#include "cppdefs.h" MODULE ad_v2dbc_mod #ifdef ADJOINT ! !svn $Id: ad_v2dbc_im.F 352 2009-05-29 20:57:39Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2009 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt ! !======================================================================= ! ! ! This subroutine sets adjoint lateral boundary conditions for ! ! vertically integrated V-velocity. It updates the specified ! ! "kout" index. ! ! ! ! BASIC STATE variables needed: zeta ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: ad_v2dbc, ad_v2dbc_tile CONTAINS ! !*********************************************************************** SUBROUTINE ad_v2dbc (ng, tile, kout) !*********************************************************************** ! USE mod_param USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, kout ! ! Local variable declarations. ! # include "tile.h" ! CALL ad_v2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs(ng), kstp(ng), kout, & & OCEAN(ng) % ubar, & & OCEAN(ng) % vbar, & & OCEAN(ng) % zeta, & & OCEAN(ng) % ad_ubar, & & OCEAN(ng) % ad_vbar, & & OCEAN(ng) % ad_zeta) RETURN END SUBROUTINE ad_v2dbc ! !*********************************************************************** SUBROUTINE ad_v2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, kout, & & ubar, vbar, zeta, & & ad_ubar, ad_vbar, ad_zeta) !*********************************************************************** ! USE mod_param USE mod_boundary USE mod_forces USE mod_grid USE mod_ncparam USE mod_scalars ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: krhs, kstp, kout ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: ubar(LBi:,LBj:,:) real(r8), intent(in) :: vbar(LBi:,LBj:,:) real(r8), intent(in) :: zeta(LBi:,LBj:,:) real(r8), intent(inout) :: ad_ubar(LBi:,LBj:,:) real(r8), intent(inout) :: ad_vbar(LBi:,LBj:,:) real(r8), intent(inout) :: ad_zeta(LBi:,LBj:,:) # else real(r8), intent(in) :: ubar(LBi:UBi,LBj:UBj,3) real(r8), intent(in) :: vbar(LBi:UBi,LBj:UBj,3) real(r8), intent(in) :: zeta(LBi:UBi,LBj:UBj,3) real(r8), intent(inout) :: ad_ubar(LBi:UBi,LBj:UBj,3) real(r8), intent(inout) :: ad_vbar(LBi:UBi,LBj:UBj,3) real(r8), intent(inout) :: ad_zeta(LBi:UBi,LBj:UBj,3) # endif ! ! Local variable declarations. ! integer :: i, j, know real(r8) :: Ce, Cx real(r8) :: bry_pgr, bry_cor, bry_str, bry_val real(r8) :: cff, cff1, cff2, dt2d, tau real(r8) :: ad_Ce, ad_Cx real(r8) :: ad_bry_pgr, ad_bry_cor, ad_bry_str, ad_bry_val real(r8) :: ad_cff, ad_cff1, ad_cff2 real(r8) :: adfac real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_grad # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Ce=0.0_r8 ad_Cx=0.0_r8 ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_bry_pgr=0.0_r8 ad_bry_cor=0.0_r8 ad_bry_str=0.0_r8 ad_bry_val=0.0_r8 ad_grad(LBi:UBi,LBj:UBj)=0.0_r8 ! !----------------------------------------------------------------------- ! Set time-indices !----------------------------------------------------------------------- ! IF (FIRST_2D_STEP) THEN know=krhs dt2d=dtfast(ng) ELSE IF (PREDICTOR_2D_STEP(ng)) THEN know=krhs dt2d=2.0_r8*dtfast(ng) ELSE know=kstp dt2d=dtfast(ng) END IF # if defined WET_DRY_NOT_YET ! !----------------------------------------------------------------------- ! Impose wetting and drying conditions. ! ! HGA: need ADM code here for the NLM code below. !----------------------------------------------------------------------- ! # ifndef EW_PERIODIC IF (WESTERN_EDGE) THEN DO j=JstrV,Jend !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Istr-1,j))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Istr-1,j,kout))* & !> & GRID(ng)%vmask_wet(Istr-1,j) !> cff=0.5_r8*GRID(ng)%vmask_wet(Istr-1,j)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Istr,j,kout)=vbar(Istr,j,kout)*cff END DO END IF IF (EASTERN_EDGE) THEN DO j=JstrV,Jend !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Iend+1,j))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Iend+1,j,kout))* & !> & GRID(ng)%vmask_wet(Iend+1,j) !> cff=0.5_r8*GRID(ng)%vmask_wet(Iend+1,j)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)*cff END DO END IF # endif # ifndef NS_PERIODIC IF (SOUTHERN_EDGE) THEN DO i=Istr,Iend !> cff1=ABS(ABS(GRID(ng)%vmask_wet(i,Jstr))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(i,Jstr,kout))* & !> & GRID(ng)%vmask_wet(i,Jstr) !> cff=0.5_r8*GRID(ng)%vmask_wet(i,Jstr)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(i,Jstr,kout)=vbar(i,Jstr,kout)*cff END DO END IF IF (NORTHERN_EDGE) THEN DO i=Istr,Iend !> cff1=ABS(ABS(GRID(ng)%vmask_wet(i,Jend+1))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(i,Jend+1,kout))* & !> & GRID(ng)%vmask_wet(i,Jend+1) !> cff=0.5_r8*GRID(ng)%vmask_wet(i,Jend+1)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)*cff END DO END IF # endif # if !defined EW_PERIODIC && !defined NS_PERIODIC IF ((SOUTHERN_EDGE).and.(WESTERN_EDGE)) THEN !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Istr-1,Jstr))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Istr-1,Jstr,kout))* & !> & GRID(ng)%vmask_wet(Istr-1,Jstr) !> cff=0.5_r8*GRID(ng)%vmask_wet(Istr-1,Jstr)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Istr-1,Jstr,kout)=vbar(Istr-1,Jstr,kout)*cff END IF IF ((SOUTHERN_EDGE).and.(EASTERN_EDGE)) THEN !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Iend+1,Jstr))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Iend+1,Jstr,kout))* & !> & GRID(ng)%vmask_wet(Iend+1,Jstr) !> cff=0.5_r8*GRID(ng)%vmask_wet(Iend+1,Jstr)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Iend+1,Jstr,kout)=vbar(Iend+1,Jstr,kout)*cff END IF IF ((NORTHERN_EDGE).and.(WESTERN_EDGE)) THEN !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Istr-1,Jend+1))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Istr-1,Jend+1,kout))* & !> & GRID(ng)%vmask_wet(Istr-1,Jend+1) !> cff=0.5_r8*GRID(ng)%vmask_wet(Istr-1,Jend+1)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Istr-1,Jend+1,kout)=vbar(Istr-1,Jend+1,kout)*cff END IF IF ((NORTHERN_EDGE).and.(EASTERN_EDGE)) THEN !> cff1=ABS(ABS(GRID(ng)%vmask_wet(Iend+1,Jend+1))-1.0_r8) !> cff2=0.5_r8+DSIGN(0.5_r8,vbar(Iend+1,Jend+1,kout))* & !> & GRID(ng)%vmask_wet(Iend+1,Jend+1) !> cff=0.5_r8*GRID(ng)%vmask_wet(Iend+1,Jend+1)*cff1+ & !> & cff2*(1.0_r8-cff1) !> vbar(Iend+1,Jend+1,kout)=vbar(Iend+1,Jend+1,kout)*cff END IF # endif # endif # if !defined EW_PERIODIC && !defined NS_PERIODIC ! !----------------------------------------------------------------------- ! Boundary corners. !----------------------------------------------------------------------- ! IF ((NORTHERN_EDGE).and.(EASTERN_EDGE)) THEN !> tl_vbar(Iend+1,Jend+1,kout)=0.5_r8* & !> & (tl_vbar(Iend+1,Jend ,kout)+ & !> & tl_vbar(Iend ,Jend+1,kout)) !> adfac=0.5_r8*ad_vbar(Iend+1,Jend+1,kout) ad_vbar(Iend+1,Jend ,kout)=ad_vbar(Iend+1,Jend ,kout)+adfac ad_vbar(Iend ,Jend+1,kout)=ad_vbar(Iend ,Jend+1,kout)+adfac ad_vbar(Iend+1,Jend+1,kout)=0.0_r8 END IF IF ((NORTHERN_EDGE).and.(WESTERN_EDGE)) THEN !> tl_vbar(Istr-1,Jend+1,kout)=0.5_r8* & !> & (tl_vbar(Istr-1,Jend ,kout)+ & !> & tl_vbar(Istr ,Jend+1,kout)) !> adfac=0.5_r8*ad_vbar(Istr-1,Jend+1,kout) ad_vbar(Istr-1,Jend ,kout)=ad_vbar(Istr-1,Jend ,kout)+adfac ad_vbar(Istr ,Jend+1,kout)=ad_vbar(Istr ,Jend+1,kout)+adfac ad_vbar(Istr-1,Jend+1,kout)=0.0_r8 END IF IF ((SOUTHERN_EDGE).and.(EASTERN_EDGE)) THEN !> tl_vbar(Iend+1,Jstr,kout)=0.5_r8* & !> & (tl_vbar(Iend ,Jstr ,kout)+ & !> & tl_vbar(Iend+1,Jstr+1,kout)) !> adfac=0.5_r8*ad_vbar(Iend+1,Jstr,kout) ad_vbar(Iend ,Jstr ,kout)=ad_vbar(Iend ,Jstr ,kout)+adfac ad_vbar(Iend+1,Jstr+1,kout)=ad_vbar(Iend+1,Jstr+1,kout)+adfac ad_vbar(Iend+1,Jstr ,kout)=0.0_r8 END IF IF ((SOUTHERN_EDGE).and.(WESTERN_EDGE)) THEN !> tl_vbar(Istr-1,Jstr,kout)=0.5_r8* & !> & (tl_vbar(Istr ,Jstr ,kout)+ & !> & tl_vbar(Istr-1,Jstr+1,kout)) !> adfac=0.5_r8*ad_vbar(Istr-1,Jstr,kout) ad_vbar(Istr ,Jstr ,kout)=ad_vbar(Istr ,Jstr ,kout)+adfac ad_vbar(Istr-1,Jstr+1,kout)=ad_vbar(Istr-1,Jstr+1,kout)+adfac ad_vbar(Istr-1,Jstr ,kout)=0.0_r8 END IF # endif # ifndef EW_PERIODIC ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the eastern edge. !----------------------------------------------------------------------- ! IF (EASTERN_EDGE) THEN # if defined EAST_M2RADIATION_NOT_YET IF (iic(ng).ne.0) THEN ! ! Eastern edge, implicit upstream radiation condition. ! DO j=JstrV,Jend # ifdef EAST_M2NUDGING IF (BOUNDARY(ng)%vbar_east_Cx(j).eq.0.0_r8) THEN tau=M2obc_in(ng,ieast) ELSE tau=M2obc_out(ng,ieast) END IF tau=tau*dt2d # endif Cx=BOUNDARY(ng)%vbar_east_Cx(j) # ifdef RADIATION_2D Ce=BOUNDARY(ng)%vbar_east_Ce(j) # else Ce=0.0_r8 # endif cff=BOUNDARY(ng)%vbar_east_C2(j) # ifdef MASKING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)* & !> & GRID(ng)%vmask(Iend+1,j) !> ad_vbar(Iend+1,j,kout)=ad_vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif # ifdef EAST_M2NUDGING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)- & !> & tau*tl_vbar(Iend+1,j,know) !> ad_vbar(Iend+1 ,j,know)=ad_vbar(Iend+1 ,j,know)- & & tau*ad_vbar(Iend+1,j,kout) # endif !> tl_vbar(Iend+1,j,kout)=(cff*tl_vbar(Iend+1,j,know)+ & !> & Cx *tl_vbar(Iend ,j,kout)- & !> & MAX(Ce,0.0_r8)*tl_grad(Iend+1,j-1)- & !> & MIN(Ce,0.0_r8)*tl_grad(Iend+1,j ))/& !> & (cff+Cx) !> adfac=ad_vbar(Iend+1,j,kout)/(cff+Cx) ad_grad(Iend+1,j-1)=ad_grad(Iend+1,j-1)-MAX(Ce,0.0_r8)*adfac ad_grad(Iend+1,j )=ad_grad(Iend+1,j )-MIN(Ce,0.0_r8)*adfac ad_vbar(Iend ,j,kout)=ad_vbar(Iend ,j,kout)+Cx* adfac ad_vbar(Iend+1,j,know)=ad_vbar(Iend+1,j,know)+cff*adfac ad_vbar(Iend+1,j,kout)=0.0_r8 END DO END IF # elif defined EAST_M2FLATHER || defined EAST_M2REDUCED ! ! Eastern edge, Chapman boundary condition. ! DO j=JstrV,Jend cff=dt2d*0.5_r8*(GRID(ng)%pm(Iend,j-1)+ & & GRID(ng)%pm(Iend,j )) cff1=SQRT(g*0.5_r8*(GRID(ng)%h(Iend,j-1)+ & & zeta(Iend,j-1,know)+ & & GRID(ng)%h(Iend,j )+ & & zeta(Iend,j ,know))) Cx=cff*cff1 cff2=1.0_r8/(1.0_r8+Cx) # ifdef MASKING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)* & !> & GRID(ng)%vmask(Iend+1,j) !> ad_vbar(Iend+1,j,kout)=ad_vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif !> tl_vbar(Iend+1,j,kout)=tl_cff2*(vbar(Iend+1,j,know)+ & !> & Cx*vbar(Iend,j,kout))+ & !> & cff2*(tl_vbar(Iend+1,j,know)+ & !> & tl_Cx*vbar(Iend,j,kout)+ & !> & Cx*tl_vbar(Iend,j,kout)) !> adfac=cff2*ad_vbar(Iend+1,j,kout) ad_vbar(Iend ,j,kout)=ad_vbar(Iend ,j,kout)+Cx*adfac ad_vbar(Iend+1,j,know)=ad_vbar(Iend+1,j,know)+adfac ad_Cx=ad_Cx+vbar(Iend,j,kout)*adfac ad_cff2=ad_cff2+(vbar(Iend+1,j,know)+ & & Cx*vbar(Iend,j,kout))*ad_vbar(Iend+1,j,kout) ad_vbar(Iend+1,j,kout)=0.0_r8 !> tl_cff2=-cff2*cff2*tl_Cx !> ad_Cx=ad_Cx-cff2*cff2*ad_cff2 ad_cff2=0.0_r8 !> tl_Cx=cff*tl_cff1 !> ad_cff1=ad_cff1+cff*ad_Cx ad_Cx=0.0_r8 !> tl_cff1=0.25_r8*g*(GRID(ng)%tl_h(Iend,j-1)+ & !> & tl_zeta(Iend,j-1,know)+ & !> & GRID(ng)%tl_h(Iend,j )+ & !> & tl_zeta(Iend,j ,know))/cff1 !> adfac=0.25_r8*g*ad_cff1/cff1 GRID(ng)%ad_h(Iend,j-1)=GRID(ng)%ad_h(Iend,j-1)+adfac GRID(ng)%ad_h(Iend,j )=GRID(ng)%ad_h(Iend,j )+adfac ad_zeta(Iend,j-1,know)=ad_zeta(Iend,j-1,know)+adfac ad_zeta(Iend,j ,know)=ad_zeta(Iend,j ,know)+adfac ad_cff1=0.0_r8 END DO # elif defined EAST_M2CLAMPED ! ! Eastern edge, clamped boundary condition. ! DO j=JstrV,Jend # ifdef MASKING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)* & !> & GRID(ng)%vmask(Iend+1,j) !> ad_vbar(Iend+1,j,kout)=ad_vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(ieast,isVbar,ng)) THEN !> tl_vbar(Iend+1,j,kout)=BOUNDARY(ng)%tl_vbar_east(j) !> BOUNDARY(ng)%ad_vbar_east(j)=BOUNDARY(ng)%ad_vbar_east(j)+ & & ad_vbar(Iend+1,j,kout) ad_vbar(Iend+1,j,kout)=0.0_r8 ELSE !> tl_vbar(Iend+1,j,kout)=0.0_r8 !> ad_vbar(Iend+1,j,kout)=0.0_r8 END IF # else !> tl_vbar(Iend+1,j,kout)=0.0_r8 !> ad_vbar(Iend+1,j,kout)=0.0_r8 # endif END DO # elif defined EAST_M2GRADIENT ! ! Eastern edge, gradient boundary condition. ! DO j=JstrV,Jend # ifdef MASKING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)* & !> & GRID(ng)%vmask(Iend+1,j) !> ad_vbar(Iend+1,j,kout)=ad_vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend,j,kout) !> ad_vbar(Iend ,j,kout)=ad_vbar(Iend,j,kout)+ & & ad_vbar(Iend+1,j,kout) ad_vbar(Iend+1,j,kout)=0.0_r8 END DO # else ! ! Eastern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef NS_PERIODIC # define J_RANGE JstrV,Jend # else # define J_RANGE Jstr,JendR # endif DO j=J_RANGE # ifdef MASKING !> tl_vbar(Iend+1,j,kout)=tl_vbar(Iend+1,j,kout)* & !> & GRID(ng)%vmask(Iend+1,j) !> ad_vbar(Iend+1,j,kout)=ad_vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif !> tl_vbar(Iend+1,j,kout)=gamma2(ng)*tl_vbar(Iend,j,kout) !> ad_vbar(Iend ,j,kout)=ad_vbar(Iend,j,kout)+ & & gamma2(ng)*ad_vbar(Iend+1,j,kout) ad_vbar(Iend+1,j,kout)=0.0_r8 END DO # undef J_RANGE # endif END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the western edge. !----------------------------------------------------------------------- ! IF (WESTERN_EDGE) THEN # if defined WEST_M2RADIATION_NOT_YET IF (iic(ng).ne.0) THEN ! ! Western edge, implicit upstream radiation condition. ! DO j=JstrV,Jend # ifdef WEST_M2NUDGING IF (BOUNDARY(ng)%vbar_west_Cx(j).eq.0.0_r8) THEN tau=M2obc_in(ng,iwest) ELSE tau=M2obc_out(ng,iwest) END IF tau=tau*dt2d # endif Cx=BOUNDARY(ng)%vbar_west_Cx(j) # ifdef RADIATION_2D Ce=BOUNDARY(ng)%vbar_west_Ce(j) # else Ce=0.0_r8 # endif cff=BOUNDARY(ng)%vbar_west_C2(j) # ifdef MASKING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)* & !> & GRID(ng)%vmask(Istr-1,j) !> ad_vbar(Istr-1,j,kout)=ad_vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif # ifdef WEST_M2NUDGING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)- & !> & tau*tl_vbar(1,j,know) !> ad_vbar(Istr,j,know)=ad_vbar(Istr,j,know)- & & tau*ad_vbar(Istr-1,j,kout) # endif !> tl_vbar(Istr-1,j,kout)=(cff*tl_vbar(Istr-1,j,know)+ & !> & Cx *tl_vbar(1,j,kout)- & !> & MAX(Ce,0.0_r8)*tl_grad(Istr-1,j-1)- & !> & MIN(Ce,0.0_r8)*tl_grad(Istr-1,j ))/& !> & (cff+Cx) !> adfac=ad_vbar(Istr-1,j,kout)/(cff+Cx) ad_grad(Istr-1,j-1)=ad_grad(Istr-1,j-1)-MAX(Ce,0.0_r8)*adfac ad_grad(Istr-1,j )=ad_grad(Istr-1,j )-MIN(Ce,0.0_r8)*adfac ad_vbar(Istr-1,j,know)=ad_vbar(Istr-1,j,know)+cff*adfac ad_vbar(Istr ,j,kout)=ad_vbar(Istr ,j,kout)+Cx *adfac ad_vbar(Istr-1,j,kout)=0.0_r8 END DO END IF # elif defined WEST_M2FLATHER || defined WEST_M2REDUCED ! ! Western edge, Chapman boundary condition. ! DO j=JstrV,Jend cff=dt2d*0.5_r8*(GRID(ng)%pm(Istr,j-1)+ & & GRID(ng)%pm(Istr,j )) cff1=SQRT(g*0.5_r8*(GRID(ng)%h(Istr,j-1)+ & & zeta(Istr,j-1,know)+ & & GRID(ng)%h(Istr,j )+ & & zeta(Istr,j ,know))) Cx=cff*cff1 cff2=1.0_r8/(1.0_r8+Cx) # ifdef MASKING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)* & !> & GRID(ng)%vmask(Istr-1,j) !> ad_vbar(Istr-1,j,kout)=ad_vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif !> tl_vbar(Istr-1,j,kout)=tl_cff2*(vbar(Istr-1,j,know)+ & !> & Cx*vbar(Istr,j,kout))+ & !> & cff2*(tl_vbar(Istr-1,j,know)+ & !> & tl_Cx*vbar(Istr,j,kout)+ & !> & Cx*tl_vbar(Istr,j,kout)) !> adfac=cff2*ad_vbar(Istr-1,j,kout) ad_vbar(Istr-1,j,know)=ad_vbar(Istr-1,j,know)+adfac ad_vbar(Istr ,j,kout)=ad_vbar(Istr ,j,kout)+Cx*adfac ad_Cx=ad_Cx+vbar(Istr,j,kout)*adfac ad_cff2=ad_cff2+(vbar(Istr-1,j,know)+ & & Cx*vbar(Istr,j,kout))*ad_vbar(Istr-1,j,kout) ad_vbar(Istr-1,j,kout)=0.0_r8 !> tl_cff2=-cff2*cff2*tl_Cx !> ad_Cx=ad_Cx-cff2*cff2*ad_cff2 ad_cff2=0.0_r8 !> tl_Cx=cff*tl_cff1 !> ad_cff1=ad_cff1+cff*ad_Cx ad_Cx=0.0_r8 !> tl_cff1=0.25_r8*g*(GRID(ng)%tl_h(Istr,j-1)+ & !> & tl_zeta(Istr,j-1,know)+ & !> & GRID(ng)%tl_h(Istr,j )+ & !> & tl_zeta(Istr,j ,know))/cff1 !> adfac=0.25_r8*g*ad_cff1/cff1 GRID(ng)%ad_h(Istr,j-1)=GRID(ng)%ad_h(Istr,j-1)+adfac GRID(ng)%ad_h(Istr,j )=GRID(ng)%ad_h(Istr,j )+adfac ad_zeta(Istr,j-1,know)=ad_zeta(Istr,j-1,know)+adfac ad_zeta(Istr,j ,know)=ad_zeta(Istr,j ,know)+adfac ad_cff1=0.0_r8 END DO # elif defined WEST_M2CLAMPED ! ! Western edge, clamped boundary condition. ! DO j=JstrV,Jend # ifdef MASKING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)* & !> & GRID(ng)%vmask(Istr-1,j) !> ad_vbar(Istr-1,j,kout)=ad_vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(iwest,isVbar,ng)) THEN !> tl_vbar(Istr-1,j,kout)=BOUNDARY(ng)%tl_vbar_west(j) !> BOUNDARY(ng)%ad_vbar_west(j)=BOUNDARY(ng)%ad_vbar_west(j)+ & & ad_vbar(Istr-1,j,kout) ad_vbar(Istr-1,j,kout)=0.0_r8 ELSE !> tl_vbar(Istr-1,j,kout)=0.0_r8 !> ad_vbar(Istr-1,j,kout)=0.0_r8 END IF # else !> tl_vbar(Istr-1,j,kout)=0.0_r8 !> ad_vbar(Istr-1,j,kout)=0.0_r8 # endif END DO # elif defined WEST_M2GRADIENT ! ! Western edge, gradient boundary condition. ! DO j=JstrV,Jend # ifdef MASKING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)* & !> & GRID(ng)%vmask(Istr-1,j) !> ad_vbar(Istr-1,j,kout)=ad_vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr,j,kout) !> ad_vbar(Istr ,j,kout)=ad_vbar(Istr,j,kout)+ & & ad_vbar(Istr-1,j,kout) ad_vbar(Istr-1,j,kout)=0.0_r8 END DO # else ! ! Western edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef NS_PERIODIC # define J_RANGE JstrV,Jend # else # define J_RANGE Jstr,JendR # endif DO j=J_RANGE # ifdef MASKING !> tl_vbar(Istr-1,j,kout)=tl_vbar(Istr-1,j,kout)* & !> & GRID(ng)%vmask(Istr-1,j) !> ad_vbar(Istr-1,j,kout)=ad_vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif !> tl_vbar(Istr-1,j,kout)=gamma2(ng)*tl_vbar(Istr,j,kout) !> ad_vbar(Istr ,j,kout)=ad_vbar(Istr,j,kout)+ & & gamma2(ng)*ad_vbar(Istr-1,j,kout) ad_vbar(Istr-1,j,kout)=0.0_r8 END DO # undef J_RANGE # endif END IF # endif # ifndef NS_PERIODIC ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the northern edge. !----------------------------------------------------------------------- ! IF (NORTHERN_EDGE) THEN # if defined NORTH_M2RADIATION_NOT_YET IF (iic(ng).ne.0) THEN ! ! Northern edge, implicit upstream radiation condition. ! DO i=Istr,Iend # ifdef NORTH_M2NUDGING IF (BOUNDARY(ng)%vbar_north_Ce(i).eq.0.0_r8) THEN tau=M2obc_in(ng,inorth) ELSE tau=M2obc_out(ng,inorth) END IF tau=tau*dt2d # endif # ifdef RADIATION_2D Cx=BOUNDARY(ng)%vbar_north_Cx(i) # else Cx=0.0_r8 # endif Ce=BOUNDARY(ng)%vbar_north_Ce(i) cff=BOUNDARY(ng)%vbar_north_C2(i) # ifdef MASKING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)* & !> & GRID(ng)%vmask(i,Jend+1) !> ad_vbar(i,Jend+1,kout)=ad_vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif # ifdef NORTH_M2NUDGING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)- & !> & tau*tl_vbar(i,Jend+1,know) !> ad_vbar(i,Jend+1 ,know)=ad_vbar(i,Jend+1 ,know)- & & tau*ad_vbar(i,Jend+1,kout) # endif !> tl_vbar(i,Jend+1,kout)=(cff*tl_vbar(i,Jend+1,know)+ & !> & Ce *tl_vbar(i,Jend ,kout)- & !> & MAX(Cx,0.0_r8)*tl_grad(i ,Jend+1)- & !> & MIN(Cx,0.0_r8)*tl_grad(i+1,Jend+1))/& !> & (cff+Ce) !> adfac=ad_vbar(i,Jend+1,kout)/(cff+Ce) ad_grad(i ,Jend+1)=ad_grad(i ,Jend+1)-MAX(Cx,0.0_r8)*adfac ad_grad(i+1,Jend+1)=ad_grad(i+1,Jend+1)-MIN(Cx,0.0_r8)*adfac ad_vbar(i,Jend ,kout)=ad_vbar(i,Jend ,kout)+Ce*adfac ad_vbar(i,Jend+1,know)=ad_vbar(i,Jend+1,know)+cff*adfac ad_vbar(i,Jend+1,kout)=0.0_r8 END DO END IF # elif defined NORTH_M2FLATHER ! ! Northern edge, Flather boundary condition. ! DO i=Istr,Iend cff=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jend )+ & & zeta(i,Jend ,know)+ & & GRID(ng)%h(i,Jend+1)+ & & zeta(i,Jend+1,know))) Ce=SQRT(g*cff) # ifdef MASKING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)* & !> & GRID(ng)%vmask(i,Jend+1) !> ad_vbar(i,Jend+1,kout)=ad_vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(inorth,isVbar,ng)) THEN !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)- & !> & Ce*BOUNDARY(ng)%tl_zeta_north(i) !> BOUNDARY(ng)%ad_zeta_north(i)=BOUNDARY(ng)%ad_zeta_north(i)-& & Ce*ad_vbar(i,Jend+1,kout) END IF # endif !> tl_vbar(i,Jend+1,kout)=tl_bry_val+ & !> & tl_Ce*(0.5_r8*(zeta(i,Jend ,know)+ & !> & zeta(i,Jend+1,know))- & !> & BOUNDARY(ng)%zeta_north(i))+ & !> & Ce*(0.5_r8*(tl_zeta(i,Jend ,know)+ & !> & tl_zeta(i,Jend+1,know))) !> adfac=Ce*0.5_r8*ad_vbar(i,Jend+1,kout) ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac ad_Ce=ad_Ce+ & & (0.5_r8*(zeta(i,Jend ,know)+ & & zeta(i,Jend+1,know))- & & BOUNDARY(ng)%zeta_north(i))*ad_vbar(i,Jend+1,kout) ad_bry_val=ad_bry_val+ad_vbar(i,Jend+1,kout) ad_vbar(i,Jend+1,kout)=0.0_r8 !> tl_Ce=0.5_r8*g*tl_cff/Ce !> ad_cff=ad_cff+0.5_r8*g*ad_Ce/Ce ad_Ce=0.0_r8 !> tl_cff=-cff*cff*(0.5_r8*(GRID(ng)%tl_h(i,Jend )+ & !> & tl_zeta(i,Jend ,know)+ & !> & GRID(ng)%tl_h(i,Jend+1)+ & !> & tl_zeta(i,Jend+1,know))) !> adfac=-cff*cff*0.5_r8*ad_cff GRID(ng)%ad_h(i,Jend )=GRID(ng)%ad_h(i,Jend )+adfac GRID(ng)%ad_h(i,Jend+1)=GRID(ng)%ad_h(i,Jend+1)+adfac ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac ad_cff=0.0_r8 # if defined SSH_TIDES_NOT_YET && !defined UV_TIDES_NOT_YET # ifdef FSOBC_REDUCED bry_pgr=-g*(BOUNDARY(ng)%zeta_north(i)- & & zeta(i,Jend,know))* & & 0.5_r8*GRID(ng)%pn(i,Jend) # else bry_pgr=-g*(zeta(i,Jend+1,know)- & & zeta(i,Jend ,know))* & & 0.5_r8*(GRID(ng)%pn(i,Jend )+ & & GRID(ng)%pn(i,Jend+1)) # endif # ifdef UV_COR bry_cor=-0.125_r8*(ubar(i ,Jend ,know)+ & & ubar(i+1,Jend ,know)+ & & ubar(i ,Jend+1,know)+ & & ubar(i+1,Jend+1,know))* & & (GRID(ng)%f(i,Jend )+ & & GRID(ng)%f(i,Jend+1)) # else bry_cor=0.0_r8 # endif cff1=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jend )+ & & zeta(i,Jend ,know)+ & & GRID(ng)%h(i,Jend+1)+ & & zeta(i,Jend+1,know))) bry_str=cff1*(FORCES(ng)%svstr(i,Jend+1)- & & FORCES(ng)%bvstr(i,Jend+1)) Ce=1.0_r8/SQRT(g*0.5_r8*(GRID(ng)%h(i,Jend+1)+ & & zeta(i,Jend+1,know)+ & & GRID(ng)%h(i,Jend )+ & & zeta(i,Jend ,know))) cff2=GRID(ng)%on_v(i,Jend+1)*Ce !> tl_bry_val=tl_vbar(i,Jend,know)+ & !> & tl_cff2*(bry_pgr+ & !> & bry_cor+ & !> & bry_str)+ & !> & cff2*(tl_bry_pgr+ & !> & tl_bry_cor+ & !> & tl_bry_str) !> adfac=cff2*ad_bry_val ad_bry_pgr=ad_bry_pgr+adfac ad_bry_cor=ad_bry_cor+adfac ad_bry_str=ad_bry_str+adfac ad_cff2=ad_cff2+(bry_pgr+ & & bry_cor+ & & bry_str)*ad_bry_val ad_vbar(i,Jend,know)=ad_vbar(i,Jend,know)+ad_bry_val ad_bry_val=0.0_r8 !> tl_cff2=GRID(ng)%on_v(i,Jend+1)*tl_Ce !> ad_Ce=ad_Ce+GRID(ng)%on_v(i,Jend+1)*ad_cff2 ad_cff2=0.0_r8 !> tl_Ce=-Ce*Ce*Ce*0.25_r8*g*(GRID(ng)%tl_h(i,Jend+1)+ & !> & tl_zeta(i,Jend+1,know)+ & !> & GRID(ng)%tl_h(i,Jend )+ & !> & tl_zeta(i,Jend ,know)) !> adfac=-Ce*Ce*Ce*0.25_r8*g*ad_Ce ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac GRID(ng)%ad_h(i,Jend )=GRID(ng)%ad_h(i,Jend )+adfac GRID(ng)%ad_h(i,Jend+1)=GRID(ng)%ad_h(i,Jend+1)+adfac ad_Ce=0.0_r8 !> tl_bry_str=tl_cff1*(FORCES(ng)%svstr(i,Jend+1)- & !> & FORCES(ng)%bvstr(i,Jend+1))+ & !> & cff1*(FORCES(ng)%tl_svstr(i,Jend+1)- & !> & FORCES(ng)%tl_bvstr(i,Jend+1)) !> adfac=cff1*ad_bry_str FORCES(ng)%ad_svstr(i,Jend+1)=FORCES(ng)%ad_svstr(i,Jend+1)+ & & adfac FORCES(ng)%ad_bvstr(i,Jend+1)=FORCES(ng)%ad_bvstr(i,Jend+1)- & & adfac ad_cff1=ad_cff1+(FORCES(ng)%svstr(i,Jend+1)- & & FORCES(ng)%bvstr(i,Jend+1))*ad_bry_str ad_bry_str=0.0_r8 !> tl_cff1=-cff1*cff1*0.5_r8*(GRID(ng)%tl_h(i,Jend )+ & !> & tl_zeta(i,Jend ,know)+ & !> & GRID(ng)%tl_h(i,Jend+1)+ & !> & tl_zeta(i,Jend+1,know)) !> adfac=-cff1*cff1*0.5_r8*ad_cff1 ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac GRID(ng)%ad_h(i,Jend )=GRID(ng)%ad_h(i,Jend )+adfac GRID(ng)%ad_h(i,Jend+1)=GRID(ng)%ad_h(i,Jend+1)+adfac ad_cff1=0.0_r8 # ifdef UV_COR !> tl_bry_cor=-0.125_r8*(tl_ubar(i ,Jend ,know)+ & !> & tl_ubar(i+1,Jend ,know)+ & !> & tl_ubar(i ,Jend+1,know)+ & !> & tl_ubar(i+1,Jend+1,know))* & !> & (GRID(ng)%f(i,Jend )+ & !> & GRID(ng)%f(i,Jend+1)) !> adfac=0.125_r8*(GRID(ng)%f(i,Jend )+ & & GRID(ng)%f(i,Jend+1))*ad_bry_cor ad_ubar(i ,Jend ,know)=ad_ubar(i ,Jend ,know)-adfac ad_ubar(i+1,Jend ,know)=ad_ubar(i+1,Jend ,know)-adfac ad_ubar(i ,Jend+1,know)=ad_ubar(i ,Jend+1,know)-adfac ad_ubar(i+1,Jend+1,know)=ad_ubar(i+1,Jend+1,know)-adfac ad_bry_cor=0.0_r8 # else !> tl_bry_cor=0.0_r8 !> # endif # ifdef FSOBC_REDUCED # ifdef ADJUST_BOUNDARY IF (Lobc(inorth,isVbar,ng)) THEN !> tl_bry_pgr=tl_bry_pgr- & !> & g*BOUNDARY(ng)%tl_zeta_north(i)* & !> & 0.5_r8*GRID(ng)%pn(i,Jend) !> BOUNDARY(ng)%ad_zeta_north(i)=BOUNDARY(ng)%ad_zeta_north(i)-& & g*0.5_r8*GRID(ng)%pn(i,Jend)* & & ad_bry_pgr END IF # endif !> tl_bry_pgr=g*tl_zeta(i,Jend,know)* & !> & 0.5_r8*GRID(ng)%pn(i,Jend) !> ad_zeta(i,Jend,know)=ad_zeta(i,Jend,know)+ & & g*0.5_r8*GRID(ng)%pn(i,Jend)*ad_bry_pgr ad_bry_pgr=0.0_r8 # else !> tl_bry_pgr=-g*(tl_zeta(i,Jend+1,know)- & !> & tl_zeta(i,Jend ,know))* & !> & 0.5_r8*(GRID(ng)%pn(i,Jend )+ & !> & GRID(ng)%pn(i,Jend+1)) !> adfac=-g*0.5_r8*(GRID(ng)%pn(i,Jend )+ & & GRID(ng)%pn(i,Jend+1))*ad_bry_pgr ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)-adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac ad_bry_pgr=0.0_r8 # endif # else # ifdef ADJUST_BOUNDARY IF (Lobc(inorth,isVbar,ng)) THEN !> tl_bry_val=BOUNDARY(ng)%tl_vbar_north(i) !> BOUNDARY(ng)%ad_vbar_north(i)=BOUNDARY(ng)%ad_vbar_north(i)+& & ad_bry_val ad_bry_val=0.0_r8 ELSE !> tl_bry_val=0.0_r8 !> ad_bry_val=0.0_r8 END IF # else !> tl_bry_val=0.0_r8 !> ad_bry_val=0.0_r8 # endif # endif END DO # elif defined NORTH_M2CLAMPED ! ! Northern edge, clamped boundary condition. ! DO i=Istr,Iend # ifdef MASKING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)* & !> & GRID(ng)%vmask(i,Jend+1) !> ad_vbar(i,Jend+1,kout)=ad_vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(inorth,isVbar,ng)) THEN !> tl_vbar(i,Jend+1,kout)=BOUNDARY(ng)%tl_vbar_north(i) !> BOUNDARY(ng)%ad_vbar_north(i)=BOUNDARY(ng)%ad_vbar_north(i)+& & ad_vbar(i,Jend+1,kout) ad_vbar(i,Jend+1,kout)=0.0_r8 ELSE !> tl_vbar(i,Jend+1,kout)=0.0_r8 !> ad_vbar(i,Jend+1,kout)=0.0_r8 END IF # else !> tl_vbar(i,Jend+1,kout)=0.0_r8 !> ad_vbar(i,Jend+1,kout)=0.0_r8 # endif END DO # elif defined NORTH_M2GRADIENT ! ! Northern edge, gradient boundary condition. ! DO i=Istr,Iend # ifdef MASKING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)* & !> & GRID(ng)%vmask(i,Jend+1) !> ad_vbar(i,Jend+1,kout)=ad_vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend,kout) !> ad_vbar(i,Jend ,kout)=ad_vbar(i,Jend,kout)+ & & ad_vbar(i,Jend+1,kout) ad_vbar(i,Jend+1,kout)=0.0_r8 END DO # elif defined NORTH_M2REDUCED ! ! Northern edge, reduced-physics boundary condition. ! DO i=Istr,Iend cff=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jend )+ & & zeta(i,Jend ,know)+ & & GRID(ng)%h(i,Jend+1)+ & & zeta(i,Jend+1,know))) # ifdef MASKING !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,kout)* & !> & GRID(ng)%vmask(i,Jend+1) !> ad_vbar(i,Jend+1,kout)=ad_vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif !> tl_vbar(i,Jend+1,kout)=tl_vbar(i,Jend+1,know)+ & !> & dt2d*(tl_bry_pgr+ & !> & tl_bry_cor+ & !> & tl_bry_str) !> adfac=dt2d*ad_vbar(i,Jend+1,kout) ad_bry_pgr=ad_bry_pgr+adfac ad_bry_cor=ad_bry_cor+adfac ad_bry_str=ad_bry_str+adfac ad_vbar(i,Jend+1,know)=ad_vbar(i,Jend+1,know)+ & & ad_vbar(i,Jend+1,kout) ad_vbar(i,Jend+1,kout)=0.0_r8 !> tl_bry_str=tl_cff*(FORCES(ng)%svstr(i,Jend+1)- & !> & FORCES(ng)%bvstr(i,Jend+1))+ & !> & cff*(FORCES(ng)%tl_svstr(i,Jend+1)- & !> & FORCES(ng)%tl_bvstr(i,Jend+1)) !> adfac=cff*ad_bry_str FORCES(ng)%ad_svstr(i,Jend+1)=FORCES(ng)%ad_svstr(i,Jend+1)+ & & adfac FORCES(ng)%ad_bvstr(i,Jend+1)=FORCES(ng)%ad_bvstr(i,Jend+1)- & & adfac ad_cff=ad_cff+(FORCES(ng)%svstr(i,Jend+1)- & & FORCES(ng)%bvstr(i,Jend+1))*ad_bry_str ad_bry_str=0.0_r8 !> tl_cff=-cff*cff*0.5_r8*(GRID(ng)%tl_h(i,Jend )+ & !> & tl_zeta(i,Jend ,know)+ & !> & GRID(ng)%tl_h(i,Jend+1)+ & !> & tl_zeta(i,Jend+1,know)) !> adfac=-cff*cff*0.5_r8*ad_cff ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac GRID(ng)%ad_h(i,Jend )=GRID(ng)%ad_h(i,Jend )+adfac GRID(ng)%ad_h(i,Jend+1)=GRID(ng)%ad_h(i,Jend+1)+adfac ad_cff=0.0_r8 # ifdef UV_COR !> tl_bry_cor=-0.125_r8*(tl_ubar(i ,Jend ,know)+ & !> & tl_ubar(i+1,Jend ,know)+ & !> & tl_ubar(i ,Jend+1,know)+ & !> & tl_ubar(i+1,Jend+1,know))* & !> & (GRID(ng)%f(i,Jend )+ & !> & GRID(ng)%f(i,Jend+1)) !> adfac=-0.125_r8*(GRID(ng)%f(i,Jend )+ & & GRID(ng)%f(i,Jend+1))*ad_bry_cor ad_ubar(i ,Jend ,know)=ad_ubar(i ,Jend ,know)+adfac ad_ubar(i+1,Jend ,know)=ad_ubar(i+1,Jend ,know)+adfac ad_ubar(i ,Jend+1,know)=ad_ubar(i ,Jend+1,know)+adfac ad_ubar(i+1,Jend+1,know)=ad_ubar(i+1,Jend+1,know)+adfac ad_bry_cor=0.0_r8 # else !> tl_bry_cor=0.0_r8 !> ad_bry_cor=0.0_r8 # endif # ifdef FSOBC_REDUCED # ifdef ADJUST_BOUNDARY IF (Lobc(inorth,isVbar,ng)) THEN !> tl_bry_pgr=tl_bry_pgr- & !> & g*BOUNDARY(ng)%tl_zeta_north(i)* & !> & 0.5_r8*GRID(ng)%pn(i,Jend) !> BOUNDARY(ng)%ad_zeta_north(i)=BOUNDARY(ng)%ad_zeta_north(i)-& & g*0.5_r8*GRID(ng)%pn(i,Jend)* & & ad_bry_pgr END IF # endif !> tl_bry_pgr=g*tl_zeta(i,Jend,know)* & !> & 0.5_r8*GRID(ng)%pn(i,Jend) !> ad_zeta(i,Jend,know)=ad_zeta(i,Jend,know)+ & & g*0.5_r8*GRID(ng)%pn(i,Jend)*ad_bry_pgr ad_bry_pgr=0.0_r8 # else !> tl_bry_pgr=-g*(tl_zeta(i,Jend+1,know)- & !> & tl_zeta(i,Jend ,know))* & !> & 0.5_r8*(GRID(ng)%pn(i,Jend )+ & !> & GRID(ng)%pn(i,Jend+1)) !> adfac=-g*0.5_r8*(GRID(ng)%pn(i,Jend )+ & & GRID(ng)%pn(i,Jend+1))*ad_bry_pgr ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)-adfac ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+adfac ad_bry_pgr=0.0_r8 # endif END DO # else ! ! Northern edge, closed boundary condition. ! DO i=Istr,Iend !> tl_vbar(i,Jend+1,kout)=0.0_r8 !> ad_vbar(i,Jend+1,kout)=0.0_r8 END DO # endif END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the southern edge. !----------------------------------------------------------------------- ! IF (SOUTHERN_EDGE) THEN # if defined SOUTH_M2RADIATION_NOT_YET IF (iic(ng).ne.0) THEN ! ! Southern edge, implicit upstream radiation condition. ! DO i=Istr,Iend # ifdef SOUTH_M2NUDGING IF (BOUNDARY(ng)%vbar_south_Ce(i).eq.0.0_r8) THEN tau=M2obc_in(ng,isouth) ELSE tau=M2obc_out(ng,isouth) END IF tau=tau*dt2d # endif # ifdef RADIATION_2D Cx=BOUNDARY(ng)%vbar_south_Cx(i) # else Cx=0.0_r8 # endif Ce=BOUNDARY(ng)%vbar_south_Ce(i) cff=BOUNDARY(ng)%vbar_south_C2(i) # ifdef MASKING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)* & !> & GRID(ng)%vmask(i,Jstr) !> ad_vbar(i,Jstr,kout)=ad_vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif # ifdef SOUTH_M2NUDGING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)- & !> & tau*tl_vbar(i,Jstr,know) !> ad_vbar(i,Jstr,know)=ad_vbar(i,Jstr,know)- & & tau*ad_vbar(i,Jstr,kout) # endif !> tl_vbar(i,Jstr,kout)=(cff*tl_vbar(i,Jstr ,know)+ & !> & Ce *tl_vbar(i,Jstr+1,kout)- & !> & MAX(Cx,0.0_r8)*tl_grad(i ,Jstr)- & !> & MIN(Cx,0.0_r8)*tl_grad(i+1,Jstr))/ & !> & (cff+Ce) !> adfac=ad_vbar(i,Jstr,kout)/(cff+Ce) ad_grad(i ,Jstr)=ad_grad(i ,Jstr)-MAX(Cx,0.0_r8)*adfac ad_grad(i+1,Jstr)=ad_grad(i+1,Jstr)-MIN(Cx,0.0_r8)*adfac ad_vbar(i,Jstr ,know)=ad_vbar(i,Jstr ,know)+cff*adfac ad_vbar(i,Jstr-1,kout)=ad_vbar(i,Jstr-1,kout)+Ce *adfac ad_vbar(i,Jstr ,kout)=0.0_r8 END DO END IF # elif defined SOUTH_M2FLATHER ! ! Southern edge, Flather boundary condition. ! DO i=Istr,Iend cff=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & zeta(i,Jstr-1,know)+ & & GRID(ng)%h(i,Jstr )+ & & zeta(i,Jstr ,know))) Ce=SQRT(g*cff) # ifdef MASKING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)* & !> & GRID(ng)%vmask(i,Jstr) !> ad_vbar(i,Jstr,kout)=ad_vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(isouth,isVbar,ng)) THEN !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)+ & !> & Ce*BOUNDARY(ng)%tl_zeta_south(i) !> BOUNDARY(ng)%ad_zeta_south(i)=BOUNDARY(ng)%ad_zeta_south(i)+& & Ce*ad_vbar(i,Jstr,kout) END IF # endif !> tl_vbar(i,Jstr,kout)=tl_bry_val- & !> & tl_Ce*(0.5_r8*(zeta(i,Jstr-1,know)+ & !> & zeta(i,Jstr ,know))- & !> & BOUNDARY(ng)%zeta_south(i))- & !> & Ce*(0.5_r8*(tl_zeta(i,Jstr-1,know)+ & !> & tl_zeta(i,Jstr ,know))) !> adfac=Ce*0.5_r8*ad_vbar(i,Jstr,kout) ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)-adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)-adfac ad_Ce=ad_Ce- & & (0.5_r8*(zeta(i,Jstr-1,know)+ & & zeta(i,Jstr ,know))- & & BOUNDARY(ng)%zeta_south(i))*ad_vbar(i,Jstr,kout) ad_bry_val=ad_bry_val+ad_vbar(i,Jstr,kout) ad_vbar(i,Jstr,kout)=0.0_r8 !> tl_Ce=0.5_r8*g*tl_cff/Ce !> ad_cff=ad_cff+0.5_r8*g*ad_Ce/Ce ad_Ce=0.0_r8 !> tl_cff=-cff*cff*(0.5_r8*(GRID(ng)%tl_h(i,Jstr-1)+ & !> & tl_zeta(i,Jstr-1,know)+ & !> & GRID(ng)%tl_h(i,Jstr )+ & !> & tl_zeta(i,Jstr ,know))) !> adfac=-cff*cff*0.5_r8*ad_cff GRID(ng)%ad_h(i,Jstr-1)=GRID(ng)%ad_h(i,Jstr-1)+adfac GRID(ng)%ad_h(i,Jstr )=GRID(ng)%ad_h(i,Jstr )+adfac ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+adfac ad_cff=0.0_r8 # if defined SSH_TIDES_NOT_YET && !defined UV_TIDES_NOT_YET # ifdef FSOBC_REDUCED bry_pgr=-g*(zeta(i,Jstr,know)- & & BOUNDARY(ng)%zeta_south(i))* & & 0.5_r8*GRID(ng)%pn(i,Jstr) # else bry_pgr=-g*(zeta(i,Jstr ,know)- & & zeta(i,Jstr-1,know))* & & 0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & & GRID(ng)%pn(i,Jstr )) # endif # ifdef UV_COR bry_cor=-0.125_r8*(ubar(i ,Jstr-1,know)+ & & ubar(i+1,Jstr-1,know)+ & & ubar(i ,Jstr ,know)+ & & ubar(i+1,Jstr ,know))* & & (GRID(ng)%f(i,Jstr-1)+ & & GRID(ng)%f(i,Jstr )) # else bry_cor=0.0_r8 # endif cff1=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & zeta(i,Jstr-1,know)+ & & GRID(ng)%h(i,Jstr )+ & & zeta(i,Jstr ,know))) bry_str=cff1*(FORCES(ng)%svstr(i,Jstr)- & & FORCES(ng)%bvstr(i,Jstr)) Ce=1.0_r8/SQRT(g*0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & zeta(i,Jstr-1,know)+ & & GRID(ng)%h(i,Jstr )+ & & zeta(i,Jstr ,know))) cff2=GRID(ng)%on_v(i,Jstr)*Ce !> tl_bry_val=tl_vbar(i,Jstr+1,know)+ & !> & tl_cff2*(bry_pgr+ & !> & bry_cor+ & !> & bry_str)+ & !> & cff2*(tl_bry_pgr+ & !> & tl_bry_cor+ & !> & tl_bry_str) !> adfac=cff2*ad_bry_val tl_bry_pgr=tl_bry_pgr+adfac tl_bry_cor=tl_bry_cor+adfac tl_bry_str=tl_bry_str+adfac ad_cff2=ad_cff2+(bry_pgr+ & & bry_cor+ & & bry_str)*ad_bry_val ad_vbar(i,Jstr+1,know)=ad_vbar(i,Jstr+1,know)+ad_bry_val ad_bry_val=0.0_r8 !> tl_cff2=GRID(ng)%on_v(i,Jstr)*tl_Ce !> ad_Ce=ad_Ce+GRID(ng)%on_v(i,Jstr)*ad_cff2 ad_cff2=0.0_r8 !> tl_Ce=-Ce*Ce*Ce*0.25_r8*g*(GRID(ng)%tl_h(i,Jstr-1)+ & !> & tl_zeta(i,Jstr-1,know)+ & !> & GRID(ng)%tl_h(i,Jstr )+ & !> & tl_zeta(i,Jstr ,know)) !> adfac=-Ce*Ce*Ce*0.25_r8*g*ad_Ce ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+adfac GRID(ng)%ad_h(i,Jstr-1)=GRID(ng)%ad_h(i,Jstr-1)+adfac GRID(ng)%ad_h(i,Jstr )=GRID(ng)%ad_h(i,Jstr )+adfac ad_Ce=0.0_r8 !> tl_bry_str=tl_cff1*(FORCES(ng)%svstr(i,Jstr)- & !> & FORCES(ng)%bvstr(i,Jstr))+ & !> & cff1*(FORCES(ng)%tl_svstr(i,Jstr)- & !> & FORCES(ng)%tl_bvstr(i,Jstr)) !> adfac=cff1*ad_bry_str FORCES(ng)%ad_svstr(i,Jstr)=FORCES(ng)%ad_svstr(i,Jstr)+ & & adfac FORCES(ng)%ad_bvstr(i,Jstr)=FORCES(ng)%ad_bvstr(i,Jstr)- & & adfac ad_cff1=ad_cff1+(FORCES(ng)%svstr(i,Jstr)- & & FORCES(ng)%bvstr(i,Jstr))*ad_bry_str ad_bry_str=0.0_r8 !> tl_cff1=-cff1*cff1*(0.5_r8*(GRID(ng)%tl_h(i,Jstr-1)+ & !> & tl_zeta(i,Jstr-1,know)+ & !> & GRID(ng)%tl_h(i,Jstr )+ & !> & tl_zeta(i,Jstr ,know))) !> adfac=-cff1*cff1*0.5_r8*ad_cff1 ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+adfac GRID(ng)%ad_h(i,Jstr-1)=GRID(ng)%ad_h(i,Jstr-1)+adfac GRID(ng)%ad_h(i,Jstr )=GRID(ng)%ad_h(i,Jstr )+adfac ad_cff1=0.0_r8 # ifdef UV_COR !> tl_bry_cor=-0.125_r8*(tl_ubar(i ,Jstr-1,know)+ & !> & tl_ubar(i+1,Jstr-1,know)+ & !> & tl_ubar(i ,Jstr ,know)+ & !> & tl_ubar(i+1,Jstr ,know))* & !> & (GRID(ng)%f(i,Jstr-1)+ & !> & GRID(ng)%f(i,Jstr )) !> adfac=-0.125_r8*(GRID(ng)%f(i,Jstr-1)+ & & GRID(ng)%f(i,Jstr ))*ad_bry_cor ad_ubar(i ,Jstr-1,know)=ad_ubar(i ,Jstr-1,know)+adfac ad_ubar(i+1,Jstr-1,know)=ad_ubar(i+1,Jstr-1,know)+adfac ad_ubar(i ,Jstr ,know)=ad_ubar(i ,Jstr ,know)+adfac ad_ubar(i+1,Jstr ,know)=ad_ubar(i+1,Jstr ,know)+adfac ad_bry_cor=0.0_r8 # else !> tl_bry_cor=0.0_r8 !> ad_bry_cor=0.0_r8 # endif # ifdef FSOBC_REDUCED # ifdef ADJUST_BOUNDARY IF (Lobc(isouth,isVbar,ng)) THEN !> tl_bry_pgr=tl_bry_pgr+ & !> & g*BOUNDARY(ng)%tl_zeta_south(i)* & !> & 0.5_r8*GRID(ng)%pn(i,Jstr) !> BOUNDARY(ng)%ad_zeta_south(i)=BOUNDARY(ng)%ad_zeta_south(i)+& & g*0.5_r8*GRID(ng)%pn(i,Jstr)* & & ad_bry_pgr END IF # endif !> tl_bry_pgr=-g*tl_zeta(i,Jstr,know)* & !> & 0.5_r8*GRID(ng)%pn(i,Jstr) !> tl_zeta(i,Jstr,know)=tl_zeta(i,Jstr,know)- & & g*0.5_r8*GRID(ng)%pn(i,Jstr)*ad_bry_pgr ad_bry_pgr=0.0_r8 # else !> tl_bry_pgr=-g*(tl_zeta(i,Jstr ,know)- & !> & tl_zeta(i,Jstr-1,know))* & !> & 0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & !> & GRID(ng)%pn(i,Jstr )) !> adfac=-g*0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & & GRID(ng)%pn(i,Jstr ))*ad_bry_pgr ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)-adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+adfac ad_bry_pgr=0.0_r8 # endif # else # ifdef ADJUST_BOUNDARY IF (Lobc(isouth,isVbar,ng)) THEN !> tl_bry_val=BOUNDARY(ng)%tl_vbar_south(i) !> BOUNDARY(ng)%ad_vbar_south(i)=BOUNDARY(ng)%ad_vbar_south(i)+& & ad_bry_val ad_bry_val=0.0_r8 ELSE !> tl_bry_val=0.0_r8 !> ad_bry_val=0.0_r8 END IF # else !> tl_bry_val=0.0_r8 !> ad_bry_val=0.0_r8 # endif # endif END DO # elif defined SOUTH_M2CLAMPED ! ! Southern edge, clamped boundary condition. ! DO i=Istr,Iend # ifdef MASKING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)* & !> & GRID(ng)%vmask(i,Jstr) !> ad_vbar(i,Jstr,kout)=ad_vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif # ifdef ADJUST_BOUNDARY IF (Lobc(isouth,isVbar,ng)) THEN !> tl_vbar(i,Jstr,kout)=BOUNDARY(ng)%tl_vbar_south(i) !> BOUNDARY(ng)%ad_vbar_south(i)=BOUNDARY(ng)%ad_vbar_south(i)+& & ad_vbar(i,Jstr,kout) ad_vbar(i,Jstr,kout)=0.0_r8 ELSE !> tl_vbar(i,Jstr,kout)=0.0_r8 !> ad_vbar(i,Jstr,kout)=0.0_r8 END IF # else !> tl_vbar(i,Jstr,kout)=0.0_r8 !> ad_vbar(i,Jstr,kout)=0.0_r8 # endif END DO # elif defined SOUTH_M2GRADIENT ! ! Southern edge, gradient boundary condition. ! DO i=Istr,Iend # ifdef MASKING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)* & !> & GRID(ng)%vmask(i,Jstr) !> ad_vbar(i,Jstr ,kout)=ad_vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr+1,kout) !> ad_vbar(i,Jstr+1,kout)=ad_vbar(i,Jstr+1,kout)+ & & ad_vbar(i,Jstr,kout) ad_vbar(i,Jstr ,kout)=0.0_r8 END DO # elif defined SOUTH_M2REDUCED ! ! Southern edge, reduced-physics boundary condition. ! DO i=Istr,Iend cff=1.0_r8/(0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & zeta(i,Jstr-1,know)+ & & GRID(ng)%h(i,Jstr )+ & & zeta(i,Jstr ,know))) # ifdef MASKING !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,kout)* & !> & GRID(ng)%vmask(i,Jstr) !> ad_vbar(i,Jstr,kout)=ad_vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif !> tl_vbar(i,Jstr,kout)=tl_vbar(i,Jstr,know)+ & !> & dt2d*(tl_bry_pgr+ & !> & tl_bry_cor+ & !> & tl_bry_str) !> adfac=dt2d*ad_vbar(i,Jstr,kout) ad_bry_pgr=ad_bry_pgr+adfac ad_bry_cor=ad_bry_cor+adfac ad_bry_str=ad_bry_str+adfac ad_vbar(i,Jstr,know)=ad_vbar(i,Jstr,know)+ & & ad_vbar(i,Jstr,kout) ad_vbar(i,Jstr,kout)=0.0_r8 !> tl_bry_str=tl_cff*(FORCES(ng)%svstr(i,Jstr)- & !> & FORCES(ng)%bvstr(i,Jstr))+ & !> & cff*(FORCES(ng)%tl_svstr(i,Jstr)- & !> & FORCES(ng)%tl_bvstr(i,Jstr)) !> adfac=cff*ad_bry_str FORCES(ng)%ad_svstr(i,Jstr)=FORCES(ng)%ad_svstr(i,Jstr)+ & & adfac FORCES(ng)%ad_bvstr(i,Jstr)=FORCES(ng)%ad_bvstr(i,Jstr)- & & adfac ad_cff=ad_cff+(FORCES(ng)%svstr(i,Jstr)- & & FORCES(ng)%bvstr(i,Jstr))*ad_bry_str ad_bry_str=0.0_r8 tl_cff=-cff*cff*0.5_r8*(GRID(ng)%tl_h(i,Jstr-1)+ & & tl_zeta(i,Jstr-1,know)+ & & GRID(ng)%tl_h(i,Jstr )+ & & tl_zeta(i,Jstr ,know)) adfac=-cff*cff*0.5_r8*ad_cff ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+adfac ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+adfac GRID(ng)%ad_h(i,Jstr-1)=GRID(ng)%ad_h(i,Jstr-1)+adfac GRID(ng)%ad_h(i,Jstr )=GRID(ng)%ad_h(i,Jstr )+adfac ad_cff=0.0_r8 # ifdef UV_COR !> tl_bry_cor=-0.125_r8*(tl_ubar(i ,Jstr-1,know)+ & !> & tl_ubar(i+1,Jstr-1,know)+ & !> & tl_ubar(i ,Jstr ,know)+ & !> & tl_ubar(i+1,Jstr ,know))* & !> & (GRID(ng)%f(i,Jstr-1)+ & !> & GRID(ng)%f(i,Jstr )) !> adfac=-0.125_r8*(GRID(ng)%f(i,Jstr-1)+ & & GRID(ng)%f(i,Jstr ))*ad_bry_cor ad_ubar(i ,Jstr-1,know)=ad_ubar(i ,Jstr-1,know)+adfac ad_ubar(i+1,Jstr-1,know)=ad_ubar(i+1,Jstr-1,know)+adfac ad_ubar(i ,Jstr ,know)=ad_ubar(i ,Jstr ,know)+adfac ad_ubar(i+1,Jstr ,know)=ad_ubar(i+1,Jstr ,know)+adfac ad_bry_cor=0.0_r8 # else !> bry_cor=0.0_r8 !> tl_bry_cor=0.0_r8 # endif # ifdef FSOBC_REDUCED # ifdef ADJUST_BOUNDARY IF (Lobc(isouth,isVbar,ng)) THEN !> tl_bry_pgr=tl_bry_pgr+ & !> & g*BOUNDARY(ng)%tl_zeta_south(i)* & !> & 0.5_r8*GRID(ng)%pn(i,Jstr) !> BOUNDARY(ng)%ad_zeta_south(i)=BOUNDARY(ng)%ad_zeta_south(i)+& & g*0.5_r8*GRID(ng)%pn(i,Jstr)* & & ad_bry_pgr END IF # endif !> tl_bry_pgr=-g*tl_zeta(i,Jstr,know)* & !> & 0.5_r8*GRID(ng)%pn(i,Jstr) !> tl_zeta(i,Jstr,know)=tl_zeta(i,Jstr,know)- & & g*0.5_r8*GRID(ng)%pn(i,Jstr)*ad_bry_pgr ad_bry_pgr=0.0_r8 # else !> tl_bry_pgr=-g*(tl_zeta(i,Jstr ,know)- & !> & tl_zeta(i,Jstr-1,know))* & !> & 0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & !> & GRID(ng)%pn(i,Jstr )) !> adfac=-g*0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & & GRID(ng)%pn(i,Jstr ))*ad_bry_pgr ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)-adfac ad_zeta(i,Jstr ,know)=tl_zeta(i,Jstr ,know)+adfac ad_bry_pgr=0.0_r8 # endif END DO # else ! ! Southern edge, closed boundary condition. ! DO i=Istr,Iend !> tl_vbar(i,Jstr,kout)=0.0_r8 !> ad_vbar(i,Jstr,kout)=0.0_r8 END DO # endif END IF # endif RETURN END SUBROUTINE ad_v2dbc_tile #endif END MODULE ad_v2dbc_mod