#include "cppdefs.h" MODULE t3dbc_mod #ifdef SOLVE3D ! !git $Id$ !svn $Id: t3dbc_im.F 1151 2023-02-09 03:08:53Z 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 the ITRC-th ! ! tracer field. ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: t3dbc_tile ! CONTAINS ! !*********************************************************************** SUBROUTINE t3dbc (ng, tile, nout, itrc, ic) !*********************************************************************** ! USE mod_param USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, nout, itrc, ic ! ! Local variable declarations. ! # include "tile.h" ! CALL t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp(ng), nout, & & OCEAN(ng)% t) RETURN END SUBROUTINE t3dbc ! !*********************************************************************** SUBROUTINE t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, UBk, UBt, & & IminS, ImaxS, JminS, JmaxS, & & nstp, nout, & & t) !*********************************************************************** ! USE mod_param USE mod_boundary USE mod_clima USE mod_grid USE mod_ncparam USE mod_scalars ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, itrc, ic integer, intent(in) :: LBi, UBi, LBj, UBj, UBk, UBt integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nstp, nout ! # ifdef ASSUMED_SHAPE real(r8), intent(inout) :: t(LBi:,LBj:,:,:,:) # else real(r8), intent(inout) :: t(LBi:UBi,LBj:UBj,UBk,3,UBt) # endif ! ! Local variable declarations. ! integer :: i, j, k real(r8), parameter :: eps =1.0E-20_r8 real(r8) :: Ce, Cx, cff, dTde, dTdt, dTdx real(r8) :: obc_in, obc_out, tau real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the western edge. !----------------------------------------------------------------------- ! IF (DOMAIN(ng)%Western_Edge(tile)) THEN ! ! Western edge, implicit upstream radiation condition. ! IF (LBC(iwest,isTvar(itrc),ng)%radiation) THEN DO k=1,N(ng) DO j=Jstr,Jend+1 grad(Istr-1,j)=t(Istr-1,j ,k,nstp,itrc)- & & t(Istr-1,j-1,k,nstp,itrc) # ifdef MASKING grad(Istr-1,j)=grad(Istr-1,j)* & & GRID(ng)%vmask(Istr-1,j) # endif grad(Istr ,j)=t(Istr ,j ,k,nstp,itrc)- & & t(Istr ,j-1,k,nstp,itrc) # ifdef MASKING grad(Istr ,j)=grad(Istr ,j)* & & GRID(ng)%vmask(Istr ,j) # endif END DO DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN dTdt=t(Istr,j,k,nstp,itrc)-t(Istr ,j,k,nout,itrc) dTdx=t(Istr,j,k,nout,itrc)-t(Istr+1,j,k,nout,itrc) IF (LBC(iwest,isTvar(itrc),ng)%nudging) THEN IF (LnudgeTCLM(itrc,ng)) THEN obc_out=CLIMA(ng)%Tnudgcof(Istr-1,j,k,ic) obc_in =obcfac(ng)*obc_out ELSE obc_out=Tobc_out(itrc,ng,iwest) obc_in =Tobc_in (itrc,ng,iwest) END IF IF ((dTdt*dTdx).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt(ng) END IF IF ((dTdt*dTdx).lt.0.0_r8) dTdt=0.0_r8 IF ((dTdt*(grad(Istr,j )+ & & grad(Istr,j+1))).gt.0.0_r8) THEN dTde=grad(Istr,j ) ELSE dTde=grad(Istr,j+1) END IF cff=MAX(dTdx*dTdx+dTde*dTde,eps) Cx=dTdt*dTdx # ifdef RADIATION_2D Ce=MIN(cff,MAX(dTdt*dTde,-cff)) # else Ce=0.0_r8 # endif # if defined CELERITY_WRITE && defined FORWARD_WRITE BOUNDARY(ng)%t_west_Cx(j,k,itrc)=Cx BOUNDARY(ng)%t_west_Ce(j,k,itrc)=Ce BOUNDARY(ng)%t_west_C2(j,k,itrc)=cff # endif t(Istr-1,j,k,nout,itrc)=(cff*t(Istr-1,j,k,nstp,itrc)+ & & Cx *t(Istr ,j,k,nout,itrc)- & & MAX(Ce,0.0_r8)* & & grad(Istr-1,j )- & & MIN(Ce,0.0_r8)* & & grad(Istr-1,j+1))/ & & (cff+Cx) IF (LBC(iwest,isTvar(itrc),ng)%nudging) THEN t(Istr-1,j,k,nout,itrc)=t(Istr-1,j,k,nout,itrc)+ & & tau* & & (BOUNDARY(ng)%t_west(j,k, & & itrc)- & & t(Istr-1,j,k,nstp,itrc)) END IF # ifdef MASKING t(Istr-1,j,k,nout,itrc)=t(Istr-1,j,k,nout,itrc)* & & GRID(ng)%rmask(Istr-1,j) # endif END IF END DO END DO ! ! Western edge, clamped boundary condition. ! ELSE IF (LBC(iwest,isTvar(itrc),ng)%clamped) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN t(Istr-1,j,k,nout,itrc)=BOUNDARY(ng)%t_west(j,k,itrc) # ifdef MASKING t(Istr-1,j,k,nout,itrc)=t(Istr-1,j,k,nout,itrc)* & & GRID(ng)%rmask(Istr-1,j) # endif END IF END DO END DO ! ! Western edge, gradient boundary condition. ! ELSE IF (LBC(iwest,isTvar(itrc),ng)%gradient) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN t(Istr-1,j,k,nout,itrc)=t(Istr,j,k,nout,itrc) # ifdef MASKING t(Istr-1,j,k,nout,itrc)=t(Istr-1,j,k,nout,itrc)* & & GRID(ng)%rmask(Istr-1,j) # endif END IF END DO END DO ! ! Western edge, closed boundary condition. ! ELSE IF (LBC(iwest,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%west(j)) THEN t(Istr-1,j,k,nout,itrc)=t(Istr,j,k,nout,itrc) # ifdef MASKING t(Istr-1,j,k,nout,itrc)=t(Istr-1,j,k,nout,itrc)* & & GRID(ng)%rmask(Istr-1,j) # endif END IF END DO 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,isTvar(itrc),ng)%radiation) THEN DO k=1,N(ng) DO j=Jstr,Jend+1 grad(Iend ,j)=t(Iend ,j ,k,nstp,itrc)- & & t(Iend ,j-1,k,nstp,itrc) # ifdef MASKING grad(Iend ,j)=grad(Iend ,j)* & & GRID(ng)%vmask(Iend ,j) # endif grad(Iend+1,j)=t(Iend+1,j ,k,nstp,itrc)- & & t(Iend+1,j-1,k,nstp,itrc) # ifdef MASKING grad(Iend+1,j)=grad(Iend+1,j)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN dTdt=t(Iend,j,k,nstp,itrc)-t(Iend ,j,k,nout,itrc) dTdx=t(Iend,j,k,nout,itrc)-t(Iend-1,j,k,nout,itrc) IF (LBC(ieast,isTvar(itrc),ng)%nudging) THEN IF (LnudgeTCLM(itrc,ng)) THEN obc_out=CLIMA(ng)%Tnudgcof(Iend+1,j,k,ic) obc_in =obcfac(ng)*obc_out ELSE obc_out=Tobc_out(itrc,ng,ieast) obc_in =Tobc_in (itrc,ng,ieast) END IF IF ((dTdt*dTdx).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt(ng) END IF IF ((dTdt*dTdx).lt.0.0_r8) dTdt=0.0_r8 IF ((dTdt*(grad(Iend,j )+ & & grad(Iend,j+1))).gt.0.0_r8) THEN dTde=grad(Iend,j ) ELSE dTde=grad(Iend,j+1) END IF cff=MAX(dTdx*dTdx+dTde*dTde,eps) Cx=dTdt*dTdx # ifdef RADIATION_2D Ce=MIN(cff,MAX(dTdt*dTde,-cff)) # else Ce=0.0_r8 # endif # if defined CELERITY_WRITE && defined FORWARD_WRITE BOUNDARY(ng)%t_east_Cx(j,k,itrc)=Cx BOUNDARY(ng)%t_east_Ce(j,k,itrc)=Ce BOUNDARY(ng)%t_east_C2(j,k,itrc)=cff # endif t(Iend+1,j,k,nout,itrc)=(cff*t(Iend+1,j,k,nstp,itrc)+ & & Cx *t(Iend ,j,k,nout,itrc)- & & MAX(Ce,0.0_r8)* & & grad(Iend+1,j )- & & MIN(Ce,0.0_r8)* & & grad(Iend+1,j+1))/ & & (cff+Cx) IF (LBC(ieast,isTvar(itrc),ng)%nudging) THEN t(Iend+1,j,k,nout,itrc)=t(Iend+1,j,k,nout,itrc)+ & & tau* & & (BOUNDARY(ng)%t_east(j,k, & & itrc)- & & t(Iend+1,j,k,nstp,itrc)) END IF # ifdef MASKING t(Iend+1,j,k,nout,itrc)=t(Iend+1,j,k,nout,itrc)* & & GRID(ng)%rmask(Iend+1,j) # endif END IF END DO END DO ! ! Eastern edge, clamped boundary condition. ! ELSE IF (LBC(ieast,isTvar(itrc),ng)%clamped) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN t(Iend+1,j,k,nout,itrc)=BOUNDARY(ng)%t_east(j,k,itrc) # ifdef MASKING t(Iend+1,j,k,nout,itrc)=t(Iend+1,j,k,nout,itrc)* & & GRID(ng)%rmask(Iend+1,j) # endif END IF END DO END DO ! ! Eastern edge, gradient boundary condition. ! ELSE IF (LBC(ieast,isTvar(itrc),ng)%gradient) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN t(Iend+1,j,k,nout,itrc)=t(Iend,j,k,nout,itrc) # ifdef MASKING t(Iend+1,j,k,nout,itrc)=t(Iend+1,j,k,nout,itrc)* & & GRID(ng)%rmask(Iend+1,j) # endif END IF END DO END DO ! ! Eastern edge, closed boundary condition. ! ELSE IF (LBC(ieast,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jstr,Jend IF (LBC_apply(ng)%east(j)) THEN t(Iend+1,j,k,nout,itrc)=t(Iend,j,k,nout,itrc) # ifdef MASKING t(Iend+1,j,k,nout,itrc)=t(Iend+1,j,k,nout,itrc)* & & GRID(ng)%rmask(Iend+1,j) # endif END IF END DO 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 (LBC(isouth,isTvar(itrc),ng)%radiation) THEN DO k=1,N(ng) DO i=Istr,Iend+1 grad(i,Jstr )=t(i ,Jstr ,k,nstp,itrc)- & & t(i-1,Jstr ,k,nstp,itrc) # ifdef MASKING grad(i,Jstr )=grad(i,Jstr )* & & GRID(ng)%umask(i,Jstr ) # endif grad(i,Jstr-1)=t(i ,Jstr-1,k,nstp,itrc)- & & t(i-1,Jstr-1,k,nstp,itrc) # ifdef MASKING grad(i,Jstr-1)=grad(i,Jstr-1)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN dTdt=t(i,Jstr,k,nstp,itrc)-t(i,Jstr ,k,nout,itrc) dTde=t(i,Jstr,k,nout,itrc)-t(i,Jstr+1,k,nout,itrc) IF (LBC(isouth,isTvar(itrc),ng)%nudging) THEN IF (LnudgeTCLM(itrc,ng)) THEN obc_out=CLIMA(ng)%Tnudgcof(i,Jstr-1,k,ic) obc_in =obcfac(ng)*obc_out ELSE obc_out=Tobc_out(itrc,ng,isouth) obc_in =Tobc_in (itrc,ng,isouth) END IF IF ((dTdt*dTde).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt(ng) END IF IF ((dTdt*dTde).lt.0.0_r8) dTdt=0.0_r8 IF ((dTdt*(grad(i ,Jstr)+ & & grad(i+1,Jstr))).gt.0.0_r8) THEN dTdx=grad(i ,Jstr) ELSE dTdx=grad(i+1,Jstr) END IF cff=MAX(dTdx*dTdx+dTde*dTde,eps) # ifdef RADIATION_2D Cx=MIN(cff,MAX(dTdt*dTdx,-cff)) # else Cx=0.0_r8 # endif Ce=dTdt*dTde # if defined CELERITY_WRITE && defined FORWARD_WRITE BOUNDARY(ng)%t_south_Cx(i,k,itrc)=Cx BOUNDARY(ng)%t_south_Ce(i,k,itrc)=Ce BOUNDARY(ng)%t_south_C2(i,k,itrc)=cff # endif t(i,Jstr-1,k,nout,itrc)=(cff*t(i,Jstr-1,k,nstp,itrc)+ & & Ce *t(i,Jstr ,k,nout,itrc )- & & MAX(Cx,0.0_r8)* & & grad(i ,Jstr-1)- & & MIN(Cx,0.0_r8)* & & grad(i+1,Jstr-1))/ & & (cff+Ce) IF (LBC(isouth,isTvar(itrc),ng)%nudging) THEN t(i,Jstr-1,k,nout,itrc)=t(i,Jstr-1,k,nout,itrc)+ & & tau* & & (BOUNDARY(ng)%t_south(i,k, & & itrc)- & & t(i,Jstr-1,k,nstp,itrc)) END IF # ifdef MASKING t(i,Jstr-1,k,nout,itrc)=t(i,Jstr-1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jstr-1) # endif END IF END DO END DO ! ! Southern edge, clamped boundary condition. ! ELSE IF (LBC(isouth,isTvar(itrc),ng)%clamped) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN t(i,Jstr-1,k,nout,itrc)=BOUNDARY(ng)%t_south(i,k,itrc) # ifdef MASKING t(i,Jstr-1,k,nout,itrc)=t(i,Jstr-1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jstr-1) # endif END IF END DO END DO ! ! Southern edge, gradient boundary condition. ! ELSE IF (LBC(isouth,isTvar(itrc),ng)%gradient) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN t(i,Jstr-1,k,nout,itrc)=t(i,Jstr,k,nout,itrc) # ifdef MASKING t(i,Jstr-1,k,nout,itrc)=t(i,Jstr-1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jstr-1) # endif END IF END DO END DO ! ! Southern edge, closed boundary condition. ! ELSE IF (LBC(isouth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%south(i)) THEN t(i,Jstr-1,k,nout,itrc)=t(i,Jstr,k,nout,itrc) # ifdef MASKING t(i,Jstr-1,k,nout,itrc)=t(i,Jstr-1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jstr-1) # endif END IF END DO 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,isTvar(itrc),ng)%radiation) THEN DO k=1,N(ng) DO i=Istr,Iend+1 grad(i,Jend )=t(i ,Jend ,k,nstp,itrc)- & & t(i-1,Jend ,k,nstp,itrc) # ifdef MASKING grad(i,Jend )=grad(i,Jend )* & & GRID(ng)%umask(i,Jend ) # endif grad(i,Jend+1)=t(i ,Jend+1,k,nstp,itrc)- & & t(i-1,Jend+1,k,nstp,itrc) # ifdef MASKING grad(i,Jend+1)=grad(i,Jend+1)* & & GRID(ng)%umask(i,Jend+1) # endif END DO DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN dTdt=t(i,Jend,k,nstp,itrc)-t(i,Jend ,k,nout,itrc) dTde=t(i,Jend,k,nout,itrc)-t(i,Jend-1,k,nout,itrc) IF (LBC(inorth,isTvar(itrc),ng)%nudging) THEN IF (LnudgeTCLM(itrc,ng)) THEN obc_out=CLIMA(ng)%Tnudgcof(i,Jend+1,k,ic) obc_in =obcfac(ng)*obc_out ELSE obc_out=Tobc_out(itrc,ng,inorth) obc_in =Tobc_in (itrc,ng,inorth) END IF IF ((dTdt*dTde).lt.0.0_r8) THEN tau=obc_in ELSE tau=obc_out END IF tau=tau*dt(ng) END IF IF ((dTdt*dTde).lt.0.0_r8) dTdt=0.0_r8 IF ((dTdt*(grad(i ,Jend)+ & & grad(i+1,Jend))).gt.0.0_r8) THEN dTdx=grad(i ,Jend) ELSE dTdx=grad(i+1,Jend) END IF cff=MAX(dTdx*dTdx+dTde*dTde,eps) # ifdef RADIATION_2D Cx=MIN(cff,MAX(dTdt*dTdx,-cff)) # else Cx=0.0_r8 # endif Ce=dTdt*dTde # if defined CELERITY_WRITE && defined FORWARD_WRITE BOUNDARY(ng)%t_north_Cx(i,k,itrc)=Cx BOUNDARY(ng)%t_north_Ce(i,k,itrc)=Ce BOUNDARY(ng)%t_north_C2(i,k,itrc)=cff # endif t(i,Jend+1,k,nout,itrc)=(cff*t(i,Jend+1,k,nstp,itrc)+ & & Ce *t(i,Jend ,k,nout,itrc)- & & MAX(Cx,0.0_r8)* & & grad(i ,Jend+1)- & & MIN(Cx,0.0_r8)* & & grad(i+1,Jend+1))/ & & (cff+Ce) IF (LBC(inorth,isTvar(itrc),ng)%nudging) THEN t(i,Jend+1,k,nout,itrc)=t(i,Jend+1,k,nout,itrc)+ & & tau* & & (BOUNDARY(ng)%t_north(i,k, & & itrc)- & & t(i,Jend+1,k,nstp,itrc)) END IF # ifdef MASKING t(i,Jend+1,k,nout,itrc)=t(i,Jend+1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jend+1) # endif END IF END DO END DO ! ! Northern edge, clamped boundary condition. ! ELSE IF (LBC(inorth,isTvar(itrc),ng)%clamped) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN t(i,Jend+1,k,nout,itrc)=BOUNDARY(ng)%t_north(i,k,itrc) # ifdef MASKING t(i,Jend+1,k,nout,itrc)=t(i,Jend+1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jend+1) # endif END IF END DO END DO ! ! Northern edge, gradient boundary condition. ! ELSE IF (LBC(inorth,isTvar(itrc),ng)%gradient) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN t(i,Jend+1,k,nout,itrc)=t(i,Jend,k,nout,itrc) # ifdef MASKING t(i,Jend+1,k,nout,itrc)=t(i,Jend+1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jend+1) # endif END IF END DO END DO ! ! Northern edge, closed boundary condition. ! ELSE IF (LBC(inorth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Istr,Iend IF (LBC_apply(ng)%north(i)) THEN t(i,Jend+1,k,nout,itrc)=t(i,Jend,k,nout,itrc) # ifdef MASKING t(i,Jend+1,k,nout,itrc)=t(i,Jend+1,k,nout,itrc)* & & GRID(ng)%rmask(i,Jend+1) # endif END IF END DO 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-1)) THEN DO k=1,N(ng) t(Istr-1,Jstr-1,k,nout,itrc)=0.5_r8* & & (t(Istr ,Jstr-1,k,nout, & & itrc)+ & & t(Istr-1,Jstr ,k,nout, & & itrc)) END DO 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 DO k=1,N(ng) t(Iend+1,Jstr-1,k,nout,itrc)=0.5_r8* & & (t(Iend ,Jstr-1,k,nout, & & itrc)+ & & t(Iend+1,Jstr ,k,nout, & & itrc)) END DO 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 DO k=1,N(ng) t(Istr-1,Jend+1,k,nout,itrc)=0.5_r8* & & (t(Istr-1,Jend ,k,nout, & & itrc)+ & & t(Istr ,Jend+1,k,nout, & & itrc)) END DO 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 DO k=1,N(ng) t(Iend+1,Jend+1,k,nout,itrc)=0.5_r8* & & (t(Iend+1,Jend ,k,nout, & & itrc)+ & & t(Iend ,Jend+1,k,nout, & & itrc)) END DO END IF END IF END IF RETURN END SUBROUTINE t3dbc_tile #endif END MODULE t3dbc_mod