pkg/generic_advdiff/gad_calc_rhs.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.12 2001/09/27 20:12:11 heimbach 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,
     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 "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 only for KPP)
C  advectionScheme      :: advection scheme to use
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
      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.
      IF (.NOT. multiDimAdvection .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
     &    advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_4TH ) THEN
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         gTracer(i,j,k,bi,bj)=0. _d 0
        ENDDO
       ENDDO
      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 (.NOT. multiDimAdvection .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
     &    advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_4TH ) 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,
     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 (.NOT. multiDimAdvection .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
     &    advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_4TH ) 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,
     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

C-    Advective flux in R
      IF (.NOT. multiDimAdvection .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
     &    advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
     &    advectionScheme.EQ.ENUM_CENTERED_4TH ) 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
c     DO j=1-Oly,sNy+Oly
c      DO i=1-Olx,sNx+Olx
c       fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
c      ENDDO
c     ENDDO

#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,
     U     df,
     I     myThid)
c      DO j=1-Oly,sNy+Oly
c       DO i=1-Olx,sNx+Olx
c        fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
c       ENDDO
c      ENDDO
      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 )
       ELSE
        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

      RETURN
      END
1	heimbach	1.13	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 1.12 2001/09/27 20:12:11 heimbach 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	adcroft	1.3	I tracerIdentity, advectionScheme,
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			#include "GAD.h"
45
46	heimbach	1.13	#ifdef ALLOW_AUTODIFF_TAMC
47			#include "tamc.h"
48			#include "tamc_keys.h"
49			#endif /* ALLOW_AUTODIFF_TAMC */
50
51	adcroft	1.11	C !INPUT PARAMETERS: ===================================================
52			C bi,bj :: tile indices
53			C iMin,iMax,jMin,jMax :: loop range for called routines
54			C kup :: index into 2 1/2D array, toggles between 1 and 2
55			C kdown :: index into 2 1/2D array, toggles between 2 and 1
56			C kp1 :: =k+1 for k<Nr, =Nr for k=Nr
57			C xA,yA :: areas of X and Y face of tracer cells
58			C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
59			C maskUp :: 2-D array for mask at W points
60			C diffKh :: horizontal diffusion coefficient
61			C diffK4 :: bi-harmonic diffusion coefficient
62			C KappaRT :: 3-D array for vertical diffusion coefficient
63			C Tracer :: tracer field
64			C tracerIdentity :: identifier for the tracer (required only for KPP)
65			C advectionScheme :: advection scheme to use
66			C myThid :: thread number
67			INTEGER bi,bj,iMin,iMax,jMin,jMax
68	adcroft	1.1	INTEGER k,kUp,kDown,kM1
69			_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
70			_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
72			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
73			_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74			_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75			_RL diffKh, diffK4
76			_RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
77			_RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
78			INTEGER tracerIdentity
79	adcroft	1.3	INTEGER advectionScheme
80	adcroft	1.11	INTEGER myThid
81
82			C !OUTPUT PARAMETERS: ==================================================
83			C gTracer :: tendancy array
84			C fVerT :: 2 1/2D arrays for vertical advective flux
85			_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
86	adcroft	1.1	_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
87
88	adcroft	1.11	C !LOCAL VARIABLES: ====================================================
89			C i,j :: loop indices
90			C df4 :: used for storing del^2 T for bi-harmonic term
91			C fZon :: zonal flux
92			C fmer :: meridional flux
93			C af :: advective flux
94			C df :: diffusive flux
95			C localT :: local copy of tracer field
96	adcroft	1.1	INTEGER i,j
97			_RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
98			_RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
99			_RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
100			_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
101			_RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
102			_RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
103	adcroft	1.11	CEOP
104	adcroft	1.1
105			#ifdef ALLOW_AUTODIFF_TAMC
106			C-- only the kUp part of fverT is set in this subroutine
107			C-- the kDown is still required
108			fVerT(1,1,kDown) = fVerT(1,1,kDown)
109			#endif
110	heimbach	1.13
111	adcroft	1.1	DO j=1-OLy,sNy+OLy
112			DO i=1-OLx,sNx+OLx
113	heimbach	1.12	fZon(i,j) = 0. _d 0
114			fMer(i,j) = 0. _d 0
115			fVerT(i,j,kUp) = 0. _d 0
116	heimbach	1.13	df(i,j) = 0. _d 0
117			df4(i,j) = 0. _d 0
118			localT(i,j) = 0. _d 0
119	adcroft	1.1	ENDDO
120			ENDDO
121
122			C-- Make local copy of tracer array
123			DO j=1-OLy,sNy+OLy
124			DO i=1-OLx,sNx+OLx
125			localT(i,j)=tracer(i,j,k,bi,bj)
126			ENDDO
127			ENDDO
128
129	adcroft	1.8	C-- Unless we have already calculated the advection terms we initialize
130			C the tendency to zero.
131			IF (.NOT. multiDimAdvection .OR.
132			& advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
133			& advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
134			& advectionScheme.EQ.ENUM_CENTERED_4TH ) THEN
135			DO j=1-Oly,sNy+Oly
136			DO i=1-Olx,sNx+Olx
137	heimbach	1.12	gTracer(i,j,k,bi,bj)=0. _d 0
138	adcroft	1.8	ENDDO
139			ENDDO
140			ENDIF
141	adcroft	1.1
142			C-- Pre-calculate del^2 T if bi-harmonic coefficient is non-zero
143			IF (diffK4 .NE. 0.) THEN
144			CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid)
145			CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid)
146			CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid)
147			ENDIF
148
149			C-- Initialize net flux in X direction
150			DO j=1-Oly,sNy+Oly
151			DO i=1-Olx,sNx+Olx
152	heimbach	1.12	fZon(i,j) = 0. _d 0
153	adcroft	1.1	ENDDO
154			ENDDO
155
156			C- Advective flux in X
157	adcroft	1.8	IF (.NOT. multiDimAdvection .OR.
158			& advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
159			& advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
160			& advectionScheme.EQ.ENUM_CENTERED_4TH ) THEN
161	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
162	adcroft	1.1	CALL GAD_C2_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
163	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
164	adcroft	1.1	CALL GAD_FLUXLIMIT_ADV_X(
165			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
166	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
167	jmc	1.2	CALL GAD_U3_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
168	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
169	adcroft	1.1	CALL GAD_C4_ADV_X(bi,bj,k,uTrans,localT,af,myThid)
170	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
171			CALL GAD_DST3_ADV_X(
172			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
173			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
174			CALL GAD_DST3FL_ADV_X(
175			& bi,bj,k,deltaTtracer,uTrans,uVel,localT,af,myThid)
176	adcroft	1.1	ELSE
177	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (X)'
178	adcroft	1.1	ENDIF
179	adcroft	1.5	DO j=1-Oly,sNy+Oly
180			DO i=1-Olx,sNx+Olx
181	adcroft	1.1	fZon(i,j) = fZon(i,j) + af(i,j)
182			ENDDO
183			ENDDO
184	adcroft	1.8	ENDIF
185	adcroft	1.1
186			C- Diffusive flux in X
187			IF (diffKh.NE.0.) THEN
188			CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid)
189			ELSE
190	adcroft	1.5	DO j=1-Oly,sNy+Oly
191			DO i=1-Olx,sNx+Olx
192	heimbach	1.12	df(i,j) = 0. _d 0
193	adcroft	1.1	ENDDO
194			ENDDO
195			ENDIF
196
197			#ifdef ALLOW_GMREDI
198			C- GM/Redi flux in X
199			IF (useGMRedi) THEN
200			C note should update GMREDI_XTRANSPORT to use localT and set df aja
201			CALL GMREDI_XTRANSPORT(
202			I iMin,iMax,jMin,jMax,bi,bj,K,
203			I xA,Tracer,
204			U df,
205			I myThid)
206			ENDIF
207			#endif
208	adcroft	1.5	DO j=1-Oly,sNy+Oly
209			DO i=1-Olx,sNx+Olx
210	adcroft	1.1	fZon(i,j) = fZon(i,j) + df(i,j)
211			ENDDO
212			ENDDO
213
214			C- Bi-harmonic duffusive flux in X
215			IF (diffK4 .NE. 0.) THEN
216			CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid)
217	adcroft	1.5	DO j=1-Oly,sNy+Oly
218			DO i=1-Olx,sNx+Olx
219	adcroft	1.1	fZon(i,j) = fZon(i,j) + df(i,j)
220			ENDDO
221			ENDDO
222			ENDIF
223
224			C-- Initialize net flux in Y direction
225			DO j=1-Oly,sNy+Oly
226			DO i=1-Olx,sNx+Olx
227	heimbach	1.12	fMer(i,j) = 0. _d 0
228	adcroft	1.1	ENDDO
229			ENDDO
230
231			C- Advective flux in Y
232	adcroft	1.8	IF (.NOT. multiDimAdvection .OR.
233			& advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
234			& advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
235			& advectionScheme.EQ.ENUM_CENTERED_4TH ) THEN
236	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
237	adcroft	1.1	CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
238	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
239	adcroft	1.1	CALL GAD_FLUXLIMIT_ADV_Y(
240			& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
241	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
242	jmc	1.2	CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
243	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
244	adcroft	1.1	CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,localT,af,myThid)
245	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
246			CALL GAD_DST3_ADV_Y(
247			& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
248			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
249			CALL GAD_DST3FL_ADV_Y(
250			& bi,bj,k,deltaTtracer,vTrans,vVel,localT,af,myThid)
251	adcroft	1.1	ELSE
252	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)'
253	adcroft	1.1	ENDIF
254			DO j=1-Oly,sNy+Oly
255			DO i=1-Olx,sNx+Olx
256			fMer(i,j) = fMer(i,j) + af(i,j)
257			ENDDO
258			ENDDO
259	adcroft	1.8	ENDIF
260	adcroft	1.1
261			C- Diffusive flux in Y
262			IF (diffKh.NE.0.) THEN
263			CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid)
264			ELSE
265			DO j=1-Oly,sNy+Oly
266			DO i=1-Olx,sNx+Olx
267	heimbach	1.12	df(i,j) = 0. _d 0
268	adcroft	1.1	ENDDO
269			ENDDO
270			ENDIF
271
272			#ifdef ALLOW_GMREDI
273			C- GM/Redi flux in Y
274			IF (useGMRedi) THEN
275	heimbach	1.7	C note should update GMREDI_YTRANSPORT to use localT and set df aja
276	adcroft	1.1	CALL GMREDI_YTRANSPORT(
277			I iMin,iMax,jMin,jMax,bi,bj,K,
278			I yA,Tracer,
279			U df,
280			I myThid)
281			ENDIF
282			#endif
283			DO j=1-Oly,sNy+Oly
284			DO i=1-Olx,sNx+Olx
285			fMer(i,j) = fMer(i,j) + df(i,j)
286			ENDDO
287			ENDDO
288
289			C- Bi-harmonic flux in Y
290			IF (diffK4 .NE. 0.) THEN
291			CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid)
292			DO j=1-Oly,sNy+Oly
293			DO i=1-Olx,sNx+Olx
294			fMer(i,j) = fMer(i,j) + df(i,j)
295			ENDDO
296			ENDDO
297			ENDIF
298
299			C- Advective flux in R
300	adcroft	1.8	IF (.NOT. multiDimAdvection .OR.
301			& advectionScheme.EQ.ENUM_CENTERED_2ND .OR.
302			& advectionScheme.EQ.ENUM_UPWIND_3RD .OR.
303			& advectionScheme.EQ.ENUM_CENTERED_4TH ) THEN
304	jmc	1.2	C Note: wVel needs to be masked
305			IF (K.GE.2) THEN
306			C- Compute vertical advective flux in the interior:
307	adcroft	1.3	IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
308	jmc	1.2	CALL GAD_C2_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
309	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
310	jmc	1.2	CALL GAD_FLUXLIMIT_ADV_R(
311	adcroft	1.1	& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
312	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
313	jmc	1.2	CALL GAD_U3_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
314	adcroft	1.3	ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
315	jmc	1.2	CALL GAD_C4_ADV_R(bi,bj,k,rTrans,tracer,af,myThid)
316	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
317	adcroft	1.9	CALL GAD_DST3_ADV_R(
318			& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
319	adcroft	1.4	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
320	adcroft	1.9	CALL GAD_DST3FL_ADV_R(
321			& bi,bj,k,deltaTtracer,rTrans,wVel,tracer,af,myThid)
322	jmc	1.2	ELSE
323	adcroft	1.3	STOP 'GAD_CALC_RHS: Bad advectionScheme (R)'
324	jmc	1.2	ENDIF
325			C- Surface "correction" term at k>1 :
326			DO j=1-Oly,sNy+Oly
327			DO i=1-Olx,sNx+Olx
328			af(i,j) = af(i,j)
329			& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))*
330			& rTrans(i,j)*Tracer(i,j,k,bi,bj)
331			ENDDO
332			ENDDO
333	adcroft	1.1	ELSE
334	jmc	1.2	C- Surface "correction" term at k=1 :
335			DO j=1-Oly,sNy+Oly
336			DO i=1-Olx,sNx+Olx
337			af(i,j) = rTrans(i,j)*Tracer(i,j,k,bi,bj)
338			ENDDO
339			ENDDO
340	adcroft	1.1	ENDIF
341	jmc	1.2	C- add the advective flux to fVerT
342	adcroft	1.5	DO j=1-Oly,sNy+Oly
343			DO i=1-Olx,sNx+Olx
344	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j)
345	adcroft	1.1	ENDDO
346			ENDDO
347	adcroft	1.8	ENDIF
348	adcroft	1.1
349			C- Diffusive flux in R
350			C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper
351			C boundary condition.
352			IF (implicitDiffusion) THEN
353	adcroft	1.5	DO j=1-Oly,sNy+Oly
354			DO i=1-Olx,sNx+Olx
355	heimbach	1.12	df(i,j) = 0. _d 0
356	adcroft	1.1	ENDDO
357			ENDDO
358			ELSE
359			CALL GAD_DIFF_R(bi,bj,k,KappaRT,tracer,df,myThid)
360			ENDIF
361	adcroft	1.5	c DO j=1-Oly,sNy+Oly
362			c DO i=1-Olx,sNx+Olx
363	adcroft	1.11	c fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
364	adcroft	1.1	c ENDDO
365			c ENDDO
366
367			#ifdef ALLOW_GMREDI
368			C- GM/Redi flux in R
369			IF (useGMRedi) THEN
370			C note should update GMREDI_RTRANSPORT to set df aja
371			CALL GMREDI_RTRANSPORT(
372			I iMin,iMax,jMin,jMax,bi,bj,K,
373	adcroft	1.6	I Tracer,
374	adcroft	1.1	U df,
375			I myThid)
376	adcroft	1.5	c DO j=1-Oly,sNy+Oly
377			c DO i=1-Olx,sNx+Olx
378	adcroft	1.11	c fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
379	adcroft	1.1	c ENDDO
380			c ENDDO
381			ENDIF
382			#endif
383
384	adcroft	1.5	DO j=1-Oly,sNy+Oly
385			DO i=1-Olx,sNx+Olx
386	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
387	adcroft	1.1	ENDDO
388			ENDDO
389
390			#ifdef ALLOW_KPP
391			C- Add non local KPP transport term (ghat) to diffusive T flux.
392			IF (useKPP) THEN
393	adcroft	1.5	DO j=1-Oly,sNy+Oly
394			DO i=1-Olx,sNx+Olx
395	heimbach	1.12	df(i,j) = 0. _d 0
396	adcroft	1.1	ENDDO
397			ENDDO
398			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
399			C note should update KPP_TRANSPORT_T to set df aja
400			CALL KPP_TRANSPORT_T(
401			I iMin,iMax,jMin,jMax,bi,bj,k,km1,
402			I KappaRT,
403			U df )
404			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
405			CALL KPP_TRANSPORT_S(
406			I iMin,iMax,jMin,jMax,bi,bj,k,km1,
407			I KappaRT,
408			U df )
409			ELSE
410			STOP 'GAD_CALC_RHS: Ooops'
411			ENDIF
412	adcroft	1.5	DO j=1-Oly,sNy+Oly
413			DO i=1-Olx,sNx+Olx
414	adcroft	1.11	fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
415	adcroft	1.1	ENDDO
416			ENDDO
417			ENDIF
418			#endif
419
420			C-- Divergence of fluxes
421	adcroft	1.10	DO j=1-Oly,sNy+Oly-1
422			DO i=1-Olx,sNx+Olx-1
423	adcroft	1.8	gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj)
424	adcroft	1.1	& -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
425			& *recip_rA(i,j,bi,bj)
426			& *(
427			& +( fZon(i+1,j)-fZon(i,j) )
428			& +( fMer(i,j+1)-fMer(i,j) )
429			& +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac
430			& )
431			ENDDO
432			ENDDO
433
434			RETURN
435			END