pkg/generic_advdiff/gad_advection.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.13 2002/07/13 04:59:42 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)
     &         STOP 'maxpass seems smaller than tracerIdentity'
#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	1.14	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.13 2002/07/13 04:59:42 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			if (tracerIdentity.GT.maxpass)
146			& STOP 'maxpass seems smaller than tracerIdentity'
147	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
148
149	adcroft	1.1	C-- Set up work arrays with valid (i.e. not NaN) values
150			C These inital values do not alter the numerical results. They
151			C just ensure that all memory references are to valid floating
152			C point numbers. This prevents spurious hardware signals due to
153			C uninitialised but inert locations.
154			DO j=1-OLy,sNy+OLy
155			DO i=1-OLx,sNx+OLx
156			xA(i,j) = 0. _d 0
157			yA(i,j) = 0. _d 0
158			uTrans(i,j) = 0. _d 0
159			vTrans(i,j) = 0. _d 0
160			rTrans(i,j) = 0. _d 0
161			fVerT(i,j,1) = 0. _d 0
162			fVerT(i,j,2) = 0. _d 0
163	jmc	1.11	rTransKp1(i,j)= 0. _d 0
164	adcroft	1.1	ENDDO
165			ENDDO
166
167			iMin = 1-OLx
168			iMax = sNx+OLx
169			jMin = 1-OLy
170			jMax = sNy+OLy
171
172			C-- Start of k loop for horizontal fluxes
173			DO k=1,Nr
174	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
175	heimbach	1.14	kkey = (igadkey-1)*Nr + k
176			CADJ STORE tracer(:,:,k,bi,bj) =
177			CADJ & comlev1_bibj_k_gad, key=kkey, byte=isbyte
178	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
179	adcroft	1.1
180			C-- Get temporary terms used by tendency routines
181			CALL CALC_COMMON_FACTORS (
182			I bi,bj,iMin,iMax,jMin,jMax,k,
183			O xA,yA,uTrans,vTrans,rTrans,maskUp,
184			I myThid)
185
186	jmc	1.11	#ifdef ALLOW_GMREDI
187			C-- Residual transp = Bolus transp + Eulerian transp
188			IF (useGMRedi)
189			& CALL GMREDI_CALC_UVFLOW(
190			& uTrans, vTrans, bi, bj, k, myThid)
191			#endif /* ALLOW_GMREDI */
192
193	adcroft	1.1	C-- Make local copy of tracer array
194			DO j=1-OLy,sNy+OLy
195			DO i=1-OLx,sNx+OLx
196			localTij(i,j)=tracer(i,j,k,bi,bj)
197			ENDDO
198			ENDDO
199
200	adcroft	1.3	IF (useCubedSphereExchange) THEN
201			nipass=3
202	heimbach	1.14	#ifdef ALLOW_AUTODIFF_TAMC
203			if ( nipass.GT.maxcube )
204			& STOP 'maxcube needs to be = 3'
205			#endif
206	adcroft	1.3	ELSE
207			nipass=1
208			ENDIF
209	heimbach	1.6	cph nipass=1
210	adcroft	1.3
211			C-- Multiple passes for different directions on different tiles
212			DO ipass=1,nipass
213	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
214	heimbach	1.14	passkey = ipass + (k-1) *maxcube
215			& + (igadkey-1)maxcubeNr
216	heimbach	1.6	IF (nipass .GT. maxpass) THEN
217	heimbach	1.14	STOP 'GAD_ADVECTION: nipass > maxcube. check tamc.h'
218	heimbach	1.6	ENDIF
219			#endif /* ALLOW_AUTODIFF_TAMC */
220	adcroft	1.3
221			IF (nipass.EQ.3) THEN
222			calc_fluxes_X=.FALSE.
223			calc_fluxes_Y=.FALSE.
224			IF (ipass.EQ.1 .AND. (bi.EQ.1 .OR. bi.EQ.2) ) THEN
225			calc_fluxes_X=.TRUE.
226			ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN
227			calc_fluxes_Y=.TRUE.
228			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN
229			calc_fluxes_Y=.TRUE.
230			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN
231			calc_fluxes_X=.TRUE.
232			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN
233			calc_fluxes_Y=.TRUE.
234			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.EQ.6) ) THEN
235			calc_fluxes_X=.TRUE.
236			ENDIF
237			ELSE
238			calc_fluxes_X=.TRUE.
239			calc_fluxes_Y=.TRUE.
240			ENDIF
241
242			C-- X direction
243			IF (calc_fluxes_X) THEN
244
245			C-- Internal exchange for calculations in X
246			IF (useCubedSphereExchange) THEN
247			DO j=1,Oly
248			DO i=1,Olx
249			localTij( 1-i , 1-j )=localTij( 1-j , i )
250			localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i )
251			localTij(sNx+i, 1-j )=localTij(sNx+j, i )
252			localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i )
253			ENDDO
254			ENDDO
255			ENDIF
256
257	adcroft	1.1	C- Advective flux in X
258			DO j=1-Oly,sNy+Oly
259			DO i=1-Olx,sNx+Olx
260			af(i,j) = 0.
261			ENDDO
262			ENDDO
263	heimbach	1.6
264			#ifdef ALLOW_AUTODIFF_TAMC
265	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
266	heimbach	1.14	CADJ STORE localTij(:,:) =
267			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
268	heimbach	1.6	#endif
269			#endif /* ALLOW_AUTODIFF_TAMC */
270
271	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
272			CALL GAD_FLUXLIMIT_ADV_X(
273			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
274			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
275			CALL GAD_DST3_ADV_X(
276			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
277			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
278			CALL GAD_DST3FL_ADV_X(
279			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
280			ELSE
281	adcroft	1.9	STOP 'GAD_ADVECTION: adv. scheme incompatibale with multi-dim'
282	adcroft	1.1	ENDIF
283	heimbach	1.6
284	adcroft	1.1	DO j=1-Oly,sNy+Oly
285			DO i=1-Olx,sNx+Olx-1
286			localTij(i,j)=localTij(i,j)-deltaTtracer*
287			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
288			& *recip_rA(i,j,bi,bj)
289			& *( af(i+1,j)-af(i,j)
290			& -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j))
291			& )
292			ENDDO
293			ENDDO
294
295			#ifdef ALLOW_OBCS
296			C-- Apply open boundary conditions
297			IF (useOBCS) THEN
298			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
299			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
300			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
301			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
302			END IF
303			END IF
304			#endif /* ALLOW_OBCS */
305
306	adcroft	1.3	C-- End of X direction
307			ENDIF
308
309			C-- Y direction
310			IF (calc_fluxes_Y) THEN
311
312			C-- Internal exchange for calculations in Y
313			IF (useCubedSphereExchange) THEN
314			DO j=1,Oly
315			DO i=1,Olx
316			localTij( 1-i , 1-j )=localTij( j , 1-i )
317			localTij( 1-i ,sNy+j)=localTij( j ,sNy+i)
318			localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i )
319			localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i)
320			ENDDO
321			ENDDO
322			ENDIF
323
324	adcroft	1.1	C- Advective flux in Y
325			DO j=1-Oly,sNy+Oly
326			DO i=1-Olx,sNx+Olx
327			af(i,j) = 0.
328			ENDDO
329			ENDDO
330	heimbach	1.6
331			#ifdef ALLOW_AUTODIFF_TAMC
332	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
333	heimbach	1.14	CADJ STORE localTij(:,:) =
334			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
335	heimbach	1.6	#endif
336			#endif /* ALLOW_AUTODIFF_TAMC */
337
338	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
339			CALL GAD_FLUXLIMIT_ADV_Y(
340			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
341			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
342			CALL GAD_DST3_ADV_Y(
343			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
344			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
345			CALL GAD_DST3FL_ADV_Y(
346			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
347			ELSE
348			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
349			ENDIF
350	heimbach	1.6
351	adcroft	1.1	DO j=1-Oly,sNy+Oly-1
352			DO i=1-Olx,sNx+Olx
353			localTij(i,j)=localTij(i,j)-deltaTtracer*
354			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
355			& *recip_rA(i,j,bi,bj)
356			& *( af(i,j+1)-af(i,j)
357			& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j))
358			& )
359			ENDDO
360			ENDDO
361	adcroft	1.3
362	adcroft	1.1	#ifdef ALLOW_OBCS
363			C-- Apply open boundary conditions
364			IF (useOBCS) THEN
365			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
366			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
367			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
368			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
369			END IF
370			END IF
371			#endif /* ALLOW_OBCS */
372	adcroft	1.3
373			C-- End of Y direction
374			ENDIF
375
376			DO j=1-Oly,sNy+Oly
377	adcroft	1.1	DO i=1-Olx,sNx+Olx
378			localTijk(i,j,k)=localTij(i,j)
379			ENDDO
380			ENDDO
381
382	adcroft	1.3	C-- End of ipass loop
383			ENDDO
384	adcroft	1.1
385			C-- End of K loop for horizontal fluxes
386			ENDDO
387
388			C-- Start of k loop for vertical flux
389			DO k=Nr,1,-1
390	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
391			kkey = (ikey-1)*Nr + k
392			#endif /* ALLOW_AUTODIFF_TAMC */
393	adcroft	1.1
394			C-- kup Cycles through 1,2 to point to w-layer above
395			C-- kDown Cycles through 2,1 to point to w-layer below
396			kup = 1+MOD(k+1,2)
397			kDown= 1+MOD(k,2)
398	jmc	1.11	c kp1=min(Nr,k+1)
399			kp1Msk=1.
400			if (k.EQ.Nr) kp1Msk=0.
401	heimbach	1.6
402			#ifdef ALLOW_AUTODIFF_TAMC
403			CADJ STORE localTijk(:,:,k)
404	heimbach	1.14	CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
405	heimbach	1.12	CADJ STORE rTrans(:,:)
406	heimbach	1.14	CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
407	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
408	adcroft	1.1
409	jmc	1.11	C-- Compute Vertical transport
410	adcroft	1.1	C Note: wVel needs to be masked
411	jmc	1.11
412			IF (k.EQ.1) THEN
413			C- Surface interface :
414
415			DO j=1-Oly,sNy+Oly
416			DO i=1-Olx,sNx+Olx
417			rTransKp1(i,j) = rTrans(i,j)
418			rTrans(i,j) = 0.
419			fVerT(i,j,kUp) = 0.
420			ENDDO
421			ENDDO
422
423			ELSE
424			C- Interior interface :
425			DO j=1-Oly,sNy+Oly
426			DO i=1-Olx,sNx+Olx
427			rTransKp1(i,j) = kp1Msk*rTrans(i,j)
428			rTrans(i,j) = wVel(i,j,k,bi,bj)*rA(i,j,bi,bj)
429			& *maskC(i,j,k-1,bi,bj)
430			af(i,j) = 0.
431			ENDDO
432			ENDDO
433
434			#ifdef ALLOW_GMREDI
435			C-- Residual transp = Bolus transp + Eulerian transp
436			IF (useGMRedi)
437			& CALL GMREDI_CALC_WFLOW(
438			& rTrans, bi, bj, k, myThid)
439			#endif /* ALLOW_GMREDI */
440
441	adcroft	1.1	C- Compute vertical advective flux in the interior:
442			IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
443			CALL GAD_FLUXLIMIT_ADV_R(
444			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
445			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
446	adcroft	1.2	CALL GAD_DST3_ADV_R(
447			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
448	adcroft	1.1	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
449	adcroft	1.2	CALL GAD_DST3FL_ADV_R(
450			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
451	adcroft	1.1	ELSE
452			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
453			ENDIF
454	jmc	1.11	C- add the advective flux to fVerT
455	adcroft	1.1	DO j=1-Oly,sNy+Oly
456			DO i=1-Olx,sNx+Olx
457	jmc	1.11	fVerT(i,j,kUp) = af(i,j)
458	adcroft	1.1	ENDDO
459	jmc	1.11	ENDDO
460
461			C- end Surface/Interior if bloc
462	adcroft	1.1	ENDIF
463
464			C-- Divergence of fluxes
465			DO j=1-Oly,sNy+Oly
466			DO i=1-Olx,sNx+Olx
467			localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
468			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
469			& *recip_rA(i,j,bi,bj)
470			& *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
471	jmc	1.11	& -tracer(i,j,k,bi,bj)*(rTrans(i,j)-rTransKp1(i,j))
472	adcroft	1.1	& )*rkFac
473			gTracer(i,j,k,bi,bj)=
474			& (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
475			ENDDO
476			ENDDO
477
478			C-- End of K loop for vertical flux
479			ENDDO
480
481			RETURN
482			END