C $Header: /u/gcmpack/MITgcm/model/src/ini_spherical_polar_grid.F,v 1.27 2010/04/17 18:25:12 jmc Exp $
C $Name: $
c#include "PACKAGES_CONFIG.h"
#include "CPP_OPTIONS.h"
#undef USE_BACKWARD_COMPATIBLE_GRID
CBOP
C !ROUTINE: INI_SPHERICAL_POLAR_GRID
C !INTERFACE:
SUBROUTINE INI_SPHERICAL_POLAR_GRID( myThid )
C !DESCRIPTION: \bv
C *==========================================================*
C | SUBROUTINE INI_SPHERICAL_POLAR_GRID
C | o Initialise model coordinate system arrays
C *==========================================================*
C | These arrays are used throughout the code in evaluating
C | gradients, integrals and spatial avarages. This routine
C | is called separately by each thread and initialise only
C | the region of the domain it is "responsible" for.
C | Under the spherical polar grid mode primitive distances
C | in X and Y are in degrees. Distance in Z are in m or Pa
C | depending on the vertical gridding mode.
C *==========================================================*
C \ev
C !USES:
IMPLICIT NONE
C === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
c#ifdef ALLOW_EXCH2
c#include "W2_EXCH2_SIZE.h"
c#include "W2_EXCH2_TOPOLOGY.h"
c#include "W2_EXCH2_PARAMS.h"
c#endif /* ALLOW_EXCH2 */
C !INPUT/OUTPUT PARAMETERS:
C == Routine arguments ==
C myThid :: my Thread Id Number
INTEGER myThid
C !LOCAL VARIABLES:
C == Local variables ==
C xG0,yG0 :: coordinate of South-West tile-corner
C iG, jG :: Global coordinate index. Usually used to hold
C :: the south-west global coordinate of a tile.
C lat :: Temporary variables used to hold latitude values.
C bi,bj :: tile indices
C i, j :: loop counters
INTEGER iG, jG
INTEGER bi, bj
INTEGER i, j
_RL lat, dlat, dlon, xG0, yG0
C "Long" real for temporary coordinate calculation
C NOTICE the extended range of indices!!
_RL xGloc(1-Olx:sNx+Olx+1,1-Oly:sNy+Oly+1)
_RL yGloc(1-Olx:sNx+Olx+1,1-Oly:sNy+Oly+1)
C The functions iGl, jGl return the "global" index with valid values beyond
C halo regions
C cnh wrote:
C > I dont understand why we would ever have to multiply the
C > overlap by the total domain size e.g
C > OLx*Nx, OLy*Ny.
C > Can anybody explain? Lines are in ini_spherical_polar_grid.F.
C > Surprised the code works if its wrong, so I am puzzled.
C jmc replied:
C Yes, I can explain this since I put this modification to work
C with small domain (where Oly > Ny, as for instance, zonal-average
C case):
C This has no effect on the acuracy of the evaluation of iGl(I,bi)
C and jGl(j,bj) since we take mod(a+OLx*Nx,Nx) and mod(b+OLy*Ny,Ny).
C But in case a or b is negative, then the FORTRAN function "mod"
C does not return the matematical value of the "modulus" function,
C and this is not good for your purpose.
C This is why I add +OLx*Nx and +OLy*Ny to be sure that the 1rst
C argument of the mod function is positive.
INTEGER iGl,jGl
iGl(i,bi) = 1+MOD(myXGlobalLo-1+(bi-1)*sNx+i+Olx*Nx-1,Nx)
jGl(j,bj) = 1+MOD(myYGlobalLo-1+(bj-1)*sNy+j+Oly*Ny-1,Ny)
c#ifdef ALLOW_EXCH2
c INTEGER tN
c#endif /* ALLOW_EXCH2 */
CEOP
C For each tile ...
DO bj = myByLo(myThid), myByHi(myThid)
DO bi = myBxLo(myThid), myBxHi(myThid)
C-- "Global" index (place holder)
jG = myYGlobalLo + (bj-1)*sNy
iG = myXGlobalLo + (bi-1)*sNx
c#ifdef ALLOW_EXCH2
c IF ( W2_useE2ioLayOut ) THEN
cC- note: does not work for non-uniform delX or delY
c tN = W2_myTileList(bi,bj)
c iG = exch2_txGlobalo(tN)
c jG = exch2_tyGlobalo(tN)
c ENDIF
c#endif /* ALLOW_EXCH2 */
C-- First find coordinate of tile corner (meaning outer corner of halo)
xG0 = xgOrigin
C Find the X-coordinate of the outer grid-line of the "real" tile
DO i=1, iG-1
xG0 = xG0 + delX(i)
ENDDO
C Back-step to the outer grid-line of the "halo" region
DO i=1, Olx
xG0 = xG0 - delX( 1+MOD(Olx*Nx-1+iG-i,Nx) )
ENDDO
C Find the Y-coordinate of the outer grid-line of the "real" tile
yG0 = ygOrigin
DO j=1, jG-1
yG0 = yG0 + delY(j)
ENDDO
C Back-step to the outer grid-line of the "halo" region
DO j=1, Oly
yG0 = yG0 - delY( 1+MOD(Oly*Ny-1+jG-j,Ny) )
ENDDO
C-- Calculate coordinates of cell corners for N+1 grid-lines
DO j=1-Oly,sNy+Oly +1
xGloc(1-Olx,j) = xG0
DO i=1-Olx,sNx+Olx
c xGloc(i+1,j) = xGloc(i,j) + delX(1+mod(Nx-1+iG-1+i,Nx))
xGloc(i+1,j) = xGloc(i,j) + delX( iGl(i,bi) )
ENDDO
ENDDO
DO i=1-Olx,sNx+Olx +1
yGloc(i,1-Oly) = yG0
DO j=1-Oly,sNy+Oly
c yGloc(i,j+1) = yGloc(i,j) + delY(1+mod(Ny-1+jG-1+j,Ny))
yGloc(i,j+1) = yGloc(i,j) + delY( jGl(j,bj) )
ENDDO
ENDDO
C-- Make a permanent copy of [xGloc,yGloc] in [xG,yG]
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
xG(i,j,bi,bj) = xGloc(i,j)
yG(i,j,bi,bj) = yGloc(i,j)
ENDDO
ENDDO
C-- Calculate [xC,yC], coordinates of cell centers
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
C by averaging
xC(i,j,bi,bj) = 0.25 _d 0*(
& xGloc(i,j)+xGloc(i+1,j)+xGloc(i,j+1)+xGloc(i+1,j+1) )
yC(i,j,bi,bj) = 0.25 _d 0*(
& yGloc(i,j)+yGloc(i+1,j)+yGloc(i,j+1)+yGloc(i+1,j+1) )
ENDDO
ENDDO
C-- Calculate [dxF,dyF], lengths between cell faces (through center)
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
C by averaging
c dxF(i,j,bi,bj) = 0.5*(dxG(i,j,bi,bj)+dxG(i,j+1,bi,bj))
c dyF(i,j,bi,bj) = 0.5*(dyG(i,j,bi,bj)+dyG(i+1,j,bi,bj))
C by formula
lat = yC(i,j,bi,bj)
dlon = delX( iGl(i,bi) )
dlat = delY( jGl(j,bj) )
dxF(i,j,bi,bj) = rSphere*COS(deg2rad*lat)*dlon*deg2rad
#ifdef USE_BACKWARD_COMPATIBLE_GRID
dxF(i,j,bi,bj) = delX(iGl(i,bi))*deg2rad*rSphere*
& COS(yC(i,j,bi,bj)*deg2rad)
#endif /* USE_BACKWARD_COMPATIBLE_GRID */
dyF(i,j,bi,bj) = rSphere*dlat*deg2rad
ENDDO
ENDDO
C-- Calculate [dxG,dyG], lengths along cell boundaries
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
C by averaging
c dxG(i,j,bi,bj) = 0.5*(dxF(i,j,bi,bj)+dxF(i,j-1,bi,bj))
c dyG(i,j,bi,bj) = 0.5*(dyF(i,j,bi,bj)+dyF(i-1,j,bi,bj))
C by formula
lat = 0.5 _d 0*(yGloc(i,j)+yGloc(i+1,j))
dlon = delX( iGl(i,bi) )
dlat = delY( jGl(j,bj) )
dxG(i,j,bi,bj) = rSphere*COS(deg2rad*lat)*dlon*deg2rad
if (dxG(i,j,bi,bj).LT.1.) dxG(i,j,bi,bj)=0.
dyG(i,j,bi,bj) = rSphere*dlat*deg2rad
ENDDO
ENDDO
C-- The following arrays are not defined in some parts of the halo
C region. We set them to zero here for safety. If they are ever
C referred to, especially in the denominator then it is a mistake!
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
dxC(i,j,bi,bj) = 0.
dyC(i,j,bi,bj) = 0.
dxV(i,j,bi,bj) = 0.
dyU(i,j,bi,bj) = 0.
rAw(i,j,bi,bj) = 0.
rAs(i,j,bi,bj) = 0.
ENDDO
ENDDO
C-- Calculate [dxC], zonal length between cell centers
DO j=1-Oly,sNy+Oly
DO i=1-Olx+1,sNx+Olx ! NOTE range
C by averaging
dxC(i,j,bi,bj) = 0.5 _d 0*(dxF(i,j,bi,bj)+dxF(i-1,j,bi,bj))
C by formula
c lat = 0.5*(yC(i,j,bi,bj)+yC(i-1,j,bi,bj))
c dlon = 0.5*(delX( iGl(i,bi) ) + delX( iGl(i-1,bi) ))
c dxC(i,j,bi,bj) = rSphere*COS(deg2rad*lat)*dlon*deg2rad
C by difference
c lat = 0.5*(yC(i,j,bi,bj)+yC(i-1,j,bi,bj))
c dlon = (xC(i,j,bi,bj)+xC(i-1,j,bi,bj))
c dxC(i,j,bi,bj) = rSphere*COS(deg2rad*lat)*dlon*deg2rad
ENDDO
ENDDO
C-- Calculate [dyC], meridional length between cell centers
DO j=1-Oly+1,sNy+Oly ! NOTE range
DO i=1-Olx,sNx+Olx
C by averaging
dyC(i,j,bi,bj) = 0.5 _d 0*(dyF(i,j,bi,bj)+dyF(i,j-1,bi,bj))
C by formula
c dlat = 0.5*(delY( jGl(j,bj) ) + delY( jGl(j-1,bj) ))
c dyC(i,j,bi,bj) = rSphere*dlat*deg2rad
C by difference
c dlat = (yC(i,j,bi,bj)+yC(i,j-1,bi,bj))
c dyC(i,j,bi,bj) = rSphere*dlat*deg2rad
ENDDO
ENDDO
C-- Calculate [dxV,dyU], length between velocity points (through corners)
DO j=1-Oly+1,sNy+Oly ! NOTE range
DO i=1-Olx+1,sNx+Olx ! NOTE range
C by averaging (method I)
dxV(i,j,bi,bj) = 0.5 _d 0*(dxG(i,j,bi,bj)+dxG(i-1,j,bi,bj))
dyU(i,j,bi,bj) = 0.5 _d 0*(dyG(i,j,bi,bj)+dyG(i,j-1,bi,bj))
C by averaging (method II)
c dxV(i,j,bi,bj) = 0.5*(dxG(i,j,bi,bj)+dxG(i-1,j,bi,bj))
c dyU(i,j,bi,bj) = 0.5*(dyC(i,j,bi,bj)+dyC(i-1,j,bi,bj))
ENDDO
ENDDO
C-- Calculate vertical face area (tracer cells)
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
lat=0.5 _d 0*(yGloc(i,j)+yGloc(i+1,j))
dlon=delX( iGl(i,bi) )
dlat=delY( jGl(j,bj) )
rA(i,j,bi,bj) = rSphere*rSphere*dlon*deg2rad
& *ABS( SIN((lat+dlat)*deg2rad)-SIN(lat*deg2rad) )
#ifdef USE_BACKWARD_COMPATIBLE_GRID
lat=yC(i,j,bi,bj)-delY( jGl(j,bj) )*0.5 _d 0
lon=yC(i,j,bi,bj)+delY( jGl(j,bj) )*0.5 _d 0
rA(i,j,bi,bj) = dyF(i,j,bi,bj)
& *rSphere*(SIN(lon*deg2rad)-SIN(lat*deg2rad))
#endif /* USE_BACKWARD_COMPATIBLE_GRID */
ENDDO
ENDDO
C-- Calculate vertical face area (u cells)
DO j=1-Oly,sNy+Oly
DO i=1-Olx+1,sNx+Olx ! NOTE range
C by averaging
rAw(i,j,bi,bj) = 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj))
C by formula
c lat=yGloc(i,j)
c dlon=0.5*( delX( iGl(i,bi) ) + delX( iGl(i-1,bi) ) )
c dlat=delY( jGl(j,bj) )
c rAw(i,j,bi,bj) = rSphere*rSphere*dlon*deg2rad
c & *abs( sin((lat+dlat)*deg2rad)-sin(lat*deg2rad) )
ENDDO
ENDDO
C-- Calculate vertical face area (v cells)
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
C by formula
lat=yC(i,j,bi,bj)
dlon=delX( iGl(i,bi) )
dlat=0.5 _d 0*( delY( jGl(j,bj) ) + delY( jGl(j-1,bj) ) )
rAs(i,j,bi,bj) = rSphere*rSphere*dlon*deg2rad
& *ABS( SIN(lat*deg2rad)-SIN((lat-dlat)*deg2rad) )
#ifdef USE_BACKWARD_COMPATIBLE_GRID
lon=yC(i,j,bi,bj)-delY( jGl(j,bj) )
lat=yC(i,j,bi,bj)
rAs(i,j,bi,bj) = rSphere*delX(iGl(i,bi))*deg2rad
& *rSphere*(SIN(lat*deg2rad)-SIN(lon*deg2rad))
#endif /* USE_BACKWARD_COMPATIBLE_GRID */
IF (ABS(lat).GT.90..OR.ABS(lat-dlat).GT.90.) rAs(i,j,bi,bj)=0.
ENDDO
ENDDO
C-- Calculate vertical face area (vorticity points)
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
C by formula
lat =0.5 _d 0*(yGloc(i,j)+yGloc(i,j+1))
dlon=0.5 _d 0*( delX( iGl(i,bi) ) + delX( iGl(i-1,bi) ) )
dlat=0.5 _d 0*( delY( jGl(j,bj) ) + delY( jGl(j-1,bj) ) )
rAz(i,j,bi,bj) = rSphere*rSphere*dlon*deg2rad
& *ABS( SIN(lat*deg2rad)-SIN((lat-dlat)*deg2rad) )
IF (ABS(lat).GT.90..OR.ABS(lat-dlat).GT.90.) rAz(i,j,bi,bj)=0.
ENDDO
ENDDO
C-- Calculate trigonometric terms & grid orientation:
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
lat=0.5 _d 0*(yGloc(i,j)+yGloc(i,j+1))
tanPhiAtU(i,j,bi,bj)=TAN(lat*deg2rad)
lat=0.5 _d 0*(yGloc(i,j)+yGloc(i+1,j))
tanPhiAtV(i,j,bi,bj)=TAN(lat*deg2rad)
angleCosC(i,j,bi,bj) = 1.
angleSinC(i,j,bi,bj) = 0.
ENDDO
ENDDO
C-- Cosine(lat) scaling
DO j=1-OLy,sNy+OLy
jG = myYGlobalLo + (bj-1)*sNy + j-1
jG = MIN(MAX(1,jG),Ny)
IF (cosPower.NE.0.) THEN
cosFacU(j,bi,bj)=COS(yC(1,j,bi,bj)*deg2rad)
& **cosPower
cosFacV(j,bi,bj)=COS((yC(1,j,bi,bj)-0.5*delY(jG))*deg2rad)
& **cosPower
cosFacU(j,bi,bj)=ABS(cosFacU(j,bi,bj))
cosFacV(j,bi,bj)=ABS(cosFacV(j,bi,bj))
sqcosFacU(j,bi,bj)=SQRT(cosFacU(j,bi,bj))
sqcosFacV(j,bi,bj)=SQRT(cosFacV(j,bi,bj))
ELSE
cosFacU(j,bi,bj)=1.
cosFacV(j,bi,bj)=1.
sqcosFacU(j,bi,bj)=1.
sqcosFacV(j,bi,bj)=1.
ENDIF
ENDDO
ENDDO ! bi
ENDDO ! bj
IF ( rotateGrid ) THEN
CALL ROTATE_SPHERICAL_POLAR_GRID( xC, yC, myThid )
CALL ROTATE_SPHERICAL_POLAR_GRID( xG, yG, myThid )
CALL CALC_ANGLES( myThid )
ENDIF
RETURN
END