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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_implicit_r.F,v 1.26 2016/10/26 00:46:00 jmc Exp $ |
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C $Name: $ |
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|
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#include "GAD_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GAD_IMPLICIT_R |
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C !INTERFACE: |
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SUBROUTINE GAD_IMPLICIT_R( |
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I implicitAdvection, advectionScheme, tracerIdentity, |
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I deltaTLev, |
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I kappaRX, recip_hFac, wFld, tracer, |
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U gTracer, |
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I bi, bj, myTime, myIter, myThid ) |
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C !DESCRIPTION: |
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C Solve implicitly vertical advection and diffusion for one tracer. |
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|
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C !USES: |
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IMPLICIT NONE |
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C == Global data == |
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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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#include "GRID.h" |
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#include "SURFACE.h" |
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#include "GAD.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 implicitAdvection :: if True, treat vertical advection implicitly |
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C advectionScheme :: advection scheme to use |
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C tracerIdentity :: Identifier for the tracer |
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C kappaRX :: 3-D array for vertical diffusion coefficient |
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C recip_hFac :: inverse of cell open-depth factor |
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C wFld :: Advection velocity field, vertical component |
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C tracer :: tracer field at current time step |
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C gTracer :: future tracer field |
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C bi,bj :: tile indices |
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C myTime :: current time |
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C myIter :: current iteration number |
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C myThid :: thread number |
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LOGICAL implicitAdvection |
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INTEGER advectionScheme |
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INTEGER tracerIdentity |
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_RL deltaTLev(Nr) |
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_RL kappaRX (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RS recip_hFac(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL wFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL tracer (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL gTracer (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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INTEGER bi, bj |
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_RL myTime |
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INTEGER myIter, myThid |
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|
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#ifdef ALLOW_DIAGNOSTICS |
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C !FUNCTIONS: |
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CHARACTER*4 GAD_DIAG_SUFX |
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EXTERNAL GAD_DIAG_SUFX |
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LOGICAL DIAGNOSTICS_IS_ON |
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EXTERNAL DIAGNOSTICS_IS_ON |
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#endif |
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|
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C !LOCAL VARIABLES: |
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C == Local variables == |
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C iMin,iMax,jMin,jMax :: computational domain |
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C i,j,k :: loop indices |
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C a5d :: 2nd lower diagonal of the pentadiagonal matrix |
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C b5d :: 1rst lower diagonal of the pentadiagonal matrix |
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C c5d :: main diagonal of the pentadiagonal matrix |
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C d5d :: 1rst upper diagonal of the pentadiagonal matrix |
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C e5d :: 2nd upper diagonal of the pentadiagonal matrix |
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C rTrans :: vertical volume transport at interface k |
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C localTr :: local copy of tracer (for Non-Lin Adv.Scheme) |
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C diagonalNumber :: number of non-zero diagonals in the matrix |
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C errCode :: > 0 if singular matrix |
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C msgBuf :: Informational/error message buffer |
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INTEGER iMin,iMax,jMin,jMax |
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PARAMETER( iMin = 1, iMax = sNx ) |
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PARAMETER( jMin = 1, jMax = sNy ) |
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INTEGER i,j,k |
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INTEGER diagonalNumber, errCode |
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_RL a5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL b5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL c5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL d5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL e5d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL rTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL localTr(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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#ifdef ALLOW_DIAGNOSTICS |
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CHARACTER*8 diagName |
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CHARACTER*4 diagSufx |
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LOGICAL diagDif, diagAdv |
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INTEGER km1, km2, kp1, kp2 |
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_RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL div(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL flx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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# ifdef SOLVE_DIAGONAL_LOWMEMORY |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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# endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
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#endif /* ALLOW_DIAGNOSTICS */ |
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CEOP |
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|
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C-- no need to solve anything with only 1 level: |
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IF (Nr.GT.1) THEN |
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|
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C-- Initialise |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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a5d(i,j,k) = 0. _d 0 |
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b5d(i,j,k) = 0. _d 0 |
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c5d(i,j,k) = 1. _d 0 |
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d5d(i,j,k) = 0. _d 0 |
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e5d(i,j,k) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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diagonalNumber = 1 |
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|
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IF (implicitDiffusion) THEN |
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C-- set the tri-diagonal matrix to solve the implicit diffusion problem |
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diagonalNumber = 3 |
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C- 1rst lower diagonal : |
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DO k=2,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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b5d(i,j,k) = -deltaTLev(k)*maskC(i,j,k-1,bi,bj) |
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& *recip_hFac(i,j,k)*recip_drF(k) |
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& *recip_deepFac2C(k)*recip_rhoFacC(k) |
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& *kappaRX(i,j, k )*recip_drC( k ) |
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& *deepFac2F( k )*rhoFacF( k ) |
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ENDDO |
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ENDDO |
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ENDDO |
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C- 1rst upper diagonal : |
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DO k=1,Nr-1 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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d5d(i,j,k) = -deltaTLev(k)*maskC(i,j,k+1,bi,bj) |
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& *recip_hFac(i,j,k)*recip_drF(k) |
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& *recip_deepFac2C(k)*recip_rhoFacC(k) |
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& *kappaRX(i,j,k+1)*recip_drC(k+1) |
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& *deepFac2F(k+1)*rhoFacF(k+1) |
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ENDDO |
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ENDDO |
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ENDDO |
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C- Main diagonal : |
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DO k=1,Nr |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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c5d(i,j,k) = 1. _d 0 - ( b5d(i,j,k) + d5d(i,j,k) ) |
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C to recover older (prior to 2016-10-05) results: |
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c c5d(i,j,k) = 1. _d 0 - b5d(i,j,k) - d5d(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C-- end if implicitDiffusion |
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ENDIF |
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|
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IF (implicitAdvection) THEN |
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|
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C-- Non-Linear Advection scheme: keep a local copy of tracer field |
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IF ( advectionScheme.EQ.ENUM_FLUX_LIMIT .OR. |
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& advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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IF ( multiDimAdvection ) THEN |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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localTr(i,j,k) = gTracer(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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localTr(i,j,k) = tracer(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDIF |
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ENDIF |
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|
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DO k=Nr,1,-1 |
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|
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C-- Compute transport |
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IF (k.EQ.1) THEN |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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rTrans(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ELSE |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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rTrans(i,j) = wFld(i,j,k)*rA(i,j,bi,bj) |
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& *deepFac2F(k)*rhoFacF(k) |
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& *maskC(i,j,k-1,bi,bj) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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#ifdef ALLOW_AIM |
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C- a hack to prevent Water-Vapor vert.transport into the stratospheric level Nr |
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IF ( k.GE.2 .AND. |
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& (.NOT.useAIM .OR.tracerIdentity.NE.GAD_SALINITY .OR.k.LT.Nr) |
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& ) THEN |
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#else |
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IF ( k.GE.2 ) THEN |
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#endif |
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|
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IF ( advectionScheme.EQ.ENUM_CENTERED_2ND ) THEN |
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diagonalNumber = 3 |
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CALL GAD_C2_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_1RST |
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& .OR. advectionScheme.EQ.ENUM_DST2 ) THEN |
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diagonalNumber = 3 |
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CALL GAD_DST2U1_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I advectionScheme, deltaTLev, |
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I rTrans, recip_hFac, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_FLUX_LIMIT ) THEN |
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diagonalNumber = 3 |
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CALL GAD_FLUXLIMIT_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, localTr, |
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U b5d, c5d, d5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_3RD |
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& .OR. advectionScheme.EQ.ENUM_CENTERED_4TH |
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& .OR. advectionScheme.EQ.ENUM_DST3 ) THEN |
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diagonalNumber = 5 |
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CALL GAD_U3C4_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I advectionScheme, deltaTLev, |
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I rTrans, recip_hFac, |
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U a5d, b5d, c5d, d5d, e5d, |
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I myThid ) |
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ELSEIF ( advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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diagonalNumber = 5 |
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CALL GAD_DST3FL_IMPL_R( bi,bj,k, iMin,iMax,jMin,jMax, |
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I deltaTLev, rTrans, recip_hFac, localTr, |
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U a5d, b5d, c5d, d5d, e5d, |
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I myThid ) |
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ELSE |
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STOP 'GAD_IMPLICIT_R: Adv.Scheme in Impl form not yet coded' |
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ENDIF |
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|
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ENDIF |
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|
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C-- end k loop |
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ENDDO |
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|
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C-- end if implicitAdvection |
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ENDIF |
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|
| 261 |
IF ( diagonalNumber .EQ. 3 ) THEN |
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C-- Solve tri-diagonal system : |
| 263 |
errCode = -1 |
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CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax, |
| 265 |
I b5d, c5d, d5d, |
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U gTracer, |
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O errCode, |
| 268 |
I bi, bj, myThid ) |
| 269 |
IF (errCode.GE.1) THEN |
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STOP 'GAD_IMPLICIT_R: error when solving 3-Diag problem' |
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ENDIF |
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ELSEIF ( diagonalNumber .EQ. 5 ) THEN |
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C-- Solve penta-diagonal system : |
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errCode = -1 |
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CALL SOLVE_PENTADIAGONAL( iMin,iMax, jMin,jMax, |
| 276 |
I a5d, b5d, c5d, d5d, e5d, |
| 277 |
U gTracer, |
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O errCode, |
| 279 |
I bi, bj, myThid ) |
| 280 |
IF (errCode.GE.1) THEN |
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STOP 'GAD_IMPLICIT_R: error when solving 5-Diag problem' |
| 282 |
ENDIF |
| 283 |
ELSEIF ( diagonalNumber .NE. 1 ) THEN |
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STOP 'GAD_IMPLICIT_R: no solver available' |
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ENDIF |
| 286 |
|
| 287 |
#ifdef ALLOW_DIAGNOSTICS |
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C-- Set diagnostic suffix for the current tracer |
| 289 |
IF ( useDiagnostics ) THEN |
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diagSufx = GAD_DIAG_SUFX( tracerIdentity, myThid ) |
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diagName = 'DFrI'//diagSufx |
| 292 |
diagDif = implicitDiffusion |
| 293 |
IF ( diagDif ) diagDif = DIAGNOSTICS_IS_ON(diagName,myThid) |
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diagName = 'ADVr'//diagSufx |
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diagAdv = implicitAdvection |
| 296 |
IF ( diagAdv ) diagAdv = DIAGNOSTICS_IS_ON(diagName,myThid) |
| 297 |
|
| 298 |
IF ( diagDif .OR. diagAdv ) THEN |
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DO j=1-OLy,sNy+OLy |
| 300 |
DO i=1-OLx,sNx+OLx |
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flx(i,j) = 0. _d 0 |
| 302 |
ENDDO |
| 303 |
ENDDO |
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C-- start diagnostics k loop |
| 305 |
DO k= Nr,1,-1 |
| 306 |
|
| 307 |
IF ( implicitDiffusion .AND. k.GE.2 ) THEN |
| 308 |
DO j=jMin,jMax |
| 309 |
DO i=iMin,iMax |
| 310 |
df(i,j) = |
| 311 |
cc#ifdef ALLOW_AUTODIFF_OPENAD |
| 312 |
cc & -rA(i,j,bi,bj)%v |
| 313 |
cc#else |
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& -rA(i,j,bi,bj)*deepFac2F(k)*rhoFacF(k) |
| 315 |
cc#endif |
| 316 |
& * kappaRX(i,j,k)*recip_drC(k)*rkSign |
| 317 |
& * (gTracer(i,j,k) - gTracer(i,j,k-1)) |
| 318 |
& * maskC(i,j,k,bi,bj) |
| 319 |
& * maskC(i,j,k-1,bi,bj) |
| 320 |
ENDDO |
| 321 |
ENDDO |
| 322 |
ELSE |
| 323 |
DO j=1-OLy,sNy+OLy |
| 324 |
DO i=1-OLx,sNx+OLx |
| 325 |
df(i,j) = 0. _d 0 |
| 326 |
ENDDO |
| 327 |
ENDDO |
| 328 |
ENDIF |
| 329 |
|
| 330 |
C- Note: Needs to explicitly increment counter (call DIAGNOSTICS_COUNT) |
| 331 |
C since skipping k=1 DIAGNOSTICS_FILL call. |
| 332 |
IF ( diagDif .AND. k.GE.2 ) THEN |
| 333 |
diagName = 'DFrI'//diagSufx |
| 334 |
CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid) |
| 335 |
IF ( k.EQ.2 ) CALL DIAGNOSTICS_COUNT(diagName,bi,bj,myThid) |
| 336 |
#ifdef ALLOW_LAYERS |
| 337 |
IF ( useLayers ) THEN |
| 338 |
CALL LAYERS_FILL( df, tracerIdentity, 'DFR', |
| 339 |
& k, 1, 2,bi,bj, myThid ) |
| 340 |
ENDIF |
| 341 |
#endif /* ALLOW_LAYERS */ |
| 342 |
ENDIF |
| 343 |
|
| 344 |
IF ( diagAdv ) THEN |
| 345 |
#ifdef SOLVE_DIAGONAL_LOWMEMORY |
| 346 |
diagName = 'ADVr'//diagSufx |
| 347 |
WRITE(msgBuf,'(4A)') 'GAD_IMPLICIT_R: ', |
| 348 |
& 'unable to compute Diagnostic "', diagName, '" with' |
| 349 |
CALL PRINT_MESSAGE( msgBuf, errorMessageUnit, |
| 350 |
& SQUEEZE_RIGHT, myThid ) |
| 351 |
WRITE(msgBuf,'(4A)') 'GAD_IMPLICIT_R: ', |
| 352 |
& '#define SOLVE_DIAGONAL_LOWMEMORY (in CPP_OPTIONS.h)' |
| 353 |
CALL PRINT_MESSAGE( msgBuf, errorMessageUnit, |
| 354 |
& SQUEEZE_RIGHT, myThid ) |
| 355 |
STOP 'ABNORMAL END: S/R GAD_IMPLICIT_R' |
| 356 |
#endif /* SOLVE_DIAGONAL_LOWMEMORY */ |
| 357 |
km1=MAX(1,k-1) |
| 358 |
km2=MAX(1,k-2) |
| 359 |
kp1=MIN(Nr,k+1) |
| 360 |
kp2=MIN(Nr,k+2) |
| 361 |
C-- Flux_divergence*deltaT = Tr^n - Tr^n+1 = [A-I](Tr^n+1) |
| 362 |
C = deltaT*rkSign*[ Flx_k+1 - Flx_k ]/dz |
| 363 |
DO j=jMin,jMax |
| 364 |
DO i=iMin,iMax |
| 365 |
div(i,j) = gTracer(i,j,k)*( c5d(i,j,k) - 1. _d 0 ) |
| 366 |
& + gTracer(i,j,km1)*b5d(i,j,k) |
| 367 |
& + gTracer(i,j,kp1)*d5d(i,j,k) |
| 368 |
ENDDO |
| 369 |
ENDDO |
| 370 |
IF ( diagonalNumber .EQ. 5 ) THEN |
| 371 |
DO j=jMin,jMax |
| 372 |
DO i=iMin,iMax |
| 373 |
div(i,j) = div(i,j) |
| 374 |
& + gTracer(i,j,km2)*a5d(i,j,k) |
| 375 |
& + gTracer(i,j,kp2)*e5d(i,j,k) |
| 376 |
ENDDO |
| 377 |
ENDDO |
| 378 |
ENDIF |
| 379 |
#ifdef NONLIN_FRSURF |
| 380 |
IF ( nonlinFreeSurf.GT.0 ) THEN |
| 381 |
C-- use future hFac to stay consistent with solver matrix |
| 382 |
IF ( select_rStar.GT.0 ) THEN |
| 383 |
DO j=jMin,jMax |
| 384 |
DO i=iMin,iMax |
| 385 |
div(i,j) = div(i,j)*h0FacC(i,j,k,bi,bj)*drF(k) |
| 386 |
& *rStarFacC(i,j,bi,bj) |
| 387 |
ENDDO |
| 388 |
ENDDO |
| 389 |
ELSEIF ( selectSigmaCoord.NE.0 ) THEN |
| 390 |
DO j=jMin,jMax |
| 391 |
DO i=iMin,iMax |
| 392 |
div(i,j) = div(i,j)*( |
| 393 |
& _hFacC(i,j,k,bi,bj)*drF(k) |
| 394 |
& + dBHybSigF(k)*dEtaHdt(i,j,bi,bj)*deltaTFreeSurf |
| 395 |
& ) |
| 396 |
ENDDO |
| 397 |
ENDDO |
| 398 |
ELSE |
| 399 |
DO j=jMin,jMax |
| 400 |
DO i=iMin,iMax |
| 401 |
IF ( k.EQ.kSurfC(i,j,bi,bj) ) THEN |
| 402 |
div(i,j) = div(i,j)*hFac_surfC(i,j,bi,bj)*drF(k) |
| 403 |
ELSE |
| 404 |
div(i,j) = div(i,j)*_hFacC(i,j,k,bi,bj)*drF(k) |
| 405 |
ENDIF |
| 406 |
ENDDO |
| 407 |
ENDDO |
| 408 |
ENDIF |
| 409 |
ELSE |
| 410 |
#else /* NONLIN_FRSURF */ |
| 411 |
IF ( .TRUE. ) THEN |
| 412 |
#endif /* NONLIN_FRSURF */ |
| 413 |
C-- use current hFac (consistent with solver matrix) |
| 414 |
DO j=jMin,jMax |
| 415 |
DO i=iMin,iMax |
| 416 |
div(i,j) = div(i,j)*_hFacC(i,j,k,bi,bj)*drF(k) |
| 417 |
ENDDO |
| 418 |
ENDDO |
| 419 |
ENDIF |
| 420 |
DO j=jMin,jMax |
| 421 |
DO i=iMin,iMax |
| 422 |
flx(i,j) = flx(i,j) |
| 423 |
cc#ifdef ALLOW_AUTODIFF_OPENAD |
| 424 |
cc & - rkSign*div(i,j)*rA(i,j,bi,bj)%v/deltaTLev(k) |
| 425 |
cc#else |
| 426 |
& - rkSign*div(i,j)*rA(i,j,bi,bj) |
| 427 |
& *deepFac2C(k)*rhoFacC(k)/deltaTLev(k) |
| 428 |
cc#endif |
| 429 |
af(i,j) = flx(i,j) - df(i,j) |
| 430 |
ENDDO |
| 431 |
ENDDO |
| 432 |
diagName = 'ADVr'//diagSufx |
| 433 |
CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid) |
| 434 |
#ifdef ALLOW_LAYERS |
| 435 |
IF ( useLayers ) THEN |
| 436 |
CALL LAYERS_FILL(af,tracerIdentity,'AFR', |
| 437 |
& k,1,2,bi,bj,myThid) |
| 438 |
ENDIF |
| 439 |
#endif /* ALLOW_LAYERS */ |
| 440 |
ENDIF |
| 441 |
|
| 442 |
C-- end diagnostics k loop |
| 443 |
ENDDO |
| 444 |
ENDIF |
| 445 |
ENDIF |
| 446 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 447 |
|
| 448 |
C-- end if Nr > 1 |
| 449 |
ENDIF |
| 450 |
|
| 451 |
RETURN |
| 452 |
END |
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