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michaesp |
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PROGRAM inv_cart
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c ********************************************************************************
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c * CALCULATES FOR A PV AND THETA DISTRIBUTION OTHER PROGNOSTIC FIELDS BY *
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c * MEANS OF A PV INVERSION *
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c * *
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c * Rene Fehlmann 1994 / Code re-organization: Michael Sprenger, 2006 *
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c ********************************************************************************
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c --------------------------------------------------------------------------------
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c Declaration of variables, parameters, externals and common blocks
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c --------------------------------------------------------------------------------
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implicit none
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c Grid parameters
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integer nx,ny,nz
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real xmin,ymin,zmin,xmax,ymax,zmax
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real dx,dy,dz
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real deltax,deltay,deltaz
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real mdv
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real, allocatable,dimension (:,:) :: coriol
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c Reference state
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real, allocatable,dimension (:) :: nsqref
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real, allocatable,dimension (:) :: thetaref
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real, allocatable,dimension (:) :: rhoref
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real, allocatable,dimension (:) :: pressref
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real, allocatable,dimension (:) :: zref
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C Boundary conditions
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real, allocatable,dimension (:,:) :: thetatop
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real, allocatable,dimension (:,:) :: thetabot
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real, allocatable,dimension (:,:) :: ua
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real, allocatable,dimension (:,:) :: ub
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real, allocatable,dimension (:,:) :: va
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real, allocatable,dimension (:,:) :: vb
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c Potentiual vorticity and stream function
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real, allocatable,dimension (:,:,:) :: psi
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real, allocatable,dimension (:,:,:) :: pv
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c Auxiliary arrays for numerics
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real, allocatable,dimension (:,:,:) :: a
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real, allocatable,dimension (:,:,:) :: b
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real, allocatable,dimension (:,:,:) :: c
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c Input parameters
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character*80 pvsrcfile
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character*80 referfile
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c Auxiliary variables
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integer i,j,k
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integer stat
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c --------------------------------------------------------------------------------
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c Preparations
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c --------------------------------------------------------------------------------
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print*,'********************************************************'
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print*,'* INV_CART *'
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print*,'********************************************************'
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c Read parameter file
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open(10,file='fort.10')
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read(10,*) pvsrcfile
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read(10,*) referfile
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close(10)
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print*
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print*,trim(pvsrcfile)
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c Get lat/lon gid parameters from input file
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call read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
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> pvsrcfile)
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print*
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print*,'Read_Dim: nx,ny,nz = ',nx,ny,nz
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print*,' dx,dy,dz = ',dx,dy,dz
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print*,' xmin,ymin,zmin = ',xmin,ymin,zmin
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print*,' mdv = ',mdv
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print*
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c Count from 0, not from 1
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nx=nx-1
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ny=ny-1
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nz=nz-1
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c Allocate memory for boundary conditions
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allocate(thetatop(0:nx,0:ny),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array thetatop ***'
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allocate(thetabot(0:nx,0:ny),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array thetabot ***'
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allocate(ua(0:nx,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array ua ***'
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allocate(ub(0:nx,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array ub ***'
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allocate(va(0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array va ***'
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allocate(vb(0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array vb ***'
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c Allocate memory for 3d PV and stream function
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allocate(psi(0:nx,0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array psi ***'
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allocate(pv(0:nx,0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array pv ***'
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c Alllocate memory for matrix elements for inversion operator
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allocate(a(0:nx,0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array a ***'
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allocate(b(0:nx,0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array b ***'
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allocate(c(0:nx,0:ny,0:nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array c ***'
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c Allocate memory for reference profile
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allocate(nsqref(0:2*nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array nsqref ***'
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allocate(thetaref(0:2*nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array thetaref ***'
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allocate(rhoref(0:2*nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array rhoref ***'
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allocate(pressref(0:2*nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array pressref ***'
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allocate(zref(0:2*nz),stat=stat)
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if (stat.ne.0) print*,'*** error allocating array zref ***'
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c Allocate memory for Coriolis parameter
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allocate(coriol(0:nx,0:ny),STAT=stat)
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if (stat.ne.0) print*,'error allocating coriol'
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c --------------------------------------------------------------------------------
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c Input
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c --------------------------------------------------------------------------------
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c Read reference profile and grid parameters
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call read_ref (nsqref,rhoref,thetaref,pressref,zref,
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> nx,ny,nz,deltax,deltay,deltaz,coriol,
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> referfile)
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deltax=1000.*deltax
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deltay=1000.*deltay
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c Read input fields from netcdf
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call read_inp (pv,thetabot,thetatop,ua,ub,va,vb,
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> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,
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> pvsrcfile)
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c --------------------------------------------------------------------------------
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c Perform the inversion
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c --------------------------------------------------------------------------------
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C Init matrix elements for inversion
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call matrixel(a,b,c,coriol,nx,ny,nz,nsqref,rhoref,
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> deltax,deltay,deltaz)
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c Inversion
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call sor(psi,nsqref,thetatop,thetabot,thetaref,rhoref,coriol,
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> pv,ua,ub,va,vb,a,b,c,nx,ny,nz,deltax,deltay,deltaz)
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c --------------------------------------------------------------------------------
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c Output
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c --------------------------------------------------------------------------------
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c Write output to netcdf
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print*
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call write_out (psi,thetabot,thetatop,ua,ub,va,vb,
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> nx,ny,nz,deltax,deltay,deltaz,
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> coriol,thetaref,rhoref,pressref,pvsrcfile)
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END
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c ********************************************************************************
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c * NETCDF AND ASCII INPUT AND OUTPUT *
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c ********************************************************************************
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c --------------------------------------------------------------------------------
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c Output to netcdf file
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c --------------------------------------------------------------------------------
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SUBROUTINE write_out (psi,thetabot,thetatop,ua,ub,va,vb,nx,ny,nz,
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> dx,dy,dz,coriol,thetaref,rhoref,pref,
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> pvsrcfile)
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c Write the result of the inversion to output netcdf
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c
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c psi : streamm function as calculated from inversion
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c thetabot,thetatop : potential temperature at lower and upper boundary
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c ua,ub : Zonal wind at western and eastern boundary
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c va,vb : Meridional wind at southern and northern boundary
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c nx,ny,nz : Grid dimension in x, y and z direction
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c dx,dy,dz : Grid resolution
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c coriol : Coriolis parameter
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c thetaref : Reference profile of potential temperature
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c rhoref : Reference profile of density
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c pref : Reference profile of pressure
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c pvsrcfile : Name of the output netcdf file
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implicit none
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c Declaration of subroutine parameters
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integer nx,ny,nz
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real psi(0:nx,0:ny,0:nz)
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real thetatop(0:nx,0:ny)
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real thetabot(0:nx,0:ny)
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real ua(0:nx,0:nz)
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real ub(0:nx,0:nz)
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real va(0:ny,0:nz)
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real vb(0:ny,0:nz)
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character*(30) pvsrcfile
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real dx,dy,dz
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real thetaref(0:2*nz)
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real rhoref(0:2*nz)
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real pref(0:2*nz)
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real coriol(0:nx,0:ny)
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c Numerical and physical parameters
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real eps
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parameter (eps=0.01)
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real g
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parameter (g=9.81)
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real preunit
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parameter (preunit=0.01)
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real kappa
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parameter (kappa=0.286)
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c Auxiliary variables
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integer cdfid,stat
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integer vardim(4)
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real misdat
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integer ndimin
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real varmin(4),varmax(4),stag(4)
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integer i,j,k,nf1,jj,kk
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real tmp(0:nx,0:ny,0:nz)
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real pr (0:nx,0:ny,0:nz)
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real th (0:nx,0:ny,0:nz)
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integer ntimes
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real time(200)
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character*80 vnam(100),varname
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integer nvars
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integer isok,ierr
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real meanpsi,meancnt
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c Get grid description
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call cdfopn(pvsrcfile,cdfid,stat)
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if (stat.ne.0) goto 997
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call getvars(cdfid,nvars,vnam,stat)
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if (stat.ne.0) goto 997
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isok=0
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varname='QGPV'
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call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) goto 997
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call getdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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time(1)=0.
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call gettimes(cdfid,time,ntimes,stat)
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if (stat.ne.0) goto 997
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call clscdf(cdfid,stat)
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if (stat.ne.0) goto 997
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c Open output netcdf file
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call cdfwopn(pvsrcfile,cdfid,stat)
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if (stat.ne.0) goto 997
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c Create the variable if necessary
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call getvars(cdfid,nvars,vnam,stat)
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if (stat.ne.0) goto 997
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isok=0
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varname='PSI'
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call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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call putdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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isok=0
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varname='U'
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281 |
call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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call putdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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isok=0
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varname='V'
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call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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call putdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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isok=0
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varname='TH'
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297 |
call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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call putdef(cdfid,varname,ndimin,misdat,vardim,
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300 |
> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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isok=0
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varname='T'
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call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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call putdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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isok=0
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varname='P'
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call check_varok(isok,varname,vnam,nvars)
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if (isok.eq.0) then
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315 |
call putdef(cdfid,varname,ndimin,misdat,vardim,
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> varmin,varmax,stag,stat)
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if (stat.ne.0) goto 997
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endif
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c Write stream function
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varname='PSI'
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call putdat(cdfid,varname,time(1),0,psi,ierr)
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if (stat.ne.0) goto 997
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print*,'W PSI ',trim(pvsrcfile)
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c Calculate and write velocity U: keep southern and northern boundary
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327 |
do k=0,nz
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328 |
do i=0,nx
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329 |
do j=1,ny-1
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tmp(i,j,k)=(psi(i,j-1,k)-psi(i,j+1,k))/
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> (2.*dy*coriol(i,j))
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enddo
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tmp(i,0,k) =ua(i,k)
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tmp(i,ny,k)=ub(i,k)
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enddo
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enddo
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varname='U'
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call putdat(cdfid,varname,time(1),0,tmp,ierr)
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339 |
if (stat.ne.0) goto 997
|
|
|
340 |
print*,'W U ',trim(pvsrcfile)
|
|
|
341 |
|
|
|
342 |
C Calculate and write velocity V: keep western and eastern boundary
|
|
|
343 |
do k=0,nz
|
|
|
344 |
do j=0,ny
|
|
|
345 |
do i=1,nx-1
|
|
|
346 |
tmp(i,j,k)=(psi(i+1,j,k)-psi(i-1,j,k))/
|
|
|
347 |
> (2.*dx*coriol(i,j))
|
|
|
348 |
enddo
|
|
|
349 |
tmp(0,j,k)=va(j,k)
|
|
|
350 |
tmp(nx,j,k)=vb(j,k)
|
|
|
351 |
enddo
|
|
|
352 |
enddo
|
|
|
353 |
varname='V'
|
|
|
354 |
call putdat(cdfid,varname,time(1),0,tmp,ierr)
|
|
|
355 |
if (stat.ne.0) goto 997
|
|
|
356 |
print*,'W V ',trim(pvsrcfile)
|
|
|
357 |
|
|
|
358 |
c Calculate and write potential temperature: keep lower and upper boundary
|
|
|
359 |
c Potential temperature is needed for calculation of temperature: keep it
|
|
|
360 |
do i=0,nx
|
|
|
361 |
do j=0,ny
|
|
|
362 |
th(i,j,0)=thetabot(i,j)
|
|
|
363 |
do k=1,nz-1
|
|
|
364 |
th(i,j,k)=thetaref(2*k)*
|
|
|
365 |
> (psi(i,j,k+1)-psi(i,j,k-1))/(2.*dz*g)
|
|
|
366 |
|
|
|
367 |
enddo
|
|
|
368 |
th(i,j,nz)=thetatop(i,j)
|
|
|
369 |
enddo
|
|
|
370 |
enddo
|
|
|
371 |
varname='TH'
|
|
|
372 |
call putdat(cdfid,varname,time(1),0,th,ierr)
|
|
|
373 |
if (stat.ne.0) goto 997
|
|
|
374 |
print*,'W TH ',trim(pvsrcfile)
|
|
|
375 |
|
|
|
376 |
c Calculate and write pressure: The pressure is directly proportional to the
|
|
|
377 |
c streamfunction. But the streamfunction is determined only up to an additive
|
|
|
378 |
c constant. Shift the streamfunction in such a way that it vanish in the mean
|
|
|
379 |
c on the boundaries. Pressure is needed for calculation of temperature: keep it
|
|
|
380 |
meanpsi=0.
|
|
|
381 |
meancnt=0.
|
|
|
382 |
do i=0,nx
|
|
|
383 |
do j=0,ny
|
|
|
384 |
meanpsi=meanpsi+psi(i,j,0)+psi(i,j,nz)
|
|
|
385 |
meancnt=meancnt+2
|
|
|
386 |
enddo
|
|
|
387 |
enddo
|
|
|
388 |
do i=0,nx
|
|
|
389 |
do k=0,nz
|
|
|
390 |
meanpsi=meanpsi+psi(i,0,k)+psi(i,ny,k)
|
|
|
391 |
meancnt=meancnt+2
|
|
|
392 |
enddo
|
|
|
393 |
enddo
|
|
|
394 |
do j=0,ny
|
|
|
395 |
do k=0,nz
|
|
|
396 |
meanpsi=meanpsi+psi(0,j,k)+psi(nx,j,k)
|
|
|
397 |
meancnt=meancnt+2
|
|
|
398 |
enddo
|
|
|
399 |
enddo
|
|
|
400 |
meanpsi=meanpsi/meancnt
|
|
|
401 |
do i=0,nx
|
|
|
402 |
do j=0,ny
|
|
|
403 |
do k=0,nz
|
|
|
404 |
kk=2*k
|
|
|
405 |
pr(i,j,k)=preunit*rhoref(kk)*(psi(i,j,k)-meanpsi)
|
|
|
406 |
enddo
|
|
|
407 |
enddo
|
|
|
408 |
enddo
|
|
|
409 |
varname='P'
|
|
|
410 |
call putdat(cdfid,varname,time(1),0,pr,ierr)
|
|
|
411 |
if (stat.ne.0) goto 997
|
|
|
412 |
print*,'W P ',trim(pvsrcfile)
|
|
|
413 |
|
|
|
414 |
c Calculate and write temperature
|
|
|
415 |
do i=0,nx
|
|
|
416 |
do j=0,ny
|
|
|
417 |
do k=0,nz
|
|
|
418 |
kk=2*k
|
|
|
419 |
tmp(i,j,k)=((pref(kk)/1000.)**kappa) *
|
|
|
420 |
> (th(i,j,k)+kappa*thetaref(kk)*pr(i,j,k)/pref(kk))
|
|
|
421 |
enddo
|
|
|
422 |
enddo
|
|
|
423 |
enddo
|
|
|
424 |
varname='T'
|
|
|
425 |
call putdat(cdfid,varname,time(1),0,tmp,ierr)
|
|
|
426 |
if (stat.ne.0) goto 997
|
|
|
427 |
print*,'W T ',trim(pvsrcfile)
|
|
|
428 |
|
|
|
429 |
c Close output netcdf file
|
|
|
430 |
call clscdf(cdfid,stat)
|
|
|
431 |
if (stat.ne.0) goto 997
|
|
|
432 |
|
|
|
433 |
return
|
|
|
434 |
|
|
|
435 |
c Exception handling
|
|
|
436 |
997 print*,'Problem with output netcdf file... Stop'
|
|
|
437 |
stop
|
|
|
438 |
|
|
|
439 |
end
|
|
|
440 |
|
|
|
441 |
|
|
|
442 |
c --------------------------------------------------------------------------------
|
|
|
443 |
c Read the reference file
|
|
|
444 |
c --------------------------------------------------------------------------------
|
|
|
445 |
|
|
|
446 |
SUBROUTINE read_ref (nsqref,rhoref,thetaref,pressref,zref,
|
|
|
447 |
> nx,ny,nz,deltax,deltay,deltaz,coriol,
|
|
|
448 |
> pvsrcfile)
|
|
|
449 |
|
|
|
450 |
c Read the reference profile from file
|
|
|
451 |
c
|
|
|
452 |
c thetaref : Reference potential temperature (K)
|
|
|
453 |
c pressref : Reference pressure (Pa)
|
|
|
454 |
c rhoref : Reference density (kg/m^3)
|
|
|
455 |
c nsqref : Stratification (s^-1)
|
|
|
456 |
c zref : Reference height (m)
|
|
|
457 |
c nx,nny,nz : Grid dimension in x,y,z direction
|
|
|
458 |
c deltax,deltay,deltaz : Grid spacings used for calculations (m)
|
|
|
459 |
c coriol : Coriolis parameter (s^-1)
|
|
|
460 |
c pvsrcfile : Input file
|
|
|
461 |
|
|
|
462 |
implicit none
|
|
|
463 |
|
|
|
464 |
c Declaration of subroutine parameters
|
|
|
465 |
integer nx,ny,nz
|
|
|
466 |
real nsqref (0:2*nz)
|
|
|
467 |
real thetaref(0:2*nz)
|
|
|
468 |
real rhoref (0:2*nz)
|
|
|
469 |
real pressref(0:2*nz)
|
|
|
470 |
real zref (0:2*nz)
|
|
|
471 |
real deltax,deltay,deltaz
|
|
|
472 |
real coriol (0:nx,0:ny)
|
|
|
473 |
character*80 pvsrcfile
|
|
|
474 |
|
|
|
475 |
c Numerical and physical parameters
|
|
|
476 |
real eps
|
|
|
477 |
parameter (eps=0.01)
|
|
|
478 |
|
|
|
479 |
c Auxiliary variables
|
|
|
480 |
integer cdfid,stat
|
|
|
481 |
integer vardim(4)
|
|
|
482 |
real misdat
|
|
|
483 |
integer ndimin
|
|
|
484 |
real varmin(4),varmax(4),stag(4)
|
|
|
485 |
integer i,j,k,nf1
|
|
|
486 |
integer ntimes
|
|
|
487 |
real time(200)
|
|
|
488 |
character*80 vnam(100),varname
|
|
|
489 |
integer nvars
|
|
|
490 |
integer isok,ierr
|
|
|
491 |
real x(0:nx,0:ny),y(0:nx,0:ny)
|
|
|
492 |
real mean,count
|
|
|
493 |
|
|
|
494 |
c Get grid description from topography
|
|
|
495 |
call cdfopn(pvsrcfile,cdfid,stat)
|
|
|
496 |
if (stat.ne.0) goto 997
|
|
|
497 |
call getvars(cdfid,nvars,vnam,stat)
|
|
|
498 |
if (stat.ne.0) goto 997
|
|
|
499 |
isok=0
|
|
|
500 |
varname='ORO'
|
|
|
501 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
502 |
if (isok.eq.0) goto 997
|
|
|
503 |
call getdef(cdfid,varname,ndimin,misdat,vardim,
|
|
|
504 |
> varmin,varmax,stag,stat)
|
|
|
505 |
if (stat.ne.0) goto 997
|
|
|
506 |
time(1)=0.
|
|
|
507 |
call gettimes(cdfid,time,ntimes,stat)
|
|
|
508 |
if (stat.ne.0) goto 997
|
|
|
509 |
call clscdf(cdfid,stat)
|
|
|
510 |
if (stat.ne.0) goto 997
|
|
|
511 |
|
|
|
512 |
c Open output netcdf file
|
|
|
513 |
call cdfopn(pvsrcfile,cdfid,stat)
|
|
|
514 |
if (stat.ne.0) goto 997
|
|
|
515 |
|
|
|
516 |
c Create the variable if necessary
|
|
|
517 |
call getvars(cdfid,nvars,vnam,stat)
|
|
|
518 |
if (stat.ne.0) goto 997
|
|
|
519 |
|
|
|
520 |
c Read data from netcdf file
|
|
|
521 |
isok=0
|
|
|
522 |
varname='NSQREF'
|
|
|
523 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
524 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
525 |
if (isok.eq.0) goto 997
|
|
|
526 |
call getdat(cdfid,varname,time(1),0,nsqref,stat)
|
|
|
527 |
if (stat.ne.0) goto 997
|
|
|
528 |
|
|
|
529 |
isok=0
|
|
|
530 |
varname='RHOREF'
|
|
|
531 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
532 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
533 |
if (isok.eq.0) goto 997
|
|
|
534 |
call getdat(cdfid,varname,time(1),0,rhoref,stat)
|
|
|
535 |
if (stat.ne.0) goto 997
|
|
|
536 |
|
|
|
537 |
isok=0
|
|
|
538 |
varname='THETAREF'
|
|
|
539 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
540 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
541 |
if (isok.eq.0) goto 997
|
|
|
542 |
call getdat(cdfid,varname,time(1),0,thetaref,stat)
|
|
|
543 |
if (stat.ne.0) goto 997
|
|
|
544 |
|
|
|
545 |
isok=0
|
|
|
546 |
varname='PREREF'
|
|
|
547 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
548 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
549 |
if (isok.eq.0) goto 997
|
|
|
550 |
call getdat(cdfid,varname,time(1),0,pressref,stat)
|
|
|
551 |
if (stat.ne.0) goto 997
|
|
|
552 |
|
|
|
553 |
isok=0
|
|
|
554 |
varname='ZREF'
|
|
|
555 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
556 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
557 |
if (isok.eq.0) goto 997
|
|
|
558 |
call getdat(cdfid,varname,time(1),0,zref,stat)
|
|
|
559 |
if (stat.ne.0) goto 997
|
|
|
560 |
|
|
|
561 |
isok=0
|
|
|
562 |
varname='CORIOL'
|
|
|
563 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
564 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
565 |
if (isok.eq.0) goto 997
|
|
|
566 |
call getdat(cdfid,varname,time(1),0,coriol,stat)
|
|
|
567 |
if (stat.ne.0) goto 997
|
|
|
568 |
|
|
|
569 |
isok=0
|
|
|
570 |
varname='X'
|
|
|
571 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
572 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
573 |
if (isok.eq.0) goto 997
|
|
|
574 |
call getdat(cdfid,varname,time(1),0,x,stat)
|
|
|
575 |
if (stat.ne.0) goto 997
|
|
|
576 |
|
|
|
577 |
isok=0
|
|
|
578 |
varname='Y'
|
|
|
579 |
print*,'R ',trim(varname),' ',trim(pvsrcfile)
|
|
|
580 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
581 |
if (isok.eq.0) goto 997
|
|
|
582 |
call getdat(cdfid,varname,time(1),0,y,stat)
|
|
|
583 |
if (stat.ne.0) goto 997
|
|
|
584 |
|
|
|
585 |
c Close netcdf file
|
|
|
586 |
call clscdf(cdfid,stat)
|
|
|
587 |
if (stat.ne.0) goto 997
|
|
|
588 |
|
|
|
589 |
c Determine the grid spacings <deltax, deltay, deltaz>
|
|
|
590 |
mean=0.
|
|
|
591 |
count=0.
|
|
|
592 |
do i=1,nx
|
|
|
593 |
do j=0,ny
|
|
|
594 |
mean=mean+abs(x(i,j)-x(i-1,j))
|
|
|
595 |
count=count+1.
|
|
|
596 |
enddo
|
|
|
597 |
enddo
|
|
|
598 |
deltax=mean/count
|
|
|
599 |
|
|
|
600 |
mean=0.
|
|
|
601 |
count=0.
|
|
|
602 |
do j=1,ny
|
|
|
603 |
do i=0,nx
|
|
|
604 |
mean=mean+abs(y(i,j)-y(i,j-1))
|
|
|
605 |
count=count+1.
|
|
|
606 |
enddo
|
|
|
607 |
enddo
|
|
|
608 |
deltay=mean/count
|
|
|
609 |
|
|
|
610 |
mean=0.
|
|
|
611 |
count=0.
|
|
|
612 |
do k=1,nz-1
|
|
|
613 |
mean=mean+abs(zref(k+1)-zref(k-1))
|
|
|
614 |
count=count+1.
|
|
|
615 |
enddo
|
|
|
616 |
deltaz=mean/count
|
|
|
617 |
|
|
|
618 |
return
|
|
|
619 |
|
|
|
620 |
c Exception handling
|
|
|
621 |
997 print*,'Read_Ref: Problem with input netcdf file... Stop'
|
|
|
622 |
stop
|
|
|
623 |
|
|
|
624 |
end
|
|
|
625 |
|
|
|
626 |
|
|
|
627 |
c --------------------------------------------------------------------------------
|
|
|
628 |
c Get grid parameters
|
|
|
629 |
c --------------------------------------------------------------------------------
|
|
|
630 |
|
|
|
631 |
subroutine read_dim (nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,mdv,
|
|
|
632 |
> pvsrcfile)
|
|
|
633 |
|
|
|
634 |
c Get the grid parameters from the variable <THETA> on the input file <pvsrcfile>.
|
|
|
635 |
c The grid parameters are
|
|
|
636 |
c nx,ny,nz : Number of grid points in x, y and z direction
|
|
|
637 |
c xmin,ymin,zmin : Minimum domain coordinates in x, y and z direction
|
|
|
638 |
c xmax,ymax,zmax : Maximal domain coordinates in x, y and z direction
|
|
|
639 |
c dx,dy,dz : Horizontal and vertical resolution
|
|
|
640 |
c Additionally, it is checked whether the vertical grid is equally spaced. If ok,
|
|
|
641 |
c the grid paramters are transformed from lon/lat to distance (in meters)
|
|
|
642 |
|
|
|
643 |
implicit none
|
|
|
644 |
|
|
|
645 |
c Declaration of subroutine parameters
|
|
|
646 |
character*80 pvsrcfile
|
|
|
647 |
integer nx,ny,nz
|
|
|
648 |
real dx,dy,dz
|
|
|
649 |
real xmin,ymin,zmin,xmax,ymax,zmax
|
|
|
650 |
real mdv
|
|
|
651 |
|
|
|
652 |
c Numerical epsilon and other physical/geoemtrical parameters
|
|
|
653 |
real eps
|
|
|
654 |
parameter (eps=0.01)
|
|
|
655 |
|
|
|
656 |
c Auxiliary variables
|
|
|
657 |
integer cdfid,cstid
|
|
|
658 |
integer ierr
|
|
|
659 |
character*80 vnam(100),varname
|
|
|
660 |
integer nvars
|
|
|
661 |
integer isok
|
|
|
662 |
integer vardim(4)
|
|
|
663 |
real misdat
|
|
|
664 |
real varmin(4),varmax(4),stag(4)
|
|
|
665 |
real aklev(1000),bklev(1000),aklay(1000),bklay(1000)
|
|
|
666 |
real dh
|
|
|
667 |
character*80 csn
|
|
|
668 |
integer ndim
|
|
|
669 |
integer i
|
|
|
670 |
|
|
|
671 |
c Get all grid parameters
|
|
|
672 |
call cdfopn(pvsrcfile,cdfid,ierr)
|
|
|
673 |
if (ierr.ne.0) goto 998
|
|
|
674 |
call getvars(cdfid,nvars,vnam,ierr)
|
|
|
675 |
if (ierr.ne.0) goto 998
|
|
|
676 |
isok=0
|
|
|
677 |
varname='QGPV'
|
|
|
678 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
679 |
if (isok.eq.0) goto 998
|
|
|
680 |
call getcfn(cdfid,csn,ierr)
|
|
|
681 |
if (ierr.ne.0) goto 998
|
|
|
682 |
call cdfopn(csn,cstid,ierr)
|
|
|
683 |
if (ierr.ne.0) goto 998
|
|
|
684 |
call getdef(cdfid,varname,ndim,misdat,vardim,varmin,varmax,
|
|
|
685 |
> stag,ierr)
|
|
|
686 |
if (ierr.ne.0) goto 998
|
|
|
687 |
nx=vardim(1)
|
|
|
688 |
ny=vardim(2)
|
|
|
689 |
nz=vardim(3)
|
|
|
690 |
xmin=varmin(1)
|
|
|
691 |
ymin=varmin(2)
|
|
|
692 |
zmin=varmin(3)
|
|
|
693 |
call getlevs(cstid,nz,aklev,bklev,aklay,bklay,ierr)
|
|
|
694 |
if (ierr.ne.0) goto 998
|
|
|
695 |
call getgrid(cstid,dx,dy,ierr)
|
|
|
696 |
if (ierr.ne.0) goto 998
|
|
|
697 |
xmax=varmax(1)
|
|
|
698 |
ymax=varmax(2)
|
|
|
699 |
zmax=varmax(3)
|
|
|
700 |
dz=(zmax-zmin)/real(nz-1)
|
|
|
701 |
call clscdf(cstid,ierr)
|
|
|
702 |
if (ierr.ne.0) goto 998
|
|
|
703 |
call clscdf(cdfid,ierr)
|
|
|
704 |
if (ierr.ne.0) goto 998
|
|
|
705 |
|
|
|
706 |
c Check whether the grid is equallay spaced in the vertical
|
|
|
707 |
do i=1,nz-1
|
|
|
708 |
dh=aklev(i+1)-aklev(i)
|
|
|
709 |
if (abs(dh-dz).gt.eps) then
|
|
|
710 |
print*,'Aklev: Vertical grid must be equally spaced... Stop'
|
|
|
711 |
print*,(aklev(i),i=1,nz)
|
|
|
712 |
stop
|
|
|
713 |
endif
|
|
|
714 |
dh=aklay(i+1)-aklay(i)
|
|
|
715 |
if (abs(dh-dz).gt.eps) then
|
|
|
716 |
print*,'Aklay: Vertical grid must be equally spaced... Stop'
|
|
|
717 |
print*,(aklay(i),i=1,nz)
|
|
|
718 |
stop
|
|
|
719 |
endif
|
|
|
720 |
enddo
|
|
|
721 |
|
|
|
722 |
c Set missing data value
|
|
|
723 |
mdv=misdat
|
|
|
724 |
|
|
|
725 |
return
|
|
|
726 |
|
|
|
727 |
c Exception handling
|
|
|
728 |
998 print*,'Read_Dim: Problem with input netcdf file... Stop'
|
|
|
729 |
stop
|
|
|
730 |
|
|
|
731 |
end
|
|
|
732 |
|
|
|
733 |
|
|
|
734 |
c -------------------------------------------------------------------------------
|
|
|
735 |
c Read the input netcdf file
|
|
|
736 |
c --------------------------------------------------------------------------------
|
|
|
737 |
|
|
|
738 |
SUBROUTINE read_inp (pv,thetabot,thetatop,ua,ub,va,vb,
|
|
|
739 |
> nx,ny,nz,dx,dy,dz,xmin,ymin,zmin,
|
|
|
740 |
> pvsrcfile)
|
|
|
741 |
|
|
|
742 |
c Read all needed field from netcdf file <pvsrcfile>. The input fields are:
|
|
|
743 |
c pv : quasigeostrophic potential vorticity
|
|
|
744 |
c thetabot,thetatop : potential temperature at lower and upper boundary
|
|
|
745 |
c ua,ub : Zonal wind at western and eastern boundary
|
|
|
746 |
c va,vb : Meridional wind at southern and northern boundary
|
|
|
747 |
c The grid is specified by <nx,ny,nz,dx,dy,dz,xmin,ymin,zmin>. A check is performed
|
|
|
748 |
c whether the input files are consitent with this grid. The input netcdf file must
|
|
|
749 |
c contain the variables <QGPV,THETA,U,V>. If the netcdf file also contains the fields
|
|
|
750 |
c <DQGPV,DTHETA,DU,DV>, these increments are added to <QGPV,THETA,U,V>.
|
|
|
751 |
|
|
|
752 |
implicit none
|
|
|
753 |
|
|
|
754 |
c Declaration of subroutine parameters
|
|
|
755 |
integer nx,ny,nz
|
|
|
756 |
real pv(0:nx,0:ny,0:nz)
|
|
|
757 |
real thetatop(0:nx,0:ny)
|
|
|
758 |
real thetabot(0:nx,0:ny)
|
|
|
759 |
real ua(0:nx,0:nz)
|
|
|
760 |
real ub(0:nx,0:nz)
|
|
|
761 |
real va(0:ny,0:nz)
|
|
|
762 |
real vb(0:ny,0:nz)
|
|
|
763 |
character*(30) pvsrcfile
|
|
|
764 |
real dx,dy,dz,xmin,ymin,zmin
|
|
|
765 |
|
|
|
766 |
c Numerical and physical parameters
|
|
|
767 |
real eps
|
|
|
768 |
parameter (eps=0.01)
|
|
|
769 |
|
|
|
770 |
c Auxiliary variables
|
|
|
771 |
integer cdfid,stat
|
|
|
772 |
integer vardim(4)
|
|
|
773 |
real misdat
|
|
|
774 |
real varmin(4),varmax(4),stag(4)
|
|
|
775 |
integer ndimin,outid,i,j,k
|
|
|
776 |
real max_th
|
|
|
777 |
real tmp(0:nx,0:ny,0:nz)
|
|
|
778 |
integer ntimes
|
|
|
779 |
real time(200)
|
|
|
780 |
integer nvars
|
|
|
781 |
character*80 vnam(100),varname
|
|
|
782 |
integer isok
|
|
|
783 |
|
|
|
784 |
c Open the input netcdf file
|
|
|
785 |
call cdfopn(pvsrcfile,cdfid,stat)
|
|
|
786 |
if (stat.ne.0) goto 998
|
|
|
787 |
|
|
|
788 |
c Check whether needed variables are on file
|
|
|
789 |
call getvars(cdfid,nvars,vnam,stat)
|
|
|
790 |
if (stat.ne.0) goto 998
|
|
|
791 |
isok=0
|
|
|
792 |
varname='TH'
|
|
|
793 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
794 |
varname='U'
|
|
|
795 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
796 |
varname='V'
|
|
|
797 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
798 |
varname='QGPV'
|
|
|
799 |
call check_varok(isok,varname,vnam,nvars)
|
|
|
800 |
if (isok.ne.4) goto 998
|
|
|
801 |
|
|
|
802 |
c Get the grid parameters
|
|
|
803 |
varname='QGPV'
|
|
|
804 |
call getdef(cdfid,varname,ndimin,misdat,vardim,
|
|
|
805 |
> varmin,varmax,stag,stat)
|
|
|
806 |
if (stat.ne.0) goto 998
|
|
|
807 |
time(1)=0.
|
|
|
808 |
call gettimes(cdfid,time,ntimes,stat)
|
|
|
809 |
if (stat.ne.0) goto 998
|
|
|
810 |
|
|
|
811 |
c Check whether grid parameters are consitent
|
|
|
812 |
if ( (vardim(1).ne.nx+1).or.
|
|
|
813 |
> (vardim(2).ne.ny+1).or.
|
|
|
814 |
> (vardim(3).ne.nz+1).or.
|
|
|
815 |
> (abs(varmin(1)-xmin).gt.eps).or.
|
|
|
816 |
> (abs(varmin(2)-ymin).gt.eps).or.
|
|
|
817 |
> (abs(varmin(3)-zmin).gt.eps).or.
|
|
|
818 |
> (abs((varmax(1)-varmin(1))/real(nx)-dx).gt.eps).or.
|
|
|
819 |
> (abs((varmax(2)-varmin(2))/real(ny)-dy).gt.eps).or.
|
|
|
820 |
> (abs((varmax(3)-varmin(3))/real(nz)-dz).gt.eps) ) then
|
|
|
821 |
print*,'Input grid inconsitency...'
|
|
|
822 |
print*,'xmin : ',xmin,varmin(1)
|
|
|
823 |
print*,'ymin : ',ymin,varmin(2)
|
|
|
824 |
print*,'zmin : ',zmin,varmin(3)
|
|
|
825 |
print*,'dx : ',dx,(varmax(1)-varmin(1))/real(nx)
|
|
|
826 |
print*,'dy : ',dy,(varmax(2)-varmin(2))/real(ny)
|
|
|
827 |
print*,'dz : ',dz,(varmax(3)-varmin(3))/real(nz)
|
|
|
828 |
print*,'nx : ',nx
|
|
|
829 |
print*,'ny : ',ny
|
|
|
830 |
print*,'nz : ',nz
|
|
|
831 |
goto 998
|
|
|
832 |
endif
|
|
|
833 |
|
|
|
834 |
c THETA: Load upper and lower boundary values
|
|
|
835 |
varname='TH'
|
|
|
836 |
call getdat(cdfid,varname,time(1),0,tmp,stat)
|
|
|
837 |
print*,'R TH ',trim(pvsrcfile)
|
|
|
838 |
if (stat.ne.0) goto 998
|
|
|
839 |
do i=0,nx
|
|
|
840 |
do j=0,ny
|
|
|
841 |
if ( abs(tmp(i,j,0)-misdat).lt.eps ) then
|
|
|
842 |
thetabot(i,j)=0.
|
|
|
843 |
else
|
|
|
844 |
thetabot(i,j)=tmp(i,j,0)
|
|
|
845 |
endif
|
|
|
846 |
if ( abs(tmp(i,j,nz)-misdat).lt.eps ) then
|
|
|
847 |
thetatop(i,j)=0.
|
|
|
848 |
else
|
|
|
849 |
thetatop(i,j)=tmp(i,j,nz)
|
|
|
850 |
endif
|
|
|
851 |
enddo
|
|
|
852 |
enddo
|
|
|
853 |
|
|
|
854 |
c U: Load zonal velocity at southern and northern boundary
|
|
|
855 |
varname='U'
|
|
|
856 |
call getdef(cdfid,varname,ndimin,misdat,vardim,
|
|
|
857 |
> varmin,varmax,stag,stat)
|
|
|
858 |
if (stat.ne.0) goto 998
|
|
|
859 |
call getdat(cdfid,varname,time(1),0,tmp,stat)
|
|
|
860 |
print*,'R U ',trim(pvsrcfile)
|
|
|
861 |
if (stat.ne.0) goto 998
|
|
|
862 |
do i=0,nx
|
|
|
863 |
do k=0,nz
|
|
|
864 |
if ( abs(tmp(i,0,k)-misdat).lt.eps ) then
|
|
|
865 |
ua(i,k)=0.
|
|
|
866 |
else
|
|
|
867 |
ua(i,k)=tmp(i,0,k)
|
|
|
868 |
endif
|
|
|
869 |
if ( abs(tmp(i,ny,k)-misdat).lt.eps ) then
|
|
|
870 |
ub(i,k)=0.
|
|
|
871 |
else
|
|
|
872 |
ub(i,k)=tmp(i,ny,k)
|
|
|
873 |
endif
|
|
|
874 |
enddo
|
|
|
875 |
enddo
|
|
|
876 |
|
|
|
877 |
c Load meridional velocity at western and eastern boundary
|
|
|
878 |
varname='V'
|
|
|
879 |
call getdef(cdfid,varname,ndimin,misdat,vardim,
|
|
|
880 |
> varmin,varmax,stag,stat)
|
|
|
881 |
if (stat.ne.0) goto 998
|
|
|
882 |
call getdat(cdfid,varname,time(1),0,tmp,stat)
|
|
|
883 |
print*,'R V ',trim(pvsrcfile)
|
|
|
884 |
if (stat.ne.0) goto 998
|
|
|
885 |
do j=0,ny
|
|
|
886 |
do k=0,nz
|
|
|
887 |
if ( abs(tmp(0,j,k)-misdat).lt.eps ) then
|
|
|
888 |
va(j,k)=0.
|
|
|
889 |
else
|
|
|
890 |
va(j,k)=tmp(0,j,k)
|
|
|
891 |
endif
|
|
|
892 |
if ( abs(tmp(nx,j,k)-misdat).lt.eps ) then
|
|
|
893 |
vb(j,k)=0.
|
|
|
894 |
else
|
|
|
895 |
vb(j,k)=tmp(nx,j,k)
|
|
|
896 |
endif
|
|
|
897 |
enddo
|
|
|
898 |
enddo
|
|
|
899 |
|
|
|
900 |
c Load qgPV
|
|
|
901 |
varname='QGPV'
|
|
|
902 |
call getdef(cdfid,varname,ndimin,misdat,vardim,
|
|
|
903 |
> varmin,varmax,stag,stat)
|
|
|
904 |
if (stat.ne.0) goto 998
|
|
|
905 |
call getdat(cdfid,varname,time(1),0,tmp,stat)
|
|
|
906 |
print*,'R QGPV ',trim(pvsrcfile)
|
|
|
907 |
if (stat.ne.0) goto 998
|
|
|
908 |
do i=0,nx
|
|
|
909 |
do j=0,ny
|
|
|
910 |
do k=0,nz
|
|
|
911 |
if ( abs(tmp(i,j,k)-misdat).lt.eps ) then
|
|
|
912 |
pv(i,j,k)=0.
|
|
|
913 |
else
|
|
|
914 |
pv(i,j,k)=tmp(i,j,k)
|
|
|
915 |
endif
|
|
|
916 |
enddo
|
|
|
917 |
enddo
|
|
|
918 |
enddo
|
|
|
919 |
|
|
|
920 |
c Close input netcdf file
|
|
|
921 |
call clscdf(cdfid,stat)
|
|
|
922 |
if (stat.ne.0) goto 998
|
|
|
923 |
|
|
|
924 |
return
|
|
|
925 |
|
|
|
926 |
c Exception handling
|
|
|
927 |
998 print*,'Problem with input netcdf file... Stop'
|
|
|
928 |
stop
|
|
|
929 |
|
|
|
930 |
end
|
|
|
931 |
|
|
|
932 |
c --------------------------------------------------------------------------------
|
|
|
933 |
c Check whether variable is found on netcdf file
|
|
|
934 |
c --------------------------------------------------------------------------------
|
|
|
935 |
|
|
|
936 |
subroutine check_varok (isok,varname,varlist,nvars)
|
|
|
937 |
|
|
|
938 |
c Check whether the variable <varname> is in the list <varlist(nvars)>. If this is
|
|
|
939 |
C the case, <isok> is incremented by 1. Otherwise <isok> keeps its value.
|
|
|
940 |
|
|
|
941 |
implicit none
|
|
|
942 |
|
|
|
943 |
c Declaraion of subroutine parameters
|
|
|
944 |
integer isok
|
|
|
945 |
integer nvars
|
|
|
946 |
character*80 varname
|
|
|
947 |
character*80 varlist(nvars)
|
|
|
948 |
|
|
|
949 |
c Auxiliary variables
|
|
|
950 |
integer i
|
|
|
951 |
|
|
|
952 |
c Main
|
|
|
953 |
do i=1,nvars
|
|
|
954 |
if (trim(varname).eq.trim(varlist(i))) isok=isok+1
|
|
|
955 |
enddo
|
|
|
956 |
|
|
|
957 |
end
|
|
|
958 |
|
|
|
959 |
|
|
|
960 |
c ********************************************************************************
|
|
|
961 |
c * INVERSION ROUTINES *
|
|
|
962 |
c ********************************************************************************
|
|
|
963 |
|
|
|
964 |
c --------------------------------------------------------------------------------
|
|
|
965 |
c SOR algorithm (successive over relaxation)
|
|
|
966 |
c --------------------------------------------------------------------------------
|
|
|
967 |
|
|
|
968 |
SUBROUTINE sor(psi,nsq,thetatop,thetabot,thetaref,rhoref,
|
|
|
969 |
> coriol,pv,ua,ub,va,vb,a,b,c,nx,ny,nz,dx,dy,dz)
|
|
|
970 |
|
|
|
971 |
c Solve the qgPV equation by succesive over relaxation (SOR). The subroutine
|
|
|
972 |
c parameters are:
|
|
|
973 |
c
|
|
|
974 |
c psi : Streamfunction, i.e. result of the PV inversion
|
|
|
975 |
c nsq,rhoref,thetaref : Reference profile
|
|
|
976 |
c thetatop,thetabot : Upper and lower boundary condition
|
|
|
977 |
c pv : quasigeostrophic potential vorticity (qgPV)
|
|
|
978 |
c ua,ub,va,vb : lateral boundary condition for wind
|
|
|
979 |
c a,b,c : Matrices for the inversion operator
|
|
|
980 |
c nx,ny,nz,dx,dy,dz : Grid specification
|
|
|
981 |
c coriol : Coriolis parameter
|
|
|
982 |
|
|
|
983 |
implicit none
|
|
|
984 |
|
|
|
985 |
c Declaration of subroutine parameters
|
|
|
986 |
integer nx,ny,nz
|
|
|
987 |
real dx,dy,dz
|
|
|
988 |
real psi (0:nx,0:ny,0:nz)
|
|
|
989 |
real nsq (0:2*nz)
|
|
|
990 |
real thetatop(0:nx,0:ny)
|
|
|
991 |
real thetabot(0:nx,0:ny)
|
|
|
992 |
real thetaref(0:2*nz)
|
|
|
993 |
real rhoref (0:2*nz)
|
|
|
994 |
real pv (0:nx,0:ny,0:nz)
|
|
|
995 |
real ua (0:nx,0:nz)
|
|
|
996 |
real ub (0:nx,0:nz)
|
|
|
997 |
real va (0:ny,0:nz)
|
|
|
998 |
real vb (0:ny,0:nz)
|
|
|
999 |
real a (0:nx,0:ny,0:nz)
|
|
|
1000 |
real b (0:nx,0:ny,0:nz)
|
|
|
1001 |
real c (0:nx,0:ny,0:nz)
|
|
|
1002 |
real coriol (0:nx,0:ny)
|
|
|
1003 |
|
|
|
1004 |
c Numerical and physical parameters
|
|
|
1005 |
real maxspec
|
|
|
1006 |
parameter (maxspec=2.0)
|
|
|
1007 |
integer nofiter
|
|
|
1008 |
parameter (nofiter=500)
|
|
|
1009 |
real omega
|
|
|
1010 |
parameter (omega=1.81)
|
|
|
1011 |
|
|
|
1012 |
c Auxiliary variables
|
|
|
1013 |
integer counter
|
|
|
1014 |
integer i,j,k
|
|
|
1015 |
real deltasq,psigauge
|
|
|
1016 |
real specx,specy,specz
|
|
|
1017 |
real helpx,helpy,helpz
|
|
|
1018 |
|
|
|
1019 |
c Init the output array
|
|
|
1020 |
do i=0,nx
|
|
|
1021 |
do j=0,ny
|
|
|
1022 |
do k=0,nz
|
|
|
1023 |
psi(i,j,k)=0.
|
|
|
1024 |
enddo
|
|
|
1025 |
enddo
|
|
|
1026 |
enddo
|
|
|
1027 |
|
|
|
1028 |
c Calculate the spectrum of the matrix
|
|
|
1029 |
i=nx/2
|
|
|
1030 |
specx=4.*a(i,0,0)/
|
|
|
1031 |
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
|
|
|
1032 |
specy=2.*(b(i,0,0)+b(i,1,0))/
|
|
|
1033 |
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
|
|
|
1034 |
specz=2.*(c(i,0,0)+c(i,0,1))/
|
|
|
1035 |
> (2.*a(i,0,0)+b(i,0,0)+b(i,1,0)+c(i,0,0)+c(i,0,1))
|
|
|
1036 |
do k=1,nz-2
|
|
|
1037 |
do j=1,ny-2
|
|
|
1038 |
|
|
|
1039 |
helpx=4.*a(i,j,k)/
|
|
|
1040 |
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
|
|
|
1041 |
if (helpx.gt.specx) specx=helpx
|
|
|
1042 |
|
|
|
1043 |
helpy=2.*(b(i,j,k)+b(i,j+1,k))/
|
|
|
1044 |
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
|
|
|
1045 |
if (helpy.gt.specy) specy=helpy
|
|
|
1046 |
|
|
|
1047 |
helpz=2.*(c(i,j,k)+c(i,j,k+1))/
|
|
|
1048 |
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k)+c(i,j,k-1))
|
|
|
1049 |
if (helpz.gt.specz) specz=helpz
|
|
|
1050 |
|
|
|
1051 |
enddo
|
|
|
1052 |
enddo
|
|
|
1053 |
|
|
|
1054 |
c Check whether the dimensions of the grid are sufficient
|
|
|
1055 |
print *
|
|
|
1056 |
print *, 'Spectrum of the matrix in each direction '
|
|
|
1057 |
print *, 'Spectrum = ', specx, specy, specz
|
|
|
1058 |
print *
|
|
|
1059 |
if ((maxspec*specx.lt.specy).or.(maxspec*specx.lt.specz)) then
|
|
|
1060 |
print*,' Nx too small... Stop'
|
|
|
1061 |
stop
|
|
|
1062 |
endif
|
|
|
1063 |
if ((maxspec*specy.lt.specx).or.(maxspec*specy.lt.specz)) then
|
|
|
1064 |
print*,'Ny too small... Stop'
|
|
|
1065 |
stop
|
|
|
1066 |
endif
|
|
|
1067 |
if ((maxspec*specz.lt.specx).or.(maxspec*specz.lt.specy)) then
|
|
|
1068 |
print*,'Nz too small... Stop'
|
|
|
1069 |
stop
|
|
|
1070 |
endif
|
|
|
1071 |
|
|
|
1072 |
c Calculate error: control variable for the iteration
|
|
|
1073 |
psigauge=0.
|
|
|
1074 |
deltasq=0.
|
|
|
1075 |
do k=1,nz-1
|
|
|
1076 |
do i=1,nx-1
|
|
|
1077 |
do j=1,ny-1
|
|
|
1078 |
deltasq=deltasq+(-pv(i,j,k)+(
|
|
|
1079 |
> a(i,j,k)*(psi(i+1,j,k)+psi(i-1,j,k)-
|
|
|
1080 |
> 2.*psi(i,j,k)) +
|
|
|
1081 |
> b(i,j,k)*(psi(i,j+1,k)-psi(i,j,k))-
|
|
|
1082 |
> b(i,j-1,k)*(psi(i,j,k)-psi(i,j-1,k))+
|
|
|
1083 |
> c(i,j,k)*(psi(i,j,k+1)-psi(i,j,k))-
|
|
|
1084 |
> c(i,j,k-1)*(psi(i,j,k)-psi(i,j,k-1))
|
|
|
1085 |
> )/(dx*dy*dz*rhoref(2*k)))**2.
|
|
|
1086 |
|
|
|
1087 |
enddo
|
|
|
1088 |
enddo
|
|
|
1089 |
enddo
|
|
|
1090 |
print 102, 'psigauge', psigauge, 'deltasq',
|
|
|
1091 |
> deltasq/(real(nx)*real(ny)*real(nz))
|
|
|
1092 |
|
|
|
1093 |
c Iterations
|
|
|
1094 |
do counter=1,nofiter
|
|
|
1095 |
|
|
|
1096 |
C Perform one iteration step
|
|
|
1097 |
call psiappsor(omega,pv,psi,nsq,rhoref,thetatop,
|
|
|
1098 |
> thetabot,thetaref,coriol,ua,ub,va,vb,
|
|
|
1099 |
> a,b,c,nx,ny,nz,dx,dy,dz)
|
|
|
1100 |
|
|
|
1101 |
|
|
|
1102 |
c Adjustment
|
|
|
1103 |
if (mod(counter,100).eq.0) then
|
|
|
1104 |
psigauge=0.
|
|
|
1105 |
do i=0,nx
|
|
|
1106 |
do j=0,ny
|
|
|
1107 |
if (psi(i,j,0).lt.psigauge) then
|
|
|
1108 |
psigauge=psi(i,j,0)
|
|
|
1109 |
endif
|
|
|
1110 |
enddo
|
|
|
1111 |
enddo
|
|
|
1112 |
do k=0,nz
|
|
|
1113 |
do i=0,nx
|
|
|
1114 |
do j=0,ny
|
|
|
1115 |
psi(i,j,k)=psi(i,j,k)-psigauge
|
|
|
1116 |
enddo
|
|
|
1117 |
enddo
|
|
|
1118 |
enddo
|
|
|
1119 |
endif
|
|
|
1120 |
|
|
|
1121 |
c Calculate error: control variable for the iteration
|
|
|
1122 |
if (mod(counter,nofiter/10).eq.0) then
|
|
|
1123 |
deltasq=0.
|
|
|
1124 |
do k=1,nz-1
|
|
|
1125 |
do i=1,nx-1
|
|
|
1126 |
do j=1,ny-1
|
|
|
1127 |
deltasq=deltasq+(-pv(i,j,k)+(
|
|
|
1128 |
> a(i,j,k)*(psi(i+1,j,k)+psi(i-1,j,k)-
|
|
|
1129 |
> 2.*psi(i,j,k)) +
|
|
|
1130 |
> b(i,j,k)*(psi(i,j+1,k)-psi(i,j,k))-
|
|
|
1131 |
> b(i,j-1,k)*(psi(i,j,k)-psi(i,j-1,k))+
|
|
|
1132 |
> c(i,j,k)*(psi(i,j,k+1)-psi(i,j,k))-
|
|
|
1133 |
> c(i,j,k-1)*(psi(i,j,k)-psi(i,j,k-1))
|
|
|
1134 |
> )/(dx*dy*dz*rhoref(2*k)))**2.
|
|
|
1135 |
enddo
|
|
|
1136 |
enddo
|
|
|
1137 |
enddo
|
|
|
1138 |
print 102, 'psigauge', psigauge, 'deltasq',
|
|
|
1139 |
> deltasq/(real(nx)*real(ny)*real(nz))
|
|
|
1140 |
endif
|
|
|
1141 |
|
|
|
1142 |
enddo
|
|
|
1143 |
|
|
|
1144 |
return
|
|
|
1145 |
|
|
|
1146 |
c Format specifications
|
|
|
1147 |
102 format (a11, ' = ',e10.3,a11, ' = ',e10.3)
|
|
|
1148 |
|
|
|
1149 |
end
|
|
|
1150 |
|
|
|
1151 |
c --------------------------------------------------------------------------------
|
|
|
1152 |
c SOR algorithm (successive over relaxation)
|
|
|
1153 |
c --------------------------------------------------------------------------------
|
|
|
1154 |
|
|
|
1155 |
subroutine psiappsor(omega,pv,psi,nsq,rhoref,thetatop,
|
|
|
1156 |
> thetabot,thetaref,coriol,ua,ub,va,vb,
|
|
|
1157 |
> a,b,c,nx,ny,nz,dx,dy,dz)
|
|
|
1158 |
|
|
|
1159 |
c Perform one relaxation step
|
|
|
1160 |
c
|
|
|
1161 |
c psi : Streamfunction, i.e. result of the PV inversion
|
|
|
1162 |
c nsq,rhoref,thetaref : Reference profile
|
|
|
1163 |
c thetatop,thetabot : Upper and lower boundary condition
|
|
|
1164 |
c pv : quasigeostrophic potential vorticity (qgPV)
|
|
|
1165 |
c ua,ub,va,vb : lateral boundary condition for wind
|
|
|
1166 |
c a,b,c : Matrices for the inversion operator
|
|
|
1167 |
c nx,ny,nz,dx,dy,dz : Grid specification
|
|
|
1168 |
c nofiter : Number of iterations
|
|
|
1169 |
c omega : Relaxation parameter
|
|
|
1170 |
c coriol : Coriolis parameter
|
|
|
1171 |
|
|
|
1172 |
implicit none
|
|
|
1173 |
|
|
|
1174 |
c Declaration of subroutine parameters
|
|
|
1175 |
integer nx,ny,nz
|
|
|
1176 |
real pv(0:nx,0:ny,0:nz)
|
|
|
1177 |
real psi(0:nx,0:ny,0:nz)
|
|
|
1178 |
real nsq(0:2*nz)
|
|
|
1179 |
real rhoref(0:2*nz)
|
|
|
1180 |
real thetatop(0:nx,0:ny)
|
|
|
1181 |
real thetabot(0:nx,0:ny)
|
|
|
1182 |
real thetaref(0:2*nz)
|
|
|
1183 |
real ua(0:nx,0:nz)
|
|
|
1184 |
real ub(0:nx,0:nz)
|
|
|
1185 |
real va(0:ny,0:nz)
|
|
|
1186 |
real vb(0:ny,0:nz)
|
|
|
1187 |
real a(0:nx,0:ny,0:nz)
|
|
|
1188 |
real b(0:nx,0:ny,0:nz)
|
|
|
1189 |
real c(0:nx,0:ny,0:nz)
|
|
|
1190 |
real coriol(0:nx,0:ny)
|
|
|
1191 |
real dx,dy,dz
|
|
|
1192 |
real omega
|
|
|
1193 |
|
|
|
1194 |
c Numerical and physical parameters
|
|
|
1195 |
real g
|
|
|
1196 |
parameter (g=9.81)
|
|
|
1197 |
|
|
|
1198 |
c Auxiliary variables
|
|
|
1199 |
integer i,j,k
|
|
|
1200 |
real dxy,dxz,dyz,dxyz
|
|
|
1201 |
|
|
|
1202 |
c Set the area and volume infinitesimals for integration
|
|
|
1203 |
dxy=dx*dy
|
|
|
1204 |
dxz=dx*dz
|
|
|
1205 |
dyz=dy*dz
|
|
|
1206 |
dxyz=dx*dy*dz
|
|
|
1207 |
|
|
|
1208 |
c Inner
|
|
|
1209 |
do k=1,nz-1
|
|
|
1210 |
do i=1,nx-1
|
|
|
1211 |
do j=1,ny-1
|
|
|
1212 |
psi(i,j,k)=omega*(-dxyz*
|
|
|
1213 |
> rhoref(2*k)*pv(i,j,k)+a(i,j,k)*
|
|
|
1214 |
> (psi(i+1,j,k)+psi(i-1,j,k))+b(i,j,k)*
|
|
|
1215 |
> psi(i,j+1,k)+b(i,j-1,k)*psi(i,j-1,k)+c(i,j,k)*
|
|
|
1216 |
> psi(i,j,k+1)+c(i,j,k-1)*psi(i,j,k-1))/
|
|
|
1217 |
> (2.*a(i,j,k)+b(i,j,k)+b(i,j-1,k)+c(i,j,k-1)+
|
|
|
1218 |
> c(i,j,k))+(1.-omega)*psi(i,j,k)
|
|
|
1219 |
enddo
|
|
|
1220 |
enddo
|
|
|
1221 |
enddo
|
|
|
1222 |
|
|
|
1223 |
c ZY plane
|
|
|
1224 |
do k=1,nz-1
|
|
|
1225 |
do j=1,ny-1
|
|
|
1226 |
psi(0,j,k)=omega*(-dyz*
|
|
|
1227 |
> rhoref(2*k)*(dx*pv(0,j,k)+va(j,k))+
|
|
|
1228 |
> a(0,j,k)*psi(1,j,k)+
|
|
|
1229 |
> b(0,j,k)*psi(0,j+1,k)+b(0,j-1,k)*psi(0,j-1,k)+
|
|
|
1230 |
> c(0,j,k)*psi(0,j,k+1)+c(0,j,k-1)*psi(0,j,k-1))/
|
|
|
1231 |
> (a(0,j,k)+b(0,j,k)+b(0,j-1,k)+c(0,j,k-1)+c(0,j,k))
|
|
|
1232 |
> +(1.-omega)*psi(0,j,k)
|
|
|
1233 |
c
|
|
|
1234 |
psi(nx,j,k)=omega*(-dyz*
|
|
|
1235 |
> rhoref(2*k)*(dx*pv(nx,j,k)-vb(j,k))+
|
|
|
1236 |
> a(nx,j,k)*psi(nx-1,j,k)+
|
|
|
1237 |
> b(nx,j,k)*psi(nx,j+1,k)+b(nx,j-1,k)*psi(nx,j-1,k)+
|
|
|
1238 |
> c(nx,j,k)*psi(nx,j,k+1)+c(nx,j,k-1)*psi(nx,j,k-1))/
|
|
|
1239 |
> (a(nx,j,k)+b(nx,j-1,k)+b(nx,j,k)+c(nx,j,k-1)+c(nx,j,k))
|
|
|
1240 |
> +(1.-omega)*psi(nx,j,k)
|
|
|
1241 |
enddo
|
|
|
1242 |
enddo
|
|
|
1243 |
|
|
|
1244 |
c ZX plane
|
|
|
1245 |
do k=1,nz-1
|
|
|
1246 |
do i=1,nx-1
|
|
|
1247 |
psi(i,0,k)=omega*(-dxz*
|
|
|
1248 |
> rhoref(2*k)*(dy*pv(i,0,k)-ua(i,k))+
|
|
|
1249 |
> a(i,0,k)*(psi(i+1,0,k)+psi(i-1,0,k))+
|
|
|
1250 |
> b(i,0,k)*psi(i,1,k)+
|
|
|
1251 |
> c(i,0,k)*psi(i,0,k+1)+c(i,0,k-1)*psi(i,0,k-1))/
|
|
|
1252 |
> (2.*a(i,0,k)+b(i,0,k)+c(i,0,k-1)+c(i,0,k))
|
|
|
1253 |
> +(1.-omega)*psi(i,0,k)
|
|
|
1254 |
c
|
|
|
1255 |
psi(i,ny,k)=omega*(-dxz*
|
|
|
1256 |
> rhoref(2*k)*(dy*pv(i,ny,k)+ub(i,k))+
|
|
|
1257 |
> a(i,ny-1,k)*(psi(i+1,ny,k)+psi(i-1,ny,k))+
|
|
|
1258 |
> b(i,ny-1,k)*psi(i,ny-1,k)+
|
|
|
1259 |
> c(i,ny-1,k)*psi(i,ny,k+1)+c(i,ny-1,k-1)*
|
|
|
1260 |
> psi(i,ny,k-1))/(2.*a(i,ny-1,k)+b(i,ny-1,k)+
|
|
|
1261 |
> c(i,ny-1,k-1)+c(i,ny-1,k))
|
|
|
1262 |
> +(1.-omega)*psi(i,ny,k)
|
|
|
1263 |
enddo
|
|
|
1264 |
enddo
|
|
|
1265 |
|
|
|
1266 |
c XY plane
|
|
|
1267 |
do i=1,nx-1
|
|
|
1268 |
do j=1,ny-1
|
|
|
1269 |
psi(i,j,0)=omega*(-dxy*rhoref(0)*(
|
|
|
1270 |
> dz*pv(i,j,0)+g*coriol(i,j)*thetabot(i,j)/
|
|
|
1271 |
> (nsq(0)*thetaref(0)))+
|
|
|
1272 |
> a(i,j,0)*(psi(i+1,j,0)+psi(i-1,j,0))+
|
|
|
1273 |
> b(i,j,0)*psi(i,j+1,0)+b(i,j-1,0)*psi(i,j-1,0)+
|
|
|
1274 |
> c(i,j,0)*psi(i,j,1))/
|
|
|
1275 |
> (2.*a(i,j,0)+b(i,j-1,0)+b(i,j,0)+c(i,j,0))
|
|
|
1276 |
> +(1.-omega)*psi(i,j,0)
|
|
|
1277 |
c
|
|
|
1278 |
psi(i,j,nz)=omega*(-dxy*rhoref(2*nz)*(
|
|
|
1279 |
> dz*pv(i,j,nz)-g*coriol(i,j)*thetatop(i,j)/
|
|
|
1280 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1281 |
> a(i,j,nz)*(psi(i+1,j,nz)+psi(i-1,j,nz))+
|
|
|
1282 |
> b(i,j,nz)*psi(i,j+1,nz)+b(i,j-1,nz)*psi(i,j-1,nz)+
|
|
|
1283 |
> c(i,j,nz-1)*psi(i,j,nz-1))/
|
|
|
1284 |
> (2.*a(i,j,nz)+b(i,j-1,nz)+b(i,j,nz)+c(i,j,nz-1))
|
|
|
1285 |
> +(1.-omega)*psi(i,j,nz)
|
|
|
1286 |
enddo
|
|
|
1287 |
enddo
|
|
|
1288 |
|
|
|
1289 |
c Y edges
|
|
|
1290 |
do j=1,ny-1
|
|
|
1291 |
psi(0,j,0)=omega*(-dy*rhoref(0)*(dxz*pv(0,j,0)+
|
|
|
1292 |
> dz*va(j,0)+dx*g*coriol(0,j)*thetabot(0,j)/
|
|
|
1293 |
> (nsq(0)*thetaref(0)))+
|
|
|
1294 |
> a(0,j,0)*psi(1,j,0)+
|
|
|
1295 |
> b(0,j,0)*psi(0,j+1,0)+b(0,j-1,0)*psi(0,j-1,0)+
|
|
|
1296 |
> c(0,j,0)*psi(0,j,1))/
|
|
|
1297 |
> (a(0,j,0)+b(0,j-1,0)+b(0,j,0)+c(0,j,0))
|
|
|
1298 |
> +(1.-omega)*psi(0,j,0)
|
|
|
1299 |
c
|
|
|
1300 |
psi(nx,j,0)=omega*(-dy*rhoref(0)*(dxz*pv(nx,j,0)-
|
|
|
1301 |
> dz*vb(j,0)+dx*g*coriol(nx,j)*thetabot(nx,j)/
|
|
|
1302 |
> (nsq(0)*thetaref(0)))+
|
|
|
1303 |
> a(nx,j,0)*psi(nx-1,j,0)+
|
|
|
1304 |
> b(nx,j,0)*psi(nx,j+1,0)+b(nx,j-1,0)*psi(nx,j-1,0)+
|
|
|
1305 |
> c(nx,j,0)*psi(nx,j,1))/
|
|
|
1306 |
> (a(nx,j,0)+b(nx,j-1,0)+b(nx,j,0)+c(nx,j,0))
|
|
|
1307 |
> +(1.-omega)*psi(nx,j,0)
|
|
|
1308 |
c
|
|
|
1309 |
psi(0,j,nz)=omega*(-dy*rhoref(2*nz)*(dxz*pv(0,j,nz)+
|
|
|
1310 |
> dz*va(j,nz)-dx*g*coriol(0,j)*thetatop(0,j)/
|
|
|
1311 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1312 |
> a(0,j,nz)*psi(1,j,nz)+
|
|
|
1313 |
> b(0,j,nz)*psi(0,j+1,nz)+b(0,j-1,nz)*psi(0,j-1,nz)+
|
|
|
1314 |
> c(0,j,nz-1)*psi(0,j,nz-1))/
|
|
|
1315 |
> (a(0,j,nz)+b(0,j-1,nz)+b(0,j,nz)+c(0,j,nz-1))
|
|
|
1316 |
> +(1.-omega)*psi(0,j,nz)
|
|
|
1317 |
c
|
|
|
1318 |
psi(nx,j,nz)=omega*(-dy*rhoref(2*nz)*(dxz*pv(nx,j,nz)-
|
|
|
1319 |
> dz*vb(j,nz)-dx*g*coriol(nx,j)*thetatop(nx,j)/
|
|
|
1320 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1321 |
> a(nx,j,nz)*psi(nx-1,j,nz)+
|
|
|
1322 |
> b(nx,j,nz)*psi(nx,j+1,nz)+b(nx,j-1,nz)*psi(nx,j-1,nz)+
|
|
|
1323 |
> c(nx,j,nz-1)*psi(nx,j,nz-1))/
|
|
|
1324 |
> (a(nx,j,nz)+b(nx,j-1,nz)+b(nx,j,nz)+c(nx,j,nz-1))
|
|
|
1325 |
> +(1.-omega)*psi(nx,j,nz)
|
|
|
1326 |
enddo
|
|
|
1327 |
|
|
|
1328 |
c X edges
|
|
|
1329 |
do i=1,nx-1
|
|
|
1330 |
psi(i,0,0)=omega*(-dx*rhoref(0)*(dyz*pv(i,0,0)-
|
|
|
1331 |
> dz*ua(i,0)+dy*g*coriol(i,0)*thetabot(i,0)/
|
|
|
1332 |
> (nsq(0)*thetaref(0)))+
|
|
|
1333 |
> a(i,0,0)*(psi(i+1,0,0)+psi(i-1,0,0))+
|
|
|
1334 |
> b(i,0,0)*psi(i,1,0)+
|
|
|
1335 |
> c(i,0,0)*psi(i,0,1))/
|
|
|
1336 |
> (2.*a(i,0,0)+b(i,0,0)+c(i,0,0))
|
|
|
1337 |
> +(1.-omega)*psi(i,0,0)
|
|
|
1338 |
c
|
|
|
1339 |
psi(i,ny,0)=omega*(-dx*rhoref(0)*(dyz*pv(i,ny,0)+
|
|
|
1340 |
> dz*ub(i,0)+dy*g*coriol(i,ny)*thetabot(i,ny)/
|
|
|
1341 |
> (nsq(0)*thetaref(0)))+
|
|
|
1342 |
> a(i,ny,0)*(psi(i+1,ny,0)+psi(i-1,ny,0))+
|
|
|
1343 |
> b(i,ny-1,0)*psi(i,ny-1,0)+
|
|
|
1344 |
> c(i,ny,0)*psi(i,ny,1))/
|
|
|
1345 |
> (2.*a(i,ny,0)+b(i,ny-1,0)+c(i,ny,0))
|
|
|
1346 |
> +(1.-omega)*psi(i,ny,0)
|
|
|
1347 |
c
|
|
|
1348 |
psi(i,0,nz)=omega*(-dx*rhoref(2*nz)*(dyz*pv(i,0,nz)-
|
|
|
1349 |
> dz*ua(i,nz)-dy*g*coriol(i,0)*thetatop(i,0)/
|
|
|
1350 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1351 |
> a(i,0,nz)*(psi(i+1,0,nz)+psi(i-1,0,nz))+
|
|
|
1352 |
> b(i,0,nz)*psi(i,1,nz)+
|
|
|
1353 |
> c(i,0,nz-1)*psi(i,0,nz-1))/
|
|
|
1354 |
> (2.*a(i,0,nz)+b(i,0,nz)+c(i,0,nz-1))
|
|
|
1355 |
> +(1.-omega)*psi(i,0,nz)
|
|
|
1356 |
c
|
|
|
1357 |
psi(i,ny,nz)=omega*(-dx*rhoref(2*nz)*(dyz*pv(i,ny,nz)+
|
|
|
1358 |
> dz*ub(i,nz)-dy*g*coriol(i,ny)*thetatop(i,ny)/
|
|
|
1359 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1360 |
> a(i,ny,nz)*(psi(i+1,ny,nz)+psi(i-1,ny,nz))+
|
|
|
1361 |
> b(i,ny-1,nz)*psi(i,ny-1,nz)+
|
|
|
1362 |
> c(i,ny,nz-1)*psi(i,ny,nz-1))/
|
|
|
1363 |
> (2.*a(i,ny,nz)+b(i,ny-1,nz)+c(i,ny,nz-1))
|
|
|
1364 |
> +(1.-omega)*psi(i,ny,nz)
|
|
|
1365 |
enddo
|
|
|
1366 |
|
|
|
1367 |
c Z edges
|
|
|
1368 |
do k=1,nz-1
|
|
|
1369 |
psi(0,0,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(0,0,k)+
|
|
|
1370 |
> dy*va(0,k)-dx*ua(0,k))+
|
|
|
1371 |
> a(0,0,k)*psi(1,0,k)+
|
|
|
1372 |
> b(0,0,k)*psi(0,1,k)+
|
|
|
1373 |
> c(0,0,k)*psi(0,0,k+1)+c(0,0,k-1)*psi(0,0,k-1))/
|
|
|
1374 |
> (a(0,0,k)+b(0,0,k)+c(0,0,k-1)+c(0,0,k))
|
|
|
1375 |
> +(1.-omega)*psi(0,0,k)
|
|
|
1376 |
c
|
|
|
1377 |
psi(nx,0,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(nx,0,k)-
|
|
|
1378 |
> dy*vb(0,k)-dx*ua(nx,k))+
|
|
|
1379 |
> a(nx,0,k)*psi(nx-1,0,k)+
|
|
|
1380 |
> b(nx,0,k)*psi(nx,1,k)+
|
|
|
1381 |
> c(nx,0,k)*psi(nx,0,k+1)+c(nx,0,k-1)*psi(nx,0,k-1))/
|
|
|
1382 |
> (a(nx,0,k)+b(nx,0,k)+c(nx,0,k-1)+c(nx,0,k))
|
|
|
1383 |
> +(1.-omega)*psi(nx,0,k)
|
|
|
1384 |
c
|
|
|
1385 |
psi(0,ny,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(0,ny,k)+
|
|
|
1386 |
> dy*va(ny,k)+dx*ub(0,k))+
|
|
|
1387 |
> a(0,ny,k)*psi(1,ny,k)+
|
|
|
1388 |
> b(0,ny-1,k)*psi(0,ny-1,k)+
|
|
|
1389 |
> c(0,ny,k)*psi(0,ny,k+1)+c(0,ny,k-1)*psi(0,ny,k-1))/
|
|
|
1390 |
> (a(0,ny,k)+b(0,ny-1,k)+c(0,ny,k-1)+c(0,ny,k))
|
|
|
1391 |
> +(1.-omega)*psi(0,ny,k)
|
|
|
1392 |
c
|
|
|
1393 |
psi(nx,ny,k)=omega*(-dz*rhoref(2*k)*(dxy*pv(nx,ny,k)-
|
|
|
1394 |
> dy*vb(ny,k)+dx*ub(nx,k))+
|
|
|
1395 |
> a(nx,ny,k)*psi(nx-1,ny,k)+
|
|
|
1396 |
> b(nx,ny-1,k)*psi(nx,ny-1,k)+
|
|
|
1397 |
> c(nx,ny,k)*psi(nx,ny,k+1)+c(nx,ny,k-1)*psi(nx,ny,k-1))/
|
|
|
1398 |
> (a(nx,ny,k)+b(nx,ny-1,k)+c(nx,ny,k-1)+c(nx,ny,k))
|
|
|
1399 |
> +(1.-omega)*psi(nx,ny,k)
|
|
|
1400 |
enddo
|
|
|
1401 |
|
|
|
1402 |
c Points
|
|
|
1403 |
psi(0,0,0)=omega*(-rhoref(0)*(dxyz*pv(0,0,0)+dyz*va(0,0)-
|
|
|
1404 |
> dxz*ua(0,0)+dxy*g*coriol(0,0)*thetabot(0,0)/
|
|
|
1405 |
> (nsq(0)*thetaref(0)))+
|
|
|
1406 |
> a(0,0,0)*psi(1,0,0)+
|
|
|
1407 |
> b(0,0,0)*psi(0,1,0)+
|
|
|
1408 |
> c(0,0,0)*psi(0,0,1))/
|
|
|
1409 |
> (a(0,0,0)+b(0,0,0)+c(0,0,0))+
|
|
|
1410 |
> (1.-omega)*psi(0,0,0)
|
|
|
1411 |
c
|
|
|
1412 |
psi(nx,0,0)=omega*(-rhoref(0)*(dxyz*pv(nx,0,0)-dyz*vb(0,0)-
|
|
|
1413 |
> dxz*ua(nx,0)+dxy*g*coriol(nx,0)*thetabot(nx,0)/
|
|
|
1414 |
> (nsq(0)*thetaref(0)))+
|
|
|
1415 |
> a(nx,0,0)*psi(nx-1,0,0)+
|
|
|
1416 |
> b(nx,0,0)*psi(nx,1,0)+
|
|
|
1417 |
> c(nx,0,0)*psi(nx,0,1))/
|
|
|
1418 |
> (a(nx,0,0)+b(nx,0,0)+c(nx,0,0))+
|
|
|
1419 |
> (1.-omega)*psi(nx,0,0)
|
|
|
1420 |
c
|
|
|
1421 |
psi(0,ny,0)=omega*(-rhoref(0)*(dxyz*pv(0,ny,0)+dyz*va(ny,0)+
|
|
|
1422 |
> dxz*ub(0,0)+dxy*g*coriol(0,ny)*thetabot(0,ny)/
|
|
|
1423 |
> (nsq(0)*thetaref(0)))+
|
|
|
1424 |
> a(0,ny,0)*psi(1,ny,0)+
|
|
|
1425 |
> b(0,ny-1,0)*psi(0,ny-1,0)+
|
|
|
1426 |
> c(0,ny,0)*psi(0,ny,1))/
|
|
|
1427 |
> (a(0,ny,0)+b(0,ny-1,0)+c(0,ny,0))+
|
|
|
1428 |
> (1.-omega)*psi(0,ny,0)
|
|
|
1429 |
c
|
|
|
1430 |
psi(nx,ny,0)=omega*(-rhoref(0)*(dxyz*pv(nx,ny,0)-dyz*vb(ny,0)+
|
|
|
1431 |
> dxz*ub(nx,0)+dxy*g*coriol(nx,ny)*thetabot(nx,ny)/
|
|
|
1432 |
> (nsq(0)*thetaref(0)))+
|
|
|
1433 |
> a(nx,ny,0)*psi(nx-1,ny,0)+
|
|
|
1434 |
> b(nx,ny-1,0)*psi(nx,ny-1,0)+
|
|
|
1435 |
> c(nx,ny,0)*psi(nx,ny,1))/
|
|
|
1436 |
> (a(nx,ny,0)+b(nx,ny-1,0)+c(nx,ny,0))+
|
|
|
1437 |
> (1.-omega)*psi(nx,ny,0)
|
|
|
1438 |
c
|
|
|
1439 |
psi(0,0,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(0,0,nz)+dyz*va(0,nz)-
|
|
|
1440 |
> dxz*ua(0,nz)-dxy*g*coriol(0,0)*thetatop(0,0)/
|
|
|
1441 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1442 |
> a(0,0,nz)*psi(1,0,nz)+
|
|
|
1443 |
> b(0,0,nz)*psi(0,1,nz)+
|
|
|
1444 |
> c(0,0,nz-1)*psi(0,0,nz-1))/
|
|
|
1445 |
> (a(0,0,nz)+b(0,0,nz)+c(0,0,nz-1))+
|
|
|
1446 |
> (1.-omega)*psi(0,0,nz)
|
|
|
1447 |
c
|
|
|
1448 |
psi(nx,0,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(nx,0,nz)-dyz*vb(0,nz)
|
|
|
1449 |
> -dxz*ua(nx,nz)-dxy*g*coriol(nx,0)*thetatop(nx,0)/
|
|
|
1450 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1451 |
> a(nx,0,nz)*psi(nx-1,0,nz)+
|
|
|
1452 |
> b(nx,0,nz)*psi(nx,1,nz)+
|
|
|
1453 |
> c(nx,0,nz-1)*psi(nx,0,nz-1))/
|
|
|
1454 |
> (a(nx,0,nz)+b(nx,0,nz)+c(nx,0,nz-1))+
|
|
|
1455 |
> (1.-omega)*psi(nx,0,nz)
|
|
|
1456 |
c
|
|
|
1457 |
psi(0,ny,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(0,ny,nz)+
|
|
|
1458 |
> dyz*va(ny,nz)+dxz*ub(0,nz)-
|
|
|
1459 |
> dxy*g*coriol(0,ny)*thetatop(0,ny)/
|
|
|
1460 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1461 |
> a(0,ny,nz)*psi(1,ny,nz)+
|
|
|
1462 |
> b(0,ny-1,nz)*psi(0,ny-1,nz)+
|
|
|
1463 |
> c(0,ny,nz-1)*psi(0,ny,nz-1))/
|
|
|
1464 |
> (a(0,ny,nz)+b(0,ny-1,nz)+c(0,ny,nz-1))+
|
|
|
1465 |
> (1.-omega)*psi(0,ny,nz)
|
|
|
1466 |
c
|
|
|
1467 |
psi(nx,ny,nz)=omega*(-rhoref(2*nz)*(dxyz*pv(nx,ny,nz)-
|
|
|
1468 |
> dyz*vb(ny,nz)+dxz*ub(nx,nz)-
|
|
|
1469 |
> dxy*g*coriol(nx,ny)*thetatop(nx,ny)/
|
|
|
1470 |
> (nsq(2*nz)*thetaref(2*nz)))+
|
|
|
1471 |
> a(nx,ny,nz)*psi(nx-1,ny,nz)+
|
|
|
1472 |
> b(nx,ny-1,nz)*psi(nx,ny-1,nz)+
|
|
|
1473 |
> c(nx,ny,nz-1)*psi(nx,ny,nz-1))/
|
|
|
1474 |
> (a(nx,ny,nz)+b(nx,ny-1,nz)+c(nx,ny,nz-1))+
|
|
|
1475 |
> (1.-omega)*psi(nx,ny,nz)
|
|
|
1476 |
c
|
|
|
1477 |
|
|
|
1478 |
end
|
|
|
1479 |
|
|
|
1480 |
c --------------------------------------------------------------------------------
|
|
|
1481 |
c Init matrix elements for the inversion
|
|
|
1482 |
c --------------------------------------------------------------------------------
|
|
|
1483 |
|
|
|
1484 |
subroutine matrixel(a,b,c,coriol,nx,ny,nz,nsq,rhoref,dx,dy,dz)
|
|
|
1485 |
|
|
|
1486 |
c Define the coefficients for the inversion problem (see page 119ff in Rene's
|
|
|
1487 |
c dissertation).
|
|
|
1488 |
|
|
|
1489 |
implicit none
|
|
|
1490 |
|
|
|
1491 |
c Declaration of subroutine parameters
|
|
|
1492 |
integer nx,nz,ny
|
|
|
1493 |
real a (0:nx,0:ny,0:nz)
|
|
|
1494 |
real b (0:nx,0:ny,0:nz)
|
|
|
1495 |
real c (0:nx,0:ny,0:nz)
|
|
|
1496 |
real coriol(0:nx,0:ny)
|
|
|
1497 |
real nsq (0:2*nz)
|
|
|
1498 |
real rhoref(0:2*nz)
|
|
|
1499 |
real dx,dy,dz
|
|
|
1500 |
|
|
|
1501 |
c Auxiliary variables
|
|
|
1502 |
integer i,j,k
|
|
|
1503 |
|
|
|
1504 |
c Calculate coefficients
|
|
|
1505 |
do i=0,nx
|
|
|
1506 |
do j=0,ny
|
|
|
1507 |
do k=0,nz
|
|
|
1508 |
a(i,j,k)=dy*dz*rhoref(2*k)/(dx*coriol(i,j))
|
|
|
1509 |
if (j.lt.ny) then
|
|
|
1510 |
b(i,j,k)=dx*dz*rhoref(2*k)/
|
|
|
1511 |
> (dy*0.5*(coriol(i,j)+coriol(i,j+1)))
|
|
|
1512 |
else
|
|
|
1513 |
b(i,j,k)=0.
|
|
|
1514 |
endif
|
|
|
1515 |
if (k.lt.nz) then
|
|
|
1516 |
c(i,j,k)=dx*dy*rhoref(2*k+1)*coriol(i,j)/
|
|
|
1517 |
> (dz*nsq(2*k+1))
|
|
|
1518 |
else
|
|
|
1519 |
c(i,j,k)=0.
|
|
|
1520 |
endif
|
|
|
1521 |
enddo
|
|
|
1522 |
enddo
|
|
|
1523 |
enddo
|
|
|
1524 |
|
|
|
1525 |
end
|
|
|
1526 |
|
|
|
1527 |
|
|
|
1528 |
|
|
|
1529 |
|