MODULE eosbn2 !!============================================================================== !! *** MODULE eosbn2 *** !! Ocean diagnostic variable : equation of state - in situ and potential 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 !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA !! - ! 2010-10 (G. Nurser, G. Madec) add eos_alpbet used in ldfslp !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! 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 !! eos_bn2 : Compute the Brunt-Vaisala frequency !! eos_alpbet : calculates the in situ thermal and haline expansion coeff. !! tfreez : Compute the surface freezing temperature !! eos_init : set eos parameters (namelist) !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE zdfddm ! vertical physics: double diffusion USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE prtctl ! Print control IMPLICIT NONE PRIVATE ! !! * Interface INTERFACE eos MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d END INTERFACE INTERFACE bn2 MODULE PROCEDURE eos_bn2 END INTERFACE PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules PUBLIC eos_init ! called by istate module PUBLIC bn2 ! called by step module PUBLIC eos_alpbet ! called by ldfslp module PUBLIC tfreez ! called by sbcice_... modules ! !!* Namelist (nameos) * INTEGER , PUBLIC :: nn_eos = 0 !: = 0/1/2 type of eq. of state and Brunt-Vaisala frequ. REAL(wp), PUBLIC :: rn_alpha = 2.0e-4_wp !: thermal expension coeff. (linear equation of state) REAL(wp), PUBLIC :: rn_beta = 7.7e-4_wp !: saline expension coeff. (linear equation of state) REAL(wp), PUBLIC :: ralpbet !: alpha / beta ratio !! * Control permutation of array indices # include "dom_oce_ftrans.h90" # include "zdfddm_ftrans.h90" !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE eos_insitu( pts, prd ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) from !! potential temperature and salinity using an equation of state !! defined through the namelist parameter nn_eos. !! !! ** Method : 3 cases: !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! nn_eos = 1 : linear equation of state function of temperature only !! prd(t) = 0.0285 - rn_alpha * t !! nn_eos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. !! Note that no boundary condition problem occurs in this routine !! as pts are defined over the whole domain. !! !! ** Action : compute prd , the in situ density (no units) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !!---------------------------------------------------------------------- USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released USE wrk_nemo, ONLY: zws => wrk_3d_1 ! 3D workspace !! !FTRANS zws :I :I :z !FTRANS pts :I :I :z :I !FTRANS prd :I :I :z REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! 2 : salinity [psu] REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-] !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt , zs , zh , zsr ! local scalars REAL(wp) :: zr1, zr2, zr3, zr4 ! - - REAL(wp) :: zrhop, ze, zbw, zb ! - - REAL(wp) :: zd , zc , zaw, za ! - - REAL(wp) :: zb1, za1, zkw, zk0 ! - - REAL(wp) :: zrau0r ! - - !!---------------------------------------------------------------------- IF( wrk_in_use(3, 1) ) THEN CALL ctl_stop('eos_insitu: requested workspace array unavailable') ; RETURN ENDIF SELECT CASE( nn_eos ) ! CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! zrau0r = 1.e0 / rau0 !CDIR NOVERRCHK zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) ) ! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 #else DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi #endif zt = pts (ji,jj,jk,jp_tem) zs = pts (ji,jj,jk,jp_sal) zh = fsdept(ji,jj,jk) ! depth zsr= zws (ji,jj,jk) ! square root salinity ! ! compute volumic mass pure water at atm pressure zr1= ( ( ( ( 6.536332e-9_wp *zt - 1.120083e-6_wp )*zt + 1.001685e-4_wp )*zt & & -9.095290e-3_wp )*zt + 6.793952e-2_wp )*zt + 999.842594_wp ! seawater volumic mass atm pressure zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & & -4.0899e-3_wp ) *zt+0.824493_wp zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp zr4= 4.8314e-4_wp ! ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! ! add the compression terms ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp zb = zbw + ze * zs ! zd = -2.042967e-2_wp zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp za = ( zd*zsr + zc ) *zs + zaw ! zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp za1= ( ( 2.326469e-3_wp*zt+1.553190_wp) *zt-65.00517_wp ) *zt+1044.077_wp zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp zk0= ( zb1*zsr + za1 )*zs + zkw ! ! masked in situ density anomaly prd(ji,jj,jk) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & & - rau0 ) * zrau0r * tmask(ji,jj,jk) END DO END DO END DO ! CASE( 1 ) !== Linear formulation function of temperature only ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 prd(ji,jj,jk) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jk,jp_tem) ) * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 1, jpkm1 prd(:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) END DO #endif ! CASE( 2 ) !== Linear formulation function of temperature and salinity ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 prd(ji,jj,jk) = ( rn_beta * pts(ji,jj,jk,jp_sal) - rn_alpha * pts(ji,jj,jk,jp_tem) ) * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 1, jpkm1 prd(:,:,jk) = ( rn_beta * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) END DO #endif ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos : ', ovlap=1, kdim=jpk ) ! IF( wrk_not_released(3, 1) ) CALL ctl_stop('eos_insitu: failed to release workspace array') ! !! * Reset control of array index permutation !FTRANS CLEAR # include "dom_oce_ftrans.h90" # include "zdfddm_ftrans.h90" END SUBROUTINE eos_insitu SUBROUTINE eos_insitu_pot( pts, prd, prhop ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu_pot *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) and the !! potential volumic mass (Kg/m3) from potential temperature and !! salinity fields using an equation of state defined through the !! namelist parameter nn_eos. !! !! ** Method : !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! rhop(t,s) = rho(t,s,0) !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! !! nn_eos = 1 : linear equation of state function of temperature only !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - rn_alpha * t !! rhop(t,s) = rho(t,s) !! !! nn_eos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 !! = rn_beta * s - rn_alpha * tn - 1. !! rhop(t,s) = rho(t,s) !! Note that no boundary condition problem occurs in this routine !! as (tn,sn) or (ta,sa) are defined over the whole domain. !! !! ** Action : - prd , the in situ density (no units) !! - prhop, the potential volumic mass (Kg/m3) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !! Brown and Campana, Mon. Weather Rev., 1978 !!---------------------------------------------------------------------- USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released USE wrk_nemo, ONLY: zws => wrk_3d_1 ! 3D workspace !! !FTRANS zws :I :I :z !FTRANS pts :I :I :z :I !FTRANS prd :I :I :z !FTRANS prhop :I :I :z !!DCSE NEMO: This style defeats ftrans ! REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! ! 2 : salinity [psu] ! REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prd ! in situ density [-] ! REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prhop ! potential density (surface referenced) REAL(wp), INTENT(in ) :: pts(jpi,jpj,jpk,jpts) ! 1 : potential temperature [Celcius] ! ! 2 : salinity [psu] REAL(wp), INTENT( out) :: prd(jpi,jpj,jpk) ! in situ density [-] REAL(wp), INTENT( out) :: prhop(jpi,jpj,jpk) ! potential density (surface referenced) ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw ! local scalars REAL(wp) :: zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, zrau0r ! - - !!---------------------------------------------------------------------- IF( wrk_in_use(3, 1) ) THEN CALL ctl_stop('eos_insitu_pot: requested workspace array unavailable') ; RETURN ENDIF SELECT CASE ( nn_eos ) ! CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! zrau0r = 1.e0 / rau0 !CDIR NOVERRCHK zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) ) ! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 #else DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi #endif zt = pts (ji,jj,jk,jp_tem) zs = pts (ji,jj,jk,jp_sal) zh = fsdept(ji,jj,jk) ! depth zsr= zws (ji,jj,jk) ! square root salinity ! ! compute volumic mass pure water at atm pressure zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt & & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp ! seawater volumic mass atm pressure zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & & -4.0899e-3_wp ) *zt+0.824493_wp zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp zr4= 4.8314e-4_wp ! ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! ! save potential volumic mass prhop(ji,jj,jk) = zrhop * tmask(ji,jj,jk) ! ! add the compression terms ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp zb = zbw + ze * zs ! zd = -2.042967e-2_wp zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp za = ( zd*zsr + zc ) *zs + zaw ! zb1= ( -0.1909078_wp *zt+7.390729_wp ) *zt-55.87545_wp za1= ( ( 2.326469e-3_wp*zt+1.553190_wp ) *zt-65.00517_wp ) *zt + 1044.077_wp zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp zk0= ( zb1*zsr + za1 )*zs + zkw ! ! masked in situ density anomaly prd(ji,jj,jk) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & & - rau0 ) * zrau0r * tmask(ji,jj,jk) END DO END DO END DO ! CASE( 1 ) !== Linear formulation = F( temperature ) ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 prd (ji,jj,jk) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jk,jp_tem) ) * tmask(ji,jj,jk) prhop(ji,jj,jk) = ( 1.e0_wp + prd(ji,jj,jk) ) * rau0 * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 1, jpkm1 prd (:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) prhop(:,:,jk) = ( 1.e0_wp + prd (:,:,jk) ) * rau0 * tmask(:,:,jk) END DO #endif ! CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpkm1 prd (ji,jj,jk) = ( rn_beta * pts(ji,jj,jk,jp_sal) - rn_alpha * pts(ji,jj,jk,jp_tem) ) * tmask(ji,jj,jk) prhop(ji,jj,jk) = ( 1.e0_wp + prd(ji,jj,jk) ) * rau0 * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 1, jpkm1 prd (:,:,jk) = ( rn_beta * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) prhop(:,:,jk) = ( 1.e0_wp + prd (:,:,jk) ) * rau0 * tmask(:,:,jk) END DO #endif ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-p: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk ) ! IF( wrk_not_released(3, 1) ) CALL ctl_stop('eos_insitu_pot: failed to release workspace array') ! !! * Reset control of array index permutation !FTRANS CLEAR # include "dom_oce_ftrans.h90" # include "zdfddm_ftrans.h90" END SUBROUTINE eos_insitu_pot SUBROUTINE eos_insitu_2d( pts, pdep, prd ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu_2d *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) from !! potential temperature and salinity using an equation of state !! defined through the namelist parameter nn_eos. * 2D field case !! !! ** Method : !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! nn_eos = 1 : linear equation of state function of temperature only !! prd(t) = 0.0285 - rn_alpha * t !! nn_eos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. !! Note that no boundary condition problem occurs in this routine !! as pts are defined over the whole domain. !! !! ** Action : - prd , the in situ density (no units) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !!---------------------------------------------------------------------- USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released USE wrk_nemo, ONLY: zws => wrk_2d_5 ! 2D workspace !! REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! 2 : salinity [psu] REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: pdep ! depth [m] REAL(wp), DIMENSION(jpi,jpj) , INTENT( out) :: prd ! in situ density !! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw ! temporary scalars REAL(wp) :: zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, zmask ! - - !!---------------------------------------------------------------------- IF( wrk_in_use(2, 5) ) THEN CALL ctl_stop('eos_insitu_2d: requested workspace array unavailable') ; RETURN ENDIF prd(:,:) = 0._wp SELECT CASE( nn_eos ) ! CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! ! !CDIR NOVERRCHK DO jj = 1, jpjm1 !CDIR NOVERRCHK DO ji = 1, fs_jpim1 ! vector opt. zws(ji,jj) = SQRT( ABS( pts(ji,jj,jp_sal) ) ) END DO END DO DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. #if defined key_z_first zmask = tmask_1(ji,jj) ! land/sea bottom mask = surf. mask #else zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask #endif zt = pts (ji,jj,jp_tem) ! interpolated T zs = pts (ji,jj,jp_sal) ! interpolated S zsr = zws (ji,jj) ! square root of interpolated S zh = pdep (ji,jj) ! depth at the partial step level ! ! compute volumic mass pure water at atm pressure zr1 = ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt & & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp ! seawater volumic mass atm pressure zr2 = ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp )*zt+7.6438e-5_wp ) *zt & & -4.0899e-3_wp ) *zt+0.824493_wp zr3 = ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp zr4 = 4.8314e-4_wp ! ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! ! add the compression terms ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp zb = zbw + ze * zs ! zd = -2.042967e-2_wp zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt -4.721788_wp za = ( zd*zsr + zc ) *zs + zaw ! zb1= (-0.1909078_wp *zt+7.390729_wp ) *zt-55.87545_wp za1= ( ( 2.326469e-3_wp*zt+1.553190_wp ) *zt-65.00517_wp ) *zt+1044.077_wp zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt & & +2098.925_wp ) *zt+190925.6_wp zk0= ( zb1*zsr + za1 )*zs + zkw ! ! masked in situ density anomaly prd(ji,jj) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) - rau0 ) / rau0 * zmask END DO END DO ! CASE( 1 ) !== Linear formulation = F( temperature ) ==! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. #if defined key_z_first prd(ji,jj) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jp_tem) ) * tmask_1(ji,jj) #else prd(ji,jj) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1) #endif END DO END DO ! CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. #if defined key_z_first prd(ji,jj) = ( rn_beta * pts(ji,jj,jp_sal) - rn_alpha * pts(ji,jj,jp_tem) ) * tmask_1(ji,jj) #else prd(ji,jj) = ( rn_beta * pts(ji,jj,jp_sal) - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1) #endif END DO END DO ! END SELECT IF(ln_ctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' ) ! IF( wrk_not_released(2, 5) ) CALL ctl_stop('eos_insitu_2d: failed to release workspace array') ! END SUBROUTINE eos_insitu_2d SUBROUTINE eos_bn2( pts, pn2 ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_bn2 *** !! !! ** Purpose : Compute the local Brunt-Vaisala frequency at the time- !! step of the input arguments !! !! ** Method : !! * nn_eos = 0 : UNESCO sea water properties !! The brunt-vaisala frequency is computed using the polynomial !! polynomial expression of McDougall (1987): !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is !! computed and used in zdfddm module : !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) !! * nn_eos = 1 : linear equation of state (temperature only) !! N^2 = grav * rn_alpha * dk[ t ]/e3w !! * nn_eos = 2 : linear equation of state (temperature & salinity) !! N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w !! The use of potential density to compute N^2 introduces e r r o r !! in the sign of N^2 at great depths. We recommand the use of !! nn_eos = 0, except for academical studies. !! Macro-tasked on horizontal slab (jk-loop) !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr !! and is never used at this level. !! !! ** Action : - pn2 : the brunt-vaisala frequency !! !! References : McDougall, J. Phys. Oceanogr., 17, 1950-1964, 1987. !!---------------------------------------------------------------------- !FTRANS pts :I :I :z :I !FTRANS pn2 :I :I :z !!DCSE_NEMO: This style defeats ftrans ! REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! ! 2 : salinity [psu] ! REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency [s-1] REAL(wp), INTENT(in ) :: pts(jpi,jpj,jpk,jpts) ! 1 : potential temperature [Celcius] ! ! 2 : salinity [psu] REAL(wp), INTENT( out) :: pn2(jpi,jpj,jpk) ! Brunt-Vaisala frequency [s-1] !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zgde3w, zt, zs, zh, zalbet, zbeta ! local scalars #if defined key_zdfddm REAL(wp) :: zds ! local scalars #endif !!---------------------------------------------------------------------- ! pn2 : interior points only (2=< jk =< jpkm1 ) ! -------------------------- ! SELECT CASE( nn_eos ) ! CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 2, jpkm1 #else DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi #endif zgde3w = grav / fse3w(ji,jj,jk) zt = 0.5 * ( pts(ji,jj,jk,jp_tem) + pts(ji,jj,jk-1,jp_tem) ) ! potential temperature at w-pt zs = 0.5 * ( pts(ji,jj,jk,jp_sal) + pts(ji,jj,jk-1,jp_sal) ) - 35.0 ! salinity anomaly (s-35) at w-pt zh = fsdepw(ji,jj,jk) ! depth in meters at w-point ! zalbet = ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & ! ratio alpha/beta & - 0.203814e-03_wp ) * zt & & + 0.170907e-01_wp ) * zt & & + 0.665157e-01_wp & & + ( - 0.678662e-05_wp * zs & & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & & + ( ( - 0.302285e-13_wp * zh & & - 0.251520e-11_wp * zs & & + 0.512857e-12_wp * zt * zt ) * zh & & - 0.164759e-06_wp * zs & & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & & + 0.380374e-04_wp ) * zh ! zbeta = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt & ! beta & - 0.301985e-05_wp ) * zt & & + 0.785567e-03_wp & & + ( 0.515032e-08_wp * zs & & + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs & & + ( ( 0.121551e-17_wp * zh & & - 0.602281e-15_wp * zs & & - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh & & + 0.408195e-10_wp * zs & & + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt & & - 0.121555e-07_wp ) * zh ! pn2(ji,jj,jk) = zgde3w * zbeta * tmask(ji,jj,jk) & ! N^2 & * ( zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) & & - ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) #if defined key_zdfddm ! !!bug **** caution a traiter zds=dk[S]= 0 !!!! zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ! Rrau = (alpha / beta) (dk[t] / dk[s]) IF ( ABS( zds) <= 1.e-20_wp ) zds = 1.e-20_wp rrau(ji,jj,jk) = zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds #endif END DO END DO END DO ! CASE( 1 ) !== Linear formulation = F( temperature ) ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 2, jpkm1 pn2(ji,jj,jk) = grav * rn_alpha * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) & & / fse3w(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 2, jpkm1 pn2(:,:,jk) = grav * rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) ) / fse3w(:,:,jk) * tmask(:,:,jk) END DO #endif ! CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 2, jpkm1 pn2(ji,jj,jk) = grav * ( rn_alpha * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) & & - rn_beta * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) & & / fse3w(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO #else DO jk = 2, jpkm1 pn2(:,:,jk) = grav * ( rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) ) & & - rn_beta * ( pts(:,:,jk-1,jp_sal) - pts(:,:,jk,jp_sal) ) ) & & / fse3w(:,:,jk) * tmask(:,:,jk) END DO #endif #if defined key_zdfddm #if defined key_z_first DO jj = 1, jpj ! Rrau = (alpha / beta) (dk[t] / dk[s]) DO ji = 1, jpi DO jk = 2, jpkm1 #else DO jk = 2, jpkm1 ! Rrau = (alpha / beta) (dk[t] / dk[s]) DO jj = 1, jpj DO ji = 1, jpi #endif zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) IF ( ABS( zds ) <= 1.e-20_wp ) zds = 1.e-20_wp rrau(ji,jj,jk) = ralpbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds END DO END DO END DO #endif END SELECT IF(ln_ctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', ovlap=1, kdim=jpk ) #if defined key_zdfddm IF(ln_ctl) CALL prt_ctl( tab3d_1=rrau, clinfo1=' rrau : ', ovlap=1, kdim=jpk ) #endif ! !! * Reset control of array index permutation !FTRANS CLEAR # include "dom_oce_ftrans.h90" # include "zdfddm_ftrans.h90" END SUBROUTINE eos_bn2 SUBROUTINE eos_alpbet( pts, palph, pbeta ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_grif *** !! !! ** Purpose : Calculates the thermal and haline expansion coefficients at T-points. !! !! ** Method : calculates alpha and beta at T-points !! * nn_eos = 0 : UNESCO sea water properties !! The brunt-vaisala frequency is computed using the polynomial !! polynomial expression of McDougall (1987): !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is !! computed and used in zdfddm module : !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) !! * nn_eos = 1 : linear equation of state (temperature only) !! N^2 = grav * rn_alpha * dk[ t ]/e3w !! * nn_eos = 2 : linear equation of state (temperature & salinity) !! N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w !! * nn_eos = 3 : Jackett JAOT 2003 ??? !! !! ** Action : - palph, pbeta : thermal and haline expansion coeff. at T-point !!---------------------------------------------------------------------- !FTRANS pts :I :I :z :I !FTRANS palph :I :I :z !FTRANS pbeta :I :I :z !!DCSE_NEMO: This style defeats ftrans ! REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity ! REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: palph, pbeta ! thermal & haline expansion coeff. REAL(wp), INTENT(in ) :: pts(jpi,jpj,jpk,jpts) ! pot. temperature & salinity REAL(wp), INTENT( out) :: palph(jpi,jpj,jpk) ! thermal expansion coeff. REAL(wp), INTENT( out) :: pbeta(jpi,jpj,jpk) ! haline expansion coeff. ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt, zs, zh ! local scalars !!---------------------------------------------------------------------- ! SELECT CASE ( nn_eos ) ! CASE ( 0 ) ! Jackett and McDougall (1994) formulation #if defined key_z_first DO jj = 1, jpj DO ji = 1, jpi DO jk = 1, jpk #else DO jk = 1, jpk DO jj = 1, jpj DO ji = 1, jpi #endif zt = pts(ji,jj,jk,jp_tem) ! potential temperature zs = pts(ji,jj,jk,jp_sal) - 35._wp ! salinity anomaly (s-35) zh = fsdept(ji,jj,jk) ! depth in meters ! pbeta(ji,jj,jk) = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt & & - 0.301985e-05_wp ) * zt & & + 0.785567e-03_wp & & + ( 0.515032e-08_wp * zs & & + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs & & + ( ( 0.121551e-17_wp * zh & & - 0.602281e-15_wp * zs & & - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh & & + 0.408195e-10_wp * zs & & + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt & & - 0.121555e-07_wp ) * zh ! palph(ji,jj,jk) = - pbeta(ji,jj,jk) * & & ((( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & & - 0.203814e-03_wp ) * zt & & + 0.170907e-01_wp ) * zt & & + 0.665157e-01_wp & & + ( - 0.678662e-05_wp * zs & & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & & + ( ( - 0.302285e-13_wp * zh & & - 0.251520e-11_wp * zs & & + 0.512857e-12_wp * zt * zt ) * zh & & - 0.164759e-06_wp * zs & & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & & + 0.380374e-04_wp ) * zh) END DO END DO END DO ! CASE ( 1 ) palph(:,:,:) = - rn_alpha pbeta(:,:,:) = 0._wp ! CASE ( 2 ) palph(:,:,:) = - rn_alpha pbeta(:,:,:) = rn_beta ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! !! * Reset control of array index permutation !FTRANS CLEAR # include "dom_oce_ftrans.h90" # include "zdfddm_ftrans.h90" END SUBROUTINE eos_alpbet FUNCTION tfreez( psal ) RESULT( ptf ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : Compute the sea surface freezing temperature [Celcius] !! !! ** Method : UNESCO freezing point at the surface (pressure = 0???) !! freezing point [Celcius]=(-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s-7.53e-4*p !! checkvalue: tf= -2.588567 Celsius for s=40.0psu, p=500. decibars !! !! Reference : UNESCO tech. papers in the marine science no. 28. 1978 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] ! Leave result array automatic rather than making explicitly allocated REAL(wp), DIMENSION(jpi,jpj) :: ptf ! freezing temperature [Celcius] !!---------------------------------------------------------------------- ! ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) & & - 2.154996e-4_wp * psal(:,:) ) * psal(:,:) ! END FUNCTION tfreez SUBROUTINE eos_init !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : initializations for the equation of state !! !! ** Method : Read the namelist nameos and control the parameters !!---------------------------------------------------------------------- NAMELIST/nameos/ nn_eos, rn_alpha, rn_beta !!---------------------------------------------------------------------- ! REWIND( numnam ) ! Read Namelist nameos : equation of state READ ( numnam, nameos ) ! IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'eos_init : equation of state' WRITE(numout,*) '~~~~~~~~' WRITE(numout,*) ' Namelist nameos : set eos parameters' WRITE(numout,*) ' flag for eq. of state and N^2 nn_eos = ', nn_eos WRITE(numout,*) ' thermal exp. coef. (linear) rn_alpha = ', rn_alpha WRITE(numout,*) ' saline exp. coef. (linear) rn_beta = ', rn_beta ENDIF ! SELECT CASE( nn_eos ) ! check option ! CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of Jackett & McDougall (1994) equation of state and' IF(lwp) WRITE(numout,*) ' McDougall (1987) Brunt-Vaisala frequency' ! CASE( 1 ) !== Linear formulation = F( temperature ) ==! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of linear eos rho(T) = rau0 * ( 1.0285 - rn_alpha * T )' IF( lk_zdfddm ) CALL ctl_stop( ' double diffusive mixing parameterization requires', & & ' that T and S are used as state variables' ) ! CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! ralpbet = rn_alpha / rn_beta IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of linear eos rho(T,S) = rau0 * ( rn_beta * S - rn_alpha * T )' ! CASE DEFAULT !== ERROR in nn_eos ==! WRITE(ctmp1,*) ' bad flag value for nn_eos = ', nn_eos CALL ctl_stop( ctmp1 ) ! END SELECT ! END SUBROUTINE eos_init !!====================================================================== END MODULE eosbn2