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Nemo-NAA10km_nemo_4.2.2/tests/ISOMIP+/MY_SRC/eosbn2.F90
Robinson Hordoir 4fa5daa6c3 First commit of Nemo-NAA10km_nemo_4.2.2
2025-09-05 09:42:21 +02:00

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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
LOGICAL , PUBLIC :: ln_LEOS ! determine if linear eos is used
! 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
INTEGER , PARAMETER :: np_leos = 2 ! parameter for using linear equation of state (ISOMIP+)
! !!! 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 10425 2018-12-19 21:54:16Z 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
!!
!! ln_leos : linear ISOMIP equation of state
!! prd(t,s,z) = ( -a0*(T-T0) + b0*(S-S0) ) / rho0
!! setup for ISOMIP linear eos
!!
!! ** 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
!
CASE( np_leos ) !== linear ISOMIP EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
zs = pts (ji,jj,jk,jp_sal) - 34.2_wp
zh = pdep (ji,jj,jk)
ztm = tmask(ji,jj,jk)
!
zn = rho0 * ( - rn_a0 * zt + rn_b0 * 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
!
CASE( np_leos ) !== linear ISOMIP EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
zs = pts (ji,jj,jk,jp_sal) - 34.2_wp
zh = pdep (ji,jj,jk)
ztm = tmask(ji,jj,jk)
! ! potential density referenced at the surface
zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
! ! density anomaly (masked)
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
!
CASE( np_leos ) !== ISOMIP EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) - (-1._wp)
zs = pts (ji,jj,jp_sal) - 34.2_wp
zh = pdep (ji,jj) ! depth at the partial step level
!
zn = rho0 * ( - rn_a0 * zt + rn_b0 * 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
!
CASE( np_leos ) !== ISOMIP EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) - (-1._wp)
zs = pts (ji,jj,jp_sal) - 34.2_wp
!zh = pdep (ji,jj) ! depth at the partial step level
!
zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
!
prhop(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
!
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( np_leos ) !== linear ISOMIP EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
zs = pts (ji,jj,jk,jp_sal) - 34.2_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 * rho0
pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
!
zn = rn_b0 * rho0
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( np_leos ) !== linear ISOMIP EOS ==!
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = pts (ji,jj,jp_tem) - (-1._wp) ! pot. temperature anomaly (t-T0)
zs = pts (ji,jj,jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
zh = pdep (ji,jj) ! depth at the partial step level
!
zn = rn_a0 * rho0
pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
!
zn = rn_b0 * rho0
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( np_leos ) !== linear ISOMIP EOS ==!
!
zt = pts(jp_tem) - (-1._wp) ! pot. temperature anomaly (t-T0)
zs = pts(jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
zh = pdep ! depth at the partial step level
!
zn = rn_a0 * rho0
pab(jp_tem) = zn * r1_rho0 ! alpha
!
zn = rn_b0 * rho0
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]
!!
CALL bn2_t( pts, pab, is_tile(pab), pn2, is_tile(pn2), Kmm )
END SUBROUTINE bn2
SUBROUTINE bn2_t( pts, pab, ktab, pn2, ktn2, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE bn2 ***
!!
!! ** Purpose : Compute the local Brunt-Vaisala frequency at the
!! time-step of the input arguments
!!
!! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
!! where alpha and beta are given in pab, and computed on T-points.
!! N.B. N^2 is set one for all to zero at jk=1 in istate module.
!!
!! ** Action : pn2 : square of the brunt-vaisala frequency at w-point
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
INTEGER , INTENT(in ) :: ktab, ktn2
REAL(wp), DIMENSION(jpi,jpj, jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
REAL(wp), DIMENSION(A2D_T(ktn2),JPK ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zaw, zbw, zrw ! local scalars
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('bn2')
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 2, jpkm1 ) ! interior points only (2=< jk =< jpkm1 ); surface and bottom value set to zero one for all in istate.F90
zrw = ( gdepw(ji,jj,jk ,Kmm) - gdept(ji,jj,jk,Kmm) ) &
& / ( gdept(ji,jj,jk-1,Kmm) - gdept(ji,jj,jk,Kmm) )
!
zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw
zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
!
pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) &
& - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) &
& / e3w(ji,jj,jk,Kmm) * wmask(ji,jj,jk)
END_3D
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', kdim=jpk )
!
IF( ln_timing ) CALL timing_stop('bn2')
!
END SUBROUTINE bn2_t
FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_pt_from_ct ***
!!
!! ** Purpose : Compute pot.temp. from cons. temp. [Celsius]
!!
!! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm
!! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
!!
!! Reference : TEOS-10, UNESCO
!! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celsius]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
! Leave result array automatic rather than making explicitly allocated
REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celsius]
!
INTEGER :: ji, jj ! dummy loop indices
REAL(wp) :: zt , zs , ztm ! local scalars
REAL(wp) :: zn , zd ! local scalars
REAL(wp) :: zdeltaS , z1_S0 , z1_T0
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos_pt_from_ct')
!
zdeltaS = 5._wp
z1_S0 = 0.875_wp/35.16504_wp
z1_T0 = 1._wp/40._wp
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
zt = ctmp (ji,jj) * z1_T0
zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * z1_S0 )
ztm = tmask(ji,jj,1)
!
zn = ((((-2.1385727895e-01_wp*zt &
& - 2.7674419971e-01_wp*zs+1.0728094330_wp)*zt &
& + (2.6366564313_wp*zs+3.3546960647_wp)*zs-7.8012209473_wp)*zt &
& + ((1.8835586562_wp*zs+7.3949191679_wp)*zs-3.3937395875_wp)*zs-5.6414948432_wp)*zt &
& + (((3.5737370589_wp*zs-1.5512427389e+01_wp)*zs+2.4625741105e+01_wp)*zs &
& +1.9912291000e+01_wp)*zs-3.2191146312e+01_wp)*zt &
& + ((((5.7153204649e-01_wp*zs-3.0943149543_wp)*zs+9.3052495181_wp)*zs &
& -9.4528934807_wp)*zs+3.1066408996_wp)*zs-4.3504021262e-01_wp
!
zd = (2.0035003456_wp*zt &
& -3.4570358592e-01_wp*zs+5.6471810638_wp)*zt &
& + (1.5393993508_wp*zs-6.9394762624_wp)*zs+1.2750522650e+01_wp
!
ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
!
END_2D
!
IF( ln_timing ) CALL timing_stop('eos_pt_from_ct')
!
END FUNCTION eos_pt_from_ct
SUBROUTINE eos_fzp_2d( psal, ptf, pdep )
!!
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
REAL(wp), DIMENSION(:,:) , INTENT(out ) :: ptf ! freezing temperature [Celsius]
!!
CALL eos_fzp_2d_t( psal, ptf, is_tile(ptf), pdep )
END SUBROUTINE eos_fzp_2d
SUBROUTINE eos_fzp_2d_t( psal, ptf, kttf, pdep )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_fzp ***
!!
!! ** Purpose : Compute the freezing point temperature [Celsius]
!!
!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
!! ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z
!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
!!
!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kttf
REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: psal ! salinity [psu]
REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ), OPTIONAL :: pdep ! depth [m]
REAL(wp), DIMENSION(A2D_T(kttf)), INTENT(out ) :: ptf ! freezing temperature [Celsius]
!
INTEGER :: ji, jj ! dummy loop indices
REAL(wp) :: zt, zs, z1_S0 ! local scalars
!!----------------------------------------------------------------------
!
SELECT CASE ( neos )
!
CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
!
z1_S0 = 1._wp / 35.16504_wp
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zs= SQRT( ABS( psal(ji,jj) ) * z1_S0 ) ! square root salinity
ptf(ji,jj) = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs &
& - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp
END_2D
ptf(:,:) = ptf(:,:) * psal(:,:)
!
IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
!
CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
!
ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) &
& - 2.154996e-4_wp * psal(:,:) ) * psal(:,:)
!
IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'eos_fzp_2d:', ctmp1 )
!
END SELECT
!
END SUBROUTINE eos_fzp_2d_t
SUBROUTINE eos_fzp_0d( psal, ptf, pdep )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_fzp ***
!!
!! ** Purpose : Compute the freezing point temperature [Celsius]
!!
!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
!! ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z
!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
!!
!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
!!----------------------------------------------------------------------
REAL(wp), INTENT(in ) :: psal ! salinity [psu]
REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m]
REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celsius]
!
REAL(wp) :: zs ! local scalars
!!----------------------------------------------------------------------
!
SELECT CASE ( neos )
!
CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
!
zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity
ptf = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs &
& - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp
ptf = ptf * psal
!
IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
!
CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
!
ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) &
& - 2.154996e-4_wp * psal ) * psal
!
IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'eos_fzp_0d:', ctmp1 )
!
END SELECT
!
END SUBROUTINE eos_fzp_0d
SUBROUTINE eos_pen( pts, pab_pe, ppen, Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE eos_pen ***
!!
!! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
!!
!! ** Method : PE is defined analytically as the vertical
!! primitive of EOS times -g integrated between 0 and z>0.
!! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rho0 gz ) / rho0 gz - rd
!! = 1/z * /int_0^z rd dz - rd
!! where rd is the density anomaly (see eos_rhd function)
!! ab_pe are partial derivatives of PE anomaly with respect to T and S:
!! ab_pe(1) = - 1/(rho0 gz) * dPE/dT + drd/dT = - d(pen)/dT
!! ab_pe(2) = 1/(rho0 gz) * dPE/dS + drd/dS = d(pen)/dS
!!
!! ** Action : - pen : PE anomaly given at T-points
!! : - pab_pe : given at T-points
!! pab_pe(:,:,:,jp_tem) is alpha_pe
!! pab_pe(:,:,:,jp_sal) is beta_pe
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe
REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly
!
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zt , zh , zs , ztm ! local scalars
REAL(wp) :: zn , zn0, zn1, zn2 ! - -
!!----------------------------------------------------------------------
!
IF( ln_timing ) CALL timing_start('eos_pen')
!
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
!
! potential energy non-linear anomaly
zn2 = (PEN012)*zt &
& + PEN102*zs+PEN002
!
zn1 = ((PEN021)*zt &
& + PEN111*zs+PEN011)*zt &
& + (PEN201*zs+PEN101)*zs+PEN001
!
zn0 = ((((PEN040)*zt &
& + PEN130*zs+PEN030)*zt &
& + (PEN220*zs+PEN120)*zs+PEN020)*zt &
& + ((PEN310*zs+PEN210)*zs+PEN110)*zs+PEN010)*zt &
& + (((PEN400*zs+PEN300)*zs+PEN200)*zs+PEN100)*zs+PEN000
!
zn = ( zn2 * zh + zn1 ) * zh + zn0
!
ppen(ji,jj,jk) = zn * zh * r1_rho0 * ztm
!
! alphaPE non-linear anomaly
zn2 = APE002
!
zn1 = (APE011)*zt &
& + APE101*zs+APE001
!
zn0 = (((APE030)*zt &
& + APE120*zs+APE020)*zt &
& + (APE210*zs+APE110)*zs+APE010)*zt &
& + ((APE300*zs+APE200)*zs+APE100)*zs+APE000
!
zn = ( zn2 * zh + zn1 ) * zh + zn0
!
pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rho0 * ztm
!
! betaPE non-linear anomaly
zn2 = BPE002
!
zn1 = (BPE011)*zt &
& + BPE101*zs+BPE001
!
zn0 = (((BPE030)*zt &
& + BPE120*zs+BPE020)*zt &
& + (BPE210*zs+BPE110)*zs+BPE010)*zt &
& + ((BPE300*zs+BPE200)*zs+BPE100)*zs+BPE000
!
zn = ( zn2 * zh + zn1 ) * zh + zn0
!
pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rho0 * ztm
!
END_3D
!
CASE( np_seos ) !== Vallis (2006) simplified EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts(ji,jj,jk,jp_tem) - 10._wp ! 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) ! tmask
zn = 0.5_wp * zh * r1_rho0 * ztm
! ! Potential Energy
ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
! ! alphaPE
pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn
!
END_3D
!
CASE( np_leos ) !== linear ISOMIP EOS ==!
!
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
zt = pts(ji,jj,jk,jp_tem) - (-1._wp) ! temperature anomaly (t-T0)
zs = pts (ji,jj,jk,jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
ztm = tmask(ji,jj,jk) ! tmask
zn = 0.5_wp * zh * r1_rho0 * ztm
! ! Potential Energy
ppen(ji,jj,jk) = 0.
! ! alphaPE
pab_pe(ji,jj,jk,jp_tem) = 0.
pab_pe(ji,jj,jk,jp_sal) = 0.
!
END_3D
!
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for neos = ', neos
CALL ctl_stop( 'eos_pen:', ctmp1 )
!
END SELECT
!
IF( ln_timing ) CALL timing_stop('eos_pen')
!
END SUBROUTINE eos_pen
SUBROUTINE eos_init
!!----------------------------------------------------------------------
!! *** ROUTINE eos_init ***
!!
!! ** Purpose : initializations for the equation of state
!!
!! ** Method : Read the namelist nameos and control the parameters
!!----------------------------------------------------------------------
INTEGER :: ios ! local integer
INTEGER :: ioptio ! local integer
!!
NAMELIST/nameos/ ln_TEOS10, ln_EOS80, ln_SEOS, ln_LEOS, rn_a0, rn_b0, &
& rn_lambda1, rn_mu1, rn_lambda2, rn_mu2, rn_nu
!!----------------------------------------------------------------------
!
READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist' )
!
READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist' )
IF(lwm) WRITE( numond, nameos )
!
rho0 = 1027.51_wp !: volumic mass of reference [kg/m3]
rcp = 3974.00_wp !: heat capacity [J/K]
!
IF(lwp) THEN ! Control print
WRITE(numout,*)
WRITE(numout,*) 'eos_init : equation of state'
WRITE(numout,*) '~~~~~~~~'
WRITE(numout,*) ' Namelist nameos : Chosen the Equation Of Seawater (EOS)'
WRITE(numout,*) ' TEOS-10 : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_TEOS10 = ', ln_TEOS10
WRITE(numout,*) ' EOS-80 : rho=F(Potential Temperature, Practical Salinity, depth) ln_EOS80 = ', ln_EOS80
WRITE(numout,*) ' S-EOS : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_SEOS = ', ln_SEOS
WRITE(numout,*) ' L-EOS : rho=F(Potential Temperature, Practical Salinity, depth) ln_LEOS = ', ln_LEOS
ENDIF
! Check options for equation of state & set neos based on logical flags
ioptio = 0
IF( ln_TEOS10 ) THEN ; ioptio = ioptio+1 ; neos = np_teos10 ; ENDIF
IF( ln_EOS80 ) THEN ; ioptio = ioptio+1 ; neos = np_eos80 ; ENDIF
IF( ln_SEOS ) THEN ; ioptio = ioptio+1 ; neos = np_seos ; ENDIF
IF( ln_LEOS ) THEN ; ioptio = ioptio+1 ; neos = np_leos ; ENDIF
IF( ioptio /= 1 ) CALL ctl_stop("Exactly one equation of state option must be selected")
!
SELECT CASE( neos ) ! check option
!
CASE( np_teos10 ) !== polynomial TEOS-10 ==!
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
!
l_useCT = .TRUE. ! model temperature is Conservative temperature
!
rdeltaS = 32._wp
r1_S0 = 0.875_wp/35.16504_wp
r1_T0 = 1._wp/40._wp
r1_Z0 = 1.e-4_wp
!
EOS000 = 8.0189615746e+02_wp
EOS100 = 8.6672408165e+02_wp
EOS200 = -1.7864682637e+03_wp
EOS300 = 2.0375295546e+03_wp
EOS400 = -1.2849161071e+03_wp
EOS500 = 4.3227585684e+02_wp
EOS600 = -6.0579916612e+01_wp
EOS010 = 2.6010145068e+01_wp
EOS110 = -6.5281885265e+01_wp
EOS210 = 8.1770425108e+01_wp
EOS310 = -5.6888046321e+01_wp
EOS410 = 1.7681814114e+01_wp
EOS510 = -1.9193502195_wp
EOS020 = -3.7074170417e+01_wp
EOS120 = 6.1548258127e+01_wp
EOS220 = -6.0362551501e+01_wp
EOS320 = 2.9130021253e+01_wp
EOS420 = -5.4723692739_wp
EOS030 = 2.1661789529e+01_wp
EOS130 = -3.3449108469e+01_wp
EOS230 = 1.9717078466e+01_wp
EOS330 = -3.1742946532_wp
EOS040 = -8.3627885467_wp
EOS140 = 1.1311538584e+01_wp
EOS240 = -5.3563304045_wp
EOS050 = 5.4048723791e-01_wp
EOS150 = 4.8169980163e-01_wp
EOS060 = -1.9083568888e-01_wp
EOS001 = 1.9681925209e+01_wp
EOS101 = -4.2549998214e+01_wp
EOS201 = 5.0774768218e+01_wp
EOS301 = -3.0938076334e+01_wp
EOS401 = 6.6051753097_wp
EOS011 = -1.3336301113e+01_wp
EOS111 = -4.4870114575_wp
EOS211 = 5.0042598061_wp
EOS311 = -6.5399043664e-01_wp
EOS021 = 6.7080479603_wp
EOS121 = 3.5063081279_wp
EOS221 = -1.8795372996_wp
EOS031 = -2.4649669534_wp
EOS131 = -5.5077101279e-01_wp
EOS041 = 5.5927935970e-01_wp
EOS002 = 2.0660924175_wp
EOS102 = -4.9527603989_wp
EOS202 = 2.5019633244_wp
EOS012 = 2.0564311499_wp
EOS112 = -2.1311365518e-01_wp
EOS022 = -1.2419983026_wp
EOS003 = -2.3342758797e-02_wp
EOS103 = -1.8507636718e-02_wp
EOS013 = 3.7969820455e-01_wp
!
ALP000 = -6.5025362670e-01_wp
ALP100 = 1.6320471316_wp
ALP200 = -2.0442606277_wp
ALP300 = 1.4222011580_wp
ALP400 = -4.4204535284e-01_wp
ALP500 = 4.7983755487e-02_wp
ALP010 = 1.8537085209_wp
ALP110 = -3.0774129064_wp
ALP210 = 3.0181275751_wp
ALP310 = -1.4565010626_wp
ALP410 = 2.7361846370e-01_wp
ALP020 = -1.6246342147_wp
ALP120 = 2.5086831352_wp
ALP220 = -1.4787808849_wp
ALP320 = 2.3807209899e-01_wp
ALP030 = 8.3627885467e-01_wp
ALP130 = -1.1311538584_wp
ALP230 = 5.3563304045e-01_wp
ALP040 = -6.7560904739e-02_wp
ALP140 = -6.0212475204e-02_wp
ALP050 = 2.8625353333e-02_wp
ALP001 = 3.3340752782e-01_wp
ALP101 = 1.1217528644e-01_wp
ALP201 = -1.2510649515e-01_wp
ALP301 = 1.6349760916e-02_wp
ALP011 = -3.3540239802e-01_wp
ALP111 = -1.7531540640e-01_wp
ALP211 = 9.3976864981e-02_wp
ALP021 = 1.8487252150e-01_wp
ALP121 = 4.1307825959e-02_wp
ALP031 = -5.5927935970e-02_wp
ALP002 = -5.1410778748e-02_wp
ALP102 = 5.3278413794e-03_wp
ALP012 = 6.2099915132e-02_wp
ALP003 = -9.4924551138e-03_wp
!
BET000 = 1.0783203594e+01_wp
BET100 = -4.4452095908e+01_wp
BET200 = 7.6048755820e+01_wp
BET300 = -6.3944280668e+01_wp
BET400 = 2.6890441098e+01_wp
BET500 = -4.5221697773_wp
BET010 = -8.1219372432e-01_wp
BET110 = 2.0346663041_wp
BET210 = -2.1232895170_wp
BET310 = 8.7994140485e-01_wp
BET410 = -1.1939638360e-01_wp
BET020 = 7.6574242289e-01_wp
BET120 = -1.5019813020_wp
BET220 = 1.0872489522_wp
BET320 = -2.7233429080e-01_wp
BET030 = -4.1615152308e-01_wp
BET130 = 4.9061350869e-01_wp
BET230 = -1.1847737788e-01_wp
BET040 = 1.4073062708e-01_wp
BET140 = -1.3327978879e-01_wp
BET050 = 5.9929880134e-03_wp
BET001 = -5.2937873009e-01_wp
BET101 = 1.2634116779_wp
BET201 = -1.1547328025_wp
BET301 = 3.2870876279e-01_wp
BET011 = -5.5824407214e-02_wp
BET111 = 1.2451933313e-01_wp
BET211 = -2.4409539932e-02_wp
BET021 = 4.3623149752e-02_wp
BET121 = -4.6767901790e-02_wp
BET031 = -6.8523260060e-03_wp
BET002 = -6.1618945251e-02_wp
BET102 = 6.2255521644e-02_wp
BET012 = -2.6514181169e-03_wp
BET003 = -2.3025968587e-04_wp
!
PEN000 = -9.8409626043_wp
PEN100 = 2.1274999107e+01_wp
PEN200 = -2.5387384109e+01_wp
PEN300 = 1.5469038167e+01_wp
PEN400 = -3.3025876549_wp
PEN010 = 6.6681505563_wp
PEN110 = 2.2435057288_wp
PEN210 = -2.5021299030_wp
PEN310 = 3.2699521832e-01_wp
PEN020 = -3.3540239802_wp
PEN120 = -1.7531540640_wp
PEN220 = 9.3976864981e-01_wp
PEN030 = 1.2324834767_wp
PEN130 = 2.7538550639e-01_wp
PEN040 = -2.7963967985e-01_wp
PEN001 = -1.3773949450_wp
PEN101 = 3.3018402659_wp
PEN201 = -1.6679755496_wp
PEN011 = -1.3709540999_wp
PEN111 = 1.4207577012e-01_wp
PEN021 = 8.2799886843e-01_wp
PEN002 = 1.7507069098e-02_wp
PEN102 = 1.3880727538e-02_wp
PEN012 = -2.8477365341e-01_wp
!
APE000 = -1.6670376391e-01_wp
APE100 = -5.6087643219e-02_wp
APE200 = 6.2553247576e-02_wp
APE300 = -8.1748804580e-03_wp
APE010 = 1.6770119901e-01_wp
APE110 = 8.7657703198e-02_wp
APE210 = -4.6988432490e-02_wp
APE020 = -9.2436260751e-02_wp
APE120 = -2.0653912979e-02_wp
APE030 = 2.7963967985e-02_wp
APE001 = 3.4273852498e-02_wp
APE101 = -3.5518942529e-03_wp
APE011 = -4.1399943421e-02_wp
APE002 = 7.1193413354e-03_wp
!
BPE000 = 2.6468936504e-01_wp
BPE100 = -6.3170583896e-01_wp
BPE200 = 5.7736640125e-01_wp
BPE300 = -1.6435438140e-01_wp
BPE010 = 2.7912203607e-02_wp
BPE110 = -6.2259666565e-02_wp
BPE210 = 1.2204769966e-02_wp
BPE020 = -2.1811574876e-02_wp
BPE120 = 2.3383950895e-02_wp
BPE030 = 3.4261630030e-03_wp
BPE001 = 4.1079296834e-02_wp
BPE101 = -4.1503681096e-02_wp
BPE011 = 1.7676120780e-03_wp
BPE002 = 1.7269476440e-04_wp
!
CASE( np_eos80 ) !== polynomial EOS-80 formulation ==!
!
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> use of EOS-80 equation of state (pot. temp. and pract. salinity)'
!
l_useCT = .FALSE. ! model temperature is Potential temperature
rdeltaS = 20._wp
r1_S0 = 1._wp/40._wp
r1_T0 = 1._wp/40._wp
r1_Z0 = 1.e-4_wp
!
EOS000 = 9.5356891948e+02_wp
EOS100 = 1.7136499189e+02_wp
EOS200 = -3.7501039454e+02_wp
EOS300 = 5.1856810420e+02_wp
EOS400 = -3.7264470465e+02_wp
EOS500 = 1.4302533998e+02_wp
EOS600 = -2.2856621162e+01_wp
EOS010 = 1.0087518651e+01_wp
EOS110 = -1.3647741861e+01_wp
EOS210 = 8.8478359933_wp
EOS310 = -7.2329388377_wp
EOS410 = 1.4774410611_wp
EOS510 = 2.0036720553e-01_wp
EOS020 = -2.5579830599e+01_wp
EOS120 = 2.4043512327e+01_wp
EOS220 = -1.6807503990e+01_wp
EOS320 = 8.3811577084_wp
EOS420 = -1.9771060192_wp
EOS030 = 1.6846451198e+01_wp
EOS130 = -2.1482926901e+01_wp
EOS230 = 1.0108954054e+01_wp
EOS330 = -6.2675951440e-01_wp
EOS040 = -8.0812310102_wp
EOS140 = 1.0102374985e+01_wp
EOS240 = -4.8340368631_wp
EOS050 = 1.2079167803_wp
EOS150 = 1.1515380987e-01_wp
EOS060 = -2.4520288837e-01_wp
EOS001 = 1.0748601068e+01_wp
EOS101 = -1.7817043500e+01_wp
EOS201 = 2.2181366768e+01_wp
EOS301 = -1.6750916338e+01_wp
EOS401 = 4.1202230403_wp
EOS011 = -1.5852644587e+01_wp
EOS111 = -7.6639383522e-01_wp
EOS211 = 4.1144627302_wp
EOS311 = -6.6955877448e-01_wp
EOS021 = 9.9994861860_wp
EOS121 = -1.9467067787e-01_wp
EOS221 = -1.2177554330_wp
EOS031 = -3.4866102017_wp
EOS131 = 2.2229155620e-01_wp
EOS041 = 5.9503008642e-01_wp
EOS002 = 1.0375676547_wp
EOS102 = -3.4249470629_wp
EOS202 = 2.0542026429_wp
EOS012 = 2.1836324814_wp
EOS112 = -3.4453674320e-01_wp
EOS022 = -1.2548163097_wp
EOS003 = 1.8729078427e-02_wp
EOS103 = -5.7238495240e-02_wp
EOS013 = 3.8306136687e-01_wp
!
ALP000 = -2.5218796628e-01_wp
ALP100 = 3.4119354654e-01_wp
ALP200 = -2.2119589983e-01_wp
ALP300 = 1.8082347094e-01_wp
ALP400 = -3.6936026529e-02_wp
ALP500 = -5.0091801383e-03_wp
ALP010 = 1.2789915300_wp
ALP110 = -1.2021756164_wp
ALP210 = 8.4037519952e-01_wp
ALP310 = -4.1905788542e-01_wp
ALP410 = 9.8855300959e-02_wp
ALP020 = -1.2634838399_wp
ALP120 = 1.6112195176_wp
ALP220 = -7.5817155402e-01_wp
ALP320 = 4.7006963580e-02_wp
ALP030 = 8.0812310102e-01_wp
ALP130 = -1.0102374985_wp
ALP230 = 4.8340368631e-01_wp
ALP040 = -1.5098959754e-01_wp
ALP140 = -1.4394226233e-02_wp
ALP050 = 3.6780433255e-02_wp
ALP001 = 3.9631611467e-01_wp
ALP101 = 1.9159845880e-02_wp
ALP201 = -1.0286156825e-01_wp
ALP301 = 1.6738969362e-02_wp
ALP011 = -4.9997430930e-01_wp
ALP111 = 9.7335338937e-03_wp
ALP211 = 6.0887771651e-02_wp
ALP021 = 2.6149576513e-01_wp
ALP121 = -1.6671866715e-02_wp
ALP031 = -5.9503008642e-02_wp
ALP002 = -5.4590812035e-02_wp
ALP102 = 8.6134185799e-03_wp
ALP012 = 6.2740815484e-02_wp
ALP003 = -9.5765341718e-03_wp
!
BET000 = 2.1420623987_wp
BET100 = -9.3752598635_wp
BET200 = 1.9446303907e+01_wp
BET300 = -1.8632235232e+01_wp
BET400 = 8.9390837485_wp
BET500 = -1.7142465871_wp
BET010 = -1.7059677327e-01_wp
BET110 = 2.2119589983e-01_wp
BET210 = -2.7123520642e-01_wp
BET310 = 7.3872053057e-02_wp
BET410 = 1.2522950346e-02_wp
BET020 = 3.0054390409e-01_wp
BET120 = -4.2018759976e-01_wp
BET220 = 3.1429341406e-01_wp
BET320 = -9.8855300959e-02_wp
BET030 = -2.6853658626e-01_wp
BET130 = 2.5272385134e-01_wp
BET230 = -2.3503481790e-02_wp
BET040 = 1.2627968731e-01_wp
BET140 = -1.2085092158e-01_wp
BET050 = 1.4394226233e-03_wp
BET001 = -2.2271304375e-01_wp
BET101 = 5.5453416919e-01_wp
BET201 = -6.2815936268e-01_wp
BET301 = 2.0601115202e-01_wp
BET011 = -9.5799229402e-03_wp
BET111 = 1.0286156825e-01_wp
BET211 = -2.5108454043e-02_wp
BET021 = -2.4333834734e-03_wp
BET121 = -3.0443885826e-02_wp
BET031 = 2.7786444526e-03_wp
BET002 = -4.2811838287e-02_wp
BET102 = 5.1355066072e-02_wp
BET012 = -4.3067092900e-03_wp
BET003 = -7.1548119050e-04_wp
!
PEN000 = -5.3743005340_wp
PEN100 = 8.9085217499_wp
PEN200 = -1.1090683384e+01_wp
PEN300 = 8.3754581690_wp
PEN400 = -2.0601115202_wp
PEN010 = 7.9263222935_wp
PEN110 = 3.8319691761e-01_wp
PEN210 = -2.0572313651_wp
PEN310 = 3.3477938724e-01_wp
PEN020 = -4.9997430930_wp
PEN120 = 9.7335338937e-02_wp
PEN220 = 6.0887771651e-01_wp
PEN030 = 1.7433051009_wp
PEN130 = -1.1114577810e-01_wp
PEN040 = -2.9751504321e-01_wp
PEN001 = -6.9171176978e-01_wp
PEN101 = 2.2832980419_wp
PEN201 = -1.3694684286_wp
PEN011 = -1.4557549876_wp
PEN111 = 2.2969116213e-01_wp
PEN021 = 8.3654420645e-01_wp
PEN002 = -1.4046808820e-02_wp
PEN102 = 4.2928871430e-02_wp
PEN012 = -2.8729602515e-01_wp
!
APE000 = -1.9815805734e-01_wp
APE100 = -9.5799229402e-03_wp
APE200 = 5.1430784127e-02_wp
APE300 = -8.3694846809e-03_wp
APE010 = 2.4998715465e-01_wp
APE110 = -4.8667669469e-03_wp
APE210 = -3.0443885826e-02_wp
APE020 = -1.3074788257e-01_wp
APE120 = 8.3359333577e-03_wp
APE030 = 2.9751504321e-02_wp
APE001 = 3.6393874690e-02_wp
APE101 = -5.7422790533e-03_wp
APE011 = -4.1827210323e-02_wp
APE002 = 7.1824006288e-03_wp
!
BPE000 = 1.1135652187e-01_wp
BPE100 = -2.7726708459e-01_wp
BPE200 = 3.1407968134e-01_wp
BPE300 = -1.0300557601e-01_wp
BPE010 = 4.7899614701e-03_wp
BPE110 = -5.1430784127e-02_wp
BPE210 = 1.2554227021e-02_wp
BPE020 = 1.2166917367e-03_wp
BPE120 = 1.5221942913e-02_wp
BPE030 = -1.3893222263e-03_wp
BPE001 = 2.8541225524e-02_wp
BPE101 = -3.4236710714e-02_wp
BPE011 = 2.8711395266e-03_wp
BPE002 = 5.3661089288e-04_wp
!
CASE( np_seos ) !== Simplified EOS ==!
r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
IF(lwp) THEN
WRITE(numout,*)
WRITE(numout,*) ' ==>>> use of simplified eos: '
WRITE(numout,*) ' rhd(dT=T-10,dS=S-35,Z) = [-a0*(1+lambda1/2*dT+mu1*Z)*dT '
WRITE(numout,*) ' + b0*(1+lambda2/2*dT+mu2*Z)*dS - nu*dT*dS] / rho0'
WRITE(numout,*) ' with the following coefficients :'
WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1
WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2
WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1
WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2
WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu
WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization '
ENDIF
l_useCT = .TRUE. ! Use conservative temperature
!
CASE( np_leos ) !== Linear ISOMIP EOS ==!
r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
IF(lwp) THEN
WRITE(numout,*)
WRITE(numout,*) ' use of linear ISOMIP eos: rhd(dT=T-(-1),dS=S-(34.2),Z) = '
WRITE(numout,*) ' [ -a0*dT + b0*dS ]/rho0'
WRITE(numout,*)
WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
ENDIF
l_useCT = .TRUE. ! Use conservative temperature
!
CASE DEFAULT !== ERROR in neos ==!
WRITE(ctmp1,*) ' bad flag value for neos = ', neos, '. You should never see this error'
CALL ctl_stop( ctmp1 )
!
END SELECT
!
rho0_rcp = rho0 * rcp
r1_rho0 = 1._wp / rho0
r1_rcp = 1._wp / rcp
r1_rho0_rcp = 1._wp / rho0_rcp
!
IF(lwp) THEN
IF( l_useCT ) THEN
WRITE(numout,*)
WRITE(numout,*) ' ==>>> model uses Conservative Temperature'
WRITE(numout,*) ' Important: model must be initialized with CT and SA fields'
ELSE
WRITE(numout,*)
WRITE(numout,*) ' ==>>> model does not use Conservative Temperature'
ENDIF
ENDIF
!
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' Associated physical constant'
IF(lwp) WRITE(numout,*) ' volumic mass of reference rho0 = ', rho0 , ' kg/m^3'
IF(lwp) WRITE(numout,*) ' 1. / rho0 r1_rho0 = ', r1_rho0, ' m^3/kg'
IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin'
IF(lwp) WRITE(numout,*) ' rho0 * rcp rho0_rcp = ', rho0_rcp
IF(lwp) WRITE(numout,*) ' 1. / ( rho0 * rcp ) r1_rho0_rcp = ', r1_rho0_rcp
!
END SUBROUTINE eos_init
!!======================================================================
END MODULE eosbn2
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