MODULE v2dbc_mod ! !git $Id$ !svn $Id: v2dbc_im.F 1178 2023-07-11 17:50:57Z arango $ !======================================================================= ! Copyright (c) 2002-2023 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md Hernan G. Arango ! !========================================== Alexander F. Shchepetkin === ! ! ! This subroutine sets lateral boundary conditions for vertically ! ! integrated V-velocity. ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: v2dbc, v2dbc_tile ! CONTAINS ! !*********************************************************************** SUBROUTINE 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. ! 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 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) RETURN END SUBROUTINE v2dbc ! !*********************************************************************** SUBROUTINE v2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, kout, & & ubar, vbar, 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) :: zeta(LBi:,LBj:,:) real(r8), intent(inout) :: vbar(LBi:,LBj:,:) ! ! Local variable declarations. ! integer :: Jmin, Jmax integer :: i, j, know real(r8), parameter :: eps = 1.0E-20_r8 real(r8) :: Ce, Cx, Ze real(r8) :: bry_pgr, bry_cor, bry_str, bry_wec, bry_val real(r8) :: cff, cff1, cff2, cff3, dt2d, dVde, dVdt, dVdx real(r8) :: obc_in, obc_out, phi, tau real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: 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 southern edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Southern_Edge(tile)) THEN ! ! Southern edge, implicit upstream radiation condition. ! IF (LBC(isouth,isVbar,ng)%radiation) THEN DO i=Istr,Iend+1 grad(i,Jstr )=vbar(i ,Jstr ,know)- & & vbar(i-1,Jstr ,know) grad(i,Jstr+1)=vbar(i ,Jstr+1,know)- & & vbar(i-1,Jstr+1,know) END DO DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN dVdt=vbar(i,Jstr+1,know)-vbar(i,Jstr+1,kout) dVde=vbar(i,Jstr+1,kout)-vbar(i,Jstr+2,kout) IF (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 ((dVdt*dVde).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF IF ((dVdt*dVde).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(i ,Jstr+1)+ & & grad(i+1,Jstr+1))).gt.0.0_r8) THEN dVdx=grad(i ,Jstr+1) ELSE dVdx=grad(i+1,Jstr+1) END IF cff=MAX(dVdx*dVdx+dVde*dVde,eps) Cx=MIN(cff,MAX(dVdt*dVdx,-cff)) Ce=dVdt*dVde vbar(i,Jstr,kout)=(cff*vbar(i,Jstr ,know)+ & & Ce *vbar(i,Jstr+1,kout)- & & MAX(Cx,0.0_r8)*grad(i ,Jstr)- & & MIN(Cx,0.0_r8)*grad(i+1,Jstr))/ & & (cff+Ce) IF (LBC(isouth,isVbar,ng)%nudging) THEN vbar(i,Jstr,kout)=vbar(i,Jstr,kout)+ & & tau*(BOUNDARY(ng)%vbar_south(i)- & & vbar(i,Jstr,know)) END IF vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, Flather boundary condition. ! ELSE IF (LBC(isouth,isVbar,ng)%Flather) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN bry_val=BOUNDARY(ng)%vbar_south(i) 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) vbar(i,Jstr,kout)=bry_val- & & Ce*(0.5_r8*(zeta(i,Jstr-1,know)+ & & zeta(i,Jstr ,know))- & & BOUNDARY(ng)%zeta_south(i)) vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (LBC(isouth,isVbar,ng)%Shchepetkin) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN bry_val=BOUNDARY(ng)%vbar_south(i) 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 vbar(i,Jstr,kout)=0.5_r8* & & ((1.0_r8-Ce)*vbar(i,Jstr,know)+ & & Ce*vbar(i,Jstr+1,know)+ & & bry_val- & & cff1*(Ze-BOUNDARY(ng)%zeta_south(i))) vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, clamped boundary condition. ! ELSE IF (LBC(isouth,isVbar,ng)%clamped) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN vbar(i,Jstr,kout)=BOUNDARY(ng)%vbar_south(i) vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, gradient boundary condition. ! ELSE IF (LBC(isouth,isVbar,ng)%gradient) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN vbar(i,Jstr,kout)=vbar(i,Jstr+1,kout) vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, reduced-physics boundary condition. ! ELSE IF (LBC(isouth,isVbar,ng)%reduced) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN IF (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 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 )) 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))) bry_str=cff*(FORCES(ng)%svstr(i,Jstr)- & & FORCES(ng)%bvstr(i,Jstr)) vbar(i,Jstr,kout)=vbar(i,Jstr,know)+ & & dt2d*(bry_pgr+ & & bry_cor+ & & bry_str) vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) END IF END DO ! ! Southern edge, closed boundary condition. ! ELSE IF (LBC(isouth,isVbar,ng)%closed) THEN DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN vbar(i,Jstr,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 (LBC(inorth,isVbar,ng)%radiation) THEN DO i=Istr,Iend+1 grad(i,Jend )=vbar(i ,Jend ,know)- & & vbar(i-1,Jend ,know) grad(i,Jend+1)=vbar(i ,Jend+1,know)- & & vbar(i-1,Jend+1,know) END DO DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN dVdt=vbar(i,Jend,know)-vbar(i,Jend ,kout) dVde=vbar(i,Jend,kout)-vbar(i,Jend-1,kout) IF (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 ((dVdt*dVde).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF IF ((dVdt*dVde).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(i ,Jend)+ & & grad(i+1,Jend))).gt.0.0_r8) THEN dVdx=grad(i ,Jend) ELSE dVdx=grad(i+1,Jend) END IF cff=MAX(dVdx*dVdx+dVde*dVde,eps) Cx=MIN(cff,MAX(dVdt*dVdx,-cff)) Ce=dVdt*dVde vbar(i,Jend+1,kout)=(cff*vbar(i,Jend+1,know)+ & & Ce *vbar(i,Jend ,kout)- & & MAX(Cx,0.0_r8)*grad(i ,Jend+1)- & & MIN(Cx,0.0_r8)*grad(i+1,Jend+1))/ & & (cff+Ce) IF (LBC(inorth,isVbar,ng)%nudging) THEN vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)+ & & tau*(BOUNDARY(ng)%vbar_north(i)- & & vbar(i,Jend+1,know)) END IF vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, Flather boundary condition. ! ELSE IF (LBC(inorth,isVbar,ng)%Flather) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN bry_val=BOUNDARY(ng)%vbar_north(i) 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) vbar(i,Jend+1,kout)=bry_val+ & & Ce*(0.5_r8*(zeta(i,Jend ,know)+ & & zeta(i,Jend+1,know))- & & BOUNDARY(ng)%zeta_north(i)) vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, Shchepetkin boundary condition (Maison et al., 2010). ! ELSE IF (LBC(inorth,isVbar,ng)%Shchepetkin) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN bry_val=BOUNDARY(ng)%vbar_north(i) 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 vbar(i,Jend+1,kout)=0.5_r8* & & ((1.0_r8-Ce)*vbar(i,Jend+1,know)+ & & Ce*vbar(i,Jend,know)+ & & bry_val+ & & cff1*(Ze-BOUNDARY(ng)%zeta_north(i))) vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, clamped boundary condition. ! ELSE IF (LBC(inorth,isVbar,ng)%clamped) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN vbar(i,Jend+1,kout)=BOUNDARY(ng)%vbar_north(i) vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, gradient boundary condition. ! ELSE IF (LBC(inorth,isVbar,ng)%gradient) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN vbar(i,Jend+1,kout)=vbar(i,Jend,kout) vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, reduced-physics boundary condition. ! ELSE IF (LBC(inorth,isVbar,ng)%reduced) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN IF (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 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)) 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))) bry_str=cff*(FORCES(ng)%svstr(i,Jend+1)- & & FORCES(ng)%bvstr(i,Jend+1)) vbar(i,Jend+1,kout)=vbar(i,Jend+1,know)+ & & dt2d*(bry_pgr+ & & bry_cor+ & & bry_str) vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) END IF END DO ! ! Northern edge, closed boundary condition. ! ELSE IF (LBC(inorth,isVbar,ng)%closed) THEN DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN vbar(i,Jend+1,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 (LBC(iwest,isVbar,ng)%radiation) THEN DO j=JstrV-1,Jend grad(Istr-1,j)=vbar(Istr-1,j+1,know)- & & vbar(Istr-1,j ,know) grad(Istr ,j)=vbar(Istr ,j+1,know)- & & vbar(Istr ,j ,know) END DO DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN dVdt=vbar(Istr,j,know)-vbar(Istr ,j,kout) dVdx=vbar(Istr,j,kout)-vbar(Istr+1,j,kout) IF (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 ((dVdt*dVdx).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF IF ((dVdt*dVdx).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(Istr,j-1)+ & & grad(Istr,j ))).gt.0.0_r8) THEN dVde=grad(Istr,j-1) ELSE dVde=grad(Istr,j ) END IF cff=MAX(dVdx*dVdx+dVde*dVde,eps) Cx=dVdt*dVdx Ce=MIN(cff,MAX(dVdt*dVde,-cff)) vbar(Istr-1,j,kout)=(cff*vbar(Istr-1,j,know)+ & & Cx *vbar(Istr ,j,kout)- & & MAX(Ce,0.0_r8)*grad(Istr-1,j-1)- & & MIN(Ce,0.0_r8)*grad(Istr-1,j ))/ & & (cff+Cx) IF (LBC(iwest,isVbar,ng)%nudging) THEN vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)+ & & tau*(BOUNDARY(ng)%vbar_west(j)- & & vbar(Istr-1,j,know)) END IF vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) END IF END DO ! ! Western edge, Chapman boundary condition. ! ELSE IF (LBC(iwest,isVbar,ng)%Flather.or. & & LBC(iwest,isVbar,ng)%reduced.or. & & 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) vbar(Istr-1,j,kout)=cff2*(vbar(Istr-1,j,know)+ & & Cx*vbar(Istr,j,kout)) vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) END IF END DO ! ! Western edge, clamped boundary condition. ! ELSE IF (LBC(iwest,isVbar,ng)%clamped) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN vbar(Istr-1,j,kout)=BOUNDARY(ng)%vbar_west(j) vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) END IF END DO ! ! Western edge, gradient boundary condition. ! ELSE IF (LBC(iwest,isVbar,ng)%gradient) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%west(j)) THEN vbar(Istr-1,j,kout)=vbar(Istr,j,kout) vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) END IF END DO ! ! Western edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (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 vbar(Istr-1,j,kout)=gamma2(ng)*vbar(Istr,j,kout) vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) 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 (LBC(ieast,isVbar,ng)%radiation) THEN DO j=JstrV-1,Jend grad(Iend ,j)=vbar(Iend ,j+1,know)- & & vbar(Iend ,j ,know) grad(Iend+1,j)=vbar(Iend+1,j+1,know)- & & vbar(Iend+1,j ,know) END DO DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN dVdt=vbar(Iend,j,know)-vbar(Iend ,j,kout) dVdx=vbar(Iend,j,kout)-vbar(Iend-1,j,kout) IF (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 ((dVdt*dVdx).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt2d END IF IF ((dVdt*dVdx).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(Iend,j-1)+ & & grad(Iend,j ))).gt.0.0_r8) THEN dVde=grad(Iend,j-1) ELSE dVde=grad(Iend,j ) END IF cff=MAX(dVdx*dVdx+dVde*dVde,eps) Cx=dVdt*dVdx Ce=MIN(cff,MAX(dVdt*dVde,-cff)) vbar(Iend+1,j,kout)=(cff*vbar(Iend+1,j,know)+ & & Cx *vbar(Iend ,j,kout)- & & MAX(Ce,0.0_r8)*grad(Iend+1,j-1)- & & MIN(Ce,0.0_r8)*grad(Iend+1,j ))/ & & (cff+Cx) IF (LBC(ieast,isVbar,ng)%nudging) THEN vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)+ & & tau*(BOUNDARY(ng)%vbar_east(j)- & & vbar(Iend+1,j,know)) END IF vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) END IF END DO ! ! Eastern edge, Chapman boundary condition. ! ELSE IF (LBC(ieast,isVbar,ng)%Flather.or. & & LBC(ieast,isVbar,ng)%reduced.or. & & 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) vbar(Iend+1,j,kout)=cff2*(vbar(Iend+1,j,know)+ & & Cx*vbar(Iend,j,kout)) vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) END IF END DO ! ! Eastern edge, clamped boundary condition. ! ELSE IF (LBC(ieast,isVbar,ng)%clamped) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN vbar(Iend+1,j,kout)=BOUNDARY(ng)%vbar_east(j) vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) END IF END DO ! ! Eastern edge, gradient boundary condition. ! ELSE IF (LBC(ieast,isVbar,ng)%gradient) THEN DO j=JstrV,Jend IF (LBC_apply(ng)%east(j)) THEN vbar(Iend+1,j,kout)=vbar(Iend,j,kout) vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) END IF END DO ! ! Eastern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! ELSE IF (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 vbar(Iend+1,j,kout)=gamma2(ng)*vbar(Iend,j,kout) vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) 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-1).and. & & LBC_apply(ng)%west (Jstr )) THEN vbar(Istr-1,Jstr,kout)=0.5_r8*(vbar(Istr ,Jstr ,kout)+ & & vbar(Istr-1,Jstr+1,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 )) THEN vbar(Iend+1,Jstr,kout)=0.5_r8*(vbar(Iend ,Jstr ,kout)+ & & vbar(Iend+1,Jstr+1,kout)) 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 vbar(Istr-1,Jend+1,kout)=0.5_r8*(vbar(Istr-1,Jend ,kout)+ & & vbar(Istr ,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 vbar(Iend+1,Jend+1,kout)=0.5_r8*(vbar(Iend+1,Jend ,kout)+ & & vbar(Iend ,Jend+1,kout)) END IF END IF END IF RETURN END SUBROUTINE v2dbc_tile END MODULE v2dbc_mod