#include "cppdefs.h" MODULE ad_rho_eos_mod #if defined ADJOINT && defined SOLVE3D ! !git $Id$ !svn $Id: ad_rho_eos.F 1188 2023-08-03 19:26:47Z 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 routine computes "in situ" density and other associated ! ! quantitites as a function of potential temperature, salinity, ! ! and pressure from a polynomial expression (Jackett and McDougall, ! ! 1992). The polynomial expression was found from fitting to 248 ! ! values in the oceanographic ranges of salinity, potential ! ! temperature, and pressure. It assumes no pressure variation ! ! along geopotential surfaces, that is, depth (meters; negative) ! ! and pressure (dbar; assumed negative here) are interchangeable. ! ! ! ! Check Values: (T=3 C, S=35.5 PSU, Z=-5000 m) ! ! ! ! alpha = 2.1014611551470d-04 (1/Celsius) ! ! beta = 7.2575037309946d-04 (1/PSU) ! ! gamma = 3.9684764511766d-06 (1/Pa) ! ! den = 1050.3639165364 (kg/m3) ! ! den1 = 1028.2845117925 (kg/m3) ! ! sound = 1548.8815240223 (m/s) ! ! bulk = 23786.056026320 (Pa) ! ! ! ! Reference: ! ! ! ! Jackett, D. R. and T. J. McDougall, 1995, Minimal Adjustment of ! ! Hydrostatic Profiles to Achieve Static Stability, J. of Atmos. ! ! and Oceanic Techn., vol. 12, pp. 381-389. ! ! ! !======================================================================= ! implicit none ! PRIVATE PUBLIC :: ad_rho_eos ! CONTAINS ! !*********************************************************************** SUBROUTINE ad_rho_eos (ng, tile, model) !*********************************************************************** ! USE mod_param USE mod_parallel USE mod_coupling USE mod_grid USE mod_mixing USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & __FILE__ ! # include "tile.h" ! # ifdef PROFILE CALL wclock_on (ng, model, 14, __LINE__, MyFile) # endif CALL ad_rho_eos_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & # ifdef MASKING & GRID(ng) % rmask, & # endif # ifdef VAR_RHO_2D_NOT_YET & GRID(ng) % Hz, & & GRID(ng) % ad_Hz, & # endif & GRID(ng) % z_r, & & GRID(ng) % ad_z_r, & # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET & GRID(ng) % z_w, & & GRID(ng) % ad_z_w, & # endif & OCEAN(ng) % t, & & OCEAN(ng) % ad_t, & # ifdef VAR_RHO_2D_NOT_YET & COUPLING(ng) % ad_rhoA, & & COUPLING(ng) % ad_rhoS, & # endif # ifdef BV_FREQUENCY_NOT_YET & MIXING(ng) % ad_bvf, & # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET & MIXING(ng) % ad_alpha, & & MIXING(ng) % ad_beta, & # ifdef LMD_DDMIX_NOT_YET & MIXING(ng) % ad_alfaobeta, & # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET & OCEAN(ng) % ad_pden, & # endif & OCEAN(ng) % rho, & & OCEAN(ng) % ad_rho) # ifdef PROFILE CALL wclock_off (ng, model, 14, __LINE__, MyFile) # endif ! RETURN END SUBROUTINE ad_rho_eos # ifdef NONLIN_EOS ! !*********************************************************************** SUBROUTINE ad_rho_eos_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & # ifdef MASKING & rmask, & # endif # ifdef VAR_RHO_2D_NOT_YET & Hz, ad_Hz, & # endif & z_r, ad_z_r, & # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET & z_w, ad_z_w, & # endif & t, ad_t, & # ifdef VAR_RHO_2D_NOT_YET & ad_rhoA, ad_rhoS, & # endif # ifdef BV_FREQUENCY_NOT_YET & ad_bvf, & # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET & ad_alpha, ad_beta, & # ifdef LMD_DDMIX_NOT_YET & ad_alfaobeta, & # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET & ad_pden, & # endif & rho, ad_rho) !*********************************************************************** ! USE mod_param USE mod_eoscoef USE mod_scalars # ifdef SEDIMENT_NOT_YET USE mod_sediment # endif ! USE ad_exchange_2d_mod USE ad_exchange_3d_mod # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d, ad_mp_exchange3d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs ! # ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) # endif # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: Hz(LBi:,LBj:,:) # endif real(r8), intent(in) :: z_r(LBi:,LBj:,:) # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET real(r8), intent(in) :: z_w(LBi:,LBj:,0:) # endif real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) real(r8), intent(in) :: rho(LBi:,LBj:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_Hz(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ad_z_r(LBi:,LBj:,:) # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_z_w(LBi:,LBj:,0:) # endif real(r8), intent(inout) :: ad_t(LBi:,LBj:,:,:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_rhoA(LBi:,LBj:) real(r8), intent(inout) :: ad_rhoS(LBi:,LBj:) # endif # ifdef BV_FREQUENCY_NOT_YET real(r8), intent(inout) :: ad_bvf(LBi:,LBj:,0:) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET real(r8), intent(inout) :: ad_alpha(LBi:,LBj:) real(r8), intent(inout) :: ad_beta(LBi:,LBj:) # ifdef LMD_DDMIX_NOT_YET real(r8), intent(inout) :: ad_alfaobeta(LBi:,LBj:,0:) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET real(r8), intent(inout) :: ad_pden(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ad_rho(LBi:,LBj:,:) # else # ifdef MASKING real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) # endif # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) # endif real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(in) :: rho(LBi:UBi,LBj:UBj,N(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_Hz(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ad_z_r(LBi:UBi,LBj:UBj,N(ng)) # if defined BV_FREQUENCY_NOT_YET || defined VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_z_w(LBi:UBi,LBj:UBj,0:N(ng)) # endif real(r8), intent(inout) :: ad_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_rhoA(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rhoS(LBi:UBi,LBj:UBj) # endif # ifdef BV_FREQUENCY_NOT_YET real(r8), intent(inout) :: ad_bvf(LBi:UBi,LBj:UBj,0:N(ng)) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET real(r8), intent(inout) :: ad_alpha(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_beta(LBi:UBi,LBj:UBj) # ifdef LMD_DDMIX_NOT_YET real(r8), intent(inout) :: ad_alfaobeta(LBi:UBi,LBj:UBj,0:N(ng)) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET real(r8), intent(inout) :: ad_pden(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ad_rho(LBi:UBi,LBj:UBj,N(ng)) # endif ! ! Local variable declarations. ! integer :: i, ised, itrc, j, k real(r8) :: SedDen, Tp, Tpr10, Ts, Tt, sqrtTs real(r8) :: ad_SedDen, ad_Tp, ad_Tpr10, ad_Ts, ad_Tt, ad_sqrtTs # ifdef BV_FREQUENCY_NOT_YET real(r8) :: bulk_dn, bulk_up, den_dn, den_up real(r8) :: ad_bulk_dn, ad_bulk_up, ad_den_dn, ad_den_up # endif real(r8) :: cff, cff1, cff2, cff3 real(r8) :: ad_cff, ad_cff1, ad_cff2, ad_cff3 real(r8) :: adfac, adfac1, adfac2, adfac3 real(r8), dimension(0:9) :: C real(r8), dimension(0:9) :: ad_C # ifdef EOS_TDERIVATIVE real(r8), dimension(0:9) :: dCdT(0:9) real(r8), dimension(0:9) :: ad_dCdT(0:9) real(r8), dimension(0:9) :: d2Cd2T(0:9) real(r8), dimension(IminS:ImaxS,N(ng)) :: DbulkDS real(r8), dimension(IminS:ImaxS,N(ng)) :: DbulkDT real(r8), dimension(IminS:ImaxS,N(ng)) :: Dden1DS real(r8), dimension(IminS:ImaxS,N(ng)) :: Dden1DT real(r8), dimension(IminS:ImaxS,N(ng)) :: Scof real(r8), dimension(IminS:ImaxS,N(ng)) :: Tcof real(r8), dimension(IminS:ImaxS,N(ng)) :: wrk real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_DbulkDS real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_DbulkDT real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_Dden1DS real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_Dden1DT real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_Scof real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_Tcof real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_wrk # endif real(r8), dimension(IminS:ImaxS,N(ng)) :: bulk real(r8), dimension(IminS:ImaxS,N(ng)) :: bulk0 real(r8), dimension(IminS:ImaxS,N(ng)) :: bulk1 real(r8), dimension(IminS:ImaxS,N(ng)) :: bulk2 real(r8), dimension(IminS:ImaxS,N(ng)) :: den real(r8), dimension(IminS:ImaxS,N(ng)) :: den1 real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_bulk real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_bulk0 real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_bulk1 real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_bulk2 real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_den real(r8), dimension(IminS:ImaxS,N(ng)) :: ad_den1 # ifdef VAR_RHO_2D_NOT_YET real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhoA1 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhoS1 # endif # include "set_bounds.h" ! !------------------------------------------------------------------------- ! Initialize adjoint private variables. !------------------------------------------------------------------------- ! ad_Tt=0.0_r8 ad_Ts=0.0_r8 ad_Tp=0.0_r8 ad_Tpr10=0.0_r8 # ifdef BV_FREQUENCY_NOT_YET ad_bulk_dn=0.0_r8 ad_bulk_up=0.0_r8 ad_den_dn=0.0_r8 ad_den_up=0.0_r8 # endif ad_sqrtTs=0.0_r8 ad_cff=0.0_r8 ad_cff1=0.0_r8 ad_cff2=0.0_r8 ad_cff3=0.0_r8 ad_C=0.0_r8 ad_dCdT=0.0_r8 DO k=1,N(ng) DO i=IminS,ImaxS # ifdef EOS_TDERIVATIVE ad_DbulkDS(i,k)=0.0_r8 ad_DbulkDT(i,k)=0.0_r8 ad_Dden1DS(i,k)=0.0_r8 ad_Dden1DT(i,k)=0.0_r8 ad_Scof(i,k)=0.0_r8 ad_Tcof(i,k)=0.0_r8 ad_wrk(i,k)=0.0_r8 # endif ad_bulk(i,k)=0.0_r8 ad_bulk0(i,k)=0.0_r8 ad_bulk1(i,k)=0.0_r8 ad_bulk2(i,k)=0.0_r8 ad_den(i,k)=0.0_r8 ad_den1(i,k)=0.0_r8 END DO END DO ! !======================================================================= ! Adjoint nonlinear equation of state. Notice that this equation ! of state is only valid for potential temperature range of -2C to 40C ! and a salinity range of 0 PSU to 42 PSU. !======================================================================= ! !----------------------------------------------------------------------- ! Exchange boundary data. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE # ifdef BV_FREQUENCY_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_bvf) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 0, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_bvf) # endif # ifdef VAR_RHO_2D_NOT_YET !^ CALL mp_exchange2d (ng, tile, model, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_rhoA, tl_rhoS) !^ CALL ad_mp_exchange2d (ng, tile, model, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_rhoA, ad_rhoS) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET !^ CALL mp_exchange2d (ng, tile, model, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_alpha, tl_beta) !^ CALL ad_mp_exchange2d (ng, tile, model, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_alpha, ad_beta) # ifdef LMD_DDMIX_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_alfaobeta) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 0, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_alfaobeta) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_pden) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_pden) # endif !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_rho) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_rho) ! # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN # ifdef BV_FREQUENCY_NOT_YET !^ CALL exchange_w3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & tl_bvf) !^ CALL ad_exchange_w3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 0, N(ng), & & ad_bvf) # endif # ifdef VAR_RHO_2D_NOT_YET !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_rhoS) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_rhoS) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_rhoA) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_rhoA) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_beta) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_beta) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_alpha) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_alpha) # ifdef LMD_DDMIX_NOT_YET !^ CALL exchange_w3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & tl_alfaobeta) !^ CALL ad_exchange_w3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 0, N(ng), & & ad_alfaobeta) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_pden) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_pden) # endif !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_rho) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_rho) END IF ! !----------------------------------------------------------------------- ! Compute BASIC STATE related variables. !----------------------------------------------------------------------- ! DO j=JstrT,JendT DO k=1,N(ng) DO i=IstrT,IendT Tt=MAX(-2.0_r8,t(i,j,k,nrhs,itemp)) # ifdef SALINITY Ts=MAX(0.0_r8,t(i,j,k,nrhs,isalt)) sqrtTs=SQRT(Ts) # else Ts=0.0_r8 sqrtTs=0.0_r8 # endif Tp=z_r(i,j,k) Tpr10=0.1_r8*Tp ! ! Compute local nonlinear equation of state coefficients and their ! derivatives when appropriate. ! C(0)=Q00+Tt*(Q01+Tt*(Q02+Tt*(Q03+Tt*(Q04+Tt*Q05)))) C(1)=U00+Tt*(U01+Tt*(U02+Tt*(U03+Tt*U04))) C(2)=V00+Tt*(V01+Tt*V02) C(3)=A00+Tt*(A01+Tt*(A02+Tt*(A03+Tt*A04))) C(4)=B00+Tt*(B01+Tt*(B02+Tt*B03)) C(5)=D00+Tt*(D01+Tt*D02) C(6)=E00+Tt*(E01+Tt*(E02+Tt*E03)) C(7)=F00+Tt*(F01+Tt*F02) C(8)=G01+Tt*(G02+Tt*G03) C(9)=H00+Tt*(H01+Tt*H02) # ifdef EOS_TDERIVATIVE ! dCdT(0)=Q01+Tt*(2.0_r8*Q02+Tt*(3.0_r8*Q03+Tt*(4.0_r8*Q04+ & & Tt*5.0_r8*Q05))) dCdT(1)=U01+Tt*(2.0_r8*U02+Tt*(3.0_r8*U03+Tt*4.0_r8*U04)) dCdT(2)=V01+Tt*2.0_r8*V02 dCdT(3)=A01+Tt*(2.0_r8*A02+Tt*(3.0_r8*A03+Tt*4.0_r8*A04)) dCdT(4)=B01+Tt*(2.0_r8*B02+Tt*3.0_r8*B03) dCdT(5)=D01+Tt*2.0_r8*D02 dCdT(6)=E01+Tt*(2.0_r8*E02+Tt*3.0_r8*E03) dCdT(7)=F01+Tt*2.0_r8*F02 dCdT(8)=G02+Tt*2.0_r8*G03 dCdT(9)=H01+Tt*2.0_r8*H02 ! d2Cd2T(0)=2.0_r8*Q02+Tt*(6.0_r8*Q03+Tt*(12.0_r8*Q04+ & & Tt*20.0_r8*Q05)) d2Cd2T(1)=2.0_r8*U02+Tt*(6.0_r8*U03+Tt*12.0_r8*U04) d2Cd2T(2)=2.0_r8*V02 d2Cd2T(3)=2.0_r8*A02+Tt*(6.0_r8*A03+Tt*12.0_r8*A04) d2Cd2T(4)=2.0_r8*B02+Tt*6.0_r8*B03 d2Cd2T(5)=2.0_r8*D02 d2Cd2T(6)=2.0_r8*E02+Tt*6.0_r8*E03 d2Cd2T(7)=2.0_r8*F02 d2Cd2T(8)=2.0_r8*G03 d2Cd2T(9)=2.0_r8*H02 # endif ! ! Compute BASIC STATE density (kg/m3) at standard one atmosphere ! pressure. ! den1(i,k)=C(0)+Ts*(C(1)+sqrtTs*C(2)+Ts*W00) # ifdef EOS_TDERIVATIVE ! ! Compute BASIC STATE d(den1)/d(S) and d(den1)/d(T) derivatives used ! in the computation of thermal expansion and saline contraction ! coefficients. ! Dden1DS(i,k)=C(1)+1.5_r8*C(2)*sqrtTs+2.0_r8*W00*Ts Dden1DT(i,k)=dCdT(0)+Ts*(dCdT(1)+sqrtTs*dCdT(2)) # endif ! ! Compute BASIC STATE secant bulk modulus. ! bulk0(i,k)=C(3)+Ts*(C(4)+sqrtTs*C(5)) bulk1(i,k)=C(6)+Ts*(C(7)+sqrtTs*G00) bulk2(i,k)=C(8)+Ts*C(9) bulk (i,k)=bulk0(i,k)-Tp*(bulk1(i,k)-Tp*bulk2(i,k)) # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET ! ! Compute BASIC STATE d(bulk)/d(S) and d(bulk)/d(T) derivatives used ! in the computation of thermal expansion and saline contraction ! coefficients. ! DbulkDS(i,k)=C(4)+sqrtTs*1.5_r8*C(5)- & & Tp*(C(7)+sqrtTs*1.5_r8*G00-Tp*C(9)) DbulkDT(i,k)=dCdT(3)+Ts*(dCdT(4)+sqrtTs*dCdT(5))- & & Tp*(dCdT(6)+Ts*dCdT(7)- & & Tp*(dCdT(8)+Ts*dCdT(9))) # endif ! ! Compute local "in situ" density anomaly (kg/m3 - 1000). The (i,k) ! DO-loop is closed here because of the adjoint to facilitate vertical ! integrals of the BASIC STATE. ! cff=1.0_r8/(bulk(i,k)+Tpr10) den(i,k)=den1(i,k)*bulk(i,k)*cff # if defined SEDIMENT_NOT_YET && defined SED_DENS_NOT_YET SedDen=0.0_r8 DO ised=1,NST cff1=1.0_r8/Srho(ised,ng) SedDen=SedDen+ & & t(i,j,k,nrhs,idsed(ised))* & & (Srho(ised,ng)-den(i,k))*cff1 END DO den(i,k)=den(i,k)+SedDen # endif den(i,k)=den(i,k)-1000.0_r8 # ifdef MASKING den(i,k)=den(i,k)*rmask(i,j) # endif END DO END DO # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET ! !----------------------------------------------------------------------- ! Compute BASIC STATE thermal expansion (1/Celsius) and saline ! contraction (1/PSU) coefficients. !----------------------------------------------------------------------- ! # ifdef LMD_DDMIX_NOT_YET DO k=1,N(ng) # else DO k=N(ng),N(ng) # endif DO i=IstrT,IendT Tpr10=0.1_r8*z_r(i,j,k) ! ! Compute thermal expansion and saline contraction coefficients. ! cff=bulk(i,k)+Tpr10 cff1=Tpr10*den1(i,k) cff2=bulk(i,k)*cff wrk(i,k)=(den(i,k)+1000.0_r8)*cff*cff Tcof(i,k)=-(DbulkDT(i,k)*cff1+ & & Dden1DT(i,k)*cff2) Scof(i,k)= (DbulkDS(i,k)*cff1+ & & Dden1DS(i,k)*cff2) END DO END DO # endif ! !----------------------------------------------------------------------- ! Load adjoint "in situ" density anomaly (kg/m3 - 1000) and adjoint ! potential density anomaly (kg/m3 - 1000) referenced to the surface ! into global arrays. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO i=IstrT,IendT # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET # ifdef MASKING !^ tl_pden(i,j,k)=tl_pden(i,k)*rmask(i,j) !^ ad_pden(i,j,k)=ad_pden(i,k)*rmask(i,j) # endif !^ tl_pden(i,j,k)=tl_den1(i,k) ! This gives a fatal !^ ! result in 4D-Var ad_den1(i,k)=ad_den1(i,k)+ad_pden(i,j,k)! posterior error... ad_pden(i,j,k)=0.0_r8 # endif !^ tl_rho(i,j,k)=tl_den(i,k) !^ ad_den(i,k)=ad_den(i,k)+ad_rho(i,j,k) ad_rho(i,j,k)=0.0_r8 END DO END DO # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET ! !----------------------------------------------------------------------- ! Compute adjoint thermal expansion (1/Celsius) and adjoint saline ! contraction (1/PSU) coefficients. !----------------------------------------------------------------------- ! # ifdef LMD_DDMIX_NOT_YET !^ DO k=1,N(ng) !^ DO k=N(ng),1,-1 # else DO k=N(ng),N(ng) # endif IF (k.eq.N(ng)) THEN DO i=IstrT,IendT cff=1.0_r8/wrk(i,N(ng)) !^ tl_beta (i,j)=tl_cff*Scof(i,N(ng))+cff*tl_Scof(i,N(ng)) !^ tl_alpha(i,j)=tl_cff*Tcof(i,N(ng))+cff*tl_Tcof(i,N(ng)) !^ ad_Scof(i,N(ng))=ad_Scof(i,N(ng))+cff*ad_beta (i,j) ad_Tcof(i,N(ng))=ad_Tcof(i,N(ng))+cff*ad_alpha(i,j) ad_cff=ad_beta (i,j)*Scof(i,N(ng))+ & & ad_alpha(i,j)*Tcof(i,N(ng)) ad_beta (i,j)=0.0_r8 ad_alpha(i,j)=0.0_r8 !^ tl_cff=-cff*cff*tl_wrk(i,N(ng)) !^ ad_wrk(i,N(ng))=ad_wrk(i,N(ng))-cff*cff*ad_cff ad_cff=0.0_r8 END DO END IF DO i=IstrT,IendT Tpr10=0.1_r8*z_r(i,j,k) cff=bulk(i,k)+Tpr10 cff1=Tpr10*den1(i,k) cff2=bulk(i,k)*cff # ifdef LMD_DDMIX_NOT_YET !^ tl_alfaobeta(i,j,k)=(tl_Tcof(i,k)*Scof(i,k)- & !^ & Tcof(i,k)*tl_Scof(i,k))/ & !^ & (Scof(i,k)*Scof(i,k)) !^ adfac=ad_alfaobeta(i,j,k)/(Scof(i,k)*Scof(i,k)) ad_Tcof(i,k)=ad_Tcof(i,k)+Scof(i,k)*adfac ad_Scof(i,k)=ad_Scof(i,k)-Tcof(i,k)*adfac ad_alfaobeta(i,j,k)=0.0_r8 # endif !^ tl_Scof(i,k)= (tl_DbulkDS(i,k)*cff1+ & !^ & DbulkDS(i,k)*tl_cff1+ & !^ & tl_Dden1DS(i,k)*cff2+ & !^ & Dden1DS(i,k)*tl_cff2) !^ ad_DbulkDS(i,k)=ad_DbulkDS(i,k)+ad_Scof(i,k)*cff1 ad_Dden1DS(i,k)=ad_Dden1DS(i,k)+ad_Scof(i,k)*cff2 ad_cff1=DbulkDS(i,k)*ad_Scof(i,k) ad_cff2=Dden1DS(i,k)*ad_Scof(i,k) ad_Scof(i,k)=0.0_r8 !^ tl_Tcof(i,k)=-(tl_DbulkDT(i,k)*cff1+ & !^ & DbulkDT(i,k)*tl_cff1+ & !^ & tl_Dden1DT(i,k)*cff2+ & !^ & Dden1DT(i,k)*tl_cff2) !^ ad_DbulkDT(i,k)=ad_DbulkDT(i,k)-ad_Tcof(i,k)*cff1 ad_Dden1DT(i,k)=ad_Dden1DT(i,k)-ad_Tcof(i,k)*cff2 ad_cff1=ad_cff1-DbulkDT(i,k)*ad_Tcof(i,k) ad_cff2=ad_cff2-Dden1DT(i,k)*ad_Tcof(i,k) ad_Tcof(i,k)=0.0_r8 !^ tl_wrk(i,k)=cff*(cff*tl_den(i,k)+ & !^ & 2.0_r8*tl_cff*(den(i,k)+1000.0_r8)) !^ adfac=cff*ad_wrk(i,k) ad_den(i,k)=ad_den(i,k)+cff*adfac ad_cff=ad_cff+2.0_r8*(den(i,k)+1000.0_r8)*adfac ad_wrk(i,k)=0.0_r8 !^ tl_cff2=tl_bulk(i,k)*cff+bulk(i,k)*tl_cff !^ ad_bulk(i,k)=ad_bulk(i,k)+ad_cff2*cff ad_cff=ad_cff+bulk(i,k)*ad_cff2 ad_cff2=0.0_r8 !^ tl_cff1=tl_Tpr10*den1(i,k)+Tpr10*tl_den1(i,k) !^ ad_Tpr10=ad_Tpr10+ad_cff1*den1(i,k) ad_den1(i,k)=ad_den1(i,k)+Tpr10*ad_cff1 ad_cff1=0.0_r8 !^ tl_cff=tl_bulk(i,k)+tl_Tpr10 !^ ad_bulk(i,k)=ad_bulk(i,k)+ad_cff ad_Tpr10=ad_Tpr10+ad_cff ad_cff=0.0_r8 !^ tl_Tpr10=0.1_r8*tl_z_r(i,j,k) !^ ad_z_r(i,j,k)=ad_z_r(i,j,k)+0.1_r8*ad_Tpr10 ad_Tpr10=0.0_r8 END DO END DO # endif # if defined BV_FREQUENCY_NOT_YET ! !----------------------------------------------------------------------- ! Compute adjoint Brunt-Vaisala frequency (1/s2) at horizontal ! RHO-points and vertical W-points. !----------------------------------------------------------------------- ! DO i=IstrT,IendT !^ tl_bvf(i,j,N(ng))=0.0_r8 !^ ad_bvf(i,j,N(ng))=0.0_r8 !^ tl_bvf(i,j,0)=0.0_r8 !^ ad_bvf(i,j,0)=0.0_r8 END DO DO k=1,N(ng)-1 DO i=IstrT,IendT bulk_up=bulk0(i,k+1)- & & z_w(i,j,k)*(bulk1(i,k+1)- & & bulk2(i,k+1)*z_w(i,j,k)) bulk_dn=bulk0(i,k )- & & z_w(i,j,k)*(bulk1(i,k )- & & bulk2(i,k )*z_w(i,j,k)) cff1=1.0_r8/(bulk_up+0.1_r8*z_w(i,j,k)) cff2=1.0_r8/(bulk_dn+0.1_r8*z_w(i,j,k)) den_up=cff1*(den1(i,k+1)*bulk_up) den_dn=cff2*(den1(i,k )*bulk_dn) cff3=1.0_r8/(0.5_r8*(den_up+den_dn)* & & (z_r(i,j,k+1)-z_r(i,j,k))) !^ tl_bvf(i,j,k)=-g*((tl_den_up-tl_den_dn)*cff3+ & !^ & (den_up-den_dn)*tl_cff3) !^ adfac=-g*ad_bvf(i,j,k) adfac1=adfac*cff3 ad_cff3=ad_cff3+(den_up-den_dn)*adfac ad_den_up=ad_den_up+adfac1 ad_den_dn=ad_den_dn-adfac1 ad_bvf(i,j,k)=0.0_r8 !^ tl_cff3=-cff3*cff3* & !^ & 0.5_r8*((tl_den_up+tl_den_dn)* & !^ & (z_r(i,j,k+1)-z_r(i,j,k))+ & !^ & (den_up+den_dn)* & !^ & (tl_z_r(i,j,k+1)-tl_z_r(i,j,k))) !^ adfac=-cff3*cff3*0.5_r8*ad_cff3 adfac1=adfac*(z_r(i,j,k+1)-z_r(i,j,k)) adfac2=adfac*(den_up+den_dn) 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_den_up=ad_den_up+adfac1 ad_den_dn=ad_den_dn+adfac1 ad_cff3=0.0_r8 !^ tl_den_dn=tl_cff2*(den1(i,k )*bulk_dn)+ & !^ & cff2*(tl_den1(i,k )*bulk_dn+ & !^ & den1(i,k )*tl_bulk_dn) !^ tl_den_up=tl_cff1*(den1(i,k+1)*bulk_up)+ & !^ & cff1*(tl_den1(i,k+1)*bulk_up+ & !^ & den1(i,k+1)*tl_bulk_up) !^ adfac1=cff2*ad_den_dn adfac2=cff1*ad_den_up ad_cff2=ad_cff2+(den1(i,k )*bulk_dn)*ad_den_dn ad_cff1=ad_cff1+(den1(i,k+1)*bulk_up)*ad_den_up ad_den1(i,k )=ad_den1(i,k )+bulk_dn*adfac1 ad_den1(i,k+1)=ad_den1(i,k+1)+bulk_up*adfac2 ad_bulk_dn=ad_bulk_dn+den1(i,k )*adfac1 ad_bulk_up=ad_bulk_up+den1(i,k+1)*adfac2 ad_den_dn=0.0_r8 ad_den_up=0.0_r8 !^ tl_cff2=-cff2*cff2*(tl_bulk_dn+0.1_r8*tl_z_w(i,j,k)) !^ tl_cff1=-cff1*cff1*(tl_bulk_up+0.1_r8*tl_z_w(i,j,k)) !^ adfac1=-cff2*cff2*ad_cff2 adfac2=-cff1*cff1*ad_cff1 ad_bulk_dn=ad_bulk_dn+adfac1 ad_bulk_up=ad_bulk_up+adfac2 ad_z_w(i,j,k)=ad_z_w(i,j,k)+ & & 0.1_r8*(adfac1+adfac2) ad_cff2=0.0_r8 ad_cff1=0.0_r8 !^ tl_bulk_dn=tl_bulk0(i,k )- & !^ & tl_z_w(i,j,k)*(bulk1(i,k )- & !^ & bulk2(i,k )*z_w(i,j,k))- & !^ & z_w(i,j,k)*(tl_bulk1(i,k )- & !^ & tl_bulk2(i,k )*z_w(i,j,k)- & !^ & bulk2(i,k )*tl_z_w(i,j,k)) !^ tl_bulk_up=tl_bulk0(i,k+1)- & !^ & tl_z_w(i,j,k)*(bulk1(i,k+1)- & !^ & bulk2(i,k+1)*z_w(i,j,k))- & !^ & z_w(i,j,k)*(tl_bulk1(i,k+1)- & !^ & tl_bulk2(i,k+1)*z_w(i,j,k)- & !^ & bulk2(i,k+1)*tl_z_w(i,j,k)) !^ adfac1=z_w(i,j,k)*ad_bulk_dn adfac2=z_w(i,j,k)*ad_bulk_up ad_bulk0(i,k )=ad_bulk0(i,k )+ad_bulk_dn ad_bulk0(i,k+1)=ad_bulk0(i,k+1)+ad_bulk_up ad_z_w(i,j,k)=ad_z_w(i,j,k)- & & (bulk1(i,k )- & & bulk2(i,k )*z_w(i,j,k)- & & bulk2(i,k ))*ad_bulk_dn- & & (bulk1(i,k+1)- & & bulk2(i,k+1)*z_w(i,j,k)- & & bulk2(i,k+1))*ad_bulk_up ad_bulk1(i,k )=ad_bulk1(i,k )-adfac1 ad_bulk1(i,k+1)=ad_bulk1(i,k+1)-adfac2 ad_bulk2(i,k )=ad_bulk2(i,k )+z_w(i,j,k)*adfac1 ad_bulk2(i,k+1)=ad_bulk2(i,k+1)+z_w(i,j,k)*adfac2 ad_bulk_dn=0.0_r8 ad_bulk_up=0.0_r8 END DO END DO # endif # ifdef VAR_RHO_2D_NOT_YET ! !----------------------------------------------------------------------- ! Compute adjoint vertical averaged density (ad_rhoA) and adjoint ! density perturbation (ad_rhoS) used in adjoint barotropic pressure ! gradient. !----------------------------------------------------------------------- ! ! Compute temporary intermediate BASIC STATE "rhoS1" and "rhoA1". ! DO i=IstrT,IendT cff1=den(i,N(ng))*Hz(i,j,N(ng)) rhoS1(i,j)=0.5_r8*cff1*Hz(i,j,N(ng)) rhoA1(i,j)=cff1 END DO DO k=N(ng)-1,1,-1 DO i=IstrT,IendT cff1=den(i,k)*Hz(i,j,k) rhoS1(i,j)=rhoS1(i,j)+Hz(i,j,k)*(rhoA1(i,j)+0.5_r8*cff1) rhoA1(i,j)=rhoA1(i,j)+cff1 END DO END DO ! cff2=1.0_r8/rho0 DO i=IstrT,IendT cff1=1.0_r8/(z_w(i,j,N(ng))-z_w(i,j,0)) !^ tl_rhoS(i,j)=2.0_r8*cff2* & !^ & cff1*(2.0_r8*tl_cff1*rhoS1(i,j)+ & !^ & cff1*tl_rhoS(i,j)) !^ adfac=2.0_r8*cff2*cff1*ad_rhoS(i,j) ad_cff1=2.0_r8*rhoS1(i,j)*adfac ad_rhoS(i,j)=cff1*adfac !^ tl_rhoA(i,j)=cff2*(tl_cff1*rhoA1(i,j)+cff1*tl_rhoA(i,j)) !^ adfac=cff2*ad_rhoA(i,j) ad_cff1=ad_cff1+rhoA1(i,j)*adfac ad_rhoA(i,j)=cff1*adfac !^ tl_cff1=-cff1*cff1*(tl_z_w(i,j,N(ng))-tl_z_w(i,j,0)) !^ adfac=-cff1*cff1*ad_cff1 ad_z_w(i,j,N(ng))=ad_z_w(i,j,N(ng))+adfac ad_z_w(i,j,0 )=ad_z_w(i,j,0 )-adfac ad_cff1=0.0_r8 END DO ! ! Compute appropriate intermediate BASIC STATE "rhoA1". ! DO i=IstrT,IendT cff1=den(i,N(ng))*Hz(i,j,N(ng)) rhoA1(i,j)=cff1 END DO DO k=N(ng)-1,1,-1 DO i=IstrT,IendT cff1=den(i,k)*Hz(i,j,k) !^ tl_rhoA(i,j)=tl_rhoA(i,j)+tl_cff1 !^ ad_cff1=ad_rhoA(i,j) !^ tl_rhoS(i,j)=tl_rhoS(i,j)+ & !^ & tl_Hz(i,j,k)*(rhoA1(i,j)+0.5_r8*cff1)+ & !^ & Hz(i,j,k)*(tl_rhoA(i,j)+0.5_r8*tl_cff1) !^ adfac=Hz(i,j,k)*ad_rhoS(i,j) ad_rhoA(i,j)=ad_rhoA(i,j)+adfac ad_cff1=ad_cff1+0.5_r8*adfac ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & (rhoA1(i,j)+0.5_r8*cff1)*ad_rhoS(i,j) !^ tl_cff1=tl_den(i,k)*Hz(i,j,k)+ & !^ & den(i,k)*tl_Hz(i,j,k) !^ ad_den(i,k)=ad_den(i,k)+Hz(i,j,k)*ad_cff1 ad_Hz(i,j,k)=ad_Hz(i,j,k)+den(i,k)*ad_cff1 ad_cff1=0.0_r8 rhoA1(i,j)=rhoA1(i,j)+cff1 END DO END DO DO i=IstrT,IendT cff1=den(i,N(ng))*Hz(i,j,N(ng)) !^ tl_rhoA(i,j)=tl_cff1 !^ ad_cff1=ad_rhoA(i,j) ad_rhoA(i,j)=0.0_r8 !^ tl_rhoS(i,j)=0.5_r8*(tl_cff1*Hz(i,j,N(ng))+ & !^ & cff1*tl_Hz(i,j,N(ng))) !^ adfac=0.5_r8*ad_rhoS(i,j) ad_cff1=ad_cff1+Hz(i,j,N(ng))*adfac ad_Hz(i,j,N(ng))=ad_Hz(i,j,N(ng))+cff1*adfac ad_rhoS(i,j)=0.0_r8 !^ tl_cff1=tl_den(i,N(ng))*Hz(i,j,N(ng))+ & !^ & den(i,N(ng))*tl_Hz(i,j,N(ng)) !^ ad_den(i,N(ng))=ad_den(i,N(ng))+Hz(i,j,N(ng))*ad_cff1 ad_Hz(i,j,N(ng))=ad_Hz(i,j,N(ng))+den(i,N(ng))*ad_cff1 ad_cff1=0.0_r8 END DO # endif ! !----------------------------------------------------------------------- ! Adjoint nonlinear equation of state. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO i=IstrT,IendT ! ! Check temperature and salinity minimum valid values. Assign depth ! to the pressure. ! Tt=MAX(-2.0_r8,t(i,j,k,nrhs,itemp)) # ifdef SALINITY Ts=MAX(0.0_r8,t(i,j,k,nrhs,isalt)) sqrtTs=SQRT(Ts) # else Ts=0.0_r8 sqrtTs=0.0_r8 # endif Tp=z_r(i,j,k) Tpr10=0.1_r8*Tp ! ! Compute local nonlinear equation of state coefficients and their ! derivatives when appropriate. These coefficients can be stored ! in slab (i,k) arrays to avoid recompute them twice. However, the ! equivalent of 50 slabs arrays are required. ! C(0)=Q00+Tt*(Q01+Tt*(Q02+Tt*(Q03+Tt*(Q04+Tt*Q05)))) C(1)=U00+Tt*(U01+Tt*(U02+Tt*(U03+Tt*U04))) C(2)=V00+Tt*(V01+Tt*V02) C(3)=A00+Tt*(A01+Tt*(A02+Tt*(A03+Tt*A04))) C(4)=B00+Tt*(B01+Tt*(B02+Tt*B03)) C(5)=D00+Tt*(D01+Tt*D02) C(6)=E00+Tt*(E01+Tt*(E02+Tt*E03)) C(7)=F00+Tt*(F01+Tt*F02) C(8)=G01+Tt*(G02+Tt*G03) C(9)=H00+Tt*(H01+Tt*H02) # ifdef EOS_TDERIVATIVE ! dCdT(0)=Q01+Tt*(2.0_r8*Q02+Tt*(3.0_r8*Q03+Tt*(4.0_r8*Q04+ & & Tt*5.0_r8*Q05))) dCdT(1)=U01+Tt*(2.0_r8*U02+Tt*(3.0_r8*U03+Tt*4.0_r8*U04)) dCdT(2)=V01+Tt*2.0_r8*V02 dCdT(3)=A01+Tt*(2.0_r8*A02+Tt*(3.0_r8*A03+Tt*4.0_r8*A04)) dCdT(4)=B01+Tt*(2.0_r8*B02+Tt*3.0_r8*B03) dCdT(5)=D01+Tt*2.0_r8*D02 dCdT(6)=E01+Tt*(2.0_r8*E02+Tt*3.0_r8*E03) dCdT(7)=F01+Tt*2.0_r8*F02 dCdT(8)=G02+Tt*2.0_r8*G03 dCdT(9)=H01+Tt*2.0_r8*H02 ! d2Cd2T(0)=2.0_r8*Q02+Tt*(6.0_r8*Q03+Tt*(12.0_r8*Q04+ & & Tt*20.0_r8*Q05)) d2Cd2T(1)=2.0_r8*U02+Tt*(6.0_r8*U03+Tt*12.0_r8*U04) d2Cd2T(2)=2.0_r8*V02 d2Cd2T(3)=2.0_r8*A02+Tt*(6.0_r8*A03+Tt*12.0_r8*A04) d2Cd2T(4)=2.0_r8*B02+Tt*6.0_r8*B03 d2Cd2T(5)=2.0_r8*D02 d2Cd2T(6)=2.0_r8*E02+Tt*6.0_r8*E03 d2Cd2T(7)=2.0_r8*F02 d2Cd2T(8)=2.0_r8*G03 d2Cd2T(9)=2.0_r8*H02 # endif ! !----------------------------------------------------------------------- ! Compute local adjoint "in situ" density anomaly (kg/m3 - 1000). !----------------------------------------------------------------------- ! cff=1.0_r8/(bulk(i,k)+Tpr10) # ifdef MASKING !^ tl_den(i,k)=tl_den(i,k)*rmask(i,j) !^ ad_den(i,k)=ad_den(i,k)*rmask(i,j) # endif # if defined SEDIMENT_NOT_YET && defined SED_DENS_NOT_YET !^ tl_den(i,k)=tl_den(i,k)+tl_SedDen !^ ad_SedDen=ad_SedDen+ad_den(i,k) DO ised=1,NST itrc=idsed(ised) cff1=1.0_r8/Srho(ised,ng) !^ tl_SedDen=tl_SedDen+ & !^ & (tl_t(i,j,k,nrhs,itrc)* & !^ & (Srho(ised,ng)-den(i,k))- & !^ & t(i,j,k,nrhs,itrc)* & !^ & tl_den(i,k))*cff1 !^ adfac=cff1*ad_SedDen ad_den(i,k)=ad_den(i,k)- & & t(i,j,k,nrhs,idsed(ised))*adfac ad_t(i,j,k,nrhs,itrc)=ad_t(i,j,k,nrhs,itrc)+ & & (Srho(ised,ng)-den(i,k))*adfac END DO !^ tl_SedDen=0.0_r8 !^ ad_SedDen=0.0_r8 # endif !^ tl_den(i,k)=tl_den1(i,k)*bulk(i,k)*cff+ & !^ & den1(i,k)*(tl_bulk(i,k)*cff+ & !^ & bulk(i,k)*tl_cff) !^ adfac1=den1(i,k)*ad_den(i,k) ad_den1(i,k)=ad_den1(i,k)+bulk(i,k)*cff*ad_den(i,k) ad_bulk(i,k)=ad_bulk(i,k)+cff*adfac1 ad_cff=ad_cff+bulk(i,k)*adfac1 ad_den(i,k)=0.0_r8 !^ tl_cff=-cff*cff*(tl_bulk(i,k)+tl_Tpr10) !^ adfac=-cff*cff*ad_cff ad_bulk(i,k)=ad_bulk(i,k)+adfac ad_Tpr10=ad_Tpr10+adfac ad_cff=0.0_r8 # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET ! ! Compute d(bulk)/d(S) and d(bulk)/d(T) derivatives used ! in the computation of thermal expansion and saline contraction ! coefficients. ! !^ tl_DbulkDT(i,k)=tl_dCdT(3)+ & !^ & tl_Ts*(dCdT(4)+sqrtTs*dCdT(5))+ & !^ & Ts*(tl_dCdT(4)+tl_sqrtTs*dCdT(5)+ & !^ & sqrtTs*tl_dCdT(5))- & !^ & tl_Tp*(dCdT(6)+Ts*dCdT(7)- & !^ & Tp*(dCdT(8)+Ts*dCdT(9)))- & !^ & Tp*(tl_dCdT(6)+tl_Ts*dCdT(7)+Ts*tl_dCdT(7)- & !^ & tl_Tp*(dCdT(8)+Ts*dCdT(9))- & !^ & Tp*(tl_dCdT(8)+tl_Ts*dCdT(9)+ & !^ & Ts*tl_dCdT(9))) !^ adfac1=Ts*ad_DbulkDT(i,k) adfac2=Tp*ad_DbulkDT(i,k) adfac3=adfac2*Tp ad_dCdT(3)=ad_dCdT(3)+ad_DbulkDT(i,k) ad_dCdT(4)=ad_dCdT(4)+adfac1 ad_dCdT(5)=ad_dCdT(5)+sqrtTs*adfac1 ad_dCdT(6)=ad_dCdT(6)-adfac2 ad_dCdT(7)=ad_dCdT(7)-Ts*adfac2 ad_dCdT(8)=ad_dCdT(8)+adfac3 ad_dCdT(9)=ad_dCdT(9)+Ts*adfac3 ad_sqrtTs=ad_sqrtTs+dCdT(5)*adfac1 ad_Ts=ad_Ts+ & & ad_DbulkDT(i,k)* & & (dCdT(4)+sqrtTs*dCdT(5)- & & Tp*(dCdT(7)-Tp*dCdT(9))) ad_Tp=ad_Tp- & & ad_DbulkDT(i,k)* & & (dCdT(6)+Ts*dCdT(7)- & & 2.0_r8*Tp*(dCdT(8)+Ts*dCdT(9))) ad_DbulkDT(i,k)=0.0_r8 !^ tl_DbulkDS(i,k)=tl_C(4)+ & !^ & 1.5_r8*(tl_sqrtTs*C(5)+ & !^ & sqrtTs*tl_C(5))- & !^ & tl_Tp*(C(7)+sqrtTs*1.5_r8*G00- & !^ & Tp*C(9))- & !^ & Tp*(tl_C(7)+tl_sqrtTs*1.5_r8*G00- & !^ & tl_Tp*C(9)-Tp*tl_C(9)) !^ adfac1=1.5_r8*ad_DbulkDS(i,k) adfac2=Tp*ad_DbulkDS(i,k) ad_C(4)=ad_C(4)+ad_DbulkDS(i,k) ad_C(5)=ad_C(5)+sqrtTs*adfac1 ad_C(7)=ad_C(7)-adfac2 ad_C(9)=ad_C(9)+Tp*adfac2 ad_sqrtTs=ad_sqrtTs+ & & (C(5)-Tp*G00)*adfac1 ad_Tp=ad_Tp- & & ad_DbulkDS(i,k)* & & (C(7)+sqrtTs*1.5_r8*G00-Tp*C(9)- & & Tp*C(9)) ad_DbulkDS(i,k)=0.0_r8 !^ tl_dCdT(9)=tl_Tt*d2Cd2T(9) !^ tl_dCdT(8)=tl_Tt*d2Cd2T(8) !^ tl_dCdT(7)=tl_Tt*d2Cd2T(7) !^ tl_dCdT(6)=tl_Tt*d2Cd2T(6) !^ tl_dCdT(5)=tl_Tt*d2Cd2T(5) !^ tl_dCdT(4)=tl_Tt*d2Cd2T(4) !^ tl_dCdT(3)=tl_Tt*d2Cd2T(3) !^ ad_Tt=ad_Tt+d2Cd2T(9)*ad_dCdT(9)+ & & d2Cd2T(8)*ad_dCdT(8)+ & & d2Cd2T(7)*ad_dCdT(7)+ & & d2Cd2T(6)*ad_dCdT(6)+ & & d2Cd2T(5)*ad_dCdT(5)+ & & d2Cd2T(4)*ad_dCdT(4)+ & & d2Cd2T(3)*ad_dCdT(3) ad_dCdT(9)=0.0_r8 ad_dCdT(8)=0.0_r8 ad_dCdT(7)=0.0_r8 ad_dCdT(6)=0.0_r8 ad_dCdT(5)=0.0_r8 ad_dCdT(4)=0.0_r8 ad_dCdT(3)=0.0_r8 # endif ! ! Compute adjoint secant bulk modulus. ! !^ tl_bulk (i,k)=tl_bulk0(i,k)- & !^ & tl_Tp*(bulk1(i,k)-Tp*bulk2(i,k))- & !^ & Tp*(tl_bulk1(i,k)- & !^ & tl_Tp*bulk2(i,k)- & !^ & Tp*tl_bulk2(i,k)) !^ adfac=Tp*ad_bulk(i,k) ad_bulk0(i,k)=ad_bulk0(i,k)+ad_bulk(i,k) ad_bulk1(i,k)=ad_bulk1(i,k)-adfac ad_bulk2(i,k)=ad_bulk2(i,k)+adfac*Tp ad_Tp=ad_Tp- & & ad_bulk(i,k)*(bulk1(i,k)-Tp*bulk2(i,k))+ & & adfac*bulk2(i,k) ad_bulk(i,k)=0.0_r8 !^ tl_bulk2(i,k)=tl_C(8)+tl_Ts*C(9)+Ts*tl_C(9) !^ ad_C(8)=ad_C(8)+ad_bulk2(i,k) ad_C(9)=ad_C(9)+Ts*ad_bulk2(i,k) ad_Ts=ad_Ts+ad_bulk2(i,k)*C(9) ad_bulk2(i,k)=0.0_r8 !^ tl_bulk1(i,k)=tl_C(6)+ & !^ & tl_Ts*(C(7)+sqrtTs*G00)+ & !^ & Ts*(tl_C(7)+tl_sqrtTs*G00) !^ adfac=Ts*ad_bulk1(i,k) ad_C(6)=ad_C(6)+ad_bulk1(i,k) ad_C(7)=ad_C(7)+adfac ad_Ts=ad_Ts+ad_bulk1(i,k)*(C(7)+sqrtTs*G00) ad_sqrtTs=ad_sqrtTs+adfac*G00 ad_bulk1(i,k)=0.0_r8 !^ tl_bulk0(i,k)=tl_C(3)+ & !^ & tl_Ts*(C(4)+sqrtTs*C(5))+ & !^ & Ts*(tl_C(4)+tl_sqrtTs*C(5)+ & !^ & sqrtTs*tl_C(5)) !^ adfac=Ts*ad_bulk0(i,k) ad_C(3)=ad_C(3)+ad_bulk0(i,k) ad_C(4)=ad_C(4)+adfac ad_C(5)=ad_C(5)+sqrtTs*adfac ad_Ts=ad_Ts+ad_bulk0(i,k)*(C(4)+sqrtTs*C(5)) ad_sqrtTs=ad_sqrtTs+C(5)*adfac ad_bulk0(i,k)=0.0_r8 !^ tl_C(9)=tl_Tt*dCdT(9) !^ tl_C(8)=tl_Tt*dCdT(8) !^ tl_C(7)=tl_Tt*dCdT(7) !^ tl_C(6)=tl_Tt*dCdT(6) !^ tl_C(5)=tl_Tt*dCdT(5) !^ tl_C(4)=tl_Tt*dCdT(4) !^ tl_C(3)=tl_Tt*dCdT(3) !^ ad_Tt=ad_Tt+ad_C(9)*dCdT(9)+ & & ad_C(8)*dCdT(8)+ & & ad_C(7)*dCdT(7)+ & & ad_C(6)*dCdT(6)+ & & ad_C(5)*dCdT(5)+ & & ad_C(4)*dCdT(4)+ & & ad_C(3)*dCdT(3) ad_C(9)=0.0_r8 ad_C(8)=0.0_r8 ad_C(7)=0.0_r8 ad_C(6)=0.0_r8 ad_C(5)=0.0_r8 ad_C(4)=0.0_r8 ad_C(3)=0.0_r8 # ifdef EOS_TDERIVATIVE ! ! Compute d(den1)/d(S) and d(den1)/d(T) derivatives used in the ! computation of thermal expansion and saline contraction ! coefficients. ! !^ tl_Dden1DT(i,k)=tl_dCdT(0)+ & !^ & tl_Ts*(dCdT(1)+sqrtTs*dCdT(2))+ & !^ & Ts*(tl_dCdT(1)+tl_sqrtTs*dCdT(2)+ & !^ & sqrtTs*tl_dCdT(2)) !^ adfac1=Ts*ad_Dden1DT(i,k) ad_dCdT(0)=ad_dCdT(0)+ad_Dden1DT(i,k) ad_dCdT(1)=ad_dCdT(1)+adfac1 ad_dCdT(2)=ad_dCdT(2)+sqrtTs*adfac1 ad_Ts=ad_Ts+ & & (dCdT(1)+sqrtTs*dCdT(2))*ad_Dden1DT(i,k) ad_sqrtTs=ad_sqrtTs+dCdT(2)*adfac1 ad_Dden1DT(i,k)=0.0_r8 !^ tl_Dden1DS(i,k)=tl_C(1)+ & !^ & 1.5_r8*(tl_C(2)*sqrtTs+ & !^ & C(2)*tl_sqrtTs)+ & !^ & 2.0_r8*W00*tl_Ts !^ adfac1=1.5_r8*ad_Dden1DS(i,k) ad_C(1)=ad_C(1)+ad_Dden1DS(i,k) ad_C(2)=ad_C(2)+sqrtTs*adfac1 ad_Ts=ad_Ts+2.0_r8*W00*ad_Dden1DS(i,k) ad_sqrtTs=ad_sqrtTs+C(2)*adfac1 ad_Dden1DS(i,k)=0.0_r8 !^ tl_dCdT(2)=tl_Tt*d2Cd2T(2) !^ tl_dCdT(1)=tl_Tt*d2Cd2T(1) !^ tl_dCdT(0)=tl_Tt*d2Cd2T(0) !^ ad_Tt=ad_Tt+d2Cd2T(2)*ad_dCdT(2)+ & & d2Cd2T(1)*ad_dCdT(1)+ & & d2Cd2T(0)*ad_dCdT(0) ad_dCdT(2)=0.0_r8 ad_dCdT(1)=0.0_r8 ad_dCdT(0)=0.0_r8 # endif ! ! Compute basic state and tangent linear density (kg/m3) at standard ! one atmosphere pressure. ! !^ tl_den1(i,k)=tl_C(0)+ & !^ & tl_Ts*(C(1)+sqrtTs*C(2)+Ts*W00)+ & !^ & Ts*(tl_C(1)+tl_sqrtTs*C(2)+ & !^ & sqrtTs*tl_C(2)+tl_Ts*W00) !^ adfac=Ts*ad_den1(i,k) ad_C(0)=ad_C(0)+ad_den1(i,k) ad_C(1)=ad_C(1)+adfac ad_C(2)=ad_C(2)+adfac*sqrtTs ad_Ts=ad_Ts+ & & ad_den1(i,k)*(C(1)+sqrtTs*C(2)+Ts*W00)+ & & adfac*W00 ad_sqrtTs=ad_sqrtTs+adfac*C(2) ad_den1(i,k)=0.0_r8 !^ tl_C(2)=tl_Tt*dCdT(2) !^ tl_C(1)=tl_Tt*dCdT(1) !^ tl_C(0)=tl_Tt*dCdT(0) !^ ad_Tt=ad_Tt+ad_C(2)*dCdT(2)+ & & ad_C(1)*dCdT(1)+ & & ad_C(0)*dCdT(0) ad_C(2)=0.0_r8 ad_C(1)=0.0_r8 ad_C(0)=0.0_r8 ! ! Check temperature and salinity minimum valid values. Assign depth ! to the pressure. ! !^ tl_Tpr10=0.1_r8*tl_Tp !^ ad_Tp=ad_Tp+0.1_r8*ad_Tpr10 ad_Tpr10=0.0_r8 !^ tl_Tp=tl_z_r(i,j,k) !^ ad_z_r(i,j,k)=ad_z_r(i,j,k)+ad_Tp ad_Tp=0.0_r8 # ifdef SALINITY IF (Ts.ne.0.0_r8) THEN !^ tl_sqrtTs=0.5_r8*tl_Ts/SQRT(Ts) !^ ad_Ts=ad_Ts+0.5_r8*ad_sqrtTs/SQRT(Ts) ad_sqrtTs=0.0_r8 ELSE !^ tl_sqrtTs=0.0_r8 !^ ad_sqrtTs=0.0_r8 END IF !^ tl_Ts=(0.5_r8-SIGN(0.5_r8,-t(i,j,k,nrhs,isalt)))* !^ & tl_t(i,j,k,nrhs,isalt) !^ ad_t(i,j,k,nrhs,isalt)=ad_t(i,j,k,nrhs,isalt)+ & & (0.5_r8-SIGN(0.5_r8, & & -t(i,j,k,nrhs,isalt)))* & & ad_Ts ad_Ts=0.0_r8 # else !^ tl_sqrtTs=0.0_r8 !^ ad_sqrtTs=0.0_r8 !^ tl_Ts=0.0_r8 !^ ad_Ts=0.0_r8 # endif !^ tl_Tt=(0.5_r8-SIGN(0.5_r8,-2.0_r8-t(i,j,k,nrhs,itemp)))* !^ & tl_t(i,j,k,nrhs,itemp) !^ ad_t(i,j,k,nrhs,itemp)=ad_t(i,j,k,nrhs,itemp)+ & & (0.5_r8-SIGN(0.5_r8,-2.0_r8- & & t(i,j,k,nrhs,itemp)))* & & ad_Tt ad_Tt=0.0_r8 END DO END DO END DO ! RETURN END SUBROUTINE ad_rho_eos_tile # endif # ifndef NONLIN_EOS ! !*********************************************************************** SUBROUTINE ad_rho_eos_tile (ng, tile, model, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & # ifdef MASKING & rmask, & # endif # ifdef VAR_RHO_2D_NOT_YET & Hz, ad_Hz, & # endif & z_r, ad_z_r, & # ifdef VAR_RHO_2D_NOT_YET & z_w, ad_z_w, & # endif & t, ad_t, & # ifdef VAR_RHO_2D_NOT_YET & ad_rhoA, ad_rhoS, & # endif # ifdef BV_FREQUENCY_NOT_YET & ad_bvf, & # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET & ad_alpha, ad_beta, & # ifdef LMD_DDMIX_NOT_YET & ad_alfaobeta, & # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET & ad_pden, & # endif & rho, ad_rho) !*********************************************************************** ! USE mod_param USE mod_parallel USE mod_scalars # ifdef SEDIMENT_NOT_YET USE mod_sediment # endif ! USE ad_exchange_2d_mod USE ad_exchange_3d_mod # ifdef DISTRIBUTE USE mp_exchange_mod, ONLY : ad_mp_exchange2d, ad_mp_exchange3d # endif ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile, model integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: IminS, ImaxS, JminS, JmaxS integer, intent(in) :: nrhs ! # ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: rmask(LBi:,LBj:) # endif # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: Hz(LBi:,LBj:,:) # endif real(r8), intent(in) :: z_r(LBi:,LBj:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: z_w(LBi:,LBj:,0:) # endif real(r8), intent(in) :: t(LBi:,LBj:,:,:,:) real(r8), intent(in) :: rho(LBi:,LBj:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_Hz(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ad_z_r(LBi:,LBj:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_z_w(LBi:,LBj:,0:) # endif real(r8), intent(inout) :: ad_t(LBi:,LBj:,:,:,:) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_rhoA(LBi:,LBj:) real(r8), intent(inout) :: ad_rhoS(LBi:,LBj:) # endif # ifdef BV_FREQUENCY_NOT_YET real(r8), intent(inout) :: tl_bvf(LBi:,LBj:,0:) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET real(r8), intent(inout) :: ad_alpha(LBi:,LBj:) real(r8), intent(inout) :: ad_beta(LBi:,LBj:) # ifdef LMD_DDMIX_NOT_YET real(r8), intent(inout) :: ad_alfaobeta(LBi:,LBj:,0:) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET real(r8), intent(inout) :: ad_pden(LBi:,LBj:,:) # endif real(r8), intent(inout) :: ad_rho(LBi:,LBj:,:) # else # ifdef MASKING real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj) # endif # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) # endif real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) real(r8), intent(inout) :: rho(LBi:UBi,LBj:UBj,N(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_Hz(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ad_z_r(LBi:UBi,LBj:UBj,N(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_z_w(LBi:UBi,LBj:UBj,0:N(ng)) # endif real(r8), intent(inout) :: ad_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng)) # ifdef VAR_RHO_2D_NOT_YET real(r8), intent(inout) :: ad_rhoA(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_rhoS(LBi:UBi,LBj:UBj) # endif # ifdef BV_FREQUENCY_NOT_YET real(r8), intent(inout) :: ad_bvf(LBi:UBi,LBj:UBj,0:N(ng)) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET real(r8), intent(inout) :: ad_alpha(LBi:UBi,LBj:UBj) real(r8), intent(inout) :: ad_beta(LBi:UBi,LBj:UBj) # ifdef LMD_DDMIX_NOT_YET real(r8), intent(inout) :: ad_alfaobeta(LBi:UBi,LBj:UBj,0:N(ng)) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET real(r8), intent(inout) :: ad_pden(LBi:UBi,LBj:UBj,N(ng)) # endif real(r8), intent(inout) :: ad_rho(LBi:UBi,LBj:UBj,N(ng)) # endif ! ! Local variable declarations. ! integer :: i, ised, itrc, j, k real(r8) :: SedDen, cff, cff1, cff2 real(r8) :: ad_SedDen, ad_cff, ad_cff1 real(r8) :: adfac, adfac1 # ifdef VAR_RHO_2D_NOT_YET real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhoA1 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhoS1 # endif # include "set_bounds.h" ! !======================================================================= ! Adjoint linear equation of state. !======================================================================= ! !----------------------------------------------------------------------- ! Exchange boundary data. !----------------------------------------------------------------------- ! # ifdef DISTRIBUTE # ifdef BV_FREQUENCY_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_bvf) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 0, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_bvf) # endif # ifdef VAR_RHO_2D_NOT_YET !^ CALL mp_exchange2d (ng, tile, model, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_rhoA, tl_rhoS) !^ CALL ad_mp_exchange2d (ng, tile, model, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_rhoA, ad_rhoS) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET !^ CALL mp_exchange2d (ng, tile, model, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_alpha, tl_beta) !^ CALL ad_mp_exchange2d (ng, tile, model, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_alpha, ad_beta) # ifdef LMD_DDMIX_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_alfaobeta) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 0, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_alfaobeta) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_pden) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_pden) # endif !^ CALL mp_exchange3d (ng, tile, model, 1, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & tl_rho) !^ CALL ad_mp_exchange3d (ng, tile, model, 1, & & LBi, UBi, LBj, UBj, 1, N(ng), & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & ad_rho) ! # endif IF (EWperiodic(ng).or.NSperiodic(ng)) THEN # ifdef BV_FREQUENCY_NOT_YET !^ CALL exchange_w3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & tl_bvf) !^ CALL ad_exchange_w3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 0, N(ng), & & ad_bvf) # endif # ifdef VAR_RHO_2D_NOT_YET !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_rhoS) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_rhoS) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_rhoA) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_rhoA) # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_beta) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_beta) !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & tl_alpha) !^ CALL ad_exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & ad_alpha) # ifdef LMD_DDMIX_NOT_YET !^ CALL exchange_w3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 0, N(ng), & !^ & tl_alfaobeta) !^ CALL ad_exchange_w3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 0, N(ng), & & ad_alfaobeta) # endif # endif # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_pden) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_pden) # endif !^ CALL exchange_r3d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, 1, N(ng), & !^ & tl_rho) !^ CALL ad_exchange_r3d_tile (ng, tile, & & LBi, UBi, LBj, UBj, 1, N(ng), & & ad_rho) END IF ! DO j=JstrT,JendT # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \ defined BULK_FLUXES_NOT_YET ! !----------------------------------------------------------------------- ! Compute adjoint thermal expansion (1/Celsius) and saline contraction ! (1/PSU) coefficients. !----------------------------------------------------------------------- # ifdef LMD_DDMIX_NOT_YET ! ! Compute ratio of thermal expansion and saline contraction ! coefficients. ! IF (Scoef(ng).eq.0.0_r8) THEN cff=1.0_r8 ELSE cff=1.0_r8/Scoef(ng) END IF DO k=1,N(ng) DO i=IstrT,IendT !^ tl_alfaobeta(i,j,k)=0.0_r8 !^ ad_alfaobeta(i,j,k)=0.0_r8 END DO END DO # endif ! ! Set thermal expansion and saline contraction coefficients. ! DO i=IstrT,IendT # ifdef SALINITY !^ tl_beta(i,j)=0.0_r8 !^ ad_beta(i,j)=0.0_r8 # else !^ beta(i,j)=0.0_r8 !^ ad_beta(i,j)=0.0_r8 # endif !^ tl_alpha(i,j)=0.0_r8 !^ ad_alpha(i,j)=0.0_r8 END DO # endif # ifdef BV_FREQUENCY_NOT_YET ! !----------------------------------------------------------------------- ! Compute Brunt-Vaisala frequency (1/s2) at horizontal RHO-points ! and vertical W-points. !----------------------------------------------------------------------- ! ad_cff=0.0_r8 DO k=1,N(ng) DO i=IstrT,IendT cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k)) !^ tl_bvf(i,j,k)=-gorho0* & !^ & (cff*(tl_rho(i,j,k+1)-tl_rho(i,j,k))+ & !^ & tl_cff*(rho(i,j,k+1)-rho(i,j,k))) !^ adfac=-gorho0*ad_bvf(i,j,k) adfac1=adfac*cff ad_rho(i,j,k+1)=ad_rho(i,j,k+1)+adfac1 ad_rho(i,j,k )=ad_rho(i,j,k )-adfac1 ad_cff=ad_cff+(rho(i,j,k+1)-rho(i,j,k))*adfac ad_bvf(i,j,k)=0.0_r8 !^ tl_cff=-cff*cff*(tl_z_r(i,j,k+1)-tl_z_r(i,j,k)) !^ adfac=-cff*cff*ad_cff ad_z_r(i,j,k+1)=ad_z_r(i,j,k+1)+adfac ad_z_r(i,j,k )=ad_z_r(i,j,k )-adfac ad_cff=0.0_r8 END DO END DO # endif # ifdef VAR_RHO_2D_NOT_YET ! !--------------------------------------------------------------------- ! Compute adjoint vertical averaged density (ad_rhoA) and adjoint ! density perturbation (ad_rhoS) used in adjoint barotropic pressure ! gradient. !--------------------------------------------------------------------- ! ! Compute intermediate BASIC STATE rhoS1 and rhoA1. ! DO i=IstrT,IendT cff1=rho(i,j,N(ng))*Hz(i,j,N(ng)) rhoS1(i,j)=0.5_r8*cff1*Hz(i,j,N(ng)) rhoA1(i,j)=cff1 END DO DO k=N(ng)-1,1,-1 DO i=IstrT,IendT cff1=rho(i,j,k)*Hz(i,j,k) rhoS1(i,j)=rhoS1(i,j)+Hz(i,j,k)*(rhoA1(i,j)+0.5_r8*cff1) rhoA1(i,j)=rhoA1(i,j)+cff1 END DO END DO ! cff2=1.0_r8/rho0 DO i=IstrT,IendT cff1=1.0_r8/(z_w(i,j,N(ng))-z_w(i,j,0)) !^ tl_rhoS(i,j)=2.0_r8*cff2* & !^ & cff1*(2.0_r8*tl_cff1*rhoS1(i,j)+ & !^ & cff1*tl_rhoS(i,j)) !^ adfac=2.0_r8*cff2*cff1*ad_rhoS(i,j) ad_cff1=2.0_r8*rhoS1(i,j)*adfac ad_rhoS(i,j)=cff1*adfac !^ tl_rhoA(i,j)=cff2*(tl_cff1*rhoA1(i,j)+cff1*tl_rhoA(i,j)) !^ adfac=cff2*ad_rhoA(i,j) ad_cff1=ad_cff1+rhoA1(i,j)*adfac ad_rhoA(i,j)=cff1*adfac !^ tl_cff1=-cff1*cff1*(tl_z_w(i,j,N(ng))-tl_z_w(i,j,0)) !^ adfac=-cff1*cff1*ad_cff1 ad_z_w(i,j,N(ng))=ad_z_w(i,j,N(ng))+adfac ad_z_w(i,j,0 )=ad_z_w(i,j,0 )-adfac ad_cff1=0.0_r8 END DO ! ! Compute appropriate intermediate BASIC STATE "rhoA1". ! DO i=IstrT,IendT cff1=rho(i,j,N(ng))*Hz(i,j,N(ng)) rhoA1(i,j)=cff1 END DO DO k=N(ng)-1,1,-1 DO i=IstrT,IendT cff1=rho(i,j,k)*Hz(i,j,k) !^ tl_rhoA(i,j)=tl_rhoA(i,j)+tl_cff1 !^ ad_cff1=ad_rhoA(i,j) !^ tl_rhoS(i,j)=tl_rhoS(i,j)+ & !^ & tl_Hz(i,j,k)*(rhoA1(i,j)+0.5_r8*cff1)+ & !^ & Hz(i,j,k)*(tl_rhoA(i,j)+0.5_r8*tl_cff1) !^ adfac=Hz(i,j,k)*ad_rhoS(i,j) ad_rhoA(i,j)=ad_rhoA(i,j)+adfac ad_cff1=ad_cff1+0.5_r8*adfac ad_Hz(i,j,k)=ad_Hz(i,j,k)+ & & (rhoA1(i,j)+0.5_r8*cff1)*ad_rhoS(i,j) !^ tl_cff1=tl_rho(i,j,k)*Hz(i,j,k)+ & !^ & rho(i,j,k)*tl_Hz(i,j,k) !^ ad_rho(i,j,k)=ad_rho(i,j,k)+Hz(i,j,k)*ad_cff1 ad_Hz(i,j,k)=ad_Hz(i,j,k)+rho(i,j,k)*ad_cff1 ad_cff1=0.0_r8 rhoA1(i,j)=rhoA1(i,j)+cff1 END DO END DO DO i=IstrT,IendT cff1=rho(i,j,N(ng))*Hz(i,j,N(ng)) !^ tl_rhoA(i,j)=tl_cff1 !^ ad_cff1=ad_rhoA(i,j) ad_rhoA(i,j)=0.0_r8 !^ tl_rhoS(i,j)=0.5_r8*(tl_cff1*Hz(i,j,N(ng))+ !^ & cff1*tl_Hz(i,j,N(ng))) !^ adfac=0.5_r8*ad_rhoS(i,j) ad_cff1=ad_cff1+Hz(i,j,N(ng))*adfac ad_Hz(i,j,N(ng))=ad_Hz(i,j,N(ng))+cff1*adfac ad_rhoS(i,j)=0.0_r8 !^ tl_cff1=tl_rho(i,j,N(ng))*Hz(i,j,N(ng))+ !^ & rho(i,j,N(ng))*tl_Hz(i,j,N(ng)) !^ ad_rho(i,j,N(ng))=ad_rho(i,j,N(ng))+Hz(i,j,N(ng))*ad_cff1 ad_Hz(i,j,N(ng))=ad_Hz(i,j,N(ng))+rho(i,j,N(ng))*ad_cff1 ad_cff1=0.0_r8 END DO # endif ! !----------------------------------------------------------------------- ! Compute adjoint "in situ" density anomaly (kg/m3 - 1000) using linear ! equation of state. !----------------------------------------------------------------------- ! DO k=1,N(ng) DO i=IstrT,IendT # if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET !^ tl_pden(i,j,k)=tl_rho(i,j,k) !^ ad_rho(i,j,k)=ad_rho(i,j,k)+ad_pden(i,j,k) ad_pden(i,j,k)=0.0 # endif # ifdef MASKING !^ tl_rho(i,j,k)=tl_rho(i,j,k)*rmask(i,j) !^ ad_rho(i,j,k)=ad_rho(i,j,k)*rmask(i,j) # endif # if defined SEDIMENT_NOT_YET && defined SED_DENS_NOT_YET !^ tl_rho(i,j,k)=tl_rho(i,j,k)+tl_SedDen !^ ad_SedDen=ad_SedDen+tl_rho(i,j,k) DO ised=1,NST itrc=idsed(ised) cff1=1.0_r8/Srho(ised,ng) !^ tl_SedDen=tl_SedDen+ & !^ & (tl_t(i,j,k,nrhs,itrc)* & !^ & (Srho(ised,ng)-rho(i,j,k))- & !^ & t(i,j,k,nrhs,itrc)* & !^ & tl_rho(i,j,k))*cff1 !^ adfac=cff1*ad_SedDen ad_rho(i,j,k)=ad_rho(i,j,k)- & & t(i,j,k,nrhs,itrc)*adfac tl_t(i,j,k,nrhs,itrc)=tl_t(i,j,k,nrhs,itrc)+ & & (Srho(ised,ng)-rho(i,j,k))*adfac END DO !^ tl_SedDen=0.0_r8 !^ ad_SedDen=0.0_r8 # endif # ifdef SALINITY !^ tl_rho(i,j,k)=tl_rho(i,j,k)+ & !^ & R0(ng)*Scoef(ng)*t(i,j,k,nrhs,isalt) !^ ad_t(i,j,k,nrhs,isalt)=ad_t(i,j,k,nrhs,isalt)+ & & R0(ng)*Scoef(ng)*ad_rho(i,j,k) # endif !^ tl_rho(i,j,k)=-R0(ng)*Tcoef*tl_t(i,j,k,nrhs,itemp) !^ ad_t(i,j,k,nrhs,itemp)=ad_t(i,j,k,nrhs,itemp)- & & R0(ng)*Tcoef(ng)*ad_rho(i,j,k) ad_rho(i,j,k)=0.0_r8 END DO END DO END DO ! RETURN END SUBROUTINE ad_rho_eos_tile # endif #endif END MODULE ad_rho_eos_mod