#include "cppdefs.h" MODULE ad_v2dbc_mod #ifdef ADJOINT ! !git $Id$ !svn $Id: ad_v2dbc_im.F 1180 2023-07-13 02:42:10Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! 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_clima 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,:) real(r8), intent(in) :: vbar(LBi:UBi,LBj:UBj,:) real(r8), intent(in) :: zeta(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_ubar(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_vbar(LBi:UBi,LBj:UBj,:) real(r8), intent(inout) :: ad_zeta(LBi:UBi,LBj:UBj,:) # endif ! ! Local variable declarations. ! integer :: Jmin, Jmax integer :: i, j, know real(r8) :: Ce, Cx, Ze real(r8) :: bry_pgr, bry_cor, bry_str, bry_val real(r8) :: cff, cff1, cff2, cff3, dt2d real(r8) :: obc_in, obc_out, tau # if defined ATM_PRESS && defined PRESS_COMPENSATE real(r8) :: OneAtm, fac # endif real(r8) :: ad_Ce, ad_Cx real(r8) :: ad_bry_pgr, ad_bry_cor, ad_bry_str, ad_bry_val, ad_Ze real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3 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_Ze=0.0_r8 ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_cff3=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 ATM_PRESS && defined PRESS_COMPENSATE OneAtm=1013.25_r8 ! 1 atm = 1013.25 mb fac=100.0_r8/(g*rho0) # endif # if defined WET_DRY_NOT_YET ! !----------------------------------------------------------------------- ! Impose wetting and drying conditions. ! ! HGA: need ADM code here for the NLM code below. !----------------------------------------------------------------------- ! IF (.not.(EWperiodic(ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN IF ((LBC_apply(ng)%north(Iend+1).and. & & LBC_apply(ng)%east (Jend+1)).or. & & (LBC(ieast,isVbar,ng)%nested.and. & & LBC(inorth,isVbar,ng)%nested)) 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 END IF IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN IF ((LBC_apply(ng)%north(Istr-1).and. & & LBC_apply(ng)%west (Jend+1)).or. & & (LBC(iwest,isVbar,ng)%nested.and. & & LBC(inorth,isVbar,ng)%nested)) 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 END IF IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN IF ((LBC_apply(ng)%south(Iend+1).and. & & LBC_apply(ng)%east (Jstr )).or. & & (LBC(ieast,isVbar,ng)%nested.and. & & LBC(isouth,isVbar,ng)%nested)) 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 END IF IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN IF ((LBC_apply(ng)%south(Istr-1).and. & & LBC_apply(ng)%west (Jstr )).or. & & (LBC(iwest,isVbar,ng)%nested.and. & & LBC(isouth,isVbar,ng)%nested)) 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 END IF END IF ! IF (.not.NSperiodic(ng)) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i).or. & & LBC(inorth,isVbar,ng)%nested) THEN !^ 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 IF END DO END IF IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i).or. & & LBC(isouth,isVbar,ng)%nested) THEN !^ 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 IF END DO END IF END IF ! IF (.not.EWperiodic(ng)) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j).or. & & LBC(ieast,isVbar,ng)%nested) THEN !^ 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 IF END DO END IF IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j).or. & & LBC(iwest,isVbar,ng)%nested) THEN !^ 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 IF END DO END IF ENDIF # endif ! !----------------------------------------------------------------------- ! Boundary corners. !----------------------------------------------------------------------- ! IF (.not.(EWperiodic(ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN IF (LBC_apply(ng)%north(Iend+1).and. & & LBC_apply(ng)%east (Jend+1)) 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 END IF IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN IF (LBC_apply(ng)%north(Istr-1).and. & & LBC_apply(ng)%west (Jend+1)) 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 END IF IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN IF (LBC_apply(ng)%south(Iend+1).and. & & LBC_apply(ng)%east (Jstr )) 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 END IF IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN IF (LBC_apply(ng)%south(Istr-1).and. & & LBC_apply(ng)%west (Jstr )) 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 END IF END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the eastern edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN ! ! Eastern edge, implicit upstream radiation condition. ! IF (ad_LBC(ieast,isVbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN # if defined CELERITY_READ && defined FORWARD_READ IF (ad_LBC(ieast,isVbar,ng)%nudging) THEN IF (LnudgeM2CLM(ng)) THEN obc_out=0.5_r8* & & (CLIMA(ng)%M2nudgcof(Iend+1,j-1)+ & & CLIMA(ng)%M2nudgcof(Iend+1,j )) obc_in =obcfac(ng)*obc_out ELSE obc_out=M2obc_out(ng,ieast) obc_in =M2obc_in (ng,ieast) END IF IF (BOUNDARY(ng)%vbar_east_Cx(j).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF 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) # endif # 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 IF (ad_LBC(ieast,isVbar,ng)%nudging) THEN !^ 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) END IF !^ 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 IF END DO END IF ! ! Eastern edge, Chapman boundary condition. ! ELSE IF (ad_LBC(ieast,isVbar,ng)%Flather.or. & & ad_LBC(ieast,isVbar,ng)%reduced.or. & & ad_LBC(ieast,isVbar,ng)%Shchepetkin) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN 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 IF END DO ! ! Eastern edge, clamped boundary condition. ! ELSE IF (ad_LBC(ieast,isVbar,ng)%clamped) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN # 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 IF END DO ! ! Eastern edge, gradient boundary condition. ! ELSE IF (ad_LBC(ieast,isVbar,ng)%gradient) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN # 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 IF END DO ! ! Eastern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (ad_LBC(ieast,isVbar,ng)%closed) THEN IF (NSperiodic(ng)) THEN Jmin=JstrV Jmax=Jend ELSE Jmin=Jstr Jmax=JendR END IF DO j=Jmin,Jmax IF (LBC_apply(ng)%east(j)) THEN # 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 IF END DO END IF END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the western edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Western_Edge(tile)) THEN ! ! Western edge, implicit upstream radiation condition. ! IF (ad_LBC(iwest,isVbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN # if defined CELERITY_READ && defined FORWARD_READ IF (ad_LBC(iwest,isVbar,ng)%nudging) THEN IF (LnudgeM2CLM(ng)) THEN obc_out=0.5_r8* & & (CLIMA(ng)%M2nudgcof(Istr-1,j-1)+ & & CLIMA(ng)%M2nudgcof(Istr-1,j )) obc_in =obcfac(ng)*obc_out ELSE obc_out=M2obc_out(ng,iwest) obc_in =M2obc_in (ng,iwest) END IF IF (BOUNDARY(ng)%vbar_west_Cx(j).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF 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) # endif # 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 IF (ad_LBC(iwest,isVbar,ng)%nudging) THEN !^ 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) END IF !^ 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 IF END DO END IF ! ! Western edge, Chapman boundary condition. ! ELSE IF (ad_LBC(iwest,isVbar,ng)%Flather.or. & & ad_LBC(iwest,isVbar,ng)%reduced.or. & & ad_LBC(iwest,isVbar,ng)%Shchepetkin) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN 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 IF END DO ! ! Western edge, clamped boundary condition. ! ELSE IF (ad_LBC(iwest,isVbar,ng)%clamped) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN # 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 IF END DO ! ! Western edge, gradient boundary condition. ! ELSE IF (ad_LBC(iwest,isVbar,ng)%gradient) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN # 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 IF END DO ! ! Western edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (ad_LBC(iwest,isVbar,ng)%closed) THEN IF (NSperiodic(ng)) THEN Jmin=JstrV Jmax=Jend ELSE Jmin=Jstr Jmax=JendR END IF DO j=Jmin,Jmax IF (LBC_apply(ng)%west(j)) THEN # 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 IF END DO END IF END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the northern edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Northern_Edge(tile)) THEN ! ! Northern edge, implicit upstream radiation condition. ! IF (ad_LBC(inorth,isVbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN # if defined CELERITY_READ && defined FORWARD_READ IF (ad_LBC(inorth,isVbar,ng)%nudging) THEN IF (LnudgeM2CLM(ng)) THEN obc_out=0.5_r8* & & (CLIMA(ng)%M2nudgcof(i,Jend )+ & & CLIMA(ng)%M2nudgcof(i,Jend+1)) obc_in =obcfac(ng)*obc_out ELSE obc_out=M2obc_out(ng,inorth) obc_in =M2obc_in (ng,inorth) END IF IF (BOUNDARY(ng)%vbar_north_Ce(i).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF # 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) # endif # 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 IF (ad_LBC(inorth,isVbar,ng)%nudging) THEN !^ 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) END IF !^ 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 IF END DO END IF ! ! Northern edge, Flather boundary condition. ! ELSE IF (ad_LBC(inorth,isVbar,ng)%Flather) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN 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 # if defined ATM_PRESS && defined PRESS_COMPENSATE !^ tl_vbar(i,Jstr,kout)=tl_bry_val- & !^ & tl_Ce* & !^ & (0.5_r8* & !^ & (zeta(i,Jstr-1,know)+ & !^ & zeta(i,Jstr ,know)+ & !^ & fac*(FORCES(ng)%Pair(i,Jstr-1)+ & !^ & FORCES(ng)%Pair(i,Jstr )- & !^ & 2.0_r8*OneAtm))- & !^ & 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,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)+ & & fac*(FORCES(ng)%Pair(i,Jstr-1)+ & & FORCES(ng)%Pair(i,Jstr )- & & 2.0_r8*OneAtm))- & & 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 # else !^ 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 # endif !^ 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 IF (ad_LBC(inorth,isFsur,ng)%acquire) THEN 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)) END IF # 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 IF (ad_LBC(inorth,isFsur,ng)%acquire) THEN # 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 END IF # 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 IF END DO ! ! Northern edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (ad_LBC(inorth,isVbar,ng)%Shchepetkin) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN cff=0.5_r8*(GRID(ng)%h(i,Jend )+ & & GRID(ng)%h(i,Jend+1)) cff1=SQRT(g/cff) Ce=dt2d*cff1*cff*0.5_r8*(GRID(ng)%pn(i,Jend )+ & & GRID(ng)%pn(i,Jend+1)) Ze=(0.5_r8+Ce)*zeta(i,Jend ,know)+ & & (0.5_r8-Ce)*zeta(i,Jend+1,know) IF (Ce.gt.Co) THEN cff2=(1.0_r8-Co/Ce)**2 cff3=zeta(i,Jend,kout)+ & & Ce*zeta(i,Jend+1,know)- & & (1.0_r8+Ce)*zeta(i,Jend,know) Ze=Ze+cff2*cff3 END IF # 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)=0.5_r8* & !^ & ((1.0_r8-Ce)* & !^ & tl_vbar(i,Jend+1,know)+ & !^ & tl_Ce*(vbar(i,Jend ,know)- & !^ & vbar(i,Jend+1,know))+ & !^ & Ce*tl_vbar(i,Jend,know)+ & !^ & tl_bry_val+ & !^ & tl_cff1* & !^ & (Ze-BOUNDARY(ng)%zeta_north(i))- & !^ & cff1*tl_ze) !^ adfac=0.5_r8*ad_vbar(i,Jend+1,kout) ad_vbar(i,Jend+1,know)=ad_vbar(i,Jend+1,know)+ & & (1.0_r8-Ce)*adfac ad_vbar(i,Jend ,know)=ad_vbar(i,Jend ,know)+ & & Ce*adfac ad_Ce=ad_Ce+ & & (vbar(i,Jend ,know)- & & vbar(i,Jend+1,know))*adfac ad_cff1=ad_cff1+ & & (Ze-BOUNDARY(ng)%zeta_north(i))*adfac ad_ze=ad_ze-cff1*adfac ad_vbar(i,Jend+1,kout)=0.0_r8 IF (Ce.gt.Co) THEN !^ tl_Ze=tl_Ze+cff2*tl_cff3+ & !^ & tl_cff2*cff3 !^ ad_cff2=ad_cff2+cff3*ad_Ze ad_cff3=ad_cff3+cff2*ad_Ze !^ tl_cff3=tl_zeta(i,Jend,kout)+ & !^ & Ce*tl_zeta(i,Jend+1,know)+ & !^ & tl_Ce*(zeta(i,Jend ,know)+ & !^ & zeta(i,Jend+1,know))- & !^ & (1.0_r8+Ce)*tl_zeta(i,Jend,know) !^ ad_zeta(i,Jend ,kout)=ad_zeta(i,Jend ,kout)+ & & ad_cff3 ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)- & & (1.0_r8+Ce)*ad_cff3 ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+ & & Ce*ad_cff3 ad_Ce=ad_Ce+ & & (zeta(i,Jend ,know)+ & & zeta(i,Jend+1,know))*ad_cff3 ad_cff3=0.0_r8 !^ tl_cff2=2.0_r8*cff2*Co*tl_Ce/(Ce*Ce) !^ ad_Ce=ad_Ce+ & & 2.0_r8*cff2*Co*ad_cff2/(Ce*Ce) ad_cff2=0.0_r8 END IF !^ tl_Ze=(0.5_r8+Ce)*tl_zeta(i,Jend ,know)+ & !^ & (0.5_r8-Ce)*tl_zeta(i,Jend+1,know)+ & !^ & tl_Ce*(zeta(i,Jend ,know)- & !^ & zeta(i,Jend+1,know)) !^ ad_zeta(i,Jend ,know)=ad_zeta(i,Jend ,know)+ & & (0.5_r8+Ce)*ad_Ze ad_zeta(i,Jend+1,know)=ad_zeta(i,Jend+1,know)+ & & (0.5_r8-Ce)*ad_Ze ad_Ce=ad_Ce+ & & (zeta(i,Jend ,know)- & & zeta(i,Jend+1,know))*ad_Ze ad_Ze=0.0_r8 !^ tl_Ce=dt2d*0.5_r8*(GRID(ng)%pn(i,Jend )+ & !^ & GRID(ng)%pn(i,Jend+1))* & !^ & (cff1*tl_cff+ & !^ & tl_cff1*cff) !^ adfac=dt2d*0.5_r8*(GRID(ng)%pn(i,Jend )+ & & GRID(ng)%pn(i,Jend+1))*ad_Ce ad_cff=ad_cff+cff1*adfac ad_cff1=ad_cff1+cff*adfac ad_Ce=0.0_r8 !^ tl_cff1=-0.5_r8*cff1*tl_cff/cff !^ ad_cff=ad_cff- & & 0.5_r8*cff1*ad_cff1/cff ad_cff1=0.0_r8 # ifdef WET_DRY_NOT_YET !^ tl_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=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 # else !^ tl_cff=0.5_r8*(GRID(ng)%tl_h(i,Jend )+ & !^ & GRID(ng)%tl_h(i,Jend+1)) !^ adfac=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_cff=0.0_r8 # endif # if defined SSH_TIDES_NOT_YET && !defined UV_TIDES_NOT_YET IF (ad_LBC(inorth,isFsur,ng)%acquire) THEN 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)) END IF # 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 IF (ad_LBC(inorth,isFsur,ng)%acquire) THEN # 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 END IF # 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 IF END DO ! ! Northern edge, clamped boundary condition. ! ELSE IF (ad_LBC(inorth,isVbar,ng)%clamped) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN # 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 IF END DO ! ! Northern edge, gradient boundary condition. ! ELSE IF (ad_LBC(inorth,isVbar,ng)%gradient) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN # 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 IF END DO ! ! Northern edge, reduced-physics boundary condition. ! ELSE IF (ad_LBC(inorth,isVbar,ng)%reduced) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN 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 IF (ad_LBC(inorth,isFsur,ng)%acquire) THEN # 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 END IF END IF END DO ! ! Northern edge, closed boundary condition. ! ELSE IF (ad_LBC(inorth,isVbar,ng)%closed) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN !^ tl_vbar(i,Jend+1,kout)=0.0_r8 !^ ad_vbar(i,Jend+1,kout)=0.0_r8 END IF END DO END IF END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the southern edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Southern_Edge(tile)) THEN ! ! Southern edge, implicit upstream radiation condition. ! IF (ad_LBC(isouth,isVbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN # if defined CELERITY_READ && defined FORWARD_READ IF (ad_LBC(isouth,isVbar,ng)%nudging) THEN IF (LnudgeM2CLM(ng)) THEN obc_out=0.5_r8* & & (CLIMA(ng)%M2nudgcof(i,Jstr-1)+ & & CLIMA(ng)%M2nudgcof(i,Jstr )) obc_in =obcfac(ng)*obc_out ELSE obc_out=M2obc_out(ng,isouth) obc_in =M2obc_in (ng,isouth) END IF IF (BOUNDARY(ng)%vbar_south_Ce(i).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF # 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) # endif # 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 IF (ad_LBC(isouth,isVbar,ng)%nudging) THEN !^ 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) END IF !^ 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 IF END DO END IF ! ! Southern edge, Flather boundary condition. ! ELSE IF (ad_LBC(isouth,isVbar,ng)%Flather) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN 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 # if defined ATM_PRESS && defined PRESS_COMPENSATE !^ tl_vbar(i,Jstr,kout)=tl_bry_val- & !^ & tl_Ce* & !^ & (0.5_r8* & !^ & (zeta(i,Jstr-1,know)+ & !^ & zeta(i,Jstr ,know)+ & !^ & fac*(FORCES(ng)%Pair(i,Jstr-1)+ & !^ & FORCES(ng)%Pair(i,Jstr )- & !^ & 2.0_r8*OneAtm))- & !^ & 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)+ & & fac*(FORCES(ng)%Pair(i,Jstr-1)+ & & FORCES(ng)%Pair(i,Jstr )- & & 2.0_r8*OneAtm))- & & 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 # else !^ 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 # endif !^ 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 IF (ad_LBC(isouth,isFsur,ng)%acquire) THEN 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 )) END IF # 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 IF (ad_LBC(isouth,isFsur,ng)%acquire) THEN # 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 END IF # 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 IF END DO ! ! Southern edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (ad_LBC(isouth,isVbar,ng)%Shchepetkin) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN cff=0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & GRID(ng)%h(i,Jstr )) cff1=SQRT(g/cff) Ce=dt2d*cff1*cff*0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & & GRID(ng)%pn(i,Jstr )) Ze=(0.5_r8+Ce)*zeta(i,Jstr ,know)+ & & (0.5_r8-Ce)*zeta(i,Jstr-1,know) IF (Ce.gt.Co) THEN cff2=(1.0_r8-Co/Ce)**2 cff3=zeta(i,Jstr,kout)+ & & Ce*zeta(i,Jstr-1,know)- & & (1.0_r8+Ce)*zeta(i,Jstr,know) Ze=Ze+cff2*cff3 END IF # 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)=0.5_r8* & !^ & ((1.0_r8-Ce)* & !^ & tl_vbar(i,Jstr,know)- & !^ & tl_Ce*(vbar(i,Jstr ,know)- & !^ & vbar(i,Jstr+1,know))+ & !^ & Ce*tl_vbar(i,Jstr+1,know)+ & !^ & tl_bry_val- & !^ & tl_cff1* & !^ & (Ze-BOUNDARY(ng)%zeta_south(i))- & !^ & cff1*tl_Ze) !^ adfac=0.5_r8*ad_vbar(i,Jstr,kout) ad_vbar(i,Jstr ,know)=ad_vbar(i,Jstr,know)+ & & (1.0_r8-Ce)*adfac ad_vbar(i,Jstr+1,know)=ad_vbar(i,Jstr+1,know)+ & & Ce*adfac ad_Ce=ad_Ce- & & (vbar(i,Jstr ,know)- & & vbar(i,Jstr+1,know))*adfac ad_bry_val=ad_bry_val+adfac ad_cff1=ad_cff1- & & (Ze-BOUNDARY(ng)%zeta_south(i))*adfac ad_Ze=ad_Ze+cff1*adfac ad_vbar(i,Jstr,kout)=0.0_r8 IF (Ce.gt.Co) THEN !^ tl_Ze=tl_Ze+cff2*tl_cff3+ & !^ & tl_cff2*cff3 !^ ad_cff2=ad_cff2+cff3*ad_Ze ad_cff3=ad_cff3+cff2*ad_Ze !^ tl_cff3=tl_zeta(i,Jstr,kout)+ & !^ & Ce*tl_zeta(i,Jstr-1,know)+ & !^ & tl_Ce*(zeta(i,Jstr-1,know)+ & !^ & zeta(i,Jstr ,know))- & !^ & (1.0_r8+Ce)*tl_zeta(i,Jstr,know) !^ ad_zeta(i,Jstr ,kout)=ad_zeta(i,Jstr ,kout)+ & & ad_cff3 ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)- & & (1.0_r8+Ce)*ad_cff3 ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+ & & Ce*ad_cff3 ad_Ce=ad_Ce+ & & (zeta(i,Jstr-1,know)+ & & zeta(i,Jstr ,know))*ad_cff3 ad_cff3=0.0_r8 !^ tl_cff2=2.0_r8*cff2*Co*tl_Ce/(Ce*Ce) !^ ad_Ce=ad_Ce+ & & 2.0_r8*cff2*Co*ad_cff2/(Ce*Ce) ad_cff2=0.0_r8 END IF !^ tl_Ze=(0.5_r8+Ce)*tl_zeta(i,Jstr ,know)+ & !^ & (0.5_r8-Ce)*tl_zeta(i,Jstr-1,know)+ & !^ & tl_Ce*(zeta(i,Jstr ,know)- & !^ & zeta(i,Jstr-1,know)) !^ ad_zeta(i,Jstr ,know)=ad_zeta(i,Jstr ,know)+ & & (0.5_r8+Ce)*ad_Ze ad_zeta(i,Jstr-1,know)=ad_zeta(i,Jstr-1,know)+ & & (0.5_r8-Ce)*ad_Ze ad_Ce=ad_Ce+ & & (zeta(i,Jstr ,know)- & & zeta(i,Jstr-1,know))*ad_Ze ad_Ze=0.0_r8 !^ tl_Ce=dt2d*0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & !^ & GRID(ng)%pn(i,Jstr ))* & !^ & (cff1*tl_cff+ & !^ & tl_cff1*cff) !^ adfac=dt2d*0.5_r8*(GRID(ng)%pn(i,Jstr-1)+ & & GRID(ng)%pn(i,Jstr ))*ad_Ce ad_cff=ad_cff+cff1*adfac ad_cff1=ad_cff1+cff*adfac ad_Ce=0.0_r8 !^ tl_cff1=-0.5_r8*cff1*tl_cff/cff !^ ad_cff=ad_cff- & & 0.5_r8*cff1*ad_cff1/cff ad_cff1=0.0_r8 # ifdef WET_DRY_NOT_YET !^ tl_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=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 # else !^ tl_cff=0.5_r8*(GRID(ng)%tl_h(i,Jstr-1)+ & !^ & GRID(ng)%tl_h(i,Jstr )) !^ adfac=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_cff=0.0_r8 # endif # if defined SSH_TIDES_NOT_YET && !defined UV_TIDES_NOT_YET IF (ad_LBC(isouth,isFsur,ng)%acquire) THEN 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 )) END IF # 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 IF (ad_LBC(isouth,isFsur,ng)%acquire) THEN # 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 END IF # 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 IF END DO ! ! Southern edge, clamped boundary condition. ! ELSE IF (ad_LBC(isouth,isVbar,ng)%clamped) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN # 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 IF END DO ! ! Southern edge, gradient boundary condition. ! ELSE IF (ad_LBC(isouth,isVbar,ng)%gradient) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN # 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 IF END DO ! ! Southern edge, reduced-physics boundary condition. ! ELSE IF (ad_LBC(isouth,isVbar,ng)%reduced) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN 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 IF (ad_LBC(isouth,isFsur,ng)%acquire) THEN # 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) !^ ad_zeta(i,Jstr,know)=ad_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 END IF END IF END DO ! ! Southern edge, closed boundary condition. ! ELSE IF (ad_LBC(isouth,isVbar,ng)%closed) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN !^ tl_vbar(i,Jstr,kout)=0.0_r8 !^ ad_vbar(i,Jstr,kout)=0.0_r8 END IF END DO END IF END IF RETURN END SUBROUTINE ad_v2dbc_tile #endif END MODULE ad_v2dbc_mod