SUBROUTINE ad_t3dmix4 (ng, tile) ! !svn $Id: ad_t3dmix4_iso.h 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 subroutine computes adjoint horizontal biharmonic mixing of ! ! tracers along isopycnic surfaces. ! ! ! ! BASIC STATE variables needed: diff4, Hz, t, rho, z_r ! ! ! !*********************************************************************** ! USE mod_param #ifdef TS_MIX_CLIMA USE mod_clima #endif #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, 29, __LINE__, __FILE__) #endif CALL ad_t3dmix4_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), nstp(ng), nnew(ng), & #ifdef MASKING & GRID(ng) % umask, & & GRID(ng) % vmask, & #endif #ifdef WET_DRY_NOT_YET & GRID(ng) % umask_wet, & & GRID(ng) % vmask_wet, & #endif & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % pm, & & GRID(ng) % pn, & & GRID(ng) % Hz, & & GRID(ng) % ad_Hz, & & GRID(ng) % z_r, & & GRID(ng) % ad_z_r, & #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT & MIXING(ng) % diff3d_u, & & MIXING(ng) % diff3d_v, & # else & MIXING(ng) % diff3d_r, & # endif #else & MIXING(ng) % diff4, & #endif & OCEAN(ng) % pden, & & OCEAN(ng) % ad_pden, & #ifdef TS_MIX_CLIMA & CLIMA(ng) % tclm, & #endif #ifdef DIAGNOSTICS_TS !! & DIAGS(ng) % DiaTwrk, & #endif & OCEAN(ng) % t, & & OCEAN(ng) % ad_t) #ifdef PROFILE CALL wclock_off (ng, iADM, 29, __LINE__, __FILE__) #endif RETURN END SUBROUTINE ad_t3dmix4 ! !*********************************************************************** SUBROUTINE ad_t3dmix4_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & #ifdef MASKING & umask, vmask, & #endif #ifdef WET_DRY_NOT_YET & umask_wet, vmask_wet, & #endif & om_v, on_u, pm, pn, & & Hz, ad_Hz, & & z_r, ad_z_r, & #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT & diff3d_u, diff3d_v, & # else & diff3d_r, & # endif #else & diff4, & #endif & pden, ad_pden, & #ifdef TS_MIX_CLIMA & tclm, & #endif #ifdef DIAGNOSTICS_TS !! & DiaTwrk, & #endif & t, ad_t) !*********************************************************************** ! USE mod_param USE mod_ncparam USE mod_scalars ! ! 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) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif # ifdef WET_DRY_NOT_YET real(r8), intent(in) :: umask_wet(LBi:,LBj:) real(r8), intent(in) :: vmask_wet(LBi:,LBj:) # endif # ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT real(r8), intent(in) :: diff3d_u(LBi:,LBj:,:) real(r8), intent(in) :: diff3d_v(LBi:,LBj:,:) # else real(r8), intent(in) :: diff3d_r(LBi:,LBj:,:) # endif # else real(r8), intent(in) :: diff4(LBi:,LBj:,:) # endif real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: pm(LBi:,LBj:) real(r8), intent(in) :: pn(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: pden(LBi:,LBj:,:) real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) # ifdef TS_MIX_CLIMA real(r8), intent(in) :: tclm(LBi:,LBj:,:,:) # endif # ifdef DIAGNOSTICS_TS real(r8), intent(inout) :: DiaTwrk(LBi:,LBj:,:,:,:) # endif real(r8), intent(inout) :: ad_Hz(LBi:,LBj:,:) real(r8), intent(inout) :: ad_z_r(LBi:,LBj:,:) real(r8), intent(inout) :: ad_pden(LBi:,LBj:,:) real(r8), intent(inout) :: ad_t(LBi:,LBj:,:,:,:) #else # ifdef MASKING real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif # ifdef WET_DRY_NOT_YET real(r8), intent(in) :: umask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask_wet(LBi:UBi,LBj:UBj) # endif # ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT real(r8), intent(in) :: diff3d_u(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: diff3d_v(LBi:UBi,LBj:UBj,N(ng)) # else real(r8), intent(in) :: diff3d_r(LBi:UBi,LBj:UBj,N(ng)) # endif # else real(r8), intent(in) :: diff4(LBi:UBi,LBj:UBj,NT(ng)) # endif real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pm(LBi:UBi,LBj:UBj) real(r8), intent(in) :: pn(LBi:UBi,LBj:UBj) real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: pden(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # ifdef TS_MIX_CLIMA real(r8), intent(in) :: tclm(LBi:UBi,LBj:UBj,N(ng),NT(ng)) # endif # 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_z_r(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_pden(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(inout) :: ad_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) #endif ! ! Local variable declarations. ! integer :: Imin, Imax, Jmin, Jmax integer :: i, itrc, j, k, kk, kt, k1, k1b, k2, k2b real(r8), parameter :: eps = 0.5_r8 real(r8), parameter :: small = 1.0E-14_r8 real(r8), parameter :: slope_max = 0.0001_r8 real(r8), parameter :: strat_min = 0.1_r8 real(r8) :: cff, cff1, cff2, cff3, cff4, dife, difx real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3, ad_cff4 real(r8) :: adfac, adfac1, adfac2, adfac3, adfac4 real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: LapT real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: ad_LapT real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX 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,2) :: FS real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: FS1 real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dRde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dRdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dTde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dTdr real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: dTdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_FS real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dRde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dRdx real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dTde real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dTdr real(r8), dimension(IminS:ImaxS,JminS:JmaxS,2) :: ad_dTdx #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 ad_cff4=0.0_r8 ad_FE(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FX(IminS:ImaxS,JminS:JmaxS)=0.0_r8 ad_FS(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dRde(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dRdx(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dTde(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dTdr(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_dTdx(IminS:ImaxS,JminS:JmaxS,1:2)=0.0_r8 ad_LapT(IminS:ImaxS,JminS:JmaxS,1:N(ng))=0.0_r8 ! !---------------------------------------------------------------------- ! Compute horizontal biharmonic diffusion along isopycnic surfaces. ! The biharmonic operator is computed by applying the harmonic ! operator twice. !---------------------------------------------------------------------- ! ! Set local I- and J-ranges. ! IF (EWperiodic(ng)) THEN Imin=Istr-1 Imax=Iend+1 ELSE Imin=MAX(Istr-1,1) Imax=MIN(Iend+1,Lm(ng)) END IF IF (NSperiodic(ng)) THEN Jmin=Jstr-1 Jmax=Jend+1 ELSE Jmin=MAX(Jstr-1,1) Jmax=MIN(Jend+1,Mm(ng)) END IF ! ! Compute horizontal and density gradients for the BASIC STATE. Notice ! the recursive blocking sequence. The vertical placement of the ! gradients is: ! ! dTdx,dTde(:,:,k1) k rho-points ! dTdx,dTde(:,:,k2) k+1 rho-points ! FS,dTdr(:,:,k1) k-1/2 W-points ! FS,dTdr(:,:,k2) k+1/2 W-points ! #ifdef TS_MIX_STABILITY ! In order to increase stability, the biharmonic operator is applied ! as: 3/4 t(:,:,:,nrhs,:) + 1/4 t(:,:,:,nstp,:). ! #endif T_LOOP : DO itrc=1,NT(ng) k2=1 K_LOOP1 : DO k=0,N(ng) k1=k2 k2=3-k1 IF (k.lt.N(ng)) THEN DO j=Jmin,Jmax DO i=Imin,Imax+1 cff=0.5_r8*(pm(i,j)+pm(i-1,j)) #ifdef MASKING cff=cff*umask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*umask_wet(i,j) #endif dRdx(i,j,k2)=cff*(pden(i ,j,k+1)- & & pden(i-1,j,k+1)) #if defined TS_MIX_STABILITY dTdx(i,j,k2)=cff*(0.75_r8*(t(i ,j,k+1,nrhs,itrc)- & & t(i-1,j,k+1,nrhs,itrc))+ & & 0.25_r8*(t(i ,j,k+1,nstp,itrc)- & & t(i-1,j,k+1,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTdx(i,j,k2)=cff*((t(i ,j,k+1,nrhs,itrc)- & & tclm(i ,j,k+1,itrc))- & & (t(i-1,j,k+1,nrhs,itrc)- & & tclm(i-1,j,k+1,itrc))) ELSE dTdx(i,j,k2)=cff*(t(i ,j,k+1,nrhs,itrc)- & & t(i-1,j,k+1,nrhs,itrc)) END IF #else dTdx(i,j,k2)=cff*(t(i ,j,k+1,nrhs,itrc)- & & t(i-1,j,k+1,nrhs,itrc)) #endif END DO END DO DO j=Jmin,Jmax+1 DO i=Imin,Imax cff=0.5_r8*(pn(i,j)+pn(i,j-1)) #ifdef MASKING cff=cff*vmask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*vmask_wet(i,j) #endif dRde(i,j,k2)=cff*(pden(i,j ,k+1)- & & pden(i,j-1,k+1)) #if defined TS_MIX_STABILITY dTde(i,j,k2)=cff*(0.75_r8*(t(i,j ,k+1,nrhs,itrc)- & & t(i,j-1,k+1,nrhs,itrc))+ & & 0.25_r8*(t(i,j ,k+1,nstp,itrc)- & & t(i,j-1,k+1,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTde(i,j,k2)=cff*((t(i,j ,k+1,nrhs,itrc)- & & tclm(i,j ,k+1,itrc))- & & (t(i,j-1,k+1,nrhs,itrc)- & & tclm(i,j-1,k+1,itrc))) ELSE dTde(i,j,k2)=cff*(t(i,j ,k+1,nrhs,itrc)- & & t(i,j-1,k+1,nrhs,itrc)) END IF #else dTde(i,j,k2)=cff*(t(i,j ,k+1,nrhs,itrc)- & & t(i,j-1,k+1,nrhs,itrc)) #endif END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 dTdr(i,j,k2)=0.0_r8 FS(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 #if defined TS_MIX_MAX_SLOPE cff1=SQRT(dRdx(i,j,k2)**2+dRdx(i+1,j,k2)**2+ & & dRdx(i,j,k1)**2+dRdx(i+1,j,k1)**2+ & & dRde(i,j,k2)**2+dRde(i,j+1,k2)**2+ & & dRde(i,j,k1)**2+dRde(i,j+1,k1)**2) cff2=0.25_r8*slope_max* & & (z_r(i,j,k+1)-z_r(i,j,k))*cff1 cff3=MAX(pden(i,j,k)-pden(i,j,k+1),small) cff4=MAX(cff2,cff3) cff=-1.0_r8/cff4 #elif defined TS_MIX_MIN_STRAT cff1=MAX(pden(i,j,k)-pden(i,j,k+1), & & strat_min*(z_r(i,j,k+1)-z_r(i,j,k))) cff=-1.0_r8/cff1 #else cff1=MAX(pden(i,j,k)-pden(i,j,k+1),eps) cff=-1.0_r8/cff1 #endif #if defined TS_MIX_STABILITY dTdr(i,j,k2)=cff*(0.75_r8*(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc))+ & & 0.25_r8*(t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTdr(i,j,k2)=cff*((t(i,j,k+1,nrhs,itrc)- & & tclm(i,j,k+1,itrc))- & & (t(i,j,k ,nrhs,itrc)- & & tclm(i,j,k ,itrc))) ELSE dTdr(i,j,k2)=cff*(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc)) END IF #else dTdr(i,j,k2)=cff*(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc)) #endif FS(i,j,k2)=cff*(z_r(i,j,k+1)- & & z_r(i,j,k )) END DO END DO END IF IF (k.gt.0) THEN DO j=Jmin,Jmax DO i=Imin,Imax+1 #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_u(i,j,k)*on_u(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i-1,j,k))* & & on_u(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i-1,j,itrc))* & & on_u(i,j) #endif FX(i,j)=cff* & & (Hz(i,j,k)+Hz(i-1,j,k))* & & (dTdx(i,j,k1)- & & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k1)+ & & dTdr(i ,j,k2))+ & & MIN(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k2)+ & & dTdr(i ,j,k1)))) END DO END DO DO j=Jmin,Jmax+1 DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_v(i,j,k)*om_v(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i,j-1,k))* & & om_v(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i,j-1,itrc))* & & om_v(i,j) #endif FE(i,j)=cff* & & (Hz(i,j,k)+Hz(i,j-1,k))* & & (dTde(i,j,k1)- & & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k1)+ & & dTdr(i,j ,k2))+ & & MIN(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k2)+ & & dTdr(i,j ,k1)))) END DO END DO IF (k.lt.N(ng)) THEN DO j=Jmin,Jmax DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT difx=0.125_r8*(diff3d_u(i,j,k )+diff3d_u(i+1,j,k )+ & & diff3d_u(i,j,k+1)+diff3d_u(i+1,j,k+1)) dife=0.125_r8*(diff3d_v(i,j,k )+diff3d_v(i,j+1,k )+ & & diff3d_v(i,j,k+1)+diff3d_v(i,j+1,k+1)) # else difx=0.5_r8*diff3d_r(i,j,k) dife=difx # endif #else difx=0.5_r8*diff4(i,j,itrc) dife=difx #endif cff1=MAX(dRdx(i ,j,k1),0.0_r8) cff2=MAX(dRdx(i+1,j,k2),0.0_r8) cff3=MIN(dRdx(i ,j,k2),0.0_r8) cff4=MIN(dRdx(i+1,j,k1),0.0_r8) cff=difx* & & (cff1*(cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))) cff1=MAX(dRde(i,j ,k1),0.0_r8) cff2=MAX(dRde(i,j+1,k2),0.0_r8) cff3=MIN(dRde(i,j ,k2),0.0_r8) cff4=MIN(dRde(i,j+1,k1),0.0_r8) cff=cff+ & & dife* & & (cff1*(cff1*dTdr(i,j,k2)-dTde(i,j ,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTde(i,j ,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))) FS(i,j,k2)=cff*FS(i,j,k2) END DO END DO END IF ! ! Compute first BASIC STATE harmonic operator, without mixing ! coefficient. Multiply by the metrics of the second harmonic ! operator. Save into work array "LapT". ! DO j=Jmin,Jmax DO i=Imin,Imax cff=pm(i,j)*pn(i,j) cff1=1.0_r8/Hz(i,j,k) LapT(i,j,k)=cff1*(cff* & & (FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j))+ & & (FS(i,j,k2)-FS(i,j,k1))) END DO END DO END IF END DO K_LOOP1 ! ! Apply boundary conditions (except periodic; closed or gradient) ! to the first BASIC STATE harmonic operator. ! IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN IF (ad_LBC(iwest,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jmin,Jmax LapT(Istr-1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jmin,Jmax LapT(Istr-1,j,k)=LapT(Istr,j,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN IF (ad_LBC(ieast,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jmin,Jmax LapT(Iend+1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jmin,Jmax LapT(Iend+1,j,k)=LapT(Iend,j,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN IF (ad_LBC(isouth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Imin,Imax LapT(i,Jstr-1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Imin,Imax LapT(i,Jstr-1,k)=LapT(i,Jstr,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN IF (ad_LBC(inorth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Imin,Imax LapT(i,Jend+1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Imin,Imax LapT(i,Jend+1,k)=LapT(i,Jend,k) END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN DO k=1,N(ng) LapT(Istr-1,Jstr-1,k)=0.5_r8* & & (LapT(Istr ,Jstr-1,k)+ & & LapT(Istr-1,Jstr ,k)) END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN DO k=1,N(ng) LapT(Iend+1,Jstr-1,k)=0.5_r8* & & (LapT(Iend ,Jstr-1,k)+ & & LapT(Iend+1,Jstr ,k)) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN DO k=1,N(ng) LapT(Istr-1,Jend+1,k)=0.5_r8* & & (LapT(Istr ,Jend+1,k)+ & & LapT(Istr-1,Jend ,k)) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN DO k=1,N(ng) LapT(Iend+1,Jend+1,k)=0.5_r8* & & (LapT(Iend ,Jend+1,k)+ & & LapT(Iend+1,Jend ,k)) END DO END IF END IF ! ! Compute adjoint of starting storage recursive indices k1 and k2. ! k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of the above code. !! k1=k2 k2=3-k1 END DO ! ! Compute required basic state fields. Need to look forward in ! recursive kk index. ! K_LOOP2: DO k=N(ng),0,-1 k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b ! ! Compute components of the rotated tracer flux (T m3/s) along ! isopycnic surfaces (required BASIC STATE fields). ! IF (kk.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i,j)+pm(i-1,j)) #ifdef MASKING cff=cff*umask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*umask_wet(i,j) #endif dRdx(i,j,k2b)=cff*(pden(i ,j,kk+1)- & & pden(i-1,j,kk+1)) dTdx(i,j,k2b)=cff*(LapT(i ,j,kk+1)- & & LapT(i-1,j,kk+1)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend DO i=Istr,Iend+1 dRdx(i,j,k1b)=0.0_r8 dTdx(i,j,k1b)=0.0_r8 END DO END DO END IF DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j)+pn(i,j-1)) #ifdef MASKING cff=cff*vmask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*vmask_wet(i,j) #endif dRde(i,j,k2b)=cff*(pden(i,j ,kk+1)- & & pden(i,j-1,kk+1)) dTde(i,j,k2b)=cff*(LapT(i,j ,kk+1)- & & LapT(i,j-1,kk+1)) END DO END DO IF (kk.eq.0) THEN DO j=Jstr,Jend+1 DO i=Istr,Iend dRde(i,j,k1b)=0.0_r8 dTde(i,j,k1b)=0.0_r8 END DO END DO END IF END IF IF ((kk.eq.0).or.(kk.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 dTdr(i,j,k2b)=0.0_r8 FS(i,j,k2b)=0.0_r8 END DO END DO IF (kk.eq.0) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 dTdr(i,j,k1b)=0.0_r8 FS(i,j,k1b)=0.0_r8 END DO END DO END IF ELSE DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 #if defined TS_MIX_MAX_SLOPE cff1=SQRT(dRdx(i,j,k2b)**2+dRdx(i+1,j,k2b)**2+ & & dRdx(i,j,k1b)**2+dRdx(i+1,j,k1b)**2+ & & dRde(i,j,k2b)**2+dRde(i,j+1,k2b)**2+ & & dRde(i,j,k1b)**2+dRde(i,j+1,k1b)**2) cff2=0.25_r8*slope_max* & & (z_r(i,j,kk+1)-z_r(i,j,kk))*cff1 cff3=MAX(pden(i,j,kk)-pden(i,j,kk+1),small) cff4=MAX(cff2,cff3) cff=-1.0_r8/cff4 #elif defined TS_MIX_MIN_STRAT cff1=MAX(pden(i,j,kk)-pden(i,j,kk+1), & & strat_min*(z_r(i,j,kk+1)-z_r(i,j,kk))) cff=-1.0_r8/cff1 #else cff1=MAX(pden(i,j,kk)-pden(i,j,kk+1),eps) cff=-1.0_r8/cff1 #endif dTdr(i,j,k2b)=cff*(LapT(i,j,kk+1)- & & LapT(i,j,kk )) FS(i,j,k2b)=cff*(z_r(i,j,kk+1)- & & z_r(i,j,kk )) END DO END DO END IF END DO ! IF (k.gt.0) THEN ! ! Time-step biharmonic, isopycnal diffusion term (m Tunits). ! DO j=Jstr,Jend DO i=Istr,Iend #ifdef DIAGNOSTICS_TS !! DiaTwrk(i,j,k,itrc,iThdif)=-cff #endif !> tl_t(i,j,k,nnew,itrc)=tl_t(i,j,k,nnew,itrc)-tl_cff !> ad_cff=ad_cff-ad_t(i,j,k,nnew,itrc) !> tl_cff=dt(ng)*pm(i,j)*pn(i,j)* & !> & (tl_FX(i+1,j)-tl_FX(i,j)+ & !> & tl_FE(i,j+1)-tl_FE(i,j))+ & !> & dt(ng)*(tl_FS(i,j,k2)-tl_FS(i,j,k1)) !> adfac=dt(ng)*ad_cff adfac1=adfac*pm(i,j)*pn(i,j) ad_FS(i,j,k1)=ad_FS(i,j,k1)-adfac ad_FS(i,j,k2)=ad_FS(i,j,k2)+adfac ad_FX(i ,j)=ad_FX(i ,j)-adfac1 ad_FX(i+1,j)=ad_FX(i+1,j)+adfac1 ad_FE(i,j )=ad_FE(i,j )-adfac1 ad_FE(i,j+1)=ad_FE(i,j+1)+adfac1 ad_cff=0.0_r8 END DO END DO IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT difx=0.125_r8*(diff3d_u(i,j,k )+diff3d_u(i+1,j,k )+ & & diff3d_u(i,j,k+1)+diff3d_u(i+1,j,k+1)) dife=0.125_r8*(diff3d_v(i,j,k )+diff3d_v(i,j+1,k )+ & & diff3d_v(i,j,k+1)+diff3d_v(i,j+1,k+1)) # else difx=0.5_r8*diff3d_r(i,j,k) dife=difx # endif #else difx=0.5_r8*diff4(i,j,itrc) dife=difx #endif cff1=MAX(dRdx(i ,j,k1),0.0_r8) cff2=MAX(dRdx(i+1,j,k2),0.0_r8) cff3=MIN(dRdx(i ,j,k2),0.0_r8) cff4=MIN(dRdx(i+1,j,k1),0.0_r8) cff=difx* & & (cff1*(cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))) cff1=MAX(dRde(i,j ,k1),0.0_r8) cff2=MAX(dRde(i,j+1,k2),0.0_r8) cff3=MIN(dRde(i,j ,k2),0.0_r8) cff4=MIN(dRde(i,j+1,k1),0.0_r8) cff=cff+ & & dife* & & (cff1*(cff1*dTdr(i,j,k2)-dTde(i,j ,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTde(i,j ,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))) !> tl_FS(i,j,k2)=tl_cff*FS(i,j,k2)+ & !> & cff*tl_FS(i,j,k2 !> ad_cff=ad_cff+FS(i,j,k2)*ad_FS(i,j,k2) ad_FS(i,j,k2)=cff*ad_FS(i,j,k2) !> tl_cff=tl_cff+ & !> & dife* & !> & (tl_cff1*(cff1*dTdr(i,j,k2)- & !> & dTde(i,j ,k1))+ & !> & tl_cff2*(cff2*dTdr(i,j,k2)- & !> & dTde(i,j+1,k2))+ & !> & tl_cff3*(cff3*dTdr(i,j,k2)- & !> & dTde(i,j ,k2))+ & !> & tl_cff4*(cff4*dTdr(i,j,k2)- & !> & dTde(i,j+1,k1))+ & !> & cff1*(tl_cff1*dTdr(i,j,k2)+ & !> & cff1*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j ,k1))+ & !> & cff2*(tl_cff2*dTdr(i,j,k2)+ & !> & cff2*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j+1,k2))+ & !> & cff3*(tl_cff3*dTdr(i,j,k2)+ & !> & cff3*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j ,k2))+ & !> & cff4*(tl_cff4*dTdr(i,j,k2)+ & !> & cff4*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j+1,k1))) !> adfac=dife*ad_cff ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTde(i,j ,k1))* & & adfac ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))* & & adfac ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTde(i,j ,k2))* & & adfac ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))* & & adfac ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dTde(i,j ,k1)=ad_dTde(i,j ,k1)-cff1*adfac ad_dTde(i,j+1,k2)=ad_dTde(i,j+1,k2)-cff2*adfac ad_dTde(i,j ,k2)=ad_dTde(i,j ,k2)-cff3*adfac ad_dTde(i,j+1,k1)=ad_dTde(i,j+1,k1)-cff4*adfac !> tl_cff4=(0.5_r8+SIGN(0.5_r8,-dRde(i,j+1,k1)))* & !> & tl_dRde(i,j+1,k1) !> ad_dRde(i,j+1,k1)=ad_dRde(i,j+1,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRde(i,j+1,k1)))* & & ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,-dRde(i,j ,k2)))* & !> & tl_dRde(i,j ,k2) !> ad_dRde(i,j ,k2)=ad_dRde(i,j ,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRde(i,j ,k2)))* & & ad_cff3 ad_cff3=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8, dRde(i,j+1,k2)))* & !> & tl_dRde(i,j+1,k2) !> ad_dRde(i,j+1,k2)=ad_dRde(i,j+1,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & dRde(i,j+1,k2)))* & & ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, dRde(i,j ,k1)))* & !> & tl_dRde(i,j ,k1) !> ad_dRde(i,j ,k1)=ad_dRde(i,j ,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & dRde(i,j ,k1)))* & & ad_cff1 ad_cff1=0.0_r8 cff1=MAX(dRdx(i ,j,k1),0.0_r8) cff2=MAX(dRdx(i+1,j,k2),0.0_r8) cff3=MIN(dRdx(i ,j,k2),0.0_r8) cff4=MIN(dRdx(i+1,j,k1),0.0_r8) !> tl_cff=difx* & !> & (tl_cff1*(cff1*dTdr(i,j,k2)- & !> & dTdx(i ,j,k1))+ & !> & tl_cff2*(cff2*dTdr(i,j,k2)- & !> & dTdx(i+1,j,k2))+ & !> & tl_cff3*(cff3*dTdr(i,j,k2)- & !> & dTdx(i ,j,k2))+ & !> & tl_cff4*(cff4*dTdr(i,j,k2)- & !> & dTdx(i+1,j,k1))+ & !> & cff1*(tl_cff1*dTdr(i,j,k2)+ & !> & cff1*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i ,j,k1))+ & !> & cff2*(tl_cff2*dTdr(i,j,k2)+ & !> & cff2*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i+1,j,k2))+ & !> & cff3*(tl_cff3*dTdr(i,j,k2)+ & !> & cff3*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i ,j,k2))+ & !> & cff4*(tl_cff4*dTdr(i,j,k2)+ & !> & cff4*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i+1,j,k1))) !> adfac=difx*ad_cff ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))* & & adfac ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))* & & adfac ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))* & & adfac ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))* & & adfac ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dTdx(i ,j,k1)=ad_dTdx(i ,j,k1)-cff1*adfac ad_dTdx(i+1,j,k2)=ad_dTdx(i+1,j,k2)-cff2*adfac ad_dTdx(i ,j,k2)=ad_dTdx(i ,j,k2)-cff3*adfac ad_dTdx(i+1,j,k1)=ad_dTdx(i+1,j,k1)-cff4*adfac ad_cff=0.0_r8 !> tl_cff4=(0.5_r8+SIGN(0.5_r8,-dRdx(i+1,j,k1)))* & !> & tl_dRdx(i+1,j,k1) !> ad_dRdx(i+1,j,k1)=ad_dRdx(i+1,j,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRdx(i+1,j,k1)))* & & ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,-dRdx(i ,j,k2)))* & !> & tl_dRdx(i ,j,k2) !> ad_dRdx(i ,j,k2)=ad_dRdx(i ,j,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRdx(i ,j,k2)))* & & ad_cff3 ad_cff3=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8, dRdx(i+1,j,k2)))* & !> & tl_dRdx(i+1,j,k2) !> ad_dRdx(i+1,j,k2)=ad_dRdx(i+1,j,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & dRdx(i+1,j,k2)))* & & ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, dRdx(i ,j,k1)))* & !> & tl_dRdx(i ,j,k1) !> ad_dRdx(i ,j,k1)=ad_dRdx(i ,j,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & dRdx(i ,j,k1)))* & & ad_cff1 ad_cff1=0.0_r8 END DO END DO END IF DO j=Jstr,Jend+1 DO i=Istr,Iend #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_v(i,j,k)*om_v(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i,j-1,k))* & & om_v(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i,j-1,itrc))* & & om_v(i,j) #endif !> tl_FE(i,j)=cff* & !> & ((tl_Hz(i,j,k)+tl_Hz(i,j-1,k))* & !> & (dTde(i,j,k1)- & !> & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & !> & (dTdr(i,j-1,k1)+ & !> & dTdr(i,j ,k2))+ & !> & MIN(dRde(i,j,k1),0.0_r8)* & !> & (dTdr(i,j-1,k2)+ & !> & dTdr(i,j ,k1))))+ & !> & (Hz(i,j,k)+Hz(i,j-1,k))* & !> & (tl_dTde(i,j,k1)- & !> & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i,j-1,k1)+ & !> & tl_dTdr(i ,j,k2))+ & !> & MIN(dRde(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i,j-1,k2)+ & !> & tl_dTdr(i,j ,k1)))- & !> & 0.5_r8*((0.5_r8+ & !> & SIGN(0.5_r8, dRde(i,j,k1)))* & !> & tl_dRde(i,j,k1)* & !> & (dTdr(i,j-1,k1)+dTdr(i,j,k2))+ & !> & (0.5_r8+ & !> & SIGN(0.5_r8,-dRde(i,j,k1)))* & !> & tl_dRde(i,j,k1)* & !> & (dTdr(i,j-1,k2)+dTdr(i,j,k1))))) !> adfac=cff*ad_FE(i,j) adfac1=adfac*(dTde(i,j,k1)- & & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k1)+ & & dTdr(i,j ,k2))+ & & MIN(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k2)+ & & dTdr(i,j ,k1)))) adfac2=adfac*(Hz(i,j,k)+Hz(i,j-1,k)) adfac3=adfac2*0.5_r8*MAX(dRde(i,j,k1),0.0_r8) adfac4=adfac2*0.5_r8*MIN(dRde(i,j,k1),0.0_r8) 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_dTde(i,j,k1)=ad_dTde(i,j,k1)+adfac2 ad_dTdr(i,j-1,k1)=ad_dTdr(i,j-1,k1)-adfac3 ad_dTdr(i,j ,k2)=ad_dTdr(i,j ,k2)-adfac3 ad_dTdr(i,j-1,k2)=ad_dTdr(i,j-1,k2)-adfac4 ad_dTdr(i,j ,k1)=ad_dTdr(i,j ,k1)-adfac4 ad_dRde(i,j,k1)=ad_dRde(i,j,k1)- & & adfac2*0.5_r8* & & ((0.5_r8+SIGN(0.5_r8, dRde(i,j,k1)))* & & (dTdr(i,j-1,k1)+dTdr(i,j,k2))+ & & (0.5_r8+SIGN(0.5_r8,-dRde(i,j,k1)))* & & (dTdr(i,j-1,k2)+dTdr(i,j,k1))) ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_u(i,j,k)*on_u(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i-1,j,k))* & & on_u(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i-1,j,itrc))* & & on_u(i,j) #endif !> tl_FX(i,j)=cff* & !> & ((tl_Hz(i,j,k)+tl_Hz(i-1,j,k))* & !> & (dTdx(i,j,k1)- & !> & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & !> & (dTdr(i-1,j,k1)+ & !> & dTdr(i ,j,k2))+ & !> & MIN(dRdx(i,j,k1),0.0_r8)* & !> & (dTdr(i-1,j,k2)+ & !> & dTdr(i ,j,k1))))+ & !> & (Hz(i,j,k)+Hz(i-1,j,k))* & !> & (tl_dTdx(i,j,k1)- & !> & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i-1,j,k1)+ & !> & tl_dTdr(i ,j,k2))+ & !> & MIN(dRdx(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i-1,j,k2)+ & !> & tl_dTdr(i ,j,k1)))- & !> & 0.5_r8*((0.5_r8+ & !> & SIGN(0.5_r8, dRdx(i,j,k1)))* & !> & tl_dRdx(i,j,k1)* & !> & (dTdr(i-1,j,k1)+dTdr(i,j,k2))+ & !> & (0.5_r8+ & !> & SIGN(0.5_r8,-dRdx(i,j,k1)))* & !> & tl_dRdx(i,j,k1)* & !> & (dTdr(i-1,j,k2)+dTdr(i,j,k1))))) !> adfac=cff*ad_FX(i,j) adfac1=adfac*(dTdx(i ,j,k1)- & & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k1)+ & & dTdr(i ,j,k2))+ & & MIN(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k2)+ & & dTdr(i ,j,k1)))) adfac2=adfac*(Hz(i,j,k)+Hz(i-1,j,k)) adfac3=adfac2*0.5_r8*MAX(dRdx(i,j,k1),0.0_r8) adfac4=adfac2*0.5_r8*MIN(dRdx(i,j,k1),0.0_r8) 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_dTdx(i ,j,k1)=ad_dTdx(i ,j,k1)+adfac2 ad_dTdr(i-1,j,k1)=ad_dTdr(i-1,j,k1)-adfac3 ad_dTdr(i ,j,k2)=ad_dTdr(i ,j,k2)-adfac3 ad_dTdr(i-1,j,k2)=ad_dTdr(i-1,j,k2)-adfac4 ad_dTdr(i ,j,k1)=ad_dTdr(i ,j,k1)-adfac4 ad_dRdx(i,j,k1)=ad_dRdx(i,j,k1)- & & adfac2*0.5_r8* & & ((0.5_r8+SIGN(0.5_r8, dRdx(i,j,k1)))* & & (dTdr(i-1,j,k1)+dTdr(i,j,k2))+ & & (0.5_r8+SIGN(0.5_r8,-dRdx(i,j,k1)))* & & (dTdr(i-1,j,k2)+dTdr(i,j,k1))) ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 !> tl_FS(i,j,k2)=0.0_r8 !> ad_FS(i,j,k2)=0.0_r8 !> tl_dTdr(i,j,k2)=0.0_r8 !> ad_dTdr(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 #if defined TS_MIX_MAX_SLOPE cff1=SQRT(dRdx(i,j,k2)**2+dRdx(i+1,j,k2)**2+ & & dRdx(i,j,k1)**2+dRdx(i+1,j,k1)**2+ & & dRde(i,j,k2)**2+dRde(i,j+1,k2)**2+ & & dRde(i,j,k1)**2+dRde(i,j+1,k1)**2) cff2=0.25_r8*slope_max* & & (z_r(i,j,k+1)-z_r(i,j,k))*cff1 cff3=MAX(pden(i,j,k)-pden(i,j,k+1),small) cff4=MAX(cff2,cff3) cff=-1.0_r8/cff4 #elif defined TS_MIX_MIN_STRAT cff1=MAX(pden(i,j,k)-pden(i,j,k+1), & & strat_min*(z_r(i,j,k+1)-z_r(i,j,k))) cff=-1.0_r8/cff1 #else cff1=MAX(pden(i,j,k)-pden(i,j,k+1),eps) cff=-1.0_r8/cff1 #endif !> tl_FS(i,j,k2)=tl_cff*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))+ & !> & cff*(tl_z_r(i,j,k+1)- & !> & tl_z_r(i,j,k )) !> adfac=cff*ad_FS(i,j,k2) 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=ad_cff+(z_r(i,j,k+1)- & & z_r(i,j,k ))*ad_FS(i,j,k2) ad_FS(i,j,k2)=0.0_r8 !> tl_dTdr(i,j,k2)=tl_cff*(LapT(i,j,k+1)- & !> & LapT(i,j,k ))+ & !> & cff*(tl_LapT(i,j,k+1)- & !> & tl_LapT(i,j,k )) !> adfac=cff*ad_dTdr(i,j,k2) ad_LapT(i,j,k )=ad_LapT(i,j,k )-adfac ad_LapT(i,j,k+1)=ad_LapT(i,j,k+1)+adfac ad_cff=ad_cff+(LapT(i,j,k+1)- & & LapT(i,j,k ))*ad_dTdr(i,j,k2) ad_dTdr(i,j,k2)=0.0_r8 #if defined TS_MIX_MAX_SLOPE !> tl_cff=cff*cff*tl_cff4 !> ad_cff4=ad_cff4+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff4=(0.5_r8+SIGN(0.5_r8,cff2-cff3))*tl_cff2+ & !> & (0.5_r8-SIGN(0.5_r8,cff2-cff3))*tl_cff3 !> ad_cff3=ad_cff3+ & & (0.5_r8-SIGN(0.5_r8,cff2-cff3))*ad_cff4 ad_cff2=ad_cff2+ & & (0.5_r8+SIGN(0.5_r8,cff2-cff3))*ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,pden(i,j,k)-pden(i,j,k+1)- & !> & small))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1)) !> adfac=(0.5_r8+SIGN(0.5_r8,pden(i,j,k)-pden(i,j,k+1)- & & small))*ad_cff3 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac ad_cff3=0.0_r8 !> tl_cff2=0.25_r8*slope_max* & !> & ((tl_z_r(i,j,k+1)-tl_z_r(i,j,k))*cff1+ & !> & (z_r(i,j,k+1)-z_r(i,j,k))*tl_cff1) !> adfac=0.25_r8*slope_max*ad_cff2 adfac1=adfac*cff1 ad_cff1=ad_cff1+(z_r(i,j,k+1)-z_r(i,j,k))*adfac ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac1 ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac1 ad_cff2=0.0_r8 IF (cff1.ne.0.0_r8) THEN !> tl_cff1=(dRdx(i ,j,k2)*tl_dRdx(i ,j,k2)+ & !> & dRdx(i+1,j,k2)*tl_dRdx(i+1,j,k2)+ & !> & dRdx(i ,j,k1)*tl_dRdx(i ,j,k1)+ & !> & dRdx(i+1,j,k1)*tl_dRdx(i+1,j,k1)+ & !> & dRde(i,j ,k2)*tl_dRde(i,j ,k2)+ & !> & dRde(i,j+1,k2)*tl_dRde(i,j+1,k2)+ & !> & dRde(i,j ,k1)*tl_dRde(i,j ,k1)+ & !> & dRde(i,j+1,k1)*tl_dRde(i,j+1,k1))/cff1 !> adfac=ad_cff1/cff1 ad_dRdx(i ,j,k1)=ad_dRdx(i ,j,k1)+ & & dRdx(i ,j,k1)*adfac ad_dRdx(i+1,j,k1)=ad_dRdx(i+1,j,k1)+ & & dRdx(i+1,j,k1)*adfac ad_dRdx(i ,j,k2)=ad_dRdx(i ,j,k2)+ & & dRdx(i ,j,k2)*adfac ad_dRdx(i+1,j,k2)=ad_dRdx(i+1,j,k2)+ & & dRdx(i+1,j,k2)*adfac ad_dRde(i,j ,k2)=ad_dRde(i,j ,k2)+ & & dRde(i,j ,k2)*adfac ad_dRde(i,j+1,k2)=ad_dRde(i,j+1,k2)+ & & dRde(i,j+1,k2)*adfac ad_dRde(i,j ,k1)=ad_dRde(i,j ,k1)+ & & dRde(i,j ,k1)*adfac ad_dRde(i,j+1,k1)=ad_dRde(i,j+1,k1)+ & & dRde(i,j+1,k1)*adfac ad_cff1=0.0_r8 ELSE !> tl_cff1=0.0_r8 !> ad_cff1=0.0_r8 END IF #elif defined TS_MIX_MIN_STRAT !> tl_cff=cff*cff*tl_cff1 !> ad_cff1=ad_cff1+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)- & !> & strat_min*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1))+ & !> & (0.5_r8-SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)- & !> & strat_min*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))))* & !> & (strat_min*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k ))) !> adfac1=(0.5_r8+SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)- & & strat_min*(z_r(i,j,k+1)- & & z_r(i,j,k ))))* & & ad_cff1 adfac2=(0.5_r8-SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)- & & strat_min*(z_r(i,j,k+1)- & & z_r(i,j,k ))))* & & strat_min*ad_cff1 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac1 ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac1 ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac2 ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac2 ad_cff1=0.0_r8 #else !> tl_cff=cff*cff*tl_cff1 !> ad_cff1=ad_cff1+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)-eps))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1)) !> adfac=(0.5_r8+SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)-eps))* & & ad_cff1 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac ad_cff1=0.0_r8 #endif END DO END DO END IF IF (k.lt.N(ng)) THEN DO j=Jstr,Jend+1 DO i=Istr,Iend cff=0.5_r8*(pn(i,j)+pn(i,j-1)) #ifdef MASKING cff=cff*vmask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*vmask_wet(i,j) #endif !> tl_dTde(i,j,k2)=cff*(tl_LapT(i,j ,k+1)- & !> & tl_LapT(i,j-1,k+1)) !> adfac=cff*ad_dTde(i,j,k2) ad_LapT(i,j-1,k+1)=ad_LapT(i,j-1,k+1)-adfac ad_LapT(i,j ,k+1)=ad_LapT(i,j ,k+1)+adfac ad_dTde(i,j,k2)=0.0_r8 !> tl_dRde(i,j,k2)=cff*(tl_pden(i,j ,k+1)- & !> & tl_pden(i,j-1,k+1)) !> adfac=cff*ad_dRde(i,j,k2) ad_pden(i,j-1,k+1)=ad_pden(i,j-1,k+1)-adfac ad_pden(i,j ,k+1)=ad_pden(i,j ,k+1)+adfac ad_dRde(i,j,k2)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.5_r8*(pm(i,j)+pm(i-1,j)) #ifdef MASKING cff=cff*umask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*umask_wet(i,j) #endif !> tl_dTdx(i,j,k2)=cff*(tl_LapT(i ,j,k+1)- & !> & tl_LapT(i-1,j,k+1)) !> adfac=cff*ad_dTdx(i,j,k2) ad_LapT(i-1,j,k+1)=ad_LapT(i-1,j,k+1)-adfac ad_LapT(i ,j,k+1)=ad_LapT(i ,j,k+1)+adfac ad_dTdx(i,j,k2)=0.0_r8 !> tl_dRdx(i,j,k2)=cff*(tl_pden(i ,j,k+1)- & !> & tl_pden(i-1,j,k+1)) !> adfac=cff*ad_dRdx(i,j,k2) ad_pden(i-1,j,k+1)=ad_pden(i-1,j,k+1)-adfac ad_pden(i ,j,k+1)=ad_pden(i ,j,k+1)+adfac ad_dRdx(i,j,k2)=0.0_r8 END DO END DO END IF ! ! Compute new storage recursive indices. ! kt=k2 k2=k1 k1=kt END DO K_LOOP2 ! ! Apply adjoint boundary conditions (except periodic; closed or ! gradient) to the first harmonic operator. ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN DO k=1,N(ng) !> tl_LapT(Iend+1,Jend+1,k)=0.5_r8* & !> & (tl_LapT(Iend ,Jend+1,k)+ & !> & tl_LapT(Iend+1,Jend ,k)) !> adfac=0.5_r8*ad_LapT(Iend+1,Jend+1,k) ad_LapT(Iend+1,Jend ,k)=ad_LapT(Iend+1,Jend ,k)+adfac ad_LapT(Iend ,Jend+1,k)=ad_LapT(Iend ,Jend+1,k)+adfac ad_LapT(Iend+1,Jend+1,k)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN DO k=1,N(ng) !> tl_LapT(Istr-1,Jend+1,k)=0.5_r8* & !> & (tl_LapT(Istr ,Jend+1,k)+ & !> & tl_LapT(Istr-1,Jend ,k)) !> adfac=0.5_r8*ad_LapT(Istr-1,Jend+1,k) ad_LapT(Istr-1,Jend ,k)=ad_LapT(Istr-1,Jend ,k)+adfac ad_LapT(Istr ,Jend+1,k)=ad_LapT(Istr ,Jend+1,k)+adfac ad_LapT(Istr-1,Jend+1,k)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(ieast ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN DO k=1,N(ng) !> tl_LapT(Iend+1,Jstr-1,k)=0.5_r8* & !> & (tl_LapT(Iend ,Jstr-1,k)+ & !> & tl_LapT(Iend+1,Jstr ,k)) !> adfac=0.5_r8*ad_LapT(Iend+1,Jstr-1,k) ad_LapT(Iend ,Jstr-1,k)=ad_LapT(Iend ,Jstr-1,k)+adfac ad_LapT(Iend+1,Jstr ,k)=ad_LapT(Iend+1,Jstr ,k)+adfac ad_LapT(Iend+1,Jstr-1,k)=0.0_r8 END DO END IF END IF IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng).or. & & CompositeGrid(iwest ,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN DO k=1,N(ng) !> tl_LapT(Istr-1,Jstr-1,k)=0.5_r8* & !> & (tl_LapT(Istr ,Jstr-1,k)+ & !> tl_LapT(Istr-1,Jstr ,k)) !> adfac=0.5_r8*ad_LapT(Istr-1,Jstr-1,k) ad_LapT(Istr ,Jstr-1,k)=ad_LapT(Istr ,Jstr-1,k)+adfac ad_LapT(Istr-1,Jstr ,k)=ad_LapT(Istr-1,Jstr ,k)+adfac ad_LapT(Istr-1,Jstr-1,k)=0.0_r8 END DO END IF END IF ! IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN IF (ad_LBC(inorth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Imin,Imax !> tl_LapT(i,Jend+1,k)=0.0_r8 !> ad_LapT(i,Jend+1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Imin,Imax !> tl_LapT(i,Jend+1,k)=tl_LapT(i,Jend,k) !> ad_LapT(i,Jend,k)=ad_LapT(i,Jend,k)+ & & ad_LapT(i,Jend+1,k) ad_LapT(i,Jend+1,k)=0.0_r8 END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN IF (ad_LBC(isouth,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO i=Imin,Imax !> tl_LapT(i,Jstr-1,k)=0.0_r8 !> ad_LapT(i,Jstr-1,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO i=Imin,Imax !> tl_LapT(i,Jstr-1,k)=tl_LapT(i,Jstr,k) !> ad_LapT(i,Jstr,k)=ad_LapT(i,Jstr,k)+ & & ad_LapT(i,Jstr-1,k) ad_LapT(i,Jstr-1,k)=0.0_r8 END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN IF (ad_LBC(ieast,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jmin,Jmax !> tl_LapT(Iend+1,j,k)=0.0_r8 !> ad_LapT(Iend+1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jmin,Jmax !> tl_LapT(Iend+1,j,k)=tl_LapT(Iend,j,k) !> ad_LapT(Iend,j,k)=ad_LapT(Iend,j,k)+ & & ad_LapT(Iend+1,j,k) ad_LapT(Iend+1,j,k)=0.0_r8 END DO END DO END IF END IF END IF ! IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN IF (ad_LBC(iwest,isTvar(itrc),ng)%closed) THEN DO k=1,N(ng) DO j=Jmin,Jmax !> tl_LapT(Istr-1,j,k)=0.0_r8 !> ad_LapT(Istr-1,j,k)=0.0_r8 END DO END DO ELSE DO k=1,N(ng) DO j=Jmin,Jmax !> tl_LapT(Istr-1,j,k)=tl_LapT(Istr,j,k) !> ad_LapT(Istr,j,k)=ad_LapT(Istr,j,k)+ & & ad_LapT(Istr-1,j,k) ad_LapT(Istr-1,j,k)=0.0_r8 END DO END DO END IF END IF END IF ! !----------------------------------------------------------------------- ! Compute first adjoint harmonic operator, without mixing coefficient. ! Multiply by the metrics of the second harmonic operator. !----------------------------------------------------------------------- ! ! Compute adjoint of starting recursive indices k1 and k2. ! k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of above code. !! k1=k2 k2=3-k1 END DO ! ! Compute required basic state fields. Need to look forward in "kk" ! index. ! K_LOOP3: DO k=N(ng),0,-1 k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b IF (kk.lt.N(ng)) THEN DO j=Jmin,Jmax DO i=Imin,Imax+1 cff=0.5_r8*(pm(i,j)+pm(i-1,j)) #ifdef MASKING cff=cff*umask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*umask_wet(i,j) #endif dRdx(i,j,k2b)=cff*(pden(i ,j,kk+1)- & & pden(i-1,j,kk+1)) #if defined TS_MIX_STABILITY dTdx(i,j,k2b)=cff*(0.75_r8*(t(i ,j,kk+1,nrhs,itrc)- & & t(i-1,j,kk+1,nrhs,itrc))+ & & 0.25_r8*(t(i ,j,kk+1,nstp,itrc)- & & t(i-1,j,kk+1,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTdx(i,j,k2b)=cff*((t(i ,j,kk+1,nrhs,itrc)- & & tclm(i ,j,kk+1,itrc))- & & (t(i-1,j,kk+1,nrhs,itrc)- & & tclm(i-1,j,kk+1,itrc))) ELSE dTdx(i,j,k2b)=cff*(t(i ,j,kk+1,nrhs,itrc)- & & t(i-1,j,kk+1,nrhs,itrc)) END IF #else dTdx(i,j,k2b)=cff*(t(i ,j,kk+1,nrhs,itrc)- & & t(i-1,j,kk+1,nrhs,itrc)) #endif END DO END DO IF (kk.eq.0) THEN DO j=Jmin,Jmax DO i=Imin,Imax+1 dRdx(i,j,k1b)=0.0_r8 dTdx(i,j,k1b)=0.0_r8 END DO END DO END IF DO j=Jmin,Jmax+1 DO i=Imin,Imax cff=0.5_r8*(pn(i,j)+pn(i,j-1)) #ifdef MASKING cff=cff*vmask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*vmask_wet(i,j) #endif dRde(i,j,k2b)=cff*(pden(i,j ,kk+1)- & & pden(i,j-1,kk+1)) #if defined TS_MIX_STABILITY dTde(i,j,k2b)=cff*(0.75_r8*(t(i,j ,kk+1,nrhs,itrc)- & & t(i,j-1,kk+1,nrhs,itrc))+ & & 0.25_r8*(t(i,j ,kk+1,nstp,itrc)- & & t(i,j-1,kk+1,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTde(i,j,k2b)=cff*((t(i,j ,kk+1,nrhs,itrc)- & & tclm(i,j ,kk+1,itrc))- & & (t(i,j-1,kk+1,nrhs,itrc)- & & tclm(i,j-1,kk+1,itrc))) ELSE dTde(i,j,k2b)=cff*(t(i,j ,kk+1,nrhs,itrc)- & & t(i,j-1,kk+1,nrhs,itrc)) END IF #else dTde(i,j,k2b)=cff*(t(i,j ,kk+1,nrhs,itrc)- & & t(i,j-1,kk+1,nrhs,itrc)) #endif END DO END DO IF (kk.eq.0) THEN DO j=Jmin,Jmax+1 DO i=Imin,Imax dRde(i,j,k1b)=0.0_r8 dTde(i,j,k1b)=0.0_r8 END DO END DO END IF END IF IF ((kk.eq.0).or.(kk.eq.N(ng))) THEN DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 dTdr(i,j,k2b)=0.0_r8 FS(i,j,k2b)=0.0_r8 END DO END DO IF (kk.eq.0) THEN DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 dTdr(i,j,k1b)=0.0_r8 FS(i,j,k1b)=0.0_r8 END DO END DO END IF ELSE DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 #if defined TS_MIX_MAX_SLOPE cff1=SQRT(dRdx(i,j,k2b)**2+dRdx(i+1,j,k2b)**2+ & & dRdx(i,j,k1b)**2+dRdx(i+1,j,k1b)**2+ & & dRde(i,j,k2b)**2+dRde(i,j+1,k2b)**2+ & & dRde(i,j,k1b)**2+dRde(i,j+1,k1b)**2) cff2=0.25_r8*slope_max* & & (z_r(i,j,kk+1)-z_r(i,j,kk))*cff1 cff3=MAX(pden(i,j,kk)-pden(i,j,kk+1),small) cff4=MAX(cff2,cff3) cff=-1.0_r8/cff4 #elif defined TS_MIX_MIN_STRAT cff1=MAX(pden(i,j,kk)-pden(i,j,kk+1), & & strat_min*(z_r(i,j,kk+1)-z_r(i,j,kk))) cff=-1.0_r8/cff1 #else cff1=MAX(pden(i,j,kk)-pden(i,j,kk+1),eps) cff=-1.0_r8/cff1 #endif #if defined TS_MIX_STABILITY dTdr(i,j,k2b)=cff*(0.75_r8*(t(i,j,kk+1,nrhs,itrc)- & & t(i,j,kk ,nrhs,itrc))+ & & 0.25_r8*(t(i,j,kk+1,nstp,itrc)- & & t(i,j,kk ,nstp,itrc))) #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN dTdr(i,j,k2b)=cff*((t(i,j,kk+1,nrhs,itrc)- & & tclm(i,j,kk+1,itrc))- & & (t(i,j,kk ,nrhs,itrc)- & & tclm(i,j,kk ,itrc))) ELSE dTdr(i,j,k2b)=cff*(t(i,j,kk+1,nrhs,itrc)- & & t(i,j,kk ,nrhs,itrc)) END IF #else dTdr(i,j,k2b)=cff*(t(i,j,kk+1,nrhs,itrc)- & & t(i,j,kk ,nrhs,itrc)) #endif FS(i,j,k2b)=cff*(z_r(i,j,kk+1)- & & z_r(i,j,kk )) END DO END DO END IF IF (kk.gt.0) THEN DO j=Jmin,Jmax DO i=Imin,Imax+1 #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_u(i,j,k)*on_u(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i-1,j,k))* & & on_u(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i-1,j,itrc))* & & on_u(i,j) #endif FX(i,j)=cff* & & (Hz(i,j,kk)+Hz(i-1,j,kk))* & & (dTdx(i ,j,k1b)- & & 0.5_r8*(MAX(dRdx(i,j,k1b),0.0_r8)* & & (dTdr(i-1,j,k1b)+ & & dTdr(i ,j,k2b))+ & & MIN(dRdx(i,j,k1b),0.0_r8)* & & (dTdr(i-1,j,k2b)+ & & dTdr(i ,j,k1b)))) END DO END DO DO j=Jmin,Jmax+1 DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_v(i,j,k)*om_v(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i,j-1,k))* & & om_v(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i,j-1,itrc))* & & om_v(i,j) #endif FE(i,j)=cff* & & (Hz(i,j,kk)+Hz(i,j-1,kk))* & & (dTde(i,j,k1b)- & & 0.5_r8*(MAX(dRde(i,j,k1b),0.0_r8)* & & (dTdr(i,j-1,k1b)+ & & dTdr(i,j ,k2b))+ & & MIN(dRde(i,j,k1b),0.0_r8)* & & (dTdr(i,j-1,k2b)+ & & dTdr(i,j ,k1b)))) END DO END DO IF (kk.lt.N(ng)) THEN DO j=Jmin,Jmax DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT difx=0.125_r8* & & (diff3d_u(i,j,kk )+diff3d_u(i+1,j,kk )+ & & diff3d_u(i,j,kk+1)+diff3d_u(i+1,j,kk+1)) dife=0.125_r8* & & (diff3d_v(i,j,kk )+diff3d_v(i,j+1,kk )+ & & diff3d_v(i,j,kk+1)+diff3d_v(i,j+1,kk+1)) # else difx=0.5_r8*diff3d_r(i,j,kk) dife=difx # endif #else difx=0.5_r8*diff4(i,j,itrc) dife=difx #endif cff1=MAX(dRdx(i ,j,k1b),0.0_r8) cff2=MAX(dRdx(i+1,j,k2b),0.0_r8) cff3=MIN(dRdx(i ,j,k2b),0.0_r8) cff4=MIN(dRdx(i+1,j,k1b),0.0_r8) cff=difx* & & (cff1*(cff1*dTdr(i,j,k2b)-dTdx(i ,j,k1b))+ & & cff2*(cff2*dTdr(i,j,k2b)-dTdx(i+1,j,k2b))+ & & cff3*(cff3*dTdr(i,j,k2b)-dTdx(i ,j,k2b))+ & & cff4*(cff4*dTdr(i,j,k2b)-dTdx(i+1,j,k1b))) cff1=MAX(dRde(i,j ,k1b),0.0_r8) cff2=MAX(dRde(i,j+1,k2b),0.0_r8) cff3=MIN(dRde(i,j ,k2b),0.0_r8) cff4=MIN(dRde(i,j+1,k1b),0.0_r8) cff=cff+ & & dife* & & (cff1*(cff1*dTdr(i,j,k2b)-dTde(i,j ,k1b))+ & & cff2*(cff2*dTdr(i,j,k2b)-dTde(i,j+1,k2b))+ & & cff3*(cff3*dTdr(i,j,k2b)-dTde(i,j ,k2b))+ & & cff4*(cff4*dTdr(i,j,k2b)-dTde(i,j+1,k1b))) FS1(i,j,k2b)=FS(i,j,k2b) ! recursive FS (i,j,k2b)=cff*FS(i,j,k2b) END DO END DO IF (kk.eq.0) THEN DO j=Jmin,Jmax DO i=Imin,Imax FS1(i,j,k1b)=0.0_r8 FS (i,j,k1b)=0.0_r8 END DO END DO END IF END IF END IF END DO ! ! Compute adjoint first harmonic operator, without mixing coefficient. ! Multiply by the metrics of the second harmonic operator. Save ! into work array "LapT". ! IF (k.gt.0) THEN DO j=Jmin,Jmax DO i=Imin,Imax cff=pm(i,j)*pn(i,j) cff1=1.0_r8/Hz(i,j,k) !> tl_LapT(i,j,k)=tl_cff1*(cff* & !> & (FX(i+1,j)-FX(i,j)+ & !> & FE(i,j+1)-FE(i,j))+ & !> & (FS(i,j,k2)-FS(i,j,k1)))+ & !> & cff1*(cff* & !> & (tl_FX(i+1,j)-tl_FX(i,j)+ & !> & tl_FE(i,j+1)-tl_FE(i,j))+ & !> & (tl_FS(i,j,k2)-tl_FS(i,j,k1))) !> adfac=cff1*ad_LapT(i,j,k) adfac1=adfac*cff ad_FS(i,j,k1)=ad_FS(i,j,k1)-adfac ad_FS(i,j,k2)=ad_FS(i,j,k2)+adfac ad_FE(i,j )=ad_FE(i,j )-adfac1 ad_FE(i,j+1)=ad_FE(i,j+1)+adfac1 ad_FX(i ,j)=ad_FX(i ,j)-adfac1 ad_FX(i+1,j)=ad_FX(i+1,j)+adfac1 ad_cff1=ad_cff1+(cff* & & (FX(i+1,j)-FX(i,j)+ & & FE(i,j+1)-FE(i,j))+ & & (FS(i,j,k2)-FS(i,j,k1)))* & & ad_LapT(i,j,k) ad_LapT(i,j,k)=0.0_r8 !> tl_cff1=-cff1*cff1*tl_Hz(i,j,k) !> ad_Hz(i,j,k)=ad_Hz(i,j,k)-cff1*cff1*ad_cff1 ad_cff1=0.0_r8 END DO END DO IF (k.lt.N(ng)) THEN DO j=Jmin,Jmax DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT difx=0.125_r8*(diff3d_u(i,j,k )+diff3d_u(i+1,j,k )+ & & diff3d_u(i,j,k+1)+diff3d_u(i+1,j,k+1)) dife=0.125_r8*(diff3d_v(i,j,k )+diff3d_v(i,j+1,k )+ & & diff3d_v(i,j,k+1)+diff3d_v(i,j+1,k+1)) # else difx=0.5_r8*diff3d_r(i,j,k) dife=difx # endif #else difx=0.5_r8*diff4(i,j,itrc) dife=difx #endif cff1=MAX(dRdx(i ,j,k1),0.0_r8) cff2=MAX(dRdx(i+1,j,k2),0.0_r8) cff3=MIN(dRdx(i ,j,k2),0.0_r8) cff4=MIN(dRdx(i+1,j,k1),0.0_r8) cff=difx* & & (cff1*(cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))) cff1=MAX(dRde(i,j ,k1),0.0_r8) cff2=MAX(dRde(i,j+1,k2),0.0_r8) cff3=MIN(dRde(i,j ,k2),0.0_r8) cff4=MIN(dRde(i,j+1,k1),0.0_r8) cff=cff+ & & dife* & & (cff1*(cff1*dTdr(i,j,k2)-dTde(i,j ,k1))+ & & cff2*(cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))+ & & cff3*(cff3*dTdr(i,j,k2)-dTde(i,j ,k2))+ & & cff4*(cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))) !> tl_FS(i,j,k2)=tl_cff*FS(i,j,k2)+ & !> & cff*tl_FS(i,j,k2) ! recursive !> ! use FS1 !> ad_FS(i,j,k2)=cff*ad_FS(i,j,k2) ad_cff=ad_cff+FS1(i,j,k2)*ad_FS(i,j,k2) !> tl_cff=tl_cff+ & !> & dife* & !> & (tl_cff1*(cff1*dTdr(i,j,k2)- & !> & dTde(i,j ,k1))+ & !> & tl_cff2*(cff2*dTdr(i,j,k2)- & !> & dTde(i,j+1,k2))+ & !> & tl_cff3*(cff3*dTdr(i,j,k2)- & !> & dTde(i,j ,k2))+ & !> & tl_cff4*(cff4*dTdr(i,j,k2)- & !> & dTde(i,j+1,k1))+ & !> & cff1*(tl_cff1*dTdr(i,j,k2)+ & !> & cff1*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j ,k1))+ & !> & cff2*(tl_cff2*dTdr(i,j,k2)+ & !> & cff2*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j+1,k2))+ & !> & cff3*(tl_cff3*dTdr(i,j,k2)+ & !> & cff3*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j ,k2))+ & !> & cff4*(tl_cff4*dTdr(i,j,k2)+ & !> & cff4*tl_dTdr(i,j,k2)- & !> & tl_dTde(i,j+1,k1))) !> adfac*dife*ad_cff ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTde(i,j ,k1))* & & adfac ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))* & & adfac ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTde(i,j ,k2))* & & adfac ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))* & & adfac ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dTde(i,j ,k1)=ad_dTde(i,j ,k1)-cff1*adfac ad_dTde(i,j+1,k2)=ad_dTde(i,j+1,k2)-cff2*adfac ad_dTde(i,j ,k2)=ad_dTde(i,j ,k2)-cff3*adfac ad_dTde(i,j+1,k1)=ad_dTde(i,j+1,k1)-cff4*adfac !> tl_cff4=(0.5_r8+SIGN(0.5_r8,-dRde(i,j+1,k1)))* & !> & tl_dRde(i,j+1,k1) !> ad_dRde(i,j+1,k1)=ad_dRde(i,j+1,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRde(i,j+1,k1)))* & & ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,-dRde(i,j ,k2)))* & !> & tl_dRde(i,j ,k2) !> ad_dRde(i,j ,k2)=ad_dRde(i,j ,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRde(i,j ,k2)))* & & ad_cff3 ad_cff3=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8, dRde(i,j+1,k2)))* & !> & tl_dRde(i,j+1,k2) !> ad_dRde(i,j+1,k2)=ad_dRde(i,j+1,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & dRde(i,j+1,k2)))* & & ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, dRde(i,j ,k1)))* & !> & tl_dRde(i,j ,k1) !> ad_dRde(i ,j,k1)=ad_dRde(i ,j,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & dRde(i ,j,k1)))* & & ad_cff1 ad_cff1=0.0_r8 cff1=MAX(dRdx(i ,j,k1),0.0_r8) cff2=MAX(dRdx(i+1,j,k2),0.0_r8) cff3=MIN(dRdx(i ,j,k2),0.0_r8) cff4=MIN(dRdx(i+1,j,k1),0.0_r8) !> tl_cff=difx* & !> & (tl_cff1*(cff1*dTdr(i ,j,k2)- & !> & dTdx(i ,j,k1))+ & !> & tl_cff2*(cff2*dTdr(i,j,k2)- & !> & dTdx(i+1,j,k2))+ & !> & tl_cff3*(cff3*dTdr(i,j,k2)- & !> & dTdx(i ,j,k2))+ & !> & tl_cff4*(cff4*dTdr(i,j,k2)- & !> & dTdx(i+1,j,k1))+ & !> & cff1*(tl_cff1*dTdr(i,j,k2)+ & !> & cff1*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i ,j,k1))+ & !> & cff2*(tl_cff2*dTdr(i,j,k2)+ & !> & cff2*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i+1,j,k2))+ & !> & cff3*(tl_cff3*dTdr(i,j,k2)+ & !> & cff3*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i ,j,k2))+ & !> & cff4*(tl_cff4*dTdr(i,j,k2)+ & !> & cff4*tl_dTdr(i,j,k2)- & !> & tl_dTdx(i+1,j,k1))) !> adfac=difx*ad_cff ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))* & & adfac ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))* & & adfac ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))* & & adfac ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))* & & adfac ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*adfac ad_dTdx(i ,j,k1)=ad_dTdx(i ,j,k1)-cff1*adfac ad_dTdx(i+1,j,k2)=ad_dTdx(i+1,j,k2)-cff2*adfac ad_dTdx(i ,j,k2)=ad_dTdx(i ,j,k2)-cff3*adfac ad_dTdx(i+1,j,k1)=ad_dTdx(i+1,j,k1)-cff4*adfac ad_cff=0.0_r8 !> tl_cff4=(0.5_r8+SIGN(0.5_r8,-dRdx(i+1,j,k1)))* & !> & tl_dRdx(i+1,j,k1) !> ad_dRdx(i+1,j,k1)=ad_dRdx(i+1,j,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRdx(i+1,j,k1)))* & & ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,-dRdx(i ,j,k2)))* & !> & tl_dRdx(i ,j,k2) !> ad_dRdx(i ,j,k2)=ad_dRdx(i ,j,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & -dRdx(i ,j,k2)))* & & ad_cff3 ad_cff3=0.0_r8 !> tl_cff2=(0.5_r8+SIGN(0.5_r8, dRdx(i+1,j,k2)))* & !> & tl_dRdx(i+1,j,k2) !> ad_dRdx(i+1,j,k2)=ad_dRdx(i+1,j,k2)+ & & (0.5_r8+SIGN(0.5_r8, & & dRdx(i+1,j,k2)))* & & ad_cff2 ad_cff2=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, dRdx(i ,j,k1)))* & !> & tl_dRdx(i ,j,k1) !> ad_dRdx(i ,j,k1)=ad_dRdx(i ,j,k1)+ & & (0.5_r8+SIGN(0.5_r8, & & dRdx(i ,j,k1)))* & & ad_cff1 ad_cff1=0.0_r8 END DO END DO END IF DO j=Jmin,Jmax+1 DO i=Imin,Imax #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_v(i,j,k)*om_v(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i,j-1,k))* & & om_v(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i,j-1,itrc))* & & om_v(i,j) #endif !> tl_FE(i,j)=cff* & !> & ((tl_Hz(i,j,k)+tl_Hz(i,j-1,k))* & !> & (dTde(i,j,k1)- & !> & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & !> & (dTdr(i,j-1,k1)+ & !> & dTdr(i,j ,k2))+ & !> & MIN(dRde(i,j,k1),0.0_r8)* & !> & (dTdr(i,j-1,k2)+ & !> & dTdr(i,j ,k1))))+ & !> & (Hz(i,j,k)+Hz(i,j-1,k))* & !> & (tl_dTde(i,j,k1)- & !> & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i,j-1,k1)+ & !> & tl_dTdr(i,j ,k2))+ & !> & MIN(dRde(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i,j-1,k2)+ & !> & tl_dTdr(i,j ,k1)))- & !> & 0.5_r8*((0.5_r8+ & !> & SIGN(0.5_r8, dRde(i,j,k1)))* & !> & tl_dRde(i,j,k1)* & !> & (dTdr(i,j-1,k1)+dTdr(i,j,k2))+ & !> & (0.5_r8+ & !> & SIGN(0.5_r8,-dRde(i,j,k1)))* & !> & tl_dRde(i,j,k1)* & !> & (dTdr(i,j-1,k2)+dTdr(i,j,k1))))) !> adfac=cff*ad_FE(i,j) adfac1=adfac*(dTde(i,j,k1)- & & 0.5_r8*(MAX(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k1)+ & & dTdr(i ,j,k2))+ & & MIN(dRde(i,j,k1),0.0_r8)* & & (dTdr(i,j-1,k2)+ & & dTdr(i ,j,k1)))) adfac2=adfac*(Hz(i,j,k)+Hz(i,j-1,k)) adfac3=adfac2*0.5_r8*MAX(dRde(i,j,k1),0.0_r8) adfac4=adfac2*0.5_r8*MIN(dRde(i,j,k1),0.0_r8) 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_dTde(i,j,k1)=ad_dTde(i,j,k1)+adfac2 ad_dTdr(i,j-1,k1)=ad_dTdr(i,j-1,k1)-adfac3 ad_dTdr(i,j, k2)=ad_dTdr(i,j ,k2)-adfac3 ad_dTdr(i,j-1,k2)=ad_dTdr(i,j-1,k2)-adfac4 ad_dTdr(i,j ,k1)=ad_dTdr(i,j ,k1)-adfac4 ad_dRde(i,j,k1)=ad_dRde(i,j,k1)- & & adfac2*0.5_r8* & & ((0.5_r8+SIGN(0.5_r8, dRde(i,j,k1)))* & & (dTdr(i,j-1,k1)+dTdr(i,j,k2))+ & & (0.5_r8+SIGN(0.5_r8,-dRde(i,j,k1)))* & & (dTdr(i,j-1,k2)+dTdr(i,j,k1))) ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jmin,Jmax DO i=Imin,Imax+1 #ifdef DIFF_3DCOEF # ifdef TS_U3ADV_SPLIT cff=0.5_r8*diff3d_u(i,j,k)*on_u(i,j) # else cff=0.25_r8*(diff3d_r(i,j,k)+diff3d_r(i-1,j,k))* & & on_u(i,j) # endif #else cff=0.25_r8*(diff4(i,j,itrc)+diff4(i-1,j,itrc))* & & on_u(i,j) #endif !> tl_FX(i,j)=cff* & !> & ((tl_Hz(i,j,k)+tl_Hz(i-1,j,k))* & !> & (dTdx(i,j,k1)- & !> & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & !> & (dTdr(i-1,j,k1)+ & !> & dTdr(i ,j,k2))+ & !> & MIN(dRdx(i,j,k1),0.0_r8)* & !> & (dTdr(i-1,j,k2)+ & !> & dTdr(i ,j,k1))))+ & !> & (Hz(i,j,k)+Hz(i-1,j,k))* & !> & (tl_dTdx(i,j,k1)- & !> & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i-1,j,k1)+ & !> & tl_dTdr(i ,j,k2))+ & !> & MIN(dRdx(i,j,k1),0.0_r8)* & !> & (tl_dTdr(i-1,j,k2)+ & !> & tl_dTdr(i ,j,k1)))- & !> & 0.5_r8*((0.5_r8+ & !> & SIGN(0.5_r8, dRdx(i,j,k1)))* & !> & tl_dRdx(i,j,k1)* & !> & (dTdr(i-1,j,k1)+dTdr(i,j,k2))+ & !> & (0.5_r8+ & !> & SIGN(0.5_r8,-dRdx(i,j,k1)))* & !> & tl_dRdx(i,j,k1)* & !> & (dTdr(i-1,j,k2)+dTdr(i,j,k1))))) !> adfac=cff*ad_FX(i,j) adfac1=adfac*(dTdx(i,j,k1)- & & 0.5_r8*(MAX(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k1)+ & & dTdr(i ,j,k2))+ & & MIN(dRdx(i,j,k1),0.0_r8)* & & (dTdr(i-1,j,k2)+ & & dTdr(i ,j,k1)))) adfac2=adfac*(Hz(i,j,k)+Hz(i-1,j,k)) adfac3=adfac2*0.5_r8*MAX(dRdx(i,j,k1),0.0_r8) adfac4=adfac2*0.5_r8*MIN(dRdx(i,j,k1),0.0_r8) 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_dTdx(i,j,k1)=ad_dTdx(i,j,k1)+adfac2 ad_dTdr(i-1,j,k1)=ad_dTdr(i-1,j,k1)-adfac3 ad_dTdr(i ,j,k2)=ad_dTdr(i ,j,k2)-adfac3 ad_dTdr(i-1,j,k2)=ad_dTdr(i-1,j,k2)-adfac4 ad_dTdr(i ,j,k1)=ad_dTdr(i ,j,k1)-adfac4 ad_dRdx(i,j,k1)=ad_dRdx(i,j,k1)- & & adfac2*0.5_r8* & & ((0.5_r8+SIGN(0.5_r8, dRdx(i,j,k1)))* & & (dTdr(i-1,j,k1)+dTdr(i,j,k2))+ & & (0.5_r8+SIGN(0.5_r8,-dRdx(i,j,k1)))* & & (dTdr(i-1,j,k2)+dTdr(i,j,k1))) ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 !> tl_dTdr(i,j,k2)=0.0_r8 !> ad_dTdr(i,j,k2)=0.0_r8 !> tl_FS(i,j,k2)=0.0_r8 !> ad_FS(i,j,k2)=0.0_r8 END DO END DO ELSE DO j=-1+Jmin,Jmax+1 DO i=-1+Imin,Imax+1 #if defined TS_MIX_MAX_SLOPE cff1=SQRT(dRdx(i,j,k2)**2+dRdx(i+1,j,k2)**2+ & & dRdx(i,j,k1)**2+dRdx(i+1,j,k1)**2+ & & dRde(i,j,k2)**2+dRde(i,j+1,k2)**2+ & & dRde(i,j,k1)**2+dRde(i,j+1,k1)**2) cff2=0.25_r8*slope_max* & & (z_r(i,j,k+1)-z_r(i,j,k))*cff1 cff3=MAX(pden(i,j,k)-pden(i,j,k+1),small) cff4=MAX(cff2,cff3) cff=-1.0_r8/cff4 #elif defined TS_MIX_MIN_STRAT cff1=MAX(pden(i,j,k)-pden(i,j,k+1), & & strat_min*(z_r(i,j,k+1)-z_r(i,j,k))) cff=-1.0_r8/cff1 #else cff1=MAX(pden(i,j,k)-pden(i,j,k+1),eps) cff=-1.0_r8/cff1 #endif !> tl_FS(i,j,k2)=tl_cff*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))+ & !> & cff*(tl_z_r(i,j,k+1)- & !> & tl_z_r(i,j,k )) !> adfac=cff*ad_FS(i,j,k2) 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=ad_cff+(z_r(i,j,k+1)- & & z_r(i,j,k ))*ad_FS(i,j,k2) ad_FS(i,j,k2)=0.0_r8 #if defined TS_MIX_STABILITY !> tl_dTdr(i,j,k2)=tl_cff* & !> & (0.75_r8*(t(i,j,k+1,nrhs,itrc)- & !> & t(i,j,k ,nrhs,itrc))+ & !> & 0.25_r8*(t(i,j,k+1,nstp,itrc)- & !> & t(i,j,k ,nstp,itrc)))+ & !> & cff* !> & (0.75_r8*(tl_t(i,j,k+1,nrhs,itrc)- & !> & tl_t(i,j,k ,nrhs,itrc))+ & !> & 0.25_r8*(tl_t(i,j,k+1,nstp,itrc)- & !> & tl_t(i,j,k ,nstp,itrc))) !> adfac=cff*ad_dTdr(i,j,k2) adfac1=adfac*0.75_r8 adfac2=adfac*0.25_r8 ad_t(i,j,k ,nrhs,itrc)=ad_t(i,j,k ,nrhs,itrc)-adfac1 ad_t(i,j,k+1,nrhs,itrc)=ad_t(i,j,k+1,nrhs,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+(0.75_r8*(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc))+ & & 0.25_r8*(t(i,j,k+1,nstp,itrc)- & & t(i,j,k ,nstp,itrc)))* & & ad_dTdz(i,j,k2) ad_dTdz(i,j,k2)=0.0_r8 #elif defined TS_MIX_CLIMA IF (LtracerCLM(itrc,ng)) THEN !> tl_dTdr(i,j,k2)=tl_cff*((t(i,j,k+1,nrhs,itrc)- & !> & tclm(i,j,k+1,itrc))- & !> & (t(i,j,k ,nrhs,itrc)- & !> & tclm(i,j,k ,itrc)))+ & !> & cff*(tl_t(i,j,k+1,nrhs,itrc)- & !> & tl_t(i,j,k ,nrhs,itrc)) !> adfac=cff*ad_dTdr(i,j,k2) ad_t(i,j,k ,nrhs,itrc)=ad_t(i,j,k ,nrhs,itrc)-adfac ad_t(i,j,k+1,nrhs,itrc)=ad_t(i,j,k+1,nrhs,itrc)+adfac ad_cff=ad_cff+((t(i,j,k+1,nrhs,itrc)- & & tclm(i,j,k+1,itrc))- & & (t(i,j,k ,nrhs,itrc)- & & tclm(i,j,k ,itrc)))*ad_dTdr(i,j,k2) ad_dTdr(i,j,k2)=0.0_r8 ELSE !> tl_dTdr(i,j,k2)=tl_cff*(t(i,j,k+1,nrhs,itrc)- & !> & t(i,j,k ,nrhs,itrc))+ & !> & cff*(tl_t(i,j,k+1,nrhs,itrc)- & !> & tl_t(i,j,k ,nrhs,itrc)) !> END IF #else !> tl_dTdr(i,j,k2)=tl_cff*(t(i,j,k+1,nrhs,itrc)- & !> & t(i,j,k ,nrhs,itrc))+ & !> & cff*(tl_t(i,j,k+1,nrhs,itrc)- & !> & tl_t(i,j,k ,nrhs,itrc)) !> adfac=cff*ad_dTdr(i,j,k2) ad_t(i,j,k ,nrhs,itrc)=ad_t(i,j,k ,nrhs,itrc)-adfac ad_t(i,j,k+1,nrhs,itrc)=ad_t(i,j,k+1,nrhs,itrc)+adfac ad_cff=ad_cff+(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc))*ad_dTdr(i,j,k2) ad_dTdr(i,j,k2)=0.0_r8 #endif #if defined TS_MIX_MAX_SLOPE !> tl_cff=cff*cff*tl_cff4 !> ad_cff4=ad_cff4+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff4=(0.5_r8+SIGN(0.5_r8,cff2-cff3))*tl_cff2+ & !> & (0.5_r8-SIGN(0.5_r8,cff2-cff3))*tl_cff3 !> ad_cff3=ad_cff3+ & & (0.5_r8-SIGN(0.5_r8,cff2-cff3))*ad_cff4 ad_cff2=ad_cff2+ & & (0.5_r8+SIGN(0.5_r8,cff2-cff3))*ad_cff4 ad_cff4=0.0_r8 !> tl_cff3=(0.5_r8+SIGN(0.5_r8,pden(i,j,k)-pden(i,j,k+1)- & !> & small))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1)) !> adfac=(0.5_r8+SIGN(0.5_r8,pden(i,j,k)-pden(i,j,k+1)- & & small))*ad_cff3 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac ad_cff3=0.0_r8 !> tl_cff2=0.25_r8*slope_max* & !> & ((tl_z_r(i,j,k+1)-tl_z_r(i,j,k))*cff1+ & !> & (z_r(i,j,k+1)-z_r(i,j,k))*tl_cff1) !> adfac=0.25_r8*slope_max*ad_cff2 adfac1=adfac*cff1 ad_cff1=ad_cff1+(z_r(i,j,k+1)-z_r(i,j,k))*adfac ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac1 ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac1 ad_cff2=0.0_r8 IF (cff1.ne.0.0_r8) THEN !> tl_cff1=(dRdx(i ,j,k2)*tl_dRdx(i ,j,k2)+ & !> & dRdx(i+1,j,k2)*tl_dRdx(i+1,j,k2)+ & !> & dRdx(i ,j,k1)*tl_dRdx(i ,j,k1)+ & !> & dRdx(i+1,j,k1)*tl_dRdx(i+1,j,k1)+ & !> & dRde(i,j ,k2)*tl_dRde(i,j ,k2)+ & !> & dRde(i,j+1,k2)*tl_dRde(i,j+1,k2)+ & !> & dRde(i,j ,k1)*tl_dRde(i,j ,k1)+ & !> & dRde(i,j+1,k1)*tl_dRde(i,j+1,k1))/cff1 !> adfac=ad_cff1/cff1 ad_dRdx(i ,j,k1)=ad_dRdx(i ,j,k1)+ & & dRdx(i ,j,k1)*adfac ad_dRdx(i+1,j,k1)=ad_dRdx(i+1,j,k1)+ & & dRdx(i+1,j,k1)*adfac ad_dRdx(i ,j,k2)=ad_dRdx(i ,j,k2)+ & & dRdx(i ,j,k2)*adfac ad_dRdx(i+1,j,k2)=ad_dRdx(i+1,j,k2)+ & & dRdx(i+1,j,k2)*adfac ad_dRde(i,j ,k2)=ad_dRde(i,j ,k2)+ & & dRde(i,j ,k2)*adfac ad_dRde(i,j+1,k2)=ad_dRde(i,j+1,k2)+ & & dRde(i,j+1,k2)*adfac ad_dRde(i,j ,k1)=ad_dRde(i,j ,k1)+ & & dRde(i,j ,k1)*adfac ad_dRde(i,j+1,k1)=ad_dRde(i,j+1,k1)+ & & dRde(i,j+1,k1)*adfac ad_cff1=0.0_r8 ELSE !> tl_cff1=0.0_r8 !> ad_cff1=0.0_r8 END IF #elif defined TS_MIX_MIN_STRAT !> tl_cff=cff*cff*tl_cff1 !> ad_cff1=ad_cff1+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)- & !> & strat_min*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1))+ & !> & (0.5_r8-SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)- & !> & strat_min*(z_r(i,j,k+1)- & !> & z_r(i,j,k ))))* & !> & (strat_min*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k ))) !> adfac1=(0.5_r8+SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)- & & strat_min*(z_r(i,j,k+1)- & & z_r(i,j,k ))))* & & ad_cff1 adfac2=(0.5_r8-SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)- & & strat_min*(z_r(i,j,k+1)- & & z_r(i,j,k ))))* & & strat_min*ad_cff1 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac1 ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac1 ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac2 ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac2 ad_cff1=0.0_r8 #else !> tl_cff=cff*cff*tl_cff1 !> ad_cff1=ad_cff1+cff*cff*ad_cff ad_cff=0.0_r8 !> tl_cff1=(0.5_r8+SIGN(0.5_r8, & !> & pden(i,j,k)-pden(i,j,k+1)-eps))* & !> & (tl_pden(i,j,k)-tl_pden(i,j,k+1)) !> adfac=(0.5_r8+SIGN(0.5_r8, & & pden(i,j,k)-pden(i,j,k+1)-eps))* & & ad_cff1 ad_pden(i,j,k )=ad_pden(i,j,k )+adfac ad_pden(i,j,k+1)=ad_pden(i,j,k+1)-adfac ad_cff1=0.0_r8 #endif END DO END DO END IF IF (k.lt.N(ng)) THEN DO j=Jmin,Jmax+1 DO i=Imin,Imax cff=0.5_r8*(pn(i,j)+pn(i,j-1)) #ifdef MASKING cff=cff*vmask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*vmask_wet(i,j) #endif #if defined TS_MIX_STABILITY !> tl_dTde(i,j,k2)=cff* & !> & (0.75_r8*(tl_t(i,j ,k+1,nrhs,itrc)- & !> & tl_t(i,j-1,k+1,nrhs,itrc))+ & !> & 0.25_r8*(tl_t(i,j ,k+1,nstp,itrc)- & !> & tl_t(i,j-1,k+1,nstp,itrc))) !> adfac=cff*ad_dTde(i,j,k2) adfac1=adfac*0.75_r8 adfac2=adfac*0.25_r8 ad_t(i,j-1,k+1,nrhs,itrc)=ad_t(i,j-1,k+1,nrhs,itrc)- & & adfac1 ad_t(i,j ,k+1,nrhs,itrc)=ad_t(i,j ,k+1,nrhs,itrc)+ & & adfac1 ad_t(i,j-1,k+1,nstp,itrc)=ad_t(i,j-1,k+1,nstp,itrc)- & & adfac2 ad_t(i,j ,k+1,nstp,itrc)=ad_t(i,j ,k+1,nstp,itrc)+ & & adfac2 ad_dTde(i,j,k2)=0.0_r8 #elif defined TS_MIX_CLIMA !> tl_dTde(i,j,k2)=cff*(tl_t(i,j ,k+1,nrhs,itrc)- & !> & tl_t(i,j-1,k+1,nrhs,itrc)) !> adfac=cff*ad_dTde(i,j,k2) ad_t(i,j-1,k+1,nrhs,itrc)=ad_t(i,j-1,k+1,nrhs,itrc)- & & adfac ad_t(i,j ,k+1,nrhs,itrc)=ad_t(i,j ,k+1,nrhs,itrc)+ & & adfac ad_dTde(i,j,k2)=0.0_r8 #else !> tl_dTde(i,j,k2)=cff*(tl_t(i,j ,k+1,nrhs,itrc)- & !> & tl_t(i,j-1,k+1,nrhs,itrc)) !> adfac=cff*ad_dTde(i,j,k2) ad_t(i,j-1,k+1,nrhs,itrc)=ad_t(i,j-1,k+1,nrhs,itrc)- & & adfac ad_t(i,j ,k+1,nrhs,itrc)=ad_t(i,j ,k+1,nrhs,itrc)+ & & adfac ad_dTde(i,j,k2)=0.0_r8 #endif !> tl_dRde(i,j,k2)=cff*(tl_pden(i,j ,k+1)- & !> & tl_pden(i,j-1,k+1)) !> adfac=cff*ad_dRde(i,j,k2) ad_pden(i,j-1,k+1)=ad_pden(i,j-1,k+1)-adfac ad_pden(i,j ,k+1)=ad_pden(i,j ,k+1)+adfac ad_dRde(i,j,k2)=0.0_r8 END DO END DO DO j=Jmin,Jmax DO i=Imin,Imax+1 cff=0.5_r8*(pm(i,j)+pm(i-1,j)) #ifdef MASKING cff=cff*umask(i,j) #endif #ifdef WET_DRY_NOT_YET cff=cff*umask_wet(i,j) #endif #if defined TS_MIX_STABILITY !> tl_dTdx(i,j,k2)=cff* & !> & (0.75_r8*(tl_t(i ,j,k+1,nrhs,itrc)- & !> & tl_t(i-1,j,k+1,nrhs,itrc))+ & !> & 0.25_r8*(tl_t(i ,j,k+1,nstp,itrc)- & !> & tl_t(i-1,j,k+1,nstp,itrc))) !> adfac=cff*ad_dTdx(i,j,k2) adfac1=adfac*0.75_r8 adfac2=adfac*0.25_r8 ad_t(i-1,j,k+1,nrhs,itrc)=ad_t(i-1,j,k+1,nrhs,itrc)- & & adfac1 ad_t(i ,j,k+1,nrhs,itrc)=ad_t(i ,j,k+1,nrhs,itrc)+ & & adfac1 ad_t(i-1,j,k+1,nstp,itrc)=ad_t(i-1,j,k+1,nstp,itrc)- & & adfac2 ad_t(i ,j,k+1,nstp,itrc)=ad_t(i ,j,k+1,nstp,itrc)+ & & adfac2 ad_dTdx(i,j,k2)=0.0_r8 #elif defined TS_MIX_CLIMA !> tl_dTdx(i,j,k2)=cff*(tl_t(i ,j,k+1,nrhs,itrc)- & !> & tl_t(i-1,j,k+1,nrhs,itrc)) !> adfac=cff*ad_dTdx(i,j,k2) ad_t(i-1,j,k+1,nrhs,itrc)=ad_t(i-1,j,k+1,nrhs,itrc)- & & adfac ad_t(i ,j,k+1,nrhs,itrc)=ad_t(i ,j,k+1,nrhs,itrc)+ & & adfac ad_dTdx(i,j,k2)=0.0_r8 #else !> tl_dTdx(i,j,k2)=cff*(tl_t(i ,j,k+1,nrhs,itrc)- & !> & tl_t(i-1,j,k+1,nrhs,itrc)) !> adfac=cff*ad_dTdx(i,j,k2) ad_t(i-1,j,k+1,nrhs,itrc)=ad_t(i-1,j,k+1,nrhs,itrc)- & & adfac ad_t(i ,j,k+1,nrhs,itrc)=ad_t(i ,j,k+1,nrhs,itrc)+ & & adfac ad_dTdx(i,j,k2)=0.0_r8 #endif !> tl_dRdx(i,j,k2)=cff*(tl_pden(i ,j,k+1)- & !> & tl_pden(i-1,j,k+1)) !> adfac=cff*ad_dRdx(i,j,k2) ad_pden(i-1,j,k+1)=ad_pden(i-1,j,k+1)-adfac ad_pden(i ,j,k+1)=ad_pden(i ,j,k+1)+adfac ad_dRdx(i,j,k2)=0.0_r8 END DO END DO END IF ! ! Compute new storage recursive indices. ! kt=k2 k2=k1 k1=kt END DO K_LOOP3 END DO T_LOOP RETURN END SUBROUTINE ad_t3dmix4_tile