[MITgcm-devel] Fwd: TAF issue for "special" parameter lists

Patrick Heimbach heimbach at MIT.EDU
Sat Feb 25 01:44:53 EST 2006


Well, I agree.
-p.



Quoting Chris Hill <cnh at MIT.EDU>:

> P. (JM),
>
>  It would be better not do it this way even for forward code.
>
>  The reason is that certain compiler optimizations will assume "no 
> aliasing" which means assuming that localT and locaABT refer to 
> different pieces of memory and therefore certain transformations that 
> safely permute the ordering of computations are allowed. Aliased 
> arguments can lead to extremely hard to track down bugs suddenly 
> appearing with some compiler all of a sudden. Some compilers provide 
> assume_alising flags but that tends to harm performance since it 
> assumes just about everything might be aliased with everything and 
> the compiler gets paranoid about lots of useful optimizations.
>
>  So far we have avoided any aliasing in the core code (not sure about 
> sea-ice, fizhi etc....) for just this reason. It would be much better 
> to continue the practice of not having aliased dummy arguments even 
> if it means adding some more logic in gad_calc_rhs.
>
>
> Chris
>
> Patrick Heimbach wrote:
>>
>> ----- Forwarded message from heimbach at MIT.EDU -----
>>     Date: Fri, 24 Feb 2006 17:57:15 -0500
>>     From: Patrick Heimbach <heimbach at MIT.EDU>
>> Reply-To: heimbach at MIT.EDU
>>  Subject: TAF issue for "special" parameter lists
>>       To: Ralf Giering <Ralf.Giering at FastOpt.com>
>>
>>
>> Ralf,
>>
>> some of my colleagues have recently introduced a construct
>> into the model which breaks the adjoint.
>> It's not very clean programming, but works well for them
>> in pure forward to be able to switch between different
>> variations of Adams-Bashforth.
>>
>> The general structure is as following (the underlying code
>> is calls of S/R gad_calc_rhs by S/R calc_gt, S/R calc_gs
>> for the case NOT AB_3)
>>
>>        call foo( ..., var, var, ... )
>>
>>        subroutine foo( ..., var1, var2, ... )
>>
>>        u = f1(var1)
>>        v = f2(var2)
>>
>> var is pure input to S/R foo, not modified.
>> The reason for doing this is to be able to use the same
>> argument list for a variation of AB (the AB_3) for which
>>        call gad_calc_rhs( ..., theta, theta, ... )   ! AB_2
>> is modified into
>>        call gad_calc_rhs( ..., gTnm1, theta, ... )   ! AB_3
>>
>> Sensitivities for this construct are not
>> properly accumulated, here's why:
>>
>>        call adfoo( ..., advar, advar, ... )
>>
>>        subroutine adfoo( ..., advar1, advar2, ...)
>>
>>        advar2 = advar2 + adf2(advar2)
>>        advar1 = advar1 + adf1(advar1)
>>
>> The link of accumulating advar1 and advar2 onto advar
>> (because they're the same) is missing; strictly:
>>        advar = advar1 + advar2
>>
>> I have actually hand-coded this variation, i.e.
>> introduce an auxiliary variable advarh in the call
>> and then accumulate advarh onto advar, something like
>>        call adfoo( ..., advar, advarh, ... )
>>        advar = advar + advarh
>>        advarh = 0.
>> It works.
>> This seems to show a strategy for TAF to properly
>> handle the construct.
>>
>> The effect is subtle, not visible at first (and in
>> gradient checks), but after 13yr integration, the "ECCO"
>> gradient is messed up.
>>
>> I am appending the routines where this problem occurs:
>>
>> calc_gt.F        (has the call to "foo" = gad_calc_rhs with
>>                   the problematic parameter list)
>> gad_calc_rhs.F   ( = "foo" where theta=Tracer, and theta=TracAB)
>> adgad_calc_rhs   (just to show how adTracer and adTracAB
>>                   are treated separately)
>> adcalc_gt_broken (the code generated by TAF,
>>                   it has adtheta twice in param. list)
>> adcalc_gt_fixed  (I introduced on auxiliary variable adthetah,
>>                   which after the call gets added onto adtheta).
>>
>> Hope this is enough info.
>> I think you'll quickly recognize the general problem.
>> It's not urgent, we'll re-write with a workaround,
>> but I think, you can modify TAF in above way to
>> handle this, provided TAF is able to recognize that
>> theta is twice in the argument list
>> (which might not be easy/general though).
>>
>> Cheers
>> -Patrick
>>
>>
>>
>> ------------------------------------------------------------------------
>>
>> C $Header: /u/gcmpack/MITgcm/model/src/calc_gt.F,v 1.46 2005/12/08 
>> 15:44:33 heimbach Exp $
>> C $Name:  $
>>
>> #include "PACKAGES_CONFIG.h"
>> #include "CPP_OPTIONS.h"
>>
>> CBOP
>> C     !ROUTINE: CALC_GT
>> C     !INTERFACE:
>>       SUBROUTINE CALC_GT(      I           
>> bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
>>      I           xA,yA,uTrans,vTrans,rTrans,rTransKp1,maskUp,
>>      I           KappaRT,
>>      U           fVerT,
>>      I           myTime,myIter,myThid )
>> C     !DESCRIPTION: \bv
>> C     *==========================================================*
>> C     | SUBROUTINE CALC_GT                                        C  
>>    | o Calculate the temperature tendency terms.               C     
>> *==========================================================*
>> C     | A procedure called EXTERNAL_FORCING_T is called from      C  
>>    | here. These procedures can be used to add per problem     C     
>> | heat flux source terms.                                   C     | 
>> Note: Although it is slightly counter-intuitive the       C     |    
>>    EXTERNAL_FORCING routine is not the place to put    C     |       
>> file I/O. Instead files that are required to        C     |       
>> calculate the external source terms are generally   C     |       
>> read during the model main loop. This makes the     C     |       
>> logisitics of multi-processing simpler and also     C     |       
>> makes the adjoint generation simpler. It also       C     |       
>> allows for I/O to overlap computation where that    C     |       is 
>> supported by hardware.                           C     | Aside from 
>> the problem specific term the code here        C     | forms the 
>> tendency terms due to advection and mixing      C     | The baseline 
>> implementation here uses a centered          C     | difference form 
>> for the advection term and a tensorial    C     | divergence of a 
>> flux form for the diffusive term. The     C     | diffusive term is 
>> formulated so that isopycnal mixing and C     | GM-style 
>> subgrid-scale terms can be incorporated b simply C     | setting the 
>> diffusion tensor terms appropriately.         C     
>> *==========================================================*
>> C     \ev
>>
>> C     !USES:
>>       IMPLICIT NONE
>> C     == GLobal variables ==
>> #include "SIZE.h"
>> #include "DYNVARS.h"
>> #include "EEPARAMS.h"
>> #include "PARAMS.h"
>> #ifdef ALLOW_GENERIC_ADVDIFF
>> #include "GAD.h"
>> #endif
>> #ifdef ALLOW_AUTODIFF_TAMC
>> # include "tamc.h"
>> # include "tamc_keys.h"
>> #endif
>>
>> C     !INPUT/OUTPUT PARAMETERS:
>> C     == Routine arguments ==
>> C     fVerT   :: Flux of temperature (T) in the vertical C           
>>      direction at the upper(U) and lower(D) faces of a cell.
>> C     maskUp  :: Land mask used to denote base of the domain.
>> C     xA      :: Tracer cell face area normal to X
>> C     yA      :: Tracer cell face area normal to X
>> C     uTrans  :: Zonal volume transport through cell face
>> C     vTrans  :: Meridional volume transport through cell face
>> C     rTrans  ::   Vertical volume transport at interface k
>> C     rTransKp1 :: Vertical volume transport at inteface k+1
>> C     bi, bj, iMin, iMax, jMin, jMax :: Range of points for which 
>> calculation
>> C                                       results will be set.
>> C     myThid :: Instance number for this innvocation of CALC_GT
>>       _RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
>>       _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)
>>       _RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       INTEGER k,kUp,kDown,kM1
>>       INTEGER bi,bj,iMin,iMax,jMin,jMax
>>       _RL     myTime
>>       INTEGER myIter
>>       INTEGER myThid
>> CEOP
>>
>> #ifdef ALLOW_GENERIC_ADVDIFF
>> C     === Local variables ===
>>       LOGICAL calcAdvection
>>       INTEGER iterNb
>> #ifdef ALLOW_ADAMSBASHFORTH_3
>>       INTEGER m1, m2
>> #endif
>>
>> #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
>>           itdkey = (act1 + 1) + act2*max1
>>      &                      + act3*max1*max2
>>      &                      + act4*max1*max2*max3
>>           kkey = (itdkey-1)*Nr + k
>> #endif /* ALLOW_AUTODIFF_TAMC */
>>
>> #ifdef ALLOW_AUTODIFF_TAMC
>> C--   only the kUp part of fverT is set in this subroutine
>> C--   the kDown is still required
>>       fVerT(1,1,kDown) = fVerT(1,1,kDown)
>> # ifdef NONLIN_FRSURF
>> CADJ STORE fVerT(:,:,:) = comlev1_bibj_k, key=kkey, byte=isbyte
>> # endif
>> #endif
>>
>> C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
>>
>>       calcAdvection = tempAdvection .AND. .NOT.tempMultiDimAdvec
>>       iterNb = myIter
>>       IF (staggerTimeStep) iterNb = myIter -1
>>
>> #ifdef ALLOW_ADAMSBASHFORTH_3
>>       IF ( AdamsBashforth_T ) THEN
>>         m1 = 1 + MOD(iterNb+1,2)
>>         m2 = 1 + MOD( iterNb ,2)
>>         CALL GAD_CALC_RHS(
>>      I           bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
>>      I           xA,yA,uTrans,vTrans,rTrans,rTransKp1,maskUp,
>>      I           uVel, vVel, wVel,
>>      I           diffKhT, diffK4T, KappaRT,
>>      I           gtNm(1-Olx,1-Oly,1,1,1,m2), theta,
>>      I           GAD_TEMPERATURE, tempAdvScheme, tempVertAdvScheme,
>>      I           calcAdvection, tempImplVertAdv,
>>      U           fVerT, gT,
>>      I           myTime, myIter, myThid )
>>       ELSE
>> #endif /* ALLOW_ADAMSBASHFORTH_3 */
>>         CALL GAD_CALC_RHS(
>>      I           bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
>>      I           xA,yA,uTrans,vTrans,rTrans,rTransKp1,maskUp,
>>      I           uVel, vVel, wVel,
>>      I           diffKhT, diffK4T, KappaRT, theta, theta,
>>      I           GAD_TEMPERATURE, tempAdvScheme, tempVertAdvScheme,
>>      I           calcAdvection, tempImplVertAdv,
>>      U           fVerT, gT,
>>      I           myTime, myIter, myThid )
>> #ifdef ALLOW_ADAMSBASHFORTH_3
>>       ENDIF
>> #endif
>>
>> C--   External thermal forcing term(s) inside Adams-Bashforth:
>>       IF ( tempForcing .AND. forcing_In_AB )
>>      & CALL EXTERNAL_FORCING_T(
>>      I     iMin,iMax,jMin,jMax,bi,bj,k,
>>      I     myTime,myThid)
>>
>>       IF ( AdamsBashforthGt ) THEN
>> #ifdef ALLOW_ADAMSBASHFORTH_3
>>         CALL ADAMS_BASHFORTH3(
>>      I                        bi, bj, k,
>>      U                        gT, gtNm,
>>      I                        tempStartAB, iterNb, myThid )
>> #else
>>         CALL ADAMS_BASHFORTH2(
>>      I                        bi, bj, k,
>>      U                        gT, gtNm1,
>>      I                        iterNb, myThid )
>> #endif
>>       ENDIF
>>
>> C--   External thermal forcing term(s) outside Adams-Bashforth:
>>       IF ( tempForcing .AND. .NOT.forcing_In_AB )
>>      & CALL EXTERNAL_FORCING_T(
>>      I     iMin,iMax,jMin,jMax,bi,bj,k,
>>      I     myTime,myThid)
>>
>> #ifdef NONLIN_FRSURF
>>       IF (nonlinFreeSurf.GT.0) THEN
>>         CALL FREESURF_RESCALE_G(
>>      I                          bi, bj, k,
>>      U                          gT,
>>      I                          myThid )
>>         IF ( AdamsBashforthGt ) THEN
>> #ifdef ALLOW_ADAMSBASHFORTH_3
>>         CALL FREESURF_RESCALE_G(
>>      I                          bi, bj, k,
>>      U                          gtNm(1-Olx,1-Oly,1,1,1,1),
>>      I                          myThid )
>>         CALL FREESURF_RESCALE_G(
>>      I                          bi, bj, k,
>>      U                          gtNm(1-Olx,1-Oly,1,1,1,2),
>>      I                          myThid )
>> #else
>>         CALL FREESURF_RESCALE_G(
>>      I                          bi, bj, k,
>>      U                          gtNm1,
>>      I                          myThid )
>> #endif
>>         ENDIF
>>       ENDIF
>> #endif /* NONLIN_FRSURF */
>>
>> #endif /* ALLOW_GENERIC_ADVDIFF */
>>
>>       RETURN
>>       END
>>
>>
>> ------------------------------------------------------------------------
>>
>> C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_calc_rhs.F,v 
>> 1.38 2005/11/06 22:14:02 jmc Exp $
>> C $Name:  $
>>
>> #include "GAD_OPTIONS.h"
>>
>> CBOP
>> C !ROUTINE: GAD_CALC_RHS
>>
>> C !INTERFACE: ==========================================================
>>       SUBROUTINE GAD_CALC_RHS(      I           
>> bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
>>      I           xA,yA,uTrans,vTrans,rTrans,rTransKp1,maskUp,
>>      I           uVel, vVel, wVel,
>>      I           diffKh, diffK4, KappaR, Tracer, TracAB,
>>      I           tracerIdentity, advectionScheme, vertAdvecScheme,
>>      I           calcAdvection, implicitAdvection,
>>      U           fVerT, gTracer,
>>      I           myTime, myIter, myThid )
>>
>> C !DESCRIPTION:
>> C Calculates the tendency of a tracer due to advection and diffusion.
>> C It calculates the fluxes in each direction indepentently and then
>> C sets the tendency to the divergence of these fluxes. The advective
>> C fluxes are only calculated here when using the linear advection schemes
>> C otherwise only the diffusive and parameterized fluxes are calculated.
>> C
>> C Contributions to the flux are calculated and added:
>> C \begin{equation*}
>> C {\bf F} = {\bf F}_{adv} + {\bf F}_{diff} +{\bf F}_{GM} + {\bf F}_{KPP}
>> C \end{equation*}
>> C
>> C The tendency is the divergence of the fluxes:
>> C \begin{equation*}
>> C G_\theta = G_\theta + \nabla \cdot {\bf F}
>> C \end{equation*}
>> C
>> C The tendency is assumed to contain data on entry.
>>
>> C !USES: ===============================================================
>>       IMPLICIT NONE
>> #include "SIZE.h"
>> #include "EEPARAMS.h"
>> #include "PARAMS.h"
>> #include "GRID.h"
>> #include "SURFACE.h"
>> #include "GAD.h"
>>
>> #ifdef ALLOW_AUTODIFF_TAMC
>> #include "tamc.h"
>> #include "tamc_keys.h"
>> #endif /* ALLOW_AUTODIFF_TAMC */
>>
>> C !INPUT PARAMETERS: ===================================================
>> C bi,bj            :: tile indices
>> C iMin,iMax        :: loop range for called routines
>> C jMin,jMax        :: loop range for called routines
>> C kup              :: index into 2 1/2D array, toggles between 1|2
>> C kdown            :: index into 2 1/2D array, toggles between 2|1
>> C kp1              :: =k+1 for k<Nr, =Nr for k=Nr
>> C xA,yA            :: areas of X and Y face of tracer cells
>> C uTrans,vTrans    :: 2-D arrays of volume transports at U,V points
>> C rTrans           :: 2-D arrays of volume transports at W points
>> C rTransKp1        :: 2-D array of volume trans at W pts, interf k+1
>> C maskUp           :: 2-D array for mask at W points
>> C uVel,vVel,wVel   :: 3 components of the velcity field (3-D array)
>> C diffKh           :: horizontal diffusion coefficient
>> C diffK4           :: bi-harmonic diffusion coefficient
>> C KappaR           :: 2-D array for vertical diffusion coefficient, interf k
>> C Tracer           :: tracer field
>> C TracAB           :: tracer field but extrapolated fwd in time (to 
>> nIter+1/2)
>> C                     if applying AB on tracer field (instead of on 
>> tendency)
>> C tracerIdentity   :: tracer identifier (required for KPP,GM)
>> C advectionScheme  :: advection scheme to use (Horizontal plane)
>> C vertAdvecScheme  :: advection scheme to use (Vertical direction)
>> C calcAdvection    :: =False if Advec computed with multiDim scheme
>> C implicitAdvection:: =True if vertical Advec computed implicitly
>> C myTime           :: current time
>> C myIter           :: iteration number
>> C myThid           :: thread number
>>       INTEGER bi,bj,iMin,iMax,jMin,jMax
>>       INTEGER k,kUp,kDown,kM1
>>       _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)
>>       _RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL uVel  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       _RL vVel  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       _RL wVel  (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       _RL diffKh, diffK4
>>       _RL KappaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL Tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       _RL TracAB(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       INTEGER tracerIdentity
>>       INTEGER advectionScheme, vertAdvecScheme
>>       LOGICAL calcAdvection
>>       LOGICAL implicitAdvection
>>       _RL     myTime
>>       INTEGER myIter, myThid
>>
>> C !OUTPUT PARAMETERS: ==================================================
>> C gTracer          :: tendency array
>> C fVerT            :: 2 1/2D arrays for vertical advective flux
>>       _RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
>>       _RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
>>
>> C !LOCAL VARIABLES: ====================================================
>> C i,j              :: loop indices
>> C df4              :: used for storing del^2 T for bi-harmonic term
>> C fZon             :: zonal flux
>> C fMer             :: meridional flux
>> C af               :: advective flux
>> C df               :: diffusive flux
>> C localT           :: local copy of tracer field
>> C locABT           :: local copy of (AB-extrapolated) tracer field
>> #ifdef ALLOW_DIAGNOSTICS
>>       CHARACTER*8 diagName
>>       CHARACTER*4 GAD_DIAG_SUFX, diagSufx       EXTERNAL    GAD_DIAG_SUFX
>> #endif
>>       INTEGER i,j
>>       _RL df4   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL fZon  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL fMer  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL af    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL df    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL localT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL locABT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
>>       _RL advFac, rAdvFac
>> CEOP
>>
>> #ifdef ALLOW_AUTODIFF_TAMC
>> C--   only the kUp part of fverT is set in this subroutine
>> C--   the kDown is still required
>>       fVerT(1,1,kDown) = fVerT(1,1,kDown)
>> #endif
>>
>> #ifdef ALLOW_DIAGNOSTICS
>> C--   Set diagnostic suffix for the current tracer
>>       IF ( useDiagnostics ) THEN
>>         diagSufx = GAD_DIAG_SUFX( tracerIdentity, myThid )
>>       ENDIF
>> #endif
>>
>>       advFac  = 0. _d 0
>>       IF (calcAdvection) advFac = 1. _d 0
>>       rAdvFac = rkSign*advFac
>>       IF (implicitAdvection) rAdvFac = 0. _d 0
>>
>>       DO j=1-OLy,sNy+OLy
>>        DO i=1-OLx,sNx+OLx
>>         fZon(i,j)      = 0. _d 0
>>         fMer(i,j)      = 0. _d 0
>>         fVerT(i,j,kUp) = 0. _d 0
>>         df(i,j)        = 0. _d 0
>>         df4(i,j)       = 0. _d 0
>>        ENDDO
>>       ENDDO
>>
>> C--   Make local copy of tracer array
>>       DO j=1-OLy,sNy+OLy
>>        DO i=1-OLx,sNx+OLx
>>         localT(i,j)=Tracer(i,j,k,bi,bj)
>>         locABT(i,j)=TracAB(i,j,k,bi,bj)
>>        ENDDO
>>       ENDDO
>>
>> C--   Unless we have already calculated the advection terms we initialize
>> C     the tendency to zero.
>> C     <== now done earlier at the beginning of thermodynamics.
>> c     IF (calcAdvection) THEN
>> c      DO j=1-Oly,sNy+Oly
>> c       DO i=1-Olx,sNx+Olx
>> c        gTracer(i,j,k,bi,bj)=0. _d 0
>> c       ENDDO
>> c      ENDDO
>> c     ENDIF
>>
>> C--   Pre-calculate del^2 T if bi-harmonic coefficient is non-zero
>>       IF (diffK4 .NE. 0.) THEN
>>        CALL GAD_GRAD_X(bi,bj,k,xA,localT,fZon,myThid)
>>        CALL GAD_GRAD_Y(bi,bj,k,yA,localT,fMer,myThid)
>>        CALL GAD_DEL2(bi,bj,k,fZon,fMer,df4,myThid)
>>       ENDIF
>>
>> C--   Initialize net flux in X direction
>>       DO j=1-Oly,sNy+Oly
>>        DO i=1-Olx,sNx+Olx
>>         fZon(i,j) = 0. _d 0
>>        ENDDO
>>       ENDDO
>>
>> C-    Advective flux in X
>>       IF (calcAdvection) THEN
>>         IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
>>           CALL GAD_C2_ADV_X(bi,bj,k,uTrans,locABT,af,myThid)
>>         ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_1RST      &          
>> .OR. advectionScheme.EQ.ENUM_DST2 ) THEN
>>           CALL GAD_DST2U1_ADV_X( bi,bj,k, advectionScheme,      I    
>>         dTtracerLev(k), uTrans, uVel, locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
>>           CALL GAD_FLUXLIMIT_ADV_X( bi,bj,k, dTtracerLev(k),
>>      I            uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
>>           CALL GAD_U3_ADV_X(bi,bj,k,uTrans,locABT,af,myThid)
>>         ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
>>           CALL GAD_C4_ADV_X(bi,bj,k,uTrans,locABT,af,myThid)
>>         ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
>>           CALL GAD_DST3_ADV_X( bi,bj,k, dTtracerLev(k),
>>      I            uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
>>          IF ( inAdMode ) THEN
>> cph This block is to trick the adjoint:
>> cph IF inAdExact=.FALSE., we want to use DST3 cph with limiters in 
>> forward, but without limiters in reverse.
>>           CALL GAD_DST3_ADV_X( bi,bj,k, dTtracerLev(k),
>>      I           uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O           af, myThid )
>>          ELSE
>>           CALL GAD_DST3FL_ADV_X( bi,bj,k, dTtracerLev(k),
>>      I           uTrans, uVel, maskW(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O           af, myThid )
>>          ENDIF
>>         ELSE
>>          STOP 'GAD_CALC_RHS: Bad advectionScheme (X)'
>>         ENDIF
>>         DO j=1-Oly,sNy+Oly
>>          DO i=1-Olx,sNx+Olx
>>           fZon(i,j) = fZon(i,j) + af(i,j)
>>          ENDDO
>>         ENDDO
>> #ifdef ALLOW_DIAGNOSTICS
>>         IF ( useDiagnostics ) THEN
>>           diagName = 'ADVx'//diagSufx
>>           CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
>>         ENDIF
>> #endif
>>       ENDIF
>>
>> C-    Diffusive flux in X
>>       IF (diffKh.NE.0.) THEN
>>        CALL GAD_DIFF_X(bi,bj,k,xA,diffKh,localT,df,myThid)
>>       ELSE
>>        DO j=1-Oly,sNy+Oly
>>         DO i=1-Olx,sNx+Olx
>>          df(i,j) = 0. _d 0
>>         ENDDO
>>        ENDDO
>>       ENDIF
>>
>> C-    Add bi-harmonic diffusive flux in X
>>       IF (diffK4 .NE. 0.) THEN
>>        CALL GAD_BIHARM_X(bi,bj,k,xA,df4,diffK4,df,myThid)
>>       ENDIF
>>
>> #ifdef ALLOW_GMREDI
>> C-    GM/Redi flux in X
>>       IF (useGMRedi) THEN
>> C *note* should update GMREDI_XTRANSPORT to set df  *aja*
>>         CALL GMREDI_XTRANSPORT(
>>      I     iMin,iMax,jMin,jMax,bi,bj,K,
>>      I     xA,Tracer,tracerIdentity,
>>      U     df,
>>      I     myThid)
>>       ENDIF
>> #endif
>>       DO j=1-Oly,sNy+Oly
>>        DO i=1-Olx,sNx+Olx
>>         fZon(i,j) = fZon(i,j) + df(i,j)
>>        ENDDO
>>       ENDDO
>>
>> #ifdef ALLOW_DIAGNOSTICS
>> C-    Diagnostics of Tracer flux in X dir (mainly Diffusive term),
>> C       excluding advective terms:
>>       IF ( useDiagnostics .AND.
>>      &    (diffKh.NE.0. .OR. diffK4 .NE.0. .OR. useGMRedi) ) THEN
>>           diagName = 'DIFx'//diagSufx
>>           CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
>>       ENDIF
>> #endif
>>
>> C--   Initialize net flux in Y direction
>>       DO j=1-Oly,sNy+Oly
>>        DO i=1-Olx,sNx+Olx
>>         fMer(i,j) = 0. _d 0
>>        ENDDO
>>       ENDDO
>>
>> C-    Advective flux in Y
>>       IF (calcAdvection) THEN
>>         IF (advectionScheme.EQ.ENUM_CENTERED_2ND) THEN
>>           CALL GAD_C2_ADV_Y(bi,bj,k,vTrans,locABT,af,myThid)
>>         ELSEIF ( advectionScheme.EQ.ENUM_UPWIND_1RST      &          
>> .OR. advectionScheme.EQ.ENUM_DST2 ) THEN
>>           CALL GAD_DST2U1_ADV_Y( bi,bj,k, advectionScheme,      I    
>>         dTtracerLev(k), vTrans, vVel, locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN
>>           CALL GAD_FLUXLIMIT_ADV_Y( bi,bj,k, dTtracerLev(k),
>>      I            vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_UPWIND_3RD ) THEN
>>           CALL GAD_U3_ADV_Y(bi,bj,k,vTrans,locABT,af,myThid)
>>         ELSEIF (advectionScheme.EQ.ENUM_CENTERED_4TH) THEN
>>           CALL GAD_C4_ADV_Y(bi,bj,k,vTrans,locABT,af,myThid)
>>         ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN
>>           CALL GAD_DST3_ADV_Y( bi,bj,k, dTtracerLev(k),
>>      I            vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O            af, myThid )
>>         ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
>>          IF ( inAdMode ) THEN
>> cph This block is to trick the adjoint:
>> cph IF inAdExact=.FALSE., we want to use DST3 cph with limiters in 
>> forward, but without limiters in reverse.
>>           CALL GAD_DST3_ADV_Y( bi,bj,k, dTtracerLev(k),
>>      I           vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O           af, myThid )
>>          ELSE
>>           CALL GAD_DST3FL_ADV_Y( bi,bj,k, dTtracerLev(k),
>>      I           vTrans, vVel, maskS(1-Olx,1-Oly,k,bi,bj), locABT,
>>      O           af, myThid )
>>          ENDIF
>>         ELSE
>>           STOP 'GAD_CALC_RHS: Bad advectionScheme (Y)'
>>         ENDIF
>>         DO j=1-Oly,sNy+Oly
>>          DO i=1-Olx,sNx+Olx
>>           fMer(i,j) = fMer(i,j) + af(i,j)
>>          ENDDO
>>         ENDDO
>> #ifdef ALLOW_DIAGNOSTICS
>>         IF ( useDiagnostics ) THEN
>>           diagName = 'ADVy'//diagSufx
>>           CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
>>         ENDIF
>> #endif
>>       ENDIF
>>
>> C-    Diffusive flux in Y
>>       IF (diffKh.NE.0.) THEN
>>        CALL GAD_DIFF_Y(bi,bj,k,yA,diffKh,localT,df,myThid)
>>       ELSE
>>        DO j=1-Oly,sNy+Oly
>>         DO i=1-Olx,sNx+Olx
>>          df(i,j) = 0. _d 0
>>         ENDDO
>>        ENDDO
>>       ENDIF
>>
>> C-    Add bi-harmonic flux in Y
>>       IF (diffK4 .NE. 0.) THEN
>>        CALL GAD_BIHARM_Y(bi,bj,k,yA,df4,diffK4,df,myThid)
>>       ENDIF
>>
>> #ifdef ALLOW_GMREDI
>> C-    GM/Redi flux in Y
>>       IF (useGMRedi) THEN
>> C *note* should update GMREDI_YTRANSPORT to set df  *aja*
>>        CALL GMREDI_YTRANSPORT(
>>      I     iMin,iMax,jMin,jMax,bi,bj,K,
>>      I     yA,Tracer,tracerIdentity,
>>      U     df,
>>      I     myThid)
>>       ENDIF
>> #endif
>>       DO j=1-Oly,sNy+Oly
>>        DO i=1-Olx,sNx+Olx
>>         fMer(i,j) = fMer(i,j) + df(i,j)
>>        ENDDO
>>       ENDDO
>>
>> #ifdef ALLOW_DIAGNOSTICS
>> C-    Diagnostics of Tracer flux in Y dir (mainly Diffusive terms),
>> C       excluding advective terms:
>>       IF ( useDiagnostics .AND.
>>      &    (diffKh.NE.0. .OR. diffK4 .NE.0. .OR. useGMRedi) ) THEN
>>           diagName = 'DIFy'//diagSufx
>>           CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
>>       ENDIF
>> #endif
>>
>> C--   Compute vertical flux fVerT(kUp) at interface k (between k-1 & k):
>> C-    Advective flux in R
>> #ifdef ALLOW_AIM
>> C- a hack to prevent Water-Vapor vert.transport into the 
>> stratospheric level Nr
>>       IF (calcAdvection .AND. .NOT.implicitAdvection .AND. K.GE.2 .AND.
>>      &     (.NOT.useAIM .OR.tracerIdentity.NE.GAD_SALINITY .OR.K.LT.Nr)
>>      &   ) THEN
>> #else
>>       IF (calcAdvection .AND. .NOT.implicitAdvection .AND. K.GE.2) THEN
>> #endif
>> C-    Compute vertical advective flux in the interior:
>>         IF (vertAdvecScheme.EQ.ENUM_CENTERED_2ND) THEN
>>           CALL GAD_C2_ADV_R(bi,bj,k,rTrans,TracAB,af,myThid)
>>         ELSEIF ( vertAdvecScheme.EQ.ENUM_UPWIND_1RST      &          
>> .OR. vertAdvecScheme.EQ.ENUM_DST2 ) THEN
>>           CALL GAD_DST2U1_ADV_R( bi,bj,k, vertAdvecScheme,      I    
>>      dTtracerLev(k),rTrans,wVel,TracAB(1-Olx,1-Oly,1,bi,bj),
>>      O         af, myThid )
>>         ELSEIF (vertAdvecScheme.EQ.ENUM_FLUX_LIMIT) THEN
>>           CALL GAD_FLUXLIMIT_ADV_R( bi,bj,k,
>>      I         dTtracerLev(k),rTrans,wVel,TracAB(1-Olx,1-Oly,1,bi,bj),
>>      O         af, myThid )
>>         ELSEIF (vertAdvecScheme.EQ.ENUM_UPWIND_3RD ) THEN
>>           CALL GAD_U3_ADV_R(bi,bj,k,rTrans,TracAB,af,myThid)
>>         ELSEIF (vertAdvecScheme.EQ.ENUM_CENTERED_4TH) THEN
>>           CALL GAD_C4_ADV_R(bi,bj,k,rTrans,TracAB,af,myThid)
>>         ELSEIF (vertAdvecScheme.EQ.ENUM_DST3 ) THEN
>>           CALL GAD_DST3_ADV_R( bi,bj,k,
>>      I         dTtracerLev(k),rTrans,wVel,TracAB(1-Olx,1-Oly,1,bi,bj),
>>      O         af, myThid )
>>         ELSEIF (vertAdvecScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN
>> cph This block is to trick the adjoint:
>> cph IF inAdExact=.FALSE., we want to use DST3 cph with limiters in 
>> forward, but without limiters in reverse.
>>           IF ( inAdMode ) THEN
>>            CALL GAD_DST3_ADV_R( bi,bj,k,
>>      I         dTtracerLev(k),rTrans,wVel,TracAB(1-Olx,1-Oly,1,bi,bj),
>>      O         af, myThid )
>>           ELSE
>>            CALL GAD_DST3FL_ADV_R( bi,bj,k,
>>      I         dTtracerLev(k),rTrans,wVel,TracAB(1-Olx,1-Oly,1,bi,bj),
>>      O         af, myThid )
>>           ENDIF
>>         ELSE
>>           STOP 'GAD_CALC_RHS: Bad vertAdvecScheme (R)'
>>         ENDIF
>> C-     add the advective flux to fVerT
>>         DO j=1-Oly,sNy+Oly
>>          DO i=1-Olx,sNx+Olx
>>           fVerT(i,j,kUp) = fVerT(i,j,kUp) + af(i,j)
>>          ENDDO
>>         ENDDO
>> #ifdef ALLOW_DIAGNOSTICS
>>         IF ( useDiagnostics ) THEN
>>           diagName = 'ADVr'//diagSufx
>>           CALL DIAGNOSTICS_FILL(af,diagName, k,1, 2,bi,bj, myThid)
>> C- note: needs to explicitly increment the counter since DIAGNOSTICS_FILL
>> C        does it only if k=1 (never the case here)
>>           IF ( k.EQ.2 ) CALL DIAGNOSTICS_COUNT(diagName,bi,bj,myThid)
>>         ENDIF
>> #endif
>>       ENDIF
>>
>> C-    Diffusive flux in R
>> C     Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper
>> C           boundary condition.
>>       IF (implicitDiffusion) THEN
>>        DO j=1-Oly,sNy+Oly
>>         DO i=1-Olx,sNx+Olx
>>          df(i,j) = 0. _d 0
>>         ENDDO
>>        ENDDO
>>       ELSE
>>        CALL GAD_DIFF_R(bi,bj,k,KappaR,Tracer,df,myThid)
>>       ENDIF
>>
>> #ifdef ALLOW_GMREDI
>> C-    GM/Redi flux in R
>>       IF (useGMRedi) THEN
>> C *note* should update GMREDI_RTRANSPORT to set df  *aja*
>>        CALL GMREDI_RTRANSPORT(
>>      I     iMin,iMax,jMin,jMax,bi,bj,K,
>>      I     Tracer,tracerIdentity,
>>      U     df,
>>      I     myThid)
>>       ENDIF
>> #endif
>>
>>       DO j=1-Oly,sNy+Oly
>>        DO i=1-Olx,sNx+Olx
>>         fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
>>        ENDDO
>>       ENDDO
>>
>> #ifdef ALLOW_DIAGNOSTICS
>> C-    Diagnostics of Tracer flux in R dir (mainly Diffusive terms), 
>> C       Explicit terms only & excluding advective terms:
>>       IF ( useDiagnostics .AND.
>>      &    (.NOT.implicitDiffusion .OR. useGMRedi) ) THEN
>>           diagName = 'DFrE'//diagSufx
>>           CALL DIAGNOSTICS_FILL(df,diagName, k,1, 2,bi,bj, myThid)
>>       ENDIF
>> #endif
>>
>> #ifdef ALLOW_KPP
>> C-    Set non local KPP transport term (ghat):
>>       IF ( useKPP .AND. k.GE.2 ) THEN
>>        DO j=1-Oly,sNy+Oly
>>         DO i=1-Olx,sNx+Olx
>>          df(i,j) = 0. _d 0
>>         ENDDO
>>        ENDDO
>>        IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN
>>         CALL KPP_TRANSPORT_T(
>>      I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
>>      O     df )
>>        ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN
>>         CALL KPP_TRANSPORT_S(
>>      I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
>>      O     df )
>> #ifdef ALLOW_PTRACERS
>>        ELSEIF (tracerIdentity .GE. GAD_TR1) THEN
>>         CALL KPP_TRANSPORT_PTR(
>>      I     iMin,iMax,jMin,jMax,bi,bj,k,km1,
>>      I     tracerIdentity-GAD_TR1+1,
>>      O     df )
>> #endif
>>        ELSE
>>         PRINT*,'invalid tracer indentity: ', tracerIdentity
>>         STOP 'GAD_CALC_RHS: Ooops'
>>        ENDIF
>>        DO j=1-Oly,sNy+Oly
>>         DO i=1-Olx,sNx+Olx
>>          fVerT(i,j,kUp) = fVerT(i,j,kUp) + df(i,j)*maskUp(i,j)
>>         ENDDO
>>        ENDDO
>>       ENDIF
>> #endif
>>
>> C--   Divergence of fluxes
>>       DO j=1-Oly,sNy+Oly-1
>>        DO i=1-Olx,sNx+Olx-1
>>         gTracer(i,j,k,bi,bj)=gTracer(i,j,k,bi,bj)
>>      &   -_recip_hFacC(i,j,k,bi,bj)*recip_drF(k)*recip_rA(i,j,bi,bj)
>>      &   *( (fZon(i+1,j)-fZon(i,j))
>>      &     +(fMer(i,j+1)-fMer(i,j))
>>      &     +(fVerT(i,j,kDown)-fVerT(i,j,kUp))*rkSign
>>      &     -localT(i,j)*( (uTrans(i+1,j)-uTrans(i,j))
>>      &                   +(vTrans(i,j+1)-vTrans(i,j))
>>      &                   +(rTransKp1(i,j)-rTrans(i,j))*rAdvFac
>>      &                  )*advFac
>>      &    )
>>        ENDDO
>>       ENDDO
>>
>> #ifdef ALLOW_DEBUG
>>       IF ( debugLevel .GE. debLevB
>>      &   .AND. tracerIdentity.EQ.GAD_TEMPERATURE
>>      &   .AND. k.EQ.2 .AND. myIter.EQ.1+nIter0
>>      &   .AND. nPx.EQ.1 .AND. nPy.EQ.1
>>      &   .AND. useCubedSphereExchange ) THEN
>>         CALL DEBUG_CS_CORNER_UV( ' fZon,fMer from GAD_CALC_RHS',
>>      &             fZon,fMer, k, standardMessageUnit,bi,bj,myThid )
>>       ENDIF
>> #endif /* ALLOW_DEBUG */
>>        RETURN
>>       END
>>
>>
>> ------------------------------------------------------------------------
>>
>>
>>       subroutine adgad_calc_rhs( bi, bj, imin, imax, jmin, jmax, k, km1,
>>      $ kup, kdown, xa, ya, utrans, vtrans, rtrans, rtranskp1, 
>> maskup,      $diffkh, diffk4, kappar, tracer, tracab, 
>> traceridentity,      $advectionscheme, vertadvecscheme, 
>> calcadvection,      $implicitadvection, mythid, adutrans, advtrans, 
>> adrtrans,      $adrtranskp1, adkappar, adtracer, adtracab, adfvert, 
>> adgtracer )
>>
>> ...
>>
>> C----------------------------------------------
>> C RESET LOCAL ADJOINT VARIABLES
>> C----------------------------------------------
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           adaf(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           addf(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           addf4(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           adfmer(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           adfzon(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           adlocabt(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>       do ip2 = 1-oly, sny+oly
>>         do ip1 = 1-olx, snx+olx
>>           adlocalt(ip1,ip2) = 0.d0
>>         end do
>>       end do
>>
>> C----------------------------------------------
>> C ROUTINE BODY
>> C----------------------------------------------
>>       advfac = 0.d0
>>       if (calcadvection) then
>>         advfac = 1.d0
>>       endif
>>       radvfac = rksign*advfac
>>       if (implicitadvection) then
>>         radvfac = 0.d0
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           localt(i,j) = tracer(i,j,k,bi,bj)
>>           locabt(i,j) = tracab(i,j,k,bi,bj)
>>         end do
>>       end do
>>       do j = 1-oly, sny+oly-1
>>         do i = 1-olx, snx+olx-1
>>           adfmer(i,j+1) = adfmer(i,j+1)-adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)
>>           adfmer(i,j) = adfmer(i,j)+adgtracer(i,j,k,bi,bj)*recip_hfacc(
>>      $i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)
>>           adfvert(i,j,kdown) = adfvert(i,j,kdown)-adgtracer(i,j,k,bi,bj)
>>      $*recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*rksign
>>           adfvert(i,j,kup) = adfvert(i,j,kup)+adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*rksign
>>           adfzon(i+1,j) = adfzon(i+1,j)-adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)
>>           adfzon(i,j) = adfzon(i,j)+adgtracer(i,j,k,bi,bj)*recip_hfacc(
>>      $i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)
>>           adlocalt(i,j) = adlocalt(i,j)+adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*(utrans(
>>      $i+1,j)-utrans(i,j)+vtrans(i,j+1)-vtrans(i,j)+(rtranskp1(i,j)-
>>      $rtrans(i,j))*radvfac)*advfac
>>           adrtrans(i,j) = adrtrans(i,j)-adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*radvfac*advfac
>>           adrtranskp1(i,j) = adrtranskp1(i,j)+adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*radvfac*advfac
>>           adutrans(i+1,j) = adutrans(i+1,j)+adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*advfac
>>           adutrans(i,j) = adutrans(i,j)-adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*advfac
>>           advtrans(i,j+1) = advtrans(i,j+1)+adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*advfac
>>           advtrans(i,j) = advtrans(i,j)-adgtracer(i,j,k,bi,bj)*
>>      $recip_hfacc(i,j,k,bi,bj)*recip_drf(k)*recip_ra(i,j,bi,bj)*localt(
>>      $i,j)*advfac
>>         end do
>>       end do
>>       if (usekpp .and. k .ge. 2) then
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             addf(i,j) = addf(i,j)+adfvert(i,j,kup)*maskup(i,j)
>>           end do
>>         end do
>>         if (traceridentity .eq. gad_temperature) then
>>           call adkpp_transport_t( imin,imax,jmin,jmax,bi,bj,k,km1,addf )
>>         else if (traceridentity .eq. gad_salinity) then
>>           call adkpp_transport_s( imin,imax,jmin,jmax,bi,bj,k,km1,addf )
>>         endif
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             addf(i,j) = 0.d0
>>           end do
>>         end do
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           addf(i,j) = addf(i,j)+adfvert(i,j,kup)*maskup(i,j)
>>         end do
>>       end do
>>       if (usegmredi) then
>>         call adgmredi_rtransport( imin,imax,jmin,jmax,bi,bj,k,tracer,
>>      $adtracer,addf )
>>       endif
>>       if (implicitdiffusion) then
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             addf(i,j) = 0.d0
>>           end do
>>         end do
>>       else
>>         call adgad_diff_r( 
>> bi,bj,k,kappar,tracer,adkappar,adtracer,addf      $)
>>       endif
>>       if (calcadvection .and. ( .not. implicitadvection) .and. k .ge. 2)
>>      $ then
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             adaf(i,j) = adaf(i,j)+adfvert(i,j,kup)
>>           end do
>>         end do
>>         if (vertadvecscheme .eq. enum_centered_2nd) then
>>           call adgad_c2_adv_r( bi,bj,k,rtrans,tracab,adrtrans,adtracab,
>>      $adaf )
>>         else if (vertadvecscheme .eq. enum_upwind_1rst .or.      
>> $vertadvecscheme .eq. enum_dst2) then
>>           call adgad_dst2u1_adv_r( bi,bj,k,vertadvecscheme,dttracerlev(
>>      $k),rtrans,tracab(1-olx,1-oly,1,bi,bj),adrtrans,adtracab(1-olx,1-
>>      $oly,1,bi,bj),adaf )
>>         else if (vertadvecscheme .eq. enum_flux_limit) then
>>           call adgad_fluxlimit_adv_r( bi,bj,k,dttracerlev(k),rtrans,
>>      $tracab(1-olx,1-oly,1,bi,bj),adrtrans,adtracab(1-olx,1-oly,1,bi,bj)
>>      $,adaf )
>>         else if (vertadvecscheme .eq. enum_upwind_3rd) then
>>           call adgad_u3_adv_r( bi,bj,k,rtrans,tracab,adrtrans,adtracab,
>>      $adaf )
>>         else if (vertadvecscheme .eq. enum_centered_4th) then
>>           call adgad_c4_adv_r( bi,bj,k,rtrans,tracab,adrtrans,adtracab,
>>      $adaf )
>>         else if (vertadvecscheme .eq. enum_dst3) then
>>           call adgad_dst3_adv_r( bi,bj,k,dttracerlev(k),rtrans,tracab(1-
>>      $olx,1-oly,1,bi,bj),adrtrans,adtracab(1-olx,1-oly,1,bi,bj),adaf )
>>         else if (vertadvecscheme .eq. enum_dst3_flux_limit) then
>>           if (inadmode) then
>>             call adgad_dst3_adv_r( bi,bj,k,dttracerlev(k),rtrans,tracab(
>>      $1-olx,1-oly,1,bi,bj),adrtrans,adtracab(1-olx,1-oly,1,bi,bj),adaf )
>>           else
>>             call adgad_dst3fl_adv_r( bi,bj,k,dttracerlev(k),rtrans,
>>      $tracab(1-olx,1-oly,1,bi,bj),adrtrans,adtracab(1-olx,1-oly,1,bi,bj)
>>      $,adaf )
>>           endif
>>         endif
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           addf(i,j) = addf(i,j)+adfmer(i,j)
>>         end do
>>       end do
>>       if (usegmredi) then
>>         call adgmredi_ytransport( imin,imax,jmin,jmax,bi,bj,k,ya,tracer,
>>      $traceridentity,mythid,adtracer,addf )
>>       endif
>>       if (diffk4 .ne. 0.) then
>>         call adgad_biharm_y( bi,bj,ya,diffk4,addf4,addf )
>>       endif
>>       if (diffkh .ne. 0.) then
>>         call adgad_diff_y( bi,bj,ya,diffkh,adlocalt,addf )
>>       else
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             addf(i,j) = 0.d0
>>           end do
>>         end do
>>       endif
>>       if (calcadvection) then
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             adaf(i,j) = adaf(i,j)+adfmer(i,j)
>>           end do
>>         end do
>>         if (advectionscheme .eq. enum_centered_2nd) then
>>           call adgad_c2_adv_y( vtrans,locabt,advtrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_upwind_1rst .or.      
>> $advectionscheme .eq. enum_dst2) then
>>           call adgad_dst2u1_adv_y( bi,bj,k,advectionscheme,dttracerlev(
>>      $k),vtrans,locabt,advtrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_flux_limit) then
>>           call adgad_fluxlimit_adv_y( bi,bj,k,dttracerlev(k),vtrans,
>>      $masks(1-olx,1-oly,k,bi,bj),locabt,advtrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_upwind_3rd) then
>>           call adgad_u3_adv_y( bi,bj,k,vtrans,locabt,advtrans,adlocabt,
>>      $adaf )
>>         else if (advectionscheme .eq. enum_centered_4th) then
>>           call adgad_c4_adv_y( bi,bj,k,vtrans,locabt,advtrans,adlocabt,
>>      $adaf )
>>         else if (advectionscheme .eq. enum_dst3) then
>>           call adgad_dst3_adv_y( bi,bj,k,dttracerlev(k),vtrans,masks(1-
>>      $olx,1-oly,k,bi,bj),locabt,advtrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_dst3_flux_limit) then
>>           if (inadmode) then
>>             call adgad_dst3_adv_y( bi,bj,k,dttracerlev(k),vtrans,masks(
>>      $1-olx,1-oly,k,bi,bj),locabt,advtrans,adlocabt,adaf )
>>           else
>>             call adgad_dst3fl_adv_y( bi,bj,k,dttracerlev(k),vtrans,
>>      $masks(1-olx,1-oly,k,bi,bj),locabt,advtrans,adlocabt,adaf )
>>           endif
>>         endif
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adfmer(i,j) = 0.d0
>>         end do
>>       end do
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           addf(i,j) = addf(i,j)+adfzon(i,j)
>>         end do
>>       end do
>>       if (usegmredi) then
>>         call adgmredi_xtransport( imin,imax,jmin,jmax,bi,bj,k,xa,tracer,
>>      $traceridentity,mythid,adtracer,addf )
>>       endif
>>       if (diffk4 .ne. 0.) then
>>         call adgad_biharm_x( bi,bj,xa,diffk4,addf4,addf )
>>       endif
>>       if (diffkh .ne. 0.) then
>>         call adgad_diff_x( bi,bj,xa,diffkh,adlocalt,addf )
>>       endif
>>       if (calcadvection) then
>>         do j = 1-oly, sny+oly
>>           do i = 1-olx, snx+olx
>>             adaf(i,j) = adaf(i,j)+adfzon(i,j)
>>           end do
>>         end do
>>         if (advectionscheme .eq. enum_centered_2nd) then
>>           call adgad_c2_adv_x( utrans,locabt,adutrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_upwind_1rst .or.      
>> $advectionscheme .eq. enum_dst2) then
>>           call adgad_dst2u1_adv_x( bi,bj,k,advectionscheme,dttracerlev(
>>      $k),utrans,locabt,adutrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_flux_limit) then
>>           call adgad_fluxlimit_adv_x( bi,bj,k,dttracerlev(k),utrans,
>>      $maskw(1-olx,1-oly,k,bi,bj),locabt,adutrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_upwind_3rd) then
>>           call adgad_u3_adv_x( bi,bj,k,utrans,locabt,adutrans,adlocabt,
>>      $adaf )
>>         else if (advectionscheme .eq. enum_centered_4th) then
>>           call adgad_c4_adv_x( bi,bj,k,utrans,locabt,adutrans,adlocabt,
>>      $adaf )
>>         else if (advectionscheme .eq. enum_dst3) then
>>           call adgad_dst3_adv_x( bi,bj,k,dttracerlev(k),utrans,maskw(1-
>>      $olx,1-oly,k,bi,bj),locabt,adutrans,adlocabt,adaf )
>>         else if (advectionscheme .eq. enum_dst3_flux_limit) then
>>           if (inadmode) then
>>             call adgad_dst3_adv_x( bi,bj,k,dttracerlev(k),utrans,maskw(
>>      $1-olx,1-oly,k,bi,bj),locabt,adutrans,adlocabt,adaf )
>>           else
>>             call adgad_dst3fl_adv_x( bi,bj,k,dttracerlev(k),utrans,
>>      $maskw(1-olx,1-oly,k,bi,bj),locabt,adutrans,adlocabt,adaf )
>>           endif
>>         endif
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adfzon(i,j) = 0.d0
>>         end do
>>       end do
>>       if (diffk4 .ne. 0.) then
>>         call adgad_del2( bi,bj,k,adfzon,adfmer,addf4 )
>>         call adgad_grad_y( bi,bj,ya,adlocalt,adfmer )
>>         call adgad_grad_x( bi,bj,xa,adlocalt,adfzon )
>>       endif
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adtracab(i,j,k,bi,bj) = adtracab(i,j,k,bi,bj)+adlocabt(i,j)
>>           adlocabt(i,j) = 0.d0
>>           adtracer(i,j,k,bi,bj) = adtracer(i,j,k,bi,bj)+adlocalt(i,j)
>>           adlocalt(i,j) = 0.d0
>>         end do
>>       end do
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adfvert(i,j,kup) = 0.d0
>>         end do
>>       end do
>>
>>       end
>>
>>
>>
>> ------------------------------------------------------------------------
>>
>>
>>       subroutine adcalc_gt( bi, bj, imin, imax, jmin, jmax, k, km1, kup,
>>      $ kdown, xa, ya, utrans, vtrans, rtrans, rtranskp1, maskup,     
>>  $kappart, myiter, mythid, adutrans, advtrans, adrtrans,      
>> $adrtranskp1, adkappart, adfvert )
>>
>> ...
>>
>>
>> C----------------------------------------------
>> C ROUTINE BODY
>> C----------------------------------------------
>>       calcadvection = tempadvection .and. ( .not. tempmultidimadvec)
>>       iternb = myiter
>>       if (staggertimestep) then
>>         iternb = myiter-1
>>       endif
>>       if (tempforcing .and. ( .not. forcing_in_ab)) then
>>         call adexternal_forcing_t( bi,bj,k )
>>       endif
>>       if (adamsbashforthgt) then
>>         call adadams_bashforth2( bi,bj,k,iternb,adgt,adgtnm1 )
>>       endif
>>       if (tempforcing .and. forcing_in_ab) then
>>         call adexternal_forcing_t( bi,bj,k )
>>       endif
>>       call adgad_calc_rhs( bi,bj,imin,imax,jmin,jmax,k,km1,kup,kdown,xa,
>>      $ya,utrans,vtrans,rtrans,rtranskp1,maskup,diffkht,diffk4t,kappart,
>>      $theta,theta,gad_temperature,tempadvscheme,tempvertadvscheme,
>>      $calcadvection,tempimplvertadv,mythid,adutrans,advtrans,adrtrans,
>>      $adrtranskp1,adkappart,adtheta,adtheta,adfvert,adgt )
>>
>>       end
>>
>>
>> ------------------------------------------------------------------------
>>
>>
>>       subroutine adcalc_gt( bi, bj, imin, imax, jmin, jmax, k, km1, kup,
>>      $ kdown, xa, ya, utrans, vtrans, rtrans, rtranskp1, maskup,     
>>  $kappart, myiter, mythid, adutrans, advtrans, adrtrans,      
>> $adrtranskp1, adkappart, adfvert )
>>
>> ...
>>
>> C----------------------------------------------
>> C ROUTINE BODY
>> C----------------------------------------------
>> cph(
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adthetah(i,j,k,bi,bj) = 0.D0
>>           adthetah(i,j,km1,bi,bj) = 0.D0
>>         end do
>>       end do
>> cph)
>>       calcadvection = tempadvection .and. ( .not. tempmultidimadvec)
>>       iternb = myiter
>>       if (staggertimestep) then
>>         iternb = myiter-1
>>       endif
>>       if (tempforcing .and. ( .not. forcing_in_ab)) then
>>         call adexternal_forcing_t( bi,bj,k )
>>       endif
>>       if (adamsbashforthgt) then
>>         call adadams_bashforth2( bi,bj,k,iternb,adgt,adgtnm1 )
>>       endif
>>       if (tempforcing .and. forcing_in_ab) then
>>         call adexternal_forcing_t( bi,bj,k )
>>       endif
>>       call adgad_calc_rhs( bi,bj,imin,imax,jmin,jmax,k,km1,kup,kdown,xa,
>>      $ya,utrans,vtrans,rtrans,rtranskp1,maskup,diffkht,diffk4t,kappart,
>>      $theta,theta,gad_temperature,tempadvscheme,tempvertadvscheme,
>>      $calcadvection,tempimplvertadv,mythid,adutrans,advtrans,adrtrans,
>>      $adrtranskp1,adkappart,adtheta,adthetah,adfvert,adgt )
>> cph(
>>       do j = 1-oly, sny+oly
>>         do i = 1-olx, snx+olx
>>           adtheta(i,j,k,bi,bj) = adtheta(i,j,k,bi,bj) +      &       
>>                     adthetah(i,j,k,bi,bj)
>>           adthetah(i,j,k,bi,bj) = 0.D0
>>           adtheta(i,j,km1,bi,bj) = adtheta(i,j,km1,bi,bj) +
>>      &                             adthetah(i,j,km1,bi,bj)
>>           adthetah(i,j,km1,bi,bj) = 0.D0
>>         end do
>>       end do
>> cph)
>>
>>       end
>>
>>
>> ------------------------------------------------------------------------
>>
>> _______________________________________________
>> MITgcm-devel mailing list
>> MITgcm-devel at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-devel
>
> _______________________________________________
> MITgcm-devel mailing list
> MITgcm-devel at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-devel
>



--------------------------------------------------------
Patrick Heimbach   Massachusetts Institute of Technology
FON: +1/617/253-5259                  EAPS, Room 54-1518
FAX: +1/617/253-4464             77 Massachusetts Avenue
mailto:heimbach at mit.edu               Cambridge MA 02139
http://www.mit.edu/~heimbach/                        USA




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