#include "cppdefs.h" MODULE ad_conv_2d_mod #if defined ADJOINT && defined FOUR_DVAR ! !git $Id$ !svn $Id: ad_conv_2d.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 explicit (inefficient) algorithm. ! ! ! ! For Gaussian (bell-shaped) correlations, the space convolution ! ! of the diffusion operator is an efficient way to estimate the ! ! finite domain error covariances. ! ! ! ! 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. ! ! Nghost Number of ghost points. ! ! NHsteps Number of horizontal diffusion integration steps. ! ! DTsizeH Horizontal diffusion pseudo time-step size. ! ! Kh Horizontal diffusion coefficients. ! ! ad_A 2D adjoint state variable to diffuse. ! ! ! ! On Output: ! ! ! ! ad_A Diffused 2D adjoint state variable. ! ! ! ! Routines: ! ! ! ! ad_conv_r2d_tile Adjoint 2D convolution at RHO-points ! ! ad_conv_u2d_tile Adjoint 2D convolution at U-points ! ! ad_conv_v2d_tile Adjoint 2D convolution at V-points ! ! ! !======================================================================= ! implicit none ! PUBLIC ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_conv_r2d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, DTsizeH, & & Kh, & & pm, pn, pmon_u, pnom_v, & # ifdef MASKING & rmask, umask, vmask, & # endif & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_2d_mod, ONLY: ad_dabc_r2d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps real(r8), intent(in) :: DTsizeH ! # ifdef ASSUMED_SHAPE 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:) # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(inout) :: ad_A(LBi:,LBj:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_v(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, step real(r8) :: adfac, cff real(r8), dimension(LBi:UBi,LBj:UBj,2) :: ad_Awrk 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) :: Hfac # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,1:2)=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 factor. ! DO j=Jstr,Jend DO i=Istr,Iend Hfac(i,j)=DTsizeH*pm(i,j)*pn(i,j) END DO END DO Nold=1 Nnew=2 ! !------------------------------------------------------------------------ ! Adjoint of load convolved solution. !------------------------------------------------------------------------ ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) DO j=Jstr,Jend DO i=Istr,Iend !^ tl_A(i,j)=tl_Awrk(i,j,Nold) !^ ad_Awrk(i,j,Nold)=ad_Awrk(i,j,Nold)+ad_A(i,j) ad_A(i,j)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion terms. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. If applicable, exchange boundary ! data. ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,Nnew)) # endif !^ CALL dabc_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_dabc_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_Awrk(:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion terms. ! DO j=Jstr,Jend DO i=Istr,Iend !^ tl_Awrk(i,j,Nnew)=tl_Awrk(i,j,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,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,Nold)=ad_Awrk(i,j,Nold)+ad_Awrk(i,j,Nnew) ad_Awrk(i,j,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 # ifdef MASKING !^ tl_FE(i,j)=tl_FE(i,j)*vmask(i,j) !^ ad_FE(i,j)=ad_FE(i,j)*vmask(i,j) # endif !^ tl_FE(i,j)=pnom_v(i,j)*0.5_r8*(Kh(i,j-1)+Kh(i,j))* & !^ & (tl_Awrk(i,j,Nold)-tl_Awrk(i,j-1,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,Nold)=ad_Awrk(i,j-1,Nold)-adfac ad_Awrk(i,j ,Nold)=ad_Awrk(i,j ,Nold)+adfac ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 # ifdef MASKING !^ tl_FX(i,j)=tl_FX(i,j)*umask(i,j) !^ ad_FX(i,j)=ad_FX(i,j)*umask(i,j) # endif !^ tl_FX(i,j)=pmon_u(i,j)*0.5_r8*(Kh(i-1,j)+Kh(i,j))* & !^ & (tl_Awrk(i,j,Nold)-tl_Awrk(i-1,j,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,Nold)=ad_Awrk(i-1,j,Nold)-adfac ad_Awrk(i ,j,Nold)=ad_Awrk(i ,j,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO ! ! Set adjoint initial conditions. ! DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_Awrk(i,j,Nold)=tl_A(i,j) !^ ad_A(i,j)=ad_A(i,j)+ad_Awrk(i,j,Nold) ad_Awrk(i,j,Nold)=0.0_r8 END DO END DO # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) RETURN END SUBROUTINE ad_conv_r2d_tile ! !*********************************************************************** SUBROUTINE ad_conv_u2d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, DTsizeH, & & Kh, & & pm, pn, pmon_r, pnom_p, & # ifdef MASKING & umask, pmask, & # endif & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_2d_mod, ONLY: ad_dabc_u2d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps real(r8), intent(in) :: DTsizeH ! # ifdef ASSUMED_SHAPE 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:) # ifdef MASKING real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(inout) :: ad_A(LBi:,LBj:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_p(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, step real(r8) :: adfac, cff real(r8), dimension(LBi:UBi,LBj:UBj,2) :: ad_Awrk 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) :: Hfac # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,1:2)=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 U-points. !----------------------------------------------------------------------- ! ! Compute metrics factor. ! cff=DTsizeH*0.25_r8 DO j=Jstr,Jend DO i=IstrU,Iend Hfac(i,j)=cff*(pm(i-1,j)+pm(i,j))*(pn(i-1,j)+pn(i,j)) END DO END DO Nold=1 Nnew=2 ! !------------------------------------------------------------------------ ! Adjoint of load convolved solution. !------------------------------------------------------------------------ ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_A(i,j)=tl_Awrk(i,j,Nold) !^ ad_Awrk(i,j,Nold)=ad_Awrk(i,j,Nold)+ad_A(i,j) ad_A(i,j)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion terms. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. If applicable, exchange boundary ! data. ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,Nnew)) # endif !^ CALL dabc_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_dabc_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_Awrk(:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion terms. ! DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_Awrk(i,j,Nnew)=tl_Awrk(i,j,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,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,Nold)=ad_Awrk(i,j,Nold)+ad_Awrk(i,j,Nnew) ad_Awrk(i,j,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 # ifdef MASKING !^ tl_FE(i,j)=tl_FE(i,j)*pmask(i,j) !^ ad_FE(i,j)=ad_FE(i,j)*pmask(i,j) # endif !^ 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,Nold)-tl_Awrk(i,j-1,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,Nold)=ad_Awrk(i,j-1,Nold)-adfac ad_Awrk(i,j ,Nold)=ad_Awrk(i,j ,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,Nold)-tl_Awrk(i,j,Nold)) !^ adfac=pmon_r(i,j)*Kh(i,j)*ad_FX(i,j) ad_Awrk(i ,j,Nold)=ad_Awrk(i ,j,Nold)-adfac ad_Awrk(i+1,j,Nold)=ad_Awrk(i+1,j,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO ! ! Set adjoint initial conditions. ! DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 !^ tl_Awrk(i,j,Nold)=tl_A(i,j) !^ ad_A(i,j)=ad_A(i,j)+ad_Awrk(i,j,Nold) ad_Awrk(i,j,Nold)=0.0_r8 END DO END DO # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) RETURN END SUBROUTINE ad_conv_u2d_tile ! !*********************************************************************** SUBROUTINE ad_conv_v2d_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & Nghost, NHsteps, DTsizeH, & & Kh, & & pm, pn, pmon_p, pnom_r, & # ifdef MASKING & vmask, pmask, & # endif & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_2d_mod, ONLY: ad_dabc_v2d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: Nghost, NHsteps real(r8), intent(in) :: DTsizeH ! # ifdef ASSUMED_SHAPE 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:) # ifdef MASKING real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif real(r8), intent(in) :: Kh(LBi:,LBj:) real(r8), intent(inout) :: ad_A(LBi:,LBj:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmon_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_r(LBi:UBi,LBj:UBj) # ifdef MASKING real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj) # endif ! ! Local variable declarations. ! integer :: Nnew, Nold, Nsav, i, j, step real(r8) :: adfac, cff real(r8), dimension(LBi:UBi,LBj:UBj,2) :: ad_Awrk 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) :: Hfac # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,1:2)=0.0_r8 ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ! !----------------------------------------------------------------------- ! Space convolution of the diffusion equation for a 2D state variable ! at V-points. !----------------------------------------------------------------------- ! ! Compute metrics factor. ! cff=DTsizeH*0.25_r8 DO j=JstrV,Jend DO i=Istr,Iend Hfac(i,j)=cff*(pm(i,j-1)+pm(i,j))*(pn(i,j-1)+pn(i,j)) END DO END DO Nold=1 Nnew=2 ! !------------------------------------------------------------------------ ! Adjoint of load convolved solution. !------------------------------------------------------------------------ ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) DO j=JstrV,Jend DO i=Istr,Iend !^ tl_A(i,j)=tl_Awrk(i,j,Nold) !^ ad_Awrk(i,j,Nold)=ad_Awrk(i,j,Nold)+ad_A(i,j) ad_A(i,j)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion terms. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. If applicable, exchange boundary ! data. ! # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_Awrk(:,:,Nnew)) # endif !^ CALL dabc_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_Awrk(:,:,Nnew)) !^ CALL ad_dabc_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_Awrk(:,:,Nnew)) ! ! Time-step adjoint horizontal diffusion terms. ! DO j=JstrV,Jend DO i=Istr,Iend !^ tl_Awrk(i,j,Nnew)=tl_Awrk(i,j,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,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,Nold)=ad_Awrk(i,j,Nold)+ad_Awrk(i,j,Nnew) ad_Awrk(i,j,Nnew)=0.0_r8 END DO END DO ! ! Compute XI- and ETA-components of the adjoint 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,Nold)-tl_Awrk(i,j,Nold)) !^ adfac=pnom_r(i,j)*Kh(i,j)*ad_FE(i,j) ad_Awrk(i,j ,Nold)=ad_Awrk(i,j ,Nold)-adfac ad_Awrk(i,j+1,Nold)=ad_Awrk(i,j+1,Nold)+adfac ad_FE(i,j)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 # ifdef MASKING !^ tl_FX(i,j)=tl_FX(i,j)*pmask(i,j) !^ ad_FX(i,j)=ad_FX(i,j)*pmask(i,j) # endif !^ 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,Nold)-tl_Awrk(i-1,j,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,Nold)=ad_Awrk(i-1,j,Nold)-adfac ad_Awrk(i ,j,Nold)=ad_Awrk(i ,j,Nold)+adfac ad_FX(i,j)=0.0_r8 END DO END DO END DO ! ! Set adjoint initial conditions. ! DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_Awrk(i,j,Nold)=tl_A(i,j) !^ ad_A(i,j)=ad_A(i,j)+ad_Awrk(i,j,Nold) ad_Awrk(i,j,Nold)=0.0_r8 END DO END DO # ifdef DISTRIBUTE !^ CALL mp_exchange2d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & Nghost, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_A) !^ CALL ad_mp_exchange2d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, & & Nghost, & & EWperiodic(ng), NSperiodic(ng), & & ad_A) # endif !^ CALL dabc_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_A) !^ CALL ad_dabc_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_A) RETURN END SUBROUTINE ad_conv_v2d_tile #endif END MODULE ad_conv_2d_mod