MODULE ad_prsgrd_mod ! !git $Id$ !svn $Id: ad_prsgrd32.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 sub routine evaluates the adjoint baroclinic, hydrostatic ! ! pressure gradient term using a nonconservative Density-Jacobian ! ! scheme, based on cubic polynomial fits for "rho" and "z_r" as ! ! functions of nondimensional coordinates (XI,ETA,s), that is, its ! ! respective array indices. The cubic polynomials are monotonized ! ! by using harmonic mean instead of linear averages to interpolate ! ! slopes. This scheme retains exact anti-symmetry: ! ! ! ! J(rho,z_r)=-J(z_r,rho). ! ! ! ! If parameter OneFifth (below) is set to zero, the scheme becomes ! ! identical to standard Jacobian. ! ! ! ! Reference: ! ! ! ! Shchepetkin A.F and J.C. McWilliams, 2003: A method for ! ! computing horizontal pressure gradient force in an ocean ! ! model with non-aligned vertical coordinate, JGR, 108, ! ! 1-34. ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: ad_prsgrd ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_prsgrd (ng, tile) !*********************************************************************** ! USE mod_param USE mod_grid USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & "ROMS/Adjoint/ad_prsgrd32.h" ! integer :: IminS, ImaxS, JminS, JmaxS integer :: LBi, UBi, LBj, UBj, LBij, UBij ! ! Set horizontal starting and ending indices for automatic private ! storage arrays. ! IminS=BOUNDS(ng)%Istr(tile)-3 ImaxS=BOUNDS(ng)%Iend(tile)+3 JminS=BOUNDS(ng)%Jstr(tile)-3 JmaxS=BOUNDS(ng)%Jend(tile)+3 ! ! Determine array lower and upper bounds in the I- and J-directions. ! LBi=BOUNDS(ng)%LBi(tile) UBi=BOUNDS(ng)%UBi(tile) LBj=BOUNDS(ng)%LBj(tile) UBj=BOUNDS(ng)%UBj(tile) ! ! Set array lower and upper bounds for MIN(I,J) directions and ! MAX(I,J) directions. ! LBij=BOUNDS(ng)%LBij UBij=BOUNDS(ng)%UBij ! CALL wclock_on (ng, iADM, 23, 67, MyFile) CALL ad_prsgrd32_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & & GRID(ng) % umask, & & GRID(ng) % vmask, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % Hz, & & GRID(ng) % ad_Hz, & & GRID(ng) % z_r, & & GRID(ng) % ad_z_r, & & GRID(ng) % z_w, & & GRID(ng) % ad_z_w, & & OCEAN(ng) % rho, & & OCEAN(ng) % ad_rho, & & OCEAN(ng) % ad_ru, & & OCEAN(ng) % ad_rv) CALL wclock_off (ng, iADM, 23, 101, MyFile) ! RETURN END SUBROUTINE ad_prsgrd ! !*********************************************************************** SUBROUTINE ad_prsgrd32_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & & umask, vmask, & & om_v, on_u, & & Hz, ad_Hz, & & z_r, ad_z_r, & & z_w, ad_z_w, & & rho, ad_rho, & & ad_ru, ad_rv) !*********************************************************************** ! 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 real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: z_r(LBi:,LBj:,:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) real(r8), intent(in) :: rho(LBi:,LBj:,:) real(r8), intent(inout) :: ad_Hz(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_rho(LBi:,LBj:,:) real(r8), intent(inout) :: ad_ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: ad_rv(LBi:,LBj:,0:,:) ! ! Local variable declarations. ! integer :: i, j, k real(r8), parameter :: OneFifth = 0.2_r8 real(r8), parameter :: OneTwelfth = 1.0_r8/12.0_r8 real(r8), parameter :: eps = 1.0E-10_r8 real(r8) :: GRho, GRho0, HalfGRho real(r8) :: cff, cff1, cff2 real(r8) :: ad_cff, ad_cff1, ad_cff2, adfac real(r8) :: adfac1, adfac2, adfac3, adfac4, adfac5, adfac6 real(r8) :: adfac7, adfac8, adfac9, adfac10, adfac11, adfac12 real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: P real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: ad_P real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dR real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dR1 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dZ real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dZ1 real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_dR real(r8), dimension(IminS:ImaxS,0:N(ng)) :: ad_dZ real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FC real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: aux real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dRx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: dZx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_FC real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_aux real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_dRx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: ad_dZx ! !----------------------------------------------------------------------- ! Set lower and upper tile bounds and staggered variables bounds for ! this horizontal domain partition. Notice that if tile=-1, it will ! set the values for the global grid. !----------------------------------------------------------------------- ! integer :: Istr, IstrB, IstrP, IstrR, IstrT, IstrM, IstrU integer :: Iend, IendB, IendP, IendR, IendT integer :: Jstr, JstrB, JstrP, JstrR, JstrT, JstrM, JstrV integer :: Jend, JendB, JendP, JendR, JendT integer :: Istrm3, Istrm2, Istrm1, IstrUm2, IstrUm1 integer :: Iendp1, Iendp2, Iendp2i, Iendp3 integer :: Jstrm3, Jstrm2, Jstrm1, JstrVm2, JstrVm1 integer :: Jendp1, Jendp2, Jendp2i, Jendp3 ! Istr =BOUNDS(ng) % Istr (tile) IstrB =BOUNDS(ng) % IstrB (tile) IstrM =BOUNDS(ng) % IstrM (tile) IstrP =BOUNDS(ng) % IstrP (tile) IstrR =BOUNDS(ng) % IstrR (tile) IstrT =BOUNDS(ng) % IstrT (tile) IstrU =BOUNDS(ng) % IstrU (tile) Iend =BOUNDS(ng) % Iend (tile) IendB =BOUNDS(ng) % IendB (tile) IendP =BOUNDS(ng) % IendP (tile) IendR =BOUNDS(ng) % IendR (tile) IendT =BOUNDS(ng) % IendT (tile) Jstr =BOUNDS(ng) % Jstr (tile) JstrB =BOUNDS(ng) % JstrB (tile) JstrM =BOUNDS(ng) % JstrM (tile) JstrP =BOUNDS(ng) % JstrP (tile) JstrR =BOUNDS(ng) % JstrR (tile) JstrT =BOUNDS(ng) % JstrT (tile) JstrV =BOUNDS(ng) % JstrV (tile) Jend =BOUNDS(ng) % Jend (tile) JendB =BOUNDS(ng) % JendB (tile) JendP =BOUNDS(ng) % JendP (tile) JendR =BOUNDS(ng) % JendR (tile) JendT =BOUNDS(ng) % JendT (tile) ! Istrm3 =BOUNDS(ng) % Istrm3 (tile) ! Istr-3 Istrm2 =BOUNDS(ng) % Istrm2 (tile) ! Istr-2 Istrm1 =BOUNDS(ng) % Istrm1 (tile) ! Istr-1 IstrUm2=BOUNDS(ng) % IstrUm2(tile) ! IstrU-2 IstrUm1=BOUNDS(ng) % IstrUm1(tile) ! IstrU-1 Iendp1 =BOUNDS(ng) % Iendp1 (tile) ! Iend+1 Iendp2 =BOUNDS(ng) % Iendp2 (tile) ! Iend+2 Iendp2i=BOUNDS(ng) % Iendp2i(tile) ! Iend+2 interior Iendp3 =BOUNDS(ng) % Iendp3 (tile) ! Iend+3 Jstrm3 =BOUNDS(ng) % Jstrm3 (tile) ! Jstr-3 Jstrm2 =BOUNDS(ng) % Jstrm2 (tile) ! Jstr-2 Jstrm1 =BOUNDS(ng) % Jstrm1 (tile) ! Jstr-1 JstrVm2=BOUNDS(ng) % JstrVm2(tile) ! JstrV-2 JstrVm1=BOUNDS(ng) % JstrVm1(tile) ! JstrV-1 Jendp1 =BOUNDS(ng) % Jendp1 (tile) ! Jend+1 Jendp2 =BOUNDS(ng) % Jendp2 (tile) ! Jend+2 Jendp2i=BOUNDS(ng) % Jendp2i(tile) ! Jend+2 interior Jendp3 =BOUNDS(ng) % Jendp3 (tile) ! Jend+3 ! !----------------------------------------------------------------------- ! Initialize adjoint private variables. !----------------------------------------------------------------------- ! ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 DO j=JminS,JmaxS DO i=IminS,ImaxS ad_FC(i,j)=0.0_r8 ad_aux(i,j)=0.0_r8 ad_dRx(i,j)=0.0_r8 ad_dZx(i,j)=0.0_r8 END DO DO k=1,N(ng) DO i=IminS,ImaxS ad_P(i,j,k)=0.0_r8 END DO END DO END DO DO k=0,N(ng) DO i=IminS,ImaxS ad_dR(i,k)=0.0_r8 ad_dZ(i,k)=0.0_r8 END DO END DO ! !----------------------------------------------------------------------- ! Preliminary step (same for XI- and ETA-components): !----------------------------------------------------------------------- ! ! Compute BASIC STATE dynamic pressure, P. ! GRho=g/rho0 GRho0=1000.0_r8*GRho HalfGRho=0.5_r8*GRho ! DO j=JstrV-1,Jend DO k=1,N(ng)-1 DO i=IstrU-1,Iend dR(i,k)=rho(i,j,k+1)-rho(i,j,k) dZ(i,k)=z_r(i,j,k+1)-z_r(i,j,k) END DO END DO DO i=IstrU-1,Iend dR(i,N(ng))=dR(i,N(ng)-1) dZ(i,N(ng))=dZ(i,N(ng)-1) dR(i,0)=dR(i,1) dZ(i,0)=dZ(i,1) END DO DO k=N(ng),1,-1 DO i=IstrU-1,Iend cff=2.0_r8*dR(i,k)*dR(i,k-1) IF (cff.gt.eps) THEN dR(i,k)=cff/(dR(i,k)+dR(i,k-1)) ELSE dR(i,k)=0.0_r8 END IF dZ(i,k)=2.0_r8*dZ(i,k)*dZ(i,k-1)/(dZ(i,k)+dZ(i,k-1)) END DO END DO DO i=IstrU-1,Iend cff1=1.0_r8/(z_r(i,j,N(ng))-z_r(i,j,N(ng)-1)) cff2=0.5_r8*(rho(i,j,N(ng))-rho(i,j,N(ng)-1))* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))*cff1 P(i,j,N(ng))=g*z_w(i,j,N(ng))+ & & GRho*(rho(i,j,N(ng))+cff2)* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng))) END DO DO k=N(ng)-1,1,-1 DO i=IstrU-1,Iend P(i,j,k)=P(i,j,k+1)+ & & HalfGRho*((rho(i,j,k+1)+rho(i,j,k))* & & (z_r(i,j,k+1)-z_r(i,j,k))- & & OneFifth* & & ((dR(i,k+1)-dR(i,k))* & & (z_r(i,j,k+1)-z_r(i,j,k)- & & OneTwelfth* & & (dZ(i,k+1)+dZ(i,k)))- & & (dZ(i,k+1)-dZ(i,k))* & & (rho(i,j,k+1)-rho(i,j,k)- & & OneTwelfth* & & (dR(i,k+1)+dR(i,k))))) END DO END DO END DO ! !----------------------------------------------------------------------- ! Adjoint ETA-component pressure gradient term. !----------------------------------------------------------------------- ! DO k=1,N(ng) ! ! Compute BASIC STATE variables. ! DO j=JstrV-1,Jend+1 DO i=Istr,Iend aux(i,j)=z_r(i,j,k)-z_r(i,j-1,k) aux(i,j)=aux(i,j)*vmask(i,j) FC(i,j)=rho(i,j,k)-rho(i,j-1,k) FC(i,j)=FC(i,j)*vmask(i,j) END DO END DO ! DO j=JstrV-1,Jend DO i=Istr,Iend cff=2.0_r8*aux(i,j)*aux(i,j+1) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i,j+1)) dZx(i,j)=cff*cff1 ELSE dZx(i,j)=0.0_r8 END IF cff1=2.0_r8*FC(i,j)*FC(i,j+1) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i,j+1)) dRx(i,j)=cff1*cff2 ELSE dRx(i,j)=0.0_r8 END IF END DO END DO ! DO j=JstrV,Jend DO i=Istr,Iend !^ tl_rv(i,j,k,nrhs)=om_v(i,j)*0.5_r8* & !^ & ((tl_Hz(i,j,k)+tl_Hz(i,j-1,k))* & !^ & (P(i,j-1,k)-P(i,j,k)- & !^ & HalfGRho* & !^ & ((rho(i,j,k)+rho(i,j-1,k))* & !^ & (z_r(i,j,k)-z_r(i,j-1,k))- & !^ & OneFifth* & !^ & ((dRx(i,j)-dRx(i,j-1))* & !^ & (z_r(i,j,k)-z_r(i,j-1,k)- & !^ & OneTwelfth* & !^ & (dZx(i,j)+dZx(i,j-1)))- & !^ & (dZx(i,j)-dZx(i,j-1))* & !^ & (rho(i,j,k)-rho(i,j-1,k)- & !^ & OneTwelfth* & !^ & (dRx(i,j)+dRx(i,j-1))))))+ & !^ & (Hz(i,j,k)+Hz(i,j-1,k))* & !^ & (tl_P(i,j-1,k)-tl_P(i,j,k)- & !^ & HalfGRho* & !^ & ((tl_rho(i,j,k)+tl_rho(i,j-1,k))* & !^ & (z_r(i,j,k)-z_r(i,j-1,k))+ & !^ & (rho(i,j,k)+rho(i,j-1,k))* & !^ & (tl_z_r(i,j,k)-tl_z_r(i,j-1,k))- & !^ & OneFifth* & !^ & ((tl_dRx(i,j)-tl_dRx(i,j-1))* & !^ & (z_r(i,j,k)-z_r(i,j-1,k)- & !^ & OneTwelfth* & !^ & (dZx(i,j)+dZx(i,j-1)))+ & !^ & (dRx(i,j)-dRx(i,j-1))* & !^ & (tl_z_r(i,j,k)-tl_z_r(i,j-1,k)- & !^ & OneTwelfth* & !^ & (tl_dZx(i,j)+tl_dZx(i,j-1)))- & !^ & (tl_dZx(i,j)-tl_dZx(i,j-1))* & !^ & (rho(i,j,k)-rho(i,j-1,k)- & !^ & OneTwelfth* & !^ & (dRx(i,j)+dRx(i,j-1)))- & !^ & (dZx(i,j)-dZx(i,j-1))* & !^ & (tl_rho(i,j,k)-tl_rho(i,j-1,k)- & !^ & OneTwelfth* & !^ & (tl_dRx(i,j)+tl_dRx(i,j-1))))))) !^ adfac=om_v(i,j)*0.5_r8*ad_rv(i,j,k,nrhs) adfac1=adfac*(P(i,j-1,k)-P(i,j,k)- & & HalfGRho* & & ((rho(i,j,k)+rho(i,j-1,k))* & & (z_r(i,j,k)-z_r(i,j-1,k))- & & OneFifth* & & ((dRx(i,j)-dRx(i,j-1))* & & (z_r(i,j,k)-z_r(i,j-1,k)- & & OneTwelfth* & & (dZx(i,j)+dZx(i,j-1)))- & & (dZx(i,j)-dZx(i,j-1))* & & (rho(i,j,k)-rho(i,j-1,k)- & & OneTwelfth* & & (dRx(i,j)+dRx(i,j-1)))))) adfac2=adfac*(Hz(i,j,k)+Hz(i,j-1,k)) adfac3=adfac2*HalfGRho adfac4=adfac3*(z_r(i,j,k)-z_r(i,j-1,k)) adfac5=adfac3*(rho(i,j,k)+rho(i,j-1,k)) adfac6=adfac3*OneFifth adfac7=adfac6*(z_r(i,j,k)-z_r(i,j-1,k)- & & OneTwelfth*(dZx(i,j)+dZx(i,j-1))) adfac8=adfac6*(dRx(i,j)-dRx(i,j-1)) adfac9=adfac8*OneTwelfth adfac10=adfac6*(rho(i,j,k)-rho(i,j-1,k)- & & OneTwelfth*(dRx(i,j)+dRx(i,j-1))) adfac11=adfac6*(dZx(i,j)-dZx(i,j-1)) adfac12=adfac11*OneTwelfth 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_P(i,j-1,k)=ad_P(i,j-1,k)+adfac2 ad_P(i,j ,k)=ad_P(i,j ,k)-adfac2 ad_rho(i,j-1,k)=ad_rho(i,j-1,k)-adfac4+adfac11 ad_rho(i,j ,k)=ad_rho(i,j ,k)-adfac4-adfac11 ad_z_r(i,j-1,k)=ad_z_r(i,j-1,k)+adfac5-adfac8 ad_z_r(i,j ,k)=ad_z_r(i,j ,k)-adfac5+adfac8 ad_dRx(i,j-1)=ad_dRx(i,j-1)-adfac7+adfac12 ad_dRx(i,j )=ad_dRx(i,j )+adfac7+adfac12 ad_dZx(i,j-1)=ad_dZx(i,j-1)-adfac9+adfac10 ad_dZx(i,j )=ad_dZx(i,j )-adfac9-adfac10 ad_rv(i,j,k,nrhs)=0.0_r8 END DO END DO ! DO j=JstrV-1,Jend DO i=Istr,Iend cff1=2.0_r8*FC(i,j)*FC(i,j+1) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i,j+1)) !^ tl_dRx(i,j)=tl_cff1*cff2+cff1*tl_cff2 !^ ad_cff1=ad_cff1+cff2*ad_dRx(i,j) ad_cff2=ad_cff2+cff1*ad_dRx(i,j) ad_dRx(i,j)=0.0_r8 !^ tl_cff2=-cff2*cff2*(tl_FC(i,j)+tl_FC(i,j+1)) !^ adfac=-cff2*cff2*ad_cff2 ad_FC(i,j )=ad_FC(i,j )+adfac ad_FC(i,j+1)=ad_FC(i,j+1)+adfac ad_cff2=0.0_r8 ELSE !^ tl_dRx(i,j)=0.0_r8 !^ ad_dRx(i,j)=0.0_r8 END IF !^ tl_cff1=2.0_r8*(tl_FC(i,j)*FC(i,j+1)+ & !^ & FC(i,j)*tl_FC(i,j+1)) !^ adfac=2.0_r8*ad_cff1 ad_FC(i,j )=ad_FC(i,j )+FC(i,j+1)*adfac ad_FC(i,j+1)=ad_FC(i,j+1)+FC(i,j )*adfac ad_cff1=0.0_r8 cff=2.0_r8*aux(i,j)*aux(i,j+1) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i,j+1)) !^ tl_dZx(i,j)=tl_cff*cff1+cff*tl_cff1 !^ ad_cff=ad_cff+cff1*ad_dZx(i,j) ad_cff1=ad_cff1+cff*ad_dZx(i,j) ad_dZx(i,j)=0.0_r8 !^ tl_cff1=-cff1*cff1*(tl_aux(i,j)+tl_aux(i,j+1)) !^ adfac=-cff1*cff1*ad_cff1 ad_aux(i,j )=ad_aux(i,j )+adfac ad_aux(i,j+1)=ad_aux(i,j+1)+adfac ad_cff1=0.0_r8 ELSE !^ tl_dZx(i,j)=0.0_r8 !^ ad_dZx(i,j)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_aux(i,j)*aux(i,j+1)+ & !^ & aux(i,j)*tl_aux(i,j+1)) !^ adfac=2.0_r8*ad_cff ad_aux(i,j )=ad_aux(i,j )+aux(i,j+1)*adfac ad_aux(i,j+1)=ad_aux(i,j+1)+aux(i,j )*adfac ad_cff=0.0_r8 END DO END DO DO j=JstrV-1,Jend+1 DO i=Istr,Iend !^ tl_FC(i,j)=tl_FC(i,j)*vmask(i,j) !^ ad_FC(i,j)=ad_FC(i,j)*vmask(i,j) !^ tl_FC(i,j)=tl_rho(i,j,k)-tl_rho(i,j-1,k) !^ ad_rho(i,j-1,k)=ad_rho(i,j-1,k)-ad_FC(i,j) ad_rho(i,j, k)=ad_rho(i,j ,k)+ad_FC(i,j) ad_FC(i,j)=0.0_r8 !^ tl_aux(i,j)=tl_aux(i,j)*vmask(i,j) !^ ad_aux(i,j)=ad_aux(i,j)*vmask(i,j) !^ tl_aux(i,j)=tl_z_r(i,j,k)-tl_z_r(i,j-1,k) !^ ad_z_r(i,j-1,k)=ad_z_r(i,j-1,k)-ad_aux(i,j) ad_z_r(i,j ,k)=ad_z_r(i,j ,k)+ad_aux(i,j) ad_aux(i,j)=0.0_r8 END DO END DO END DO ! !----------------------------------------------------------------------- ! Compute adjoint XI-component pressure gradient term. !----------------------------------------------------------------------- ! DO k=1,N(ng) ! ! Compute BASIC STATE variables. ! DO j=Jstr,Jend DO i=IstrU-1,Iend+1 aux(i,j)=z_r(i,j,k)-z_r(i-1,j,k) aux(i,j)=aux(i,j)*umask(i,j) FC(i,j)=rho(i,j,k)-rho(i-1,j,k) FC(i,j)=FC(i,j)*umask(i,j) END DO END DO ! DO j=Jstr,Jend DO i=IstrU-1,Iend cff=2.0_r8*aux(i,j)*aux(i+1,j) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i+1,j)) dZx(i,j)=cff*cff1 ELSE dZx(i,j)=0.0_r8 END IF cff1=2.0_r8*FC(i,j)*FC(i+1,j) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i+1,j)) dRx(i,j)=cff1*cff2 ELSE dRx(i,j)=0.0_r8 END IF END DO END DO ! DO j=Jstr,Jend DO i=IstrU,Iend !^ tl_ru(i,j,k,nrhs)=on_u(i,j)*0.5_r8* & !^ & ((tl_Hz(i,j,k)+tl_Hz(i-1,j,k))* & !^ & (P(i-1,j,k)-P(i,j,k)- & !^ & HalfGRho* & !^ & ((rho(i,j,k)+rho(i-1,j,k))* & !^ & (z_r(i,j,k)-z_r(i-1,j,k))- & !^ & OneFifth* & !^ & ((dRx(i,j)-dRx(i-1,j))* & !^ & (z_r(i,j,k)-z_r(i-1,j,k)- & !^ & OneTwelfth* & !^ & (dZx(i,j)+dZx(i-1,j)))- & !^ & (dZx(i,j)-dZx(i-1,j))* & !^ & (rho(i,j,k)-rho(i-1,j,k)- & !^ & OneTwelfth* & !^ & (dRx(i,j)+dRx(i-1,j))))))+ & !^ & (Hz(i,j,k)+Hz(i-1,j,k))* & !^ & (tl_P(i-1,j,k)-tl_P(i,j,k)- & !^ & HalfGRho* & !^ & ((tl_rho(i,j,k)+tl_rho(i-1,j,k))* & !^ & (z_r(i,j,k)-z_r(i-1,j,k))+ & !^ & (rho(i,j,k)+rho(i-1,j,k))* & !^ & (tl_z_r(i,j,k)-tl_z_r(i-1,j,k))- & !^ & OneFifth* & !^ & ((tl_dRx(i,j)-tl_dRx(i-1,j))* & !^ & (z_r(i,j,k)-z_r(i-1,j,k)- & !^ & OneTwelfth* & !^ & (dZx(i,j)+dZx(i-1,j)))+ & !^ & (dRx(i,j)-dRx(i-1,j))* & !^ & (tl_z_r(i,j,k)-tl_z_r(i-1,j,k)- & !^ & OneTwelfth* & !^ & (tl_dZx(i,j)+tl_dZx(i-1,j)))- & !^ & (tl_dZx(i,j)-tl_dZx(i-1,j))* & !^ & (rho(i,j,k)-rho(i-1,j,k)- & !^ & OneTwelfth* & !^ & (dRx(i,j)+dRx(i-1,j)))- & !^ & (dZx(i,j)-dZx(i-1,j))* & !^ & (tl_rho(i,j,k)-tl_rho(i-1,j,k)- & !^ & OneTwelfth* & !^ & (tl_dRx(i,j)+tl_dRx(i-1,j))))))) !^ adfac=on_u(i,j)*0.5_r8*ad_ru(i,j,k,nrhs) adfac1=adfac*(P(i-1,j,k)-P(i,j,k)- & & HalfGRho* & & ((rho(i,j,k)+rho(i-1,j,k))* & & (z_r(i,j,k)-z_r(i-1,j,k))- & & OneFifth* & & ((dRx(i,j)-dRx(i-1,j))* & & (z_r(i,j,k)-z_r(i-1,j,k)- & & OneTwelfth* & & (dZx(i,j)+dZx(i-1,j)))- & & (dZx(i,j)-dZx(i-1,j))* & & (rho(i,j,k)-rho(i-1,j,k)- & & OneTwelfth* & & (dRx(i,j)+dRx(i-1,j)))))) adfac2=adfac*(Hz(i,j,k)+Hz(i-1,j,k)) adfac3=adfac2*HalfGRho adfac4=adfac3*(z_r(i,j,k)-z_r(i-1,j,k)) adfac5=adfac3*(rho(i,j,k)+rho(i-1,j,k)) adfac6=adfac3*OneFifth adfac7=adfac6*(z_r(i,j,k)-z_r(i-1,j,k)- & & OneTwelfth*(dZx(i,j)+dZx(i-1,j))) adfac8=adfac6*(dRx(i,j)-dRx(i-1,j)) adfac9=adfac8*OneTwelfth adfac10=adfac6*(rho(i,j,k)-rho(i-1,j,k)- & & OneTwelfth*(dRx(i,j)+dRx(i-1,j))) adfac11=adfac6*(dZx(i,j)-dZx(i-1,j)) adfac12=adfac11*OneTwelfth 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_P(i-1,j,k)=ad_P(i-1,j,k)+adfac2 ad_P(i ,j,k)=ad_P(i ,j,k)-adfac2 ad_rho(i-1,j,k)=ad_rho(i-1,j,k)-adfac4+adfac11 ad_rho(i ,j,k)=ad_rho(i ,j,k)-adfac4-adfac11 ad_z_r(i-1,j,k)=ad_z_r(i-1,j,k)+adfac5-adfac8 ad_z_r(i ,j,k)=ad_z_r(i ,j,k)-adfac5+adfac8 ad_dRx(i-1,j)=ad_dRx(i-1,j)-adfac7+adfac12 ad_dRx(i ,j)=ad_dRx(i ,j)+adfac7+adfac12 ad_dZx(i-1,j)=ad_dZx(i-1,j)-adfac9+adfac10 ad_dZx(i ,j)=ad_dZx(i ,j)-adfac9-adfac10 ad_ru(i,j,k,nrhs)=0.0_r8 END DO END DO ! DO j=Jstr,Jend DO i=IstrU-1,Iend cff1=2.0_r8*FC(i,j)*FC(i+1,j) IF (cff1.gt.eps) THEN cff2=1.0_r8/(FC(i,j)+FC(i+1,j)) !^ tl_dRx(i,j)=tl_cff1*cff2+cff1*tl_cff2 !^ ad_cff1=ad_cff1+cff2*ad_dRx(i,j) ad_cff2=ad_cff2+cff1*ad_dRx(i,j) ad_dRx(i,j)=0.0_r8 !^ tl_cff2=-cff2*cff2*(tl_FC(i,j)+tl_FC(i+1,j)) !^ adfac=-cff2*cff2*ad_cff2 ad_FC(i ,j)=ad_FC(i ,j)+adfac ad_FC(i+1,j)=ad_FC(i+1,j)+adfac ad_cff2=0.0_r8 ELSE !^ tl_dRx(i,j)=0.0_r8 !^ ad_dRx(i,j)=0.0_r8 END IF !^ tl_cff1=2.0_r8*(tl_FC(i,j)*FC(i+1,j)+ & !^ & FC(i,j)*tl_FC(i+1,j) !^ adfac=2.0_r8*ad_cff1 ad_FC(i ,j)=ad_FC(i ,j)+FC(i+1,j)*adfac ad_FC(i+1,j)=ad_FC(i+1,j)+FC(i ,j)*adfac ad_cff1=0.0_r8 cff=2.0_r8*aux(i,j)*aux(i+1,j) IF (cff.gt.eps) THEN cff1=1.0_r8/(aux(i,j)+aux(i+1,j)) !^ tl_dZx(i,j)=tl_cff*cff1+cff*tl_cff1 !^ ad_cff=ad_cff+cff1*ad_dZx(i,j) ad_cff1=ad_cff1+cff*ad_dZx(i,j) ad_dZx(i,j)=0.0_r8 !^ tl_cff1=-cff1*cff1*(tl_aux(i,j)+tl_aux(i+1,j)) !^ adfac=-cff1*cff1*ad_cff1 ad_aux(i ,j)=ad_aux(i ,j)+adfac ad_aux(i+1,j)=ad_aux(i+1,j)+adfac ad_cff1=0.0_r8 ELSE !^ tl_dZx(i,j)=0.0_r8 !^ ad_dZx(i,j)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_aux(i,j)*aux(i+1,j)+ & !^ & aux(i,j)*tl_aux(i+1,j) !^ adfac=2.0_r8*ad_cff ad_aux(i ,j)=ad_aux(i ,j)+aux(i+1,j)*adfac ad_aux(i+1,j)=ad_aux(i+1,j)+aux(i ,j)*adfac ad_cff=0.0_r8 END DO END DO DO j=Jstr,Jend DO i=IstrU-1,Iend+1 !^ tl_FC(i,j)=tl_FC(i,j)*umask(i,j) !^ ad_FC(i,j)=ad_FC(i,j)*umask(i,j) !^ tl_FC(i,j)=tl_rho(i,j,k)-tl_rho(i-1,j,k) !^ ad_rho(i-1,j,k)=ad_rho(i-1,j,k)-ad_FC(i,j) ad_rho(i ,j,k)=ad_rho(i ,j,k)+ad_FC(i,j) ad_FC(i,j)=0.0_r8 !^ tl_aux(i,j)=tl_aux(i,j)*umask(i,j) !^ ad_aux(i,j)=ad_aux(i,j)*umask(i,j) !^ tl_aux(i,j)=tl_z_r(i,j,k)-tl_z_r(i-1,j,k) !^ ad_z_r(i-1,j,k)=ad_z_r(i-1,j,k)-ad_aux(i,j) ad_z_r(i ,j,k)=ad_z_r(i ,j,k)+ad_aux(i,j) ad_aux(i,j)=0.0_r8 END DO END DO END DO ! !----------------------------------------------------------------------- ! Adjoint of Preliminary step (same for XI- and ETA-components): !----------------------------------------------------------------------- ! DO j=JstrV-1,Jend DO k=1,N(ng)-1 DO i=IstrU-1,Iend dR(i,k)=rho(i,j,k+1)-rho(i,j,k) dZ(i,k)=z_r(i,j,k+1)-z_r(i,j,k) dR1(i,k)=dR(i,k) dZ1(i,k)=dZ(i,k) END DO END DO DO i=IstrU-1,Iend dR(i,N(ng))=dR(i,N(ng)-1) dR1(i,N(ng))=dR(i,N(ng)) dZ(i,N(ng))=dZ(i,N(ng)-1) dZ1(i,N(ng))=dZ(i,N(ng)) dR(i,0)=dR(i,1) dR1(i,0)=dR(i,0) dZ(i,0)=dZ(i,1) dZ1(i,0)=dZ(i,0) END DO DO k=N(ng),1,-1 DO i=IstrU-1,Iend cff=2.0_r8*dR(i,k)*dR(i,k-1) IF (cff.gt.eps) THEN dR(i,k)=cff/(dR(i,k)+dR(i,k-1)) ELSE dR(i,k)=0.0_r8 END IF dZ(i,k)=2.0_r8*dZ(i,k)*dZ(i,k-1)/(dZ(i,k)+dZ(i,k-1)) END DO END DO ! DO k=1,N(ng)-1 DO i=IstrU-1,Iend !^ tl_P(i,j,k)=tl_P(i,j,k+1)+tl_cff !^ ad_cff=ad_cff+ad_P(i,j,k) !^ tl_cff=HalfGRho*((tl_rho(i,j,k+1)+tl_rho(i,j,k))* & !^ & (z_r(i,j,k+1)-z_r(i,j,k))+ & !^ & (rho(i,j,k+1)+rho(i,j,k))* & !^ & (tl_z_r(i,j,k+1)-tl_z_r(i,j,k))- & !^ & OneFifth* & !^ & ((tl_dR(i,k+1)-tl_dR(i,k))* & !^ & (z_r(i,j,k+1)-z_r(i,j,k)- & !^ & OneTwelfth* & !^ & (dZ(i,k+1)+dZ(i,k)))+ & !^ & (dR(i,k+1)-dR(i,k))* & !^ & (tl_z_r(i,j,k+1)-tl_z_r(i,j,k)- & !^ & OneTwelfth* & !^ & (tl_dZ(i,k+1)+tl_dZ(i,k)))- & !^ & (tl_dZ(i,k+1)-tl_dZ(i,k))* & !^ & (rho(i,j,k+1)-rho(i,j,k)- & !^ & OneTwelfth* & !^ & (dR(i,k+1)+dR(i,k)))- & !^ & (dZ(i,k+1)-dZ(i,k))* & !^ & (tl_rho(i,j,k+1)-tl_rho(i,j,k)- & !^ & OneTwelfth* & !^ & (tl_dR(i,k+1)+tl_dR(i,k))))) !^ adfac=HalfGRho*ad_cff adfac1=adfac*(z_r(i,j,k+1)-z_r(i,j,k)) adfac2=adfac*(rho(i,j,k+1)+rho(i,j,k)) adfac3=adfac*OneFifth adfac4=adfac3*(z_r(i,j,k+1)-z_r(i,j,k)- & & OneTwelfth*(dZ(i,k+1)+dZ(i,k))) adfac5=adfac3*(dR(i,k+1)-dR(i,k)) adfac6=adfac5*OneTwelfth adfac7=adfac3*(rho(i,j,k+1)-rho(i,j,k)- & & OneTwelfth*(dR(i,k+1)+dR(i,k))) adfac8=adfac3*(dZ(i,k+1)-dZ(i,k)) adfac9=adfac8*OneTwelfth ad_P(i,j,k+1)=ad_P(i,j,k+1)+ad_P(i,j,k) ad_rho(i,j,k )=ad_rho(i,j,k )+adfac1-adfac8 ad_rho(i,j,k+1)=ad_rho(i,j,k+1)+adfac1+adfac8 ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac2+adfac5 ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac2-adfac5 ad_dR(i,k )=ad_dR(i,k )+adfac4-adfac9 ad_dR(i,k+1)=ad_dR(i,k+1)-adfac4-adfac9 ad_dZ(i,k )=ad_dZ(i,k )+adfac6-adfac7 ad_dZ(i,k+1)=ad_dZ(i,k+1)+adfac6+adfac7 ad_cff=0.0_r8 END DO END DO DO i=IstrU-1,Iend cff1=1.0_r8/(z_r(i,j,N(ng))-z_r(i,j,N(ng)-1)) cff2=0.5_r8*(rho(i,j,N(ng))-rho(i,j,N(ng)-1))* & & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))*cff1 !^ tl_P(i,j,N(ng))=g*tl_z_w(i,j,N(ng))+ & !^ & GRho*((tl_rho(i,j,N(ng))+tl_cff2)* & !^ & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))+ & !^ & (rho(i,j,N(ng))+cff2)* & !^ & (tl_z_w(i,j,N(ng))-tl_z_r(i,j,N(ng)))) !^ adfac=GRho*ad_P(i,j,N(ng)) adfac1=adfac*(z_w(i,j,N(ng))-z_r(i,j,N(ng))) adfac2=adfac*(rho(i,j,N(ng))+cff2) ad_z_r(i,j,N(ng))=ad_z_r(i,j,N(ng))-adfac2 ad_z_w(i,j,N(ng))=ad_z_w(i,j,N(ng))+adfac2+ & & g*ad_P(i,j,N(ng)) ad_rho(i,j,N(ng))=ad_rho(i,j,N(ng))+adfac1 ad_cff2=ad_cff2+adfac1 ad_P(i,j,N(ng))=0.0_r8 !^ tl_cff2=0.5_r8*((tl_rho(i,j,N(ng))-tl_rho(i,j,N(ng)-1))* & !^ & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))*cff1+ & !^ & (rho(i,j,N(ng))-rho(i,j,N(ng)-1))* & !^ & ((tl_z_w(i,j,N(ng))-tl_z_r(i,j,N(ng)))*cff1+ & !^ & (z_w(i,j,N(ng))-z_r(i,j,N(ng)))*tl_cff1)) !^ adfac=0.5_r8*ad_cff2 adfac1=adfac*(z_w(i,j,N(ng))-z_r(i,j,N(ng)))*cff1 adfac2=adfac*(rho(i,j,N(ng))-rho(i,j,N(ng)-1)) adfac3=adfac2*cff1 ad_rho(i,j,N(ng)-1)=ad_rho(i,j,N(ng)-1)-adfac1 ad_rho(i,j,N(ng) )=ad_rho(i,j,N(ng) )+adfac1 ad_z_r(i,j,N(ng))=ad_z_r(i,j,N(ng))-adfac3 ad_z_w(i,j,N(ng))=ad_z_w(i,j,N(ng))+adfac3 ad_cff1=ad_cff1+(z_w(i,j,N(ng))-z_r(i,j,N(ng)))*adfac2 ad_cff2=0.0_r8 !^ tl_cff1=-cff1*cff1*(tl_z_r(i,j,N(ng))-tl_z_r(i,j,N(ng)-1)) !^ adfac=-cff1*cff1*ad_cff1 ad_z_r(i,j,N(ng)-1)=ad_z_r(i,j,N(ng)-1)-adfac ad_z_r(i,j,N(ng) )=ad_z_r(i,j,N(ng) )+adfac ad_cff1=0.0_r8 END DO ! ! The forward code has recursive statements, so we need to dR1(ik) and ! dZ1(i,k) for BOTH terms in denominator of adjoint code. ! DO k=1,N(ng) DO i=IstrU-1,Iend !^ tl_dZ(i,k)=(2.0_r8*(tl_dZ(i,k)*dZ1(i,k-1)+ & !^ & dZ1(i,k)*tl_dZ(i,k-1))- !^ & dZ(i,k)*(tl_dZ(i,k)+tl_dZ(i,k-1)))/ !^ & (dZ1(i,k)+dZ1(i,k-1)) !^ recursive adfac=ad_dZ(i,k)/(dZ1(i,k)+dZ1(i,k-1)) adfac1=adfac*2.0_r8 adfac2=adfac*dZ(i,k) ad_dZ(i,k-1)=ad_dZ(i,k-1)+dZ1(i,k)*adfac1-adfac2 ad_dZ(i,k )=dZ1(i,k-1)*adfac1-adfac2 cff=2.0_r8*dR1(i,k)*dR1(i,k-1) IF (cff.gt.eps) THEN !^ tl_dR(i,k)=(tl_cff-dR(i,k)*(tl_dR(i,k)+tl_dR(i,k-1)))/ & !^ & (dR1(i,k)+dR1(i,k-1)) !^ adfac=ad_dR(i,k)/(dR1(i,k)+dR1(i,k-1)) adfac1=adfac*dR(i,k) ad_dR(i,k-1)=ad_dR(i,k-1)-adfac1 ad_dR(i,k )=-adfac1 ad_cff=ad_cff+adfac ELSE !^ tl_dR(i,k)=0.0_r8 !^ ad_dR(i,k)=0.0_r8 END IF !^ tl_cff=2.0_r8*(tl_dR(i,k)*dR1(i,k-1)+ & !^ & dR1(i,k)*tl_dR(i,k-1)) !^ adfac=2.0_r8*ad_cff ad_dR(i,k-1)=ad_dR(i,k-1)+dR1(i,k )*adfac ad_dR(i,k )=ad_dR(i,k )+dR1(i,k-1)*adfac ad_cff=0.0_r8 END DO END DO DO i=IstrU-1,Iend !^ tl_dZ(i,0)=tl_dZ(i,1) !^ ad_dZ(i,1)=ad_dZ(i,1)+ad_dZ(i,0) ad_dZ(i,0)=0.0_r8 !^ tl_dR(i,0)=tl_dR(i,1) !^ ad_dR(i,1)=ad_dR(i,1)+ad_dR(i,0) ad_dR(i,0)=0.0_r8 !^ tl_dZ(i,N(ng))=tl_dZ(i,N(ng)-1) !^ ad_dZ(i,N(ng)-1)=ad_dZ(i,N(ng)-1)+ad_dZ(i,N(ng)) ad_dZ(i,N(ng))=0.0_r8 !^ tl_dR(i,N(ng))=tl_dR(i,N(ng)-1) !^ ad_dR(i,N(ng)-1)=ad_dR(i,N(ng)-1)+ad_dR(i,N(ng)) ad_dR(i,N(ng))=0.0_r8 END DO DO k=N(ng)-1,1,-1 DO i=IstrU-1,Iend !^ tl_dZ(i,k)=tl_z_r(i,j,k+1)-tl_z_r(i,j,k) !^ ad_z_r(i,j,k )=ad_z_r(i,j,k )-ad_dZ(i,k) ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+ad_dZ(i,k) ad_dZ(i,k)=0.0_r8 !^ tl_dR(i,k)=tl_rho(i,j,k+1)-tl_rho(i,j,k) !^ ad_rho(i,j,k )=ad_rho(i,j,k )-ad_dR(i,k) ad_rho(i,j,k+1)=ad_rho(i,j,k+1)+ad_dR(i,k) ad_dR(i,k)=0.0_r8 END DO END DO END DO ! RETURN END SUBROUTINE ad_prsgrd32_tile END MODULE ad_prsgrd_mod