MODULE ad_bc_2d_mod
!
!git $Id$
!svn $Id: ad_bc_2d.F 1151 2023-02-09 03:08:53Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2023 The ROMS/TOMS Group !
! Licensed under a MIT/X style license !
! See License_ROMS.md !
!=======================================================================
! !
! These routines apply close, gradient or periodic boundary !
! conditions to generic 2D adjoint fields. !
! !
! On Input: !
! !
! ng Nested grid number. !
! tile Domain partition. !
! LBi I-dimension Lower bound. !
! UBi I-dimension Upper bound. !
! LBj J-dimension Lower bound. !
! UBj J-dimension Upper bound. !
! ad_A 2D adjoint field. !
! !
! On Output: !
! !
! ad_A Processed 2D adjoint field. !
! !
! Routines: !
! !
! ad_bc_r2d_tile Boundary conditions for field at RHO-points !
! ad_bc_u2d_tile Boundary conditions for field at U-points !
! ad_bc_v2d_tile Boundary conditions for field at V-points !
! !
!=======================================================================
!
implicit none
!
CONTAINS
!
!***********************************************************************
SUBROUTINE ad_bc_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_r2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=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_A(Istr-1,Jend+1)=0.5_r8*(tl_A(Istr-1,Jend )+ &
!^ & tl_A(Istr ,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jend+1)
ad_A(Istr-1,Jend )=ad_A(Istr-1,Jend )+adfac
ad_A(Istr ,Jend+1)=ad_A(Istr ,Jend+1)+adfac
ad_A(Istr-1,Jend+1)=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-1)) THEN
!^ tl_A(Iend+1,Jstr-1)=0.5_r8*(tl_A(Iend ,Jstr-1)+ &
!^ & tl_A(Iend+1,Jstr ))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr-1)
ad_A(Iend ,Jstr-1)=ad_A(Iend ,Jstr-1)+adfac
ad_A(Iend+1,Jstr )=ad_A(Iend+1,Jstr )+adfac
ad_A(Iend+1,Jstr-1)=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-1)) THEN
!^ tl_A(Istr-1,Jstr-1)=0.5_r8*(tl_A(Istr ,Jstr-1)+ &
!^ & tl_A(Istr-1,Jstr ))
!^
adfac=0.5_r8*ad_A(Istr-1,Jstr-1)
ad_A(Istr ,Jstr-1)=ad_A(Istr ,Jstr-1)+adfac
ad_A(Istr-1,Jstr )=ad_A(Istr-1,Jstr )+adfac
ad_A(Istr-1,Jstr-1)=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr-1)=tl_A(i,Jstr)
!^
ad_A(i,Jstr )=ad_A(i,Jstr)+ad_A(i,Jstr-1)
ad_A(i,Jstr-1)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend )=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr-1,j)=tl_A(Istr,j)
!^
ad_A(Istr ,j)=ad_A(Istr,j)+ad_A(Istr-1,j)
ad_A(Istr-1,j)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_bc_r2d_tile
!
!***********************************************************************
SUBROUTINE ad_bc_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_grid
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_u2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: Imin, Imax
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=0.0_r8
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
!^ tl_A(Istr ,Jend+1)=0.5_r8*(tl_A(Istr ,Jend )+ &
!^ & tl_A(Istr+1,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr,Jend+1)
ad_A(Istr ,Jend )=ad_A(Istr ,Jend )+adfac
ad_A(Istr+1,Jend+1)=ad_A(Istr+1,Jend+1)+adfac
ad_A(Istr ,Jend+1)=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-1)) THEN
!^ tl_A(Iend+1,Jstr-1)=0.5_r8*(tl_A(Iend ,Jstr-1)+ &
!^ & tl_A(Iend+1,Jstr ))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr-1)
ad_A(Iend ,Jstr-1)=ad_A(Iend ,Jstr-1)+adfac
ad_A(Iend+1,Jstr )=ad_A(Iend+1,Jstr )+adfac
ad_A(Iend+1,Jstr-1)=0.0_r8
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
!^ tl_A(Istr ,Jstr-1)=0.5_r8*(tl_A(Istr+1,Jstr-1)+ &
!^ & tl_A(Istr ,Jstr ))
!^
adfac=0.5_r8*ad_A(Istr,Jstr-1)
ad_A(Istr+1,Jstr-1)=ad_A(Istr+1,Jstr-1)+adfac
ad_A(Istr ,Jstr )=ad_A(Istr ,Jstr )+adfac
ad_A(Istr ,Jstr-1)=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South boundary conditions: Closed (free-slip/no-slip)
! or gradient.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
IF (ad_LBC(isouth,isBu2d,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
!^ tl_A(i,Jstr-1)=tl_A(i,Jstr-1)*GRID(ng)%umask(i,Jstr-1)
!^
ad_A(i,Jstr-1)=ad_A(i,Jstr-1)*GRID(ng)%umask(i,Jstr-1)
!^ tl_A(i,Jstr-1)=gamma2(ng)*tl_A(i,Jstr)
!^
ad_A(i,Jstr)=ad_A(i,Jstr)+gamma2(ng)*ad_A(i,Jstr-1)
ad_A(i,Jstr-1)=0.0_r8
END IF
END DO
ELSE
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr-1)=tl_A(i,Jstr)
!^
ad_A(i,Jstr )=ad_A(i,Jstr)+ad_A(i,Jstr-1)
ad_A(i,Jstr-1)=0.0_r8
END IF
END DO
END IF
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
IF (ad_LBC(inorth,isBu2d,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
!^ tl_A(i,Jend+1)=tl_A(i,Jend+1)*GRID(ng)%umask(i,Jend+1)
!^
ad_A(i,Jend+1)=ad_A(i,Jend+1)*GRID(ng)%umask(i,Jend+1)
!^ tl_A(i,Jend+1)=gamma2(ng)*tl_A(i,Jend)
!^
ad_A(i,Jend)=ad_A(i,Jend)+gamma2(ng)*ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
ELSE
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend )=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West boundary conditions: Closed or gradient.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
IF (ad_LBC(iwest,isBu2d,ng)%closed) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr,j)=0.0_r8
!^
ad_A(Istr,j)=0.0_r8
END IF
END DO
ELSE
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr,j)=tl_A(Istr+1,j)
!^
ad_A(Istr+1,j)=ad_A(Istr+1,j)+ad_A(Istr,j)
ad_A(Istr ,j)=0.0_r8
END IF
END DO
END IF
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
IF (ad_LBC(ieast,isBu2d,ng)%closed) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ A(Iend+1,j)=0.0_r8
!^
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
ELSE
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
END IF
RETURN
END SUBROUTINE ad_bc_u2d_tile
!
!***********************************************************************
SUBROUTINE ad_bc_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_grid
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_v2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: Jmin, Jmax
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=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_A(Istr-1,Jend+1)=0.5_r8*(tl_A(Istr-1,Jend )+ &
!^ & tl_A(Istr ,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jend+1)
ad_A(Istr-1,Jend )=ad_A(Istr-1,Jend )+adfac
ad_A(Istr ,Jend+1)=ad_A(Istr ,Jend+1)+adfac
ad_A(Istr-1,Jend+1)=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_A(Iend+1,Jstr )=0.5_r8*(tl_A(Iend ,Jstr )+ &
!^ & tl_A(Iend+1,Jstr+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr )
ad_A(Iend ,Jstr )=ad_A(Iend ,Jstr )+adfac
ad_A(Iend+1,Jstr+1)=ad_A(Iend+1,Jstr+1)+adfac
ad_A(Iend+1,Jstr )=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_A(Istr-1,Jstr )=0.5_r8*(tl_A(Istr ,Jstr )+ &
!^ & tl_A(Istr-1,Jstr+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jstr )
ad_A(Istr ,Jstr )=ad_A(Istr ,Jstr )+adfac
ad_A(Istr-1,Jstr+1)=ad_A(Istr-1,Jstr+1)+adfac
ad_A(Istr-1,Jstr )=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South boundary conditions: Closed or Gradient.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
IF (ad_LBC(isouth,isBv2d,ng)%closed) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr)=0.0_r8
!^
ad_A(i,Jstr)=0.0_r8
END IF
END DO
ELSE
DO i=Istr,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr)=tl_A(i,Jstr+1)
!^
ad_A(i,Jstr+1)=ad_A(i,Jstr+1)+ad_A(i,Jstr)
ad_A(i,Jstr)=0.0_r8
END IF
END DO
END IF
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
IF (ad_LBC(inorth,isBv2d,ng)%closed) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=0.0_r8
!^
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
ELSE
DO i=Istr,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend)=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
IF (ad_LBC(iwest,isBv2d,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
!^ tl_A(Istr-1,j)=tl_A(Istr-1,j)*GRID(ng)%vmask(Istr-1,j)
!^
ad_A(Istr-1,j)=ad_A(Istr-1,j)*GRID(ng)%vmask(Istr-1,j)
!^ tl_A(Istr-1,j)=gamma2(ng)*tl_A(Istr,j)
!^
ad_A(Istr ,j)=ad_A(Istr,j)+gamma2(ng)*ad_A(Istr-1,j)
ad_A(Istr-1,j)=0.0_r8
END IF
END DO
ELSE
DO j=JstrV,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr-1,j)=tl_A(Istr,j)
!^
ad_A(Istr ,j)=ad_A(Istr,j)+ad_A(Istr-1,j)
ad_A(Istr-1,j)=0.0_r8
END IF
END DO
END IF
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
IF (ad_LBC(ieast,isBv2d,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
!^ tl_A(Iend+1,j)=tl_A(Iend+1,j)*GRID(ng)%vmask(Iend+1,j)
!^
ad_A(Iend+1,j)=ad_A(Iend+1,j)*GRID(ng)%vmask(Iend+1,j)
!^ tl_A(Iend+1,j)=gamma2(ng)*tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
ELSE
DO j=JstrV,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
END IF
RETURN
END SUBROUTINE ad_bc_v2d_tile
!
!***********************************************************************
SUBROUTINE ad_dabc_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_r2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=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_A(Istr-1,Jend+1)=0.5_r8*(tl_A(Istr-1,Jend )+ &
!^ & tl_A(Istr ,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jend+1)
ad_A(Istr-1,Jend )=ad_A(Istr-1,Jend )+adfac
ad_A(Istr ,Jend+1)=ad_A(Istr ,Jend+1)+adfac
ad_A(Istr-1,Jend+1)=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-1)) THEN
!^ tl_A(Iend+1,Jstr-1)=0.5_r8*(tl_A(Iend ,Jstr-1)+ &
!^ & tl_A(Iend+1,Jstr ))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr-1)
ad_A(Iend ,Jstr-1)=ad_A(Iend ,Jstr-1)+adfac
ad_A(Iend+1,Jstr )=ad_A(Iend+1,Jstr )+adfac
ad_A(Iend+1,Jstr-1)=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-1)) THEN
!^ tl_A(Istr-1,Jstr-1)=0.5_r8*(tl_A(Istr ,Jstr-1)+ &
!^ & tl_A(Istr-1,Jstr ))
!^
adfac=0.5_r8*ad_A(Istr-1,Jstr-1)
ad_A(Istr ,Jstr-1)=ad_A(Istr ,Jstr-1)+adfac
ad_A(Istr-1,Jstr )=ad_A(Istr-1,Jstr )+adfac
ad_A(Istr-1,Jstr-1)=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr-1)=tl_A(i,Jstr)
!^
ad_A(i,Jstr )=ad_A(i,Jstr)+ad_A(i,Jstr-1)
ad_A(i,Jstr-1)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend )=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr-1,j)=tl_A(Istr,j)
!^
ad_A(Istr ,j)=ad_A(Istr,j)+ad_A(Istr-1,j)
ad_A(Istr-1,j)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_dabc_r2d_tile
!
!***********************************************************************
SUBROUTINE ad_dabc_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_grid
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_u2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: Imin, Imax
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=0.0_r8
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
!^ tl_A(Istr ,Jend+1)=0.5_r8*(tl_A(Istr ,Jend )+ &
!^ & tl_A(Istr+1,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr,Jend+1)
ad_A(Istr ,Jend )=ad_A(Istr ,Jend )+adfac
ad_A(Istr+1,Jend+1)=ad_A(Istr+1,Jend+1)+adfac
ad_A(Istr ,Jend+1)=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-1)) THEN
!^ tl_A(Iend+1,Jstr-1)=0.5_r8*(tl_A(Iend ,Jstr-1)+ &
!^ & tl_A(Iend+1,Jstr ))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr-1)
ad_A(Iend ,Jstr-1)=ad_A(Iend ,Jstr-1)+adfac
ad_A(Iend+1,Jstr )=ad_A(Iend+1,Jstr )+adfac
ad_A(Iend+1,Jstr-1)=0.0_r8
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
!^ tl_A(Istr ,Jstr-1)=0.5_r8*(tl_A(Istr+1,Jstr-1)+ &
!^ & tl_A(Istr ,Jstr ))
!^
adfac=0.5_r8*ad_A(Istr,Jstr-1)
ad_A(Istr+1,Jstr-1)=ad_A(Istr+1,Jstr-1)+adfac
ad_A(Istr ,Jstr )=ad_A(Istr ,Jstr )+adfac
ad_A(Istr ,Jstr-1)=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr-1)=tl_A(i,Jstr)
!^
ad_A(i,Jstr )=ad_A(i,Jstr)+ad_A(i,Jstr-1)
ad_A(i,Jstr-1)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend )=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr,j)=tl_A(Istr+1,j)
!^
ad_A(Istr+1,j)=ad_A(Istr+1,j)+ad_A(Istr,j)
ad_A(Istr ,j)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_dabc_u2d_tile
!
!***********************************************************************
SUBROUTINE ad_dabc_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_grid
USE mod_ncparam
USE mod_scalars
!
USE ad_exchange_2d_mod, ONLY : ad_exchange_v2d_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
!
real(r8), intent(inout) :: ad_A(LBi:,LBj:)
!
! Local variable declarations.
!
integer :: Jmin, Jmax
integer :: i, j
real(r8) :: adfac
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Apply adjoint periodic boundary conditons.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL ad_exchange_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_A)
END IF
!
!-----------------------------------------------------------------------
! 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_A(Iend+1,Jend+1)=0.5_r8*(tl_A(Iend+1,Jend )+ &
!^ & tl_A(Iend ,Jend+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jend+1)
ad_A(Iend+1,Jend )=ad_A(Iend+1,Jend )+adfac
ad_A(Iend ,Jend+1)=ad_A(Iend ,Jend+1)+adfac
ad_A(Iend+1,Jend+1)=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_A(Istr-1,Jend+1)=0.5_r8*(tl_A(Istr-1,Jend )+ &
!^ & tl_A(Istr ,Jend+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jend+1)
ad_A(Istr-1,Jend )=ad_A(Istr-1,Jend )+adfac
ad_A(Istr ,Jend+1)=ad_A(Istr ,Jend+1)+adfac
ad_A(Istr-1,Jend+1)=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_A(Iend+1,Jstr )=0.5_r8*(tl_A(Iend ,Jstr )+ &
!^ & tl_A(Iend+1,Jstr+1))
!^
adfac=0.5_r8*ad_A(Iend+1,Jstr )
ad_A(Iend ,Jstr )=ad_A(Iend ,Jstr )+adfac
ad_A(Iend+1,Jstr+1)=ad_A(Iend+1,Jstr+1)+adfac
ad_A(Iend+1,Jstr )=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_A(Istr-1,Jstr )=0.5_r8*(tl_A(Istr ,Jstr )+ &
!^ & tl_A(Istr-1,Jstr+1))
!^
adfac=0.5_r8*ad_A(Istr-1,Jstr )
ad_A(Istr ,Jstr )=ad_A(Istr ,Jstr )+adfac
ad_A(Istr-1,Jstr+1)=ad_A(Istr-1,Jstr+1)+adfac
ad_A(Istr-1,Jstr )=0.0_r8
END IF
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint North-South gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.NSperiodic(ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%south(i)) THEN
!^ tl_A(i,Jstr)=tl_A(i,Jstr+1)
!^
ad_A(i,Jstr+1)=ad_A(i,Jstr+1)+ad_A(i,Jstr)
ad_A(i,Jstr)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
IF (LBC_apply(ng)%north(i)) THEN
!^ tl_A(i,Jend+1)=tl_A(i,Jend)
!^
ad_A(i,Jend)=ad_A(i,Jend)+ad_A(i,Jend+1)
ad_A(i,Jend+1)=0.0_r8
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Adjoint East-West gradient boundary conditions.
!-----------------------------------------------------------------------
!
IF (.not.EWperiodic(ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=JstrV,Jend
IF (LBC_apply(ng)%west(j)) THEN
!^ tl_A(Istr-1,j)=tl_A(Istr,j)
!^
ad_A(Istr ,j)=ad_A(Istr,j)+ad_A(Istr-1,j)
ad_A(Istr-1,j)=0.0_r8
END IF
END DO
END IF
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=JstrV,Jend
IF (LBC_apply(ng)%east(j)) THEN
!^ tl_A(Iend+1,j)=tl_A(Iend,j)
!^
ad_A(Iend ,j)=ad_A(Iend,j)+ad_A(Iend+1,j)
ad_A(Iend+1,j)=0.0_r8
END IF
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_dabc_v2d_tile
END MODULE ad_bc_2d_mod