------------------------
c Write output
c --------------------------------------------------------------------
 
c Open output file and set some general parameters
call cdfwopn(reffile,cdfid,ierr)
if (ierr.ne.0) goto 998
vardim(1)=1
vardim(2)=1
vardim(3)=nmax
ndim=3
 
c Write LAT
isok=0
varname='COAST_LAT'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,lat,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Write LON
isok=0
varname='COAST_LON'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,lon,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Write RLAT
isok=0
varname='COAST_RLAT'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,rlat,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Write RLON
isok=0
varname='COAST_RLON'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,rlon,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Write Y
isok=0
varname='COAST_Y'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,ypos,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Write X
isok=0
varname='COAST_X'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,xpos,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(reffile)
 
c Close output file
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
 
c --------------------------------------------------------------------
c Exception handling
c --------------------------------------------------------------------
stop
 
998 print*,'Problems with input netcdf file'
stop
 
END
 
c --------------------------------------------------------------------------------
c Subroutine to get environment of strcof
c --------------------------------------------------------------------------------
 
SUBROUTINE getenvir (clon,clat,rotation,
> xcor,ycor,rnx,rny,rxmin,rymin,rdx,rdy,mdv,
> lon,lat,rlon,rlat,xpos,ypos,n)
 
c Rotate from a local quasi-cartesian coordiante system into lat/lon coordinate
c system.
 
implicit none
 
c Declaration of input and output parameters
integer n
real clon,clat,rotation
real lon(n), lat(n)
real rlon(n),rlat(n)
real xpos(n),ypos(n)
integer rnx,rny
real xcor(rnx,rny),ycor(rnx,rny)
real rxmin,rymin,rdx,rdy
real mdv
 
c Set numerical and physical constants
real g2r
parameter (g2r=0.0174533)
real pi180
parameter (pi180=3.14159265359/180.)
real eps
parameter (eps=0.0001)
 
c Auxiliary variables
real pollon,pollat
integer i,j
real xind,yind
real rindx,rindy
integer indx,indy,indr,indu
real frac0i,frac0j,frac1i,frac1j
real rlon1(n),rlat1(n)
 
c Externals
real lmtolms,phtophs
external lmtolms,phtophs
 
c First rotation
pollon=clon-180.
if (pollon.lt.-180.) pollon=pollon+360.
pollat=90.-clat
do i=1,n
 
if ( (abs(lon(i)-mdv).gt.eps).and.
> (abs(lat(i)-mdv).gt.eps) ) then
 
c First rotation
pollon=clon-180.
if (pollon.lt.-180.) pollon=pollon+360.
pollat=90.-clat
rlon1(i)=lmtolms(lat(i),lon(i),pollat,pollon)
rlat1(i)=phtophs(lat(i),lon(i),pollat,pollon)
 
c Second coordinate transformation
pollon=-180.
pollat=90.+rotation
rlon(i)=90.+lmtolms(rlat1(i),rlon1(i)-90.,pollat,pollon)
rlat(i)=phtophs(rlat1(i),rlon1(i)-90.,pollat,pollon)
 
c Get rotated latitude and longitude
100 if (rlon(i).lt.rxmin) then
rlon(i)=rlon(i)+360.
goto 100
endif
102 if (rlon(i).gt.(rxmin+real(rnx-1)*rdx)) then
rlon(i)=rlon(i)-360.
goto 102
endif
if ( (rlon(i).lt.rxmin).or.
> (rlon(i).gt.(rxmin+real(rnx-1)*rdx)).or.
> (rlat(i).lt.rymin).or.
> (rlat(i).gt.(rymin+real(rny-1)*rdy)) ) then
rlon(i)=mdv
rlat(i)=mdv
endif
 
c Get x and y coordinates
rindx=(rlon(i)-rxmin)/rdx+1.
rindy=(rlat(i)-rymin)/rdy+1.
indx=int(rindx)
indy=int(rindy)
if ((indx.gt.1).and.(indx.lt.rnx).and.
> (indy.gt.1).and.(indy.lt.rny)) then
 
indr=indx+1
if (indr.gt.rnx) indr=1
indu=indy+1
if (indu.gt.rny) indu=rny
 
frac0i=rindx-float(indx)
frac0j=rindy-float(indy)
frac1i=1.-frac0i
frac1j=1.-frac0j
xpos(i) = xcor(indx ,indy) * frac1i * frac1j
& + xcor(indx ,indu) * frac1i * frac0j
& + xcor(indr ,indy) * frac0i * frac1j
& + xcor(indr ,indu) * frac0i * frac0j
ypos(i) = ycor(indx ,indy) * frac1i * frac1j
& + ycor(indx ,indu) * frac1i * frac0j
& + ycor(indr ,indy) * frac0i * frac1j
& + ycor(indr ,indu) * frac0i * frac0j
 
else
 
xpos(i)=mdv
ypos(i)=mdv
 
endif
 
else
rlon(i)=mdv
rlat(i)=mdv
xpos(i)=mdv
ypos(i)=mdv
endif
 
enddo
 
END
 
c --------------------------------------------------------------------------------
c Transformation routine: LMSTOLM and PHSTOPH from library gm2em
c --------------------------------------------------------------------------------
 
REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** LMTOLMS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMTOLMS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG1 = - SIN(ZLAM-ZLAMPOL)*COS(ZPHI)
ZARG2 = - ZSINPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL)+ZCOSPOL*SIN(ZPHI)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMTOLMS = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMTOLMS = 90.0
ELSE
LMTOLMS = -90.0
ENDIF
ELSE
LMTOLMS = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
 
 
REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
C
C**** PHTOPHS - FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI
C**** AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHTOPHS (PHI, LAM, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI AUF
C** EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHI REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
C** LAM REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
C** POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
C** POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
C** AUSGABE-
C** PARAMETER: ROTIERTE BREITE PHIS ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: G. DE MORSIER
REAL LAM,PHI,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHI = ZPIR18*PHI
ZLAM = LAM
IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
ZLAM = ZPIR18*ZLAM
ZARG = ZCOSPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL) + ZSINPOL*SIN(ZPHI)
PHTOPHS = ZRPI18*ASIN(ZARG)
RETURN
END
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
 
Property changes:
Added: svn:executable
/tags/1.0/prep/coastline.m
0,0 → 1,15
 
% Read input file
inp = ncget('REF_20060116_18');
 
% Plot continental boundaries (rotated latitude/longitude)
figure;
inp.COAST_RLON.data ( inp.COAST_RLON.data< -900 ) = NaN;
inp.COAST_RLAT.data ( inp.COAST_RLAT.data< -900 ) = NaN;
plot(inp.COAST_RLON.data,inp.COAST_RLAT.data,'k');
 
% Plot continental boundaries (x/y)
figure;
inp.COAST_X.data ( inp.COAST_X.data< -5000 ) = NaN;
inp.COAST_Y.data ( inp.COAST_Y.data< -5000 ) = NaN;
plot(inp.COAST_X.data,inp.COAST_Y.data,'k');
Property changes:
Added: svn:executable
/tags/1.0/prep/cutnetcdf.f
0,0 → 1,201
PROGRAM Cutnetcdf
 
c -----------------------------------------------------------------------
c Cut and split an input netcdf
c Michael Sprenger / Summer 2006
c -----------------------------------------------------------------------
 
implicit none
 
c -----------------------------------------------------------------------
c Declaration of variables
c -----------------------------------------------------------------------
 
c Maximum domain size
integer nxmax,nymax,nzmax,ntmax
parameter (nxmax=400,nymax=400,nzmax=400,ntmax=5)
 
c Variables for input and output netcdf file
integer cdfid
real phymin(4),phymax(4),stag(4), misdat
integer ndim, vardim(4), error, nlev
integer cstid
real dx, dy
real aklev(nzmax),bklev(nzmax),aklay(nzmax),bklay(nzmax)
real pollon, pollat
integer stdate(5)
integer ncdfid
integer datar(14)
character*80 cfn
real varold(nxmax*nymax*nzmax)
real time(ntmax)
 
c Parameters
character*80 oldfile(400),newfile(400)
character*80 oldname(400),newname(400)
integer novars
 
c Auxiliary variables
integer i,j,k,l,t,ntimes
integer imin, imax, jmin, jmax, tmin, tmax
integer nx,ny,nz
integer crename(400),crefile(400)
integer isnew
character*80 varname
 
c -----------------------------------------------------------------------
c Preparations
c -----------------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* cutnetcdf *'
print*,'*********************************************************'
 
c Read entries from argument file
open(10,file='fort.10')
novars=1
100 read(10,*,end=110) oldname(novars),newname(novars),
> oldfile(novars),newfile(novars)
novars=novars+1
goto 100
110 close(10)
novars=novars-1
 
c Init the flags for creating files and variables
do i=1,novars
crename(i)=0
crefile(i)=0
enddo
 
c -----------------------------------------------------------------------
c Loop through data points
c -----------------------------------------------------------------------
 
do t=1,novars
 
c Write info
write(*,'(a10,a5,3x,a5,3x,a15,3x,a15)')
> ' Split ',trim(oldname(t)),
> trim(newname(t)),
> trim(oldfile(t)),
> trim(newfile(t))
 
c Open input file and read some parametersq
call cdfopn(oldfile(t),cdfid,error)
if (error.ne.0) goto 997
call getcfn(cdfid,cfn,error)
if (error.ne.0) goto 997
call cdfopn(cfn,cstid,error)
if (error.ne.0) goto 997
call gettimes(cdfid, time, ntimes, error)
if (error.ne.0) goto 997
call getgrid(cstid, dx, dy, error)
if (error.ne.0) goto 997
call getlevs(cstid, nlev, aklev, bklev, aklay, bklay, error)
if (error.ne.0) goto 997
call getpole(cstid,pollon,pollat,error)
if (error.ne.0) goto 997
call getstart(cstid,stdate,error)
if (error.ne.0) goto 997
 
c Set new grid parameters and read data of subdomain
call getdef(cdfid,oldname(t),ndim,misdat,
> vardim,phymin,phymax,stag,error)
if (error.ne.0) goto 997
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
 
c Load data
varname=oldname(t)
call getdat(cdfid,varname,time(1),0,varold,error)
if (error.ne.0) goto 997
 
c Create file if necessary (otherwise open it for writing)
isnew=1
do k=1,novars
if ((crefile(k).eq.1).and.
> (newfile(t).eq.newfile(k))) then
isnew=0
endif
enddo
if (isnew.eq.1) then
cfn=trim(newfile(t))//'_cst'
datar(1) = vardim(1)
datar(2) = vardim(2)
datar(3) = 1000.*phymax(2)
datar(4) = 1000.*phymin(1)
datar(5) = 1000.*phymin(2)
datar(6) = 1000.*phymax(1)
datar(7) = 1000.*dx
datar(8) = 1000.*dy
datar(9) = nlev
datar(10) = 1
datar(11) = 0
datar(12) = 0
datar(13) = 1000.*pollon
datar(14) = 1000.*pollat
call wricst(cfn,datar,
> aklev,bklev,aklay,bklay,stdate)
call crecdf(trim(newfile(t)),ncdfid, phymin, phymax,
> ndim,cfn,error)
if (error.ne.0) goto 998
else
call cdfwopn(trim(newfile(t)),ncdfid,error)
if (error.ne.0) goto 998
endif
do k=1,novars
if (newfile(k).eq.newfile(t)) then
crefile(k)=1
endif
enddo
 
c Create variable if necessary
isnew=1
do k=1,novars
if ((newfile(t).eq.newfile(k)).and.
> (newname(t).eq.newname(k)).and.
> (crename(t).eq.1)) then
isnew=0
endif
enddo
if (isnew.eq.1) then
call putdef(ncdfid, newname(t), ndim, misdat, vardim,
> phymin, phymax, stag, error)
if (error.ne.0) goto 998
endif
do k=1,novars
if ((newname(k).eq.newname(t)).and.
> (crefile(k).eq.1)) then
crename(k)=1
endif
enddo
 
c Write data
call putdat(ncdfid,newname(t),time(1),0,varold,error)
if (error.ne.0) goto 998
 
c Close files
call clscdf(cdfid, error)
if (error.ne.0) goto 997
call clscdf(ncdfid, error)
if (error.ne.0) goto 998
call clscdf(cstid, error)
if (error.ne.0) goto 997
 
enddo
 
c -----------------------------------------------------------------------
c Exception handling
c -----------------------------------------------------------------------
 
stop
 
997 print*,'Problems with input file... Stop'
stop
 
998 print*,'Problems with output file... Stop'
stop
 
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/def_anomaly.f
0,0 → 1,745
 
PROGRAM def_anomaly
 
c ************************************************************************
c * Define a PV anomaly and set it up for inversion. Additionally, the *
c * lateral and upper/lower boundary values for potential temperature *
c * and wind are set *
c * Michael Sprenger / Spring 2005 *
c ************************************************************************
 
implicit none
 
c ------------------------------------------------------------------------
c Declaration of subroutine parameters
c ------------------------------------------------------------------------
 
c Numerical epsilon
real eps
parameter (eps=0.01)
 
c Variables for input Z file : height level
character*80 in_zfn,in_varname
real in_varmin(4),in_varmax(4),in_stag(4)
integer in_vardim(4)
real in_mdv
integer in_ndim
integer in_nx,in_ny,in_nz
real in_xmin,in_xmax,in_ymin,in_ymax,in_dx,in_dy
integer in_ntimes
real in_aklev(1000),in_bklev(1000)
real in_aklay(1000),in_bklay(1000)
 
real in_time
real in_pollon,in_pollat
integer in_idate(5)
integer in_nvars
character*80 in_vnam(100)
real,allocatable, dimension (:,:,:) :: in_field
real,allocatable, dimension (:,:,:) :: in_filt
real,allocatable, dimension (:,:,:) :: in_anom
real,allocatable, dimension (:,:) :: in_x,in_y
real,allocatable, dimension (:,:,:) :: th_anom
real,allocatable, dimension (:,:,:) :: uu_anom,vv_anom
 
c Filtering
real f_xmin,f_xmax
real f_ymin,f_ymax
real f_zmin,f_zmax
integer nfilt
real boundxy,boundz
real,allocatable, dimension (:,:) :: tmp
 
c Auxiliary variables
integer i,j,k,l,n
integer cdfid,cstid
integer ierr,stat
character*80 cfn
real xpt,ypt,zpt
integer isok
character*80 varname,cdfname
character*80 parfile
real distxy,distz,distz1,distz2
integer indx,indy,indz
real sum
integer count
character*80 name
 
c Externals
real kink
external kink
c ------------------------------------------------------------------------
c Preparations
c ------------------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* def_anomaly *'
print*,'*********************************************************'
 
c Set name of the PV variable
in_varname='PV'
 
c Read parameters
open(10,file='fort.10')
read(10,*) in_zfn
read(10,*) name,f_xmin
if ( trim(name).ne.'BOX_XMIN') stop
read(10,*) name,f_xmax
if ( trim(name).ne.'BOX_XMAX') stop
read(10,*) name,f_ymin
if ( trim(name).ne.'BOX_YMIN') stop
read(10,*) name,f_ymax
if ( trim(name).ne.'BOX_YMAX') stop
read(10,*) name,f_zmin
if ( trim(name).ne.'BOX_ZMIN') stop
read(10,*) name,f_zmax
if ( trim(name).ne.'BOX_ZMAX') stop
read(10,*) name,nfilt
if ( trim(name).ne.'NFILTER' ) stop
read(10,*) name,boundxy
if ( trim(name).ne.'BOUND_XY') stop
read(10,*) name,boundz
if ( trim(name).ne.'BOUND_Z') stop
close(10)
 
print*,'Filter domain, x: ', f_xmin,f_xmax
print*,' y: ', f_ymin,f_ymax
print*,' z: ', f_zmin,f_zmax
print*,'Nfilt: ',nfilt
print*,'Boundxy,z: ',boundxy,boundz
c Get grid description for Z file : height levels
call cdfopn(in_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,in_nvars,in_vnam,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,in_varname,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 998
in_nx =in_vardim(1)
in_ny =in_vardim(2)
in_nz =in_vardim(3)
in_xmin=in_varmin(1)
in_ymin=in_varmin(2)
call getlevs(cstid,in_nz,in_aklev,in_bklev,in_aklay,in_bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,in_dx,in_dy,ierr)
if (ierr.ne.0) goto 998
in_xmax=in_xmin+real(in_nx-1)*in_dx
in_ymax=in_ymin+real(in_ny-1)*in_dy
call gettimes(cdfid,in_time,in_ntimes,ierr)
if (ierr.ne.0) goto 998
call getstart(cstid,in_idate,ierr)
if (ierr.ne.0) goto 998
call getpole(cstid,in_pollon,in_pollat,ierr)
if (ierr.ne.0) goto 998
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Allocate memory for grid description
allocate(in_x(in_nx,in_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_x ***'
allocate(in_y(in_nx,in_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_y ***'
 
c Allocate memory for input and output fields
allocate(in_field(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_field ***'
allocate(in_anom(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_anom ***'
allocate(in_filt(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_filt ***'
allocate(th_anom(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array th_anom ***'
allocate(uu_anom(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array uu_anom ***'
allocate(vv_anom(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array vvnom ***'
 
c Allocate memory for filtering
allocate(tmp(in_nx,in_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array tmp ***'
 
c Read variables from file
call cdfopn(in_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
 
varname=trim(in_varname)
print*,'R ',trim(varname),' ',trim(in_zfn)
call gettimes(cdfid,in_time,in_ntimes,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,in_time,0,in_field,ierr)
if (ierr.ne.0) goto 998
 
varname='X'
print*,'R ',trim(varname),' ',trim(in_zfn)
call gettimes(cdfid,in_time,in_ntimes,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,in_time,0,in_x,ierr)
if (ierr.ne.0) goto 998
 
varname='Y'
print*,'R ',trim(varname),' ',trim(in_zfn)
call gettimes(cdfid,in_time,in_ntimes,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,in_time,0,in_y,ierr)
if (ierr.ne.0) goto 998
 
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c ------------------------------------------------------------------------
c Get the average along the x axis: "zonal" average
c ------------------------------------------------------------------------
 
print*,'A ',trim(in_varname)
do k=1,in_nz
do j=1,in_ny
 
c Get the mean along x axis
sum=0.
count=0
do i=1,in_nx
if (abs(in_field(i,j,k)-in_mdv).gt.eps) then
sum=sum+in_field(i,j,k)
count=count+1
endif
enddo
if (count.ge.1) then
sum=sum/real(count)
else
sum=in_mdv
endif
 
c Get the difference relative to the "zonal" mean
do i=1,in_nx
xpt=in_x(i,j)
ypt=in_y(i,j)
zpt=in_aklay(k)
if ( (xpt.ge.f_xmin).and.
> (xpt.le.f_xmax).and.
> (ypt.ge.f_ymin).and.
> (ypt.le.f_ymax).and.
> (zpt.ge.f_zmin).and.
> (zpt.le.f_zmax)) then
in_filt(i,j,k)=sum
else
in_filt(i,j,k)=in_field(i,j,k)
endif
enddo
enddo
enddo
 
c ------------------------------------------------------------------------
c Get the anomaly field
c ------------------------------------------------------------------------
c
c Determine the difference between filtered and unfiltered field
do i=1,in_nx
do j=1,in_ny
do k=1,in_nz
if ( (abs(in_field(i,j,k)-in_mdv).gt.eps).and.
> (abs(in_filt (i,j,k)-in_mdv).gt.eps)) then
in_anom(i,j,k)=in_field(i,j,k)-in_filt(i,j,k)
else
in_anom(i,j,k)=in_mdv
endif
enddo
enddo
enddo
 
c Take only the positive part of the difference (mdv is set to 0)
do i=1,in_nx
do j=1,in_ny
do k=1,in_nz
if ( (abs(in_anom(i,j,k)-in_mdv).lt.eps) ) then
in_anom(i,j,k)=0.
else if ( in_anom(i,j,k).lt.0.) then
in_anom(i,j,k)=0.
endif
enddo
enddo
enddo
 
c Smooth transition to zero at boundaries
do i=1,in_nx
do j=1,in_ny
do k=1,in_nz
if ( (abs(in_anom (i,j,k)-in_mdv).gt.eps) ) then
in_anom(i,j,k)=in_anom(i,j,k)*
> kink(f_zmax -in_aklay(k),boundz )*
> kink(in_aklay(k)-f_zmin ,boundz )*
> kink(in_x(i,j) -f_xmin ,boundxy)*
> kink(f_xmax -in_x(i,j) ,boundxy)*
> kink(in_y(i,j) -f_ymin ,boundxy)*
> kink(f_ymax -in_y(i,j) ,boundxy)
 
endif
enddo
enddo
enddo
 
c ------------------------------------------------------------------------
c Apply a digital filter to the anomaly field
c ------------------------------------------------------------------------
 
print*,'F ',trim(in_varname)
do k=1,in_nz
do i=1,in_nx
do j=1,in_ny
tmp(i,j)=in_anom(i,j,k)
enddo
enddo
do n=1,nfilt
call filt2d (tmp,tmp,in_nx,in_ny,1.,in_mdv,0,0,0,0)
enddo
do i=1,in_nx
do j=1,in_ny
in_anom(i,j,k)=tmp(i,j)
enddo
enddo
enddo
 
c ------------------------------------------------------------------------
c Get the modified PV field (original minus anomaly)
c ------------------------------------------------------------------------
 
do i=1,in_nx
do j=1,in_ny
do k=1,in_nz
if ( (abs(in_anom (i,j,k)-in_mdv).gt.eps).and.
> (abs(in_field(i,j,k)-in_mdv).gt.eps) ) then
in_filt(i,j,k)=in_field(i,j,k)-in_anom(i,j,k)
else
in_filt(i,j,k)=in_mdv
endif
enddo
enddo
enddo
 
c -----------------------------------------------------------------
c Define the boundary values for wind and potential temperature
c -----------------------------------------------------------------
 
do i=1,in_nx
do j=1,in_ny
do k=1,in_nz
th_anom(i,j,k)=0.
uu_anom(i,j,k)=0.
vv_anom(i,j,k)=0.
enddo
enddo
enddo
c -----------------------------------------------------------------
c Write output
c -----------------------------------------------------------------
 
c Open output netcdf file
call cdfwopn(in_zfn,cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Write the 3d filtered field
isok=0
varname=trim(in_varname)//'_FILT'
print*,'Write ',trim(varname),' ',trim(in_zfn)
call check_varok(isok,varname,in_vnam,in_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,4,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,in_time,0,in_filt,ierr)
if (ierr.ne.0) goto 997
 
c Write the 3d anomaly field
isok=0
varname=trim(in_varname)//'_ANOM'
print*,'Write ',trim(varname),' ',trim(in_zfn)
call check_varok(isok,varname,in_vnam,in_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,4,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,in_time,0,in_anom,ierr)
if (ierr.ne.0) goto 997
 
c Write lower and upper boundary
isok=0
varname='TH_ANOM'
print*,'Write ',trim(varname),' ',trim(in_zfn)
call check_varok(isok,varname,in_vnam,in_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,4,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,in_time,0,th_anom,ierr)
if (ierr.ne.0) goto 997
 
c Write lateral boundary
isok=0
varname='UU_ANOM'
print*,'Write ',trim(varname),' ',trim(in_zfn)
call check_varok(isok,varname,in_vnam,in_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,4,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,in_time,0,uu_anom,ierr)
if (ierr.ne.0) goto 997
isok=0
varname='VV_ANOM'
print*,'Write ',trim(varname),' ',trim(in_zfn)
call check_varok(isok,varname,in_vnam,in_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,4,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,in_time,0,vv_anom,ierr)
if (ierr.ne.0) goto 997
 
c Close output netcdf file
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 997
 
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Problems with input netcdf file'
stop
 
997 print*,'Problems with output netcdf file'
stop
 
END
 
 
c ******************************************************************
c * 2D FILTERING *
c ******************************************************************
 
c -----------------------------------------------------------------
c Horizontal filter
c -----------------------------------------------------------------
 
subroutine filt2d (a,af,nx,ny,fil,misdat,
& iperx,ipery,ispol,inpol)
 
c Apply a conservative diffusion operator onto the 2d field a,
c with full missing data checking.
c
c a real inp array to be filtered, dimensioned (nx,ny)
c af real out filtered array, dimensioned (nx,ny), can be
c equivalenced with array a in the calling routine
c f1 real workarray, dimensioned (nx+1,ny)
c f2 real workarray, dimensioned (nx,ny+1)
c fil real inp filter-coeff., 0<afil<=1. Maximum filtering with afil=1
c corresponds to one application of the linear filter.
c misdat real inp missing-data value, a(i,j)=misdat indicates that
c the corresponding value is not available. The
c misdat-checking can be switched off with with misdat=0.
c iperx int inp periodic boundaries in the x-direction (1=yes,0=no)
c ipery int inp periodic boundaries in the y-direction (1=yes,0=no)
c inpol int inp northpole at j=ny (1=yes,0=no)
c ispol int inp southpole at j=1 (1=yes,0=no)
c
c Christoph Schaer, 1993
 
c argument declaration
integer nx,ny
real a(nx,ny),af(nx,ny),fil,misdat
integer iperx,ipery,inpol,ispol
 
c local variable declaration
integer i,j,is
real fh
real f1(nx+1,ny),f2(nx,ny+1)
 
c compute constant fh
fh=0.125*fil
 
c compute fluxes in x-direction
if (misdat.eq.0.) then
do j=1,ny
do i=2,nx
f1(i,j)=a(i-1,j)-a(i,j)
enddo
enddo
else
do j=1,ny
do i=2,nx
if ((a(i,j).eq.misdat).or.(a(i-1,j).eq.misdat)) then
f1(i,j)=0.
else
f1(i,j)=a(i-1,j)-a(i,j)
endif
enddo
enddo
endif
if (iperx.eq.1) then
c do periodic boundaries in the x-direction
do j=1,ny
f1(1,j)=f1(nx,j)
f1(nx+1,j)=f1(2,j)
enddo
else
c set boundary-fluxes to zero
do j=1,ny
f1(1,j)=0.
f1(nx+1,j)=0.
enddo
endif
 
c compute fluxes in y-direction
if (misdat.eq.0.) then
do j=2,ny
do i=1,nx
f2(i,j)=a(i,j-1)-a(i,j)
enddo
enddo
else
do j=2,ny
do i=1,nx
if ((a(i,j).eq.misdat).or.(a(i,j-1).eq.misdat)) then
f2(i,j)=0.
else
f2(i,j)=a(i,j-1)-a(i,j)
endif
enddo
enddo
endif
c set boundary-fluxes to zero
do i=1,nx
f2(i,1)=0.
f2(i,ny+1)=0.
enddo
if (ipery.eq.1) then
c do periodic boundaries in the x-direction
do i=1,nx
f2(i,1)=f2(i,ny)
f2(i,ny+1)=f2(i,2)
enddo
endif
if (iperx.eq.1) then
if (ispol.eq.1) then
c do south-pole
is=(nx-1)/2
do i=1,nx
f2(i,1)=-f2(mod(i-1+is,nx)+1,2)
enddo
endif
if (inpol.eq.1) then
c do north-pole
is=(nx-1)/2
do i=1,nx
f2(i,ny+1)=-f2(mod(i-1+is,nx)+1,ny)
enddo
endif
endif
 
c compute flux-convergence -> filter
if (misdat.eq.0.) then
do j=1,ny
do i=1,nx
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
enddo
enddo
else
do j=1,ny
do i=1,nx
if (a(i,j).eq.misdat) then
af(i,j)=misdat
else
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
endif
enddo
enddo
endif
 
end
 
 
c ******************************************************************
c * AUXILIARY SUBROUTINES *
c ******************************************************************
C -----------------------------------------------------------------
c Rene's KINK function (for smoothing at bounadries)
C -----------------------------------------------------------------
 
real function kink (x,a)
 
implicit none
 
c declaration of parameters
real x,a
 
c parameters
real pi
parameter (pi=3.1415926535)
 
if (x.lt.0.) then
kink=0.
elseif (x.gt.a) then
kink=1.
else
kink=(1.+cos(pi*(x-a)/a))/2.
endif
return
end
 
 
c ---------------------------------------------------------
c Subroutines to write the netcdf output file
c ---------------------------------------------------------
 
subroutine writecdf2D(cdfname,
> varname,arr,time,
> dx,dy,xmin,ymin,nx,ny,
> crefile,crevar)
 
c Create and write to the netcdf file <cdfname>. The variable
c with name <varname> and with time <time> is written. The data
c are in the two-dimensional array <arr>. The list <dx,dy,xmin,
c ymin,nx,ny> specifies the output grid. The flags <crefile> and
c <crevar> determine whether the file and/or the variable should
c be created. 1: create / 0: not created
 
IMPLICIT NONE
 
c Declaration of input parameters
character*80 cdfname,varname
integer nx,ny
real arr(nx,ny)
real dx,dy,xmin,ymin
real time
integer crefile,crevar
 
c Further variables
real varmin(4),varmax(4),stag(4)
integer ierr,cdfid,ndim,vardim(4)
character*80 cstname
real mdv
integer datar(14),stdate(5)
integer i
 
C Definitions
varmin(1)=xmin
varmin(2)=ymin
varmin(3)=1050.
varmax(1)=xmin+real(nx-1)*dx
varmax(2)=ymin+real(ny-1)*dy
varmax(3)=1050.
cstname=trim(cdfname)//'_cst'
ndim=4
vardim(1)=nx
vardim(2)=ny
vardim(3)=1
stag(1)=0.
stag(2)=0.
stag(3)=0.
mdv=-999.98999
 
C Create the file
if (crefile.eq.0) then
call cdfwopn(cdfname,cdfid,ierr)
if (ierr.ne.0) goto 906
else if (crefile.eq.1) then
call crecdf(cdfname,cdfid,
> varmin,varmax,ndim,cstname,ierr)
if (ierr.ne.0) goto 903
 
C Write the constants file
datar(1)=vardim(1)
datar(2)=vardim(2)
datar(3)=int(1000.*varmax(2))
datar(4)=int(1000.*varmin(1))
datar(5)=int(1000.*varmin(2))
datar(6)=int(1000.*varmax(1))
datar(7)=int(1000.*dx)
datar(8)=int(1000.*dy)
datar(9)=1
datar(10)=1
datar(11)=0 ! data version
datar(12)=0 ! cstfile version
datar(13)=0 ! longitude of pole
datar(14)=90000 ! latitude of pole
do i=1,5
stdate(i)=0
enddo
call wricst(cstname,datar,0.,0.,0.,0.,stdate)
endif
 
c Write the data to the netcdf file, and close the file
if (crevar.eq.1) then
call putdef(cdfid,varname,ndim,mdv,
> vardim,varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 904
endif
call putdat(cdfid,varname,time,0,arr,ierr)
if (ierr.ne.0) goto 905
call clscdf(cdfid,ierr)
 
return
c Error handling
903 print*,'*** Problem to create netcdf file ***'
stop
904 print*,'*** Problem to write definition ***'
stop
905 print*,'*** Problem to write data ***'
stop
906 print*,'*** Problem to open netcdf file ***'
stop
 
END
 
 
c ------------------------------------------------------------------
c Auxiliary routines
c ------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok> keeps
c its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/def_anomaly.m
0,0 → 1,674
 
% -------------------------------------------------------------------------
% Load files
% -------------------------------------------------------------------------
 
% Base directory and filename
base = '/net/rossby/lhome/sprenger/PV_Inversion_Tool/real/inp/';
folder = base;
filename = 'H20060116_18';
disp([folder filename])
 
% First image (otherwise first image is not correctly written)
figname = [base '/test.eps'];
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% Load variables from file (on model levels)
m_th = cdf_loadV(folder,filename,'TH');
m_pv = cdf_loadV(folder,filename,'PV');
m_fl = cdf_loadV(folder,filename,'PV_FILT');
m_an = cdf_loadV(folder,filename,'PV_ANOM');
 
% Specify the plot domain
lonmin =-100;
lonmax = -20;
latmin = 10;
latmax = 80;
 
% Region for smoothing
lon1=-75;lon2=-50;
lat1= 30;lat2=55;
lev1=2000;lev2=10000;
 
% Plotting parameters
plotting=cellstr([ 'ew'; 'ns'; '2d'; 'pv'; 'an'; 'fl' ]);
%plotting=cellstr([ 'ew'; 'pv'; 'an'; 'fl' ]);
 
% -------------------------------------------------------------------------
% PV (HORIZONTAL)
% -------------------------------------------------------------------------
 
if ( any(strcmp('2d',plotting)) & any(strcmp('pv',plotting)) )
 
disp('2D PV');
% Loop over all levels
for ilev=1:m_th.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[lonmin lonmax],'lat',[latmin latmax]);
 
% Scale the plotting field for color map
fld=squeeze(m_pv.var(ilev,:,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(m_th.aklay(ilev)));
 
% Add region of smoothing
if ( (m_th.aklay(ilev) > lev1) & (m_th.aklay(ilev) < lev2) )
m_line([lon1 lon1],[lat1 lat2],'color','k','linewidth',2);
m_line([lon1 lon2],[lat2 lat2],'color','k','linewidth',2);
m_line([lon2 lon2],[lat2 lat1],'color','k','linewidth',2);
m_line([lon1 lon2],[lat1 lat1],'color','k','linewidth',2);
end
 
% Save figure
pre='';
if ( m_th.aklay(ilev) < 10 )
pre='0';
end
if ( m_th.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/pv_2d_' filename '_' pre num2str(m_th.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_FILT (HORIZONTAL)
% -------------------------------------------------------------------------
 
if ( any(strcmp('2d',plotting)) & any(strcmp('fl',plotting)) )
 
disp('2D FL');
 
% Loop over all levels
for ilev=1:m_th.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[lonmin lonmax],'lat',[latmin latmax]);
 
% Scale the plotting field for color map
fld=squeeze(m_fl.var(ilev,:,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(m_th.aklay(ilev)));
 
% Add region for smootrhing
if ( (m_th.aklay(ilev) > lev1) & (m_th.aklay(ilev) < lev2) )
m_line([lon1 lon1],[lat1 lat2],'color','k','linewidth',2);
m_line([lon1 lon2],[lat2 lat2],'color','k','linewidth',2);
m_line([lon2 lon2],[lat2 lat1],'color','k','linewidth',2);
m_line([lon1 lon2],[lat1 lat1],'color','k','linewidth',2);
end
 
% Save figure
pre='';
if ( m_th.aklay(ilev) < 10 )
pre='0';
end
if ( m_th.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/fl_2d_' filename '_' pre num2str(m_th.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_ANOM (HORIZONTAL)
% -------------------------------------------------------------------------
 
if ( any(strcmp('2d',plotting)) & any(strcmp('an',plotting)) )
 
disp('2D AN');
 
% Loop over all levels
for ilev=1:m_th.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[lonmin lonmax],'lat',[latmin latmax]);
 
% Scale the plotting field for color map
fld=squeeze(m_an.var(ilev,:,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(m_th.aklay(ilev)));
 
% Add region for smootrhing
if ( (m_th.aklay(ilev) > lev1) & (m_th.aklay(ilev) < lev2) )
m_line([lon1 lon1],[lat1 lat2],'color','k','linewidth',2);
m_line([lon1 lon2],[lat2 lat2],'color','k','linewidth',2);
m_line([lon2 lon2],[lat2 lat1],'color','k','linewidth',2);
m_line([lon1 lon2],[lat1 lat1],'color','k','linewidth',2);
end
 
% Save figure
pre='';
if ( m_th.aklay(ilev) < 10 )
pre='0';
end
if ( m_th.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( m_th.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/an_2d_' filename '_' pre num2str(m_th.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV (VERTICAL EAST/WEST)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ew',plotting)) & any(strcmp('pv',plotting)) )
disp('EW PV');
 
% Loop over all levels
for lat=latmin:latmax
 
% Get the y index of the latitude in the grid
ilat=floor((lat-m_pv.ymin)/(m_pv.dy)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_pv.var(:,ilat,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
lev=m_pv.aklay;
mask=(lon>=lonmin) & (lon<=lonmax);
[C,h]=contourf(lon(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Latitude = ' num2str(lat) ]);
 
% Add region for smootrhing
if ( (lat > lat1) & (lat < lat2) )
line([lon1 lon2],[lev1 lev1],'color','k','linewidth',2);
line([lon2 lon2],[lev1 lev2],'color','k','linewidth',2);
line([lon2 lon1],[lev2 lev2],'color','k','linewidth',2);
line([lon1 lon1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lat < 0 )
pre='s'
else
pre='n'
end
if ( abs(lat) < 10 )
pre=[ pre '0'];
end
 
figname = [ base '/pv_ew_' filename '_' pre num2str(abs(lat)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_FILT (VERTICAL EAST/WEST)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ew',plotting)) & any(strcmp('fl',plotting)) )
disp('EW FL');
 
% Loop over all levels
for lat=latmin:latmax
 
% Get the y index of the latitude in the grid
ilat=floor((lat-m_pv.ymin)/(m_pv.dy)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_fl.var(:,ilat,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV_FILT
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
lev=m_pv.aklay;
mask=(lon>=lonmin) & (lon<=lonmax);
[C,h]=contourf(lon(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Latitude = ' num2str(lat) ]);
 
% Add region for smootrhing
if ( (lat > lat1) & (lat < lat2) )
line([lon1 lon2],[lev1 lev1],'color','k','linewidth',2);
line([lon2 lon2],[lev1 lev2],'color','k','linewidth',2);
line([lon2 lon1],[lev2 lev2],'color','k','linewidth',2);
line([lon1 lon1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lat < 0 )
pre='s'
else
pre='n'
end
if ( abs(lat) < 10 )
pre=[ pre '0'];
end
 
figname = [ base '/fl_ew_' filename '_' pre num2str(abs(lat)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_ANOM (VERTICAL EAST/WEST)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ew',plotting)) & any(strcmp('an',plotting)) )
 
disp('EW AN');
 
% Loop over all levels
for lat=latmin:latmax
 
% Get the y index of the latitude in the grid
ilat=floor((lat-m_pv.ymin)/(m_pv.dy)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_an.var(:,ilat,:));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV_FILT
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
lev=m_pv.aklay;
mask=(lon>=lonmin) & (lon<=lonmax);
[C,h]=contourf(lon(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Latitude = ' num2str(lat) ]);
 
% Add region for smootrhing
if ( (lat > lat1) & (lat < lat2) )
line([lon1 lon2],[lev1 lev1],'color','k','linewidth',2);
line([lon2 lon2],[lev1 lev2],'color','k','linewidth',2);
line([lon2 lon1],[lev2 lev2],'color','k','linewidth',2);
line([lon1 lon1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lat < 0 )
pre='s'
else
pre='n'
end
if ( abs(lat) < 10 )
pre=[ pre '0'];
end
 
figname = [ base '/an_ew_' filename '_' pre num2str(abs(lat)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV (VERTICAL NORTH/SOUTH)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ns',plotting)) & any(strcmp('pv',plotting)) )
disp('NS PV');
% Loop over all levels
for lon=lonmin:lonmax
 
% Get the y index of the latitude in the grid
ilon=floor((lon-m_pv.xmin)/(m_pv.dx)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_pv.var(:,:,ilon));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lev=m_pv.aklay;
mask=(lat>=latmin) & (lat<=latmax);
[C,h]=contourf(lat(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Longitude = ' num2str(lon) ]);
 
% Add region for smootrhing
if ( (lon > lon1) & (lon < lon2) )
line([lat1 lat2],[lev1 lev1],'color','k','linewidth',2);
line([lat2 lat2],[lev1 lev2],'color','k','linewidth',2);
line([lat2 lat1],[lev2 lev2],'color','k','linewidth',2);
line([lat1 lat1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lon < 0 )
pre='w'
else
pre='e'
end
if ( abs(lon) < 10 )
pre=[ pre '00'];
elseif ( abs(lon) < 100 )
pre=[ pre '0'];
end
 
figname = [ base '/pv_ns_' filename '_' pre num2str(abs(lon)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_FILT (VERTICAL NORTH/SOUTH)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ns',plotting)) & any(strcmp('fl',plotting)) )
disp('NS FL');
 
% Loop over all levels
for lon=lonmin:lonmax
 
% Get the y index of the latitude in the grid
ilon=floor((lon-m_pv.xmin)/(m_pv.dx)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_fl.var(:,:,ilon));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lev=m_pv.aklay;
mask=(lat>=latmin) & (lat<=latmax);
[C,h]=contourf(lat(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Longitude = ' num2str(lon) ]);
 
% Add region for smootrhing
if ( (lon > lon1) & (lon < lon2) )
line([lat1 lat2],[lev1 lev1],'color','k','linewidth',2);
line([lat2 lat2],[lev1 lev2],'color','k','linewidth',2);
line([lat2 lat1],[lev2 lev2],'color','k','linewidth',2);
line([lat1 lat1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lon < 0 )
pre='w'
else
pre='e'
end
if ( abs(lon) < 10 )
pre=[ pre '00'];
elseif ( abs(lon) < 100 )
pre=[ pre '0'];
end
 
figname = [ base '/fl_ns_' filename '_' pre num2str(abs(lon)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
 
% -------------------------------------------------------------------------
% PV_ANOM (VERTICAL NORTH/SOUTH)
% -------------------------------------------------------------------------
 
if ( any(strcmp('ns',plotting)) & any(strcmp('an',plotting)) )
disp('NS AN');
 
% Loop over all levels
for lon=lonmin:lonmax
 
% Get the y index of the latitude in the grid
ilon=floor((lon-m_pv.xmin)/(m_pv.dx)+1);
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Scale the plotting field for color map
fld=squeeze(m_an.var(:,:,ilon));
c_map = scale_col([-.5,-.2,0.,.2,.5,1.,1.5,2.,3.,4.,6.,8.,10.],fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lev=m_pv.aklay;
mask=(lat>=latmin) & (lat<=latmax);
[C,h]=contourf(lat(mask),lev,c_map.data(:,mask),c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
title([ 'Longitude = ' num2str(lon) ]);
 
% Add region for smootrhing
if ( (lon > lon1) & (lon < lon2) )
line([lat1 lat2],[lev1 lev1],'color','k','linewidth',2);
line([lat2 lat2],[lev1 lev2],'color','k','linewidth',2);
line([lat2 lat1],[lev2 lev2],'color','k','linewidth',2);
line([lat1 lat1],[lev2 lev1],'color','k','linewidth',2);
end
 
% Save figure
if ( lon < 0 )
pre='w'
else
pre='e'
end
if ( abs(lon) < 10 )
pre=[ pre '00'];
elseif ( abs(lon) < 100 )
pre=[ pre '0'];
end
 
figname = [ base '/an_ns_' filename '_' pre num2str(abs(lon)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/p2z.f
0,0 → 1,846
PROGRAM p2z
 
c Calculate the geopotential and add it to the P file
c Michael Sprenger / Spring 2006
 
implicit none
 
c ---------------------------------------------------------------
c Declaration of variables
c ---------------------------------------------------------------
 
c Variables for input P file : model level
character*80 ml_pfn
real ml_varmin(4),ml_varmax(4),ml_stag(4)
integer ml_vardim(4)
real ml_mdv
integer ml_ndim
integer ml_nx,ml_ny,ml_nz
real ml_xmin,ml_xmax,ml_ymin,ml_ymax,ml_dx,ml_dy
integer ml_ntimes
real ml_aklev(500),ml_bklev(500)
real ml_aklay(500),ml_bklay(500)
real ml_time
real ml_pollon,ml_pollat
integer ml_nvars
character*80 ml_vnam(100)
integer ml_idate(5)
real,allocatable, dimension (:,:) :: ml_ps,ml_zb
real,allocatable, dimension (:,:,:) :: ml_t3,ml_q3,ml_p3,ml_tv3
real,allocatable, dimension (:,:,:) :: ml_z3
 
c Variables for input Z file : pressure level
character*80 pl_zfn
real pl_varmin(4),pl_varmax(4),pl_stag(4)
integer pl_vardim(4)
real pl_mdv
integer pl_ndim
integer pl_nx,pl_ny,pl_nz
real pl_xmin,pl_xmax,pl_ymin,pl_ymax,pl_dx,pl_dy
integer pl_ntimes
real pl_aklev(500),pl_bklev(500)
real pl_aklay(500),pl_bklay(500)
real pl_time
real pl_pollon,pl_pollat
integer pl_nvars
character*80 pl_vnam(100)
integer pl_idate(5)
real,allocatable, dimension (:,:,:) :: pl_z3,pl_p3
 
c Variables for output Z file : height level
character*80 zl_ofn
real zl_varmin(4),zl_varmax(4),zl_stag(4)
integer zl_vardim(4)
real zl_mdv
integer zl_ndim
integer zl_nx,zl_ny,zl_nz
real zl_xmin,zl_xmax,zl_ymin,zl_ymax,zl_dx,zl_dy
integer zl_ntimes
real zl_aklev(500),zl_bklev(500)
real zl_aklay(500),zl_bklay(500)
real zl_time
real zl_pollon,zl_pollat
integer zl_idate(5)
real,allocatable, dimension (:,:,:) :: zl_field
real,allocatable, dimension (:,:,:) :: zl_p
 
c Variables for input P,S file : model level
character*80 in_ofn
real in_varmin(4),in_varmax(4),in_stag(4)
integer in_vardim(4)
real in_mdv
integer in_ndim
integer in_nx,in_ny,in_nz
real in_xmin,in_xmax,in_ymin,in_ymax,in_dx,in_dy
integer in_ntimes
real in_aklev(500),in_bklev(500)
real in_aklay(500),in_bklay(500)
real in_time
real in_pollon,in_pollat
integer in_nvars
character*80 in_vnam(100)
integer in_idate(5)
real,allocatable, dimension (:,:,:) :: in_field
 
c Physical and numerical parameters
real g
parameter (g=9.80665)
real eps
parameter (eps=0.01)
real tzero
parameter (tzero=273.15)
real kappa
parameter (kappa=0.6078)
real zerodiv
parameter (zerodiv=0.0000000001)
real dpmin
parameter (dpmin=10.)
real rdg
parameter (rdg=29.271)
 
c Flag for test mode
integer test
parameter (test=0)
character*80 testfile
parameter (testfile='TEST')
 
c Variables and levels for interpolation onto z levels
character*80 levelfile,varfile
integer nvar,nlev
character*80 varinp(100),varout(100),varsrc(100)
real zlev(500)
 
c Auxiliary variables
integer ierr
integer cdfid,cstid
character*80 cfn
integer stat
real time
real tv1(1000),z1(1000),p1(1000),f1(1000)
real spline_tv1(1000),spline_f1(1000),spline_z1(1000)
real pu,po,zu,zo,p,z,dp,p0,tvu,tvo,ff
integer i,j,k,l
integer lmin,n
character*80 varname,cdfname
integer idate(5),stdate(5),datar(14)
integer isok
character*80 name
real zmin,dz
 
c -----------------------------------------------------------------
c Read input fields
c -----------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* p2z *'
print*,'*********************************************************'
 
c Read in the parameter file
open(10,file='fort.10')
 
read(10,*) ml_pfn
read(10,*) pl_zfn
read(10,*) zl_ofn
 
read(10,*) name,zmin
if ( trim(name).ne.'GEO_ZMIN') stop
read(10,*) name,nlev
if ( trim(name).ne.'GEO_NZ' ) stop
read(10,*) name,dz
if ( trim(name).ne.'GEO_DZ' ) stop
do i=1,nlev
zlev(i)=zmin+real(i-1)*dz
enddo
 
nvar=1
102 continue
read(10,*,end=103) varinp(nvar),varout(nvar),varsrc(nvar)
nvar=nvar+1
goto 102
103 continue
nvar=nvar-1
print*
do i=1,nvar
write(*,'(a10,a10,a30)') trim(varinp(i)),trim(varout(i)),
> trim(varsrc(i))
enddo
print*
 
close(10)
 
 
c Get grid description for P file : model level
call cdfopn(ml_pfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,ml_nvars,ml_vnam,ierr)
varname='T'
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 998
ml_nx =ml_vardim(1)
ml_ny =ml_vardim(2)
ml_nz =ml_vardim(3)
ml_xmin=ml_varmin(1)
ml_ymin=ml_varmin(2)
call getlevs(cstid,ml_nz,ml_aklev,ml_bklev,ml_aklay,ml_bklay,ierr)
call getgrid(cstid,ml_dx,ml_dy,ierr)
ml_xmax=ml_xmin+real(ml_nx-1)*ml_dx
ml_ymax=ml_ymin+real(ml_ny-1)*ml_dy
call gettimes(cdfid,ml_time,ml_ntimes,ierr)
call getstart(cstid,ml_idate,ierr)
call getpole(cstid,ml_pollon,ml_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Get grid description for Z file : pressure level
call cdfopn(pl_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,pl_nvars,pl_vnam,ierr)
varname='Z'
isok=0
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
call getdef(cdfid,varname,pl_ndim,pl_mdv,pl_vardim,
> pl_varmin,pl_varmax,pl_stag,ierr)
if (ierr.ne.0) goto 998
pl_nx =pl_vardim(1)
pl_ny =pl_vardim(2)
pl_nz =pl_vardim(3)
pl_xmin=pl_varmin(1)
pl_ymin=pl_varmin(2)
call getlevs(cstid,pl_nz,pl_aklev,pl_bklev,pl_aklay,pl_bklay,ierr)
call getgrid(cstid,pl_dx,pl_dy,ierr)
pl_xmax=pl_xmin+real(pl_nx-1)*pl_dx
pl_ymax=pl_ymin+real(pl_ny-1)*pl_dy
call gettimes(cdfid,pl_time,pl_ntimes,ierr)
call getstart(cstid,pl_idate,ierr)
call getpole(cstid,pl_pollon,pl_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Set grid description for output file : height level
zl_vardim(1) = pl_vardim(1)
zl_vardim(2) = pl_vardim(2)
zl_vardim(3) = nlev
zl_varmin(1) = pl_varmin(1)
zl_varmin(2) = pl_varmin(2)
zl_varmin(3) = zlev(1)
zl_varmax(1) = pl_varmax(1)
zl_varmax(2) = pl_varmax(2)
zl_varmax(3) = zlev(nlev)
do i=1,nlev
zl_aklay(i) = zlev(i)
zl_bklay(i) = 0.
zl_aklev(i) = zlev(i)
zl_bklev(i) = 0.
enddo
zl_dx = pl_dx
zl_dy = pl_dy
zl_time = pl_time
zl_ntimes = pl_ntimes
zl_ndim = 4
zl_mdv = pl_mdv
zl_nx = zl_vardim(1)
zl_ny = zl_vardim(2)
zl_nz = zl_vardim(3)
zl_xmin = zl_varmin(1)
zl_ymin = zl_varmin(2)
zl_pollon = ml_pollon
zl_pollat = ml_pollat
do i=1,5
zl_idate(i) = ml_idate(i)
enddo
 
c Consitency check for the grids
if ( (ml_nx.ne.pl_nx).or.
> (ml_ny.ne.pl_ny).or.
> (abs(ml_xmin-pl_xmin ).gt.eps).or.
> (abs(ml_ymin-pl_ymin ).gt.eps).or.
> (abs(ml_xmax-pl_xmax ).gt.eps).or.
> (abs(ml_ymax-pl_ymax ).gt.eps).or.
> (abs(ml_dx -pl_dx ).gt.eps).or.
> (abs(ml_dy -pl_dy ).gt.eps).or.
> (abs(ml_time-pl_time ).gt.eps).or.
> (abs(ml_pollon-pl_pollon).gt.eps).or.
> (abs(ml_pollat-pl_pollat).gt.eps)) then
print*,'Input P and Z grids are not consistent... Stop'
print*
print*,'Xmin : ',ml_xmin,pl_xmin
print*,'Ymin : ',ml_ymin,pl_ymin
print*,'Xmax : ',ml_xmax,pl_xmax
print*,'Ymax : ',ml_ymax,pl_ymax
print*,'Dx : ',ml_dx, pl_dx
print*,'Dy : ',ml_dy, pl_dy
print*,'Time : ',ml_time,pl_time
print*,'Pollon : ',ml_pollon,pl_pollon
print*,'Pollat : ',ml_pollat,pl_pollat
stop
endif
 
c Allocate memory for all fields
allocate(ml_ps(ml_nx,ml_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_ps ***'
allocate(ml_zb(ml_nx,ml_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_zb ***'
allocate(ml_p3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_p3 ***'
allocate(ml_t3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_t3 ***'
allocate(ml_q3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_q3 ***'
allocate(ml_tv3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_tv3 ***'
allocate(ml_z3(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ml_z3 ***'
 
allocate(in_field(ml_nx,ml_ny,ml_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_field ***'
 
allocate(pl_z3(pl_nx,pl_ny,pl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pl_z3 ***'
allocate(pl_p3(pl_nx,pl_ny,pl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pl_p3 ***'
 
allocate(zl_field(zl_nx,zl_ny,zl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array zl_field ***'
allocate(zl_p(zl_nx,zl_ny,zl_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array zl_p ***'
 
c Read T, Q, PS from P file
call cdfopn(ml_pfn,cdfid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='T'
call check_varok (isok,varname, ml_vnam,ml_nvars)
varname='Q'
call check_varok (isok,varname, ml_vnam,ml_nvars)
varname='PS'
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.ne.3) goto 998
print*,'R T ',trim(ml_pfn)
call getdat(cdfid,'T',ml_time,0,ml_t3,ierr)
print*,'R Q ',trim(ml_pfn)
call getdat(cdfid,'Q',ml_time,0,ml_q3,ierr)
print*,'R PS ',trim(ml_pfn)
call getdat(cdfid,'PS',ml_time,1,ml_ps,ierr)
call clscdf(cdfid,ierr)
 
c Read Z from Z file
call cdfopn(pl_zfn,cdfid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='Z'
call check_varok (isok,varname,pl_vnam,pl_nvars)
if (isok.ne.1) goto 998
print*,'R Z ',trim(pl_zfn)
call getdat(cdfid,varname,pl_time,0,pl_z3,ierr)
call clscdf(cdfid,ierr)
 
c Set the values for the pressure on the pressure levels
do i=1,pl_nx
do j=1,pl_ny
do k=1,pl_nz
pl_p3(i,j,k)=pl_aklay(k)
enddo
enddo
enddo
 
c -----------------------------------------------------------------
c Calculate geopotential on layers
c -----------------------------------------------------------------
 
c Calculate 3d pressure field
print*,'C P'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
ml_p3(i,j,k)=ml_aklay(k)+ml_bklay(k)*ml_ps(i,j)
enddo
enddo
enddo
 
c Calculate 3d virtual temperature
print*,'C TV'
do k=1,ml_nz
do i=1,ml_nx
do j=1,ml_ny
ml_tv3(i,j,k) = (ml_t3(i,j,k)+tzero)*
> (1.+kappa*ml_q3(i,j,k))
enddo
enddo
enddo
 
c Loop over all grid points
print*,'C HYDROSTATIC EQUATION'
do i=1,ml_nx
do j=1,ml_ny
 
c Make the virtual temperature profile available
do k=1,ml_nz
p1 (ml_nz-k+1)=ml_p3 (i,j,k)
tv1(ml_nz-k+1)=ml_tv3(i,j,k)
enddo
call spline (p1,tv1,ml_nz,1.e30,1.e30,spline_tv1)
 
c Loop over all model levels
do k=1,ml_nz
 
c Get pressure at the grid point
p = ml_p3(i,j,k)
 
c Find nearest pressure level which is above topography
lmin=pl_nz
do l=1,pl_nz
if ((abs(p-pl_p3(i,j,l))).lt.(abs(p-pl_p3(i,j,lmin)))
> .and.
> (pl_p3(i,j,l).lt.ml_ps(i,j)) ) then
lmin=l
endif
enddo
 
c Integrate hydrostatic equation from this level to the grid point
p0 = pl_p3(i,j,lmin)
n = nint(abs(p-p0)/dpmin)
if (n.lt.1) n=1
dp = (p-p0)/real(n)
 
pu = p0
z = pl_z3(i,j,lmin)
call splint(p1,tv1,spline_tv1,ml_nz,pu,tvu)
do l=1,n
po = pu+dp
call splint(p1,tv1,spline_tv1,ml_nz,po,tvo)
z = z + rdg*0.5*(tvu+tvo)*alog(pu/po)
tvu = tvo
pu = po
enddo
c Set the geopotential at the grid point
ml_z3(i,j,k) = z
enddo
 
enddo
enddo
 
c -----------------------------------------------------------------
c Calculate height of topography
c -----------------------------------------------------------------
 
print*,'C TOPOGRAPHY'
do i=1,ml_nx
do j=1,ml_ny
 
c Make the z/p profile available
do k=1,ml_nz
p1(ml_nz-k+1)=ml_p3(i,j,k)
z1(ml_nz-k+1)=ml_z3(i,j,k)
enddo
 
c Cubic spline interpolation
call spline (p1,z1,ml_nz,1.e30,1.e30,spline_z1)
call splint (p1,z1,spline_z1,ml_nz,ml_ps(i,j),ml_zb(i,j))
enddo
enddo
 
c -----------------------------------------------------------------
c Interpolate pressure onto z levels
c -----------------------------------------------------------------
 
do i=1,zl_nx
do j=1,zl_ny
c Make 1d profile available
do k=1,ml_nz
z1(k)=ml_z3(i,j,k)
f1(k)=ml_p3(i,j,k)
enddo
call spline (z1,f1,ml_nz,1.e30,1.e30,spline_f1)
do k=1,zl_nz
if (zl_aklay(k).gt.ml_zb(i,j)) then
call splint(z1,f1,spline_f1,ml_nz,zl_aklay(k),ff)
zl_p(i,j,k)=ff
else
zl_p(i,j,k)=zl_mdv
endif
enddo
enddo
enddo
 
c -----------------------------------------------------------------
c Write output to netcdf file
c -----------------------------------------------------------------
 
if (test.eq.1) then
 
c Create the output file (grid taken from temperature)
cdfname=testfile
call cdfopn(ml_pfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
call crecdf(cdfname,cdfid,
> ml_varmin,ml_varmax,ml_ndim,cfn,ierr)
if (ierr.ne.0) goto 997
 
c Write the definitions of the output variables
varname='PS'
ml_vardim(3)=1
call putdef(cdfid,varname,ml_ndim,ml_mdv,
> ml_vardim,ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 997
varname='ORO'
call putdef(cdfid,varname,ml_ndim,ml_mdv,
> ml_vardim,ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 997
ml_vardim(3)=ml_nz
varname='Z'
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 997
 
c Write output fields
print*,'W PS TEST'
varname='PS'
call putdat(cdfid,varname,ml_time,1,ml_ps,ierr)
if (ierr.ne.0) goto 997
print*,'W ZB TEST'
varname='ORO'
call putdat(cdfid,varname,ml_time,1,ml_zb,ierr)
if (ierr.ne.0) goto 997
print*,'W Z TEST'
varname='Z'
call putdat(cdfid,varname,ml_time,0,ml_z3,ierr)
if (ierr.ne.0) goto 997
 
c Close cdf file
call clscdf(cdfid,ierr)
endif
 
c -----------------------------------------------------------------
c Interpolate fields onto a stack of z levels and write new file
c -----------------------------------------------------------------
 
c Create output file
cfn=trim(zl_ofn)//'_cst'
call crecdf(trim(zl_ofn),cdfid,zl_varmin,zl_varmax,
> zl_ndim,trim(cfn),ierr)
if (ierr.ne.0) goto 995
 
c Write topography
print*,'W ZB ',trim(zl_ofn)
varname='ORO'
zl_vardim(3)=1
call putdef(cdfid,varname,zl_ndim,zl_mdv,zl_vardim,
> zl_varmin,zl_varmax,zl_stag,ierr)
zl_vardim(3)=zl_nz
if (ierr.ne.0) goto 995
call putdat(cdfid,varname,zl_time,1,ml_zb,ierr)
if (ierr.ne.0) goto 995
 
c Write pressure
print*,'W P ',trim(zl_ofn)
varname='P'
call putdef(cdfid,varname,4,zl_mdv,zl_vardim,
> zl_varmin,zl_varmax,zl_stag,ierr)
if (ierr.ne.0) goto 995
call putdat(cdfid,varname,zl_time,0,zl_p,ierr)
if (ierr.ne.0) goto 995
 
c Close output file
call clscdf(cdfid,ierr)
c Loop over all variables
do l=1,nvar
print*,'I ',trim(varinp(l))
 
c Get grid description for variable
call cdfopn(varsrc(l),cdfid,ierr)
if (ierr.ne.0) goto 996
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 996
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 996
call getvars(cdfid,in_nvars,in_vnam,ierr)
isok=0
varname=varinp(l)
call check_varok (isok,varname, in_vnam,in_nvars)
if (isok.ne.1) goto 996
call getdef(cdfid,varinp(l),in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 996
in_nx =in_vardim(1)
in_ny =in_vardim(2)
in_nz =in_vardim(3)
in_xmin=in_varmin(1)
in_ymin=in_varmin(2)
call getlevs(cstid,in_nz,in_aklev,in_bklev,
> in_aklay,in_bklay,ierr)
call getgrid(cstid,in_dx,in_dy,ierr)
in_xmax=in_xmin+real(in_nx-1)*in_dx
in_ymax=in_ymin+real(in_ny-1)*in_dy
call gettimes(cdfid,in_time,in_ntimes,ierr)
call getstart(cstid,in_idate,ierr)
call getpole(cstid,in_pollon,in_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Check whether this grid is consistent with P grid
if ( (ml_nx.ne.in_nx).or.
> (ml_ny.ne.in_ny).or.
> (ml_nz.ne.in_nz).or.
> (abs(ml_xmin-in_xmin ).gt.eps).or.
> (abs(ml_ymin-in_ymin ).gt.eps).or.
> (abs(ml_xmax-in_xmax ).gt.eps).or.
> (abs(ml_ymax-in_ymax ).gt.eps).or.
> (abs(ml_dx -in_dx ).gt.eps).or.
> (abs(ml_dy -in_dy ).gt.eps).or.
> (abs(ml_time-in_time ).gt.eps).or.
> (abs(ml_stag(1)-in_stag(1)).gt.eps).or.
> (abs(ml_stag(2)-in_stag(2)).gt.eps).or.
> (abs(ml_stag(3)-in_stag(3)).gt.eps).or.
> (abs(ml_pollon-in_pollon ).gt.eps).or.
> (abs(ml_pollat-in_pollat ).gt.eps)) then
print*,trim(varinp(l)),
> ' :Input P and FIELD grids are not consistent... Stop'
print*,'Stag: ',ml_stag, in_stag
print*,'Pol: ',ml_pollon,in_pollon,ml_pollat,in_pollat
stop
endif
 
c Read variable from file
call cdfopn(varsrc(l),cdfid,ierr)
if (ierr.ne.0) goto 996
call getdat(cdfid,varinp(l),in_time,0,in_field,ierr)
if (ierr.ne.0) goto 996
call clscdf(cdfid,ierr)
 
c Write the constants file
if (l.eq.1) then
datar(1)=zl_nx
datar(2)=zl_ny
datar(3)=int(1000.*zl_varmax(2))
datar(4)=int(1000.*zl_varmin(1))
datar(5)=int(1000.*zl_varmin(2))
datar(6)=int(1000.*zl_varmax(1))
datar(7)=int(1000.*zl_dx)
datar(8)=int(1000.*zl_dy)
datar(9)=zl_nz
datar(10)=1
datar(11)=1
datar(12)=0
datar(13)=int(1000.*zl_pollon)
datar(14)=int(1000.*zl_pollat)
 
cfn=trim(zl_ofn)//'_cst'
call wricst(cfn,datar,zl_aklev,zl_bklev,
> zl_aklay,zl_bklay,zl_idate)
 
endif
 
c Do the interpolation
do i=1,zl_nx
do j=1,zl_ny
c Make 1d profile available
do k=1,ml_nz
z1(k)=ml_z3 (i,j,k)
f1(k)=in_field(i,j,k)
enddo
call spline (z1,f1,ml_nz,1.e30,1.e30,spline_f1)
do k=1,zl_nz
if (zl_aklay(k).gt.ml_zb(i,j)) then
call splint(z1,f1,spline_f1,ml_nz,zl_aklay(k),ff)
zl_field(i,j,k)=ff
else
zl_field(i,j,k)=zl_mdv
endif
enddo
 
enddo
enddo
 
c Write the output field
print*,'W ',trim(varout(l)),' ',trim(zl_ofn)
call cdfwopn(trim(zl_ofn),cdfid,ierr)
varname=trim(varout(l))
call putdef(cdfid,varname,4,zl_mdv,zl_vardim,
> zl_varmin,zl_varmax,zl_stag,ierr)
if (ierr.ne.0) goto 995
call putdat(cdfid,varname,zl_time,0,zl_field,ierr)
if (ierr.ne.0) goto 995
call clscdf(cdfid,ierr)
enddo
c -----------------------------------------------------------------
c Write topography and geopotential also to the input P file
c -----------------------------------------------------------------
 
c Open the P file
call cdfwopn(trim(ml_pfn),cdfid,ierr)
 
c Write topography
varname='ORO'
print*,'W ',trim(varname),' ',trim(ml_pfn)
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
ml_vardim(3)=1
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
ml_vardim(3)=ml_nz
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,ml_time,1,ml_zb,ierr)
if (ierr.ne.0) goto 997
 
c Write geopotential height
varname='Z'
print*,'W ',trim(varname),' ',trim(ml_pfn)
isok=0
call check_varok (isok,varname,ml_vnam,ml_nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ml_ndim,ml_mdv,ml_vardim,
> ml_varmin,ml_varmax,ml_stag,ierr)
if (ierr.ne.0) goto 997
endif
call putdat(cdfid,varname,ml_time,0,ml_z3,ierr)
if (ierr.ne.0) goto 997
 
c Close P file
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Z: Problems with input from m level'
stop
 
997 print*,'Z: Problems with output on m level'
stop
 
996 print*,'F: Problems with input from m level'
stop
 
995 print*,'F: Problems with output on z level'
stop
 
 
end
 
c -------------------------------------------------------------
c Natural cubic spline
c -------------------------------------------------------------
 
SUBROUTINE spline(x,y,n,yp1,ypn,y2)
INTEGER n,NMAX
REAL yp1,ypn,x(n),y(n),y2(n)
PARAMETER (NMAX=500)
INTEGER i,k
REAL p,qn,sig,un,u(NMAX)
if (yp1.gt..99e30) then
y2(1)=0.
u(1)=0.
else
y2(1)=-0.5
u(1)=(3./(x(2)-x(1)))*((y(2)-y(1))/(x(2)-x(1))-yp1)
endif
do 11 i=2,n-1
sig=(x(i)-x(i-1))/(x(i+1)-x(i-1))
p=sig*y2(i-1)+2.
y2(i)=(sig-1.)/p
u(i)=(6.*((y(i+1)-y(i))/(x(i+
*1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*
*u(i-1))/p
11 continue
if (ypn.gt..99e30) then
qn=0.
un=0.
else
qn=0.5
un=(3./(x(n)-x(n-1)))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1)))
endif
y2(n)=(un-qn*u(n-1))/(qn*y2(n-1)+1.)
do 12 k=n-1,1,-1
y2(k)=y2(k)*y2(k+1)+u(k)
12 continue
return
END
 
 
SUBROUTINE splint(xa,ya,y2a,n,x,y)
INTEGER n
REAL x,y,xa(n),y2a(n),ya(n)
INTEGER k,khi,klo
REAL a,b,h
klo=1
khi=n
1 if (khi-klo.gt.1) then
k=(khi+klo)/2
if(xa(k).gt.x)then
khi=k
else
klo=k
endif
goto 1
endif
h=xa(khi)-xa(klo)
if (h.eq.0.) pause 'bad xa input in splint'
a=(xa(khi)-x)/h
b=(x-xa(klo))/h
y=a*ya(klo)+b*ya(khi)+((a**3-a)*y2a(klo)+(b**3-b)*y2a(khi))*(h**
*2)/6.
return
END
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/ref_profile.f
0,0 → 1,723
PROGRAM inv_prep
 
c ********************************************************************************
c * CALCULATE REFERENCE PROFILE, CORIOLIS PARAMETER AND GRID PARAMETERS *
c * Rene Fehlmann 1994 / Code re-organization: Michael Sprenger, 2006 *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Declaration of variables, parameters, externals and common blocks
c --------------------------------------------------------------------------------
 
implicit none
 
c Input and output file
character*80 pvsrcfile,referfile
integer mode
real radius
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real mdv
 
c Reference state
real, allocatable,dimension (:) :: nsqref
real, allocatable,dimension (:) :: thetaref
real, allocatable,dimension (:) :: rhoref
real, allocatable,dimension (:) :: pressref
real, allocatable,dimension (:) :: zref
real pressn,thetan
 
c 3d fields for calculation of reference profile
real,allocatable,dimension (:,:,:) :: th,rho,nsq,p,z
 
c 2d weight for mean
real,allocatable,dimension (:,:) :: weight
 
c Auxiliary variables
integer i,j,k
integer stat
integer jj,kk
character*80 varname
integer istep
real sum,max,min
integer cnt,nmd
integer step
integer i0,j0
real lon0,lat0,lon1,lat1,dist
integer vardim(4),ndim,cdfid,ierr
real varmin(4),varmax(4),stag(4)
real mdv
character*80 name
 
c Externals
real sdis
external sdis
 
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* ref_grid *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) pvsrcfile
read(10,*) referfile
read(10,*) name,radius
if ( trim(name).ne.'REF_R') stop
close(10)
print*
print*,trim(pvsrcfile)
print*,trim(referfile)
print*,radius
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
xmax = xmin + real(nx-1) * dx
ymax = ymin + real(ny-1) * dy
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for reference profile
allocate(rhoref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rhoref'
allocate(pressref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pressref'
allocate(thetaref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating thetaref'
allocate(nsqref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsqref'
allocate(zref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating zref'
c Allocate memory for calculatation of reference profile
allocate(th (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating th'
allocate(rho(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rho'
allocate(p (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating p'
allocate(nsq(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsq'
allocate(z(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating z'
 
c Allocate memory for weight
allocate(weight(0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating weight'
 
c --------------------------------------------------------------------------------
c Calculate the reference profile and put it onto netcdf file
c --------------------------------------------------------------------------------
 
c Read data from file
varname='TH'
call read_inp (th,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='RHO'
call read_inp (rho,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='NSQ'
call read_inp (nsq,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='P'
call read_inp (p,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Init the height field (not really necessary, but code becomes more symmetrical)
do i=0,nx
do j=0,ny
do k=0,nz
z(i,j,k)=zmin+real(k)*dz
enddo
enddo
enddo
 
c Define the weight
if ( radius.lt.0 ) then
do i=0,nx
do j=0,ny
weight(i,j) = 1.
enddo
enddo
else
i0 = nx/2
j0 = ny/2
lon0 = xmin + real(i0-1) * dx
lat0 = ymin + real(j0-1) * dy
weight(i0,j0)=1.
do i=0,nx
do j=0,ny
lon1 = xmin + real(i-1) * dx
lat1 = ymin + real(j-1) * dy
dist = sdis(lon0,lat0,lon1,lat1)
if ( dist.lt.radius ) then
weight(i,j) = 1.
else
weight(i,j) = 0.
endif
enddo
enddo
endif
 
c Determine the reference profile (mean over domain, split levels and layers)
call mean(zref, z, nx,ny,nz,mdv,weight)
call mean(nsqref, nsq,nx,ny,nz,mdv,weight)
call mean(rhoref, rho,nx,ny,nz,mdv,weight)
call mean(thetaref,th, nx,ny,nz,mdv,weight)
call mean(pressref,p, nx,ny,nz,mdv,weight)
 
c Write reference file to netcdf file
call write_ref (nsqref,rhoref,thetaref,pressref,zref,
> nz,referfile)
 
c Write some info
print*
print*,'Ref: z p rho nsq theta'
step=2*nz/10
if (step.lt.1) step=1
do k=0,2*nz,step
write(*,'(8x,f10.1,2f10.2,f10.6,f10.2)')
> zref(k),pressref(k),rhoref(k),nsqref(k),thetaref(k)
enddo
print*
 
c Write weighht to REF file
call cdfwopn(trim(referfile),cdfid,ierr)
varname='WEIGHT'
vardim(1)=nx+1
vardim(2)=ny+1
vardim(3)=1
vardim(4)=1
varmin(1)=xmin
varmin(2)=ymin
varmin(3)=0.
varmax(1)=xmax
varmax(2)=ymax
varmax(3)=0.
ndim=3
mdv=-999.
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
call putdat(cdfid,varname,0.,1,weight,ierr)
 
c --------------------------------------------------------------------------------
c Format specifications
c --------------------------------------------------------------------------------
 
111 format (5f20.9)
106 format (2f20.9)
end
 
c --------------------------------------------------------------------------
c Spherical distance between lat/lon points
c --------------------------------------------------------------------------
 
real function sdis(xp,yp,xq,yq)
c
c calculates spherical distance (in km) between two points given
c by their spherical coordinates (xp,yp) and (xq,yq), respectively.
c
real re
parameter (re=6370.)
real pi180
parameter (pi180=3.14159/180.)
real xp,yp,xq,yq,arg
 
arg=sin(pi180*yp)*sin(pi180*yq)+
> cos(pi180*yp)*cos(pi180*yq)*cos(pi180*(xp-xq))
if (arg.lt.-1.) arg=-1.
if (arg.gt.1.) arg=1.
 
sdis=re*acos(arg)
 
end
 
c ********************************************************************************
c * NETCDF INPUT AND OUTPUT *
c ********************************************************************************
 
 
c --------------------------------------------------------------------------------
c Write reference file to netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE write_ref (nsqref,rhoref,thetaref,pressref,zref,
> nz,pvsrcfile)
 
c Write the reference profile to file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nz : Grid dimension in z direction
c pvsrcfile : Output file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='NSQREF'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
vardim(1)=1
vardim(2)=1
vardim(3)=2*nz+1
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='RHOREF'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
vardim(1)=1
vardim(2)=1
vardim(3)=2*nz+1
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='PREREF'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
vardim(1)=1
vardim(2)=1
vardim(3)=2*nz+1
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='THETAREF'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
vardim(1)=1
vardim(2)=1
vardim(3)=2*nz+1
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='ZREF'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
vardim(1)=1
vardim(2)=1
vardim(3)=2*nz+1
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
 
c Write data
varname='NSQREF'
print*,'W NSQREF ',trim(pvsrcfile)
call putdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
varname='RHOREF'
print*,'W RHOREF ',trim(pvsrcfile)
call putdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
varname='THETAREF'
print*,'W THETAREF ',trim(pvsrcfile)
call putdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
varname='PREREF'
print*,'W PREREF ',trim(pvsrcfile)
call putdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
varname='ZREF'
print*,'W ZREF ',trim(pvsrcfile)
call putdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
c Close output netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
return
 
c Exception handling
997 print*,'Write_Ref: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read input fields for reference profile
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*,'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <TH> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='T'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
c ********************************************************************************
c * DEFINE REFERENCE PROFILE *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Calculate area mean
c --------------------------------------------------------------------------------
 
SUBROUTINE mean(a,m,nx,ny,nz,mdv,weight)
 
c Calculate the area-mean of <m> and save it on <a>.
 
implicit none
 
c Declaration of subroutine parameters
real mdv
integer nx,ny,nz
real m(0:nx,0:ny,0:nz),a(0:2*nz)
real weight(0:nx,0:ny)
 
c Numerical epsilon
real eps
parameter (eps=0.01)
 
c Auxiliary varaibles
real mea(0:nz)
integer i,j,k,kk
real counter
 
c Determine the mean over all levels (handle missing data)
do k=0,nz
mea(k)=0.
counter=0.
do i=0,nx
do j=0,ny
if (abs(m(i,j,k)-mdv).gt.eps) then
mea(k)=mea(k)+m(i,j,k)*weight(i,j)
counter=counter+weight(i,j)
endif
enddo
enddo
if (counter.gt.0) then
mea(k)=mea(k)/counter
else
mea(k)=mdv
endif
enddo
 
c Prepare the output array: split layers and levels
do k=0,nz-1
kk=2*k
a(kk)=mea(k)
a(kk+1)=0.5*(mea(k)+mea(k+1))
enddo
a(2*nz)=mea(nz)
end
Property changes:
Added: svn:executable
/tags/1.0/prep/ref_profile.m
0,0 → 1,75
 
mode=2;
folder ='/lhome/sprenger/PV_Inversion_Tool/';
filename='Z1_20060115_18';
 
% First image (otherwise first image is not correctly written)
figname = 'test.eps';
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% --------------------------------------------------------------------------
% Plot Coriolis parameter and get grid parameters
% --------------------------------------------------------------------------
 
if ( mode == 2 )
 
m_deltax = cdf_loadV(folder,filename,'DELTAX');
m_deltay = cdf_loadV(folder,filename,'DELTAY');
m_deltaz = cdf_loadV(folder,filename,'DELTAZ');
m_corlat = cdf_loadV(folder,filename,'CORLAT');
m_coriol = cdf_loadV(folder,filename,'CORIOL');
plot(m_coriol.var,m_corlat.var,'LineWidth',2)
ylabel('Latitude','FontSize',15);
xlabel('Coriolis parameter f','FontSize',15);
figname = [ 'coriolis.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
end
 
 
% --------------------------------------------------------------------------
% Plot reference profile
% --------------------------------------------------------------------------
 
if ( mode == 3 )
 
m_zref = cdf_loadV(folder,filename,'ZREF');
m_preref = cdf_loadV(folder,filename,'PREREF');
m_nsqref = cdf_loadV(folder,filename,'NSQREF');
m_rhoref = cdf_loadV(folder,filename,'RHOREF');
m_thetaref = cdf_loadV(folder,filename,'THETAREF');
 
title('Reference profile');
subplot(2,3,1);plot(10000*m_nsqref.var, m_zref.var/1000);
xlabel('N^2 [10^{-4}s^{-2}]','FontSize',12);ylabel('Z [km]','FontSize',12);ylim([0 20]);
subplot(2,3,2);plot(m_rhoref.var, m_zref.var/1000);
xlabel('\rho [kg/m^3]','FontSize',12);ylim([0 20]);
subplot(2,3,3);plot(m_thetaref.var,m_zref.var/1000);
xlabel('\theta [K]','FontSize',12); ylim([0 20]);
subplot(2,3,4);plot(10000*m_nsqref.var, m_preref.var);
xlabel('N^2 [10^-{-4}s^{-2}]','FontSize',12);ylabel('P [hPa]','FontSize',12);set(gca,'YDir','reverse'); ylim([0 1020]);
subplot(2,3,5);plot(m_rhoref.var, m_preref.var);
xlabel('\rho [kg/m^3]','FontSize',12);set(gca,'YDir','reverse'); ylim([0 1020]);
subplot(2,3,6);plot(m_thetaref.var,m_preref.var);
xlabel('\theta [K]','FontSize',12);set(gca,'YDir','reverse'); ylim([0 1020]);
figname = [ 'reference.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
end
 
 
Property changes:
Added: svn:executable
/tags/1.0/prep/rotate_grid.f
0,0 → 1,1218
PROGRAM rotate_grid
 
c *******************************************************************
c * Rotate to a grid with the PV anomaly at its center *
c * Michael Sprenger / Autumn 2006 *
c *******************************************************************
 
implicit none
 
c -------------------------------------------------------------------
c Declaration of parameters and variables
c -------------------------------------------------------------------
 
c Specification of input parameters
real clon,clat,rotation
integer rnx,rny
real rdx,rdy
integer nfield
character*80 fieldname(100)
 
c Numerical and physical parameters
real degrad
parameter (degrad=0.0174532925)
real omegaerd
parameter (omegaerd=7.292e-5 )
real eps
parameter (eps=0.001)
 
c Variables for input Z file : height level
character*80 in_cfn
real in_varmin(4),in_varmax(4),in_stag(4)
integer in_vardim(4)
real in_mdv
integer in_ndim
integer in_nx,in_ny,in_nz
real in_xmin,in_xmax,in_ymin,in_ymax,in_dx,in_dy
integer in_ntimes
real in_aklev(500),in_bklev(500)
real in_aklay(500),in_bklay(500)
real in_time
real in_pollon,in_pollat
integer in_nvars
character*80 in_vnam(100)
integer in_idate(5)
real,allocatable, dimension (:,:,:) :: in_field3
real,allocatable, dimension (:,:,:) :: in_vect1
real,allocatable, dimension (:,:,:) :: in_vect2
 
c Variables for output Z file : height level
character*80 out_cfn
real out_varmin(4),out_varmax(4),out_stag(4)
integer out_vardim(4)
real out_mdv
integer out_ndim
integer out_nx,out_ny,out_nz
real out_xmin,out_xmax,out_ymin,out_ymax,out_dx,out_dy
integer out_ntimes
real out_aklev(500),out_bklev(500)
real out_aklay(500),out_bklay(500)
real out_time
real out_pollon,out_pollat
integer out_idate(5)
real,allocatable, dimension (:,:,:) :: out_field3
real,allocatable, dimension (:,:,:) :: out_vect1
real,allocatable, dimension (:,:,:) :: out_vect2
real,allocatable, dimension (:,:) :: out_lat,out_lon
real,allocatable, dimension (:,:) :: out_x,out_y
real,allocatable, dimension (:,:) :: out_coriol
 
c Auxiliary variables
integer ifield
integer i,j,k
integer cdfid,cstid
character*80 cfn
integer stat,ierr,isok
real time
character*80 varname,cdfname,varname1,varname2
integer idate(5),stdate(5),datar(14)
integer rotmode
integer i1,i2,i3,i4
integer isvector
real lat
character*80 name
 
c Externals
real sdis
external sdis
 
c -------------------------------------------------------------------
c Preparations
c -------------------------------------------------------------------
print*,'*********************************************************'
print*,'* rotate_grid *'
print*,'*********************************************************'
 
c Read parameter file
open(10,file='fort.10')
 
read(10,*) in_cfn
read(10,*) out_cfn
 
read(10,*) name,rnx
if ( trim(name).ne.'ROT_NX') stop
read(10,*) name,rny
if ( trim(name).ne.'ROT_NY') stop
read(10,*) name,rdx
if ( trim(name).ne.'ROT_DX') stop
read(10,*) name,rdy
if ( trim(name).ne.'ROT_DY') stop
read(10,*) name,clon
if ( trim(name).ne.'CLON' ) stop
read(10,*) name,clat
if ( trim(name).ne.'CLAT' ) stop
read(10,*) name,rotation
if ( trim(name).ne.'CROT' ) stop
 
read(10,*) nfield
do i=1,nfield
read(10,*) fieldname(i)
enddo
 
close(10)
print*,clon,clat,rotation
print*,rnx,rny,rdx,rdy
print*,trim(in_cfn),' -> ',trim(out_cfn)
 
c Get grid description for input Z file : height level
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,in_nvars,in_vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname=fieldname(1)
call check_varok (isok,varname,in_vnam,in_nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
if (ierr.ne.0) goto 998
in_nx =in_vardim(1)
in_ny =in_vardim(2)
in_xmin=in_varmin(1)
in_ymin=in_varmin(2)
call getlevs(cstid,in_nz,in_aklev,in_bklev,in_aklay,in_bklay,ierr)
call getgrid(cstid,in_dx,in_dy,ierr)
in_xmax=in_xmin+real(in_nx-1)*in_dx
in_ymax=in_ymin+real(in_ny-1)*in_dy
call gettimes(cdfid,in_time,in_ntimes,ierr)
call getstart(cstid,in_idate,ierr)
call getpole(cstid,in_pollon,in_pollat,ierr)
call clscdf(cstid,ierr)
call clscdf(cdfid,ierr)
 
c Set grid description for output file : height level
out_vardim(1) = rnx
out_vardim(2) = rny
out_vardim(3) = in_nz
out_varmin(1) = -real(rnx/2)*rdx
out_varmin(2) = -real(rny/2)*rdy
out_varmin(3) = in_varmin(3)
out_varmax(1) = real(rnx/2)*rdx
out_varmax(2) = real(rny/2)*rdy
out_varmax(3) = in_varmax(3)
do i=1,in_nz
out_aklay(i) = in_aklay(i)
out_bklay(i) = in_bklay(i)
out_aklev(i) = in_aklev(i)
out_bklev(i) = in_bklev(i)
enddo
out_dx = rdx
out_dy = rdy
out_time = in_time
out_ntimes = in_ntimes
out_ndim = 4
out_mdv = in_mdv
out_nx = out_vardim(1)
out_ny = out_vardim(2)
out_nz = out_vardim(3)
out_xmin = out_varmin(1)
out_ymin = out_varmin(2)
out_pollon = clon
out_pollat = clat
do i=1,5
out_idate(i) = in_idate(i)
enddo
 
c Allocate memory for all fields
allocate(in_field3(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_field3 ***'
allocate(in_vect1(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_vect1 ***'
allocate(in_vect2(in_nx,in_ny,in_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array in_vect2 ***'
allocate(out_field3(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_field3 ***'
allocate(out_vect1(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_vect1 ***'
allocate(out_vect2(out_nx,out_ny,out_nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_vect2 ***'
allocate(out_lat(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_lat ***'
allocate(out_lon(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_lon ***'
allocate(out_x(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_x ***'
allocate(out_y(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_y ***'
allocate(out_coriol(out_nx,out_ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array out_coriol ***'
 
c Create constants file
datar(1)=out_nx
datar(2)=out_ny
datar(3)=int(1000.*out_varmax(2))
datar(4)=int(1000.*out_varmin(1))
datar(5)=int(1000.*out_varmin(2))
datar(6)=int(1000.*out_varmax(1))
datar(7)=int(1000.*out_dx)
datar(8)=int(1000.*out_dy)
datar(9)=out_nz
datar(10)=1
datar(11)=1
datar(12)=0
datar(13)=int(1000.*out_pollon)
datar(14)=int(1000.*out_pollat)
 
cfn=trim(out_cfn)//'_cst'
call wricst(cfn,datar,out_aklev,out_bklev,
> out_aklay,out_bklay,out_idate)
 
call crecdf(trim(out_cfn),cdfid,out_varmin,out_varmax,
> out_ndim,trim(cfn),ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Loop through all fields - rotate to new grid
c -----------------------------------------------------------------
 
do ifield=1,nfield
 
c Check if scalar or vectorial field (X for scalar, U.V for vector)
varname=fieldname(ifield)
i1=1
i2=1
i3=0
i4=0
100 if (varname(i1:i1).eq.' ') then
i1=i1+1
goto 100
endif
i2=i1
101 if ((varname(i2:i2).ne.' ').and.(varname(i2:i2).ne.'.')) then
i2=i2+1
goto 101
endif
if (varname(i2:i2).eq.'.') then
i3=i2+1
102 if (varname(i3:i3).eq.' ') then
i3=i3+1
goto 102
endif
i4=i3
104 if (varname(i4:i4).ne.' ') then
i4=i4+1
goto 104
endif
endif
if ((i3.ne.0).and.(i4.ne.0)) then
isvector=1
i2=i2-1
varname1=varname(i1:i2)
i4=i4-1
varname2=varname(i3:i4)
print*,'Rotating vector : ',
> trim(varname1),' / ',trim(varname2)
else
isvector=0
i2=i2-1
varname=varname(i1:i2)
print*,'Rotating scalar : ',trim(varname)
endif
c Rotate a scalar field
if (isvector.eq.0) then
 
c Read input field
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,in_time,0,in_field3,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Rotate to new coordinate system
out_nz=in_nz
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
 
c Write output scalar field
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
out_vardim(3)=out_nz
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_field3,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
c Rotate vector field
else if (isvector.eq.1) then
c Read input vector field
call cdfopn(in_cfn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname1,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname1,in_time,0,in_vect1,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname2,in_ndim,in_mdv,in_vardim,
> in_varmin,in_varmax,in_stag,ierr)
in_nz=in_vardim(3)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname2,in_time,0,in_vect2,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
 
c Get new vector component in x direction
out_nz=in_nz
call getenvir (clon,clat,rotation,1,
> in_vect1,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
out_vect1(i,j,k)=out_field3(i,j,k)
enddo
enddo
enddo
call getenvir (clon,clat,rotation,2,
> in_vect2,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
if ( (abs(out_vect1 (i,j,k)-out_mdv).gt.eps).and.
> (abs(out_field3(i,j,k)-out_mdv).gt.eps) ) then
out_vect1(i,j,k)=out_vect1(i,j,k)-
> out_field3(i,j,k)
endif
enddo
enddo
enddo
 
c Get new vector component in y direction
out_nz=in_nz
call getenvir (clon,clat,rotation,2,
> in_vect1,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
out_vect2(i,j,k)=out_field3(i,j,k)
enddo
enddo
enddo
call getenvir (clon,clat,rotation,1,
> in_vect2,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,in_nz,in_mdv,
> out_field3,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,out_nz)
do i=1,out_nx
do j=1,out_ny
do k=1,out_nz
if ( (abs(out_vect2 (i,j,k)-out_mdv).gt.eps).and.
> (abs(out_field3(i,j,k)-out_mdv).gt.eps) ) then
out_vect2(i,j,k)=out_vect2(i,j,k)+
> out_field3(i,j,k)
endif
enddo
enddo
enddo
 
c Write output vector field
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
out_vardim(3)=out_nz
call putdef(cdfid,varname1,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname1,out_time,0,out_vect1,ierr)
if (ierr.ne.0) goto 997
call putdef(cdfid,varname2,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname2,out_time,0,out_vect2,ierr)
if (ierr.ne.0) goto 997
call clscdf(cdfid,ierr)
 
endif
 
enddo
 
c -----------------------------------------------------------------
c Write additional fields: latitude, longitude, Coriolis parameter
c -----------------------------------------------------------------
 
c Open the output file
call cdfwopn(trim(out_cfn),cdfid,ierr)
if (ierr.ne.0) goto 997
 
c Geographical latitude
varname='LAT'
print*,'Rotating scalar : ',trim(varname)
do i=1,in_nx
do j=1,in_ny
in_field3(i,j,1)=in_ymin+real(j-1)*in_dy
enddo
enddo
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,1,in_mdv,
> out_lat,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,1)
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_lat,ierr)
if (ierr.ne.0) goto 997
 
c Geographical longitude
varname='LON'
print*,'Rotating scalar : ',trim(varname)
do i=1,in_nx
do j=1,in_ny
in_field3(i,j,1)=in_xmin+real(i-1)*in_dx
enddo
enddo
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,1,in_mdv,
> out_lon,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,1)
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_lon,ierr)
if (ierr.ne.0) goto 997
 
c Coriolis parameter
varname='CORIOL'
print*,'Rotating scalar : ',trim(varname)
do i=1,in_nx
do j=1,in_ny
lat=in_ymin+real(j-1)*in_dy
in_field3(i,j,1)=2.*omegaerd*sin(lat*degrad)
enddo
enddo
call getenvir (clon,clat,rotation,0,
> in_field3,in_dx,in_dy,
> in_xmin,in_ymin,in_nx,in_ny,1,in_mdv,
> out_coriol,out_dx,out_dy,
> out_xmin,out_ymin,out_nx,out_ny,1)
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_coriol,ierr)
if (ierr.ne.0) goto 997
 
c X coordinate
varname='X'
print*,'Getting X grid : ',trim(varname)
do j=1,out_ny
out_x(out_nx/2,j)=0.
do i=out_nx/2+1,out_nx
out_x(i,j)=out_x(i-1,j)+
> sdis(out_lon(i-1,j),out_lat(i-1,j),
> out_lon(i ,j),out_lat(i ,j))
enddo
do i=out_nx/2-1,1,-1
out_x(i,j)=out_x(i+1,j)-
> sdis(out_lon(i+1,j),out_lat(i+1,j),
> out_lon(i ,j),out_lat(i ,j))
enddo
enddo
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_x,ierr)
if (ierr.ne.0) goto 997
 
c Y coordinate
varname='Y'
print*,'Getting Y grid : ',trim(varname)
do i=1,out_nx
out_y(i,out_ny/2)=0.
do j=out_ny/2+1,out_ny
out_y(i,j)=out_y(i,j-1)+
> sdis(out_lon(i,j-1),out_lat(i,j-1),
> out_lon(i ,j),out_lat(i ,j))
enddo
do j=out_ny/2-1,1,-1
out_y(i,j)=out_y(i,j+1)-
> sdis(out_lon(i,j+1),out_lat(i,j+1),
> out_lon(i ,j),out_lat(i ,j))
enddo
enddo
out_vardim(3)=1
call putdef(cdfid,varname,4,out_mdv,out_vardim,
> out_varmin,out_varmax,out_stag,ierr)
if (ierr.ne.0) goto 997
call putdat(cdfid,varname,out_time,0,out_y,ierr)
if (ierr.ne.0) goto 997
c Close output file
call clscdf(cdfid,ierr)
 
c -----------------------------------------------------------------
c Exception handling and format specs
c -----------------------------------------------------------------
 
stop
 
998 print*,'Z: Problems with input lat/lon grid'
stop
 
997 print*,'Z: Problems with output to rotated grid'
stop
 
end
 
 
c ********************************************************************************
c * SUBROUTINE: ROTATION TO LOCAL CARTESIAN COORDINATE SYSTEM *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Subroutine to get environment (vector+scalar)
c --------------------------------------------------------------------------------
 
SUBROUTINE getenvir (clon,clat,rotation,rotmode,
> inar, dx, dy, xmin, ymin, nx, ny, nz,mdv,
> outar,rdx,rdy,rxmin,rymin,rnx,rny,rnz)
 
c Get an input field <inar> and the center <clon,clat> of a structure. The input
c array is defined on a lat/lon grid with grid specification <dx,dy,xmin,ymin,nx,ny>.
c The input field is then rotated to an output grid <rdx,rdy,rxmin,rymin,rnx,rny>,
c whereby the structure <clon,clat> is at the center of the new grid and the output
c grid is rotated with rotation angle <rotation>. This routine rotates the components
c of a vector field for <rotmode=1|2>: <rotmode=1> refers to the x xomponent of the
c field, <rotmode=2> to the y component. If <rotmode=0>, scalar field is assumed.
 
implicit none
 
c Declaration of input parameters
integer nx,ny,nz
real dx,dy,xmin,ymin
real inar(nx,ny,nz)
real clon,clat,rotation
real mdv
integer rotmode
 
c Declaration of output parameters
integer rnx,rny,rnz
real rdx,rdy,rxmin,rymin
real outar(rnx,rny,rnz)
 
c Set numerical and physical constants
real g2r
parameter (g2r=0.0174533)
real pi180
parameter (pi180=3.14159265359/180.)
real eps
parameter (eps=0.0001)
 
 
c Flag for test mode
integer test
parameter (test=0)
character*80 testfile
parameter (testfile='ROTGRID')
 
c Auxiliary variables
real pollon,pollat
integer i,j,k,l
real rlon1(rnx,rny),rlat1(rnx,rny)
real rlon2(rnx,rny),rlat2(rnx,rny)
real lon(rnx,rny),lat(rnx,rny)
real rotangle1(rnx,rny),rotangle2(rnx,rny)
real rotangle(rnx,rny)
real sinoutar(rnx,rny,rnz),cosoutar(rnx,rny,rnz)
real xmax,ymax
real xind,yind,pind
real outval
integer ix,iy
real ax,ay,az,bx,by,bz,zx,zy,zz
real clon1,clat1,clon2,clat2
real rindx,rindy
integer indx,indy,indr,indu
real frac0i,frac0j,frac1i,frac1j
real lonmean,latmean
character*80 cdfname,varname,cstname
real vx1,vx2,vy1,vy2,angle,vx2min
integer s
 
c Externals
real lmstolm,phstoph
external lmstolm,phstoph
 
c Get rotated coordinates
do i=1,rnx
do j=1,rny
rlon1(i,j)=rxmin+real(i-1)*rdx
rlat1(i,j)=rymin+real(j-1)*rdy
enddo
enddo
 
c First coordinate transformation (make the local coordinate system parallel to equator)
pollon=-180.
pollat=90.+rotation
do i=1,rnx
do j=1,rny
rlon2(i,j)=90.+lmstolm(rlat1(i,j),rlon1(i,j)-90.,pollat,pollon)
rlat2(i,j)=phstoph(rlat1(i,j),rlon1(i,j)-90.,pollat,pollon)
enddo
enddo
 
c Second coordinate transformation (make the local coordinate system parallel to equator)
pollon=clon-180.
if (pollon.lt.-180.) pollon=pollon+360.
pollat=90.-clat
do i=1,rnx
do j=1,rny
lon(i,j)=lmstolm(rlat2(i,j),rlon2(i,j),pollat,pollon)
lat(i,j)=phstoph(rlat2(i,j),rlon2(i,j),pollat,pollon)
enddo
enddo
 
c Get the angle between the rotated and non-rotated coordinate frame
if ((rotmode.eq.1).or.(rotmode.eq.2)) then
do i=2,rnx-1
do j=2,rny-1
c Angle between latitude circles
vx1=1.
vy1=0.
vx2min=(lon(i+1,j)-lon(i-1,j))*cos(pi180*lat(i,j))
do s=-1,1,2
vx2=(lon(i+1,j)-lon(i-1,j)+real(s)*360.)*
> cos(pi180*lat(i,j))
if (abs(vx2).lt.abs(vx2min)) vx2min=vx2
enddo
vx2=vx2min
vy2=lat(i+1,j)-lat(i-1,j)
call getangle(vx1,vy1,vx2,vy2,angle)
rotangle1(i,j)=angle
 
c Angle between longitude circles
vx1=0.
vy1=1.
vx2min=(lon(i,j+1)-lon(i,j-1))*cos(pi180*lat(i,j))
do s=-1,1,2
vx2=(lon(i+1,j)-lon(i-1,j)+real(s)*360.)*
> cos(pi180*lat(i,j))
if (abs(vx2).lt.abs(vx2min)) vx2min=vx2
enddo
vx2=vx2min
vy2=lat(i,j+1)-lat(i,j-1)
call getangle(vx1,vy1,vx2,vy2,angle)
rotangle2(i,j)=angle
enddo
enddo
 
c Set the angle at the boundaries
do i=1,rnx
rotangle1(i,rny)=2.0*rotangle1(i,rny-1)-rotangle1(i,rny-2)
rotangle1(i,1) =2.0*rotangle1(i,2)-rotangle1(i,3)
rotangle2(i,rny)=2.0*rotangle2(i,rny-1)-rotangle2(i,rny-2)
rotangle2(i,1) =2.0*rotangle2(i,2)-rotangle2(i,3)
enddo
do j=1,rny
rotangle1(rnx,j)=2.0*rotangle1(rnx-1,j)-rotangle1(rnx-2,j)
rotangle1(1,j) =2.0*rotangle1(2,j)-rotangle1(3,j)
rotangle2(rnx,j)=2.0*rotangle2(rnx-1,j)-rotangle2(rnx-2,j)
rotangle2(1,j) =2.0*rotangle2(2,j)-rotangle2(3,j)
enddo
c Set the final rotation angle
do i=1,rnx
do j=1,rny
rotangle(i,j)=0.5*(rotangle1(i,j)+rotangle2(i,j))
enddo
enddo
 
endif
 
c Bring longitude into domain of geographical grid (shift by 360 deg)
do i=1,rnx
do j=1,rny
100 if (lon(i,j).lt.xmin) then
lon(i,j)=lon(i,j)+360.
goto 100
endif
102 if (lon(i,j).gt.(xmin+real(nx-1)*dx)) then
lon(i,j)=lon(i,j)-360.
goto 102
endif
enddo
enddo
 
c Rotate the scalar or the vector component
do i=1,rnx
do j=1,rny
do k=1,rnz
 
c Get index
rindx=(lon(i,j)-xmin)/dx+1.
rindy=(lat(i,j)-ymin)/dy+1.
indx=int(rindx)
indy=int(rindy)
if ((indx.lt.1).or.(indx.gt.nx).or.
> (indy.lt.1).or.(indy.gt.ny)) then
print*,'lat/lon interpolation not possible....'
print*,i,j,k,indx,indy,lon(i,j),lat(i,j)
stop
endif
 
c Get inidices of left and upper neighbours
indr=indx+1
if (indr.gt.nx) indr=1
indu=indy+1
if (indu.gt.ny) indu=ny
c Do linear interpolation
if ( ( abs(inar(indx ,indy, k)-mdv).gt.eps ).and.
& ( abs(inar(indx ,indu, k)-mdv).gt.eps ).and.
& ( abs(inar(indr ,indy, k)-mdv).gt.eps ).and.
& ( abs(inar(indr ,indu, k)-mdv).gt.eps ) ) then
frac0i=rindx-float(indx)
frac0j=rindy-float(indy)
frac1i=1.-frac0i
frac1j=1.-frac0j
outval = inar(indx ,indy, k ) * frac1i * frac1j
& + inar(indx ,indu, k ) * frac1i * frac0j
& + inar(indr ,indy, k ) * frac0i * frac1j
& + inar(indr ,indu, k ) * frac0i * frac0j
else
outval=mdv
endif
 
c Update output array
outar(i,j,k)=outval
 
enddo
enddo
enddo
 
c Get components for tests
if (test.eq.1) then
do i=1,rnx
do j=1,rny
do k=1,rnz
cosoutar(i,j,k)=outar(i,j,k)*cos(pi180*rotangle(i,j))
sinoutar(i,j,k)=-outar(i,j,k)*sin(pi180*rotangle(i,j))
enddo
enddo
enddo
endif
 
c Get correct component of rotated field
do i=1,rnx
do j=1,rny
do k=1,rnz
if ( abs(outar(i,j,k)-mdv).gt.eps ) then
if (rotmode.eq.1) then
outar(i,j,k)= outar(i,j,k)*cos(pi180*rotangle(i,j))
else if (rotmode.eq.2) then
outar(i,j,k)=-outar(i,j,k)*sin(pi180*rotangle(i,j))
else if (rotmode.eq.0) then
outar(i,j,k)=outar(i,j,k)
endif
endif
enddo
enddo
enddo
 
c Test mode: Write grids to cdf file
if (test.eq.1) then
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLON1'
call writecdf2D(cdfname,cstname,
> varname,rlon1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 1,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLON2'
call writecdf2D(cdfname,cstname,
> varname,rlon2,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='LON'
call writecdf2D(cdfname,cstname,
> varname,lon,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLAT1'
call writecdf2D(cdfname,cstname,
> varname,rlat1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='RLAT2'
call writecdf2D(cdfname,cstname,
> varname,rlat2,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='LAT'
call writecdf2D(cdfname,cstname,
> varname,lat,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='ANGLE1'
call writecdf2D(cdfname,cstname,
> varname,rotangle1,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='ANGLE2'
call writecdf2D(cdfname,cstname,
> varname,rotangle2,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='U'
call writecdf2D(cdfname,cstname,
> varname,cosoutar,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
cdfname=testfile
cstname=trim(testfile)//'_cst'
varname='V'
call writecdf2D(cdfname,cstname,
> varname,sinoutar,0.,
> rdx,rdy,rxmin,rymin,rnx,rny,
> 0,1)
 
endif
 
END
 
 
c --------------------------------------------------------------------------------
c Auxiliary routines: angle between two vectors
c --------------------------------------------------------------------------------
 
SUBROUTINE getangle (vx1,vy1,vx2,vy2,angle)
 
c Given two vectors <vx1,vy1> and <vx2,vy2>, determine the angle (in deg)
c between the two vectors.
 
implicit none
 
c Declaration of subroutine parameters
real vx1,vy1
real vx2,vy2
real angle
 
c Auxiliary variables and parameters
real len1,len2,len3
real val1,val2,val3
real pi
parameter (pi=3.14159265359)
 
len1=sqrt(vx1*vx1+vy1*vy1)
len2=sqrt(vx2*vx2+vy2*vy2)
 
if ((len1.gt.0.).and.(len2.gt.0.)) then
vx1=vx1/len1
vy1=vy1/len1
vx2=vx2/len2
vy2=vy2/len2
 
val1=vx1*vx2+vy1*vy2
val2=-vy1*vx2+vx1*vy2
 
len3=sqrt(val1*val1+val2*val2)
 
if ( (val1.ge.0.).and.(val2.ge.0.) ) then
val3=acos(val1/len3)
else if ( (val1.lt.0.).and.(val2.ge.0.) ) then
val3=pi-acos(abs(val1)/len3)
else if ( (val1.ge.0.).and.(val2.le.0.) ) then
val3=-acos(val1/len3)
else if ( (val1.lt.0.).and.(val2.le.0.) ) then
val3=-pi+acos(abs(val1)/len3)
endif
else
val3=0.
endif
 
angle=180./pi*val3
 
END
 
c --------------------------------------------------------------------------------
c Transformation routine: LMSTOLM and PHSTOPH from library gm2em
c --------------------------------------------------------------------------------
 
REAL FUNCTION LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C
C**** LMSTOLM - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C**** IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : LAM = LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
C** IM ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
ZSINPOL = SIN(ZPIR18*POLPHI)
ZCOSPOL = COS(ZPIR18*POLPHI)
ZLAMPOL = ZPIR18*POLLAM
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ZARG1 = SIN(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) -
2 COS(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
ZARG2 = COS(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS) +
1 ZCOSPOL* SIN(ZPHIS)) +
2 SIN(ZLAMPOL)* SIN(ZLAMS)*COS(ZPHIS)
IF (ABS(ZARG2).LT.1.E-30) THEN
IF (ABS(ZARG1).LT.1.E-30) THEN
LMSTOLM = 0.0
ELSEIF (ZARG1.GT.0.) THEN
LMSTOLAM = 90.0
ELSE
LMSTOLAM = -90.0
ENDIF
ELSE
LMSTOLM = ZRPI18*ATAN2(ZARG1,ZARG2)
ENDIF
RETURN
END
 
 
REAL FUNCTION PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C
C**** PHSTOPH - FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C**** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C**** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C**** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** AUFRUF : PHI = PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
C** ENTRIES : KEINE
C** ZWECK : BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
C** EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
C** ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
C** DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
C** VERSIONS-
C** DATUM : 03.05.90
C**
C** EXTERNALS: KEINE
C** EINGABE-
C** PARAMETER: PHIS REAL GEOGR. BREITE DES PUNKTES IM ROT.SYS.
C** LAMS REAL GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
C** POLPHI REAL WAHRE GEOGR. BREITE DES NORDPOLS
C** POLLAM REAL WAHRE GEOGR. LAENGE DES NORDPOLS
C** AUSGABE-
C** PARAMETER: WAHRE GEOGRAPHISCHE BREITE ALS WERT DER FUNKTION
C** ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
C**
C** COMMON-
C** BLOECKE : KEINE
C**
C** FEHLERBE-
C** HANDLUNG : KEINE
C** VERFASSER: D.MAJEWSKI
REAL LAMS,PHIS,POLPHI,POLLAM
DATA ZRPI18 , ZPIR18 / 57.2957795 , 0.0174532925 /
SINPOL = SIN(ZPIR18*POLPHI)
COSPOL = COS(ZPIR18*POLPHI)
ZPHIS = ZPIR18*PHIS
ZLAMS = LAMS
IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
ZLAMS = ZPIR18*ZLAMS
ARG = COSPOL*COS(ZPHIS)*COS(ZLAMS) + SINPOL*SIN(ZPHIS)
PHSTOPH = ZRPI18*ASIN(ARG)
RETURN
END
 
 
c ---------------------------------------------------------
c Spherical distance between two lat/lon points
c ---------------------------------------------------------
 
real function sdis(xp,yp,xq,yq)
c
c calculates spherical distance (in km) between two points given
c by their spherical coordinates (xp,yp) and (xq,yq), respectively.
c
real re
parameter (re=6370.)
real xp,yp,xq,yq,arg
arg=sind(yp)*sind(yq)+cosd(yp)*cosd(yq)*cosd(xp-xq)
if (arg.lt.-1.) arg=-1.
if (arg.gt.1.) arg=1.
sdis=re*acos(arg)
end
 
 
c ********************************************************************************
c * NETCDF INPUT/OUTPUT *
c ********************************************************************************
 
c ---------------------------------------------------------
c Subroutines to write the netcdf output file
c ---------------------------------------------------------
 
subroutine writecdf2D(cdfname,cstname,
> varname,arr,ctime,
> dx,dy,xmin,ymin,nx,ny,
> crefile,crevar)
 
c Create and write to the netcdf file <cdfname>. The variable
c with name <varname> and with time <time> is written. The data
c are in the two-dimensional array <arr>. The list <dx,dy,xmin,
c ymin,nx,ny> specifies the output grid. The flags <crefile> and
c <crevar> determine whether the file and/or the variable should
c be created. 1: create / 0: not created
 
IMPLICIT NONE
 
c Declaration of input parameters
character*80 cdfname,cstname,varname
integer nx,ny
real arr(nx,ny)
real dx,dy,xmin,ymin
integer ctime
integer crefile,crevar
 
c Further variables
real varmin(4),varmax(4),stag(4)
integer ierr,cdfid,ndim,vardim(4)
real mdv
integer datar(14),stdate(5)
integer i
real time
C Definitions
varmin(1)=xmin
varmin(2)=ymin
varmin(3)=1050.
varmax(1)=xmin+real(nx-1)*dx
varmax(2)=ymin+real(ny-1)*dy
varmax(3)=1050.
ndim=4
vardim(1)=nx
vardim(2)=ny
vardim(3)=1
stag(1)=0.
stag(2)=0.
stag(3)=0.
mdv=-999.98999
time=real(ctime)
 
C Create the file
if (crefile.eq.0) then
call cdfwopn(cdfname,cdfid,ierr)
if (ierr.ne.0) goto 906
else if (crefile.eq.1) then
call crecdf(cdfname,cdfid,
> varmin,varmax,ndim,cstname,ierr)
if (ierr.ne.0) goto 903
 
C Write the constants file
datar(1)=vardim(1)
datar(2)=vardim(2)
datar(3)=int(1000.*varmax(2))
datar(4)=int(1000.*varmin(1))
datar(5)=int(1000.*varmin(2))
datar(6)=int(1000.*varmax(1))
datar(7)=int(1000.*dx)
datar(8)=int(1000.*dy)
datar(9)=1
datar(10)=1
datar(11)=0 ! data version
datar(12)=0 ! cstfile version
datar(13)=0 ! longitude of pole
datar(14)=90000 ! latitude of pole
do i=1,5
stdate(i)=0
enddo
call wricst(cstname,datar,0.,0.,0.,0.,stdate)
endif
 
c Write the data to the netcdf file, and close the file
if (crevar.eq.1) then
call putdef(cdfid,varname,ndim,mdv,
> vardim,varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 904
endif
call putdat(cdfid,varname,time,0,arr,ierr)
if (ierr.ne.0) goto 905
call clscdf(cdfid,ierr)
 
return
c Error handling
903 print*,'*** Problem to create netcdf file ***'
stop
904 print*,'*** Problem to write definition ***'
stop
905 print*,'*** Problem to write data ***'
stop
906 print*,'*** Problem to open netcdf file ***'
stop
 
END
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
Property changes:
Added: svn:executable
/tags/1.0/prep/z2s.f
0,0 → 1,978
PROGRAM z2s
 
c Calculate secondary fields on z levels
c Michael Sprenger / Summer 2006
 
implicit none
 
c ---------------------------------------------------------------
c Declaration of variables
c ---------------------------------------------------------------
 
c Variables for output Z file : height level
character*80 cfn
real varmin(4),varmax(4),stag(4)
integer vardim(4)
real mdv
integer ndim
integer nx,ny,nz
real xmin,xmax,ymin,ymax,dx,dy
integer ntimes
real aklev(1000),bklev(1000)
real aklay(1000),bklay(1000)
real time
real pollon,pollat
integer idate(5)
integer nfields
character*80 field_nam(100)
real,allocatable, dimension (:,:,:,:) :: field_dat
real,allocatable, dimension (:,:,:) :: z3
real,allocatable, dimension (:,:) :: x2,y2,f2
real,allocatable, dimension (:,:,:) :: out
real,allocatable, dimension (:,:,:) :: inp
integer nvars
character*80 vnam(100),varname
integer isok
integer cdfid,cstid
 
c Parameter file
character*80 fieldname
integer nfilt
character*80 ofn,gri
 
c Auxiliary variables
integer ierr,stat
integer i,j,k,n
real,allocatable, dimension (:,:) :: out2
character*80 vnam2(100)
integer nvars2
 
c ---------------------------------------------------------------
c Preparations
c ---------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* z2s *'
print*,'*********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) fieldname
read(10,*) ofn
read(10,*) gri
read(10,*) nfilt
close(10)
 
c Get grid description for Z file : height level
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,'T',ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
nx =vardim(1)
ny =vardim(2)
nz =vardim(3)
xmin=varmin(1)
ymin=varmin(2)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
call gettimes(cdfid,time,ntimes,ierr)
if (ierr.ne.0) goto 998
call getstart(cstid,idate,ierr)
if (ierr.ne.0) goto 998
call getpole(cstid,pollon,pollat,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Get a list of all variables on the GRID file
if (trim(gri).ne.trim(ofn)) then
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars2,vnam2,ierr)
if (ierr.ne.0) goto 998
do i=1,nvars2
vnam(nvars+i)=vnam2(i)
enddo
nvars=nvars+nvars2
endif
 
c Check whether calculation of <fieldname> is supported
if ( (fieldname.ne.'TH' ).and.
> (fieldname.ne.'NSQ') .and.
> (fieldname.ne.'PV' ) .and.
> (fieldname.ne.'RHO')) then
print*,'Variable not supported ',trim(fieldname)
stop
endif
c Set dependencies
if (fieldname.eq.'TH') then
nfields=2
field_nam(1)='T'
field_nam(2)='P'
else if (fieldname.eq.'RHO') then
nfields=2
field_nam(1)='T'
field_nam(2)='P'
else if (fieldname.eq.'NSQ') then
nfields=2
field_nam(1)='T'
field_nam(2)='Q'
else if (fieldname.eq.'PV') then
nfields=4
field_nam(1)='T'
field_nam(2)='P'
field_nam(3)='U'
field_nam(4)='V'
endif
 
c Allocate memory
allocate(field_dat(nfields,nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating field_dat'
allocate(out(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating out'
allocate(inp(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating inp'
allocate(z3(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating z3'
allocate(x2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating x2'
allocate(y2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating y2'
allocate(f2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating f2'
 
c Allocate auxiliary fields
allocate(out2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating out2'
c Read X grid
varname='X'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,x2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Read Y grid
varname='Y'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,y2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
c Read Coriolis parametzer
varname='CORIOL'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,f2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Init height levels
do i=1,nx
do j=1,ny
do k=1,nz
z3(i,j,k)=aklay(k)
enddo
enddo
enddo
 
c Load needed variables
do n=1,nfields
 
c Check whether variable is available on file
varname=field_nam(n)
isok=0
call check_varok (isok,varname,vnam,nvars)
 
c Variable is available on file
if (isok.eq.1) then
 
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,inp,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(ofn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=inp(i,j,k)
enddo
enddo
enddo
else
print*,'Variable missing : ',trim(varname)
stop
endif
 
enddo
 
c Change unit of pressure from hPa to Pa
n=0
do i=1,nfields
if (field_nam(i).eq.'P') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=100.*field_dat(n,i,j,k)
enddo
enddo
enddo
endif
 
c ----------------------------------------------------------------
c Calculations
c ----------------------------------------------------------------
 
c Call to the defining routines
if (fieldname.eq.'RHO') then
 
print*,'C ',trim(fieldname)
call calc_rho (out, ! RHO
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> nx,ny,nz,mdv)
 
else if (fieldname.eq.'TH') then
 
print*,'C ',trim(fieldname)
call calc_theta (out, ! TH
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> nx,ny,nz,mdv)
 
else if (fieldname.eq.'NSQ') then
 
print*,'C ',trim(fieldname)
call calc_nsq (out, ! NSQ
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! Q
> z3, ! Z
> nx,ny,nz,mdv)
else if (fieldname.eq.'PV') then
 
print*,'C ',trim(fieldname)
call calc_pv (out, ! PV
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> field_dat(3,:,:,:), ! U
> field_dat(4,:,:,:), ! V
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
endif
 
c Horizontal filtering of the resulting fields
print*,'F ',trim(fieldname)
do k=1,nz
do i=1,nx
do j=1,ny
out2(i,j)=out(i,j,k)
enddo
enddo
do n=1,nfilt
call filt2d (out2,out2,nx,ny,1.,mdv,0,0,0,0)
enddo
 
do i=1,nx
do j=1,ny
out(i,j,k)=out2(i,j)
enddo
enddo
enddo
 
c ----------------------------------------------------------------
c Save result onto netcdf file
c ----------------------------------------------------------------
call cdfwopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
 
c ----------------------------------------------------------------
c Exception handling
c ----------------------------------------------------------------
stop
 
998 print*,'Problem with netcdf file'
stop
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: AUXILIARY ROUTINES *
c ****************************************************************
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: CALCULATE SECONDARY FIELDS *
c ****************************************************************
 
c -----------------------------------------------------------------
c Calculate density
c -----------------------------------------------------------------
 
subroutine calc_rho (rho3,t3,p3,
> nx,ny,nz,mdv)
 
c Calculate the density <rho3> (in kg/m^3) from temperature <t3>
c (in deg C) and pressure <p3> (in hPa).
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real mdv
real rho3(nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
 
c Declaration of physical constants
real eps
parameter (eps=0.01)
real rd
parameter (rd=287.)
real tzero
parameter (tzero=273.15)
 
c Auxiliary variables
integer i,j,k
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(p3(i,j,k)-mdv).gt.eps)) then
rho3(i,j,k)=1./rd*p3(i,j,k)/(t3(i,j,k)+tzero)
 
else
rho3(i,j,k)=mdv
endif
enddo
enddo
enddo
 
end
 
 
c -----------------------------------------------------------------
c Calculate potential temperature
c -----------------------------------------------------------------
 
subroutine calc_theta (th3,t3,p3,
> nx,ny,nz,mdv)
 
c Calculate potential temperature <th3> (in K) from temperature <t3>
c (in deg C) and pressure <p3> (in hPa).
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real mdv
real th3(nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
c Declaration of physical constants
real rdcp,tzero,p0
parameter (rdcp=0.286)
parameter (tzero=273.15)
parameter (p0=100000.)
real eps
parameter (eps=0.01)
c Auxiliary variables
integer i,j,k
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(p3(i,j,k)-mdv).gt.eps)) then
th3(i,j,k)=(t3(i,j,k)+tzero)*( (p0/p3(i,j,k))**rdcp )
 
else
th3(i,j,k)=mdv
endif
enddo
enddo
enddo
 
end
 
c -----------------------------------------------------------------
c Calculate stratification
c -----------------------------------------------------------------
 
subroutine calc_nsq (nsq3,t3,q3,
> z3,nx,ny,nz,mdv)
 
c Calculate stratification <nsq3> on the model grid. The grid is
c specified in the horizontal by <xmin,ymin,dx,dy,nx,ny>. The number
c of vertical levels is <nz>. The input field are: temperature <t3>,
c specific humidity <q3>, height <z3> and horizontal grid <x2>, <y2>.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real nsq3(nx,ny,nz)
real t3 (nx,ny,nz)
real q3 (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real mdv
 
c Physical and numerical parameters
real scale
parameter (scale=1.)
real g
parameter (g=9.80665)
real eps
parameter (eps=0.01)
real tzero
parameter (tzero=273.15)
real kappa
parameter (kappa=0.6078)
real cp
parameter (cp=1005.)
real zerodiv
parameter (zerodiv=0.0000000001)
real R
parameter (R=287.)
 
c Auxiliary variables
real tv (nx,ny,nz)
real dtvdz(nx,ny,nz)
integer i,j,k
real scaledz
 
c Calculate 3d virtual temperature
do k=1,nz
do i=1,nx
do j=1,ny
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(q3(i,j,k)-mdv).gt.eps))
> then
tv(i,j,k) = (t3(i,j,k)+tzero)*(1.+kappa*q3(i,j,k))
else
tv(i,j,k) = mdv
endif
enddo
enddo
enddo
 
c Vertical derivative of virtual temperature
call deriv (dtvdz,tv,'z',z3,x2,y2,nx,ny,nz,mdv)
 
c Stratification
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(dtvdz(i,j,k)-mdv).gt.eps).and.
> (abs(tv (i,j,k)-mdv).gt.eps))
> then
nsq3(i,j,k) = g/tv(i,j,k) * (dtvdz(i,j,k) + g/cp)
else
nsq3(i,j,k) = mdv
endif
enddo
enddo
enddo
 
end
c -----------------------------------------------------------------
c Calculate potential vorticity
c -----------------------------------------------------------------
 
subroutine calc_pv (pv3,t3,p3,u3,v3,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate potential vorticity <pv3> on the model grid. The grid is
c specified in the horizontal by <xmin,ymin,dx,dy,nx,ny>. The number
c of vertical levels is <nz>. The input field are: potential temperature
c <th3>, horizontal wind <u3> and <v3>, density <rho3>, height <z3>.
c The terms including the vertical velocity are neglected in the calculation
c of the PV.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real pv3 (nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
real u3 (nx,ny,nz)
real v3 (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
 
real mdv
 
c Physical and numerical parameters
real scale
parameter (scale=1.E6)
real omega
parameter (omega=7.292E-5)
real pi180
parameter (pi180=3.141592654/180.)
real eps
parameter (eps=0.01)
c Auxiliary variables
real dtdz(nx,ny,nz)
real dtdx(nx,ny,nz)
real dtdy(nx,ny,nz)
real dudz(nx,ny,nz)
real dvdz(nx,ny,nz)
real dvdx(nx,ny,nz)
real dudy(nx,ny,nz)
real rho3(nx,ny,nz)
real th3 (nx,ny,nz)
 
integer i,j,k
 
c Calculate density and potential temperature
call calc_rho (rho3,t3,p3,nx,ny,nz,mdv)
call calc_theta (th3 ,t3,p3,nx,ny,nz,mdv)
 
c Calculate needed derivatives
call deriv (dudz, u3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdz, v3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdz,th3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdx,th3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdy,th3,'y',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdx, v3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dudy, u3,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate potential vorticity
do j=1,ny
do i=1,nx
do k=1,nz
 
c Evaluate PV formula with missing data check
if ((abs(dtdz(i,j,k)-mdv).gt.eps).and.
> (abs(dudz(i,j,k)-mdv).gt.eps).and.
> (abs(dtdy(i,j,k)-mdv).gt.eps).and.
> (abs(dvdz(i,j,k)-mdv).gt.eps).and.
> (abs(rho3(i,j,k)-mdv).gt.eps).and.
> (abs(dtdx(i,j,k)-mdv).gt.eps).and.
> (abs(dvdx(i,j,k)-mdv).gt.eps).and.
> (abs(dudy(i,j,k)-mdv).gt.eps)) then
 
pv3(i,j,k)=scale*1./rho3(i,j,k)*
> ((dvdx(i,j,k)-dudy(i,j,k)+f2(i,j))*dtdz(i,j,k)
> +dudz(i,j,k)*dtdy(i,j,k)
> -dvdz(i,j,k)*dtdx(i,j,k))
else
pv3(i,j,k)=mdv
endif
 
enddo
enddo
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: GRID HANDLING *
c ****************************************************************
 
c -----------------------------------------------------------------
c Horizontal and vertical derivatives for 3d fields
c -----------------------------------------------------------------
 
subroutine deriv (df,f,direction,
> z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate horizontal and vertical derivatives of the 3d field <f>.
c The direction of the derivative is specified in <direction>
c 'x','y' : Horizontal derivative in x and y direction
c 'p','z','t','m' : Vertical derivative (pressure, height, theta, model)
c The 3d field <z3> specifies the isosurfaces along which the horizontal
c derivatives are calculated or the levels for the vertical derivatives.
 
implicit none
 
c Input and output parameters
integer nx,ny,nz
real df (nx,ny,nz)
real f (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
character direction
real mdv
c Numerical and physical parameters
real pi180
parameter (pi180=3.141592654/180.)
real zerodiv
parameter (zerodiv=0.00000001)
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
real vmin,vmax
real scale,lat
real vu,vl,vuvl,vlvu
integer o,u,w,e,n,s
 
c Vertical derivative
if ((direction.eq.'z').or.
> (direction.eq.'th').or.
> (direction.eq.'p').or.
> (direction.eq.'m').and.
> (nz.gt.1)) then
 
do i=1,nx
do j=1,ny
do k=1,nz
o=k+1
if (o.gt.nz) o=nz
u=k-1
if (u.lt.1) u=1
 
if ((abs(f(i,j,o)-mdv).gt.eps).and.
> (abs(f(i,j,u)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps)) then
 
vu = z3(i,j,k)-z3(i,j,o)
vl = z3(i,j,u)-z3(i,j,k)
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
 
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,j,u)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,j,o)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Horizontal derivative in the y direction: 3d
elseif (direction.eq.'y') then
do i=1,nx
do j=1,ny
do k=1,nz
s=j-1
if (s.lt.1) s=1
n=j+1
if (n.gt.ny) n=ny
 
if ((abs(f(i,n,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(i,s,k)-mdv).gt.eps)) then
vu = 1000.*(y2(i,j)-y2(i,n))
vl = 1000.*(y2(i,s)-y2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,s,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,n,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
 
c Horizontal derivative in the x direction: 3d
elseif (direction.eq.'x') then
 
do i=1,nx
do j=1,ny
do k=1,nz
w=i-1
if (w.lt.1) w=1
e=i+1
if (e.gt.nx) e=nx
 
if ((abs(f(w,j,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(e,j,k)-mdv).gt.eps)) then
vu = 1000.*(x2(i,j)-x2(e,j))
vl = 1000.*(x2(w,j)-x2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(w,j,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(e,j,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Undefined direction for derivative
else
print*,'Invalid direction of derivative... Stop'
stop
endif
 
end
 
c -----------------------------------------------------------------
c Horizontal filter
c -----------------------------------------------------------------
 
subroutine filt2d (a,af,nx,ny,fil,misdat,
& iperx,ipery,ispol,inpol)
 
c Apply a conservative diffusion operator onto the 2d field a,
c with full missing data checking.
c
c a real inp array to be filtered, dimensioned (nx,ny)
c af real out filtered array, dimensioned (nx,ny), can be
c equivalenced with array a in the calling routine
c f1 real workarray, dimensioned (nx+1,ny)
c f2 real workarray, dimensioned (nx,ny+1)
c fil real inp filter-coeff., 0<afil<=1. Maximum filtering with afil=1
c corresponds to one application of the linear filter.
c misdat real inp missing-data value, a(i,j)=misdat indicates that
c the corresponding value is not available. The
c misdat-checking can be switched off with with misdat=0.
c iperx int inp periodic boundaries in the x-direction (1=yes,0=no)
c ipery int inp periodic boundaries in the y-direction (1=yes,0=no)
c inpol int inp northpole at j=ny (1=yes,0=no)
c ispol int inp southpole at j=1 (1=yes,0=no)
c
c Christoph Schaer, 1993
 
c argument declaration
integer nx,ny
real a(nx,ny),af(nx,ny),fil,misdat
integer iperx,ipery,inpol,ispol
 
c local variable declaration
integer i,j,is
real fh
real f1(nx+1,ny),f2(nx,ny+1)
 
c compute constant fh
fh=0.125*fil
 
c compute fluxes in x-direction
if (misdat.eq.0.) then
do j=1,ny
do i=2,nx
f1(i,j)=a(i-1,j)-a(i,j)
enddo
enddo
else
do j=1,ny
do i=2,nx
if ((a(i,j).eq.misdat).or.(a(i-1,j).eq.misdat)) then
f1(i,j)=0.
else
f1(i,j)=a(i-1,j)-a(i,j)
endif
enddo
enddo
endif
if (iperx.eq.1) then
c do periodic boundaries in the x-direction
do j=1,ny
f1(1,j)=f1(nx,j)
f1(nx+1,j)=f1(2,j)
enddo
else
c set boundary-fluxes to zero
do j=1,ny
f1(1,j)=0.
f1(nx+1,j)=0.
enddo
endif
 
c compute fluxes in y-direction
if (misdat.eq.0.) then
do j=2,ny
do i=1,nx
f2(i,j)=a(i,j-1)-a(i,j)
enddo
enddo
else
do j=2,ny
do i=1,nx
if ((a(i,j).eq.misdat).or.(a(i,j-1).eq.misdat)) then
f2(i,j)=0.
else
f2(i,j)=a(i,j-1)-a(i,j)
endif
enddo
enddo
endif
c set boundary-fluxes to zero
do i=1,nx
f2(i,1)=0.
f2(i,ny+1)=0.
enddo
if (ipery.eq.1) then
c do periodic boundaries in the x-direction
do i=1,nx
f2(i,1)=f2(i,ny)
f2(i,ny+1)=f2(i,2)
enddo
endif
if (iperx.eq.1) then
if (ispol.eq.1) then
c do south-pole
is=(nx-1)/2
do i=1,nx
f2(i,1)=-f2(mod(i-1+is,nx)+1,2)
enddo
endif
if (inpol.eq.1) then
c do north-pole
is=(nx-1)/2
do i=1,nx
f2(i,ny+1)=-f2(mod(i-1+is,nx)+1,ny)
enddo
endif
endif
 
c compute flux-convergence -> filter
if (misdat.eq.0.) then
do j=1,ny
do i=1,nx
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
enddo
enddo
else
do j=1,ny
do i=1,nx
if (a(i,j).eq.misdat) then
af(i,j)=misdat
else
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
endif
enddo
enddo
endif
end
Property changes:
Added: svn:executable
/tags/1.0/pvin/inv_cart.f
0,0 → 1,1529
PROGRAM inv_cart
 
c ********************************************************************************
c * CALCULATES FOR A PV AND THETA DISTRIBUTION OTHER PROGNOSTIC FIELDS BY *
c * MEANS OF A PV INVERSION *
c * *
c * Rene Fehlmann 1994 / Code re-organization: Michael Sprenger, 2006 *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Declaration of variables, parameters, externals and common blocks
c --------------------------------------------------------------------------------
 
implicit none
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real deltax,deltay,deltaz
real mdv
real, allocatable,dimension (:,:) :: coriol
 
c Reference state
real, allocatable,dimension (:) :: nsqref
real, allocatable,dimension (:) :: thetaref
real, allocatable,dimension (:) :: rhoref
real, allocatable,dimension (:) :: pressref
real, allocatable,dimension (:) :: zref
 
 
C Boundary conditions
real, allocatable,dimension (:,:) :: thetatop
real, allocatable,dimension (:,:) :: thetabot
real, allocatable,dimension (:,:) :: ua
real, allocatable,dimension (:,:) :: ub
real, allocatable,dimension (:,:) :: va
real, allocatable,dimension (:,:) :: vb
 
c Potentiual vorticity and stream function
real, allocatable,dimension (:,:,:) :: psi
real, allocatable,dimension (:,:,:) :: pv
 
c Auxiliary arrays for numerics
real, allocatable,dimension (:,:,:) :: a
real, allocatable,dimension (:,:,:) :: b
real, allocatable,dimension (:,:,:) :: c
 
c Input parameters
character*80 pvsrcfile
character*80 referfile
 
c Auxiliary variables
integer i,j,k
integer stat
 
c --------------------------------------------------------------------------------
c Preparations
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* INV_CART *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) pvsrcfile
read(10,*) referfile
close(10)
print*
print*,trim(pvsrcfile)
 
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
print*
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1
nx=nx-1
ny=ny-1
nz=nz-1
c Allocate memory for boundary conditions
allocate(thetatop(0:nx,0:ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array thetatop ***'
allocate(thetabot(0:nx,0:ny),stat=stat)
if (stat.ne.0) print*,'*** error allocating array thetabot ***'
allocate(ua(0:nx,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ua ***'
allocate(ub(0:nx,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array ub ***'
allocate(va(0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array va ***'
allocate(vb(0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array vb ***'
 
c Allocate memory for 3d PV and stream function
allocate(psi(0:nx,0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array psi ***'
allocate(pv(0:nx,0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pv ***'
 
c Alllocate memory for matrix elements for inversion operator
allocate(a(0:nx,0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array a ***'
allocate(b(0:nx,0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array b ***'
allocate(c(0:nx,0:ny,0:nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array c ***'
 
c Allocate memory for reference profile
allocate(nsqref(0:2*nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array nsqref ***'
allocate(thetaref(0:2*nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array thetaref ***'
allocate(rhoref(0:2*nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array rhoref ***'
allocate(pressref(0:2*nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array pressref ***'
allocate(zref(0:2*nz),stat=stat)
if (stat.ne.0) print*,'*** error allocating array zref ***'
 
c Allocate memory for Coriolis parameter
allocate(coriol(0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating coriol'
 
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
c Read reference profile and grid parameters
call read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> referfile)
deltax=1000.*deltax
deltay=1000.*deltay
 
c Read input fields from netcdf
call read_inp (pv,thetabot,thetatop,ua,ub,va,vb,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,
> pvsrcfile)
 
c --------------------------------------------------------------------------------
c Perform the inversion
c --------------------------------------------------------------------------------
 
C Init matrix elements for inversion
call matrixel(a,b,c,coriol,nx,ny,nz,nsqref,rhoref,
> deltax,deltay,deltaz)
 
c Inversion
call sor(psi,nsqref,thetatop,thetabot,thetaref,rhoref,coriol,
> pv,ua,ub,va,vb,a,b,c,nx,ny,nz,deltax,deltay,deltaz)
 
c --------------------------------------------------------------------------------
c Output
c --------------------------------------------------------------------------------
 
c Write output to netcdf
print*
call write_out (psi,thetabot,thetatop,ua,ub,va,vb,
> nx,ny,nz,deltax,deltay,deltaz,
> coriol,thetaref,rhoref,pressref,pvsrcfile)
 
 
END
 
 
c ********************************************************************************
c * NETCDF AND ASCII INPUT AND OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Output to netcdf file
c --------------------------------------------------------------------------------
 
SUBROUTINE write_out (psi,thetabot,thetatop,ua,ub,va,vb,nx,ny,nz,
> dx,dy,dz,coriol,thetaref,rhoref,pref,
> pvsrcfile)
 
c Write the result of the inversion to output netcdf
c
c psi : streamm function as calculated from inversion
c thetabot,thetatop : potential temperature at lower and upper boundary
c ua,ub : Zonal wind at western and eastern boundary
c va,vb : Meridional wind at southern and northern boundary
c nx,ny,nz : Grid dimension in x, y and z direction
c dx,dy,dz : Grid resolution
c coriol : Coriolis parameter
c thetaref : Reference profile of potential temperature
c rhoref : Reference profile of density
c pref : Reference profile of pressure
c pvsrcfile : Name of the output netcdf file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real psi(0:nx,0:ny,0:nz)
real thetatop(0:nx,0:ny)
real thetabot(0:nx,0:ny)
real ua(0:nx,0:nz)
real ub(0:nx,0:nz)
real va(0:ny,0:nz)
real vb(0:ny,0:nz)
character*(30) pvsrcfile
real dx,dy,dz
real thetaref(0:2*nz)
real rhoref(0:2*nz)
real pref(0:2*nz)
real coriol(0:nx,0:ny)
c Numerical and physical parameters
real eps
parameter (eps=0.01)
real g
parameter (g=9.81)
real preunit
parameter (preunit=0.01)
real kappa
parameter (kappa=0.286)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1,jj,kk
real tmp(0:nx,0:ny,0:nz)
real pr (0:nx,0:ny,0:nz)
real th (0:nx,0:ny,0:nz)
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real meanpsi,meancnt
 
c Get grid description
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='QGPV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='PSI'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='U'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='V'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='T'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
isok=0
varname='P'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
endif
 
c Write stream function
varname='PSI'
call putdat(cdfid,varname,time(1),0,psi,ierr)
if (stat.ne.0) goto 997
print*,'W PSI ',trim(pvsrcfile)
 
c Calculate and write velocity U: keep southern and northern boundary
do k=0,nz
do i=0,nx
do j=1,ny-1
tmp(i,j,k)=(psi(i,j-1,k)-psi(i,j+1,k))/
> (2.*dy*coriol(i,j))
enddo
tmp(i,0,k) =ua(i,k)
tmp(i,ny,k)=ub(i,k)
enddo
enddo
varname='U'
call putdat(cdfid,varname,time(1),0,tmp,ierr)
if (stat.ne.0) goto 997
print*,'W U ',trim(pvsrcfile)
 
C Calculate and write velocity V: keep western and eastern boundary
do k=0,nz
do j=0,ny
do i=1,nx-1
tmp(i,j,k)=(psi(i+1,j,k)-psi(i-1,j,k))/
> (2.*dx*coriol(i,j))
enddo
tmp(0,j,k)=va(j,k)
tmp(nx,j,k)=vb(j,k)
enddo
enddo
varname='V'
call putdat(cdfid,varname,time(1),0,tmp,ierr)
if (stat.ne.0) goto 997
print*,'W V ',trim(pvsrcfile)
c Calculate and write potential temperature: keep lower and upper boundary
c Potential temperature is needed for calculation of temperature: keep it
do i=0,nx
do j=0,ny
th(i,j,0)=thetabot(i,j)
do k=1,nz-1
th(i,j,k)=thetaref(2*k)*
> (psi(i,j,k+1)-psi(i,j,k-1))/(2.*dz*g)
 
enddo
th(i,j,nz)=thetatop(i,j)
enddo
enddo
varname='TH'
call putdat(cdfid,varname,time(1),0,th,ierr)
if (stat.ne.0) goto 997
print*,'W TH ',trim(pvsrcfile)
 
c Calculate and write pressure: The pressure is directly proportional to the
c streamfunction. But the streamfunction is determined only up to an additive
c constant. Shift the streamfunction in such a way that it vanish in the mean
c on the boundaries. Pressure is needed for calculation of temperature: keep it
meanpsi=0.
meancnt=0.
do i=0,nx
do j=0,ny
meanpsi=meanpsi+psi(i,j,0)+psi(i,j,nz)
meancnt=meancnt+2
enddo
enddo
do i=0,nx
do k=0,nz
meanpsi=meanpsi+psi(i,0,k)+psi(i,ny,k)
meancnt=meancnt+2
enddo
enddo
do j=0,ny
do k=0,nz
meanpsi=meanpsi+psi(0,j,k)+psi(nx,j,k)
meancnt=meancnt+2
enddo
enddo
meanpsi=meanpsi/meancnt
do i=0,nx
do j=0,ny
do k=0,nz
kk=2*k
pr(i,j,k)=preunit*rhoref(kk)*(psi(i,j,k)-meanpsi)
enddo
enddo
enddo
varname='P'
call putdat(cdfid,varname,time(1),0,pr,ierr)
if (stat.ne.0) goto 997
print*,'W P ',trim(pvsrcfile)
 
c Calculate and write temperature
do i=0,nx
do j=0,ny
do k=0,nz
kk=2*k
tmp(i,j,k)=((pref(kk)/1000.)**kappa) *
> (th(i,j,k)+kappa*thetaref(kk)*pr(i,j,k)/pref(kk))
enddo
enddo
enddo
varname='T'
call putdat(cdfid,varname,time(1),0,tmp,ierr)
if (stat.ne.0) goto 997
print*,'W T ',trim(pvsrcfile)
 
c Close output netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
return
 
c Exception handling
997 print*,'Problem with output netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read the reference file
c --------------------------------------------------------------------------------
 
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,
> pvsrcfile)
 
c Read the reference profile from file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nx,nny,nz : Grid dimension in x,y,z direction
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
c coriol : Coriolis parameter (s^-1)
c pvsrcfile : Input file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
real deltax,deltay,deltaz
real coriol (0:nx,0:ny)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real x(0:nx,0:ny),y(0:nx,0:ny)
real mean,count
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
 
c Read data from netcdf file
isok=0
varname='NSQREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='RHOREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
isok=0
varname='THETAREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='PREREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ZREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='CORIOL'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,coriol,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='X'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,x,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='Y'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,y,stat)
if (stat.ne.0) goto 997
 
c Close netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Determine the grid spacings <deltax, deltay, deltaz>
mean=0.
count=0.
do i=1,nx
do j=0,ny
mean=mean+abs(x(i,j)-x(i-1,j))
count=count+1.
enddo
enddo
deltax=mean/count
 
mean=0.
count=0.
do j=1,ny
do i=0,nx
mean=mean+abs(y(i,j)-y(i,j-1))
count=count+1.
enddo
enddo
deltay=mean/count
 
mean=0.
count=0.
do k=1,nz-1
mean=mean+abs(zref(k+1)-zref(k-1))
count=count+1.
enddo
deltaz=mean/count
 
return
 
c Exception handling
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='QGPV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
c -------------------------------------------------------------------------------
c Read the input netcdf file
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (pv,thetabot,thetatop,ua,ub,va,vb,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,
> pvsrcfile)
 
c Read all needed field from netcdf file <pvsrcfile>. The input fields are:
c pv : quasigeostrophic potential vorticity
c thetabot,thetatop : potential temperature at lower and upper boundary
c ua,ub : Zonal wind at western and eastern boundary
c va,vb : Meridional wind at southern and northern boundary
c The grid is specified by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed
c whether the input files are consitent with this grid. The input netcdf file must
c contain the variables <QGPV,THETA,U,V>. If the netcdf file also contains the fields
c <DQGPV,DTHETA,DU,DV>, these increments are added to <QGPV,THETA,U,V>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real pv(0:nx,0:ny,0:nz)
real thetatop(0:nx,0:ny)
real thetabot(0:nx,0:ny)
real ua(0:nx,0:nz)
real ub(0:nx,0:nz)
real va(0:ny,0:nz)
real vb(0:ny,0:nz)
character*(30) pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(0:nx,0:ny,0:nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
varname='U'
call check_varok(isok,varname,vnam,nvars)
varname='V'
call check_varok(isok,varname,vnam,nvars)
varname='QGPV'
call check_varok(isok,varname,vnam,nvars)
if (isok.ne.4) goto 998
 
c Get the grid parameters
varname='QGPV'
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consitent
if ( (vardim(1).ne.nx+1).or.
> (vardim(2).ne.ny+1).or.
> (vardim(3).ne.nz+1).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(nx)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(ny)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(nz)-dz).gt.eps) ) then
print*,'Input grid inconsitency...'
print*,'xmin : ',xmin,varmin(1)
print*,'ymin : ',ymin,varmin(2)
print*,'zmin : ',zmin,varmin(3)
print*,'dx : ',dx,(varmax(1)-varmin(1))/real(nx)
print*,'dy : ',dy,(varmax(2)-varmin(2))/real(ny)
print*,'dz : ',dz,(varmax(3)-varmin(3))/real(nz)
print*,'nx : ',nx
print*,'ny : ',ny
print*,'nz : ',nz
goto 998
endif
 
c THETA: Load upper and lower boundary values
varname='TH'
call getdat(cdfid,varname,time(1),0,tmp,stat)
print*,'R TH ',trim(pvsrcfile)
if (stat.ne.0) goto 998
do i=0,nx
do j=0,ny
if ( abs(tmp(i,j,0)-misdat).lt.eps ) then
thetabot(i,j)=0.
else
thetabot(i,j)=tmp(i,j,0)
endif
if ( abs(tmp(i,j,nz)-misdat).lt.eps ) then
thetatop(i,j)=0.
else
thetatop(i,j)=tmp(i,j,nz)
endif
enddo
enddo
 
c U: Load zonal velocity at southern and northern boundary
varname='U'
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,tmp,stat)
print*,'R U ',trim(pvsrcfile)
if (stat.ne.0) goto 998
do i=0,nx
do k=0,nz
if ( abs(tmp(i,0,k)-misdat).lt.eps ) then
ua(i,k)=0.
else
ua(i,k)=tmp(i,0,k)
endif
if ( abs(tmp(i,ny,k)-misdat).lt.eps ) then
ub(i,k)=0.
else
ub(i,k)=tmp(i,ny,k)
endif
enddo
enddo
 
c Load meridional velocity at western and eastern boundary
varname='V'
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,tmp,stat)
print*,'R V ',trim(pvsrcfile)
if (stat.ne.0) goto 998
do j=0,ny
do k=0,nz
if ( abs(tmp(0,j,k)-misdat).lt.eps ) then
va(j,k)=0.
else
va(j,k)=tmp(0,j,k)
endif
if ( abs(tmp(nx,j,k)-misdat).lt.eps ) then
vb(j,k)=0.
else
vb(j,k)=tmp(nx,j,k)
endif
enddo
enddo
 
c Load qgPV
varname='QGPV'
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,tmp,stat)
print*,'R QGPV ',trim(pvsrcfile)
if (stat.ne.0) goto 998
do i=0,nx
do j=0,ny
do k=0,nz
if ( abs(tmp(i,j,k)-misdat).lt.eps ) then
pv(i,j,k)=0.
else
pv(i,j,k)=tmp(i,j,k)
endif
enddo
enddo
enddo
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
return
 
c Exception handling
998 print*,'Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
 
c ********************************************************************************
c * INVERSION ROUTINES *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c SOR algorithm (successive over relaxation)
c --------------------------------------------------------------------------------
 
SUBROUTINE sor(psi,nsq,thetatop,thetabot,thetaref,rhoref,
> coriol,pv,ua,ub,va,vb,a,b,c,nx,ny,nz,dx,dy,dz)
 
c Solve the qgPV equation by succesive over relaxation (SOR). The subroutine
c parameters are:
c
c psi : Streamfunction, i.e. result of the PV inversion
c nsq,rhoref,thetaref : Reference profile
c thetatop,thetabot : Upper and lower boundary condition
c pv : quasigeostrophic potential vorticity (qgPV)
c ua,ub,va,vb : lateral boundary condition for wind
c a,b,c : Matrices for the inversion operator
c nx,ny,nz,dx,dy,dz : Grid specification
c coriol : Coriolis parameter
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real dx,dy,dz
real psi (0:nx,0:ny,0:nz)
real nsq (0:2*nz)
real thetatop(0:nx,0:ny)
real thetabot(0:nx,0:ny)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pv (0:nx,0:ny,0:nz)
real ua (0:nx,0:nz)
real ub (0:nx,0:nz)
real va (0:ny,0:nz)
real vb (0:ny,0:nz)
real a (0:nx,0:ny,0:nz)
real b (0:nx,0:ny,0:nz)
real c (0:nx,0:ny,0:nz)
real coriol (0:nx,0:ny)
 
c Numerical and physical parameters
real maxspec
parameter (maxspec=2.0)
integer nofiter
parameter (nofiter=500)
real omega
parameter (omega=1.81)
c Auxiliary variables
integer counter
integer i,j,k
real deltasq,psigauge
real specx,specy,specz
real helpx,helpy,helpz
 
c Init the output array
do i=0,nx
do j=0,ny
do k=0,nz
psi(i,j,k)=0.
enddo
enddo
enddo
 
c Calculate the spectrum of the matrix
i=nx/2
specx=4.*a(i,0,0)/
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
specy=2.*(b(i,0,0)+b(i,1,0))/
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
specz=2.*(c(i,0,0)+c(i,0,1))/
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
do k=1,nz-2
do j=1,ny-2
 
helpx=4.*a(i,j,k)/
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
if (helpx.gt.specx) specx=helpx
helpy=2.*(b(i,j,k)+b(i,j+1,k))/
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
if (helpy.gt.specy) specy=helpy
 
helpz=2.*(c(i,j,k)+c(i,j,k+1))/
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
if (helpz.gt.specz) specz=helpz
 
enddo
enddo
 
c Check whether the dimensions of the grid are sufficient
print *
print *, 'Spectrum of the matrix in each direction '
print *, 'Spectrum = ', specx, specy, specz
print *
if ((maxspec*specx.lt.specy).or.(maxspec*specx.lt.specz)) then
print*,' Nx too small... Stop'
stop
endif
if ((maxspec*specy.lt.specx).or.(maxspec*specy.lt.specz)) then
print*,'Ny too small... Stop'
stop
endif
if ((maxspec*specz.lt.specx).or.(maxspec*specz.lt.specy)) then
print*,'Nz too small... Stop'
stop
endif
 
c Calculate error: control variable for the iteration
psigauge=0.
deltasq=0.
do k=1,nz-1
do i=1,nx-1
do j=1,ny-1
deltasq=deltasq+(-pv(i,j,k)+(
> a(i,j,k)*(psi(i+1,j,k)+psi(i-1,j,k)-
> 2.*psi(i,j,k)) +
> b(i,j,k)*(psi(i,j+1,k)-psi(i,j,k))-
> b(i,j-1,k)*(psi(i,j,k)-psi(i,j-1,k))+
> c(i,j,k)*(psi(i,j,k+1)-psi(i,j,k))-
> c(i,j,k-1)*(psi(i,j,k)-psi(i,j,k-1))
> )/(dx*dy*dz*rhoref(2*k)))**2.
enddo
enddo
enddo
print 102, 'psigauge', psigauge, 'deltasq',
> deltasq/(real(nx)*real(ny)*real(nz))
 
c Iterations
do counter=1,nofiter
 
C Perform one iteration step
call psiappsor(omega,pv,psi,nsq,rhoref,thetatop,
> thetabot,thetaref,coriol,ua,ub,va,vb,
> a,b,c,nx,ny,nz,dx,dy,dz)
 
 
c Adjustment
if (mod(counter,100).eq.0) then
psigauge=0.
do i=0,nx
do j=0,ny
if (psi(i,j,0).lt.psigauge) then
psigauge=psi(i,j,0)
endif
enddo
enddo
do k=0,nz
do i=0,nx
do j=0,ny
psi(i,j,k)=psi(i,j,k)-psigauge
enddo
enddo
enddo
endif
 
c Calculate error: control variable for the iteration
if (mod(counter,nofiter/10).eq.0) then
deltasq=0.
do k=1,nz-1
do i=1,nx-1
do j=1,ny-1
deltasq=deltasq+(-pv(i,j,k)+(
> a(i,j,k)*(psi(i+1,j,k)+psi(i-1,j,k)-
> 2.*psi(i,j,k)) +
> b(i,j,k)*(psi(i,j+1,k)-psi(i,j,k))-
> b(i,j-1,k)*(psi(i,j,k)-psi(i,j-1,k))+
> c(i,j,k)*(psi(i,j,k+1)-psi(i,j,k))-
> c(i,j,k-1)*(psi(i,j,k)-psi(i,j,k-1))
> )/(dx*dy*dz*rhoref(2*k)))**2.
enddo
enddo
enddo
print 102, 'psigauge', psigauge, 'deltasq',
> deltasq/(real(nx)*real(ny)*real(nz))
endif
 
enddo
 
return
 
c Format specifications
102 format (a11, ' = ',e10.3,a11, ' = ',e10.3)
 
end
 
c --------------------------------------------------------------------------------
c SOR algorithm (successive over relaxation)
c --------------------------------------------------------------------------------
 
subroutine psiappsor(omega,pv,psi,nsq,rhoref,thetatop,
> thetabot,thetaref,coriol,ua,ub,va,vb,
> a,b,c,nx,ny,nz,dx,dy,dz)
 
c Perform one relaxation step
c
c psi : Streamfunction, i.e. result of the PV inversion
c nsq,rhoref,thetaref : Reference profile
c thetatop,thetabot : Upper and lower boundary condition
c pv : quasigeostrophic potential vorticity (qgPV)
c ua,ub,va,vb : lateral boundary condition for wind
c a,b,c : Matrices for the inversion operator
c nx,ny,nz,dx,dy,dz : Grid specification
c nofiter : Number of iterations
c omega : Relaxation parameter
c coriol : Coriolis parameter
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real pv(0:nx,0:ny,0:nz)
real psi(0:nx,0:ny,0:nz)
real nsq(0:2*nz)
real rhoref(0:2*nz)
real thetatop(0:nx,0:ny)
real thetabot(0:nx,0:ny)
real thetaref(0:2*nz)
real ua(0:nx,0:nz)
real ub(0:nx,0:nz)
real va(0:ny,0:nz)
real vb(0:ny,0:nz)
real a(0:nx,0:ny,0:nz)
real b(0:nx,0:ny,0:nz)
real c(0:nx,0:ny,0:nz)
real coriol(0:nx,0:ny)
real dx,dy,dz
real omega
 
c Numerical and physical parameters
real g
parameter (g=9.81)
 
c Auxiliary variables
integer i,j,k
real dxy,dxz,dyz,dxyz
 
c Set the area and volume infinitesimals for integration
dxy=dx*dy
dxz=dx*dz
dyz=dy*dz
dxyz=dx*dy*dz
 
c Inner
do k=1,nz-1
do i=1,nx-1
do j=1,ny-1
psi(i,j,k)=omega*(-dxyz*
> rhoref(2*k)*pv(i,j,k)+a(i,j,k)*
> (psi(i+1,j,k)+psi(i-1,j,k))+b(i,j,k)*
> psi(i,j+1,k)+b(i,j-1,k)*psi(i,j-1,k)+c(i,j,k)*
> psi(i,j,k+1)+c(i,j,k-1)*psi(i,j,k-1))/
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k-1)+
> c(i,j,k))+(1.-omega)*psi(i,j,k)
enddo
enddo
enddo
 
c ZY plane
do k=1,nz-1
do j=1,ny-1
psi(0,j,k)=omega*(-dyz*
> rhoref(2*k)*(dx*pv(0,j,k)+va(j,k))+
> a(0,j,k)*psi(1,j,k)+
> b(0,j,k)*psi(0,j+1,k)+b(0,j-1,k)*psi(0,j-1,k)+
> c(0,j,k)*psi(0,j,k+1)+c(0,j,k-1)*psi(0,j,k-1))/
> (a(0,j,k)+b(0,j,k)+b(0,j-1,k)+c(0,j,k-1)+c(0,j,k))
> +(1.-omega)*psi(0,j,k)
c
psi(nx,j,k)=omega*(-dyz*
> rhoref(2*k)*(dx*pv(nx,j,k)-vb(j,k))+
> a(nx,j,k)*psi(nx-1,j,k)+
> b(nx,j,k)*psi(nx,j+1,k)+b(nx,j-1,k)*psi(nx,j-1,k)+
> c(nx,j,k)*psi(nx,j,k+1)+c(nx,j,k-1)*psi(nx,j,k-1))/
> (a(nx,j,k)+b(nx,j-1,k)+b(nx,j,k)+c(nx,j,k-1)+c(nx,j,k))
> +(1.-omega)*psi(nx,j,k)
enddo
enddo
 
c ZX plane
do k=1,nz-1
do i=1,nx-1
psi(i,0,k)=omega*(-dxz*
> rhoref(2*k)*(dy*pv(i,0,k)-ua(i,k))+
> a(i,0,k)*(psi(i+1,0,k)+psi(i-1,0,k))+
> b(i,0,k)*psi(i,1,k)+
> c(i,0,k)*psi(i,0,k+1)+c(i,0,k-1)*psi(i,0,k-1))/
> (2.*a(i,0,k)+b(i,0,k)+c(i,0,k-1)+c(i,0,k))
> +(1.-omega)*psi(i,0,k)
c
psi(i,ny,k)=omega*(-dxz*
> rhoref(2*k)*(dy*pv(i,ny,k)+ub(i,k))+
> a(i,ny-1,k)*(psi(i+1,ny,k)+psi(i-1,ny,k))+
> b(i,ny-1,k)*psi(i,ny-1,k)+
> c(i,ny-1,k)*psi(i,ny,k+1)+c(i,ny-1,k-1)*
> psi(i,ny,k-1))/(2.*a(i,ny-1,k)+b(i,ny-1,k)+
> c(i,ny-1,k-1)+c(i,ny-1,k))
> +(1.-omega)*psi(i,ny,k)
enddo
enddo
 
c XY plane
do i=1,nx-1
do j=1,ny-1
psi(i,j,0)=omega*(-dxy*rhoref(0)*(
> dz*pv(i,j,0)+g*coriol(i,j)*thetabot(i,j)/
> (nsq(0)*thetaref(0)))+
> a(i,j,0)*(psi(i+1,j,0)+psi(i-1,j,0))+
> b(i,j,0)*psi(i,j+1,0)+b(i,j-1,0)*psi(i,j-1,0)+
> c(i,j,0)*psi(i,j,1))/
> (2.*a(i,j,0)+b(i,j-1,0)+b(i,j,0)+c(i,j,0))
> +(1.-omega)*psi(i,j,0)
c
psi(i,j,nz)=omega*(-dxy*rhoref(2*nz)*(
> dz*pv(i,j,nz)-g*coriol(i,j)*thetatop(i,j)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(i,j,nz)*(psi(i+1,j,nz)+psi(i-1,j,nz))+
> b(i,j,nz)*psi(i,j+1,nz)+b(i,j-1,nz)*psi(i,j-1,nz)+
> c(i,j,nz-1)*psi(i,j,nz-1))/
> (2.*a(i,j,nz)+b(i,j-1,nz)+b(i,j,nz)+c(i,j,nz-1))
> +(1.-omega)*psi(i,j,nz)
enddo
enddo
 
c Y edges
do j=1,ny-1
psi(0,j,0)=omega*(-dy*rhoref(0)*(dxz*pv(0,j,0)+
> dz*va(j,0)+dx*g*coriol(0,j)*thetabot(0,j)/
> (nsq(0)*thetaref(0)))+
> a(0,j,0)*psi(1,j,0)+
> b(0,j,0)*psi(0,j+1,0)+b(0,j-1,0)*psi(0,j-1,0)+
> c(0,j,0)*psi(0,j,1))/
> (a(0,j,0)+b(0,j-1,0)+b(0,j,0)+c(0,j,0))
> +(1.-omega)*psi(0,j,0)
c
psi(nx,j,0)=omega*(-dy*rhoref(0)*(dxz*pv(nx,j,0)-
> dz*vb(j,0)+dx*g*coriol(nx,j)*thetabot(nx,j)/
> (nsq(0)*thetaref(0)))+
> a(nx,j,0)*psi(nx-1,j,0)+
> b(nx,j,0)*psi(nx,j+1,0)+b(nx,j-1,0)*psi(nx,j-1,0)+
> c(nx,j,0)*psi(nx,j,1))/
> (a(nx,j,0)+b(nx,j-1,0)+b(nx,j,0)+c(nx,j,0))
> +(1.-omega)*psi(nx,j,0)
c
psi(0,j,nz)=omega*(-dy*rhoref(2*nz)*(dxz*pv(0,j,nz)+
> dz*va(j,nz)-dx*g*coriol(0,j)*thetatop(0,j)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(0,j,nz)*psi(1,j,nz)+
> b(0,j,nz)*psi(0,j+1,nz)+b(0,j-1,nz)*psi(0,j-1,nz)+
> c(0,j,nz-1)*psi(0,j,nz-1))/
> (a(0,j,nz)+b(0,j-1,nz)+b(0,j,nz)+c(0,j,nz-1))
> +(1.-omega)*psi(0,j,nz)
c
psi(nx,j,nz)=omega*(-dy*rhoref(2*nz)*(dxz*pv(nx,j,nz)-
> dz*vb(j,nz)-dx*g*coriol(nx,j)*thetatop(nx,j)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(nx,j,nz)*psi(nx-1,j,nz)+
> b(nx,j,nz)*psi(nx,j+1,nz)+b(nx,j-1,nz)*psi(nx,j-1,nz)+
> c(nx,j,nz-1)*psi(nx,j,nz-1))/
> (a(nx,j,nz)+b(nx,j-1,nz)+b(nx,j,nz)+c(nx,j,nz-1))
> +(1.-omega)*psi(nx,j,nz)
enddo
 
c X edges
do i=1,nx-1
psi(i,0,0)=omega*(-dx*rhoref(0)*(dyz*pv(i,0,0)-
> dz*ua(i,0)+dy*g*coriol(i,0)*thetabot(i,0)/
> (nsq(0)*thetaref(0)))+
> a(i,0,0)*(psi(i+1,0,0)+psi(i-1,0,0))+
> b(i,0,0)*psi(i,1,0)+
> c(i,0,0)*psi(i,0,1))/
> (2.*a(i,0,0)+b(i,0,0)+c(i,0,0))
> +(1.-omega)*psi(i,0,0)
c
psi(i,ny,0)=omega*(-dx*rhoref(0)*(dyz*pv(i,ny,0)+
> dz*ub(i,0)+dy*g*coriol(i,ny)*thetabot(i,ny)/
> (nsq(0)*thetaref(0)))+
> a(i,ny,0)*(psi(i+1,ny,0)+psi(i-1,ny,0))+
> b(i,ny-1,0)*psi(i,ny-1,0)+
> c(i,ny,0)*psi(i,ny,1))/
> (2.*a(i,ny,0)+b(i,ny-1,0)+c(i,ny,0))
> +(1.-omega)*psi(i,ny,0)
c
psi(i,0,nz)=omega*(-dx*rhoref(2*nz)*(dyz*pv(i,0,nz)-
> dz*ua(i,nz)-dy*g*coriol(i,0)*thetatop(i,0)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(i,0,nz)*(psi(i+1,0,nz)+psi(i-1,0,nz))+
> b(i,0,nz)*psi(i,1,nz)+
> c(i,0,nz-1)*psi(i,0,nz-1))/
> (2.*a(i,0,nz)+b(i,0,nz)+c(i,0,nz-1))
> +(1.-omega)*psi(i,0,nz)
c
psi(i,ny,nz)=omega*(-dx*rhoref(2*nz)*(dyz*pv(i,ny,nz)+
> dz*ub(i,nz)-dy*g*coriol(i,ny)*thetatop(i,ny)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(i,ny,nz)*(psi(i+1,ny,nz)+psi(i-1,ny,nz))+
> b(i,ny-1,nz)*psi(i,ny-1,nz)+
> c(i,ny,nz-1)*psi(i,ny,nz-1))/
> (2.*a(i,ny,nz)+b(i,ny-1,nz)+c(i,ny,nz-1))
> +(1.-omega)*psi(i,ny,nz)
enddo
 
c Z edges
do k=1,nz-1
psi(0,0,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(0,0,k)+
> dy*va(0,k)-dx*ua(0,k))+
> a(0,0,k)*psi(1,0,k)+
> b(0,0,k)*psi(0,1,k)+
> c(0,0,k)*psi(0,0,k+1)+c(0,0,k-1)*psi(0,0,k-1))/
> (a(0,0,k)+b(0,0,k)+c(0,0,k-1)+c(0,0,k))
> +(1.-omega)*psi(0,0,k)
c
psi(nx,0,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(nx,0,k)-
> dy*vb(0,k)-dx*ua(nx,k))+
> a(nx,0,k)*psi(nx-1,0,k)+
> b(nx,0,k)*psi(nx,1,k)+
> c(nx,0,k)*psi(nx,0,k+1)+c(nx,0,k-1)*psi(nx,0,k-1))/
> (a(nx,0,k)+b(nx,0,k)+c(nx,0,k-1)+c(nx,0,k))
> +(1.-omega)*psi(nx,0,k)
c
psi(0,ny,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(0,ny,k)+
> dy*va(ny,k)+dx*ub(0,k))+
> a(0,ny,k)*psi(1,ny,k)+
> b(0,ny-1,k)*psi(0,ny-1,k)+
> c(0,ny,k)*psi(0,ny,k+1)+c(0,ny,k-1)*psi(0,ny,k-1))/
> (a(0,ny,k)+b(0,ny-1,k)+c(0,ny,k-1)+c(0,ny,k))
> +(1.-omega)*psi(0,ny,k)
c
psi(nx,ny,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(nx,ny,k)-
> dy*vb(ny,k)+dx*ub(nx,k))+
> a(nx,ny,k)*psi(nx-1,ny,k)+
> b(nx,ny-1,k)*psi(nx,ny-1,k)+
> c(nx,ny,k)*psi(nx,ny,k+1)+c(nx,ny,k-1)*psi(nx,ny,k-1))/
> (a(nx,ny,k)+b(nx,ny-1,k)+c(nx,ny,k-1)+c(nx,ny,k))
> +(1.-omega)*psi(nx,ny,k)
enddo
 
c Points
psi(0,0,0)=omega*(-rhoref(0)*(dxyz*pv(0,0,0)+dyz*va(0,0)-
> dxz*ua(0,0)+dxy*g*coriol(0,0)*thetabot(0,0)/
> (nsq(0)*thetaref(0)))+
> a(0,0,0)*psi(1,0,0)+
> b(0,0,0)*psi(0,1,0)+
> c(0,0,0)*psi(0,0,1))/
> (a(0,0,0)+b(0,0,0)+c(0,0,0))+
> (1.-omega)*psi(0,0,0)
c
psi(nx,0,0)=omega*(-rhoref(0)*(dxyz*pv(nx,0,0)-dyz*vb(0,0)-
> dxz*ua(nx,0)+dxy*g*coriol(nx,0)*thetabot(nx,0)/
> (nsq(0)*thetaref(0)))+
> a(nx,0,0)*psi(nx-1,0,0)+
> b(nx,0,0)*psi(nx,1,0)+
> c(nx,0,0)*psi(nx,0,1))/
> (a(nx,0,0)+b(nx,0,0)+c(nx,0,0))+
> (1.-omega)*psi(nx,0,0)
c
psi(0,ny,0)=omega*(-rhoref(0)*(dxyz*pv(0,ny,0)+dyz*va(ny,0)+
> dxz*ub(0,0)+dxy*g*coriol(0,ny)*thetabot(0,ny)/
> (nsq(0)*thetaref(0)))+
> a(0,ny,0)*psi(1,ny,0)+
> b(0,ny-1,0)*psi(0,ny-1,0)+
> c(0,ny,0)*psi(0,ny,1))/
> (a(0,ny,0)+b(0,ny-1,0)+c(0,ny,0))+
> (1.-omega)*psi(0,ny,0)
c
psi(nx,ny,0)=omega*(-rhoref(0)*(dxyz*pv(nx,ny,0)-dyz*vb(ny,0)+
> dxz*ub(nx,0)+dxy*g*coriol(nx,ny)*thetabot(nx,ny)/
> (nsq(0)*thetaref(0)))+
> a(nx,ny,0)*psi(nx-1,ny,0)+
> b(nx,ny-1,0)*psi(nx,ny-1,0)+
> c(nx,ny,0)*psi(nx,ny,1))/
> (a(nx,ny,0)+b(nx,ny-1,0)+c(nx,ny,0))+
> (1.-omega)*psi(nx,ny,0)
c
psi(0,0,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(0,0,nz)+dyz*va(0,nz)-
> dxz*ua(0,nz)-dxy*g*coriol(0,0)*thetatop(0,0)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(0,0,nz)*psi(1,0,nz)+
> b(0,0,nz)*psi(0,1,nz)+
> c(0,0,nz-1)*psi(0,0,nz-1))/
> (a(0,0,nz)+b(0,0,nz)+c(0,0,nz-1))+
> (1.-omega)*psi(0,0,nz)
c
psi(nx,0,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(nx,0,nz)-dyz*vb(0,nz)
> -dxz*ua(nx,nz)-dxy*g*coriol(nx,0)*thetatop(nx,0)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(nx,0,nz)*psi(nx-1,0,nz)+
> b(nx,0,nz)*psi(nx,1,nz)+
> c(nx,0,nz-1)*psi(nx,0,nz-1))/
> (a(nx,0,nz)+b(nx,0,nz)+c(nx,0,nz-1))+
> (1.-omega)*psi(nx,0,nz)
c
psi(0,ny,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(0,ny,nz)+
> dyz*va(ny,nz)+dxz*ub(0,nz)-
> dxy*g*coriol(0,ny)*thetatop(0,ny)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(0,ny,nz)*psi(1,ny,nz)+
> b(0,ny-1,nz)*psi(0,ny-1,nz)+
> c(0,ny,nz-1)*psi(0,ny,nz-1))/
> (a(0,ny,nz)+b(0,ny-1,nz)+c(0,ny,nz-1))+
> (1.-omega)*psi(0,ny,nz)
c
psi(nx,ny,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(nx,ny,nz)-
> dyz*vb(ny,nz)+dxz*ub(nx,nz)-
> dxy*g*coriol(nx,ny)*thetatop(nx,ny)/
> (nsq(2*nz)*thetaref(2*nz)))+
> a(nx,ny,nz)*psi(nx-1,ny,nz)+
> b(nx,ny-1,nz)*psi(nx,ny-1,nz)+
> c(nx,ny,nz-1)*psi(nx,ny,nz-1))/
> (a(nx,ny,nz)+b(nx,ny-1,nz)+c(nx,ny,nz-1))+
> (1.-omega)*psi(nx,ny,nz)
c
 
end
 
c --------------------------------------------------------------------------------
c Init matrix elements for the inversion
c --------------------------------------------------------------------------------
 
subroutine matrixel(a,b,c,coriol,nx,ny,nz,nsq,rhoref,dx,dy,dz)
 
c Define the coefficients for the inversion problem (see page 119ff in Rene's
c dissertation).
 
implicit none
 
c Declaration of subroutine parameters
integer nx,nz,ny
real a (0:nx,0:ny,0:nz)
real b (0:nx,0:ny,0:nz)
real c (0:nx,0:ny,0:nz)
real coriol(0:nx,0:ny)
real nsq (0:2*nz)
real rhoref(0:2*nz)
real dx,dy,dz
 
c Auxiliary variables
integer i,j,k
 
c Calculate coefficients
do i=0,nx
do j=0,ny
do k=0,nz
a(i,j,k)=dy*dz*rhoref(2*k)/(dx*coriol(i,j))
if (j.lt.ny) then
b(i,j,k)=dx*dz*rhoref(2*k)/
> (dy*0.5*(coriol(i,j)+coriol(i,j+1)))
else
b(i,j,k)=0.
endif
if (k.lt.nz) then
c(i,j,k)=dx*dy*rhoref(2*k+1)*coriol(i,j)/
> (dz*nsq(2*k+1))
else
c(i,j,k)=0.
endif
enddo
enddo
enddo
 
end
 
 
 
 
Property changes:
Added: svn:executable
/tags/1.0/pvin/inv_cart.m
0,0 → 1,259
% -------------------------------------------------------------------------
% Load files
% -------------------------------------------------------------------------
 
% Base directory and filename
base = '/net/rossby/lhome/sprenger/PV_Inversion_Tool/run/';
folder = base;
filename = 'ANO_20060115_18';
disp([folder filename])
 
% First image (otherwise first image is not correctly written)
figname = [base '/test.eps'];
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% Load variables from file (on model levels)
z_th = cdf_loadV(folder,filename,'TH');
z_uu = cdf_loadV(folder,filename,'U');
z_vv = cdf_loadV(folder,filename,'V');
z_qgpv = cdf_loadV(folder,filename,'QGPV');
z_psi = cdf_loadV(folder,filename,'PSI');
 
% -------------------------------------------------------------------------
% Plot stream function
% -------------------------------------------------------------------------
 
for ilev=1:z_psi.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[z_psi.lonmin z_psi.lonmax],'lat',[z_psi.latmin z_psi.latmax]);
 
% Scale the plotting field for color map
fld=squeeze(z_psi.var(ilev,:,:));
c_map = scale_col(-4000:500:4000,fld);
 
% Plot Stream Function PSI
lat=z_psi.ymin + (0:z_psi.ny-1) * z_psi.dy;
lon=z_psi.xmin + (0:z_psi.nx-1) * z_psi.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(z_psi.aklay(ilev)));
 
% Save figure
pre='';
if ( z_psi.aklay(ilev) < 10 )
pre='0';
end
if ( z_psi.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( z_psi.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( z_psi.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/sf_2d_' filename '_' pre num2str(z_psi.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
% -------------------------------------------------------------------------
% Plot anomaly of potential temperature
% -------------------------------------------------------------------------
 
for ilev=1:z_th.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[z_th.lonmin z_th.lonmax],'lat',[z_th.latmin z_th.latmax]);
 
% Scale the plotting field for color map
fld=squeeze(z_th.var(ilev,:,:));
c_map = scale_col(-20:2.5:20,fld);
 
% Plot potential temperature
lat=z_th.ymin + (0:z_th.ny-1) * z_th.dy;
lon=z_th.xmin + (0:z_th.nx-1) * z_th.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(z_th.aklay(ilev)));
 
% Save figure
pre='';
if ( z_th.aklay(ilev) < 10 )
pre='0';
end
if ( z_th.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( z_th.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( z_th.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/ta_2d_' filename '_' pre num2str(z_th.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
% -------------------------------------------------------------------------
% Plot anomaly of meridional wind
% -------------------------------------------------------------------------
 
for ilev=1:z_vv.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[z_vv.lonmin z_vv.lonmax],'lat',[z_vv.latmin z_vv.latmax]);
 
% Scale the plotting field for color map
fld=squeeze(z_vv.var(ilev,:,:));
c_map = scale_col(-30:3:30,fld);
 
% Plot potential temperature
lat=z_vv.ymin + (0:z_vv.ny-1) * z_vv.dy;
lon=z_vv.xmin + (0:z_vv.nx-1) * z_vv.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(z_vv.aklay(ilev)));
 
% Save figure
pre='';
if ( z_vv.aklay(ilev) < 10 )
pre='0';
end
if ( z_vv.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( z_vv.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( z_vv.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/va_2d_' filename '_' pre num2str(z_vv.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
% -------------------------------------------------------------------------
% Plot anomaly of zonal wind
% -------------------------------------------------------------------------
 
for ilev=1:z_uu.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[z_uu.lonmin z_uu.lonmax],'lat',[z_uu.latmin z_uu.latmax]);
 
% Scale the plotting field for color map
fld=squeeze(z_uu.var(ilev,:,:));
c_map = scale_col(-30:3:30,fld);
 
% Plot potential temperature
lat=z_uu.ymin + (0:z_uu.ny-1) * z_uu.dy;
lon=z_uu.xmin + (0:z_uu.nx-1) * z_uu.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('vert');
set(q,'ytick',c_map.xtick,'YTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(z_uu.aklay(ilev)));
 
% Save figure
pre='';
if ( z_uu.aklay(ilev) < 10 )
pre='0';
end
if ( z_uu.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( z_uu.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( z_uu.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/ua_2d_' filename '_' pre num2str(z_uu.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
Property changes:
Added: svn:executable
/tags/1.0/pvin/prep_iteration.f
0,0 → 1,513
PROGRAM prep_iteration
 
c ************************************************************************
c * Prepare the next step for the PV inversion *
c * Michael Sprenger / Summer, Autumn 2006 *
c ************************************************************************
 
implicit none
 
c ------------------------------------------------------------------------
c Declaration of variables and parameters
c ------------------------------------------------------------------------
c Input and output file
character*80 anomafile
character*80 iterafile
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real mdv
 
c Numerical epsilon and other variables
real eps
parameter (eps=0.01)
real alpha
 
c 3d arrays
real,allocatable,dimension (:,:,:) :: v_iter,v_anom
real,allocatable,dimension (:,:,:) :: u_iter,u_anom
real,allocatable,dimension (:,:,:) :: t_iter,t_anom
real,allocatable,dimension (:,:,:) :: p_iter,p_anom
 
c Auciliary variables
integer i,j,k
integer stat
character*80 varname
character*80 name
 
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* PREP_ITERATION *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) iterafile
read(10,*) anomafile
read(10,*) name,alpha
if ( trim(name).ne.'ALPHA' ) stop
close(10)
print*
print*,trim(anomafile)
print*,trim(iterafile)
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> anomafile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for 3d arrays
allocate(u_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating u_anom'
allocate(v_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating v_anom'
allocate(t_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating t_anom'
allocate(p_anom (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating p_anom'
allocate(u_iter (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating u_iter'
allocate(v_iter (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating v_iter'
allocate(t_iter (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating t_iter'
allocate(p_iter (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating p_iter'
c Read anomaly and iteration fields
varname='U'
call read_inp (u_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='V'
call read_inp (v_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='T'
call read_inp (t_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='P'
call read_inp (p_anom,varname,anomafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='U'
call read_inp (u_iter,varname,iterafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='V'
call read_inp (v_iter,varname,iterafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='T'
call read_inp (t_iter,varname,iterafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='P'
call read_inp (p_iter,varname,iterafile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c --------------------------------------------------------------------------------
c Modify the iteration fields
c --------------------------------------------------------------------------------
 
do i=0,nx
do j=0,ny
do k=0,nz
 
c Update zonal velocity
if ((abs(u_anom(i,j,k)-mdv).gt.eps).and.
> (abs(u_iter(i,j,k)-mdv).gt.eps)) then
u_iter(i,j,k)=u_iter(i,j,k)-alpha*u_anom(i,j,k)
else
u_iter(i,j,k)=mdv
endif
 
c Update meridional velocity
if ((abs(v_anom(i,j,k)-mdv).gt.eps).and.
> (abs(v_iter(i,j,k)-mdv).gt.eps)) then
v_iter(i,j,k)=v_iter(i,j,k)-alpha*v_anom(i,j,k)
else
v_iter(i,j,k)=mdv
endif
 
c Update temperature
if ((abs(t_anom(i,j,k)-mdv).gt.eps).and.
> (abs(t_iter(i,j,k)-mdv).gt.eps)) then
t_iter(i,j,k)=t_iter(i,j,k)-alpha*t_anom(i,j,k)
else
t_iter(i,j,k)=mdv
endif
 
c Update pressure
if ((abs(p_anom(i,j,k)-mdv).gt.eps).and.
> (abs(p_iter(i,j,k)-mdv).gt.eps)) then
p_iter(i,j,k)=p_iter(i,j,k)-alpha*p_anom(i,j,k)
else
p_iter(i,j,k)=mdv
endif
 
enddo
enddo
enddo
 
 
c --------------------------------------------------------------------------------
c Write output
c --------------------------------------------------------------------------------
 
varname='U'
call write_inp (u_iter,varname,iterafile,nx,ny,nz)
varname='V'
call write_inp (v_iter,varname,iterafile,nx,ny,nz)
varname='T'
call write_inp (t_iter,varname,iterafile,nx,ny,nz)
varname='P'
call write_inp (p_iter,varname,iterafile,nx,ny,nz)
 
 
end
 
 
 
 
c ********************************************************************************
c * NETCDF INPUT AND OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Write input field to netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE write_inp (field,fieldname,pvsrcfile,nx,ny,nz)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field (0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(0:nx,0:ny,0:nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Get grid parameters
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Save variables (write definition, if necessary)
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
endif
call putdat(cdfid,varname,time(1),0,field,stat)
print*,'W ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
return
 
c Exception handling
998 print*,'Write_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read input fields for reference profile
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real max_th
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters from theta
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*, 'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='TH'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
Property changes:
Added: svn:executable
/tags/1.0/pvin/pv_to_qgpv.f
0,0 → 1,894
PROGRAM pv_to_qgpv
 
c ********************************************************************************
c * TRANSFORM ERTEL'S PV TO QUASI-GEOSTROPHIC PV *
c * Rene Fehlmann 1994 / Code re-organization: Michael Sprenger, 2006 *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Declaration of variables, parameters, externals and common blocks
c --------------------------------------------------------------------------------
 
implicit none
 
c Input and output file
character*80 pvsrcfile
character*80 referfile
character*80 anomafile
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real mdv
 
c Numerical and physical parameters
real pi180 ! Pi/180
parameter (pi180=3.141592654/180.)
real rerd ! Earth's radius
parameter (rerd=6.371229e6)
real eps ! Numerical epsilon
parameter (eps=0.01)
real scale ! Scale for PV unit
parameter (scale=1e6)
real minagl ! No PV and qgPV below this height AGL
parameter (minagl=1000.)
 
c Reference state and grid parameters
real, allocatable,dimension (:) :: nsqref
real, allocatable,dimension (:) :: thetaref
real, allocatable,dimension (:) :: rhoref
real, allocatable,dimension (:) :: pressref
real, allocatable,dimension (:) :: zref
real, allocatable,dimension (:,:) :: coriol
real, allocatable,dimension (:,:) :: oro
real deltax,deltay,deltaz
 
c 3d fields for calculation of qgPV and Ertel's PV
real,allocatable,dimension (:,:,:) :: qgpv,pv1,pv2,pv
 
c Auxiliary variables
real zpos
integer i,j,k
integer stat
character*80 varname
integer istep
real mean,rmsq,min,max
integer step
real,allocatable,dimension (:,:) :: tmp
c --------------------------------------------------------------------------------
c Input
c --------------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* PV_TO_QGPV *'
print*,'********************************************************'
 
 
c Read parameter file
open(10,file='fort.10')
read(10,*) pvsrcfile
read(10,*) referfile
read(10,*) anomafile
close(10)
print*
print*,trim(pvsrcfile)
print*,trim(referfile)
print*,trim(anomafile)
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for reference profile and grid parameters
allocate(rhoref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating rhoref'
allocate(pressref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pressref'
allocate(thetaref(0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating thetaref'
allocate(nsqref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating nsqref'
allocate(zref (0:2*nz),STAT=stat)
if (stat.ne.0) print*,'error allocating zref'
allocate(coriol (0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating coriol'
allocate(oro (0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating oro'
c Allocate memory for calculation of qgPV and Ertel's PV
allocate(pv1 (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv1'
allocate(pv2 (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv2'
allocate(pv (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv'
allocate(qgpv(0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating qgpv'
 
c Allocate memory for temporary array
allocate(tmp(0:nx,0:ny),STAT=stat)
if (stat.ne.0) print*,'error allocating tmp'
 
c --------------------------------------------------------------------------------
c Calculate the qgPV from Ertel's PV and put it onto file
c --------------------------------------------------------------------------------
 
c Read data from file
varname='PV'
call read_inp (pv1,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='PV_AIM'
call read_inp (pv2,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
c Read reference profile and grid parameters
call read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,oro,
> referfile)
 
c If the PV is negative, set it to zero
do i=0,nx
do j=0,ny
do k=0,nz
if (pv1(i,j,k).lt.0.) pv1(i,j,k)=0.
if (pv2(i,j,k).lt.0.) pv2(i,j,k)=0.
enddo
enddo
enddo
 
c Get the difference of Ertel's PV and set all missing values to 0
do i=0,nx
do j=0,ny
do k=0,nz
if ((abs(pv1(i,j,k)-mdv).gt.eps).and.
> (abs(pv2(i,j,k)-mdv).gt.eps)) then
pv(i,j,k)=pv1(i,j,k)-pv2(i,j,k)
else
pv(i,j,k)=0.
endif
enddo
enddo
enddo
 
c Calculate qgPV
call epv_to_qgpv (qgpv,pv,
> rhoref,pressref,nsqref,thetaref,
> nx,ny,nz,mdv)
 
c Set values on the boundaries to zero
do i=0,nx
do j=0,ny
qgpv(i,j, 0)=0.
qgpv(i,j,nz)=0.
enddo
enddo
do i=0,nx
do k=0,nz
qgpv(i, 0,k)=0.
qgpv(i,ny,k)=0.
enddo
enddo
do j=0,ny
do k=0,nz
qgpv( 0,j,k)=0.
qgpv(nx,j,k)=0.
enddo
enddo
 
c Set all values to zero which are too near to the surface
do i=0,nx
do j=0,ny
do k=0,nz
zpos=zmin+real(k)*dz
if (zpos.lt.(oro(i,j)+minagl)) then
pv(i,j,k)=0.
qgpv(i,j,k)=0.
endif
enddo
enddo
enddo
 
c Write result to netcdf file
varname='QGPV'
call write_inp (qgpv,varname,anomafile,nx,ny,nz)
varname='PV'
call write_inp (pv,varname,anomafile,nx,ny,nz)
 
c Write some info
print*
print*,'PV -> qgPV: k z min max mean rmsq'
step=nz/10
if (step.lt.1) step=1
do k=0,nz,step
do i=0,nx
do j=0,ny
tmp(i,j)=qgpv(i,j,k)
enddo
enddo
call calc_error(min,max,mean,rmsq,tmp,nx,ny)
write(*,'(8x,i3,f10.1,4f10.2)')
> k,zmin+real(k)*dz,scale*min,scale*max,
> scale*mean,scale*rmsq
enddo
print*
 
c --------------------------------------------------------------------------------
c Format specifications
c --------------------------------------------------------------------------------
 
111 format (5f20.9)
106 format (2f20.9)
end
 
 
c ********************************************************************************
c * NETCDF INPUT AND OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Write input field to netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE write_inp (field,fieldname,pvsrcfile,nx,ny,nz)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field (0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real tmp(0:nx,0:ny,0:nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Get grid parameters from PV
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname='PV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Save variables (write definition, if necessary)
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
endif
call putdat(cdfid,varname,time(1),0,field,stat)
print*,'W ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
return
 
c Exception handling
998 print*,'Write_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read input fields for reference profile
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters from theta
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*, 'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Read refernece profile from netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
> nx,ny,nz,deltax,deltay,deltaz,coriol,oro,
> pvsrcfile)
 
c Read the reference profile from file
c
c thetaref : Reference potential temperature (K)
c pressref : Reference pressure (Pa)
c rhoref : Reference density (kg/m^3)
c nsqref : Stratification (s^-1)
c zref : Reference height (m)
c nx,nny,nz : Grid dimension in x,y,z direction
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
c coriol : Coriolis parameter (s^-1)
c oro : Height of orography (m)
c pvsrcfile : Input file
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real rhoref (0:2*nz)
real pressref(0:2*nz)
real zref (0:2*nz)
real deltax,deltay,deltaz
real coriol (0:nx,0:ny)
real oro (0:nx,0:ny)
character*80 pvsrcfile
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
integer ndimin
real varmin(4),varmax(4),stag(4)
integer i,j,k,nf1
integer ntimes
real time(200)
character*80 vnam(100),varname
integer nvars
integer isok,ierr
real x(0:nx,0:ny),y(0:nx,0:ny)
real mean,count
 
c Get grid description from topography
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
isok=0
varname='ORO'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 997
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 997
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Open output netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 997
c Create the variable if necessary
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 997
 
c Read data from netcdf file
isok=0
varname='NSQREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,nsqref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='RHOREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,rhoref,stat)
if (stat.ne.0) goto 997
isok=0
varname='THETAREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,thetaref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='PREREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,pressref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ZREF'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,zref,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='CORIOL'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,coriol,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='ORO'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,oro,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='X'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,x,stat)
if (stat.ne.0) goto 997
 
isok=0
varname='Y'
print*,'R ',trim(varname),' ',trim(pvsrcfile)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 997
call getdat(cdfid,varname,time(1),0,y,stat)
if (stat.ne.0) goto 997
 
c Close netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 997
 
c Determine the grid spacings <deltax, deltay, deltaz>
mean=0.
count=0.
do i=1,nx
do j=0,ny
mean=mean+abs(x(i)-x(i-1))
count=count+1.
enddo
enddo
deltax=mean/count
 
mean=0.
count=0.
do j=1,ny
do i=0,nx
mean=mean+abs(y(j)-y(j-1))
count=count+1.
enddo
enddo
deltay=mean/count
 
mean=0.
count=0.
do k=1,nz-1
mean=mean+abs(zref(k+1)-zref(k-1))
count=count+1.
enddo
deltaz=mean/count
 
return
 
c Exception handling
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='PV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
 
 
c ********************************************************************************
c * CALCULATION *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Calculate qgPV from Ertels's PV
c --------------------------------------------------------------------------------
 
subroutine epv_to_qgpv (qgpv,pv,
> rhoref,pressref,nsqref,thetaref,
> nx,ny,nz,mdv)
 
c Calculate the qgPV from Ertel's PV according to equation 2.11 p16, Thesis
c from Rene Fehlmann.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real qgpv(0:nx,0:ny,0:nz),pv(0:nx,0:ny,0:nz)
real rhoref (0:2*nz)
real nsqref (0:2*nz)
real thetaref(0:2*nz)
real pressref(0:2*nz)
real mdv
 
c Numerical epsilon
real g
parameter (g=9.81)
real eps
parameter (eps=0.01)
real scale
parameter (scale=1e6)
 
c Auxiliary variables
integer i,j,k
integer kk
 
c Calculation
do i=0,nx
do j=0,ny
do k=0,nz
 
kk=2*k
if (( abs(rhoref(kk) -mdv).gt.eps).and.
> ( abs(thetaref(kk)-mdv).gt.eps).and.
> ( abs(nsqref(kk) -mdv).gt.eps).and.
> ( abs(pv(i,j,k) -mdv).gt.eps)) then
 
qgpv(i,j,k)=rhoref(kk)*g*pv(i,j,k)/thetaref(kk)/
> nsqref(kk)/scale
else
qgpv(i,j,k)=0.
endif
 
enddo
enddo
enddo
 
end
 
c --------------------------------------------------------------------------------
c Calculate error statistics
c --------------------------------------------------------------------------------
 
subroutine calc_error (min,max,mean,rmsq,tmp,nx,ny)
 
c Calculate the error statistics for the two-dimensional error field <tmp>. The
c following error measures are calculated: the minimum <min>, the maximum <max>,
c the mean <mean>, the root-mean square <rmsq>
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny
real tmp(0:nx,0:ny)
real mean,rmsq
real min,max
 
c Auxiliary variables
integer i,j
real sum
integer cnt
 
c Calculate the minimum and maximum
min=tmp(0,0)
max=tmp(0,0)
do i=0,nx
do j=0,ny
if (tmp(i,j).lt.min) min=tmp(i,j)
if (tmp(i,j).gt.max) max=tmp(i,j)
enddo
enddo
 
c Calculate the mean
sum=0.
cnt=0
do i=0,nx
do j=0,ny
cnt=cnt+1
sum=sum+tmp(i,j)
enddo
enddo
if (cnt.ge.1) then
mean=sum/real(cnt)
else
mean=0.
endif
 
c Calculate rmsq
rmsq=0.
cnt=0
do i=0,nx
do j=0,ny
cnt=cnt+1
rmsq=rmsq+(tmp(i,j)-mean)**2
enddo
enddo
if (cnt.ge.1) then
rmsq=1./real(cnt)*sqrt(rmsq)
else
rmsq=0.
endif
 
end
 
 
Property changes:
Added: svn:executable
/tags/1.0/pvin/pv_to_qgpv.m
0,0 → 1,81
 
folder ='/lhome/sprenger/PV_Inversion_Tool/';
filename='Z1_20060115_18';
 
% --------------------------------------------------------------------------
% Plot qgPV anomaly (horizontal sections)
% --------------------------------------------------------------------------
 
% Base directory and filename
base = '/net/rossby/lhome/sprenger/PV_Inversion_Tool/';
folder = base;
filename = 'Z1_20060115_18';
disp([folder filename])
 
% First image (otherwise first image is not correctly written)
figname = [base '/test.eps'];
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% Load variables from file (on model levels)
m_pv = cdf_loadV(folder,filename,'QGPV_ANOM');
 
% Loop over all levels
for ilev=1:m_pv.nz
 
% Create a new figure
close;
fh=figure('Units','pixels','Position',[100 100 900 900])
 
% Set the geographical projection
m_proj('Equidistant Cylindrical','long',[m_pv.lonmin m_pv.lonmax],'lat',[m_pv.latmin m_pv.latmax]);
 
% Scale the plotting field for color map
fld=1e6*squeeze(m_pv.var(ilev,:,:));
c_map = scale_col(0:50:600,fld);
 
% Plot PV
lat=m_pv.ymin + (0:m_pv.ny-1) * m_pv.dy;
lon=m_pv.xmin + (0:m_pv.nx-1) * m_pv.dx;
[C,h]=m_contourf(lon,lat,c_map.data,c_map.xtick);
for icnt = 1: length(h)
set( h(icnt), 'EdgeColor', 'none' )
end
 
% Add color bar
colormap('default');
ctb(['/home/sprenger/ECFC_STE_Forecast/ctb_isen'],c_map.xtick,1);
caxis(c_map.caxis);
q=colorbar('hori');
set(q,'xtick',c_map.xtick,'XTickLabel',c_map.label);
 
% Add the grid and the coast lines to the plot
m_grid;
m_coast('linewidth',1,'color','k');
title(num2str(m_pv.aklay(ilev)));
 
% Save figure
pre='';
if ( m_pv.aklay(ilev) < 10 )
pre='0';
end
if ( m_pv.aklay(ilev) < 100 )
pre=[pre '0' ];
end
if ( m_pv.aklay(ilev) < 1000 )
pre=[pre '0' ];
end
if ( m_pv.aklay(ilev) < 10000 )
pre=[pre '0' ];
end
 
figname = [ base '/qg_2d_' filename '_' pre num2str(m_pv.aklay(ilev)) '.eps' ];
set(gcf, 'PaperPosition', [2 1 15 10]);
print('-depsc2','-r0',figname);
 
% End loop over all levels
end
 
 
Property changes:
Added: svn:executable
/tags/1.0/pvin/z2s.f
0,0 → 1,978
PROGRAM z2s
 
c Calculate secondary fields on z levels
c Michael Sprenger / Summer 2006
 
implicit none
 
c ---------------------------------------------------------------
c Declaration of variables
c ---------------------------------------------------------------
 
c Variables for output Z file : height level
character*80 cfn
real varmin(4),varmax(4),stag(4)
integer vardim(4)
real mdv
integer ndim
integer nx,ny,nz
real xmin,xmax,ymin,ymax,dx,dy
integer ntimes
real aklev(1000),bklev(1000)
real aklay(1000),bklay(1000)
real time
real pollon,pollat
integer idate(5)
integer nfields
character*80 field_nam(100)
real,allocatable, dimension (:,:,:,:) :: field_dat
real,allocatable, dimension (:,:,:) :: z3
real,allocatable, dimension (:,:) :: x2,y2,f2
real,allocatable, dimension (:,:,:) :: out
real,allocatable, dimension (:,:,:) :: inp
integer nvars
character*80 vnam(100),varname
integer isok
integer cdfid,cstid
 
c Parameter file
character*80 fieldname
integer nfilt
character*80 ofn,gri
 
c Auxiliary variables
integer ierr,stat
integer i,j,k,n
real,allocatable, dimension (:,:) :: out2
character*80 vnam2(100)
integer nvars2
 
c ---------------------------------------------------------------
c Preparations
c ---------------------------------------------------------------
 
print*,'*********************************************************'
print*,'* z2s *'
print*,'*********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) fieldname
read(10,*) ofn
read(10,*) gri
read(10,*) nfilt
close(10)
 
c Get grid description for Z file : height level
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getcfn(cdfid,cfn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(cfn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,'T',ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
nx =vardim(1)
ny =vardim(2)
nz =vardim(3)
xmin=varmin(1)
ymin=varmin(2)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
call gettimes(cdfid,time,ntimes,ierr)
if (ierr.ne.0) goto 998
call getstart(cstid,idate,ierr)
if (ierr.ne.0) goto 998
call getpole(cstid,pollon,pollat,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Get a list of all variables on the GRID file
if (trim(gri).ne.trim(ofn)) then
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars2,vnam2,ierr)
if (ierr.ne.0) goto 998
do i=1,nvars2
vnam(nvars+i)=vnam2(i)
enddo
nvars=nvars+nvars2
endif
 
c Check whether calculation of <fieldname> is supported
if ( (fieldname.ne.'TH' ).and.
> (fieldname.ne.'NSQ') .and.
> (fieldname.ne.'PV' ) .and.
> (fieldname.ne.'RHO')) then
print*,'Variable not supported ',trim(fieldname)
stop
endif
c Set dependencies
if (fieldname.eq.'TH') then
nfields=2
field_nam(1)='T'
field_nam(2)='P'
else if (fieldname.eq.'RHO') then
nfields=2
field_nam(1)='T'
field_nam(2)='P'
else if (fieldname.eq.'NSQ') then
nfields=2
field_nam(1)='T'
field_nam(2)='Q'
else if (fieldname.eq.'PV') then
nfields=4
field_nam(1)='T'
field_nam(2)='P'
field_nam(3)='U'
field_nam(4)='V'
endif
 
c Allocate memory
allocate(field_dat(nfields,nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating field_dat'
allocate(out(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating out'
allocate(inp(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating inp'
allocate(z3(nx,ny,nz),stat=stat)
if (stat.ne.0) print*,'error allocating z3'
allocate(x2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating x2'
allocate(y2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating y2'
allocate(f2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating f2'
 
c Allocate auxiliary fields
allocate(out2(nx,ny),stat=stat)
if (stat.ne.0) print*,'error allocating out2'
c Read X grid
varname='X'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,x2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Read Y grid
varname='Y'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,y2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
c Read Coriolis parametzer
varname='CORIOL'
isok=0
call check_varok (isok,varname,vnam,nvars)
if (isok.eq.0) then
print*,'Variable ',trim(varname),' missing... Stop'
stop
endif
call cdfopn(gri,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,f2,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(gri)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Init height levels
do i=1,nx
do j=1,ny
do k=1,nz
z3(i,j,k)=aklay(k)
enddo
enddo
enddo
 
c Load needed variables
do n=1,nfields
 
c Check whether variable is available on file
varname=field_nam(n)
isok=0
call check_varok (isok,varname,vnam,nvars)
 
c Variable is available on file
if (isok.eq.1) then
 
call cdfopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
call getdat(cdfid,varname,time,0,inp,ierr)
if (ierr.ne.0) goto 998
print*,'R ',trim(varname),' ',trim(ofn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=inp(i,j,k)
enddo
enddo
enddo
else
print*,'Variable missing : ',trim(varname)
stop
endif
 
enddo
 
c Change unit of pressure from hPa to Pa
n=0
do i=1,nfields
if (field_nam(i).eq.'P') n=i
enddo
if (n.ne.0) then
do i=1,nx
do j=1,ny
do k=1,nz
field_dat(n,i,j,k)=100.*field_dat(n,i,j,k)
enddo
enddo
enddo
endif
 
c ----------------------------------------------------------------
c Calculations
c ----------------------------------------------------------------
 
c Call to the defining routines
if (fieldname.eq.'RHO') then
 
print*,'C ',trim(fieldname)
call calc_rho (out, ! RHO
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> nx,ny,nz,mdv)
 
else if (fieldname.eq.'TH') then
 
print*,'C ',trim(fieldname)
call calc_theta (out, ! TH
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> nx,ny,nz,mdv)
 
else if (fieldname.eq.'NSQ') then
 
print*,'C ',trim(fieldname)
call calc_nsq (out, ! NSQ
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! Q
> z3, ! Z
> nx,ny,nz,mdv)
else if (fieldname.eq.'PV') then
 
print*,'C ',trim(fieldname)
call calc_pv (out, ! PV
> field_dat(1,:,:,:), ! T
> field_dat(2,:,:,:), ! P
> field_dat(3,:,:,:), ! U
> field_dat(4,:,:,:), ! V
> z3,x2,y2,f2, ! Z,X,Y,CORIOL
> nx,ny,nz,mdv)
 
endif
 
c Horizontal filtering of the resulting fields
print*,'F ',trim(fieldname)
do k=1,nz
do i=1,nx
do j=1,ny
out2(i,j)=out(i,j,k)
enddo
enddo
do n=1,nfilt
call filt2d (out2,out2,nx,ny,1.,mdv,0,0,0,0)
enddo
 
do i=1,nx
do j=1,ny
out(i,j,k)=out2(i,j)
enddo
enddo
enddo
 
c ----------------------------------------------------------------
c Save result onto netcdf file
c ----------------------------------------------------------------
call cdfwopn(ofn,cdfid,ierr)
if (ierr.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndim,mdv,vardim,
> varmin,varmax,stag,ierr)
if (ierr.ne.0) goto 998
endif
call putdat(cdfid,varname,time,0,out,ierr)
if (ierr.ne.0) goto 998
print*,'W ',trim(varname),' ',trim(ofn)
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
 
c ----------------------------------------------------------------
c Exception handling
c ----------------------------------------------------------------
stop
 
998 print*,'Problem with netcdf file'
stop
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: AUXILIARY ROUTINES *
c ****************************************************************
 
c ----------------------------------------------------------------
c Check whether variable is found on netcdf file
c ----------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>.
c If this is the case, <isok> is incremented by 1. Otherwise <isok>
c keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: CALCULATE SECONDARY FIELDS *
c ****************************************************************
 
c -----------------------------------------------------------------
c Calculate density
c -----------------------------------------------------------------
 
subroutine calc_rho (rho3,t3,p3,
> nx,ny,nz,mdv)
 
c Calculate the density <rho3> (in kg/m^3) from temperature <t3>
c (in deg C) and pressure <p3> (in hPa).
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real mdv
real rho3(nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
 
c Declaration of physical constants
real eps
parameter (eps=0.01)
real rd
parameter (rd=287.)
real tzero
parameter (tzero=273.15)
 
c Auxiliary variables
integer i,j,k
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(p3(i,j,k)-mdv).gt.eps)) then
rho3(i,j,k)=1./rd*p3(i,j,k)/(t3(i,j,k)+tzero)
 
else
rho3(i,j,k)=mdv
endif
enddo
enddo
enddo
 
end
 
 
c -----------------------------------------------------------------
c Calculate potential temperature
c -----------------------------------------------------------------
 
subroutine calc_theta (th3,t3,p3,
> nx,ny,nz,mdv)
 
c Calculate potential temperature <th3> (in K) from temperature <t3>
c (in deg C) and pressure <p3> (in hPa).
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real mdv
real th3(nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
c Declaration of physical constants
real rdcp,tzero,p0
parameter (rdcp=0.286)
parameter (tzero=273.15)
parameter (p0=100000.)
real eps
parameter (eps=0.01)
c Auxiliary variables
integer i,j,k
 
c Calculation
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(p3(i,j,k)-mdv).gt.eps)) then
th3(i,j,k)=(t3(i,j,k)+tzero)*( (p0/p3(i,j,k))**rdcp )
 
else
th3(i,j,k)=mdv
endif
enddo
enddo
enddo
 
end
 
c -----------------------------------------------------------------
c Calculate stratification
c -----------------------------------------------------------------
 
subroutine calc_nsq (nsq3,t3,q3,
> z3,nx,ny,nz,mdv)
 
c Calculate stratification <nsq3> on the model grid. The grid is
c specified in the horizontal by <xmin,ymin,dx,dy,nx,ny>. The number
c of vertical levels is <nz>. The input field are: temperature <t3>,
c specific humidity <q3>, height <z3> and horizontal grid <x2>, <y2>.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real nsq3(nx,ny,nz)
real t3 (nx,ny,nz)
real q3 (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real mdv
 
c Physical and numerical parameters
real scale
parameter (scale=1.)
real g
parameter (g=9.80665)
real eps
parameter (eps=0.01)
real tzero
parameter (tzero=273.15)
real kappa
parameter (kappa=0.6078)
real cp
parameter (cp=1005.)
real zerodiv
parameter (zerodiv=0.0000000001)
real R
parameter (R=287.)
 
c Auxiliary variables
real tv (nx,ny,nz)
real dtvdz(nx,ny,nz)
integer i,j,k
real scaledz
 
c Calculate 3d virtual temperature
do k=1,nz
do i=1,nx
do j=1,ny
if ((abs(t3(i,j,k)-mdv).gt.eps).and.
> (abs(q3(i,j,k)-mdv).gt.eps))
> then
tv(i,j,k) = (t3(i,j,k)+tzero)*(1.+kappa*q3(i,j,k))
else
tv(i,j,k) = mdv
endif
enddo
enddo
enddo
 
c Vertical derivative of virtual temperature
call deriv (dtvdz,tv,'z',z3,x2,y2,nx,ny,nz,mdv)
 
c Stratification
do i=1,nx
do j=1,ny
do k=1,nz
if ((abs(dtvdz(i,j,k)-mdv).gt.eps).and.
> (abs(tv (i,j,k)-mdv).gt.eps))
> then
nsq3(i,j,k) = g/tv(i,j,k) * (dtvdz(i,j,k) + g/cp)
else
nsq3(i,j,k) = mdv
endif
enddo
enddo
enddo
 
end
c -----------------------------------------------------------------
c Calculate potential vorticity
c -----------------------------------------------------------------
 
subroutine calc_pv (pv3,t3,p3,u3,v3,
> z3,x2,y2,f2,nx,ny,nz,mdv)
 
c Calculate potential vorticity <pv3> on the model grid. The grid is
c specified in the horizontal by <xmin,ymin,dx,dy,nx,ny>. The number
c of vertical levels is <nz>. The input field are: potential temperature
c <th3>, horizontal wind <u3> and <v3>, density <rho3>, height <z3>.
c The terms including the vertical velocity are neglected in the calculation
c of the PV.
 
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real pv3 (nx,ny,nz)
real t3 (nx,ny,nz)
real p3 (nx,ny,nz)
real u3 (nx,ny,nz)
real v3 (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
real f2 (nx,ny)
 
real mdv
 
c Physical and numerical parameters
real scale
parameter (scale=1.E6)
real omega
parameter (omega=7.292E-5)
real pi180
parameter (pi180=3.141592654/180.)
real eps
parameter (eps=0.01)
c Auxiliary variables
real dtdz(nx,ny,nz)
real dtdx(nx,ny,nz)
real dtdy(nx,ny,nz)
real dudz(nx,ny,nz)
real dvdz(nx,ny,nz)
real dvdx(nx,ny,nz)
real dudy(nx,ny,nz)
real rho3(nx,ny,nz)
real th3 (nx,ny,nz)
 
integer i,j,k
 
c Calculate density and potential temperature
call calc_rho (rho3,t3,p3,nx,ny,nz,mdv)
call calc_theta (th3 ,t3,p3,nx,ny,nz,mdv)
 
c Calculate needed derivatives
call deriv (dudz, u3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdz, v3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdz,th3,'z',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdx,th3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dtdy,th3,'y',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dvdx, v3,'x',z3,x2,y2,nx,ny,nz,mdv)
call deriv (dudy, u3,'y',z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate potential vorticity
do j=1,ny
do i=1,nx
do k=1,nz
 
c Evaluate PV formula with missing data check
if ((abs(dtdz(i,j,k)-mdv).gt.eps).and.
> (abs(dudz(i,j,k)-mdv).gt.eps).and.
> (abs(dtdy(i,j,k)-mdv).gt.eps).and.
> (abs(dvdz(i,j,k)-mdv).gt.eps).and.
> (abs(rho3(i,j,k)-mdv).gt.eps).and.
> (abs(dtdx(i,j,k)-mdv).gt.eps).and.
> (abs(dvdx(i,j,k)-mdv).gt.eps).and.
> (abs(dudy(i,j,k)-mdv).gt.eps)) then
 
pv3(i,j,k)=scale*1./rho3(i,j,k)*
> ((dvdx(i,j,k)-dudy(i,j,k)+f2(i,j))*dtdz(i,j,k)
> +dudz(i,j,k)*dtdy(i,j,k)
> -dvdz(i,j,k)*dtdx(i,j,k))
else
pv3(i,j,k)=mdv
endif
 
enddo
enddo
enddo
 
end
 
 
c ****************************************************************
c * SUBROUTINE SECTION: GRID HANDLING *
c ****************************************************************
 
c -----------------------------------------------------------------
c Horizontal and vertical derivatives for 3d fields
c -----------------------------------------------------------------
 
subroutine deriv (df,f,direction,
> z3,x2,y2,nx,ny,nz,mdv)
 
c Calculate horizontal and vertical derivatives of the 3d field <f>.
c The direction of the derivative is specified in <direction>
c 'x','y' : Horizontal derivative in x and y direction
c 'p','z','t','m' : Vertical derivative (pressure, height, theta, model)
c The 3d field <z3> specifies the isosurfaces along which the horizontal
c derivatives are calculated or the levels for the vertical derivatives.
 
implicit none
 
c Input and output parameters
integer nx,ny,nz
real df (nx,ny,nz)
real f (nx,ny,nz)
real z3 (nx,ny,nz)
real x2 (nx,ny)
real y2 (nx,ny)
character direction
real mdv
c Numerical and physical parameters
real pi180
parameter (pi180=3.141592654/180.)
real zerodiv
parameter (zerodiv=0.00000001)
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
real vmin,vmax
real scale,lat
real vu,vl,vuvl,vlvu
integer o,u,w,e,n,s
 
c Vertical derivative
if ((direction.eq.'z').or.
> (direction.eq.'th').or.
> (direction.eq.'p').or.
> (direction.eq.'m').and.
> (nz.gt.1)) then
 
do i=1,nx
do j=1,ny
do k=1,nz
o=k+1
if (o.gt.nz) o=nz
u=k-1
if (u.lt.1) u=1
 
if ((abs(f(i,j,o)-mdv).gt.eps).and.
> (abs(f(i,j,u)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps)) then
 
vu = z3(i,j,k)-z3(i,j,o)
vl = z3(i,j,u)-z3(i,j,k)
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
 
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,j,u)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,j,o)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Horizontal derivative in the y direction: 3d
elseif (direction.eq.'y') then
do i=1,nx
do j=1,ny
do k=1,nz
s=j-1
if (s.lt.1) s=1
n=j+1
if (n.gt.ny) n=ny
 
if ((abs(f(i,n,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(i,s,k)-mdv).gt.eps)) then
vu = 1000.*(y2(i,j)-y2(i,n))
vl = 1000.*(y2(i,s)-y2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(i,s,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(i,n,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
 
c Horizontal derivative in the x direction: 3d
elseif (direction.eq.'x') then
 
do i=1,nx
do j=1,ny
do k=1,nz
w=i-1
if (w.lt.1) w=1
e=i+1
if (e.gt.nx) e=nx
 
if ((abs(f(w,j,k)-mdv).gt.eps).and.
> (abs(f(i,j,k)-mdv).gt.eps).and.
> (abs(f(e,j,k)-mdv).gt.eps)) then
vu = 1000.*(x2(i,j)-x2(e,j))
vl = 1000.*(x2(w,j)-x2(i,j))
vuvl = vu/(vl+zerodiv)
vlvu = 1./(vuvl+zerodiv)
df(i,j,k) = 1./(vu+vl)
> * (vuvl*(f(w,j,k)-f(i,j,k))
> + vlvu*(f(i,j,k)-f(e,j,k)))
 
else
df(i,j,k) = mdv
endif
 
enddo
enddo
enddo
c Undefined direction for derivative
else
print*,'Invalid direction of derivative... Stop'
stop
endif
 
end
 
c -----------------------------------------------------------------
c Horizontal filter
c -----------------------------------------------------------------
 
subroutine filt2d (a,af,nx,ny,fil,misdat,
& iperx,ipery,ispol,inpol)
 
c Apply a conservative diffusion operator onto the 2d field a,
c with full missing data checking.
c
c a real inp array to be filtered, dimensioned (nx,ny)
c af real out filtered array, dimensioned (nx,ny), can be
c equivalenced with array a in the calling routine
c f1 real workarray, dimensioned (nx+1,ny)
c f2 real workarray, dimensioned (nx,ny+1)
c fil real inp filter-coeff., 0<afil<=1. Maximum filtering with afil=1
c corresponds to one application of the linear filter.
c misdat real inp missing-data value, a(i,j)=misdat indicates that
c the corresponding value is not available. The
c misdat-checking can be switched off with with misdat=0.
c iperx int inp periodic boundaries in the x-direction (1=yes,0=no)
c ipery int inp periodic boundaries in the y-direction (1=yes,0=no)
c inpol int inp northpole at j=ny (1=yes,0=no)
c ispol int inp southpole at j=1 (1=yes,0=no)
c
c Christoph Schaer, 1993
 
c argument declaration
integer nx,ny
real a(nx,ny),af(nx,ny),fil,misdat
integer iperx,ipery,inpol,ispol
 
c local variable declaration
integer i,j,is
real fh
real f1(nx+1,ny),f2(nx,ny+1)
 
c compute constant fh
fh=0.125*fil
 
c compute fluxes in x-direction
if (misdat.eq.0.) then
do j=1,ny
do i=2,nx
f1(i,j)=a(i-1,j)-a(i,j)
enddo
enddo
else
do j=1,ny
do i=2,nx
if ((a(i,j).eq.misdat).or.(a(i-1,j).eq.misdat)) then
f1(i,j)=0.
else
f1(i,j)=a(i-1,j)-a(i,j)
endif
enddo
enddo
endif
if (iperx.eq.1) then
c do periodic boundaries in the x-direction
do j=1,ny
f1(1,j)=f1(nx,j)
f1(nx+1,j)=f1(2,j)
enddo
else
c set boundary-fluxes to zero
do j=1,ny
f1(1,j)=0.
f1(nx+1,j)=0.
enddo
endif
 
c compute fluxes in y-direction
if (misdat.eq.0.) then
do j=2,ny
do i=1,nx
f2(i,j)=a(i,j-1)-a(i,j)
enddo
enddo
else
do j=2,ny
do i=1,nx
if ((a(i,j).eq.misdat).or.(a(i,j-1).eq.misdat)) then
f2(i,j)=0.
else
f2(i,j)=a(i,j-1)-a(i,j)
endif
enddo
enddo
endif
c set boundary-fluxes to zero
do i=1,nx
f2(i,1)=0.
f2(i,ny+1)=0.
enddo
if (ipery.eq.1) then
c do periodic boundaries in the x-direction
do i=1,nx
f2(i,1)=f2(i,ny)
f2(i,ny+1)=f2(i,2)
enddo
endif
if (iperx.eq.1) then
if (ispol.eq.1) then
c do south-pole
is=(nx-1)/2
do i=1,nx
f2(i,1)=-f2(mod(i-1+is,nx)+1,2)
enddo
endif
if (inpol.eq.1) then
c do north-pole
is=(nx-1)/2
do i=1,nx
f2(i,ny+1)=-f2(mod(i-1+is,nx)+1,ny)
enddo
endif
endif
 
c compute flux-convergence -> filter
if (misdat.eq.0.) then
do j=1,ny
do i=1,nx
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
enddo
enddo
else
do j=1,ny
do i=1,nx
if (a(i,j).eq.misdat) then
af(i,j)=misdat
else
af(i,j)=a(i,j)+fh*(f1(i,j)-f1(i+1,j)+f2(i,j)-f2(i,j+1))
endif
enddo
enddo
endif
end
Property changes:
Added: svn:executable
/tags/1.0/spec/modify_anomaly.f
0,0 → 1,970
PROGRAM modify_anomaly
 
c ******************************************************************************
c * Read the modified and unmodified PV from the R file and *
c * perform some non-standard modifications: (a) Change of amplitude, *
c * (b) Stretching and shrinking along an axis, (c) rotation, or *
c * (d) change in position.
c *
c # modify_anomaly.sh R_20060116_18 shifty=-10,rot=10,stretchy=1.5,rot=-10,shifty=10
c # modify_anomaly.sh R_20060116_18 fac=2
c # modify_anomaly.sh R_20060116_18 cex=-30,cey=-30,rot=20
c * *
c * Michael Sprenger / Spring, Summer 2007 *
c ******************************************************************************
 
implicit none
 
c -----------------------------------------------------------------------------
c Declaration of parameters and variables
c -----------------------------------------------------------------------------
 
c Input/output file and command string
character*80 pvsrcfile
character*80 commandstr
 
c Grid parameters
integer nx,ny,nz
real xmin,ymin,zmin,xmax,ymax,zmax
real dx,dy,dz
real mdv
 
c 3d fields for calculation of qgPV and Ertel's PV
real,allocatable,dimension (:,:,:) :: pv1,pv2,ano
 
c Numerical epsilon
real eps
parameter (eps=0.01)
 
c Parameters for the transformations
real cex,cey ! Centre point for rotation
real angle ! Rotation angle
 
c Auxiliary variables
real zpos
integer i,j,k
integer stat
character*80 varname
integer n
real par
character*80 com
 
c -----------------------------------------------------------------------------
c Preparations
c -----------------------------------------------------------------------------
 
print*,'********************************************************'
print*,'* MODIFY_ANOMALY *'
print*,'********************************************************'
 
c Read parameter file
open(10,file='fort.10')
read(10,*) pvsrcfile
read(10,*) commandstr
close(10)
print*
print*,'Input file : ',trim(pvsrcfile)
print*,'Command : ',trim(commandstr)
print*
 
c Get lat/lon gid parameters from input file
call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
print*,' dx,dy,dz = ',dx,dy,dz
print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
print*,' mdv = ',mdv
print*
 
c Count from 0, not from 1: consistent with <inv_cart.f>.
nx=nx-1
ny=ny-1
nz=nz-1
 
c Allocate memory for modified and non-modified PV
allocate(pv1 (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv1'
allocate(pv2 (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating pv2'
allocate(ano (0:nx,0:ny,0:nz),STAT=stat)
if (stat.ne.0) print*,'error allocating ano'
c Read data from file
varname='PV'
call read_inp (pv1,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
varname='PV_FILT'
call read_inp (pv2,varname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Define the anomaly
do i=0,nx
do j=0,ny
do k=0,nz
if ( (abs(pv1(i,j,k)-mdv).gt.eps).and.
> (abs(pv2(i,j,k)-mdv).gt.eps) ) then
ano(i,j,k)=pv1(i,j,k)-pv2(i,j,k)
else
ano(i,j,k)=0.
endif
enddo
enddo
enddo
 
 
c -------------------------------------------------------------------------------
c Modifications
c -------------------------------------------------------------------------------
 
c Set the default values for parameters
cex = 0.
cey = 0.
angle = 0.
 
c Set the counter for the command string
n=1
 
c Loop over all commands
100 continue
 
c Extract new command/parameter pair; exit if no new command
call next_command(commandstr,n,com,par)
if (com.eq.'nil') goto 200
print*,trim(com),par
 
c Multiply the anomaly by a constant factor
if (com.eq.'fac') then
call mod_factor (ano,par,nx,ny,nz,mdv)
endif
 
c Set the centre point (needed for rotations)
if (com.eq.'cex') then
cex=par
endif
if (com.eq.'cey') then
cey=par
endif
 
c Rotation around the centrre point
if (com.eq.'rot') then
call mod_rotation (ano,par,cex,cey,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
endif
 
c Shift in x or in y direction
if (com.eq.'shiftx') then
call mod_shift (ano,par,0.,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
endif
if (com.eq.'shifty') then
call mod_shift (ano,0.,par,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
endif
 
c Stretch/shrink in x or in y direction
if (com.eq.'stretchx') then
call mod_stretch (ano,par,1.,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
endif
if (com.eq.'stretchy') then
call mod_stretch (ano,1.,par,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
endif
 
 
c Goto next command/parameter pair
goto 100
 
c All commands handled
200 continue
 
c --------------------------------------------------------------------------------
c Write modified fields
c --------------------------------------------------------------------------------
 
c Build the modified PV distribution from the anomaly
do i=0,nx
do j=0,ny
do k=0,nz
if ( (abs(pv1(i,j,k)-mdv).gt.eps).and.
> (abs(ano(i,j,k)-mdv).gt.eps) ) then
pv2(i,j,k)=pv1(i,j,k)-ano(i,j,k)
else
pv2(i,j,k)=mdv
endif
enddo
enddo
enddo
 
c Write result to netcdf file
varname='PV_FILT'
call write_inp (pv2,varname,pvsrcfile,nx,ny,nz)
 
c Write the modified anomaly also to the file
varname='PV_ANOM'
call write_inp (ano,varname,pvsrcfile,nx,ny,nz)
 
end
 
c ********************************************************************************
c * Command handling and transformations *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Extract next command from command string
c --------------------------------------------------------------------------------
subroutine next_command (commandstr,n,com,par)
c Given the command string <commandstr>, extract the next command/parameter pair
c <com,par> starting at position <n> of the command string.
 
implicit none
c Declaration of subroutine parameters
character*80 commandstr
character*80 com
real par
integer n
 
c Auxiliary variables
integer i,j,k
 
c Check whether end of command line reached
if (n.ge.80) then
com='nil'
par=0.
goto 120
endif
 
c Set indices to next next command/parameter pair
i=n
j=n
100 if ( (commandstr(j:j).ne.'=').and.(j.lt.80) ) then
j=j+1
goto 100
endif
k=j+1
110 if ( (commandstr(k:k).ne.',' ).and.
> (commandstr(k:k).ne.';' ).and.
> (commandstr(k:k).ne.' ' ).and.
> (k .lt.80 ) ) then
k=k+1
goto 110
endif
 
c Check whether this is a valid command/parameter pair
if ( ((j-1).lt.i).or.((k-1).lt.(j+1)) ) then
com='nil'
par=0.
goto 120
endif
 
c Extract tzhe command and the parameter
com=commandstr(i:j-1)
read(commandstr(j+1:k-1),*) par
 
c Set the counter to the next command/parameter pair
n=k+1
 
c Exit point
120 continue
 
end
 
c --------------------------------------------------------------------------------
c Multiply the anomaly by a factor
c --------------------------------------------------------------------------------
subroutine mod_factor (field,factor,nx,ny,nz,mdv)
c Multiply the anomaly <field> by a constant factor <factor>. The grid and the
c missing data value are given by <nx,ny,nz,mdv>.
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
real mdv
real factor
c Parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
 
c Do the transformation
do i=0,nx
do j=0,ny
do k=0,nz
if ( (abs(field(i,j,k)-mdv).gt.eps) ) then
field(i,j,k)=factor*field(i,j,k)
endif
enddo
enddo
enddo
end
 
c --------------------------------------------------------------------------------
c Rotate the anomaly
c --------------------------------------------------------------------------------
 
subroutine mod_rotation (field,angle,cex,cey,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
 
c Rotate the anomaly <field> in the horizontal by the angle <angle>. The centre
c for the rotation is given by <cex,cey>, expressed in rotated longitude, latitude.
c The grid and the missing data value are given by <nx,ny,nz,xmin,ymin,dx,dy,mdv>.
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
real xmin,ymin,dx,dy
real mdv
real angle
real cex,cey
c Parameters
real eps
parameter (eps=0.01)
real pi180
parameter (pi180=3.14159/180.)
 
c Auxiliary variables
integer i,j,k
real lon,lat,rlon,rlat
real xmax,ymax
real tmp1(0:nx,0:ny),tmp2(0:nx,0:ny)
 
c Externals
real int2d
external int2d
 
c Maximal grid extension
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
 
c Do the Transformation
do k=0,nz
 
c Copy level to 2d array
do i=0,nx
do j=0,ny
tmp1(i,j)=field(i,j,k)
enddo
enddo
 
c Rotate each grid point
do i=0,nx
do j=0,ny
c Lon/lat coordinates of grid point
lon=xmin+real(i)*dx-cex
lat=ymin+real(j)*dy-cey
 
c Rotation
rlon = cex + lon*cos(angle*pi180) + lat*sin(angle*pi180)
rlat = cey - lon*sin(angle*pi180) + lat*cos(angle*pi180)
 
c Do the interpolation
if ( (rlon.gt.xmin).and.(rlon.lt.xmax).and.
> (rlat.gt.ymin).and.(rlat.lt.ymax) )
> then
tmp2(i,j)=int2d(tmp1,rlon,rlat,
> dx,dy,xmin,ymin,nx,ny,mdv)
else
tmp2(i,j)=0.
endif
enddo
enddo
c Copy 2d array to level
do i=0,nx
do j=0,ny
field(i,j,k)=tmp2(i,j)
enddo
enddo
enddo
 
end
 
c --------------------------------------------------------------------------------
c Shift the anomaly in x and y direction
c --------------------------------------------------------------------------------
 
subroutine mod_shift (field,shiftx,shifty,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
 
c Shift the anomaly <field> in the horizontal by the vector <shiftx,shifty>.
c The grid and the missing data value are given by <nx,ny,nz,xmin,ymin,dx,dy,mdv>.
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
real xmin,ymin,dx,dy
real mdv
real shiftx,shifty
c Parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
real lon,lat,rlon,rlat
real xmax,ymax
real tmp1(0:nx,0:ny),tmp2(0:nx,0:ny)
 
c Externals
real int2d
external int2d
 
c Maximal grid extension
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
 
c Do the Transformation
do k=0,nz
 
c Copy level to 2d array
do i=0,nx
do j=0,ny
tmp1(i,j)=field(i,j,k)
enddo
enddo
 
c Rotate each grid point
do i=0,nx
do j=0,ny
c Lon/lat coordinates of grid point
lon=xmin+real(i)*dx
lat=ymin+real(j)*dy
 
c shifted coordinates
rlon = lon - shiftx
rlat = lat - shifty
 
c Do the interpolation
if ( (rlon.gt.xmin).and.(rlon.lt.xmax).and.
> (rlat.gt.ymin).and.(rlat.lt.ymax) )
> then
tmp2(i,j)=int2d(tmp1,rlon,rlat,
> dx,dy,xmin,ymin,nx,ny,mdv)
else
tmp2(i,j)=0.
endif
enddo
enddo
c Copy 2d array to level
do i=0,nx
do j=0,ny
field(i,j,k)=tmp2(i,j)
enddo
enddo
enddo
 
end
 
c --------------------------------------------------------------------------------
c Stretch/shrink the anomaly in x and y direction
c --------------------------------------------------------------------------------
 
subroutine mod_stretch (field,stretchx,stretchy,
> nx,ny,nz,xmin,ymin,dx,dy,mdv)
 
c Stretch the anomaly <field> in the horizontal by the fatcors <stretchx,stretchy>.
c The grid and the missing data value are given by <nx,ny,nz,xmin,ymin,dx,dy,mdv>.
implicit none
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
real xmin,ymin,dx,dy
real mdv
real stretchx,stretchy
c Parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer i,j,k
real lon,lat,rlon,rlat
real xmax,ymax
real tmp1(0:nx,0:ny),tmp2(0:nx,0:ny)
 
c Externals
real int2d
external int2d
 
c Maximal grid extension
xmax=xmin+real(nx-1)*dx
ymax=ymin+real(ny-1)*dy
 
c Do the Transformation
do k=0,nz
 
c Copy level to 2d array
do i=0,nx
do j=0,ny
tmp1(i,j)=field(i,j,k)
enddo
enddo
 
c Rotate each grid point
do i=0,nx
do j=0,ny
c Lon/lat coordinates of grid point
lon=xmin+real(i)*dx
lat=ymin+real(j)*dy
 
c shifted coordinates
rlon = 1./stretchx * lon
rlat = 1./stretchy * lat
 
c Do the interpolation
if ( (rlon.gt.xmin).and.(rlon.lt.xmax).and.
> (rlat.gt.ymin).and.(rlat.lt.ymax) )
> then
tmp2(i,j)=int2d(tmp1,rlon,rlat,
> dx,dy,xmin,ymin,nx,ny,mdv)
else
tmp2(i,j)=0.
endif
enddo
enddo
c Copy 2d array to level
do i=0,nx
do j=0,ny
field(i,j,k)=tmp2(i,j)
enddo
enddo
enddo
 
end
 
c ------------------------------------------------------------------------
c Two-dimensional interpolation
c ------------------------------------------------------------------------
 
real function int2d(ar,lon,lat,
> dx,dy,xmin,ymin,nx,ny,mdv)
 
c Interpolate the field <ar(nx,ny)> to the position <lon,lat>. The
c grid is specified by <dx,dy,xmin,ymin,nx,ny>.
 
implicit none
 
c Declaration of subroutine paramters
integer nx,ny
real ar(0:nx,0:ny)
real lon,lat
real dx,dy,xmin,ymin
real mdv
 
c Parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
real ri,rj
integer i,j,ir,ju
real frac0i,frac0j,frac1i,frac1j
real tmp,nor
 
c Get index
ri=(lon-xmin)/dx
rj=(lat-ymin)/dy
i=int(ri)
j=int(rj)
if ((i.lt.0).or.(i.gt.nx).or.
> (j.lt.0).or.(j.gt.ny)) then
print*,'lat/lon interpolation not possible....'
stop
endif
c Get inidices of left and upper neighbours
ir=i+1
if (ir.gt.nx) ir=nx
ju=j+1
if (ju.gt.ny) ju=ny
 
c Get the weights for the bilinear interpolation
frac0i=ri-float(i)
frac0j=rj-float(j)
frac1i=1.-frac0i
frac1j=1.-frac0j
 
c Bilinear interpolation with missing data check
tmp=0.
nor=0.
if ( (abs(ar(i ,j )-mdv).gt.eps) ) then
tmp = tmp + ar(i ,j ) * frac1i * frac1j
nor = nor + frac1i * frac1j
endif
if ( (abs(ar(i ,ju)-mdv).gt.eps) ) then
tmp = tmp + ar(i ,ju) * frac1i * frac0j
nor = nor + frac1i * frac0j
endif
if ( (abs(ar(ir,j )-mdv).gt.eps) ) then
tmp = tmp + ar(ir,j ) * frac0i * frac1j
nor = nor + frac0i * frac1j
endif
if ( (abs(ar(ir,ju)-mdv).gt.eps) ) then
tmp = tmp + ar(ir,ju) * frac0i * frac0j
nor = nor + frac0i * frac0j
endif
 
c Return result
int2d=tmp/nor
 
end
 
c ********************************************************************************
c * NETCDF INPUT AND OUTPUT *
c ********************************************************************************
 
c --------------------------------------------------------------------------------
c Write input field to netcdf
c --------------------------------------------------------------------------------
 
SUBROUTINE write_inp (field,fieldname,pvsrcfile,nx,ny,nz)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field (0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
 
c Auxiliary variables
integer cdfid,stat
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real tmp(0:nx,0:ny,0:nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Get grid parameters from PV
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname='PV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Save variables (write definition, if necessary)
call cdfwopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
isok=0
varname=fieldname
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) then
call putdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
endif
call putdat(cdfid,varname,time(1),0,field,stat)
print*,'W ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
return
 
c Exception handling
998 print*,'Write_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
 
c --------------------------------------------------------------------------------
c Read input fields for reference profile
c --------------------------------------------------------------------------------
 
SUBROUTINE read_inp (field,fieldname,pvsrcfile,
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv)
 
c Read <fieldname> from netcdf file <pvsrcfile> into <field>. The grid is specified
c by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed whether the input
c files are consitent with this grid. The missing data value is set to <mdv>.
 
implicit none
 
c Declaration of subroutine parameters
integer nx,ny,nz
real field(0:nx,0:ny,0:nz)
character*80 fieldname
character*80 pvsrcfile
real dx,dy,dz,xmin,ymin,zmin
real mdv
 
c Numerical and physical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,stat,cdfid99
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
integer ndimin,outid,i,j,k
real tmp(nx,ny,nz)
integer ntimes
real time(200)
integer nvars
character*80 vnam(100),varname
integer isok
 
c Open the input netcdf file
call cdfopn(pvsrcfile,cdfid,stat)
if (stat.ne.0) goto 998
 
c Check whether needed variables are on file
call getvars(cdfid,nvars,vnam,stat)
if (stat.ne.0) goto 998
isok=0
varname=trim(fieldname)
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
 
c Get the grid parameters from theta
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
time(1)=0.
call gettimes(cdfid,time,ntimes,stat)
if (stat.ne.0) goto 998
 
c Check whether grid parameters are consistent
if ( (vardim(1).ne.(nx+1)).or.
> (vardim(2).ne.(ny+1)).or.
> (vardim(3).ne.(nz+1)).or.
> (abs(varmin(1)-xmin).gt.eps).or.
> (abs(varmin(2)-ymin).gt.eps).or.
> (abs(varmin(3)-zmin).gt.eps).or.
> (abs((varmax(1)-varmin(1))/real(vardim(1)-1)-dx).gt.eps).or.
> (abs((varmax(2)-varmin(2))/real(vardim(2)-1)-dy).gt.eps).or.
> (abs((varmax(3)-varmin(3))/real(vardim(3)-1)-dz).gt.eps) )
>then
print*,'Input grid inconsitency...'
print*,' Nx = ',vardim(1),nx+1
print*,' Ny = ',vardim(2),ny+1
print*,' Nz = ',vardim(3),nz+1
print*,' Varminx = ',varmin(1),xmin
print*,' Varminy = ',varmin(2),ymin
print*,' Varminz = ',varmin(3),zmin
print*,' Dx = ',(varmax(1)-varmin(1))/real(nx-1),dx
print*,' Dy = ',(varmax(2)-varmin(2))/real(ny-1),dy
print*,' Dz = ',(varmax(3)-varmin(3))/real(nz-1),dz
goto 998
endif
 
c Load variables
call getdef(cdfid,varname,ndimin,misdat,vardim,
> varmin,varmax,stag,stat)
if (stat.ne.0) goto 998
call getdat(cdfid,varname,time(1),0,field,stat)
print*, 'R ',trim(varname),' ',trim(pvsrcfile)
if (stat.ne.0) goto 998
 
c Close input netcdf file
call clscdf(cdfid,stat)
if (stat.ne.0) goto 998
 
c Set missing data value to <mdv>
do i=1,nx
do j=1,ny
do k=1,nz
if (abs(field(i,j,k)-misdat).lt.eps) then
field(i,j,k)=mdv
endif
enddo
enddo
enddo
 
return
 
c Exception handling
998 print*,'Read_Inp: Problem with input netcdf file... Stop'
stop
 
end
 
c --------------------------------------------------------------------------------
c Check whether variable is found on netcdf file
c --------------------------------------------------------------------------------
 
subroutine check_varok (isok,varname,varlist,nvars)
 
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
 
implicit none
 
c Declaraion of subroutine parameters
integer isok
integer nvars
character*80 varname
character*80 varlist(nvars)
 
c Auxiliary variables
integer i
 
c Main
do i=1,nvars
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
enddo
 
end
 
c --------------------------------------------------------------------------------
c Get grid parameters
c --------------------------------------------------------------------------------
 
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
> pvsrcfile)
 
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
c The grid parameters are
c nx,ny,nz : Number of grid points in x, y and z direction
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
c dx,dy,dz : Horizontal and vertical resolution
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
c the grid paramters are transformed from lon/lat to distance (in meters)
 
implicit none
 
c Declaration of subroutine parameters
character*80 pvsrcfile
integer nx,ny,nz
real dx,dy,dz
real xmin,ymin,zmin,xmax,ymax,zmax
real mdv
 
c Numerical epsilon and other physical/geoemtrical parameters
real eps
parameter (eps=0.01)
 
c Auxiliary variables
integer cdfid,cstid
integer ierr
character*80 vnam(100),varname
integer nvars
integer isok
integer vardim(4)
real misdat
real varmin(4),varmax(4),stag(4)
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
real dh
character*80 csn
integer ndim
integer i
 
c Get all grid parameters
call cdfopn(pvsrcfile,cdfid,ierr)
if (ierr.ne.0) goto 998
call getvars(cdfid,nvars,vnam,ierr)
if (ierr.ne.0) goto 998
isok=0
varname='PV'
call check_varok(isok,varname,vnam,nvars)
if (isok.eq.0) goto 998
call getcfn(cdfid,csn,ierr)
if (ierr.ne.0) goto 998
call cdfopn(csn,cstid,ierr)
if (ierr.ne.0) goto 998
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
> stag,ierr)
if (ierr.ne.0) goto 998
nx=vardim(1)
ny=vardim(2)
nz=vardim(3)
xmin=varmin(1)
ymin=varmin(2)
zmin=varmin(3)
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
if (ierr.ne.0) goto 998
call getgrid(cstid,dx,dy,ierr)
if (ierr.ne.0) goto 998
xmax=varmax(1)
ymax=varmax(2)
zmax=varmax(3)
dz=(zmax-zmin)/real(nz-1)
call clscdf(cstid,ierr)
if (ierr.ne.0) goto 998
call clscdf(cdfid,ierr)
if (ierr.ne.0) goto 998
 
c Check whether the grid is equallay spaced in the vertical
do i=1,nz-1
dh=aklev(i+1)-aklev(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklev: Vertical grid must be equally spaced... Stop'
print*,(aklev(i),i=1,nz)
stop
endif
dh=aklay(i+1)-aklay(i)
if (abs(dh-dz).gt.eps) then
print*,'Aklay: Vertical grid must be equally spaced... Stop'
print*,(aklay(i),i=1,nz)
stop
endif
enddo
 
c Set missing data value
mdv=misdat
 
return
 
c Exception handling
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
stop
 
end
Property changes:
Added: svn:executable