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MODULE eosbn2
!!==============================================================================
!! *** MODULE eosbn2 ***
!! Equation Of Seawater : in situ density - Brunt-Vaisala frequency
!!==============================================================================
!! History : OPA ! 1989-03 (O. Marti) Original code
!! 6.0 ! 1994-07 (G. Madec, M. Imbard) add bn2
!! 6.0 ! 1994-08 (G. Madec) Add Jackett & McDougall eos
!! 7.0 ! 1996-01 (G. Madec) statement function for e3
!! 8.1 ! 1997-07 (G. Madec) density instead of volumic mass
!! - ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure gradient
!! 8.2 ! 2001-09 (M. Ben Jelloul) bugfix on linear eos
!! NEMO 1.0 ! 2002-10 (G. Madec) add eos_init
!! - ! 2002-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d
!! - ! 2003-08 (G. Madec) F90, free form
!! 3.0 ! 2006-08 (G. Madec) add tfreez function (now eos_fzp function)
!! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA
!! - ! 2010-10 (G. Nurser, G. Madec) add alpha/beta used in ldfslp
!! 3.7 ! 2012-03 (F. Roquet, G. Madec) add primitive of alpha and beta used in PE computation
!! - ! 2012-05 (F. Roquet) add Vallis and original JM95 equation of state
!! - ! 2013-04 (F. Roquet, G. Madec) add eos_rab, change bn2 computation and reorganize the module
!! - ! 2014-09 (F. Roquet) add TEOS-10, S-EOS, and modify EOS-80
!! - ! 2015-06 (P.A. Bouttier) eos_fzp functions changed to subroutines for AGRIF
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! eos : generic interface of the equation of state
!! eos_insitu : Compute the in situ density
!! eos_insitu_pot: Compute the insitu and surface referenced potential volumic mass
!! eos_insitu_2d : Compute the in situ density for 2d fields
!! bn2 : compute the Brunt-Vaisala frequency
!! eos_pt_from_ct: compute the potential temperature from the Conservative Temperature
!! eos_rab : generic interface of in situ thermal/haline expansion ratio
!! eos_rab_3d : compute in situ thermal/haline expansion ratio
!! eos_rab_2d : compute in situ thermal/haline expansion ratio for 2d fields
!! eos_fzp_2d : freezing temperature for 2d fields
!! eos_fzp_0d : freezing temperature for scalar
!! eos_init : set eos parameters (namelist)
!!----------------------------------------------------------------------
USE dom_oce ! ocean space and time domain
USE domutl, ONLY : is_tile
USE phycst ! physical constants
USE stopar ! Stochastic T/S fluctuations
USE stopts ! Stochastic T/S fluctuations
!
USE in_out_manager ! I/O manager
USE lib_mpp ! MPP library
USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
USE prtctl ! Print control
USE lbclnk ! ocean lateral boundary conditions
USE timing ! Timing
IMPLICIT NONE
PRIVATE
! !! * Interface
INTERFACE eos
MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d, eos_insitu_pot_2d
END INTERFACE
!
INTERFACE eos_rab
MODULE PROCEDURE rab_3d, rab_2d, rab_0d
END INTERFACE
!
INTERFACE eos_fzp
MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
END INTERFACE
!
PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules
PUBLIC bn2 ! called by step module
PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl
PUBLIC eos_pt_from_ct ! called by sbcssm
PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules
PUBLIC eos_pen ! used for pe diagnostics in trdpen module
PUBLIC eos_init ! called by istate module
! !!** Namelist nameos **
LOGICAL , PUBLIC :: ln_TEOS10
LOGICAL , PUBLIC :: ln_EOS80
LOGICAL , PUBLIC :: ln_SEOS
! Parameters
LOGICAL , PUBLIC :: l_useCT ! =T in ln_TEOS10=T (i.e. use eos_pt_from_ct to compute sst_m), =F otherwise
INTEGER , PUBLIC :: neos ! Identifier for equation of state used
INTEGER , PARAMETER :: np_teos10 = -1 ! parameter for using TEOS10
INTEGER , PARAMETER :: np_eos80 = 0 ! parameter for using EOS80
INTEGER , PARAMETER :: np_seos = 1 ! parameter for using Simplified Equation of state
! !!! simplified eos coefficients (default value: Vallis 2006)
REAL(wp), PUBLIC :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff.
REAL(wp), PUBLIC :: rn_b0 = 7.6554e-1_wp ! saline expansion coeff.
REAL(wp) :: rn_lambda1 = 5.9520e-2_wp ! cabbeling coeff. in T^2
REAL(wp) :: rn_lambda2 = 5.4914e-4_wp ! cabbeling coeff. in S^2
REAL(wp) :: rn_mu1 = 1.4970e-4_wp ! thermobaric coeff. in T
REAL(wp) :: rn_mu2 = 1.1090e-5_wp ! thermobaric coeff. in S
REAL(wp) :: rn_nu = 2.4341e-3_wp ! cabbeling coeff. in theta*salt
! TEOS10/EOS80 parameters
REAL(wp) :: r1_S0, r1_T0, r1_Z0, rdeltaS
! EOS parameters
REAL(wp) :: EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600
REAL(wp) :: EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510
REAL(wp) :: EOS020 , EOS120 , EOS220 , EOS320 , EOS420
REAL(wp) :: EOS030 , EOS130 , EOS230 , EOS330
REAL(wp) :: EOS040 , EOS140 , EOS240
REAL(wp) :: EOS050 , EOS150
REAL(wp) :: EOS060
REAL(wp) :: EOS001 , EOS101 , EOS201 , EOS301 , EOS401
REAL(wp) :: EOS011 , EOS111 , EOS211 , EOS311
REAL(wp) :: EOS021 , EOS121 , EOS221
REAL(wp) :: EOS031 , EOS131
REAL(wp) :: EOS041
REAL(wp) :: EOS002 , EOS102 , EOS202
REAL(wp) :: EOS012 , EOS112
REAL(wp) :: EOS022
REAL(wp) :: EOS003 , EOS103
REAL(wp) :: EOS013
! ALPHA parameters
REAL(wp) :: ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500
REAL(wp) :: ALP010 , ALP110 , ALP210 , ALP310 , ALP410
REAL(wp) :: ALP020 , ALP120 , ALP220 , ALP320
REAL(wp) :: ALP030 , ALP130 , ALP230
REAL(wp) :: ALP040 , ALP140
REAL(wp) :: ALP050
REAL(wp) :: ALP001 , ALP101 , ALP201 , ALP301
REAL(wp) :: ALP011 , ALP111 , ALP211
REAL(wp) :: ALP021 , ALP121
REAL(wp) :: ALP031
REAL(wp) :: ALP002 , ALP102
REAL(wp) :: ALP012
REAL(wp) :: ALP003
! BETA parameters
REAL(wp) :: BET000 , BET100 , BET200 , BET300 , BET400 , BET500
REAL(wp) :: BET010 , BET110 , BET210 , BET310 , BET410
REAL(wp) :: BET020 , BET120 , BET220 , BET320
REAL(wp) :: BET030 , BET130 , BET230
REAL(wp) :: BET040 , BET140
REAL(wp) :: BET050
REAL(wp) :: BET001 , BET101 , BET201 , BET301
REAL(wp) :: BET011 , BET111 , BET211
REAL(wp) :: BET021 , BET121
REAL(wp) :: BET031
REAL(wp) :: BET002 , BET102
REAL(wp) :: BET012
REAL(wp) :: BET003
! PEN parameters
REAL(wp) :: PEN000 , PEN100 , PEN200 , PEN300 , PEN400
REAL(wp) :: PEN010 , PEN110 , PEN210 , PEN310
REAL(wp) :: PEN020 , PEN120 , PEN220
REAL(wp) :: PEN030 , PEN130
REAL(wp) :: PEN040
REAL(wp) :: PEN001 , PEN101 , PEN201
REAL(wp) :: PEN011 , PEN111
REAL(wp) :: PEN021
REAL(wp) :: PEN002 , PEN102
REAL(wp) :: PEN012
! ALPHA_PEN parameters
REAL(wp) :: APE000 , APE100 , APE200 , APE300
REAL(wp) :: APE010 , APE110 , APE210
REAL(wp) :: APE020 , APE120
REAL(wp) :: APE030
REAL(wp) :: APE001 , APE101
REAL(wp) :: APE011
REAL(wp) :: APE002
! BETA_PEN parameters
REAL(wp) :: BPE000 , BPE100 , BPE200 , BPE300
REAL(wp) :: BPE010 , BPE110 , BPE210
REAL(wp) :: BPE020 , BPE120
REAL(wp) :: BPE030
REAL(wp) :: BPE001 , BPE101
REAL(wp) :: BPE011
REAL(wp) :: BPE002
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: eosbn2.F90 15136 2021-07-23 10:07:28Z smasson $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE eos_insitu( pts, prd, pdep )
!!
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
!!
CALL eos_insitu_t( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
END SUBROUTINE eos_insitu
SUBROUTINE eos_insitu_t( pts, ktts, prd, ktrd, pdep, ktdep )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_insitu ***
!!
!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
!! potential temperature and salinity using an equation of state
!! selected in the nameos namelist
!!
!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
!! with prd in situ density anomaly no units
!! t TEOS10: CT or EOS80: PT Celsius
!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
!! z depth meters
!! rho in situ density kg/m^3
!! rho0 reference density kg/m^3
!!
!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
!!
!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
!!
!! ln_seos : simplified equation of state
!! prd(t,s,z) = ( -a0*(1+lambda/2*(T-T0)+mu*z+nu*(S-S0))*(T-T0) + b0*(S-S0) ) / rho0
!! linear case function of T only: rn_alpha<>0, other coefficients = 0
!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
!! Vallis like equation: use default values of coefficients
!!
!! ** Action : compute prd , the in situ density (no units)
!!
!! References : Roquet et al, Ocean Modelling, in preparation (2014)
!! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
!! TEOS-10 Manual, 2010
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: ktts, ktrd, ktdep
REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
REAL(wp), DIMENSION(A2D_T(ktdep),JPK ), INTENT(in ) :: pdep ! depth [m]
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zt , zh , zs , ztm ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos-insitu')
!
SELECT CASE( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
!
zh = pdep(ji,jj,jk) * r1_Z0 ! depth
zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
ztm = tmask(ji,jj,jk) ! tmask
!
zn3 = EOS013*zt &
& + EOS103*zs+EOS003
!
zn2 = (EOS022*zt &
& + EOS112*zs+EOS012)*zt &
& + (EOS202*zs+EOS102)*zs+EOS002
!
zn1 = (((EOS041*zt &
& + EOS131*zs+EOS031)*zt &
& + (EOS221*zs+EOS121)*zs+EOS021)*zt &
& + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt &
& + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001
!
zn0 = (((((EOS060*zt &
& + EOS150*zs+EOS050)*zt &
& + (EOS240*zs+EOS140)*zs+EOS040)*zt &
& + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt &
& + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt &
& + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt &
& + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
!
END_3D
!
CASE( np_seos ) !== simplified EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - 10._wp
zs = pts (ji,jj,jk,jp_sal) - 35._wp
zh = pdep (ji,jj,jk)
ztm = tmask(ji,jj,jk)
!
zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt &
& + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs &
& - rn_nu * zt * zs
!
prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
END_3D
!
END SELECT
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', kdim=jpk )
!
IF( ln_timing ) CALL timing_stop('eos-insitu')
!
END SUBROUTINE eos_insitu_t
SUBROUTINE eos_insitu_pot( pts, prd, prhop, pdep )
!!
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
!!
CALL eos_insitu_pot_t( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
END SUBROUTINE eos_insitu_pot
SUBROUTINE eos_insitu_pot_t( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_insitu_pot ***
!!
!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
!! potential volumic mass (Kg/m3) from potential temperature and
!! salinity fields using an equation of state selected in the
!! namelist.
!!
!! ** Action : - prd , the in situ density (no units)
!! - prhop, the potential volumic mass (Kg/m3)
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
REAL(wp), DIMENSION(A2D_T(ktrhop),JPK ), INTENT( out) :: prhop ! potential density (surface referenced)
REAL(wp), DIMENSION(A2D_T(ktdep) ,JPK ), INTENT(in ) :: pdep ! depth [m]
!
INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
INTEGER :: jdof
REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos-pot')
!
SELECT CASE ( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
! Stochastic equation of state
IF ( ln_sto_eos ) THEN
ALLOCATE(zn0_sto(1:2*nn_sto_eos))
ALLOCATE(zn_sto(1:2*nn_sto_eos))
ALLOCATE(zsign(1:2*nn_sto_eos))
DO jsmp = 1, 2*nn_sto_eos, 2
zsign(jsmp) = 1._wp
zsign(jsmp+1) = -1._wp
END DO
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
!
! compute density (2*nn_sto_eos) times:
! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
! (2) for t-dt, s-ds (with the opposite fluctuation)
DO jsmp = 1, nn_sto_eos*2
jdof = (jsmp + 1) / 2
zh = pdep(ji,jj,jk) * r1_Z0 ! depth
zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
ztm = tmask(ji,jj,jk) ! tmask
!
zn3 = EOS013*zt &
& + EOS103*zs+EOS003
!
zn2 = (EOS022*zt &
& + EOS112*zs+EOS012)*zt &
& + (EOS202*zs+EOS102)*zs+EOS002
!
zn1 = (((EOS041*zt &
& + EOS131*zs+EOS031)*zt &
& + (EOS221*zs+EOS121)*zs+EOS021)*zt &
& + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt &
& + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001
!
zn0_sto(jsmp) = (((((EOS060*zt &
& + EOS150*zs+EOS050)*zt &
& + (EOS240*zs+EOS140)*zs+EOS040)*zt &
& + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt &
& + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt &
& + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt &
& + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000
!
zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
END DO
!
! compute stochastic density as the mean of the (2*nn_sto_eos) densities
prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
DO jsmp = 1, nn_sto_eos*2
prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
!
prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
END DO
prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
END_3D
DEALLOCATE(zn0_sto,zn_sto,zsign)
! Non-stochastic equation of state
ELSE
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
!
zh = pdep(ji,jj,jk) * r1_Z0 ! depth
zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
ztm = tmask(ji,jj,jk) ! tmask
!
zn3 = EOS013*zt &
& + EOS103*zs+EOS003
!
zn2 = (EOS022*zt &
& + EOS112*zs+EOS012)*zt &
& + (EOS202*zs+EOS102)*zs+EOS002
!
zn1 = (((EOS041*zt &
& + EOS131*zs+EOS031)*zt &
& + (EOS221*zs+EOS121)*zs+EOS021)*zt &
& + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt &
& + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001
!
zn0 = (((((EOS060*zt &
& + EOS150*zs+EOS050)*zt &
& + (EOS240*zs+EOS140)*zs+EOS040)*zt &
& + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt &
& + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt &
& + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt &
& + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
!
prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
END_3D
ENDIF
CASE( np_seos ) !== simplified EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - 10._wp
zs = pts (ji,jj,jk,jp_sal) - 35._wp
zh = pdep (ji,jj,jk)
ztm = tmask(ji,jj,jk)
! ! potential density referenced at the surface
zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt ) * zt &
& + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs ) * zs &
& - rn_nu * zt * zs
prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
! ! density anomaly (masked)
zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
prd(ji,jj,jk) = zn * r1_rho0 * ztm
!
END_3D
!
END SELECT
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', &
& tab3d_2=prhop, clinfo2=' pot : ', kdim=jpk )
!
IF( ln_timing ) CALL timing_stop('eos-pot')
!
END SUBROUTINE eos_insitu_pot_t
SUBROUTINE eos_insitu_2d( pts, pdep, prd )
!!
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
REAL(wp), DIMENSION(:,:) , INTENT( out) :: prd ! in situ density
!!
CALL eos_insitu_2d_t( pts, is_tile(pts), pdep, is_tile(pdep), prd, is_tile(prd) )
END SUBROUTINE eos_insitu_2d
SUBROUTINE eos_insitu_2d_t( pts, ktts, pdep, ktdep, prd, ktrd )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_insitu_2d ***
!!
!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
!! potential temperature and salinity using an equation of state
!! selected in the nameos namelist. * 2D field case
!!
!! ** Action : - prd , the in situ density (no units) (unmasked)
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: ktts, ktdep, ktrd
REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
REAL(wp), DIMENSION(A2D_T(ktrd) ), INTENT( out) :: prd ! in situ density
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zt , zh , zs ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos2d')
!
prd(:,:) = 0._wp
!
SELECT CASE( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zh = pdep(ji,jj) * r1_Z0 ! depth
zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
!
zn3 = EOS013*zt &
& + EOS103*zs+EOS003
!
zn2 = (EOS022*zt &
& + EOS112*zs+EOS012)*zt &
& + (EOS202*zs+EOS102)*zs+EOS002
!
zn1 = (((EOS041*zt &
& + EOS131*zs+EOS031)*zt &
& + (EOS221*zs+EOS121)*zs+EOS021)*zt &
& + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt &
& + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001
!
zn0 = (((((EOS060*zt &
& + EOS150*zs+EOS050)*zt &
& + (EOS240*zs+EOS140)*zs+EOS040)*zt &
& + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt &
& + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt &
& + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt &
& + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
prd(ji,jj) = zn * r1_rho0 - 1._wp ! unmasked in situ density anomaly
!
END_2D
!
CASE( np_seos ) !== simplified EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) - 10._wp
zs = pts (ji,jj,jp_sal) - 35._wp
zh = pdep (ji,jj) ! depth at the partial step level
!
zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt &
& + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs &
& - rn_nu * zt * zs
!
prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
!
END_2D
!
END SELECT
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' )
!
IF( ln_timing ) CALL timing_stop('eos2d')
!
END SUBROUTINE eos_insitu_2d_t
SUBROUTINE eos_insitu_pot_2d( pts, prhop )
!!
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
!!
CALL eos_insitu_pot_2d_t( pts, is_tile(pts), prhop, is_tile(prhop) )
END SUBROUTINE eos_insitu_pot_2d
SUBROUTINE eos_insitu_pot_2d_t( pts, ktts, prhop, ktrhop )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_insitu_pot ***
!!
!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
!! potential volumic mass (Kg/m3) from potential temperature and
!! salinity fields using an equation of state selected in the
!! namelist.
!!
!! ** Action :
!! - prhop, the potential volumic mass (Kg/m3)
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: ktts, ktrhop
REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
! ! 2 : salinity [psu]
REAL(wp), DIMENSION(A2D_T(ktrhop) ), INTENT( out) :: prhop ! potential density (surface referenced)
!
INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
INTEGER :: jdof
REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos-pot')
!
SELECT CASE ( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
ztm = tmask(ji,jj,1) ! tmask
!
zn0 = (((((EOS060*zt &
& + EOS150*zs+EOS050)*zt &
& + (EOS240*zs+EOS140)*zs+EOS040)*zt &
& + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt &
& + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt &
& + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt &
& + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000
!
!
prhop(ji,jj) = zn0 * ztm ! potential density referenced at the surface
!
END_2D
CASE( np_seos ) !== simplified EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zt = pts (ji,jj,jp_tem) - 10._wp
zs = pts (ji,jj,jp_sal) - 35._wp
ztm = tmask(ji,jj,1)
! ! potential density referenced at the surface
zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt ) * zt &
& + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs ) * zs &
& - rn_nu * zt * zs
prhop(ji,jj) = ( rho0 + zn ) * ztm
!
END_2D
!
END SELECT
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prhop, clinfo1=' pot: ', kdim=1 )
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prhop, clinfo1=' eos-pot: ' )
!
IF( ln_timing ) CALL timing_stop('eos-pot')
!
END SUBROUTINE eos_insitu_pot_2d_t
SUBROUTINE rab_3d( pts, pab, Kmm )
!!
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
!!
CALL rab_3d_t( pts, is_tile(pts), pab, is_tile(pab), Kmm )
END SUBROUTINE rab_3d
SUBROUTINE rab_3d_t( pts, ktts, pab, ktab, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE rab_3d ***
!!
!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
!!
!! ** Method : calculates alpha / beta at T-points
!!
!! ** Action : - pab : thermal/haline expansion ratio at T-points
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
INTEGER , INTENT(in ) :: ktts, ktab
REAL(wp), DIMENSION(A2D_T(ktts),JPK,JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zt , zh , zs , ztm ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('rab_3d')
!
SELECT CASE ( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
!
zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
ztm = tmask(ji,jj,jk) ! tmask
!
! alpha
zn3 = ALP003
!
zn2 = ALP012*zt + ALP102*zs+ALP002
!
zn1 = ((ALP031*zt &
& + ALP121*zs+ALP021)*zt &
& + (ALP211*zs+ALP111)*zs+ALP011)*zt &
& + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
!
zn0 = ((((ALP050*zt &
& + ALP140*zs+ALP040)*zt &
& + (ALP230*zs+ALP130)*zs+ALP030)*zt &
& + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt &
& + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt &
& + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
!
! beta
zn3 = BET003
!
zn2 = BET012*zt + BET102*zs+BET002
!
zn1 = ((BET031*zt &
& + BET121*zs+BET021)*zt &
& + (BET211*zs+BET111)*zs+BET011)*zt &
& + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
!
zn0 = ((((BET050*zt &
& + BET140*zs+BET040)*zt &
& + (BET230*zs+BET130)*zs+BET030)*zt &
& + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt &
& + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt &
& + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
!
END_3D
!
CASE( np_seos ) !== simplified EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
!
zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
!
zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
!
END_3D
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'rab_3d:', ctmp1 )
!
END SELECT
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', &
& tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', kdim=jpk )
!
IF( ln_timing ) CALL timing_stop('rab_3d')
!
END SUBROUTINE rab_3d_t
SUBROUTINE rab_2d( pts, pdep, pab, Kmm )
!!
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
REAL(wp), DIMENSION(:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
!!
CALL rab_2d_t(pts, is_tile(pts), pdep, is_tile(pdep), pab, is_tile(pab), Kmm)
END SUBROUTINE rab_2d
SUBROUTINE rab_2d_t( pts, ktts, pdep, ktdep, pab, ktab, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE rab_2d ***
!!
!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
!!
!! ** Action : - pab : thermal/haline expansion ratio at T-points
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
INTEGER , INTENT(in ) :: ktts, ktdep, ktab
REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
REAL(wp), DIMENSION(A2D_T(ktab),JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zt , zh , zs ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('rab_2d')
!
pab(:,:,:) = 0._wp
!
SELECT CASE ( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zh = pdep(ji,jj) * r1_Z0 ! depth
zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
!
! alpha
zn3 = ALP003
!
zn2 = ALP012*zt + ALP102*zs+ALP002
!
zn1 = ((ALP031*zt &
& + ALP121*zs+ALP021)*zt &
& + (ALP211*zs+ALP111)*zs+ALP011)*zt &
& + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
!
zn0 = ((((ALP050*zt &
& + ALP140*zs+ALP040)*zt &
& + (ALP230*zs+ALP130)*zs+ALP030)*zt &
& + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt &
& + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt &
& + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(ji,jj,jp_tem) = zn * r1_rho0
!
! beta
zn3 = BET003
!
zn2 = BET012*zt + BET102*zs+BET002
!
zn1 = ((BET031*zt &
& + BET121*zs+BET021)*zt &
& + (BET211*zs+BET111)*zs+BET011)*zt &
& + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
!
zn0 = ((((BET050*zt &
& + BET140*zs+BET040)*zt &
& + (BET230*zs+BET130)*zs+BET030)*zt &
& + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt &
& + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt &
& + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(ji,jj,jp_sal) = zn / zs * r1_rho0
!
!
END_2D
!
CASE( np_seos ) !== simplified EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
zh = pdep (ji,jj) ! depth at the partial step level
!
zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
!
zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
!
END_2D
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'rab_2d:', ctmp1 )
!
END SELECT
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', &
& tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' )
!
IF( ln_timing ) CALL timing_stop('rab_2d')
!
END SUBROUTINE rab_2d_t
SUBROUTINE rab_0d( pts, pdep, pab, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE rab_0d ***
!!
!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
!!
!! ** Action : - pab : thermal/haline expansion ratio at T-points
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), INTENT(in ) :: pdep ! depth [m]
REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio
!
REAL(wp) :: zt , zh , zs ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('rab_0d')
!
pab(:) = 0._wp
!
SELECT CASE ( neos )
!
CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
!
!
zh = pdep * r1_Z0 ! depth
zt = pts (jp_tem) * r1_T0 ! temperature
zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
!
! alpha
zn3 = ALP003
!
zn2 = ALP012*zt + ALP102*zs+ALP002
!
zn1 = ((ALP031*zt &
& + ALP121*zs+ALP021)*zt &
& + (ALP211*zs+ALP111)*zs+ALP011)*zt &
& + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
!
zn0 = ((((ALP050*zt &
& + ALP140*zs+ALP040)*zt &
& + (ALP230*zs+ALP130)*zs+ALP030)*zt &
& + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt &
& + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt &
& + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(jp_tem) = zn * r1_rho0
!
! beta
zn3 = BET003
!
zn2 = BET012*zt + BET102*zs+BET002
!
zn1 = ((BET031*zt &
& + BET121*zs+BET021)*zt &
& + (BET211*zs+BET111)*zs+BET011)*zt &
& + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
!
zn0 = ((((BET050*zt &
& + BET140*zs+BET040)*zt &
& + (BET230*zs+BET130)*zs+BET030)*zt &
& + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt &
& + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt &
& + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
!
zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
!
pab(jp_sal) = zn / zs * r1_rho0
!
!
!
CASE( np_seos ) !== simplified EOS ==!
!
zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
zh = pdep ! depth at the partial step level
!
zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
pab(jp_tem) = zn * r1_rho0 ! alpha
!
zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
pab(jp_sal) = zn * r1_rho0 ! beta
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'rab_0d:', ctmp1 )
!
END SELECT
!
IF( ln_timing ) CALL timing_stop('rab_0d')
!
END SUBROUTINE rab_0d
SUBROUTINE bn2( pts, pab, pn2, Kmm )
!!
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]