#include "cppdefs.h" MODULE ad_step3d_t_mod #if !defined TS_FIXED && (defined ADJOINT && defined SOLVE3D) ! !svn $Id: ad_step3d_t.F 889 2018-02-10 03:32:52Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2019 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt ! !======================================================================= ! ! ! 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. ! ! ! ! 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. ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, iADM, 35, __LINE__, __FILE__) # 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 TS_MPDATA_NOT_YET # 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, & # endif & 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__, __FILE__) # 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 TS_MPDATA_NOT_YET # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & omn, om_u, om_v, on_u, on_v, & # endif & 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 # if defined FLOATS_NOT_YET && defined FLOAT_VWALK !! USE mp_exchange_mod, ONLY : mp_exchange3d # endif USE mp_exchange_mod, ONLY : ad_mp_exchange4d # endif # ifdef TS_MPDATA_NOT_YET !! USE ad_mpdata_adiff_mod # 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 TS_MPDATA_NOT_YET # 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:) # endif 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 TS_MPDATA_NOT_YET # 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) # endif 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. ! 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 # ifdef TS_MPDATA_NOT_YET # ifdef DIAGNOSTICS_TS !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS,3) :: Dhadv !! real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng),NT(ng)) :: Dvadv # endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS, & & N(ng),NT(ng)) :: Ta real(r8), dimension(IminS:ImaxS,JminS:JmaxS, & & N(ng),NT(ng)) :: ad_Ta real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: Ua real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: Va real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: Wa real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: ad_Ua real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: ad_Va real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: ad_Wa # endif # include "set_bounds.h" ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! 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 # ifdef TS_MPDATA_NOT_YET DO k=1,N(ng) DO i=IminS,ImaxS ad_Ua(i,j,k)=0.0_r8 ad_Va(i,j,k)=0.0_r8 END DO END DO DO k=0,N(ng) DO i=IminS,ImaxS ad_Wa(i,j,k)=0.0_r8 END DO END DO DO itrc=1,NT(ng) DO k=1,N(ng) DO i=IminS,ImaxS ad_Ta(i,j,k,itrc)=0.0_r8 END DO END DO END DO # endif 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 ! 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 ! ! 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 !> tl_t(i,j,k,nnew,iage)=tl_t(i,j,k,nnew,iage)+ & !> & dt(ng)* & # ifdef TS_MPDATA !> & tl_t(i,j,k,nnew,inert(itrc)) # else !> & tl_t(i,j,k,3,inert(itrc)) # endif !> # ifdef TS_MPDATA ad_t(i,j,k,nnew,inert(itrc))=ad_t(i,j,k,nnew,inert(itrc))+& & dt(ng)*ad_t(i,j,k,nnew,iage) # else 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) # endif END DO END DO END DO END DO # endif ! !----------------------------------------------------------------------- ! Time-step adjoint vertical diffusion term. !----------------------------------------------------------------------- ! ! Compute BASIC STATE inverse thickness. ! # ifdef TS_MPDATA_NOT_YET # define I_RANGE Istrm2,Iendp2 # define J_RANGE Jstrm2,Jendp2 # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif DO k=1,N(ng) DO j=J_RANGE DO i=I_RANGE oHz(i,j,k)=1.0_r8/Hz(i,j,k) END DO END DO END DO # undef I_RANGE # undef J_RANGE ! ! Compute adjoint vertical diffusion term. ! DO j=Jstr,Jend DO itrc=1,NT(ng) ltrc=MIN(NAT,itrc) # if defined SPLINES_VDIFF && !defined TS_MPDATA_NOT_YET ! ! 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 ! ! 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 # endif END DO END DO # ifdef TS_MPDATA_NOT_YET ! !----------------------------------------------------------------------- ! Compute adjoint anti-diffusive velocities and correct advected ! tracers using MPDATA recursive method. Notice that pipelined ! J-loop ended. !----------------------------------------------------------------------- ! ! 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 (EWperiodic(ng).or.NSperiodic(ng)) THEN DO itrc=1,NT(ng) CALL exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & t(:,:,:,nnew,itrc)) END DO END IF # ifdef DISTRIBUTE CALL mp_exchange4d (ng, tile, iNLM, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & t(:,:,:,nnew,:)) # endif ! ! Compute BASIC STATE private tracer diffusion and anti-diffusive ! velocities. ! ! NOTE: the BASIC STATE retrived is already in Tunits so it is not ! necessary to divide by Hz. ! DO itrc=1,NT(ng) DO k=1,N(ng) DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp3 cff1=MAX(Huon(i,j,k),0.0_r8) cff2=MIN(Huon(i,j,k),0.0_r8) FX(i,j)=cff1*t(i-1,j,k,3,itrc)+ & & cff2*t(i ,j,k,3,itrc) END DO END DO DO j=JstrVm2,Jendp3 DO i=IstrUm2,Iendp2i cff1=MAX(Hvom(i,j,k),0.0_r8) cff2=MIN(Hvom(i,j,k),0.0_r8) FE(i,j)=cff1*t(i,j-1,k,3,itrc)+ & & cff2*t(i,j ,k,3,itrc) END DO END DO ! ! Apply tracers point sources to the BASIC STATE horizontal advection ! terms. ! IF (LuvSrc(ng).and.ANY(LtracerSrc(:,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 # ifdef TS_MPDATA_NOT_YET IF (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp3)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp2i))) THEN # else IF (((Istr.le.Isrc).and.(Isrc.le.Iend+1)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc ,Jsrc).eq.0.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.1.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc-1,Jsrc,k,3,itrc) ELSE IF ((rmask(Isrc ,Jsrc).eq.1.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.0.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc ,Jsrc,k,3,itrc) END IF # endif END IF END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN # ifdef TS_MPDATA_NOT_YET IF (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp2i)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp3))) THEN # else IF (((Istr.le.Isrc).and.(Isrc.le.Iend)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend+1))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc,Jsrc ).eq.0.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.1.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc-1,k,3,itrc) ELSE IF ((rmask(Isrc,Jsrc ).eq.1.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.0.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc ,k,3,itrc) END IF # endif END IF END IF END IF END DO END IF ! ! Time-step BASIC STATE horizontal advection term (m Tunits). ! DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp2i cff=dt(ng)*pm(i,j)*pn(i,j) cff1=cff*(FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j)) Ta(i,j,k,itrc)=t(i,j,k,nnew,itrc)-cff1 END DO END DO END DO END DO ! ! First_order, upstream differences vertical BASIC STATE advective ! flux. ! DO j=JstrVm2,Jendp2i DO itrc=1,NT(ng) DO i=IstrUm2,Iendp2i DO k=1,N(ng)-1 cff1=MAX(W(i,j,k),0.0_r8) cff2=MIN(W(i,j,k),0.0_r8) FC(i,k)=cff1*t(i,j,k ,3,itrc)+ & & cff2*t(i,j,k+1,3,itrc) END DO # 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 ! ! Time-step BASIC STATE vertical advection term (Tunits). ! DO i=IstrUm2,Iendp2i CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO ! ! Apply mass point sources (volume vertical influx), if any. ! IF (LwSrc(ng).and.ANY(LtracerSrc(:,ng))) THEN DO is=1,Nsrc(ng) Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (LtracerSrc(itrc,ng).and. & # ifdef TS_MPDATA_NOT_YET & ((IstrUm2.le.Isrc).and.(Isrc.le.Iendp2i)).and. & # else & ((IstrR.le.Isrc).and.(Isrc.le.IendR)).and. & # endif & (j.eq.Jsrc)) THEN DO k=1,N(ng)-1 FC(Isrc,k)=FC(Isrc,k)+0.5_r8* & & (SOURCES(ng)%Qsrc(is,k )* & & SOURCES(ng)%Tsrc(is,k ,itrc)+ & & SOURCES(ng)%Qsrc(is,k+1)* & & SOURCES(ng)%Tsrc(is,k+1,itrc)) END DO END IF END DO END IF ! DO k=1,N(ng) DO i=IstrUm2,Iendp2i cff1=CF(i,0)*(FC(i,k)-FC(i,k-1))*oHz(i,j,k) Ta(i,j,k,itrc)=Ta(i,j,k,itrc)-cff1 END DO END DO END DO END DO # undef I_RANGE # undef J_RANGE ! ! Compute BASIC STATE anti-diffusive velocities to corrected advected ! tracers using MPDATA recursive method. ! DO itrc=1,NT(ng) CALL mpdata_adiff_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & pm, pn, omn, om_u, on_v, & & z_r, oHz, & & Huon, Hvom, W, & & t(:,:,:,3,itrc), & & Ta(:,:,:,itrc), Ua, Va, Wa) ! ! Compute BASIC STATE anti-diffusive corrected advection fluxes. ! DO k=1,N(ng) DO j=Jstr,Jend DO i=Istr,Iend+1 cff1=MAX(Ua(i,j,k),0.0_r8) cff2=MIN(Ua(i,j,k),0.0_r8) FX(i,j)=(cff1*Ta(i-1,j,k,itrc)+ & & cff2*Ta(i ,j,k,itrc))* & & 0.5_r8*(Hz(i,j,k)+Hz(i-1,j,k))*on_u(i,j) END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend cff1=MAX(Va(i,j,k),0.0_r8) cff2=MIN(Va(i,j,k),0.0_r8) FE(i,j)=(cff1*Ta(i,j-1,k,itrc)+ & & cff2*Ta(i,j ,k,itrc))* & & 0.5_r8*(Hz(i,j,k)+Hz(i,j-1,k))*om_v(i,j) END DO END DO END DO ! ! Compute BASIC anti-diffusive corrected vertical advection flux. ! DO j=Jstr,Jend DO k=1,N(ng)-1 DO i=Istr,Iend cff1=MAX(Wa(i,j,k),0.0_r8) cff2=MIN(Wa(i,j,k),0.0_r8) FC(i,k)=cff1*Ta(i,j,k ,itrc)+ & & cff2*Ta(i,j,k+1,itrc) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ! Time-step adjoint corrected vertical advection (Tunits). # ifdef DIAGNOSTICS_TS ! Convert units of tracer diagnostic terms to Tunits. # endif ! 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 # ifdef DIAGNOSTICS_TS !! DO idiag=1,NDT !! DiaTwrk(i,j,k,itrc,idiag)=DiaTwrk(i,j,k,itrc,idiag)* & !! & oHz(i,j,k) !! END DO !! DiaTwrk(i,j,k,itrc,iTvadv)=Dvadv(i,j,k,itrc)- & !! & 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=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 ! ! Compute adjoint anti-diffusive corrected vertical advection flux. ! 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 DO k=1,N(ng)-1 DO i=Istr,Iend cff1=MAX(Wa(i,j,k),0.0_r8) cff2=MIN(Wa(i,j,k),0.0_r8) !> tl_FC(i,k)=tl_cff1*Ta(i,j,k ,itrc)+ & !> & cff1*tl_Ta(i,j,k ,itrc)+ & !> & tl_cff2*Ta(i,j,k+1,itrc)+ & !> & cff2*tl_Ta(i,j,k+1,itrc) !> ad_Ta(i,j,k ,itrc)=ad_Ta(i,j,k ,itrc)+cff1*ad_FC(i,k) ad_Ta(i,j,k+1,itrc)=ad_Ta(i,j,k+1,itrc)+cff2*ad_FC(i,k) ad_cff1=ad_cff1+Ta(i,j,k ,itrc)*ad_FC(i,k) ad_cff2=ad_cff2+Ta(i,j,k+1,itrc)*ad_FC(i,k) ad_FC(i,k)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5,-Wa(i,j,k)))*tl_Wa(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5, Wa(i,j,k)))*tl_Wa(i,j,k) !> ad_Wa(i,j,k)=ad_Wa(i,j,k)+ & & (0.5_r8+SIGN(0.5,-Wa(i,j,k)))*ad_cff2+ & & (0.5_r8+SIGN(0.5, Wa(i,j,k)))*ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO END DO ! ! Time-step adjoint corrected horizontal advection (Tunits). ! DO k=1,N(ng) 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)=DiaTwrk(i,j,k,itrc,iThadv)- & !! & cff3 !! DiaTwrk(i,j,k,itrc,iTyadv)=DiaTwrk(i,j,k,itrc,iTyadv)- & !! & cff2 !! DiaTwrk(i,j,k,itrc,iTxadv)=DiaTwrk(i,j,k,itrc,iTxadv)- & !! & cff1 # endif !> tl_t(i,j,k,nnew,itrc)=tl_Ta(i,j,k,itrc)*Hz(i,j,k)+ & !> & Ta(i,j,k,itrc)*tl_Hz(i,j,k)-tl_cff3 !> ad_Ta(i,j,k,itrc)=ad_Ta(i,j,k,itrc)+ & & Hz(i,j,k)*ad_t(i,j,k,nnew,itrc) ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & Ta(i,j,k,itrc)*ad_t(i,j,k,nnew,itrc) ad_cff3=ad_cff3-ad_t(i,j,k,nnew,itrc) ad_t(i,j,k,nnew,itrc)=0.0_r8 !> 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 ! ! Compute adjoint anti-diffusive corrected advection fluxes. ! DO j=Jstr,Jend+1 DO i=Istr,Iend cff1=MAX(Va(i,j,k),0.0_r8) cff2=MIN(Va(i,j,k),0.0_r8) !> tl_FE(i,j)=0.5_r8*om_v(i,j)* & !> & ((tl_Hz(i,j,k)+tl_Hz(i,j-1,k))* & !> & (cff1*Ta(i,j-1,k,itrc)+ & !> & cff2*Ta(i,j ,k,itrc))+ & !> & (Hz(i,j,k)+Hz(i,j-1,k))* & !> & (tl_cff1*Ta(i,j-1,k,itrc)+ & !> & cff1*tl_Ta(i,j-1,k,itrc)+ & !> & tl_cff2*Ta(i,j ,k,itrc)+ & !> & cff2*tl_Ta(i,j ,k,itrc))) !> adfac=0.5_r8*om_v(i,j)*ad_FE(i,j) adfac1=adfac*(cff1*Ta(i,j-1,k,itrc)+ & & cff2*Ta(i,j ,k,itrc)) adfac2=adfac*(Hz(i,j,k)+Hz(i,j-1,k)) ad_Hz(i,j-1,k)=ad_Hz(i,j-1,k)+adfac1 ad_Hz(i,j ,k)=ad_Hz(i,j,k)+adfac1 ad_Ta(i,j-1,k,itrc)=ad_Ta(i,j-1,k,itrc)+cff1*adfac2 ad_Ta(i,j ,k,itrc)=ad_Ta(i,j ,k,itrc)+cff2*adfac2 ad_cff1=ad_cff1+Ta(i,j-1,k,itrc)*adfac2 ad_cff2=ad_cff2+Ta(i,j ,k,itrc)*adfac2 ad_FE(i,j)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8,-Va(i,j,k)))*tl_Va(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5_r8, Va(i,j,k)))*tl_Va(i,j,k) !> ad_Va(i,j,k)=ad_Va(i,j,k)+ & & (0.5_r8+SIGN(0.5_r8,-Va(i,j,k)))*ad_cff2+ & & (0.5_r8+SIGN(0.5_r8, Va(i,j,k)))*ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 cff1=MAX(Ua(i,j,k),0.0_r8) cff2=MIN(Ua(i,j,k),0.0_r8) !> tl_FX(i,j)=0.5_r8*on_u(i,j)* & !> & ((tl_Hz(i,j,k)+tl_Hz(i-1,j,k))* & !> & (cff1*Ta(i-1,j,k,itrc)+ & !> & cff2*Ta(i ,j,k,itrc))+ & !> & (Hz(i,j,k)+Hz(i-1,j,k))* & !> & (tl_cff1*Ta(i-1,j,k,itrc)+ & !> & cff1*tl_Ta(i-1,j,k,itrc)+ & !> & tl_cff2*Ta(i ,j,k,itrc)+ & !> & cff2*tl_Ta(i ,j,k,itrc))) !> adfac=0.5_r8*on_u(i,j)*ad_FX(i,j) adfac1=adfac*(cff1*Ta(i-1,j,k,itrc)+ & & cff2*Ta(i ,j,k,itrc)) adfac2=adfac*(Hz(i,j,k)+Hz(i-1,j,k)) ad_Hz(i-1,j,k)=ad_Hz(i-1,j,k)+adfac1 ad_Hz(i ,j,k)=ad_Hz(i ,j,k)+adfac1 ad_Ta(i-1,j,k,itrc)=ad_Ta(i-1,j,k,itrc)+cff1*adfac2 ad_Ta(i ,j,k,itrc)=ad_Ta(i ,j,k,itrc)+cff2*adfac2 ad_cff1=ad_cff1+Ta(i-1,j,k,itrc)*adfac1 ad_cff2=ad_cff2+Ta(i ,j,k,itrc)*adfac2 ad_FX(i,j)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8,-Ua(i,j,k)))*tl_Ua(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5_r8, Ua(i,j,k)))*tl_Ua(i,j,k) !> ad_Ua(i,j,k)=ad_Ua(i,j,k)+ & & (0.5_r8+SIGN(0.5_r8,-Ua(i,j,k)))*ad_cff2+ & & (0.5_r8+SIGN(0.5_r8, Ua(i,j,k)))*ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO END DO ! ! Compute adjoint anti-diffusive velocities to corrected advected ! tracers using MPDATA recursive method. ! !> CALL tl_mpdata_adiff_tile (ng, tile, & !> & LBi, UBi, LBj, UBj, & !> & IminS, ImaxS, JminS, JmaxS, & # ifdef MASKING !> & rmask, umask, vmask, & # endif # ifdef WET_DRY !> & rmask_wet, umask_wet, vmask_wet, & # endif !> & pm, pn, omn, om_u, on_v, & !> & z_r, tl_z_r, & !> & oHz, tl_oHz, & !> & Huon, tl_Huon, & !> & Hvom, tl_Hvom, & !> & W, tl_W, & !> & t(:,:,:,3,itrc), tl_t(:,:,:,3,itrc), & !> & Ta(:,:,:,itrc), tl_Ta(:,:,:,itrc), & !> & Ua, tl_Ua, & !> & Va, tl_Va, & !> & Wa, tl_Wa) !> CALL ad_mpdata_adiff_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & # ifdef MASKING & rmask, umask, vmask, & # endif # ifdef WET_DRY & rmask_wet, umask_wet, vmask_wet, & # endif & pm, pn, omn, om_u, on_v, & & z_r, ad_z_r, & & oHz, ad_oHz, & & Huon, ad_Huon, & & Hvom, ad_Hvom, & & W, ad_W, & & t(:,:,:,3,itrc), ad_t(:,:,:,3,itrc), & & Ta(:,:,:,itrc), ad_Ta(:,:,:,itrc), & & Ua, ad_Ua, & & Va, ad_Va, & & Wa, ad_Wa) END DO # endif /* TS_MPDATA_NOT_YET */ ! !----------------------------------------------------------------------- ! Time-step adjoint vertical advection term. !----------------------------------------------------------------------- # ifdef TS_MPDATA_NOT_YET ! ! Compute BASIC STATE Ta due to horizontal advection only. ! ! NOTE: the BASIC STATE retrived is already in Tunits so it is not ! necessary to divide by Hz. ! DO itrc=1,NT(ng) DO k=1,N(ng) DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp3 cff1=MAX(Huon(i,j,k),0.0_r8) cff2=MIN(Huon(i,j,k),0.0_r8) FX(i,j)=cff1*t(i-1,j,k,3,itrc)+ & & cff2*t(i ,j,k,3,itrc) END DO END DO DO j=JstrVm2,Jendp3 DO i=IstrUm2,Iendp2i cff1=MAX(Hvom(i,j,k),0.0_r8) cff2=MIN(Hvom(i,j,k),0.0_r8) FE(i,j)=cff1*t(i,j-1,k,3,itrc)+ & & cff2*t(i,j ,k,3,itrc) END DO END DO ! ! Apply tracers point sources to the BASIC STATE horizontal advection ! terms, if any. ! IF (LuvSrc(ng).and.ANY(LtracerSrc(:,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 (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp3)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp2i))) THEN IF (LtracerSrc(itrc,ng)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc ,Jsrc).eq.0.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.1.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc-1,Jsrc,k,3,itrc) ELSE IF ((rmask(Isrc ,Jsrc).eq.1.0_r8).and. & & (rmask(Isrc-1,Jsrc).eq.0.0_r8)) THEN FX(Isrc,Jsrc)=Huon(Isrc,Jsrc,k)* & & t(Isrc ,Jsrc,k,3,itrc) END IF # endif END IF END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN IF (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp2i)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp3))) THEN IF (LtracerSrc(itrc,ng)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & SOURCES(ng)%Tsrc(is,k,itrc) # ifdef MASKING ELSE IF ((rmask(Isrc,Jsrc ).eq.0.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.1.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc-1,k,3,itrc) ELSE IF ((rmask(Isrc,Jsrc ).eq.1.0_r8).and. & & (rmask(Isrc,Jsrc-1).eq.0.0_r8)) THEN FE(Isrc,Jsrc)=Hvom(Isrc,Jsrc,k)* & & t(Isrc,Jsrc ,k,3,itrc) END IF # endif END IF END IF END IF END DO END IF ! ! Time-step BASIC STATE horizontal advection term (Tunits). ! DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp2i cff=dt(ng)*pm(i,j)*pn(i,j)*oHz(i,j,k) cff1=cff*(FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j)) Ta(i,j,k,itrc)=t(i,j,k,nnew,itrc)-cff1 END DO END DO END DO END DO # endif ! ! Time-step adjoint vertical advection term. Compute first BASIC ! STATE vertical advection flux, FC. ! # ifdef TS_MPDATA_NOT_YET # define I_RANGE IstrUm2,Iendp2i # define J_RANGE JstrVm2,Jendp2i # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif DO j=J_RANGE DO itrc=1,NT(ng) # if defined TS_SVADVECTION_TL ! ! 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 # elif defined TS_A4VADVECTION_TL ! ! 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 # elif defined TS_C2VADVECTION_TL ! ! 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 # elif defined TS_MPDATA_NOT_YET ! ! First_order, BASIC STATE upstream differences vertical advective ! flux. ! DO i=I_RANGE DO k=1,N(ng)-1 cff1=MAX(W(i,j,k),0.0_r8) cff2=MIN(W(i,j,k),0.0_r8) FC(i,k)=cff1*t(i,j,k ,3,itrc)+ & & cff2*t(i,j,k+1,3,itrc) END DO # 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 !! !! 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 # endif ! ! 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 ! DO i=Istr,Iend CF(i,0)=dt(ng)*pm(i,j)*pn(i,j) END DO DO k=1,N(ng) DO i=I_RANGE !! cff1=CF(i,0)*(FC(i,k)-FC(i,k-1)) ! not needed HGA # ifdef TS_MPDATA_NOT_YET # ifdef DIAGNOSTICS_TS !! Dvadv(i,j,k,itrc)=-cff1 # endif !> tl_Ta(i,j,k,itrc)=(tl_Ta(i,j,k,itrc)-tl_cff1)* & !> & oHz(i,j,k)+ & !> & (Ta(i,j,k,itrc)-cff1)* & !> & tl_oHz(i,j,k) !> adfac=ad_Ta(i,j,k,itrc)*oHz(i,j,k) ad_oHz(i,j,k)=ad_oHz(i,j,k)+ & & (Ta(i,j,k,itrc)-cff1)*ad_Ta(i,j,k,itrc) ad_Ta(i,j,k,itrc)=adfac ad_cff1=ad_cff1-adfac # else # ifdef DIAGNOSTICS_TS !! DO idiag=1,NDT !! DiaTwrk(i,j,k,itrc,idiag)=DiaTwrk(i,j,k,itrc,idiag)* & !! & oHz(i,j,k) !! END DO !! DiaTwrk(i,j,k,itrc,iTvadv)=-cff1 # 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) # endif !> 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 ! ! Apply mass point sources (volume vertical influx), if any. ! IF (LwSrc(ng).and.ANY(LtracerSrc(:,ng))) THEN DO is=1,Nsrc(ng) Isrc=SOURCES(ng)%Isrc(is) Jsrc=SOURCES(ng)%Jsrc(is) IF (LtracerSrc(itrc,ng).and. & # ifdef TS_MPDATA_NOT_YET & ((IstrUm2.le.Isrc).and.(Isrc.le.Iendp2i)).and. & # else & ((IstrR.le.Isrc).and.(Isrc.le.IendR)).and. & # endif & (j.eq.Jsrc)) THEN DO k=1,N(ng)-1 !> tl_FC(Isrc,k)=tl_FC(Isrc,k)+0.0_r8 !> END DO END IF END DO END IF # ifdef TS_SVADVECTION_TL ! ! 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 # elif defined TS_A4VADVECTION_TL ! ! 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 # elif defined TS_C2VADVECTION_TL ! ! 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 # elif defined TS_MPDATA_NOT_YET ! ! First_order, upstream differences vertical advective flux. ! DO i=I_RANGE !> 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 DO k=1,N(ng)-1 cff1=MAX(W(i,j,k),0.0_r8) cff2=MIN(W(i,j,k),0.0_r8) !> tl_FC(i,k)=tl_cff1*t(i,j,k ,3,itrc)+ & !> & cff1*tl_t(i,j,k ,3,itrc)+ & !> & tl_cff2*t(i,j,k+1,3,itrc)+ & !> & cff2*tl_t(i,j,k+1,3,itrc) !> ad_t(i,j,k ,3,itrc)=ad_t(i,j,k ,3,itrc)+cff1*ad_FC(i,k) ad_t(i,j,k+1,3,itrc)=ad_t(i,j,k+1,3,itrc)+cff2*ad_FC(i,k) ad_cff1=ad_cff1+t(i,j,k ,3,itrc)*ad_FC(i,k) ad_cff2=ad_cff2+t(i,j,k+1,3,itrc)*ad_FC(i,k) ad_FC(i,k)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8,-W(i,j,k)))*tl_W(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5_r8, W(i,j,k)))*tl_W(i,j,k) !> ad_W(i,j,k)=ad_W(i,j,k)+ & & (0.5_r8+SIGN(0.5_r8,-W(i,j,k)))*ad_cff2+ & & (0.5_r8+SIGN(0.5_r8, W(i,j,k)))*ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO # else ! ! 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 # endif END DO END DO # undef I_RANGE # undef J_RANGE ! !----------------------------------------------------------------------- ! Time-step adjoint horizontal advection term. !----------------------------------------------------------------------- ! T_LOOP : DO itrc=1,NT(ng) K_LOOP : DO k=1,N(ng) ! ! Time-step adjoint horizontal advection term. ! # ifdef TS_MPDATA_NOT_YET # define I_RANGE IstrUm2,Iendp2i # define J_RANGE JstrVm2,Jendp2i # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif # if defined DIAGNOSTICS_TS && defined TS_MPDATA_NOT_YET !! DO j=Jstr,Jend !! DO i=Istr,Iend !! DiaTwrk(i,j,k,itrc,iThadv)=Dhadv(i,j,iThadv) !! DiaTwrk(i,j,k,itrc,iTyadv)=Dhadv(i,j,iTyadv) !! DiaTwrk(i,j,k,itrc,iTxadv)=Dhadv(i,j,iTxadv) !! END DO !! END DO # endif DO j=J_RANGE DO i=I_RANGE cff=dt(ng)*pm(i,j)*pn(i,j) # ifdef DIAGNOSTICS_TS # ifdef TS_MPDATA_NOT_YET !! Dhadv(i,j,iThadv)=-cff3 !! Dhadv(i,j,iTyadv)=-cff2 !! Dhadv(i,j,iTxadv)=-cff1 # else !! DiaTwrk(i,j,k,itrc,iThadv)=-cff3 !! DiaTwrk(i,j,k,itrc,iTyadv)=-cff2 !! DiaTwrk(i,j,k,itrc,iTxadv)=-cff1 # endif # endif # ifdef TS_MPDATA_NOT_YET !> tl_Ta(i,j,k,itrc)=tl_t(i,j,k,nnew,itrc)-tl_cff3 !> ad_cff3=ad_cff3-ad_Ta(i,j,k,itrc) ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)+ & & ad_Ta(i,j,k,itrc) ad_Ta(i,j,k,itrc)=0.0_r8 # else !> 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) # endif !> 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 # undef I_RANGE # undef J_RANGE ! ! Apply adjoint tracers point sources to the horizontal advection ! terms, if any. ! IF (LuvSrc(ng).and.ANY(LtracerSrc(:,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 # ifdef TS_MPDATA_NOT_YET IF (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp3)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp2i))) THEN # else IF (((Istr.le.Isrc).and.(Isrc.le.Iend+1)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN !> tl_FX(Isrc,Jsrc)=tl_Huon(Isrc,Jsrc,k)* & !> & SOURCES(ng)%Tsrc(is,k,itrc) !> ad_Huon(Isrc,Jsrc,k)=ad_Huon(Isrc,Jsrc,k)+ & & SOURCES(ng)%Tsrc(is,k,itrc)* & & 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 # ifdef TS_MPDATA_NOT_YET IF (((IstrUm2.le.Isrc).and.(Isrc.le.Iendp2i)).and. & & ((JstrVm2.le.Jsrc).and.(Jsrc.le.Jendp3))) THEN # else IF (((Istr.le.Isrc).and.(Isrc.le.Iend)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend+1))) THEN # endif IF (LtracerSrc(itrc,ng)) THEN !> tl_FE(Isrc,Jsrc)=tl_Hvom(Isrc,Jsrc,k)* & !> & SOURCES(ng)%Tsrc(is,k,itrc) !> ad_Hvom(Isrc,Jsrc,k)=ad_Hvom(Isrc,Jsrc,k)+ & & SOURCES(ng)%Tsrc(is,k,itrc)* & & 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 # if defined TS_C2HADVECTION_TL ! ! 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 # elif defined TS_MPDATA_NOT_YET ! ! First-order, upstream differences adjoint horizontal advective ! fluxes. ! DO j=JstrVm2,Jendp3 DO i=IstrUm2,Iendp2i cff1=MAX(Hvom(i,j,k),0.0_r8) cff2=MIN(Hvom(i,j,k),0.0_r8) !> tl_FE(i,j)=tl_cff1*t(i,j-1,k,3,itrc)+ & !> & cff1*tl_t(i,j-1,k,3,itrc)+ & !> & tl_cff2*t(i,j ,k,3,itrc)+ & !> & cff2*tl_t(i,j ,k,3,itrc) !> ad_t(i,j-1,k,3,itrc)=ad_t(i,j-1,k,3,itrc)+ & & cff1*ad_FE(i,j) ad_t(i,j ,k,3,itrc)=ad_t(i,j ,k,3,itrc)+ & & cff2*ad_FE(i,j) ad_cff1=ad_cff1+t(i,j-1,k,3,itrc)*ad_FE(i,j) ad_cff2=ad_cff2+t(i,j ,k,3,itrc)*ad_FE(i,j) ad_FE(i,j)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k)))*tl_Hvom(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))*tl_Hvom(i,j,k) !> ad_Hvom(i,j,k)=ad_Hvom(i,j,k)+ & & (0.5_r8+SIGN(0.5_r8,-Hvom(i,j,k)))* & & ad_cff2+ & & (0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))* & & ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO DO j=JstrVm2,Jendp2i DO i=IstrUm2,Iendp3 cff1=MAX(Huon(i,j,k),0.0_r8) cff2=MIN(Huon(i,j,k),0.0_r8) !> tl_FX(i,j)=tl_cff1*t(i-1,j,k,3,itrc)+ & !> & cff1*tl_t(i-1,j,k,3,itrc)+ & !> & tl_cff2*t(i ,j,k,3,itrc)+ & !> & cff2*tl_t(i ,j,k,3,itrc) !> ad_t(i ,j,k,3,itrc)=ad_t(i ,j,k,3,itrc)+ & & cff2*ad_FX(i,j) ad_t(i-1,j,k,3,itrc)=ad_t(i-1,j,k,3,itrc)+ & & cff1*ad_FX(i,j) ad_cff1=ad_cff1+t(i-1,j,k,3,itrc)*ad_FX(i,j) ad_cff2=ad_cff2+t(i ,j,k,3,itrc)*ad_FX(i,j) ad_FX(i,j)=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8,-Huon(i,j,k)))*tl_Huon(i,j,k) !> tl_cff1=(0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))*tl_Huon(i,j,k) !> ad_Huon(i,j,k)=ad_Huon(i,j,k)+ & & (0.5_r8+SIGN(0.5_r8,-Huon(i,j,k)))* & & ad_cff2+ & & (0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))* & & ad_cff1 ad_cff2=0.0_r8 ad_cff1=0.0_r8 END DO END DO # else ! # if defined TS_U3HADVECTION_TL ! Third-order, uptream-biased horizontal advective fluxes. # elif defined TS_A4HADVECTION_TL ! Fourth-order, Akima horizontal advective fluxes. # else ! Fourth-order, centered differences horizontal advective fluxes. # endif ! Compute BASIC STATE "curv" and "grad" scratch arrays. ! 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 defined TS_U3HADVECTION_TL curv(i,j)=FE(i,j+1)-FE(i,j) # elif defined TS_A4HADVECTION_TL 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 grad(i,j)=0.5_r8*(FE(i,j+1)+FE(i,j)) # endif 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 # ifdef TS_U3HADVECTION_TL !> 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 !> 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 # endif END DO END DO ! DO j=Jstr-1,Jend+1 DO i=Istr,Iend # if defined TS_U3HADVECTION_TL !> 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 # elif defined TS_A4HADVECTION_TL 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 !> 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 # endif 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 defined TS_U3HADVECTION_TL curv(i,j)=FX(i+1,j)-FX(i,j) # elif defined TS_A4HADVECTION_TL 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 grad(i,j)=0.5_r8*(FX(i+1,j)+FX(i,j)) # endif 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 # ifdef TS_U3HADVECTION_TL !> 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 !> 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 # endif END DO END DO ! DO j=Jstr,Jend DO i=Istr-1,Iend+1 # if defined TS_U3HADVECTION_TL !> 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 # elif defined TS_A4HADVECTION_TL 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 !> 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 # endif !> 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 # endif END DO K_LOOP END DO T_LOOP # ifdef TS_MPDATA_NOT_YET ! ! 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. ! # ifdef DISTRIBUTE !> CALL mp_exchange4d (ng, tile, iNLM, 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 IF (EWperiodic(ng).or.NSperiodic(ng)) THEN DO itrc=1,NT(ng) !> 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 DO END IF # endif ! ! Compute adjoint inverse thickness. ! # ifdef TS_MPDATA_NOT_YET # define I_RANGE Istrm2,Iendp2 # define J_RANGE Jstrm2,Jendp2 # else # define I_RANGE Istr,Iend # define J_RANGE Jstr,Jend # endif DO k=1,N(ng) DO j=J_RANGE DO i=I_RANGE 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 #undef I_RANGE #undef J_RANGE RETURN END SUBROUTINE ad_step3d_t_tile #endif END MODULE ad_step3d_t_mod