MODULE tl_u2dbc_mod ! !git $Id$ !svn $Id: tl_u2dbc_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 tangent linear lateral boundary conditions for ! ! vertically integrated U-velocity. It updates the specified "kout" ! ! index. ! ! ! ! BASIC STATE variables needed: ubar ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: tl_u2dbc, tl_u2dbc_tile ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_u2dbc (ng, tile, kout) !*********************************************************************** ! USE mod_param USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, kout ! ! Local variable declarations. ! integer :: IminS, ImaxS, JminS, JmaxS integer :: LBi, UBi, LBj, UBj, LBij, UBij ! ! Set horizontal starting and ending indices for automatic private ! storage arrays. ! IminS=BOUNDS(ng)%Istr(tile)-3 ImaxS=BOUNDS(ng)%Iend(tile)+3 JminS=BOUNDS(ng)%Jstr(tile)-3 JmaxS=BOUNDS(ng)%Jend(tile)+3 ! ! Determine array lower and upper bounds in the I- and J-directions. ! LBi=BOUNDS(ng)%LBi(tile) UBi=BOUNDS(ng)%UBi(tile) LBj=BOUNDS(ng)%LBj(tile) UBj=BOUNDS(ng)%UBj(tile) ! ! Set array lower and upper bounds for MIN(I,J) directions and ! MAX(I,J) directions. ! LBij=BOUNDS(ng)%LBij UBij=BOUNDS(ng)%UBij ! CALL tl_u2dbc_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) % tl_ubar, & & OCEAN(ng) % tl_vbar, & & OCEAN(ng) % tl_zeta) RETURN END SUBROUTINE tl_u2dbc ! !*********************************************************************** SUBROUTINE tl_u2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, kout, & & ubar, vbar, zeta, & & tl_ubar, tl_vbar, tl_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 ! real(r8), intent(in) :: ubar(LBi:,LBj:,:) real(r8), intent(in) :: vbar(LBi:,LBj:,:) real(r8), intent(in) :: zeta(LBi:,LBj:,:) real(r8), intent(in) :: tl_vbar(LBi:,LBj:,:) real(r8), intent(in) :: tl_zeta(LBi:,LBj:,:) real(r8), intent(inout) :: tl_ubar(LBi:,LBj:,:) ! ! Local variable declarations. ! integer :: Imin, Imax integer :: i, j, know real(r8) :: Ce, Cx, Zx real(r8) :: bry_pgr, bry_cor, bry_str real(r8) :: cff, cff1, cff2, cff3, dt2d real(r8) :: obc_in, obc_out, tau real(r8) :: tl_Ce, tl_Cx, tl_Zx real(r8) :: tl_bry_pgr, tl_bry_cor, tl_bry_str, tl_bry_val real(r8) :: tl_cff, tl_cff1, tl_cff2, tl_cff3 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_grad ! !----------------------------------------------------------------------- ! Set lower and upper tile bounds and staggered variables bounds for ! this horizontal domain partition. Notice that if tile=-1, it will ! set the values for the global grid. !----------------------------------------------------------------------- ! integer :: Istr, IstrB, IstrP, IstrR, IstrT, IstrM, IstrU integer :: Iend, IendB, IendP, IendR, IendT integer :: Jstr, JstrB, JstrP, JstrR, JstrT, JstrM, JstrV integer :: Jend, JendB, JendP, JendR, JendT integer :: Istrm3, Istrm2, Istrm1, IstrUm2, IstrUm1 integer :: Iendp1, Iendp2, Iendp2i, Iendp3 integer :: Jstrm3, Jstrm2, Jstrm1, JstrVm2, JstrVm1 integer :: Jendp1, Jendp2, Jendp2i, Jendp3 ! Istr =BOUNDS(ng) % Istr (tile) IstrB =BOUNDS(ng) % IstrB (tile) IstrM =BOUNDS(ng) % IstrM (tile) IstrP =BOUNDS(ng) % IstrP (tile) IstrR =BOUNDS(ng) % IstrR (tile) IstrT =BOUNDS(ng) % IstrT (tile) IstrU =BOUNDS(ng) % IstrU (tile) Iend =BOUNDS(ng) % Iend (tile) IendB =BOUNDS(ng) % IendB (tile) IendP =BOUNDS(ng) % IendP (tile) IendR =BOUNDS(ng) % IendR (tile) IendT =BOUNDS(ng) % IendT (tile) Jstr =BOUNDS(ng) % Jstr (tile) JstrB =BOUNDS(ng) % JstrB (tile) JstrM =BOUNDS(ng) % JstrM (tile) JstrP =BOUNDS(ng) % JstrP (tile) JstrR =BOUNDS(ng) % JstrR (tile) JstrT =BOUNDS(ng) % JstrT (tile) JstrV =BOUNDS(ng) % JstrV (tile) Jend =BOUNDS(ng) % Jend (tile) JendB =BOUNDS(ng) % JendB (tile) JendP =BOUNDS(ng) % JendP (tile) JendR =BOUNDS(ng) % JendR (tile) JendT =BOUNDS(ng) % JendT (tile) ! Istrm3 =BOUNDS(ng) % Istrm3 (tile) ! Istr-3 Istrm2 =BOUNDS(ng) % Istrm2 (tile) ! Istr-2 Istrm1 =BOUNDS(ng) % Istrm1 (tile) ! Istr-1 IstrUm2=BOUNDS(ng) % IstrUm2(tile) ! IstrU-2 IstrUm1=BOUNDS(ng) % IstrUm1(tile) ! IstrU-1 Iendp1 =BOUNDS(ng) % Iendp1 (tile) ! Iend+1 Iendp2 =BOUNDS(ng) % Iendp2 (tile) ! Iend+2 Iendp2i=BOUNDS(ng) % Iendp2i(tile) ! Iend+2 interior Iendp3 =BOUNDS(ng) % Iendp3 (tile) ! Iend+3 Jstrm3 =BOUNDS(ng) % Jstrm3 (tile) ! Jstr-3 Jstrm2 =BOUNDS(ng) % Jstrm2 (tile) ! Jstr-2 Jstrm1 =BOUNDS(ng) % Jstrm1 (tile) ! Jstr-1 JstrVm2=BOUNDS(ng) % JstrVm2(tile) ! JstrV-2 JstrVm1=BOUNDS(ng) % JstrVm1(tile) ! JstrV-1 Jendp1 =BOUNDS(ng) % Jendp1 (tile) ! Jend+1 Jendp2 =BOUNDS(ng) % Jendp2 (tile) ! Jend+2 Jendp2i=BOUNDS(ng) % Jendp2i(tile) ! Jend+2 interior Jendp3 =BOUNDS(ng) % Jendp3 (tile) ! Jend+3 ! !----------------------------------------------------------------------- ! Set time-indices !----------------------------------------------------------------------- ! IF (iif(ng).eq.1) 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 ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the western edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Western_Edge(tile)) THEN ! ! Western edge, implicit upstream radiation condition. ! IF (tl_LBC(iwest,isUbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO j=Jstr,Jend+1 !^ grad(Istr,j)=ubar(Istr,j ,know)- & !^ & ubar(Istr,j-1,know) !^ tl_grad(Istr,j)=0.0_r8 END DO DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ ubar(Istr,j,kout)=(cff*ubar(Istr ,j,know)+ & !^ & Cx *ubar(Istr+1,j,kout)- & !^ & MAX(Ce,0.0_r8)*grad(Istr,j )- & !^ & MIN(Ce,0.0_r8)*grad(Istr,j+1))/ & !^ & (cff+Cx) !^ tl_ubar(Istr,j,kout)=(cff*tl_ubar(Istr ,j,know)+ & & Cx *tl_ubar(Istr+1,j,kout)- & & MAX(Ce,0.0_r8)* & & tl_grad(Istr,j )- & & MIN(Ce,0.0_r8)* & & tl_grad(Istr,j+1))/ & & (cff+Cx) IF (tl_LBC(iwest,isUbar,ng)%nudging) THEN !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)+ & !^ & tau*(BOUNDARY(ng)%ubar_west(j)- & !^ & ubar(Istr,j,know)) & !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)- & & tau*tl_ubar(Istr,j,know) END IF !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO END IF ! ! Western edge, Flather boundary condition. ! ELSE IF (tl_LBC(iwest,isUbar,ng)%Flather) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ bry_val=BOUNDARY(ng)%ubar_west(j) !^ tl_bry_val=0.0_r8 cff=1.0_r8/(0.5_r8*(GRID(ng)%h(Istr-1,j)+ & & zeta(Istr-1,j,know)+ & & GRID(ng)%h(Istr ,j)+ & & zeta(Istr ,j,know))) tl_cff=-cff*cff*(0.5_r8*(GRID(ng)%tl_h(Istr-1,j)+ & & tl_zeta(Istr-1,j,know)+ & & GRID(ng)%tl_h(Istr ,j)+ & & tl_zeta(Istr ,j,know))) Cx=SQRT(g*cff) tl_Cx=0.5_r8*g*tl_cff/Cx !^ ubar(Istr,j,kout)=bry_val- & !^ & Cx*(0.5_r8*(zeta(Istr-1,j,know)+ & !^ & zeta(Istr ,j,know))- & !^ & BOUNDARY(ng)%zeta_west(j)) !^ tl_ubar(Istr,j,kout)=tl_bry_val- & & tl_Cx* & & (0.5_r8*(zeta(Istr-1,j,know)+ & & zeta(Istr ,j,know))- & & BOUNDARY(ng)%zeta_west(j))- & & Cx* & & (0.5_r8*(tl_zeta(Istr-1,j,know)+ & & tl_zeta(Istr ,j,know))) !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO ! ! Western edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (tl_LBC(iwest,isUbar,ng)%Shchepetkin) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ bry_val=BOUNDARY(ng)%ubar_west(j) !^ tl_bry_val=0.0_r8 cff=0.5_r8*(GRID(ng)%h(Istr-1,j)+ & & GRID(ng)%h(Istr ,j)) tl_cff=0.5_r8*(GRID(ng)%tl_h(Istr-1,j)+ & & GRID(ng)%tl_h(Istr ,j)) cff1=SQRT(g/cff) tl_cff1=-0.5_r8*cff1*tl_cff/cff Cx=dt2d*cff1*cff*0.5_r8*(GRID(ng)%pm(Istr-1,j)+ & & GRID(ng)%pm(Istr ,j)) tl_Cx=dt2d*0.5_r8*(GRID(ng)%pm(Istr-1,j)+ & & GRID(ng)%pm(Istr ,j))* & & (cff1*tl_cff+ & & tl_cff1*cff) Zx=(0.5_r8+Cx)*zeta(Istr ,j,know)+ & & (0.5_r8-Cx)*zeta(Istr-1,j,know) tl_Zx=(0.5_r8+Cx)*tl_zeta(Istr ,j,know)+ & & (0.5_r8-Cx)*tl_zeta(Istr-1,j,know)+ & & tl_Cx*(zeta(Istr ,j,know)- & & zeta(Istr-1,j,know)) IF (Cx.gt.Co) THEN cff2=(1.0_r8-Co/Cx)**2 tl_cff2=2.0_r8*cff2*Co*tl_Cx/(Cx*Cx) cff3=zeta(Istr,j,kout)+ & & Cx*zeta(Istr-1,j,know)- & & (1.0_r8+Cx)*zeta(Istr,j,know) tl_cff3=tl_zeta(Istr,j,kout)+ & & Cx*tl_zeta(Istr-1,j,know)+ & & tl_Cx*(zeta(Istr-1,j,know)+ & & zeta(Istr ,j,know))- & & (1.0_r8+Cx)*tl_zeta(Istr,j,know) Zx=Zx+cff2*cff3 tl_Zx=tl_Zx+cff2*tl_cff3+ & & tl_cff2*cff3 END IF !^ ubar(Istr,j,kout)=0.5_r8* & !^ & ((1.0_r8-Cx)*ubar(Istr,j,know)+ & !^ & Cx*ubar(Istr+1,j,know)+ & !^ & bry_val- & !^ & cff1*(Zx-BOUNDARY(ng)%zeta_west(j))) !^ tl_ubar(Istr,j,kout)=0.5_r8* & & ((1.0_r8-Cx)* & & tl_ubar(Istr,j,know)- & & tl_Cx*(ubar(Istr ,j,know)- & & ubar(Istr+1,j,know))+ & & Cx*tl_ubar(Istr+1,j,know)+ & & tl_bry_val- & & tl_cff1* & & (Zx-BOUNDARY(ng)%zeta_west(j))- & & cff1*tl_Zx) !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO ! ! Western edge, clamped boundary condition. ! ELSE IF (tl_LBC(iwest,isUbar,ng)%clamped) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ ubar(Istr,j,kout)=BOUNDARY(ng)%ubar_west(j) !^ tl_ubar(Istr,j,kout)=0.0_r8 !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO ! ! Western edge, gradient boundary condition. ! ELSE IF (tl_LBC(iwest,isUbar,ng)%gradient) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ ubar(Istr,j,kout)=ubar(Istr+1,j,kout) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr+1,j,kout) !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO ! ! Western edge, reduced-physics boundary condition. ! ELSE IF (tl_LBC(iwest,isUbar,ng)%reduced) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN IF (tl_LBC(iwest,isFsur,ng)%acquire) THEN !^ bry_pgr=-g*(zeta(Istr,j,know)- & !^ & BOUNDARY(ng)%zeta_west(j))* & !^ & 0.5_r8*GRID(ng)%pm(Istr,j) !^ tl_bry_pgr=-g*tl_zeta(Istr,j,know)* & & 0.5_r8*GRID(ng)%pm(Istr,j) ELSE !^ bry_pgr=-g*(zeta(Istr,j,know)- & !^ & zeta(Istr-1,j,know))* & !^ & 0.5_r8*(GRID(ng)%pm(Istr-1,j)+ & !^ & GRID(ng)%pm(Istr ,j)) !^ tl_bry_pgr=-g*(tl_zeta(Istr ,j,know)- & & tl_zeta(Istr-1,j,know))* & & 0.5_r8*(GRID(ng)%pm(Istr-1,j)+ & & GRID(ng)%pm(Istr ,j)) END IF !^ bry_cor=0.125_r8*(vbar(Istr-1,j ,know)+ & !^ & vbar(Istr-1,j+1,know)+ & !^ & vbar(Istr ,j ,know)+ & !^ & vbar(Istr ,j+1,know))* & !^ & (GRID(ng)%f(Istr-1,j)+ & !^ & GRID(ng)%f(Istr ,j)) !^ tl_bry_cor=0.125_r8*(tl_vbar(Istr-1,j ,know)+ & & tl_vbar(Istr-1,j+1,know)+ & & tl_vbar(Istr ,j ,know)+ & & tl_vbar(Istr ,j+1,know))* & & (GRID(ng)%f(Istr-1,j)+ & & GRID(ng)%f(Istr ,j)) cff=1.0_r8/(0.5_r8*(GRID(ng)%h(Istr-1,j)+ & & zeta(Istr-1,j,know)+ & & GRID(ng)%h(Istr ,j)+ & & zeta(Istr ,j,know))) tl_cff=-cff*cff*0.5_r8*(GRID(ng)%tl_h(Istr-1,j)+ & & tl_zeta(Istr-1,j,know)+ & & GRID(ng)%tl_h(Istr ,j)+ & & tl_zeta(Istr ,j,know)) !^ bry_str=cff*(FORCES(ng)%sustr(Istr,j)- & !^ & FORCES(ng)%bustr(Istr,j)) !^ tl_bry_str=tl_cff*(FORCES(ng)%sustr(Istr,j)- & & FORCES(ng)%bustr(Istr,j))+ & & cff*(FORCES(ng)%tl_sustr(Istr,j)- & & FORCES(ng)%tl_bustr(Istr,j)) !^ ubar(Istr,j,kout)=ubar(Istr,j,know)+ & !^ & dt2d*(bry_pgr+ & !^ & bry_cor+ & !^ & bry_str) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,know)+ & & dt2d*(tl_bry_pgr+ & & tl_bry_cor+ & & tl_bry_str) !^ ubar(Istr,j,kout)=ubar(Istr,j,kout)* & !^ & GRID(ng)%umask(Istr,j) !^ tl_ubar(Istr,j,kout)=tl_ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) END IF END DO ! ! Western edge, closed boundary condition. ! ELSE IF (tl_LBC(iwest,isUbar,ng)%closed) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN !^ ubar(Istr,j,kout)=0.0_r8 !^ tl_ubar(Istr,j,kout)=0.0_r8 END IF END DO 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 (tl_LBC(ieast,isUbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO j=Jstr,Jend+1 !^ grad(Iend+1,j)=ubar(Iend+1,j ,know)- & !^ & ubar(Iend+1,j-1,know) !^ tl_grad(Iend+1,j)=0.0_r8 END DO DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ ubar(Iend+1,j,kout)=(cff*ubar(Iend+1,j,know)+ & !^ & Cx *ubar(Iend ,j,kout)- & !^ & MAX(Ce,0.0_r8)*grad(Iend+1,j )- & !^ & MIN(Ce,0.0_r8)*grad(Iend+1,j+1))/ & !^ & (cff+Cx) !^ tl_ubar(Iend+1,j,kout)=(cff*tl_ubar(Iend+1,j,know)+ & & Cx *tl_ubar(Iend ,j,kout)- & & MAX(Ce,0.0_r8)* & & tl_grad(Iend+1,j )- & & MIN(Ce,0.0_r8)* & & tl_grad(Iend+1,j+1))/ & & (cff+Cx) IF (tl_LBC(ieast,isUbar,ng)%nudging) THEN !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)+ & !^ & tau*(BOUNDARY(ng)%ubar_east(j)- & !^ & ubar(Iend+1,j,know)) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)- & & tau*tl_ubar(Iend+1,j,know) END IF !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO END IF ! ! Eastern edge, Flather boundary condition. ! ELSE IF (tl_LBC(ieast,isUbar,ng)%Flather) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ bry_val=BOUNDARY(ng)%ubar_east(j) !^ tl_bry_val=0.0_r8 cff=1.0_r8/(0.5_r8*(GRID(ng)%h(Iend ,j)+ & & zeta(Iend ,j,know)+ & & GRID(ng)%h(Iend+1,j)+ & & zeta(Iend+1,j,know))) tl_cff=-cff*cff*(0.5_r8*(GRID(ng)%tl_h(Iend ,j)+ & & tl_zeta(Iend ,j,know)+ & & GRID(ng)%tl_h(Iend+1,j)+ & & tl_zeta(Iend+1,j,know))) Cx=SQRT(g*cff) tl_Cx=0.5_r8*g*tl_cff/Cx !^ ubar(Iend+1,j,kout)=bry_val+ & !^ & Cx*(0.5_r8*(zeta(Iend ,j,know)+ & !^ & zeta(Iend+1,j,know))- & !^ & BOUNDARY(ng)%zeta_east(j)) !^ tl_ubar(Iend+1,j,kout)=tl_bry_val+ & & tl_Cx* & & (0.5_r8*(zeta(Iend ,j,know)+ & & zeta(Iend+1,j,know))- & & BOUNDARY(ng)%zeta_east(j))+ & & Cx* & & (0.5_r8*(tl_zeta(Iend ,j,know)+ & & tl_zeta(Iend+1,j,know))) !^ & ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO ! ! Eastern edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (tl_LBC(ieast,isUbar,ng)%Shchepetkin) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ bry_val=BOUNDARY(ng)%ubar_east(j) !^ tl_bry_val=0.0_r8 cff=0.5_r8*(GRID(ng)%h(Iend ,j)+ & & GRID(ng)%h(Iend+1,j)) tl_cff=0.5_r8*(GRID(ng)%tl_h(Iend ,j)+ & & GRID(ng)%tl_h(Iend+1,j)) cff1=SQRT(g/cff) tl_cff1=-0.5_r8*cff1*tl_cff/cff Cx=dt2d*cff1*cff*0.5_r8*(GRID(ng)%pm(Iend ,j)+ & & GRID(ng)%pm(Iend+1,j)) tl_Cx=dt2d*0.5_r8*(GRID(ng)%pm(Iend ,j)+ & & GRID(ng)%pm(Iend+1,j))* & & (cff1*tl_cff+ & & tl_cff1*cff) Zx=(0.5_r8+Cx)*zeta(Iend ,j,know)+ & & (0.5_r8-Cx)*zeta(Iend+1,j,know) tl_Zx=(0.5_r8+Cx)*tl_zeta(Iend ,j,know)+ & & (0.5_r8-Cx)*tl_zeta(Iend+1,j,know)+ & & tl_Cx*(zeta(Iend ,j,know)- & & zeta(Iend+1,j,know)) IF (Cx.gt.Co) THEN cff2=(1.0_r8-Co/Cx)**2 tl_cff2=2.0_r8*cff2*Co*tl_Cx/(Cx*Cx) cff3=zeta(Iend,j,kout)+ & & Cx*zeta(Iend+1,j,know)- & & (1.0_r8+Cx)*zeta(Iend,j,know) tl_cff3=tl_zeta(Iend,j,kout)+ & & Cx*tl_zeta(Iend+1,j,know)+ & & tl_Cx*(zeta(Iend ,j,know)+ & & zeta(Iend+1,j,know))- & & (1.0_r8+Cx)*tl_zeta(Iend,j,know) Zx=Zx+cff2*cff3 tl_Zx=tl_Zx+cff2*tl_cff3+ & & tl_cff2*cff3 END IF !^ ubar(Iend+1,j,kout)=0.5_r8* & !^ & ((1.0_r8-Cx)*ubar(Iend+1,j,know)+ & !^ & Cx*ubar(Iend,j,know)+ & !^ & bry_val+ & !^ & cff1*(Zx-BOUNDARY(ng)%zeta_east(j))) !^ tl_ubar(Iend+1,j,kout)=0.5_r8* & & ((1.0_r8-Cx)* & & tl_ubar(Iend+1,j,know)+ & & tl_Cx*(ubar(Iend ,j,know)- & & ubar(Iend+1,j,know))+ & & Cx*tl_ubar(Iend,j,know)+ & & tl_bry_val+ & & tl_cff1* & & (Zx-BOUNDARY(ng)%zeta_east(j))- & & cff1*tl_Zx) !^ & ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO ! ! Eastern edge, clamped boundary condition. ! ELSE IF (tl_LBC(ieast,isUbar,ng)%clamped) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ ubar(Iend+1,j,kout)=BOUNDARY(ng)%ubar_east(j) !^ tl_ubar(Iend+1,j,kout)=0.0_r8 !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO ! ! Eastern edge, gradient boundary condition. ! ELSE IF (tl_LBC(ieast,isUbar,ng)%gradient) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ ubar(Iend+1,j,kout)=ubar(Iend,j,kout) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend,j,kout) !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO ! ! Eastern edge, reduced-physics boundary condition. ! ELSE IF (tl_LBC(ieast,isUbar,ng)%reduced) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN IF (tl_LBC(ieast,isFsur,ng)%acquire) THEN !^ bry_pgr=-g*(BOUNDARY(ng)%zeta_east(j)- & !^ & zeta(Iend,j,know))* & !^ & 0.5_r8*GRID(ng)%pm(Iend,j) !^ tl_bry_pgr=g*tl_zeta(Iend,j,know)* & & 0.5_r8*GRID(ng)%pm(Iend,j) ELSE !^ bry_pgr=-g*(zeta(Iend+1,j,know)- & !^ & zeta(Iend ,j,know))* & !^ & 0.5_r8*(GRID(ng)%pm(Iend ,j)+ & !^ & GRID(ng)%pm(Iend+1,j)) !^ tl_bry_pgr=-g*(tl_zeta(Iend+1,j,know)- & & tl_zeta(Iend ,j,know))* & & 0.5_r8*(GRID(ng)%pm(Iend ,j)+ & & GRID(ng)%pm(Iend+1,j)) END IF !^ bry_cor=0.125_r8*(vbar(Iend ,j ,know)+ & !^ & vbar(Iend ,j+1,know)+ & !^ & vbar(Iend+1,j ,know)+ & !^ & vbar(Iend+1,j+1,know))* & !^ & (GRID(ng)%f(Iend ,j)+ & !^ & GRID(ng)%f(Iend+1,j)) !^ tl_bry_cor=0.125_r8*(tl_vbar(Iend, j ,know)+ & & tl_vbar(Iend ,j+1,know)+ & & tl_vbar(Iend+1,j ,know)+ & & tl_vbar(Iend+1,j+1,know))* & & (GRID(ng)%f(Iend ,j)+ & & GRID(ng)%f(Iend+1,j)) cff=1.0_r8/(0.5_r8*(GRID(ng)%h(Iend ,j)+ & & zeta(Iend ,j,know)+ & & GRID(ng)%h(Iend+1,j)+ & & zeta(Iend+1,j,know))) tl_cff=-cff*cff*0.5_r8*(GRID(ng)%tl_h(Iend ,j)+ & & tl_zeta(Iend ,j,know)+ & & GRID(ng)%tl_h(Iend+1,j)+ & & tl_zeta(Iend+1,j,know)) !^ bry_str=cff*(FORCES(ng)%sustr(Iend+1,j)- & !^ & FORCES(ng)%bustr(Iend+1,j)) !^ tl_bry_str=tl_cff*(FORCES(ng)%sustr(Iend+1,j)- & & FORCES(ng)%bustr(Iend+1,j))+ & & cff*(FORCES(ng)%tl_sustr(Iend+1,j)- & & FORCES(ng)%tl_bustr(Iend+1,j)) !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,know)+ & !^ & dt2d*(bry_pgr+ & !^ & bry_cor+ & !^ & bry_str) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,know)+ & & dt2d*(tl_bry_pgr+ & & tl_bry_cor+ & & tl_bry_str) !^ ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & !^ & GRID(ng)%umask(Iend+1,j) !^ tl_ubar(Iend+1,j,kout)=tl_ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) END IF END DO ! ! Eastern edge, closed boundary condition. ! ELSE IF (tl_LBC(ieast,isUbar,ng)%closed) THEN DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN !^ ubar(Iend+1,j,kout)=0.0_r8 !^ tl_ubar(Iend+1,j,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 (tl_LBC(isouth,isUbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO i=IstrU-1,Iend !^ grad(i,Jstr-1)=ubar(i+1,Jstr-1,know)- & !^ & ubar(i ,Jstr-1,know) !^ tl_grad(i,Jstr-1)=0.0_r8 END DO DO i=IstrU,Iend IF (LBC_apply(ng)%south(i)) THEN !^ ubar(i,Jstr-1,kout)=(cff*ubar(i,Jstr-1,know)+ & !^ & Ce *ubar(i,Jstr ,kout)- & !^ & MAX(Cx,0.0_r8)*grad(i-1,Jstr-1)- & !^ & MIN(Cx,0.0_r8)*grad(i ,Jstr-1))/ & !^ & (cff+Ce) !^ tl_ubar(i,Jstr-1,kout)=(cff*tl_ubar(i,Jstr-1,know)+ & & Ce *tl_ubar(i,Jstr ,kout)- & & MAX(Cx,0.0_r8)* & & tl_grad(i-1,Jstr-1)- & & MIN(Cx,0.0_r8)* & & tl_grad(i ,Jstr-1))/ & & (cff+Ce) IF (tl_LBC(isouth,isUbar,ng)%nudging) THEN !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)+ & !^ & tau*(BOUNDARY(ng)%ubar_south(i)- & !^ & ubar(i,Jstr-1,know)) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)- & & tau*tl_ubar(i,Jstr-1,know) END IF !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & !^ & GRID(ng)%umask(i,Jstr-1) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) END IF END DO END IF ! ! Southern edge, Chapman boundary condition. ! ELSE IF (tl_LBC(isouth,isUbar,ng)%Flather.or. & & tl_LBC(isouth,isUbar,ng)%reduced.or. & & tl_LBC(isouth,isUbar,ng)%Shchepetkin) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%south(i)) THEN cff=dt2d*0.5_r8*(GRID(ng)%pn(i-1,Jstr)+ & & GRID(ng)%pn(i ,Jstr)) cff1=SQRT(g*0.5_r8*(GRID(ng)%h(i-1,Jstr)+ & & zeta(i-1,Jstr,know)+ & & GRID(ng)%h(i ,Jstr)+ & & zeta(i ,Jstr,know))) tl_cff1=0.25_r8*g*(GRID(ng)%tl_h(i-1,Jstr)+ & & tl_zeta(i-1,Jstr,know)+ & & GRID(ng)%tl_h(i ,Jstr)+ & & tl_zeta(i ,Jstr,know))/cff1 Ce=cff*cff1 tl_Ce=cff*tl_cff1 cff2=1.0_r8/(1.0_r8+Ce) tl_cff2=-cff2*cff2*tl_Ce !^ ubar(i,Jstr-1,kout)=cff2*(ubar(i,Jstr-1,know)+ & !^ & Ce*ubar(i,Jstr,kout)) !^ tl_ubar(i,Jstr-1,kout)=tl_cff2*(ubar(i,Jstr-1,know)+ & & Ce*ubar(i,Jstr,kout))+ & & cff2*(tl_ubar(i,Jstr-1,know)+ & & tl_Ce*ubar(i,Jstr,kout)+ & & Ce*tl_ubar(i,Jstr,kout)) !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & !^ & GRID(ng)%umask(i,Jstr-1) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) END IF END DO ! ! Southern edge, clamped boundary condition. ! ELSE IF (tl_LBC(isouth,isUbar,ng)%clamped) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%south(i)) THEN !^ ubar(i,Jstr-1,kout)=BOUNDARY(ng)%ubar_south(i) !^ tl_ubar(i,Jstr-1,kout)=0.0_r8 !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & !^ & GRID(ng)%umask(i,Jstr-1) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) END IF END DO ! ! Southern edge, gradient boundary condition. ! ELSE IF (tl_LBC(isouth,isUbar,ng)%gradient) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%south(i)) THEN !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr,kout) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr,kout) !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & !^ & GRID(ng)%umask(i,Jstr-1) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) END IF END DO ! ! Southern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (tl_LBC(isouth,isUbar,ng)%closed) THEN IF (EWperiodic(ng)) THEN Imin=IstrU Imax=Iend ELSE Imin=Istr Imax=IendR END IF DO i=Imin,Imax IF (LBC_apply(ng)%south(i)) THEN !^ ubar(i,Jstr-1,kout)=gamma2(ng)*ubar(i,Jstr,kout) !^ tl_ubar(i,Jstr-1,kout)=gamma2(ng)*tl_ubar(i,Jstr,kout) !^ ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & !^ & GRID(ng)%umask(i,Jstr-1) !^ tl_ubar(i,Jstr-1,kout)=tl_ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) 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 (tl_LBC(inorth,isUbar,ng)%radiation) THEN IF (iic(ng).ne.0) THEN DO i=IstrU-1,Iend !^ grad(i,Jend+1)=ubar(i+1,Jend+1,know)- & !^ & ubar(i ,Jend+1,know) !^ tl_grad(i,Jend+1)=0.0_r8 END DO DO i=IstrU,Iend IF (LBC_apply(ng)%north(i)) THEN !^ ubar(i,Jend+1,kout)=(cff*ubar(i,Jend+1,know)+ & !^ & Ce *ubar(i,Jend ,kout)- & !^ & MAX(Cx,0.0_r8)*grad(i-1,Jend+1)- & !^ & MIN(Cx,0.0_r8)*grad(i ,Jend+1))/ & !^ & (cff+Ce) !^ tl_ubar(i,Jend+1,kout)=(cff*tl_ubar(i,Jend+1,know)+ & & Ce *tl_ubar(i,Jend ,kout)- & & MAX(Cx,0.0_r8)* & & tl_grad(i-1,Jend+1)- & & MIN(Cx,0.0_r8)* & & tl_grad(i ,Jend+1))/ & & (cff+Ce) IF (tl_LBC(inorth,isUbar,ng)%nudging) THEN !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)+ & !^ & tau*(BOUNDARY(ng)%ubar_north(i)- & !^ & ubar(i,Jend+1,know)) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)- & & tau*tl_ubar(i,Jend+1,know) END IF !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & !^ & GRID(ng)%umask(i,Jend+1) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) END IF END DO END IF ! ! Northern edge, Chapman boundary condition. ! ELSE IF (tl_LBC(inorth,isUbar,ng)%Flather.or. & & tl_LBC(inorth,isUbar,ng)%reduced.or. & & tl_LBC(inorth,isUbar,ng)%Shchepetkin) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%north(i)) THEN cff=dt2d*0.5_r8*(GRID(ng)%pn(i-1,Jend)+ & & GRID(ng)%pn(i ,Jend)) cff1=SQRT(g*0.5_r8*(GRID(ng)%h(i-1,Jend)+ & & zeta(i-1,Jend,know)+ & & GRID(ng)%h(i ,Jend)+ & & zeta(i ,Jend,know))) tl_cff1=0.25_r8*g*(GRID(ng)%tl_h(i-1,Jend)+ & & tl_zeta(i-1,Jend,know)+ & & GRID(ng)%tl_h(i ,Jend)+ & & tl_zeta(i ,Jend,know))/cff1 Ce=cff*cff1 tl_Ce=cff*tl_cff1 cff2=1.0_r8/(1.0_r8+Ce) tl_cff2=-cff2*cff2*tl_Ce !^ ubar(i,Jend+1,kout)=cff2*(ubar(i,Jend+1,know)+ & !^ & Ce*ubar(i,Jend,kout)) !^ tl_ubar(i,Jend+1,kout)=tl_cff2*(ubar(i,Jend+1,know)+ & & Ce*ubar(i,Jend,kout))+ & & cff2*(tl_ubar(i,Jend+1,know)+ & & tl_Ce*ubar(i,Jend,kout)+ & & Ce*tl_ubar(i,Jend,kout)) !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & !^ & GRID(ng)%umask(i,Jend+1) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) END IF END DO ! ! Northern edge, clamped boundary condition. ! ELSE IF (tl_LBC(inorth,isUbar,ng)%clamped) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%north(i)) THEN !^ ubar(i,Jend+1,kout)=BOUNDARY(ng)%ubar_north(i) !^ tl_ubar(i,Jend+1,kout)=0.0_r8 !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & !^ & GRID(ng)%umask(i,Jend+1) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) END IF END DO ! ! Northern edge, gradient boundary condition. ! ELSE IF (tl_LBC(inorth,isUbar,ng)%gradient) THEN DO i=IstrU,Iend IF (LBC_apply(ng)%north(i)) THEN !^ ubar(i,Jend+1,kout)=ubar(i,Jend,kout) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend,kout) !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & !^ & GRID(ng)%umask(i,Jend+1) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) END IF END DO ! ! Northern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (tl_LBC(inorth,isUbar,ng)%closed) THEN IF (EWperiodic(ng)) THEN Imin=IstrU Imax=Iend ELSE Imin=Istr Imax=IendR END IF DO i=Imin,Imax IF (LBC_apply(ng)%north(i)) THEN !^ ubar(i,Jend+1,kout)=gamma2(ng)*ubar(i,Jend,kout) !^ tl_ubar(i,Jend+1,kout)=gamma2(ng)*tl_ubar(i,Jend,kout) !^ ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & !^ & GRID(ng)%GRID(ng)%umask(i,Jend+1) !^ tl_ubar(i,Jend+1,kout)=tl_ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) END IF END DO END IF END IF ! !----------------------------------------------------------------------- ! Boundary corners. !----------------------------------------------------------------------- ! IF (.not.(EWperiodic(ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN IF (LBC_apply(ng)%south(Istr ).and. & & LBC_apply(ng)%west (Jstr-1)) THEN !^ ubar(Istr,Jstr-1,kout)=0.5_r8*(ubar(Istr+1,Jstr-1,kout)+ & !^ & ubar(Istr ,Jstr ,kout)) !^ tl_ubar(Istr,Jstr-1,kout)=0.5_r8* & & (tl_ubar(Istr+1,Jstr-1,kout)+ & & tl_ubar(Istr ,Jstr ,kout)) END IF END IF IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN IF (LBC_apply(ng)%south(Iend+1).and. & & LBC_apply(ng)%east (Jstr-1)) THEN !^ ubar(Iend+1,Jstr-1,kout)=0.5_r8*(ubar(Iend ,Jstr-1,kout)+ & !^ & ubar(Iend+1,Jstr ,kout)) !^ tl_ubar(Iend+1,Jstr-1,kout)=0.5_r8* & & (tl_ubar(Iend ,Jstr-1,kout)+ & & tl_ubar(Iend+1,Jstr ,kout)) END IF END IF IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN IF (LBC_apply(ng)%north(Istr ).and. & & LBC_apply(ng)%west (Jend+1)) THEN !^ ubar(Istr,Jend+1,kout)=0.5_r8*(ubar(Istr ,Jend ,kout)+ & !^ & ubar(Istr+1,Jend+1,kout)) !^ tl_ubar(Istr,Jend+1,kout)=0.5_r8* & & (tl_ubar(Istr ,Jend ,kout)+ & & tl_ubar(Istr+1,Jend+1,kout)) END IF END IF IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN IF (LBC_apply(ng)%north(Iend+1).and. & & LBC_apply(ng)%east (Jend+1)) THEN !^ ubar(Iend+1,Jend+1,kout)=0.5_r8*(ubar(Iend+1,Jend ,kout)+ & !^ & ubar(Iend ,Jend+1,kout)) !^ tl_ubar(Iend+1,Jend+1,kout)=0.5_r8* & & (tl_ubar(Iend+1,Jend ,kout)+ & & tl_ubar(Iend ,Jend+1,kout)) END IF END IF END IF ! RETURN END SUBROUTINE tl_u2dbc_tile END MODULE tl_u2dbc_mod