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C $Header: /u/gcmpack/models/MITgcmUV/pkg/generic_advdiff/gad_advection.F,v 1.4 2001/09/19 20:45:09 adcroft Exp $ |
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C $Name: $ |
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|
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CBOI |
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C !TITLE: pkg/generic\_advdiff |
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C !AUTHORS: adcroft@mit.edu |
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C !INTRODUCTION: |
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C \section{Generica Advection Diffusion Package} |
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C |
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C Package "generic\_advdiff" provides a common set of routines for calculating |
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C advective/diffusive fluxes for tracers (cell centered quantities on a C-grid). |
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C |
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C Many different advection schemes are available: the standard centered |
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C second order, centered fourth order and upwind biased third order schemes |
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C are known as linear methods and require some stable time-stepping method |
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C such as Adams-Bashforth. Alternatives such as flux-limited schemes are |
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C stable in the forward sense and are best combined with the multi-dimensional |
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C method provided in gad\_advection. |
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C |
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C There are two high-level routines: |
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C \begin{itemize} |
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C \item{GAD\_CALC\_RHS} calculates all fluxes at time level "n" and is used |
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C for the standard linear schemes. This must be used in conjuction with |
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C Adams-Bashforth time-stepping. Diffusive and parameterized fluxes are |
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C always calculated here. |
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C \item{GAD\_ADVECTION} calculates just the advective fluxes using the |
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C non-linear schemes and can not be used in conjuction with Adams-Bashforth |
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C time-stepping. |
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C \end{itemize} |
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CEOI |
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|
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#include "GAD_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GAD_ADVECTION |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_ADVECTION(bi,bj,advectionScheme,tracerIdentity, |
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U Tracer,Gtracer, |
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I myTime,myIter,myThid) |
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|
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C !DESCRIPTION: |
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C Calculates the tendancy of a tracer due to advection. |
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C It uses the multi-dimensional method given in \ref{sect:multiDimAdvection} |
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C and can only be used for the non-linear advection schemes such as the |
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C direct-space-time method and flux-limiters. |
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C |
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C The algorithm is as follows: |
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C \begin{itemize} |
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C \item{$\theta^{(n+1/3)} = \theta^{(n)} |
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C - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$} |
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C \item{$\theta^{(n+2/3)} = \theta^{(n+1/3)} |
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C - \Delta t \partial_y (v\theta^{(n+1/3)}) + \theta^{(n)} \partial_y v$} |
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C \item{$\theta^{(n+3/3)} = \theta^{(n+2/3)} |
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C - \Delta t \partial_r (w\theta^{(n+2/3)}) + \theta^{(n)} \partial_r w$} |
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C \item{$G_\theta = ( \theta^{(n+3/3)} - \theta^{(n)} )/\Delta t$} |
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C \end{itemize} |
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C |
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C The tendancy (output) is over-written by this routine. |
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|
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C !USES: =============================================================== |
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IMPLICIT NONE |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "GRID.h" |
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#include "GAD.h" |
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|
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C advectionScheme :: advection scheme to use |
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C tracerIdentity :: identifier for the tracer (required only for OBCS) |
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C Tracer :: tracer field |
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C myTime :: current time |
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C myIter :: iteration number |
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C myThid :: thread number |
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INTEGER bi,bj |
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INTEGER advectionScheme |
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INTEGER tracerIdentity |
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_RL Gtracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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|
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C !OUTPUT PARAMETERS: ================================================== |
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C gTracer :: tendancy array |
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_RL Tracer(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C maskUp :: 2-D array for mask at W points |
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C iMin,iMax,jMin,jMax :: loop range for called routines |
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C i,j,k :: loop indices |
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C kup :: index into 2 1/2D array, toggles between 1 and 2 |
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C kdown :: index into 2 1/2D array, toggles between 2 and 1 |
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C kp1 :: =k+1 for k<Nr, =Nr for k=Nr |
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C xA,yA :: areas of X and Y face of tracer cells |
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C uTrans,vTrans,rTrans :: 2-D arrays of volume transports at U,V and W points |
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C af :: 2-D array for horizontal advective flux |
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C fVerT :: 2 1/2D arrays for vertical advective flux |
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C localTij :: 2-D array used as temporary local copy of tracer fld |
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C localTijk :: 3-D array used as temporary local copy of tracer fld |
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C kp1Msk :: flag (0,1) to act as over-riding mask for W levels |
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C calc_fluxes_X :: logical to indicate to calculate fluxes in X dir |
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C calc_fluxes_Y :: logical to indicate to calculate fluxes in Y dir |
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C nipass :: number of passes to make in multi-dimensional method |
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C ipass :: number of the current pass being made |
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_RS maskUp (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER iMin,iMax,jMin,jMax |
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INTEGER i,j,k,kup,kDown,kp1 |
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_RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL rTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL localTij(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL localTijk(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL kp1Msk |
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LOGICAL calc_fluxes_X,calc_fluxes_Y |
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INTEGER nipass,ipass |
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CEOP |
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|
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C-- Set up work arrays with valid (i.e. not NaN) values |
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C These inital values do not alter the numerical results. They |
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C just ensure that all memory references are to valid floating |
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C point numbers. This prevents spurious hardware signals due to |
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C uninitialised but inert locations. |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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xA(i,j) = 0. _d 0 |
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yA(i,j) = 0. _d 0 |
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uTrans(i,j) = 0. _d 0 |
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vTrans(i,j) = 0. _d 0 |
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rTrans(i,j) = 0. _d 0 |
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fVerT(i,j,1) = 0. _d 0 |
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fVerT(i,j,2) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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iMin = 1-OLx |
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iMax = sNx+OLx |
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jMin = 1-OLy |
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jMax = sNy+OLy |
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|
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C-- Start of k loop for horizontal fluxes |
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DO k=1,Nr |
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|
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C-- Get temporary terms used by tendency routines |
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CALL CALC_COMMON_FACTORS ( |
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I bi,bj,iMin,iMax,jMin,jMax,k, |
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O xA,yA,uTrans,vTrans,rTrans,maskUp, |
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I myThid) |
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|
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C-- Make local copy of tracer array |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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localTij(i,j)=tracer(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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|
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IF (useCubedSphereExchange) THEN |
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nipass=3 |
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ELSE |
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nipass=1 |
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ENDIF |
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nipass=1 |
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|
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C-- Multiple passes for different directions on different tiles |
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DO ipass=1,nipass |
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|
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IF (nipass.EQ.3) THEN |
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calc_fluxes_X=.FALSE. |
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calc_fluxes_Y=.FALSE. |
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IF (ipass.EQ.1 .AND. (bi.EQ.1 .OR. bi.EQ.2) ) THEN |
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calc_fluxes_X=.TRUE. |
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ELSEIF (ipass.EQ.1 .AND. (bi.EQ.4 .OR. bi.EQ.5) ) THEN |
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calc_fluxes_Y=.TRUE. |
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ELSEIF (ipass.EQ.2 .AND. (bi.EQ.1 .OR. bi.EQ.6) ) THEN |
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calc_fluxes_Y=.TRUE. |
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ELSEIF (ipass.EQ.2 .AND. (bi.EQ.3 .OR. bi.EQ.4) ) THEN |
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calc_fluxes_X=.TRUE. |
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ELSEIF (ipass.EQ.3 .AND. (bi.EQ.2 .OR. bi.EQ.3) ) THEN |
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calc_fluxes_Y=.TRUE. |
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ELSEIF (ipass.EQ.3 .AND. (bi.EQ.5 .OR. bi.EQ.6) ) THEN |
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calc_fluxes_X=.TRUE. |
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ENDIF |
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ELSE |
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calc_fluxes_X=.TRUE. |
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calc_fluxes_Y=.TRUE. |
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ENDIF |
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|
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C-- X direction |
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IF (calc_fluxes_X) THEN |
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|
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C-- Internal exchange for calculations in X |
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IF (useCubedSphereExchange) THEN |
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DO j=1,Oly |
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DO i=1,Olx |
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localTij( 1-i , 1-j )=localTij( 1-j , i ) |
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localTij( 1-i ,sNy+j)=localTij( 1-j , sNy+1-i ) |
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localTij(sNx+i, 1-j )=localTij(sNx+j, i ) |
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localTij(sNx+i,sNy+j)=localTij(sNx+j, sNy+1-i ) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C- Advective flux in X |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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af(i,j) = 0. |
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ENDDO |
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ENDDO |
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IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
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CALL GAD_DST3_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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CALL GAD_DST3FL_ADV_X( |
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& bi,bj,k,deltaTtracer,uTrans,uVel,localTij,af,myThid) |
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ELSE |
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STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim' |
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ENDIF |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx-1 |
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localTij(i,j)=localTij(i,j)-deltaTtracer* |
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& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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& *recip_rA(i,j,bi,bj) |
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& *( af(i+1,j)-af(i,j) |
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& -tracer(i,j,k,bi,bj)*(uTrans(i+1,j)-uTrans(i,j)) |
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& ) |
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ENDDO |
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ENDDO |
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|
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#ifdef ALLOW_OBCS |
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C-- Apply open boundary conditions |
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IF (useOBCS) THEN |
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IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
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CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid ) |
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ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
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CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid ) |
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END IF |
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END IF |
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#endif /* ALLOW_OBCS */ |
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|
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C-- End of X direction |
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ENDIF |
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|
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C-- Y direction |
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IF (calc_fluxes_Y) THEN |
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|
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C-- Internal exchange for calculations in Y |
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IF (useCubedSphereExchange) THEN |
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DO j=1,Oly |
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DO i=1,Olx |
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localTij( 1-i , 1-j )=localTij( j , 1-i ) |
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localTij( 1-i ,sNy+j)=localTij( j ,sNy+i) |
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localTij(sNx+i, 1-j )=localTij(sNx+1-j, 1-i ) |
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localTij(sNx+i,sNy+j)=localTij(sNx+1-j,sNy+i) |
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ENDDO |
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ENDDO |
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ENDIF |
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|
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C- Advective flux in Y |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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af(i,j) = 0. |
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ENDDO |
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ENDDO |
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IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
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CALL GAD_FLUXLIMIT_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
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CALL GAD_DST3_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid) |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
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CALL GAD_DST3FL_ADV_Y( |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid) |
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ELSE |
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STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim' |
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ENDIF |
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DO j=1-Oly,sNy+Oly-1 |
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DO i=1-Olx,sNx+Olx |
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localTij(i,j)=localTij(i,j)-deltaTtracer* |
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& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
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& *recip_rA(i,j,bi,bj) |
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& *( af(i,j+1)-af(i,j) |
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& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j)) |
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& ) |
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ENDDO |
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ENDDO |
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|
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#ifdef ALLOW_OBCS |
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C-- Apply open boundary conditions |
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IF (useOBCS) THEN |
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IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
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CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid ) |
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ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
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CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid ) |
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END IF |
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END IF |
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#endif /* ALLOW_OBCS */ |
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|
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C-- End of Y direction |
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ENDIF |
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|
| 310 |
DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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localTijk(i,j,k)=localTij(i,j) |
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ENDDO |
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ENDDO |
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|
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C-- End of ipass loop |
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ENDDO |
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|
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C-- End of K loop for horizontal fluxes |
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ENDDO |
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|
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C-- Start of k loop for vertical flux |
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DO k=Nr,1,-1 |
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|
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C-- kup Cycles through 1,2 to point to w-layer above |
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C-- kDown Cycles through 2,1 to point to w-layer below |
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kup = 1+MOD(k+1,2) |
| 328 |
kDown= 1+MOD(k,2) |
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|
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C-- Get temporary terms used by tendency routines |
| 331 |
CALL CALC_COMMON_FACTORS ( |
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I bi,bj,iMin,iMax,jMin,jMax,k, |
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O xA,yA,uTrans,vTrans,rTrans,maskUp, |
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I myThid) |
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|
| 336 |
C- Advective flux in R |
| 337 |
DO j=1-Oly,sNy+Oly |
| 338 |
DO i=1-Olx,sNx+Olx |
| 339 |
af(i,j) = 0. |
| 340 |
ENDDO |
| 341 |
ENDDO |
| 342 |
|
| 343 |
C Note: wVel needs to be masked |
| 344 |
IF (K.GE.2) THEN |
| 345 |
C- Compute vertical advective flux in the interior: |
| 346 |
IF (advectionScheme.EQ.ENUM_FLUX_LIMIT) THEN |
| 347 |
CALL GAD_FLUXLIMIT_ADV_R( |
| 348 |
& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid) |
| 349 |
ELSEIF (advectionScheme.EQ.ENUM_DST3 ) THEN |
| 350 |
CALL GAD_DST3_ADV_R( |
| 351 |
& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid) |
| 352 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
| 353 |
CALL GAD_DST3FL_ADV_R( |
| 354 |
& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid) |
| 355 |
ELSE |
| 356 |
STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim' |
| 357 |
ENDIF |
| 358 |
C- Surface "correction" term at k>1 : |
| 359 |
DO j=1-Oly,sNy+Oly |
| 360 |
DO i=1-Olx,sNx+Olx |
| 361 |
af(i,j) = af(i,j) |
| 362 |
& + (maskC(i,j,k,bi,bj)-maskC(i,j,k-1,bi,bj))* |
| 363 |
& rTrans(i,j)*localTijk(i,j,k) |
| 364 |
ENDDO |
| 365 |
ENDDO |
| 366 |
ELSE |
| 367 |
C- Surface "correction" term at k=1 : |
| 368 |
DO j=1-Oly,sNy+Oly |
| 369 |
DO i=1-Olx,sNx+Olx |
| 370 |
af(i,j) = rTrans(i,j)*localTijk(i,j,k) |
| 371 |
ENDDO |
| 372 |
ENDDO |
| 373 |
ENDIF |
| 374 |
C- add the advective flux to fVerT |
| 375 |
DO j=1-Oly,sNy+Oly |
| 376 |
DO i=1-Olx,sNx+Olx |
| 377 |
fVerT(i,j,kUp) = af(i,j) |
| 378 |
ENDDO |
| 379 |
ENDDO |
| 380 |
|
| 381 |
C-- Divergence of fluxes |
| 382 |
kp1=min(Nr,k+1) |
| 383 |
kp1Msk=1. |
| 384 |
if (k.EQ.Nr) kp1Msk=0. |
| 385 |
DO j=1-Oly,sNy+Oly |
| 386 |
DO i=1-Olx,sNx+Olx |
| 387 |
localTij(i,j)=localTijk(i,j,k)-deltaTtracer* |
| 388 |
& _recip_hFacC(i,j,k,bi,bj)*recip_drF(k) |
| 389 |
& *recip_rA(i,j,bi,bj) |
| 390 |
& *( fVerT(i,j,kUp)-fVerT(i,j,kDown) |
| 391 |
& -tracer(i,j,k,bi,bj)*rA(i,j,bi,bj)* |
| 392 |
& (wVel(i,j,k,bi,bj)-kp1Msk*wVel(i,j,kp1,bi,bj)) |
| 393 |
& )*rkFac |
| 394 |
gTracer(i,j,k,bi,bj)= |
| 395 |
& (localTij(i,j)-tracer(i,j,k,bi,bj))/deltaTtracer |
| 396 |
ENDDO |
| 397 |
ENDDO |
| 398 |
|
| 399 |
C-- End of K loop for vertical flux |
| 400 |
ENDDO |
| 401 |
|
| 402 |
RETURN |
| 403 |
END |
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