| 1 | MODULE eosbn2 |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE eosbn2 *** |
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| 4 | !! Ocean diagnostic variable : equation of state - in situ and potential density |
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| 5 | !! - Brunt-Vaisala frequency |
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| 6 | !!============================================================================== |
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| 7 | |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | !! eos : generic interface of the equation of state |
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| 10 | !! eos_insitu : Compute the in situ density |
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| 11 | !! eos_insitu_pot : Compute the insitu and surface referenced potential |
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| 12 | !! volumic mass |
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| 13 | !! eos_insitu_2d : Compute the in situ density for 2d fields |
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| 14 | !! eos_bn2 : Compute the Brunt-Vaisala frequency |
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| 15 | !! eos_init : set eos parameters (namelist) |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | !! * Modules used |
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| 18 | USE dom_oce ! ocean space and time domain |
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| 19 | USE phycst ! physical constants |
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| 20 | USE in_out_manager ! I/O manager |
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| 21 | USE zdfddm ! vertical physics: double diffusion |
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| 22 | USE prtctl ! Print control |
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| 23 | |
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| 24 | IMPLICIT NONE |
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| 25 | PRIVATE |
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| 26 | |
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| 27 | !! * Interface |
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| 28 | INTERFACE eos |
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| 29 | MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d |
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| 30 | END INTERFACE |
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| 31 | INTERFACE bn2 |
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| 32 | MODULE PROCEDURE eos_bn2 |
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| 33 | END INTERFACE |
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| 34 | |
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| 35 | !! * Routine accessibility |
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| 36 | PUBLIC eos ! called by step.F90, inidtr.F90, tranpc.F90 and intgrd.F90 |
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| 37 | PUBLIC bn2 ! called by step.F90 |
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| 38 | PUBLIC eos_init ! called by step.F90 |
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| 39 | |
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| 40 | !! * Share module variables |
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| 41 | INTEGER , PUBLIC :: & !: nameos : ocean physical parameters |
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| 42 | neos = 0, & !: = 0/1/2 type of eq. of state and Brunt-Vaisala frequ. |
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| 43 | neos_init = 0 !: control flag for initialization |
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| 44 | |
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| 45 | REAL(wp), PUBLIC :: & !: nameos : ocean physical parameters |
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| 46 | ralpha = 2.0e-4, & !: thermal expension coeff. (linear equation of state) |
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| 47 | rbeta = 7.7e-4 !: saline expension coeff. (linear equation of state) |
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| 48 | |
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| 49 | !! * Substitutions |
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| 50 | # include "domzgr_substitute.h90" |
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| 51 | # include "vectopt_loop_substitute.h90" |
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| 52 | !!---------------------------------------------------------------------- |
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| 53 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 54 | !! $Header$ |
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| 55 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 56 | !!---------------------------------------------------------------------- |
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| 57 | |
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| 58 | CONTAINS |
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| 59 | |
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| 60 | SUBROUTINE eos_insitu ( ptem, psal, prd ) |
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| 61 | !!---------------------------------------------------------------------- |
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| 62 | !! *** ROUTINE eos_insitu *** |
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| 63 | !! |
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| 64 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) from |
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| 65 | !! potential temperature and salinity using an equation of state |
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| 66 | !! defined through the namelist parameter neos. |
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| 67 | !! |
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| 68 | !! ** Method : 3 cases: |
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| 69 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
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| 70 | !! the in situ density is computed directly as a function of |
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| 71 | !! potential temperature relative to the surface (the opa t |
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| 72 | !! variable), salt and pressure (assuming no pressure variation |
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| 73 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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| 74 | !! is approximated by the depth in meters. |
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| 75 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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| 76 | !! with pressure p decibars |
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| 77 | !! potential temperature t deg celsius |
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| 78 | !! salinity s psu |
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| 79 | !! reference volumic mass rau0 kg/m**3 |
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| 80 | !! in situ volumic mass rho kg/m**3 |
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| 81 | !! in situ density anomalie prd no units |
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| 82 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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| 83 | !! t = 40 deg celcius, s=40 psu |
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| 84 | !! neos = 1 : linear equation of state function of temperature only |
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| 85 | !! prd(t) = 0.0285 - ralpha * t |
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| 86 | !! neos = 2 : linear equation of state function of temperature and |
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| 87 | !! salinity |
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| 88 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
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| 89 | !! Note that no boundary condition problem occurs in this routine |
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| 90 | !! as (ptem,psal) are defined over the whole domain. |
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| 91 | !! |
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| 92 | !! ** Action : compute prd , the in situ density (no units) |
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| 93 | !! |
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| 94 | !! References : |
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| 95 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
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| 96 | !! |
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| 97 | !! History : |
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| 98 | !! ! 89-03 (o. Marti) Original code |
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| 99 | !! ! 94-08 (G. Madec) |
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| 100 | !! ! 96-01 (G. Madec) statement function for e3 |
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| 101 | !! ! 97-07 (G. Madec) introduction of neos, OPA8.1 |
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| 102 | !! ! 97-07 (G. Madec) density instead of volumic mass |
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| 103 | !! ! 99-02 (G. Madec, N. Grima) semi-implicit pressure gradient |
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| 104 | !! ! 01-09 (M. Ben Jelloul) bugfix |
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| 105 | !!---------------------------------------------------------------------- |
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| 106 | !! * Arguments |
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| 107 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
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| 108 | ptem, & ! potential temperature |
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| 109 | psal ! salinity |
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| 110 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
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| 111 | prd ! potential density (surface referenced) |
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| 112 | |
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| 113 | !! * Local declarations |
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| 114 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 115 | REAL(wp) :: & |
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| 116 | zt , zs , zh , zsr, & ! temporary scalars |
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| 117 | zr1, zr2, zr3, zr4, & ! " " |
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| 118 | zrhop, ze, zbw, zb, & ! " " |
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| 119 | zd , zc , zaw, za , & ! " " |
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| 120 | zb1, za1, zkw, zk0 ! " " |
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| 121 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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| 122 | zws ! temporary workspace |
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| 123 | !!---------------------------------------------------------------------- |
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| 124 | |
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| 125 | |
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| 126 | ! initialization (in not already done) |
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| 127 | IF( neos_init == 0 ) CALL eos_init |
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| 128 | |
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| 129 | |
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| 130 | SELECT CASE ( neos ) |
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| 131 | |
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| 132 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
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| 133 | |
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| 134 | !CDIR NOVERRCHK |
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| 135 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
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| 136 | |
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| 137 | ! ! =============== |
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| 138 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 139 | ! ! =============== |
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| 140 | DO jj = 1, jpj |
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| 141 | DO ji = 1, jpi |
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| 142 | zt = ptem(ji,jj,jk) |
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| 143 | zs = psal(ji,jj,jk) |
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| 144 | ! depth |
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| 145 | zh = fsdept(ji,jj,jk) |
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| 146 | ! square root salinity |
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| 147 | zsr= zws(ji,jj,jk) |
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| 148 | ! compute volumic mass pure water at atm pressure |
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| 149 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
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| 150 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
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| 151 | ! seawater volumic mass atm pressure |
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| 152 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
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| 153 | -4.0899e-3 ) *zt+0.824493 |
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| 154 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
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| 155 | zr4= 4.8314e-4 |
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| 156 | |
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| 157 | ! potential volumic mass (reference to the surface) |
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| 158 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
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| 159 | |
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| 160 | ! add the compression terms |
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| 161 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
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| 162 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
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| 163 | zb = zbw + ze * zs |
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| 164 | |
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| 165 | zd = -2.042967e-2 |
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| 166 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
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| 167 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
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| 168 | za = ( zd*zsr + zc ) *zs + zaw |
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| 169 | |
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| 170 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
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| 171 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
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| 172 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
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| 173 | zk0= ( zb1*zsr + za1 )*zs + zkw |
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| 174 | |
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| 175 | ! masked in situ density anomaly |
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| 176 | prd(ji,jj,jk) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & |
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| 177 | - rau0 ) / rau0 * tmask(ji,jj,jk) |
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| 178 | END DO |
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| 179 | END DO |
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| 180 | ! ! =============== |
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| 181 | END DO ! End of slab |
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| 182 | ! ! =============== |
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| 183 | |
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| 184 | |
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| 185 | CASE ( 1 ) ! Linear formulation function of temperature only |
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| 186 | |
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| 187 | ! ! =============== |
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| 188 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 189 | ! ! =============== |
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| 190 | DO jj = 1, jpj |
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| 191 | DO ji = 1, jpi |
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| 192 | zt = ptem(ji,jj,jk) |
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| 193 | zs = psal(ji,jj,jk) |
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| 194 | ! ... density and potential volumic mass |
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| 195 | prd(ji,jj,jk) = ( 0.0285 - ralpha * zt ) * tmask(ji,jj,jk) |
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| 196 | END DO |
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| 197 | END DO |
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| 198 | ! ! =============== |
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| 199 | END DO ! End of slab |
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| 200 | ! ! =============== |
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| 201 | |
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| 202 | |
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| 203 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
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| 204 | |
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| 205 | ! ! =============== |
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| 206 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 207 | ! ! =============== |
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| 208 | DO jj = 1, jpj |
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| 209 | DO ji = 1, jpi |
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| 210 | zt = ptem(ji,jj,jk) |
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| 211 | zs = psal(ji,jj,jk) |
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| 212 | ! ... density and potential volumic mass |
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| 213 | prd(ji,jj,jk) = ( rbeta * zs - ralpha * zt ) * tmask(ji,jj,jk) |
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| 214 | END DO |
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| 215 | END DO |
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| 216 | ! ! =============== |
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| 217 | END DO ! End of slab |
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| 218 | ! ! =============== |
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| 219 | |
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| 220 | CASE DEFAULT |
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| 221 | |
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| 222 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
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| 223 | CALL ctl_stop( ctmp1 ) |
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| 224 | |
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| 225 | END SELECT |
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| 226 | |
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| 227 | IF(ln_ctl) THEN |
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| 228 | CALL prt_ctl(tab3d_1=prd, clinfo1=' eos : ', ovlap=1, kdim=jpk) |
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| 229 | ENDIF |
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| 230 | |
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| 231 | END SUBROUTINE eos_insitu |
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| 232 | |
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| 233 | |
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| 234 | SUBROUTINE eos_insitu_pot ( ptem, psal, prd, prhop) |
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| 235 | !!---------------------------------------------------------------------- |
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| 236 | !! *** ROUTINE eos_insitu_pot *** |
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| 237 | !! |
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| 238 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) and the |
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| 239 | !! potential volumic mass (Kg/m3) from potential temperature and |
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| 240 | !! salinity fields using an equation of state defined through the |
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| 241 | !! namelist parameter neos. |
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| 242 | !! |
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| 243 | !! ** Method : |
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| 244 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
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| 245 | !! the in situ density is computed directly as a function of |
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| 246 | !! potential temperature relative to the surface (the opa t |
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| 247 | !! variable), salt and pressure (assuming no pressure variation |
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| 248 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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| 249 | !! is approximated by the depth in meters. |
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| 250 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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| 251 | !! rhop(t,s) = rho(t,s,0) |
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| 252 | !! with pressure p decibars |
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| 253 | !! potential temperature t deg celsius |
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| 254 | !! salinity s psu |
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| 255 | !! reference volumic mass rau0 kg/m**3 |
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| 256 | !! in situ volumic mass rho kg/m**3 |
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| 257 | !! in situ density anomalie prd no units |
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| 258 | !! |
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| 259 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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| 260 | !! t = 40 deg celcius, s=40 psu |
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| 261 | !! |
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| 262 | !! neos = 1 : linear equation of state function of temperature only |
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| 263 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - ralpha * t |
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| 264 | !! rhop(t,s) = rho(t,s) |
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| 265 | !! |
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| 266 | !! neos = 2 : linear equation of state function of temperature and |
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| 267 | !! salinity |
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| 268 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
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| 269 | !! = rbeta * s - ralpha * tn - 1. |
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| 270 | !! rhop(t,s) = rho(t,s) |
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| 271 | !! Note that no boundary condition problem occurs in this routine |
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| 272 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
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| 273 | !! |
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| 274 | !! ** Action : - prd , the in situ density (no units) |
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| 275 | !! - prhop, the potential volumic mass (Kg/m3) |
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| 276 | !! |
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| 277 | !! References : |
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| 278 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
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| 279 | !! Brown, J. A. and K. A. Campana. Mon. Weather Rev., 1978 |
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| 280 | !! |
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| 281 | !! History : |
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| 282 | !! 4.0 ! 89-03 (O. Marti) |
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| 283 | !! ! 94-08 (G. Madec) |
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| 284 | !! ! 96-01 (G. Madec) statement function for e3 |
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| 285 | !! ! 97-07 (G. Madec) introduction of neos, OPA8.1 |
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| 286 | !! ! 97-07 (G. Madec) density instead of volumic mass |
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| 287 | !! ! 99-02 (G. Madec, N. Grima) semi-implicit pressure gradient |
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| 288 | !! ! 01-09 (M. Ben Jelloul) bugfix |
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| 289 | !! 9.0 ! 03-08 (G. Madec) F90, free form |
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| 290 | !!---------------------------------------------------------------------- |
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| 291 | !! * Arguments |
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| 292 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
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| 293 | ptem, & ! potential temperature |
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| 294 | psal ! salinity |
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| 295 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
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| 296 | prd, & ! potential density (surface referenced) |
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| 297 | prhop ! potential density (surface referenced) |
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| 298 | |
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| 299 | !! * Local declarations |
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| 300 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 301 | REAL(wp) :: & ! temporary scalars |
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| 302 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
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| 303 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0 |
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| 304 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws |
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| 305 | !!---------------------------------------------------------------------- |
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| 306 | |
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| 307 | ! initialization (in not already done) |
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| 308 | IF( neos_init == 0 ) CALL eos_init |
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| 309 | |
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| 310 | |
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| 311 | SELECT CASE ( neos ) |
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| 312 | |
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| 313 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
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| 314 | |
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| 315 | !CDIR NOVERRCHK |
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| 316 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
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| 317 | |
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| 318 | ! ! =============== |
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| 319 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 320 | ! ! =============== |
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| 321 | DO jj = 1, jpj |
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| 322 | DO ji = 1, jpi |
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| 323 | zt = ptem(ji,jj,jk) |
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| 324 | zs = psal(ji,jj,jk) |
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| 325 | ! depth |
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| 326 | zh = fsdept(ji,jj,jk) |
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| 327 | ! square root salinity |
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| 328 | !!Edmee zsr= SQRT( ABS( zs ) ) |
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| 329 | zsr= zws(ji,jj,jk) |
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| 330 | ! compute volumic mass pure water at atm pressure |
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| 331 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
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| 332 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
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| 333 | ! seawater volumic mass atm pressure |
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| 334 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
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| 335 | -4.0899e-3 ) *zt+0.824493 |
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| 336 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
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| 337 | zr4= 4.8314e-4 |
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| 338 | |
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| 339 | ! potential volumic mass (reference to the surface) |
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| 340 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
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| 341 | |
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| 342 | ! save potential volumic mass |
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| 343 | prhop(ji,jj,jk) = zrhop * tmask(ji,jj,jk) |
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| 344 | |
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| 345 | ! add the compression terms |
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| 346 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
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| 347 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
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| 348 | zb = zbw + ze * zs |
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| 349 | |
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| 350 | zd = -2.042967e-2 |
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| 351 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
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| 352 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
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| 353 | za = ( zd*zsr + zc ) *zs + zaw |
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| 354 | |
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| 355 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
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| 356 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
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| 357 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
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| 358 | zk0= ( zb1*zsr + za1 )*zs + zkw |
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| 359 | |
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| 360 | ! masked in situ density anomaly |
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| 361 | prd(ji,jj,jk) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & |
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| 362 | - rau0 ) / rau0 * tmask(ji,jj,jk) |
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| 363 | END DO |
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| 364 | END DO |
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| 365 | ! ! =============== |
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| 366 | END DO ! End of slab |
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| 367 | ! ! =============== |
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| 368 | |
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| 369 | |
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| 370 | CASE ( 1 ) ! Linear formulation function of temperature only |
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| 371 | |
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| 372 | ! ! =============== |
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| 373 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 374 | ! ! =============== |
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| 375 | DO jj = 1, jpj |
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| 376 | DO ji = 1, jpi |
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| 377 | zt = ptem(ji,jj,jk) |
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| 378 | zs = psal(ji,jj,jk) |
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| 379 | ! ... density and potential volumic mass |
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| 380 | prd (ji,jj,jk) = ( 0.0285 - ralpha * zt ) * tmask(ji,jj,jk) |
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| 381 | prhop(ji,jj,jk) = ( rau0 * prd(ji,jj,jk) + rau0 ) * tmask(ji,jj,jk) |
|---|
| 382 | END DO |
|---|
| 383 | END DO |
|---|
| 384 | ! ! =============== |
|---|
| 385 | END DO ! End of slab |
|---|
| 386 | ! ! =============== |
|---|
| 387 | |
|---|
| 388 | |
|---|
| 389 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
|---|
| 390 | |
|---|
| 391 | ! ! =============== |
|---|
| 392 | DO jk = 1, jpkm1 ! Horizontal slab |
|---|
| 393 | ! ! =============== |
|---|
| 394 | DO jj = 1, jpj |
|---|
| 395 | DO ji = 1, jpi |
|---|
| 396 | zt = ptem(ji,jj,jk) |
|---|
| 397 | zs = psal(ji,jj,jk) |
|---|
| 398 | ! ... density and potential volumic mass |
|---|
| 399 | prd (ji,jj,jk) = ( rbeta * zs - ralpha * zt ) * tmask(ji,jj,jk) |
|---|
| 400 | prhop(ji,jj,jk) = ( rau0 * prd(ji,jj,jk) + rau0 ) * tmask(ji,jj,jk) |
|---|
| 401 | END DO |
|---|
| 402 | END DO |
|---|
| 403 | ! ! =============== |
|---|
| 404 | END DO ! End of slab |
|---|
| 405 | ! ! =============== |
|---|
| 406 | |
|---|
| 407 | CASE DEFAULT |
|---|
| 408 | |
|---|
| 409 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
|---|
| 410 | CALL ctl_stop( ctmp1 ) |
|---|
| 411 | |
|---|
| 412 | END SELECT |
|---|
| 413 | |
|---|
| 414 | IF(ln_ctl) THEN |
|---|
| 415 | CALL prt_ctl(tab3d_1=prd, clinfo1=' eos-p: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk) |
|---|
| 416 | ENDIF |
|---|
| 417 | |
|---|
| 418 | END SUBROUTINE eos_insitu_pot |
|---|
| 419 | |
|---|
| 420 | SUBROUTINE eos_insitu_2d ( ptem, psal, pdep, prd ) |
|---|
| 421 | !!---------------------------------------------------------------------- |
|---|
| 422 | !! *** ROUTINE eos_insitu_2d *** |
|---|
| 423 | !! |
|---|
| 424 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) from |
|---|
| 425 | !! potential temperature and salinity using an equation of state |
|---|
| 426 | !! defined through the namelist parameter neos. * 2D field case |
|---|
| 427 | !! |
|---|
| 428 | !! ** Method : |
|---|
| 429 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
|---|
| 430 | !! the in situ density is computed directly as a function of |
|---|
| 431 | !! potential temperature relative to the surface (the opa t |
|---|
| 432 | !! variable), salt and pressure (assuming no pressure variation |
|---|
| 433 | !! along geopotential surfaces, i.e. the pressure p in decibars |
|---|
| 434 | !! is approximated by the depth in meters. |
|---|
| 435 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
|---|
| 436 | !! with pressure p decibars |
|---|
| 437 | !! potential temperature t deg celsius |
|---|
| 438 | !! salinity s psu |
|---|
| 439 | !! reference volumic mass rau0 kg/m**3 |
|---|
| 440 | !! in situ volumic mass rho kg/m**3 |
|---|
| 441 | !! in situ density anomalie prd no units |
|---|
| 442 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
|---|
| 443 | !! t = 40 deg celcius, s=40 psu |
|---|
| 444 | !! neos = 1 : linear equation of state function of temperature only |
|---|
| 445 | !! prd(t) = 0.0285 - ralpha * t |
|---|
| 446 | !! neos = 2 : linear equation of state function of temperature and |
|---|
| 447 | !! salinity |
|---|
| 448 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
|---|
| 449 | !! Note that no boundary condition problem occurs in this routine |
|---|
| 450 | !! as (ptem,psal) are defined over the whole domain. |
|---|
| 451 | !! |
|---|
| 452 | !! ** Action : - prd , the in situ density (no units) |
|---|
| 453 | !! |
|---|
| 454 | !! References : |
|---|
| 455 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
|---|
| 456 | !! |
|---|
| 457 | !! History : |
|---|
| 458 | !! 8.5 ! 02-11 (G. Madec, A. Bozec) partial step |
|---|
| 459 | !!---------------------------------------------------------------------- |
|---|
| 460 | !! * Arguments |
|---|
| 461 | REAL(wp), DIMENSION(jpi,jpj), INTENT( in ) :: & |
|---|
| 462 | ptem, & ! potential temperature |
|---|
| 463 | psal, & ! salinity |
|---|
| 464 | pdep ! depth |
|---|
| 465 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out ) :: & |
|---|
| 466 | prd ! potential density (surface referenced) |
|---|
| 467 | |
|---|
| 468 | !! * Local declarations |
|---|
| 469 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 470 | REAL(wp) :: & ! temporary scalars |
|---|
| 471 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
|---|
| 472 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
|---|
| 473 | zmask |
|---|
| 474 | REAL(wp), DIMENSION(jpi,jpj) :: zws |
|---|
| 475 | !!---------------------------------------------------------------------- |
|---|
| 476 | |
|---|
| 477 | |
|---|
| 478 | ! initialization (in not already done) |
|---|
| 479 | IF( neos_init == 0 ) CALL eos_init |
|---|
| 480 | |
|---|
| 481 | prd(:,:) = 0.e0 |
|---|
| 482 | |
|---|
| 483 | SELECT CASE ( neos ) |
|---|
| 484 | |
|---|
| 485 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
|---|
| 486 | |
|---|
| 487 | !CDIR NOVERRCHK |
|---|
| 488 | DO jj = 1, jpjm1 |
|---|
| 489 | !CDIR NOVERRCHK |
|---|
| 490 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 491 | zws(ji,jj) = SQRT( ABS( psal(ji,jj) ) ) |
|---|
| 492 | END DO |
|---|
| 493 | END DO |
|---|
| 494 | |
|---|
| 495 | ! ! =============== |
|---|
| 496 | DO jj = 1, jpjm1 ! Horizontal slab |
|---|
| 497 | ! ! =============== |
|---|
| 498 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 499 | |
|---|
| 500 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
|---|
| 501 | |
|---|
| 502 | zt = ptem (ji,jj) ! interpolated T |
|---|
| 503 | zs = psal (ji,jj) ! interpolated S |
|---|
| 504 | zsr= zws(ji,jj) ! square root of interpolated S |
|---|
| 505 | zh = pdep(ji,jj) ! depth at the partial step level |
|---|
| 506 | |
|---|
| 507 | ! compute volumic mass pure water at atm pressure |
|---|
| 508 | zr1 = ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
|---|
| 509 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
|---|
| 510 | ! seawater volumic mass atm pressure |
|---|
| 511 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 )*zt+7.6438e-5 ) *zt & |
|---|
| 512 | -4.0899e-3 ) *zt+0.824493 |
|---|
| 513 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
|---|
| 514 | zr4= 4.8314e-4 |
|---|
| 515 | |
|---|
| 516 | ! potential volumic mass (reference to the surface) |
|---|
| 517 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
|---|
| 518 | |
|---|
| 519 | ! add the compression terms |
|---|
| 520 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
|---|
| 521 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
|---|
| 522 | zb = zbw + ze * zs |
|---|
| 523 | |
|---|
| 524 | zd = -2.042967e-2 |
|---|
| 525 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
|---|
| 526 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt -4.721788 |
|---|
| 527 | za = ( zd*zsr + zc ) *zs + zaw |
|---|
| 528 | |
|---|
| 529 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
|---|
| 530 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
|---|
| 531 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt & |
|---|
| 532 | +2098.925 ) *zt+190925.6 |
|---|
| 533 | zk0= ( zb1*zsr + za1 )*zs + zkw |
|---|
| 534 | |
|---|
| 535 | ! masked in situ density anomaly |
|---|
| 536 | prd(ji,jj) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) - rau0 ) & |
|---|
| 537 | / rau0 * zmask |
|---|
| 538 | END DO |
|---|
| 539 | ! ! =============== |
|---|
| 540 | END DO ! End of slab |
|---|
| 541 | ! ! =============== |
|---|
| 542 | |
|---|
| 543 | |
|---|
| 544 | CASE ( 1 ) ! Linear formulation function of temperature only |
|---|
| 545 | |
|---|
| 546 | ! ! =============== |
|---|
| 547 | DO jj = 1, jpjm1 ! Horizontal slab |
|---|
| 548 | ! ! =============== |
|---|
| 549 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 550 | prd(ji,jj) = ( 0.0285 - ralpha * ptem(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 551 | END DO |
|---|
| 552 | ! ! =============== |
|---|
| 553 | END DO ! End of slab |
|---|
| 554 | ! ! =============== |
|---|
| 555 | |
|---|
| 556 | |
|---|
| 557 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
|---|
| 558 | |
|---|
| 559 | ! ! =============== |
|---|
| 560 | DO jj = 1, jpjm1 ! Horizontal slab |
|---|
| 561 | ! ! =============== |
|---|
| 562 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 563 | prd(ji,jj) = ( rbeta * psal(ji,jj) - ralpha * ptem(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 564 | END DO |
|---|
| 565 | ! ! =============== |
|---|
| 566 | END DO ! End of slab |
|---|
| 567 | ! ! =============== |
|---|
| 568 | |
|---|
| 569 | CASE DEFAULT |
|---|
| 570 | |
|---|
| 571 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
|---|
| 572 | CALL ctl_stop( ctmp1 ) |
|---|
| 573 | |
|---|
| 574 | END SELECT |
|---|
| 575 | |
|---|
| 576 | IF(ln_ctl) CALL prt_ctl(tab2d_1=prd, clinfo1=' eos2d: ') |
|---|
| 577 | |
|---|
| 578 | END SUBROUTINE eos_insitu_2d |
|---|
| 579 | |
|---|
| 580 | |
|---|
| 581 | SUBROUTINE eos_bn2( ptem, psal, pn2 ) |
|---|
| 582 | !!---------------------------------------------------------------------- |
|---|
| 583 | !! *** ROUTINE eos_bn2 *** |
|---|
| 584 | !! |
|---|
| 585 | !! ** Purpose : Compute the local Brunt-Vaisala frequency at the time- |
|---|
| 586 | !! step of the input arguments |
|---|
| 587 | !! |
|---|
| 588 | !! ** Method : |
|---|
| 589 | !! * neos = 0 : UNESCO sea water properties |
|---|
| 590 | !! The brunt-vaisala frequency is computed using the polynomial |
|---|
| 591 | !! polynomial expression of McDougall (1987): |
|---|
| 592 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
|---|
| 593 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
|---|
| 594 | !! computed and used in zdfddm module : |
|---|
| 595 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
|---|
| 596 | !! * neos = 1 : linear equation of state (temperature only) |
|---|
| 597 | !! N^2 = grav * ralpha * dk[ t ]/e3w |
|---|
| 598 | !! * neos = 2 : linear equation of state (temperature & salinity) |
|---|
| 599 | !! N^2 = grav * (ralpha * dk[ t ] - rbeta * dk[ s ] ) / e3w |
|---|
| 600 | !! The use of potential density to compute N^2 introduces e r r o r |
|---|
| 601 | !! in the sign of N^2 at great depths. We recommand the use of |
|---|
| 602 | !! neos = 0, except for academical studies. |
|---|
| 603 | !! Macro-tasked on horizontal slab (jk-loop) |
|---|
| 604 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
|---|
| 605 | !! and is never used at this level. |
|---|
| 606 | !! |
|---|
| 607 | !! ** Action : - pn2 : the brunt-vaisala frequency |
|---|
| 608 | !! |
|---|
| 609 | !! References : |
|---|
| 610 | !! McDougall, T. J., J. Phys. Oceanogr., 17, 1950-1964, 1987. |
|---|
| 611 | !! |
|---|
| 612 | !! History : |
|---|
| 613 | !! 6.0 ! 94-07 (G. Madec, M. Imbard) Original code |
|---|
| 614 | !! 8.0 ! 97-07 (G. Madec) introduction of statement functions |
|---|
| 615 | !! 8.5 ! 02-07 (G. Madec) Free form, F90 |
|---|
| 616 | !! 8.5 ! 02-08 (G. Madec) introduction of arguments |
|---|
| 617 | !!---------------------------------------------------------------------- |
|---|
| 618 | !! * Arguments |
|---|
| 619 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
|---|
| 620 | ptem, & ! potential temperature |
|---|
| 621 | psal ! salinity |
|---|
| 622 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
|---|
| 623 | pn2 ! Brunt-Vaisala frequency |
|---|
| 624 | |
|---|
| 625 | !! * Local declarations |
|---|
| 626 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 627 | REAL(wp) :: & |
|---|
| 628 | zgde3w, zt, zs, zh, & ! temporary scalars |
|---|
| 629 | zalbet, zbeta ! " " |
|---|
| 630 | #if defined key_zdfddm |
|---|
| 631 | REAL(wp) :: zds ! temporary scalars |
|---|
| 632 | #endif |
|---|
| 633 | !!---------------------------------------------------------------------- |
|---|
| 634 | !! OPA8.5, LODYC-IPSL (2002) |
|---|
| 635 | !!---------------------------------------------------------------------- |
|---|
| 636 | |
|---|
| 637 | ! pn2 : first and last levels |
|---|
| 638 | ! --------------------------- |
|---|
| 639 | ! bn^2=0. at jk=1 and jpk set in inidtr.F : no computation |
|---|
| 640 | |
|---|
| 641 | |
|---|
| 642 | ! pn2 : interior points only (2=< jk =< jpkm1 ) |
|---|
| 643 | ! -------------------------- |
|---|
| 644 | |
|---|
| 645 | SELECT CASE ( neos ) |
|---|
| 646 | |
|---|
| 647 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
|---|
| 648 | |
|---|
| 649 | ! ! =============== |
|---|
| 650 | DO jk = 2, jpkm1 ! Horizontal slab |
|---|
| 651 | ! ! =============== |
|---|
| 652 | DO jj = 1, jpj |
|---|
| 653 | DO ji = 1, jpi |
|---|
| 654 | zgde3w = grav / fse3w(ji,jj,jk) |
|---|
| 655 | zt = 0.5 * ( ptem(ji,jj,jk) + ptem(ji,jj,jk-1) ) ! potential temperature at w-point |
|---|
| 656 | zs = 0.5 * ( psal(ji,jj,jk) + psal(ji,jj,jk-1) ) - 35.0 ! salinity anomaly (s-35) at w-point |
|---|
| 657 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
|---|
| 658 | |
|---|
| 659 | zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta |
|---|
| 660 | & - 0.203814e-03 ) * zt & |
|---|
| 661 | & + 0.170907e-01 ) * zt & |
|---|
| 662 | & + 0.665157e-01 & |
|---|
| 663 | & + ( - 0.678662e-05 * zs & |
|---|
| 664 | & - 0.846960e-04 * zt + 0.378110e-02 ) * zs & |
|---|
| 665 | & + ( ( - 0.302285e-13 * zh & |
|---|
| 666 | & - 0.251520e-11 * zs & |
|---|
| 667 | & + 0.512857e-12 * zt * zt ) * zh & |
|---|
| 668 | & - 0.164759e-06 * zs & |
|---|
| 669 | & +( 0.791325e-08 * zt - 0.933746e-06 ) * zt & |
|---|
| 670 | & + 0.380374e-04 ) * zh |
|---|
| 671 | |
|---|
| 672 | zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta |
|---|
| 673 | & - 0.301985e-05 ) * zt & |
|---|
| 674 | & + 0.785567e-03 & |
|---|
| 675 | & + ( 0.515032e-08 * zs & |
|---|
| 676 | & + 0.788212e-08 * zt - 0.356603e-06 ) * zs & |
|---|
| 677 | & +( ( 0.121551e-17 * zh & |
|---|
| 678 | & - 0.602281e-15 * zs & |
|---|
| 679 | & - 0.175379e-14 * zt + 0.176621e-12 ) * zh & |
|---|
| 680 | & + 0.408195e-10 * zs & |
|---|
| 681 | & + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt & |
|---|
| 682 | & - 0.121555e-07 ) * zh |
|---|
| 683 | |
|---|
| 684 | pn2(ji,jj,jk) = zgde3w * zbeta * tmask(ji,jj,jk) & ! N^2 |
|---|
| 685 | & * ( zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) & |
|---|
| 686 | & - ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ) |
|---|
| 687 | #if defined key_zdfddm |
|---|
| 688 | ! !!bug **** caution a traiter zds=dk[S]= 0 !!!! |
|---|
| 689 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ! Rrau = (alpha / beta) (dk[t] / dk[s]) |
|---|
| 690 | IF ( ABS( zds) <= 1.e-20 ) zds = 1.e-20 |
|---|
| 691 | rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds |
|---|
| 692 | #endif |
|---|
| 693 | END DO |
|---|
| 694 | END DO |
|---|
| 695 | ! ! =============== |
|---|
| 696 | END DO ! End of slab |
|---|
| 697 | ! ! =============== |
|---|
| 698 | |
|---|
| 699 | |
|---|
| 700 | CASE ( 1 ) ! Linear formulation function of temperature only |
|---|
| 701 | |
|---|
| 702 | ! ! =============== |
|---|
| 703 | DO jk = 2, jpkm1 ! Horizontal slab |
|---|
| 704 | ! ! =============== |
|---|
| 705 | DO jj = 1, jpj |
|---|
| 706 | DO ji = 1, jpi |
|---|
| 707 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
|---|
| 708 | pn2(ji,jj,jk) = zgde3w * ralpha * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) |
|---|
| 709 | END DO |
|---|
| 710 | END DO |
|---|
| 711 | ! ! =============== |
|---|
| 712 | END DO ! End of slab |
|---|
| 713 | ! ! =============== |
|---|
| 714 | |
|---|
| 715 | |
|---|
| 716 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
|---|
| 717 | |
|---|
| 718 | ! ! =============== |
|---|
| 719 | DO jk = 2, jpkm1 ! Horizontal slab |
|---|
| 720 | ! ! =============== |
|---|
| 721 | DO jj = 1, jpj |
|---|
| 722 | DO ji = 1, jpi |
|---|
| 723 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
|---|
| 724 | pn2(ji,jj,jk) = zgde3w * ( ralpha * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) & |
|---|
| 725 | & - rbeta * ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ) |
|---|
| 726 | END DO |
|---|
| 727 | END DO |
|---|
| 728 | #if defined key_zdfddm |
|---|
| 729 | ! ! Rrau = (alpha / beta) (dk[t] / dk[s]) |
|---|
| 730 | zalbet = ralpha / rbeta |
|---|
| 731 | DO jj = 1, jpj |
|---|
| 732 | DO ji = 1, jpi |
|---|
| 733 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) |
|---|
| 734 | IF ( ABS( zds ) <= 1.e-20 ) zds = 1.e-20 |
|---|
| 735 | rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds |
|---|
| 736 | END DO |
|---|
| 737 | END DO |
|---|
| 738 | #endif |
|---|
| 739 | ! ! =============== |
|---|
| 740 | END DO ! End of slab |
|---|
| 741 | ! ! =============== |
|---|
| 742 | |
|---|
| 743 | CASE DEFAULT |
|---|
| 744 | |
|---|
| 745 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
|---|
| 746 | CALL ctl_stop( ctmp1 ) |
|---|
| 747 | |
|---|
| 748 | END SELECT |
|---|
| 749 | |
|---|
| 750 | IF(ln_ctl) THEN |
|---|
| 751 | CALL prt_ctl(tab3d_1=pn2, clinfo1=' bn2 : ', ovlap=1, kdim=jpk) |
|---|
| 752 | #if defined key_zdfddm |
|---|
| 753 | CALL prt_ctl(tab3d_1=rrau, clinfo1=' rrau : ', ovlap=1, kdim=jpk) |
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| 754 | #endif |
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| 755 | ENDIF |
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| 756 | |
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| 757 | END SUBROUTINE eos_bn2 |
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| 758 | |
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| 759 | |
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| 760 | SUBROUTINE eos_init |
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| 761 | !!---------------------------------------------------------------------- |
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| 762 | !! *** ROUTINE eos_init *** |
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| 763 | !! |
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| 764 | !! ** Purpose : initializations for the equation of state |
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| 765 | !! |
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| 766 | !! ** Method : Read the namelist nameos |
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| 767 | !! |
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| 768 | !! ** Action : blahblah.... |
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| 769 | !! |
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| 770 | !! History : |
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| 771 | !! 8.5 ! 02-10 (G. Madec) Original code |
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| 772 | !!---------------------------------------------------------------------- |
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| 773 | NAMELIST/nameos/ neos, ralpha, rbeta |
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| 774 | !!---------------------------------------------------------------------- |
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| 775 | !! OPA 8.5, LODYC-IPSL (2002) |
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| 776 | !!---------------------------------------------------------------------- |
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| 777 | |
|---|
| 778 | ! set the initialization flag to 1 |
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| 779 | neos_init = 1 ! indicate that the initialization has been done |
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| 780 | |
|---|
| 781 | ! namelist nameos : ocean physical parameters |
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| 782 | |
|---|
| 783 | ! Read Namelist nameos : equation of state |
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| 784 | REWIND( numnam ) |
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| 785 | READ ( numnam, nameos ) |
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| 786 | |
|---|
| 787 | ! Control print |
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| 788 | IF(lwp) THEN |
|---|
| 789 | WRITE(numout,*) |
|---|
| 790 | WRITE(numout,*) 'eos_init : equation of state' |
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| 791 | WRITE(numout,*) '~~~~~~~~' |
|---|
| 792 | WRITE(numout,*) ' Namelist nameos : set eos parameters' |
|---|
| 793 | WRITE(numout,*) |
|---|
| 794 | WRITE(numout,*) ' flag for eq. of state and N^2 neos = ', neos |
|---|
| 795 | WRITE(numout,*) ' thermal exp. coef. (linear) ralpha = ', ralpha |
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| 796 | WRITE(numout,*) ' saline exp. coef. (linear) rbeta = ', rbeta |
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| 797 | WRITE(numout,*) |
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| 798 | ENDIF |
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| 799 | |
|---|
| 800 | SELECT CASE ( neos ) |
|---|
| 801 | |
|---|
| 802 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
|---|
| 803 | |
|---|
| 804 | IF(lwp) WRITE(numout,*) ' use of Jackett & McDougall (1994) equation of state and' |
|---|
| 805 | IF(lwp) WRITE(numout,*) ' McDougall (1987) Brunt-Vaisala frequency' |
|---|
| 806 | |
|---|
| 807 | CASE ( 1 ) ! Linear formulation function of temperature only |
|---|
| 808 | |
|---|
| 809 | IF(lwp) WRITE(numout,*) ' use of linear eos rho(T) = rau0 * ( 1.0285 - ralpha * T )' |
|---|
| 810 | IF( lk_zdfddm ) CALL ctl_stop( ' double diffusive mixing parameterization requires', & |
|---|
| 811 | & ' that T and S are used as state variables' ) |
|---|
| 812 | |
|---|
| 813 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
|---|
| 814 | |
|---|
| 815 | IF(lwp) WRITE(numout,*) ' use of linear eos rho(T,S) = rau0 * ( rbeta * S - ralpha * T )' |
|---|
| 816 | |
|---|
| 817 | CASE DEFAULT |
|---|
| 818 | |
|---|
| 819 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
|---|
| 820 | CALL ctl_stop( ctmp1 ) |
|---|
| 821 | |
|---|
| 822 | END SELECT |
|---|
| 823 | |
|---|
| 824 | END SUBROUTINE eos_init |
|---|
| 825 | |
|---|
| 826 | !!====================================================================== |
|---|
| 827 | END MODULE eosbn2 |
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