#include "cppdefs.h" MODULE ad_pre_step3d_mod #if defined ADJOINT && defined SOLVE3D # define NEUMANN ! !git $Id$ !svn $Id: ad_pre_step3d.F 1180 2023-07-13 02:42:10Z 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 subroutine initialize computations for new time step of the ! ! adjoint 3D primitive variables. ! ! ! ! Both n-1 and n-2 time-step contributions of the Adams/Bashforth ! ! scheme are added here to u and v at time index "nnew", since the ! ! right-hand-side arrays ru and rv at n-2 will be overwriten in ! ! subsequent calls to routines within the 3D engine. ! ! ! ! It also computes the time "n" vertical viscosity and diffusion ! ! contributions of the Crank-Nicholson implicit scheme because the ! ! thicknesses "Hz" will be overwriten at the end of the 2D engine ! ! (barotropic mode) computations. ! ! ! ! The actual time step will be carried out in routines "step3d_uv" ! ! and "step3d_t". ! ! ! ! BASIC STATE variables needed: AKt, AKv, Huon, Hvom, Hz, Tsrc, W, ! ! bustr, bvstr, ghats, srflx, sustr, ! ! svstr, t, z_r, z_w ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: ad_pre_step3d ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_pre_step3d (ng, tile) !*********************************************************************** ! USE mod_param # ifdef DIAGNOSTICS !! USE mod_diags # endif USE mod_forces 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, 22, __LINE__, MyFile) # endif CALL ad_pre_step3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & # ifdef FOUR_DVAR & kstp(ng), knew(ng), & # endif & nrhs(ng), nstp(ng), nnew(ng), & # ifdef MASKING & GRID(ng) % rmask, & & GRID(ng) % umask, & & GRID(ng) % vmask, & # if defined SOLAR_SOURCE && defined WET_DRY & GRID(ng) % rmask_wet, & # endif # endif # ifdef FOUR_DVAR & GRID(ng) % om_v, & & GRID(ng) % on_u, & # 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, & & GRID(ng) % z_w, & & GRID(ng) % ad_z_w, & & FORCES(ng) % ad_btflx, & & FORCES(ng) % ad_bustr, & & FORCES(ng) % ad_bvstr, & & FORCES(ng) % ad_stflx, & & FORCES(ng) % ad_sustr, & & FORCES(ng) % ad_svstr, & # ifdef SOLAR_SOURCE & FORCES(ng) % srflx, & # endif & MIXING(ng) % Akt, & & MIXING(ng) % ad_Akt, & & MIXING(ng) % Akv, & & MIXING(ng) % ad_Akv, & # ifdef LMD_NONLOCAL_NOT_YET & MIXING(ng) % ad_ghats, & # endif # ifdef FOUR_DVAR & OCEAN(ng) % ad_ubar, & & OCEAN(ng) % ad_vbar, & # endif & OCEAN(ng) % W, & & OCEAN(ng) % ad_W, & & OCEAN(ng) % ad_ru, & & OCEAN(ng) % ad_rv, & # ifdef DIAGNOSTICS_TS !! & DIAGS(ng) % DiaTwrk, & # endif # ifdef DIAGNOSTICS_UV !! & DIAGS(ng) % DiaU3wrk, & !! & DIAGS(ng) % DiaV3wrk, & !! & DIAGS(ng) % DiaRU, & !! & DIAGS(ng) % DiaRV, & # endif & OCEAN(ng) % t, & & OCEAN(ng) % ad_t, & & OCEAN(ng) % u, & & OCEAN(ng) % ad_u, & & OCEAN(ng) % v, & & OCEAN(ng) % ad_v) # ifdef PROFILE CALL wclock_off (ng, iADM, 22, __LINE__, MyFile) # endif ! RETURN END SUBROUTINE ad_pre_step3d ! !*********************************************************************** SUBROUTINE ad_pre_step3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & # ifdef FOUR_DVAR & kstp, knew, & # endif & nrhs, nstp, nnew, & # ifdef MASKING & rmask, umask, vmask, & # if defined SOLAR_SOURCE && defined WET_DRY & rmask_wet, & # endif # endif # ifdef FOUR_DVAR & om_v, on_u, & # endif & pm, pn, & & Hz, ad_Hz, & & Huon, ad_Huon, & & Hvom, ad_Hvom, & & z_r, ad_z_r, & & z_w, ad_z_w, & & ad_btflx, ad_bustr, ad_bvstr, & & ad_stflx, ad_sustr, ad_svstr, & # ifdef SOLAR_SOURCE & srflx, & # endif & Akt, ad_Akt, & & Akv, ad_Akv, & # ifdef LMD_NONLOCAL_NOT_YET & ad_ghats, & # endif # ifdef FOUR_DVAR & ad_ubar, ad_vbar, & # endif & W, ad_W, & & ad_ru, ad_rv, & # ifdef DIAGNOSTICS_TS !! & DiaTwrk, & # endif # ifdef DIAGNOSTICS_UV !! & DiaU3wrk, DiaV3wrk, & !! & DiaRU, DiaRV, & # endif & t, ad_t, & & u, ad_u, & & v, ad_v) !*********************************************************************** ! USE mod_param 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_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 # ifdef FOUR_DVAR integer, intent(in) :: kstp, knew # endif 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:) # if defined SOLAR_SOURCE && defined WET_DRY real(r8), intent(in) :: rmask_wet(LBi:,LBj:) # endif # endif # ifdef FOUR_DVAR real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(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:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) # ifdef SOLAR_SOURCE real(r8), intent(in) :: srflx(LBi:,LBj:) # endif # ifdef SUN real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) # else real(r8), intent(in) :: Akt(LBi:,LBj:,0:,:) # endif real(r8), intent(in) :: Akv(LBi:,LBj:,0:) # ifdef FOUR_DVAR real(r8), intent(in) :: ad_ubar(LBi:,LBj:,:) real(r8), intent(in) :: ad_vbar(LBi:,LBj:,:) # endif real(r8), intent(in) :: W(LBi:,LBj:,0:) # ifdef SUN real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # else real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) # endif real(r8), intent(in) :: u(LBi:,LBj:,:,:) real(r8), intent(in) :: v(LBi:,LBj:,:,:) # ifdef DIAGNOSTICS_TS !! real(r8), intent(inout) :: DiaTwrk(LBi:,LBj:,:,:,:) # endif # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaU3wrk(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaV3wrk(LBi:,LBj:,:,:) !! real(r8), intent(inout) :: DiaRU(LBi:,LBj:,:,:,:) !! real(r8), intent(inout) :: DiaRV(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:,:) real(r8), intent(inout) :: ad_z_w(LBi:,LBj:,0:) real(r8), intent(inout) :: ad_btflx(LBi:,LBj:,:) real(r8), intent(inout) :: ad_bustr(LBi:,LBj:) real(r8), intent(inout) :: ad_bvstr(LBi:,LBj:) real(r8), intent(inout) :: ad_stflx(LBi:,LBj:,:) real(r8), intent(inout) :: ad_sustr(LBi:,LBj:) real(r8), intent(inout) :: ad_svstr(LBi:,LBj:) real(r8), intent(inout) :: ad_ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: ad_rv(LBi:,LBj:,0:,:) # ifdef LMD_NONLOCAL_NOT_YET real(r8), intent(inout) :: ad_ghats(LBi:,LBj:,0:,:) # endif # 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_Akv(LBi:,LBj:,0:) 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 real(r8), intent(inout) :: ad_u(LBi:,LBj:,:,:) real(r8), intent(inout) :: ad_v(LBi:,LBj:,:,:) # 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) # if defined SOLAR_SOURCE && defined WET_DRY real(r8), intent(in) :: rmask_wet(LBi:UBi,LBj:UBj) # endif # endif # ifdef FOUR_DVAR real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(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) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef SOLAR_SOURCE real(r8), intent(in) :: srflx(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(in) :: Akv(LBi:UBi,LBj:UBj,0:N(ng)) # ifdef FOUR_DVAR real(r8), intent(in) :: ad_ubar(LBi:UBi,LBj:UBj,:) real(r8), intent(in) :: ad_vbar(LBi:UBi,LBj:UBj,:) # endif real(r8), intent(in) :: W(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(in) :: u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(in) :: v(LBi:UBi,LBj:UBj,N(ng),2) # ifdef DIAGNOSTICS_TS !! real(r8), intent(inout) :: DiaTwrk(LBi:UBi,LBj:UBj,N(ng),NT(ng), & !! & NDT) # endif # ifdef DIAGNOSTICS_UV !! real(r8), intent(inout) :: DiaU3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) !! real(r8), intent(inout) :: DiaV3wrk(LBi:UBi,LBj:UBj,N(ng),NDM3d) !! real(r8), intent(inout) :: DiaRU(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) !! real(r8), intent(inout) :: DiaRV(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) # 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_z_w(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(inout) :: ad_btflx(LBi:UBi,LBj:UBj,NT(ng)) real(r8), intent(inout) :: ad_bustr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_bvstr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_stflx(LBi:UBi,LBj:UBj,NT(ng)) real(r8), intent(inout) :: ad_sustr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_svstr(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: ad_rv(LBi:UBi,LBj:UBj,0:N(ng),2) # ifdef LMD_NONLOCAL_NOT_YET real(r8), intent(inout) :: ad_ghats(LBi:UBi,LBj:UBj,0:N(ng),NAT) # endif real(r8), intent(inout) :: ad_Akt(LBi:UBi,LBj:UBj,0:N(ng),NAT) real(r8), intent(inout) :: ad_Akv(LBi:UBi,LBj:UBj,0:N(ng)) 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)) real(r8), intent(inout) :: ad_u(LBi:UBi,LBj:UBj,N(ng),2) real(r8), intent(inout) :: ad_v(LBi:UBi,LBj:UBj,N(ng),2) # endif ! ! Local variable declarations. ! integer :: Isrc, Jsrc integer :: i, ic, indx, is, itrc, j, k, ltrc # if defined AGE_MEAN && defined T_PASSIVE integer :: iage # endif # if defined DIAGNOSTICS_TS || defined DIAGNOSTICS_UV integer :: idiag # endif real(r8), parameter :: eps = 1.0E-16_r8 real(r8) :: cff, cff1, cff2, cff3, cff4 real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3, ad_cff4 real(r8) :: adfac, adfac1, adfac2, adfac3 real(r8) :: Gamma real(r8), dimension(IminS:ImaxS,0:N(ng)) :: CF real(r8), dimension(IminS:ImaxS,0:N(ng)) :: DC 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_DC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_FC # ifdef SOLAR_SOURCE real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: ad_swdk # endif 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 # include "set_bounds.h" ! ! In the tangent model, we have: ! !^ ! nnew=3-nstp !^ indx=3-nrhs ! nrhs=nstp !^ indx=nnew ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_cff3=0.0_r8 ad_cff4=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 # ifdef SOLAR_SOURCE DO k=0,N(ng) DO i=IminS,ImaxS ad_swdk(i,j,k)=0.0_r8 END DO END DO # endif END DO DO k=0,N(ng) DO i=IminS,ImaxS ad_CF(i,k)=0.0_r8 ad_DC(i,k)=0.0_r8 ad_FC(i,k)=0.0_r8 END DO END DO # ifndef TS_FIXED ! !======================================================================= ! Apply tracers lateral boundary conditions. !======================================================================= ! # ifdef DISTRIBUTE !^ CALL mp_exchange4d (ng, tile, iTLM, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), 1, NT(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_t(:,:,:,3,:)) !^ 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(:,:,:,3,:)) ! # endif ! ic=0 DO itrc=1,NT(ng) IF (LtracerCLM(itrc,ng).and.LnudgeTCLM(itrc,ng)) THEN ic=ic+1 END IF IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_t(:,:,:,3,itrc)) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_t(:,:,:,3,itrc)) END IF !^ CALL tl_t3dbc_tile (ng, tile, itrc, ic, & !^ & LBi, UBi, LBj, UBj, N(ng), NT(ng), & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & nstp, 3, & !^ & tl_t) !^ CALL ad_t3dbc_tile (ng, tile, itrc, ic, & & LBi, UBi, LBj, UBj, N(ng), NT(ng), & & IminS, ImaxS, JminS, JmaxS, & & nstp, 3, & & ad_t) END DO # endif ! !======================================================================= ! 3D adjoint momentum equation in the ETA-direction. !======================================================================= ! J_LOOP2 : DO j=Jstr,Jend IF (j.ge.JstrV) THEN ! ! Compute new V-momentum (m m/s). ! cff=dt(ng)*0.25_r8 DO i=Istr,Iend DC(i,0)=cff*(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) END DO IF (iic(ng).eq.ntfirst(ng)) THEN DO k=1,N(ng) DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaV3wrk(i,j,k,M3rate)=cff1 !! DiaV3wrk(i,j,k,M3vvis)=cff2 !! DO idiag=1,M3pgrd !! DiaV3wrk(i,j,k,idiag)=0.0_r8 !! END DO # endif !^ tl_v(i,j,k,nnew)=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_v(i,j,k,nnew) ad_cff2=ad_cff2+ad_v(i,j,k,nnew) ad_v(i,j,k,nnew)=0.0_r8 !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff2 ad_FC(i,k )=ad_FC(i,k )+ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(tl_v(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i,j-1,k))+ & !^ & v(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ adfac=0.5_r8*ad_cff1 adfac1=adfac*v(i,j,k,nstp) ad_v(i,j,k,nstp)=ad_v(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i,j-1,k))*adfac 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_cff1=0.0_r8 END DO END DO ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN DO k=1,N(ng) DO i=Istr,Iend cff3=0.5_r8*DC(i,0) # ifdef DIAGNOSTICS_UV !! DiaV3wrk(i,j,k,M3rate)=cff1 # ifdef BODYFORCE !! DiaV3wrk(i,j,k,M3vvis)=DiaV3wrk(i,j,k,M3vvis)- & !! & cff3*DiaRV(i,j,k,indx,M3vvis) # endif !! DiaV3wrk(i,j,k,M3vvis)=cff2 !! DO idiag=1,M3pgrd !! DiaV3wrk(i,j,k,idiag)=-cff3*DiaRV(i,j,k,indx,idiag) !! END DO # endif !^ tl_v(i,j,k,nnew)=tl_cff1- & !^ & cff3*tl_rv(i,j,k,indx)+ & !^ & tl_cff2 ! ad_rv(i,j,k,indx)=ad_rv(i,j,k,indx)- & & cff3*ad_v(i,j,k,nnew) ad_cff1=ad_cff1+ad_v(i,j,k,nnew) ad_cff2=ad_cff2+ad_v(i,j,k,nnew) ad_v(i,j,k,nnew)=0.0_r8 !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff2 ad_FC(i,k )=ad_FC(i,k )+ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(tl_v(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i,j-1,k))+ & !^ & v(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ adfac=0.5_r8*ad_cff1 adfac1=adfac*v(i,j,k,nstp) 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_v(i,j,k,nstp)=ad_v(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i,j-1,k))*adfac ad_cff1=0.0_r8 END DO END DO ELSE cff1= 5.0_r8/12.0_r8 cff2=16.0_r8/12.0_r8 DO k=1,N(ng) DO i=Istr,Iend # ifdef DIAGNOSTICS_UV !! DiaV3wrk(i,j,k,M3rate)=cff3 # ifdef BODYFORCE !! DiaV3wrk(i,j,k,M3vvis)=DiaV3wrk(i,j,k,M3vvis)+ & !! & DC(i,0)* & !! & (cff1*DiaRV(i,j,k,nrhs,M3vvis)- & !! & cff2*DiaRV(i,j,k,indx,M3vvis)) # endif !! DiaV3wrk(i,j,k,M3vvis)=cff4 !! DO idiag=1,M3pgrd !! DiaV3wrk(i,j,k,idiag)=DC(i,0)* & !! & (cff1*DiaRV(i,j,k,nrhs,idiag)- & !! & cff2*DiaRV(i,j,k,indx,idiag)) !! END DO # endif !^ tl_v(i,j,k,nnew)=tl_cff3+ & !^ & DC(i,0)*(cff1*tl_rv(i,j,k,nrhs)- & !^ & cff2*tl_rv(i,j,k,indx))+ & !^ & tl_cff4 !^ adfac=DC(i,0)*ad_v(i,j,k,nnew) ad_rv(i,j,k,nrhs)=ad_rv(i,j,k,nrhs)+cff1*adfac ad_rv(i,j,k,indx)=ad_rv(i,j,k,indx)-cff2*adfac ad_cff3=ad_cff3+ad_v(i,j,k,nnew) ad_cff4=ad_cff4+ad_v(i,j,k,nnew) ad_v(i,j,k,nnew)=0.0_r8 !^ tl_cff4=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff4 ad_FC(i,k )=ad_FC(i,k )+ad_cff4 ad_cff4=0.0_r8 !^ tl_cff3=0.5_r8*(tl_v(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i,j-1,k))+ & !^ & v(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i,j-1,k))) !^ adfac=0.5_r8*ad_cff3 adfac1=adfac*v(i,j,k,nstp) 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_v(i,j,k,nstp)=ad_v(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i,j-1,k))*adfac ad_cff3=0.0_r8 END DO END DO END IF ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=Istr,Iend # ifdef BODYFORCE !^ 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 # else !^ tl_FC(i,N(ng))=dt(ng)*tl_svstr(i,j) !^ ad_svstr(i,j)=ad_svstr(i,j)+dt(ng)*ad_FC(i,N(ng)) ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=dt(ng)*tl_bvstr(i,j) !^ ad_bvstr(i,j)=ad_bvstr(i,j)+dt(ng)*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # endif END DO ! ! Compute adjoint V-component viscous vertical momentum fluxes "FC" ! at current time-step n, and at horizontal V-points and vertical ! W-points. ! cff3=dt(ng)*(1.0_r8-lambda) DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(z_r(i,j,k+1)+z_r(i,j-1,k+1)- & & z_r(i,j,k )-z_r(i,j-1,k )) !^ tl_FC(i,k)=cff3* & !^ & (cff*((tl_v(i,j,k+1,nstp)-tl_v(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i,j-1,k))+ & !^ & (v(i,j,k+1,nstp)-v(i,j,k,nstp))* & !^ & (tl_Akv(i,j,k)+tl_Akv(i,j-1,k)))+ & !^ & tl_cff*(v(i,j,k+1,nstp)-v(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i,j-1,k))) !^ adfac=cff3*ad_FC(i,k) adfac1=adfac*cff adfac2=adfac1*(Akv(i,j,k)+Akv(i,j-1,k)) adfac3=adfac1*(v(i,j,k+1,nstp)-v(i,j,k,nstp)) ad_v(i,j,k ,nstp)=ad_v(i,j,k ,nstp)-adfac2 ad_v(i,j,k+1,nstp)=ad_v(i,j,k+1,nstp)+adfac2 ad_Akv(i,j-1,k)=ad_Akv(i,j-1,k)+adfac3 ad_Akv(i,j ,k)=ad_Akv(i,j ,k)+adfac3 ad_cff=ad_cff+ & & (v(i,j,k+1,nstp)-v(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i,j-1,k))*adfac ad_FC(i,k)=0.0_r8 !^ tl_cff=-cff*cff*(tl_z_r(i,j,k+1)+tl_z_r(i,j-1,k+1)- & !^ & tl_z_r(i,j,k )-tl_z_r(i,j-1,k )) !^ adfac=-cff*cff*ad_cff ad_z_r(i,j-1,k )=ad_z_r(i,j-1,k )-adfac ad_z_r(i,j ,k )=ad_z_r(i,j ,k )-adfac ad_z_r(i,j-1,k+1)=ad_z_r(i,j-1,k+1)+adfac ad_z_r(i,j ,k+1)=ad_z_r(i,j ,k+1)+adfac ad_cff=0.0_r8 END DO END DO END IF ! !===================================================================== ! 3D adjoint momentum equation in the XI-direction. !===================================================================== ! ! Compute new U-momentum (m m/s). ! cff=dt(ng)*0.25_r8 DO i=IstrU,Iend DC(i,0)=cff*(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) END DO IF (iic(ng).eq.ntfirst(ng)) THEN DO k=1,N(ng) DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaU3wrk(i,j,k,M3rate)=cff1 !! DiaU3wrk(i,j,k,M3vvis)=cff2 !! DO idiag=1,M3pgrd !! DiaU3wrk(i,j,k,idiag)=0.0_r8 !! END DO # endif !^ tl_u(i,j,k,nnew)=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_u(i,j,k,nnew) ad_cff2=ad_cff2+ad_u(i,j,k,nnew) ad_u(i,j,k,nnew)=0.0_r8 !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff2 ad_FC(i,k )=ad_FC(i,k )+ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(tl_u(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i-1,j,k))+ & !^ & u(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ adfac=0.5_r8*ad_cff1 adfac1=adfac*u(i,j,k,nstp) 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_u(i,j,k,nstp)=ad_u(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i-1,j,k))*adfac ad_cff1=0.0_r8 END DO END DO ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN DO k=1,N(ng) DO i=IstrU,Iend cff3=0.5_r8*DC(i,0) # ifdef DIAGNOSTICS_UV !! DiaU3wrk(i,j,k,M3rate)=cff1 # ifdef BODYFORCE !! DiaU3wrk(i,j,k,M3vvis)=DiaU3wrk(i,j,k,M3vvis)- & !! & cff3*DiaRU(i,j,k,indx,M3vvis) # endif !! DO idiag=1,M3pgrd !! DiaU3wrk(i,j,k,idiag)=-cff3*DiaRU(i,j,k,indx,idiag) !! END DO !! DiaU3wrk(i,j,k,M3vvis)=cff2 # endif !^ tl_u(i,j,k,nnew)=tl_cff1- & !^ & cff3*tl_ru(i,j,k,indx)+ & !^ & tl_cff2 !^ ad_ru(i,j,k,indx)=ad_ru(i,j,k,indx)- & & cff3*ad_u(i,j,k,nnew) ad_cff1=ad_cff1+ad_u(i,j,k,nnew) ad_cff2=ad_cff2+ad_u(i,j,k,nnew) ad_u(i,j,k,nnew)=0.0_r8 !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff2 ad_FC(i,k )=ad_FC(i,k )+ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=0.5_r8*(tl_u(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i-1,j,k))+ & !^ & u(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ adfac=0.5_r8*ad_cff1 adfac1=adfac*u(i,j,k,nstp) 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_u(i,j,k,nstp)=ad_u(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i-1,j,k))*adfac ad_cff1=0.0_r8 END DO END DO ELSE cff1= 5.0_r8/12.0_r8 cff2=16.0_r8/12.0_r8 DO k=1,N(ng) DO i=IstrU,Iend # ifdef DIAGNOSTICS_UV !! DiaU3wrk(i,j,k,M3rate)=cff3 # ifdef BODYFORCE !! DiaU3wrk(i,j,k,M3vvis)=DiaU3wrk(i,j,k,M3vvis)+ & !! & DC(i,0)* & !! & (cff1*DiaRU(i,j,k,nrhs,M3vvis)- & !! & cff2*DiaRU(i,j,k,indx,M3vvis)) # endif !! DiaU3wrk(i,j,k,M3vvis)=cff4 !! DO idiag=1,M3pgrd !! DiaU3wrk(i,j,k,idiag)=DC(i,0)* & !! & (cff1*DiaRU(i,j,k,nrhs,idiag)- & !! & cff2*DiaRU(i,j,k,indx,idiag)) !! END DO # endif !^ tl_u(i,j,k,nnew)=tl_cff3+ & !^ & DC(i,0)*(cff1*tl_ru(i,j,k,nrhs)- & !^ & cff2*tl_ru(i,j,k,indx))+ & !^ & tl_cff4 !^ adfac=DC(i,0)*ad_u(i,j,k,nnew) ad_ru(i,j,k,nrhs)=ad_ru(i,j,k,nrhs)+cff1*adfac ad_ru(i,j,k,indx)=ad_ru(i,j,k,indx)-cff2*adfac ad_cff3=ad_cff3+ad_u(i,j,k,nnew) ad_cff4=ad_cff4+ad_u(i,j,k,nnew) ad_u(i,j,k,nnew)=0.0_r8 !^ tl_cff4=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff4 ad_FC(i,k )=ad_FC(i,k )+ad_cff4 ad_cff4=0.0_r8 !^ tl_cff3=0.5_r8*(tl_u(i,j,k,nstp)* & !^ & (Hz(i,j,k)+Hz(i-1,j,k))+ & !^ & u(i,j,k,nstp)* & !^ & (tl_Hz(i,j,k)+tl_Hz(i-1,j,k))) !^ adfac=0.5_r8*ad_cff3 adfac1=adfac*u(i,j,k,nstp) 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_u(i,j,k,nstp)=ad_u(i,j,k,nstp)+ & & (Hz(i,j,k)+Hz(i-1,j,k))*adfac ad_cff3=0.0_r8 END DO END DO END IF ! ! Apply bottom and surface stresses, if so is prescribed. ! DO i=IstrU,Iend # ifdef BODYFORCE !^ 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 # else !^ tl_FC(i,N(ng))=dt(ng)*tl_sustr(i,j) !^ ad_sustr(i,j)=ad_sustr(i,j)+dt(ng)*ad_FC(i,N(ng)) ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=dt(ng)*tl_bustr(i,j) !^ ad_bustr(i,j)=ad_bustr(i,j)+dt(ng)*ad_FC(i,0) ad_FC(i,0)=0.0_r8 # endif END DO ! ! Compute adjoint U-component viscous vertical momentum fluxes "FC" ! at current time-step n, and at horizontal U-points and vertical ! W-points. ! cff3=dt(ng)*(1.0_r8-lambda) DO k=1,N(ng)-1 DO i=IstrU,Iend cff=1.0/(z_r(i,j,k+1)+z_r(i-1,j,k+1)- & & z_r(i,j,k )-z_r(i-1,j,k )) !^ tl_FC(i,k)=cff3* & !^ & (cff*((tl_u(i,j,k+1,nstp)-tl_u(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i-1,j,k))+ & !^ & (u(i,j,k+1,nstp)-u(i,j,k,nstp))* & !^ & (tl_Akv(i,j,k)+tl_Akv(i-1,j,k)))+ & !^ & tl_cff*(u(i,j,k+1,nstp)-u(i,j,k,nstp))* & !^ & (Akv(i,j,k)+Akv(i-1,j,k))) !^ adfac=cff3*ad_FC(i,k) adfac1=adfac*cff adfac2=adfac1*(Akv(i,j,k)+Akv(i-1,j,k)) adfac3=adfac1*(u(i,j,k+1,nstp)-u(i,j,k,nstp)) ad_u(i,j,k ,nstp)=ad_u(i,j,k ,nstp)-adfac2 ad_u(i,j,k+1,nstp)=ad_u(i,j,k+1,nstp)+adfac2 ad_Akv(i-1,j,k)=ad_Akv(i-1,j,k)+adfac3 ad_Akv(i ,j,k)=ad_Akv(i ,j,k)+adfac3 ad_cff=ad_cff+ & & (u(i,j,k+1,nstp)-u(i,j,k,nstp))* & & (Akv(i,j,k)+Akv(i-1,j,k))*adfac ad_FC(i,k)=0.0_r8 !^ tl_cff=-cff*cff*(tl_z_r(i,j,k+1)+tl_z_r(i-1,j,k+1)- & !^ & tl_z_r(i,j,k )-tl_z_r(i-1,j,k )) !^ adfac=-cff*cff*ad_cff ad_z_r(i-1,j,k )=ad_z_r(i-1,j,k )-adfac ad_z_r(i ,j,k )=ad_z_r(i ,j,k )-adfac ad_z_r(i-1,j,k+1)=ad_z_r(i-1,j,k+1)+adfac ad_z_r(i ,j,k+1)=ad_z_r(i ,j,k+1)+adfac ad_cff=0.0_r8 END DO END DO END DO J_LOOP2 # ifndef TS_FIXED ! !======================================================================= ! Adjoint tracer equation(s). !======================================================================= ! !----------------------------------------------------------------------- ! Start computation of tracers at n+1 time-step, t(i,j,k,nnew,itrc). !----------------------------------------------------------------------- ! ! Compute vertical diffusive fluxes "FC" of the tracer fields at ! current time step n, and at horizontal RHO-points and vertical ! W-points. ! DO j=Jstr,Jend DO itrc=1,NT(ng) ! ! Compute new tracer field (m Tunits). ! DO k=1,N(ng) DO i=Istr,Iend # ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iTvdif)=cff2 !! DiaTwrk(i,j,k,itrc,iTrate)=cff1 # endif !^ tl_t(i,j,k,nnew,itrc)=tl_cff1+tl_cff2 !^ ad_cff1=ad_cff1+ad_t(i,j,k,nnew,itrc) ad_cff2=ad_cff2+ad_t(i,j,k,nnew,itrc) ad_t(i,j,k,nnew,itrc)=0.0_r8 !^ tl_cff2=tl_FC(i,k)-tl_FC(i,k-1) !^ ad_FC(i,k-1)=ad_FC(i,k-1)-ad_cff2 ad_FC(i,k )=ad_FC(i,k )+ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=tl_Hz(i,j,k)*t(i,j,k,nstp,itrc)+ & !^ & Hz(i,j,k)*tl_t(i,j,k,nstp,itrc) !^ ad_t(i,j,k,nstp,itrc)=ad_t(i,j,k,nstp,itrc)+ & & Hz(i,j,k)*ad_cff1 ad_Hz(i,j,k)=ad_Hz(i,j,k)+t(i,j,k,nstp,itrc)*ad_cff1 ad_cff1=0.0_r8 END DO END DO ! ! Apply bottom and surface tracer flux conditions. ! DO i=Istr,Iend !^ tl_FC(i,N(ng))=dt(ng)*tl_stflx(i,j,itrc) !^ ad_stflx(i,j,itrc)=ad_stflx(i,j,itrc)+dt(ng)*ad_FC(i,N(ng)) ad_FC(i,N(ng))=0.0_r8 !^ tl_FC(i,0)=dt(ng)*tl_btflx(i,j,itrc) !^ ad_btflx(i,j,itrc)=ad_btflx(i,j,itrc)+dt(ng)*ad_FC(i,0) ad_FC(i,0)=0.0_r8 END DO # ifdef SOLAR_SOURCE ! ! Add in incoming solar radiation at interior W-points using decay ! decay penetration function based on Jerlov water type. ! IF (itrc.eq.itemp) THEN DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k)=tl_FC(i,k)+ & !^ & dt(ng)*srflx(i,j)* & # ifdef WET_DRY_NOT_YET !^ & rmask_wet(i,j)* & # endif !^ & tl_swdk(i,j,k) !^ ad_swdk(i,j,k)=ad_swdk(i,j,k)+ & & dt(ng)*srflx(i,j)* & # ifdef WET_DRY_NOT_YET & rmask_wet(i,j)* & # endif & ad_FC(i,k) END DO END DO END IF # endif # ifdef LMD_NONLOCAL_NOT_YET ! ! Add in the nonlocal transport flux for unstable (convective) ! forcing conditions into matrix FC when using the Large et al. ! KPP scheme. The nonlocal transport is only applied to active ! tracers. ! IF (itrc.le.NAT) THEN DO k=1,N(ng)-1 DO i=Istr,Iend !^ tl_FC(i,k)=tl_FC(i,k)- & !^ & dt(ng)*(tl_Akt(i,j,k,itrc)* & !^ & ghats(i,j,k,itrc)+ & !^ & Akt(i,j,k,itrc)* & !^ & tl_ghats(i,j,k,itrc)) !^ adfac=dt(ng)*ad_FC(i,k) ad_ghats(i,j,k,itrc)=ad_ghats(i,j,k,itrc)- & & Akt(i,j,k,itrc)*adfac ad_Akt(i,j,k,itrc)=ad_Akt(i,j,k,itrc)- & & ghats(i,j,k,itrc)*adfac END DO END DO END IF # endif ! ! Compute adjoint vertical diffusive fluxes "FC" of the tracer fields ! at current time step n, and at horizontal RHO-points and vertical ! W-points. Notice that the vertical diffusion coefficients for ! passive tracers is the same as that for salinity (ltrc=NAT). ! cff3=dt(ng)*(1.0_r8-lambda) ltrc=MIN(NAT,itrc) DO k=1,N(ng)-1 DO i=Istr,Iend cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) !^ tl_FC(i,k)=cff3* & !^ & (cff*(tl_Akt(i,j,k,ltrc)* & !^ & (t(i,j,k+1,nstp,itrc)- & !^ & t(i,j,k ,nstp,itrc))+ & !^ & Akt(i,j,k,ltrc)* & !^ & (tl_t(i,j,k+1,nstp,itrc)- & !^ & tl_t(i,j,k ,nstp,itrc)))+ & !^ & tl_cff*(Akt(i,j,k,ltrc)* & !^ & (t(i,j,k+1,nstp,itrc)- & !^ & t(i,j,k,nstp,itrc)))) !^ adfac=cff3*ad_FC(i,k) adfac1=adfac*cff adfac2=adfac1*Akt(i,j,k,ltrc) ad_Akt(i,j,k,ltrc)=ad_Akt(i,j,k,ltrc)+ & & (t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc))*adfac1 ad_t(i,j,k ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)-adfac2 ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+adfac2 ad_cff=ad_cff+ & & (Akt(i,j,k,ltrc)* & & (t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc)))*adfac ad_FC(i,k)=0.0_r8 !^ tl_cff=-cff*cff*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k)) !^ adfac=-cff*cff*ad_cff 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_cff=0.0_r8 END DO END DO END DO END DO ! !------------------------------------------------------------------------ ! Time-step adjoint vertical advection of tracers. Impose artificial ! continuity equation. !------------------------------------------------------------------------ ! J_LOOP1 : DO j=Jstr,Jend T_LOOP2 : DO itrc=1,NT(ng) ! VADV_FLUX1 : IF (ad_Vadvection(itrc,ng)%SPLINES) THEN ! ! Build BASIC 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,nstp,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,nstp,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,nstp,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,nstp,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),nstp,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),nstp,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,nstp,itrc)- & & t(i,j,k ,nstp,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 ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc)- & & cff1*(CF(i,k+1)-CF(i,k))) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 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 ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc)) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ELSE IF ((ad_Vadvection(itrc,ng)%MPDATA).or. & & (ad_Vadvection(itrc,ng)%HSIMT)) THEN ! ! First_order, BASIC STATE upstream differences vertical advective ! flux. ! DO i=Istr,Iend 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 ,nstp,itrc)+ & & cff2*t(i,j,k+1,nstp,itrc) END DO FC(i,0)=0.0_r8 FC(i,N(ng))=0.0_r8 END DO ! ELSE IF ((ad_Vadvection(itrc,ng)%CENTERED4).or. & & (ad_Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, BASIC STATE central differences vertical advective ! flux. ! 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 ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))- & & cff3*(t(i,j,k-1,nstp,itrc)+ & & t(i,j,k+2,nstp,itrc))) END DO END DO DO i=Istr,Iend FC(i,0)=0.0_r8 FC(i,1)=W(i,j,1)* & & (cff1*t(i,j,1,nstp,itrc)+ & & cff2*t(i,j,2,nstp,itrc)- & & cff3*t(i,j,3,nstp,itrc)) FC(i,N(ng)-1)=W(i,j,N(ng)-1)* & & (cff1*t(i,j,N(ng) ,nstp,itrc)+ & & cff2*t(i,j,N(ng)-1,nstp,itrc)- & & cff3*t(i,j,N(ng)-2,nstp,itrc)) FC(i,N(ng))=0.0_r8 END DO END IF VADV_FLUX1 ! ! Compute BASIC STATE artificial continuity equation and load it ! into private array DC (1/m). It is needed to preserve tracer ! constancy. It is not the same for all the tracer advection ! schemes because of the Gamma value. ! IF ((Vadvection(itrc,ng)%MPDATA).or. & & (Vadvection(itrc,ng)%HSIMT)) THEN Gamma=0.5_r8 ELSE Gamma=1.0_r8/6.0_r8 END IF IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) ELSE cff=(1.0_r8-Gamma)*dt(ng) END IF DO k=1,N(ng) DO i=Istr,Iend DC(i,k)=1.0_r8/(Hz(i,j,k)- & & cff*pm(i,j)*pn(i,j)* & & (Huon(i+1,j,k)-Huon(i,j,k)+ & & Hvom(i,j+1,k)-Hvom(i,j,k)+ & & (W(i,j,k)-W(i,j,k-1)))) END DO END DO ! ! Adjoint of Time-step vertical advection of tracers (Tunits). ! ! WARNING: t(:,:,:,3,itrc) at this point should be in units of ! ======= m Tunits. But, t(:,:,:,3,itrc) is read from a BASIC ! STATE file and is in Tunits, so we need to multiply ! by level thickness (Hz). ! DO k=1,N(ng) DO i=Istr,Iend cff1=cff*pm(i,j)*pn(i,j) !^ tl_t(i,j,k,3,itrc)=tl_DC(i,k)* & !^ & (t(i,j,k,3,itrc)*Hz(i,j,k)- & !^ & cff1*(FC(i,k)-FC(i,k-1)))+ & !^ & DC(i,k)* & !^ & (tl_t(i,j,k,3,itrc)- & !^ & cff1*(tl_FC(i,k)-tl_FC(i,k-1))) !^ adfac=DC(i,k)*ad_t(i,j,k,3,itrc) adfac1=adfac*cff1 ad_DC(i,k)=ad_DC(i,k)+ & & (t(i,j,k,3,itrc)*Hz(i,j,k)- & & cff1*(FC(i,k)-FC(i,k-1)))* & & ad_t(i,j,k,3,itrc) ad_FC(i,k-1)=ad_FC(i,k-1)+adfac1 ad_FC(i,k )=ad_FC(i,k )-adfac1 ad_t(i,j,k,3,itrc)=adfac END DO END DO ! ! Compute adjoint artificial continuity equation (same for all tracers) ! and load it into private array DC (1/m). Notice that "cff" has not ! changed from above. ! DO k=1,N(ng) DO i=Istr,Iend !^ tl_DC(i,k)=-DC(i,k)*DC(i,k)* & !^ & (tl_Hz(i,j,k)- & !^ & cff*pm(i,j)*pn(i,j)* & !^ & (tl_Huon(i+1,j,k)-tl_Huon(i,j,k)+ & !^ & tl_Hvom(i,j+1,k)-tl_Hvom(i,j,k)+ & !^ & (tl_W(i,j,k)-tl_W(i,j,k-1)))) !^ adfac=-DC(i,k)*DC(i,k)*ad_DC(i,k) adfac1=adfac*cff*pm(i,j)*pn(i,j) ad_Hz(i,j,k)=ad_Hz(i,j,k)+adfac ad_Huon(i ,j,k)=ad_Huon(i ,j,k)+adfac1 ad_Huon(i+1,j,k)=ad_Huon(i+1,j,k)-adfac1 ad_Hvom(i,j ,k)=ad_Hvom(i,j ,k)+adfac1 ad_Hvom(i,j+1,k)=ad_Hvom(i,j+1,k)-adfac1 ad_W(i,j,k-1)=ad_W(i,j,k-1)+adfac1 ad_W(i,j,k )=ad_W(i,j,k )-adfac1 ad_DC(i,k)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Compute adjoint time rate of change of intermediate tracer due to ! vertical advection. !----------------------------------------------------------------------- ! VADV_FLUX2 : IF (ad_Vadvection(itrc,ng)%SPLINES) THEN ! ! Construct BASIC STATE conservative parabolic splines for the vertical ! derivatives "CF" of the tracer. ! DO i=Istr,Iend # ifdef NEUMANN FC(i,0)=1.5_r8*t(i,j,1,nstp,itrc) CF(i,1)=0.5_r8 # else FC(i,0)=2.0_r8*t(i,j,1,nstp,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,nstp,itrc)+ & & Hz(i,j,k+1)*t(i,j,k ,nstp,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),nstp,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),nstp,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 spline 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),nstp,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),nstp,itrc)=ad_t(i,j,N(ng),nstp,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),nstp,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),nstp,itrc)=ad_t(i,j,N(ng),nstp,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_r8 # 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,nstp,itrc)+ & !^ & Hz(i,j,k+1)* & !^ & tl_t(i,j,k ,nstp,itrc)+ & !^ & tl_Hz(i,j,k )* & !^ & t(i,j,k+1,nstp,itrc)+ & !^ & tl_Hz(i,j,k+1)* & !^ & t(i,j,k ,nstp,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 ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)+ & & Hz(i,j,k+1)*adfac1 ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+ & & Hz(i,j,k )*adfac1 ad_Hz(i,j,k )=ad_Hz(i,j,k )+ & & t(i,j,k+1,nstp,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 ,nstp,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,nstp,itrc) !^ ad_t(i,j,1,nstp,itrc)=ad_t(i,j,1,nstp,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,nstp,itrc) !^ ad_t(i,j,1,nstp,itrc)=ad_t(i,j,1,nstp,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, adjoint Akima vertical advective flux. ! DO k=1,N(ng)-1 DO i=Istr,Iend FC(i,k)=t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,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 !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 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 ,nstp,itrc)+ & !^ & t(i,j,k+1,nstp,itrc)- & !^ & cff1*(CF(i,k+1)-CF(i,k)))+ & !^ & W(i,j,k)* & !^ & (tl_t(i,j,k ,nstp,itrc)+ & !^ & tl_t(i,j,k+1,nstp,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 ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)+adfac1 ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+adfac1 ad_W(i,j,k)=ad_W(i,j,k)+ & & (t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,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,nstp,itrc)- & !^ & tl_t(i,j,k ,nstp,itrc) !^ ad_t(i,j,k ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)- & & ad_FC(i,k) ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,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 vertical advective 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 !^ tl_FC(i,k)=0.5_r8* & !^ & (tl_W(i,j,k)* & !^ & (t(i,j,k ,nstp,itrc)+ & !^ & t(i,j,k+1,nstp,itrc))+ & !^ & W(i,j,k)* & !^ & (tl_t(i,j,k ,nstp,itrc)+ & !^ & tl_t(i,j,k+1,nstp,itrc))) !^ adfac=0.5_r8*ad_FC(i,k) adfac1=adfac*W(i,j,k) ad_W(i,j,k)=ad_W(i,j,k)+ & & (t(i,j,k ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))*adfac ad_t(i,j,k ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)+adfac1 ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+adfac1 ad_FC(i,k)=0.0_r8 END DO END DO ! ELSE IF ((ad_Vadvection(itrc,ng)%MPDATA).or. & & (ad_Vadvection(itrc,ng)%HSIMT)) THEN ! ! First_order, upstream differences vertical advective 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(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 ,nstp,itrc)+ & !^ & cff1*tl_t(i,j,k ,nstp,itrc)+ & !^ & tl_cff2*t(i,j,k+1,nstp,itrc)+ & !^ & cff2*tl_t(i,j,k+1,nstp,itrc) !^ ad_t(i,j,k ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)+ & & cff1*ad_FC(i,k) ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+ & & cff2*ad_FC(i,k) ad_cff1=ad_cff1+t(i,j,k ,nstp,itrc)*ad_FC(i,k) ad_cff2=ad_cff2+t(i,j,k+1,nstp,itrc)*ad_FC(i,k) ad_FC(i,k)=0.0_r8 !^ tl_cff1=(0.5_r8+SIGN(0.5_r8, W(i,j,k)))*tl_W(i,j,k) !^ tl_cff2=(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 IF ((ad_Vadvection(itrc,ng)%CENTERED4).or. & & (ad_Vadvection(itrc,ng)%SPLIT_U3)) THEN ! ! Fourth-order, central differences 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) ,nstp,itrc)+ & !^ & cff2*t(i,j,N(ng)-1,nstp,itrc)- & !^ & cff3*t(i,j,N(ng)-2,nstp,itrc))+ & !^ & W(i,j,N(ng)-1)* & !^ & (cff1*tl_t(i,j,N(ng) ,nstp,itrc)+ & !^ & cff2*tl_t(i,j,N(ng)-1,nstp,itrc)- & !^ & cff3*tl_t(i,j,N(ng)-2,nstp,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) ,nstp,itrc)+ & & cff2*t(i,j,N(ng)-1,nstp,itrc)- & & cff3*t(i,j,N(ng)-2,nstp,itrc))* & & ad_FC(i,N(ng)-1) ad_t(i,j,N(ng)-2,nstp,itrc)=ad_t(i,j,N(ng)-2,nstp,itrc)- & & cff3*adfac ad_t(i,j,N(ng)-1,nstp,itrc)=ad_t(i,j,N(ng)-1,nstp,itrc)+ & & cff2*adfac ad_t(i,j,N(ng) ,nstp,itrc)=ad_t(i,j,N(ng) ,nstp,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,nstp,itrc)+ & !^ & cff2*t(i,j,2,nstp,itrc)- & !^ & cff3*t(i,j,3,nstp,itrc))+ & !^ & W(i,j,1)* & !^ & (cff1*tl_t(i,j,1,nstp,itrc)+ & !^ & cff2*tl_t(i,j,2,nstp,itrc)- & !^ & cff3*tl_t(i,j,3,nstp,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,nstp,itrc)+ & & cff2*t(i,j,2,nstp,itrc)- & & cff3*t(i,j,3,nstp,itrc))*ad_FC(i,1) ad_t(i,j,1,nstp,itrc)=ad_t(i,j,1,nstp,itrc)+cff1*adfac ad_t(i,j,2,nstp,itrc)=ad_t(i,j,2,nstp,itrc)+cff2*adfac ad_t(i,j,3,nstp,itrc)=ad_t(i,j,3,nstp,itrc)-cff3*adfac ad_FC(i,1)=0.0_r8 !^ tl_FC(i,0)=0.0_r8 !^ ad_FC(i,0)=0.0_r8 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 ,nstp,itrc)+ & !^ & t(i,j,k+1,nstp,itrc))- & !^ & cff3*(t(i,j,k-1,nstp,itrc)+ & !^ & t(i,j,k+2,nstp,itrc)))+ & !^ & W(i,j,k)* & !^ & (cff2*(tl_t(i,j,k ,nstp,itrc)+ & !^ & tl_t(i,j,k+1,nstp,itrc))- & !^ & cff3*(tl_t(i,j,k-1,nstp,itrc)+ & !^ & tl_t(i,j,k+2,nstp,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 ,nstp,itrc)+ & & t(i,j,k+1,nstp,itrc))- & & cff3*(t(i,j,k-1,nstp,itrc)+ & & t(i,j,k+2,nstp,itrc)))*ad_FC(i,k) ad_t(i,j,k-1,nstp,itrc)=ad_t(i,j,k-1,nstp,itrc)-adfac2 ad_t(i,j,k ,nstp,itrc)=ad_t(i,j,k ,nstp,itrc)+adfac1 ad_t(i,j,k+1,nstp,itrc)=ad_t(i,j,k+1,nstp,itrc)+adfac1 ad_t(i,j,k+2,nstp,itrc)=ad_t(i,j,k+2,nstp,itrc)-adfac2 ad_FC(i,k)=0.0_r8 END DO END DO END IF VADV_FLUX2 END DO T_LOOP2 END DO J_LOOP1 # 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). ! Implemented and tested by W.G. Zhang and J. Wilkin. (m Tunits) ! DO itrc=1,NPT,2 IF (.not.((ad_Hadvection(inert(itrc),ng)%MPDATA).or. & & (ad_Hadvection(inert(itrc),ng)%HSIMT))) THEN IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) ELSE Gamma=1.0_r8/6.0_r8 cff=(1.0_r8-Gamma)*dt(ng) END IF 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,3,iage)=tl_t(i,j,k,3,iage)+ & !^ & cff* & !^ & (Hz(i,j,k)* & !^ & tl_t(i,j,k,nnew,inert(itrc))+ & !^ & tl_Hz(i,j,k)* & !^ & t(i,j,k,nnew,inert(itrc))) !^ adfac=cff*ad_t(i,j,k,3,iage) ad_t(i,j,k,nnew,inert(itrc))=ad_t(i,j,k,nnew, & & inert(itrc))+ & & Hz(i,j,k)*adfac ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & t(i,j,k,nnew,inert(itrc))*adfac END DO END DO END DO END IF END DO # endif ! ! Compute adjoint time rate of change of intermediate tracer due to ! horizontal advection. ! T_LOOP1 :DO itrc=1,NT(ng) K_LOOP: DO k=1,N(ng) ! ! Time-step horizontal advection (m Tunits). ! IF ((ad_Hadvection(itrc,ng)%MPDATA).or. & & (ad_Hadvection(itrc,ng)%HSIMT)) THEN Gamma=0.5_r8 ELSE Gamma=1.0_r8/6.0_r8 END IF IF (iic(ng).eq.ntfirst(ng)) THEN cff=0.5_r8*dt(ng) cff1=1.0_r8 cff2=0.0_r8 ELSE cff=(1.0_r8-Gamma)*dt(ng) cff1=0.5_r8+Gamma cff2=0.5_r8-Gamma END IF DO j=Jstr,Jend DO i=Istr,Iend !^ tl_t(i,j,k,3,itrc)=tl_Hz(i,j,k)* & !^ & (cff1*t(i,j,k,nstp,itrc)+ & !^ & cff2*t(i,j,k,nnew,itrc))+ & !^ & Hz(i,j,k)* & !^ & (cff1*tl_t(i,j,k,nstp,itrc)+ & !^ & cff2*tl_t(i,j,k,nnew,itrc))- & !^ & cff*pm(i,j)*pn(i,j)* & !^ & (tl_FX(i+1,j)-tl_FX(i,j)+ & !^ & tl_FE(i,j+1)-tl_FE(i,j)) !^ adfac1=Hz(i,j,k)*ad_t(i,j,k,3,itrc) adfac2=cff*pm(i,j)*pn(i,j)*ad_t(i,j,k,3,itrc) ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & (cff1*t(i,j,k,nstp,itrc)+ & & cff2*t(i,j,k,nnew,itrc))*ad_t(i,j,k,3,itrc) ad_t(i,j,k,nstp,itrc)=ad_t(i,j,k,nstp,itrc)+cff1*adfac1 ad_t(i,j,k,nnew,itrc)=ad_t(i,j,k,nnew,itrc)+cff2*adfac1 ad_FE(i,j )=ad_FE(i,j )+adfac2 ad_FE(i,j+1)=ad_FE(i,j+1)-adfac2 ad_FX(i ,j)=ad_FX(i ,j)+adfac2 ad_FX(i+1,j)=ad_FX(i+1,j)-adfac2 ad_t(i,j,k,3,itrc)=0.0_r8 END DO END DO ! ! Apply 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 (((Istr.le.Isrc).and.(Isrc.le.Iend+1)).and. & & ((Jstr.le.Jsrc).and.(Jsrc.le.Jend+1))) THEN IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) 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 ELSE !^ tl_FX(Isrc,Jsrc)=0.0_r8 !^ ad_FX(Isrc,Jsrc)=0.0_r8 END IF ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) 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 ELSE !^ tl_FE(Isrc,Jsrc)=0.0_r8 !^ ad_FE(Isrc,Jsrc)=0.0_r8 END IF END IF END IF END DO END IF ! ! Compute adjoint of intermediate tracer horizontal advection fluxes. ! HADV_FLUX : IF (ad_Hadvection(itrc,ng)%CENTERED2) THEN ! ! Second-order, centered differences 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,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc))+ & !^ & Hvom(i,j,k)* & !^ & (tl_t(i,j-1,k,nstp,itrc)+ & !^ & tl_t(i,j ,k,nstp,itrc))) !^ adfac=0.5_r8*ad_FE(i,j) adfac1=adfac*Hvom(i,j,k) ad_Hvom(i,j,k)=ad_Hvom(i,j,k)+ & & adfac*(t(i,j ,k,nstp,itrc)+ & & t(i,j-1,k,nstp,itrc)) ad_t(i,j-1,k,nstp,itrc)=ad_t(i,j-1,k,nstp,itrc)+adfac1 ad_t(i,j ,k,nstp,itrc)=ad_t(i,j ,k,nstp,itrc)+adfac1 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,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc))+ & !^ & Huon(i,j,k)* & !^ & (tl_t(i-1,j,k,nstp,itrc)+ & !^ & tl_t(i ,j,k,nstp,itrc))) !^ adfac=0.5_r8*ad_FX(i,j) adfac1=adfac*Huon(i,j,k) ad_Huon(i,j,k)=ad_Huon(i,j,k)+ & & adfac*(t(i-1,j,k,nstp,itrc)+ & & t(i ,j,k,nstp,itrc)) ad_t(i-1,j,k,nstp,itrc)=ad_t(i-1,j,k,nstp,itrc)+adfac1 ad_t(i ,j,k,nstp,itrc)=ad_t(i ,j,k,nstp,itrc)+adfac1 ad_FX(i,j)=0.0_r8 END DO END DO ! ELSE IF ((ad_Hadvection(itrc,ng)%MPDATA).or. & & (ad_Hadvection(itrc,ng)%HSIMT)) THEN ! ! First-order, upstream differences horizontal advective fluxes. ! DO j=Jstr,Jend+1 DO i=Istr,Iend 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,nstp,itrc)+ & !^ & cff1*tl_t(i,j-1,k,nstp,itrc)+ & !^ & tl_cff2*t(i,j ,k,nstp,itrc)+ & !^ & cff2*tl_t(i,j ,k,nstp,itrc) !^ ad_t(i,j-1,k,nstp,itrc)=ad_t(i,j-1,k,nstp,itrc)+ & & cff1*ad_FE(i,j) ad_t(i,j ,k,nstp,itrc)=ad_t(i,j ,k,nstp,itrc)+ & & cff2*ad_FE(i,j) ad_cff1=ad_cff1+t(i,j-1,k,nstp,itrc)*ad_FE(i,j) ad_cff2=ad_cff2+t(i,j ,k,nstp,itrc)*ad_FE(i,j) ad_FE(i,j)=0.0_r8 !^ tl_cff1=(0.5_r8+SIGN(0.5_r8, Hvom(i,j,k)))* & !^ & tl_Hvom(i,j,k) !^ tl_cff2=(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=Jstr,Jend DO i=Istr,Iend+1 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,nstp,itrc)+ & !^ & cff1*tl_t(i-1,j,k,nstp,itrc)+ & !^ & tl_cff2*t(i ,j,k,nstp,itrc)+ & !^ & cff2*tl_t(i ,j,k,nstp,itrc) !^ ad_t(i ,j,k,nstp,itrc)=ad_t(i ,j,k,nstp,itrc)+ & & cff2*ad_FX(i,j) ad_t(i-1,j,k,nstp,itrc)=ad_t(i-1,j,k,nstp,itrc)+ & & cff1*ad_FX(i,j) ad_cff1=ad_cff1+t(i-1,j,k,nstp,itrc)*ad_FX(i,j) ad_cff2=ad_cff2+t(i ,j,k,nstp,itrc)*ad_FX(i,j) ad_FX(i,j)=0.0_r8 !^ tl_cff1=(0.5_r8+SIGN(0.5_r8, Huon(i,j,k)))* & !^ & tl_Huon(i,j,k) !^ tl_cff2=(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 ((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. ! Compute BASIC STATE "curv" and "grad" scratch arrays. ! DO j=Jstrm1,Jendp2 DO i=Istr,Iend FE(i,j)=t(i,j ,k,nstp,itrc)- & & t(i,j-1,k,nstp,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,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc))+ & !^ & Hvom(i,j,k)* & !^ & (tl_t(i,j-1,k,nstp,itrc)+ & !^ & tl_t(i,j ,k,nstp,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,nstp,itrc)+ & & t(i,j ,k,nstp,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,nstp,itrc)=ad_t(i,j-1,k,nstp,itrc)+adfac1 ad_t(i,j ,k,nstp,itrc)=ad_t(i,j ,k,nstp,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,nstp,itrc)+ & !^ & t(i,j ,k,nstp,itrc)- & !^ & cff2*(grad(i,j )- & !^ & grad(i,j-1)))+ & !^ & Hvom(i,j,k)* & !^ & (tl_t(i,j-1,k,nstp,itrc)+ & !^ & tl_t(i,j ,k,nstp,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,nstp,itrc)+ & & t(i,j ,k,nstp,itrc)- & & cff2*(grad(i,j )- & & grad(i,j-1))) ad_t(i,j-1,k,nstp,itrc)=ad_t(i,j-1,k,nstp,itrc)+adfac1 ad_t(i,j ,k,nstp,itrc)=ad_t(i,j ,k,nstp,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,nstp,itrc)- & !^ & tl_t(i,j-1,k,nstp,itrc) !^ ad_t(i,j-1,k,nstp,itrc)=ad_t(i,j-1,k,nstp,itrc)- & & ad_FE(i,j) ad_t(i,j ,k,nstp,itrc)=ad_t(i,j ,k,nstp,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,nstp,itrc)- & & t(i-1,j,k,nstp,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,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc))+ & !^ & Huon(i,j,k)* & !^ & (tl_t(i-1,j,k,nstp,itrc)+ & !^ & tl_t(i ,j,k,nstp,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,nstp,itrc)+ & & t(i ,j,k,nstp,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,nstp,itrc)=ad_t(i-1,j,k,nstp,itrc)+adfac1 ad_t(i ,j,k,nstp,itrc)=ad_t(i ,j,k,nstp,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,nstp,itrc)+ & !^ & t(i ,j,k,nstp,itrc)- & !^ & cff2*(grad(i ,j)- & !^ & grad(i-1,j)))+ & !^ & Huon(i,j,k)* & !^ & (tl_t(i-1,j,k,nstp,itrc)+ & !^ & tl_t(i ,j,k,nstp,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,nstp,itrc)+ & & t(i ,j,k,nstp,itrc)- & & cff2*(grad(i ,j)- & & grad(i-1,j))) ad_t(i-1,j,k,nstp,itrc)=ad_t(i-1,j,k,nstp,itrc)+adfac1 ad_t(i ,j,k,nstp,itrc)=ad_t(i ,j,k,nstp,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,nstp,itrc)=ad_t(i-1,j,k,nstp,itrc)- & & ad_FX(i,j) ad_t(i ,j,k,nstp,itrc)=ad_t(i ,j,k,nstp,itrc)+ & & ad_FX(i,j) ad_FX(i,j)=0.0_r8 END DO END DO END IF HADV_FLUX END DO K_LOOP END DO T_LOOP1 # ifdef SOLAR_SOURCE ! ! Compute fraction of the solar shortwave radiation, "swdk" ! (at vertical W-points) penetrating water column. First, compute ! BASIC STATE arrays. ! DO k=1,N(ng)-1 DO j=Jstr,Jend DO i=Istr,Iend FX(i,j)=z_w(i,j,N(ng))-z_w(i,j,k) END DO END DO DO j=Jstr,Jend DO i=Istr,Iend !^ tl_swdk(i,j,k)=tl_FE(i,j) !^ ad_FE(i,j)=ad_FE(i,j)+ad_swdk(i,j,k) ad_swdk(i,j,k)=0.0_r8 END DO END DO !^ CALL tl_lmd_swfrac_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & -1.0_r8, FX, tl_FX, tl_FE) !^ CALL ad_lmd_swfrac_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & -1.0_r8, FX, ad_FX, ad_FE) DO j=Jstr,Jend DO i=Istr,Iend !^ tl_FX(i,j)=tl_z_w(i,j,N(ng))-tl_z_w(i,j,k) !^ ad_z_w(i,j,k )=ad_z_w(i,j,k )-ad_FX(i,j) ad_z_w(i,j,N(ng))=ad_z_w(i,j,N(ng))+ad_FX(i,j) ad_FX(i,j)=0.0_r8 END DO END DO END DO # endif # endif /* !TS_FIXED */ ! RETURN END SUBROUTINE ad_pre_step3d_tile #endif END MODULE ad_pre_step3d_mod