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C $Header: /u/gcmpack/MITgcm/model/src/rotate_spherical_polar_grid.F,v 1.3 2011/02/21 17:57:36 jmc Exp $ |
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C $Name: $ |
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#include "CPP_OPTIONS.h" |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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CBOP |
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C !ROUTINE: ROTATE_SPHERICAL_POLAR_GRID |
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C !INTERFACE: |
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SUBROUTINE ROTATE_SPHERICAL_POLAR_GRID( |
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U X, Y, |
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I myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *===================================================================* |
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C | SUBROUTINE ROTATE_SPHERICAL_POLAR_GRID |
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C | o rotate the model coordinates on the input arrays to |
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C | geographical coordinates |
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C | o this is useful when a rotated spherical grid is used, |
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C | e.g., in order to avoid the pole singularity. |
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C | The three Euler angles PhiEuler, ThetaEuler, and PsiEuler |
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C | define the rotation about the original z-axis (of an sphere |
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C | centered cartesian grid), the new x-axis, and the new z-axis, |
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C | respectively. |
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C | The input coordinates X, Y are assumed to be the model coordinates |
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C | on a rotated grid defined by the Euler angles. In this S/R they |
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C | are rotated *BACK* to the geographical coordinate; that is why |
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C | all rotation matrices are the inverses of the original matrices. |
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C | On exit X and Y are the geographical coordinates, that are |
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C | used to compute the Coriolis parameter and also to interpolate |
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C | forcing fields to as in pkg/exf/exf_interf.F |
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C | Naturally, this feature does not work with all packages, so the |
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C | some combinations are prohibited in config_summary (flt, |
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C | flt_zonal, ecco, profiles), because there the coordinates are |
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C | assumed to be regular spherical grid coordinates. |
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C *===================================================================* |
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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine arguments == |
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C X, Y :: on entry: model coordinate location |
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C :: on exit: geographical coordinate location |
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C myThid :: my Thread Id Number |
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_RS X(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RS Y(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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INTEGER myThid |
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CEOP |
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|
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C !LOCAL VARIABLES: |
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C == Local variables == |
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C bi,bj :: Tile indices |
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C i, j :: Loop counters |
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INTEGER bi, bj |
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INTEGER I, J, iA, jA, kA |
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C Euler angles in radians |
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_RL phiRad, thetaRad, psiRad |
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C inverted rotation matrix |
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_RL Ainv(3,3), Binv(3,3), Cinv(3,3), Dinv(3,3), CB(3,3) |
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C cartesian coordinates |
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_RL XYZgeo(3), XYZrot(3) |
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C some auxilliary variables |
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_RL hypotxy |
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CEOP |
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|
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C convert to radians |
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phiRad = phiEuler *deg2rad |
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thetaRad = thetaEuler*deg2rad |
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psiRad = psiEuler *deg2rad |
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|
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C create inverse of full rotation matrix |
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Dinv(1,1) = COS(phiRad) |
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Dinv(1,2) = -SIN(phiRad) |
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Dinv(1,3) = 0. _d 0 |
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C |
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Dinv(2,1) = SIN(phiRad) |
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Dinv(2,2) = COS(phiRad) |
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Dinv(2,3) = 0. _d 0 |
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C |
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Dinv(3,1) = 0. _d 0 |
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Dinv(3,2) = 0. _d 0 |
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Dinv(3,3) = 1. _d 0 |
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C |
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Cinv(1,1) = 1. _d 0 |
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Cinv(1,2) = 0. _d 0 |
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Cinv(1,3) = 0. _d 0 |
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C |
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Cinv(2,1) = 0. _d 0 |
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Cinv(2,2) = COS(thetaRad) |
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Cinv(2,3) = -SIN(thetaRad) |
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C |
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Cinv(3,1) = 0. _d 0 |
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Cinv(3,2) = SIN(thetaRad) |
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Cinv(3,3) = COS(thetaRad) |
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C |
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Binv(1,1) = COS(psiRad) |
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Binv(1,2) = -SIN(psiRad) |
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Binv(1,3) = 0. _d 0 |
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C |
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Binv(2,1) = SIN(psiRad) |
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Binv(2,2) = COS(psiRad) |
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Binv(2,3) = 0. _d 0 |
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C |
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Binv(3,1) = 0. _d 0 |
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Binv(3,2) = 0. _d 0 |
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Binv(3,3) = 1. _d 0 |
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C Ainv = Binv*Cinv*Dinv (matrix multiplications) |
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DO jA=1,3 |
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DO iA=1,3 |
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Ainv(iA,jA) = 0. _d 0 |
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CB (iA,jA) = 0. _d 0 |
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ENDDO |
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ENDDO |
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DO jA=1,3 |
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DO iA=1,3 |
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DO kA=1,3 |
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CB (iA,jA) = CB (iA,jA) + Cinv(iA,kA)*Binv(kA,jA) |
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ENDDO |
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ENDDO |
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ENDDO |
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DO jA=1,3 |
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DO iA=1,3 |
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DO kA=1,3 |
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Ainv(iA,jA) = Ainv(iA,jA) + Dinv(iA,kA)*CB(kA,jA) |
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ENDDO |
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ENDDO |
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ENDDO |
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C |
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|
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C For each tile ... |
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DO bj = myByLo(myThid), myByHi(myThid) |
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DO bi = myBxLo(myThid), myBxHi(myThid) |
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|
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C loop over grid points |
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DO J = 1-OLy,sNy+OLy |
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DO I = 1-OLx,sNx+OLx |
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C transform spherical coordinates with unit radius |
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C to sphere centered cartesian coordinates |
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XYZrot(1) = |
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& COS( Y(I,J,bi,bj)*deg2rad )*COS( X(I,J,bi,bj)*deg2rad ) |
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XYZrot(2) = |
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& COS( Y(I,J,bi,bj)*deg2rad )*SIN( X(I,J,bi,bj)*deg2rad ) |
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XYZrot(3) = SIN( Y(I,J,bi,bj)*deg2rad ) |
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C rotate cartesian coordinate (matrix multiplication) |
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DO iA=1,3 |
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XYZgeo(iA) = 0. _d 0 |
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ENDDO |
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DO iA=1,3 |
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DO jA=1,3 |
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XYZgeo(iA) = XYZgeo(iA) + Ainv(iA,jA)*XYZrot(jA) |
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ENDDO |
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ENDDO |
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C tranform cartesian coordinates back to spherical coordinates |
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hypotxy = SQRT( ABS(XYZgeo(1))*ABS(XYZgeo(1)) |
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& + ABS(XYZgeo(2))*ABS(XYZgeo(2)) ) |
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IF(XYZgeo(1) .EQ. 0. _d 0 .AND. XYZgeo(2) .EQ. 0. _d 0)THEN |
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C happens exactly at the poles |
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X(I,J,bi,bj) = 0. _d 0 |
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ELSE |
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X(I,J,bi,bj) = ATAN2(XYZgeo(2),XYZgeo(1))/deg2rad |
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IF ( X(I,J,bi,bj) .LT. 0. _d 0 ) |
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& X(I,J,bi,bj) = X(I,J,bi,bj) + 360. _d 0 |
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ENDIF |
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IF(hypotxy .EQ. 0. _d 0 .AND. XYZgeo(3) .EQ. 0. _d 0)THEN |
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C this can not happen for a sphere with unit radius |
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Y(I,J,bi,bj) = 0. _d 0 |
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ELSE |
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Y(I,J,bi,bj) = ATAN2(XYZgeo(3),hypotxy)/deg2rad |
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ENDIF |
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ENDDO |
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ENDDO |
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C bi,bj-loops |
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ENDDO |
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ENDDO |
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|
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RETURN |
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END |
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