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michaesp |
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c *************************************************************
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c * This package provides a general interpolaton routine *
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c *************************************************************
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c The main interface routines are:
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c get_index3,4 : get the grid indices for interpolation
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c int_index3,4 : interpolate to the grid position
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c -------------------------------------------------------------
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c Get index in grid space for interpolation
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c -------------------------------------------------------------
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subroutine get_index4 (rid,rjd,rkd,xpo,ypo,ppo,rtp,
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> vert0,vert1,surf0,surf1,mode,
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> nx,ny,nz,lonw,lats,dlon,dlat,misdat)
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c Purpose:
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c This subroutine determines the indices (rid,rjd,rkd) in grid
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c space for a point in physical space (xpo,ypo,ppo). The
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c horizontal grid is specified by the south-west point (lats,lonw)
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c and the grid spacing (dlat,dlon). The vertical grid is given
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c by <vert(n1,n2,n3)>. The lower boundary (typicall surface
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c pressure) is given by <surf(n1,n2)>.
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c Arguments:
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c rid,rjd,rkd real output grid location to be interpolated to
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c xpo,ypo,ppo real input physical coordinates
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c rtp real input relative time position (0=beginning, 1=end)
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c n1,n2,n3 int input grid dimensions in x-, y- and p-direction
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c lats,lonw real input south and west boundary of grid space
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c vert real input vertical coordinate grid
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c surf real input lower boundary (surface pressure)
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c mode int input direction of vertical axis (p=1,th=-1)
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c 1: linear, 1 -> nz (th)
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c 2: linear, nz -> 1 (pv)
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c 3: binary (z)
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c 4: binary (p)
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implicit none
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c Declartion of function parameters
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integer nx,ny,nz
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real xpo,ypo,ppo,rtp
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real vert0(nx*ny*nz),vert1(nx*ny*nz)
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real surf0(nx*ny) ,surf1(nx*ny*nz)
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real rid,rjd,rkd
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real dlat,dlon,lats,lonw
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real misdat
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integer mode
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c Set numerical parameters
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real eps
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parameter (eps=1.e-10)
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c Auxiliary variables
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real rid0,rjd0,rkd0,rid1,rjd1,rkd1
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c Externals
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real int_time
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external int_time
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c Get the inidices
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if (abs(rtp).lt.eps) then
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call get_index3 (rid,rjd,rkd,xpo,ypo,ppo,mode,
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> vert0,surf0,nx,ny,nz,lonw,lats,dlon,dlat)
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elseif (abs(rtp-1.).lt.eps) then
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call get_index3 (rid,rjd,rkd,xpo,ypo,ppo,mode,
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> vert1,surf1,nx,ny,nz,lonw,lats,dlon,dlat)
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else
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call get_index3 (rid0,rjd0,rkd0,xpo,ypo,ppo,mode,
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> vert0,surf0,nx,ny,nz,lonw,lats,dlon,dlat)
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call get_index3 (rid1,rjd1,rkd1,xpo,ypo,ppo,mode,
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> vert1,surf1,nx,ny,nz,lonw,lats,dlon,dlat)
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rid = int_time (rid0,rid1,rtp,misdat)
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rjd = int_time (rjd0,rjd1,rtp,misdat)
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rkd = int_time (rkd0,rkd1,rtp,misdat)
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endif
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end
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c -------------------------------------------------------------
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c Interpolate to an arbitrary position in grid space and time
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c -------------------------------------------------------------
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real function int_index4 (ar0,ar1,n1,n2,n3,rid,rjd,rkd,rtp,misdat)
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c Purpose:
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c This subroutine interpolates a 3d-array to an arbitrary
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c location within the grid including a linear time-interpolation.
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c Arguments:
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c rid,rjd,rkd real output grid location to be interpolated to
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c xpo,ypo,ppo real input physical coordinates
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c n1,n2,n3 int input grid dimensions in x-, y- and p-direction
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c lats,lonw real input south and west boundary of grid space
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c vert real input vertical coordinate grid
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c surf real input lower boundary (surface pressure)
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implicit none
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c Declartion of function parameters
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integer n1,n2,n3
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real ar0(n1*n2*n3),ar1(n1*n2*n3)
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real rid,rjd,rkd
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real rtp
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real misdat
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c Set numerical parameters
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real eps
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parameter (eps=1.e-10)
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c Externals
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real int_index3,int_time
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external int_index3,int_time
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c Auxiliary variables
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real val0,val1,val
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c Do the 3d-interpolation
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if (abs(rtp).lt.eps) then
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val = int_index3 (ar0,n1,n2,n3,rid,rjd,rkd,misdat)
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elseif (abs(rtp-1.).lt.eps) then
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val = int_index3 (ar1,n1,n2,n3,rid,rjd,rkd,misdat)
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else
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val0 = int_index3 (ar0,n1,n2,n3,rid,rjd,rkd,misdat)
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val1 = int_index3 (ar1,n1,n2,n3,rid,rjd,rkd,misdat)
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val = int_time (val0,val1,rtp,misdat)
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endif
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c Return value
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int_index4 = val
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return
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end
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c -------------------------------------------------------------
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c Interpolate to an arbitrary position in grid space
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c -------------------------------------------------------------
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real function int_index3 (ar,n1,n2,n3,rid,rjd,rkd,misdat)
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c Purpose:
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c This subroutine interpolates a 3d-array to an arbitrary
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c location within the grid. The interpolation includes the
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c testing of the missing data flag 'misdat'. If one dimension
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c is 1, a 2d-interpolation is performed; if two dimensions
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c are 1, it is a 1d-interpolation; if all three dimensions are
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c 1, no interpolation is performed and the input value is
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c returned.
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c Arguments:
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c ar real input input data array
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c n1,n2,n3 int input dimensions of ar
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c ri,rj,rk real input grid location to be interpolated to
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c misdat real input missing data flag (on if misdat<>0)
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implicit none
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c Declartion of function parameters
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integer n1,n2,n3
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real ar(n1*n2*n3)
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real rid,rjd,rkd
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real misdat
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c Set numerical parameters
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real eps
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parameter (eps=1.e-10)
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c Local variables
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integer i,j,k,ip1,jp1,kp1
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real frac0i,frac0j,frac0k,frac1i,frac1j,frac1k
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real ri,rj,rk
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real val000,val001,val010,val011,val100,val101,val110,val111
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real frc000,frc001,frc010,frc011,frc100,frc101,frc110,frc111
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real frc
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real mdv
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real val
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c Elementary test for dimensions
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if ( (n1.lt.1).or.(n2.lt.1).or.(n3.lt.1) ) then
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print*,'Invalid grid dimensions ',n1,n2,n3
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stop
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endif
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c Activate or inactive the missing data check (quick and dirty)
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if (misdat.ne.0.) then
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mdv = misdat
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else
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mdv = 257.22725394015
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endif
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c Bring the indices into the grid space
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ri = amax1(1.,amin1(float(n1),rid))
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rj = amax1(1.,amin1(float(n2),rjd))
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rk = amax1(1.,amin1(float(n3),rkd))
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c Get the index of the west-south-bottom corner of the box
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i = min0(int(ri),n1-1)
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ip1 = i+1
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j = min0(int(rj),n2-1)
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jp1 = j+1
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k = min0(int(rk),n3-1)
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kp1 = k+1
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c Special handling for 2d arrays
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if (n3.eq.1) then
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k=1
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kp1=1
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endif
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c Get location relative to grid box
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if ( i.ne.ip1 ) then
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frac0i = ri-float(i)
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frac1i = 1.-frac0i
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else
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frac0i = 0.
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frac1i = 1.
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endif
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if ( j.ne.jp1 ) then
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frac0j = rj-float(j)
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frac1j = 1.-frac0j
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else
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frac0j = 0.
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frac1j = 1.
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endif
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if ( k.ne.kp1 ) then
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frac0k = rk-float(k)
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frac1k = 1.-frac0k
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else
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frac0k = 0.
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frac1k = 1.
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endif
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c On a grid point - take the grid point value
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if ( ( abs(frac0i).lt.eps ).and.
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> ( abs(frac0j).lt.eps ).and.
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> ( abs(frac0k).lt.eps ) ) then
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val = ar( i + n1*(j -1) + n1*n2*(k -1) )
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goto 100
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endif
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c Init the fractions
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frc000 = frac1i * frac1j * frac1k
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frc001 = frac0i * frac1j * frac1k
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frc010 = frac1i * frac0j * frac1k
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frc011 = frac0i * frac0j * frac1k
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frc100 = frac1i * frac1j * frac0k
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frc101 = frac0i * frac1j * frac0k
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frc110 = frac1i * frac0j * frac0k
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frc111 = frac0i * frac0j * frac0k
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c Init the values
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val000 = ar( i + n1*(j -1) + n1*n2*(k -1) )
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val001 = ar( ip1 + n1*(j -1) + n1*n2*(k -1) )
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val010 = ar( i + n1*(jp1-1) + n1*n2*(k -1) )
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val011 = ar( ip1 + n1*(jp1-1) + n1*n2*(k -1) )
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val100 = ar( i + n1*(j -1) + n1*n2*(kp1-1) )
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val101 = ar( ip1 + n1*(j -1) + n1*n2*(kp1-1) )
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val110 = ar( i + n1*(jp1-1) + n1*n2*(kp1-1) )
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val111 = ar( ip1 + n1*(jp1-1) + n1*n2*(kp1-1) )
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c Handle missing data
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if ( abs(val000-mdv).lt.eps ) frc000 = 0.
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if ( abs(val001-mdv).lt.eps ) frc001 = 0.
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if ( abs(val010-mdv).lt.eps ) frc010 = 0.
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if ( abs(val011-mdv).lt.eps ) frc011 = 0.
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if ( abs(val100-mdv).lt.eps ) frc100 = 0.
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if ( abs(val101-mdv).lt.eps ) frc101 = 0.
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if ( abs(val110-mdv).lt.eps ) frc110 = 0.
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if ( abs(val111-mdv).lt.eps ) frc111 = 0.
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c Build the final value
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frc = frc000 + frc001 + frc010 + frc011 +
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> frc100 + frc101 + frc110 + frc111
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if ( frc.gt.0. ) then
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val = 1./frc * ( frc000 * val000 + frc001 * val001 +
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> frc010 * val010 + frc011 * val011 +
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> frc100 * val100 + frc101 * val101 +
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> frc110 * val110 + frc111 * val111 )
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else
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val = misdat
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endif
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c Return the value
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100 continue
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int_index3 = val
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end
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c -------------------------------------------------------------
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295 |
c Time interpolation
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296 |
c -------------------------------------------------------------
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297 |
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298 |
real function int_time (val0,val1,reltpos,misdat)
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299 |
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300 |
c Purpose:
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c This subroutine interpolates linearly in time between two
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c values.
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c Arguments:
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c val0 real input value at time 0
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c val1 real input value at time 1
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c reltpos real input relative time (between 0 and 1)
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c misdat real input missing data flag (on if misdat<>0)
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308 |
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implicit none
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310 |
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311 |
c Declaration of parameters
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312 |
real val0
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313 |
real val1
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real reltpos
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real misdat
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c Numerical epsilon
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318 |
real eps
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parameter (eps=1.e-10)
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320 |
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c Local variables
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322 |
real val
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real mdv
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324 |
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325 |
c Activate or inactive the missing data check (quick and dirty)
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326 |
if (misdat.ne.0.) then
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mdv = misdat
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else
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mdv = 257.22725394015
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endif
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c Do the linear interpolation
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333 |
if ( abs(reltpos).lt.eps ) then
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val = val0
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elseif ( abs(reltpos-1.).lt.eps ) then
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336 |
val = val1
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337 |
elseif ( (abs(val0-mdv).gt.eps).and.
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> (abs(val1-mdv).gt.eps) ) then
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val = (1.-reltpos)*val0+reltpos*val1
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else
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341 |
val = mdv
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342 |
endif
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343 |
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344 |
c Return value
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|
345 |
int_time = val
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346 |
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|
347 |
end
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348 |
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349 |
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350 |
c -------------------------------------------------------------
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351 |
c Get the position of a physical point in grid space
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352 |
c -------------------------------------------------------------
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353 |
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354 |
subroutine get_index3 (rid,rjd,rkd,xpo,ypo,ppo,mode,
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355 |
> vert,surf,nx,ny,nz,lonw,lats,dlon,dlat)
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356 |
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357 |
c Purpose:
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358 |
c This subroutine determines the indices (rid,rjd,rkd) in grid
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359 |
c space for a point in physical space (xpo,ypo,ppo). The
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360 |
c horizontal grid is specified by the south-west point (lats,lonw)
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361 |
c and the grid spacing (dlat,dlon). The vertical grid is given
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362 |
c by <vert(n1,n2,n3)>. The lower boundary (typicall surface
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363 |
c pressure) is given by <surf(n1,n2)>.
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364 |
c Arguments:
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365 |
c rid,rjd,rkd real output grid location to be interpolated to
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366 |
c xpo,ypo,ppo real input physical coordinates
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367 |
c n1,n2,n3 int input grid dimensions in x-, y- and p-direction
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368 |
c lats,lonw real input south and west boundary of grid space
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369 |
c vert real input vertical coordinate grid
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370 |
c surf real input lower boundary (surface pressure)
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371 |
c mode int input direction of vertical axis
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372 |
c 1: linear, 1 -> nz (th)
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373 |
c 2: linear, nz -> 1 (pv)
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374 |
c 3: binary (z)
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375 |
c 4: binary (p)
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376 |
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377 |
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378 |
implicit none
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379 |
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380 |
c Declartion of function parameters
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381 |
integer nx,ny,nz
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382 |
real vert(nx*ny*nz)
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383 |
real surf(nx*ny)
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384 |
real rid,rjd,rkd
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|
385 |
real xpo,ypo,ppo
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386 |
real dlat,dlon,lats,lonw
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387 |
integer mode
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388 |
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389 |
c Numerical epsilon
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390 |
real eps
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391 |
parameter (eps=1.e-10)
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392 |
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393 |
c Local variables
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394 |
integer i,j,k
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395 |
real ppo0,ppo1,ppom,psur
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|
396 |
integer i0,im,i1
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397 |
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398 |
c Externals
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|
399 |
real int_index3
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|
400 |
external int_index3
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401 |
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402 |
c Get the horizontal grid indices
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403 |
rid=(xpo-lonw)/dlon+1.
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404 |
rjd=(ypo-lats)/dlat+1.
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405 |
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|
406 |
c Two-dimensional interpolation on horizontal plane: return
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407 |
if ( nz.eq.1 ) then
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|
408 |
rkd = 1.
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|
409 |
goto 100
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|
410 |
endif
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411 |
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412 |
c Lowest-level interpolation: return
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413 |
if ( abs(ppo).lt.eps ) then
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|
414 |
rkd = 1.
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415 |
goto 100
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416 |
endif
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417 |
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418 |
c Get the pressure at the lowest level and at the surface
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|
419 |
ppo0 = int_index3(vert,nx,ny,nz,rid,rjd,real(1),0.)
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|
420 |
psur = int_index3(surf,nx,ny, 1,rid,rjd,real(1),0.)
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421 |
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422 |
c Decide whether the pressure is ascending or descending
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|
423 |
if ( mode.eq.4 ) then
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|
424 |
ppo1 = int_index3(vert,nx,ny,nz,rid,rjd,real(nz),0.)
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|
425 |
if ( ppo1.gt.ppo0 ) then
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|
426 |
ppo0 = ppo1
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|
427 |
endif
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|
428 |
endif
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|
429 |
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|
430 |
c (p-mode) The point is between the surface and the lowest level: return
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|
431 |
if ( mode.eq.4 ) then
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|
432 |
if ( (ppo.ge.ppo0).and.(ppo.le.psur).or.
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|
433 |
> (ppo.le.ppo0).and.(ppo.ge.psur) )
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|
434 |
> then
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|
435 |
psur = int_index3(surf,nx,ny, 1,rid,rjd,real(1),0.)
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|
436 |
rkd = (psur-ppo)/(psur-ppo0)
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|
437 |
goto 100
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|
438 |
endif
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|
439 |
endif
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|
440 |
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|
441 |
c (z-mode) The point is between the surface and the lowest level: return
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|
442 |
if ( mode.eq.3 ) then
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|
443 |
if ( (ppo.ge.ppo0).and.(ppo.le.psur).or.
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|
444 |
> (ppo.le.ppo0).and.(ppo.ge.psur) )
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|
445 |
> then
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|
446 |
psur = int_index3(surf,nx,ny, 1,rid,rjd,real(1),0.)
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|
447 |
rkd = 1.
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|
448 |
goto 100
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|
449 |
endif
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|
450 |
endif
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|
451 |
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|
452 |
c Full-level search (TH): linear ascending scanning through all levels
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|
453 |
if ( mode.eq.1 ) then
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|
454 |
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|
455 |
ppo0 = int_index3(vert,nx,ny,nz,rid,rjd,real(1),0.)
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|
456 |
rkd=0
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|
457 |
do i=1,nz-1
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|
458 |
ppo1 = int_index3(vert,nx,ny,nz,rid,rjd,real(i+1),0.)
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|
459 |
if ( (ppo0.lt.ppo).and.(ppo1.ge.ppo) ) then
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|
460 |
rkd=real(i)+(ppo0-ppo)/(ppo0-ppo1)
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|
461 |
goto 100
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|
462 |
endif
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|
463 |
ppo0 = ppo1
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|
464 |
enddo
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|
465 |
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|
466 |
c Full-level search (PV): linear descending scanning through all levels
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|
467 |
elseif ( mode.eq.2 ) then
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|
468 |
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|
469 |
ppo1 = int_index3(vert,nx,ny,nz,rid,rjd,real(nz),0.)
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|
470 |
rkd=0
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|
471 |
do i=nz-1,1,-1
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|
472 |
ppo0 = int_index3(vert,nx,ny,nz,rid,rjd,real(i),0.)
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|
473 |
if ( (ppo1.gt.ppo).and.(ppo0.le.ppo) ) then
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|
474 |
rkd=real(i)+(ppo0-ppo)/(ppo0-ppo1)
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|
475 |
goto 100
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|
476 |
endif
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|
477 |
ppo1 = ppo0
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|
478 |
enddo
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|
479 |
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|
480 |
c Full-level search (Z): binary search
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|
481 |
elseif ( mode.eq.3 ) then
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|
482 |
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|
483 |
rkd = 0
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|
484 |
i0 = 1
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|
|
485 |
i1 = nz
|
|
|
486 |
ppo0 = int_index3(vert,nx,ny,nz,rid,rjd,real( 1),0.)
|
|
|
487 |
ppo1 = int_index3(vert,nx,ny,nz,rid,rjd,real(nz),0.)
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|
488 |
|
|
|
489 |
do while ( i1.gt.(i0+1) )
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|
490 |
im = (i0+i1)/2
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|
|
491 |
ppom = int_index3(vert,nx,ny,nz,rid,rjd,real(im),0.)
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|
492 |
if (ppom.gt.ppo) then
|
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|
493 |
i1 = im
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|
|
494 |
ppo1 = ppom
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|
|
495 |
else
|
|
|
496 |
i0 = im
|
|
|
497 |
ppo0 = ppom
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|
498 |
endif
|
|
|
499 |
|
|
|
500 |
enddo
|
|
|
501 |
|
|
|
502 |
rkd=real(i0)+(ppo0-ppo)/(ppo0-ppo1)
|
|
|
503 |
|
|
|
504 |
c Full-level search (P): binary search
|
|
|
505 |
elseif ( mode.eq.4 ) then
|
|
|
506 |
|
|
|
507 |
rkd = 0
|
|
|
508 |
i0 = 1
|
|
|
509 |
i1 = nz
|
|
|
510 |
ppo0 = int_index3(vert,nx,ny,nz,rid,rjd,real( 1),0.)
|
|
|
511 |
ppo1 = int_index3(vert,nx,ny,nz,rid,rjd,real(nz),0.)
|
|
|
512 |
|
|
|
513 |
do while ( i1.gt.(i0+1) )
|
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|
514 |
im = (i0+i1)/2
|
|
|
515 |
ppom = int_index3(vert,nx,ny,nz,rid,rjd,real(im),0.)
|
|
|
516 |
if (ppom.lt.ppo) then
|
|
|
517 |
i1 = im
|
|
|
518 |
ppo1 = ppom
|
|
|
519 |
else
|
|
|
520 |
i0 = im
|
|
|
521 |
ppo0 = ppom
|
|
|
522 |
endif
|
|
|
523 |
enddo
|
|
|
524 |
|
|
|
525 |
rkd=real(i0)+(ppo0-ppo)/(ppo0-ppo1)
|
|
|
526 |
|
|
|
527 |
endif
|
|
|
528 |
|
|
|
529 |
c Exit point for subroutine
|
|
|
530 |
100 continue
|
|
|
531 |
|
|
|
532 |
end
|
|
|
533 |
|