pkg/generic_advdiff/gad_advection.F

C $Header: /u/gcmpack/models/MITgcmUV/pkg/generic_advdiff/gad_advection.F,v 1.7 2001/09/28 02:26:57 adcroft 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 Gtracer(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 Tracer(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  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,kp1
      _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 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
          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
          ikey = (act1 + 1) + act2*max1
     &                      + act3*max1*max2
     &                      + act4*max1*max2*max3
#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
       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 = (ikey-1)*Nr + k
CADJ STORE tracer(:,:,k,bi,bj) = comlev1_bibj_k, 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)

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
      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)   *maxpass
     &                   + (ikey-1)*maxpass*Nr
         IF (nipass .GT. maxpass) THEN
          STOP 'GAD_ADVECTION: nipass > maxpass. 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(:,:)  = comlev1_bibj_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 mutli-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(:,:)  = comlev1_bibj_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--   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)

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

#ifdef ALLOW_AUTODIFF_TAMC 
CADJ STORE localTijk(:,:,k)  
CADJ &     = comlev1_bibj_k, key=kkey, byte=isbyte
#endif /* ALLOW_AUTODIFF_TAMC */

C     Note: wVel needs to be masked 
      IF (K.GE.2) THEN
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-    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)*localTijk(i,j,k)
        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)*localTijk(i,j,k)
        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) = af(i,j)
       ENDDO
      ENDDO

C--   Divergence of fluxes
      kp1=min(Nr,k+1)
      kp1Msk=1.
      if (k.EQ.Nr) kp1Msk=0.
      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)*rA(i,j,bi,bj)*
     &        (wVel(i,j,k,bi,bj)-kp1Msk*wVel(i,j,kp1,bi,bj))
     &     )*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	adcroft	1.8	C $Header: /u/gcmpack/models/MITgcmUV/pkg/generic_advdiff/gad_advection.F,v 1.7 2001/09/28 02:26:57 adcroft 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			_RL Gtracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
85			_RL myTime
86			INTEGER myIter
87			INTEGER myThid
88
89	adcroft	1.4	C !OUTPUT PARAMETERS: ==================================================
90			C gTracer :: tendancy array
91			_RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
92
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			C af :: 2-D array for horizontal advective flux
103			C fVerT :: 2 1/2D arrays for vertical advective flux
104			C localTij :: 2-D array used as temporary local copy of tracer fld
105			C localTijk :: 3-D array used as temporary local copy of tracer fld
106			C kp1Msk :: flag (0,1) to act as over-riding mask for W levels
107			C calc_fluxes_X :: logical to indicate to calculate fluxes in X dir
108			C calc_fluxes_Y :: logical to indicate to calculate fluxes in Y dir
109			C nipass :: number of passes to make in multi-dimensional method
110			C ipass :: number of the current pass being made
111	adcroft	1.1	_RS maskUp (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
112			INTEGER iMin,iMax,jMin,jMax
113			INTEGER i,j,k,kup,kDown,kp1
114			_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
115			_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
116			_RL uTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
117			_RL vTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
118			_RL rTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119			_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120			_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
121			_RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122			_RL localTijk(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
123			_RL kp1Msk
124	adcroft	1.3	LOGICAL calc_fluxes_X,calc_fluxes_Y
125			INTEGER nipass,ipass
126	adcroft	1.4	CEOP
127	adcroft	1.1
128	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
129			act1 = bi - myBxLo(myThid)
130			max1 = myBxHi(myThid) - myBxLo(myThid) + 1
131			act2 = bj - myByLo(myThid)
132			max2 = myByHi(myThid) - myByLo(myThid) + 1
133			act3 = myThid - 1
134			max3 = nTx*nTy
135			act4 = ikey_dynamics - 1
136			ikey = (act1 + 1) + act2*max1
137			& + act3max1max2
138			& + act4max1max2*max3
139			#endif /* ALLOW_AUTODIFF_TAMC */
140
141	adcroft	1.1	C-- Set up work arrays with valid (i.e. not NaN) values
142			C These inital values do not alter the numerical results. They
143			C just ensure that all memory references are to valid floating
144			C point numbers. This prevents spurious hardware signals due to
145			C uninitialised but inert locations.
146			DO j=1-OLy,sNy+OLy
147			DO i=1-OLx,sNx+OLx
148			xA(i,j) = 0. _d 0
149			yA(i,j) = 0. _d 0
150			uTrans(i,j) = 0. _d 0
151			vTrans(i,j) = 0. _d 0
152			rTrans(i,j) = 0. _d 0
153			fVerT(i,j,1) = 0. _d 0
154			fVerT(i,j,2) = 0. _d 0
155			ENDDO
156			ENDDO
157
158			iMin = 1-OLx
159			iMax = sNx+OLx
160			jMin = 1-OLy
161			jMax = sNy+OLy
162
163			C-- Start of k loop for horizontal fluxes
164			DO k=1,Nr
165	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
166			kkey = (ikey-1)*Nr + k
167			CADJ STORE tracer(:,:,k,bi,bj) = comlev1_bibj_k, key=kkey, byte=isbyte
168			#endif /* ALLOW_AUTODIFF_TAMC */
169	adcroft	1.1
170			C-- Get temporary terms used by tendency routines
171			CALL CALC_COMMON_FACTORS (
172			I bi,bj,iMin,iMax,jMin,jMax,k,
173			O xA,yA,uTrans,vTrans,rTrans,maskUp,
174			I myThid)
175
176			C-- Make local copy of tracer array
177			DO j=1-OLy,sNy+OLy
178			DO i=1-OLx,sNx+OLx
179			localTij(i,j)=tracer(i,j,k,bi,bj)
180			ENDDO
181			ENDDO
182
183	adcroft	1.3	IF (useCubedSphereExchange) THEN
184			nipass=3
185			ELSE
186			nipass=1
187			ENDIF
188	heimbach	1.6	cph nipass=1
189	adcroft	1.3
190			C-- Multiple passes for different directions on different tiles
191			DO ipass=1,nipass
192	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
193			passkey = ipass + (k-1) *maxpass
194			& + (ikey-1)maxpassNr
195			IF (nipass .GT. maxpass) THEN
196			STOP 'GAD_ADVECTION: nipass > maxpass. check tamc.h'
197			ENDIF
198			#endif /* ALLOW_AUTODIFF_TAMC */
199	adcroft	1.3
200			IF (nipass.EQ.3) THEN
201			calc_fluxes_X=.FALSE.
202			calc_fluxes_Y=.FALSE.
203			IF (ipass.EQ.1 .AND. (bi.EQ.1 .OR. bi.EQ.2) ) THEN
204			calc_fluxes_X=.TRUE.
205			ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN
206			calc_fluxes_Y=.TRUE.
207			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN
208			calc_fluxes_Y=.TRUE.
209			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN
210			calc_fluxes_X=.TRUE.
211			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN
212			calc_fluxes_Y=.TRUE.
213			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.EQ.6) ) THEN
214			calc_fluxes_X=.TRUE.
215			ENDIF
216			ELSE
217			calc_fluxes_X=.TRUE.
218			calc_fluxes_Y=.TRUE.
219			ENDIF
220
221			C-- X direction
222			IF (calc_fluxes_X) THEN
223
224			C-- Internal exchange for calculations in X
225			IF (useCubedSphereExchange) THEN
226			DO j=1,Oly
227			DO i=1,Olx
228			localTij( 1-i , 1-j )=localTij( 1-j , i )
229			localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i )
230			localTij(sNx+i, 1-j )=localTij(sNx+j, i )
231			localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i )
232			ENDDO
233			ENDDO
234			ENDIF
235
236	adcroft	1.1	C- Advective flux in X
237			DO j=1-Oly,sNy+Oly
238			DO i=1-Olx,sNx+Olx
239			af(i,j) = 0.
240			ENDDO
241			ENDDO
242	heimbach	1.6
243			#ifdef ALLOW_AUTODIFF_TAMC
244	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
245	heimbach	1.6	CADJ STORE localTij(:,:) = comlev1_bibj_pass, key=passkey, byte=isbyte
246			#endif
247			#endif /* ALLOW_AUTODIFF_TAMC */
248
249	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
250			CALL GAD_FLUXLIMIT_ADV_X(
251			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
252			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
253			CALL GAD_DST3_ADV_X(
254			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
255			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
256			CALL GAD_DST3FL_ADV_X(
257			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
258			ELSE
259			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
260			ENDIF
261	heimbach	1.6
262	adcroft	1.1	DO j=1-Oly,sNy+Oly
263			DO i=1-Olx,sNx+Olx-1
264			localTij(i,j)=localTij(i,j)-deltaTtracer*
265			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
266			& *recip_rA(i,j,bi,bj)
267			& *( af(i+1,j)-af(i,j)
268			& -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j))
269			& )
270			ENDDO
271			ENDDO
272
273			#ifdef ALLOW_OBCS
274			C-- Apply open boundary conditions
275			IF (useOBCS) THEN
276			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
277			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
278			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
279			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
280			END IF
281			END IF
282			#endif /* ALLOW_OBCS */
283
284	adcroft	1.3	C-- End of X direction
285			ENDIF
286
287			C-- Y direction
288			IF (calc_fluxes_Y) THEN
289
290			C-- Internal exchange for calculations in Y
291			IF (useCubedSphereExchange) THEN
292			DO j=1,Oly
293			DO i=1,Olx
294			localTij( 1-i , 1-j )=localTij( j , 1-i )
295			localTij( 1-i ,sNy+j)=localTij( j ,sNy+i)
296			localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i )
297			localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i)
298			ENDDO
299			ENDDO
300			ENDIF
301
302	adcroft	1.1	C- Advective flux in Y
303			DO j=1-Oly,sNy+Oly
304			DO i=1-Olx,sNx+Olx
305			af(i,j) = 0.
306			ENDDO
307			ENDDO
308	heimbach	1.6
309			#ifdef ALLOW_AUTODIFF_TAMC
310	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
311	heimbach	1.6	CADJ STORE localTij(:,:) = comlev1_bibj_pass, key=passkey, byte=isbyte
312			#endif
313			#endif /* ALLOW_AUTODIFF_TAMC */
314
315	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
316			CALL GAD_FLUXLIMIT_ADV_Y(
317			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
318			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
319			CALL GAD_DST3_ADV_Y(
320			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
321			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
322			CALL GAD_DST3FL_ADV_Y(
323			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
324			ELSE
325			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
326			ENDIF
327	heimbach	1.6
328	adcroft	1.1	DO j=1-Oly,sNy+Oly-1
329			DO i=1-Olx,sNx+Olx
330			localTij(i,j)=localTij(i,j)-deltaTtracer*
331			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
332			& *recip_rA(i,j,bi,bj)
333			& *( af(i,j+1)-af(i,j)
334			& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j))
335			& )
336			ENDDO
337			ENDDO
338	adcroft	1.3
339	adcroft	1.1	#ifdef ALLOW_OBCS
340			C-- Apply open boundary conditions
341			IF (useOBCS) THEN
342			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
343			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
344			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
345			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
346			END IF
347			END IF
348			#endif /* ALLOW_OBCS */
349	adcroft	1.3
350			C-- End of Y direction
351			ENDIF
352
353			DO j=1-Oly,sNy+Oly
354	adcroft	1.1	DO i=1-Olx,sNx+Olx
355			localTijk(i,j,k)=localTij(i,j)
356			ENDDO
357			ENDDO
358
359	adcroft	1.3	C-- End of ipass loop
360			ENDDO
361	adcroft	1.1
362			C-- End of K loop for horizontal fluxes
363			ENDDO
364
365			C-- Start of k loop for vertical flux
366			DO k=Nr,1,-1
367	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
368			kkey = (ikey-1)*Nr + k
369			#endif /* ALLOW_AUTODIFF_TAMC */
370	adcroft	1.1
371			C-- kup Cycles through 1,2 to point to w-layer above
372			C-- kDown Cycles through 2,1 to point to w-layer below
373			kup = 1+MOD(k+1,2)
374			kDown= 1+MOD(k,2)
375
376			C-- Get temporary terms used by tendency routines
377			CALL CALC_COMMON_FACTORS (
378			I bi,bj,iMin,iMax,jMin,jMax,k,
379			O xA,yA,uTrans,vTrans,rTrans,maskUp,
380			I myThid)
381
382			C- Advective flux in R
383			DO j=1-Oly,sNy+Oly
384			DO i=1-Olx,sNx+Olx
385			af(i,j) = 0.
386			ENDDO
387			ENDDO
388	heimbach	1.6
389			#ifdef ALLOW_AUTODIFF_TAMC
390			CADJ STORE localTijk(:,:,k)
391			CADJ & = comlev1_bibj_k, key=kkey, byte=isbyte
392			#endif /* ALLOW_AUTODIFF_TAMC */
393	adcroft	1.1
394			C Note: wVel needs to be masked
395			IF (K.GE.2) THEN
396			C- Compute vertical advective flux in the interior:
397			IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
398			CALL GAD_FLUXLIMIT_ADV_R(
399			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
400			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
401	adcroft	1.2	CALL GAD_DST3_ADV_R(
402			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
403	adcroft	1.1	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
404	adcroft	1.2	CALL GAD_DST3FL_ADV_R(
405			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
406	adcroft	1.1	ELSE
407			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
408			ENDIF
409			C- Surface "correction" term at k>1 :
410			DO j=1-Oly,sNy+Oly
411			DO i=1-Olx,sNx+Olx
412			af(i,j) = af(i,j)
413			& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))*
414			& rTrans(i,j)*localTijk(i,j,k)
415			ENDDO
416			ENDDO
417			ELSE
418			C- Surface "correction" term at k=1 :
419			DO j=1-Oly,sNy+Oly
420			DO i=1-Olx,sNx+Olx
421			af(i,j) = rTrans(i,j)*localTijk(i,j,k)
422			ENDDO
423			ENDDO
424			ENDIF
425			C- add the advective flux to fVerT
426			DO j=1-Oly,sNy+Oly
427			DO i=1-Olx,sNx+Olx
428			fVerT(i,j,kUp) = af(i,j)
429			ENDDO
430			ENDDO
431
432			C-- Divergence of fluxes
433			kp1=min(Nr,k+1)
434			kp1Msk=1.
435			if (k.EQ.Nr) kp1Msk=0.
436			DO j=1-Oly,sNy+Oly
437			DO i=1-Olx,sNx+Olx
438			localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
439			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
440			& *recip_rA(i,j,bi,bj)
441			& *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
442			& -tracer(i,j,k,bi,bj)rA(i,j,bi,bj)
443			& (wVel(i,j,k,bi,bj)-kp1Msk*wVel(i,j,kp1,bi,bj))
444			& )*rkFac
445			gTracer(i,j,k,bi,bj)=
446			& (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
447			ENDDO
448			ENDDO
449
450			C-- End of K loop for vertical flux
451			ENDDO
452
453			RETURN
454			END