MODULE ad_obc_volcons_mod
!
!git $Id$
!svn $Id: ad_obc_volcons.F 1180 2023-07-13 02:42:10Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore !
! Licensed under a MIT/X style license !
! See License_ROMS.md !
!=======================================================================
! !
! This routines computes adjoint integral mass flux "obc_flux" !
! across the open boundaries, which is needed to enforce global !
! mass conservation constraint. !
! !
!=======================================================================
!
implicit none
PRIVATE
PUBLIC :: ad_obc_flux_tile, ad_set_DUV_bc_tile
CONTAINS
!
!***********************************************************************
SUBROUTINE ad_obc_flux (ng, tile, kinp)
!***********************************************************************
!
USE mod_param
USE mod_grid
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, kinp
!
! 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_obc_flux_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& kinp, &
& GRID(ng) % umask, &
& GRID(ng) % vmask, &
& GRID(ng) % h, &
& GRID(ng) % ad_h, &
& GRID(ng) % om_v, &
& GRID(ng) % on_u, &
& OCEAN(ng) % ubar, &
& OCEAN(ng) % vbar, &
& OCEAN(ng) % zeta, &
& OCEAN(ng) % ad_ubar, &
& OCEAN(ng) % ad_vbar, &
& OCEAN(ng) % ad_zeta)
RETURN
END SUBROUTINE ad_obc_flux
!
!***********************************************************************
SUBROUTINE ad_obc_flux_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& kinp, &
& umask, vmask, &
& h, ad_h, &
& om_v, on_u, &
& ubar, vbar, zeta, &
& ad_ubar, ad_vbar, ad_zeta)
!***********************************************************************
!
USE mod_param
USE mod_parallel
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) :: kinp
!
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(in) :: h(LBi:,LBj:)
real(r8), intent(in) :: om_v(LBi:,LBj:)
real(r8), intent(in) :: on_u(LBi:,LBj:)
real(r8), intent(in) :: ubar(LBi:,LBj:,:)
real(r8), intent(in) :: vbar(LBi:,LBj:,:)
real(r8), intent(in) :: zeta(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_h(LBi:,LBj:)
real(r8), intent(inout) :: ad_ubar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_vbar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_zeta(LBi:,LBj:,:)
!
! Local variable declarations.
!
integer :: i, j
real(r8) :: cff, my_area, my_flux
real(r8) :: adfac, ad_cff, ad_my_area, ad_my_flux
real(r8), dimension(2) :: rbuffer
character (len=3), dimension(2) :: op_handle
!
!
!-----------------------------------------------------------------------
! 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_cff=0.0_r8
!
!-----------------------------------------------------------------------
! Perform adjoint global summation and compute correction velocity.
!-----------------------------------------------------------------------
!
IF (ANY(ad_VolCons(:,ng))) THEN
!^ tl_ubar_xs=tl_bc_flux/bc_area- &
!^ & tl_bc_area*ubar_xs/bc_area
!^
ad_bc_area=-ad_ubar_xs*ubar_xs/bc_area
ad_bc_flux=ad_ubar_xs/bc_area
ad_ubar_xs=0.0_r8
!^ tl_bc_flux=tl_bc_flux+tl_my_flux
!^
ad_my_flux=ad_bc_flux
!^ tl_bc_area=tl_bc_area+tl_my_area
!^
ad_my_area=ad_bc_area
END IF
!
!-----------------------------------------------------------------------
! Compute open segments cross-section area and mass flux.
!-----------------------------------------------------------------------
!
IF (ad_VolCons(inorth,ng)) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
cff=0.5_r8*om_v(i,Jend+1)* &
& (zeta(i,Jend ,kinp)+h(i,Jend )+ &
& zeta(i,Jend+1,kinp)+h(i,Jend+1))
cff=cff*vmask(i,Jend+1)
!^ tl_my_flux=tl_my_flux- &
!^ & tl_cff*vbar(i,Jend+1,kinp)- &
!^ & cff*tl_vbar(i,Jend+1,kinp)
!^
ad_vbar(i,Jend+1,kinp)=ad_vbar(i,Jend+1,kinp)- &
& cff*ad_my_flux
ad_cff=ad_cff-ad_my_flux*vbar(i,Jend+1,kinp)
!^ tl_my_area=tl_my_area+tl_cff
!^
ad_cff=ad_cff+ad_my_area
!^ tl_cff=tl_cff*vmask(i,Jend+1)
!^
ad_cff=ad_cff*vmask(i,Jend+1)
!^ tl_cff=0.5_r8*om_v(i,Jend+1)* &
!^ & (tl_zeta(i,Jend ,kinp)+tl_h(i,Jend )+ &
!^ & tl_zeta(i,Jend+1,kinp)+tl_h(i,Jend+1))
!^
adfac=0.5_r8*om_v(i,Jend+1)*ad_cff
ad_zeta(i,Jend ,kinp)=ad_zeta(i,Jend ,kinp)+adfac
ad_zeta(i,Jend+1,kinp)=ad_zeta(i,Jend+1,kinp)+adfac
ad_h(i,Jend )=ad_h(i,Jend )+adfac
ad_h(i,Jend+1)=ad_h(i,Jend+1)+adfac
ad_cff=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(isouth,ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
cff=0.5_r8*om_v(i,Jstr)* &
& (zeta(i,Jstr-1,kinp)+h(i,Jstr-1)+ &
& zeta(i,Jstr ,kinp)+h(i,Jstr ))
cff=cff*vmask(i,Jstr)
!^ tl_my_flux=tl_my_flux+ &
!^ & tl_cff*vbar(i,JstrV-1,kinp)+ &
!^ & cff*tl_vbar(i,JstrV-1,kinp)
!^
ad_vbar(i,JstrV-1,kinp)=ad_vbar(i,JstrV-1,kinp)+ &
& cff*ad_my_flux
ad_cff=ad_cff+ad_my_flux*vbar(i,JstrV-1,kinp)
!^ tl_my_area=tl_my_area+tl_cff
!^
ad_cff=ad_cff+ad_my_area
!^ tl_cff=tl_cff*vmask(i,Jstr)
!^
ad_cff=ad_cff*vmask(i,Jstr)
!^ tl_cff=0.5_r8*om_v(i,Jstr)* &
!^ & (tl_zeta(i,Jstr-1,kinp)+tl_h(i,Jstr-1)+ &
!^ & tl_zeta(i,Jstr ,kinp)+tl_h(i,Jstr ))
!^
adfac=0.5_r8*om_v(i,Jstr)*ad_cff
ad_zeta(i,Jstr-1,kinp)=ad_zeta(i,Jstr-1,kinp)+adfac
ad_zeta(i,Jstr ,kinp)=ad_zeta(i,Jstr ,kinp)+adfac
ad_h(i,Jstr-1)=ad_h(i,Jstr-1)+adfac
ad_h(i,Jstr )=ad_h(i,Jstr )+adfac
ad_cff=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(ieast,ng)) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
cff=0.5_r8*on_u(Iend+1,j)* &
& (zeta(Iend ,j,kinp)+h(Iend ,j)+ &
& zeta(Iend+1,j,kinp)+h(Iend+1,j))
cff=cff*umask(Iend+1,j)
!^ tl_my_flux=tl_my_flux- &
!^ & tl_cff*ubar(Iend+1,j,kinp)- &
!^ & cff*tl_ubar(Iend+1,j,kinp)
!^
ad_ubar(Iend+1,j,kinp)=ad_ubar(Iend+1,j,kinp)- &
& cff*ad_my_flux
ad_cff=ad_cff-ad_my_flux*ubar(Iend+1,j,kinp)
!^ tl_my_area=tl_my_area+tl_cff
!^
ad_cff=ad_cff+ad_my_area
!^ tl_cff=tl_cff*umask(Iend+1,j)
!^
ad_cff=ad_cff*umask(Iend+1,j)
!^ tl_cff=0.5_r8*on_u(Iend+1,j)* &
!^ & (tl_zeta(Iend ,j,kinp)+tl_h(Iend ,j)+ &
!^ & tl_zeta(Iend+1,j,kinp)+tl_h(Iend+1,j))
!^
adfac=0.5_r8*on_u(Iend+1,j)*ad_cff
ad_zeta(Iend ,j,kinp)=ad_zeta(Iend ,j,kinp)+adfac
ad_zeta(Iend+1,j,kinp)=ad_zeta(Iend+1,j,kinp)+adfac
ad_h(Iend ,j)=ad_h(Iend ,j)+adfac
ad_h(Iend+1,j)=ad_h(Iend+1,j)+adfac
ad_cff=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(iwest,ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
cff=0.5_r8*on_u(Istr,j)* &
& (zeta(Istr-1,j,kinp)+h(Istr-1,j)+ &
& zeta(Istr ,j,kinp)+h(Istr ,j))
cff=cff*umask(Istr,j)
!^ tl_my_flux=tl_my_flux+ &
!^ & tl_cff*ubar(Istr,j,kinp)+ &
!^ & cff*tl_ubar(Istr,j,kinp)
!^
ad_ubar(Istr,j,kinp)=ad_ubar(Istr,j,kinp)+ &
& cff*ad_my_flux
ad_cff=ad_cff+ad_my_flux*ubar(Istr,j,kinp)
!^ tl_my_area=tl_my_area+tl_cff
!^
ad_cff=ad_cff+ad_my_area
!^ tl_cff=tl_cff*umask(Istr,j)
!^
ad_cff=ad_cff*umask(Istr,j)
!^ tl_cff=0.5_r8*on_u(Istr,j)* &
!^ & (tl_zeta(Istr-1,j,kinp)+tl_h(Istr-1,j)+ &
!^ & tl_zeta(Istr ,j,kinp)+tl_h(Istr ,j))
!^
adfac=0.5_r8*on_u(Istr,j)*ad_cff
ad_zeta(Istr-1,j,kinp)=ad_zeta(Istr-1,j,kinp)+adfac
ad_zeta(Istr ,j,kinp)=ad_zeta(Istr ,j,kinp)+adfac
ad_h(Istr-1,j)=ad_h(Istr-1,j)+adfac
ad_h(Istr-1,j)=ad_h(Istr-1,j)+adfac
ad_cff=0.0_r8
END DO
END IF
END IF
!^ tl_my_area=0.0_r8
!^ tl_my_flux=0.0_r8
!^
ad_my_area=0.0_r8
ad_my_flux=0.0_r8
RETURN
END SUBROUTINE ad_obc_flux_tile
!
!***********************************************************************
SUBROUTINE ad_set_DUV_bc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& kinp, &
& umask, vmask, &
& om_v, on_u, &
& ubar, vbar, &
& ad_ubar, ad_vbar, &
& Drhs, Duon, Dvom, &
& ad_Drhs, ad_Duon, ad_Dvom)
!***********************************************************************
!
USE mod_param
USE mod_scalars
USE mod_parallel
!
USE mp_exchange_mod, ONLY : ad_mp_exchange2d
USE distribute_mod, ONLY : mp_reduce
!
! 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) :: kinp
!
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(in) :: om_v(LBi:,LBj:)
real(r8), intent(in) :: on_u(LBi:,LBj:)
real(r8), intent(in) :: ubar(LBi:,LBj:,:)
real(r8), intent(in) :: vbar(LBi:,LBj:,:)
real(r8), intent(in) :: Drhs(IminS:,JminS:)
real(r8), intent(in) :: Duon(IminS:,JminS:)
real(r8), intent(in) :: Dvom(IminS:,JminS:)
real(r8), intent(inout) :: ad_ubar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_vbar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_Drhs(IminS:,JminS:)
real(r8), intent(inout) :: ad_Duon(IminS:,JminS:)
real(r8), intent(inout) :: ad_Dvom(IminS:,JminS:)
!
! Local variable declarations.
!
integer :: NSUB, i, j
real(r8) :: adfac, adfac1, adfac2, adfac3
real(r8) :: ad_my_ubar_xs
real(r8) :: rbuffer
character (len=3) :: op_handle
!
!-----------------------------------------------------------------------
! 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 vertically integrated mass fluxes "Duon" and "Dvom" along
! the open boundaries in such a way that the integral volume is
! conserved. This is done by applying "ubar_xs" correction to
! the velocities.
!-----------------------------------------------------------------------
!
ad_my_ubar_xs=0.0_r8
!
! Do a special exchange to avoid having three ghost points for high
! order numerical stencil.
!
IF (ad_VolCons(isouth,ng).or.ad_VolCons(inorth,ng)) THEN
!^ CALL mp_exchange2d (ng, tile, iTLM, 1, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_Dvom)
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 1, &
& IminS, ImaxS, JminS, JmaxS, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_Dvom)
END IF
IF (ad_VolCons(iwest,ng).or.ad_VolCons(ieast,ng)) THEN
!^ CALL mp_exchange2d (ng, tile, iTLM, 1, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_Duon)
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 1, &
& IminS, ImaxS, JminS, JmaxS, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_Duon)
END IF
IF (ad_VolCons(inorth,ng)) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=-2+IstrU,MIN(Iend+1,Lm(ng))+1
!^ tl_Dvom(i,Jend+1)=tl_Dvom(i,Jend+1)*vmask(i,Jend+1)
!^
ad_Dvom(i,Jend+1)=ad_Dvom(i,Jend+1)*vmask(i,Jend+1)
!^ tl_Dvom(i,Jend+1)=0.5_r8* &
!^ & ((tl_Drhs(i,Jend+1)+tl_Drhs(i,Jend))* &
!^ & (vbar(i,Jend+1,kinp)+ubar_xs)+ &
!^ & (Drhs(i,Jend+1)+Drhs(i,Jend))* &
!^ & (tl_vbar(i,Jend+1,kinp)+tl_ubar_xs))* &
!^ & om_v(i,Jend+1)
!^
adfac=0.5_r8*om_v(i,Jend+1)*ad_Dvom(i,Jend+1)
adfac1=adfac*(vbar(i,Jend+1,kinp)+ubar_xs)
adfac2=adfac*(Drhs(i,Jend+1)+Drhs(i,Jend))
ad_Drhs(i,Jend+1)=ad_Drhs(i,Jend+1)+adfac1
ad_Drhs(i,Jend )=ad_Drhs(i,Jend )+adfac1
ad_vbar(i,Jend+1,kinp)=ad_vbar(i,Jend+1,kinp)+adfac2
ad_my_ubar_xs=ad_my_ubar_xs+adfac2
ad_Dvom(i,Jend+1)=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(isouth,ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=-2+IstrU,MIN(Iend+1,Lm(ng))+1
!^ tl_Dvom(i,Jstr)=tl_Dvom(i,Jstr)*vmask(i,Jstr)
!^
ad_Dvom(i,Jstr)=ad_Dvom(i,Jstr)*vmask(i,Jstr)
!^ tl_Dvom(i,Jstr)=0.5_r8* &
!^ & ((tl_Drhs(i,Jstr)+tl_Drhs(i,Jstr-1))* &
!^ & (vbar(i,Jstr,kinp)-ubar_xs)+ &
!^ & (Drhs(i,Jstr)+Drhs(i,Jstr-1))* &
!^ & (tl_vbar(i,Jstr,kinp)-tl_ubar_xs))* &
!^ & om_v(i,Jstr)
!^
adfac=0.5_r8*om_v(i,Jstr)*ad_Dvom(i,Jstr)
adfac1=adfac*(vbar(i,Jstr,kinp)-ubar_xs)
adfac2=adfac*(Drhs(i,Jstr)+Drhs(i,Jstr-1))
ad_Drhs(i,Jstr-1)=ad_Drhs(i,Jstr-1)+adfac1
ad_Drhs(i,Jstr )=ad_Drhs(i,Jstr )+adfac1
ad_vbar(i,Jstr,kinp)=ad_vbar(i,Jstr,kinp)+adfac2
ad_my_ubar_xs=ad_my_ubar_xs-adfac2
ad_Dvom(i,Jstr)=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(ieast,ng)) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=-2+JstrV,MIN(Jend+1,Mm(ng))+1
!^ tl_Duon(Iend+1,j)=tl_Duon(Iend+1,j)*umask(Iend+1,j)
!^
ad_Duon(Iend+1,j)=ad_Duon(Iend+1,j)*umask(Iend+1,j)
!^ tl_Duon(Iend+1,j)=0.5_r8* &
!^ & ((tl_Drhs(Iend+1,j)+tl_Drhs(Iend,j))* &
!^ & (ubar(Iend+1,j,kinp)+ubar_xs)+ &
!^ & (Drhs(Iend+1,j)+Drhs(Iend,j))* &
!^ & (tl_ubar(Iend+1,j,kinp)+tl_ubar_xs))* &
!^ & on_u(Iend+1,j)
!^
adfac=0.5_r8*on_u(Iend+1,j)*ad_Duon(Iend+1,j)
adfac1=adfac*(ubar(Iend+1,j,kinp)+ubar_xs)
adfac2=adfac*(Drhs(Iend+1,j)+Drhs(Iend,j))
ad_Drhs(Iend ,j)=ad_Drhs(Iend ,j)+adfac1
ad_Drhs(Iend+1,j)=ad_Drhs(Iend+1,j)+adfac1
ad_ubar(Iend+1,j,kinp)=ad_ubar(Iend+1,j,kinp)+adfac2
ad_my_ubar_xs=ad_my_ubar_xs+adfac2
ad_Duon(Iend+1,j)=0.0_r8
END DO
END IF
END IF
IF (ad_VolCons(iwest,ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=-2+JstrV,MIN(Jend+1,Mm(ng))+1
!^ tl_Duon(Istr,j)=tl_Duon(Istr,j)*umask(Istr,j)
!^
ad_Duon(Istr,j)=ad_Duon(Istr,j)*umask(Istr,j)
!^ tl_Duon(Istr,j)=0.5_r8* &
!^ & ((tl_Drhs(Istr,j)+tl_Drhs(Istr-1,j))* &
!^ & (ubar(Istr,j,kinp)-ubar_xs)+ &
!^ & (Drhs(Istr,j)+Drhs(Istr-1,j))* &
!^ & (tl_ubar(Istr,j,kinp)-tl_ubar_xs))* &
!^ & on_u(Istr,j)
!^
adfac=0.5_r8*on_u(Istr,j)*ad_Duon(Istr,j)
adfac1=adfac*(ubar(Istr,j,kinp)-ubar_xs)
adfac2=adfac*(Drhs(Istr,j)+Drhs(Istr-1,j))
ad_Drhs(Istr-1,j)=ad_Drhs(Istr-1,j)+adfac1
ad_Drhs(Istr ,j)=ad_Drhs(Istr ,j)+adfac1
ad_ubar(Istr,j,kinp)=ad_ubar(Istr,j,kinp)+adfac2
ad_my_ubar_xs=ad_my_ubar_xs-adfac2
ad_Duon(Istr,j)=0.0_r8
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Perform global summation and compute correction velocity.
!-----------------------------------------------------------------------
!
IF (ANY(ad_VolCons(:,ng))) THEN
NSUB=1 ! distributed-memory
!$OMP CRITICAL (AD_OBC_VOLUME)
IF (tile_count.eq.0) THEN
adfac3=0.0_r8
END IF
adfac3=adfac3+ad_my_ubar_xs
tile_count=tile_count+1
IF (tile_count.eq.NSUB) THEN
tile_count=0
rbuffer=adfac3
op_handle='SUM'
CALL mp_reduce (ng, iADM, 1, rbuffer, op_handle)
adfac3=rbuffer
IF (iif(ng).eq.nfast(ng)+1) THEN
ad_ubar_xs=ad_ubar_xs+adfac3
ELSE
ad_ubar_xs=adfac3
ENDIF
END IF
!$OMP END CRITICAL (AD_OBC_VOLUME)
END IF
RETURN
END SUBROUTINE ad_set_DUV_bc_tile
!
!***********************************************************************
SUBROUTINE ad_conserve_mass_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& kinp, &
& umask, vmask, &
& ad_ubar, ad_vbar)
!***********************************************************************
!
USE mod_param
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) :: kinp
!
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(inout) :: ad_ubar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_vbar(LBi:,LBj:,:)
!
! Local variable declarations.
!
integer :: i, j
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Corrects velocities across the open boundaries to enforce global
! mass conservation constraint.
!-----------------------------------------------------------------------
!
IF (ad_VolCons(inorth,ng)) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
!^ vbar(i,Jend+1,kinp)=vbar(i,Jend+1,kinp)* &
!^ & vmask(i,Jend+1)
!^
ad_vbar(i,Jend+1,kinp)=ad_vbar(i,Jend+1,kinp)* &
& vmask(i,Jend+1)
!^ tl_vbar(i,Jend+1,kinp)=(tl_vbar(i,Jend+1,kinp)+tl_ubar_xs)
!^
ad_ubar_xs=ad_ubar_xs+ad_vbar(i,Jend+1,kinp)
END DO
END IF
END IF
IF (ad_VolCons(isouth,ng)) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
!^ tl_vbar(i,Jstr,kinp)=tl_vbar(i,Jstr,kinp)* &
!^ & vmask(i,Jstr)
!^
ad_vbar(i,Jstr,kinp)=ad_vbar(i,Jstr,kinp)* &
& vmask(i,Jstr)
!^ tl_vbar(i,Jstr,kinp)=(tl_vbar(i,Jstr,kinp)-tl_ubar_xs)
!^
ad_ubar_xs=ad_ubar_xs-ad_vbar(i,Jstr,kinp)
END DO
END IF
END IF
IF (ad_VolCons(ieast,ng)) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
!^ tl_ubar(Iend+1,j,kinp)=tl_ubar(Iend+1,j,kinp)* &
!^ & umask(Iend+1,j)
!^
ad_ubar(Iend+1,j,kinp)=ad_ubar(Iend+1,j,kinp)* &
& umask(Iend+1,j)
!^ tl_ubar(Iend+1,j,kinp)=tl_ubar(Iend+1,j,kinp)+tl_ubar_xs
!^
ad_ubar_xs=ad_ubar_xs+ad_ubar(Iend+1,j,kinp)
END DO
END IF
END IF
IF (ad_VolCons(iwest,ng)) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
!^ tl_ubar(Istr,j,kinp)=tl_ubar(Istr,j,kinp)* &
!^ & umask(Istr,j)
!^
ad_ubar(Istr,j,kinp)=ad_ubar(Istr,j,kinp)* &
& umask(Istr,j)
!^ tl_ubar(Istr,j,kinp)=tl_ubar(Istr,j,kinp)-tl_ubar_xs
!^
ad_ubar_xs=ad_ubar_xs-ad_ubar(Istr,j,kinp)
END DO
END IF
END IF
RETURN
END SUBROUTINE ad_conserve_mass_tile
END MODULE ad_obc_volcons_mod