MODULE ad_t3dmix2_mod ! !git $Id$ !svn $Id: ad_t3dmix2_iso.h 1151 2023-02-09 03:08:53Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! This subroutine computes adjoint horizontal harmonic mixing of ! ! tracers along isopycnic surfaces. ! ! ! ! BASIC STATE variables needed: diff2, Hz, rho, t, z_r ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC ad_t3dmix2 ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_t3dmix2 (ng, tile) !*********************************************************************** ! 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. ! character (len=*), parameter :: MyFile = & & __FILE__ ! #include "tile.h" ! #ifdef PROFILE CALL wclock_on (ng, iADM, 26, __LINE__, MyFile) #endif CALL ad_t3dmix2_iso_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 & 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, & & MIXING(ng) % diff2, & & 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, 26, __LINE__, MyFile) #endif ! RETURN END SUBROUTINE ad_t3dmix2 ! !*********************************************************************** SUBROUTINE ad_t3dmix2_iso_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, nstp, nnew, & #ifdef MASKING & umask, vmask, & #endif & om_v, on_u, pm, pn, & & Hz, ad_Hz, & & z_r, ad_z_r, & & diff2, & & pden, ad_pden, & #ifdef TS_MIX_CLIMA & tclm, & #endif #ifdef DIAGNOSTICS_TS !! & DiaTwrk, & #endif & t, ad_t) !*********************************************************************** ! USE mod_param 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 real(r8), intent(in) :: diff2(LBi:,LBj:,:) 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 real(r8), intent(in) :: diff2(LBi:UBi,LBj:UBj,NT(ng)) 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 :: 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 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) :: 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) :: 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 ! !---------------------------------------------------------------------- ! Compute horizontal harmonic diffusion along isopycnic surfaces. !---------------------------------------------------------------------- ! ! Compute horizontal and density gradients. 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 ! ! Compute adjoint of starting values of k1 and k2. ! T_LOOP : DO itrc=1,NT(ng) k1=2 k2=1 DO k=0,N(ng) !! !! Note: The following code is equivalent to !! !! kt=k1 !! k1=k2 !! k2=kt !! !! We use the adjoint of above code. !! k1=k2 k2=3-k1 END DO K_LOOP : DO k=N(ng),0,-1 ! ! Compute required BASIC STATE fields. Need to look forward in ! recursive kk index. ! k2b=1 DO kk=0,k k1b=k2b k2b=3-k1b ! ! Compute components of the rotated tracer flux (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 dRdx(i,j,k2b)=cff*(pden(i ,j,kk+1)- & & pden(i-1,j,kk+1)) #ifdef TS_MIX_CLIMA dTdx(i,j,k2b)=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,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=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 dRde(i,j,k2b)=cff*(pden(i,j ,kk+1)- & & pden(i,j-1,kk+1)) #ifdef TS_MIX_CLIMA dTde(i,j,k2b)=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,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=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 #ifdef TS_MIX_CLIMA dTdr(i,j,k2b)=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,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 END DO ! IF (k.gt.0) THEN ! ! Time-step harmonic, isopycnic diffusion term. ! 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,k2)=ad_FS(i,j,k2)+adfac ad_FS(i,j,k1)=ad_FS(i,j,k1)-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_cff=0.0_r8 END DO END DO ! ! Compute components of the rotated tracer flux (T m4/s) along ! isopycnic surfaces. ! IF (k.lt.N(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend 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=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+ & & 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)=0.5_r8*diff2(i,j,itrc)* & !^ & (tl_cff*FS(i,j,k2)+ & !^ & cff*tl_FS(i,j,k2)) !^ adfac=0.5_r8*diff2(i,j,itrc)*ad_FS(i,j,k2) ad_cff=ad_cff+adfac*FS(i,j,k2) ad_FS(i,j,k2)=cff*adfac !^ tl_cff=tl_cff+ & !^ & 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)) !^ ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTde(i,j ,k1))* & & ad_cff ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTde(i,j+1,k2))* & & ad_cff ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTde(i,j ,k2))* & & ad_cff ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTde(i,j+1,k1))* & & ad_cff ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*ad_cff ad_dTde(i,j ,k1)=ad_dTde(i,j ,k1)-cff1*ad_cff ad_dTde(i,j+1,k2)=ad_dTde(i,j+1,k2)-cff2*ad_cff ad_dTde(i,j ,k2)=ad_dTde(i,j ,k2)-cff3*ad_cff ad_dTde(i,j+1,k1)=ad_dTde(i,j+1,k1)-cff4*ad_cff !^ 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=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)) !^ ad_cff1=ad_cff1+ & & (2.0_r8*cff1*dTdr(i,j,k2)-dTdx(i ,j,k1))* & & ad_cff ad_cff2=ad_cff2+ & & (2.0_r8*cff2*dTdr(i,j,k2)-dTdx(i+1,j,k2))* & & ad_cff ad_cff3=ad_cff3+ & & (2.0_r8*cff3*dTdr(i,j,k2)-dTdx(i ,j,k2))* & & ad_cff ad_cff4=ad_cff4+ & & (2.0_r8*cff4*dTdr(i,j,k2)-dTdx(i+1,j,k1))* & & ad_cff ad_dTdr(i,j,k2)=ad_dTdr(i,j,k2)+ & & (cff1*cff1+ & & cff2*cff2+ & & cff3*cff3+ & & cff4*cff4)*ad_cff ad_dTdx(i ,j,k1)=ad_dTdx(i ,j,k1)-cff1*ad_cff ad_dTdx(i+1,j,k2)=ad_dTdx(i+1,j,k2)-cff2*ad_cff ad_dTdx(i ,j,k2)=ad_dTdx(i ,j,k2)-cff3*ad_cff ad_dTdx(i+1,j,k1)=ad_dTdx(i+1,j,k1)-cff4*ad_cff 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 cff=0.25_r8*(diff2(i,j,itrc)+diff2(i,j-1,itrc))* & & om_v(i,j) !^ 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)- & & 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)))*adfac2 ad_FE(i,j)=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=Istr,Iend+1 cff=0.25_r8*(diff2(i,j,itrc)+diff2(i-1,j,itrc))* & & on_u(i,j) !^ 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)- & & 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)))*adfac2 ad_FX(i,j)=0.0_r8 END DO END DO END IF IF ((k.eq.0).or.(k.eq.N(ng))) THEN DO j=Jstr-1,Jend+1 DO i=Istr-1,Iend+1 !^ tl_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 #ifdef TS_MIX_CLIMA !^ 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)) #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)) #endif !^ 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 #ifdef TS_MIX_CLIMA 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) #else ad_cff=ad_cff+(t(i,j,k+1,nrhs,itrc)- & & t(i,j,k ,nrhs,itrc))*ad_dTdr(i,j,k2) #endif 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 !^ 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 !^ 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 !^ 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 !^ 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_LOOP END DO T_LOOP ! RETURN END SUBROUTINE ad_t3dmix2_iso_tile END MODULE ad_t3dmix2_mod