#include "cppdefs.h" MODULE ad_conv_3d_mod #if defined ADJOINT && defined FOUR_DVAR && defined SOLVE3D ! !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, & # ifdef GEOPOTENTIAL_HCONV & on_u, om_v, & # else & pmon_u, pnom_v, & # endif # ifdef MASKING & rmask, umask, vmask, & # endif & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_r3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange3d # endif ! ! 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 ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) # else real(r8), intent(in) :: pmon_u(LBi:,LBj:) real(r8), intent(in) :: pnom_v(LBi:,LBj:) # endif # 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) :: 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:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_v(LBi:UBi,LBj:UBj) # endif # 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) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! 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 # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC # endif real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAde # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 # else ad_FS(IminS:ImaxS,0:N(ng))=0.0_r8 # endif # endif ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 # ifdef GEOPOTENTIAL_HCONV ad_FZ(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdz(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdx(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAde(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 # endif ! !----------------------------------------------------------------------- ! 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) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV FC(i,j,k)=-DTsizeV*Kv(i,j,k)/(z_r(i,j,k+1)-z_r(i,j,k)) # else FC(i,j,k)=DTsizeV*Kv(i,j,k)/(z_r(i,j,k+1)-z_r(i,j,k)) # endif END DO FC(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO # endif # endif END DO END DO Nold=1 Nnew=2 ! !------------------------------------------------------------------------ ! Adjoint of load convolved solution. !------------------------------------------------------------------------ ! # ifdef DISTRIBUTE !^ 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) # endif !^ 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 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate adjoint vertical diffusion equation implicitly using ! parabolic splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav DO j=Jstr,Jend ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! ! Compute basic state time-invariant coefficients. ! cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=cff1*Hz(i,j,k )- & & DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hz(i,j,k+1)- & & DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 END DO ! cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend BC(i,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ & & DTsizeV*Kv(i,j,k)*(oHz(i,j,k)+oHz(i,j,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) END DO END DO ! ! Adjoint backward substitution. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & DTsizeV*oHz(i,j,k)* & !^ & (tl_DC(i,k)-tl_DC(i,k-1)) !^ adfac=DTsizeV*oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_DC(i,k-1)=ad_DC(i,k-1)-adfac ad_DC(i,k )=ad_DC(i,k )+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 !^ tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !^ ad_DC(i,k)=ad_DC(i,k)*Kv(i,j,k) END DO END DO DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_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_DC(i,N(ng))=0.0_r8 !^ ad_DC(i,N(ng))=0.0_r8 END DO ! ! Adjoint LU decomposition and forward substitution. ! DO k=N(ng)-1,1,-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)- & !^ & FC(i,k)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,k)*adfac ad_DC(i,k)=0.0_r8 END DO END DO ! DO i=Istr,Iend !^ tl_DC(i,0)=0.0_r8 !^ ad_DC(i,0)=0.0_r8 END DO END DO END DO # else ! !----------------------------------------------------------------------- ! 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 # ifdef MASKING !^ 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) # endif !^ 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 # ifdef MASKING !^ 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) # endif !^ 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 # endif # else ! !----------------------------------------------------------------------- ! Integrate adjoint vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav DO j=Jstr,Jend ! ! Time-step adjoint vertical diffusive term. Notice that "oHz" is ! assumed to be time invariant. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & oHz(i,j,k)*(tl_FS(i,k )- & !^ & tl_FS(i,k-1)) !^ adfac=oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_FS(i,k-1)=ad_FS(i,k-1)-adfac ad_FS(i,k )=ad_FS(i,k )+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 adjoint vertical diffusive flux. Notice that "FC" is ! assumed to be time invariant. ! DO i=Istr,Iend !^ tl_FS(i,N(ng))=0.0_r8 !^ ad_FS(i,N(ng))=0.0_r8 !^ tl_FS(i,0)=0.0_r8 !^ ad_FS(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend # ifdef MASKING !^ tl_FS(i,k)=tl_FS(i,k)*rmask(i,j) !^ ad_FS(i,k)=ad_FS(i,k)*rmask(i,j) # endif !^ tl_FS(i,k)=FC(i,j,k)*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=FC(i,j,k)*ad_FS(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_FS(i,k)=0.0_r8 END DO END DO END DO END DO # endif # endif ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! # ifdef DISTRIBUTE !^ 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)) # endif !^ 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)) # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! ! Compute adjoint of starting values of k1 and k2. ! k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of above code. !! k1=k2 k2=3-k1 END DO ! K_LOOP : DO k=N(ng),0,-1 ! ! Compute required BASIC STATE fields. Need to look forward in ! recursive kk index. ! k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b ! ! Compute components of the rotated tracer flux (A m3/s) along ! geopotential surfaces (required BASIC STATE fields). ! IF (kk.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j,k2)=cff*(z_r(i ,j,kk+1)- & & z_r(i-1,j,kk+1)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 dZdx(i,j,k1b)=0.0_r8 END DO END DO END IF DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j,k2)=cff*(z_r(i,j ,kk+1)- & & z_r(i,j-1,kk+1)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend+1 DO i=Istr,Iend dZde(i,j,k1b)=0.0_r8 END DO END DO END IF END IF END DO ! IF (k.gt.0) THEN ! ! Time-step adjoint harmonic, geopotential diffusion term. ! 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))+ & !^ & DTsizeH* & !^ & (tl_FZ(i,j,k2)-tl_FZ(i,j,k1)) !^ adfac1=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) adfac2=DTsizeH*ad_Awrk(i,j,k,Nnew) ad_FE(i,j )=ad_FE(i,j )-adfac1 ad_FE(i,j+1)=ad_FE(i,j+1)+adfac1 ad_FX(i ,j)=ad_FX(i ,j)-adfac1 ad_FX(i+1,j)=ad_FX(i+1,j)+adfac1 ad_FZ(i,j,k1)=ad_FZ(i,j,k1)-adfac2 ad_FZ(i,j,k2)=ad_FZ(i,j,k2)+adfac2 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 components of the adjoint rotated A flux (A m3/s) along ! geopotential surfaces. ! IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend cff=0.5_r8*Kh(i,j) cff1=MIN(dZde(i,j ,k1),0.0_r8) cff2=MIN(dZde(i,j+1,k2),0.0_r8) cff3=MAX(dZde(i,j ,k2),0.0_r8) cff4=MAX(dZde(i,j+1,k1),0.0_r8) !^ tl_FZ(i,j,k2)=tl_FZ(i,j,k2)+ & !^ & cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j+1,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j+1,k1))) !^ adfac=cff*ad_FZ(i,j,k2) ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAde(i,j ,k1)=ad_dAde(i,j ,k1)-cff1*adfac ad_dAde(i,j+1,k2)=ad_dAde(i,j+1,k2)-cff2*adfac ad_dAde(i,j ,k2)=ad_dAde(i,j ,k2)-cff3*adfac ad_dAde(i,j+1,k1)=ad_dade(i,j+1,k1)-cff4*adfac ! cff1=MIN(dZdx(i ,j,k1),0.0_r8) cff2=MIN(dZdx(i+1,j,k2),0.0_r8) cff3=MAX(dZdx(i ,j,k2),0.0_r8) cff4=MAX(dZdx(i+1,j,k1),0.0_r8) !^ tl_FZ(i,j,k2)=cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i+1,j,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i+1,j,k1))) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAdx(i ,j,k1)=ad_dAdx(i ,j,k1)-cff1*adfac ad_dAdx(i+1,j,k2)=ad_dAdx(i+1,j,k2)-cff2*adfac ad_dAdx(i ,j,k2)=ad_dAdx(i ,j,k2)-cff3*adfac ad_dAdx(i+1,j,k1)=ad_dAdx(i+1,j,k1)-cff4*adfac ad_FZ(i,j,k2)=0.0_r8 END DO END DO END IF DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.25_r8*(Kh(i,j-1)+Kh(i,j))*om_v(i,j) cff1=MIN(dZde(i,j,k1),0.0_r8) cff2=MAX(dZde(i,j,k1),0.0_r8) !^ tl_FE(i,j)=cff* & !^ & (Hz(i,j,k)+Hz(i,j-1,k))* & !^ & (tl_dAde(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i,j-1,k1)+ & !^ & tl_dAdz(i,j ,k2))+ & !^ & cff2*(tl_dAdz(i,j-1,k2)+ & !^ & tl_dAdz(i,j ,k1)))) !^ adfac=cff*(Hz(i,j,k)+Hz(i,j-1,k))*ad_FE(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAde(i,j,k1)=ad_dAde(i,j,k1)+adfac ad_dAdz(i,j-1,k1)=ad_dAdz(i,j-1,k1)-adfac1 ad_dAdz(i,j ,k2)=ad_dAdz(i,j ,k2)-adfac1 ad_dAdz(i,j-1,k2)=ad_dAdz(i,j-1,k2)-adfac2 ad_dAdz(i,j ,k1)=ad_dAdz(i,j ,k1)-adfac2 ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.25_r8*(Kh(i-1,j)+Kh(i-1,j))*on_u(i,j) cff1=MIN(dZdx(i,j,k1),0.0_r8) cff2=MAX(dZdx(i,j,k1),0.0_r8) !^ tl_FX(i,j)=cff* & !^ & (Hz(i,j,k)+Hz(i-1,j,k))* & !^ & (tl_dAdx(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i-1,j,k1)+ & !^ & tl_dAdz(i ,j,k2))+ & !^ & cff2*(tl_dAdz(i-1,j,k2)+ & !^ & tl_dAdz(i ,j,k1)))) !^ adfac=cff*(Hz(i,j,k)+Hz(i-1,j,k))*ad_FX(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAdx(i,j,k1)=ad_dAdx(i,j,k1)+adfac ad_dAdz(i-1,j,k1)=ad_dAdz(i-1,j,k1)-adfac1 ad_dAdz(i ,j,k2)=ad_dAdz(i ,j,k2)-adfac1 ad_dAdz(i-1,j,k2)=ad_dAdz(i-1,j,k2)-adfac2 ad_dAdz(i ,j,k1)=ad_dAdz(i ,j,k1)-adfac2 ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_FZ(i,j,k2)=0.0_r8 !^ ad_FZ(i,j,k2)=0.0_r8 !^ tl_dAdz(i,j,k2)=0.0_r8 !^ ad_dAdz(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) # ifdef MASKING !^ tl_dAdz(i,j,k2)=tl_dAdz(i,j,k2)*rmask(i,j) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)*rmask(i,j) # endif !^ tl_dAdz(i,j,k2)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=cff*ad_dAdz(i,j,k2) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_dAdz(i,j,k2)=0.0_r8 END DO END DO END IF IF (k.lt.N(ng)) THEN DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) !^ tl_dAde(i,j,k2)=cff* !^ & (tl_Awrk(i,j ,k+1,Nold)*rmask(i,j )- & !^ & tl_Awrk(i,j-1,k+1,Nold)*rmask(i,j-1)) !^ adfac=cff*ad_dAde(i,j,k2) ad_Awrk(i,j-1,k+1,Nold)=ad_Awrk(i,j-1,k+1,Nold)- & & rmask(i,j-1)*adfac ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)+ & & rmask(i,j )*adfac ad_dAde(i,j,k2)=0.0_r8 # else !^ tl_dAde(i,j,k2)=cff*(tl_Awrk(i,j ,k+1,Nold)- & !^ & tl_Awrk(i,j-1,k+1,Nold)) !^ adfac=cff*ad_dAde(i,j,k2) ad_Awrk(i,j-1,k+1,Nold)=ad_Awrk(i,j-1,k+1,Nold)-adfac ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)+adfac ad_dAde(i,j,k2)=0.0_r8 # endif END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) !^ dAdx(i,j,k2)=cff*(Awrk(i ,j,k+1,Nold)*rmask(i ,j)- & !^ & Awrk(i-1,j,k+1,Nold)*rmask(i-1,j)) !^ adfac=cff*ad_dAdx(i,j,k2) ad_Awrk(i-1,j,k+1,Nold)=ad_Awrk(i-1,j,k+1,Nold)- & & rmask(i-1,j)*adfac ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)+ & & rmask(i ,j)*adfac ad_dAdx(i,j,k2)=0.0_r8 # else !^ tl_dAdx(i,j,k2)=cff*(tl_Awrk(i ,j,k+1,Nold)- & !^ & tl_Awrk(i-1,j,k+1,Nold)) !^ adfac=cff*ad_dAdx(i,j,k2) ad_Awrk(i-1,j,k+1,Nold)=ad_Awrk(i-1,j,k+1,Nold)-adfac ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)+adfac ad_dAdx(i,j,k2)=0.0_r8 # endif END DO END DO END IF ! ! Compute new storage recursive indices. ! kt=k2 k2=k1 k1=kt END DO K_LOOP # else ! ! 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 # 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,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 # 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,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 # endif 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 # ifdef DISTRIBUTE !^ 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) # endif !^ 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, & # ifdef GEOPOTENTIAL_HCONV & on_r, om_p, & # else & pmon_r, pnom_p, & # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV & pmask, rmask, umask, vmask, & # else & umask, pmask, & # endif # endif & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_u3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange3d # endif ! ! 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 ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_r(LBi:,LBj:) real(r8), intent(in) :: om_p(LBi:,LBj:) # else real(r8), intent(in) :: pmon_r(LBi:,LBj:) real(r8), intent(in) :: pnom_p(LBi:,LBj:) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV 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:) # else real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif # endif 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:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_p(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_r(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_p(LBi:UBi,LBj:UBj) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) 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) # else real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! 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 # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,N(ng)) :: Hzk # endif real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAde # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 # else ad_FS(IminS:ImaxS,0:N(ng))=0.0_r8 # endif # endif ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 # ifdef GEOPOTENTIAL_HCONV ad_FZ(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdz(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdx(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAde(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 # endif ! !----------------------------------------------------------------------- ! 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)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV 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 )) # else 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 )) # endif END DO FC(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=2.0_r8/(Hz(i-1,j,k)+Hz(i,j,k)) END DO # endif # endif END DO END DO Nold=1 Nnew=2 ! !----------------------------------------------------------------------- ! Adjoint of load convolved solution. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE !^ 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) # endif !^ 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 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate adjoint vertical diffusion equation implicitly using ! parabolic splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! ! Compute basic state time-invariant coefficients. ! DO j=Jstr,Jend DO k=1,N(ng) DO i=IstrU,Iend Hzk(i,k)=0.5_r8*(Hz(i-1,j,k)+ & & Hz(i ,j,k)) END DO END DO cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend FC(i,k)=cff1*Hzk(i,k )-DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hzk(i,k+1)-DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=IstrU,Iend CF(i,0)=0.0_r8 END DO ! cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=IstrU,Iend BC(i,k)=cff1*(Hzk(i,k)+Hzk(i,k+1))+ & & DTsizeV*Kv(i,j,k)*(oHz(i,j,k)+oHz(i,j,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) END DO END DO ! ! Adjoint backward substitution. ! DO k=1,N(ng) DO i=IstrU,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & DTsizeV*oHz(i,j,k)* & !^ & (tl_DC(i,k)-tl_DC(i,k-1)) !^ adfac=DTsizeV*oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_DC(i,k-1)=ad_DC(i,k-1)-adfac ad_DC(i,k )=ad_DC(i,k )+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 !^ tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !^ ad_DC(i,k)=ad_DC(i,k)*Kv(i,j,k) END DO END DO DO k=1,N(ng)-1 DO i=IstrU,Iend !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_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_DC(i,N(ng))=0.0_r8 !^ ad_DC(i,N(ng))=0.0_r8 END DO ! ! Adjoint LU decomposition and forward substitution. ! DO k=N(ng)-1,1,-1 DO i=IstrU,Iend cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)- & !^ & FC(i,k)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,k)*adfac ad_DC(i,k)=0.0_r8 END DO END DO DO i=IstrU,Iend !^ tl_DC(i,0)=0.0_r8 !^ ad_DC(i,0)=0.0_r8 END DO END DO END DO # else ! !----------------------------------------------------------------------- ! 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 # ifdef MASKING !^ 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) # endif !^ 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 # ifdef MASKING !^ 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) # endif !^ 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 # endif # else ! !----------------------------------------------------------------------- ! Integerate adjoint vertical diffusion equation explicitly. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Time-step adjoint vertical diffusive term. Notice that "oHz" is ! assumed to be time invariant. ! DO j=Jstr,Jend DO k=1,N(ng) DO i=IstrU,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & oHz(i,j,k)*(tl_FS(i,k )- & !^ & tl_FS(i,k-1)) !^ adfac=oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_FS(i,k-1)=ad_FS(i,k-1)-adfac ad_FS(i,k )=ad_FS(i,k )+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 adjoint vertical diffusive flux. Notice that "FC" is ! assumed to be time invariant. ! DO i=IstrU,Iend !^ tl_FS(i,N(ng))=0.0_r8 !^ ad_FS(i,N(ng))=0.0_r8 !^ tl_FS(i,0)=0.0_r8 !^ ad_FS(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=IstrU,Iend # ifdef MASKING !^ tl_FS(i,k)=tl_FS(i,k)*umask(i,j) !^ ad_FS(i,k)=ad_FS(i,k)*umask(i,j) # endif !^ tl_FS(i,k)=FC(i,j,k)*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=FC(i,j,k)*ad_FS(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_FS(i,k)=0.0_r8 END DO END DO END DO END DO # endif # endif ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! # ifdef DISTRIBUTE !^ 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)) # endif !^ 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)) # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! ! Compute adjoint of starting values of k1 and k2. ! k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of above code. !! k1=k2 k2=3-k1 END DO ! K_LOOP : DO k=N(ng),0,-1 ! Compute required BASIC STATE fields. Need to look forward in ! recursive kk index. ! k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b ! ! Compute components of the rotated tracer flux (A m3/s) along ! geopotential surfaces (required BASIC STATE fields). ! IF (kk.lt.N(ng)) THEN DO j=Jstr,Jend DO i=IstrU-1,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j)=cff*(z_r(i ,j,kk+1)- & & z_r(i-1,j,kk+1)) END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend dZdx_r(i,j,k2)=0.5_r8*(dZdx(i ,j)+ & & dZdx(i+1,j)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend DO i=IstrU-1,Iend dZdx_r(i,j,k1b)=0.0_r8 END DO END DO END IF ! DO j=Jstr,Jend+1 DO i=IstrU-1,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j)=cff*(z_r(i,j ,kk+1)- & & z_r(i,j-1,kk+1)) END DO END DO DO j=Jstr,Jend+1 DO i=IstrU,Iend dZde_p(i,j,k2)=0.5_r8*(dZde(i-1,j)+ & & dZde(i ,j)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend+1 DO i=IstrU,Iend dZde_p(i,j,k1b)=0.0_r8 END DO END DO END IF END IF END DO ! IF (k.gt.0) THEN ! ! Time-step adjoint harmonic, geopotential diffusion term. ! 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))+ & !^ & DTsizeH* & !^ & (tl_FZ(i,j,k2)-tl_FZ(i,j,k1)) !^ adfac1=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) adfac2=DTsizeH*ad_Awrk(i,j,k,Nnew) ad_FE(i,j )=ad_FE(i,j )-adfac1 ad_FE(i,j+1)=ad_FE(i,j+1)+adfac1 ad_FX(i-1,j)=ad_FX(i-1,j)-adfac1 ad_FX(i ,j)=ad_FX(i ,j)+adfac1 ad_FZ(i,j,k1)=ad_FZ(i,j,k1)-adfac2 ad_FZ(i,j,k2)=ad_FZ(i,j,k2)+adfac2 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 components of the adjoint rotated A flux (A m3/s) along ! geopotential surfaces. ! IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(Kh(i-1,j)+Kh(i,j)) cff1=MIN(dZde_p(i,j ,k1),0.0_r8) cff2=MIN(dZde_p(i,j+1,k2),0.0_r8) cff3=MAX(dZde_p(i,j ,k2),0.0_r8) cff4=MAX(dZde_p(i,j+1,k1),0.0_r8) !^ tl_FZ(i,j,k2)=tl_FZ(i,j,k2)+ & !^ & cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j+1,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j+1,k1))) !^ adfac=cff*ad_FZ(i,j,k2) ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAde(i,j ,k1)=ad_dAde(i,j ,k1)-cff1*adfac ad_dAde(i,j+1,k2)=ad_dAde(i,j+1,k2)-cff2*adfac ad_dAde(i,j ,k2)=ad_dAde(i,j ,k2)-cff3*adfac ad_dAde(i,j+1,k1)=ad_dade(i,j+1,k1)-cff4*adfac ! cff1=MIN(dZdx_r(i-1,j,k1),0.0_r8) cff2=MIN(dZdx_r(i ,j,k2),0.0_r8) cff3=MAX(dZdx_r(i-1,j,k2),0.0_r8) cff4=MAX(dZdx_r(i ,j,k1),0.0_r8) !^ tl_FZ(i,j,k2)=cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i-1,j,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i-1,j,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k1))) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAdx(i-1,j,k1)=ad_dAdx(i-1,j,k1)-cff1*adfac ad_dAdx(i ,j,k2)=ad_dAdx(i ,j,k2)-cff2*adfac ad_dAdx(i-1,j,k2)=ad_dAdx(i-1,j,k2)-cff3*adfac ad_dAdx(i ,j,k1)=ad_dAdx(i ,j,k1)-cff4*adfac ad_FZ(i,j,k2)=0.0_r8 END DO END DO END IF DO j=Jstr,Jend+1 DO i=IstrU,Iend cff=0.0625_r8*(Kh(i-1,j-1)+Kh(i-1,j)+ & & Kh(i ,j-1)+Kh(i ,j))*om_p(i,j) cff1=MIN(dZde_p(i,j,k1),0.0_r8) cff2=MAX(dZde_p(i,j,k1),0.0_r8) !^ tl_FE(i,j)=cff* & !^ & (Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & !^ & Hz(i ,j-1,k)+Hz(i ,j,k))* & !^ & (tl_dAde(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i,j-1,k1)+ & !^ & tl_dAdz(i,j ,k2))+ & !^ & cff2*(tl_dAdz(i,j-1,k2)+ & !^ & tl_dAdz(i,j ,k1)))) !^ adfac=cff*(Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & & Hz(i ,j-1,k)+Hz(i ,j,k))*ad_FE(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAde(i,j,k1)=ad_dAde(i,j,k1)+adfac ad_dAdz(i,j-1,k1)=ad_dAdz(i,j-1,k1)-adfac1 ad_dAdz(i,j ,k2)=ad_dAdz(i,j ,k2)-adfac1 ad_dAdz(i,j-1,k2)=ad_dAdz(i,j-1,k2)-adfac2 ad_dAdz(i,j ,k1)=ad_dAdz(i,j ,k1)-adfac2 ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend cff=Kh(i,j)*on_r(i,j) cff1=MIN(dZdx_r(i,j,k1),0.0_r8) cff2=MAX(dZdx_r(i,j,k1),0.0_r8) !^ tl_FX(i,j)=cff* & !^ & Hz(i,j,k)* & !^ & (tl_dAdx(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i ,j,k1)+ & !^ & tl_dAdz(i+1,j,k2))+ & !^ & cff2*(tl_dAdz(i ,j,k2)+ & !^ & tl_dAdz(i+1,j,k1)))) !^ adfac=cff*Hz(i,j,k)*ad_FX(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAdx(i,j,k1)=ad_dAdx(i,j,k1)+adfac ad_dAdz(i ,j,k1)=ad_dAdz(i ,j,k1)-adfac1 ad_dAdz(i+1,j,k2)=ad_dAdz(i+1,j,k2)-adfac1 ad_dAdz(i ,j,k2)=ad_dAdz(i ,j,k2)-adfac2 ad_dAdz(i+1,j,k1)=ad_dAdz(i+1,j,k1)-adfac2 ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 !^ tl_FZ(i,j,k2)=0.0_r8 !^ ad_FZ(i,j,k2)=0.0_r8 !^ tl_dAdz(i,j,k2)=0.0_r8 !^ ad_dAdz(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=IstrU-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) # ifdef MASKING !^ tl_dAdz(i,j,k2)=tl_dAdz(i,j,k2)*umask(i,j) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)*umask(i,j) # endif !^ tl_dAdz(i,j,k2)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=cff*ad_dAdz(i,j,k2) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_dAdz(i,j,k2)=0.0_r8 END DO END DO END IF IF (k.lt.N(ng)) THEN DO j=Jstr,Jend+1 DO i=IstrU,Iend cff=0.25_r8*(pn(i-1,j )+pn(i,j )+ & & pn(i-1,j-1)+pn(i,j-1)) # ifdef MASKING !^ tl_dAde(i,j,k2)=tl_dAde(i,j,k2)*pmask(i,j) !^ ad_dAde(i,j,k2)=ad_dAde(i,j,k2)*pmask(i,j) !^ tl_dAde(i,j,k2)=cff* & !^ & (tl_Awrk(i,j ,k+1,Nold)*umask(i,j )- & !^ & tl_Awrk(i,j-1,k+1,Nold)*umask(i,j-1)) !^ adfac=cff*ad_dAde(i,j,k2) ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)+ & & umask(i,j )*adfac ad_Awrk(i,j-1,k+1,Nold)=ad_Awrk(i,j-1,k+1,Nold)- & & umask(i,j-1)*adfac ad_dAde(i,j,k2)=0.0_r8 # else !^ tl_dAde(i,j,k2)=cff*(tl_Awrk(i,j ,k+1,Nold)- & !^ & tl_Awrk(i,j-1,k+1,Nold)) !^ adfac=cff*ad_dAde(i,j,k2) ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)+ & & adfac ad_Awrk(i,j-1,k+1,Nold)=ad_Awrk(i,j-1,k+1,Nold)- & & adfac ad_dAde(i,j,k2)=0.0_r8 # endif END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend # ifdef MASKING !^ tl_dAdx(i,j,k2)=tl_dAdx(i,j,k2)*rmask(i,j) !^ ad_dAdx(i,j,k2)=ad_dAdx(i,j,k2)*rmask(i,j) !^ tl_dAdx(i,j,k2)=pm(i,j)* & !^ & (tl_Awrk(i+1,j,k+1,Nold)*umask(i+1,j)- & !^ & tl_Awrk(i ,j,k+1,Nold)*umask(i ,j)) !^ adfac=pm(i,j)*ad_dAdx(i,j,k2) ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)- & & umask(i ,j)*adfac ad_Awrk(i+1,j,k+1,Nold)=ad_Awrk(i+1,j,k+1,Nold)+ & & umask(i+1,j)*adfac ad_dAdx(i,j,k2)=0.0_r8 # else !^ tl_dAdx(i,j,k2)=pm(i,j)*(tl_Awrk(i+1,j,k+1,Nold)- & !^ & tl_Awrk(i ,j,k+1,Nold)) !^ adfac=pm(i,j)*ad_dAdx(i,j,k2) ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)- & & adfac ad_Awrk(i+1,j,k+1,Nold)=ad_Awrk(i+1,j,k+1,Nold)+ & & adfac ad_dAdx(i,j,k2)=0.0_r8 # endif END DO END DO END IF ! ! Compute new storage recursive indices. ! kt=k2 k2=k1 k1=kt END DO K_LOOP # else ! ! 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 # 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,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 # endif 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 # ifdef DISTRIBUTE !^ 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) # endif !^ 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, & # ifdef GEOPOTENTIAL_HCONV & on_p, om_r, & # else & pmon_p, pnom_r, & # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV & pmask, rmask, umask, vmask, & # else & vmask, pmask, & # endif # endif & Hz, z_r, & & ad_A) !*********************************************************************** ! USE mod_param USE mod_scalars ! USE ad_bc_3d_mod, ONLY: ad_dabc_v3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange3d # endif ! ! 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 ! # ifdef ASSUMED_SHAPE real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_p(LBi:,LBj:) real(r8), intent(in) :: om_r(LBi:,LBj:) # else real(r8), intent(in) :: pmon_p(LBi:,LBj:) real(r8), intent(in) :: pnom_r(LBi:,LBj:) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV 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:) # else real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: pmask(LBi:,LBj:) # endif # endif 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:) # else real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: on_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_r(LBi:UBi,LBj:UBj) # else real(r8), intent(in) :: pmon_p(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pnom_r(LBi:UBi,LBj:UBj) # endif # ifdef MASKING # ifdef GEOPOTENTIAL_HCONV real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) 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) # else real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pmask(LBi:UBi,LBj:UBj) # endif # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Kh(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Kv(LBi:UBi,LBj:UBj,0:UBk) real(r8), intent(inout) :: ad_A(LBi:UBi,LBj:UBj,LBk:UBk) # endif ! ! 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 # ifdef VCONVOLUTION # ifndef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FC # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz # endif # if defined IMPLICIT_VCONV || defined SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF # ifdef SPLINES_VCONV real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,N(ng)) :: Hzk # endif real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC # else real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_FS # endif # endif # ifdef GEOPOTENTIAL_HCONV real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZdx_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dZde_r real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_FZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dAde # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_Awrk(LBi:UBi,LBj:UBj,LBk:UBk,1:2)=0.0_r8 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV ad_DC(IminS:ImaxS,0:N(ng))=0.0_r8 # else ad_FS(IminS:ImaxS,0:N(ng))=0.0_r8 # endif # endif ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 # ifdef GEOPOTENTIAL_HCONV ad_FZ(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdz(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAdx(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dAde(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 # endif ! !----------------------------------------------------------------------- ! 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)) # ifdef VCONVOLUTION # ifndef SPLINES_VCONV FC(i,j,N(ng))=0.0_r8 DO k=1,N(ng)-1 # ifdef IMPLICIT_VCONV 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 )) # else 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 )) # endif END DO FC(i,j,0)=0.0_r8 # endif # if !defined IMPLICIT_VCONV || defined SPLINES_VCONV DO k=1,N(ng) oHz(i,j,k)=2.0_r8/(Hz(i,j-1,k)+Hz(i,j,k)) END DO # endif # endif END DO END DO Nold=1 Nnew=2 ! !----------------------------------------------------------------------- ! Adjoint of load convolved adjoint solution. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE !^ 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) # endif !^ 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 # ifdef VCONVOLUTION # ifdef IMPLICIT_VCONV # ifdef SPLINES_VCONV ! !----------------------------------------------------------------------- ! Integrate adjoint vertical diffusion equation implicitly using ! parabolic splines. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Use conservative, parabolic spline reconstruction of vertical ! diffusion derivatives. Then, time step vertical diffusion term ! implicitly. ! ! Compute basic state time-invariant coefficients. ! DO j=JstrV,Jend DO k=1,N(ng) DO i=Istr,Iend Hzk(i,k)=0.5_r8*(Hz(i,j-1,k)+ & & Hz(i,j ,k)) END DO END DO cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=cff1*Hzk(i,k )-DTsizeV*Kv(i,j,k-1)*oHz(i,j,k ) CF(i,k)=cff1*Hzk(i,k+1)-DTsizeV*Kv(i,j,k+1)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 END DO ! cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend BC(i,k)=cff1*(Hzk(i,k)+Hzk(i,k+1))+ & & DTsizeV*Kv(i,j,k)*(oHz(i,j,k)+oHz(i,j,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) CF(i,k)=cff*CF(i,k) END DO END DO ! ! Adjoint backward substitution. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & DTsizeV*oHz(i,j,k)* & !^ & (tl_DC(i,k)-tl_DC(i,k-1)) !^ adfac=DTsizeV*oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_DC(i,k-1)=ad_DC(i,k-1)-adfac ad_DC(i,k )=ad_DC(i,k )+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 !^ tl_DC(i,k)=tl_DC(i,k)*Kv(i,j,k) !^ ad_DC(i,k)=ad_DC(i,k)*Kv(i,j,k) END DO END DO DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_DC(i,k)=tl_DC(i,k)-CF(i,k)*tl_DC(i,k+1) !^ ad_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_DC(i,N(ng))=0.0_r8 !^ ad_DC(i,N(ng))=0.0_r8 END DO ! ! Adjoint LU decomposition and forward substitution. ! DO k=N(ng)-1,1,-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)- & !^ & FC(i,k)*tl_DC(i,k-1)) adfac=cff*ad_DC(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,k)*adfac ad_DC(i,k)=0.0_r8 END DO END DO DO i=Istr,Iend !^ tl_DC(i,0)=0.0_r8 !^ ad_DC(i,0)=0.0_r8 END DO END DO END DO # else ! !----------------------------------------------------------------------- ! 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 # ifdef MASKING !^ 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) # endif !^ 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 # ifdef MASKING !^ 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) # endif !^ 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 # endif # else ! !----------------------------------------------------------------------- ! Integerate adjoint vertical diffusion term. !----------------------------------------------------------------------- ! DO step=1,NVsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Time-step vertical diffusive term. Notice that "oHz" is assumed to ! be time invariant. ! DO j=JstrV,Jend DO k=1,N(ng) DO i=Istr,Iend !^ tl_Awrk(i,j,k,Nnew)=tl_Awrk(i,j,k,Nold)+ & !^ & oHz(i,j,k)*(tl_FS(i,k )- & !^ & tl_FS(i,k-1)) !^ adfac=oHz(i,j,k)*ad_Awrk(i,j,k,Nnew) ad_FS(i,k-1)=ad_FS(i,k-1)-adfac ad_FS(i,k )=ad_FS(i,k )+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 vertical diffusive flux. Notice that "FC" is assumed to ! be time invariant. ! DO i=Istr,Iend !^ tl_FS(i,N(ng))=0.0_r8 !^ ad_FS(i,N(ng))=0.0_r8 !^ tl_FS(i,0)=0.0_r8 !^ ad_FS(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend # ifdef MASKING !^ tl_FS(i,k)=tl_FS(i,k)*vmask(i,j) !^ ad_FS(i,k)=ad_FS(i,k)*vmask(i,j) # endif !^ tl_FS(i,k)=FC(i,j,k)*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=FC(i,j,k)*ad_FS(i,k) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_FS(i,k)=0.0_r8 END DO END DO END DO END DO # endif # endif ! !----------------------------------------------------------------------- ! Integrate adjoint horizontal diffusion equation. !----------------------------------------------------------------------- ! DO step=1,NHsteps ! ! Update integration indices. ! Nsav=Nnew Nnew=Nold Nold=Nsav ! ! Apply adjoint boundary conditions. ! # ifdef DISTRIBUTE !^ 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)) # endif !^ 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)) # ifdef GEOPOTENTIAL_HCONV ! ! Diffusion along geopotential surfaces: Compute horizontal and ! vertical gradients. Notice the recursive blocking sequence. The ! vertical placement of the gradients is: ! ! dAdx,dAde(:,:,k1) k rho-points ! dAdx,dAde(:,:,k2) k+1 rho-points ! FZ,dAdz(:,:,k1) k-1/2 W-points ! FZ,dAdz(:,:,k2) k+1/2 W-points ! ! Compute adjoint of starting values of k1 and k2. ! k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of above code. !! k1=k2 k2=3-k1 END DO ! K_LOOP : DO k=N(ng),0,-1 ! Compute required BASIC STATE fields. Need to look forward in ! recursive kk index. ! k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b ! ! Compute components of the rotated tracer flux (A m3/s) along ! geopotential surfaces (required BASIC STATE fields). ! IF (kk.lt.N(ng)) THEN DO j=JstrV-1,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i-1,j)+pm(i,j)) # ifdef MASKING cff=cff*umask(i,j) # endif dZdx(i,j)=cff*(z_r(i ,j,kk+1)- & & z_r(i-1,j,kk+1)) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 dZdx_p(i,j,k2)=0.5_r8*(dZdx(i,j-1)+ & & dZdx(i,j )) END DO END DO IF (kk.eq.0) THEN DO j=JstrV,Jend DO i=Istr,Iend+1 dZdx_p(i,j,k1b)=0.0_r8 END DO END DO END IF ! DO j=JstrV-1,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j-1)+pn(i,j)) # ifdef MASKING cff=cff*vmask(i,j) # endif dZde(i,j)=cff*(z_r(i,j ,k+1)- & & z_r(i,j-1,k+1)) END DO END DO DO j=JstrV-1,Jend DO i=Istr,Iend dZde_r(i,j,k2)=0.5_r8*(dZde(i,j )+ & & dZde(i,j+1)) END DO END DO IF (kk.eq.0) THEN DO j=JstrV-1,Jend DO i=Istr,Iend dZde_r(i,j,k2)=0.0_r8 END DO END DO END IF END IF END DO ! IF (k.gt.0) THEN ! ! Time-step adjoint harmonic, geopotential diffusion term. ! 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))+ & !^ & DTsizeH* & !^ & (tl_FZ(i,j,k2)-tl_FZ(i,j,k1)) !^ adfac1=Hfac(i,j)*ad_Awrk(i,j,k,Nnew) adfac2=DTsizeH*ad_Awrk(i,j,k,Nnew) ad_FE(i,j-1)=ad_FE(i,j-1)-adfac1 ad_FE(i,j )=ad_FE(i, j)+adfac1 ad_FX(i ,j)=ad_FX(i ,j)-adfac1 ad_FX(i+1,j)=ad_FX(i+1,j)+adfac1 ad_FZ(i,j,k1)=ad_FZ(i,j,k1)-adfac2 ad_FZ(i,j,k2)=ad_FZ(i,j,k2)+adfac2 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 components of the adjoint rotated A flux (A m3/s) along ! geopotential surfaces. ! IF (k.lt.N(ng)) THEN DO j=JstrV,Jend DO i=Istr,Iend cff=0.5_r8*(Kh(i,j-1)+Kh(i,j)) cff1=MIN(dZde_r(i,j-1,k1),0.0_r8) cff2=MIN(dZde_r(i,j ,k2),0.0_r8) cff3=MAX(dZde_r(i,j-1,k2),0.0_r8) cff4=MAX(dZde_r(i,j ,k1),0.0_r8) !^ tl_FZ(i,j,k2)=tl_FZ(i,j,k2)+ & !^ & cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j-1,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j-1,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAde(i,j ,k1))) !^ adfac=cff*ad_FZ(i,j,k2) ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAde(i,j-1,k1)=ad_dAde(i,j-1,k1)-cff1*adfac ad_dAde(i,j ,k2)=ad_dAde(i,j ,k2)-cff2*adfac ad_dAde(i,j-1,k2)=ad_dAde(i,j-1,k2)-cff3*adfac ad_dAde(i,j ,k1)=ad_dade(i,j ,k1)-cff4*adfac ! cff1=MIN(dZdx_p(i ,j,k1),0.0_r8) cff2=MIN(dZdx_p(i+1,j,k2),0.0_r8) cff3=MAX(dZdx_p(i ,j,k2),0.0_r8) cff4=MAX(dZdx_p(i+1,j,k1),0.0_r8) !^ tl_FZ(i,j,k2)=cff* & !^ & (cff1*(cff1*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k1))+ & !^ & cff2*(cff2*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i+1,j,k2))+ & !^ & cff3*(cff3*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i ,j,k2))+ & !^ & cff4*(cff4*tl_dAdz(i,j,k2)- & !^ & tl_dAdx(i+1,j,k1))) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dAdx(i ,j,k1)=ad_dAdx(i ,j,k1)-cff1*adfac ad_dAdx(i+1,j,k2)=ad_dAdx(i+1,j,k2)-cff2*adfac ad_dAdx(i ,j,k2)=ad_dAdx(i ,j,k2)-cff3*adfac ad_dAdx(i+1,j,k1)=ad_dAdx(i+1,j,k1)-cff4*adfac ad_FZ(i,j,k2)=0.0_r8 END DO END DO END IF DO j=JstrV-1,Jend DO i=Istr,Iend cff=Kh(i,j)*om_r(i,j) cff1=MIN(dZde_r(i,j,k1),0.0_r8) cff2=MAX(dZde_r(i,j,k1),0.0_r8) !^ tl_FE(i,j)=cff* & !^ & Hz(i,j,k)* & !^ & (tl_dAde(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i,j ,k1)+ & !^ & tl_dAdz(i,j+1,k2))+ & !^ & cff2*(tl_dAdz(i,j ,k2)+ & !^ & tl_dAdz(i,j+1,k1)))) !^ adfac=cff*Hz(i,j,k)*ad_FE(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAde(i,j,k1)=ad_dAde(i,j,k1)+adfac ad_dAdz(i,j ,k1)=ad_dAdz(i,j ,k1)-adfac1 ad_dAdz(i,j+1,k2)=ad_dAdz(i,j+1,k2)-adfac1 ad_dAdz(i,j ,k2)=ad_dAdz(i,j ,k2)-adfac2 ad_dAdz(i,j+1,k1)=ad_dAdz(i,j+1,k1)-adfac2 ad_FE(i,j)=0.0_r8 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 cff=0.0625_r8*(Kh(i-1,j-1)+Kh(i-1,j)+ & & Kh(i ,j-1)+Kh(i ,j))*on_p(i,j) cff1=MIN(dZdx_p(i,j,k1),0.0_r8) cff2=MAX(dZdx_p(i,j,k1),0.0_r8) !^ tl_FX(i,j)=cff* & !^ & (Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & !^ & Hz(i ,j-1,k)+Hz(i ,j,k))* & !^ & (tl_dAdx(i,j,k1)- & !^ & 0.5_r8*(cff1*(tl_dAdz(i-1,j,k1)+ & !^ & tl_dAdz(i ,j,k2))+ & !^ & cff2*(tl_dAdz(i-1,j,k2)+ & !^ & tl_dAdz(i ,j,k1)))) !^ adfac=cff*(Hz(i-1,j-1,k)+Hz(i-1,j,k)+ & & Hz(i ,j-1,k)+Hz(i ,j,k))*ad_FX(i,j) adfac1=adfac*0.5_r8*cff1 adfac2=adfac*0.5_r8*cff2 ad_dAdx(i,j,k1)=ad_dAdx(i,j,k1)+adfac ad_dAdz(i-1,j,k1)=ad_dAdz(i-1,j,k1)-adfac1 ad_dAdz(i ,j,k2)=ad_dAdz(i ,j,k2)-adfac1 ad_dAdz(i-1,j,k2)=ad_dAdz(i-1,j,k2)-adfac2 ad_dAdz(i ,j,k1)=ad_dAdz(i ,j,k1)-adfac2 ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_FZ(i,j,k2)=0.0_r8 !^ ad_FZ(i,j,k2)=0.0_r8 !^ tl_dAdz(i,j,k2)=0.0_r8 !^ ad_dAdz(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=JstrV-1,Jend+1 DO i=Istr-1,Iend+1 cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) # ifdef MASKING !^ tl_dAdz(i,j,k2)=tl_dAdz(i,j,k2)*vmask(i,j) !^ ad_dAdz(i,j,k2)=ad_dAdz(i,j,k2)*vmask(i,j) # endif !^ tl_dAdz(i,j,k2)=cff*(tl_Awrk(i,j,k+1,Nold)- & !^ & tl_Awrk(i,j,k ,Nold)) !^ adfac=cff*ad_dAdz(i,j,k2) ad_Awrk(i,j,k ,Nold)=ad_Awrk(i,j,k ,Nold)-adfac ad_Awrk(i,j,k+1,Nold)=ad_Awrk(i,j,k+1,Nold)+adfac ad_dAdz(i,j,k2)=0.0_r8 END DO END DO END IF IF (k.lt.N(ng)) THEN DO j=JstrV-1,Jend DO i=Istr,Iend # ifdef MASKING !^ tl_dAde(i,j,k2)=tl_dAde(i,j,k2)*rmask(i,j) !^ ad_dAde(i,j,k2)=ad_dAde(i,j,k2)*rmask(i,j) !^ tl_dAde(i,j,k2)=pn(i,j)* & !^ & (tl_Awrk(i,j+1,k+1,Nold)*vmask(i,j+1)- & !^ & tl_Awrk(i,j ,k+1,Nold)*vmask(i,j )) !^ adfac=pn(i,j)*ad_dAde(i,j,k2) ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)- & & vmask(i,j )*adfac ad_Awrk(i,j+1,k+1,Nold)=ad_Awrk(i,j+1,k+1,Nold)+ & & vmask(i,j+1)*adfac ad_dAde(i,j,k2)=0.0_r8 # else !^ tl_dAde(i,j,k2)=pn(i,j)*(tl_Awrk(i,j+1,k+1,Nold)- & !^ & tl_Awrk(i,j ,k+1,Nold)) !^ adfac=pn(i,j)*ad_dAde(i,j,k2) ad_Awrk(i,j ,k+1,Nold)=ad_Awrk(i,j ,k+1,Nold)- & & adfac ad_Awrk(i,j+1,k+1,Nold)=ad_Awrk(i,j+1,k+1,Nold)+ & & adfac ad_dAde(i,j,k2)=0.0_r8 # endif END DO END DO DO j=JstrV,Jend DO i=Istr,Iend+1 cff=0.25_r8*(pm(i-1,j-1)+pm(i-1,j)+ & & pm(i ,j-1)+pm(i ,j)) # ifdef MASKING !^ tl_dAdx(i,j,k2)=tl_dAdx(i,j,k2)*pmask(i,j) !^ ad_dAdx(i,j,k2)=ad_dAdx(i,j,k2)*pmask(i,j) !^ tl_dAdx(i,j,k2)=cff* & !^ & (tl_Awrk(i ,j,k+1,Nold)*vmask(i ,j)- & !^ & tl_Awrk(i-1,j,k+1,Nold)*vmask(i-1,j)) !^ adfac=cff*ad_dAdx(i,j,k2) ad_Awrk(i-1,j,k+1,Nold)=ad_Awrk(i-1,j,k+1,Nold)- & & vmask(i-1,j)*adfac ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)+ & & vmask(i ,j)*adfac ad_dAdx(i,j,k2)=0.0_r8 # else !^ tl_dAdx(i,j,k2)=cff*(tl_Awrk(i ,j,k+1,Nold)- & !^ & tl_Awrk(i-1,j,k+1,Nold)) !^ adfac=cff*ad_dAdx(i,j,k2) ad_Awrk(i-1,j,k+1,Nold)=ad_Awrk(i-1,j,k+1,Nold)- & & adfac ad_Awrk(i ,j,k+1,Nold)=ad_Awrk(i ,j,k+1,Nold)+ & & adfac ad_dAdx(i,j,k2)=0.0_r8 # endif END DO END DO END IF ! ! Compute new storage recursive indices. ! kt=k2 k2=k1 k1=kt END DO K_LOOP # else ! ! 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 # 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,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 # endif 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 # ifdef DISTRIBUTE !^ 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) # endif !^ 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 #endif END MODULE ad_conv_3d_mod