MODULE ad_u3dbc_mod
!
!git $Id$
!svn $Id: ad_u3dbc_im.F 1151 2023-02-09 03:08:53Z 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 total !
! 3D U-velocity. It updates the specified "nout" time index. !
! !
! BASIC STATE variables needed: u !
! !
!=======================================================================
!
implicit none
PRIVATE
PUBLIC :: ad_u3dbc, ad_u3dbc_tile
CONTAINS
!
!***********************************************************************
SUBROUTINE ad_u3dbc (ng, tile, nout)
!***********************************************************************
!
USE mod_param
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, nout
!
! 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 ad_u3dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, N(ng), &
& IminS, ImaxS, JminS, JmaxS, &
& nstp(ng), nout, &
& OCEAN(ng) % ad_u)
RETURN
END SUBROUTINE ad_u3dbc
!
!***********************************************************************
SUBROUTINE ad_u3dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& nstp, nout, &
& ad_u)
!***********************************************************************
!
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
integer, intent(in) :: LBi, UBi, LBj, UBj, UBk
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: nstp, nout
!
real(r8), intent(inout) :: ad_u(LBi:,LBj:,:,:)
!
! Local variable declarations.
!
integer :: Imin, Imax
integer :: i, j, k
real(r8) :: Ce, Cx, cff
real(r8) :: obc_in, obc_out, tau
real(r8) :: adfac
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_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
!
!-----------------------------------------------------------------------
! Initialize adjoint private variables.
!-----------------------------------------------------------------------
!
ad_grad(LBi:UBi,LBj:UBj)=0.0_r8
!
!-----------------------------------------------------------------------
! 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
DO k=1,N(ng)
!^ tl_u(Iend+1,Jend+1,k,nout)=0.5_r8* &
!^ & (tl_u(Iend+1,Jend ,k,nout)+ &
!^ & tl_u(Iend ,Jend+1,k,nout))
!^
adfac=0.5_r8*ad_u(Iend+1,Jend+1,k,nout)
ad_u(Iend+1,Jend ,k,nout)=ad_u(Iend+1,Jend ,k,nout)+ &
& adfac
ad_u(Iend ,Jend+1,k,nout)=ad_u(Iend ,Jend+1,k,nout)+ &
& adfac
ad_u(Iend+1,Jend+1,k,nout)=0.0_r8
END DO
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
DO k=1,N(ng)
!^ tl_u(Istr,Jend+1,k,nout)=0.5_r8* &
!^ & (tl_u(Istr ,Jend ,k,nout)+ &
!^ & tl_u(Istr+1,Jend+1,k,nout))
!^
adfac=0.5_r8*ad_u(Istr,Jend+1,k,nout)
ad_u(Istr ,Jend ,k,nout)=ad_u(Istr ,Jend ,k,nout)+ &
& adfac
ad_u(Istr+1,Jend+1,k,nout)=ad_u(Istr+1,Jend+1,k,nout)+ &
& adfac
ad_u(Istr ,Jend+1,k,nout)=0.0_r8
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)
!^ tl_u(Iend+1,Jstr-1,k,nout)=0.5_r8* &
!^ & (tl_u(Iend ,Jstr-1,k,nout)+ &
!^ & tl_u(Iend+1,Jstr ,k,nout))
!^
adfac=0.5_r8*ad_u(Iend+1,Jstr-1,k,nout)
ad_u(Iend ,Jstr-1,k,nout)=ad_u(Iend ,Jstr-1,k,nout)+ &
& adfac
ad_u(Iend+1,Jstr ,k,nout)=ad_u(Iend+1,Jstr ,k,nout)+ &
& adfac
ad_u(Iend+1,Jstr-1,k,nout)=0.0_r8
END DO
END IF
END IF
IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN
IF (LBC_apply(ng)%south(Istr ).and. &
& LBC_apply(ng)%west (Jstr-1)) THEN
DO k=1,N(ng)
!^ tl_u(Istr,Jstr-1,k,nout)=0.5_r8* &
!^ & (tl_u(Istr+1,Jstr-1,k,nout)+ &
!^ & tl_u(Istr ,Jstr ,k,nout))
!^
adfac=0.5_r8*ad_u(Istr,Jstr-1,k,nout)
ad_u(Istr+1,Jstr-1,k,nout)=ad_u(Istr+1,Jstr-1,k,nout)+ &
& adfac
ad_u(Istr ,Jstr ,k,nout)=ad_u(Istr ,Jstr ,k,nout)+ &
& adfac
ad_u(Istr ,Jstr-1,k,nout)=0.0_r8
END DO
END IF
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,isUvel,ng)%radiation) THEN
IF (iic(ng).ne.0) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend+1,k,nout)* &
!^ & GRID(ng)%umask(i,Jend+1)
!^
ad_u(i,Jend+1,k,nout)=ad_u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
IF (ad_LBC(inorth,isUvel,ng)%nudging) THEN
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend+1,k,nout)- &
!^ & tau*tl_u(i,Jend+1,k,nstp)
!^
ad_u(i,Jend+1,k,nstp)=ad_u(i,Jend+1,k,nstp)- &
& tau*ad_u(i,Jend+1,k,nout)
END IF
!^ tl_u(i,Jend+1,k,nout)=(cff*tl_u(i,Jend+1,k,nstp)+ &
!^ & Ce *tl_u(i,Jend ,k,nout)- &
!^ & MAX(Cx,0.0_r8)* &
!^ & tl_grad(i-1,Jend+1)- &
!^ & MIN(Cx,0.0_r8)* &
!^ & tl_grad(i ,Jend+1))/ &
!^ & (cff+Ce)
!^
adfac=ad_u(i,Jend+1,k,nout)/(cff+Ce)
ad_grad(i-1,Jend+1)=ad_grad(i-1,Jend+1)- &
& MAX(Cx,0.0_r8)*adfac
ad_grad(i ,Jend+1)=ad_grad(i ,Jend+1)- &
& MIN(Cx,0.0_r8)*adfac
ad_u(i,Jend ,k,nout)=ad_u(i,Jend ,k,nout)+Ce *adfac
ad_u(i,Jend+1,k,nstp)=ad_u(i,Jend+1,k,nstp)+cff*adfac
ad_u(i,Jend+1,k,nout)=0.0_r8
END IF
END DO
END DO
END IF
!
! Northern edge, clamped boundary condition.
!
ELSE IF (ad_LBC(inorth,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend+1,k,nout)* &
!^ & GRID(ng)%umask(i,Jend+1)
!^
ad_u(i,Jend+1,k,nout)=ad_u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
!^ tl_u(i,Jend+1,k,nout)=0.0_r8
!^
ad_u(i,Jend+1,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Northern edge, gradient boundary condition.
!
ELSE IF (ad_LBC(inorth,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend+1,k,nout)* &
!^ & GRID(ng)%umask(i,Jend+1)
!^
ad_u(i,Jend+1,k,nout)=ad_u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend,k,nout)
!^
ad_u(i,Jend ,k,nout)=ad_u(i,Jend ,k,nout)+ &
& ad_u(i,Jend+1,k,nout)
ad_u(i,Jend+1,k,nout) = 0.0_r8
END IF
END DO
END DO
!
! Northern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (ad_LBC(inorth,isUvel,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO k=1,N(ng)
DO i=Imin,Imax
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_u(i,Jend+1,k,nout)=tl_u(i,Jend+1,k,nout)* &
!^ & GRID(ng)%umask(i,Jend+1)
!^
ad_u(i,Jend+1,k,nout)=ad_u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
!^ tl_u(i,Jend+1,k,nout)=gamma2(ng)*tl_u(i,Jend,k,nout)
!^
ad_u(i,Jend ,k,nout)=ad_u(i,Jend ,k,nout)+ &
& gamma2(ng)*ad_u(i,Jend+1,k,nout)
ad_u(i,Jend+1,k,nout)=0.0_r8
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 (ad_LBC(isouth,isUvel,ng)%radiation) THEN
IF (iic(ng).ne.0) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr-1,k,nout)* &
!^ & GRID(ng)%umask(i,Jstr-1)
!^
ad_u(i,Jstr-1,k,nout)=ad_u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
IF (ad_LBC(isouth,isUvel,ng)%nudging) THEN
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr-1,k,nout)- &
!^ & tau*tl_u(i,Jstr-1,k,nstp)
!^
ad_u(i,Jstr-1,k,nstp)=ad_u(i,Jstr-1,k,nstp)- &
& tau*ad_u(i,Jstr-1,k,nout)
END IF
!^ tl_u(i,Jstr-1,k,nout)=(cff*tl_u(i,Jstr-1,k,nstp)+ &
!^ & Ce *tl_u(i,Jstr ,k,nout)- &
!^ & MAX(Cx,0.0_r8)* &
!^ & tl_grad(i-1,Jstr-1)- &
!^ & MIN(Cx,0.0_r8)* &
!^ & tl_grad(i ,Jstr-1))/ &
!^ & (cff+Ce)
!^
adfac=ad_u(i,Jstr-1,k,nout)/(cff+Ce)
ad_grad(i-1,Jstr-1)=ad_grad(i-1,Jstr-1)- &
& MAX(Cx,0.0_r8)*adfac
ad_grad(i ,Jstr-1)=ad_grad(i ,Jstr-1)- &
& MIN(Cx,0.0_r8)*adfac
ad_u(i,Jstr-1,k,nstp)=ad_u(i,Jstr-1,k,nstp)+cff*adfac
ad_u(i,Jstr ,k,nout)=ad_u(i,Jstr ,k,nout)+Ce *adfac
ad_u(i,Jstr-1,k,nout)=0.0_r8
END IF
END DO
END DO
END IF
!
! Southern edge, clamped boundary condition.
!
ELSE IF (ad_LBC(isouth,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr-1,k,nout)* &
!^ & GRID(ng)%umask(i,Jstr-1)
!^
ad_u(i,Jstr-1,k,nout)=ad_u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
!^ tl_u(i,Jstr-1,k,nout)=0.0_r8
!^
ad_u(i,Jstr-1,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Southern edge, gradient boundary condition.
!
ELSE IF (ad_LBC(isouth,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr-1,k,nout)* &
!^ & GRID(ng)%umask(i,Jstr-1)
!^
ad_u(i,Jstr-1,k,nout)=ad_u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr,k,nout)
!^
ad_u(i,Jstr ,k,nout)=ad_u(i,Jstr ,k,nout)+ &
& ad_u(i,Jstr-1,k,nout)
ad_u(i,Jstr-1,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Southern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (ad_LBC(isouth,isUvel,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO k=1,N(ng)
DO i=Imin,Imax
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_u(i,Jstr-1,k,nout)=tl_u(i,Jstr-1,k,nout)* &
!^ & GRID(ng)%umask(i,Jstr-1)
!^
ad_u(i,Jstr-1,k,nout)=ad_u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
!^ tl_u(i,Jstr-1,k,nout)=gamma2(ng)*tl_u(i,Jstr,k,nout)
!^
ad_u(i,Jstr ,k,nout)=ad_u(i,Jstr ,k,nout)+ &
& gamma2(ng)*ad_u(i,Jstr-1,k,nout)
ad_u(i,Jstr-1,k,nout)=0.0_r8
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 (ad_LBC(ieast,isUvel,ng)%radiation) THEN
IF (iic(ng).ne.0) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_u(Iend+1,j,k,nout)=tl_u(Iend+1,j,k,nout)* &
!^ & GRID(ng)%umask(Iend+1,j)
!^
ad_u(Iend+1,j,k,nout)=ad_u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
IF (ad_LBC(ieast,isUvel,ng)%nudging) THEN
!^ tl_u(Iend+1,j,k,nout)=tl_u(Iend+1,j,k,nout)- &
!^ & tau*tl_u(Iend+1,j,k,nstp)
!^
ad_u(Iend+1,j,k,nstp)=ad_u(Iend+1,j,k,nstp)- &
& tau*ad_u(Iend+1,j,k,nout)
END IF
!^ tl_u(Iend+1,j,k,nout)=(cff*tl_u(Iend+1,j,k,nstp)+ &
!^ & Cx *tl_u(Iend ,j,k,nout)- &
!^ & MAX(Ce,0.0_r8)* &
!^ & tl_grad(Iend+1,j )- &
!^ & MIN(Ce,0.0_r8)* &
!^ & tl_grad(Iend+1,j+1))/ &
!^ & (cff+Cx)
!^
adfac=ad_u(Iend+1,j,k,nout)/(cff+Cx)
ad_grad(Iend+1,j )=ad_grad(Iend+1,j )- &
& MAX(Ce,0.0_r8)*adfac
ad_grad(Iend+1,j+1)=ad_grad(Iend+1,j+1)- &
& MIN(Ce,0.0_r8)*adfac
ad_u(Iend ,j,k,nout)=ad_u(Iend ,j,k,nout)+Cx *adfac
ad_u(Iend+1,j,k,nstp)=ad_u(Iend+1,j,k,nstp)+cff*adfac
ad_u(Iend+1,j,k,nout)=0.0_r8
END IF
END DO
END DO
END IF
!
! Eastern edge, clamped boundary condition.
!
ELSE IF (ad_LBC(ieast,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_u(Iend+1,j,k,nout)=tl_u(Iend+1,j,k,nout)* &
!^ & GRID(ng)%umask(Iend+1,j)
!^
ad_u(Iend+1,j,k,nout)=ad_u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
!^ tl_u(Iend+1,j,k,nout)=0.0_r8
!^
ad_u(Iend+1,j,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Eastern edge, gradient boundary condition.
!
ELSE IF (ad_LBC(ieast,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_u(Iend+1,j,k,nout)=tl_u(Iend+1,j,k,nout)* &
!^ & GRID(ng)%umask(Iend+1,j)
!^
ad_u(Iend+1,j,k,nout)=ad_u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
!^ tl_u(Iend+1,j,k,nout)=tl_u(Iend,j,k,nout)
!^
ad_u(Iend ,j,k,nout)=ad_u(Iend ,j,k,nout)+ &
& ad_u(Iend+1,j,k,nout)
ad_u(Iend+1,j,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Eastern edge, closed boundary condition.
!
ELSE IF (ad_LBC(ieast,isUvel,ng)%closed) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_u(Iend+1,j,k,nout)=0.0_r8
!^
ad_u(Iend+1,j,k,nout)=0.0_r8
END IF
END DO
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,isUvel,ng)%radiation) THEN
IF (iic(ng).ne.0) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_u(Istr,j,k,nout)=tl_u(Istr,j,k,nout)* &
!^ & GRID(ng)%umask(Istr,j)
!^
ad_u(Istr,j,k,nout)=ad_u(Istr,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
IF (ad_LBC(iwest,isUvel,ng)%nudging) THEN
!^ tl_u(Istr,j,k,nout)=tl_u(Istr,j,k,nout)- &
!^ & tau*tl_u(Istr,j,k,nstp)
!^
ad_u(Istr,j,k,nstp)=ad_u(Istr,j,k,nstp)- &
& tau*ad_u(Istr,j,k,nout)
END IF
!^ tl_u(Istr,j,k,nout)=(cff*tl_u(Istr ,j,k,nstp)+ &
!^ & Cx *tl_u(Istr+1,j,k,nout)- &
!^ & MAX(Ce,0.0_r8)* &
!^ & tl_grad(Istr,j )- &
!^ & MIN(Ce,0.0_r8)* &
!^ & tl_grad(Istr,j+1))/ &
!^ & (cff+Cx)
!^
adfac=ad_u(Istr,j,k,nout)/(cff+Cx)
ad_grad(Istr,j )=ad_grad(Istr,j )- &
& MAX(Ce,0.0_r8)*adfac
ad_grad(Istr,j+1)=ad_grad(Istr,j+1)- &
& MIN(Ce,0.0_r8)*adfac
ad_u(Istr ,j,k,nstp)=ad_u(Istr ,j,k,nstp)+cff*adfac
ad_u(Istr+1,j,k,nout)=ad_u(Istr+1,j,k,nout)+Cx *adfac
ad_u(Istr ,j,k,nout)=0.0_r8
END IF
END DO
END DO
END IF
!
! Western edge, clamped boundary condition.
!
ELSE IF (ad_LBC(iwest,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_u(Istr,j,k,nout)=tl_u(Istr,j,k,nout)* &
!^ & GRID(ng)%umask(Istr,j)
!^
ad_u(Istr,j,k,nout)=ad_u(Istr,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
!^ tl_u(Istr,j,k,nout)=0.0_r8
!^
ad_u(Istr,j,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Western edge, gradient boundary condition.
!
ELSE IF (ad_LBC(iwest,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_u(Istr,j,k,nout)=tl_u(Istr,j,k,nout)* &
!^ & GRID(ng)%umask(Istr,j)
!^
ad_u(Istr ,j,k,nout)=ad_u(Istr ,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
!^ tl_u(Istr,j,k,nout)=tl_u(Istr+1,j,k,nout)
!^
ad_u(Istr+1,j,k,nout)=ad_u(Istr+1,j,k,nout)+ &
& ad_u(Istr ,j,k,nout)
ad_u(Istr ,j,k,nout)=0.0_r8
END IF
END DO
END DO
!
! Western edge, closed boundary condition.
!
ELSE IF (ad_LBC(iwest,isUvel,ng)%closed) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_u(Istr,j,k,nout)=0.0_r8
!^
ad_u(Istr,j,k,nout)=0.0_r8
END IF
END DO
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_u3dbc_tile
END MODULE ad_u3dbc_mod