#include "cppdefs.h" #undef AD_SUPPORTED MODULE ad_step3d_t_mod #if !defined TS_FIXED && (defined ADJOINT && defined SOLVE3D) ! !git $Id$ !svn $Id: ad_step3d_t.F 1151 2023-02-09 03:08:53Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! This routine time-steps adjoint tracer equations. Notice that ! ! advective and diffusive terms are time-stepped differently. ! ! It applies the corrector time-step for horizontal and vertical ! ! advection, vertical diffusion, nudging if necessary, and lateral ! ! boundary conditions. ! ! ! ! A different horizontal/vertical advection scheme is allowed for ! ! each tracer. If the HSIMT monotonic scheme, it is applied to both ! ! horizontal and vertical advective fluxes. It is not coded yet, it ! ! is problematic since it requires NghostPoints=3. ! ! ! ! The MPDATA scheme is not supported in the TLM, RPM, and ADM. ! ! ! ! Notice that at input the tracer arrays have: ! ! ! ! t(:,:,:,nnew,:) m Tunits n+1 horizontal/vertical diffusion ! ! terms plus source/sink terms ! ! (biology, sediment), if any ! ! ! ! t(:,:,:,3 ,:) Tunits n+1/2 advective terms and vertical ! ! diffusion predictor step ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: ad_step3d_t ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_step3d_t (ng, tile) !*********************************************************************** ! USE mod_param # ifdef DIAGNOSTICS_TS !! USE mod_diags # endif USE mod_grid USE mod_mixing USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & __FILE__ ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iADM, 35, __LINE__, MyFile) # endif CALL ad_step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & # ifdef MASKING & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & # endif # ifdef WET_DRY & GRID(ng) % rmask_wet, & & GRID(ng) % umask_wet, & & GRID(ng) % vmask_wet, & # endif & GRID(ng) % omn, & & GRID(ng) % om_u, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % on_v, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % ad_Hz, & & GRID(ng) % Huon, & & GRID(ng) % ad_Huon, & & GRID(ng) % Hvom, & & GRID(ng) % ad_Hvom, & & GRID(ng) % z_r, & & GRID(ng) % ad_z_r, & & MIXING(ng) % Akt, & & MIXING(ng) % ad_Akt, & & OCEAN(ng) % W, & & OCEAN(ng) % ad_W, & # if defined FLOATS_NOT_YET && defined FLOAT_VWALK & MIXING(ng) % dAktdz, & # endif # ifdef DIAGNOSTICS_TS !! & DIAGS(ng) % DiaTwrk, & # endif & OCEAN(ng) % t, & & OCEAN(ng) % ad_t) # ifdef PROFILE CALL wclock_off (ng, iADM, 35, __LINE__, MyFile) # endif ! RETURN END SUBROUTINE ad_step3d_t ! !*********************************************************************** SUBROUTINE ad_step3d_t_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & omn, om_u, om_v, on_u, on_v, & & pm, pn, & & Hz, ad_Hz, & & Huon, ad_Huon, & & Hvom, ad_Hvom, & & z_r, ad_z_r, & & Akt, ad_Akt, & & W, ad_W, & # if defined FLOATS_NOT_YET && defined FLOAT_VWALK & dAktdz, & # endif # ifdef DIAGNOSTICS_TS !! & DiaTwrk, & # endif & t, & & ad_t) !*********************************************************************** ! USE mod_param USE mod_clima USE mod_ncparam USE mod_scalars USE mod_sources ! USE ad_exchange_3d_mod, ONLY : ad_exchange_r3d_tile # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange3d USE mp_exchange_mod, ONLY : ad_mp_exchange4d # endif USE ad_t3dbc_mod, ONLY : ad_t3dbc_tile ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs, nstp, nnew ! # ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif # ifdef WET_DRY real(r8), intent(in) :: rmask_wet(LBi:,LBj:) real(r8), intent(in) :: umask_wet(LBi:,LBj:) real(r8), intent(in) :: vmask_wet(LBi:,LBj:) # endif real(r8), intent(in) :: omn(LBi:,LBj:) real(r8), intent(in) :: om_u(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: on_v(LBi:,LBj:) real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: Huon(LBi:,LBj:,:) real(r8), intent(in) :: Hvom(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) # ifdef SUN real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # else real(r8), intent(in) :: Akt(LBi:,LBj:,0:,:) real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) # endif real(r8), intent(in) :: W(LBi:,LBj:,0:) # ifdef DIAGNOSTICS_TS !! real(r8), intent(inout) :: DiaTwrk(LBi:,LBj:,:,:,:) # endif real(r8), intent(inout) :: ad_Hz(LBi:,LBj:,:) real(r8), intent(inout) :: ad_Huon(LBi:,LBj:,:) real(r8), intent(inout) :: ad_Hvom(LBi:,LBj:,:) real(r8), intent(inout) :: ad_z_r(LBi:,LBj:,:) # ifdef SUN real(r8), intent(inout) :: ad_Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) # else real(r8), intent(inout) :: ad_Akt(LBi:,LBj:,0:,:) # endif real(r8), intent(inout) :: ad_W(LBi:,LBj:,0:) # ifdef SUN real(r8), intent(inout) :: ad_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # else real(r8), intent(inout) :: ad_t(LBi:,LBj:,:,:,:) # endif # if defined FLOATS_NOT_YET && defined FLOAT_VWALK real(r8), intent(out) :: dAktdz(LBi:,LBj:,:) # endif # else # 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 # ifdef WET_DRY real(r8), intent(in) :: rmask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: umask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask_wet(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: omn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Huon(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Hvom(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(in) :: W(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef DIAGNOSTICS_TS !! real(r8), intent(inout) :: DiaTwrk(LBi:UBi,LBj:UBj,N(ng),NT(ng), & !! & NDT) # endif real(r8), intent(inout) :: ad_Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_Huon(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_Hvom(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(inout) :: ad_W(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(inout) :: ad_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # if defined FLOATS_NOT_YET && defined FLOAT_VWALK real(r8), intent(out) :: dAktdz(LBi:UBi,LBj:UBj,N(ng)) # endif # endif ! ! Local variable declarations. ! logical :: LapplySrc, Lhsimt ! integer :: JminT, JmaxT integer :: Isrc, Jsrc integer :: i, ic, is, itrc, j, k, ltrc # if defined AGE_MEAN && defined T_PASSIVE integer :: iage # endif # ifdef DIAGNOSTICS_TS integer :: idiag # endif real(r8), parameter :: eps = 1.0E-16_r8 real(r8) :: cff, cff1, cff2, cff3 real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3 real(r8) :: adfac, adfac1, adfac2 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC # ifdef SPLINES_VDIFF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC1 # endif real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_BC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_FC real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: curv real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad 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) :: ad_curv real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_grad real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: oHz real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: ad_oHz # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! Lhsimt =ANY(ad_Hadvection(:,ng)%HSIMT).and. & & ANY(ad_Vadvection(:,ng)%HSIMT) ! ! Initialize. ! ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_cff3=0.0_r8 DO j=JminS,JmaxS DO i=IminS,ImaxS ad_FE(i,j)=0.0_r8 ad_FX(i,j)=0.0_r8 ad_curv(i,j)=0.0_r8 ad_grad(i,j)=0.0_r8 END DO DO k=1,N(ng) DO i=IminS,ImaxS ad_oHz(i,j,k)=0.0_r8 END DO END DO END DO DO k=0,N(ng) DO i=IminS,ImaxS ad_CF(i,k)=0.0_r8 ad_BC(i,k)=0.0_r8 ad_DC(i,k)=0.0_r8 ad_FC(i,k)=0.0_r8 END DO END DO # if defined FLOATS_NOT_YET && defined FLOAT_VWALK ! !----------------------------------------------------------------------- ! Compute vertical gradient in vertical T-diffusion coefficient for ! floats random walk. !----------------------------------------------------------------------- ! ! Exchange boundary data. ! # ifdef DISTRIBUTE CALL mp_exchange3d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & dAktdz) # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & dAktdz) END IF ! DO j=JstrR,JendR DO i=IstrR,IendR DO k=1,N(ng) dAktdz(i,j,k)=(Akt(i,j,k,1)-Akt(i,j,k-1,1))/Hz(i,j,k) END DO END DO END DO # endif ! !----------------------------------------------------------------------- ! Apply adjoint lateral boundary conditions and, if appropriate, nudge ! to tracer data and apply Land/Sea mask. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE ! Adjoint of exchange boundary data. ! !^ CALL mp_exchange4d (ng, tile, iTLM, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_t(:,:,:,nnew,:)) !^ CALL ad_mp_exchange4d (ng, tile, iADM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_t(:,:,:,nnew,:)) ! # endif ! ! Initialize tracer counter index. The "tclm" array is only allocated ! to the NTCLM fields that need to be processed. This is done to ! reduce memory. ! ic=0 ! DO itrc=1,NT(ng) ! ! Set compact reduced memory tracer index for nudging coefficients and ! climatology arrays. ! IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN ic=ic+1 END IF ! ! Apply adjoint periodic boundary conditions. ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_t(:,:,:,nnew,itrc)) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_t(:,:,:,nnew,itrc)) END IF # ifdef DIAGNOSTICS_TS !! !! Compute time-rate-of-change diagnostic term. !! !! DO k=1,N(ng) !! DO j=JstrR,JendR !! DO i=IstrR,IendR !! DiaTwrk(i,j,k,itrc,iTrate)=t(i,j,k,nnew,itrc)- & !! & t(i,j,k,nstp,itrc) !! DiaTwrk(i,j,k,itrc,iTrate)=t(i,j,k,nnew,itrc)- & !! & DiaTwrk(i,j,k,itrc,iTrate) !! END DO !! END DO !! END DO # endif # ifdef MASKING ! ! Apply Land/Sea mask. ! DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)*rmask(i,j) !^ ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)*rmask(i,j) END DO END DO END DO # endif ! ! Adjoint of nudge towards tracer climatology. ! IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN DO k=1,N(ng) DO j=JstrR,JendR DO i=IstrR,IendR !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)- & !^ & dt(ng)* & !^ & CLIMA(ng)%Tnudgcof(i,j,k,ic)* & !^ & tl_t(i,j,k,nnew,itrc) !^ ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)- & & dt(ng)* & & CLIMA(ng)%Tnudgcof(i,j,k,ic)* & & ad_t(i,j,k,nnew,itrc) END DO END DO END DO END IF ! ! Set adjoint lateral boundary conditions. ! !^ CALL tl_t3dbc_tile (ng, tile, itrc, ic, & !^ & LBi, UBi, LBj, UBj, N(ng), NT(ng), & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & nstp, nnew, & !^ & tl_t) !^ CALL ad_t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, nnew, & & ad_t) END DO # if defined AGE_MEAN && defined T_PASSIVE ! !----------------------------------------------------------------------- ! If inert passive tracer and Mean Age, compute age concentration (even ! inert index) forced by the right-hand-side term that is concentration ! of an associated conservative passive tracer (odd inert index). Mean ! Age is age concentration divided by conservative passive tracer ! concentration. Code implements NPT/2 mean age tracer pairs. ! ! Implemented and tested by W.G. Zhang and J. Wilkin. See following ! reference for details. ! ! Zhang et al. (2010): Simulation of water age and residence time in ! the New York Bight, JPO, 40,965-982, doi:10.1175/2009JPO4249.1 !----------------------------------------------------------------------- ! DO itrc=1,NPT,2 iage=inert(itrc+1) ! even inert tracer index DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend IF ((ad_Hadvection(inert(itrc),ng)%MPDATA).and. & & (ad_Vadvection(inert(itrc),ng)%MPDATA)) THEN CONTINUE ! not supported ELSE !^ tl_t(i,j,k,nnew,iage)=tl_t(i,j,k,nnew,iage)+ & !^ & dt(ng)* & !^ & tl_t(i,j,k,3,inert(itrc)) !^ ad_t(i,j,k,3,inert(itrc))=ad_t(i,j,k,3,inert(itrc))+ & & dt(ng)*ad_t(i,j,k,nnew,iage) END IF END DO END DO END DO END DO # endif ! !----------------------------------------------------------------------- ! Time-step adjoint vertical diffusion term. !----------------------------------------------------------------------- ! ! Compute BASIC STATE reciprocal thickness, 1/Hz. ! IF (Lhsimt) THEN DO k=1,N(ng) DO j=Jstrm2,Jendp2 DO i=Istrm2,Iendp2 oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO ELSE DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO END IF ! ! Compute adjoint vertical diffusion term. ! J_LOOP2 : DO j=Jstr,Jend ! start pipelined J-loop DO itrc=1,NT(ng) ltrc=MIN(NAT,itrc) # ifdef SPLINES_VDIFF IF (.not.((ad_Hadvection(itrc,ng)%MPDATA).and. & & (ad_Vadvection(itrc,ng)%MPDATA))) THEN ! ! Use conservative, parabolic spline reconstruction of BASIC STATE ! vertical diffusion derivatives. Solve BASIC STATE tridiagonal ! system. ! 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 )- & & dt(ng)*Akt(i,j,k-1,ltrc)*oHz(i,j,k ) CF(i,k)=cff1*Hz(i,j,k+1)- & & dt(ng)*Akt(i,j,k+1,ltrc)*oHz(i,j,k+1) END DO END DO DO i=Istr,Iend CF(i,0)=0.0_r8 DC(i,0)=0.0_r8 END DO ! ! LU decomposition and forward substitution. ! 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))+ & & dt(ng)*Akt(i,j,k,ltrc)*(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) DC(i,k)=cff*(t(i,j,k+1,nnew,itrc)-t(i,j,k,nnew,itrc)- & & FC(i,k)*DC(i,k-1)) END DO END DO ! ! Backward substitution. Save DC for the adjoint code below. ! DO i=Istr,Iend DC(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) END DO END DO ! ! Multiply DC by Akt and save it on DC1. ! DO k=0,N(ng) DO i=Istr,Iend DC1(i,k)=DC(i,k)*Akt(i,j,k,ltrc) END DO END DO ! ! Time-step adjoint diffusion term. ! !^ DO k=1,N(ng) !^ DO k=N(ng),1,-1 DO i=Istr,Iend # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)+ & !! & cff1 # endif !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)+tl_cff1 !^ ad_cff1=ad_cff1+ad_t(i,j,k,nnew,itrc) !^ tl_cff1=dt(ng)*(tl_oHz(i,j,k)*(DC(i,k)-DC(i,k-1))+ & !^ & oHz(i,j,k)*(tl_DC(i,k)-tl_DC(i,k-1))) !^ use DC1 instead adfac=dt(ng)*ad_cff1 adfac1=adfac*oHz(i,j,k) ad_DC(i,k-1)=ad_DC(i,k-1)-adfac1 ad_DC(i,k )=ad_DC(i,k )+adfac1 ad_oHz(i,j,k)=ad_oHz(i,j,k)+(DC1(i,k)-DC1(i,k-1))*adfac ad_cff1=0.0_r8 !^ tl_DC(i,k)=tl_DC(i,k)*Akt(i,j,k,ltrc)+ & !^ & DC(i,k)*tl_Akt(i,j,k,ltrc) !^ use DC here ad_DC(i,k)=ad_DC(i,k)*Akt(i,j,k,ltrc) ad_Akt(i,j,k,ltrc)=ad_Akt(i,j,k,ltrc)+DC(i,k)*ad_DC(i,k) END DO END DO ! ! Adjoint back substitution ! 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. ! cff1=1.0_r8/3.0_r8 DO k=N(ng)-1,1,-1 DO i=Istr,Iend BC(i,k)=cff1*(Hz(i,j,k)+Hz(i,j,k+1))+ & & dt(ng)*Akt(i,j,k,ltrc)*(oHz(i,j,k)+oHz(i,j,k+1)) cff=1.0_r8/(BC(i,k)-FC(i,k)*CF(i,k-1)) !^ tl_DC(i,k)=cff*(tl_t(i,j,k+1,nnew,itrc)- & !^ & tl_t(i,j,k ,nnew,itrc)- & !^ & (tl_FC(i,k)*DC(i,k-1)+ & !^ & tl_BC(i,k)*DC(i,k )+ & !^ & tl_CF(i,k)*DC(i,k+1))- & !^ & FC(i,k)*tl_DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,k)*adfac ad_CF(i,k)=ad_CF(i,k)-DC(i,k+1)*adfac ad_BC(i,k)=ad_BC(i,k)-DC(i,k )*adfac ad_FC(i,k)=ad_FC(i,k)-DC(i,k-1)*adfac ad_t(i,j,k ,nnew,itrc)=ad_t(i,j,k ,nnew,itrc)-adfac ad_t(i,j,k+1,nnew,itrc)=ad_t(i,j,k+1,nnew,itrc)+adfac ad_DC(i,k)=0.0_r8 !^ tl_BC(i,k)=cff1*(tl_Hz(i,j,k)+tl_Hz(i,j,k+1))+ & !^ & dt(ng)*(tl_Akt(i,j,k,ltrc)* & !^ & (oHz(i,j,k)+oHz(i,j,k+1))+ & !^ & Akt(i,j,k,ltrc)* & !^ & (tl_oHz(i,j,k)+tl_oHz(i,j,k+1))) !^ adfac=cff1*ad_BC(i,k) adfac1=dt(ng)*ad_BC(i,k) adfac2=adfac1*Akt(i,j,k,ltrc) ad_oHz(i,j,k )=ad_oHz(i,j,k )+adfac2 ad_oHz(i,j,k+1)=ad_oHz(i,j,k+1)+adfac2 ad_Akt(i,j,k,ltrc)=ad_Akt(i,j,k,ltrc)+ & & (oHz(i,j,k)+oHz(i,j,k+1))*adfac1 ad_Hz(i,j,k )=ad_Hz(i,j,k )+adfac ad_Hz(i,j,k+1)=ad_Hz(i,j,k+1)+adfac ad_BC(i,k)=0.0_r8 END DO END DO ! ! Use conservative, parabolic spline reconstruction of tangent linear ! vertical diffusion derivatives. Then, time step vertical diffusion ! term implicitly. ! ! Note that the BASIC STATE "t" must in Tunits when used in the ! tangent spline routine below, which it does in the present code. ! DO i=Istr,Iend !^ tl_CF(i,0)=0.0_r8 !^ ad_CF(i,0)=0.0_r8 !^ tl_DC(i,0)=0.0_r8 !^ ad_DC(i,0)=0.0_r8 END DO cff1=1.0_r8/6.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_CF(i,k)=cff1*tl_Hz(i,j,k+1)- & !^ & dt(ng)*(tl_Akt(i,j,k+1,ltrc)*oHz(i,j,k+1)+ & !^ & Akt(i,j,k+1,ltrc)*tl_oHz(i,j,k+1)) !^ adfac=dt(ng)*ad_CF(i,k) ad_oHz(i,j,k+1)=ad_oHz(i,j,k+1)- & & Akt(i,j,k+1,ltrc)*adfac ad_Akt(i,j,k+1,ltrc)=ad_Akt(i,j,k+1,ltrc)- & & oHz(i,j,k+1)*adfac ad_Hz(i,j,k+1)=ad_Hz(i,j,k+1)+cff1*ad_CF(i,k) ad_CF(i,k)=0.0_r8 !^ tl_FC(i,k)=cff1*tl_Hz(i,j,k )- & !^ & dt(ng)*(tl_Akt(i,j,k-1,ltrc)*oHz(i,j,k )+ & !^ & Akt(i,j,k-1,ltrc)*tl_oHz(i,j,k )) !^ adfac=dt(ng)*ad_FC(i,k) ad_oHz(i,j,k )=ad_oHz(i,j,k )- & & Akt(i,j,k-1,ltrc)*adfac ad_Akt(i,j,k-1,ltrc)=ad_Akt(i,j,k-1,ltrc)- & & oHz(i,j,k )*adfac ad_Hz(i,j,k )=ad_Hz(i,j,k )+cff1*ad_FC(i,k) ad_FC(i,k)=0.0_r8 END DO END DO ELSE # endif ! ! Compute off-diagonal BASIC STATE coefficients FC [lambda*dt*Akt/Hz] ! for the implicit vertical diffusion terms at future time step, ! located at horizontal RHO-points and vertical W-points. ! Also set FC at the top and bottom levels. ! cff=-dt(ng)*lambda DO k=1,N(ng)-1 DO i=Istr,Iend cff1=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) FC(i,k)=cff*cff1*Akt(i,j,k,ltrc) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ! Compute diagonal matrix coefficients BC. ! DO k=1,N(ng) DO i=Istr,Iend BC(i,k)=Hz(i,j,k)-FC(i,k)-FC(i,k-1) END DO END DO ! ! Compute new solution by back substitution. ! (DC is a tangent linear variable here). ! DO i=Istr,Iend cff=1.0_r8/BC(i,1) CF(i,1)=cff*FC(i,1) END DO DO k=2,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1)) CF(i,k)=cff*FC(i,k) END DO END DO !^ DO k=N(ng)-1,1,-1 !^ DO k=1,N(ng)-1 DO i=Istr,Iend # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iTvdif)=DiaTwrk(i,j,k,itrc,iTvdif)+ & !! & t(i,j,k,nnew,itrc)-cff1 # endif !^ tl_t(i,j,k,nnew,itrc)=DC(i,k) !^ ad_DC(i,k)=ad_DC(i,k)+ad_t(i,j,k,nnew,itrc) ad_t(i,j,k,nnew,itrc)=0.0_r8 !^ DC(i,k)=DC(i,k)-CF(i,k)*DC(i,k+1) !^ ad_DC(i,k+1)=-CF(i,k)*ad_DC(i,k) # ifdef DIAGNOSTICS_TS !! cff1=t(i,j,k,nnew,itrc)*oHz(i,j,k) # endif END DO END DO DO i=Istr,Iend # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,N(ng),itrc,iTvdif)= & !! & DiaTwrk(i,j,N(ng),itrc,iTvdif)+ & !! & t(i,j,N(ng),nnew,itrc)-cff1 # endif !^ tl_t(i,j,N(ng),nnew,itrc)=DC(i,N(ng)) !^ ad_DC(i,N(ng))=ad_DC(i,N(ng))+ad_t(i,j,N(ng),nnew,itrc) ad_t(i,j,N(ng),nnew,itrc)=0.0_r8 !^ DC(i,N(ng))=(DC(i,N(ng))-FC(i,N(ng)-1)*DC(i,N(ng)-1))/ & !^ & (BC(i,N(ng))-FC(i,N(ng)-1)*CF(i,N(ng)-1)) !^ adfac=ad_DC(i,N(ng))/ & & (BC(i,N(ng))-FC(i,N(ng)-1)*CF(i,N(ng)-1)) ad_DC(i,N(ng)-1)=ad_DC(i,N(ng)-1)-FC(i,N(ng)-1)*adfac ad_DC(i,N(ng) )=adfac END DO ! ! Solve the adjoint tridiagonal system. ! (DC is a tangent linear variable here). ! DO k=N(ng)-1,2,-1 DO i=Istr,Iend cff=1.0_r8/(BC(i,k)-FC(i,k-1)*CF(i,k-1)) !^ DC(i,k)=cff*(DC(i,k)-FC(i,k-1)*DC(i,k-1)) !^ adfac=cff*ad_DC(i,k) ad_DC(i,k-1)=ad_DC(i,k-1)-FC(i,k-1)*adfac ad_DC(i,k )=adfac END DO END DO DO i=Istr,Iend cff=1.0_r8/BC(i,1) !^ DC(i,1)=cff*DC(i,1) !^ ad_DC(i,1)=cff*ad_DC(i,1) END DO ! DO i=Istr,Iend !^ DC(i,N(ng))=tl_t(i,j,N(ng),nnew,itrc)- & !^ & (tl_FC(i,N(ng)-1)*t(i,j,N(ng)-1,nnew,itrc)+ & !^ & tl_BC(i,N(ng) )*t(i,j,N(ng) ,nnew,itrc)) !^ ad_BC(i,N(ng) )=-t(i,j,N(ng) ,nnew,itrc)*ad_DC(i,N(ng)) ad_FC(i,N(ng)-1)=-t(i,j,N(ng)-1,nnew,itrc)*ad_DC(i,N(ng)) ad_t(i,j,N(ng),nnew,itrc)=ad_DC(i,N(ng)) ad_DC(i,N(ng))=0.0_r8 !^ DC(i,1)=tl_t(i,j,1,nnew,itrc)- & !^ & (tl_BC(i,1)*t(i,j,1,nnew,itrc)+ & !^ & tl_FC(i,1)*t(i,j,2,nnew,itrc)) !^ ad_FC(i,1)=-t(i,j,2,nnew,itrc)*ad_DC(i,1) ad_BC(i,1)=-t(i,j,1,nnew,itrc)*ad_DC(i,1) ad_t(i,j,1,nnew,itrc)=ad_DC(i,1) ad_DC(i,1)=0.0_r8 END DO DO k=2,N(ng)-1 DO i=Istr,Iend !^ DC(i,k)=tl_t(i,j,k,nnew,itrc)- & !^ & (tl_FC(i,k-1)*t(i,j,k-1,nnew,itrc)+ & !^ & tl_BC(i,k )*t(i,j,k ,nnew,itrc)+ & !^ & tl_FC(i,k )*t(i,j,k+1,nnew,itrc)) !^ ad_FC(i,k-1)=ad_FC(i,k-1)- & & t(i,j,k-1,nnew,itrc)*ad_DC(i,k) ad_FC(i,k )=ad_FC(i,k )- & & t(i,j,k+1,nnew,itrc)*ad_DC(i,k) ad_BC(i,k)=ad_BC(i,k)- & & t(i,j,k ,nnew,itrc)*ad_DC(i,k) ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)+ad_DC(i,k) ad_DC(i,k)=0.0_r8 END DO END DO ! ! Compute diagonal matrix coefficients BC. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_BC(i,k)=tl_Hz(i,j,k)-tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_BC(i,k) ad_FC(i,k )=ad_FC(i,k )-ad_BC(i,k) ad_Hz(i,j,k)=ad_Hz(i,j,k)+ad_BC(i,k) ad_BC(i,k)=0.0_r8 END DO END DO ! ! Compute off-diagonal coefficients FC [lambda*dt*Akt/Hz] for the ! implicit vertical diffusion terms at future time step, located ! at horizontal RHO-points and vertical W-points. ! Also set FC at the top and bottom levels. ! ! NOTE: The original code solves the tridiagonal system A*t=r where ! A is a matrix and t and r are vectors. We need to solve the ! tangent linear C of this system which is A*tl_t+tl_A*t=tl_r. ! Here, tl_A*t and tl_r are known, so we must solve for tl_t ! by inverting A*tl_t=tl_r-tl_A*t. ! DO i=Istr,Iend !^ tl_FC(i,N(ng))=0.0_r8 !^ ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 END DO cff=-dt(ng)*lambda DO k=1,N(ng)-1 DO i=Istr,Iend cff1=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) !^ tl_FC(i,k)=cff*(tl_cff1*Akt(i,j,k,ltrc)+ & !^ & cff1*tl_Akt(i,j,k,ltrc)) !^ adfac=cff*ad_FC(i,k) ad_Akt(i,j,k,ltrc)=ad_Akt(i,j,k,ltrc)+cff1*adfac ad_cff1=ad_cff1+Akt(i,j,k,ltrc)*adfac ad_FC(i,k)=0.0_r8 !^ tl_cff1=-cff1*cff1*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k)) !^ adfac=-cff1*cff1*ad_cff1 ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac ad_cff1=0.0_r8 END DO END DO # ifdef SPLINES_VDIFF END IF # endif END DO END DO J_LOOP2 ! !----------------------------------------------------------------------- ! Adjoint of add tracer divergence due to cell-centered (LwSrc) point ! sources. !----------------------------------------------------------------------- ! ! When LTracerSrc is .true. the inflowing concentration is Tsrc. ! When LtracerSrc is .false. we add tracer mass to compensate for the ! added volume to keep the receiving cell concentration unchanged. ! J. Levin (Jupiter Intelligence Inc.) and J. Wilkin ! ! Dsrc(is) = 2, flow across grid cell w-face (positive or negative) ! IF (LwSrc(ng)) THEN DO itrc=1,NT(ng) IF (.not.((ad_Hadvection(itrc,ng)%MPDATA).and. & & (ad_Vadvection(itrc,ng)%MPDATA))) THEN DO is=1,Nsrc(ng) IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (((Istr.le.Isrc).and.(Isrc.le.Iend+1)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend+1))) THEN DO k=1,N(ng) cff=dt(ng)*pm(Isrc,Jsrc)*pn(Isrc,Jsrc) # ifdef SPLINES_VDIFF cff=cff*oHz(Isrc,Jsrc,k) # endif IF (LtracerSrc(itrc,ng)) THEN cff3=SOURCES(ng)%Tsrc(is,k,itrc) ELSE cff3=t(Isrc,Jsrc,k,3,itrc) END IF # ifdef SPLINES_VDIFF !^ tl_t(Isrc,Jsrc,k,nnew,itrc)= & !^ & tl_t(Isrc,Jsrc,k,nnew,itrc)+ & !^ & cff*(SOURCES(ng)%tl_Qsrc(is,k)* & !^ & cff3+ & !^ & SOURCES(ng)%Qsrc(is,k)* & !^ & tl_cff3)+ & !^ & tl_cff*SOURCES(ng)%Qsrc(is,k)* & !^ & cff3 !^ adfac=cff*ad_t(Isrc,Jsrc,k,nnew,itrc) SOURCES(ng)%ad_Qsrc(is,k)=SOURCES(ng)%ad_Qsrc(is,k)+& & cff3*adfac ad_cff3=ad_cff3+ & & SOURCES(ng)%Qsrc(is,k)*adfac ad_cff=ad_cff+ & & SOURCES(ng)%Qsrc(is,k)*cff3* & & ad_t(Isrc,Jsrc,k,nnew,itrc) # else !^ tl_t(Isrc,Jsrc,k,nnew,itrc)= & !^ & tl_t(Isrc,Jsrc,k,nnew,itrc)+ & !^ & cff*(SOURCES(ng)%tl_Qsrc(is,k)* & !^ & cff3+ & !^ & SOURCES(ng)%Qsrc(is,k)* & !^ & tl_cff3) !^ adfac=cff*ad_t(Isrc,Jsrc,k,nnew,itrc) SOURCES(ng)%ad_Qsrc(is,k)=SOURCES(ng)%ad_Qsrc(is,k)+& & cff3*adfac ad_cff3=ad_cff3+ & & SOURCES(ng)%Qsrc(is,k)*adfac # endif IF (LtracerSrc(itrc,ng)) THEN !^ tl_cff3=SOURCES(ng)%tl_Tsrc(is,k,itrc) !^ SOURCES(ng)%ad_Tsrc(is,k,itrc)= & & SOURCES(ng)%ad_Tsrc(is,k,itrc)+ & ad_cff3 ELSE !^ tl_cff3=tl_t(Isrc,Jsrc,k,3,itrc) !^ ad_t(Isrc,Jsrc,k,3,itrc)=ad_t(Isrc,Jsrc,k,3,itrc)+& & ad_cff3 END IF ad_cff3=0.0_r8 # ifdef SPLINES_VDIFF !^ tl_cff=cff*tl_oHz(Isrc,Jsrc,k) !^ ad_oHz(Isrc,Jsrc,k)=ad_oHz(Isrc,Jsrc,k)+ & & cff*ad_cff ad_cff=0.0_r8 # endif END DO END IF END IF END DO END IF END DO END IF ! !----------------------------------------------------------------------- ! Time-step adjoint vertical advection term. !----------------------------------------------------------------------- ! T_LOOP2 : DO itrc=1,NT(ng) IF (ad_Hadvection(itrc,ng)%MPDATA) THEN JminT=JstrVm2 JmaxT=Jendp2i ELSE JminT=Jstr JmaxT=Jend END IF ! J_LOOP1 : DO j=JminT,JmaxT ! start pipelined J-loop ! ! Time-step adjoint vertical advection term. Compute first BASIC ! STATE vertical advection flux, FC. ! VADV_FLUX_BASIC : IF (ad_Vadvection(itrc,ng)%SPLINES) THEN ! ! Build conservative parabolic splines for the BASIC STATE vertical ! derivatives "FC" of the tracer. Then, the interfacial "FC" values ! are converted to vertical advective flux. ! DO i=Istr,Iend # ifdef NEUMANN FC(i,0)=1.5_r8*t(i,j,1,3,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,3,itrc) CF(i,1)=1.0_r8 # endif END DO DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*Hz(i,j,k)+ & & Hz(i,j,k+1)*(2.0_r8-CF(i,k))) CF(i,k+1)=cff*Hz(i,j,k) FC(i,k)=cff*(3.0_r8*(Hz(i,j,k )*t(i,j,k+1,3,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,3,itrc))- & & Hz(i,j,k+1)*FC(i,k-1)) END DO END DO DO i=Istr,Iend # ifdef NEUMANN FC(i,N(ng))=(3.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (2.0_r8-CF(i,N(ng))) # else FC(i,N(ng))=(2.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (1.0_r8-CF(i,N(ng))) # endif END DO DO k=N(ng)-1,0,-1 DO i=Istr,Iend FC(i,k)=FC(i,k)-CF(i,k+1)*FC(i,k+1) FC(i,k+1)=W(i,j,k+1)*FC(i,k+1) END DO END DO DO i=Istr,Iend FC(i,N(ng))=0.0_r8 FC(i,0)=0.0_r8 END DO ! ELSE IF (ad_Vadvection(itrc,ng)%AKIMA4) THEN ! ! Fourth-order, BASIC STATE Akima vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=t(i,j,k+1,3,itrc)- & & t(i,j,k ,3,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=FC(i,1) FC(i,N(ng))=FC(i,N(ng)-1) END DO DO k=1,N(ng) DO i=Istr,Iend cff=2.0_r8*FC(i,k)*FC(i,k-1) IF (cff.gt.eps) THEN CF(i,k)=cff/(FC(i,k)+FC(i,k-1)) ELSE CF(i,k)=0.0_r8 END IF END DO END DO cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & 0.5_r8*(t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc)- & & cff1*(CF(i,k+1)-CF(i,k))) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF (ad_Vadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, BASIC STATE central differences vertical advective ! flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & 0.5_r8*(t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc)) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*t(i,j,1,3,itrc) # else FC(i,0)=0.0_r8 # endif FC(i,N(ng))=0.0_r8 END DO ! ELSE IF (ad_Vadvection(itrc,ng)%MPDATA) THEN ! ! First_order, BASIC STATE upstream differences vertical advective ! flux. ! CONTINUE ! not supported ! ELSE IF (ad_Vadvection(itrc,ng)%HSIMT) THEN ! ! Third High-order Spatial Interpolation at the Middle Temporal level ! (HSIMT; Wu and Zhu, 2010) with a Total Variation Diminishing (TVD) ! limiter vertical advection flux (Tunits m3/s). ! CONTINUE ! not supported ! ELSE IF ((ad_Vadvection(itrc,ng)%CENTERED4).or. & & (ad_Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, BASIC STATE central differences vertical advective ! flux. (Not really needed, HGA). ! cff1=0.5_r8 cff2=7.0_r8/12.0_r8 cff3=1.0_r8/12.0_r8 DO k=2,N(ng)-2 DO i=Istr,Iend FC(i,k)=W(i,j,k)* & & (cff2*(t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc))- & & cff3*(t(i,j,k-1,3,itrc)+ & & t(i,j,k+2,3,itrc))) END DO END DO DO i=Istr,Iend # ifdef SED_MORPH FC(i,0)=W(i,j,0)*2.0_r8* & & (cff2*t(i,j,1,3,itrc)- & & cff3*t(i,j,2,3,itrc)) # else FC(i,0)=0.0_r8 # endif FC(i,1)=W(i,j,1)* & & (cff1*t(i,j,1,3,itrc)+ & & cff2*t(i,j,2,3,itrc)- & & cff3*t(i,j,3,3,itrc)) FC(i,N(ng)-1)=W(i,j,N(ng)-1)* & & (cff1*t(i,j,N(ng) ,3,itrc)+ & & cff2*t(i,j,N(ng)-1,3,itrc)- & & cff3*t(i,j,N(ng)-2,3,itrc)) FC(i,N(ng))=0.0_r8 END DO END IF VADV_FLUX_BASIC ! ! Time-step vertical advection term. # ifdef SPLINES_VDIFF ! The BASIC STATE "t" used below must be in transport units, but "t" ! retrived is in Tunits so we multiply by "Hz". # endif ! VADV_STEPPING : IF (ad_Vadvection(itrc,ng)%MPDATA) THEN CONTINUE ! not supported ELSE DO i=Istr,Iend CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO DO k=1,N(ng) DO i=Istr,Iend cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iTvadv)=-cff1 !! DO idiag=1,NDT !! DiaTwrk(i,j,k,itrc,idiag)=DiaTwrk(i,j,k,itrc,idiag)* & !! & oHz(i,j,k) !! END DO # endif # ifdef SPLINES_VDIFF !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)* & !^ & oHz(i,j,k)+ & !^ & (t(i,j,k,nnew,itrc)*Hz(i,j,k))* & !^ & tl_oHz(i,j,k) !^ ad_oHz(i,j,k)=ad_oHz(i,j,k)+ & & (t(i,j,k,nnew,itrc)*Hz(i,j,k))* & & ad_t(i,j,k,nnew,itrc) ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)*oHz(i,j,k) # endif !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)-tl_cff1 !^ ad_cff1=ad_cff1-ad_t(i,j,k,nnew,itrc) !^ tl_cff1=CF(i,0)*(tl_FC(i,k)-tl_FC(i,k-1)) !^ adfac=CF(i,0)*ad_cff1 ad_FC(i,k-1)=ad_FC(i,k-1)-adfac ad_FC(i,k )=ad_FC(i,k )+adfac ad_cff1=0.0_r8 END DO END DO END IF VADV_STEPPING ! ! Compute adjoint of vertical advection fluxes. ! VADV_FLUX : IF (ad_Vadvection(itrc,ng)%SPLINES) THEN ! ! Build conservative parabolic splines for the vertical derivatives ! "FC" of the tracer. Then, the interfacial "FC" values are ! converted to vertical advective flux. ! DO i=Istr,Iend # ifdef NEUMANN FC(i,0)=1.5_r8*t(i,j,1,3,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,3,itrc) CF(i,1)=1.0_r8 # endif END DO DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*Hz(i,j,k)+ & & Hz(i,j,k+1)*(2.0_r8-CF(i,k))) CF(i,k+1)=cff*Hz(i,j,k) FC(i,k)=cff*(3.0_r8*(Hz(i,j,k )*t(i,j,k+1,3,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,3,itrc))- & & Hz(i,j,k+1)*FC(i,k-1)) END DO END DO DO i=Istr,Iend # ifdef NEUMANN FC(i,N(ng))=(3.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (2.0_r8-CF(i,N(ng))) # else FC(i,N(ng))=(2.0_r8*t(i,j,N(ng),3,itrc)-FC(i,N(ng)-1))/ & & (1.0_r8-CF(i,N(ng))) # endif END DO DO k=N(ng)-1,0,-1 DO i=Istr,Iend FC(i,k)=FC(i,k)-CF(i,k+1)*FC(i,k+1) END DO END DO ! ! Now the adjoint splines code. ! DO i=Istr,Iend !^ tl_FC(i,N(ng))=0.0_r8 !^ ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 END DO ! ! Adjoint back substitution. ! DO k=0,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k+1)=tl_W(i,j,k+1)*FC(i,k+1)+ & !^ & W(i,j,k+1)*tl_FC(i,k+1) !^ ad_W(i,j,k+1)=ad_W(i,j,k+1)+FC(i,k+1)*ad_FC(i,k+1) ad_FC(i,k+1)=W(i,j,k+1)*ad_FC(i,k+1) !^ tl_FC(i,k)=tl_FC(i,k)-CF(i,k+1)*tl_FC(i,k+1) !^ ad_FC(i,k+1)=ad_FC(i,k+1)-CF(i,k+1)*ad_FC(i,k) END DO END DO DO i=Istr,Iend # ifdef NEUMANN !^ tl_FC(i,N(ng))=(3.0_r8*tl_t(i,j,N(ng),3,itrc)- & !^ & tl_FC(i,N(ng)-1))/ & !^ & (2.0_r8-CF(i,N(ng))) !^ adfac=ad_FC(i,N(ng))/(2.0_r8-CF(i,N(ng))) ad_t(i,j,N(ng),3,itrc)=ad_t(i,j,N(ng),3,itrc)+3.0_r8*adfac ad_FC(i,N(ng)-1)=ad_FC(i,N(ng)-1)-adfac ad_FC(i,N(ng))=0.0_r8 # else !^ tl_FC(i,N(ng))=(2.0_r8*tl_t(i,j,N(ng),3,itrc)- & !^ & tl_FC(i,N(ng)-1))/ & !^ & (1.0_r8-CF(i,N(ng))) !^ adfac=ad_FC(i,N(ng))/(1.0_r8-CF(i,N(ng))) ad_t(i,j,N(ng),3,itrc)=ad_t(i,j,N(ng),3,itrc)+2.0_r8*adfac ad_FC(i,N(ng)-1)=ad_FC(i,N(ng)-1)-adfac ad_FC(i,N(ng))=0.0 # endif END DO DO k=N(ng)-1,1,-1 DO i=Istr,Iend cff=1.0_r8/(2.0_r8*Hz(i,j,k)+ & & Hz(i,j,k+1)*(2.0_r8-CF(i,k))) !^ tl_FC(i,k)=cff* & !^ & (3.0_r8*(Hz(i,j,k )*tl_t(i,j,k+1,3,itrc)+ & !^ & Hz(i,j,k+1)*tl_t(i,j,k ,3,itrc)+ & !^ & tl_Hz(i,j,k )*t(i,j,k+1,3,itrc)+ & !^ & tl_Hz(i,j,k+1)*t(i,j,k ,3,itrc))- & !^ & (tl_Hz(i,j,k+1)*FC(i,k-1)+ & !^ & 2.0_r8*(tl_Hz(i,j,k )+ & !^ & tl_Hz(i,j,k+1))*FC(i,k)+ & !^ & tl_Hz(i,j,k )*FC(i,k+1))- & !^ & Hz(i,j,k+1)*tl_FC(i,k-1)) !^ adfac=cff*ad_FC(i,k) adfac1=3.0_r8*adfac adfac2=2.0_r8*adfac ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)+ & & Hz(i,j,k+1)*adfac1 ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+ & & Hz(i,j,k )*adfac1 ad_Hz(i,j,k )=ad_Hz(i,j,k )+ & & t(i,j,k+1,3,itrc)*adfac1- & & FC(i,k )*adfac2- & & FC(i,k+1)*adfac ad_Hz(i,j,k+1)=ad_Hz(i,j,k+1)+ & & t(i,j,k ,3,itrc)*adfac1- & & FC(i,k-1)*adfac- & & FC(i,k )*adfac2 ad_FC(i,k-1)=ad_FC(i,k-1)-Hz(i,j,k+1)*adfac ad_FC(i,k)=0.0_r8 END DO END DO DO i=Istr,Iend # ifdef NEUMANN !^ tl_FC(i,0)=1.5_r8*tl_t(i,j,1,3,itrc) !^ ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+1.5_r8*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # else !^ tl_FC(i,0)=2.0_r8*tl_t(i,j,1,3,itrc) !^ ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+2.0_r8*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # endif END DO ! ELSE IF (ad_Vadvection(itrc,ng)%AKIMA4) THEN ! ! Fourth-order, Akima adjoint vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=t(i,j,k+1,3,itrc)- & & t(i,j,k ,3,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=FC(i,1) FC(i,N(ng))=FC(i,N(ng)-1) END DO DO k=1,N(ng) DO i=Istr,Iend cff=2.0_r8*FC(i,k)*FC(i,k-1) IF (cff.gt.eps) THEN CF(i,k)=cff/(FC(i,k)+FC(i,k-1)) ELSE CF(i,k)=0.0_r8 END IF END DO END DO DO i=Istr,Iend !^ tl_FC(i,N(ng))=0.0_r8 !^ ad_FC(i,N(ng))=0.0_r8 # ifdef SED_MORPH !^ tl_FC(i,0)=tl_W(i,j,0)*t(i,j,1,3,itrc)+ & !^ & W(i,j,0)*tl_t(i,j,1,3,itrc) !^ ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+W(i,j,0)*ad_FC(i,0) ad_W(i,j,0)=ad_W(i,j,0)+t(i,j,1,3,itrc)*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # else !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 # endif END DO cff1=1.0_r8/3.0_r8 DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k)=0.5_r8* & !^ & (tl_W(i,j,k)* & !^ & (t(i,j,k ,3,itrc)+ & !^ & t(i,j,k+1,3,itrc)- & !^ & cff1*(CF(i,k+1)-CF(i,k)))+ & !^ & W(i,j,k)* & !^ & (tl_t(i,j,k ,3,itrc)+ & !^ & tl_t(i,j,k+1,3,itrc)- & !^ & cff1*(tl_CF(i,k+1)-tl_CF(i,k)))) !^ adfac=0.5_r8*ad_FC(i,k) adfac1=adfac*W(i,j,k) adfac2=adfac1*cff1 ad_CF(i,k )=ad_CF(i,k )+adfac2 ad_CF(i,k+1)=ad_CF(i,k+1)-adfac2 ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)+adfac1 ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+adfac1 ad_W(i,j,k)=ad_W(i,j,k)+ & & (t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc)- & & cff1*(CF(i,k+1)-CF(i,k)))*adfac ad_FC(i,k)=0.0_r8 END DO END DO DO k=1,N(ng) DO i=Istr,Iend cff=2.0_r8*FC(i,k)*FC(i,k-1) IF (cff.gt.eps) THEN !^ tl_CF(i,k)=((FC(i,k)+FC(i,k-1))*tl_cff- & !^ & cff*(tl_FC(i,k)+tl_FC(i,k-1)))/ & !^ & ((FC(i,k)+FC(i,k-1))*(FC(i,k)+FC(i,k-1))) !^ adfac=ad_CF(i,k)/ & & ((FC(i,k)+FC(i,k-1))*(FC(i,k)+FC(i,k-1))) adfac1=adfac*cff ad_FC(i,k-1)=ad_FC(i,k-1)-adfac1 ad_FC(i,k )=ad_FC(i,k )-adfac1 ad_cff=ad_cff+(FC(i,k)+FC(i,k-1))*adfac ad_CF(i,k)=0.0_r8 ELSE !^ tl_CF(i,k)=0.0_r8 !^ ad_CF(i,k)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_FC(i,k)*FC(i,k-1)+ & !^ & FC(i,k)*tl_FC(i,k-1)) !^ adfac=2.0_r8*ad_cff ad_FC(i,k-1)=ad_FC(i,k-1)+FC(i,k )*adfac ad_FC(i,k )=ad_FC(i,k )+FC(i,k-1)*adfac ad_cff=0.0_r8 END DO END DO DO i=Istr,Iend !^ tl_FC(i,N(ng))=tl_FC(i,N(ng)-1) !^ ad_FC(i,N(ng)-1)=ad_FC(i,N(ng)-1)+ad_FC(i,N(ng)) ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=tl_FC(i,1) !^ ad_FC(i,1)=ad_FC(i,1)+ad_FC(i,0) ad_FC(i,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k)=tl_t(i,j,k+1,3,itrc)- & !^ & tl_t(i,j,k ,3,itrc) !^ ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)-ad_FC(i,k) ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+ad_FC(i,k) ad_FC(i,k)=0.0_r8 END DO END DO ! ELSE IF (ad_Vadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, central differences adjoint vertical advective flux. ! DO i=Istr,Iend !^ tl_FC(i,N(ng))=0.0_r8 !^ ad_FC(i,N(ng))=0.0_r8 # ifdef SED_MORPH !^ tl_FC(i,0)=tl_W(i,j,0)*t(i,j,1,3,itrc)+ & !^ & W(i,j,0)*tl_t(i,j,1,3,itrc) !^ ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+W(i,j,0)*ad_FC(i,0) ad_W(i,j,0)=ad_W(i,j,0)+t(i,j,1,3,itrc)*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # else !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 # endif END DO DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k)=0.5_r8* & !^ & (tl_W(i,j,k)* & !^ & (t(i,j,k ,3,itrc)+ & !^ & t(i,j,k+1,3,itrc))+ & !^ & W(i,j,k)* & !^ & (tl_t(i,j,k ,3,itrc)+ & !^ & tl_t(i,j,k+1,3,itrc))) !^ adfac=0.5_r8*ad_FC(i,k) adfac1=adfac*W(i,j,k) ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)+adfac1 ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+adfac1 ad_W(i,j,k)=ad_W(i,j,k)+ & & (t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc))*adfac ad_FC(i,k)=0.0_r8 END DO END DO ! ELSE IF (ad_Vadvection(itrc,ng)%MPDATA) THEN ! ! First_order, upstream differences vertical advective flux. ! CONTINUE ! not supported ! ELSE IF (ad_Vadvection(itrc,ng)%HSIMT) THEN ! ! Third High-order Spatial Interpolation at the Middle Temporal level ! (HSIMT; Wu and Zhu, 2010) with a Total Variation Diminishing (TVD) ! limiter vertical advection flux (Tunits m3/s). ! CONTINUE ! not supported ! ELSE IF ((ad_Vadvection(itrc,ng)%CENTERED4).or. & & (ad_Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, central differences adjoint vertical advective flux. ! cff1=0.5_r8 cff2=7.0_r8/12.0_r8 cff3=1.0_r8/12.0_r8 DO i=Istr,Iend !^ tl_FC(i,N(ng))=0.0_r8 !^ ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,N(ng)-1)=tl_W(i,j,N(ng)-1)* & !^ & (cff1*t(i,j,N(ng) ,3,itrc)+ & !^ & cff2*t(i,j,N(ng)-1,3,itrc)- & !^ & cff3*t(i,j,N(ng)-2,3,itrc))+ & !^ & W(i,j,N(ng)-1)* & !^ & (cff1*tl_t(i,j,N(ng) ,3,itrc)+ & !^ & cff2*tl_t(i,j,N(ng)-1,3,itrc)- & !^ & cff3*tl_t(i,j,N(ng)-2,3,itrc)) !^ adfac=W(i,j,N(ng)-1)*ad_FC(i,N(ng)-1) ad_W(i,j,N(ng)-1)=ad_W(i,j,N(ng)-1)+ & & (cff1*t(i,j,N(ng) ,3,itrc)+ & & cff2*t(i,j,N(ng)-1,3,itrc)- & & cff3*t(i,j,N(ng)-2,3,itrc))* & & ad_FC(i,N(ng)-1) ad_t(i,j,N(ng)-2,3,itrc)=ad_t(i,j,N(ng)-2,3,itrc)- & & cff3*adfac ad_t(i,j,N(ng)-1,3,itrc)=ad_t(i,j,N(ng)-1,3,itrc)+ & & cff2*adfac ad_t(i,j,N(ng) ,3,itrc)=ad_t(i,j,N(ng) ,3,itrc)+ & & cff1*adfac ad_FC(i,N(ng)-1)=0.0_r8 !^ tl_FC(i,1)=tl_W(i,j,1)* & !^ & (cff1*t(i,j,1,3,itrc)+ & !^ & cff2*t(i,j,2,3,itrc)- & !^ & cff3*t(i,j,3,3,itrc))+ & !^ & W(i,j,1)* & !^ & (cff1*tl_t(i,j,1,3,itrc)+ & !^ & cff2*tl_t(i,j,2,3,itrc)- & !^ & cff3*tl_t(i,j,3,3,itrc)) !^ adfac=W(i,j,1)*ad_FC(i,1) ad_W(i,j,1)=ad_W(i,j,1)+ & & (cff1*t(i,j,1,3,itrc)+ & & cff2*t(i,j,2,3,itrc)- & & cff3*t(i,j,3,3,itrc))*ad_FC(i,1) ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+cff1*adfac ad_t(i,j,2,3,itrc)=ad_t(i,j,2,3,itrc)+cff2*adfac ad_t(i,j,3,3,itrc)=ad_t(i,j,3,3,itrc)-cff3*adfac ad_FC(i,1)=0.0_r8 # ifdef SED_MORPH !^ tl_FC(i,0)=2.0_r8* & !^ & (tl_W(i,j,0)* & !^ & (cff2*t(i,j,1,3,itrc)- & !^ & cff3*t(i,j,2,3,itrc))+ & !^ & W(i,j,0)* & !^ & (cff2*tl_t(i,j,1,3,itrc)- & !^ & cff3*tl_t(i,j,2,3,itrc))) !^ adfac=2.0_r8*ad_FC(i,0) adfac1=adfac*W(i,j,0) ad_t(i,j,1,3,itrc)=ad_t(i,j,1,3,itrc)+cff2*adfac1 ad_t(i,j,2,3,itrc)=ad_t(i,j,2,3,itrc)-cff3*adfac1 ad_W(i,j,0)=ad_W(i,j,0)+ & & (cff2*t(i,j,1,3,itrc)- & & cff3*t(i,j,2,3,itrc))*adfac ad_FC(i,0)=0.0_r8 # else !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 # endif END DO DO k=2,N(ng)-2 DO i=Istr,Iend !^ tl_FC(i,k)=tl_W(i,j,k)* & !^ & (cff2*(t(i,j,k ,3,itrc)+ & !^ & t(i,j,k+1,3,itrc))- & !^ & cff3*(t(i,j,k-1,3,itrc)+ & !^ & t(i,j,k+2,3,itrc)))+ & !^ & W(i,j,k)* & !^ & (cff2*(tl_t(i,j,k ,3,itrc)+ & !^ & tl_t(i,j,k+1,3,itrc))- & !^ & cff3*(tl_t(i,j,k-1,3,itrc)+ & !^ & tl_t(i,j,k+2,3,itrc))) !^ adfac=W(i,j,k)*ad_FC(i,k) adfac1=adfac*cff2 adfac2=adfac*cff3 ad_W(i,j,k)=ad_W(i,j,k)+ & & (cff2*(t(i,j,k ,3,itrc)+ & & t(i,j,k+1,3,itrc))- & & cff3*(t(i,j,k-1,3,itrc)+ & & t(i,j,k+2,3,itrc)))*ad_FC(i,k) ad_t(i,j,k-1,3,itrc)=ad_t(i,j,k-1,3,itrc)-adfac2 ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)+adfac1 ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+adfac1 ad_t(i,j,k+2,3,itrc)=ad_t(i,j,k+2,3,itrc)-adfac2 ad_FC(i,k)=0.0_r8 END DO END DO END IF VADV_FLUX END DO J_LOOP1 END DO T_LOOP2 ! !----------------------------------------------------------------------- ! Time-step adjoint horizontal advection term. !----------------------------------------------------------------------- ! T_LOOP1 : DO itrc=1,NT(ng) ! K_LOOP : DO k=1,N(ng) ! ! Time-step adjoint horizontal advection term. ! HADV_STEPPING : IF (ad_Hadvection(itrc,ng)%MPDATA) THEN CONTINUE ! not supported ELSE DO j=Jstr,Jend DO i=Istr,Iend cff=dt(ng)*pm(i,j)*pn(i,j) # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iThadv)=-cff3 !! DiaTwrk(i,j,k,itrc,iTyadv)=-cff2 !! DiaTwrk(i,j,k,itrc,iTxadv)=-cff1 # endif !^ tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)-tl_cff3 !^ ad_cff3=ad_cff3-ad_t(i,j,k,nnew,itrc) !^ tl_cff3=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_cff3 ad_cff2=ad_cff2+ad_cff3 ad_cff3=0.0_r8 !^ tl_cff2=cff*(tl_FE(i,j+1)-tl_FE(i,j)) !^ adfac=cff*ad_cff2 ad_FE(i,j )=ad_FE(i,j )-adfac ad_FE(i,j+1)=ad_FE(i,j+1)+adfac ad_cff2=0.0_r8 !^ tl_cff1=cff*(tl_FX(i+1,j)-tl_FX(i,j)) !^ adfac=cff*ad_cff1 ad_FX(i ,j)=ad_FX(i ,j)-adfac ad_FX(i+1,j)=ad_FX(i+1,j)+adfac ad_cff1=0.0_r8 END DO END DO END IF HADV_STEPPING ! ! Apply adjoint tracers point sources to the horizontal advection ! terms, if any. ! ! Dsrc(is) = 0, flow across grid cell u-face (positive or negative) ! Dsrc(is) = 1, flow across grid cell v-face (positive or negative) ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN IF ((ad_Hadvection(itrc,ng)%MPDATA).or. & & (ad_Hadvection(itrc,ng)%HSIMT)) THEN LapplySrc=(IstrUm2.le.Isrc).and. & & (Isrc.le.Iendp3).and. & & (JstrVm2.le.Jsrc).and. & & (Jsrc.le.Jendp2i) ELSE LapplySrc=(Istr.le.Isrc).and. & & (Isrc.le.Iend+1).and. & & (Jstr.le.Jsrc).and. & & (Jsrc.le.Jend) END IF IF (LapplySrc) THEN IF (LtracerSrc(itrc,ng)) THEN !^ tl_FX(Isrc,Jsrc)=tl_Huon(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%Tsrc(is,k,itrc)+ & !^ & Huon(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%tl_Tsrc(is,k,itrc) !^ ad_Huon(Isrc,Jsrc,k)=ad_Huon(Isrc,Jsrc,k)+ & & SOURCES(ng)%Tsrc(is,k,itrc)* & & ad_FX(Isrc,Jsrc) SOURCES(ng)%ad_Tsrc(is,k,itrc)= & & SOURCES(ng)%ad_Tsrc(is,k,itrc)+ & & Huon(Isrc,Jsrc,k)* & & ad_FX(Isrc,Jsrc) ad_FX(Isrc,Jsrc)=0.0_r8 # ifdef MASKING ELSE IF ((rmask(Isrc ,Jsrc).eq.0.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.1.0_r8)) THEN !^ tl_FX(Isrc,Jsrc)=tl_Huon(Isrc,Jsrc,k)* & !^ & t(Isrc-1,Jsrc,k,3,itrc)+ & !^ & Huon(Isrc,Jsrc,k)* & !^ & tl_t(Isrc-1,Jsrc,k,3,itrc) !^ ad_t(Isrc-1,Jsrc,k,3,itrc)= & & ad_t(Isrc-1,Jsrc,k,3,itrc)+ & & Huon(Isrc,Jsrc,k)* & & ad_FX(Isrc,Jsrc) ad_Huon(Isrc,Jsrc,k)=ad_Huon(Isrc,Jsrc,k)+ & & t(Isrc-1,Jsrc,k,3,itrc)* & & ad_FX(Isrc,Jsrc) ad_FX(Isrc,Jsrc)=0.0_r8 ELSE IF ((rmask(Isrc ,Jsrc).eq.1.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.0.0_r8)) THEN !^ tl_FX(Isrc,Jsrc)=tl_Huon(Isrc,Jsrc,k)* & !^ & t(Isrc ,Jsrc,k,3,itrc)+ & !^ & Huon(Isrc,Jsrc,k)* !^ & tl_t(Isrc ,Jsrc,k,3,itrc) !^ ad_t(Isrc ,Jsrc,k,3,itrc)= & & ad_t(Isrc ,Jsrc,k,3,itrc)+ & & Huon(Isrc,Jsrc,k)* & & ad_FX(Isrc,Jsrc) ad_Huon(Isrc,Jsrc,k)=ad_Huon(Isrc,Jsrc,k)+ & & t(Isrc ,Jsrc,k,3,itrc)* & & ad_FX(Isrc,Jsrc) ad_FX(Isrc,Jsrc)=0.0_r8 END IF # endif END IF END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN IF ((ad_Hadvection(itrc,ng)%MPDATA).or. & & (ad_Hadvection(itrc,ng)%HSIMT)) THEN LapplySrc=(IstrUm2.le.Isrc).and. & & (Isrc.le.Iendp2i).and. & & (JstrVm2.le.Jsrc).and. & & (Jsrc.le.Jendp3) ELSE LapplySrc=(Istr.le.Isrc).and. & & (Isrc.le.Iend).and. & & (Jstr.le.Jsrc).and. & & (Jsrc.le.Jend+1) END IF IF (LapplySrc) THEN IF (LtracerSrc(itrc,ng)) THEN !^ tl_FE(Isrc,Jsrc)=tl_Hvom(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%Tsrc(is,k,itrc) !^ & Hvom(Isrc,Jsrc,k)* & !^ & SOURCES(ng)%tl_Tsrc(is,k,itrc) !^ ad_Hvom(Isrc,Jsrc,k)=ad_Hvom(Isrc,Jsrc,k)+ & & SOURCES(ng)%Tsrc(is,k,itrc)* & & ad_FE(Isrc,Jsrc) SOURCES(ng)%ad_Tsrc(is,k,itrc)= & & SOURCES(ng)%ad_Tsrc(is,k,itrc)+ & & Hvom(Isrc,Jsrc,k)* & & ad_FE(Isrc,Jsrc) ad_FE(Isrc,Jsrc)=0.0_r8 # ifdef MASKING ELSE IF ((rmask(Isrc,Jsrc ).eq.0.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.1.0_r8)) THEN !^ tl_FE(Isrc,Jsrc)=tl_Hvom(Isrc,Jsrc,k)* & !^ & t(Isrc,Jsrc-1,k,3,itrc)+ & !^ & Hvom(Isrc,Jsrc,k)* & !^ & tl_t(Isrc,Jsrc-1,k,3,itrc) !^ ad_t(Isrc,Jsrc-1,k,3,itrc)= & & ad_t(Isrc,Jsrc-1,k,3,itrc)+ & & Hvom(Isrc,Jsrc,k)* & & ad_FE(Isrc,Jsrc) ad_Hvom(Isrc,Jsrc,k)=ad_Hvom(Isrc,Jsrc,k)+ & & t(Isrc,Jsrc-1,k,3,itrc)* & & ad_FE(Isrc,Jsrc) ad_FE(Isrc,Jsrc)=0.0_r8 ELSE IF ((rmask(Isrc,Jsrc ).eq.1.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.0.0_r8)) THEN !^ tl_FE(Isrc,Jsrc)=tl_Hvom(Isrc,Jsrc,k)* & !^ & t(Isrc,Jsrc ,k,3,itrc)+ & !^ & Hvom(Isrc,Jsrc,k)* !^ & tl_t(Isrc,Jsrc ,k,3,itrc) !^ ad_t(Isrc,Jsrc ,k,3,itrc)= & & ad_t(Isrc,Jsrc ,k,3,itrc)+ & & Hvom(Isrc,Jsrc,k)* & & ad_FE(Isrc,Jsrc) ad_Hvom(Isrc,Jsrc,k)=ad_Hvom(Isrc,Jsrc,k)+ & & t(Isrc,jsrc ,k,3,itrc)* & & ad_FE(Isrc,Jsrc) ad_FE(Isrc,Jsrc)=0.0_r8 END IF # endif END IF END IF END IF END DO END IF ! ! Compute adjoint of tracer horizontal advection fluxes. ! HADV_FLUX : IF (ad_Hadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, centered differences adjoint horizontal advective fluxes. ! DO j=Jstr,Jend+1 DO i=Istr,Iend !^ tl_FE(i,j)=0.5_r8* & !^ & (tl_Hvom(i,j,k)*(t(i,j-1,k,3,itrc)+ & !^ & t(i,j ,k,3,itrc))+ & !^ & Hvom(i,j,k)*(tl_t(i,j-1,k,3,itrc)+ & !^ & tl_t(i,j ,k,3,itrc))) !^ adfac=0.5_r8*ad_FE(i,j) adfac1=adfac*Hvom(i,j,k) ad_t(i,j-1,k,3,itrc)=ad_t(i,j-1,k,3,itrc)+adfac1 ad_t(i,j ,k,3,itrc)=ad_t(i,j ,k,3,itrc)+adfac1 ad_Hvom(i,j,k)=ad_Hvom(i,j,k)+ & & (t(i,j-1,k,3,itrc)+ & & t(i,j ,k,3,itrc))*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)=0.5_r8* & !^ & (tl_Huon(i,j,k)*(t(i-1,j,k,3,itrc)+ & !^ & t(i ,j,k,3,itrc))+ & !^ & Huon(i,j,k)*(tl_t(i-1,j,k,3,itrc)+ & !^ & tl_t(i ,j,k,3,itrc))) !^ adfac=0.5_r8*ad_FX(i,j) adfac1=adfac*Huon(i,j,k) ad_t(i-1,j,k,3,itrc)=ad_t(i-1,j,k,3,itrc)+adfac1 ad_t(i ,j,k,3,itrc)=ad_t(i ,j,k,3,itrc)+adfac1 ad_Huon(i,j,k)=ad_Huon(i,j,k)+ & & (t(i-1,j,k,3,itrc)+ & & t(i ,j,k,3,itrc))*adfac ad_FX(i,j)=0.0_r8 END DO END DO ! ELSE IF (ad_Hadvection(itrc,ng)%MPDATA) THEN ! ! First-order, upstream differences adjoint horizontal advective ! fluxes. ! CONTINUE ! not supported ! ELSE IF (ad_Hadvection(itrc,ng)%HSIMT) THEN ! ! Third High-order Spatial Interpolation at the Middle Temporal level ! (HSIMT; Wu and Zhu, 2010) with a Total Variation Diminishing (TVD) ! limiter horizontal advection fluxes. ! CONTINUE ! not supported ! ELSE IF ((ad_Hadvection(itrc,ng)%AKIMA4).or. & & (ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3).or. & & (ad_Hadvection(itrc,ng)%UPSTREAM3)) THEN ! ! Fourth-order Akima, fourth-order centered differences, or third-order ! upstream-biased horizontal advective fluxes. ! DO j=Jstrm1,Jendp2 DO i=Istr,Iend FE(i,j)=t(i,j ,k,3,itrc)- & & t(i,j-1,k,3,itrc) # ifdef MASKING FE(i,j)=FE(i,j)*vmask(i,j) # endif END DO END DO IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend FE(i,Jstr-1)=FE(i,Jstr) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend FE(i,Jend+2)=FE(i,Jend+1) END DO END IF END IF ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FE(i,j+1)-FE(i,j) ELSE IF (ad_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FE(i,j+1)*FE(i,j) IF (cff.gt.eps) THEN grad(i,j)=cff/(FE(i,j+1)+FE(i,j)) ELSE grad(i,j)=0.0_r8 END IF ELSE IF ((ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FE(i,j+1)+FE(i,j)) END IF END DO END DO ! cff1=1.0_r8/6.0_r8 cff2=1.0_r8/3.0_r8 DO j=Jstr,Jend+1 DO i=Istr,Iend IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ tl_FE(i,j)=0.5_r8* & !^ & (tl_Hvom(i,j,k)* & !^ & (t(i,j-1,k,3,itrc)+ & !^ & t(i,j ,k,3,itrc))+ & !^ & Hvom(i,j,k)* & !^ & (tl_t(i,j-1,k,3,itrc)+ & !^ & tl_t(i,j ,k,3,itrc)))- & !^ & cff1* & !^ & (tl_curv(i,j-1)*MAX(Hvom(i,j,k),0.0_r8)+ & !^ & curv(i,j-1)* & !^ & (0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))* & !^ & tl_Hvom(i,j,k)+ & !^ & tl_curv(i,j )*MIN(Hvom(i,j,k),0.0_r8)+ & !^ & curv(i,j )* & !^ & (0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k)))* & !^ & tl_Hvom(i,j,k)) !^ adfac=0.5_r8*ad_FE(i,j) adfac1=adfac*Hvom(i,j,k) adfac2=cff1*ad_FE(i,j) ad_Hvom(i,j,k)=ad_Hvom(i,j,k)+ & & (t(i,j-1,k,3,itrc)+ & & t(i,j ,k,3,itrc))*adfac- & & (curv(i,j-1)* & & (0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))+ & & curv(i,j )* & & (0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k))))* & & adfac2 ad_t(i,j-1,k,3,itrc)=ad_t(i,j-1,k,3,itrc)+adfac1 ad_t(i,j ,k,3,itrc)=ad_t(i,j ,k,3,itrc)+adfac1 ad_curv(i,j-1)=ad_curv(i,j-1)- & & MAX(Hvom(i,j,k),0.0_r8)*adfac2 ad_curv(i,j )=ad_curv(i,j )- & & MIN(Hvom(i,j,k),0.0_r8)*adfac2 ad_FE(i,j)=0.0_r8 ELSE IF ((ad_Hadvection(itrc,ng)%AKIMA4).or. & & (ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ tl_FE(i,j)=0.5_r8* & !^ & (tl_Hvom(i,j,k)* & !^ & (t(i,j-1,k,3,itrc)+ & !^ & t(i,j ,k,3,itrc)- & !^ & cff2*(grad(i,j )- & !^ & grad(i,j-1)))+ & !^ & Hvom(i,j,k)* & !^ & (tl_t(i,j-1,k,3,itrc)+ & !^ & tl_t(i,j ,k,3,itrc)- & !^ & cff2*(tl_grad(i,j )- & !^ & tl_grad(i,j-1)))) !^ adfac=0.5_r8*ad_FE(i,j) adfac1=adfac*Hvom(i,j,k) adfac2=adfac1*cff2 ad_Hvom(i,j,k)=ad_Hvom(i,j,k)+ & & adfac*(t(i,j-1,k,3,itrc)+ & & t(i,j ,k,3,itrc)- & & cff2*(grad(i,j )- & & grad(i,j-1))) ad_t(i,j-1,k,3,itrc)=ad_t(i,j-1,k,3,itrc)+adfac1 ad_t(i,j ,k,3,itrc)=ad_t(i,j ,k,3,itrc)+adfac1 ad_grad(i,j-1)=ad_grad(i,j-1)+adfac2 ad_grad(i,j )=ad_grad(i,j )-adfac2 ad_FE(i,j)=0.0_r8 END IF END DO END DO ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ tl_curv(i,j)=tl_FE(i,j+1)-tl_FE(i,j) !^ ad_FE(i,j )=ad_FE(i,j )-ad_curv(i,j) ad_FE(i,j+1)=ad_FE(i,j+1)+ad_curv(i,j) ad_curv(i,j)=0.0_r8 ELSE IF (ad_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FE(i,j+1)*FE(i,j) IF (cff.gt.eps) THEN !^ tl_grad(i,j)=((FE(i,j+1)+FE(i,j))*tl_cff- & !^ & cff*(tl_FE(i,j+1)+tl_FE(i,j)))/ & !^ & ((FE(i,j+1)+FE(i,j))* & !^ & (FE(i,j+1)+FE(i,j))) !^ adfac=ad_grad(i,j)/ & & ((FE(i,j+1)+FE(i,j))*(FE(i,j+1)+FE(i,j))) adfac1=adfac*cff ad_FE(i,j )=ad_FE(i,j)-adfac1 ad_FE(i,j+1)=ad_FE(i,j+1)-adfac1 ad_cff=ad_cff+(FE(i,j+1)+FE(i,j))*adfac ad_grad(i,j)=0.0_r8 ELSE !^ tl_grad(i,j)=0.0_r8 !^ ad_grad(i,j)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_FE(i,j+1)*FE(i,j)+ & !^ & FE(i,j+1)*tl_FE(i,j)) !^ adfac=2.0_r8*ad_cff ad_FE(i,j )=ad_FE(i,j )+FE(i,j+1)*adfac ad_FE(i,j+1)=ad_FE(i,j+1)+FE(i,j )*adfac ad_cff=0.0_r8 ELSE IF ((ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ tl_grad(i,j)=0.5_r8*(tl_FE(i,j+1)+tl_FE(i,j)) !^ adfac=0.5_r8*ad_grad(i,j) ad_FE(i,j )=ad_FE(i,j )+adfac ad_FE(i,j+1)=ad_FE(i,j+1)+adfac ad_grad(i,j)=0.0_r8 END IF END DO END DO IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend !^ tl_FE(i,Jend+2)=tl_FE(i,Jend+1) !^ ad_FE(i,Jend+1)=ad_FE(i,Jend+1)+ad_FE(i,Jend+2) ad_FE(i,Jend+2)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend !^ tl_FE(i,Jstr-1)=tl_FE(i,Jstr) !^ ad_FE(i,Jstr)=ad_FE(i,Jstr)+ad_FE(i,Jstr-1) ad_FE(i,Jstr-1)=0.0_r8 END DO END IF END IF ! DO j=Jstrm1,Jendp2 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)=tl_t(i,j ,k,3,itrc)- & !^ & tl_t(i,j-1,k,3,itrc) !^ ad_t(i,j-1,k,3,itrc)=ad_t(i,j-1,k,3,itrc)-ad_FE(i,j) ad_t(i,j ,k,3,itrc)=ad_t(i,j ,k,3,itrc)+ad_FE(i,j) ad_FE(i,j)=0.0_r8 END DO END DO ! DO j=Jstr,Jend DO i=Istrm1,Iendp2 FX(i,j)=t(i ,j,k,3,itrc)- & & t(i-1,j,k,3,itrc) # ifdef MASKING FX(i,j)=FX(i,j)*umask(i,j) # endif END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend FX(Istr-1,j)=FX(Istr,j) END DO END IF END IF IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=Jstr,Jend FX(Iend+2,j)=FX(Iend+1,j) END DO END IF END IF ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN curv(i,j)=FX(i+1,j)-FX(i,j) ELSE IF (ad_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FX(i+1,j)*FX(i,j) IF (cff.gt.eps) THEN grad(i,j)=cff/(FX(i+1,j)+FX(i,j)) ELSE grad(i,j)=0.0_r8 END IF ELSE IF ((ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN grad(i,j)=0.5_r8*(FX(i+1,j)+FX(i,j)) END IF END DO END DO ! cff1=1.0_r8/6.0_r8 cff2=1.0_r8/3.0_r8 DO j=Jstr,Jend DO i=Istr,Iend+1 IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ tl_FX(i,j)=0.5_r8* & !^ & (tl_Huon(i,j,k)* & !^ & (t(i-1,j,k,3,itrc)+ & !^ & t(i ,j,k,3,itrc))+ & !^ & Huon(i,j,k)* & !^ & (tl_t(i-1,j,k,3,itrc)+ & !^ & tl_t(i ,j,k,3,itrc)))- & !^ & cff1* & !^ & (tl_curv(i-1,j)*MAX(Huon(i,j,k),0.0_r8)+ & !^ & curv(i-1,j)* & !^ & (0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))* & !^ & tl_Huon(i,j,k)+ & !^ & tl_curv(i ,j)*MIN(Huon(i,j,k),0.0_r8)+ & !^ & curv(i ,j)* & !^ & (0.5_r8+SIGN(0.5_r8,-Huon(i,j,k)))* & !^ & tl_Huon(i,j,k)) !^ adfac=0.5_r8*ad_FX(i,j) adfac1=adfac*Huon(i,j,k) adfac2=cff1*ad_FX(i,j) ad_Huon(i,j,k)=ad_Huon(i,j,k)+ & & (t(i-1,j,k,3,itrc)+ & & t(i ,j,k,3,itrc))*adfac- & & (curv(i-1,j)* & & (0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))+ & & curv(i ,j)* & & (0.5_r8+SIGN(0.5_r8,-Huon(i,j,k))))* & & adfac2 ad_t(i-1,j,k,3,itrc)=ad_t(i-1,j,k,3,itrc)+adfac1 ad_t(i ,j,k,3,itrc)=ad_t(i ,j,k,3,itrc)+adfac1 ad_curv(i-1,j)=ad_curv(i-1,j)- & & MAX(Huon(i,j,k),0.0_r8)*adfac2 ad_curv(i ,j)=ad_curv(i ,j)- & & MIN(Huon(i,j,k),0.0_r8)*adfac2 ad_FX(i,j)=0.0_r8 ELSE IF ((ad_Hadvection(itrc,ng)%AKIMA4).or. & & (ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ tl_FX(i,j)=0.5_r8* & !^ & (tl_Huon(i,j,k)* & !^ & (t(i-1,j,k,3,itrc)+ & !^ & t(i ,j,k,3,itrc)- & !^ & cff2*(grad(i ,j)- & !^ & grad(i-1,j)))+ & !^ & Huon(i,j,k)* & !^ & (tl_t(i-1,j,k,3,itrc)+ & !^ & tl_t(i ,j,k,3,itrc)- & !^ & cff2*(tl_grad(i ,j)- & !^ & tl_grad(i-1,j)))) !^ adfac=0.5_r8*ad_FX(i,j) adfac1=adfac*Huon(i,j,k) adfac2=adfac1*cff2 ad_Huon(i,j,k)=ad_Huon(i,j,k)+ & & adfac*(t(i-1,j,k,3,itrc)+ & & t(i ,j,k,3,itrc)- & & cff2*(grad(i ,j)- & & grad(i-1,j))) ad_t(i-1,j,k,3,itrc)=ad_t(i-1,j,k,3,itrc)+adfac1 ad_t(i ,j,k,3,itrc)=ad_t(i ,j,k,3,itrc)+adfac1 ad_grad(i-1,j)=ad_grad(i-1,j)+adfac2 ad_grad(i ,j)=ad_grad(i ,j)-adfac2 ad_FX(i,j)=0.0_r8 END IF END DO END DO ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 IF (ad_Hadvection(itrc,ng)%UPSTREAM3) THEN !^ tl_curv(i,j)=tl_FX(i+1,j)-tl_FX(i,j) !^ ad_FX(i ,j)=ad_FX(i ,j)-ad_curv(i,j) ad_FX(i+1,j)=ad_FX(i+1,j)+ad_curv(i,j) ad_curv(i,j)=0.0_r8 ELSE IF (ad_Hadvection(itrc,ng)%AKIMA4) THEN cff=2.0_r8*FX(i+1,j)*FX(i,j) IF (cff.gt.eps) THEN !^ tl_grad(i,j)=((FX(i+1,j)+FX(i,j))*tl_cff- & !^ & cff*(tl_FX(i+1,j)+tl_FX(i,j)))/ & !^ & ((FX(i+1,j)+FX(i,j))* & !^ & (FX(i+1,j)+FX(i,j))) !^ adfac=ad_grad(i,j)/ & & ((FX(i+1,j)+FX(i,j))*(FX(i+1,j)+FX(i,j))) adfac1=adfac*cff ad_FX(i ,j)=ad_FX(i ,j)-adfac1 ad_FX(i+1,j)=ad_FX(i+1,j)-adfac1 ad_cff=ad_cff+(FX(i+1,j)+FX(i,j))*adfac ad_grad(i,j)=0.0_r8 ELSE !^ tl_grad(i,j)=0.0_r8 !^ ad_grad(i,j)=0.0_r8 END IF ELSE IF ((ad_Hadvection(itrc,ng)%CENTERED4).or. & & (ad_Hadvection(itrc,ng)%SPLIT_U3)) THEN !^ tl_grad(i,j)=0.5_r8*(tl_FX(i+1,j)+tl_FX(i,j)) !^ adfac=0.5_r8*ad_grad(i,j) ad_FX(i ,j)=ad_FX(i ,j)+adfac ad_FX(i+1,j)=ad_FX(i+1,j)+adfac ad_grad(i,j)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_FX(i+1,j)*FX(i,j)+ & !^ & FX(i+1,j)*tl_FX(i,j)) !^ adfac=2.0_r8*ad_cff ad_FX(i ,j)=ad_FX(i ,j)+FX(i+1,j)*adfac ad_FX(i+1,j)=ad_FX(i+1,j)+FX(i ,j)*adfac ad_cff=0.0_r8 END DO END DO IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=Jstr,Jend !^ tl_FX(Iend+2,j)=tl_FX(Iend+1,j) !^ ad_FX(Iend+1,j)=ad_FX(Iend+1,j)+ad_FX(Iend+2,j) ad_FX(Iend+2,j)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend !^ tl_FX(Istr-1,j)=tl_FX(Istr,j) !^ ad_FX(Istr,j)=ad_FX(Istr,j)+ad_FX(Istr-1,j) ad_FX(Istr-1,j)=0.0_r8 END DO END IF END IF ! DO j=Jstr,Jend DO i=Istrm1,Iendp2 # 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)=tl_t(i ,j,k,nstp,itrc)- & !^ & tl_t(i-1,j,k,nstp,itrc) !^ ad_t(i-1,j,k,3,itrc)=ad_t(i-1,j,k,3,itrc)-ad_FX(i,j) ad_t(i ,j,k,3,itrc)=ad_t(i ,j,k,3,itrc)+ad_FX(i,j) ad_FX(i,j)=0.0_r8 END DO END DO END IF HADV_FLUX END DO K_LOOP # ifdef AD_SUPPORTED ! ! The MPDATA algorithm requires a three-point footprint, so exchange ! boundary data on t(:,:,:,nnew,:) so other processes computed earlier ! (horizontal diffusion, biology, or sediment) are accounted. ! IF ((ad_Hadvection(itrc,ng)%MPDATA).or. & & (ad_Hadvection(itrc,ng)%HSIMT)) THEN # ifdef DISTRIBUTE ! > CALL mp_exchange3d (ng, tile, iNLM, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_t(:,:,:,nnew,itrc)) !^ CALL ad_mp_exchange3d (ng, tile, iADM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_t(:,:,:,nnew,itrc)) # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_t(:,:,:,nnew,itrc)) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_t(:,:,:,nnew,itrc)) END IF END IF # endif END DO T_LOOP1 ! ! Compute adjoint inverse thickness. ! IF (Lhsimt) THEN DO k=1,N(ng) DO j=Jstrm2,Jendp2 DO i=Istrm2,Iendp2 oHz(i,j,k)=1.0_r8/Hz(i,j,k) !^ tl_oHz(i,j,k)=-oHz(i,j,k)*oHz(i,j,k)*tl_Hz(i,j,k) !^ ad_Hz(i,j,k)=ad_Hz(i,j,k)- & & oHz(i,j,k)*oHz(i,j,k)*ad_oHz(i,j,k) ad_oHz(i,j,k)=0.0_r8 END DO END DO END DO ELSE DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend oHz(i,j,k)=1.0_r8/Hz(i,j,k) !^ tl_oHz(i,j,k)=-oHz(i,j,k)*oHz(i,j,k)*tl_Hz(i,j,k) !^ ad_Hz(i,j,k)=ad_Hz(i,j,k)- & & oHz(i,j,k)*oHz(i,j,k)*ad_oHz(i,j,k) ad_oHz(i,j,k)=0.0_r8 END DO END DO END DO END IF ! RETURN END SUBROUTINE ad_step3d_t_tile #endif END MODULE ad_step3d_t_mod