#include "cppdefs.h"
MODULE tl_rho_eos_mod
#if defined TANGENT && defined SOLVE3D
!
!svn $Id: tl_rho_eos.F 889 2018-02-10 03:32:52Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2019 The ROMS/TOMS Group Andrew M. Moore !
! Licensed under a MIT/X style license !
! See License_ROMS.txt !
!=======================================================================
! !
! This routine computes "in situ" density and other associated !
! quantitites as a function of potential temperature, salinity, !
! and pressure from a polynomial expression (Jackett & 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 :: tl_rho_eos
!
CONTAINS
!
!***********************************************************************
SUBROUTINE tl_rho_eos (ng, tile, model)
!***********************************************************************
!
USE mod_param
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.
!
# include "tile.h"
!
# ifdef PROFILE
CALL wclock_on (ng, model, 14, __LINE__, __FILE__)
# endif
CALL tl_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
& GRID(ng) % Hz, &
& GRID(ng) % tl_Hz, &
# endif
& GRID(ng) % z_r, &
& GRID(ng) % tl_z_r, &
& GRID(ng) % z_w, &
& GRID(ng) % tl_z_w, &
& OCEAN(ng) % t, &
& OCEAN(ng) % tl_t, &
# ifdef VAR_RHO_2D
& COUPLING(ng) % rhoA, &
& COUPLING(ng) % tl_rhoA, &
& COUPLING(ng) % rhoS, &
& COUPLING(ng) % tl_rhoS, &
# endif
# ifdef BV_FREQUENCY_NOT_YET
& MIXING(ng) % tl_bvf, &
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
& MIXING(ng) % alpha, &
& MIXING(ng) % tl_alpha, &
& MIXING(ng) % beta, &
& MIXING(ng) % tl_beta, &
# ifdef LMD_DDMIX_NOT_YET
& MIXING(ng) % tl_alfaobeta, &
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
& OCEAN(ng) % tl_pden, &
# endif
& OCEAN(ng) % rho, &
& OCEAN(ng) % tl_rho)
# ifdef PROFILE
CALL wclock_off (ng, model, 14, __LINE__, __FILE__)
# endif
RETURN
END SUBROUTINE tl_rho_eos
# ifdef NONLIN_EOS
!
!***********************************************************************
SUBROUTINE tl_rho_eos_tile (ng, tile, model, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nrhs, &
# ifdef MASKING
& rmask, &
# endif
# ifdef VAR_RHO_2D
& Hz, tl_Hz, &
# endif
& z_r, tl_z_r, &
& z_w, tl_z_w, &
& t, tl_t, &
# ifdef VAR_RHO_2D
& rhoA, tl_rhoA, &
& rhoS, tl_rhoS, &
# endif
# ifdef BV_FREQUENCY_NOT_YET
& tl_bvf, &
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
& alpha, tl_alpha, &
& beta, tl_beta, &
# ifdef LMD_DDMIX_NOT_YET
& tl_alfaobeta, &
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
& tl_pden, &
# endif
& rho, tl_rho)
!***********************************************************************
!
USE mod_param
USE mod_eoscoef
USE mod_scalars
# ifdef SEDIMENT_NOT_YET
USE mod_sediment
# endif
!
USE exchange_2d_mod
USE exchange_3d_mod
# ifdef DISTRIBUTE
USE mp_exchange_mod, ONLY : mp_exchange2d, 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
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
# endif
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: z_w(LBi:,LBj:,0:)
real(r8), intent(in) :: t(LBi:,LBj:,:,:,:)
# ifdef VAR_RHO_2D
real(r8), intent(in) :: tl_Hz(LBi:,LBj:,:)
# endif
real(r8), intent(in) :: tl_z_r(LBi:,LBj:,:)
real(r8), intent(in) :: tl_z_w(LBi:,LBj:,0:)
real(r8), intent(in) :: tl_t(LBi:,LBj:,:,:,:)
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(inout) :: alpha(LBi:,LBj:)
real(r8), intent(inout) :: beta(LBi:,LBj:)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(out) :: rhoA(LBi:,LBj:)
real(r8), intent(out) :: rhoS(LBi:,LBj:)
real(r8), intent(out) :: tl_rhoA(LBi:,LBj:)
real(r8), intent(out) :: tl_rhoS(LBi:,LBj:)
# endif
# ifdef BV_FREQUENCY_NOT_YET
real(r8), intent(out) :: tl_bvf(LBi:,LBj:,0:)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(out) :: tl_alpha(LBi:,LBj:)
real(r8), intent(out) :: tl_beta(LBi:,LBj:)
# ifdef LMD_DDMIX_NOT_YET
real(r8), intent(out) :: tl_alfaobeta(LBi:,LBj:,0:)
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
real(r8), intent(out) :: tl_pden(LBi:,LBj:,:)
# endif
real(r8), intent(out) :: rho(LBi:,LBj:,:)
real(r8), intent(out) :: tl_rho(LBi:,LBj:,:)
# else
# ifdef MASKING
real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng))
real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng))
# ifdef VAR_RHO_2D
real(r8), intent(in) :: tl_Hz(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(in) :: tl_z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: tl_z_w(LBi:UBi,LBj:UBj,0:N(ng))
real(r8), intent(in) :: tl_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng))
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(inout) :: alpha(LBi:UBi,LBj:UBj)
real(r8), intent(inout) :: beta(LBi:UBi,LBj:UBj)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(out) :: rhoA(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: rhoS(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_rhoA(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_rhoS(LBi:UBi,LBj:UBj)
# endif
# ifdef BV_FREQUENCY_NOT_YET
real(r8), intent(out) :: tl_bvf(LBi:UBi,LBj:UBj,0:N(ng))
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(out) :: tl_alpha(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_beta(LBi:UBi,LBj:UBj)
# ifdef LMD_DDMIX_NOT_YET
real(r8), intent(out) :: tl_alfaobeta(LBi:UBi,LBj:UBj,0:N(ng))
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
real(r8), intent(out) :: tl_pden(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(out) :: rho(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(out) :: tl_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) :: tl_SedDen, tl_Tp, tl_Tpr10, tl_Ts, tl_Tt, tl_sqrtTs
# ifdef BV_FREQUENCY_NOT_YET
real(r8) :: bulk_dn, bulk_up, den_dn, den_up
real(r8) :: tl_bulk_dn, tl_bulk_up, tl_den_dn, tl_den_up
# endif
real(r8) :: cff, cff1, cff2, cff3
real(r8) :: tl_cff, tl_cff1, tl_cff2, tl_cff3
real(r8), dimension(0:9) :: C
real(r8), dimension(0:9) :: tl_C
# ifdef EOS_TDERIVATIVE
real(r8), dimension(0:9) :: dCdT(0:9)
real(r8), dimension(0:9) :: tl_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)) :: tl_DbulkDS
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_DbulkDT
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_Dden1DS
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_Dden1DT
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_Scof
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_Tcof
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_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)) :: tl_bulk
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_bulk0
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_bulk1
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_bulk2
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_den
real(r8), dimension(IminS:ImaxS,N(ng)) :: tl_den1
# include "set_bounds.h"
!
!=======================================================================
! 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.
!=======================================================================
!
DO j=JstrT,JendT
DO k=1,N(ng)
DO i=IstrT,IendT
!
! Check temperature and salinity lower values. Assign depth to the
! pressure.
!
Tt=MAX(-2.0_r8,t(i,j,k,nrhs,itemp))
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)
# ifdef SALINITY
Ts=MAX(0.0_r8,t(i,j,k,nrhs,isalt))
tl_Ts=(0.5_r8-SIGN(0.5_r8,-t(i,j,k,nrhs,isalt)))* &
& tl_t(i,j,k,nrhs,isalt)
sqrtTs=SQRT(Ts)
IF (Ts.ne.0.0_r8) THEN
tl_sqrtTs=0.5_r8*tl_Ts/SQRT(Ts)
ELSE
tl_sqrtTs=0.0_r8
END IF
# else
Ts=0.0_r8
tl_Ts=0.0_r8
sqrtTs=0.0_r8
tl_sqrtTs=0.0_r8
# endif
Tp=z_r(i,j,k)
tl_Tp=tl_z_r(i,j,k)
Tpr10=0.1_r8*Tp
tl_Tpr10=0.1_r8*tl_Tp
!
!-----------------------------------------------------------------------
! Compute BASIC STATE and tangent linear density (kg/m3) at standard
! one atmosphere pressure.
!-----------------------------------------------------------------------
!
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)
# 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
# endif
tl_C(0)=tl_Tt*dCdT(0)
tl_C(1)=tl_Tt*dCdT(1)
tl_C(2)=tl_Tt*dCdT(2)
!
den1(i,k)=C(0)+Ts*(C(1)+sqrtTs*C(2)+Ts*W00)
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)
# 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.
!
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
!
tl_dCdT(0)=tl_Tt*d2Cd2T(0)
tl_dCdT(1)=tl_Tt*d2Cd2T(1)
tl_dCdT(2)=tl_Tt*d2Cd2T(2)
!
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))
!
tl_Dden1DS(i,k)=tl_C(1)+ &
& 1.5_r8*(tl_C(2)*sqrtTs+ &
& C(2)*tl_sqrtTs)+ &
& 2.0_r8*W00*tl_Ts
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))
# endif
!
!-----------------------------------------------------------------------
! Compute BASIC STATE and tangent linear secant bulk modulus.
!-----------------------------------------------------------------------
!
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(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
# endif
!
tl_C(3)=tl_Tt*dCdT(3)
tl_C(4)=tl_Tt*dCdT(4)
tl_C(5)=tl_Tt*dCdT(5)
tl_C(6)=tl_Tt*dCdT(6)
tl_C(7)=tl_Tt*dCdT(7)
tl_C(8)=tl_Tt*dCdT(8)
tl_C(9)=tl_Tt*dCdT(9)
!
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))
!
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))
tl_bulk1(i,k)=tl_C(6)+ &
& tl_Ts*(C(7)+sqrtTs*G00)+ &
& Ts*(tl_C(7)+tl_sqrtTs*G00)
tl_bulk2(i,k)=tl_C(8)+tl_Ts*C(9)+Ts*tl_C(9)
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))
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
!
! Compute d(bulk)/d(S) and d(bulk)/d(T) derivatives used
! in the computation of thermal expansion and saline contraction
! coefficients.
!
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
!
tl_dCdT(3)=tl_Tt*d2Cd2T(3)
tl_dCdT(4)=tl_Tt*d2Cd2T(4)
tl_dCdT(5)=tl_Tt*d2Cd2T(5)
tl_dCdT(6)=tl_Tt*d2Cd2T(6)
tl_dCdT(7)=tl_Tt*d2Cd2T(7)
tl_dCdT(8)=tl_Tt*d2Cd2T(8)
tl_dCdT(9)=tl_Tt*d2Cd2T(9)
!
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)))
!
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))
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)))
# endif
!
!-----------------------------------------------------------------------
! Compute local "in situ" density anomaly (kg/m3 - 1000).
!-----------------------------------------------------------------------
!
cff=1.0_r8/(bulk(i,k)+Tpr10)
tl_cff=-cff*cff*(tl_bulk(i,k)+tl_Tpr10)
den(i,k)=den1(i,k)*bulk(i,k)*cff
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)
# if defined SEDIMENT_NOT_YET && defined SED_DENS_NOT_YET
SedDen=0.0_r8
tl_SedDen=0.0_r8
DO ised=1,NST
itrc=idsed(ised)
cff1=1.0_r8/Srho(ised,ng)
SedDen=SedDen+ &
& t(i,j,k,nrhs,itrc)* &
& (Srho(ised,ng)-den(i,k))*cff1
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
END DO
den(i,k)=den(i,k)+SedDen
tl_den(i,k)=tl_den(i,k)+tl_SedDen
# endif
den(i,k)=den(i,k)-1000.0_r8
# ifdef MASKING
den(i,k)=den(i,k)*rmask(i,j)
tl_den(i,k)=tl_den(i,k)*rmask(i,j)
# endif
END DO
END DO
# ifdef VAR_RHO_2D
!
!-----------------------------------------------------------------------
! Compute vertical averaged density (rhoA) and density perturbation
! (rhoS) used in barotropic pressure gradient.
!-----------------------------------------------------------------------
!
DO i=IstrT,IendT
cff1=den(i,N(ng))*Hz(i,j,N(ng))
tl_cff1=tl_den(i,N(ng))*Hz(i,j,N(ng))+ &
& den(i,N(ng))*tl_Hz(i,j,N(ng))
rhoS(i,j)=0.5_r8*cff1*Hz(i,j,N(ng))
tl_rhoS(i,j)=0.5_r8*(tl_cff1*Hz(i,j,N(ng))+ &
& cff1*tl_Hz(i,j,N(ng)))
rhoA(i,j)=cff1
tl_rhoA(i,j)=tl_cff1
END DO
DO k=N(ng)-1,1,-1
DO i=IstrT,IendT
cff1=den(i,k)*Hz(i,j,k)
tl_cff1=tl_den(i,k)*Hz(i,j,k)+ &
& den(i,k)*tl_Hz(i,j,k)
rhoS(i,j)=rhoS(i,j)+Hz(i,j,k)*(rhoA(i,j)+0.5_r8*cff1)
tl_rhoS(i,j)=tl_rhoS(i,j)+ &
& tl_Hz(i,j,k)*(rhoA(i,j)+0.5_r8*cff1)+ &
& Hz(i,j,k)*(tl_rhoA(i,j)+0.5_r8*tl_cff1)
rhoA(i,j)=rhoA(i,j)+cff1
tl_rhoA(i,j)=tl_rhoA(i,j)+tl_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_cff1=-cff1*cff1*(tl_z_w(i,j,N(ng))-tl_z_w(i,j,0))
!
! Here we reverse the order of the NL and TL operations since an
! intermeridiate value of rhoA and rhoS is needed because they are
! recursive.
!
tl_rhoA(i,j)=cff2*(tl_cff1*rhoA(i,j)+cff1*tl_rhoA(i,j))
rhoA(i,j)=cff2*cff1*rhoA(i,j)
tl_rhoS(i,j)=2.0_r8*cff2* &
& cff1*(2.0_r8*tl_cff1*rhoS(i,j)+ &
& cff1*tl_rhoS(i,j))
rhoS(i,j)=2.0_r8*cff1*cff1*cff2*rhoS(i,j)
END DO
# endif
# if defined BV_FREQUENCY_NOT_YET
!
!-----------------------------------------------------------------------
! Compute Brunt-Vaisala frequency (1/s2) at horizontal RHO-points
! and vertical W-points:
!
! bvf = - g/rho d(rho)/d(z).
!
! The density anomaly difference is computed by lowering/rising the
! water parcel above/below adiabatically at W-point depth "z_w".
!-----------------------------------------------------------------------
!
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))
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))
bulk_dn=bulk0(i,k )- &
& z_w(i,j,k)*(bulk1(i,k )- &
& bulk2(i,k )*z_w(i,j,k))
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))
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))
tl_cff1=-cff1*cff1*(tl_bulk_up+0.1_r8*tl_z_w(i,j,k))
tl_cff2=-cff2*cff2*(tl_bulk_dn+0.1_r8*tl_z_w(i,j,k))
den_up=cff1*(den1(i,k+1)*bulk_up)
den_dn=cff2*(den1(i,k )*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)
tl_den_dn=tl_cff2*(den1(i,k )*bulk_dn)+ &
& cff2*(tl_den1(i,k )*bulk_dn+ &
& den1(i,k )*tl_bulk_dn)
!> bvf(i,j,k)=-g*(den_up-den_dn)/ &
!> & (0.5_r8*(den_up+den_dn)* &
!> & (z_r(i,j,k+1)-z_r(i,j,k)))
!>
cff3=1.0_r8/(0.5_r8*(den_up+den_dn)* &
& (z_r(i,j,k+1)-z_r(i,j,k)))
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)))
tl_bvf(i,j,k)=-g*((tl_den_up-tl_den_dn)*cff3+ &
& (den_up-den_dn)*tl_cff3)
END DO
END DO
DO i=IstrT,IendT
!> bvf(i,j,0)=0.0_r8
!>
tl_bvf(i,j,0)=0.0_r8
!> bvf(i,j,N(ng))=0.0_r8
!>
tl_bvf(i,j,N(ng))=0.0_r8
END DO
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
!
!-----------------------------------------------------------------------
! Compute 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)
tl_Tpr10=0.1_r8*tl_z_r(i,j,k)
!
! Compute thermal expansion and saline contraction coefficients.
!
cff=bulk(i,k)+Tpr10
tl_cff=tl_bulk(i,k)+tl_Tpr10
cff1=Tpr10*den1(i,k)
tl_cff1=tl_Tpr10*den1(i,k)+Tpr10*tl_den1(i,k)
cff2=bulk(i,k)*cff
tl_cff2=tl_bulk(i,k)*cff+bulk(i,k)*tl_cff
wrk(i,k)=(den(i,k)+1000.0_r8)*cff*cff
tl_wrk(i,k)=cff*(cff*tl_den(i,k)+ &
& 2.0_r8*tl_cff*(den(i,k)+1000.0_r8))
Tcof(i,k)=-(DbulkDT(i,k)*cff1+ &
& Dden1DT(i,k)*cff2)
tl_Tcof(i,k)=-(tl_DbulkDT(i,k)*cff1+ &
& DbulkDT(i,k)*tl_cff1+ &
& tl_Dden1DT(i,k)*cff2+ &
& Dden1DT(i,k)*tl_cff2)
Scof(i,k)= (DbulkDS(i,k)*cff1+ &
& Dden1DS(i,k)*cff2)
tl_Scof(i,k)= (tl_DbulkDS(i,k)*cff1+ &
& DbulkDS(i,k)*tl_cff1+ &
& tl_Dden1DS(i,k)*cff2+ &
& Dden1DS(i,k)*tl_cff2)
# ifdef LMD_DDMIX_NOT_YET
!> alfaobeta(i,j,k)=Tcof(i,k)/Scof(i,k)
!>
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))
# endif
END DO
IF (k.eq.N(ng)) THEN
DO i=IstrT,IendT
cff=1.0_r8/wrk(i,N(ng))
tl_cff=-cff*cff*tl_wrk(i,N(ng))
alpha(i,j)=cff*Tcof(i,N(ng))
tl_alpha(i,j)=tl_cff*Tcof(i,N(ng))+cff*tl_Tcof(i,N(ng))
beta (i,j)=cff*Scof(i,N(ng))
tl_beta (i,j)=tl_cff*Scof(i,N(ng))+cff*tl_Scof(i,N(ng))
END DO
END IF
END DO
# endif
!
!-----------------------------------------------------------------------
! Load "in situ" density anomaly (kg/m3 - 1000) and potential
! density anomaly (kg/m3 - 1000) referenced to the surface into global
! arrays. Notice that this is done in a separate (i,k) DO-loops to
! facilitate the adjoint.
!-----------------------------------------------------------------------
!
DO k=1,N(ng)
DO i=IstrT,IendT
rho(i,j,k)=den(i,k)
tl_rho(i,j,k)=tl_den(i,k)
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
!> pden(i,j,k)=(den1(i,k)-1000.0_r8) ! This gives a fatal
!> ! result in 4D-Var
tl_pden(i,j,k)=tl_den1(i,k) ! posterior error...
# ifdef MASKING
!> pden(i,j,k)=pden(i,k)*rmask(i,j)
!>
tl_pden(i,j,k)=tl_pden(i,k)*rmask(i,j)
# endif
# endif
END DO
END DO
END DO
!
!-----------------------------------------------------------------------
! Exchange boundary data.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& rho)
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& tl_rho)
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
!> CALL exchange_r3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 1, N(ng), &
!> & pden)
!>
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& tl_pden)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES_NOT_YET
# ifdef LMD_DDMIX_NOT_YET
!> CALL exchange_w3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & alfaobeta)
!>
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& tl_alfaobeta)
# endif
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& alpha)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_alpha)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& beta)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_beta)
# endif
# ifdef VAR_RHO_2D
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& rhoA)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_rhoA)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& rhoS)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_rhoS)
# endif
# ifdef BV_FREQUENCY_NOT_YET
!> CALL exchange_w3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & bvf)
!>
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& tl_bvf)
# endif
END IF
# ifdef DISTRIBUTE
!
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& rho)
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_rho)
# 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), &
!> & pden)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_pden)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
# ifdef LMD_DDMIX_NOT_YET
!> CALL mp_exchange3d (ng, tile, model, 1, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & NghostPoints, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & alfaobeta)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_alfaobeta)
# endif
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& alpha, beta)
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_alpha, tl_beta)
# endif
# ifdef VAR_RHO_2D
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& rhoA, rhoS)
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_rhoA, tl_rhoS)
# endif
# ifdef BV_FREQUENCY_NOT_YET
!> CALL mp_exchange3d (ng, tile, model, 1, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & NghostPoints, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & bvf)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_bvf)
# endif
# endif
RETURN
END SUBROUTINE tl_rho_eos_tile
# endif
# ifndef NONLIN_EOS
!
!***********************************************************************
SUBROUTINE tl_rho_eos_tile (ng, tile, model, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nrhs, &
# ifdef MASKING
& rmask, &
# endif
# ifdef VAR_RHO_2D
& Hz, tl_Hz, &
# endif
& z_r, tl_z_r, &
& z_w, tl_z_w, &
& t, tl_t, &
# ifdef VAR_RHO_2D
& rhoA, tl_rhoA, &
& rhoS, tl_rhoS, &
# endif
# ifdef BV_FREQUENCY_NOT_YET
& tl_bvf, &
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
& alpha, tl_alpha, &
& beta, tl_beta, &
# ifdef LMD_DDMIX_NOT_YET
& tl_alfaobeta, &
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
& tl_pden, &
# endif
& rho, tl_rho)
!***********************************************************************
!
USE mod_param
USE mod_scalars
# ifdef SEDIMENT_NOT_YET
USE mod_sediment
# endif
!
USE exchange_2d_mod
USE exchange_3d_mod
# ifdef DISTRIBUTE
USE mp_exchange_mod, ONLY : mp_exchange2d, 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
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
# endif
real(r8), intent(in) :: z_r(LBi:,LBj:,:)
real(r8), intent(in) :: z_w(LBi:,LBj:,0:)
real(r8), intent(in) :: t(LBi:,LBj:,:,:,:)
# ifdef VAR_RHO_2D
real(r8), intent(in) :: tl_Hz(LBi:,LBj:,:)
# endif
real(r8), intent(in) :: tl_z_r(LBi:,LBj:,:)
real(r8), intent(in) :: tl_z_w(LBi:,LBj:,0:)
real(r8), intent(in) :: tl_t(LBi:,LBj:,:,:,:)
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(inout) :: alpha(LBi:,LBj:)
real(r8), intent(inout) :: beta(LBi:,LBj:)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(out) :: rhoA(LBi:,LBj:)
real(r8), intent(out) :: rhoS(LBi:,LBj:)
real(r8), intent(out) :: tl_rhoA(LBi:,LBj:)
real(r8), intent(out) :: tl_rhoS(LBi:,LBj:)
# endif
# ifdef BV_FREQUENCY_NOT_YET
real(r8), intent(out) :: tl_bvf(LBi:,LBj:,0:)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(out) :: tl_alpha(LBi:,LBj:)
real(r8), intent(out) :: tl_beta(LBi:,LBj:)
# ifdef LMD_DDMIX_NOT_YET
real(r8), intent(out) :: tl_alfaobeta(LBi:,LBj:,0:)
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
real(r8), intent(out) :: tl_pden(LBi:,LBj:,:)
# endif
real(r8), intent(out) :: rho(LBi:,LBj:,:)
real(r8), intent(out) :: tl_rho(LBi:,LBj:,:)
# else
# ifdef MASKING
real(r8), intent(in) :: rmask(LBi:UBi,LBj:UBj)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(in) :: z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng))
real(r8), intent(in) :: t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng))
# ifdef VAR_RHO_2D
real(r8), intent(in) :: tl_Hz(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(in) :: tl_z_r(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(in) :: tl_z_w(LBi:UBi,LBj:UBj,0:N(ng))
real(r8), intent(in) :: tl_t(LBi:UBi,LBj:UBj,N(ng),3,NT(ng))
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(inout) :: alpha(LBi:UBi,LBj:UBj)
real(r8), intent(inout) :: beta(LBi:UBi,LBj:UBj)
# endif
# ifdef VAR_RHO_2D
real(r8), intent(out) :: rhoA(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: rhoS(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_rhoA(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_rhoS(LBi:UBi,LBj:UBj)
# endif
# ifdef BV_FREQUENCY_NOT_YET
real(r8), intent(out) :: tl_bvf(LBi:UBi,LBj:UBj,0:N(ng))
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
real(r8), intent(out) :: tl_alpha(LBi:UBi,LBj:UBj)
real(r8), intent(out) :: tl_beta(LBi:UBi,LBj:UBj)
# ifdef LMD_DDMIX_NOT_YET
real(r8), intent(out) :: tl_alfaobeta(LBi:UBi,LBj:UBj,0:N(ng))
# endif
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
real(r8), intent(out) :: tl_pden(LBi:UBi,LBj:UBj,N(ng))
# endif
real(r8), intent(out) :: rho(LBi:UBi,LBj:UBj,N(ng))
real(r8), intent(out) :: tl_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) :: tl_SedDen, tl_cff, tl_cff1
# include "set_bounds.h"
!
!=======================================================================
! Tangent linear, linear equation of state.
!=======================================================================
!
!-----------------------------------------------------------------------
! Compute "in situ" density anomaly (kg/m3 - 1000) using the linear
! equation of state.
!-----------------------------------------------------------------------
!
DO j=JstrT,JendT
DO k=1,N(ng)
DO i=IstrT,IendT
rho(i,j,k)=R0(ng)- &
& R0(ng)*Tcoef(ng)*(t(i,j,k,nrhs,itemp)-T0(ng))
tl_rho(i,j,k)=-R0(ng)*Tcoef(ng)*tl_t(i,j,k,nrhs,itemp)
# ifdef SALINITY
rho(i,j,k)=rho(i,j,k)+ &
& R0(ng)*Scoef(ng)*(t(i,j,k,nrhs,isalt)-S0(ng))
tl_rho(i,j,k)=tl_rho(i,j,k)+ &
& R0(ng)*Scoef(ng)*tl_t(i,j,k,nrhs,isalt)
# endif
# if defined SEDIMENT_NOT_YET && defined SED_DENS_NOT_YET
SedDen=0.0_r8
tl_SedDen=0.0_r8
DO ised=1,NST
itrc=idsed(ised)
cff1=1.0_r8/Srho(ised,ng)
SedDen=SedDen+ &
& t(i,j,k,nrhs,itrc)* &
& (Srho(ised,ng)-rho(i,j,k))*cff1
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
END DO
rho(i,j,k)=rho(i,j,k)+SedDen
tl_rho(i,j,k)=tl_rho(i,j,k)+tl_SedDen
# endif
rho(i,j,k)=rho(i,j,k)-1000.0_r8
# ifdef MASKING
rho(i,j,k)=rho(i,j,k)*rmask(i,j)
tl_rho(i,j,k)=tl_rho(i,j,k)*rmask(i,j)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
!> pden(i,j,k)=rho(i,j,k)
!>
tl_pden(i,j,k)=tl_rho(i,j,k)
# endif
END DO
END DO
# ifdef VAR_RHO_2D
!
!-----------------------------------------------------------------------
! Compute vertical averaged density (rhoA) and density perturbation
! used (rhoS) in barotropic pressure gradient.
!-----------------------------------------------------------------------
!
DO i=IstrT,IendT
cff1=rho(i,j,N(ng))*Hz(i,j,N(ng))
tl_cff1=tl_rho(i,j,N(ng))*Hz(i,j,N(ng))+ &
& rho(i,j,N(ng))*tl_Hz(i,j,N(ng))
rhoS(i,j)=0.5_r8*cff1*Hz(i,j,N(ng))
tl_rhoS(i,j)=0.5_r8*(tl_cff1*Hz(i,j,N(ng))+ &
& cff1*tl_Hz(i,j,N(ng)))
rhoA(i,j)=cff1
tl_rhoA(i,j)=tl_cff1
END DO
DO k=N(ng)-1,1,-1
DO i=IstrT,IendT
cff1=rho(i,j,k)*Hz(i,j,k)
tl_cff1=tl_rho(i,j,k)*Hz(i,j,k)+ &
& rho(i,j,k)*tl_Hz(i,j,k)
rhoS(i,j)=rhoS(i,j)+Hz(i,j,k)*(rhoA(i,j)+0.5_r8*cff1)
tl_rhoS(i,j)=tl_rhoS(i,j)+ &
& tl_Hz(i,j,k)*(rhoA(i,j)+0.5_r8*cff1)+ &
& Hz(i,j,k)*(tl_rhoA(i,j)+0.5_r8*tl_cff1)
rhoA(i,j)=rhoA(i,j)+cff1
tl_rhoA(i,j)=tl_rhoA(i,j)+tl_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_cff1=-cff1*cff1*(tl_z_w(i,j,N(ng))-tl_z_w(i,j,0))
!
! Here we reverse the order of the NL and TL operations since an
! intermeridiate value of rhoA and rhoS is needed because they are
! recursive.
!
tl_rhoA(i,j)=cff2*(tl_cff1*rhoA(i,j)+cff1*tl_rhoA(i,j))
rhoA(i,j)=cff2*cff1*rhoA(i,j)
tl_rhoS(i,j)=2.0_r8*cff2* &
& cff1*(2.0_r8*tl_cff1*rhoS(i,j)+ &
& cff1*tl_rhoS(i,j))
rhoS(i,j)=2.0_r8*cff1*cff1*cff2*rhoS(i,j)
END DO
# endif
# ifdef BV_FREQUENCY_NOT_YET
!
!-----------------------------------------------------------------------
! Compute Brunt-Vaisala frequency (1/s2) at horizontal RHO-points
! and vertical W-points.
!-----------------------------------------------------------------------
!
DO k=1,N(ng)-1
DO i=IstrT,IendT
!> bvf(i,j,k)=-gorho0*(rho(i,j,k+1)-rho(i,j,k))/ &
!> & (z_r(i,j,k+1)-z_r(i,j,k))
!>
cff=1.0_r8/(z_r(i,j,k+1)-z_r(i,j,k))
tl_cff=-cff*cff*(tl_z_r(i,j,k+1)-tl_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)))
END DO
END DO
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
!
!-----------------------------------------------------------------------
! Compute thermal expansion (1/Celsius) and saline contraction
! (1/PSU) coefficients.
!-----------------------------------------------------------------------
!
DO i=IstrT,IendT
alpha(i,j)=ABS(Tcoef(ng))
tl_alpha(i,j)=0.0_r8
# ifdef SALINITY
beta(i,j)=ABS(Scoef(ng))
tl_beta(i,j)=0.0_r8
# else
beta(i,j)=0.0_r8
tl_beta(i,j)=0.0_r8
# endif
END DO
# 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
!> alfaobeta(i,j,k)=cff*Tcoef(ng)
!>
tl_alfaobeta(i,j,k)=0.0_r8
END DO
END DO
# endif
# endif
END DO
!
!-----------------------------------------------------------------------
! Exchange boundary data.
!-----------------------------------------------------------------------
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& rho)
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& tl_rho)
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET
!> CALL exchange_r3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 1, N(ng), &
!> & pden)
!>
CALL exchange_r3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& tl_pden)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES_NOT_YET
# ifdef LMD_DDMIX_NOT_YET
!> CALL exchange_w3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & alfaobeta)
!>
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& tl_alfaobeta)
# endif
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& alpha)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_alpha)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& beta)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_beta)
# endif
# ifdef VAR_RHO_2D
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& rhoA)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_rhoA)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& rhoS)
CALL exchange_r2d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& tl_rhoS)
# endif
# ifdef BV_FREQUENCY_NOT_YET
!> CALL exchange_w3d_tile (ng, tile, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & bvf)
!>
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& tl_bvf)
# endif
END IF
# ifdef DISTRIBUTE
!
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& rho)
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_rho)
# 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), &
!> & pden)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 1, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_pden)
# endif
# if defined LMD_SKPP_NOT_YET || defined LMD_BKPP_NOT_YET || \
defined BULK_FLUXES
# ifdef LMD_DDMIX_NOT_YET
!> CALL mp_exchange3d (ng, tile, model, 1, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & NghostPoints, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & alfaobeta)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_alfaobeta)
# endif
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& alpha, beta)
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_alpha, tl_beta)
# endif
# ifdef VAR_RHO_2D
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& rhoA, rhoS)
CALL mp_exchange2d (ng, tile, model, 2, &
& LBi, UBi, LBj, UBj, &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_rhoA, tl_rhoS)
# endif
# ifdef BV_FREQUENCY_NOT_YET
!> CALL mp_exchange3d (ng, tile, model, 1, &
!> & LBi, UBi, LBj, UBj, 0, N(ng), &
!> & NghostPoints, &
!> & EWperiodic(ng), NSperiodic(ng), &
!> & bvf)
!>
CALL mp_exchange3d (ng, tile, model, 1, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tl_bvf)
# endif
# endif
RETURN
END SUBROUTINE tl_rho_eos_tile
# endif
#endif
END MODULE tl_rho_eos_mod