pkg/generic_advdiff/gad_advection.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.14 2002/11/12 20:42:24 heimbach Exp $
C $Name:  $

CBOI
C !TITLE: pkg/generic\_advdiff
C !AUTHORS: adcroft@mit.edu
C !INTRODUCTION: Generic Advection Diffusion Package
C
C Package "generic\_advdiff" provides a common set of routines for calculating
C advective/diffusive fluxes for tracers (cell centered quantities on a C-grid).
C
C Many different advection schemes are available: the standard centered
C second order, centered fourth order and upwind biased third order schemes
C are known as linear methods and require some stable time-stepping method
C such as Adams-Bashforth. Alternatives such as flux-limited schemes are
C stable in the forward sense and are best combined with the multi-dimensional
C method provided in gad\_advection.
C
C There are two high-level routines:
C  \begin{itemize}
C  \item{GAD\_CALC\_RHS} calculates all fluxes at time level "n" and is used
C  for the standard linear schemes. This must be used in conjuction with
C  Adams-Bashforth time-stepping. Diffusive and parameterized fluxes are
C  always calculated here.
C  \item{GAD\_ADVECTION} calculates just the advective fluxes using the
C  non-linear schemes and can not be used in conjuction with Adams-Bashforth
C  time-stepping.
C  \end{itemize}
CEOI

#include "GAD_OPTIONS.h"

CBOP
C !ROUTINE: GAD_ADVECTION

C !INTERFACE: ==========================================================
      SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity,
     U                         Tracer,Gtracer,
     I                         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 "DYNVARS.h"
#include "GRID.h"
#include "GAD.h"
#ifdef ALLOW_AUTODIFF_TAMC
# include "tamc.h"
# include "tamc_keys.h"
#endif

C !INPUT PARAMETERS: ===================================================
C  bi,bj                :: tile indices
C  advectionScheme      :: advection scheme to use
C  tracerIdentity       :: identifier for the tracer (required only for OBCS)
C  Tracer               :: tracer field
C  myTime               :: current time
C  myIter               :: iteration number
C  myThid               :: thread number
      INTEGER bi,bj
      INTEGER advectionScheme
      INTEGER tracerIdentity
      _RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
      _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,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,rTrans :: 2-D arrays of volume transports at U,V and 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 used as temporary local copy of tracer fld
C  localTijk            :: 3-D array used as temporary local copy of tracer fld
C  kp1Msk               :: flag (0,1) to act as 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 to make in multi-dimensional method
C  ipass                :: number of the current pass being made
      _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
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

      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
      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. (bi.EQ.1 .OR. bi.EQ.2) ) THEN
        calc_fluxes_X=.TRUE.
       ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN
        calc_fluxes_X=.TRUE.
       ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN
        calc_fluxes_Y=.TRUE.
       ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.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
       DO j=1,Oly
        DO i=1,Olx
         localTij( 1-i , 1-j )=localTij( 1-j ,    i    )
         localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i )
         localTij(sNx+i, 1-j )=localTij(sNx+j,    i    )
         localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i )
        ENDDO
       ENDDO
      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

C--   Internal exchange for calculations in Y
      IF (useCubedSphereExchange) THEN
       DO j=1,Oly
        DO i=1,Olx
         localTij( 1-i , 1-j )=localTij(   j   , 1-i )
         localTij( 1-i ,sNy+j)=localTij(   j   ,sNy+i)
         localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i )
         localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i)
        ENDDO
       ENDDO
      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

      DO j=1-Oly,sNy+Oly
       DO i=1-Olx,sNx+Olx
        localTijk(i,j,k)=localTij(i,j)
       ENDDO
      ENDDO

C--   End of ipass loop
      ENDDO

C--   End of K loop for horizontal fluxes
      ENDDO

C--   Start of k loop for vertical flux
      DO k=Nr,1,-1
#ifdef ALLOW_AUTODIFF_TAMC 
         kkey = (ikey-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.

#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 transport
C     Note: wVel needs to be masked 

      IF (k.EQ.1) THEN
C- Surface interface :

       DO j=1-Oly,sNy+Oly
        DO i=1-Olx,sNx+Olx
         rTransKp1(i,j) = rTrans(i,j)
         rTrans(i,j) = 0.
         fVerT(i,j,kUp) = 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 */

C-    Compute vertical advective flux in the interior:
       IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
        CALL GAD_FLUXLIMIT_ADV_R(
     &       bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
       ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
        CALL GAD_DST3_ADV_R(
     &       bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
       ELSEIF (advectionScheme.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

C--   Divergence of 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

      RETURN
      END
1	heimbach	1.15	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.14 2002/11/12 20:42:24 heimbach Exp $
2	adcroft	1.2	C $Name: $
3	adcroft	1.1
4	adcroft	1.4	CBOI
5			C !TITLE: pkg/generic\_advdiff
6			C !AUTHORS: adcroft@mit.edu
7	adcroft	1.8	C !INTRODUCTION: Generic Advection Diffusion Package
8	adcroft	1.4	C
9			C Package "generic\_advdiff" provides a common set of routines for calculating
10			C advective/diffusive fluxes for tracers (cell centered quantities on a C-grid).
11			C
12			C Many different advection schemes are available: the standard centered
13			C second order, centered fourth order and upwind biased third order schemes
14			C are known as linear methods and require some stable time-stepping method
15			C such as Adams-Bashforth. Alternatives such as flux-limited schemes are
16			C stable in the forward sense and are best combined with the multi-dimensional
17			C method provided in gad\_advection.
18			C
19			C There are two high-level routines:
20			C \begin{itemize}
21			C \item{GAD\_CALC\_RHS} calculates all fluxes at time level "n" and is used
22			C for the standard linear schemes. This must be used in conjuction with
23			C Adams-Bashforth time-stepping. Diffusive and parameterized fluxes are
24			C always calculated here.
25			C \item{GAD\_ADVECTION} calculates just the advective fluxes using the
26			C non-linear schemes and can not be used in conjuction with Adams-Bashforth
27			C time-stepping.
28			C \end{itemize}
29			CEOI
30
31	adcroft	1.1	#include "GAD_OPTIONS.h"
32
33	adcroft	1.4	CBOP
34			C !ROUTINE: GAD_ADVECTION
35
36			C !INTERFACE: ==========================================================
37	adcroft	1.1	SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity,
38			U Tracer,Gtracer,
39			I myTime,myIter,myThid)
40	adcroft	1.4
41			C !DESCRIPTION:
42			C Calculates the tendancy of a tracer due to advection.
43			C It uses the multi-dimensional method given in \ref{sect:multiDimAdvection}
44			C and can only be used for the non-linear advection schemes such as the
45			C direct-space-time method and flux-limiters.
46			C
47			C The algorithm is as follows:
48			C \begin{itemize}
49			C \item{$\theta^{(n+1/3)} = \theta^{(n)}
50	adcroft	1.5	C - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$}
51	adcroft	1.4	C \item{$\theta^{(n+2/3)} = \theta^{(n+1/3)}
52	adcroft	1.5	C - \Delta t \partial_y (v\theta^{(n+1/3)}) + \theta^{(n)} \partial_y v$}
53	adcroft	1.4	C \item{$\theta^{(n+3/3)} = \theta^{(n+2/3)}
54	adcroft	1.5	C - \Delta t \partial_r (w\theta^{(n+2/3)}) + \theta^{(n)} \partial_r w$}
55	adcroft	1.4	C \item{$G_\theta = ( \theta^{(n+3/3)} - \theta^{(n)} )/\Delta t$}
56			C \end{itemize}
57			C
58			C The tendancy (output) is over-written by this routine.
59
60			C !USES: ===============================================================
61	adcroft	1.1	IMPLICIT NONE
62			#include "SIZE.h"
63			#include "EEPARAMS.h"
64			#include "PARAMS.h"
65			#include "DYNVARS.h"
66			#include "GRID.h"
67			#include "GAD.h"
68	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
69			# include "tamc.h"
70			# include "tamc_keys.h"
71			#endif
72	adcroft	1.1
73	adcroft	1.4	C !INPUT PARAMETERS: ===================================================
74			C bi,bj :: tile indices
75			C advectionScheme :: advection scheme to use
76			C tracerIdentity :: identifier for the tracer (required only for OBCS)
77			C Tracer :: tracer field
78			C myTime :: current time
79			C myIter :: iteration number
80			C myThid :: thread number
81	adcroft	1.1	INTEGER bi,bj
82			INTEGER advectionScheme
83			INTEGER tracerIdentity
84	adcroft	1.9	_RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
85	adcroft	1.1	_RL myTime
86			INTEGER myIter
87			INTEGER myThid
88
89	adcroft	1.4	C !OUTPUT PARAMETERS: ==================================================
90			C gTracer :: tendancy array
91	adcroft	1.9	_RL gTracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
92	adcroft	1.4
93			C !LOCAL VARIABLES: ====================================================
94			C maskUp :: 2-D array for mask at W points
95			C iMin,iMax,jMin,jMax :: loop range for called routines
96			C i,j,k :: loop indices
97			C kup :: index into 2 1/2D array, toggles between 1 and 2
98			C kdown :: index into 2 1/2D array, toggles between 2 and 1
99			C kp1 :: =k+1 for k<Nr, =Nr for k=Nr
100			C xA,yA :: areas of X and Y face of tracer cells
101			C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
102	jmc	1.11	C rTransKp1 :: vertical volume transport at interface k+1
103	adcroft	1.4	C af :: 2-D array for horizontal advective flux
104			C fVerT :: 2 1/2D arrays for vertical advective flux
105			C localTij :: 2-D array used as temporary local copy of tracer fld
106			C localTijk :: 3-D array used as temporary local copy of tracer fld
107			C kp1Msk :: flag (0,1) to act as over-riding mask for W levels
108			C calc_fluxes_X :: logical to indicate to calculate fluxes in X dir
109			C calc_fluxes_Y :: logical to indicate to calculate fluxes in Y dir
110			C nipass :: number of passes to make in multi-dimensional method
111			C ipass :: number of the current pass being made
112	adcroft	1.1	_RS maskUp (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
113			INTEGER iMin,iMax,jMin,jMax
114	jmc	1.11	INTEGER i,j,k,kup,kDown
115	adcroft	1.1	_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
116			_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
117			_RL uTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
118			_RL vTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119			_RL rTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120	jmc	1.11	_RL rTransKp1(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121	adcroft	1.1	_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122			_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
123			_RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
124			_RL localTijk(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
125			_RL kp1Msk
126	adcroft	1.3	LOGICAL calc_fluxes_X,calc_fluxes_Y
127			INTEGER nipass,ipass
128	adcroft	1.4	CEOP
129	adcroft	1.1
130	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
131	heimbach	1.14	act0 = tracerIdentity - 1
132			max0 = maxpass
133	heimbach	1.6	act1 = bi - myBxLo(myThid)
134			max1 = myBxHi(myThid) - myBxLo(myThid) + 1
135			act2 = bj - myByLo(myThid)
136			max2 = myByHi(myThid) - myByLo(myThid) + 1
137			act3 = myThid - 1
138			max3 = nTx*nTy
139			act4 = ikey_dynamics - 1
140	heimbach	1.14	igadkey = (act0 + 1)
141			& + act1*max0
142			& + act2max0max1
143			& + act3max0max1*max2
144			& + act4max0max1max2max3
145	heimbach	1.15	if (tracerIdentity.GT.maxpass) then
146			print *, 'ph-pass gad_advection ', maxpass, tracerIdentity
147			STOP 'maxpass seems smaller than tracerIdentity'
148			endif
149	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
150
151	adcroft	1.1	C-- Set up work arrays with valid (i.e. not NaN) values
152			C These inital values do not alter the numerical results. They
153			C just ensure that all memory references are to valid floating
154			C point numbers. This prevents spurious hardware signals due to
155			C uninitialised but inert locations.
156			DO j=1-OLy,sNy+OLy
157			DO i=1-OLx,sNx+OLx
158			xA(i,j) = 0. _d 0
159			yA(i,j) = 0. _d 0
160			uTrans(i,j) = 0. _d 0
161			vTrans(i,j) = 0. _d 0
162			rTrans(i,j) = 0. _d 0
163			fVerT(i,j,1) = 0. _d 0
164			fVerT(i,j,2) = 0. _d 0
165	jmc	1.11	rTransKp1(i,j)= 0. _d 0
166	adcroft	1.1	ENDDO
167			ENDDO
168
169			iMin = 1-OLx
170			iMax = sNx+OLx
171			jMin = 1-OLy
172			jMax = sNy+OLy
173
174			C-- Start of k loop for horizontal fluxes
175			DO k=1,Nr
176	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
177	heimbach	1.14	kkey = (igadkey-1)*Nr + k
178			CADJ STORE tracer(:,:,k,bi,bj) =
179			CADJ & comlev1_bibj_k_gad, key=kkey, byte=isbyte
180	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
181	adcroft	1.1
182			C-- Get temporary terms used by tendency routines
183			CALL CALC_COMMON_FACTORS (
184			I bi,bj,iMin,iMax,jMin,jMax,k,
185			O xA,yA,uTrans,vTrans,rTrans,maskUp,
186			I myThid)
187
188	jmc	1.11	#ifdef ALLOW_GMREDI
189			C-- Residual transp = Bolus transp + Eulerian transp
190			IF (useGMRedi)
191			& CALL GMREDI_CALC_UVFLOW(
192			& uTrans, vTrans, bi, bj, k, myThid)
193			#endif /* ALLOW_GMREDI */
194
195	adcroft	1.1	C-- Make local copy of tracer array
196			DO j=1-OLy,sNy+OLy
197			DO i=1-OLx,sNx+OLx
198			localTij(i,j)=tracer(i,j,k,bi,bj)
199			ENDDO
200			ENDDO
201
202	adcroft	1.3	IF (useCubedSphereExchange) THEN
203			nipass=3
204	heimbach	1.14	#ifdef ALLOW_AUTODIFF_TAMC
205			if ( nipass.GT.maxcube )
206			& STOP 'maxcube needs to be = 3'
207			#endif
208	adcroft	1.3	ELSE
209			nipass=1
210			ENDIF
211	heimbach	1.6	cph nipass=1
212	adcroft	1.3
213			C-- Multiple passes for different directions on different tiles
214			DO ipass=1,nipass
215	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
216	heimbach	1.14	passkey = ipass + (k-1) *maxcube
217			& + (igadkey-1)maxcubeNr
218	heimbach	1.6	IF (nipass .GT. maxpass) THEN
219	heimbach	1.14	STOP 'GAD_ADVECTION: nipass > maxcube. check tamc.h'
220	heimbach	1.6	ENDIF
221			#endif /* ALLOW_AUTODIFF_TAMC */
222	adcroft	1.3
223			IF (nipass.EQ.3) THEN
224			calc_fluxes_X=.FALSE.
225			calc_fluxes_Y=.FALSE.
226			IF (ipass.EQ.1 .AND. (bi.EQ.1 .OR. bi.EQ.2) ) THEN
227			calc_fluxes_X=.TRUE.
228			ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN
229			calc_fluxes_Y=.TRUE.
230			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN
231			calc_fluxes_Y=.TRUE.
232			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN
233			calc_fluxes_X=.TRUE.
234			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN
235			calc_fluxes_Y=.TRUE.
236			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.EQ.6) ) THEN
237			calc_fluxes_X=.TRUE.
238			ENDIF
239			ELSE
240			calc_fluxes_X=.TRUE.
241			calc_fluxes_Y=.TRUE.
242			ENDIF
243
244			C-- X direction
245			IF (calc_fluxes_X) THEN
246
247			C-- Internal exchange for calculations in X
248			IF (useCubedSphereExchange) THEN
249			DO j=1,Oly
250			DO i=1,Olx
251			localTij( 1-i , 1-j )=localTij( 1-j , i )
252			localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i )
253			localTij(sNx+i, 1-j )=localTij(sNx+j, i )
254			localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i )
255			ENDDO
256			ENDDO
257			ENDIF
258
259	adcroft	1.1	C- Advective flux in X
260			DO j=1-Oly,sNy+Oly
261			DO i=1-Olx,sNx+Olx
262			af(i,j) = 0.
263			ENDDO
264			ENDDO
265	heimbach	1.6
266			#ifdef ALLOW_AUTODIFF_TAMC
267	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
268	heimbach	1.14	CADJ STORE localTij(:,:) =
269			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
270	heimbach	1.6	#endif
271			#endif /* ALLOW_AUTODIFF_TAMC */
272
273	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
274			CALL GAD_FLUXLIMIT_ADV_X(
275			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
276			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
277			CALL GAD_DST3_ADV_X(
278			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
279			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
280			CALL GAD_DST3FL_ADV_X(
281			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
282			ELSE
283	adcroft	1.9	STOP 'GAD_ADVECTION: adv. scheme incompatibale with multi-dim'
284	adcroft	1.1	ENDIF
285	heimbach	1.6
286	adcroft	1.1	DO j=1-Oly,sNy+Oly
287			DO i=1-Olx,sNx+Olx-1
288			localTij(i,j)=localTij(i,j)-deltaTtracer*
289			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
290			& *recip_rA(i,j,bi,bj)
291			& *( af(i+1,j)-af(i,j)
292			& -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j))
293			& )
294			ENDDO
295			ENDDO
296
297			#ifdef ALLOW_OBCS
298			C-- Apply open boundary conditions
299			IF (useOBCS) THEN
300			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
301			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
302			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
303			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
304			END IF
305			END IF
306			#endif /* ALLOW_OBCS */
307
308	adcroft	1.3	C-- End of X direction
309			ENDIF
310
311			C-- Y direction
312			IF (calc_fluxes_Y) THEN
313
314			C-- Internal exchange for calculations in Y
315			IF (useCubedSphereExchange) THEN
316			DO j=1,Oly
317			DO i=1,Olx
318			localTij( 1-i , 1-j )=localTij( j , 1-i )
319			localTij( 1-i ,sNy+j)=localTij( j ,sNy+i)
320			localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i )
321			localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i)
322			ENDDO
323			ENDDO
324			ENDIF
325
326	adcroft	1.1	C- Advective flux in Y
327			DO j=1-Oly,sNy+Oly
328			DO i=1-Olx,sNx+Olx
329			af(i,j) = 0.
330			ENDDO
331			ENDDO
332	heimbach	1.6
333			#ifdef ALLOW_AUTODIFF_TAMC
334	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
335	heimbach	1.14	CADJ STORE localTij(:,:) =
336			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
337	heimbach	1.6	#endif
338			#endif /* ALLOW_AUTODIFF_TAMC */
339
340	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
341			CALL GAD_FLUXLIMIT_ADV_Y(
342			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
343			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
344			CALL GAD_DST3_ADV_Y(
345			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
346			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
347			CALL GAD_DST3FL_ADV_Y(
348			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
349			ELSE
350			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
351			ENDIF
352	heimbach	1.6
353	adcroft	1.1	DO j=1-Oly,sNy+Oly-1
354			DO i=1-Olx,sNx+Olx
355			localTij(i,j)=localTij(i,j)-deltaTtracer*
356			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
357			& *recip_rA(i,j,bi,bj)
358			& *( af(i,j+1)-af(i,j)
359			& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j))
360			& )
361			ENDDO
362			ENDDO
363	adcroft	1.3
364	adcroft	1.1	#ifdef ALLOW_OBCS
365			C-- Apply open boundary conditions
366			IF (useOBCS) THEN
367			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
368			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
369			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
370			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
371			END IF
372			END IF
373			#endif /* ALLOW_OBCS */
374	adcroft	1.3
375			C-- End of Y direction
376			ENDIF
377
378			DO j=1-Oly,sNy+Oly
379	adcroft	1.1	DO i=1-Olx,sNx+Olx
380			localTijk(i,j,k)=localTij(i,j)
381			ENDDO
382			ENDDO
383
384	adcroft	1.3	C-- End of ipass loop
385			ENDDO
386	adcroft	1.1
387			C-- End of K loop for horizontal fluxes
388			ENDDO
389
390			C-- Start of k loop for vertical flux
391			DO k=Nr,1,-1
392	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
393			kkey = (ikey-1)*Nr + k
394			#endif /* ALLOW_AUTODIFF_TAMC */
395	adcroft	1.1
396			C-- kup Cycles through 1,2 to point to w-layer above
397			C-- kDown Cycles through 2,1 to point to w-layer below
398			kup = 1+MOD(k+1,2)
399			kDown= 1+MOD(k,2)
400	jmc	1.11	c kp1=min(Nr,k+1)
401			kp1Msk=1.
402			if (k.EQ.Nr) kp1Msk=0.
403	heimbach	1.6
404			#ifdef ALLOW_AUTODIFF_TAMC
405			CADJ STORE localTijk(:,:,k)
406	heimbach	1.14	CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
407	heimbach	1.12	CADJ STORE rTrans(:,:)
408	heimbach	1.14	CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
409	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
410	adcroft	1.1
411	jmc	1.11	C-- Compute Vertical transport
412	adcroft	1.1	C Note: wVel needs to be masked
413	jmc	1.11
414			IF (k.EQ.1) THEN
415			C- Surface interface :
416
417			DO j=1-Oly,sNy+Oly
418			DO i=1-Olx,sNx+Olx
419			rTransKp1(i,j) = rTrans(i,j)
420			rTrans(i,j) = 0.
421			fVerT(i,j,kUp) = 0.
422			ENDDO
423			ENDDO
424
425			ELSE
426			C- Interior interface :
427			DO j=1-Oly,sNy+Oly
428			DO i=1-Olx,sNx+Olx
429			rTransKp1(i,j) = kp1Msk*rTrans(i,j)
430			rTrans(i,j) = wVel(i,j,k,bi,bj)*rA(i,j,bi,bj)
431			& *maskC(i,j,k-1,bi,bj)
432			af(i,j) = 0.
433			ENDDO
434			ENDDO
435
436			#ifdef ALLOW_GMREDI
437			C-- Residual transp = Bolus transp + Eulerian transp
438			IF (useGMRedi)
439			& CALL GMREDI_CALC_WFLOW(
440			& rTrans, bi, bj, k, myThid)
441			#endif /* ALLOW_GMREDI */
442
443	adcroft	1.1	C- Compute vertical advective flux in the interior:
444			IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
445			CALL GAD_FLUXLIMIT_ADV_R(
446			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
447			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
448	adcroft	1.2	CALL GAD_DST3_ADV_R(
449			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
450	adcroft	1.1	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
451	adcroft	1.2	CALL GAD_DST3FL_ADV_R(
452			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
453	adcroft	1.1	ELSE
454			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
455			ENDIF
456	jmc	1.11	C- add the advective flux to fVerT
457	adcroft	1.1	DO j=1-Oly,sNy+Oly
458			DO i=1-Olx,sNx+Olx
459	jmc	1.11	fVerT(i,j,kUp) = af(i,j)
460	adcroft	1.1	ENDDO
461	jmc	1.11	ENDDO
462
463			C- end Surface/Interior if bloc
464	adcroft	1.1	ENDIF
465
466			C-- Divergence of fluxes
467			DO j=1-Oly,sNy+Oly
468			DO i=1-Olx,sNx+Olx
469			localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
470			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
471			& *recip_rA(i,j,bi,bj)
472			& *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
473	jmc	1.11	& -tracer(i,j,k,bi,bj)*(rTrans(i,j)-rTransKp1(i,j))
474	adcroft	1.1	& )*rkFac
475			gTracer(i,j,k,bi,bj)=
476			& (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
477			ENDDO
478			ENDDO
479
480			C-- End of K loop for vertical flux
481			ENDDO
482
483			RETURN
484			END