pkg/generic_advdiff/gad_advection.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.15 2003/06/27 01:57:28 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 "PACKAGES_CONFIG.h"
#include "GAD_OPTIONS.h"
#ifdef ALLOW_AUTODIFF
# include "CPP_OPTIONS.h"
#endif

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 = (igadkey-1)*Nr + k
#endif /* ALLOW_AUTODIFF_TAMC */

C--   kup    Cycles through 1,2 to point to w-layer above
C--   kDown  Cycles through 2,1 to point to w-layer below
      kup  = 1+MOD(k+1,2)
      kDown= 1+MOD(k,2)
c     kp1=min(Nr,k+1)
      kp1Msk=1.
      if (k.EQ.Nr) kp1Msk=0.

C-- Compute Vertical transport
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.
         af(i,j) = 0.
        ENDDO
       ENDDO

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

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

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

C-    Compute vertical advective flux in the interior:
       IF (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

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

C--   Divergence of 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	1.16	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_advection.F,v 1.15 2003/06/27 01:57:28 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	heimbach	1.16	#include "PACKAGES_CONFIG.h"
32	adcroft	1.1	#include "GAD_OPTIONS.h"
33	heimbach	1.16	#ifdef ALLOW_AUTODIFF
34			# include "CPP_OPTIONS.h"
35			#endif
36	adcroft	1.1
37	adcroft	1.4	CBOP
38			C !ROUTINE: GAD_ADVECTION
39
40			C !INTERFACE: ==========================================================
41	adcroft	1.1	SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity,
42			U Tracer,Gtracer,
43			I myTime,myIter,myThid)
44	adcroft	1.4
45			C !DESCRIPTION:
46			C Calculates the tendancy of a tracer due to advection.
47			C It uses the multi-dimensional method given in \ref{sect:multiDimAdvection}
48			C and can only be used for the non-linear advection schemes such as the
49			C direct-space-time method and flux-limiters.
50			C
51			C The algorithm is as follows:
52			C \begin{itemize}
53			C \item{$\theta^{(n+1/3)} = \theta^{(n)}
54	adcroft	1.5	C - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$}
55	adcroft	1.4	C \item{$\theta^{(n+2/3)} = \theta^{(n+1/3)}
56	adcroft	1.5	C - \Delta t \partial_y (v\theta^{(n+1/3)}) + \theta^{(n)} \partial_y v$}
57	adcroft	1.4	C \item{$\theta^{(n+3/3)} = \theta^{(n+2/3)}
58	adcroft	1.5	C - \Delta t \partial_r (w\theta^{(n+2/3)}) + \theta^{(n)} \partial_r w$}
59	adcroft	1.4	C \item{$G_\theta = ( \theta^{(n+3/3)} - \theta^{(n)} )/\Delta t$}
60			C \end{itemize}
61			C
62			C The tendancy (output) is over-written by this routine.
63
64			C !USES: ===============================================================
65	adcroft	1.1	IMPLICIT NONE
66			#include "SIZE.h"
67			#include "EEPARAMS.h"
68			#include "PARAMS.h"
69			#include "DYNVARS.h"
70			#include "GRID.h"
71			#include "GAD.h"
72	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
73			# include "tamc.h"
74			# include "tamc_keys.h"
75			#endif
76	adcroft	1.1
77	adcroft	1.4	C !INPUT PARAMETERS: ===================================================
78			C bi,bj :: tile indices
79			C advectionScheme :: advection scheme to use
80			C tracerIdentity :: identifier for the tracer (required only for OBCS)
81			C Tracer :: tracer field
82			C myTime :: current time
83			C myIter :: iteration number
84			C myThid :: thread number
85	adcroft	1.1	INTEGER bi,bj
86			INTEGER advectionScheme
87			INTEGER tracerIdentity
88	adcroft	1.9	_RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
89	adcroft	1.1	_RL myTime
90			INTEGER myIter
91			INTEGER myThid
92
93	adcroft	1.4	C !OUTPUT PARAMETERS: ==================================================
94			C gTracer :: tendancy array
95	adcroft	1.9	_RL gTracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
96	adcroft	1.4
97			C !LOCAL VARIABLES: ====================================================
98			C maskUp :: 2-D array for mask at W points
99			C iMin,iMax,jMin,jMax :: loop range for called routines
100			C i,j,k :: loop indices
101			C kup :: index into 2 1/2D array, toggles between 1 and 2
102			C kdown :: index into 2 1/2D array, toggles between 2 and 1
103			C kp1 :: =k+1 for k<Nr, =Nr for k=Nr
104			C xA,yA :: areas of X and Y face of tracer cells
105			C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points
106	jmc	1.11	C rTransKp1 :: vertical volume transport at interface k+1
107	adcroft	1.4	C af :: 2-D array for horizontal advective flux
108			C fVerT :: 2 1/2D arrays for vertical advective flux
109			C localTij :: 2-D array used as temporary local copy of tracer fld
110			C localTijk :: 3-D array used as temporary local copy of tracer fld
111			C kp1Msk :: flag (0,1) to act as over-riding mask for W levels
112			C calc_fluxes_X :: logical to indicate to calculate fluxes in X dir
113			C calc_fluxes_Y :: logical to indicate to calculate fluxes in Y dir
114			C nipass :: number of passes to make in multi-dimensional method
115			C ipass :: number of the current pass being made
116	adcroft	1.1	_RS maskUp (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
117			INTEGER iMin,iMax,jMin,jMax
118	jmc	1.11	INTEGER i,j,k,kup,kDown
119	adcroft	1.1	_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120			_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121			_RL uTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122			_RL vTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
123			_RL rTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
124	jmc	1.11	_RL rTransKp1(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
125	adcroft	1.1	_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
126			_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
127			_RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
128			_RL localTijk(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
129			_RL kp1Msk
130	adcroft	1.3	LOGICAL calc_fluxes_X,calc_fluxes_Y
131			INTEGER nipass,ipass
132	adcroft	1.4	CEOP
133	adcroft	1.1
134	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
135	heimbach	1.14	act0 = tracerIdentity - 1
136			max0 = maxpass
137	heimbach	1.6	act1 = bi - myBxLo(myThid)
138			max1 = myBxHi(myThid) - myBxLo(myThid) + 1
139			act2 = bj - myByLo(myThid)
140			max2 = myByHi(myThid) - myByLo(myThid) + 1
141			act3 = myThid - 1
142			max3 = nTx*nTy
143			act4 = ikey_dynamics - 1
144	heimbach	1.14	igadkey = (act0 + 1)
145			& + act1*max0
146			& + act2max0max1
147			& + act3max0max1*max2
148			& + act4max0max1max2max3
149	heimbach	1.15	if (tracerIdentity.GT.maxpass) then
150			print *, 'ph-pass gad_advection ', maxpass, tracerIdentity
151			STOP 'maxpass seems smaller than tracerIdentity'
152			endif
153	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
154
155	adcroft	1.1	C-- Set up work arrays with valid (i.e. not NaN) values
156			C These inital values do not alter the numerical results. They
157			C just ensure that all memory references are to valid floating
158			C point numbers. This prevents spurious hardware signals due to
159			C uninitialised but inert locations.
160			DO j=1-OLy,sNy+OLy
161			DO i=1-OLx,sNx+OLx
162			xA(i,j) = 0. _d 0
163			yA(i,j) = 0. _d 0
164			uTrans(i,j) = 0. _d 0
165			vTrans(i,j) = 0. _d 0
166			rTrans(i,j) = 0. _d 0
167			fVerT(i,j,1) = 0. _d 0
168			fVerT(i,j,2) = 0. _d 0
169	jmc	1.11	rTransKp1(i,j)= 0. _d 0
170	adcroft	1.1	ENDDO
171			ENDDO
172
173			iMin = 1-OLx
174			iMax = sNx+OLx
175			jMin = 1-OLy
176			jMax = sNy+OLy
177
178			C-- Start of k loop for horizontal fluxes
179			DO k=1,Nr
180	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
181	heimbach	1.14	kkey = (igadkey-1)*Nr + k
182			CADJ STORE tracer(:,:,k,bi,bj) =
183			CADJ & comlev1_bibj_k_gad, key=kkey, byte=isbyte
184	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
185	adcroft	1.1
186			C-- Get temporary terms used by tendency routines
187			CALL CALC_COMMON_FACTORS (
188			I bi,bj,iMin,iMax,jMin,jMax,k,
189			O xA,yA,uTrans,vTrans,rTrans,maskUp,
190			I myThid)
191
192	jmc	1.11	#ifdef ALLOW_GMREDI
193			C-- Residual transp = Bolus transp + Eulerian transp
194			IF (useGMRedi)
195			& CALL GMREDI_CALC_UVFLOW(
196			& uTrans, vTrans, bi, bj, k, myThid)
197			#endif /* ALLOW_GMREDI */
198
199	adcroft	1.1	C-- Make local copy of tracer array
200			DO j=1-OLy,sNy+OLy
201			DO i=1-OLx,sNx+OLx
202			localTij(i,j)=tracer(i,j,k,bi,bj)
203			ENDDO
204			ENDDO
205
206	adcroft	1.3	IF (useCubedSphereExchange) THEN
207			nipass=3
208	heimbach	1.14	#ifdef ALLOW_AUTODIFF_TAMC
209			if ( nipass.GT.maxcube )
210			& STOP 'maxcube needs to be = 3'
211			#endif
212	adcroft	1.3	ELSE
213			nipass=1
214			ENDIF
215	heimbach	1.6	cph nipass=1
216	adcroft	1.3
217			C-- Multiple passes for different directions on different tiles
218			DO ipass=1,nipass
219	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
220	heimbach	1.14	passkey = ipass + (k-1) *maxcube
221			& + (igadkey-1)maxcubeNr
222	heimbach	1.6	IF (nipass .GT. maxpass) THEN
223	heimbach	1.14	STOP 'GAD_ADVECTION: nipass > maxcube. check tamc.h'
224	heimbach	1.6	ENDIF
225			#endif /* ALLOW_AUTODIFF_TAMC */
226	adcroft	1.3
227			IF (nipass.EQ.3) THEN
228			calc_fluxes_X=.FALSE.
229			calc_fluxes_Y=.FALSE.
230			IF (ipass.EQ.1 .AND. (bi.EQ.1 .OR. bi.EQ.2) ) THEN
231			calc_fluxes_X=.TRUE.
232			ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN
233			calc_fluxes_Y=.TRUE.
234			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN
235			calc_fluxes_Y=.TRUE.
236			ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN
237			calc_fluxes_X=.TRUE.
238			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN
239			calc_fluxes_Y=.TRUE.
240			ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.EQ.6) ) THEN
241			calc_fluxes_X=.TRUE.
242			ENDIF
243			ELSE
244			calc_fluxes_X=.TRUE.
245			calc_fluxes_Y=.TRUE.
246			ENDIF
247
248			C-- X direction
249			IF (calc_fluxes_X) THEN
250
251			C-- Internal exchange for calculations in X
252			IF (useCubedSphereExchange) THEN
253			DO j=1,Oly
254			DO i=1,Olx
255			localTij( 1-i , 1-j )=localTij( 1-j , i )
256			localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i )
257			localTij(sNx+i, 1-j )=localTij(sNx+j, i )
258			localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i )
259			ENDDO
260			ENDDO
261			ENDIF
262
263	adcroft	1.1	C- Advective flux in X
264			DO j=1-Oly,sNy+Oly
265			DO i=1-Olx,sNx+Olx
266			af(i,j) = 0.
267			ENDDO
268			ENDDO
269	heimbach	1.6
270			#ifdef ALLOW_AUTODIFF_TAMC
271	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
272	heimbach	1.14	CADJ STORE localTij(:,:) =
273			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
274	heimbach	1.6	#endif
275			#endif /* ALLOW_AUTODIFF_TAMC */
276
277	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
278			CALL GAD_FLUXLIMIT_ADV_X(
279			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
280			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
281			CALL GAD_DST3_ADV_X(
282			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
283			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
284			CALL GAD_DST3FL_ADV_X(
285			& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid)
286			ELSE
287	adcroft	1.9	STOP 'GAD_ADVECTION: adv. scheme incompatibale with multi-dim'
288	adcroft	1.1	ENDIF
289	heimbach	1.6
290	adcroft	1.1	DO j=1-Oly,sNy+Oly
291			DO i=1-Olx,sNx+Olx-1
292			localTij(i,j)=localTij(i,j)-deltaTtracer*
293			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
294			& *recip_rA(i,j,bi,bj)
295			& *( af(i+1,j)-af(i,j)
296			& -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j))
297			& )
298			ENDDO
299			ENDDO
300
301			#ifdef ALLOW_OBCS
302			C-- Apply open boundary conditions
303			IF (useOBCS) THEN
304			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
305			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
306			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
307			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
308			END IF
309			END IF
310			#endif /* ALLOW_OBCS */
311
312	adcroft	1.3	C-- End of X direction
313			ENDIF
314
315			C-- Y direction
316			IF (calc_fluxes_Y) THEN
317
318			C-- Internal exchange for calculations in Y
319			IF (useCubedSphereExchange) THEN
320			DO j=1,Oly
321			DO i=1,Olx
322			localTij( 1-i , 1-j )=localTij( j , 1-i )
323			localTij( 1-i ,sNy+j)=localTij( j ,sNy+i)
324			localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i )
325			localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i)
326			ENDDO
327			ENDDO
328			ENDIF
329
330	adcroft	1.1	C- Advective flux in Y
331			DO j=1-Oly,sNy+Oly
332			DO i=1-Olx,sNx+Olx
333			af(i,j) = 0.
334			ENDDO
335			ENDDO
336	heimbach	1.6
337			#ifdef ALLOW_AUTODIFF_TAMC
338	adcroft	1.7	#ifndef DISABLE_MULTIDIM_ADVECTION
339	heimbach	1.14	CADJ STORE localTij(:,:) =
340			CADJ & comlev1_bibj_k_gad_pass, key=passkey, byte=isbyte
341	heimbach	1.6	#endif
342			#endif /* ALLOW_AUTODIFF_TAMC */
343
344	adcroft	1.1	IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
345			CALL GAD_FLUXLIMIT_ADV_Y(
346			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
347			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
348			CALL GAD_DST3_ADV_Y(
349			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
350			ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
351			CALL GAD_DST3FL_ADV_Y(
352			& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid)
353			ELSE
354			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
355			ENDIF
356	heimbach	1.6
357	adcroft	1.1	DO j=1-Oly,sNy+Oly-1
358			DO i=1-Olx,sNx+Olx
359			localTij(i,j)=localTij(i,j)-deltaTtracer*
360			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
361			& *recip_rA(i,j,bi,bj)
362			& *( af(i,j+1)-af(i,j)
363			& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j))
364			& )
365			ENDDO
366			ENDDO
367	adcroft	1.3
368	adcroft	1.1	#ifdef ALLOW_OBCS
369			C-- Apply open boundary conditions
370			IF (useOBCS) THEN
371			IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
372			CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid )
373			ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
374			CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid )
375			END IF
376			END IF
377			#endif /* ALLOW_OBCS */
378	adcroft	1.3
379			C-- End of Y direction
380			ENDIF
381
382			DO j=1-Oly,sNy+Oly
383	adcroft	1.1	DO i=1-Olx,sNx+Olx
384			localTijk(i,j,k)=localTij(i,j)
385			ENDDO
386			ENDDO
387
388	adcroft	1.3	C-- End of ipass loop
389			ENDDO
390	adcroft	1.1
391			C-- End of K loop for horizontal fluxes
392			ENDDO
393
394			C-- Start of k loop for vertical flux
395			DO k=Nr,1,-1
396	heimbach	1.6	#ifdef ALLOW_AUTODIFF_TAMC
397	heimbach	1.16	kkey = (igadkey-1)*Nr + k
398	heimbach	1.6	#endif /* ALLOW_AUTODIFF_TAMC */
399	adcroft	1.1
400			C-- kup Cycles through 1,2 to point to w-layer above
401			C-- kDown Cycles through 2,1 to point to w-layer below
402			kup = 1+MOD(k+1,2)
403			kDown= 1+MOD(k,2)
404	jmc	1.11	c kp1=min(Nr,k+1)
405			kp1Msk=1.
406			if (k.EQ.Nr) kp1Msk=0.
407	heimbach	1.6
408	jmc	1.11	C-- Compute Vertical transport
409	adcroft	1.1	C Note: wVel needs to be masked
410	jmc	1.11
411			IF (k.EQ.1) THEN
412			C- Surface interface :
413
414			DO j=1-Oly,sNy+Oly
415			DO i=1-Olx,sNx+Olx
416			rTransKp1(i,j) = rTrans(i,j)
417			rTrans(i,j) = 0.
418			fVerT(i,j,kUp) = 0.
419	heimbach	1.16	af(i,j) = 0.
420	jmc	1.11	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	heimbach	1.16	#ifdef ALLOW_AUTODIFF_TAMC
442			CADJ STORE localTijk(:,:,k)
443			CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
444			CADJ STORE rTrans(:,:)
445			CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
446			#endif /* ALLOW_AUTODIFF_TAMC */
447
448	adcroft	1.1	C- Compute vertical advective flux in the interior:
449			IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
450			CALL GAD_FLUXLIMIT_ADV_R(
451			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
452			ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
453	adcroft	1.2	CALL GAD_DST3_ADV_R(
454			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
455	adcroft	1.1	ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
456	adcroft	1.2	CALL GAD_DST3FL_ADV_R(
457			& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid)
458	adcroft	1.1	ELSE
459			STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim'
460			ENDIF
461	jmc	1.11	C- add the advective flux to fVerT
462	adcroft	1.1	DO j=1-Oly,sNy+Oly
463			DO i=1-Olx,sNx+Olx
464	jmc	1.11	fVerT(i,j,kUp) = af(i,j)
465	adcroft	1.1	ENDDO
466	jmc	1.11	ENDDO
467
468			C- end Surface/Interior if bloc
469	adcroft	1.1	ENDIF
470	heimbach	1.16
471			#ifdef ALLOW_AUTODIFF_TAMC
472			CADJ STORE rTrans(:,:)
473			CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
474			CADJ STORE rTranskp1(:,:)
475			CADJ & = comlev1_bibj_k_gad, key=kkey, byte=isbyte
476			#endif /* ALLOW_AUTODIFF_TAMC */
477	adcroft	1.1
478			C-- Divergence of fluxes
479			DO j=1-Oly,sNy+Oly
480			DO i=1-Olx,sNx+Olx
481			localTij(i,j)=localTijk(i,j,k)-deltaTtracer*
482			& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
483			& *recip_rA(i,j,bi,bj)
484			& *( fVerT(i,j,kUp)-fVerT(i,j,kDown)
485	jmc	1.11	& -tracer(i,j,k,bi,bj)*(rTrans(i,j)-rTransKp1(i,j))
486	adcroft	1.1	& )*rkFac
487			gTracer(i,j,k,bi,bj)=
488			& (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer
489			ENDDO
490			ENDDO
491
492			C-- End of K loop for vertical flux
493			ENDDO
494
495			RETURN
496			END