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jmc |
1.4 |
C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_som_adv_r.F,v 1.3 2008/01/08 19:57:34 jmc Exp $ |
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jmc |
1.1 |
C $Name: $ |
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#include "GAD_OPTIONS.h" |
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CBOP |
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C !ROUTINE: GAD_SOM_ADV_R |
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_SOM_ADV_R( |
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I bi,bj,k, kUp, kDw, |
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I deltaTloc, rTrans, maskUp, |
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U sm_v, sm_o, sm_x, sm_y, sm_z, |
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U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
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U alp, aln, fp_v, fn_v, fp_o, fn_o, |
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U fp_x, fn_x, fp_y, fn_y, fp_z, fn_z, |
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U fp_xx, fn_xx, fp_yy, fn_yy, fp_zz, fn_zz, |
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U fp_xy, fn_xy, fp_xz, fn_xz, fp_yz, fn_yz, |
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O wT, |
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I myThid ) |
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C !DESCRIPTION: |
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C Calculates the area integrated vertical flux due to advection |
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C of a tracer using |
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C-- |
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C Second-Order Moments Advection of tracer in Z-direction |
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C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding |
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C velocity field (U,V,W). Parallel subroutine calculate |
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C advection in the X- and Y- directions. |
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C The moment [Si] are as defined in the text, Sm refers to |
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C the total mass in each grid box |
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C the moments [Fi] are similarly defined and used as temporary |
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C storage for portions of the grid boxes in transit. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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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 "SURFACE.h" |
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c #include "GRID.h" |
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#include "GAD.h" |
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C k :: vertical level |
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C kUp :: index into 2 1/2D array, toggles between 1 and 2 |
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C kDw :: index into 2 1/2D array, toggles between 2 and 1 |
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C rTrans :: vertical volume transport |
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C maskUp :: 2-D array mask for W points |
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C myThid :: my Thread Id. number |
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INTEGER bi,bj,k, kUp, kDw |
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_RL deltaTloc |
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_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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c _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER myThid |
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C !OUTPUT PARAMETERS: ================================================== |
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C sm_v :: volume of grid cell |
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C sm_o :: tracer content of grid cell (zero order moment) |
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C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction |
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C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction |
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C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz |
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C wT :: vertical advective flux |
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_RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL wT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C wLoc :: volume transported (per time step) |
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_RL two, three |
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PARAMETER( two = 2. _d 0 ) |
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PARAMETER( three = 3. _d 0 ) |
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INTEGER i,j |
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INTEGER km1 |
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jmc |
1.3 |
_RL recip_dT |
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jmc |
1.1 |
_RL wLoc, alf1, alf1q, alpmn |
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_RL alfp, alpq, alp1, locTp |
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_RL alfn, alnq, aln1, locTn |
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CEOP |
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jmc |
1.3 |
recip_dT = 0. |
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IF ( deltaTloc.GT.0. _d 0 ) recip_dT = 1.0 _d 0 / deltaTloc |
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jmc |
1.1 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C--- part.1 : calculate flux for all moments |
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jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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jmc |
1.1 |
wLoc = rTrans(i,j)*deltaTloc |
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C-- Flux from (k) to (k-1) when W>0 (i.e., take upper side of box k) |
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C- note: Linear free surface case: this takes care of w_surf advection out |
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C of the domain since for this particular case, rTrans is not masked |
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fp_v (i,j,kUp) = MAX( 0. _d 0, wLoc ) |
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alp (i,j,kUp) = fp_v(i,j,kUp)/sm_v(i,j,k) |
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alpq = alp(i,j,kUp)*alp(i,j,kUp) |
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alp1 = 1. _d 0 - alp(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "p" for positive W |
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fp_o (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_o(i,j, k ) + alp1*sm_z(i,j, k ) |
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& + alp1*(alp1-alp(i,j,kUp))*sm_zz(i,j, k ) |
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& ) |
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fp_z (i,j,kUp) = alpq* |
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& ( sm_z(i,j, k ) + three*alp1*sm_zz(i,j, k ) ) |
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fp_zz(i,j,kUp) = alp(i,j,kUp)*alpq*sm_zz(i,j, k ) |
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fp_x (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_x(i,j, k ) + alp1*sm_xz(i,j, k ) ) |
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fp_y (i,j,kUp) = alp(i,j,kUp)* |
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& ( sm_y(i,j, k ) + alp1*sm_yz(i,j, k ) ) |
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fp_xz(i,j,kUp) = alpq *sm_xz(i,j, k ) |
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fp_yz(i,j,kUp) = alpq *sm_yz(i,j, k ) |
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fp_xx(i,j,kUp) = alp(i,j,kUp)*sm_xx(i,j, k ) |
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fp_yy(i,j,kUp) = alp(i,j,kUp)*sm_yy(i,j, k ) |
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fp_xy(i,j,kUp) = alp(i,j,kUp)*sm_xy(i,j, k ) |
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ENDDO |
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ENDDO |
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IF ( k.EQ.1 ) THEN |
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C-- Linear free surface, calculate w_surf (<0) advection term |
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km1 = 1 |
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jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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jmc |
1.1 |
wLoc = rTrans(i,j)*deltaTloc |
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C- Flux from above to (k) when W<0 , surface case: |
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C take box k=1, assuming zero 1rst & 2nd moment in Z dir. |
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fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) |
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aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
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alnq = aln(i,j,kUp)*aln(i,j,kUp) |
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aln1 = 1. _d 0 - aln(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative W |
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fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) |
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fn_z (i,j,kUp) = 0. _d 0 |
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fn_zz(i,j,kUp) = 0. _d 0 |
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fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) |
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fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) |
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fn_xz(i,j,kUp) = 0. _d 0 |
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fn_yz(i,j,kUp) = 0. _d 0 |
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fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
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fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
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fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
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jmc |
1.3 |
wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
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jmc |
1.1 |
ENDDO |
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ENDDO |
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ELSE |
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C-- Interior only: mask rTrans (if not already done) |
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km1 = k-1 |
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jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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jmc |
1.1 |
wLoc = maskUp(i,j)*rTrans(i,j)*deltaTloc |
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C- Flux from (k-1) to (k) when W<0 (i.e., take lower side of box k-1) |
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fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) |
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aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
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alnq = aln(i,j,kUp)*aln(i,j,kUp) |
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aln1 = 1. _d 0 - aln(i,j,kUp) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative W |
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fn_o (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_o(i,j,km1) - aln1*sm_z(i,j,km1) |
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& + aln1*(aln1-aln(i,j,kUp))*sm_zz(i,j,km1) |
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& ) |
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fn_z (i,j,kUp) = alnq* |
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& ( sm_z(i,j,km1) - three*aln1*sm_zz(i,j,km1) ) |
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fn_zz(i,j,kUp) = aln(i,j,kUp)*alnq*sm_zz(i,j,km1) |
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fn_x (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_x(i,j,km1) - aln1*sm_xz(i,j,km1) ) |
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fn_y (i,j,kUp) = aln(i,j,kUp)* |
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& ( sm_y(i,j,km1) - aln1*sm_yz(i,j,km1) ) |
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fn_xz(i,j,kUp) = alnq *sm_xz(i,j,km1) |
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fn_yz(i,j,kUp) = alnq *sm_yz(i,j,km1) |
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fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
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fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
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fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
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jmc |
1.3 |
wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
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jmc |
1.1 |
ENDDO |
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ENDDO |
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C-- end surface/interior cases for W<0 advective fluxes |
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ENDIF |
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IF ( usingPCoords .AND. k.NE.1 .AND. |
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& .NOT.rigidLid .AND. nonlinFreeSurf.LE.0 ) THEN |
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C-- Linear free surface, but surface not @ k=1 : |
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C calculate w_surf (<0) advection term from current level |
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C moments assuming zero 1rst & 2nd moment in Z dir. ; |
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C and add to previous fluxes; note: identical to resetting fluxes |
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C since previous fluxes are zero in this case (=> let TAF decide) |
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km1 = k |
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jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
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DO i=iMinAdvR,iMaxAdvR |
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jmc |
1.1 |
wLoc = rTrans(i,j)*deltaTloc |
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IF ( k.EQ.ksurfC(i,j,bi,bj) ) THEN |
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C- Flux from (k-1) to (k) when W<0 (special surface case, take box k) |
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fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) |
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aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative W |
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fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) |
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fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) |
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fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) |
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fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) |
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fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) |
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fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) |
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C-- Save zero-order flux: |
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jmc |
1.3 |
wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT |
| 243 |
jmc |
1.1 |
ENDIF |
| 244 |
|
|
ENDDO |
| 245 |
|
|
ENDDO |
| 246 |
|
|
ENDIF |
| 247 |
|
|
|
| 248 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 249 |
|
|
C--- part.2 : re-adjust moments remaining in the box |
| 250 |
|
|
C take off from grid box (k): negative W(kDw) and positive W(kUp) |
| 251 |
jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
| 252 |
|
|
DO i=iMinAdvR,iMaxAdvR |
| 253 |
jmc |
1.1 |
alf1 = 1. _d 0 - aln(i,j,kDw) - alp(i,j,kUp) |
| 254 |
|
|
alf1q = alf1*alf1 |
| 255 |
|
|
alpmn = alp(i,j,kUp) - aln(i,j,kDw) |
| 256 |
|
|
sm_v (i,j,k) = sm_v (i,j,k) - fn_v (i,j,kDw) - fp_v (i,j,kUp) |
| 257 |
|
|
sm_o (i,j,k) = sm_o (i,j,k) - fn_o (i,j,kDw) - fp_o (i,j,kUp) |
| 258 |
|
|
sm_z (i,j,k) = alf1q*( sm_z(i,j,k) - three*alpmn*sm_zz(i,j,k) ) |
| 259 |
|
|
sm_zz(i,j,k) = alf1*alf1q*sm_zz(i,j,k) |
| 260 |
|
|
sm_xz(i,j,k) = alf1q*sm_xz(i,j,k) |
| 261 |
|
|
sm_yz(i,j,k) = alf1q*sm_yz(i,j,k) |
| 262 |
|
|
sm_x (i,j,k) = sm_x (i,j,k) - fn_x (i,j,kDw) - fp_x (i,j,kUp) |
| 263 |
|
|
sm_xx(i,j,k) = sm_xx(i,j,k) - fn_xx(i,j,kDw) - fp_xx(i,j,kUp) |
| 264 |
|
|
sm_y (i,j,k) = sm_y (i,j,k) - fn_y (i,j,kDw) - fp_y (i,j,kUp) |
| 265 |
|
|
sm_yy(i,j,k) = sm_yy(i,j,k) - fn_yy(i,j,kDw) - fp_yy(i,j,kUp) |
| 266 |
|
|
sm_xy(i,j,k) = sm_xy(i,j,k) - fn_xy(i,j,kDw) - fp_xy(i,j,kUp) |
| 267 |
|
|
ENDDO |
| 268 |
|
|
ENDDO |
| 269 |
|
|
|
| 270 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 271 |
|
|
C--- part.3 : Put the temporary moments into appropriate neighboring boxes |
| 272 |
|
|
C add into grid box (k): positive W(kDw) and negative W(kUp) |
| 273 |
jmc |
1.2 |
DO j=jMinAdvR,jMaxAdvR |
| 274 |
|
|
DO i=iMinAdvR,iMaxAdvR |
| 275 |
jmc |
1.1 |
sm_v (i,j,k) = sm_v (i,j,k) + fp_v (i,j,kDw) + fn_v (i,j,kUp) |
| 276 |
|
|
alfp = fp_v(i,j,kDw)/sm_v(i,j,k) |
| 277 |
|
|
alfn = fn_v(i,j,kUp)/sm_v(i,j,k) |
| 278 |
|
|
alf1 = 1. _d 0 - alfp - alfn |
| 279 |
|
|
alp1 = 1. _d 0 - alfp |
| 280 |
|
|
aln1 = 1. _d 0 - alfn |
| 281 |
|
|
alpmn = alfp - alfn |
| 282 |
|
|
locTp = alfp*sm_o(i,j,k) - alp1*fp_o(i,j,kDw) |
| 283 |
|
|
locTn = alfn*sm_o(i,j,k) - aln1*fn_o(i,j,kUp) |
| 284 |
|
|
sm_zz(i,j,k) = alf1*alf1*sm_zz(i,j,k) + alfp*alfp*fp_zz(i,j,kDw) |
| 285 |
|
|
& + alfn*alfn*fn_zz(i,j,kUp) |
| 286 |
|
|
& - 5. _d 0*(-alpmn*alf1*sm_z(i,j,k) + alfp*alp1*fp_z(i,j,kDw) |
| 287 |
|
|
& - alfn*aln1*fn_z(i,j,kUp) |
| 288 |
|
|
& + two*alfp*alfn*sm_o(i,j,k) + (alp1-alfp)*locTp |
| 289 |
|
|
& + (aln1-alfn)*locTn |
| 290 |
|
|
& ) |
| 291 |
|
|
sm_xz(i,j,k) = alf1*sm_xz(i,j,k) + alfp*fp_xz(i,j,kDw) |
| 292 |
|
|
& + alfn*fn_xz(i,j,kUp) |
| 293 |
|
|
& + three*( alpmn*sm_x(i,j,k) - alp1*fp_x(i,j,kDw) |
| 294 |
|
|
& + aln1*fn_x(i,j,kUp) |
| 295 |
|
|
& ) |
| 296 |
|
|
sm_yz(i,j,k) = alf1*sm_yz(i,j,k) + alfp*fp_yz(i,j,kDw) |
| 297 |
|
|
& + alfn*fn_yz(i,j,kUp) |
| 298 |
|
|
& + three*( alpmn*sm_y(i,j,k) - alp1*fp_y(i,j,kDw) |
| 299 |
|
|
& + aln1*fn_y(i,j,kUp) |
| 300 |
|
|
& ) |
| 301 |
|
|
sm_z (i,j,k) = alf1*sm_z(i,j,k) + alfp*fp_z(i,j,kDw) |
| 302 |
|
|
& + alfn*fn_z(i,j,kUp) |
| 303 |
|
|
& + three*( locTp - locTn ) |
| 304 |
|
|
sm_o (i,j,k) = sm_o (i,j,k) + fp_o (i,j,kDw) + fn_o (i,j,kUp) |
| 305 |
|
|
sm_x (i,j,k) = sm_x (i,j,k) + fp_x (i,j,kDw) + fn_x (i,j,kUp) |
| 306 |
|
|
sm_xx(i,j,k) = sm_xx(i,j,k) + fp_xx(i,j,kDw) + fn_xx(i,j,kUp) |
| 307 |
|
|
sm_y (i,j,k) = sm_y (i,j,k) + fp_y (i,j,kDw) + fn_y (i,j,kUp) |
| 308 |
|
|
sm_yy(i,j,k) = sm_yy(i,j,k) + fp_yy(i,j,kDw) + fn_yy(i,j,kUp) |
| 309 |
|
|
sm_xy(i,j,k) = sm_xy(i,j,k) + fp_xy(i,j,kDw) + fn_xy(i,j,kUp) |
| 310 |
|
|
ENDDO |
| 311 |
|
|
ENDDO |
| 312 |
|
|
|
| 313 |
|
|
RETURN |
| 314 |
|
|
END |
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