C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/generic_advdiff/gad_som_adv_r.F,v 1.3 2008/01/08 19:57:34 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_SOM_ADV_R C !INTERFACE: ========================================================== SUBROUTINE GAD_SOM_ADV_R( I bi,bj,k, kUp, kDw, I deltaTloc, rTrans, maskUp, U sm_v, sm_o, sm_x, sm_y, sm_z, U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, U alp, aln, fp_v, fn_v, fp_o, fn_o, U fp_x, fn_x, fp_y, fn_y, fp_z, fn_z, U fp_xx, fn_xx, fp_yy, fn_yy, fp_zz, fn_zz, U fp_xy, fn_xy, fp_xz, fn_xz, fp_yz, fn_yz, O wT, I myThid ) C !DESCRIPTION: C Calculates the area integrated vertical flux due to advection C of a tracer using C-- C Second-Order Moments Advection of tracer in Z-direction C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding C velocity field (U,V,W). Parallel subroutine calculate C advection in the X- and Y- directions. C The moment [Si] are as defined in the text, Sm refers to C the total mass in each grid box C the moments [Fi] are similarly defined and used as temporary C storage for portions of the grid boxes in transit. C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C !USES: =============================================================== IMPLICIT NONE #include "SIZE.h" #include "EEPARAMS.h" #include "PARAMS.h" #include "SURFACE.h" c #include "GRID.h" #include "GAD.h" C !INPUT PARAMETERS: =================================================== C bi,bj :: tile indices C k :: vertical level C kUp :: index into 2 1/2D array, toggles between 1 and 2 C kDw :: index into 2 1/2D array, toggles between 2 and 1 C rTrans :: vertical volume transport C maskUp :: 2-D array mask for W points C myThid :: my Thread Id. number INTEGER bi,bj,k, kUp, kDw _RL deltaTloc _RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) c _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy) INTEGER myThid C !OUTPUT PARAMETERS: ================================================== C sm_v :: volume of grid cell C sm_o :: tracer content of grid cell (zero order moment) C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz C wT :: vertical advective flux _RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) _RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) _RL wT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) #ifdef GAD_ALLOW_SOM_ADVECT C !LOCAL VARIABLES: ==================================================== C i,j :: loop indices C wLoc :: volume transported (per time step) _RL two, three PARAMETER( two = 2. _d 0 ) PARAMETER( three = 3. _d 0 ) INTEGER i,j INTEGER km1 _RL recip_dT _RL wLoc, alf1, alf1q, alpmn _RL alfp, alpq, alp1, locTp _RL alfn, alnq, aln1, locTn CEOP recip_dT = 0. IF ( deltaTloc.GT.0. _d 0 ) recip_dT = 1.0 _d 0 / deltaTloc C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.1 : calculate flux for all moments DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR wLoc = rTrans(i,j)*deltaTloc C-- Flux from (k) to (k-1) when W>0 (i.e., take upper side of box k) C- note: Linear free surface case: this takes care of w_surf advection out C of the domain since for this particular case, rTrans is not masked fp_v (i,j,kUp) = MAX( 0. _d 0, wLoc ) alp (i,j,kUp) = fp_v(i,j,kUp)/sm_v(i,j,k) alpq = alp(i,j,kUp)*alp(i,j,kUp) alp1 = 1. _d 0 - alp(i,j,kUp) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "p" for positive W fp_o (i,j,kUp) = alp(i,j,kUp)* & ( sm_o(i,j, k ) + alp1*sm_z(i,j, k ) & + alp1*(alp1-alp(i,j,kUp))*sm_zz(i,j, k ) & ) fp_z (i,j,kUp) = alpq* & ( sm_z(i,j, k ) + three*alp1*sm_zz(i,j, k ) ) fp_zz(i,j,kUp) = alp(i,j,kUp)*alpq*sm_zz(i,j, k ) fp_x (i,j,kUp) = alp(i,j,kUp)* & ( sm_x(i,j, k ) + alp1*sm_xz(i,j, k ) ) fp_y (i,j,kUp) = alp(i,j,kUp)* & ( sm_y(i,j, k ) + alp1*sm_yz(i,j, k ) ) fp_xz(i,j,kUp) = alpq *sm_xz(i,j, k ) fp_yz(i,j,kUp) = alpq *sm_yz(i,j, k ) fp_xx(i,j,kUp) = alp(i,j,kUp)*sm_xx(i,j, k ) fp_yy(i,j,kUp) = alp(i,j,kUp)*sm_yy(i,j, k ) fp_xy(i,j,kUp) = alp(i,j,kUp)*sm_xy(i,j, k ) ENDDO ENDDO IF ( k.EQ.1 ) THEN C-- Linear free surface, calculate w_surf (<0) advection term km1 = 1 DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR wLoc = rTrans(i,j)*deltaTloc C- Flux from above to (k) when W<0 , surface case: C take box k=1, assuming zero 1rst & 2nd moment in Z dir. fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) alnq = aln(i,j,kUp)*aln(i,j,kUp) aln1 = 1. _d 0 - aln(i,j,kUp) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "n" for negative W fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) fn_z (i,j,kUp) = 0. _d 0 fn_zz(i,j,kUp) = 0. _d 0 fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) fn_xz(i,j,kUp) = 0. _d 0 fn_yz(i,j,kUp) = 0. _d 0 fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) C-- Save zero-order flux: wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT ENDDO ENDDO ELSE C-- Interior only: mask rTrans (if not already done) km1 = k-1 DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR wLoc = maskUp(i,j)*rTrans(i,j)*deltaTloc C- Flux from (k-1) to (k) when W<0 (i.e., take lower side of box k-1) fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) alnq = aln(i,j,kUp)*aln(i,j,kUp) aln1 = 1. _d 0 - aln(i,j,kUp) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "n" for negative W fn_o (i,j,kUp) = aln(i,j,kUp)* & ( sm_o(i,j,km1) - aln1*sm_z(i,j,km1) & + aln1*(aln1-aln(i,j,kUp))*sm_zz(i,j,km1) & ) fn_z (i,j,kUp) = alnq* & ( sm_z(i,j,km1) - three*aln1*sm_zz(i,j,km1) ) fn_zz(i,j,kUp) = aln(i,j,kUp)*alnq*sm_zz(i,j,km1) fn_x (i,j,kUp) = aln(i,j,kUp)* & ( sm_x(i,j,km1) - aln1*sm_xz(i,j,km1) ) fn_y (i,j,kUp) = aln(i,j,kUp)* & ( sm_y(i,j,km1) - aln1*sm_yz(i,j,km1) ) fn_xz(i,j,kUp) = alnq *sm_xz(i,j,km1) fn_yz(i,j,kUp) = alnq *sm_yz(i,j,km1) fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) C-- Save zero-order flux: wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT ENDDO ENDDO C-- end surface/interior cases for W<0 advective fluxes ENDIF IF ( usingPCoords .AND. k.NE.1 .AND. & .NOT.rigidLid .AND. nonlinFreeSurf.LE.0 ) THEN C-- Linear free surface, but surface not @ k=1 : C calculate w_surf (<0) advection term from current level C moments assuming zero 1rst & 2nd moment in Z dir. ; C and add to previous fluxes; note: identical to resetting fluxes C since previous fluxes are zero in this case (=> let TAF decide) km1 = k DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR wLoc = rTrans(i,j)*deltaTloc IF ( k.EQ.ksurfC(i,j,bi,bj) ) THEN C- Flux from (k-1) to (k) when W<0 (special surface case, take box k) fn_v (i,j,kUp) = MAX( 0. _d 0, -wLoc ) aln (i,j,kUp) = fn_v(i,j,kUp)/sm_v(i,j,km1) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "n" for negative W fn_o (i,j,kUp) = aln(i,j,kUp)*sm_o(i,j,km1) fn_x (i,j,kUp) = aln(i,j,kUp)*sm_x(i,j,km1) fn_y (i,j,kUp) = aln(i,j,kUp)*sm_y(i,j,km1) fn_xx(i,j,kUp) = aln(i,j,kUp)*sm_xx(i,j,km1) fn_yy(i,j,kUp) = aln(i,j,kUp)*sm_yy(i,j,km1) fn_xy(i,j,kUp) = aln(i,j,kUp)*sm_xy(i,j,km1) C-- Save zero-order flux: wT(i,j) = ( fp_o(i,j,kUp) - fn_o(i,j,kUp) )*recip_dT ENDIF ENDDO ENDDO ENDIF C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.2 : re-adjust moments remaining in the box C take off from grid box (k): negative W(kDw) and positive W(kUp) DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR alf1 = 1. _d 0 - aln(i,j,kDw) - alp(i,j,kUp) alf1q = alf1*alf1 alpmn = alp(i,j,kUp) - aln(i,j,kDw) sm_v (i,j,k) = sm_v (i,j,k) - fn_v (i,j,kDw) - fp_v (i,j,kUp) sm_o (i,j,k) = sm_o (i,j,k) - fn_o (i,j,kDw) - fp_o (i,j,kUp) sm_z (i,j,k) = alf1q*( sm_z(i,j,k) - three*alpmn*sm_zz(i,j,k) ) sm_zz(i,j,k) = alf1*alf1q*sm_zz(i,j,k) sm_xz(i,j,k) = alf1q*sm_xz(i,j,k) sm_yz(i,j,k) = alf1q*sm_yz(i,j,k) sm_x (i,j,k) = sm_x (i,j,k) - fn_x (i,j,kDw) - fp_x (i,j,kUp) sm_xx(i,j,k) = sm_xx(i,j,k) - fn_xx(i,j,kDw) - fp_xx(i,j,kUp) sm_y (i,j,k) = sm_y (i,j,k) - fn_y (i,j,kDw) - fp_y (i,j,kUp) sm_yy(i,j,k) = sm_yy(i,j,k) - fn_yy(i,j,kDw) - fp_yy(i,j,kUp) sm_xy(i,j,k) = sm_xy(i,j,k) - fn_xy(i,j,kDw) - fp_xy(i,j,kUp) ENDDO ENDDO C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.3 : Put the temporary moments into appropriate neighboring boxes C add into grid box (k): positive W(kDw) and negative W(kUp) DO j=jMinAdvR,jMaxAdvR DO i=iMinAdvR,iMaxAdvR sm_v (i,j,k) = sm_v (i,j,k) + fp_v (i,j,kDw) + fn_v (i,j,kUp) alfp = fp_v(i,j,kDw)/sm_v(i,j,k) alfn = fn_v(i,j,kUp)/sm_v(i,j,k) alf1 = 1. _d 0 - alfp - alfn alp1 = 1. _d 0 - alfp aln1 = 1. _d 0 - alfn alpmn = alfp - alfn locTp = alfp*sm_o(i,j,k) - alp1*fp_o(i,j,kDw) locTn = alfn*sm_o(i,j,k) - aln1*fn_o(i,j,kUp) sm_zz(i,j,k) = alf1*alf1*sm_zz(i,j,k) + alfp*alfp*fp_zz(i,j,kDw) & + alfn*alfn*fn_zz(i,j,kUp) & - 5. _d 0*(-alpmn*alf1*sm_z(i,j,k) + alfp*alp1*fp_z(i,j,kDw) & - alfn*aln1*fn_z(i,j,kUp) & + two*alfp*alfn*sm_o(i,j,k) + (alp1-alfp)*locTp & + (aln1-alfn)*locTn & ) sm_xz(i,j,k) = alf1*sm_xz(i,j,k) + alfp*fp_xz(i,j,kDw) & + alfn*fn_xz(i,j,kUp) & + three*( alpmn*sm_x(i,j,k) - alp1*fp_x(i,j,kDw) & + aln1*fn_x(i,j,kUp) & ) sm_yz(i,j,k) = alf1*sm_yz(i,j,k) + alfp*fp_yz(i,j,kDw) & + alfn*fn_yz(i,j,kUp) & + three*( alpmn*sm_y(i,j,k) - alp1*fp_y(i,j,kDw) & + aln1*fn_y(i,j,kUp) & ) sm_z (i,j,k) = alf1*sm_z(i,j,k) + alfp*fp_z(i,j,kDw) & + alfn*fn_z(i,j,kUp) & + three*( locTp - locTn ) sm_o (i,j,k) = sm_o (i,j,k) + fp_o (i,j,kDw) + fn_o (i,j,kUp) sm_x (i,j,k) = sm_x (i,j,k) + fp_x (i,j,kDw) + fn_x (i,j,kUp) sm_xx(i,j,k) = sm_xx(i,j,k) + fp_xx(i,j,kDw) + fn_xx(i,j,kUp) sm_y (i,j,k) = sm_y (i,j,k) + fp_y (i,j,kDw) + fn_y (i,j,kUp) sm_yy(i,j,k) = sm_yy(i,j,k) + fp_yy(i,j,kDw) + fn_yy(i,j,kUp) sm_xy(i,j,k) = sm_xy(i,j,k) + fp_xy(i,j,kDw) + fn_xy(i,j,kUp) ENDDO ENDDO #endif /* GAD_ALLOW_SOM_ADVECT */ RETURN END