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C $Header: /usr/local/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.21 2003/09/24 04:52:38 dimitri 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_CALC_RHS |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_CALC_RHS( |
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I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown, |
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I xA,yA,uTrans,vTrans,rTrans,maskUp, |
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I diffKh, diffK4, KappaRT, Tracer, |
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I tracerIdentity, advectionScheme, calcAdvection, |
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U fVerT, gTracer, |
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I myThid ) |
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|
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C !DESCRIPTION: |
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C Calculates the tendancy of a tracer due to advection and diffusion. |
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C It calculates the fluxes in each direction indepentently and then |
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C sets the tendancy to the divergence of these fluxes. The advective |
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C fluxes are only calculated here when using the linear advection schemes |
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C otherwise only the diffusive and parameterized fluxes are calculated. |
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C |
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C Contributions to the flux are calculated and added: |
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C \begin{equation*} |
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C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP} |
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C \end{equation*} |
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C |
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C The tendancy is the divergence of the fluxes: |
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C \begin{equation*} |
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C G_\theta = G_\theta + \nabla \cdot {\bf F} |
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C \end{equation*} |
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C |
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C The tendancy is assumed to contain data on entry. |
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|
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C !USES: =============================================================== |
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IMPLICIT NONE |
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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 "DYNVARS.h" |
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#include "SURFACE.h" |
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#include "GAD.h" |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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#include "tamc.h" |
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#include "tamc_keys.h" |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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|
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C iMin,iMax,jMin,jMax :: loop range for called routines |
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C kup :: index into 2 1/2D array, toggles between 1 and 2 |
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C kdown :: index into 2 1/2D array, toggles between 2 and 1 |
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C kp1 :: =k+1 for k<Nr, =Nr for k=Nr |
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C xA,yA :: areas of X and Y face of tracer cells |
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C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points |
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C maskUp :: 2-D array for mask at W points |
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C diffKh :: horizontal diffusion coefficient |
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C diffK4 :: bi-harmonic diffusion coefficient |
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C KappaRT :: 3-D array for vertical diffusion coefficient |
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C Tracer :: tracer field |
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C tracerIdentity :: identifier for the tracer (required for KPP and GM) |
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C advectionScheme :: advection scheme to use |
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C calcAdvection :: =False if Advec terms computed with multiDim scheme |
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C myThid :: thread number |
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INTEGER bi,bj,iMin,iMax,jMin,jMax |
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INTEGER k,kUp,kDown,kM1 |
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_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL diffKh, diffK4 |
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_RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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INTEGER tracerIdentity |
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INTEGER advectionScheme |
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LOGICAL calcAdvection |
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INTEGER myThid |
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|
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C !OUTPUT PARAMETERS: ================================================== |
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C gTracer :: tendancy array |
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C fVerT :: 2 1/2D arrays for vertical advective flux |
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_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C df4 :: used for storing del^2 T for bi-harmonic term |
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C fZon :: zonal flux |
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C fmer :: meridional flux |
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C af :: advective flux |
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C df :: diffusive flux |
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C localT :: local copy of tracer field |
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INTEGER i,j |
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_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fMer (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 df (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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CEOP |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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C-- only the kUp part of fverT is set in this subroutine |
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C-- the kDown is still required |
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fVerT(1,1,kDown) = fVerT(1,1,kDown) |
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#endif |
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|
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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fZon(i,j) = 0. _d 0 |
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fMer(i,j) = 0. _d 0 |
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fVerT(i,j,kUp) = 0. _d 0 |
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df(i,j) = 0. _d 0 |
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df4(i,j) = 0. _d 0 |
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localT(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C-- Make local copy of tracer array |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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localT(i,j)=tracer(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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|
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C-- Unless we have already calculated the advection terms we initialize |
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C the tendency to zero. |
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C <== now done earlier at the beginning of thermodynamics. |
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c IF (calcAdvection) THEN |
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c DO j=1-Oly,sNy+Oly |
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c DO i=1-Olx,sNx+Olx |
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c gTracer(i,j,k,bi,bj)=0. _d 0 |
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c ENDDO |
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c ENDDO |
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c ENDIF |
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|
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C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero |
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IF (diffK4 .NE. 0.) THEN |
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CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid) |
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CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid) |
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CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid) |
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ENDIF |
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|
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C-- Initialize net flux in X direction |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C- Advective flux in X |
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IF (calcAdvection) THEN |
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IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
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CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
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CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
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CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
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CALL GAD_DST3_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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CALL GAD_DST3FL_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid) |
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ELSE |
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STOP 'GAD_CALC_RHS: Bad advectionScheme (X)' |
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ENDIF |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + af(i,j) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C- Diffusive flux in X |
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IF (diffKh.NE.0.) THEN |
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CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid) |
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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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df(i,j) = 0. _d 0 |
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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_GMREDI |
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C- GM/Redi flux in X |
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IF (useGMRedi) THEN |
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C *note* should update GMREDI_XTRANSPORT to use localT and set df *aja* |
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CALL GMREDI_XTRANSPORT( |
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I iMin,iMax,jMin,jMax,bi,bj,K, |
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I xA,Tracer,tracerIdentity, |
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U df, |
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I myThid) |
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ENDIF |
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#endif |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + df(i,j) |
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ENDDO |
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ENDDO |
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|
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C- Bi-harmonic duffusive flux in X |
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IF (diffK4 .NE. 0.) THEN |
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CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fZon(i,j) = fZon(i,j) + df(i,j) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C-- Initialize net flux in Y direction |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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fMer(i,j) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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C- Advective flux in Y |
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IF (calcAdvection) THEN |
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IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
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CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
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CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
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CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid) |
240 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
241 |
CALL GAD_DST3_ADV_Y( |
242 |
& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
243 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
244 |
CALL GAD_DST3FL_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid) |
246 |
ELSE |
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STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)' |
248 |
ENDIF |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
251 |
fMer(i,j) = fMer(i,j) + af(i,j) |
252 |
ENDDO |
253 |
ENDDO |
254 |
ENDIF |
255 |
|
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C- Diffusive flux in Y |
257 |
IF (diffKh.NE.0.) THEN |
258 |
CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid) |
259 |
ELSE |
260 |
DO j=1-Oly,sNy+Oly |
261 |
DO i=1-Olx,sNx+Olx |
262 |
df(i,j) = 0. _d 0 |
263 |
ENDDO |
264 |
ENDDO |
265 |
ENDIF |
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|
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#ifdef ALLOW_GMREDI |
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C- GM/Redi flux in Y |
269 |
IF (useGMRedi) THEN |
270 |
C *note* should update GMREDI_YTRANSPORT to use localT and set df *aja* |
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CALL GMREDI_YTRANSPORT( |
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I iMin,iMax,jMin,jMax,bi,bj,K, |
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I yA,Tracer,tracerIdentity, |
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U df, |
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I myThid) |
276 |
ENDIF |
277 |
#endif |
278 |
DO j=1-Oly,sNy+Oly |
279 |
DO i=1-Olx,sNx+Olx |
280 |
fMer(i,j) = fMer(i,j) + df(i,j) |
281 |
ENDDO |
282 |
ENDDO |
283 |
|
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C- Bi-harmonic flux in Y |
285 |
IF (diffK4 .NE. 0.) THEN |
286 |
CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid) |
287 |
DO j=1-Oly,sNy+Oly |
288 |
DO i=1-Olx,sNx+Olx |
289 |
fMer(i,j) = fMer(i,j) + df(i,j) |
290 |
ENDDO |
291 |
ENDDO |
292 |
ENDIF |
293 |
|
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#ifdef NONLIN_FRSURF |
295 |
C-- Compute vertical flux fVerT(kDown) at interface k+1 (between k & k+1): |
296 |
IF ( calcAdvection .AND. K.EQ.Nr .AND. |
297 |
& useRealFreshWaterFlux .AND. |
298 |
& buoyancyRelation .EQ. 'OCEANICP' ) THEN |
299 |
DO j=1-Oly,sNy+Oly |
300 |
DO i=1-Olx,sNx+Olx |
301 |
fVerT(i,j,kDown) = convertEmP2rUnit*PmEpR(i,j,bi,bj) |
302 |
& *rA(i,j,bi,bj)*maskC(i,j,k,bi,bj)*Tracer(i,j,k,bi,bj) |
303 |
ENDDO |
304 |
ENDDO |
305 |
ENDIF |
306 |
#endif /* NONLIN_FRSURF */ |
307 |
|
308 |
C-- Compute vertical flux fVerT(kUp) at interface k (between k-1 & k): |
309 |
C- Advective flux in R |
310 |
IF (calcAdvection) THEN |
311 |
C Note: wVel needs to be masked |
312 |
IF (K.GE.2) THEN |
313 |
C- Compute vertical advective flux in the interior: |
314 |
IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN |
315 |
CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
316 |
ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
317 |
CALL GAD_FLUXLIMIT_ADV_R( |
318 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
319 |
ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN |
320 |
CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
321 |
ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN |
322 |
CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid) |
323 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
324 |
CALL GAD_DST3_ADV_R( |
325 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
326 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
327 |
CALL GAD_DST3FL_ADV_R( |
328 |
& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid) |
329 |
ELSE |
330 |
STOP 'GAD_CALC_RHS: Bad advectionScheme (R)' |
331 |
ENDIF |
332 |
C- Surface "correction" term at k>1 : |
333 |
DO j=1-Oly,sNy+Oly |
334 |
DO i=1-Olx,sNx+Olx |
335 |
af(i,j) = af(i,j) |
336 |
& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))* |
337 |
& rTrans(i,j)*Tracer(i,j,k,bi,bj) |
338 |
ENDDO |
339 |
ENDDO |
340 |
ELSE |
341 |
C- Surface "correction" term at k=1 : |
342 |
DO j=1-Oly,sNy+Oly |
343 |
DO i=1-Olx,sNx+Olx |
344 |
af(i,j) = rTrans(i,j)*Tracer(i,j,k,bi,bj) |
345 |
ENDDO |
346 |
ENDDO |
347 |
ENDIF |
348 |
C- add the advective flux to fVerT |
349 |
DO j=1-Oly,sNy+Oly |
350 |
DO i=1-Olx,sNx+Olx |
351 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j) |
352 |
ENDDO |
353 |
ENDDO |
354 |
ENDIF |
355 |
|
356 |
C- Diffusive flux in R |
357 |
C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper |
358 |
C boundary condition. |
359 |
IF (implicitDiffusion) THEN |
360 |
DO j=1-Oly,sNy+Oly |
361 |
DO i=1-Olx,sNx+Olx |
362 |
df(i,j) = 0. _d 0 |
363 |
ENDDO |
364 |
ENDDO |
365 |
ELSE |
366 |
CALL GAD_DIFF_R(bi,bj,k,KappaRT,tracer,df,myThid) |
367 |
ENDIF |
368 |
|
369 |
#ifdef ALLOW_GMREDI |
370 |
C- GM/Redi flux in R |
371 |
IF (useGMRedi) THEN |
372 |
C *note* should update GMREDI_RTRANSPORT to set df *aja* |
373 |
CALL GMREDI_RTRANSPORT( |
374 |
I iMin,iMax,jMin,jMax,bi,bj,K, |
375 |
I Tracer,tracerIdentity, |
376 |
U df, |
377 |
I myThid) |
378 |
ENDIF |
379 |
#endif |
380 |
|
381 |
DO j=1-Oly,sNy+Oly |
382 |
DO i=1-Olx,sNx+Olx |
383 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
384 |
ENDDO |
385 |
ENDDO |
386 |
|
387 |
#ifdef ALLOW_KPP |
388 |
C- Add non local KPP transport term (ghat) to diffusive T flux. |
389 |
IF (useKPP) THEN |
390 |
DO j=1-Oly,sNy+Oly |
391 |
DO i=1-Olx,sNx+Olx |
392 |
df(i,j) = 0. _d 0 |
393 |
ENDDO |
394 |
ENDDO |
395 |
IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
396 |
C *note* should update KPP_TRANSPORT_T to set df *aja* |
397 |
CALL KPP_TRANSPORT_T( |
398 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
399 |
I KappaRT, |
400 |
U df ) |
401 |
ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
402 |
CALL KPP_TRANSPORT_S( |
403 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
404 |
I KappaRT, |
405 |
U df ) |
406 |
#ifdef ALLOW_PTRACERS |
407 |
ELSEIF (tracerIdentity .GE. GAD_TR1) THEN |
408 |
CALL KPP_TRANSPORT_PTR( |
409 |
I iMin,iMax,jMin,jMax,bi,bj,k,km1, |
410 |
I tracerIdentity-GAD_TR1+1,KappaRT, |
411 |
U df ) |
412 |
#endif |
413 |
ELSE |
414 |
PRINT*,'invalid tracer indentity: ', tracerIdentity |
415 |
STOP 'GAD_CALC_RHS: Ooops' |
416 |
ENDIF |
417 |
DO j=1-Oly,sNy+Oly |
418 |
DO i=1-Olx,sNx+Olx |
419 |
fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j) |
420 |
ENDDO |
421 |
ENDDO |
422 |
ENDIF |
423 |
#endif |
424 |
|
425 |
C-- Divergence of fluxes |
426 |
DO j=1-Oly,sNy+Oly-1 |
427 |
DO i=1-Olx,sNx+Olx-1 |
428 |
gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj) |
429 |
& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
430 |
& *recip_rA(i,j,bi,bj) |
431 |
& *( |
432 |
& +( fZon(i+1,j)-fZon(i,j) ) |
433 |
& +( fMer(i,j+1)-fMer(i,j) ) |
434 |
& +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac |
435 |
& ) |
436 |
ENDDO |
437 |
ENDDO |
438 |
|
439 |
#ifdef NONLIN_FRSURF |
440 |
C-- account for 3.D divergence of the flow in rStar coordinate: |
441 |
IF (calcAdvection .AND. select_rStar.GT.0) THEN |
442 |
DO j=1-Oly,sNy+Oly-1 |
443 |
DO i=1-Olx,sNx+Olx-1 |
444 |
gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj) |
445 |
& - (rStarExpC(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf |
446 |
& *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj) |
447 |
ENDDO |
448 |
ENDDO |
449 |
ENDIF |
450 |
IF (calcAdvection .AND. select_rStar.LT.0) THEN |
451 |
DO j=1-Oly,sNy+Oly-1 |
452 |
DO i=1-Olx,sNx+Olx-1 |
453 |
gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj) |
454 |
& - rStarDhCDt(i,j,bi,bj) |
455 |
& *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj) |
456 |
ENDDO |
457 |
ENDDO |
458 |
ENDIF |
459 |
#endif /* NONLIN_FRSURF */ |
460 |
|
461 |
|
462 |
RETURN |
463 |
END |