!
!git $Id$
!svn $Id: ad_step2d.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 performs a fast (predictor or corrector) time-step !
! for the free-surface and 2D momentum adjoint equations. !
! It also calculates the time filtering variables over all fast-time !
! steps to damp high frequency signals in 3D applications. !
! !
!=======================================================================
!
MODULE ad_step2d_mod
!
!git $Id$
!svn $Id: ad_step2d_LF_AM3.h 1188 2023-08-03 19:26:47Z arango $
!=======================================================================
! !
! Adjoint shallow-water primitive equations predictor (Leap-frog) !
! and corrector (Adams-Moulton) time-stepping engine. !
! !
!=======================================================================
!
implicit none
!
PRIVATE
PUBLIC :: ad_step2d
!
CONTAINS
!
!***********************************************************************
SUBROUTINE ad_step2d (ng, tile)
!***********************************************************************
!
USE mod_param
USE mod_ncparam
USE mod_coupling
USE mod_forces
USE mod_grid
USE mod_mixing
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
!
! Local variable declarations.
!
character (len=*), parameter :: MyFile = &
& "ROMS/Adjoint/ad_step2d_LF_AM3.h"
!
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 wclock_on (ng, iADM, 9, 56, MyFile)
CALL ad_step2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, N(ng), &
& IminS, ImaxS, JminS, JmaxS, &
& krhs(ng), kstp(ng), knew(ng), &
& nstp(ng), nnew(ng), &
& GRID(ng) % pmask, GRID(ng) % rmask, &
& GRID(ng) % umask, GRID(ng) % vmask, &
& GRID(ng) % fomn, &
& GRID(ng) % h, GRID(ng) % ad_h, &
& GRID(ng) % om_u, GRID(ng) % om_v, &
& GRID(ng) % on_u, GRID(ng) % on_v, &
& GRID(ng) % omn, &
& GRID(ng) % pm, GRID(ng) % pn, &
& GRID(ng) % dndx, GRID(ng) % dmde, &
& GRID(ng) % pmon_r, GRID(ng) % pnom_r, &
& GRID(ng) % pmon_p, GRID(ng) % pnom_p, &
& GRID(ng) % om_r, GRID(ng) % on_r, &
& GRID(ng) % om_p, GRID(ng) % on_p, &
& MIXING(ng) % visc2_p, MIXING(ng) % visc2_r,&
& COUPLING(ng) % ad_DU_avg1, &
& COUPLING(ng) % ad_DU_avg2, &
& COUPLING(ng) % ad_DV_avg1, &
& COUPLING(ng) % ad_DV_avg2, &
& COUPLING(ng) % Zt_avg1, &
& COUPLING(ng) % ad_Zt_avg1, &
& COUPLING(ng) % ad_rufrc, &
& COUPLING(ng) % ad_rvfrc, &
& OCEAN(ng) % ad_ru, &
& OCEAN(ng) % ad_rv, &
& OCEAN(ng) % rubar, OCEAN(ng) % ad_rubar,&
& OCEAN(ng) % rvbar, OCEAN(ng) % ad_rvbar,&
& OCEAN(ng) % rzeta, OCEAN(ng) % ad_rzeta,&
& OCEAN(ng) % ubar, OCEAN(ng) % ad_ubar, &
& OCEAN(ng) % vbar, OCEAN(ng) % ad_vbar, &
& OCEAN(ng) % zeta, OCEAN(ng) % ad_zeta)
CALL wclock_off (ng, iADM, 9, 162, MyFile)
!
RETURN
END SUBROUTINE ad_step2d
!
!***********************************************************************
SUBROUTINE ad_step2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, kstp, knew, &
& nstp, nnew, &
& pmask, rmask, umask, vmask, &
& fomn, &
& h, ad_h, &
& om_u, om_v, on_u, on_v, omn, pm, pn, &
& dndx, dmde, &
& pmon_r, pnom_r, pmon_p, pnom_p, &
& om_r, on_r, om_p, on_p, &
& visc2_p, visc2_r, &
& ad_DU_avg1, ad_DU_avg2, &
& ad_DV_avg1, ad_DV_avg2, &
& Zt_avg1, ad_Zt_avg1, &
& ad_rufrc, ad_rvfrc, &
& ad_ru, ad_rv, &
& rubar, ad_rubar, &
& rvbar, ad_rvbar, &
& rzeta, ad_rzeta, &
& ubar, ad_ubar, &
& vbar, ad_vbar, &
& zeta, ad_zeta)
!***********************************************************************
!
USE mod_param
USE mod_clima
USE mod_ncparam
USE mod_scalars
USE mod_sources
!
USE ad_exchange_2d_mod
USE exchange_2d_mod
USE mp_exchange_mod, ONLY : ad_mp_exchange2d
USE mp_exchange_mod, ONLY : mp_exchange2d
USE obc_volcons_mod
USE ad_obc_volcons_mod
USE ad_u2dbc_mod, ONLY : ad_u2dbc_tile
USE ad_v2dbc_mod, ONLY : ad_v2dbc_tile
USE ad_zetabc_mod, ONLY : ad_zetabc_tile
!
! 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) :: krhs, kstp, knew
integer, intent(in) :: nstp, nnew
!
real(r8), intent(in) :: pmask(LBi:,LBj:)
real(r8), intent(in) :: rmask(LBi:,LBj:)
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(in) :: fomn(LBi:,LBj:)
real(r8), intent(in) :: h(LBi:,LBj:)
real(r8), intent(in) :: om_u(LBi:,LBj:)
real(r8), intent(in) :: om_v(LBi:,LBj:)
real(r8), intent(in) :: on_u(LBi:,LBj:)
real(r8), intent(in) :: on_v(LBi:,LBj:)
real(r8), intent(in) :: omn(LBi:,LBj:)
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: dndx(LBi:,LBj:)
real(r8), intent(in) :: dmde(LBi:,LBj:)
real(r8), intent(in) :: pmon_r(LBi:,LBj:)
real(r8), intent(in) :: pnom_r(LBi:,LBj:)
real(r8), intent(in) :: pmon_p(LBi:,LBj:)
real(r8), intent(in) :: pnom_p(LBi:,LBj:)
real(r8), intent(in) :: om_r(LBi:,LBj:)
real(r8), intent(in) :: on_r(LBi:,LBj:)
real(r8), intent(in) :: om_p(LBi:,LBj:)
real(r8), intent(in) :: on_p(LBi:,LBj:)
real(r8), intent(in) :: visc2_p(LBi:,LBj:)
real(r8), intent(in) :: visc2_r(LBi:,LBj:)
real(r8), intent(in) :: rubar(LBi:,LBj:,:)
real(r8), intent(in) :: rvbar(LBi:,LBj:,:)
real(r8), intent(in) :: rzeta(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(in) :: Zt_avg1(LBi:,LBj:)
real(r8), intent(inout) :: ad_DU_avg1(LBi:,LBj:)
real(r8), intent(inout) :: ad_DU_avg2(LBi:,LBj:)
real(r8), intent(inout) :: ad_DV_avg1(LBi:,LBj:)
real(r8), intent(inout) :: ad_DV_avg2(LBi:,LBj:)
real(r8), intent(inout) :: ad_Zt_avg1(LBi:,LBj:)
real(r8), intent(inout) :: ad_rufrc(LBi:,LBj:)
real(r8), intent(inout) :: ad_rvfrc(LBi:,LBj:)
real(r8), intent(inout) :: ad_ru(LBi:,LBj:,0:,:)
real(r8), intent(inout) :: ad_rv(LBi:,LBj:,0:,:)
real(r8), intent(inout) :: ad_h(LBi:,LBj:)
real(r8), intent(inout) :: ad_rubar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_rvbar(LBi:,LBj:,:)
real(r8), intent(inout) :: ad_rzeta(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.
!
logical :: CORRECTOR_2D_STEP
!
integer :: i, is, j, ptsk
!
real(r8) :: cff, cff1, cff2, cff3, cff4, cff5, cff6, cff7
real(r8) :: fac, fac1, fac2, fac3
real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3, ad_cff4
real(r8) :: ad_fac, ad_fac1
real(r8) :: adfac, adfac1, adfac2, adfac3, adfac4
!
real(r8), parameter :: IniVal = 0.0_r8
!
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dgrad
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dnew
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dstp
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DUon
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DVom
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: gzeta
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: gzeta2
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_ubar
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_vbar
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_zeta
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zeta_new
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zwrk
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dgrad
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dnew
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Drhs
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Drhs_p
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_Dstp
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DUon
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_DVom
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFe
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_UFx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFe
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_VFx
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_grad
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_gzeta
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_gzeta2
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rhs_ubar
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rhs_vbar
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_rhs_zeta
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_zeta_new
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_zwrk
!
!-----------------------------------------------------------------------
! 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
!
ptsk=3-kstp
CORRECTOR_2D_STEP=.not.PREDICTOR_2D_STEP(ng)
!
!-----------------------------------------------------------------------
! Initialize adjoint private variables.
!-----------------------------------------------------------------------
!
ad_cff=IniVal
ad_cff1=IniVal
ad_cff2=IniVal
ad_cff3=IniVal
ad_cff4=IniVal
ad_fac=IniVal
ad_fac1=IniVal
DO j=JminS,JmaxS
DO i=IminS,ImaxS
ad_Dgrad(i,j)=IniVal
ad_Dnew(i,j)=IniVal
ad_Drhs(i,j)=IniVal
ad_Drhs_p(i,j)=IniVal
ad_Dstp(i,j)=IniVal
ad_DUon(i,j)=IniVal
ad_DVom(i,j)=IniVal
ad_UFe(i,j)=IniVal
ad_UFx(i,j)=IniVal
ad_VFe(i,j)=IniVal
ad_VFx(i,j)=IniVal
ad_grad(i,j)=IniVal
ad_gzeta(i,j)=IniVal
ad_gzeta2(i,j)=IniVal
ad_rhs_ubar(i,j)=IniVal
ad_rhs_vbar(i,j)=IniVal
ad_rhs_zeta(i,j)=IniVal
ad_zeta_new(i,j)=IniVal
ad_zwrk(i,j)=IniVal
ad_DUon(i,j)=IniVal
ad_DVom(i,j)=IniVal
END DO
END DO
!
!-----------------------------------------------------------------------
! Compute BASIC STATE total depth (m) arrays and vertically
! integerated mass fluxes.
!-----------------------------------------------------------------------
!
! In distributed-memory, the I- and J-ranges are different and a
! special exchange is done to avoid having three ghost points for
! high order numerical stencils. Notice that a private array is
! passed below to the exchange routine. It also applies periodic
! boundary conditions, if appropriate and no partitions in I- or
! J-directions.
!
DO j=JstrV-2,Jendp2
DO i=IstrU-2,Iendp2
Dnew(i,j)=zeta(i,j,knew)+h(i,j)
Drhs(i,j)=zeta(i,j,krhs)+h(i,j)
Dstp(i,j)=zeta(i,j,kstp)+h(i,j)
END DO
END DO
DO j=JstrV-2,Jendp2
DO i=IstrU-1,Iendp2
cff=0.5_r8*on_u(i,j)
cff1=cff*(Drhs(i,j)+Drhs(i-1,j))
DUon(i,j)=ubar(i,j,krhs)*cff1
END DO
END DO
DO j=JstrV-1,Jendp2
DO i=IstrU-2,Iendp2
cff=0.5_r8*om_v(i,j)
cff1=cff*(Drhs(i,j)+Drhs(i,j-1))
DVom(i,j)=vbar(i,j,krhs)*cff1
END DO
END DO
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL exchange_u2d_tile (ng, tile, &
& IminS, ImaxS, JminS, JmaxS, &
& DUon)
CALL exchange_v2d_tile (ng, tile, &
& IminS, ImaxS, JminS, JmaxS, &
& DVom)
END IF
CALL mp_exchange2d (ng, tile, iADM, 2, &
& IminS, ImaxS, JminS, JmaxS, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& DUon, DVom)
!
! Compute integral mass flux across open boundaries and adjust
! for volume conservation. Compute BASIC STATE value.
! This must be computed here instead of below.
!
IF (ANY(ad_VolCons(:,ng))) THEN
CALL obc_flux_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& knew, &
& umask, vmask, &
& h, om_v, on_u, &
& ubar, vbar, zeta)
!
! Set vertically integrated mass fluxes DUon and DVom along the open
! boundaries in such a way that the integral volume is conserved.
!
CALL set_DUV_bc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, &
& umask, vmask, &
& om_v, on_u, &
& ubar, vbar, &
& Drhs, DUon, DVom)
END IF
!
! Compute BASIC state depths at PSI-points for viscosity.
!
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
Drhs_p(i,j)=0.25_r8*(Drhs(i,j )+Drhs(i-1,j )+ &
& Drhs(i,j-1)+Drhs(i-1,j-1))
END DO
END DO
!
! Initialize BASIC STATE right-hand-side terms.
!
DO j=Jstr,Jend
DO i=Istr,Iend
rhs_ubar(i,j)=0.0_r8
rhs_vbar(i,j)=0.0_r8
END DO
END DO
!
! Do not perform the actual time stepping during the auxiliary
! (nfast(ng)+1) time step.
!
STEP_LOOP : IF (iif(ng).le.nfast(ng)) THEN
!
!-----------------------------------------------------------------------
! Exchange boundary information.
!-----------------------------------------------------------------------
!
!^ CALL mp_exchange2d (ng, tile, iTLM, 2, &
!^ & LBi, UBi, LBj, UBj, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_ubar(:,:,knew), &
!^ & tl_vbar(:,:,knew))
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_ubar(:,:,knew), &
& ad_vbar(:,:,knew))
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
!^ CALL exchange_v2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_vbar(:,:,knew))
!^
CALL ad_exchange_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_vbar(:,:,knew))
!^ CALL exchange_u2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_ubar(:,:,knew))
!^
CALL ad_exchange_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_ubar(:,:,knew))
END IF
!
!-----------------------------------------------------------------------
! Apply adjoint momentum transport point sources (like river runoff),
! if any.
!-----------------------------------------------------------------------
!
IF (LuvSrc(ng)) THEN
DO is=1,Nsrc(ng)
i=SOURCES(ng)%Isrc(is)
j=SOURCES(ng)%Jsrc(is)
IF (((IstrR.le.i).and.(i.le.IendR)).and. &
& ((JstrR.le.j).and.(j.le.JendR))) THEN
IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN
cff=1.0_r8/(on_u(i,j)* &
& 0.5_r8*(zeta(i-1,j,knew)+h(i-1,j)+ &
& zeta(i ,j,knew)+h(i ,j)))
!^ tl_ubar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ &
!^ & SOURCES(ng)%Qbar(is)*tl_cff
!^
SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ &
& cff*ad_ubar(i,j,knew)
ad_cff=ad_cff+ &
& SOURCES(ng)%Qbar(is)*ad_ubar(i,j,knew)
ad_ubar(i,j,knew)=0.0_r8
!^ tl_cff=-cff*cff*on_u(i,j)* &
!^ & 0.5_r8*(tl_zeta(i-1,j,knew)+tl_h(i-1,j)+ &
!^ & tl_zeta(i ,j,knew)+tl_h(i ,j))
!^
adfac=-cff*cff*on_u(i,j)*0.5_r8*ad_cff
ad_h(i-1,j)=ad_h(i-1,j)+adfac
ad_h(i ,j)=ad_h(i ,j)+adfac
ad_zeta(i-1,j,knew)=ad_zeta(i-1,j,knew)+adfac
ad_zeta(i ,j,knew)=ad_zeta(i ,j,knew)+adfac
ad_cff=0.0_r8
ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN
cff=1.0_r8/(om_v(i,j)* &
& 0.5_r8*(zeta(i,j-1,knew)+h(i,j-1)+ &
& zeta(i,j ,knew)+h(i,j )))
!^ tl_vbar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ &
!^ & SOURCES(ng)%Qbar(is)*tl_cff
!^
SOURCES(ng)%ad_Qbar(is)=SOURCES(ng)%ad_Qbar(is)+ &
& cff*ad_vbar(i,j,knew)
ad_cff=ad_cff+ &
& SOURCES(ng)%Qbar(is)*ad_vbar(i,j,knew)
ad_vbar(i,j,knew)=0.0_r8
!^ tl_cff=-cff*cff*om_v(i,j)* &
!^ & 0.5_r8*(tl_zeta(i,j-1,knew)+tl_h(i,j-1)+ &
!^ & tl_zeta(i,j ,knew)+tl_h(i,j ))
!^
adfac=-cff*cff*om_v(i,j)*0.5_r8*ad_cff
ad_h(i,j-1)=ad_h(i,j-1)+adfac
ad_h(i,j )=ad_h(i,j )+adfac
ad_zeta(i,j-1,knew)=ad_zeta(i,j-1,knew)+adfac
ad_zeta(i,j ,knew)=ad_zeta(i,j ,knew)+adfac
ad_cff=0.0_r8
END IF
END IF
END DO
END IF
!
!-----------------------------------------------------------------------
! Apply adjoint lateral boundary conditions.
!-----------------------------------------------------------------------
!
! Compute integral mass flux across open boundaries and adjust
! for adjoint volume conservation.
!
IF (ANY(ad_VolCons(:,ng))) THEN
!^ CALL tl_obc_flux_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & knew, &
!^ & umask, vmask, &
!^ & h, tl_h, om_v, on_u, &
!^ & ubar, vbar, zeta, &
!^ & tl_ubar, tl_vbar, tl_zeta)
!^
CALL ad_obc_flux_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& knew, &
& umask, vmask, &
& h, ad_h, om_v, on_u, &
& ubar, vbar, zeta, &
& ad_ubar, ad_vbar, ad_zeta)
END IF
!
! Adjoint lateral boundary conditons.
!
!^ CALL tl_v2dbc_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & krhs, kstp, knew, &
!^ & ubar, vbar, zeta, &
!^ & tl_ubar, tl_vbar, tl_zeta)
!^
CALL ad_v2dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, kstp, knew, &
& ubar, vbar, zeta, &
& ad_ubar, ad_vbar, ad_zeta)
!^ CALL tl_u2dbc_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & krhs, kstp, knew, &
!^ & ubar, vbar, zeta, &
!^ & tl_ubar, tl_vbar, tl_zeta)
!^
CALL ad_u2dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, kstp, knew, &
& ubar, vbar, zeta, &
& ad_ubar, ad_vbar, ad_zeta)
!
! If predictor step, load right-side-term into shared arrays for
! future use during the subsequent corrector step.
!
IF (PREDICTOR_2D_STEP(ng)) THEN
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rvbar(i,j,krhs)=tl_rhs_vbar(i,j)
!^
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)+ad_rvbar(i,j,krhs)
ad_rvbar(i,j,krhs)=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rubar(i,j,krhs)=tl_rhs_ubar(i,j)
!^
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)+ad_rubar(i,j,krhs)
ad_rubar(i,j,krhs)=0.0_r8
END DO
END DO
END IF
!
!=======================================================================
! Time step adjoint 2D momentum equations.
!=======================================================================
!
! During the first time-step, the predictor step is Forward-Euler
! and the corrector step is Backward-Euler. Otherwise, the predictor
! step is Leap-frog and the corrector step is Adams-Moulton.
!
IF (iif(ng).eq.1) THEN
cff1=0.5_r8*dtfast(ng)
DO j=JstrV,Jend
DO i=Istr,Iend
cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1))
fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1))
!^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j)
!^
ad_vbar(i,j,knew)=ad_vbar(i,j,knew)*vmask(i,j)
!^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & vbar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ &
!^ & cff*cff1*tl_rhs_vbar(i,j))*fac+ &
!^ & (vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & cff*cff1*rhs_vbar(i,j))*tl_fac
!^
adfac=fac*ad_vbar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i,j-1))
adfac2=adfac*cff*cff1
adfac3=adfac*vbar(i,j,kstp)
ad_vbar(i,j,kstp)=ad_vbar(i,j,kstp)+adfac1
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)+adfac2
ad_Dstp(i,j-1)=ad_Dstp(i,j-1)+adfac3
ad_Dstp(i,j )=ad_Dstp(i,j )+adfac3
ad_fac=ad_fac+ &
& (vbar(i,j,kstp)*(Dstp(i,j)+Dstp(i,j-1))+ &
& cff*cff1*rhs_vbar(i,j))*ad_vbar(i,j,knew)
ad_vbar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac
ad_Dnew(i,j )=ad_Dnew(i,j )+adfac
ad_fac=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j))
fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j))
!^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j)
!^
ad_ubar(i,j,knew)=ad_ubar(i,j,knew)*umask(i,j)
!^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & ubar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ &
!^ & cff*cff1*tl_rhs_ubar(i,j))*fac+ &
!^ & (ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & cff*cff1*rhs_ubar(i,j))*tl_fac
!^
adfac=fac*ad_ubar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i-1,j))
adfac2=adfac*cff*cff1
adfac3=adfac*ubar(i,j,kstp)
ad_ubar(i,j,kstp)=ad_ubar(i,j,kstp)+adfac1
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)+adfac2
ad_Dstp(i-1,j)=ad_Dstp(i-1,j)+adfac3
ad_Dstp(i ,j)=ad_Dstp(i ,j)+adfac3
ad_fac=ad_fac+ &
& (ubar(i,j,kstp)*(Dstp(i,j)+Dstp(i-1,j))+ &
& cff*cff1*rhs_ubar(i,j))*ad_ubar(i,j,knew)
ad_ubar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac
ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac
ad_fac=0.0_r8
END DO
END DO
ELSE IF (PREDICTOR_2D_STEP(ng)) THEN
cff1=dtfast(ng)
DO j=JstrV,Jend
DO i=Istr,Iend
cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1))
fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1))
!^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j)
!^
ad_vbar(i,j,knew)=ad_vbar(i,j,knew)*vmask(i,j)
!^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & vbar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ &
!^ & cff*cff1*tl_rhs_vbar(i,j))*fac+ &
!^ & (vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & cff*cff1*rhs_vbar(i,j))*tl_fac
!^
adfac=fac*ad_vbar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i,j-1))
adfac2=adfac*cff*cff1
adfac3=adfac*vbar(i,j,kstp)
ad_vbar(i,j,kstp)=ad_vbar(i,j,kstp)+adfac1
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)+adfac2
ad_Dstp(i,j-1)=ad_Dstp(i,j-1)+adfac3
ad_Dstp(i,j )=ad_Dstp(i,j )+adfac3
ad_fac=ad_fac+ &
& (vbar(i,j,kstp)*(Dstp(i,j)+Dstp(i,j-1))+ &
& cff*cff1*rhs_vbar(i,j))*ad_vbar(i,j,knew)
ad_vbar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac
ad_Dnew(i,j )=ad_Dnew(i,j )+adfac
ad_fac=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j))
fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j))
!^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j)
!^
ad_ubar(i,j,knew)=ad_ubar(i,j,knew)*umask(i,j)
!^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & ubar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ &
!^ & cff*cff1*tl_rhs_ubar(i,j))*fac+ &
!^ & (ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & cff*cff1*rhs_ubar(i,j))*tl_fac
!^
adfac=fac*ad_ubar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i-1,j))
adfac2=adfac*cff*cff1
adfac3=adfac*ubar(i,j,kstp)
ad_ubar(i,j,kstp)=ad_ubar(i,j,kstp)+adfac1
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)+adfac2
ad_Dstp(i-1,j)=ad_Dstp(i-1,j)+adfac3
ad_Dstp(i ,j)=ad_Dstp(i ,j)+adfac3
ad_fac=ad_fac+ &
& (ubar(i,j,kstp)*(Dstp(i,j)+Dstp(i-1,j))+ &
& cff*cff1*rhs_ubar(i,j))*ad_ubar(i,j,knew)
ad_ubar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac
ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac
ad_fac=0.0_r8
END DO
END DO
ELSE IF (CORRECTOR_2D_STEP) THEN
cff1=0.5_r8*dtfast(ng)*5.0_r8/12.0_r8
cff2=0.5_r8*dtfast(ng)*8.0_r8/12.0_r8
cff3=0.5_r8*dtfast(ng)*1.0_r8/12.0_r8
DO j=JstrV,Jend
DO i=Istr,Iend
cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1))
fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1))
!^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j)
!^
ad_vbar(i,j,knew)=ad_vbar(i,j,knew)*vmask(i,j)
!^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & vbar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ &
!^ & cff*(cff1*tl_rhs_vbar(i,j)+ &
!^ & cff2*tl_rvbar(i,j,kstp)- &
!^ & cff3*tl_rvbar(i,j,ptsk)))*fac+ &
!^ & (vbar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i,j-1))+ &
!^ & cff*(cff1*rhs_vbar(i,j)+ &
!^ & cff2*rvbar(i,j,kstp)- &
!^ & cff3*rvbar(i,j,ptsk)))*tl_fac
!^
adfac=fac*ad_vbar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i,j-1))
adfac2=adfac*cff
adfac3=adfac*vbar(i,j,kstp)
ad_vbar(i,j,kstp)=ad_vbar(i,j,kstp)+adfac1
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)+cff1*adfac2
ad_rvbar(i,j,kstp)=ad_rvbar(i,j,kstp)+cff2*adfac2
ad_rvbar(i,j,ptsk)=-cff3*adfac2
ad_Dstp(i,j-1)=ad_Dstp(i,j-1)+adfac3
ad_Dstp(i,j )=ad_Dstp(i,j )+adfac3
ad_fac=ad_fac+ &
& (vbar(i,j,kstp)*(Dstp(i,j)+Dstp(i,j-1))+ &
& cff*(cff1*rhs_vbar(i,j)+ &
& cff2*rvbar(i,j,kstp)- &
& cff3*rvbar(i,j,ptsk)))*ad_vbar(i,j,knew)
ad_vbar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i,j-1)=ad_Dnew(i,j-1)+adfac
ad_Dnew(i,j )=ad_Dnew(i,j )+adfac
ad_fac=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j))
fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j))
!^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j)
!^
ad_ubar(i,j,knew)=ad_ubar(i,j,knew)*umask(i,j)
!^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & ubar(i,j,kstp)* &
!^ & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ &
!^ & cff*(cff1*tl_rhs_ubar(i,j)+ &
!^ & cff2*tl_rubar(i,j,kstp)- &
!^ & cff3*tl_rubar(i,j,ptsk)))*fac+ &
!^ & (ubar(i,j,kstp)* &
!^ & (Dstp(i,j)+Dstp(i-1,j))+ &
!^ & cff*(cff1*rhs_ubar(i,j)+ &
!^ & cff2*rubar(i,j,kstp)- &
!^ & cff3*rubar(i,j,ptsk)))*tl_fac
!^
adfac=fac*ad_ubar(i,j,knew)
adfac1=adfac*(Dstp(i,j)+Dstp(i-1,j))
adfac2=adfac*cff
adfac3=adfac*ubar(i,j,kstp)
ad_ubar(i,j,kstp)=ad_ubar(i,j,kstp)+adfac1
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)+cff1*adfac2
ad_rubar(i,j,kstp)=ad_rubar(i,j,kstp)+cff2*adfac2
ad_rubar(i,j,ptsk)=-cff3*adfac2
ad_Dstp(i-1,j)=ad_Dstp(i-1,j)+adfac3
ad_Dstp(i ,j)=ad_Dstp(i ,j)+adfac3
ad_fac=ad_fac+ &
& (ubar(i,j,kstp)*(Dstp(i,j)+Dstp(i-1,j))+ &
& cff*(cff1*rhs_ubar(i,j)+ &
& cff2*rubar(i,j,kstp)- &
& cff3*rubar(i,j,ptsk)))*ad_ubar(i,j,knew)
ad_ubar(i,j,knew)=0.0_r8
!^ tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j))
!^
adfac=-fac*fac*ad_fac
ad_Dnew(i-1,j)=ad_Dnew(i-1,j)+adfac
ad_Dnew(i ,j)=ad_Dnew(i ,j)+adfac
ad_fac=0.0_r8
END DO
END DO
END IF
!
! Compute adjoint total water column depth.
!
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ tl_Dstp(i,j)=tl_zeta(i,j,kstp)+tl_h(i,j)
!^
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_Dstp(i,j)
ad_h(i,j)=ad_h(i,j)+ad_Dstp(i,j)
ad_Dstp(i,j)=0.0_r8
END DO
END DO
!
!=======================================================================
! Compute right-hand-side for the 2D momentum equations.
!=======================================================================
!
!-----------------------------------------------------------------------
! Adjoint Coupling between 2D and 3D equations.
!-----------------------------------------------------------------------
!
! Before the predictor step of the first barotropic time-step,
! arrays "rufrc" and "rvfrc" contain the vertical integrals of
! the 3D right-hand-side terms for momentum equations (including
! surface and bottom stresses, if so prescribed).
!
! Convert them into forcing terms by subtracting the fast time
! "rhs_ubar" and "rhs_vbar" from them; Also, immediately apply
! these forcing terms "rhs_ubar" and "rhs_vbar".
!
! From now on, these newly computed forcing terms will remain
! constant during the fast time stepping and will added to
! "rhs_ubar" and "rhs_vbar" during all subsequent time steps.
!
IF (iif(ng).eq.1.and.PREDICTOR_2D_STEP(ng)) THEN
IF (iic(ng).eq.ntfirst(ng)) THEN
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_rv(i,j,0,nstp)
ad_rv(i,j,0,nstp)=0.0_r8
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_rvfrc(i,j)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_rhs_vbar(i,j)
!^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j)
!^
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)-ad_rvfrc(i,j)
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+ad_ru(i,j,0,nstp)
ad_ru(i,j,0,nstp)=0.0_r8
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_rufrc(i,j)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+ad_rhs_ubar(i,j)
!^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j)
!^
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)-ad_rufrc(i,j)
END DO
END DO
ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_rv(i,j,0,nstp)
ad_rv(i,j,0,nstp)=0.0_r8
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ &
!^ & 1.5_r8*tl_rvfrc(i,j)- &
!^ & 0.5_r8*tl_rv(i,j,0,nnew)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+1.5_r8*ad_rhs_vbar(i,j)
ad_rv(i,j,0,nnew)=ad_rv(i,j,0,nnew)- &
& 0.5_r8*ad_rhs_vbar(i,j)
!^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j)
!^
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)-ad_rvfrc(i,j)
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+ad_ru(i,j,0,nstp)
ad_ru(i,j,0,nstp)=0.0_r8
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ &
!^ & 1.5_r8*tl_rufrc(i,j)- &
!^ & 0.5_r8*tl_ru(i,j,0,nnew)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+1.5_r8*ad_rhs_ubar(i,j)
ad_ru(i,j,0,nnew)=ad_ru(i,j,0,nnew)- &
& 0.5_r8*ad_rhs_ubar(i,j)
!^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j)
!^
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)-ad_rufrc(i,j)
END DO
END DO
ELSE
cff1=23.0_r8/12.0_r8
cff2=16.0_r8/12.0_r8
cff3= 5.0_r8/12.0_r8
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_rv(i,j,0,nstp)
ad_rv(i,j,0,nstp)=0.0_r8
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ &
!^ & cff1*tl_rvfrc(i,j)- &
!^ & cff2*tl_rv(i,j,0,nnew)+ &
!^ & cff3*tl_rv(i,j,0,nstp)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+cff1*ad_rhs_vbar(i,j)
ad_rv(i,j,0,nnew)=ad_rv(i,j,0,nnew)- &
& cff2*ad_rhs_vbar(i,j)
ad_rv(i,j,0,nstp)=ad_rv(i,j,0,nstp)+ &
& cff3*ad_rhs_vbar(i,j)
!^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j)
!^
ad_rhs_vbar(i,j)=ad_rhs_vbar(i,j)-ad_rvfrc(i,j)
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+ad_ru(i,j,0,nstp)
ad_ru(i,j,0,nstp)=0.0_r8
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ &
!^ & cff1*tl_rufrc(i,j)- &
!^ & cff2*tl_ru(i,j,0,nnew)+ &
!^ & cff3*tl_ru(i,j,0,nstp)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+cff1*ad_rhs_ubar(i,j)
ad_ru(i,j,0,nnew)=ad_ru(i,j,0,nnew)- &
& cff2*ad_rhs_ubar(i,j)
ad_ru(i,j,0,nstp)=ad_ru(i,j,0,nstp)+ &
& cff3*ad_rhs_ubar(i,j)
!^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j)
!^
ad_rhs_ubar(i,j)=ad_rhs_ubar(i,j)-ad_rufrc(i,j)
END DO
END DO
END IF
ELSE
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_rvfrc(i,j)
!^
ad_rvfrc(i,j)=ad_rvfrc(i,j)+ad_rhs_vbar(i,j)
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_rufrc(i,j)
!^
ad_rufrc(i,j)=ad_rufrc(i,j)+ad_rhs_ubar(i,j)
END DO
END DO
END IF
!
!-----------------------------------------------------------------------
! Add in adjoint nudging of 2D momentum climatology.
!-----------------------------------------------------------------------
!
IF (LnudgeM2CLM(ng)) THEN
DO j=JstrV,Jend
DO i=Istr,Iend
cff=0.25_r8*(CLIMA(ng)%M2nudgcof(i,j-1)+ &
& CLIMA(ng)%M2nudgcof(i,j ))* &
& om_v(i,j)*on_v(i,j)
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ &
!^ & cff*((Drhs(i,j-1)+Drhs(i,j))* &
!^ & (-tl_vbar(i,j,krhs))+ &
!^ & (tl_Drhs(i,j-1)+tl_Drhs(i,j))* &
!^ & (CLIMA(ng)%vbarclm(i,j)-
!^ & vbar(i,j,krhs)))
!^
adfac=cff*ad_rhs_vbar(i,j)
adfac1=adfac*(Drhs(i,j-1)+Drhs(i,j))
adfac2=adfac*(CLIMA(ng)%vbarclm(i,j)-vbar(i,j,krhs))
ad_vbar(i,j,krhs)=ad_vbar(i,j,krhs)-adfac1
ad_Drhs(i,j-1)=ad_Drhs(i,j-1)+adfac2
ad_Drhs(i,j )=ad_Drhs(i,j )+adfac2
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
cff=0.25_r8*(CLIMA(ng)%M2nudgcof(i-1,j)+ &
& CLIMA(ng)%M2nudgcof(i ,j))* &
& om_u(i,j)*on_u(i,j)
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ &
!^ & cff*((Drhs(i-1,j)+Drhs(i,j))* &
!^ & (-tl_ubar(i,j,krhs))+ &
!^ & (tl_Drhs(i-1,j)+tl_Drhs(i,j))* &
!^ & (CLIMA(ng)%ubarclm(i,j)-
!^ & ubar(i,j,krhs)))
!^
adfac=cff*ad_rhs_ubar(i,j)
adfac1=adfac*(Drhs(i-1,j)+Drhs(i,j))
adfac2=adfac*(CLIMA(ng)%ubarclm(i,j)-ubar(i,j,krhs))
ad_ubar(i,j,krhs)=ad_ubar(i,j,krhs)-adfac1
ad_Drhs(i-1,j)=ad_Drhs(i-1,j)+adfac2
ad_Drhs(i ,j)=ad_Drhs(i ,j)+adfac2
END DO
END DO
END IF
!
!-----------------------------------------------------------------------
! Compute basic state total depth at PSI-points.
!-----------------------------------------------------------------------
!
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
Drhs_p(i,j)=0.25_r8*(Drhs(i,j )+Drhs(i-1,j )+ &
& Drhs(i,j-1)+Drhs(i-1,j-1))
END DO
END DO
!
!-----------------------------------------------------------------------
! Add in adjoint horizontal harmonic viscosity.
!-----------------------------------------------------------------------
!
! Add in harmonic viscosity.
!
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_fac
!^
ad_fac=ad_fac+ad_rhs_vbar(i,j)
!^ tl_fac=tl_cff1-tl_cff2
!^
ad_cff1=ad_cff1+ad_fac
ad_cff2=ad_cff2-ad_fac
ad_fac=0.0_r8
!^ tl_cff2=0.5_r8*(pm(i,j-1)+pm(i,j))* &
!^ & (tl_VFe(i ,j)-tl_VFe(i,j-1))
!^
adfac=0.5_r8*(pm(i,j-1)+pm(i,j))*ad_cff2
ad_VFe(i,j-1)=ad_VFe(i,j-1)-adfac
ad_VFe(i ,j)=ad_VFe(i ,j)+adfac
ad_cff2=0.0_r8
!^ tl_cff1=0.5_r8*(pn(i,j-1)+pn(i,j))* &
!^ & (tl_VFx(i+1,j)-tl_VFx(i,j ))
!^
adfac=0.5_r8*(pn(i,j-1)+pn(i,j))*ad_cff1
ad_VFx(i ,j)=ad_VFx(i ,j)-adfac
ad_VFx(i+1,j)=ad_VFx(i+1,j)+adfac
ad_cff1=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac
!^
ad_fac=ad_fac+ad_rhs_ubar(i,j)
!^ tl_fac=tl_cff1+tl_cff2
!^
ad_cff1=ad_cff1+ad_fac
ad_cff2=ad_cff2+ad_fac
ad_fac=0.0_r8
!^ tl_cff2=0.5_r8*(pm(i-1,j)+pm(i,j))* &
!^ & (tl_UFe(i,j+1)-tl_UFe(i ,j))
!^
adfac=0.5_r8*(pm(i-1,j)+pm(i,j))*ad_cff2
ad_UFe(i,j )=ad_UFe(i,j )-adfac
ad_UFe(i,j+1)=ad_UFe(i,j+1)+adfac
ad_cff2=0.0_r8
!^ tl_cff1=0.5_r8*(pn(i-1,j)+pn(i,j))* &
!^ & (tl_UFx(i,j )-tl_UFx(i-1,j))
!^
adfac=0.5_r8*(pn(i-1,j)+pn(i,j))*ad_cff1
ad_UFx(i-1,j)=ad_UFx(i-1,j)-adfac
ad_UFx(i ,j)=ad_UFx(i ,j)+adfac
ad_cff1=0.0_r8
END DO
END DO
!
! Compute flux-components of the adjoint horizontal divergence of the
! stress tensor (m5/s2) in XI- and ETA-directions.
!
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
!^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*tl_cff
!^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*tl_cff
!^
ad_cff=ad_cff+ &
& on_p(i,j)*on_p(i,j)*ad_VFx(i,j)+ &
& om_p(i,j)*om_p(i,j)*ad_UFe(i,j)
ad_VFx(i,j)=0.0_r8
ad_UFe(i,j)=0.0_r8
!^ tl_cff=tl_cff*pmask(i,j)
!^
ad_cff=ad_cff*pmask(i,j)
!^ tl_cff=visc2_p(i,j)*0.5_r8* &
!^ & (tl_Drhs_p(i,j)* &
!^ & (pmon_p(i,j)* &
!^ & ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,krhs)- &
!^ & (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,krhs))+ &
!^ & pnom_p(i,j)* &
!^ & ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,krhs)- &
!^ & (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,krhs)))+ &
!^ & Drhs_p(i,j)* &
!^ & (pmon_p(i,j)* &
!^ & ((pn(i ,j-1)+pn(i ,j))*tl_vbar(i ,j,krhs)- &
!^ & (pn(i-1,j-1)+pn(i-1,j))*tl_vbar(i-1,j,krhs))+ &
!^ & pnom_p(i,j)* &
!^ & ((pm(i-1,j )+pm(i,j ))*tl_ubar(i,j ,krhs)- &
!^ & (pm(i-1,j-1)+pm(i,j-1))*tl_ubar(i,j-1,krhs))))
!^
adfac=visc2_p(i,j)*0.5_r8*ad_cff
adfac1=adfac*Drhs_p(i,j)
adfac2=adfac1*pmon_p(i,j)
adfac3=adfac1*pnom_p(i,j)
ad_Drhs_p(i,j)=ad_Drhs_p(i,j)+ &
& (pmon_p(i,j)* &
& ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,krhs)- &
& (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,krhs))+ &
& pnom_p(i,j)* &
& ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,krhs)- &
& (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,krhs)))*&
& adfac
ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)- &
& (pn(i-1,j-1)+pn(i-1,j))*adfac2
ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)+ &
& (pn(i ,j-1)+pn(i ,j))*adfac2
ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)- &
& (pm(i-1,j-1)+pm(i,j-1))*adfac3
ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)+ &
& (pm(i-1,j )+pm(i,j ))*adfac3
ad_cff=0.0_r8
END DO
END DO
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*tl_cff
!^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*tl_cff
!^
ad_cff=ad_cff+ &
& om_r(i,j)*om_r(i,j)*ad_VFe(i,j)+ &
& on_r(i,j)*on_r(i,j)*ad_UFx(i,j)
ad_VFe(i,j)=0.0_r8
ad_UFx(i,j)=0.0_r8
!^ tl_cff=visc2_r(i,j)*0.5_r8* &
!^ & (tl_Drhs(i,j)* &
!^ & (pmon_r(i,j)* &
!^ & ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,krhs)- &
!^ & (pn(i-1,j)+pn(i ,j))*ubar(i ,j,krhs))- &
!^ & pnom_r(i,j)* &
!^ & ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,krhs)- &
!^ & (pm(i,j-1)+pm(i,j ))*vbar(i,j ,krhs)))+ &
!^ & Drhs(i,j)* &
!^ & (pmon_r(i,j)* &
!^ & ((pn(i ,j)+pn(i+1,j))*tl_ubar(i+1,j,krhs)- &
!^ & (pn(i-1,j)+pn(i ,j))*tl_ubar(i ,j,krhs))- &
!^ & pnom_r(i,j)* &
!^ & ((pm(i,j )+pm(i,j+1))*tl_vbar(i,j+1,krhs)- &
!^ & (pm(i,j-1)+pm(i,j ))*tl_vbar(i,j ,krhs))))
!^
adfac=visc2_r(i,j)*0.5_r8*ad_cff
adfac1=adfac*Drhs(i,j)
adfac2=adfac1*pmon_r(i,j)
adfac3=adfac1*pnom_r(i,j)
ad_Drhs(i,j)=ad_Drhs(i,j)+ &
& (pmon_r(i,j)* &
& ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,krhs)- &
& (pn(i-1,j)+pn(i ,j))*ubar(i ,j,krhs))- &
& pnom_r(i,j)* &
& ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,krhs)- &
& (pm(i,j-1)+pm(i,j ))*vbar(i,j ,krhs)))* &
& adfac
ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)- &
& (pn(i-1,j)+pn(i ,j))*adfac2
ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+ &
& (pn(i ,j)+pn(i+1,j))*adfac2
ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+ &
& (pm(i,j-1)+pm(i,j ))*adfac3
ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)- &
& (pm(i,j )+pm(i,j+1))*adfac3
ad_cff=0.0_r8
END DO
END DO
!
!-----------------------------------------------------------------------
! If horizontal mixing, compute adjoint total depth at PSI-points.
!-----------------------------------------------------------------------
!
DO j=Jstr,Jend+1
DO i=Istr,Iend+1
Drhs_p(i,j)=0.25_r8*(Drhs(i,j )+Drhs(i-1,j )+ &
& Drhs(i,j-1)+Drhs(i-1,j-1))
!^ tl_Drhs_p(i,j)=0.25_r8*(tl_Drhs(i,j )+tl_Drhs(i-1,j )+ &
!^ & tl_Drhs(i,j-1)+tl_Drhs(i-1,j-1))
!^
adfac=0.25_r8*ad_Drhs_p(i,j)
ad_Drhs(i-1,j )=ad_Drhs(i-1,j )+adfac
ad_Drhs(i ,j )=ad_Drhs(i ,j )+adfac
ad_Drhs(i-1,j-1)=ad_Drhs(i-1,j-1)+adfac
ad_Drhs(i ,j-1)=ad_Drhs(i ,j-1)+adfac
ad_Drhs_p(i,j)=0.0_r8
END DO
END DO
!
!-----------------------------------------------------------------------
! Add in curvilinear transformation terms.
!-----------------------------------------------------------------------
!
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac1
!^
ad_fac1=ad_fac1-ad_rhs_vbar(i,j)
!^ tl_fac1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1))
!^
adfac=0.5_r8*ad_fac1
ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac
ad_VFe(i,j )=ad_VFe(i,j )+adfac
ad_fac1=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac1
!^
ad_fac1=ad_fac1+ad_rhs_ubar(i,j)
!^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j))
!^
adfac=0.5_r8*ad_fac1
ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac
ad_UFx(i ,j)=ad_UFx(i ,j)+adfac
ad_fac1=0.0_r8
END DO
END DO
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
cff1=0.5_r8*(vbar(i,j ,krhs)+ &
& vbar(i,j+1,krhs))
cff2=0.5_r8*(ubar(i ,j,krhs)+ &
& ubar(i+1,j,krhs))
cff3=cff1*dndx(i,j)
cff4=cff2*dmde(i,j)
cff=Drhs(i,j)*(cff3-cff4)
!^ tl_VFe(i,j)=tl_cff*cff2+cff*tl_cff2
!^ tl_UFx(i,j)=tl_cff*cff1+cff*tl_cff1
!^
ad_cff=ad_cff+ &
& cff1*ad_UFx(i,j)+ &
& cff2*ad_VFe(i,j)
ad_cff1=ad_cff1+cff*ad_UFx(i,j)
ad_cff2=ad_cff2+cff*ad_VFe(i,j)
ad_UFx(i,j)=0.0_r8
ad_VFe(i,j)=0.0_r8
!^ tl_cff=tl_Drhs(i,j)*(cff3-cff4)+ &
!^ & Drhs(i,j)*(tl_cff3-tl_cff4)
!^
adfac=Drhs(i,j)*ad_cff
ad_cff4=ad_cff4-adfac
ad_cff3=ad_cff3+adfac
ad_Drhs(i,j)=ad_Drhs(i,j)+(cff3-cff4)*ad_cff
ad_cff=0.0_r8
!^ tl_cff4=tl_cff2*dmde(i,j)
!^
ad_cff2=ad_cff2+dmde(i,j)*ad_cff4
ad_cff4=0.0_r8
!^ tl_cff3=tl_cff1*dndx(i,j)
!^
ad_cff1=ad_cff1+dndx(i,j)*ad_cff3
ad_cff3=0.0_r8
!^ tl_cff2=0.5_r8*(tl_ubar(i ,j,krhs)+ &
!^ & tl_ubar(i+1,j,krhs))
!^
adfac=0.5_r8*ad_cff2
ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac
ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac
ad_cff2=0.0_r8
!^ tl_cff1=0.5_r8*(tl_vbar(i,j ,krhs)+ &
!^ & tl_vbar(i,j+1,krhs))
!^
adfac=0.5_r8*ad_cff1
ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac
ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac
ad_cff1=0.0_r8
END DO
END DO
!
!-----------------------------------------------------------------------
! Add in Coriolis term.
!-----------------------------------------------------------------------
!
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac1
!^
ad_fac1=ad_fac1-ad_rhs_vbar(i,j)
!^ tl_fac1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1))
!^
adfac=0.5_r8*ad_fac1
ad_VFe(i,j-1)=ad_VFe(i,j-1)+adfac
ad_VFe(i,j )=ad_VFe(i,j )+adfac
ad_fac1=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac1
!^
ad_fac1=ad_fac1+ad_rhs_ubar(i,j)
!^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j))
!^
adfac=0.5_r8*ad_fac1
ad_UFx(i-1,j)=ad_UFx(i-1,j)+adfac
ad_UFx(i ,j)=ad_UFx(i ,j)+adfac
ad_fac1=0.0_r8
END DO
END DO
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
cff=0.5_r8*Drhs(i,j)*fomn(i,j)
!^ tl_VFe(i,j)=tl_cff*(ubar(i ,j,krhs)+ &
!^ & ubar(i+1,j,krhs))+ &
!^ & cff*(tl_ubar(i ,j,krhs)+ &
!^ & tl_ubar(i+1,j,krhs))
!^
adfac=cff*ad_VFe(i,j)
ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac
ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac
ad_cff=ad_cff+(ubar(i ,j,krhs)+ &
& ubar(i+1,j,krhs))*ad_VFe(i,j)
ad_VFe(i,j)=0.0_r8
!^ tl_UFx(i,j)=tl_cff*(vbar(i,j ,krhs)+ &
!^ & vbar(i,j+1,krhs))+ &
!^ & cff*(tl_vbar(i,j ,krhs)+ &
!^ & tl_vbar(i,j+1,krhs))
!^
adfac=cff*ad_UFx(i,j)
ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac
ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac
ad_cff=ad_cff+(vbar(i,j ,krhs)+ &
& vbar(i,j+1,krhs))*ad_UFx(i,j)
ad_UFx(i,j)=0.0_r8
!^ tl_cff=0.5_r8*tl_Drhs(i,j)*fomn(i,j)
!^
ad_Drhs(i,j)=ad_Drhs(i,j)+0.5_r8*fomn(i,j)*ad_cff
ad_cff=0.0_r8
END DO
END DO
!
!-----------------------------------------------------------------------
! Add in adjoint horizontal advection of momentum.
!-----------------------------------------------------------------------
!
DO j=JstrV,Jend
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac
!^
ad_fac=ad_fac-ad_rhs_vbar(i,j)
!^ tl_fac=tl_cff1+tl_cff2
!^
ad_cff1=ad_cff1+ad_fac
ad_cff2=ad_cff2+ad_fac
ad_fac=0.0_r8
!^ tl_cff2=tl_VFe(i,j)-tl_VFe(i,j-1)
!^
ad_VFe(i,j-1)=ad_VFe(i,j-1)-ad_cff2
ad_VFe(i,j )=ad_VFe(i,j )+ad_cff2
ad_cff2=0.0_r8
!^ tl_cff1=tl_VFx(i+1,j)-tl_VFx(i,j)
!^
ad_VFx(i ,j)=ad_VFx(i ,j)-ad_cff1
ad_VFx(i+1,j)=ad_VFx(i+1,j)+ad_cff1
ad_cff1=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)-tl_fac
!^
ad_fac=ad_fac-ad_rhs_ubar(i,j)
!^ tl_fac=tl_cff1+tl_cff2
!^
ad_cff1=ad_cff1+ad_fac
ad_cff2=ad_cff2+ad_fac
ad_fac=0.0_r8
!^ tl_cff2=tl_UFe(i,j+1)-tl_UFe(i,j)
!^
ad_UFe(i,j )=ad_UFe(i,j )-ad_cff2
ad_UFe(i,j+1)=ad_UFe(i,j+1)+ad_cff2
ad_cff2=0.0_r8
!^ tl_cff1=tl_UFx(i,j)-tl_UFx(i-1,j)
!^
ad_UFx(i-1,j)=ad_UFx(i-1,j)-ad_cff1
ad_UFx(i ,j)=ad_UFx(i ,j)+ad_cff1
ad_cff1=0.0_r8
END DO
END DO
!
! Fourth-order, centered differences advection.
!
DO j=JstrVm1,Jendp1
DO i=Istr,Iend
grad (i,j)=vbar(i,j-1,krhs)-2.0_r8*vbar(i,j,krhs)+ &
& vbar(i,j+1,krhs)
Dgrad(i,j)=DVom(i,j-1)-2.0_r8*DVom(i,j)+DVom(i,j+1)
END DO
END DO
IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
grad (i,Jend+1)=grad (i,Jend)
Dgrad(i,Jend+1)=Dgrad(i,Jend)
END DO
END IF
END IF
IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
grad (i,Jstr)=grad (i,Jstr+1)
Dgrad(i,Jstr)=Dgrad(i,Jstr+1)
END DO
END IF
END IF
cff=1.0_r8/6.0_r8
DO j=JstrV-1,Jend
DO i=Istr,Iend
!^ tl_VFe(i,j)=0.25_r8* &
!^ & ((tl_vbar(i,j ,krhs)+ &
!^ & tl_vbar(i,j+1,krhs)- &
!^ & cff*(tl_grad (i,j)+tl_grad (i,j+1)))* &
!^ & (DVom(i,j)+DVom(i,j+1)- &
!^ & cff*(Dgrad(i,j)+Dgrad(i,j+1)))+ &
!^ & (vbar(i,j ,krhs)+ &
!^ & vbar(i,j+1,krhs)- &
!^ & cff*(grad (i,j)+grad (i,j+1)))* &
!^ & (tl_DVom(i,j)+tl_DVom(i,j+1)- &
!^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j+1))))
!^
adfac=0.25_r8*ad_VFe(i,j)
adfac1=adfac*(DVom(i,j)+DVom(i,j+1)- &
& cff*(Dgrad(i,j)+Dgrad(i,j+1)))
adfac2=adfac1*cff
adfac3=adfac*(vbar(i,j ,krhs)+ &
& vbar(i,j+1,krhs)- &
& cff*(grad (i,j)+grad (i,j+1)))
adfac4=adfac3*cff
ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)+adfac1
ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+adfac1
ad_grad (i,j )=ad_grad (i,j )-adfac2
ad_grad (i,j+1)=ad_grad (i,j+1)-adfac2
ad_DVom(i,j )=ad_DVom(i,j )+adfac3
ad_DVom(i,j+1)=ad_DVom(i,j+1)+adfac3
ad_Dgrad(i,j )=ad_Dgrad(i,j )-adfac4
ad_Dgrad(i,j+1)=ad_Dgrad(i,j+1)-adfac4
ad_VFe(i,j)=0.0_r8
END DO
END DO
IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=Istr,Iend
!^ tl_Dgrad(i,Jend+1)=tl_Dgrad(i,Jend)
!^
ad_Dgrad(i,Jend)=ad_Dgrad(i,Jend)+ad_Dgrad(i,Jend+1)
ad_Dgrad(i,Jend+1)=0.0_r8
!^ tl_grad (i,Jend+1)=tl_grad (i,Jend)
!^
ad_grad (i,Jend)=ad_grad (i,Jend)+ad_grad (i,Jend+1)
ad_grad (i,Jend+1)=0.0_r8
END DO
END IF
END IF
IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=Istr,Iend
!^ tl_Dgrad(i,Jstr)=tl_Dgrad(i,Jstr+1)
!^
ad_Dgrad(i,Jstr+1)=ad_Dgrad(i,Jstr+1)+ad_Dgrad(i,Jstr)
ad_Dgrad(i,Jstr)=0.0_r8
!^ tl_grad (i,Jstr)=tl_grad (i,Jstr+1)
!^
ad_grad (i,Jstr+1)=ad_grad (i,Jstr+1)+ad_grad (i,Jstr)
ad_grad (i,Jstr)=0.0_r8
END DO
END IF
END IF
DO j=JstrVm1,Jendp1
DO i=Istr,Iend
!^ tl_Dgrad(i,j)=tl_DVom(i,j-1)-2.0_r8*tl_DVom(i,j)+ &
!^ & tl_DVom(i,j+1)
!^
ad_DVom(i,j-1)=ad_DVom(i,j-1)+ad_Dgrad(i,j)
ad_DVom(i,j )=ad_DVom(i,j )-2.0_r8*ad_Dgrad(i,j)
ad_DVom(i,j+1)=ad_DVom(i,j+1)+ad_Dgrad(i,j)
ad_Dgrad(i,j)=0.0_r8
!^ tl_grad (i,j)=tl_vbar(i,j-1,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ &
!^ & tl_vbar(i,j+1,krhs)
!^
ad_vbar(i,j-1,krhs)=ad_vbar(i,j-1,krhs)+ad_grad(i,j)
ad_vbar(i,j ,krhs)=ad_vbar(i,j ,krhs)- &
& 2.0_r8*ad_grad(i,j)
ad_vbar(i,j+1,krhs)=ad_vbar(i,j+1,krhs)+ad_grad(i,j)
ad_grad(i,j)=0.0_r8
END DO
END DO
DO j=JstrV,Jend
DO i=Istrm1,Iendp1
grad(i,j)=vbar(i-1,j,krhs)-2.0_r8*vbar(i,j,krhs)+ &
& vbar(i+1,j,krhs)
END DO
END DO
IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=JstrV,Jend
grad(Istr-1,j)=grad(Istr,j)
END DO
END IF
END IF
IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=JstrV,Jend
grad(Iend+1,j)=grad(Iend,j)
END DO
END IF
END IF
DO j=JstrV-1,Jend
DO i=Istr,Iend+1
Dgrad(i,j)=DUon(i,j-1)-2.0_r8*DUon(i,j)+DUon(i,j+1)
END DO
END DO
cff=1.0_r8/6.0_r8
DO j=JstrV,Jend
DO i=Istr,Iend+1
!^ tl_VFx(i,j)=0.25_r8* &
!^ & ((tl_vbar(i ,j,krhs)+ &
!^ & tl_vbar(i-1,j,krhs)- &
!^ & cff*(tl_grad (i,j)+tl_grad (i-1,j)))* &
!^ & (DUon(i,j)+DUon(i,j-1)- &
!^ & cff*(Dgrad(i,j)+Dgrad(i,j-1)))+ &
!^ & (vbar(i ,j,krhs)+ &
!^ & vbar(i-1,j,krhs)- &
!^ & cff*(grad (i,j)+grad (i-1,j)))* &
!^ & (tl_DUon(i,j)+tl_DUon(i,j-1)- &
!^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j-1))))
!^
adfac=0.25_r8*ad_VFx(i,j)
adfac1=adfac*(DUon(i,j)+DUon(i,j-1)- &
& cff*(Dgrad(i,j)+Dgrad(i,j-1)))
adfac2=adfac1*cff
adfac3=adfac*(vbar(i ,j,krhs)+ &
& vbar(i-1,j,krhs)- &
& cff*(grad (i,j)+grad (i-1,j)))
adfac4=adfac3*cff
ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)+adfac1
ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)+adfac1
ad_grad (i-1,j)=ad_grad (i-1,j)-adfac2
ad_grad (i ,j)=ad_grad (i ,j)-adfac2
ad_DUon(i,j-1)=ad_DUon(i,j-1)+adfac3
ad_DUon(i,j )=ad_DUon(i,j )+adfac3
ad_Dgrad(i,j-1)=ad_Dgrad(i,j-1)-adfac4
ad_Dgrad(i,j )=ad_Dgrad(i,j )-adfac4
ad_VFx(i,j)=0.0_r8
END DO
END DO
DO j=JstrV-1,Jend
DO i=Istr,Iend+1
!^ tl_Dgrad(i,j)=tl_DUon(i,j-1)-2.0_r8*tl_DUon(i,j)+ &
!^ & tl_DUon(i,j+1)
!^
ad_DUon(i,j-1)=ad_DUon(i,j-1)+ad_Dgrad(i,j)
ad_DUon(i,j )=ad_DUon(i,j )-2.0_r8*ad_Dgrad(i,j)
ad_DUon(i,j+1)=ad_DUon(i,j+1)+ad_Dgrad(i,j)
ad_Dgrad(i,j)=0.0_r8
END DO
END DO
IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=JstrV,Jend
!^ tl_grad(Iend+1,j)=tl_grad(Iend,j)
!^
ad_grad(Iend,j)=ad_grad(Iend,j)+ad_grad(Iend+1,j)
ad_grad(Iend+1,j)=0.0_r8
END DO
END IF
END IF
IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=JstrV,Jend
!^ tl_grad(Istr-1,j)=tl_grad(Istr,j)
!^
ad_grad(Istr,j)=ad_grad(Istr,j)+ad_grad(Istr-1,j)
ad_grad(Istr-1,j)=0.0_r8
END DO
END IF
END IF
DO j=JstrV,Jend
DO i=Istrm1,Iendp1
!^ tl_grad(i,j)=tl_vbar(i-1,j,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ &
!^ & tl_vbar(i+1,j,krhs)
!^
ad_vbar(i-1,j,krhs)=ad_vbar(i-1,j,krhs)+ad_grad(i,j)
ad_vbar(i ,j,krhs)=ad_vbar(i ,j,krhs)- &
& 2.0_r8*ad_grad(i,j)
ad_vbar(i+1,j,krhs)=ad_vbar(i+1,j,krhs)+ad_grad(i,j)
ad_grad(i,j)=0.0_r8
END DO
END DO
DO j=Jstrm1,Jendp1
DO i=IstrU,Iend
grad(i,j)=ubar(i,j-1,krhs)-2.0_r8*ubar(i,j,krhs)+ &
& ubar(i,j+1,krhs)
END DO
END DO
IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=IstrU,Iend
grad(i,Jstr-1)=grad(i,Jstr)
END DO
END IF
END IF
IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=IstrU,Iend
grad(i,Jend+1)=grad(i,Jend)
END DO
END IF
END IF
DO j=Jstr,Jend+1
DO i=IstrU-1,Iend
Dgrad(i,j)=DVom(i-1,j)-2.0_r8*DVom(i,j)+DVom(i+1,j)
END DO
END DO
cff=1.0_r8/6.0_r8
DO j=Jstr,Jend+1
DO i=IstrU,Iend
!^ tl_UFe(i,j)=0.25_r8* &
!^ & ((tl_ubar(i,j ,krhs)+ &
!^ & tl_ubar(i,j-1,krhs)- &
!^ & cff*(tl_grad (i,j)+tl_grad (i,j-1)))* &
!^ & (DVom(i,j)+DVom(i-1,j)- &
!^ & cff*(Dgrad(i,j)+Dgrad(i-1,j)))+ &
!^ & (ubar(i,j ,krhs)+ &
!^ & ubar(i,j-1,krhs)- &
!^ & cff*(grad (i,j)+grad (i,j-1)))* &
!^ & (tl_DVom(i,j)+tl_DVom(i-1,j)- &
!^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i-1,j))))
!^
adfac=0.25_r8*ad_UFe(i,j)
adfac1=adfac*(DVom(i,j)+DVom(i-1,j)- &
& cff*(Dgrad(i,j)+Dgrad(i-1,j)))
adfac2=adfac1*cff
adfac3=adfac*(ubar(i,j ,krhs)+ &
& ubar(i,j-1,krhs)- &
& cff*(grad (i,j)+grad (i,j-1)))
adfac4=adfac3*cff
ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)+adfac1
ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)+adfac1
ad_grad (i,j-1)=ad_grad (i,j-1)-adfac2
ad_grad (i,j )=ad_grad (i,j )-adfac2
ad_DVom(i-1,j)=ad_DVom(i-1,j)+adfac3
ad_DVom(i ,j)=ad_DVom(i ,j)+adfac3
ad_Dgrad(i-1,j)=ad_Dgrad(i-1,j)-adfac4
ad_Dgrad(i ,j)=ad_Dgrad(i ,j)-adfac4
ad_UFe(i,j)=0.0_r8
END DO
END DO
DO j=Jstr,Jend+1
DO i=IstrU-1,Iend
!^ tl_Dgrad(i,j)=tl_DVom(i-1,j)-2.0_r8*tl_DVom(i,j)+ &
!^ & tl_DVom(i+1,j)
!^
ad_DVom(i-1,j)=ad_DVom(i-1,j)+ad_Dgrad(i,j)
ad_DVom(i ,j)=ad_DVom(i ,j)-2.0_r8*ad_Dgrad(i,j)
ad_DVom(i+1,j)=ad_DVom(i+1,j)+ad_Dgrad(i,j)
ad_Dgrad(i,j)=0.0_r8
END DO
END DO
IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
DO i=IstrU,Iend
!^ tl_grad(i,Jend+1)=tl_grad(i,Jend)
!^
ad_grad(i,Jend)=ad_grad(i,Jend)+ad_grad(i,Jend+1)
ad_grad(i,Jend+1)=0.0_r8
END DO
END IF
END IF
IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
DO i=IstrU,Iend
!^ tl_grad(i,Jstr-1)=tl_grad(i,Jstr)
!^
ad_grad(i,Jstr)=ad_grad(i,Jstr)+ad_grad(i,Jstr-1)
ad_grad(i,Jstr-1)=0.0_r8
END DO
END IF
END IF
DO j=Jstrm1,Jendp1
DO i=IstrU,Iend
!^ tl_grad(i,j)=tl_ubar(i,j-1,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ &
!^ & tl_ubar(i,j+1,krhs)
!^
ad_ubar(i,j-1,krhs)=ad_ubar(i,j-1,krhs)+ad_grad(i,j)
ad_ubar(i,j ,krhs)=ad_ubar(i,j ,krhs)- &
& 2.0_r8*ad_grad(i,j)
ad_ubar(i,j+1,krhs)=ad_ubar(i,j+1,krhs)+ad_grad(i,j)
ad_grad(i,j)=0.0_r8
END DO
END DO
DO j=Jstr,Jend
DO i=IstrUm1,Iendp1
grad (i,j)=ubar(i-1,j,krhs)-2.0_r8*ubar(i,j,krhs)+ &
& ubar(i+1,j,krhs)
Dgrad(i,j)=DUon(i-1,j)-2.0_r8*DUon(i,j)+DUon(i+1,j)
END DO
END DO
IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
grad (Istr,j)=grad (Istr+1,j)
Dgrad(Istr,j)=Dgrad(Istr+1,j)
END DO
END IF
END IF
IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
grad (Iend+1,j)=grad (Iend,j)
Dgrad(Iend+1,j)=Dgrad(Iend,j)
END DO
END IF
END IF
cff=1.0_r8/6.0_r8
DO j=Jstr,Jend
DO i=IstrU-1,Iend
!^ tl_UFx(i,j)=0.25_r8* &
!^ & ((ubar(i ,j,krhs)+ &
!^ & ubar(i+1,j,krhs)- &
!^ & cff*(grad (i,j)+grad (i+1,j)))* &
!^ & (tl_DUon(i,j)+tl_DUon(i+1,j)- &
!^ & cff*(tl_Dgrad(i,j)+tl_Dgrad(i+1,j)))+ &
!^ & (tl_ubar(i ,j,krhs)+ &
!^ & tl_ubar(i+1,j,krhs)- &
!^ & cff*(tl_grad (i,j)+tl_grad (i+1,j)))* &
!^ & (DUon(i,j)+DUon(i+1,j)- &
!^ & cff*(Dgrad(i,j)+Dgrad(i+1,j))))
!^
adfac=0.25_r8*ad_UFx(i,j)
adfac1=adfac*(DUon(i,j)+DUon(i+1,j)- &
& cff*(Dgrad(i,j)+Dgrad(i+1,j)))
adfac2=adfac1*cff
adfac3=adfac*(ubar(i ,j,krhs)+ &
& ubar(i+1,j,krhs)- &
& cff*(grad (i,j)+grad (i+1,j)))
adfac4=adfac3*cff
ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)+adfac1
ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+adfac1
ad_grad (i ,j)=ad_grad (i ,j)-adfac2
ad_grad (i+1,j)=ad_grad (i+1,j)-adfac2
ad_DUon(i ,j)=ad_DUon(i ,j)+adfac3
ad_DUon(i+1,j)=ad_DUon(i+1,j)+adfac3
ad_Dgrad(i ,j)=ad_Dgrad(i ,j)-adfac4
ad_Dgrad(i+1,j)=ad_Dgrad(i+1,j)-adfac4
ad_UFx(i,j)=0.0_r8
END DO
END DO
IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
DO j=Jstr,Jend
!^ tl_Dgrad(Iend+1,j)=tl_Dgrad(Iend,j)
!^
ad_Dgrad(Iend,j)=ad_Dgrad(Iend,j)+ad_Dgrad(Iend+1,j)
ad_Dgrad(Iend+1,j)=0.0_r8
!^ tl_grad (Iend+1,j)=tl_grad (Iend,j)
!^
ad_grad (Iend,j)=ad_grad (Iend,j)+ad_grad (Iend+1,j)
ad_grad (Iend+1,j)=0.0_r8
END DO
END IF
END IF
IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
DO j=Jstr,Jend
!^ tl_Dgrad(Istr,j)=tl_Dgrad(Istr+1,j)
!^
ad_Dgrad(Istr+1,j)=ad_Dgrad(Istr+1,j)+ad_Dgrad(Istr,j)
ad_Dgrad(Istr,j)=0.0_r8
!^ tl_grad (Istr,j)=tl_grad (Istr+1,j)
!^
ad_grad (Istr+1,j)=ad_grad (Istr+1,j)+ad_grad (Istr,j)
ad_grad (Istr,j)=0.0_r8
END DO
END IF
END IF
DO j=Jstr,Jend
DO i=IstrUm1,Iendp1
!^ tl_Dgrad(i,j)=tl_DUon(i-1,j)-2.0_r8*tl_DUon(i,j)+ &
!^ & tl_DUon(i+1,j)
!^
ad_DUon(i-1,j)=ad_DUon(i-1,j)+ad_Dgrad(i,j)
ad_DUon(i ,j)=ad_DUon(i ,j)-2.0_r8*ad_Dgrad(i,j)
ad_DUon(i+1,j)=ad_DUon(i+1,j)+ad_Dgrad(i,j)
ad_Dgrad(i,j)=0.0_r8
!^ tl_grad (i,j)=tl_ubar(i-1,j,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ &
!^ & tl_ubar(i+1,j,krhs)
!^
ad_ubar(i-1,j,krhs)=ad_ubar(i-1,j,krhs)+ad_grad (i,j)
ad_ubar(i ,j,krhs)=ad_ubar(i ,j,krhs)- &
& 2.0_r8*ad_grad (i,j)
ad_ubar(i+1,j,krhs)=ad_ubar(i+1,j,krhs)+ad_grad (i,j)
ad_grad(i,j)=0.0_r8
END DO
END DO
!
!-----------------------------------------------------------------------
! Compute adjoint pressure gradient terms.
!-----------------------------------------------------------------------
!
! Compute BASIC STATE fields associated with pressure gradient and
! time-stepping of adjoint free-surface.
!
fac=1000.0_r8/rho0
IF (iif(ng).eq.1) THEN
cff1=dtfast(ng)
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ rhs_zeta(i,j)=(DUon(i,j)-DUon(i+1,j))+ &
!^ & (DVom(i,j)-DVom(i,j+1))
!^ zeta_new(i,j)=zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*cff1*rhs_zeta(i,j)
!^
!^ use background instead
zeta_new(i,j)=zeta(i,j,knew)
zeta_new(i,j)=zeta_new(i,j)*rmask(i,j)
zwrk(i,j)=0.5_r8*(zeta(i,j,kstp)+zeta_new(i,j))
gzeta(i,j)=zwrk(i,j)
gzeta2(i,j)=zwrk(i,j)*zwrk(i,j)
END DO
END DO
ELSE IF (PREDICTOR_2D_STEP(ng)) THEN
cff1=2.0_r8*dtfast(ng)
cff4=4.0_r8/25.0_r8
cff5=1.0_r8-2.0_r8*cff4
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ rhs_zeta(i,j)=(DUon(i,j)-DUon(i+1,j))+ &
!^ & (DVom(i,j)-DVom(i,j+1))
!^ zeta_new(i,j)=zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*cff1*rhs_zeta(i,j)
!^
!^ use background instead
zeta_new(i,j)=zeta(i,j,knew)
zeta_new(i,j)=zeta_new(i,j)*rmask(i,j)
zwrk(i,j)=cff5*zeta(i,j,krhs)+ &
& cff4*(zeta(i,j,kstp)+zeta_new(i,j))
gzeta(i,j)=zwrk(i,j)
gzeta2(i,j)=zwrk(i,j)*zwrk(i,j)
END DO
END DO
ELSE IF (CORRECTOR_2D_STEP) THEN
cff1=dtfast(ng)*5.0_r8/12.0_r8
cff2=dtfast(ng)*8.0_r8/12.0_r8
cff3=dtfast(ng)*1.0_r8/12.0_r8
cff4=2.0_r8/5.0_r8
cff5=1.0_r8-cff4
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ cff=cff1*((DUon(i,j)-DUon(i+1,j))+ &
!^ & (DVom(i,j)-DVom(i,j+1)))
!^ zeta_new(i,j)=zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*(cff+ &
!^ & cff2*rzeta(i,j,kstp)- &
!^ & cff3*rzeta(i,j,ptsk))
!^
!^ use background instead
zeta_new(i,j)=zeta(i,j,knew)
zeta_new(i,j)=zeta_new(i,j)*rmask(i,j)
zwrk(i,j)=cff5*zeta_new(i,j)+cff4*zeta(i,j,krhs)
gzeta(i,j)=zwrk(i,j)
gzeta2(i,j)=zwrk(i,j)*zwrk(i,j)
END DO
END DO
END IF
!
! Compute adjoint pressure gradient.
!
cff1=0.5_r8*g
cff2=1.0_r8/3.0_r8
DO j=Jstr,Jend
IF (j.ge.JstrV) THEN
DO i=Istr,Iend
!^ tl_rhs_vbar(i,j)=cff1*om_v(i,j)* &
!^ & ((tl_h(i,j-1)+ &
!^ & tl_h(i,j ))* &
!^ & (gzeta(i,j-1)- &
!^ & gzeta(i,j ))+ &
!^ & (h(i,j-1)+ &
!^ & h(i,j ))* &
!^ & (tl_gzeta(i,j-1)- &
!^ & tl_gzeta(i,j ))+ &
!^ & (tl_gzeta2(i,j-1)- &
!^ & tl_gzeta2(i,j )
!^
adfac=cff1*om_v(i,j)*ad_rhs_vbar(i,j)
adfac1=adfac*(gzeta(i,j-1)-gzeta(i,j ))
adfac2=adfac*(h(i,j-1)+h(i,j ))
ad_h(i,j-1)=ad_h(i,j-1)+adfac1
ad_h(i,j )=ad_h(i,j )+adfac1
ad_gzeta(i,j-1)=ad_gzeta(i,j-1)+adfac2
ad_gzeta(i,j )=ad_gzeta(i,j )-adfac2
ad_gzeta2(i,j-1)=ad_gzeta2(i,j-1)+adfac
ad_gzeta2(i,j )=ad_gzeta2(i,j )-adfac
ad_rhs_vbar(i,j)=0.0_r8
END DO
END IF
DO i=IstrU,Iend
!^ tl_rhs_ubar(i,j)=cff1*on_u(i,j)* &
!^ & ((tl_h(i-1,j)+ &
!^ & tl_h(i ,j))* &
!^ & (gzeta(i-1,j)- &
!^ & gzeta(i ,j))+ &
!^ & (h(i-1,j)+ &
!^ & h(i ,j))* &
!^ & (tl_gzeta(i-1,j)- &
!^ & tl_gzeta(i ,j))+ &
!^ & (tl_gzeta2(i-1,j)- &
!^ & tl_gzeta2(i ,j)))
!^
adfac=cff1*on_u(i,j)*ad_rhs_ubar(i,j)
adfac1=adfac*(gzeta(i-1,j)-gzeta(i ,j))
adfac2=adfac*(h(i-1,j)+h(i ,j))
ad_h(i-1,j)=ad_h(i-1,j)+adfac1
ad_h(i ,j)=ad_h(i ,j)+adfac1
ad_gzeta(i-1,j)=ad_gzeta(i-1,j)+adfac2
ad_gzeta(i ,j)=ad_gzeta(i ,j)-adfac2
ad_gzeta2(i-1,j)=ad_gzeta2(i-1,j)+adfac
ad_gzeta2(i ,j)=ad_gzeta2(i ,j)-adfac
ad_rhs_ubar(i,j)=0.0_r8
END DO
END DO
!
! Set adjoint free-surface lateral boundary conditions.
!
!^ CALL mp_exchange2d (ng, tile, iTLM, 1, &
!^ & LBi, UBi, LBj, UBj, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_zeta(:,:,knew))
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 1, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_zeta(:,:,knew))
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
!^ CALL exchange_r2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_zeta(:,:,knew))
!^
CALL ad_exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_zeta(:,:,knew))
END IF
!^ CALL tl_zetabc_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & krhs, kstp, knew, &
!^ & zeta, tl_zeta)
!^
CALL ad_zetabc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, kstp, knew, &
& zeta, ad_zeta)
!
! Apply adjoint mass point sources (volume vertical influx), if any.
!
! Dsrc(is) = 2, flow across grid cell w-face (positive or negative)
!
IF (LwSrc(ng)) THEN
DO is=1,Nsrc(ng)
IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN
i=SOURCES(ng)%Isrc(is)
j=SOURCES(ng)%Jsrc(is)
IF (((IstrR.le.i).and.(i.le.IendR)).and. &
& ((JstrR.le.j).and.(j.le.JendR))) THEN
!^ tl_zeta(i,j,knew)=tl_zeta(i,j,knew)+0.0_r8
!^
END IF
END IF
END DO
END IF
!
! If adjoint predictor step, load right-side-term into shared array.
!
IF (PREDICTOR_2D_STEP(ng)) THEN
!^ CALL mp_exchange2d (ng, tile, iTLM, 1, &
!^ & LBi, UBi, LBj, UBj, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_rzeta(:,:,krhs))
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 1, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_rzeta(:,:,krhs))
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
!^ CALL exchange_r2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_rzeta(:,:,krhs))
!^
CALL ad_exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_rzeta(:,:,krhs))
END IF
DO j=Jstr,Jend
DO i=Istr,Iend
!^ tl_rzeta(i,j,krhs)=tl_rhs_zeta(i,j)
!^
ad_rhs_zeta(i,j)=ad_rhs_zeta(i,j)+ad_rzeta(i,j,krhs)
ad_rzeta(i,j,krhs)=0.0
END DO
END DO
END IF
!
! Load new adjoint free-surface values into shared array at both
! predictor and corrector steps.
!
DO j=Jstr,Jend
DO i=Istr,Iend
!^ tl_zeta(i,j,knew)=tl_zeta_new(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_zeta(i,j,knew)
ad_zeta(i,j,knew)=0.0_r8
END DO
END DO
!
!=======================================================================
! Time step adjoint free-surface equation.
!=======================================================================
!
! During the first time-step, the predictor step is Forward-Euler
! and the corrector step is Backward-Euler. Otherwise, the predictor
! step is Leap-frog and the corrector step is Adams-Moulton.
!
IF (iif(ng).eq.1) THEN
cff1=dtfast(ng)
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j)
!^ tl_gzeta(i,j)=tl_zwrk(i,j)
!^
ad_zwrk(i,j)=ad_zwrk(i,j)+ &
& 2.0_r8*zwrk(i,j)*ad_gzeta2(i,j)+ &
& ad_gzeta(i,j)
ad_gzeta2(i,j)=0.0_r8
ad_gzeta(i,j)=0.0_r8
!^ tl_zwrk(i,j)=0.5_r8*(tl_zeta(i,j,kstp)+tl_zeta_new(i,j))
!^
adfac=0.5_r8*ad_zwrk(i,j)
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+adfac
ad_zeta_new(i,j)=ad_zeta_new(i,j)+adfac
ad_zwrk(i,j)=0.0_r8
!^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_Dnew(i,j)
ad_h(i,j)=ad_h(i,j)+ad_Dnew(i,j)
ad_Dnew(i,j)=0.0_r8
!^ tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)*rmask(i,j)
!^ tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*cff1*tl_rhs_zeta(i,j)
!^
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_zeta_new(i,j)
ad_rhs_zeta(i,j)=ad_rhs_zeta(i,j)+ &
& pm(i,j)*pn(i,j)*cff1*ad_zeta_new(i,j)
ad_zeta_new(i,j)=0.0_r8
!^ tl_rhs_zeta(i,j)=(tl_DUon(i,j)-tl_DUon(i+1,j))+ &
!^ & (tl_DVom(i,j)-tl_DVom(i,j+1))
!^
ad_DUon(i ,j )=ad_DUon(i ,j )+ad_rhs_zeta(i,j)
ad_DUon(i+1,j )=ad_DUon(i+1,j )-ad_rhs_zeta(i,j)
ad_DVom(i ,j )=ad_DVom(i ,j )+ad_rhs_zeta(i,j)
ad_DVom(i ,j+1)=ad_DVom(i ,j+1)-ad_rhs_zeta(i,j)
ad_rhs_zeta(i,j)=0.0_r8
END DO
END DO
ELSE IF (PREDICTOR_2D_STEP(ng)) THEN
cff1=2.0_r8*dtfast(ng)
cff4=4.0_r8/25.0_r8
cff5=1.0_r8-2.0_r8*cff4
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j)
!^ tl_gzeta(i,j)=tl_zwrk(i,j)
!^
ad_zwrk(i,j)=ad_zwrk(i,j)+ &
& 2.0_r8*zwrk(i,j)*ad_gzeta2(i,j)+ &
& ad_gzeta(i,j)
ad_gzeta2(i,j)=0.0_r8
ad_gzeta(i,j)=0.0_r8
!^ tl_zwrk(i,j)=cff5*tl_zeta(i,j,krhs)+ &
!^ & cff4*(tl_zeta(i,j,kstp)+tl_zeta_new(i,j))
!^
adfac=cff4*ad_zwrk(i,j)
ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+cff5*ad_zwrk(i,j)
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+adfac
ad_zeta_new(i,j)=ad_zeta_new(i,j)+adfac
ad_zwrk(i,j)=0.0_r8
!^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_Dnew(i,j)
ad_h(i,j)=ad_h(i,j)+ad_Dnew(i,j)
ad_Dnew(i,j)=0.0_r8
!^ tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)*rmask(i,j)
!^ tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*cff1*tl_rhs_zeta(i,j)
!^
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_zeta_new(i,j)
ad_rhs_zeta(i,j)=ad_rhs_zeta(i,j)+ &
& pm(i,j)*pn(i,j)*cff1*ad_zeta_new(i,j)
ad_zeta_new(i,j)=0.0_r8
!^ tl_rhs_zeta(i,j)=(tl_DUon(i,j)-tl_DUon(i+1,j))+ &
!^ & (tl_DVom(i,j)-tl_DVom(i,j+1))
!^
ad_DUon(i ,j )=ad_DUon(i ,j )+ad_rhs_zeta(i,j)
ad_DUon(i+1,j )=ad_DUon(i+1,j )-ad_rhs_zeta(i,j)
ad_DVom(i ,j )=ad_DVom(i ,j )+ad_rhs_zeta(i,j)
ad_DVom(i ,j+1)=ad_DVom(i ,j+1)-ad_rhs_zeta(i,j)
ad_rhs_zeta(i,j)=0.0_r8
END DO
END DO
ELSE IF (CORRECTOR_2D_STEP) THEN
cff1=dtfast(ng)*5.0_r8/12.0_r8
cff2=dtfast(ng)*8.0_r8/12.0_r8
cff3=dtfast(ng)*1.0_r8/12.0_r8
cff4=2.0_r8/5.0_r8
cff5=1.0_r8-cff4
DO j=JstrV-1,Jend
DO i=IstrU-1,Iend
!^ tl_gzeta(i,j)=tl_zwrk(i,j)
!^ tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j)
!^
ad_zwrk(i,j)=ad_zwrk(i,j)+ &
& 2.0_r8*zwrk(i,j)*ad_gzeta2(i,j)+ &
& ad_gzeta(i,j)
ad_gzeta2(i,j)=0.0_r8
ad_gzeta(i,j)=0.0_r8
!^ tl_zwrk(i,j)=cff5*tl_zeta_new(i,j)+cff4*tl_zeta(i,j,krhs)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)+cff5*ad_zwrk(i,j)
ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+cff4*ad_zwrk(i,j)
ad_zwrk(i,j)=0.0_r8
!^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)+ad_Dnew(i,j)
ad_h(i,j)=ad_h(i,j)+ad_Dnew(i,j)
ad_Dnew(i,j)=0.0_r8
!^ tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j)
!^
ad_zeta_new(i,j)=ad_zeta_new(i,j)*rmask(i,j)
!^ tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ &
!^ & pm(i,j)*pn(i,j)*(tl_cff+ &
!^ & cff2*tl_rzeta(i,j,kstp)-&
!^ & cff3*tl_rzeta(i,j,ptsk))
!^
adfac=pm(i,j)*pn(i,j)*ad_zeta_new(i,j)
ad_zeta(i,j,kstp)=ad_zeta(i,j,kstp)+ad_zeta_new(i,j)
ad_cff=ad_cff+adfac
ad_rzeta(i,j,kstp)=ad_rzeta(i,j,kstp)+adfac*cff2
ad_rzeta(i,j,ptsk)=-adfac*cff3
ad_zeta_new(i,j)=0.0_r8
!^ tl_cff=cff1*((tl_DUon(i,j)-tl_DUon(i+1,j))+ &
!^ & (tl_DVom(i,j)-tl_DVom(i,j+1)))
!^
adfac=cff1*ad_cff
ad_DUon(i ,j )=ad_DUon(i ,j )+adfac
ad_DUon(i+1,j )=ad_DUon(i+1,j )-adfac
ad_DVom(i ,j )=ad_DVom(i ,j )+adfac
ad_DVom(i ,j+1)=ad_DVom(i ,j+1)-adfac
ad_cff=0.0_r8
END DO
END DO
END IF
END IF STEP_LOOP
!
!-----------------------------------------------------------------------
! Compute adjoint time averaged fields over all short timesteps.
!-----------------------------------------------------------------------
!
! After all fast time steps are completed, recompute S-coordinate
! surfaces according to the new free surface field. Apply boundary
! conditions to time averaged fields.
!
IF ((iif(ng).eq.(nfast(ng)+1)).and.PREDICTOR_2D_STEP(ng)) THEN
!^ CALL mp_exchange2d (ng, tile, iTLM, 3, &
!^ & LBi, UBi, LBj, UBj, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_Zt_avg1, tl_DU_avg1, tl_DV_avg1)
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 3, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_Zt_avg1, ad_DU_avg1, ad_DV_avg1)
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
!^ CALL exchange_v2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_DV_avg1)
!^
CALL ad_exchange_v2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_DV_avg1)
!^ CALL exchange_u2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_DU_avg1)
!^
CALL ad_exchange_u2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_DU_avg1)
!^ CALL exchange_r2d_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & tl_Zt_avg1)
!^
CALL ad_exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& ad_Zt_avg1)
END IF
END IF
!
! Compute time-averaged fields.
!
IF (PREDICTOR_2D_STEP(ng)) THEN
IF (iif(ng).eq.1) THEN
!
! Reset arrays for 2D fields averaged within the short time-steps.
!
cff2=(-1.0_r8/12.0_r8)*weight(2,iif(ng)+1,ng)
DO j=JstrR,JendR
DO i=IstrR,IendR
!^ tl_Zt_avg1(i,j)=0.0_r8
!^
ad_Zt_avg1(i,j)=0.0_r8
END DO
DO i=Istr,IendR
!^ tl_DU_avg2(i,j)=cff2*tl_DUon(i,j)
!^
ad_DUon(i,j)=ad_DUon(i,j)+cff2*ad_DU_avg2(i,j)
ad_DU_avg2(i,j)=0.0_r8
!^ tl_DU_avg1(i,j)=0.0_r8
!^
ad_DU_avg1(i,j)=0.0_r8
END DO
END DO
DO j=Jstr,JendR
DO i=IstrR,IendR
!^ tl_DV_avg2(i,j)=cff2*tl_DVom(i,j)
!^
ad_DVom(i,j)=ad_DVom(i,j)+cff2*ad_DV_avg2(i,j)
ad_DV_avg2(i,j)=0.0_r8
!^ tl_DV_avg1(i,j)=0.0_r8
!^
ad_DV_avg1(i,j)=0.0_r8
END DO
END DO
ELSE
!
! Accumulate field averages of previous time-step after they are
! computed in the previous corrector step, updated their boundaries,
! and synchronized.
!
cff1=weight(1,iif(ng)-1,ng)
cff2=(8.0_r8/12.0_r8)*weight(2,iif(ng) ,ng)- &
& (1.0_r8/12.0_r8)*weight(2,iif(ng)+1,ng)
DO j=JstrR,JendR
DO i=IstrR,IendR
!^ tl_Zt_avg1(i,j)=tl_Zt_avg1(i,j)+cff1*tl_zeta(i,j,krhs)
!^
ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+cff1*ad_Zt_avg1(i,j)
END DO
DO i=Istr,IendR
!^ tl_DU_avg2(i,j)=tl_DU_avg2(i,j)+cff2*tl_DUon(i,j)
!^
ad_DUon(i,j)=ad_DUon(i,j)+ &
& cff2*ad_DU_avg2(i,j)
!^ tl_DU_avg1(i,j)=tl_DU_avg1(i,j)+cff1*tl_DUon(i,j)
!^
ad_DUon(i,j)=ad_DUon(i,j)+ &
& cff1*ad_DU_avg1(i,j)
END DO
END DO
DO j=Jstr,JendR
DO i=IstrR,IendR
!^ tl_DV_avg2(i,j)=tl_DV_avg2(i,j)+cff2*tl_DVom(i,j)
!^
ad_DVom(i,j)=ad_DVom(i,j)+ &
& cff2*ad_DV_avg2(i,j)
!^ tl_DV_avg1(i,j)=tl_DV_avg1(i,j)+cff1*tl_DVom(i,j)
!^
ad_DVom(i,j)=ad_DVom(i,j)+ &
& cff1*ad_DV_avg1(i,j)
END DO
END DO
END IF
ELSE
IF (iif(ng).eq.1) THEN
cff2=weight(2,iif(ng),ng)
ELSE
cff2=(5.0_r8/12.0_r8)*weight(2,iif(ng),ng)
END IF
DO j=JstrR,JendR
DO i=Istr,IendR
!^ tl_DV_avg2(i,j)=tl_DV_avg2(i,j)+cff2*tl_DVom(i,j)
!^
ad_DVom(i,j)=ad_DVom(i,j)+cff2*ad_DV_avg2(i,j)
END DO
END DO
DO j=Jstr,JendR
DO i=IstrR,IendR
!^ tl_DU_avg2(i,j)=tl_DU_avg2(i,j)+cff2*tl_DUon(i,j)
!^
ad_DUon(i,j)=ad_DUon(i,j)+cff2*ad_DU_avg2(i,j)
END DO
END DO
END IF
!
!-----------------------------------------------------------------------
! Compute total depth (m) and vertically integrated mass fluxes.
!-----------------------------------------------------------------------
!
! Set vertically integrated mass fluxes DUon and DVom along the open
! boundaries in such a way that the integral volume is conserved.
!
IF (ANY(ad_VolCons(:,ng))) THEN
!^ CALL tl_set_DUV_bc_tile (ng, tile, &
!^ & LBi, UBi, LBj, UBj, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & krhs, &
!^ & umask, vmask, &
!^ & om_v, on_u, ubar, vbar, &
!^ & tl_ubar, tl_vbar, &
!^ & Drhs, DUon, DVom, &
!^ & tl_Drhs, tl_DUon, tl_DVom)
!^
CALL ad_set_DUV_bc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& krhs, &
& umask, vmask, &
& om_v, on_u, ubar, vbar, &
& ad_ubar, ad_vbar, &
& Drhs, DUon, DVom, &
& ad_Drhs, ad_DUon, ad_DVom)
END IF
!
! In distributed-memory, the I- and J-ranges are different and a
! special exchange is done to avoid having three ghost points for
! high order numerical stencils. Notice that a private array is
! passed below to the exchange routine. It also applies periodic
! boundary conditions, if appropriate and no partitions in I- or
! J-directions.
!
!^ CALL mp_exchange2d (ng, tile, iTLM, 2, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & NghostPoints, &
!^ & EWperiodic(ng), NSperiodic(ng), &
!^ & tl_DUon, tl_DVom)
!^
CALL ad_mp_exchange2d (ng, tile, iADM, 2, &
& IminS, ImaxS, JminS, JmaxS, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& ad_DUon, ad_DVom)
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
!^ CALL exchange_u2d_tile (ng, tile, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & tl_DUon)
!^
CALL ad_exchange_u2d_tile (ng, tile, &
& IminS, ImaxS, JminS, JmaxS, &
& ad_DUon)
!^ CALL exchange_v2d_tile (ng, tile, &
!^ & IminS, ImaxS, JminS, JmaxS, &
!^ & tl_DVom)
!^
CALL ad_exchange_v2d_tile (ng, tile, &
& IminS, ImaxS, JminS, JmaxS, &
& ad_DVom)
END IF
!
! Compute adjoint adjoint vertically integrated mass fluxes.
!
DO j=JstrV-1,Jendp2
DO i=IstrU-2,Iendp2
cff=0.5_r8*om_v(i,j)
cff1=cff*(Drhs(i,j)+Drhs(i,j-1))
!^ tl_DVom(i,j)=tl_vbar(i,j,krhs)*cff1+ &
!^ & vbar(i,j,krhs)*tl_cff1
!^
ad_cff1=ad_cff1+vbar(i,j,krhs)*ad_DVom(i,j)
ad_vbar(i,j,krhs)=ad_vbar(i,j,krhs)+cff1*ad_DVom(i,j)
ad_DVom(i,j)=0.0_r8
!^ tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i,j-1))
!^
adfac=cff*ad_cff1
ad_Drhs(i,j-1)=ad_Drhs(i,j-1)+adfac
ad_Drhs(i,j )=ad_Drhs(i,j )+adfac
ad_cff1=0.0_r8
END DO
END DO
DO j=JstrV-2,Jendp2
DO i=IstrU-1,Iendp2
cff=0.5_r8*on_u(i,j)
cff1=cff*(Drhs(i,j)+Drhs(i-1,j))
!^ tl_DUon(i,j)=tl_ubar(i,j,krhs)*cff1+ &
!^ & ubar(i,j,krhs)*tl_cff1
!^
ad_cff1=ad_cff1+ubar(i,j,krhs)*ad_DUon(i,j)
ad_ubar(i,j,krhs)=ad_ubar(i,j,krhs)+cff1*ad_DUon(i,j)
ad_DUon(i,j)=0.0_r8
!^ tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i-1,j))
!^
adfac=cff*ad_cff1
ad_Drhs(i-1,j)=ad_Drhs(i-1,j)+adfac
ad_Drhs(i ,j)=ad_Drhs(i ,j)+adfac
ad_cff1=0.0_r8
END DO
END DO
!
! Compute adjoint total depth.
!
DO j=JstrV-2,Jendp2
DO i=IstrU-2,Iendp2
!^ tl_Drhs(i,j)=tl_zeta(i,j,krhs)+tl_h(i,j)
!^
ad_zeta(i,j,krhs)=ad_zeta(i,j,krhs)+ad_Drhs(i,j)
ad_h(i,j)=ad_h(i,j)+ad_Drhs(i,j)
ad_Drhs(i,j)=0.0_r8
END DO
END DO
!
RETURN
END SUBROUTINE ad_step2d_tile
END MODULE ad_step2d_mod