| 1 | MODULE eosbn2 |
|---|
| 2 | !!============================================================================== |
|---|
| 3 | !! *** MODULE eosbn2 *** |
|---|
| 4 | !! Ocean diagnostic variable : equation of state - in situ and potential density |
|---|
| 5 | !! - Brunt-Vaisala frequency |
|---|
| 6 | !!============================================================================== |
|---|
| 7 | !! History : OPA ! 1989-03 (O. Marti) Original code |
|---|
| 8 | !! 6.0 ! 1994-07 (G. Madec, M. Imbard) add bn2 |
|---|
| 9 | !! 6.0 ! 1994-08 (G. Madec) Add Jackett & McDougall eos |
|---|
| 10 | !! 7.0 ! 1996-01 (G. Madec) statement function for e3 |
|---|
| 11 | !! 8.1 ! 1997-07 (G. Madec) density instead of volumic mass |
|---|
| 12 | !! - ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure gradient |
|---|
| 13 | !! 8.2 ! 2001-09 (M. Ben Jelloul) bugfix on linear eos |
|---|
| 14 | !! NEMO 1.0 ! 2002-10 (G. Madec) add eos_init |
|---|
| 15 | !! - ! 2002-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d |
|---|
| 16 | !! - ! 2003-08 (G. Madec) F90, free form |
|---|
| 17 | !! 3.0 ! 2006-08 (G. Madec) add tfreez function |
|---|
| 18 | !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
|---|
| 19 | !! - ! 2010-10 (G. Nurser, G. Madec) add eos_alpbet used in ldfslp |
|---|
| 20 | !!---------------------------------------------------------------------- |
|---|
| 21 | |
|---|
| 22 | !!---------------------------------------------------------------------- |
|---|
| 23 | !! eos : generic interface of the equation of state |
|---|
| 24 | !! eos_insitu : Compute the in situ density |
|---|
| 25 | !! eos_insitu_pot : Compute the insitu and surface referenced potential |
|---|
| 26 | !! volumic mass |
|---|
| 27 | !! eos_insitu_2d : Compute the in situ density for 2d fields |
|---|
| 28 | !! eos_bn2 : Compute the Brunt-Vaisala frequency |
|---|
| 29 | !! eos_alpbet : calculates the in situ thermal/haline expansion ratio |
|---|
| 30 | !! tfreez : Compute the surface freezing temperature |
|---|
| 31 | !! eos_init : set eos parameters (namelist) |
|---|
| 32 | !!---------------------------------------------------------------------- |
|---|
| 33 | USE dom_oce ! ocean space and time domain |
|---|
| 34 | USE phycst ! physical constants |
|---|
| 35 | USE zdfddm ! vertical physics: double diffusion |
|---|
| 36 | USE in_out_manager ! I/O manager |
|---|
| 37 | USE lib_mpp ! MPP library |
|---|
| 38 | USE prtctl ! Print control |
|---|
| 39 | USE wrk_nemo ! Memory Allocation |
|---|
| 40 | USE timing ! Timing |
|---|
| 41 | |
|---|
| 42 | IMPLICIT NONE |
|---|
| 43 | PRIVATE |
|---|
| 44 | |
|---|
| 45 | ! !! * Interface |
|---|
| 46 | INTERFACE eos |
|---|
| 47 | MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d |
|---|
| 48 | END INTERFACE |
|---|
| 49 | INTERFACE bn2 |
|---|
| 50 | MODULE PROCEDURE eos_bn2 |
|---|
| 51 | END INTERFACE |
|---|
| 52 | |
|---|
| 53 | PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules |
|---|
| 54 | PUBLIC eos_init ! called by istate module |
|---|
| 55 | PUBLIC bn2 ! called by step module |
|---|
| 56 | PUBLIC eos_alpbet ! called by ldfslp module |
|---|
| 57 | PUBLIC tfreez ! called by sbcice_... modules |
|---|
| 58 | |
|---|
| 59 | ! !!* Namelist (nameos) * |
|---|
| 60 | INTEGER , PUBLIC :: nn_eos = 0 !: = 0/1/2 type of eq. of state and Brunt-Vaisala frequ. |
|---|
| 61 | REAL(wp), PUBLIC :: rn_alpha = 2.0e-4_wp !: thermal expension coeff. (linear equation of state) |
|---|
| 62 | REAL(wp), PUBLIC :: rn_beta = 7.7e-4_wp !: saline expension coeff. (linear equation of state) |
|---|
| 63 | |
|---|
| 64 | REAL(wp), PUBLIC :: ralpbet !: alpha / beta ratio |
|---|
| 65 | |
|---|
| 66 | !! * Substitutions |
|---|
| 67 | # include "domzgr_substitute.h90" |
|---|
| 68 | # include "vectopt_loop_substitute.h90" |
|---|
| 69 | !!---------------------------------------------------------------------- |
|---|
| 70 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
|---|
| 71 | !! $Id$ |
|---|
| 72 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
|---|
| 73 | !!---------------------------------------------------------------------- |
|---|
| 74 | CONTAINS |
|---|
| 75 | |
|---|
| 76 | SUBROUTINE eos_insitu( pts, prd ) |
|---|
| 77 | !!---------------------------------------------------------------------- |
|---|
| 78 | !! *** ROUTINE eos_insitu *** |
|---|
| 79 | !! |
|---|
| 80 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) from |
|---|
| 81 | !! potential temperature and salinity using an equation of state |
|---|
| 82 | !! defined through the namelist parameter nn_eos. |
|---|
| 83 | !! |
|---|
| 84 | !! ** Method : 3 cases: |
|---|
| 85 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
|---|
| 86 | !! the in situ density is computed directly as a function of |
|---|
| 87 | !! potential temperature relative to the surface (the opa t |
|---|
| 88 | !! variable), salt and pressure (assuming no pressure variation |
|---|
| 89 | !! along geopotential surfaces, i.e. the pressure p in decibars |
|---|
| 90 | !! is approximated by the depth in meters. |
|---|
| 91 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
|---|
| 92 | !! with pressure p decibars |
|---|
| 93 | !! potential temperature t deg celsius |
|---|
| 94 | !! salinity s psu |
|---|
| 95 | !! reference volumic mass rau0 kg/m**3 |
|---|
| 96 | !! in situ volumic mass rho kg/m**3 |
|---|
| 97 | !! in situ density anomalie prd no units |
|---|
| 98 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
|---|
| 99 | !! t = 40 deg celcius, s=40 psu |
|---|
| 100 | !! nn_eos = 1 : linear equation of state function of temperature only |
|---|
| 101 | !! prd(t) = 0.0285 - rn_alpha * t |
|---|
| 102 | !! nn_eos = 2 : linear equation of state function of temperature and |
|---|
| 103 | !! salinity |
|---|
| 104 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
|---|
| 105 | !! Note that no boundary condition problem occurs in this routine |
|---|
| 106 | !! as pts are defined over the whole domain. |
|---|
| 107 | !! |
|---|
| 108 | !! ** Action : compute prd , the in situ density (no units) |
|---|
| 109 | !! |
|---|
| 110 | !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 |
|---|
| 111 | !!---------------------------------------------------------------------- |
|---|
| 112 | !! |
|---|
| 113 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
|---|
| 114 | ! ! 2 : salinity [psu] |
|---|
| 115 | REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-] |
|---|
| 116 | !! |
|---|
| 117 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 118 | REAL(wp) :: zt , zs , zh , zsr ! local scalars |
|---|
| 119 | REAL(wp) :: zr1, zr2, zr3, zr4 ! - - |
|---|
| 120 | REAL(wp) :: zrhop, ze, zbw, zb ! - - |
|---|
| 121 | REAL(wp) :: zd , zc , zaw, za ! - - |
|---|
| 122 | REAL(wp) :: zb1, za1, zkw, zk0 ! - - |
|---|
| 123 | REAL(wp) :: zrau0r ! - - |
|---|
| 124 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
|---|
| 125 | !!---------------------------------------------------------------------- |
|---|
| 126 | |
|---|
| 127 | ! |
|---|
| 128 | IF( nn_timing == 1 ) CALL timing_start('eos') |
|---|
| 129 | ! |
|---|
| 130 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
|---|
| 131 | ! |
|---|
| 132 | SELECT CASE( nn_eos ) |
|---|
| 133 | ! |
|---|
| 134 | CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! |
|---|
| 135 | zrau0r = 1.e0 / rau0 |
|---|
| 136 | !CDIR NOVERRCHK |
|---|
| 137 | zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) ) |
|---|
| 138 | ! |
|---|
| 139 | DO jk = 1, jpkm1 |
|---|
| 140 | DO jj = 1, jpj |
|---|
| 141 | DO ji = 1, jpi |
|---|
| 142 | zt = pts (ji,jj,jk,jp_tem) |
|---|
| 143 | zs = pts (ji,jj,jk,jp_sal) |
|---|
| 144 | zh = fsdept(ji,jj,jk) ! depth |
|---|
| 145 | zsr= zws (ji,jj,jk) ! square root salinity |
|---|
| 146 | ! |
|---|
| 147 | ! compute volumic mass pure water at atm pressure |
|---|
| 148 | zr1= ( ( ( ( 6.536332e-9_wp *zt - 1.120083e-6_wp )*zt + 1.001685e-4_wp )*zt & |
|---|
| 149 | & -9.095290e-3_wp )*zt + 6.793952e-2_wp )*zt + 999.842594_wp |
|---|
| 150 | ! seawater volumic mass atm pressure |
|---|
| 151 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
|---|
| 152 | & -4.0899e-3_wp ) *zt+0.824493_wp |
|---|
| 153 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
|---|
| 154 | zr4= 4.8314e-4_wp |
|---|
| 155 | ! |
|---|
| 156 | ! potential volumic mass (reference to the surface) |
|---|
| 157 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
|---|
| 158 | ! |
|---|
| 159 | ! add the compression terms |
|---|
| 160 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
|---|
| 161 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
|---|
| 162 | zb = zbw + ze * zs |
|---|
| 163 | ! |
|---|
| 164 | zd = -2.042967e-2_wp |
|---|
| 165 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
|---|
| 166 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
|---|
| 167 | za = ( zd*zsr + zc ) *zs + zaw |
|---|
| 168 | ! |
|---|
| 169 | zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp |
|---|
| 170 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp) *zt-65.00517_wp ) *zt+1044.077_wp |
|---|
| 171 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
|---|
| 172 | zk0= ( zb1*zsr + za1 )*zs + zkw |
|---|
| 173 | ! |
|---|
| 174 | ! masked in situ density anomaly |
|---|
| 175 | prd(ji,jj,jk) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & |
|---|
| 176 | & - rau0 ) * zrau0r * tmask(ji,jj,jk) |
|---|
| 177 | END DO |
|---|
| 178 | END DO |
|---|
| 179 | END DO |
|---|
| 180 | ! |
|---|
| 181 | CASE( 1 ) !== Linear formulation function of temperature only ==! |
|---|
| 182 | DO jk = 1, jpkm1 |
|---|
| 183 | prd(:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) |
|---|
| 184 | END DO |
|---|
| 185 | ! |
|---|
| 186 | CASE( 2 ) !== Linear formulation function of temperature and salinity ==! |
|---|
| 187 | DO jk = 1, jpkm1 |
|---|
| 188 | prd(:,:,jk) = ( rn_beta * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) |
|---|
| 189 | END DO |
|---|
| 190 | ! |
|---|
| 191 | END SELECT |
|---|
| 192 | ! |
|---|
| 193 | IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos : ', ovlap=1, kdim=jpk ) |
|---|
| 194 | ! |
|---|
| 195 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
|---|
| 196 | ! |
|---|
| 197 | IF( nn_timing == 1 ) CALL timing_stop('eos') |
|---|
| 198 | ! |
|---|
| 199 | END SUBROUTINE eos_insitu |
|---|
| 200 | |
|---|
| 201 | |
|---|
| 202 | SUBROUTINE eos_insitu_pot( pts, prd, prhop ) |
|---|
| 203 | !!---------------------------------------------------------------------- |
|---|
| 204 | !! *** ROUTINE eos_insitu_pot *** |
|---|
| 205 | !! |
|---|
| 206 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) and the |
|---|
| 207 | !! potential volumic mass (Kg/m3) from potential temperature and |
|---|
| 208 | !! salinity fields using an equation of state defined through the |
|---|
| 209 | !! namelist parameter nn_eos. |
|---|
| 210 | !! |
|---|
| 211 | !! ** Method : |
|---|
| 212 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
|---|
| 213 | !! the in situ density is computed directly as a function of |
|---|
| 214 | !! potential temperature relative to the surface (the opa t |
|---|
| 215 | !! variable), salt and pressure (assuming no pressure variation |
|---|
| 216 | !! along geopotential surfaces, i.e. the pressure p in decibars |
|---|
| 217 | !! is approximated by the depth in meters. |
|---|
| 218 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
|---|
| 219 | !! rhop(t,s) = rho(t,s,0) |
|---|
| 220 | !! with pressure p decibars |
|---|
| 221 | !! potential temperature t deg celsius |
|---|
| 222 | !! salinity s psu |
|---|
| 223 | !! reference volumic mass rau0 kg/m**3 |
|---|
| 224 | !! in situ volumic mass rho kg/m**3 |
|---|
| 225 | !! in situ density anomalie prd no units |
|---|
| 226 | !! |
|---|
| 227 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
|---|
| 228 | !! t = 40 deg celcius, s=40 psu |
|---|
| 229 | !! |
|---|
| 230 | !! nn_eos = 1 : linear equation of state function of temperature only |
|---|
| 231 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - rn_alpha * t |
|---|
| 232 | !! rhop(t,s) = rho(t,s) |
|---|
| 233 | !! |
|---|
| 234 | !! nn_eos = 2 : linear equation of state function of temperature and |
|---|
| 235 | !! salinity |
|---|
| 236 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
|---|
| 237 | !! = rn_beta * s - rn_alpha * tn - 1. |
|---|
| 238 | !! rhop(t,s) = rho(t,s) |
|---|
| 239 | !! Note that no boundary condition problem occurs in this routine |
|---|
| 240 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
|---|
| 241 | !! |
|---|
| 242 | !! ** Action : - prd , the in situ density (no units) |
|---|
| 243 | !! - prhop, the potential volumic mass (Kg/m3) |
|---|
| 244 | !! |
|---|
| 245 | !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 |
|---|
| 246 | !! Brown and Campana, Mon. Weather Rev., 1978 |
|---|
| 247 | !!---------------------------------------------------------------------- |
|---|
| 248 | !! |
|---|
| 249 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
|---|
| 250 | ! ! 2 : salinity [psu] |
|---|
| 251 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prd ! in situ density [-] |
|---|
| 252 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prhop ! potential density (surface referenced) |
|---|
| 253 | ! |
|---|
| 254 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 255 | REAL(wp) :: zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw ! local scalars |
|---|
| 256 | REAL(wp) :: zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, zrau0r ! - - |
|---|
| 257 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
|---|
| 258 | !!---------------------------------------------------------------------- |
|---|
| 259 | ! |
|---|
| 260 | IF( nn_timing == 1 ) CALL timing_start('eos-p') |
|---|
| 261 | ! |
|---|
| 262 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
|---|
| 263 | ! |
|---|
| 264 | SELECT CASE ( nn_eos ) |
|---|
| 265 | ! |
|---|
| 266 | CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! |
|---|
| 267 | zrau0r = 1.e0 / rau0 |
|---|
| 268 | !CDIR NOVERRCHK |
|---|
| 269 | zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) ) |
|---|
| 270 | ! |
|---|
| 271 | DO jk = 1, jpkm1 |
|---|
| 272 | DO jj = 1, jpj |
|---|
| 273 | DO ji = 1, jpi |
|---|
| 274 | zt = pts (ji,jj,jk,jp_tem) |
|---|
| 275 | zs = pts (ji,jj,jk,jp_sal) |
|---|
| 276 | zh = fsdept(ji,jj,jk) ! depth |
|---|
| 277 | zsr= zws (ji,jj,jk) ! square root salinity |
|---|
| 278 | ! |
|---|
| 279 | ! compute volumic mass pure water at atm pressure |
|---|
| 280 | zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt & |
|---|
| 281 | & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
|---|
| 282 | ! seawater volumic mass atm pressure |
|---|
| 283 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
|---|
| 284 | & -4.0899e-3_wp ) *zt+0.824493_wp |
|---|
| 285 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
|---|
| 286 | zr4= 4.8314e-4_wp |
|---|
| 287 | ! |
|---|
| 288 | ! potential volumic mass (reference to the surface) |
|---|
| 289 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
|---|
| 290 | ! |
|---|
| 291 | ! save potential volumic mass |
|---|
| 292 | prhop(ji,jj,jk) = zrhop * tmask(ji,jj,jk) |
|---|
| 293 | ! |
|---|
| 294 | ! add the compression terms |
|---|
| 295 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
|---|
| 296 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
|---|
| 297 | zb = zbw + ze * zs |
|---|
| 298 | ! |
|---|
| 299 | zd = -2.042967e-2_wp |
|---|
| 300 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
|---|
| 301 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
|---|
| 302 | za = ( zd*zsr + zc ) *zs + zaw |
|---|
| 303 | ! |
|---|
| 304 | zb1= ( -0.1909078_wp *zt+7.390729_wp ) *zt-55.87545_wp |
|---|
| 305 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp ) *zt-65.00517_wp ) *zt + 1044.077_wp |
|---|
| 306 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
|---|
| 307 | zk0= ( zb1*zsr + za1 )*zs + zkw |
|---|
| 308 | ! |
|---|
| 309 | ! masked in situ density anomaly |
|---|
| 310 | prd(ji,jj,jk) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & |
|---|
| 311 | & - rau0 ) * zrau0r * tmask(ji,jj,jk) |
|---|
| 312 | END DO |
|---|
| 313 | END DO |
|---|
| 314 | END DO |
|---|
| 315 | ! |
|---|
| 316 | CASE( 1 ) !== Linear formulation = F( temperature ) ==! |
|---|
| 317 | DO jk = 1, jpkm1 |
|---|
| 318 | prd (:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) |
|---|
| 319 | prhop(:,:,jk) = ( 1.e0_wp + prd (:,:,jk) ) * rau0 * tmask(:,:,jk) |
|---|
| 320 | END DO |
|---|
| 321 | ! |
|---|
| 322 | CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
|---|
| 323 | DO jk = 1, jpkm1 |
|---|
| 324 | prd (:,:,jk) = ( rn_beta * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk) |
|---|
| 325 | prhop(:,:,jk) = ( 1.e0_wp + prd (:,:,jk) ) * rau0 * tmask(:,:,jk) |
|---|
| 326 | END DO |
|---|
| 327 | ! |
|---|
| 328 | END SELECT |
|---|
| 329 | ! |
|---|
| 330 | IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-p: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk ) |
|---|
| 331 | ! |
|---|
| 332 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
|---|
| 333 | ! |
|---|
| 334 | IF( nn_timing == 1 ) CALL timing_stop('eos-p') |
|---|
| 335 | ! |
|---|
| 336 | END SUBROUTINE eos_insitu_pot |
|---|
| 337 | |
|---|
| 338 | |
|---|
| 339 | SUBROUTINE eos_insitu_2d( pts, pdep, prd ) |
|---|
| 340 | !!---------------------------------------------------------------------- |
|---|
| 341 | !! *** ROUTINE eos_insitu_2d *** |
|---|
| 342 | !! |
|---|
| 343 | !! ** Purpose : Compute the in situ density (ratio rho/rau0) from |
|---|
| 344 | !! potential temperature and salinity using an equation of state |
|---|
| 345 | !! defined through the namelist parameter nn_eos. * 2D field case |
|---|
| 346 | !! |
|---|
| 347 | !! ** Method : |
|---|
| 348 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
|---|
| 349 | !! the in situ density is computed directly as a function of |
|---|
| 350 | !! potential temperature relative to the surface (the opa t |
|---|
| 351 | !! variable), salt and pressure (assuming no pressure variation |
|---|
| 352 | !! along geopotential surfaces, i.e. the pressure p in decibars |
|---|
| 353 | !! is approximated by the depth in meters. |
|---|
| 354 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
|---|
| 355 | !! with pressure p decibars |
|---|
| 356 | !! potential temperature t deg celsius |
|---|
| 357 | !! salinity s psu |
|---|
| 358 | !! reference volumic mass rau0 kg/m**3 |
|---|
| 359 | !! in situ volumic mass rho kg/m**3 |
|---|
| 360 | !! in situ density anomalie prd no units |
|---|
| 361 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
|---|
| 362 | !! t = 40 deg celcius, s=40 psu |
|---|
| 363 | !! nn_eos = 1 : linear equation of state function of temperature only |
|---|
| 364 | !! prd(t) = 0.0285 - rn_alpha * t |
|---|
| 365 | !! nn_eos = 2 : linear equation of state function of temperature and |
|---|
| 366 | !! salinity |
|---|
| 367 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
|---|
| 368 | !! Note that no boundary condition problem occurs in this routine |
|---|
| 369 | !! as pts are defined over the whole domain. |
|---|
| 370 | !! |
|---|
| 371 | !! ** Action : - prd , the in situ density (no units) |
|---|
| 372 | !! |
|---|
| 373 | !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 |
|---|
| 374 | !!---------------------------------------------------------------------- |
|---|
| 375 | !! |
|---|
| 376 | REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
|---|
| 377 | ! ! 2 : salinity [psu] |
|---|
| 378 | REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: pdep ! depth [m] |
|---|
| 379 | REAL(wp), DIMENSION(jpi,jpj) , INTENT( out) :: prd ! in situ density |
|---|
| 380 | !! |
|---|
| 381 | INTEGER :: ji, jj ! dummy loop indices |
|---|
| 382 | REAL(wp) :: zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw ! temporary scalars |
|---|
| 383 | REAL(wp) :: zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, zmask ! - - |
|---|
| 384 | REAL(wp), POINTER, DIMENSION(:,:) :: zws |
|---|
| 385 | !!---------------------------------------------------------------------- |
|---|
| 386 | ! |
|---|
| 387 | IF( nn_timing == 1 ) CALL timing_start('eos2d') |
|---|
| 388 | ! |
|---|
| 389 | CALL wrk_alloc( jpi, jpj, zws ) |
|---|
| 390 | ! |
|---|
| 391 | |
|---|
| 392 | prd(:,:) = 0._wp |
|---|
| 393 | |
|---|
| 394 | SELECT CASE( nn_eos ) |
|---|
| 395 | ! |
|---|
| 396 | CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! |
|---|
| 397 | ! |
|---|
| 398 | !CDIR NOVERRCHK |
|---|
| 399 | DO jj = 1, jpjm1 |
|---|
| 400 | !CDIR NOVERRCHK |
|---|
| 401 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 402 | zws(ji,jj) = SQRT( ABS( pts(ji,jj,jp_sal) ) ) |
|---|
| 403 | END DO |
|---|
| 404 | END DO |
|---|
| 405 | DO jj = 1, jpjm1 |
|---|
| 406 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 407 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
|---|
| 408 | zt = pts (ji,jj,jp_tem) ! interpolated T |
|---|
| 409 | zs = pts (ji,jj,jp_sal) ! interpolated S |
|---|
| 410 | zsr = zws (ji,jj) ! square root of interpolated S |
|---|
| 411 | zh = pdep (ji,jj) ! depth at the partial step level |
|---|
| 412 | ! |
|---|
| 413 | ! compute volumic mass pure water at atm pressure |
|---|
| 414 | zr1 = ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt & |
|---|
| 415 | & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
|---|
| 416 | ! seawater volumic mass atm pressure |
|---|
| 417 | zr2 = ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp )*zt+7.6438e-5_wp ) *zt & |
|---|
| 418 | & -4.0899e-3_wp ) *zt+0.824493_wp |
|---|
| 419 | zr3 = ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
|---|
| 420 | zr4 = 4.8314e-4_wp |
|---|
| 421 | ! |
|---|
| 422 | ! potential volumic mass (reference to the surface) |
|---|
| 423 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
|---|
| 424 | ! |
|---|
| 425 | ! add the compression terms |
|---|
| 426 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
|---|
| 427 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
|---|
| 428 | zb = zbw + ze * zs |
|---|
| 429 | ! |
|---|
| 430 | zd = -2.042967e-2_wp |
|---|
| 431 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
|---|
| 432 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt -4.721788_wp |
|---|
| 433 | za = ( zd*zsr + zc ) *zs + zaw |
|---|
| 434 | ! |
|---|
| 435 | zb1= (-0.1909078_wp *zt+7.390729_wp ) *zt-55.87545_wp |
|---|
| 436 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp ) *zt-65.00517_wp ) *zt+1044.077_wp |
|---|
| 437 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt & |
|---|
| 438 | & +2098.925_wp ) *zt+190925.6_wp |
|---|
| 439 | zk0= ( zb1*zsr + za1 )*zs + zkw |
|---|
| 440 | ! |
|---|
| 441 | ! masked in situ density anomaly |
|---|
| 442 | prd(ji,jj) = ( zrhop / ( 1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) ) ) - rau0 ) / rau0 * zmask |
|---|
| 443 | END DO |
|---|
| 444 | END DO |
|---|
| 445 | ! |
|---|
| 446 | CASE( 1 ) !== Linear formulation = F( temperature ) ==! |
|---|
| 447 | DO jj = 1, jpjm1 |
|---|
| 448 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 449 | prd(ji,jj) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1) |
|---|
| 450 | END DO |
|---|
| 451 | END DO |
|---|
| 452 | ! |
|---|
| 453 | CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
|---|
| 454 | DO jj = 1, jpjm1 |
|---|
| 455 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 456 | prd(ji,jj) = ( rn_beta * pts(ji,jj,jp_sal) - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1) |
|---|
| 457 | END DO |
|---|
| 458 | END DO |
|---|
| 459 | ! |
|---|
| 460 | END SELECT |
|---|
| 461 | |
|---|
| 462 | IF(ln_ctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' ) |
|---|
| 463 | ! |
|---|
| 464 | CALL wrk_dealloc( jpi, jpj, zws ) |
|---|
| 465 | ! |
|---|
| 466 | IF( nn_timing == 1 ) CALL timing_stop('eos2d') |
|---|
| 467 | ! |
|---|
| 468 | END SUBROUTINE eos_insitu_2d |
|---|
| 469 | |
|---|
| 470 | |
|---|
| 471 | SUBROUTINE eos_bn2( pts, pn2 ) |
|---|
| 472 | !!---------------------------------------------------------------------- |
|---|
| 473 | !! *** ROUTINE eos_bn2 *** |
|---|
| 474 | !! |
|---|
| 475 | !! ** Purpose : Compute the local Brunt-Vaisala frequency at the time- |
|---|
| 476 | !! step of the input arguments |
|---|
| 477 | !! |
|---|
| 478 | !! ** Method : |
|---|
| 479 | !! * nn_eos = 0 : UNESCO sea water properties |
|---|
| 480 | !! The brunt-vaisala frequency is computed using the polynomial |
|---|
| 481 | !! polynomial expression of McDougall (1987): |
|---|
| 482 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
|---|
| 483 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
|---|
| 484 | !! computed and used in zdfddm module : |
|---|
| 485 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
|---|
| 486 | !! * nn_eos = 1 : linear equation of state (temperature only) |
|---|
| 487 | !! N^2 = grav * rn_alpha * dk[ t ]/e3w |
|---|
| 488 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
|---|
| 489 | !! N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w |
|---|
| 490 | !! The use of potential density to compute N^2 introduces e r r o r |
|---|
| 491 | !! in the sign of N^2 at great depths. We recommand the use of |
|---|
| 492 | !! nn_eos = 0, except for academical studies. |
|---|
| 493 | !! Macro-tasked on horizontal slab (jk-loop) |
|---|
| 494 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
|---|
| 495 | !! and is never used at this level. |
|---|
| 496 | !! |
|---|
| 497 | !! ** Action : - pn2 : the brunt-vaisala frequency |
|---|
| 498 | !! |
|---|
| 499 | !! References : McDougall, J. Phys. Oceanogr., 17, 1950-1964, 1987. |
|---|
| 500 | !!---------------------------------------------------------------------- |
|---|
| 501 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
|---|
| 502 | ! ! 2 : salinity [psu] |
|---|
| 503 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency [s-1] |
|---|
| 504 | !! |
|---|
| 505 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 506 | REAL(wp) :: zgde3w, zt, zs, zh, zalbet, zbeta ! local scalars |
|---|
| 507 | #if defined key_zdfddm |
|---|
| 508 | REAL(wp) :: zds ! local scalars |
|---|
| 509 | #endif |
|---|
| 510 | !!---------------------------------------------------------------------- |
|---|
| 511 | |
|---|
| 512 | ! |
|---|
| 513 | IF( nn_timing == 1 ) CALL timing_start('bn2') |
|---|
| 514 | ! |
|---|
| 515 | ! pn2 : interior points only (2=< jk =< jpkm1 ) |
|---|
| 516 | ! -------------------------- |
|---|
| 517 | ! |
|---|
| 518 | SELECT CASE( nn_eos ) |
|---|
| 519 | ! |
|---|
| 520 | CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! |
|---|
| 521 | DO jk = 2, jpkm1 |
|---|
| 522 | DO jj = 1, jpj |
|---|
| 523 | DO ji = 1, jpi |
|---|
| 524 | zgde3w = grav / fse3w(ji,jj,jk) |
|---|
| 525 | zt = 0.5 * ( pts(ji,jj,jk,jp_tem) + pts(ji,jj,jk-1,jp_tem) ) ! potential temperature at w-pt |
|---|
| 526 | 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 |
|---|
| 527 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
|---|
| 528 | ! |
|---|
| 529 | zalbet = ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & ! ratio alpha/beta |
|---|
| 530 | & - 0.203814e-03_wp ) * zt & |
|---|
| 531 | & + 0.170907e-01_wp ) * zt & |
|---|
| 532 | & + 0.665157e-01_wp & |
|---|
| 533 | & + ( - 0.678662e-05_wp * zs & |
|---|
| 534 | & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & |
|---|
| 535 | & + ( ( - 0.302285e-13_wp * zh & |
|---|
| 536 | & - 0.251520e-11_wp * zs & |
|---|
| 537 | & + 0.512857e-12_wp * zt * zt ) * zh & |
|---|
| 538 | & - 0.164759e-06_wp * zs & |
|---|
| 539 | & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & |
|---|
| 540 | & + 0.380374e-04_wp ) * zh |
|---|
| 541 | ! |
|---|
| 542 | zbeta = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt & ! beta |
|---|
| 543 | & - 0.301985e-05_wp ) * zt & |
|---|
| 544 | & + 0.785567e-03_wp & |
|---|
| 545 | & + ( 0.515032e-08_wp * zs & |
|---|
| 546 | & + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs & |
|---|
| 547 | & + ( ( 0.121551e-17_wp * zh & |
|---|
| 548 | & - 0.602281e-15_wp * zs & |
|---|
| 549 | & - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh & |
|---|
| 550 | & + 0.408195e-10_wp * zs & |
|---|
| 551 | & + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt & |
|---|
| 552 | & - 0.121555e-07_wp ) * zh |
|---|
| 553 | ! |
|---|
| 554 | pn2(ji,jj,jk) = zgde3w * zbeta * tmask(ji,jj,jk) & ! N^2 |
|---|
| 555 | & * ( zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) & |
|---|
| 556 | & - ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) |
|---|
| 557 | #if defined key_zdfddm |
|---|
| 558 | ! !!bug **** caution a traiter zds=dk[S]= 0 !!!! |
|---|
| 559 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ! Rrau = (alpha / beta) (dk[t] / dk[s]) |
|---|
| 560 | IF ( ABS( zds) <= 1.e-20_wp ) zds = 1.e-20_wp |
|---|
| 561 | rrau(ji,jj,jk) = zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds |
|---|
| 562 | #endif |
|---|
| 563 | END DO |
|---|
| 564 | END DO |
|---|
| 565 | END DO |
|---|
| 566 | ! |
|---|
| 567 | CASE( 1 ) !== Linear formulation = F( temperature ) ==! |
|---|
| 568 | DO jk = 2, jpkm1 |
|---|
| 569 | pn2(:,:,jk) = grav * rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) ) / fse3w(:,:,jk) * tmask(:,:,jk) |
|---|
| 570 | END DO |
|---|
| 571 | ! |
|---|
| 572 | CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
|---|
| 573 | DO jk = 2, jpkm1 |
|---|
| 574 | pn2(:,:,jk) = grav * ( rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) ) & |
|---|
| 575 | & - rn_beta * ( pts(:,:,jk-1,jp_sal) - pts(:,:,jk,jp_sal) ) ) & |
|---|
| 576 | & / fse3w(:,:,jk) * tmask(:,:,jk) |
|---|
| 577 | END DO |
|---|
| 578 | #if defined key_zdfddm |
|---|
| 579 | DO jk = 2, jpkm1 ! Rrau = (alpha / beta) (dk[t] / dk[s]) |
|---|
| 580 | DO jj = 1, jpj |
|---|
| 581 | DO ji = 1, jpi |
|---|
| 582 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
|---|
| 583 | IF ( ABS( zds ) <= 1.e-20_wp ) zds = 1.e-20_wp |
|---|
| 584 | rrau(ji,jj,jk) = ralpbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds |
|---|
| 585 | END DO |
|---|
| 586 | END DO |
|---|
| 587 | END DO |
|---|
| 588 | #endif |
|---|
| 589 | END SELECT |
|---|
| 590 | |
|---|
| 591 | IF(ln_ctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', ovlap=1, kdim=jpk ) |
|---|
| 592 | #if defined key_zdfddm |
|---|
| 593 | IF(ln_ctl) CALL prt_ctl( tab3d_1=rrau, clinfo1=' rrau : ', ovlap=1, kdim=jpk ) |
|---|
| 594 | #endif |
|---|
| 595 | ! |
|---|
| 596 | IF( nn_timing == 1 ) CALL timing_stop('bn2') |
|---|
| 597 | ! |
|---|
| 598 | END SUBROUTINE eos_bn2 |
|---|
| 599 | |
|---|
| 600 | |
|---|
| 601 | SUBROUTINE eos_alpbet( pts, palpbet, beta0 ) |
|---|
| 602 | !!---------------------------------------------------------------------- |
|---|
| 603 | !! *** ROUTINE eos_alpbet *** |
|---|
| 604 | !! |
|---|
| 605 | !! ** Purpose : Calculates the in situ thermal/haline expansion ratio at T-points |
|---|
| 606 | !! |
|---|
| 607 | !! ** Method : calculates alpha / beta ratio at T-points |
|---|
| 608 | !! * nn_eos = 0 : UNESCO sea water properties |
|---|
| 609 | !! The alpha/beta ratio is returned as 3-D array palpbet using the polynomial |
|---|
| 610 | !! polynomial expression of McDougall (1987). |
|---|
| 611 | !! Scalar beta0 is returned = 1. |
|---|
| 612 | !! * nn_eos = 1 : linear equation of state (temperature only) |
|---|
| 613 | !! The ratio is undefined, so we return alpha as palpbet |
|---|
| 614 | !! Scalar beta0 is returned = 0. |
|---|
| 615 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
|---|
| 616 | !! The alpha/beta ratio is returned as ralpbet |
|---|
| 617 | !! Scalar beta0 is returned = 1. |
|---|
| 618 | !! |
|---|
| 619 | !! ** Action : - palpbet : thermal/haline expansion ratio at T-points |
|---|
| 620 | !! : beta0 : 1. or 0. |
|---|
| 621 | !!---------------------------------------------------------------------- |
|---|
| 622 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity |
|---|
| 623 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: palpbet ! thermal/haline expansion ratio |
|---|
| 624 | REAL(wp), INTENT( out) :: beta0 ! set = 1 except with case 1 eos, rho=rho(T) |
|---|
| 625 | !! |
|---|
| 626 | INTEGER :: ji, jj, jk ! dummy loop indices |
|---|
| 627 | REAL(wp) :: zt, zs, zh ! local scalars |
|---|
| 628 | !!---------------------------------------------------------------------- |
|---|
| 629 | ! |
|---|
| 630 | IF( nn_timing == 1 ) CALL timing_start('eos_alpbet') |
|---|
| 631 | ! |
|---|
| 632 | SELECT CASE ( nn_eos ) |
|---|
| 633 | ! |
|---|
| 634 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
|---|
| 635 | DO jk = 1, jpk |
|---|
| 636 | DO jj = 1, jpj |
|---|
| 637 | DO ji = 1, jpi |
|---|
| 638 | zt = pts(ji,jj,jk,jp_tem) ! potential temperature |
|---|
| 639 | zs = pts(ji,jj,jk,jp_sal) - 35._wp ! salinity anomaly (s-35) |
|---|
| 640 | zh = fsdept(ji,jj,jk) ! depth in meters |
|---|
| 641 | ! |
|---|
| 642 | palpbet(ji,jj,jk) = & |
|---|
| 643 | & ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & |
|---|
| 644 | & - 0.203814e-03_wp ) * zt & |
|---|
| 645 | & + 0.170907e-01_wp ) * zt & |
|---|
| 646 | & + 0.665157e-01_wp & |
|---|
| 647 | & + ( - 0.678662e-05_wp * zs & |
|---|
| 648 | & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & |
|---|
| 649 | & + ( ( - 0.302285e-13_wp * zh & |
|---|
| 650 | & - 0.251520e-11_wp * zs & |
|---|
| 651 | & + 0.512857e-12_wp * zt * zt ) * zh & |
|---|
| 652 | & - 0.164759e-06_wp * zs & |
|---|
| 653 | & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & |
|---|
| 654 | & + 0.380374e-04_wp ) * zh |
|---|
| 655 | END DO |
|---|
| 656 | END DO |
|---|
| 657 | END DO |
|---|
| 658 | beta0 = 1._wp |
|---|
| 659 | ! |
|---|
| 660 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
|---|
| 661 | palpbet(:,:,:) = rn_alpha |
|---|
| 662 | beta0 = 0._wp |
|---|
| 663 | ! |
|---|
| 664 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
|---|
| 665 | palpbet(:,:,:) = ralpbet |
|---|
| 666 | beta0 = 1._wp |
|---|
| 667 | ! |
|---|
| 668 | CASE DEFAULT |
|---|
| 669 | IF(lwp) WRITE(numout,cform_err) |
|---|
| 670 | IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos |
|---|
| 671 | nstop = nstop + 1 |
|---|
| 672 | ! |
|---|
| 673 | END SELECT |
|---|
| 674 | ! |
|---|
| 675 | IF( nn_timing == 1 ) CALL timing_stop('eos_alpbet') |
|---|
| 676 | ! |
|---|
| 677 | END SUBROUTINE eos_alpbet |
|---|
| 678 | |
|---|
| 679 | |
|---|
| 680 | FUNCTION tfreez( psal ) RESULT( ptf ) |
|---|
| 681 | !!---------------------------------------------------------------------- |
|---|
| 682 | !! *** ROUTINE eos_init *** |
|---|
| 683 | !! |
|---|
| 684 | !! ** Purpose : Compute the sea surface freezing temperature [Celcius] |
|---|
| 685 | !! |
|---|
| 686 | !! ** Method : UNESCO freezing point at the surface (pressure = 0???) |
|---|
| 687 | !! freezing point [Celcius]=(-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s-7.53e-4*p |
|---|
| 688 | !! checkvalue: tf= -2.588567 Celsius for s=40.0psu, p=500. decibars |
|---|
| 689 | !! |
|---|
| 690 | !! Reference : UNESCO tech. papers in the marine science no. 28. 1978 |
|---|
| 691 | !!---------------------------------------------------------------------- |
|---|
| 692 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] |
|---|
| 693 | ! Leave result array automatic rather than making explicitly allocated |
|---|
| 694 | REAL(wp), DIMENSION(jpi,jpj) :: ptf ! freezing temperature [Celcius] |
|---|
| 695 | !!---------------------------------------------------------------------- |
|---|
| 696 | ! |
|---|
| 697 | ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) & |
|---|
| 698 | & - 2.154996e-4_wp * psal(:,:) ) * psal(:,:) |
|---|
| 699 | ! |
|---|
| 700 | END FUNCTION tfreez |
|---|
| 701 | |
|---|
| 702 | |
|---|
| 703 | SUBROUTINE eos_init |
|---|
| 704 | !!---------------------------------------------------------------------- |
|---|
| 705 | !! *** ROUTINE eos_init *** |
|---|
| 706 | !! |
|---|
| 707 | !! ** Purpose : initializations for the equation of state |
|---|
| 708 | !! |
|---|
| 709 | !! ** Method : Read the namelist nameos and control the parameters |
|---|
| 710 | !!---------------------------------------------------------------------- |
|---|
| 711 | NAMELIST/nameos/ nn_eos, rn_alpha, rn_beta |
|---|
| 712 | !!---------------------------------------------------------------------- |
|---|
| 713 | ! |
|---|
| 714 | REWIND( numnam ) ! Read Namelist nameos : equation of state |
|---|
| 715 | READ ( numnam, nameos ) |
|---|
| 716 | ! |
|---|
| 717 | IF(lwp) THEN ! Control print |
|---|
| 718 | WRITE(numout,*) |
|---|
| 719 | WRITE(numout,*) 'eos_init : equation of state' |
|---|
| 720 | WRITE(numout,*) '~~~~~~~~' |
|---|
| 721 | WRITE(numout,*) ' Namelist nameos : set eos parameters' |
|---|
| 722 | WRITE(numout,*) ' flag for eq. of state and N^2 nn_eos = ', nn_eos |
|---|
| 723 | WRITE(numout,*) ' thermal exp. coef. (linear) rn_alpha = ', rn_alpha |
|---|
| 724 | WRITE(numout,*) ' saline exp. coef. (linear) rn_beta = ', rn_beta |
|---|
| 725 | ENDIF |
|---|
| 726 | ! |
|---|
| 727 | SELECT CASE( nn_eos ) ! check option |
|---|
| 728 | ! |
|---|
| 729 | CASE( 0 ) !== Jackett and McDougall (1994) formulation ==! |
|---|
| 730 | IF(lwp) WRITE(numout,*) |
|---|
| 731 | IF(lwp) WRITE(numout,*) ' use of Jackett & McDougall (1994) equation of state and' |
|---|
| 732 | IF(lwp) WRITE(numout,*) ' McDougall (1987) Brunt-Vaisala frequency' |
|---|
| 733 | ! |
|---|
| 734 | CASE( 1 ) !== Linear formulation = F( temperature ) ==! |
|---|
| 735 | IF(lwp) WRITE(numout,*) |
|---|
| 736 | IF(lwp) WRITE(numout,*) ' use of linear eos rho(T) = rau0 * ( 1.0285 - rn_alpha * T )' |
|---|
| 737 | IF( lk_zdfddm ) CALL ctl_stop( ' double diffusive mixing parameterization requires', & |
|---|
| 738 | & ' that T and S are used as state variables' ) |
|---|
| 739 | ! |
|---|
| 740 | CASE( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
|---|
| 741 | ralpbet = rn_alpha / rn_beta |
|---|
| 742 | IF(lwp) WRITE(numout,*) |
|---|
| 743 | IF(lwp) WRITE(numout,*) ' use of linear eos rho(T,S) = rau0 * ( rn_beta * S - rn_alpha * T )' |
|---|
| 744 | ! |
|---|
| 745 | CASE DEFAULT !== ERROR in nn_eos ==! |
|---|
| 746 | WRITE(ctmp1,*) ' bad flag value for nn_eos = ', nn_eos |
|---|
| 747 | CALL ctl_stop( ctmp1 ) |
|---|
| 748 | ! |
|---|
| 749 | END SELECT |
|---|
| 750 | ! |
|---|
| 751 | END SUBROUTINE eos_init |
|---|
| 752 | |
|---|
| 753 | !!====================================================================== |
|---|
| 754 | END MODULE eosbn2 |
|---|
