MODULE ad_conv_3d_mod ! !git $Id$ !svn $Id: ad_conv_3d.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 ! !======================================================================= ! ! ! These routines applies the background error covariance to data ! ! assimilation fields via the adjoint space convolution of the ! ! diffusion equation (filter) for 3D state variables. The filter ! ! is solved using an implicit or explicit algorithm. ! ! ! ! For Gaussian (bell-shaped) correlations, the space convolution ! ! of the diffusion operator is an efficient way to estimate the ! ! finite domain error covariances. ! ! ! ! Notice that "z_r" and "Hz" are assumed to be time invariant in ! ! the spatial convolution. That it, they are not adjointable. ! ! ! ! On Input: ! ! ! ! ng Nested grid number. ! ! model Calling model identifier. ! ! Istr Starting tile index in the I-direction. ! ! Iend Ending tile index in the I-direction. ! ! Jstr Starting tile index in the J-direction. ! ! Jend Ending tile index in the J-direction. ! ! LBi I-dimension lower bound. ! ! UBi I-dimension upper bound. ! ! LBj J-dimension lower bound. ! ! UBj J-dimension upper bound. ! ! LBk K-dimension lower bound. ! ! UBk K-dimension upper bound. ! ! Nghost Number of ghost points. ! ! NHsteps Number of horizontal diffusion integration steps. ! ! NVsteps Number of vertical diffusion integration steps. ! ! DTsizeH Horizontal diffusion pseudo time-step size. ! ! DTsizeV Vertical diffusion pseudo time-step size. ! ! Kh Horizontal diffusion coefficients. ! ! Kv Vertical diffusion coefficients. ! ! ad_A 3D adjoint state variable to diffuse. ! ! ! ! On Output: ! ! ! ! ad_A Convolved 3D adjoint state variable. ! ! ! ! Routines: ! ! ! ! ad_conv_r3d_tile Adjoint 3D convolution at RHO-points ! ! ad_conv_u3d_tile Adjoint 3D convolution at U-points ! ! ad_conv_v3d_tile Adjoint 3D convolution at V-points ! ! ! !======================================================================= ! implicit none ! PUBLIC ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_conv_r3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & & pmon_u, pnom_v, & & rmask, umask, vmask, & & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_r3d_tile USE mp_exchange_mod, ONLY : ad_mp_exchange3d ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_u(LBi:,LBj:) real(r8), intent(in) :: pnom_v(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) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: ad_A(LBi:,LBj:,LBk:) ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav integer :: i, j, k, kk, kt, k1, k1b, k2, k2b, step real(r8) :: adfac, adfac1, adfac2 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: ad_Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC ! !----------------------------------------------------------------------- ! 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_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ! !----------------------------------------------------------------------- ! Adjoint space convolution of the diffusion equation for a 2D state ! variable at RHO-points. !----------------------------------------------------------------------- ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 Hfac(i,j)=DTsizeH*pm(i,j)*pn(i,j) FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 FC(i,j,k)=-DTsizeV*Kv(i,j,k)/(z_r(i,j,k+1)-z_r(i,j,k)) END DO FC(i,j,0)=0.0_r8 END DO END DO Nold=1 Nnew=2 ! !------------------------------------------------------------------------ ! Adjoint of load convolved solution. !------------------------------------------------------------------------ ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend !^ tl_A(i,j,k)=tl_Awrk(i,j,k,Nold) !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ad_A(i,j,k) ad_A(i,j,k)=0.0_r8 END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint vertical diffusion equation implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav DO j=Jstr,Jend ! ! Compute diagonal matrix coefficients BC. ! DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=Hz(i,j,k)-FC(i,j,k)-FC(i,j,k-1) END DO END DO ! ! Compute new solution by back substitution. ! DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) END DO END DO !^ DO k=N(ng)-1,1,-1 !^ DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nnew)*rmask(i,j) !^ ad_Awrk(i,j,k,Nnew)=ad_Awrk(i,j,k,Nnew)*rmask(i,j) !^ tl_Awrk(i,j,k,Nnew)=tl_DC(i,k) !^ ad_DC(i,k)=ad_DC(i,k)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_DC(i,k+1)=-CF(i,k)*ad_DC(i,k) END DO END DO DO i=Istr,Iend !^ tl_Awrk(i,j,N(ng),Nnew)=tl_Awrk(i,j,N(ng),Nnew)*rmask(i,j) !^ ad_Awrk(i,j,N(ng),Nnew)=ad_Awrk(i,j,N(ng),Nnew)*rmask(i,j) !^ tl_Awrk(i,j,N(ng),Nnew)=tl_DC(i,N(ng)) !^ ad_DC(i,N(ng))=ad_DC(i,N(ng))+ & & ad_Awrk(i,j,N(ng),Nnew) ad_Awrk(i,j,N(ng),Nnew)=0.0_r8 !^ tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & !^ & FC(i,j,N(ng)-1)*tl_DC(i,N(ng)-1))/ & !^ & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) !^ adfac=ad_DC(i,N(ng))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) ad_DC(i,N(ng)-1)=ad_DC(i,N(ng)-1)-FC(i,j,N(ng)-1)*adfac ad_DC(i,N(ng) )=adfac END DO ! ! Solve the adjoint tridiagonal system. ! !^ DO k=2,N(ng)-1 !^ DO k=N(ng)-1,2,-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,j,k-1)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,j,k-1)*adfac ad_DC(i,k )=adfac END DO END DO DO i=Istr,Iend cff=1.0_r8/BC(i,1) !^ tl_DC(i,1)=cff*tl_DC(i,1) !^ ad_DC(i,1)=cff*ad_DC(i,1) END DO ! ! Adjoint of right-hand-side terms for the diffusion equation. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_DC(i,k)=tl_Awrk(i,j,k,Nold)*Hz(i,j,k) !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ & & Hz(i,j,k)*ad_DC(i,k) ad_DC(i,k)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,:,Nnew)) !^ CALL dabc_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_Awrk(:,:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion equation. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & Hfac(i,j)* & !^ & (tl_FX(i+1,j)-tl_FX(i,j)+ & !^ & tl_FE(i,j+1)-tl_FE(i,j)) !^ adfac=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) ad_FE(i,j )=ad_FE(i,j )-adfac ad_FE(i,j+1)=ad_FE(i,j+1)+adfac ad_FX(i ,j)=ad_FX(i ,j)-adfac ad_FX(i+1,j)=ad_FX(i+1,j)+adfac ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 END DO END DO ! ! Compute XI- and ETA-components of the adjoint diffusive flux. ! DO j=Jstr,Jend+1 DO i=Istr,Iend !^ tl_FE(i,j)=tl_FE(i,j)*vmask(i,j) !^ ad_FE(i,j)=ad_FE(i,j)*vmask(i,j) !^ tl_FE(i,j)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* & !^ & (tl_Awrk(i,j,k,Nold)-tl_Awrk(i,j-1,k,Nold)) !^ adfac=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))*ad_FE(i,j) ad_Awrk(i,j-1,k,Nold)=ad_Awrk(i,j-1,k,Nold)-adfac ad_Awrk(i,j ,k,Nold)=ad_Awrk(i,j ,k,Nold)+adfac ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 !^ tl_FX(i,j)=tl_FX(i,j)*umask(i,j) !^ ad_FX(i,j)=ad_FX(i,j)*umask(i,j) !^ tl_FX(i,j)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* & !^ & (tl_Awrk(i,j,k,Nold)-tl_Awrk(i-1,j,k,Nold)) !^ adfac=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))*ad_FX(i,j) ad_Awrk(i-1,j,k,Nold)=ad_Awrk(i-1,j,k,Nold)-adfac ad_Awrk(i ,j,k,Nold)=ad_Awrk(i ,j,k,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Set adjoint initial conditions. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_Awrk(i,j,k,Nold)=tl_A(i,j,k) !^ ad_A(i,j,k)=ad_A(i,j,k)+ad_Awrk(i,j,k,Nold) ad_Awrk(i,j,k,Nold)=0.0_r8 END DO END DO END DO !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) RETURN END SUBROUTINE ad_conv_r3d_tile ! !*********************************************************************** SUBROUTINE ad_conv_u3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & & pmon_r, pnom_p, & & umask, pmask, & & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_u3d_tile USE mp_exchange_mod, ONLY : ad_mp_exchange3d ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_r(LBi:,LBj:) real(r8), intent(in) :: pnom_p(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: ad_A(LBi:,LBj:,LBk:) ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav integer :: i, j, k, kk, kt, k1, k1b, k2, k2b, step real(r8) :: adfac, adfac1, adfac2 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: ad_Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC ! !----------------------------------------------------------------------- ! 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_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ! !----------------------------------------------------------------------- ! Adjoint space convolution of the diffusion equation for a 3D state ! variable at U-points. !----------------------------------------------------------------------- ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! cff=DTsizeH*0.25_r8 DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 Hfac(i,j)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 FC(i,j,k)=-DTsizeV*(Kv(i-1,j,k)+Kv(i,j,k))/ & & (z_r(i-1,j,k+1)+z_r(i,j,k+1)- & & z_r(i-1,j,k )-z_r(i,j,k )) END DO FC(i,j,0)=0.0_r8 END DO END DO Nold=1 Nnew=2 ! !----------------------------------------------------------------------- ! Adjoint of load convolved solution. !----------------------------------------------------------------------- ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_u3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) DO k=1,N(ng) DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_A(i,j,k)=tl_Awrk(i,j,k,Nold) !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ad_A(i,j,k) ad_A(i,j,k)=0.0_r8 END DO END DO END DO ! !----------------------------------------------------------------------- ! Integerate adjoint vertical diffusion equation implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Compute diagonal matrix coefficients BC. ! DO j=Jstr,Jend DO k=1,N(ng) DO i=IstrU,Iend BC(i,k)=0.5*(Hz(i-1,j,k)+Hz(i,j,k))- & & FC(i,j,k)-FC(i,j,k-1) END DO END DO ! ! Compute new solution by back substitution. ! DO i=IstrU,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) END DO DO k=2,N(ng)-1 DO i=IstrU,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) END DO END DO !^ DO k=N(ng)-1,1,-1 !^ DO k=1,N(ng)-1 DO i=IstrU,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nnew)*umask(i,j) !^ ad_Awrk(i,j,k,Nnew)=ad_Awrk(i,j,k,Nnew)*umask(i,j) !^ tl_Awrk(i,j,k,Nnew)=tl_DC(i,k) !^ ad_DC(i,k)=ad_DC(i,k)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_DC(i,k+1)=-CF(i,k)*ad_DC(i,k) END DO END DO DO i=IstrU,Iend !^ tl_Awrk(i,j,N(ng),Nnew)=tl_Awrk(i,j,N(ng),Nnew)*umask(i,j) !^ ad_Awrk(i,j,N(ng),Nnew)=ad_Awrk(i,j,N(ng),Nnew)*umask(i,j) !^ tl_Awrk(i,j,N(ng),Nnew)=tl_DC(i,N(ng)) !^ ad_DC(i,N(ng))=ad_DC(i,N(ng))+ & & ad_Awrk(i,j,N(ng),Nnew) ad_Awrk(i,j,N(ng),Nnew)=0.0_r8 !^ tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & !^ & FC(i,j,N(ng)-1)*tl_DC(i,N(ng)-1))/ & !^ & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) !^ adfac=ad_DC(i,N(ng))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) ad_DC(i,N(ng)-1)=ad_DC(i,N(ng)-1)-FC(i,j,N(ng)-1)*adfac ad_DC(i,N(ng) )=adfac END DO ! ! Solve the adjoint tridiagonal system. ! !^ DO k=2,N(ng)-1 !^ DO k=N(ng)-1,2,-1 DO i=IstrU,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,j,k-1)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,j,k-1)*adfac ad_DC(i,k )=adfac END DO END DO DO i=IstrU,Iend cff=1.0_r8/BC(i,1) !^ tl_DC(i,1)=cff*tl_DC(i,1) !^ ad_DC(i,1)=cff*ad_DC(i,1) END DO ! ! Adjoint of right-hand-side terms for the diffusion equation. ! DO k=1,N(ng) DO i=IstrU,Iend cff=0.5*(Hz(i-1,j,k)+Hz(i,j,k)) !^ tl_DC(i,k)=tl_Awrk(i,j,k,Nold)*cff !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+cff*ad_DC(i,k) ad_DC(i,k)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,:,Nnew)) !^ CALL dabc_u3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_Awrk(:,:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion equation. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & Hfac(i,j)* & !^ & (tl_FX(i,j)-tl_FX(i-1,j)+ & !^ & tl_FE(i,j+1)-tl_FE(i,j)) !^ adfac=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) ad_FE(i,j )=ad_FE(i,j )-adfac ad_FE(i,j+1)=ad_FE(i,j+1)+adfac ad_FX(i-1,j)=ad_FX(i-1,j)-adfac ad_FX(i ,j)=ad_FX(i ,j)+adfac ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 END DO END DO ! ! Compute XI- and ETA-components of the adjoint diffusive flux. ! DO j=Jstr,Jend+1 DO i=IstrU,Iend !^ tl_FE(i,j)=tl_FE(i,j)*pmask(i,j) !^ ad_FE(i,j)=ad_FE(i,j)*pmask(i,j) !^ tl_FE(i,j)=pnom_p(i,j)*0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & !^ & Kh(i-1,j-1)+Kh(i,j-1))* & !^ & (tl_Awrk(i,j,k,Nold)-tl_Awrk(i,j-1,k,Nold)) !^ adfac=pnom_p(i,j)*0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & & Kh(i-1,j-1)+Kh(i,j-1))* & & ad_FE(i,j) ad_Awrk(i,j-1,k,Nold)=ad_Awrk(i,j-1,k,Nold)-adfac ad_Awrk(i,j ,k,Nold)=ad_Awrk(i,j ,k,Nold)+adfac ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend !^ tl_FX(i,j)=pmon_r(i,j)*Kh(i,j)* & !^ & (tl_Awrk(i+1,j,k,Nold)-tl_Awrk(i,j,k,Nold)) !^ adfac=pmon_r(i,j)*Kh(i,j)*ad_FX(i,j) ad_Awrk(i ,j,k,Nold)=ad_Awrk(i ,j,k,Nold)-adfac ad_Awrk(i+1,j,k,Nold)=ad_Awrk(i+1,j,k,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Set adjoint initial conditions. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 !^ tl_Awrk(i,j,k,Nold)=tl_A(i,j,k) !^ ad_A(i,j,k)=ad_A(i,j,k)+ad_Awrk(i,j,k,Nold) ad_Awrk(i,j,k,Nold)=0.0_r8 END DO END DO END DO !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_u3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_u3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) RETURN END SUBROUTINE ad_conv_u3d_tile ! !*********************************************************************** SUBROUTINE ad_conv_v3d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, LBk, UBk, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, NVsteps, & & DTsizeH, DTsizeV, & & Kh, Kv, & & pm, pn, & & pmon_p, pnom_r, & & vmask, pmask, & & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_v3d_tile USE mp_exchange_mod, ONLY : ad_mp_exchange3d ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj, LBk, UBk integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps, NVsteps real(r8), intent(in) :: DTsizeH, DTsizeV ! real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: pmon_p(LBi:,LBj:) real(r8), intent(in) :: pnom_r(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(in) :: Kv(LBi:,LBj:,0:) real(r8), intent(inout) :: ad_A(LBi:,LBj:,LBk:) ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav integer :: i, j, k, kk, kt, k1, k1b, k2, k2b, step real(r8) :: adfac, adfac1, adfac2 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8), dimension(LBi:UBi,LBj:UBj,LBk:UBk,2) :: ad_Awrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Hfac real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC ! !----------------------------------------------------------------------- ! 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_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ! !----------------------------------------------------------------------- ! Adjoint space convolution of the diffusion equation for a 3D state ! variable at V-points !----------------------------------------------------------------------- ! ! Compute metrics factors. Notice that "z_r" and "Hz" are assumed to ! be time invariant in the vertical convolution. Scratch array are ! used for efficiency. ! cff=DTsizeH*0.25_r8 DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 Hfac(i,j)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j)) FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 FC(i,j,k)=-DTsizeV*(Kv(i,j-1,k)+Kv(i,j,k))/ & & (z_r(i,j-1,k+1)+z_r(i,j,k+1)- & & z_r(i,j-1,k )-z_r(i,j,k )) END DO FC(i,j,0)=0.0_r8 END DO END DO Nold=1 Nnew=2 ! !----------------------------------------------------------------------- ! Adjoint of load convolved adjoint solution. !----------------------------------------------------------------------- ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_v3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) DO k=1,N(ng) DO j=JstrV,Jend DO i=Istr,Iend !^ tl_A(i,j,k)=tl_Awrk(i,j,k,Nold) !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ad_A(i,j,k) ad_A(i,j,k)=0.0_r8 END DO END DO END DO ! !----------------------------------------------------------------------- ! Integerate adjoint vertical diffusion adjoint implicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Compute diagonal matrix coefficients BC. ! DO j=JstrV,Jend DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=0.5_r8*(Hz(i,j-1,k)+Hz(i,j,k))- & & FC(i,j,k)-FC(i,j,k-1) END DO END DO ! ! Compute new solution by back substitution. ! DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,j,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,j,k) END DO END DO !^ DO k=N(ng)-1,1,-1 !^ DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nnew)*vmask(i,j) !^ ad_Awrk(i,j,k,Nnew)=ad_Awrk(i,j,k,Nnew)*vmask(i,j) !^ tl_Awrk(i,j,k,Nnew)=tl_DC(i,k) !^ ad_DC(i,k)=ad_DC(i,k)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_DC(i,k+1)=-CF(i,k)*ad_DC(i,k) END DO END DO DO i=Istr,Iend !^ tl_Awrk(i,j,N(ng),Nnew)=tl_Awrk(i,j,N(ng),Nnew)*vmask(i,j) !^ ad_Awrk(i,j,N(ng),Nnew)=ad_Awrk(i,j,N(ng),Nnew)*vmask(i,j) !^ tl_Awrk(i,j,N(ng),Nnew)=tl_DC(i,N(ng)) !^ ad_DC(i,N(ng))=ad_DC(i,N(ng))+ & & ad_Awrk(i,j,N(ng),Nnew) ad_Awrk(i,j,N(ng),Nnew)=0.0_r8 !^ tl_DC(i,N(ng))=(tl_DC(i,N(ng))- & !^ & FC(i,j,N(ng)-1)*tl_DC(i,N(ng)-1))/ & !^ & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) !^ adfac=ad_DC(i,N(ng))/ & & (BC(i,N(ng))-FC(i,j,N(ng)-1)*CF(i,N(ng)-1)) ad_DC(i,N(ng)-1)=ad_DC(i,N(ng)-1)-FC(i,j,N(ng)-1)*adfac ad_DC(i,N(ng) )=adfac END DO ! ! Solve the adjoint tridiagonal system. ! !^ DO k=2,N(ng)-1 !^ DO k=N(ng)-1,2,-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,j,k-1)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_DC(i,k)-FC(i,j,k-1)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,j,k-1)*adfac ad_DC(i,k )=adfac END DO END DO DO i=Istr,Iend cff=1.0_r8/BC(i,1) !^ tl_DC(i,1)=cff*tl_DC(i,1) !^ ad_DC(i,1)=cff*ad_DC(i,1) END DO ! ! Adjoint of right-hand-side terms for the diffusion equation. ! DO k=1,N(ng) DO i=Istr,Iend cff=0.5*(Hz(i,j-1,k)+Hz(i,j,k)) !^ tl_DC(i,k)=tl_Awrk(i,j,k,Nold)*cff !^ ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+cff*ad_DC(i,k) ad_DC(i,k)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,:,Nnew)) !^ CALL dabc_v3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_Awrk(:,:,:,Nnew)) !^ CALL ad_dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_Awrk(:,:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion equation. ! DO k=1,N(ng) DO j=JstrV,Jend DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & Hfac(i,j)* & !^ & (tl_FX(i+1,j)-tl_FX(i,j)+ & !^ & tl_FE(i,j)-tl_FE(i,j-1)) !^ adfac=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) ad_FE(i,j-1)=ad_FE(i,j-1)-adfac ad_FE(i,j )=ad_FE(i,j )+adfac ad_FX(i ,j)=ad_FX(i ,j)-adfac ad_FX(i+1,j)=ad_FX(i+1,j)+adfac ad_Awrk(i,j,k,Nold)=ad_Awrk(i,j,k,Nold)+ & & ad_Awrk(i,j,k,Nnew) ad_Awrk(i,j,k,Nnew)=0.0_r8 END DO END DO ! ! Compute XI- and ETA-components of diffusive flux. ! DO j=JstrV-1,Jend DO i=Istr,Iend !^ tl_FE(i,j)=pnom_r(i,j)*Kh(i,j)* & !^ & (tl_Awrk(i,j+1,k,Nold)-tl_Awrk(i,j,k,Nold)) !^ adfac=pnom_r(i,j)*Kh(i,j)*ad_FE(i,j) ad_Awrk(i,j ,k,Nold)=ad_Awrk(i,j ,k,Nold)-adfac ad_Awrk(i,j+1,k,Nold)=ad_Awrk(i,j+1,k,Nold)+adfac ad_FE(i,j)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 !^ tl_FX(i,j)=tl_FX(i,j)*pmask(i,j) !^ ad_FX(i,j)=ad_FX(i,j)*pmask(i,j) !^ tl_FX(i,j)=pmon_p(i,j)*0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & !^ & Kh(i-1,j-1)+Kh(i,j-1))* & !^ & (tl_Awrk(i,j,k,Nold)-tl_Awrk(i-1,j,k,Nold)) !^ adfac=pmon_p(i,j)*0.25_r8*(Kh(i-1,j )+Kh(i,j )+ & & Kh(i-1,j-1)+Kh(i,j-1))* & & ad_FX(i,j) ad_Awrk(i-1,j,k,Nold)=ad_Awrk(i-1,j,k,Nold)-adfac ad_Awrk(i ,j,k,Nold)=ad_Awrk(i ,j,k,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO END DO ! !----------------------------------------------------------------------- ! Set adjoint initial conditions. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_Awrk(i,j,k,Nold)=tl_A(i,j,k) !^ ad_A(i,j,k)=ad_A(i,j,k)+ad_Awrk(i,j,k,Nold) ad_Awrk(i,j,k,Nold)=0.0_r8 END DO END DO END DO !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, LBk, UBk, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) !^ CALL dabc_v3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, LBk, UBk, & !^ & tl_A) !^ CALL ad_dabc_v3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, LBk, UBk, & & ad_A) RETURN END SUBROUTINE ad_conv_v3d_tile END MODULE ad_conv_3d_mod