C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.27 2004/09/17 23:02:01 heimbach Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
CBOP
C !ROUTINE: GAD_ADVECTION

C !INTERFACE: ==========================================================
      SUBROUTINE GAD_ADVECTION(
     I     implicitAdvection, advectionScheme, vertAdvecScheme,
     I     tracerIdentity,
     I     uVel, vVel, wVel, tracer,
     O     gTracer,
     I     bi,bj, myTime,myIter,myThid)

C !DESCRIPTION:
C Calculates the tendancy of a tracer due to advection.
C It uses the multi-dimensional method given in \ref{sect:multiDimAdvection}
C and can only be used for the non-linear advection schemes such as the
C direct-space-time method and flux-limiters. 
C
C The algorithm is as follows:
C \begin{itemize}
C \item{$\theta^{(n+1/3)} = \theta^{(n)}
C      - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$}
C \item{$\theta^{(n+2/3)} = \theta^{(n+1/3)}
C      - \Delta t \partial_y (v\theta^{(n+1/3)}) + \theta^{(n)} \partial_y v$}
C \item{$\theta^{(n+3/3)} = \theta^{(n+2/3)}
C      - \Delta t \partial_r (w\theta^{(n+2/3)}) + \theta^{(n)} \partial_r w$}
C \item{$G_\theta = ( \theta^{(n+3/3)} - \theta^{(n)} )/\Delta t$}
C \end{itemize}
C
C The tendancy (output) is over-written by this routine.

C !USES: ===============================================================
      IMPLICIT NONE
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "GAD.h"
#ifdef ALLOW_AUTODIFF_TAMC
# include "tamc.h"
# include "tamc_keys.h"
# ifdef ALLOW_PTRACERS
#  include "PTRACERS_SIZE.h"
# endif
#endif
#ifdef ALLOW_EXCH2
#include "W2_EXCH2_TOPOLOGY.h"
#include "W2_EXCH2_PARAMS.h"
#endif /* ALLOW_EXCH2 */

C !INPUT PARAMETERS: ===================================================
C  implicitAdvection :: implicit vertical advection (later on)
C  advectionScheme   :: advection scheme to use (Horizontal plane)
C  vertAdvecScheme   :: advection scheme to use (vertical direction)
C  tracerIdentity    :: tracer identifier (required only for OBCS)
C  uVel              :: velocity, zonal component
C  vVel              :: velocity, meridional component
C  wVel              :: velocity, vertical component
C  tracer            :: tracer field
C  bi,bj             :: tile indices
C  myTime            :: current time
C  myIter            :: iteration number
C  myThid            :: thread number
      LOGICAL implicitAdvection
      INTEGER advectionScheme, vertAdvecScheme
      INTEGER tracerIdentity
      _RL uVel  (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
      _RL vVel  (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
      _RL wVel  (1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
      _RL tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
      INTEGER bi,bj
      _RL myTime
      INTEGER myIter
      INTEGER myThid

C !OUTPUT PARAMETERS: ==================================================
C  gTracer           :: tendancy array
      _RL gTracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)

C !LOCAL VARIABLES: ====================================================
C  maskUp        :: 2-D array for mask at W points
C  iMin,iMax,    :: loop range for called routines
C  jMin,jMax     :: loop range for called routines
C  i,j,k         :: loop indices
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 :: 2-D arrays of volume transports at U,V points
C  rTrans        :: 2-D arrays of volume transports at W points
C  rTransKp1     :: vertical volume transport at interface k+1
C  af            :: 2-D array for horizontal advective flux
C  fVerT         :: 2 1/2D arrays for vertical advective flux
C  localTij      :: 2-D array, temporary local copy of tracer fld
C  localTijk     :: 3-D array, temporary local copy of tracer fld
C  kp1Msk        :: flag (0,1) for over-riding mask for W levels
C  calc_fluxes_X :: logical to indicate to calculate fluxes in X dir
C  calc_fluxes_Y :: logical to indicate to calculate fluxes in Y dir
C  nipass        :: number of passes in multi-dimensional method
C  ipass         :: number of the current pass being made
C  myTile        :: variables used to determine which cube face 
C  nCFace        :: owns a tile for cube grid runs using
C                :: multi-dim advection.
      _RS maskUp  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      INTEGER iMin,iMax,jMin,jMax
      INTEGER i,j,k,kup,kDown
      _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)
      _RL rTransKp1(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL af      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL fVerT   (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
      _RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL localTijk(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
      _RL kp1Msk
      LOGICAL calc_fluxes_X,calc_fluxes_Y
      INTEGER nipass,ipass
      INTEGER myTile, nCFace
      LOGICAL southWestCorner
      LOGICAL southEastCorner
      LOGICAL northWestCorner
      LOGICAL northEastCorner
CEOP

#ifdef ALLOW_AUTODIFF_TAMC
          act0 = tracerIdentity - 1
          max0 = maxpass
          act1 = bi - myBxLo(myThid)
          max1 = myBxHi(myThid) - myBxLo(myThid) + 1
          act2 = bj - myByLo(myThid)
          max2 = myByHi(myThid) - myByLo(myThid) + 1
          act3 = myThid - 1
          max3 = nTx*nTy
          act4 = ikey_dynamics - 1
          igadkey = (act0 + 1) 
     &                      + act1*max0
     &                      + act2*max0*max1
     &                      + act3*max0*max1*max2
     &                      + act4*max0*max1*max2*max3
          if (tracerIdentity.GT.maxpass) then
             print *, 'ph-pass gad_advection ', maxpass, tracerIdentity
             STOP 'maxpass seems smaller than tracerIdentity'
          endif
#endif /* ALLOW_AUTODIFF_TAMC */

C--   Set up work arrays with valid (i.e. not NaN) values
C     These inital values do not alter the numerical results. They
C     just ensure that all memory references are to valid floating
C     point numbers. This prevents spurious hardware signals due to
C     uninitialised but inert locations.
      DO j=1-OLy,sNy+OLy
       DO i=1-OLx,sNx+OLx
        xA(i,j)      = 0. _d 0
        yA(i,j)      = 0. _d 0
        uTrans(i,j)  = 0. _d 0
        vTrans(i,j)  = 0. _d 0
        rTrans(i,j)  = 0. _d 0
        fVerT(i,j,1) = 0. _d 0
        fVerT(i,j,2) = 0. _d 0
        rTransKp1(i,j)= 0. _d 0
       ENDDO
      ENDDO

      iMin = 1-OLx
      iMax = sNx+OLx
      jMin = 1-OLy
      jMax = sNy+OLy

C--   Start of k loop for horizontal fluxes
      DO k=1,Nr
#ifdef ALLOW_AUTODIFF_TAMC 
         kkey = (igadkey-1)*Nr + k
CADJ STORE tracer(:,:,k,bi,bj) = 
CADJ &     comlev1_bibj_k_gad, key=kkey, byte=isbyte
#endif /* ALLOW_AUTODIFF_TAMC */

C--   Get temporary terms used by tendency routines
      CALL CALC_COMMON_FACTORS (
     I         bi,bj,iMin,iMax,jMin,jMax,k,
     O         xA,yA,uTrans,vTrans,rTrans,maskUp,
     I         myThid)

#ifdef ALLOW_GMREDI
C--   Residual transp = Bolus transp + Eulerian transp
       IF (useGMRedi)
     &   CALL GMREDI_CALC_UVFLOW(
     &            uTrans, vTrans, bi, bj, k, myThid)
#endif /* ALLOW_GMREDI */

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

cph  The following block is needed for useCubedSphereExchange only,
cph  but needs to be set for all cases to avoid spurious 
cph  TAF dependencies
       southWestCorner = .TRUE.
       southEastCorner = .TRUE.
       northWestCorner = .TRUE.
       northEastCorner = .TRUE.
#ifdef ALLOW_EXCH2
       myTile = W2_myTileList(bi)
       nCFace = exch2_myFace(myTile)
       southWestCorner = exch2_isWedge(myTile).EQ.1
     &             .AND. exch2_isSedge(myTile).EQ.1
       southEastCorner = exch2_isEedge(myTile).EQ.1
     &             .AND. exch2_isSedge(myTile).EQ.1
       northEastCorner = exch2_isEedge(myTile).EQ.1
     &             .AND. exch2_isNedge(myTile).EQ.1
       northWestCorner = exch2_isWedge(myTile).EQ.1
     &             .AND. exch2_isNedge(myTile).EQ.1
#else
       nCFace = bi
#endif
      IF (useCubedSphereExchange) THEN

       nipass=3
#ifdef ALLOW_AUTODIFF_TAMC
       if ( nipass.GT.maxcube )
     &      STOP 'maxcube needs to be = 3'
#endif
      ELSE
       nipass=1
      ENDIF
cph       nipass=1

C--   Multiple passes for different directions on different tiles
C--   For cube need one pass for each of red, green and blue axes.
      DO ipass=1,nipass
#ifdef ALLOW_AUTODIFF_TAMC
         passkey = ipass + (k-1)      *maxcube
     &                   + (igadkey-1)*maxcube*Nr
         IF (nipass .GT. maxpass) THEN
          STOP 'GAD_ADVECTION: nipass > maxcube. check tamc.h'
         ENDIF
#endif /* ALLOW_AUTODIFF_TAMC */

      IF (nipass.EQ.3) THEN
       calc_fluxes_X=.FALSE.
       calc_fluxes_Y=.FALSE.
       IF (ipass.EQ.1 .AND. (nCFace.EQ.1 .OR. nCFace.EQ.2) ) THEN
        calc_fluxes_X=.TRUE.
       ELSEIF (ipass.EQ.1 .AND. (nCFace.EQ.4 .OR. nCFace.EQ.5) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.2 .AND. (nCFace.EQ.1 .OR. nCFace.EQ.6) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.2 .AND. (nCFace.EQ.3 .OR. nCFace.EQ.4) ) THEN
        calc_fluxes_X=.TRUE.
       ELSEIF (ipass.EQ.3 .AND. (nCFace.EQ.2 .OR. nCFace.EQ.3) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.3 .AND. (nCFace.EQ.5 .OR. nCFace.EQ.6) ) THEN
        calc_fluxes_X=.TRUE.
       ENDIF
      ELSE
       calc_fluxes_X=.TRUE.
       calc_fluxes_Y=.TRUE.
      ENDIF
 
C--   X direction
      IF (calc_fluxes_X) THEN

C--   Internal exchange for calculations in X
      IF (useCubedSphereExchange) THEN
C--    For cube face corners we need to duplicate the
C--    i-1 and i+1 values into the null space as follows:
C
C
C      o NW corner: copy T(    0,sNy  ) into T(    0,sNy+1) e.g.
C                      |
C         x T(0,sNy+1) |
C        /\            |
C      --||------------|-----------
C        ||            |
C         x T(0,sNy)   |   x T(1,sNy)
C                      |
C
C      o SW corner: copy T(0,1) into T(0,0) e.g.
C                      |
C         x T(0,1)     |  x T(1,1)
C        ||            |
C      --||------------|-----------
C        \/            |
C         x T(0,0)     |
C                      |
C
C      o NE corner: copy T(sNx+1,sNy  ) into T(sNx+1,sNy+1) e.g.
C                      |
C                      |   x T(sNx+1,sNy+1)
C                      |  /\
C      ----------------|--||-------
C                      |  ||
C         x T(sNx,sNy) |   x T(sNx+1,sNy  )
C                      |
C      o SE corner: copy T(sNx+1,1    ) into T(sNx+1,0    ) e.g.
C                      |
C         x T(sNx,1)   |   x T(sNx+1,    1) 
C                      |  ||
C      ----------------|--||-------
C                      |  \/
C                      |   x T(sNx+1,    0)
       IF ( southWestCorner ) THEN
        DO J=1,OLy
         DO I=1,OLx
          localTij(1-I, 1-J   )= localTij(1-J  ,1  )
         ENDDO
        ENDDO
       ENDIF
       IF ( southEastCorner ) THEN
        DO J=1,OLy
         DO I=1,OLx
          localTij(sNx+I, 1-J )=localTij(sNx+J, I  )
         ENDDO
        ENDDO
       ENDIF
       IF ( northWestCorner ) THEN
        DO J=1,OLy
         DO I=1,OLx
          localTij( 1-I ,sNy+J)=localTij( 1-J , sNy+1-I )
         ENDDO
        ENDDO
       ENDIF
       IF ( northEastCorner ) THEN
        DO J=1,OLy
         DO I=1,OLx
          localTij(sNx+I,sNy+J)=localTij(sNx+J, sNy+1-I )
         ENDDO
        ENDDO
       ENDIF
      ENDIF

C-    Advective flux in X
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        af(i,j) = 0.
       ENDDO
      ENDDO

#ifdef ALLOW_AUTODIFF_TAMC
#ifndef DISABLE_MULTIDIM_ADVECTION
CADJ STORE localTij(:,:)  = 
CADJ &     comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
#endif
#endif /* ALLOW_AUTODIFF_TAMC */

      IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
       CALL GAD_FLUXLIMIT_ADV_X(
     &      bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
       CALL GAD_DST3_ADV_X(
     &       bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
       CALL GAD_DST3FL_ADV_X(
     &       bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
      ELSE
       STOP 'GAD_ADVECTION: adv. scheme incompatibale with multi-dim'
      ENDIF

      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx-1
        localTij(i,j)=localTij(i,j)-deltaTtracer*
     &    _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
     &    *recip_rA(i,j,bi,bj)
     &    *( af(i+1,j)-af(i,j)
     &      -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j))
     &     )
       ENDDO
      ENDDO

#ifdef ALLOW_OBCS
C--   Apply open boundary conditions
      IF (useOBCS) THEN
       IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
        CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
       ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
        CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
       END IF
      END IF
#endif /* ALLOW_OBCS */

C--   End of X direction
      ENDIF

C--   Y direction
      IF (calc_fluxes_Y) THEN

      IF (useCubedSphereExchange) THEN
C--   Internal exchange for calculations in Y
C--    For cube face corners we need to duplicate the
C--    j-1 and j+1 values into the null space as follows:
C
C      o SW corner: copy T(0,1) into T(0,0) e.g.
C                      |
C                      |  x T(1,1)
C                      |
C      ----------------|-----------
C                      |
C         x T(0,0)<====== x T(1,0)
C                      |
C
C      o NW corner: copy T(    0,sNy  ) into T(    0,sNy+1) e.g.
C                      |
C         x T(0,sNy+1)<=== x T(1,sNy+1)
C                      |
C      ----------------|-----------
C                      |
C                      |   x T(1,sNy)
C                      |
C
C      o NE corner: copy T(sNx+1,sNy  ) into T(sNx+1,sNy+1) e.g.
C                      |
C      x T(sNx,sNy+1)=====>x T(sNx+1,sNy+1)
C                      |     
C      ----------------|-----------
C                      |     
C      x T(sNx,sNy)    |                       
C                      |
C      o SE corner: copy T(sNx+1,1    ) into T(sNx+1,0    ) e.g.
C                      |
C         x T(sNx,1)   |                    
C                      |    
C      ----------------|-----------
C                      |     
C         x T(sNx,0) =====>x T(sNx+1,    0)
       IF ( southWestCorner ) THEN
        DO J=1,Oly
         DO I=1,Olx
          localTij( 1-i , 1-j ) = localTij(j   , 1-i )
         ENDDO
        ENDDO
       ENDIF
       IF ( southEastCorner ) THEN
        DO J=1,Oly
         DO I=1,Olx
          localTij(sNx+i, 1-j ) = localTij(sNx+1-j, 1-i )
         ENDDO
        ENDDO
       ENDIF
       IF ( northWestCorner ) THEN
        DO J=1,Oly
         DO I=1,Olx
          localTij( 1-i ,sNy+j) = localTij(j   ,sNy+i)
         ENDDO
        ENDDO
       ENDIF
       IF ( northEastCorner ) THEN
        DO J=1,Oly
         DO I=1,Olx
          localTij(sNx+i,sNy+j) = localTij(sNx+1-j,sNy+i)
         ENDDO
        ENDDO
       ENDIF
      ENDIF

C-    Advective flux in Y
      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        af(i,j) = 0.
       ENDDO
      ENDDO

#ifdef ALLOW_AUTODIFF_TAMC 
#ifndef DISABLE_MULTIDIM_ADVECTION
CADJ STORE localTij(:,:)  = 
CADJ &     comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
#endif
#endif /* ALLOW_AUTODIFF_TAMC */

      IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
       CALL GAD_FLUXLIMIT_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
       CALL GAD_DST3_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
      ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
       CALL GAD_DST3FL_ADV_Y(
     &       bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
      ELSE
       STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
      ENDIF

      DO j=1-Oly,sNy+Oly-1
       DO i=1-Olx,sNx+Olx
        localTij(i,j)=localTij(i,j)-deltaTtracer*
     &    _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
     &    *recip_rA(i,j,bi,bj)
     &    *( af(i,j+1)-af(i,j)
     &      -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j))
     &     )
       ENDDO
      ENDDO

#ifdef ALLOW_OBCS
C--   Apply open boundary conditions
      IF (useOBCS) THEN
       IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
        CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
       ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
        CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
       END IF
      END IF
#endif /* ALLOW_OBCS */

C--   End of Y direction
      ENDIF

C--   End of ipass loop
      ENDDO

      IF ( implicitAdvection ) THEN
C-    explicit advection is done ; store tendency in gTracer:
        DO j=1-Oly,sNy+Oly
         DO i=1-Olx,sNx+Olx
          gTracer(i,j,k,bi,bj)=
     &     (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
         ENDDO
        ENDDO
      ELSE
C-    horizontal advection done; store intermediate result in 3D array:
       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         localTijk(i,j,k)=localTij(i,j)
        ENDDO
       ENDDO
      ENDIF

C--   End of K loop for horizontal fluxes
      ENDDO

      IF ( .NOT.implicitAdvection ) THEN
C--   Start of k loop for vertical flux
       DO k=Nr,1,-1
#ifdef ALLOW_AUTODIFF_TAMC 
         kkey = (igadkey-1)*Nr + k
#endif /* ALLOW_AUTODIFF_TAMC */
C--   kup    Cycles through 1,2 to point to w-layer above
C--   kDown  Cycles through 2,1 to point to w-layer below
        kup  = 1+MOD(k+1,2)
        kDown= 1+MOD(k,2)
c       kp1=min(Nr,k+1)
        kp1Msk=1.
        if (k.EQ.Nr) kp1Msk=0.

C-- Compute Vertical transport
#ifdef ALLOW_AIM
C- a hack to prevent Water-Vapor vert.transport into the stratospheric level Nr
        IF ( k.EQ.1 .OR.
     &     (useAIM .AND. tracerIdentity.EQ.GAD_SALINITY .AND. k.EQ.Nr)
     &              ) THEN
#else
        IF ( k.EQ.1 ) THEN
#endif

C- Surface interface :
         DO j=1-Oly,sNy+Oly
          DO i=1-Olx,sNx+Olx
           rTransKp1(i,j) = kp1Msk*rTrans(i,j)
           rTrans(i,j) = 0.
           fVerT(i,j,kUp) = 0.
           af(i,j) = 0.
          ENDDO
         ENDDO

        ELSE
C- Interior interface :

         DO j=1-Oly,sNy+Oly
          DO i=1-Olx,sNx+Olx
           rTransKp1(i,j) = kp1Msk*rTrans(i,j)
           rTrans(i,j) = wVel(i,j,k,bi,bj)*rA(i,j,bi,bj)
     &                 *maskC(i,j,k-1,bi,bj)
           af(i,j) = 0.
          ENDDO
         ENDDO

#ifdef ALLOW_GMREDI
C--   Residual transp = Bolus transp + Eulerian transp
         IF (useGMRedi) 
     &   CALL GMREDI_CALC_WFLOW(
     &                    rTrans, bi, bj, k, myThid)
#endif /* ALLOW_GMREDI */

#ifdef ALLOW_AUTODIFF_TAMC 
CADJ STORE localTijk(:,:,k)  
CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
CADJ STORE rTrans(:,:)  
CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
#endif /* ALLOW_AUTODIFF_TAMC */

C-    Compute vertical advective flux in the interior:
         IF (vertAdvecScheme.EQ.ENUM_FLUX_LIMIT) THEN
          CALL GAD_FLUXLIMIT_ADV_R(
     &        bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
         ELSEIF (vertAdvecScheme.EQ.ENUM_DST3 ) THEN
          CALL GAD_DST3_ADV_R(
     &        bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
         ELSEIF (vertAdvecScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
          CALL GAD_DST3FL_ADV_R(
     &        bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
         ELSE
          STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
         ENDIF
C-    add the advective flux to fVerT
         DO j=1-Oly,sNy+Oly
          DO i=1-Olx,sNx+Olx
           fVerT(i,j,kUp) = af(i,j)
          ENDDO
         ENDDO

C- end Surface/Interior if bloc
        ENDIF

#ifdef ALLOW_AUTODIFF_TAMC 
CADJ STORE rTrans(:,:)  
CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
CADJ STORE rTranskp1(:,:)  
CADJ &     = comlev1_bibj_k_gad, key=kkey, byte=isbyte
#endif /* ALLOW_AUTODIFF_TAMC */

C--   Divergence of vertical fluxes
        DO j=1-Oly,sNy+Oly
         DO i=1-Olx,sNx+Olx
          localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
     &     _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
     &     *recip_rA(i,j,bi,bj)
     &     *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
     &       -tracer(i,j,k,bi,bj)*(rTrans(i,j)-rTransKp1(i,j))
     &      )*rkFac
          gTracer(i,j,k,bi,bj)=
     &     (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
         ENDDO
        ENDDO
 
C--   End of K loop for vertical flux
       ENDDO
C--   end of if not.implicitAdvection block
      ENDIF 

      RETURN
      END