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adcroft |
1.5 |
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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adcroft |
1.2 |
C $Name: $ |
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adcroft |
1.1 |
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1.4 |
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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adcroft |
1.1 |
#include "GAD_OPTIONS.h" |
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1.4 |
CBOP |
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C !ROUTINE: GAD_ADVECTION |
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C !INTERFACE: ========================================================== |
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1.1 |
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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1.4 |
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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{$\theta^{(n+1/3)} = \theta^{(n)} |
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1.5 |
C - \Delta t \partial_x (u\theta^{(n)}) + \theta^{(n)} \partial_x u$} |
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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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1.4 |
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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C !USES: =============================================================== |
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1.1 |
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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1.4 |
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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1.1 |
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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1.4 |
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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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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1.1 |
_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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1.3 |
LOGICAL calc_fluxes_X,calc_fluxes_Y |
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INTEGER nipass,ipass |
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1.4 |
CEOP |
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1.1 |
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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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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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C-- Start of k loop for horizontal fluxes |
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DO k=1,Nr |
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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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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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adcroft |
1.3 |
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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C-- Multiple passes for different directions on different tiles |
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DO ipass=1,nipass |
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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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C-- X direction |
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IF (calc_fluxes_X) THEN |
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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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adcroft |
1.1 |
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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#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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adcroft |
1.3 |
C-- End of X direction |
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ENDIF |
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C-- Y direction |
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IF (calc_fluxes_Y) THEN |
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C-- Internal exchange for calculations in Y |
256 |
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IF (useCubedSphereExchange) THEN |
257 |
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DO j=1,Oly |
258 |
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DO i=1,Olx |
259 |
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localTij( 1-i , 1-j )=localTij( j , 1-i ) |
260 |
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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 ) |
262 |
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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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adcroft |
1.1 |
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) |
279 |
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ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
280 |
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CALL GAD_DST3FL_ADV_Y( |
281 |
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& bi,bj,k,deltaTtracer,vTrans,vVel,localTij,af,myThid) |
282 |
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ELSE |
283 |
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STOP 'GAD_ADVECTION: adv. scheme incompatibale with mutli-dim' |
284 |
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ENDIF |
285 |
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DO j=1-Oly,sNy+Oly-1 |
286 |
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DO i=1-Olx,sNx+Olx |
287 |
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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) |
291 |
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& -tracer(i,j,k,bi,bj)*(vTrans(i,j+1)-vTrans(i,j)) |
292 |
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& ) |
293 |
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ENDDO |
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ENDDO |
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adcroft |
1.3 |
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adcroft |
1.1 |
#ifdef ALLOW_OBCS |
297 |
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C-- Apply open boundary conditions |
298 |
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IF (useOBCS) THEN |
299 |
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IF (tracerIdentity.EQ.GAD_TEMPERATURE) THEN |
300 |
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CALL OBCS_APPLY_TLOC( bi, bj, k, localTij, myThid ) |
301 |
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ELSEIF (tracerIdentity.EQ.GAD_SALINITY) THEN |
302 |
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CALL OBCS_APPLY_SLOC( bi, bj, k, localTij, myThid ) |
303 |
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END IF |
304 |
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END IF |
305 |
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#endif /* ALLOW_OBCS */ |
306 |
adcroft |
1.3 |
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307 |
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C-- End of Y direction |
308 |
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ENDIF |
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310 |
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DO j=1-Oly,sNy+Oly |
311 |
adcroft |
1.1 |
DO i=1-Olx,sNx+Olx |
312 |
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localTijk(i,j,k)=localTij(i,j) |
313 |
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ENDDO |
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ENDDO |
315 |
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316 |
adcroft |
1.3 |
C-- End of ipass loop |
317 |
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ENDDO |
318 |
adcroft |
1.1 |
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319 |
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C-- End of K loop for horizontal fluxes |
320 |
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ENDDO |
321 |
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322 |
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C-- Start of k loop for vertical flux |
323 |
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|
DO k=Nr,1,-1 |
324 |
|
|
|
325 |
|
|
C-- kup Cycles through 1,2 to point to w-layer above |
326 |
|
|
C-- kDown Cycles through 2,1 to point to w-layer below |
327 |
|
|
kup = 1+MOD(k+1,2) |
328 |
|
|
kDown= 1+MOD(k,2) |
329 |
|
|
|
330 |
|
|
C-- Get temporary terms used by tendency routines |
331 |
|
|
CALL CALC_COMMON_FACTORS ( |
332 |
|
|
I bi,bj,iMin,iMax,jMin,jMax,k, |
333 |
|
|
O xA,yA,uTrans,vTrans,rTrans,maskUp, |
334 |
|
|
I myThid) |
335 |
|
|
|
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 |
adcroft |
1.2 |
CALL GAD_DST3_ADV_R( |
351 |
|
|
& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid) |
352 |
adcroft |
1.1 |
ELSEIF (advectionScheme.EQ.ENUM_DST3_FLUX_LIMIT ) THEN |
353 |
adcroft |
1.2 |
CALL GAD_DST3FL_ADV_R( |
354 |
|
|
& bi,bj,k,deltaTtracer,rTrans,wVel,localTijk,af,myThid) |
355 |
adcroft |
1.1 |
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 |