pkg/generic_advdiff/gad_calc_rhs.F

C $Header: /usr/local/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.21 2003/09/24 04:52:38 dimitri Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

CBOP
C !ROUTINE: GAD_CALC_RHS

C !INTERFACE: ==========================================================
      SUBROUTINE GAD_CALC_RHS( 
     I           bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
     I           xA,yA,uTrans,vTrans,rTrans,maskUp,
     I           diffKh, diffK4, KappaRT, Tracer,
     I           tracerIdentity, advectionScheme, calcAdvection,
     U           fVerT, gTracer,
     I           myThid )

C !DESCRIPTION:
C Calculates the tendancy of a tracer due to advection and diffusion.
C It calculates the fluxes in each direction indepentently and then
C sets the tendancy to the divergence of these fluxes. The advective
C fluxes are only calculated here when using the linear advection schemes
C otherwise only the diffusive and parameterized fluxes are calculated.
C
C Contributions to the flux are calculated and added:
C \begin{equation*}
C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP}
C \end{equation*}
C
C The tendancy is the divergence of the fluxes:
C \begin{equation*}
C G_\theta = G_\theta + \nabla \cdot {\bf F}
C \end{equation*}
C
C The tendancy is assumed to contain data on entry.

C !USES: ===============================================================
      IMPLICIT NONE
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "DYNVARS.h"
#include "SURFACE.h"
#include "GAD.h"

#ifdef ALLOW_AUTODIFF_TAMC
#include "tamc.h"
#include "tamc_keys.h"
#endif /* ALLOW_AUTODIFF_TAMC */

C !INPUT PARAMETERS: ===================================================
C  bi,bj                :: tile indices
C  iMin,iMax,jMin,jMax  :: loop range for called routines
C  kup                  :: index into 2 1/2D array, toggles between 1 and 2
C  kdown                :: index into 2 1/2D array, toggles between 2 and 1
C  kp1                  :: =k+1 for k<Nr, =Nr for k=Nr
C  xA,yA                :: areas of X and Y face of tracer cells
C  uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
C  maskUp               :: 2-D array for mask at W points
C  diffKh               :: horizontal diffusion coefficient
C  diffK4               :: bi-harmonic diffusion coefficient
C  KappaRT              :: 3-D array for vertical diffusion coefficient
C  Tracer               :: tracer field
C  tracerIdentity       :: identifier for the tracer (required for KPP and GM)
C  advectionScheme      :: advection scheme to use
C  calcAdvection        :: =False if Advec terms computed with multiDim scheme
C  myThid               :: thread number
      INTEGER bi,bj,iMin,iMax,jMin,jMax
      INTEGER k,kUp,kDown,kM1
      _RS xA    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RS yA    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL diffKh, diffK4
      _RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
      _RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      INTEGER tracerIdentity
      INTEGER advectionScheme
      LOGICAL calcAdvection
      INTEGER myThid

C !OUTPUT PARAMETERS: ==================================================
C  gTracer              :: tendancy array
C  fVerT                :: 2 1/2D arrays for vertical advective flux
      _RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
      _RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)

C !LOCAL VARIABLES: ====================================================
C  i,j                  :: loop indices
C  df4                  :: used for storing del^2 T for bi-harmonic term
C  fZon                 :: zonal flux
C  fmer                 :: meridional flux
C  af                   :: advective flux
C  df                   :: diffusive flux
C  localT               :: local copy of tracer field
      INTEGER i,j
      _RL df4   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL fZon  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL fMer  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL af    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL df    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
CEOP

#ifdef ALLOW_AUTODIFF_TAMC
C--   only the kUp part of fverT is set in this subroutine
C--   the kDown is still required
      fVerT(1,1,kDown) = fVerT(1,1,kDown)
#endif

      DO j=1-OLy,sNy+OLy
       DO i=1-OLx,sNx+OLx
        fZon(i,j)      = 0. _d 0
        fMer(i,j)      = 0. _d 0
        fVerT(i,j,kUp) = 0. _d 0
        df(i,j)        = 0. _d 0
        df4(i,j)       = 0. _d 0
        localT(i,j)    = 0. _d 0
       ENDDO
      ENDDO

C--   Make local copy of tracer array
      DO j=1-OLy,sNy+OLy
       DO i=1-OLx,sNx+OLx
        localT(i,j)=tracer(i,j,k,bi,bj)
       ENDDO
      ENDDO

C--   Unless we have already calculated the advection terms we initialize
C     the tendency to zero.
C     <== now done earlier at the beginning of thermodynamics.
c     IF (calcAdvection) THEN
c      DO j=1-Oly,sNy+Oly
c       DO i=1-Olx,sNx+Olx
c        gTracer(i,j,k,bi,bj)=0. _d 0
c       ENDDO
c      ENDDO
c     ENDIF

C--   Pre-calculate del^2 T if bi-harmonic coefficient is non-zero
      IF (diffK4 .NE. 0.) THEN
       CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid)
       CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid)
       CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid)
      ENDIF

C--   Initialize net flux in X direction
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fZon(i,j) = 0. _d 0
       ENDDO
      ENDDO

C-    Advective flux in X
      IF (calcAdvection) THEN
      IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
       CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
       CALL GAD_FLUXLIMIT_ADV_X(
     &      bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
       CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
       CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
       CALL GAD_DST3_ADV_X(
     &       bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
       CALL GAD_DST3FL_ADV_X(
     &       bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
      ELSE
       STOP 'GAD_CALC_RHS: Bad advectionScheme (X)'
      ENDIF
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fZon(i,j) = fZon(i,j) + af(i,j)
       ENDDO
      ENDDO
      ENDIF

C-    Diffusive flux in X
      IF (diffKh.NE.0.) THEN
       CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid)
      ELSE
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         df(i,j) = 0. _d 0
        ENDDO
       ENDDO
      ENDIF

#ifdef ALLOW_GMREDI
C-    GM/Redi flux in X
      IF (useGMRedi) THEN
C *note* should update GMREDI_XTRANSPORT to use localT and set df  *aja*
        CALL GMREDI_XTRANSPORT(
     I     iMin,iMax,jMin,jMax,bi,bj,K,
     I     xA,Tracer,tracerIdentity,
     U     df,
     I     myThid)
      ENDIF
#endif
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fZon(i,j) = fZon(i,j) + df(i,j)
       ENDDO
      ENDDO

C-    Bi-harmonic duffusive flux in X
      IF (diffK4 .NE. 0.) THEN
       CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid)
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         fZon(i,j) = fZon(i,j) + df(i,j)
        ENDDO
       ENDDO
      ENDIF

C--   Initialize net flux in Y direction
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fMer(i,j) = 0. _d 0
       ENDDO
      ENDDO

C-    Advective flux in Y
      IF (calcAdvection) THEN
      IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
       CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
       CALL GAD_FLUXLIMIT_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
       CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
       CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
       CALL GAD_DST3_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
       CALL GAD_DST3FL_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
      ELSE
       STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)'
      ENDIF
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fMer(i,j) = fMer(i,j) + af(i,j)
       ENDDO
      ENDDO
      ENDIF

C-    Diffusive flux in Y
      IF (diffKh.NE.0.) THEN
       CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid)
      ELSE
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         df(i,j) = 0. _d 0
        ENDDO
       ENDDO
      ENDIF

#ifdef ALLOW_GMREDI
C-    GM/Redi flux in Y
      IF (useGMRedi) THEN
C *note* should update GMREDI_YTRANSPORT to use localT and set df  *aja*
       CALL GMREDI_YTRANSPORT(
     I     iMin,iMax,jMin,jMax,bi,bj,K,
     I     yA,Tracer,tracerIdentity,
     U     df,
     I     myThid)
      ENDIF
#endif
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fMer(i,j) = fMer(i,j) + df(i,j)
       ENDDO
      ENDDO

C-    Bi-harmonic flux in Y
      IF (diffK4 .NE. 0.) THEN
       CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid)
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         fMer(i,j) = fMer(i,j) + df(i,j)
        ENDDO
       ENDDO
      ENDIF

#ifdef NONLIN_FRSURF
C--   Compute vertical flux fVerT(kDown) at interface k+1 (between k & k+1):
      IF ( calcAdvection .AND. K.EQ.Nr .AND.
     &     useRealFreshWaterFlux .AND.
     &     buoyancyRelation .EQ. 'OCEANICP' ) THEN   
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         fVerT(i,j,kDown) = convertEmP2rUnit*PmEpR(i,j,bi,bj)
     &     *rA(i,j,bi,bj)*maskC(i,j,k,bi,bj)*Tracer(i,j,k,bi,bj)
        ENDDO
       ENDDO 
      ENDIF
#endif /* NONLIN_FRSURF */

C--   Compute vertical flux fVerT(kUp) at interface k (between k-1 & k):
C-    Advective flux in R
      IF (calcAdvection) THEN
C     Note: wVel needs to be masked 
      IF (K.GE.2) THEN
C-    Compute vertical advective flux in the interior:
       IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
        CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
        CALL GAD_FLUXLIMIT_ADV_R(
     &       bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
        CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
        CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
        CALL GAD_DST3_ADV_R(
     &       bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
        CALL GAD_DST3FL_ADV_R(
     &       bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
       ELSE
        STOP 'GAD_CALC_RHS: Bad advectionScheme (R)'
       ENDIF
C-    Surface "correction" term at k>1 :
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         af(i,j) = af(i,j)
     &           + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))*
     &             rTrans(i,j)*Tracer(i,j,k,bi,bj)
        ENDDO
       ENDDO 
      ELSE
C-    Surface "correction" term at k=1 :
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         af(i,j) = rTrans(i,j)*Tracer(i,j,k,bi,bj)
        ENDDO
       ENDDO 
      ENDIF
C-    add the advective flux to fVerT
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j)
       ENDDO
      ENDDO
      ENDIF

C-    Diffusive flux in R
C     Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper
C           boundary condition.
      IF (implicitDiffusion) THEN
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         df(i,j) = 0. _d 0
        ENDDO
       ENDDO
      ELSE
       CALL GAD_DIFF_R(bi,bj,k,KappaRT,tracer,df,myThid)
      ENDIF

#ifdef ALLOW_GMREDI
C-    GM/Redi flux in R
      IF (useGMRedi) THEN
C *note* should update GMREDI_RTRANSPORT to set df  *aja*
       CALL GMREDI_RTRANSPORT(
     I     iMin,iMax,jMin,jMax,bi,bj,K,
     I     Tracer,tracerIdentity,
     U     df,
     I     myThid)
      ENDIF
#endif

      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
       ENDDO
      ENDDO

#ifdef ALLOW_KPP
C-    Add non local KPP transport term (ghat) to diffusive T flux.
      IF (useKPP) THEN
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         df(i,j) = 0. _d 0
        ENDDO
       ENDDO
       IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
C *note* should update KPP_TRANSPORT_T to set df  *aja*
        CALL KPP_TRANSPORT_T(
     I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
     I     KappaRT,
     U     df )
       ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
        CALL KPP_TRANSPORT_S(
     I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
     I     KappaRT,
     U     df )
#ifdef ALLOW_PTRACERS
       ELSEIF (tracerIdentity .GE. GAD_TR1) THEN
        CALL KPP_TRANSPORT_PTR(
     I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
     I     tracerIdentity-GAD_TR1+1,KappaRT,
     U     df )
#endif
       ELSE
        PRINT*,'invalid tracer indentity: ', tracerIdentity
        STOP 'GAD_CALC_RHS: Ooops'
       ENDIF
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
        ENDDO
       ENDDO
      ENDIF
#endif

C--   Divergence of fluxes
      DO j=1-Oly,sNy+Oly-1
       DO i=1-Olx,sNx+Olx-1
        gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj)
     &   -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
     &    *recip_rA(i,j,bi,bj)
     &    *(
     &    +( fZon(i+1,j)-fZon(i,j) )
     &    +( fMer(i,j+1)-fMer(i,j) )
     &    +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac
     &    )
       ENDDO
      ENDDO

#ifdef NONLIN_FRSURF
C-- account for 3.D divergence of the flow in rStar coordinate:
      IF (calcAdvection .AND. select_rStar.GT.0) THEN
       DO j=1-Oly,sNy+Oly-1
        DO i=1-Olx,sNx+Olx-1
         gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj)
     &     - (rStarExpC(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
     &       *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj)
        ENDDO
       ENDDO
      ENDIF
      IF (calcAdvection .AND. select_rStar.LT.0) THEN
       DO j=1-Oly,sNy+Oly-1
        DO i=1-Olx,sNx+Olx-1
         gTracer(i,j,k,bi,bj) = gTracer(i,j,k,bi,bj)
     &     - rStarDhCDt(i,j,bi,bj)
     &       *tracer(i,j,k,bi,bj)*maskC(i,j,k,bi,bj)
        ENDDO
       ENDDO
      ENDIF
#endif /* NONLIN_FRSURF */
      

      RETURN
      END
1	dimitri	1.22	C $Header: /usr/local/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.21 2003/09/24 04:52:38 dimitri Exp $
2	jmc	1.2	C $Name: $
3	adcroft	1.1
4			#include "GAD_OPTIONS.h"
5
6	adcroft	1.11	CBOP
7			C !ROUTINE: GAD_CALC_RHS
8
9			C !INTERFACE: ==========================================================
10	adcroft	1.1	SUBROUTINE GAD_CALC_RHS(
11			I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
12			I xA,yA,uTrans,vTrans,rTrans,maskUp,
13			I diffKh, diffK4, KappaRT, Tracer,
14	jmc	1.14	I tracerIdentity, advectionScheme, calcAdvection,
15	adcroft	1.1	U fVerT, gTracer,
16			I myThid )
17	adcroft	1.11
18			C !DESCRIPTION:
19			C Calculates the tendancy of a tracer due to advection and diffusion.
20			C It calculates the fluxes in each direction indepentently and then
21			C sets the tendancy to the divergence of these fluxes. The advective
22			C fluxes are only calculated here when using the linear advection schemes
23			C otherwise only the diffusive and parameterized fluxes are calculated.
24			C
25			C Contributions to the flux are calculated and added:
26			C \begin{equation*}
27			C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP}
28			C \end{equation*}
29			C
30			C The tendancy is the divergence of the fluxes:
31			C \begin{equation*}
32			C G_\theta = G_\theta + \nabla \cdot {\bf F}
33			C \end{equation*}
34			C
35			C The tendancy is assumed to contain data on entry.
36
37			C !USES: ===============================================================
38	adcroft	1.1	IMPLICIT NONE
39			#include "SIZE.h"
40			#include "EEPARAMS.h"
41			#include "PARAMS.h"
42			#include "GRID.h"
43			#include "DYNVARS.h"
44	jmc	1.16	#include "SURFACE.h"
45	adcroft	1.1	#include "GAD.h"
46
47	heimbach	1.13	#ifdef ALLOW_AUTODIFF_TAMC
48			#include "tamc.h"
49			#include "tamc_keys.h"
50			#endif /* ALLOW_AUTODIFF_TAMC */
51
52	adcroft	1.11	C !INPUT PARAMETERS: ===================================================
53			C bi,bj :: tile indices
54			C iMin,iMax,jMin,jMax :: loop range for called routines
55			C kup :: index into 2 1/2D array, toggles between 1 and 2
56			C kdown :: index into 2 1/2D array, toggles between 2 and 1
57			C kp1 :: =k+1 for k<Nr, =Nr for k=Nr
58			C xA,yA :: areas of X and Y face of tracer cells
59			C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
60			C maskUp :: 2-D array for mask at W points
61			C diffKh :: horizontal diffusion coefficient
62			C diffK4 :: bi-harmonic diffusion coefficient
63			C KappaRT :: 3-D array for vertical diffusion coefficient
64			C Tracer :: tracer field
65	dimitri	1.19	C tracerIdentity :: identifier for the tracer (required for KPP and GM)
66	adcroft	1.11	C advectionScheme :: advection scheme to use
67	jmc	1.14	C calcAdvection :: =False if Advec terms computed with multiDim scheme
68	adcroft	1.11	C myThid :: thread number
69			INTEGER bi,bj,iMin,iMax,jMin,jMax
70	adcroft	1.1	INTEGER k,kUp,kDown,kM1
71			_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
72			_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
73			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75			_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
76			_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
77			_RL diffKh, diffK4
78			_RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
79			_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
80			INTEGER tracerIdentity
81	adcroft	1.3	INTEGER advectionScheme
82	jmc	1.14	LOGICAL calcAdvection
83	adcroft	1.11	INTEGER myThid
84
85			C !OUTPUT PARAMETERS: ==================================================
86			C gTracer :: tendancy array
87			C fVerT :: 2 1/2D arrays for vertical advective flux
88			_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
89	adcroft	1.1	_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
90
91	adcroft	1.11	C !LOCAL VARIABLES: ====================================================
92			C i,j :: loop indices
93			C df4 :: used for storing del^2 T for bi-harmonic term
94			C fZon :: zonal flux
95			C fmer :: meridional flux
96			C af :: advective flux
97			C df :: diffusive flux
98			C localT :: local copy of tracer field
99	adcroft	1.1	INTEGER i,j
100			_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
101			_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
102			_RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
103			_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
104			_RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
105			_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
106	adcroft	1.11	CEOP
107	adcroft	1.1
108			#ifdef ALLOW_AUTODIFF_TAMC
109			C-- only the kUp part of fverT is set in this subroutine
110			C-- the kDown is still required
111			fVerT(1,1,kDown) = fVerT(1,1,kDown)
112			#endif
113	heimbach	1.13
114	adcroft	1.1	DO j=1-OLy,sNy+OLy
115			DO i=1-OLx,sNx+OLx
116	heimbach	1.12	fZon(i,j) = 0. _d 0
117			fMer(i,j) = 0. _d 0
118			fVerT(i,j,kUp) = 0. _d 0
119	heimbach	1.13	df(i,j) = 0. _d 0
120			df4(i,j) = 0. _d 0
121			localT(i,j) = 0. _d 0
122	adcroft	1.1	ENDDO
123			ENDDO
124
125			C-- Make local copy of tracer array
126			DO j=1-OLy,sNy+OLy
127			DO i=1-OLx,sNx+OLx
128			localT(i,j)=tracer(i,j,k,bi,bj)
129			ENDDO
130			ENDDO
131
132	adcroft	1.8	C-- Unless we have already calculated the advection terms we initialize
133			C the tendency to zero.
134	jmc	1.20	C <== now done earlier at the beginning of thermodynamics.
135			c IF (calcAdvection) THEN
136			c DO j=1-Oly,sNy+Oly
137			c DO i=1-Olx,sNx+Olx
138			c gTracer(i,j,k,bi,bj)=0. _d 0
139			c ENDDO
140			c ENDDO
141			c ENDIF
142	adcroft	1.1
143			C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero
144			IF (diffK4 .NE. 0.) THEN
145			CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid)
146			CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid)
147			CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid)
148			ENDIF
149
150			C-- Initialize net flux in X direction
151			DO j=1-Oly,sNy+Oly
152			DO i=1-Olx,sNx+Olx
153	heimbach	1.12	fZon(i,j) = 0. _d 0
154	adcroft	1.1	ENDDO
155			ENDDO
156
157			C- Advective flux in X
158	jmc	1.14	IF (calcAdvection) THEN
159	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
160	adcroft	1.1	CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
161	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
162	adcroft	1.1	CALL GAD_FLUXLIMIT_ADV_X(
163			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
164	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
165	jmc	1.2	CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
166	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
167	adcroft	1.1	CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
168	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
169			CALL GAD_DST3_ADV_X(
170			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
171			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
172			CALL GAD_DST3FL_ADV_X(
173			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
174	adcroft	1.1	ELSE
175	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (X)'
176	adcroft	1.1	ENDIF
177	adcroft	1.5	DO j=1-Oly,sNy+Oly
178			DO i=1-Olx,sNx+Olx
179	adcroft	1.1	fZon(i,j) = fZon(i,j) + af(i,j)
180			ENDDO
181			ENDDO
182	adcroft	1.8	ENDIF
183	adcroft	1.1
184			C- Diffusive flux in X
185			IF (diffKh.NE.0.) THEN
186			CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid)
187			ELSE
188	adcroft	1.5	DO j=1-Oly,sNy+Oly
189			DO i=1-Olx,sNx+Olx
190	heimbach	1.12	df(i,j) = 0. _d 0
191	adcroft	1.1	ENDDO
192			ENDDO
193			ENDIF
194
195			#ifdef ALLOW_GMREDI
196			C- GM/Redi flux in X
197			IF (useGMRedi) THEN
198			C note should update GMREDI_XTRANSPORT to use localT and set df aja
199			CALL GMREDI_XTRANSPORT(
200			I iMin,iMax,jMin,jMax,bi,bj,K,
201	heimbach	1.15	I xA,Tracer,tracerIdentity,
202	adcroft	1.1	U df,
203			I myThid)
204			ENDIF
205			#endif
206	adcroft	1.5	DO j=1-Oly,sNy+Oly
207			DO i=1-Olx,sNx+Olx
208	adcroft	1.1	fZon(i,j) = fZon(i,j) + df(i,j)
209			ENDDO
210			ENDDO
211
212			C- Bi-harmonic duffusive flux in X
213			IF (diffK4 .NE. 0.) THEN
214			CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid)
215	adcroft	1.5	DO j=1-Oly,sNy+Oly
216			DO i=1-Olx,sNx+Olx
217	adcroft	1.1	fZon(i,j) = fZon(i,j) + df(i,j)
218			ENDDO
219			ENDDO
220			ENDIF
221
222			C-- Initialize net flux in Y direction
223			DO j=1-Oly,sNy+Oly
224			DO i=1-Olx,sNx+Olx
225	heimbach	1.12	fMer(i,j) = 0. _d 0
226	adcroft	1.1	ENDDO
227			ENDDO
228
229			C- Advective flux in Y
230	jmc	1.14	IF (calcAdvection) THEN
231	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
232	adcroft	1.1	CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
233	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
234	adcroft	1.1	CALL GAD_FLUXLIMIT_ADV_Y(
235			& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
236	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
237	jmc	1.2	CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
238	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
239	adcroft	1.1	CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
240	adcroft	1.4	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(
245			& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
246	adcroft	1.1	ELSE
247	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)'
248	adcroft	1.1	ENDIF
249			DO j=1-Oly,sNy+Oly
250			DO i=1-Olx,sNx+Olx
251			fMer(i,j) = fMer(i,j) + af(i,j)
252			ENDDO
253			ENDDO
254	adcroft	1.8	ENDIF
255	adcroft	1.1
256			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	heimbach	1.12	df(i,j) = 0. _d 0
263	adcroft	1.1	ENDDO
264			ENDDO
265			ENDIF
266
267			#ifdef ALLOW_GMREDI
268			C- GM/Redi flux in Y
269			IF (useGMRedi) THEN
270	heimbach	1.7	C note should update GMREDI_YTRANSPORT to use localT and set df aja
271	adcroft	1.1	CALL GMREDI_YTRANSPORT(
272			I iMin,iMax,jMin,jMax,bi,bj,K,
273	heimbach	1.15	I yA,Tracer,tracerIdentity,
274	adcroft	1.1	U df,
275			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
284			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
294	jmc	1.16	#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	adcroft	1.1	C- Advective flux in R
310	jmc	1.14	IF (calcAdvection) THEN
311	jmc	1.2	C Note: wVel needs to be masked
312			IF (K.GE.2) THEN
313			C- Compute vertical advective flux in the interior:
314	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
315	jmc	1.2	CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
316	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
317	jmc	1.2	CALL GAD_FLUXLIMIT_ADV_R(
318	adcroft	1.1	& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
319	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
320	jmc	1.2	CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
321	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
322	jmc	1.2	CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
323	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
324	adcroft	1.9	CALL GAD_DST3_ADV_R(
325			& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
326	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
327	adcroft	1.9	CALL GAD_DST3FL_ADV_R(
328			& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
329	jmc	1.2	ELSE
330	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (R)'
331	jmc	1.2	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	adcroft	1.1	ELSE
341	jmc	1.2	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	adcroft	1.1	ENDIF
348	jmc	1.2	C- add the advective flux to fVerT
349	adcroft	1.5	DO j=1-Oly,sNy+Oly
350			DO i=1-Olx,sNx+Olx
351	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j)
352	adcroft	1.1	ENDDO
353			ENDDO
354	adcroft	1.8	ENDIF
355	adcroft	1.1
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	adcroft	1.5	DO j=1-Oly,sNy+Oly
361			DO i=1-Olx,sNx+Olx
362	heimbach	1.12	df(i,j) = 0. _d 0
363	adcroft	1.1	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	heimbach	1.15	I Tracer,tracerIdentity,
376	adcroft	1.1	U df,
377			I myThid)
378			ENDIF
379			#endif
380
381	adcroft	1.5	DO j=1-Oly,sNy+Oly
382			DO i=1-Olx,sNx+Olx
383	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
384	adcroft	1.1	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	adcroft	1.5	DO j=1-Oly,sNy+Oly
391			DO i=1-Olx,sNx+Olx
392	heimbach	1.12	df(i,j) = 0. _d 0
393	adcroft	1.1	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	mlosch	1.18	#ifdef ALLOW_PTRACERS
407	dimitri	1.22	ELSEIF (tracerIdentity .GE. GAD_TR1) THEN
408	mlosch	1.18	CALL KPP_TRANSPORT_PTR(
409			I iMin,iMax,jMin,jMax,bi,bj,k,km1,
410	dimitri	1.21	I tracerIdentity-GAD_TR1+1,KappaRT,
411	mlosch	1.18	U df )
412			#endif
413	adcroft	1.1	ELSE
414	mlosch	1.18	PRINT*,'invalid tracer indentity: ', tracerIdentity
415	adcroft	1.1	STOP 'GAD_CALC_RHS: Ooops'
416			ENDIF
417	adcroft	1.5	DO j=1-Oly,sNy+Oly
418			DO i=1-Olx,sNx+Olx
419	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
420	adcroft	1.1	ENDDO
421			ENDDO
422			ENDIF
423			#endif
424
425			C-- Divergence of fluxes
426	adcroft	1.10	DO j=1-Oly,sNy+Oly-1
427			DO i=1-Olx,sNx+Olx-1
428	adcroft	1.8	gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj)
429	adcroft	1.1	& -_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	jmc	1.17
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	adcroft	1.1
462			RETURN
463			END