1 | MODULE eosbn2_tam |
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2 | !!============================================================================== |
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3 | !! *** MODULE eosbn2_tam *** |
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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 | !! Tangent and Adjoint Module |
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7 | !!=========================================================================== !! History of the direct Module : |
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8 | !! ! 89-03 (O. Marti) Original code |
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9 | !! 6.0 ! 94-07 (G. Madec, M. Imbard) add bn2 |
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10 | !! 6.0 ! 94-08 (G. Madec) Add Jackett & McDougall eos |
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11 | !! 7.0 ! 96-01 (G. Madec) statement function for e3 |
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12 | !! 8.1 ! 97-07 (G. Madec) introduction of neos, OPA8.1 |
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13 | !! 8.1 ! 97-07 (G. Madec) density instead of volumic mass |
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14 | !! ! 99-02 (G. Madec, N. Grima) semi-implicit pressure gradient |
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15 | !! ! 01-09 (M. Ben Jelloul) bugfix onlinear eos |
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16 | !! 8.5 ! 02-10 (G. Madec) add eos_init |
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17 | !! 8.5 ! 02-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d |
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18 | !! 9.0 ! 03-08 (G. Madec) F90, free form |
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19 | !! 9.0 ! 06-08 (G. Madec) add tfreez function |
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20 | !! History of the TAM Module : |
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21 | !! 8.2 ! 05-03 (F. Van den Berghe, A. Weaver, N. Daget) |
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22 | !! - eostan.F |
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23 | !! 9.0 ! 07-07 (K. Mogensen) Initial version based on eostan.F |
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24 | !! ! 08-07 (A. Vidard) bug fix in computation of prd_tl if neos=1 |
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25 | !! ! 08-11 (A. Vidard) TAM of the 06-08 version |
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26 | !!---------------------------------------------------------------------- |
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27 | |
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28 | !!---------------------------------------------------------------------- |
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29 | !! Direct subroutines |
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30 | !! eos : generic interface of the equation of state |
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31 | !! eos_insitu : Compute the in situ density |
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32 | !! eos_insitu_pot : Compute the insitu and surface referenced potential |
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33 | !! volumic mass |
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34 | !! eos_insitu_2d : Compute the in situ density for 2d fields |
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35 | !! eos_insitu_pot_1pt : Compute the in situ density for a single point |
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36 | !! eos_bn2 : Compute the Brunt-Vaisala frequency |
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37 | !! tfreez : Compute the surface freezing temperature (NOT IN TAM) |
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38 | !! eos_init : set eos parameters (namelist) |
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39 | !!---------------------------------------------------------------------- |
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40 | !! * Modules used |
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41 | #if defined key_zdfddm |
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42 | USE oce_tam , ONLY: & |
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43 | & rrau_tl, & |
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44 | & rrau_ad |
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45 | #endif |
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46 | USE dom_oce , ONLY: & ! ocean space and time domain |
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47 | & tmask, & |
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48 | & e1t, & |
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49 | & e2t, & |
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50 | #if defined key_zco |
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51 | & e3t_0, & |
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52 | & e3w_0, & |
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53 | & gdept_0, & |
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54 | & gdepw_0, & |
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55 | #else |
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56 | & e3t, & |
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57 | & e3w, & |
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58 | & gdept, & |
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59 | & gdepw, & |
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60 | #endif |
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61 | & mig, & |
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62 | & mjg, & |
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63 | & nperio, & |
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64 | & nldi, & |
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65 | & nldj, & |
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66 | & nlei, & |
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67 | & nlej |
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68 | USE par_kind , ONLY: & |
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69 | & wp |
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70 | USE par_oce , ONLY: & |
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71 | & jpi, & |
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72 | & jpj, & |
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73 | & jpk, & |
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74 | & jpim1, & |
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75 | & jpjm1, & |
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76 | & jpkm1, & |
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77 | & jpiglo |
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78 | USE oce , ONLY: & |
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79 | & tn, & |
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80 | & sn |
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81 | USE phycst , ONLY: & ! physical constants |
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82 | & rau0, & |
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83 | & grav |
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84 | USE in_out_manager, ONLY: & ! I/O manager |
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85 | & lwp, & |
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86 | & ctmp1, & |
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87 | & numout, & |
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88 | & ctl_stop |
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89 | #if defined key_zdfddm |
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90 | USE zdfddm ! vertical physics: double diffusion |
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91 | #endif |
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92 | USE eosbn2 , ONLY: & |
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93 | & eos_init, & |
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94 | & neos_init, & |
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95 | & neos, & |
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96 | & ralpha, & |
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97 | & rbeta |
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98 | USE gridrandom , ONLY: & ! Random Gaussian noise on grids |
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99 | & grid_random |
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100 | USE dotprodfld , ONLY: & ! Computes dot product for 3D and 2D fields |
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101 | & dot_product |
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102 | USE tstool_tam , ONLY: & |
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103 | & prntst_adj, & |
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104 | & prntst_tlm, & ! |
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105 | & stds, & |
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106 | & stdt |
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107 | IMPLICIT NONE |
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108 | PRIVATE |
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109 | |
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110 | !! * Interface |
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111 | INTERFACE eos_tan |
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112 | MODULE PROCEDURE eos_insitu_tan, eos_insitu_pot_tan, eos_insitu_2d_tan |
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113 | END INTERFACE |
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114 | INTERFACE eos_adj |
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115 | MODULE PROCEDURE eos_insitu_adj, eos_insitu_pot_adj, eos_insitu_2d_adj |
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116 | END INTERFACE |
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117 | INTERFACE bn2_tan |
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118 | MODULE PROCEDURE eos_bn2_tan |
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119 | END INTERFACE |
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120 | INTERFACE bn2_adj |
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121 | MODULE PROCEDURE eos_bn2_adj |
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122 | END INTERFACE |
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123 | |
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124 | !! * Routine accessibility |
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125 | PUBLIC eos_tan ! called by step.F90, inidtr.F90, tranpc.F90 and intgrd.F90 |
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126 | PUBLIC bn2_tan ! called by step.F90 |
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127 | PUBLIC eos_adj ! called by step.F90, inidtr.F90, tranpc.F90 and intgrd.F90 |
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128 | PUBLIC bn2_adj ! called by step.F90 |
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129 | #if defined key_tam |
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130 | PUBLIC eos_adj_tst |
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131 | PUBLIC bn2_adj_tst |
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132 | PUBLIC eos_tlm_tst |
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133 | PUBLIC bn2_tlm_tst |
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134 | #endif |
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135 | |
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136 | |
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137 | !! * Substitutions |
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138 | # include "domzgr_substitute.h90" |
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139 | # include "vectopt_loop_substitute.h90" |
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140 | |
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141 | CONTAINS |
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142 | |
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143 | SUBROUTINE eos_insitu_tan( ptem, psal, ptem_tl, psal_tl, prd_tl ) |
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144 | !!----------------------------------------------------------------------- |
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145 | !! |
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146 | !! *** ROUTINE eos_insitu_tan : TL OF ROUTINE eos_insitu *** |
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147 | !! |
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148 | !! ** Purpose of direct routine : Compute the in situ density |
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149 | !! (ratio rho/rau0) from potential temperature and salinity |
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150 | !! using an equation of state defined through the namelist |
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151 | !! parameter neos. |
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152 | !! |
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153 | !! ** Method of direct routine : 3 cases: |
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154 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
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155 | !! the in situ density is computed directly as a function of |
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156 | !! potential temperature relative to the surface (the opa t |
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157 | !! variable), salt and pressure (assuming no pressure variation |
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158 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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159 | !! is approximated by the depth in meters. |
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160 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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161 | !! with pressure p decibars |
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162 | !! potential temperature t deg celsius |
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163 | !! salinity s psu |
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164 | !! reference volumic mass rau0 kg/m**3 |
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165 | !! in situ volumic mass rho kg/m**3 |
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166 | !! in situ density anomalie prd no units |
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167 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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168 | !! t = 40 deg celcius, s=40 psu |
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169 | !! neos = 1 : linear equation of state function of temperature only |
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170 | !! prd(t) = 0.0285 - ralpha * t |
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171 | !! neos = 2 : linear equation of state function of temperature and |
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172 | !! salinity |
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173 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
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174 | !! Note that no boundary condition problem occurs in this routine |
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175 | !! as (ptem,psal) are defined over the whole domain. |
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176 | !! |
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177 | !! ** Comments on Adjoint Routine : |
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178 | !! Care has been taken to avoid division by zero when computing |
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179 | !! the inverse of the square root of salinity at masked salinity |
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180 | !! points. |
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181 | !! |
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182 | !! * Arguments |
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183 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
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184 | & ptem, & ! potential temperature |
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185 | & psal, & ! salinity |
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186 | & ptem_tl, & ! TL of potential temperature |
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187 | & psal_tl ! TL of salinity |
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188 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
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189 | & prd_tl ! TL of potential density (surface referenced) |
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190 | !! * Local declarations |
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191 | INTEGER :: ji, jj, jk ! dummy loop indices |
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192 | REAL(wp) :: & ! temporary scalars |
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193 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
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194 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
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195 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
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196 | zr4tl, zrhoptl, zetl, zbwtl, & |
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197 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
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198 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
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199 | zmask |
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200 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws |
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201 | !!---------------------------------------------------------------------- |
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202 | |
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203 | |
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204 | ! initialization (in not already done) |
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205 | IF( neos_init == 0 ) CALL eos_init |
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206 | |
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207 | SELECT CASE ( neos ) |
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208 | |
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209 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
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210 | |
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211 | #ifdef key_sp |
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212 | zeps = 1.e-7 |
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213 | #else |
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214 | zeps = 1.e-14 |
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215 | #endif |
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216 | |
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217 | !CDIR NOVERRCHK |
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218 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
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219 | |
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220 | ! ! =============== |
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221 | DO jk = 1, jpkm1 ! Horizontal slab |
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222 | ! ! =============== |
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223 | DO jj = 1, jpj |
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224 | DO ji = 1, jpi |
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225 | zt = ptem(ji,jj,jk) |
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226 | zs = psal(ji,jj,jk) |
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227 | ! depth |
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228 | zh = fsdept(ji,jj,jk) |
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229 | ! square root salinity |
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230 | zsr= zws(ji,jj,jk) |
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231 | ! compute volumic mass pure water at atm pressure |
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232 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
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233 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
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234 | ! seawater volumic mass atm pressure |
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235 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
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236 | -4.0899e-3 ) *zt+0.824493 |
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237 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
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238 | zr4= 4.8314e-4 |
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239 | |
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240 | ! potential volumic mass (reference to the surface) |
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241 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
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242 | |
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243 | ! add the compression terms |
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244 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
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245 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
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246 | zb = zbw + ze * zs |
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247 | |
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248 | zd = -2.042967e-2 |
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249 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
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250 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
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251 | za = ( zd*zsr + zc ) *zs + zaw |
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252 | |
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253 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
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254 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
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255 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
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256 | zk0= ( zb1*zsr + za1 )*zs + zkw |
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257 | |
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258 | ! Tangent linear part |
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259 | |
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260 | zttl = ptem_tl(ji,jj,jk) |
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261 | zstl = psal_tl(ji,jj,jk) |
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262 | |
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263 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
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264 | & * tmask(ji,jj,jk) * zstl |
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265 | |
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266 | zr1tl= ( ( ( ( 5.*6.536332e-9 * zt & |
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267 | & -4.*1.120083e-6 ) * zt & |
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268 | & +3.*1.001685e-4 ) * zt & |
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269 | & -2.*9.095290e-3 ) * zt & |
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270 | & + 6.793952e-2 ) * zttl |
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271 | |
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272 | zr2tl= ( ( ( 4.*5.3875e-9 * zt & |
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273 | & -3.*8.2467e-7 ) * zt & |
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274 | & +2.*7.6438e-5 ) * zt & |
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275 | & - 4.0899e-3 ) * zttl |
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276 | |
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277 | zr3tl= ( -2.*1.6546e-6 * zt & |
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278 | & + 1.0227e-4 ) * zttl |
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279 | |
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280 | zrhoptl= zr1tl & |
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281 | & + zs * zr2tl & |
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282 | & + zsr * zs * zr3tl & |
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283 | & + zr3 * zs * zsrtl & |
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284 | & + ( 2. * zr4 * zs + zr2 & |
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285 | & + zr3 * zsr ) * zstl |
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286 | |
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287 | zetl = ( -2.*3.508914e-8 * zt & |
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288 | & - 1.248266e-8 ) * zttl |
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289 | |
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290 | zbwtl= ( 2.*1.296821e-6 * zt & |
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291 | & - 5.782165e-9 ) * zttl |
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292 | |
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293 | zbtl = zbwtl & |
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294 | & + zs * zetl & |
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295 | & + ze * zstl |
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296 | |
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297 | zctl = ( -2.*7.267926e-5 * zt & |
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298 | & + 2.598241e-3 ) * zttl |
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299 | |
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300 | zawtl= ( ( 3.*5.939910e-6 * zt & |
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301 | & +2.*2.512549e-3 ) * zt & |
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302 | & - 0.1028859 ) * zttl |
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303 | |
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304 | zatl = zawtl & |
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305 | & + zd * zs * zsrtl & |
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306 | & + zs * zctl & |
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307 | & + ( zd * zsr + zc ) * zstl |
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308 | |
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309 | zb1tl= ( -2.*0.1909078 * zt & |
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310 | & + 7.390729 ) * zttl |
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311 | |
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312 | za1tl= ( ( 3.*2.326469e-3 * zt & |
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313 | & +2.*1.553190 ) * zt & |
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314 | & - 65.00517 ) * zttl |
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315 | |
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316 | zkwtl= ( ( ( -4.*1.361629e-4 * zt & |
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317 | & -3.*1.852732e-2 ) * zt & |
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318 | & -2.*30.41638 ) * zt & |
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319 | & + 2098.925 ) * zttl |
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320 | |
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321 | zk0tl= zkwtl & |
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322 | & + zb1 * zs * zsrtl & |
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323 | & + zs * zsr * zb1tl & |
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324 | & + zs * za1tl & |
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325 | & + ( zb1 * zsr + za1 ) * zstl |
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326 | |
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327 | ! Masked in situ density anomaly |
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328 | |
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329 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
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330 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
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331 | |
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332 | prd_tl(ji,jj,jk) = tmask(ji,jj,jk) * zrdc2 * & |
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333 | & ( zrhoptl & |
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334 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
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335 | & * ( zk0tl & |
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336 | & - zh * ( zatl & |
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337 | & - zh * zbtl ) ) )& |
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338 | & / rau0 |
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339 | |
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340 | END DO |
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341 | |
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342 | END DO |
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343 | ! ! =============== |
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344 | END DO ! End of slab |
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345 | ! ! =============== |
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346 | |
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347 | CASE ( 1 ) ! Linear formulation function of temperature only |
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348 | |
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349 | ! ! =============== |
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350 | DO jk = 1, jpkm1 ! Horizontal slab |
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351 | ! ! =============== |
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352 | DO jj = 1, jpj |
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353 | DO ji = 1, jpi |
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354 | zttl = ptem_tl(ji,jj,jk) |
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355 | ! ... density and potential volumic mass |
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356 | prd_tl(ji,jj,jk) = ( - ralpha * zttl ) * tmask(ji,jj,jk) |
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357 | END DO |
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358 | END DO |
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359 | ! ! =============== |
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360 | END DO ! End of slab |
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361 | ! ! =============== |
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362 | |
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363 | |
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364 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
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365 | |
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366 | ! ! =============== |
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367 | DO jk = 1, jpkm1 ! Horizontal slab |
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368 | ! ! =============== |
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369 | DO jj = 1, jpj |
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370 | DO ji = 1, jpi |
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371 | zttl = ptem_tl(ji,jj,jk) |
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372 | zstl = psal_tl(ji,jj,jk) |
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373 | ! ... density and potential volumic mass |
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374 | prd_tl(ji,jj,jk) = ( rbeta * zstl - ralpha * zttl ) * tmask(ji,jj,jk) |
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375 | END DO |
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376 | END DO |
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377 | ! ! =============== |
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378 | END DO ! End of slab |
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379 | ! ! =============== |
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380 | |
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381 | CASE DEFAULT |
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382 | |
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383 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
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384 | CALL ctl_stop( ctmp1 ) |
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385 | |
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386 | END SELECT |
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387 | |
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388 | END SUBROUTINE eos_insitu_tan |
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389 | |
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390 | SUBROUTINE eos_insitu_pot_tan( ptem, psal, ptem_tl, psal_tl, prd_tl, prhop_tl) |
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391 | !!---------------------------------------------------------------------- |
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392 | !! *** ROUTINE eos_insitu_pot_tan *** |
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393 | !! |
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394 | !! ** Purpose or the direct routine: |
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395 | !! Compute the in situ density (ratio rho/rau0) and the |
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396 | !! potential volumic mass (Kg/m3) from potential temperature and |
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397 | !! salinity fields using an equation of state defined through the |
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398 | !! namelist parameter neos. |
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399 | !! |
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400 | !! ** Method : |
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401 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
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402 | !! the in situ density is computed directly as a function of |
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403 | !! potential temperature relative to the surface (the opa t |
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404 | !! variable), salt and pressure (assuming no pressure variation |
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405 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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406 | !! is approximated by the depth in meters. |
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407 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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408 | !! rhop(t,s) = rho(t,s,0) |
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409 | !! with pressure p decibars |
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410 | !! potential temperature t deg celsius |
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411 | !! salinity s psu |
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412 | !! reference volumic mass rau0 kg/m**3 |
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413 | !! in situ volumic mass rho kg/m**3 |
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414 | !! in situ density anomalie prd no units |
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415 | !! |
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416 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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417 | !! t = 40 deg celcius, s=40 psu |
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418 | !! |
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419 | !! neos = 1 : linear equation of state function of temperature only |
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420 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - ralpha * t |
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421 | !! rhop(t,s) = rho(t,s) |
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422 | !! |
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423 | !! neos = 2 : linear equation of state function of temperature and |
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424 | !! salinity |
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425 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
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426 | !! = rbeta * s - ralpha * tn - 1. |
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427 | !! rhop(t,s) = rho(t,s) |
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428 | !! Note that no boundary condition problem occurs in this routine |
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429 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
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430 | !! |
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431 | !! ** Action : - prd , the in situ density (no units) |
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432 | !! - prhop, the potential volumic mass (Kg/m3) |
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433 | !! |
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434 | !! References : |
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435 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
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436 | !! Brown, J. A. and K. A. Campana. Mon. Weather Rev., 1978 |
---|
437 | !! |
---|
438 | !!---------------------------------------------------------------------- |
---|
439 | !! * Arguments |
---|
440 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
441 | ptem, & ! potential temperature |
---|
442 | psal ! salinity |
---|
443 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
444 | ptem_tl,& ! potential temperature |
---|
445 | psal_tl ! salinity |
---|
446 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
---|
447 | prd_tl, & ! potential density (surface referenced) |
---|
448 | prhop_tl ! potential density (surface referenced) |
---|
449 | !! * Local declarations |
---|
450 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
451 | REAL(wp) :: & ! temporary scalars |
---|
452 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
453 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
454 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
---|
455 | zr4tl, zrhoptl, zetl, zbwtl, & |
---|
456 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
---|
457 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
---|
458 | zmask |
---|
459 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws |
---|
460 | !!---------------------------------------------------------------------- |
---|
461 | |
---|
462 | ! initialization (in not already done) |
---|
463 | IF( neos_init == 0 ) CALL eos_init |
---|
464 | |
---|
465 | |
---|
466 | SELECT CASE ( neos ) |
---|
467 | |
---|
468 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
469 | |
---|
470 | #ifdef key_sp |
---|
471 | zeps = 1.e-7 |
---|
472 | #else |
---|
473 | zeps = 1.e-14 |
---|
474 | #endif |
---|
475 | |
---|
476 | !CDIR NOVERRCHK |
---|
477 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
---|
478 | |
---|
479 | ! ! =============== |
---|
480 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
481 | ! ! =============== |
---|
482 | DO jj = 1, jpj |
---|
483 | DO ji = 1, jpi |
---|
484 | zt = ptem(ji,jj,jk) |
---|
485 | zs = psal(ji,jj,jk) |
---|
486 | ! depth |
---|
487 | zh = fsdept(ji,jj,jk) |
---|
488 | ! square root salinity |
---|
489 | zsr = zws(ji,jj,jk) |
---|
490 | ! compute volumic mass pure water at atm pressure |
---|
491 | zr1 = ( ( ( ( 6.536332e-9 * zt - 1.120083e-6 ) * zt & |
---|
492 | & + 1.001685e-4 ) * zt - 9.095290e-3 ) * zt & |
---|
493 | & + 6.793952e-2 ) * zt + 999.842594 |
---|
494 | ! seawater volumic mass atm pressure |
---|
495 | zr2 = ( ( ( 5.3875e-9 * zt - 8.2467e-7 ) * zt & |
---|
496 | & + 7.6438e-5 ) * zt - 4.0899e-3 ) * zt & |
---|
497 | & + 0.824493 |
---|
498 | zr3 = ( -1.6546e-6 * zt + 1.0227e-4 ) * zt - 5.72466e-3 |
---|
499 | zr4 = 4.8314e-4 |
---|
500 | |
---|
501 | ! potential volumic mass (reference to the surface) |
---|
502 | zrhop= ( zr4 * zs + zr3 * zsr + zr2 ) * zs + zr1 |
---|
503 | |
---|
504 | ! add the compression terms |
---|
505 | ze = ( -3.508914e-8 * zt - 1.248266e-8 ) * zt - 2.595994e-6 |
---|
506 | zbw = ( 1.296821e-6 * zt - 5.782165e-9 ) * zt + 1.045941e-4 |
---|
507 | zb = zbw + ze * zs |
---|
508 | |
---|
509 | zd = -2.042967e-2 |
---|
510 | zc = (-7.267926e-5 * zt + 2.598241e-3 ) * zt + 0.1571896 |
---|
511 | zaw= ( ( 5.939910e-6 * zt + 2.512549e-3 ) * zt - 0.1028859 ) * zt - 4.721788 |
---|
512 | za = ( zd * zsr + zc ) * zs + zaw |
---|
513 | |
---|
514 | zb1 = (-0.1909078 * zt + 7.390729 ) * zt - 55.87545 |
---|
515 | za1 = ( ( 2.326469e-3 * zt + 1.553190 ) * zt - 65.00517 & |
---|
516 | & ) * zt + 1044.077 |
---|
517 | zkw = ( ( (-1.361629e-4 * zt - 1.852732e-2 ) * zt - 30.41638 & |
---|
518 | & ) * zt + 2098.925 ) * zt + 190925.6 |
---|
519 | zk0 = ( zb1 * zsr + za1 ) * zs + zkw |
---|
520 | |
---|
521 | |
---|
522 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
523 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
524 | |
---|
525 | ! Tangent linear part |
---|
526 | |
---|
527 | zttl = ptem_tl(ji,jj,jk) |
---|
528 | zstl = psal_tl(ji,jj,jk) |
---|
529 | |
---|
530 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
531 | & * tmask(ji,jj,jk) * zstl |
---|
532 | |
---|
533 | zr1tl= ( ( ( ( 5.*6.536332e-9 * zt & |
---|
534 | & -4.*1.120083e-6 ) * zt & |
---|
535 | & +3.*1.001685e-4 ) * zt & |
---|
536 | & -2.*9.095290e-3 ) * zt & |
---|
537 | & + 6.793952e-2 ) * zttl |
---|
538 | |
---|
539 | zr2tl= ( ( ( 4.*5.3875e-9 * zt & |
---|
540 | & -3.*8.2467e-7 ) * zt & |
---|
541 | & +2.*7.6438e-5 ) * zt & |
---|
542 | & - 4.0899e-3 ) * zttl |
---|
543 | |
---|
544 | zr3tl= ( -2.*1.6546e-6 * zt & |
---|
545 | & + 1.0227e-4 ) * zttl |
---|
546 | |
---|
547 | zrhoptl= zr1tl & |
---|
548 | & + zs * zr2tl & |
---|
549 | & + zsr * zs * zr3tl & |
---|
550 | & + zr3 * zs * zsrtl & |
---|
551 | & + ( 2. * zr4 * zs + zr2 & |
---|
552 | & + zr3 * zsr ) * zstl |
---|
553 | |
---|
554 | prhop_tl(ji,jj,jk) = zrhoptl * tmask(ji,jj,jk) |
---|
555 | |
---|
556 | zetl = ( -2.*3.508914e-8 * zt & |
---|
557 | & - 1.248266e-8 ) * zttl |
---|
558 | |
---|
559 | zbwtl= ( 2.*1.296821e-6 * zt & |
---|
560 | & - 5.782165e-9 ) * zttl |
---|
561 | |
---|
562 | zbtl = zbwtl & |
---|
563 | & + zs * zetl & |
---|
564 | & + ze * zstl |
---|
565 | |
---|
566 | zctl = ( -2.*7.267926e-5 * zt & |
---|
567 | & + 2.598241e-3 ) * zttl |
---|
568 | |
---|
569 | zawtl= ( ( 3.*5.939910e-6 * zt & |
---|
570 | & +2.*2.512549e-3 ) * zt & |
---|
571 | & - 0.1028859 ) * zttl |
---|
572 | |
---|
573 | zatl = zawtl & |
---|
574 | & + zd * zs * zsrtl & |
---|
575 | & + zs * zctl & |
---|
576 | & + ( zd * zsr + zc ) * zstl |
---|
577 | |
---|
578 | zb1tl= ( -2.*0.1909078 * zt & |
---|
579 | & + 7.390729 ) * zttl |
---|
580 | |
---|
581 | za1tl= ( ( 3.*2.326469e-3 * zt & |
---|
582 | & +2.*1.553190 ) * zt & |
---|
583 | & - 65.00517 ) * zttl |
---|
584 | |
---|
585 | zkwtl= ( ( ( -4.*1.361629e-4 * zt & |
---|
586 | & -3.*1.852732e-2 ) * zt & |
---|
587 | & -2.*30.41638 ) * zt & |
---|
588 | & + 2098.925 ) * zttl |
---|
589 | |
---|
590 | zk0tl= zkwtl & |
---|
591 | & + zb1 * zs * zsrtl & |
---|
592 | & + zs * zsr * zb1tl & |
---|
593 | & + zs * za1tl & |
---|
594 | & + ( zb1 * zsr + za1 ) * zstl |
---|
595 | |
---|
596 | ! Masked in situ density anomaly |
---|
597 | |
---|
598 | prd_tl(ji,jj,jk) = tmask(ji,jj,jk) * zrdc2 * & |
---|
599 | & ( zrhoptl & |
---|
600 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
---|
601 | & * ( zk0tl & |
---|
602 | & - zh * ( zatl & |
---|
603 | & - zh * zbtl ) ) )& |
---|
604 | & / rau0 |
---|
605 | END DO |
---|
606 | |
---|
607 | END DO |
---|
608 | ! ! =============== |
---|
609 | END DO ! End of slab |
---|
610 | ! ! =============== |
---|
611 | |
---|
612 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
613 | |
---|
614 | ! ! =============== |
---|
615 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
616 | ! ! =============== |
---|
617 | DO jj = 1, jpj |
---|
618 | DO ji = 1, jpi |
---|
619 | zttl = ptem_tl(ji,jj,jk) |
---|
620 | ! ... density and potential volumic mass |
---|
621 | prd_tl (ji,jj,jk) = ( - ralpha * zttl ) * tmask(ji,jj,jk) |
---|
622 | prhop_tl(ji,jj,jk) = ( rau0 * prd_tl(ji,jj,jk) ) * tmask(ji,jj,jk) |
---|
623 | END DO |
---|
624 | END DO |
---|
625 | ! ! =============== |
---|
626 | END DO ! End of slab |
---|
627 | ! ! =============== |
---|
628 | |
---|
629 | |
---|
630 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
631 | |
---|
632 | ! ! =============== |
---|
633 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
634 | ! ! =============== |
---|
635 | DO jj = 1, jpj |
---|
636 | DO ji = 1, jpi |
---|
637 | zttl = ptem_tl(ji,jj,jk) |
---|
638 | zstl = psal_tl(ji,jj,jk) |
---|
639 | ! ... density and potential volumic mass |
---|
640 | prd_tl(ji,jj,jk) = ( rbeta * zstl - ralpha * zttl ) * tmask(ji,jj,jk) |
---|
641 | prhop_tl(ji,jj,jk) = ( rau0 * prd_tl(ji,jj,jk) ) * tmask(ji,jj,jk) |
---|
642 | END DO |
---|
643 | END DO |
---|
644 | ! ! =============== |
---|
645 | END DO ! End of slab |
---|
646 | ! ! =============== |
---|
647 | |
---|
648 | CASE DEFAULT |
---|
649 | |
---|
650 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
651 | CALL ctl_stop( ctmp1 ) |
---|
652 | |
---|
653 | END SELECT |
---|
654 | |
---|
655 | END SUBROUTINE eos_insitu_pot_tan |
---|
656 | SUBROUTINE eos_insitu_2d_tan( ptem, psal, pdep, ptem_tl, psal_tl, prd_tl ) |
---|
657 | !!----------------------------------------------------------------------- |
---|
658 | !! |
---|
659 | !! *** ROUTINE eos_insitu_2d_tan : TL OF ROUTINE eos_insitu_2d *** |
---|
660 | !! |
---|
661 | !! ** Purpose of direct routine : Compute the in situ density |
---|
662 | !! (ratio rho/rau0) from potential temperature and salinity |
---|
663 | !! using an equation of state defined through the namelist |
---|
664 | !! parameter neos. * 2D field case |
---|
665 | !! |
---|
666 | !! ** Method of direct routine : 3 cases: |
---|
667 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
---|
668 | !! the in situ density is computed directly as a function of |
---|
669 | !! potential temperature relative to the surface (the opa t |
---|
670 | !! variable), salt and pressure (assuming no pressure variation |
---|
671 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
672 | !! is approximated by the depth in meters. |
---|
673 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
674 | !! with pressure p decibars |
---|
675 | !! potential temperature t deg celsius |
---|
676 | !! salinity s psu |
---|
677 | !! reference volumic mass rau0 kg/m**3 |
---|
678 | !! in situ volumic mass rho kg/m**3 |
---|
679 | !! in situ density anomalie prd no units |
---|
680 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
681 | !! t = 40 deg celcius, s=40 psu |
---|
682 | !! neos = 1 : linear equation of state function of temperature only |
---|
683 | !! prd(t) = 0.0285 - ralpha * t |
---|
684 | !! neos = 2 : linear equation of state function of temperature and |
---|
685 | !! salinity |
---|
686 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
---|
687 | !! Note that no boundary condition problem occurs in this routine |
---|
688 | !! as (ptem,psal) are defined over the whole domain. |
---|
689 | !! |
---|
690 | !! ** Comments on Adjoint Routine : |
---|
691 | !! Care has been taken to avoid division by zero when computing |
---|
692 | !! the inverse of the square root of salinity at masked salinity |
---|
693 | !! points. |
---|
694 | !! |
---|
695 | !! ** Action : |
---|
696 | !! |
---|
697 | !! References : |
---|
698 | !! |
---|
699 | !! History : |
---|
700 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eostan.F |
---|
701 | !! 9.0 ! 07-07 (K. Mogensen) Initial version based on eostan.F |
---|
702 | !! ! 08-07 (A. Vidard) bug fix in computation of prd_tl if neos=1 |
---|
703 | !!----------------------------------------------------------------------- |
---|
704 | !! * Modules used |
---|
705 | !! * Arguments |
---|
706 | REAL(wp), DIMENSION(jpi,jpj), INTENT( in ) :: & |
---|
707 | & ptem, & ! potential temperature |
---|
708 | & psal, & ! salinity |
---|
709 | & pdep, & ! depth |
---|
710 | & ptem_tl, & ! TL of potential temperature |
---|
711 | & psal_tl ! TL of salinity |
---|
712 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out ) :: & |
---|
713 | & prd_tl ! TL of potential density (surface referenced) |
---|
714 | |
---|
715 | !! * Local declarations |
---|
716 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
717 | REAL(wp) :: & ! temporary scalars |
---|
718 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
719 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
720 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
---|
721 | zr4tl, zrhoptl, zetl, zbwtl, & |
---|
722 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
---|
723 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
---|
724 | zmask |
---|
725 | REAL(wp), DIMENSION(jpi,jpj) :: zws |
---|
726 | !!---------------------------------------------------------------------- |
---|
727 | |
---|
728 | |
---|
729 | ! initialization (in not already done) |
---|
730 | IF( neos_init == 0 ) CALL eos_init |
---|
731 | |
---|
732 | SELECT CASE ( neos ) |
---|
733 | |
---|
734 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
735 | |
---|
736 | #ifdef key_sp |
---|
737 | zeps = 1.e-7 |
---|
738 | #else |
---|
739 | zeps = 1.e-14 |
---|
740 | #endif |
---|
741 | |
---|
742 | !CDIR NOVERRCHK |
---|
743 | DO jj = 1, jpjm1 |
---|
744 | !CDIR NOVERRCHK |
---|
745 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
746 | zws(ji,jj) = SQRT( ABS( psal(ji,jj) ) ) |
---|
747 | END DO |
---|
748 | END DO |
---|
749 | |
---|
750 | ! ! =============== |
---|
751 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
752 | ! ! =============== |
---|
753 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
754 | |
---|
755 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
---|
756 | |
---|
757 | zt = ptem (ji,jj) ! interpolated T |
---|
758 | zs = psal (ji,jj) ! interpolated S |
---|
759 | zsr= zws(ji,jj) ! square root of interpolated S |
---|
760 | zh = pdep(ji,jj) ! depth at the partial step level |
---|
761 | ! compute volumic mass pure water at atm pressure |
---|
762 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
---|
763 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
---|
764 | ! seawater volumic mass atm pressure |
---|
765 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
---|
766 | -4.0899e-3 ) *zt+0.824493 |
---|
767 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
---|
768 | zr4= 4.8314e-4 |
---|
769 | |
---|
770 | ! potential volumic mass (reference to the surface) |
---|
771 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
---|
772 | |
---|
773 | ! add the compression terms |
---|
774 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
---|
775 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
---|
776 | zb = zbw + ze * zs |
---|
777 | |
---|
778 | zd = -2.042967e-2 |
---|
779 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
---|
780 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
---|
781 | za = ( zd*zsr + zc ) *zs + zaw |
---|
782 | |
---|
783 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
---|
784 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
---|
785 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
---|
786 | zk0= ( zb1*zsr + za1 )*zs + zkw |
---|
787 | |
---|
788 | ! Tangent linear part |
---|
789 | |
---|
790 | zttl = ptem_tl(ji,jj) |
---|
791 | zstl = psal_tl(ji,jj) |
---|
792 | |
---|
793 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
794 | & * tmask(ji,jj,1) * zstl |
---|
795 | |
---|
796 | zr1tl= ( ( ( ( 5.*6.536332e-9 * zt & |
---|
797 | & -4.*1.120083e-6 ) * zt & |
---|
798 | & +3.*1.001685e-4 ) * zt & |
---|
799 | & -2.*9.095290e-3 ) * zt & |
---|
800 | & + 6.793952e-2 ) * zttl |
---|
801 | |
---|
802 | zr2tl= ( ( ( 4.*5.3875e-9 * zt & |
---|
803 | & -3.*8.2467e-7 ) * zt & |
---|
804 | & +2.*7.6438e-5 ) * zt & |
---|
805 | & - 4.0899e-3 ) * zttl |
---|
806 | |
---|
807 | zr3tl= ( -2.*1.6546e-6 * zt & |
---|
808 | & + 1.0227e-4 ) * zttl |
---|
809 | |
---|
810 | zrhoptl= zr1tl & |
---|
811 | & + zs * zr2tl & |
---|
812 | & + zsr * zs * zr3tl & |
---|
813 | & + zr3 * zs * zsrtl & |
---|
814 | & + ( 2. * zr4 * zs + zr2 & |
---|
815 | & + zr3 * zsr ) * zstl |
---|
816 | |
---|
817 | zetl = ( -2.*3.508914e-8 * zt & |
---|
818 | & - 1.248266e-8 ) * zttl |
---|
819 | |
---|
820 | zbwtl= ( 2.*1.296821e-6 * zt & |
---|
821 | & - 5.782165e-9 ) * zttl |
---|
822 | |
---|
823 | zbtl = zbwtl & |
---|
824 | & + zs * zetl & |
---|
825 | & + ze * zstl |
---|
826 | |
---|
827 | zctl = ( -2.*7.267926e-5 * zt & |
---|
828 | & + 2.598241e-3 ) * zttl |
---|
829 | |
---|
830 | zawtl= ( ( 3.*5.939910e-6 * zt & |
---|
831 | & +2.*2.512549e-3 ) * zt & |
---|
832 | & - 0.1028859 ) * zttl |
---|
833 | |
---|
834 | zatl = zawtl & |
---|
835 | & + zd * zs * zsrtl & |
---|
836 | & + zs * zctl & |
---|
837 | & + ( zd * zsr + zc ) * zstl |
---|
838 | |
---|
839 | zb1tl= ( -2.*0.1909078 * zt & |
---|
840 | & + 7.390729 ) * zttl |
---|
841 | |
---|
842 | za1tl= ( ( 3.*2.326469e-3 * zt & |
---|
843 | & +2.*1.553190 ) * zt & |
---|
844 | & - 65.00517 ) * zttl |
---|
845 | |
---|
846 | zkwtl= ( ( ( -4.*1.361629e-4 * zt & |
---|
847 | & -3.*1.852732e-2 ) * zt & |
---|
848 | & -2.*30.41638 ) * zt & |
---|
849 | & + 2098.925 ) * zttl |
---|
850 | |
---|
851 | zk0tl= zkwtl & |
---|
852 | & + zb1 * zs * zsrtl & |
---|
853 | & + zs * zsr * zb1tl & |
---|
854 | & + zs * za1tl & |
---|
855 | & + ( zb1 * zsr + za1 ) * zstl |
---|
856 | |
---|
857 | ! Masked in situ density anomaly |
---|
858 | |
---|
859 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
860 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
861 | |
---|
862 | prd_tl(ji,jj) = tmask(ji,jj,1) * zrdc2 * & |
---|
863 | & ( zrhoptl & |
---|
864 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
---|
865 | & * ( zk0tl & |
---|
866 | & - zh * ( zatl & |
---|
867 | & - zh * zbtl ) ) )& |
---|
868 | & / rau0 |
---|
869 | |
---|
870 | |
---|
871 | END DO |
---|
872 | ! ! =============== |
---|
873 | END DO ! End of slab |
---|
874 | ! ! =============== |
---|
875 | |
---|
876 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
877 | |
---|
878 | ! ! =============== |
---|
879 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
880 | ! ! =============== |
---|
881 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
882 | zttl = ptem_tl(ji,jj) |
---|
883 | ! ... density and potential volumic mass |
---|
884 | prd_tl(ji,jj) = ( - ralpha * zttl ) * tmask(ji,jj,1) |
---|
885 | |
---|
886 | END DO |
---|
887 | ! ! =============== |
---|
888 | END DO ! End of slab |
---|
889 | ! ! =============== |
---|
890 | |
---|
891 | |
---|
892 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
893 | |
---|
894 | ! ! =============== |
---|
895 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
896 | ! ! =============== |
---|
897 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
898 | zttl = ptem_tl(ji,jj) |
---|
899 | zstl = psal_tl(ji,jj) |
---|
900 | prd_tl (ji,jj) = ( rbeta * zstl - ralpha * zttl ) * tmask(ji,jj,1) |
---|
901 | END DO |
---|
902 | ! ! =============== |
---|
903 | END DO ! End of slab |
---|
904 | ! ! =============== |
---|
905 | |
---|
906 | CASE DEFAULT |
---|
907 | |
---|
908 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
909 | CALL ctl_stop( ctmp1 ) |
---|
910 | |
---|
911 | END SELECT |
---|
912 | |
---|
913 | |
---|
914 | END SUBROUTINE eos_insitu_2d_tan |
---|
915 | |
---|
916 | SUBROUTINE eos_insitu_adj(ptem, psal, ptem_ad, psal_ad, prd_ad) |
---|
917 | !!----------------------------------------------------------------------- |
---|
918 | !! |
---|
919 | !! *** ROUTINE eos_insitu_tan : Adjoint OF ROUTINE eos_insitu *** |
---|
920 | !! |
---|
921 | !! ** Purpose of direct routine : Compute the in situ density |
---|
922 | !! (ratio rho/rau0) from potential temperature and salinity |
---|
923 | !! using an equation of state defined through the namelist |
---|
924 | !! parameter neos. |
---|
925 | !! |
---|
926 | !! ** Method of direct routine : 3 cases: |
---|
927 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
---|
928 | !! the in situ density is computed directly as a function of |
---|
929 | !! potential temperature relative to the surface (the opa t |
---|
930 | !! variable), salt and pressure (assuming no pressure variation |
---|
931 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
932 | !! is approximated by the depth in meters. |
---|
933 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
934 | !! with pressure p decibars |
---|
935 | !! potential temperature t deg celsius |
---|
936 | !! salinity s psu |
---|
937 | !! reference volumic mass rau0 kg/m**3 |
---|
938 | !! in situ volumic mass rho kg/m**3 |
---|
939 | !! in situ density anomalie prd no units |
---|
940 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
941 | !! t = 40 deg celcius, s=40 psu |
---|
942 | !! neos = 1 : linear equation of state function of temperature only |
---|
943 | !! prd(t) = 0.0285 - ralpha * t |
---|
944 | !! neos = 2 : linear equation of state function of temperature and |
---|
945 | !! salinity |
---|
946 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
---|
947 | !! Note that no boundary condition problem occurs in this routine |
---|
948 | !! as (ptem,psal) are defined over the whole domain. |
---|
949 | !! |
---|
950 | !! ** Comments on Adjoint Routine : |
---|
951 | !! Care has been taken to avoid division by zero when computing |
---|
952 | !! the inverse of the square root of salinity at masked salinity |
---|
953 | !! points. |
---|
954 | !! |
---|
955 | !! ** Action : |
---|
956 | !! |
---|
957 | !! References : |
---|
958 | !! |
---|
959 | !! History : |
---|
960 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eostan.F |
---|
961 | !! 9.0 ! 08-08 (A. Vidard) 9.0 version |
---|
962 | !!----------------------------------------------------------------------- |
---|
963 | !! * Modules used |
---|
964 | !! * Arguments |
---|
965 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
966 | ptem, & ! potential temperature |
---|
967 | psal ! salinity |
---|
968 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
969 | ptem_ad, & ! potential temperature |
---|
970 | psal_ad ! salinity |
---|
971 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
972 | prd_ad ! potential density (surface referenced) |
---|
973 | !! * Local declarations |
---|
974 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
975 | REAL(wp) :: & ! temporary scalars |
---|
976 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
977 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
978 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
979 | zr4ad, zrhopad, zead, zbwad, & |
---|
980 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
981 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
982 | zmask |
---|
983 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws |
---|
984 | !!---------------------------------------------------------------------- |
---|
985 | |
---|
986 | |
---|
987 | ! initialization (in not already done) |
---|
988 | IF( neos_init == 0 ) CALL eos_init |
---|
989 | ! initialization of adjoint variables |
---|
990 | ztad = 0.0_wp |
---|
991 | zsad = 0.0_wp |
---|
992 | zhad = 0.0_wp |
---|
993 | zsrad = 0.0_wp |
---|
994 | zr1ad = 0.0_wp |
---|
995 | zr2ad = 0.0_wp |
---|
996 | zr3ad = 0.0_wp |
---|
997 | zr4ad = 0.0_wp |
---|
998 | zrhopad = 0.0_wp |
---|
999 | zead = 0.0_wp |
---|
1000 | zbwad = 0.0_wp |
---|
1001 | zbad = 0.0_wp |
---|
1002 | zdad = 0.0_wp |
---|
1003 | zcad = 0.0_wp |
---|
1004 | zawad = 0.0_wp |
---|
1005 | zaad = 0.0_wp |
---|
1006 | zb1ad = 0.0_wp |
---|
1007 | za1ad = 0.0_wp |
---|
1008 | zkwad = 0.0_wp |
---|
1009 | zk0ad = 0.0_wp |
---|
1010 | |
---|
1011 | SELECT CASE ( neos ) |
---|
1012 | |
---|
1013 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
1014 | |
---|
1015 | #ifdef key_sp |
---|
1016 | zeps = 1.e-7 |
---|
1017 | #else |
---|
1018 | zeps = 1.e-14 |
---|
1019 | #endif |
---|
1020 | |
---|
1021 | !CDIR NOVERRCHK |
---|
1022 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
---|
1023 | |
---|
1024 | ! ! =============== |
---|
1025 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
1026 | ! ! =============== |
---|
1027 | DO jj = 1, jpj |
---|
1028 | DO ji = 1, jpi |
---|
1029 | zt = ptem(ji,jj,jk) |
---|
1030 | zs = psal(ji,jj,jk) |
---|
1031 | ! depth |
---|
1032 | zh = fsdept(ji,jj,jk) |
---|
1033 | ! square root salinity |
---|
1034 | zsr= zws(ji,jj,jk) |
---|
1035 | ! compute volumic mass pure water at atm pressure |
---|
1036 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
---|
1037 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
---|
1038 | ! seawater volumic mass atm pressure |
---|
1039 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
---|
1040 | -4.0899e-3 ) *zt+0.824493 |
---|
1041 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
---|
1042 | zr4= 4.8314e-4 |
---|
1043 | |
---|
1044 | ! potential volumic mass (reference to the surface) |
---|
1045 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
---|
1046 | |
---|
1047 | ! add the compression terms |
---|
1048 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
---|
1049 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
---|
1050 | zb = zbw + ze * zs |
---|
1051 | |
---|
1052 | zd = -2.042967e-2 |
---|
1053 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
---|
1054 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
---|
1055 | za = ( zd*zsr + zc ) *zs + zaw |
---|
1056 | |
---|
1057 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
---|
1058 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
---|
1059 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
---|
1060 | zk0= ( zb1*zsr + za1 )*zs + zkw |
---|
1061 | |
---|
1062 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
1063 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
1064 | ! ============ |
---|
1065 | ! Adjoint part |
---|
1066 | ! ============ |
---|
1067 | |
---|
1068 | ! Masked in situ density anomaly |
---|
1069 | |
---|
1070 | zrhopad = zrhopad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1071 | & * zrdc2 / rau0 |
---|
1072 | zk0ad = zk0ad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1073 | & * zrdc2 * zrdc2 * zh & |
---|
1074 | & * zrdc1**2 * zrhop & |
---|
1075 | & / rau0 |
---|
1076 | zaad = zaad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1077 | & * zrdc2 * zrdc2 * zh & |
---|
1078 | & * zrdc1**2 * zrhop & |
---|
1079 | & * zh / rau0 |
---|
1080 | zbad = zbad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1081 | & * zrdc2 * zrdc2 * zh & |
---|
1082 | & * zrdc1**2 * zrhop & |
---|
1083 | & * zh * zh / rau0 |
---|
1084 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1085 | |
---|
1086 | zkwad = zkwad + zk0ad |
---|
1087 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
1088 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
1089 | za1ad = za1ad + zk0ad * zs |
---|
1090 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
1091 | zk0ad = 0.0_wp |
---|
1092 | |
---|
1093 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4 * zt & |
---|
1094 | & -3.*1.852732e-2 ) * zt & |
---|
1095 | & -2.*30.41638 ) * zt & |
---|
1096 | & + 2098.925 ) |
---|
1097 | zkwad = 0.0_wp |
---|
1098 | |
---|
1099 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3 * zt & |
---|
1100 | & +2.*1.553190 ) * zt & |
---|
1101 | & - 65.00517 ) |
---|
1102 | za1ad = 0.0_wp |
---|
1103 | |
---|
1104 | ztad = ztad + zb1ad * (-2.*0.1909078 * zt & |
---|
1105 | & + 7.390729 ) |
---|
1106 | zb1ad = 0.0_wp |
---|
1107 | |
---|
1108 | zawad = zawad + zaad |
---|
1109 | zsrad = zsrad + zaad * zd * zs |
---|
1110 | zcad = zcad + zaad * zs |
---|
1111 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
1112 | zaad = 0.0_wp |
---|
1113 | |
---|
1114 | ztad = ztad + zawad * ( ( 3.*5.939910e-6 * zt & |
---|
1115 | & +2.*2.512549e-3 ) * zt & |
---|
1116 | & - 0.1028859 ) |
---|
1117 | zawad = 0.0_wp |
---|
1118 | |
---|
1119 | ztad = ztad + zcad * (-2.*7.267926e-5 * zt & |
---|
1120 | & + 2.598241e-3 ) |
---|
1121 | zcad = 0.0_wp |
---|
1122 | |
---|
1123 | zbwad = zbwad + zbad |
---|
1124 | zead = zead + zbad * zs |
---|
1125 | zsad = zsad + zbad * ze |
---|
1126 | zbad = 0.0_wp |
---|
1127 | |
---|
1128 | ztad = ztad + zbwad * ( 2.*1.296821e-6 * zt & |
---|
1129 | & - 5.782165e-9 ) |
---|
1130 | zbwad = 0.0_wp |
---|
1131 | |
---|
1132 | ztad = ztad + zead * (-2.*3.508914e-8 * zt & |
---|
1133 | & - 1.248266e-8 ) |
---|
1134 | zead = 0.0_wp |
---|
1135 | |
---|
1136 | zr1ad = zr1ad + zrhopad |
---|
1137 | zr2ad = zr2ad + zrhopad * zs |
---|
1138 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
1139 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
1140 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
1141 | & + zr3 * zsr ) |
---|
1142 | zrhopad = 0.0_wp |
---|
1143 | |
---|
1144 | ztad = ztad + zr3ad * (-2.*1.6546e-6 * zt & |
---|
1145 | & + 1.0227e-4 ) |
---|
1146 | zr3ad = 0.0_wp |
---|
1147 | |
---|
1148 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9 * zt & |
---|
1149 | & -3.*8.2467e-7 ) * zt & |
---|
1150 | & +2.*7.6438e-5 ) * zt & |
---|
1151 | & - 4.0899e-3 ) |
---|
1152 | zr2ad = 0.0_wp |
---|
1153 | |
---|
1154 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9 * zt & |
---|
1155 | & -4.*1.120083e-6 ) * zt & |
---|
1156 | & +3.*1.001685e-4 ) * zt & |
---|
1157 | & -2.*9.095290e-3 ) * zt & |
---|
1158 | & + 6.793952e-2 ) |
---|
1159 | zr1ad = 0.0_wp |
---|
1160 | |
---|
1161 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
1162 | & * tmask(ji,jj,jk) |
---|
1163 | zsrad = 0.0_wp |
---|
1164 | |
---|
1165 | psal_ad(ji,jj,jk) = psal_ad(ji,jj,jk) + zsad |
---|
1166 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) + ztad |
---|
1167 | ztad = 0.0_wp |
---|
1168 | zsad = 0.0_wp |
---|
1169 | END DO |
---|
1170 | |
---|
1171 | END DO |
---|
1172 | ! ! =============== |
---|
1173 | END DO ! End of slab |
---|
1174 | ! ! =============== |
---|
1175 | |
---|
1176 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
1177 | |
---|
1178 | ! ! =============== |
---|
1179 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
1180 | ! ! =============== |
---|
1181 | DO jj = 1, jpj |
---|
1182 | DO ji = 1, jpi |
---|
1183 | ! ... density and potential volumic mass |
---|
1184 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) - ralpha * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1185 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1186 | END DO |
---|
1187 | END DO |
---|
1188 | ! ! =============== |
---|
1189 | END DO ! End of slab |
---|
1190 | ! ! =============== |
---|
1191 | |
---|
1192 | |
---|
1193 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
1194 | |
---|
1195 | ! ! =============== |
---|
1196 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
1197 | ! ! =============== |
---|
1198 | DO jj = 1, jpj |
---|
1199 | DO ji = 1, jpi |
---|
1200 | ! ... density and potential volumic mass |
---|
1201 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) - ralpha * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1202 | psal_ad(ji,jj,jk) = psal_ad(ji,jj,jk) + rbeta * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1203 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1204 | END DO |
---|
1205 | END DO |
---|
1206 | ! ! =============== |
---|
1207 | END DO ! End of slab |
---|
1208 | ! ! =============== |
---|
1209 | |
---|
1210 | CASE DEFAULT |
---|
1211 | |
---|
1212 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
1213 | CALL ctl_stop( ctmp1 ) |
---|
1214 | |
---|
1215 | END SELECT |
---|
1216 | END SUBROUTINE eos_insitu_adj |
---|
1217 | SUBROUTINE eos_insitu_pot_adj ( ptem, psal, ptem_ad, psal_ad, prd_ad, prhop_ad ) |
---|
1218 | !!---------------------------------------------------------------------- |
---|
1219 | !! *** ROUTINE eos_insitu_pot_adj *** |
---|
1220 | !! |
---|
1221 | !! ** Purpose or the direct routine: |
---|
1222 | !! Compute the in situ density (ratio rho/rau0) and the |
---|
1223 | !! potential volumic mass (Kg/m3) from potential temperature and |
---|
1224 | !! salinity fields using an equation of state defined through the |
---|
1225 | !! namelist parameter neos. |
---|
1226 | !! |
---|
1227 | !! ** Method : |
---|
1228 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
---|
1229 | !! the in situ density is computed directly as a function of |
---|
1230 | !! potential temperature relative to the surface (the opa t |
---|
1231 | !! variable), salt and pressure (assuming no pressure variation |
---|
1232 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
1233 | !! is approximated by the depth in meters. |
---|
1234 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
1235 | !! rhop(t,s) = rho(t,s,0) |
---|
1236 | !! with pressure p decibars |
---|
1237 | !! potential temperature t deg celsius |
---|
1238 | !! salinity s psu |
---|
1239 | !! reference volumic mass rau0 kg/m**3 |
---|
1240 | !! in situ volumic mass rho kg/m**3 |
---|
1241 | !! in situ density anomalie prd no units |
---|
1242 | !! |
---|
1243 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
1244 | !! t = 40 deg celcius, s=40 psu |
---|
1245 | !! |
---|
1246 | !! neos = 1 : linear equation of state function of temperature only |
---|
1247 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - ralpha * t |
---|
1248 | !! rhop(t,s) = rho(t,s) |
---|
1249 | !! |
---|
1250 | !! neos = 2 : linear equation of state function of temperature and |
---|
1251 | !! salinity |
---|
1252 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
---|
1253 | !! = rbeta * s - ralpha * tn - 1. |
---|
1254 | !! rhop(t,s) = rho(t,s) |
---|
1255 | !! Note that no boundary condition problem occurs in this routine |
---|
1256 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
---|
1257 | !! |
---|
1258 | !! ** Action : - prd , the in situ density (no units) |
---|
1259 | !! - prhop, the potential volumic mass (Kg/m3) |
---|
1260 | !! |
---|
1261 | !! References : |
---|
1262 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
---|
1263 | !! Brown, J. A. and K. A. Campana. Mon. Weather Rev., 1978 |
---|
1264 | !! |
---|
1265 | !! History of the adjoint routine: |
---|
1266 | !! 9.0 ! 08-06 (A. Vidard) Initial version |
---|
1267 | !!---------------------------------------------------------------------- |
---|
1268 | !! * Arguments |
---|
1269 | |
---|
1270 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
1271 | ptem, & ! potential temperature |
---|
1272 | psal ! salinity |
---|
1273 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
1274 | ptem_ad, & ! potential temperature |
---|
1275 | psal_ad ! salinity |
---|
1276 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
1277 | prd_ad, & ! potential density (surface referenced) |
---|
1278 | prhop_ad |
---|
1279 | !! * Local declarations |
---|
1280 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1281 | REAL(wp) :: & ! temporary scalars |
---|
1282 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
1283 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
1284 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
1285 | zr4ad, zrhopad, zead, zbwad, & |
---|
1286 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
1287 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
1288 | zmask |
---|
1289 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws |
---|
1290 | !!---------------------------------------------------------------------- |
---|
1291 | ! initialization (in not already done) |
---|
1292 | IF( neos_init == 0 ) CALL eos_init |
---|
1293 | ! initialization of adjoint variables |
---|
1294 | ztad = 0.0_wp |
---|
1295 | zsad = 0.0_wp |
---|
1296 | zhad = 0.0_wp |
---|
1297 | zsrad = 0.0_wp |
---|
1298 | zr1ad = 0.0_wp |
---|
1299 | zr2ad = 0.0_wp |
---|
1300 | zr3ad = 0.0_wp |
---|
1301 | zr4ad = 0.0_wp |
---|
1302 | zrhopad = 0.0_wp |
---|
1303 | zead = 0.0_wp |
---|
1304 | zbwad = 0.0_wp |
---|
1305 | zbad = 0.0_wp |
---|
1306 | zdad = 0.0_wp |
---|
1307 | zcad = 0.0_wp |
---|
1308 | zawad = 0.0_wp |
---|
1309 | zaad = 0.0_wp |
---|
1310 | zb1ad = 0.0_wp |
---|
1311 | za1ad = 0.0_wp |
---|
1312 | zkwad = 0.0_wp |
---|
1313 | zk0ad = 0.0_wp |
---|
1314 | |
---|
1315 | SELECT CASE ( neos ) |
---|
1316 | |
---|
1317 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
1318 | |
---|
1319 | #ifdef key_sp |
---|
1320 | zeps = 1.e-7 |
---|
1321 | #else |
---|
1322 | zeps = 1.e-14 |
---|
1323 | #endif |
---|
1324 | |
---|
1325 | !CDIR NOVERRCHK |
---|
1326 | zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) |
---|
1327 | ! ! =============== |
---|
1328 | DO jk = jpkm1, 1, -1 ! Horizontal slab |
---|
1329 | ! ! =============== |
---|
1330 | DO jj = jpj, 1, -1 |
---|
1331 | DO ji = jpi, 1, -1 |
---|
1332 | ! direct recomputing |
---|
1333 | zt = ptem(ji,jj,jk) |
---|
1334 | zs = psal(ji,jj,jk) |
---|
1335 | ! depth |
---|
1336 | zh = fsdept(ji,jj,jk) |
---|
1337 | ! square root salinity |
---|
1338 | zsr = zws(ji,jj,jk) |
---|
1339 | ! compute volumic mass pure water at atm pressure |
---|
1340 | zr1 = ( ( ( ( 6.536332e-9 * zt - 1.120083e-6 ) * zt & |
---|
1341 | & + 1.001685e-4 ) * zt - 9.095290e-3 ) * zt & |
---|
1342 | & + 6.793952e-2 ) * zt + 999.842594 |
---|
1343 | ! seawater volumic mass atm pressure |
---|
1344 | zr2 = ( ( ( 5.3875e-9 * zt - 8.2467e-7 ) * zt & |
---|
1345 | & + 7.6438e-5 ) * zt - 4.0899e-3 ) * zt + 0.824493 |
---|
1346 | zr3 = ( -1.6546e-6 * zt + 1.0227e-4 ) * zt - 5.72466e-3 |
---|
1347 | zr4 = 4.8314e-4 |
---|
1348 | ! potential volumic mass (reference to the surface) |
---|
1349 | zrhop = ( zr4 * zs + zr3*zsr + zr2 ) * zs + zr1 |
---|
1350 | ! add the compression terms |
---|
1351 | ze = ( -3.508914e-8 * zt - 1.248266e-8 ) * zt - 2.595994e-6 |
---|
1352 | zbw = ( 1.296821e-6 * zt - 5.782165e-9 ) * zt + 1.045941e-4 |
---|
1353 | zb = zbw + ze * zs |
---|
1354 | |
---|
1355 | zd = -2.042967e-2 |
---|
1356 | zc = (-7.267926e-5 * zt + 2.598241e-3 ) * zt + 0.1571896 |
---|
1357 | zaw= ( ( 5.939910e-6 * zt + 2.512549e-3 ) * zt - 0.1028859 & |
---|
1358 | & ) * zt - 4.721788 |
---|
1359 | za = ( zd * zsr + zc ) * zs + zaw |
---|
1360 | |
---|
1361 | zb1= (-0.1909078 * zt + 7.390729 ) * zt - 55.87545 |
---|
1362 | za1= ( ( 2.326469e-3 * zt + 1.553190 ) * zt - 65.00517 & |
---|
1363 | & ) * zt + 1044.077 |
---|
1364 | zkw= ( ( (-1.361629e-4 * zt - 1.852732e-2 ) * zt - 30.41638 & |
---|
1365 | & ) * zt + 2098.925 ) * zt + 190925.6 |
---|
1366 | zk0= ( zb1 * zsr + za1 ) * zs + zkw |
---|
1367 | |
---|
1368 | |
---|
1369 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
1370 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
1371 | |
---|
1372 | ! ============ |
---|
1373 | ! Adjoint part |
---|
1374 | ! ============ |
---|
1375 | |
---|
1376 | ! Masked in situ density anomaly |
---|
1377 | |
---|
1378 | zrhopad = zrhopad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1379 | & * zrdc2 / rau0 |
---|
1380 | zk0ad = zk0ad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1381 | & * zrdc2 * zrdc2 * zh & |
---|
1382 | & * zrdc1**2 * zrhop & |
---|
1383 | & / rau0 |
---|
1384 | zaad = zaad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1385 | & * zrdc2 * zrdc2 * zh & |
---|
1386 | & * zrdc1**2 * zrhop & |
---|
1387 | & * zh / rau0 |
---|
1388 | zbad = zbad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
1389 | & * zrdc2 * zrdc2 * zh & |
---|
1390 | & * zrdc1**2 * zrhop & |
---|
1391 | & * zh * zh / rau0 |
---|
1392 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1393 | |
---|
1394 | zkwad = zkwad + zk0ad |
---|
1395 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
1396 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
1397 | za1ad = za1ad + zk0ad * zs |
---|
1398 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
1399 | zk0ad = 0.0_wp |
---|
1400 | |
---|
1401 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4 * zt & |
---|
1402 | & -3.*1.852732e-2 ) * zt & |
---|
1403 | & -2.*30.41638 ) * zt & |
---|
1404 | & + 2098.925 ) |
---|
1405 | zkwad = 0.0_wp |
---|
1406 | |
---|
1407 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3 * zt & |
---|
1408 | & +2.*1.553190 ) * zt & |
---|
1409 | & - 65.00517 ) |
---|
1410 | za1ad = 0.0_wp |
---|
1411 | |
---|
1412 | ztad = ztad + zb1ad * (-2.*0.1909078 * zt & |
---|
1413 | & + 7.390729 ) |
---|
1414 | zb1ad = 0.0_wp |
---|
1415 | |
---|
1416 | zawad = zawad + zaad |
---|
1417 | zsrad = zsrad + zaad * zd * zs |
---|
1418 | zcad = zcad + zaad * zs |
---|
1419 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
1420 | zaad = 0.0_wp |
---|
1421 | |
---|
1422 | ztad = ztad + zawad * ( ( 3.*5.939910e-6 * zt & |
---|
1423 | & +2.*2.512549e-3 ) * zt & |
---|
1424 | & - 0.1028859 ) |
---|
1425 | zawad = 0.0_wp |
---|
1426 | |
---|
1427 | ztad = ztad + zcad * (-2.*7.267926e-5 * zt & |
---|
1428 | & + 2.598241e-3 ) |
---|
1429 | zcad = 0.0_wp |
---|
1430 | |
---|
1431 | |
---|
1432 | zsad = zsad + zbad * ze |
---|
1433 | zead = zead + zbad * zs |
---|
1434 | zbwad = zbwad + zbad |
---|
1435 | zbad = 0.0_wp |
---|
1436 | |
---|
1437 | ztad = ztad + zbwad * ( 2.*1.296821e-6 * zt & |
---|
1438 | & - 5.782165e-9 ) |
---|
1439 | zbwad = 0.0_wp |
---|
1440 | |
---|
1441 | ztad = ztad + zead * (-2.*3.508914e-8 * zt & |
---|
1442 | & - 1.248266e-8 ) |
---|
1443 | zead = 0.0_wp |
---|
1444 | |
---|
1445 | zrhopad = zrhopad + prhop_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1446 | prhop_ad(ji,jj,jk) = 0.0_wp |
---|
1447 | |
---|
1448 | zr1ad = zr1ad + zrhopad |
---|
1449 | zr2ad = zr2ad + zrhopad * zs |
---|
1450 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
1451 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
1452 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
1453 | & + zr3 * zsr ) |
---|
1454 | zrhopad = 0.0_wp |
---|
1455 | |
---|
1456 | ztad = ztad + zr3ad * (-2.*1.6546e-6 * zt & |
---|
1457 | & + 1.0227e-4 ) |
---|
1458 | zr3ad = 0.0_wp |
---|
1459 | |
---|
1460 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9 * zt & |
---|
1461 | & -3.*8.2467e-7 ) * zt & |
---|
1462 | & +2.*7.6438e-5 ) * zt & |
---|
1463 | & - 4.0899e-3 ) |
---|
1464 | zr2ad = 0.0_wp |
---|
1465 | |
---|
1466 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9 * zt & |
---|
1467 | & -4.*1.120083e-6 ) * zt & |
---|
1468 | & +3.*1.001685e-4 ) * zt & |
---|
1469 | & -2.*9.095290e-3 ) * zt & |
---|
1470 | & + 6.793952e-2 ) |
---|
1471 | zr1ad = 0.0_wp |
---|
1472 | |
---|
1473 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
1474 | & * tmask(ji,jj,jk) |
---|
1475 | zsrad = 0.0_wp |
---|
1476 | |
---|
1477 | psal_ad(ji,jj,jk) = psal_ad(ji,jj,jk) + zsad |
---|
1478 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) + ztad |
---|
1479 | ztad = 0.0_wp |
---|
1480 | zsad = 0.0_wp |
---|
1481 | |
---|
1482 | END DO |
---|
1483 | |
---|
1484 | END DO |
---|
1485 | ! ! =============== |
---|
1486 | END DO ! End of slab |
---|
1487 | ! ! =============== |
---|
1488 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
1489 | ! ! =============== |
---|
1490 | DO jk = jpkm1, 1, -1 ! Horizontal slab |
---|
1491 | ! ! =============== |
---|
1492 | DO jj = jpj, 1, -1 |
---|
1493 | DO ji = jpi, 1, -1 |
---|
1494 | prd_ad(ji,jj,jk) = prd_ad(ji,jj,jk) & |
---|
1495 | & + rau0 * prhop_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1496 | prhop_ad(ji,jj,jk) = 0.0_wp |
---|
1497 | |
---|
1498 | ztad = ztad - ralpha * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1499 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1500 | |
---|
1501 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) + ztad |
---|
1502 | ztad = 0.0_wp |
---|
1503 | END DO |
---|
1504 | END DO |
---|
1505 | ! ! =============== |
---|
1506 | END DO ! End of slab |
---|
1507 | ! ! =============== |
---|
1508 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
1509 | ! ! =============== |
---|
1510 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
1511 | ! ! =============== |
---|
1512 | DO jj = 1, jpj |
---|
1513 | DO ji = 1, jpi |
---|
1514 | prd_ad(ji,jj,jk) = prd_ad(ji,jj,jk) & |
---|
1515 | & + rau0 * prhop_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1516 | prhop_ad(ji,jj,jk) = 0.0_wp |
---|
1517 | |
---|
1518 | |
---|
1519 | ztad = ztad - ralpha * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1520 | zsad = zsad + rbeta * prd_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
1521 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
1522 | |
---|
1523 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) + ztad |
---|
1524 | ztad = 0.0_wp |
---|
1525 | psal_ad(ji,jj,jk) = psal_ad(ji,jj,jk) + zsad |
---|
1526 | zsad = 0.0_wp |
---|
1527 | END DO |
---|
1528 | END DO |
---|
1529 | ! ! =============== |
---|
1530 | END DO ! End of slab |
---|
1531 | ! ! =============== |
---|
1532 | |
---|
1533 | CASE DEFAULT |
---|
1534 | |
---|
1535 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
1536 | CALL ctl_stop( ctmp1 ) |
---|
1537 | |
---|
1538 | END SELECT |
---|
1539 | |
---|
1540 | END SUBROUTINE eos_insitu_pot_adj |
---|
1541 | |
---|
1542 | SUBROUTINE eos_insitu_2d_adj( ptem, psal, pdep, ptem_ad, psal_ad, prd_ad ) |
---|
1543 | !!----------------------------------------------------------------------- |
---|
1544 | !! |
---|
1545 | !! *** ROUTINE eos_insitu_2d_adj : adj OF ROUTINE eos_insitu_2d *** |
---|
1546 | !! |
---|
1547 | !! ** Purpose of direct routine : Compute the in situ density |
---|
1548 | !! (ratio rho/rau0) from potential temperature and salinity |
---|
1549 | !! using an equation of state defined through the namelist |
---|
1550 | !! parameter neos. * 2D field case |
---|
1551 | !! |
---|
1552 | !! ** Method of direct routine : 3 cases: |
---|
1553 | !! neos = 0 : Jackett and McDougall (1994) equation of state. |
---|
1554 | !! the in situ density is computed directly as a function of |
---|
1555 | !! potential temperature relative to the surface (the opa t |
---|
1556 | !! variable), salt and pressure (assuming no pressure variation |
---|
1557 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
1558 | !! is approximated by the depth in meters. |
---|
1559 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
1560 | !! with pressure p decibars |
---|
1561 | !! potential temperature t deg celsius |
---|
1562 | !! salinity s psu |
---|
1563 | !! reference volumic mass rau0 kg/m**3 |
---|
1564 | !! in situ volumic mass rho kg/m**3 |
---|
1565 | !! in situ density anomalie prd no units |
---|
1566 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
1567 | !! t = 40 deg celcius, s=40 psu |
---|
1568 | !! neos = 1 : linear equation of state function of temperature only |
---|
1569 | !! prd(t) = 0.0285 - ralpha * t |
---|
1570 | !! neos = 2 : linear equation of state function of temperature and |
---|
1571 | !! salinity |
---|
1572 | !! prd(t,s) = rbeta * s - ralpha * tn - 1. |
---|
1573 | !! Note that no boundary condition problem occurs in this routine |
---|
1574 | !! as (ptem,psal) are defined over the whole domain. |
---|
1575 | !! |
---|
1576 | !! ** Comments on Adjoint Routine : |
---|
1577 | !! Care has been taken to avoid division by zero when computing |
---|
1578 | !! the inverse of the square root of salinity at masked salinity |
---|
1579 | !! points. |
---|
1580 | !! |
---|
1581 | !! ** Action : |
---|
1582 | !! |
---|
1583 | !! References : |
---|
1584 | !! |
---|
1585 | !! History : |
---|
1586 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eosadj.F |
---|
1587 | !! 9.0 ! 08-07 (A. Vidard) first version based on eosadj |
---|
1588 | !!----------------------------------------------------------------------- |
---|
1589 | !! * Modules used |
---|
1590 | !! * Arguments |
---|
1591 | REAL(wp), DIMENSION(jpi,jpj), INTENT( in ) :: & |
---|
1592 | & ptem, & ! potential temperature |
---|
1593 | & psal, & ! salinity |
---|
1594 | & pdep ! depth |
---|
1595 | REAL(wp), DIMENSION(jpi,jpj), INTENT( inout ) :: & |
---|
1596 | & ptem_ad, & ! TL of potential temperature |
---|
1597 | & psal_ad ! TL of salinity |
---|
1598 | REAL(wp), DIMENSION(jpi,jpj), INTENT( inout ) :: & |
---|
1599 | & prd_ad ! TL of potential density (surface referenced) |
---|
1600 | INTEGER :: ji, jj ! dummy loop indices |
---|
1601 | REAL(wp) :: & ! temporary scalars |
---|
1602 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
1603 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
1604 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
1605 | zr4ad, zrhopad, zead, zbwad, & |
---|
1606 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
1607 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
1608 | zmask |
---|
1609 | REAL(wp), DIMENSION(jpi,jpj) :: zws |
---|
1610 | !!---------------------------------------------------------------------- |
---|
1611 | |
---|
1612 | |
---|
1613 | ! initialization (in not already done) |
---|
1614 | IF( neos_init == 0 ) CALL eos_init |
---|
1615 | ! initialization of adjoint variables |
---|
1616 | ztad = 0.0_wp |
---|
1617 | zsad = 0.0_wp |
---|
1618 | zhad = 0.0_wp |
---|
1619 | zsrad = 0.0_wp |
---|
1620 | zr1ad = 0.0_wp |
---|
1621 | zr2ad = 0.0_wp |
---|
1622 | zr3ad = 0.0_wp |
---|
1623 | zr4ad = 0.0_wp |
---|
1624 | zrhopad = 0.0_wp |
---|
1625 | zead = 0.0_wp |
---|
1626 | zbwad = 0.0_wp |
---|
1627 | zbad = 0.0_wp |
---|
1628 | zdad = 0.0_wp |
---|
1629 | zcad = 0.0_wp |
---|
1630 | zawad = 0.0_wp |
---|
1631 | zaad = 0.0_wp |
---|
1632 | zb1ad = 0.0_wp |
---|
1633 | za1ad = 0.0_wp |
---|
1634 | zkwad = 0.0_wp |
---|
1635 | zk0ad = 0.0_wp |
---|
1636 | |
---|
1637 | |
---|
1638 | SELECT CASE ( neos ) |
---|
1639 | |
---|
1640 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
1641 | |
---|
1642 | #ifdef key_sp |
---|
1643 | zeps = 1.e-7 |
---|
1644 | #else |
---|
1645 | zeps = 1.e-14 |
---|
1646 | #endif |
---|
1647 | |
---|
1648 | !CDIR NOVERRCHK |
---|
1649 | DO jj = 1, jpjm1 |
---|
1650 | !CDIR NOVERRCHK |
---|
1651 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1652 | zws(ji,jj) = SQRT( ABS( psal(ji,jj) ) ) |
---|
1653 | END DO |
---|
1654 | END DO |
---|
1655 | |
---|
1656 | ! ! =============== |
---|
1657 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
1658 | ! ! =============== |
---|
1659 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1660 | |
---|
1661 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
---|
1662 | |
---|
1663 | zt = ptem (ji,jj) ! interpolated T |
---|
1664 | zs = psal (ji,jj) ! interpolated S |
---|
1665 | zsr= zws(ji,jj) ! square root of interpolated S |
---|
1666 | zh = pdep(ji,jj) ! depth at the partial step level |
---|
1667 | ! compute volumic mass pure water at atm pressure |
---|
1668 | zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & |
---|
1669 | -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 |
---|
1670 | ! seawater volumic mass atm pressure |
---|
1671 | zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & |
---|
1672 | -4.0899e-3 ) *zt+0.824493 |
---|
1673 | zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 |
---|
1674 | zr4= 4.8314e-4 |
---|
1675 | |
---|
1676 | ! potential volumic mass (reference to the surface) |
---|
1677 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
---|
1678 | |
---|
1679 | ! add the compression terms |
---|
1680 | ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 |
---|
1681 | zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 |
---|
1682 | zb = zbw + ze * zs |
---|
1683 | |
---|
1684 | zd = -2.042967e-2 |
---|
1685 | zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 |
---|
1686 | zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 |
---|
1687 | za = ( zd*zsr + zc ) *zs + zaw |
---|
1688 | |
---|
1689 | zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 |
---|
1690 | za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 |
---|
1691 | zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 |
---|
1692 | zk0= ( zb1*zsr + za1 )*zs + zkw |
---|
1693 | |
---|
1694 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
1695 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
1696 | ! ============ |
---|
1697 | ! Adjoint part |
---|
1698 | ! ============ |
---|
1699 | |
---|
1700 | ! Masked in situ density anomaly |
---|
1701 | |
---|
1702 | zrhopad = zrhopad + prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
1703 | & * zrdc2 / rau0 |
---|
1704 | zk0ad = zk0ad - prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
1705 | & * zrdc2 * zrdc2 * zh & |
---|
1706 | & * zrdc1**2 * zrhop & |
---|
1707 | & / rau0 |
---|
1708 | zaad = zaad + prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
1709 | & * zrdc2 * zrdc2 * zh & |
---|
1710 | & * zrdc1**2 * zrhop & |
---|
1711 | & * zh / rau0 |
---|
1712 | zbad = zbad - prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
1713 | & * zrdc2 * zrdc2 * zh & |
---|
1714 | & * zrdc1**2 * zrhop & |
---|
1715 | & * zh * zh / rau0 |
---|
1716 | prd_ad(ji,jj) = 0.0_wp |
---|
1717 | |
---|
1718 | zkwad = zkwad + zk0ad |
---|
1719 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
1720 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
1721 | za1ad = za1ad + zk0ad * zs |
---|
1722 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
1723 | zk0ad = 0.0_wp |
---|
1724 | |
---|
1725 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4 * zt & |
---|
1726 | & -3.*1.852732e-2 ) * zt & |
---|
1727 | & -2.*30.41638 ) * zt & |
---|
1728 | & + 2098.925 ) |
---|
1729 | zkwad = 0.0_wp |
---|
1730 | |
---|
1731 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3 * zt & |
---|
1732 | & +2.*1.553190 ) * zt & |
---|
1733 | & - 65.00517 ) |
---|
1734 | za1ad = 0.0_wp |
---|
1735 | |
---|
1736 | ztad = ztad + zb1ad * (-2.*0.1909078 * zt & |
---|
1737 | & + 7.390729 ) |
---|
1738 | zb1ad = 0.0_wp |
---|
1739 | |
---|
1740 | zawad = zawad + zaad |
---|
1741 | zsrad = zsrad + zaad * zd * zs |
---|
1742 | zcad = zcad + zaad * zs |
---|
1743 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
1744 | zaad = 0.0_wp |
---|
1745 | |
---|
1746 | ztad = ztad + zawad * ( ( 3.*5.939910e-6 * zt & |
---|
1747 | & +2.*2.512549e-3 ) * zt & |
---|
1748 | & - 0.1028859 ) |
---|
1749 | zawad = 0.0_wp |
---|
1750 | |
---|
1751 | ztad = ztad + zcad * (-2.*7.267926e-5 * zt & |
---|
1752 | & + 2.598241e-3 ) |
---|
1753 | zcad = 0.0_wp |
---|
1754 | |
---|
1755 | zbwad = zbwad + zbad |
---|
1756 | zead = zead + zbad * zs |
---|
1757 | zsad = zsad + zbad * ze |
---|
1758 | zbad = 0.0_wp |
---|
1759 | |
---|
1760 | ztad = ztad + zbwad * ( 2.*1.296821e-6 * zt & |
---|
1761 | & - 5.782165e-9 ) |
---|
1762 | zbwad = 0.0_wp |
---|
1763 | |
---|
1764 | ztad = ztad + zead * (-2.*3.508914e-8 * zt & |
---|
1765 | & - 1.248266e-8 ) |
---|
1766 | zead = 0.0_wp |
---|
1767 | |
---|
1768 | zr1ad = zr1ad + zrhopad |
---|
1769 | zr2ad = zr2ad + zrhopad * zs |
---|
1770 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
1771 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
1772 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
1773 | & + zr3 * zsr ) |
---|
1774 | zrhopad = 0.0_wp |
---|
1775 | |
---|
1776 | ztad = ztad + zr3ad * (-2.*1.6546e-6 * zt & |
---|
1777 | & + 1.0227e-4 ) |
---|
1778 | zr3ad = 0.0_wp |
---|
1779 | |
---|
1780 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9 * zt & |
---|
1781 | & -3.*8.2467e-7 ) * zt & |
---|
1782 | & +2.*7.6438e-5 ) * zt & |
---|
1783 | & - 4.0899e-3 ) |
---|
1784 | zr2ad = 0.0_wp |
---|
1785 | |
---|
1786 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9 * zt & |
---|
1787 | & -4.*1.120083e-6 ) * zt & |
---|
1788 | & +3.*1.001685e-4 ) * zt & |
---|
1789 | & -2.*9.095290e-3 ) * zt & |
---|
1790 | & + 6.793952e-2 ) |
---|
1791 | zr1ad = 0.0_wp |
---|
1792 | |
---|
1793 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
1794 | & * tmask(ji,jj, 1) |
---|
1795 | zsrad = 0.0_wp |
---|
1796 | |
---|
1797 | psal_ad(ji,jj) = psal_ad(ji,jj) + zsad |
---|
1798 | ptem_ad(ji,jj) = ptem_ad(ji,jj) + ztad |
---|
1799 | ztad = 0.0_wp |
---|
1800 | zsad = 0.0_wp |
---|
1801 | END DO |
---|
1802 | ! ! =============== |
---|
1803 | END DO ! End of slab |
---|
1804 | ! ! =============== |
---|
1805 | |
---|
1806 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
1807 | |
---|
1808 | ! ! =============== |
---|
1809 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
1810 | ! ! =============== |
---|
1811 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1812 | ! ... density and potential volumic mass |
---|
1813 | ptem_ad(ji,jj) = ptem_ad(ji,jj) - prd_ad(ji,jj) * ralpha * tmask(ji,jj,1) |
---|
1814 | prd_ad(ji,jj) = 0.0_wp |
---|
1815 | |
---|
1816 | END DO |
---|
1817 | ! ! =============== |
---|
1818 | END DO ! End of slab |
---|
1819 | ! ! =============== |
---|
1820 | |
---|
1821 | |
---|
1822 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
1823 | |
---|
1824 | ! ! =============== |
---|
1825 | DO jj = 1, jpjm1 ! Horizontal slab |
---|
1826 | ! ! =============== |
---|
1827 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1828 | ptem_ad(ji,jj) = ptem_ad(ji,jj) - prd_ad(ji,jj) * ralpha * tmask(ji,jj,1) |
---|
1829 | psal_ad(ji,jj) = psal_ad(ji,jj) + prd_ad(ji,jj) * rbeta * tmask(ji,jj,1) |
---|
1830 | prd_ad (ji,jj) = 0.0_wp |
---|
1831 | END DO |
---|
1832 | ! ! =============== |
---|
1833 | END DO ! End of slab |
---|
1834 | ! ! =============== |
---|
1835 | |
---|
1836 | CASE DEFAULT |
---|
1837 | |
---|
1838 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
1839 | CALL ctl_stop( ctmp1 ) |
---|
1840 | |
---|
1841 | END SELECT |
---|
1842 | END SUBROUTINE eos_insitu_2d_adj |
---|
1843 | |
---|
1844 | |
---|
1845 | |
---|
1846 | SUBROUTINE eos_bn2_tan ( ptem, psal, ptem_tl, psal_tl, pn2_tl ) |
---|
1847 | !!---------------------------------------------------------------------- |
---|
1848 | !! *** ROUTINE eos_bn2_tan *** |
---|
1849 | !! |
---|
1850 | !! ** Purpose of the direct routine: Compute the local |
---|
1851 | !! Brunt-Vaisala frequency at the time-step of the input arguments |
---|
1852 | !! |
---|
1853 | !! ** Method of the direct routine: |
---|
1854 | !! * neos = 0 : UNESCO sea water properties |
---|
1855 | !! The brunt-vaisala frequency is computed using the polynomial |
---|
1856 | !! polynomial expression of McDougall (1987): |
---|
1857 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
---|
1858 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
---|
1859 | !! computed and used in zdfddm module : |
---|
1860 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
---|
1861 | !! * neos = 1 : linear equation of state (temperature only) |
---|
1862 | !! N^2 = grav * ralpha * dk[ t ]/e3w |
---|
1863 | !! * neos = 2 : linear equation of state (temperature & salinity) |
---|
1864 | !! N^2 = grav * (ralpha * dk[ t ] - rbeta * dk[ s ] ) / e3w |
---|
1865 | !! The use of potential density to compute N^2 introduces e r r o r |
---|
1866 | !! in the sign of N^2 at great depths. We recommand the use of |
---|
1867 | !! neos = 0, except for academical studies. |
---|
1868 | !! Macro-tasked on horizontal slab (jk-loop) |
---|
1869 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
---|
1870 | !! and is never used at this level. |
---|
1871 | !! |
---|
1872 | !! ** Action : - pn2 : the brunt-vaisala frequency |
---|
1873 | !! |
---|
1874 | !! References : |
---|
1875 | !! McDougall, T. J., J. Phys. Oceanogr., 17, 1950-1964, 1987. |
---|
1876 | !! |
---|
1877 | !! History: |
---|
1878 | !! ! 08-07 (A. Vidard) First version |
---|
1879 | !!---------------------------------------------------------------------- |
---|
1880 | !! * Arguments |
---|
1881 | |
---|
1882 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
1883 | ptem, & ! potential temperature |
---|
1884 | psal ! salinity |
---|
1885 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
1886 | ptem_tl, & ! potential temperature |
---|
1887 | psal_tl ! salinity |
---|
1888 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
---|
1889 | pn2_tl ! Brunt-Vaisala frequency |
---|
1890 | |
---|
1891 | !! * Local declarations |
---|
1892 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
1893 | REAL(wp) :: & |
---|
1894 | zgde3w, zt, zs, zh, & ! temporary scalars |
---|
1895 | zalbet, zbeta ! " " |
---|
1896 | REAL(wp) :: & |
---|
1897 | zttl, zstl, & ! temporary scalars |
---|
1898 | zalbettl, zbetatl ! " " |
---|
1899 | #if defined key_zdfddm |
---|
1900 | REAL(wp) :: zds, zdstl ! temporary scalars |
---|
1901 | #endif |
---|
1902 | ! pn2_tl : first and last levels |
---|
1903 | ! --------------------------- |
---|
1904 | ! bn^2=0. at jk=1 and jpk set in inidtr.F : no computation |
---|
1905 | |
---|
1906 | |
---|
1907 | ! pn2_tl : interior points only (2=< jk =< jpkm1 ) |
---|
1908 | ! -------------------------- |
---|
1909 | |
---|
1910 | SELECT CASE ( neos ) |
---|
1911 | |
---|
1912 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
1913 | ! ! =============== |
---|
1914 | DO jk = 2, jpkm1 ! Horizontal slab |
---|
1915 | ! ! =============== |
---|
1916 | DO jj = 1, jpj |
---|
1917 | DO ji = 1, jpi |
---|
1918 | zgde3w = grav / fse3w(ji,jj,jk) |
---|
1919 | zt = 0.5 * ( ptem(ji,jj,jk) + ptem(ji,jj,jk-1) ) ! potential temperature at w-point |
---|
1920 | zs = 0.5 * ( psal(ji,jj,jk) + psal(ji,jj,jk-1) ) - 35.0 ! salinity anomaly (s-35) at w-point |
---|
1921 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
---|
1922 | |
---|
1923 | zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta |
---|
1924 | & - 0.203814e-03 ) * zt & |
---|
1925 | & + 0.170907e-01 ) * zt & |
---|
1926 | & + 0.665157e-01 & |
---|
1927 | & + ( - 0.678662e-05 * zs & |
---|
1928 | & - 0.846960e-04 * zt + 0.378110e-02 ) * zs & |
---|
1929 | & + ( ( - 0.302285e-13 * zh & |
---|
1930 | & - 0.251520e-11 * zs & |
---|
1931 | & + 0.512857e-12 * zt * zt ) * zh & |
---|
1932 | & - 0.164759e-06 * zs & |
---|
1933 | & +( 0.791325e-08 * zt - 0.933746e-06 ) * zt & |
---|
1934 | & + 0.380374e-04 ) * zh |
---|
1935 | |
---|
1936 | zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta |
---|
1937 | & - 0.301985e-05 ) * zt & |
---|
1938 | & + 0.785567e-03 & |
---|
1939 | & + ( 0.515032e-08 * zs & |
---|
1940 | & + 0.788212e-08 * zt - 0.356603e-06 ) * zs & |
---|
1941 | & +( ( 0.121551e-17 * zh & |
---|
1942 | & - 0.602281e-15 * zs & |
---|
1943 | & - 0.175379e-14 * zt + 0.176621e-12 ) * zh & |
---|
1944 | & + 0.408195e-10 * zs & |
---|
1945 | & + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt & |
---|
1946 | & - 0.121555e-07 ) * zh |
---|
1947 | |
---|
1948 | |
---|
1949 | !! tangent part |
---|
1950 | zttl = 0.5 * ( ptem_tl(ji,jj,jk) + ptem_tl(ji,jj,jk-1) ) ! potential temperature at w-point |
---|
1951 | zstl = 0.5 * ( psal_tl(ji,jj,jk) + psal_tl(ji,jj,jk-1) ) ! salinity anomaly at w-point |
---|
1952 | zalbettl = ( ( ( -4.*0.255019e-07 * zt &! ratio alpha/beta |
---|
1953 | & +3.*0.298357e-05 ) * zt & |
---|
1954 | & -2.*0.203814e-03 ) * zt & |
---|
1955 | & + 0.170907e-01 & |
---|
1956 | & - 0.846960e-04 * zs & |
---|
1957 | & - ( 0.933746e-06 & |
---|
1958 | & - ( 2.*0.791325e-08 & |
---|
1959 | & +2.*0.512857e-12 * zh ) * zt ) * zh ) * zttl & |
---|
1960 | & + ( - 2.*0.678662e-05 * zs & |
---|
1961 | & - 0.846960e-04 * zt & |
---|
1962 | & + 0.378110e-02 & |
---|
1963 | & + ( - 0.164759e-06 & |
---|
1964 | & - 0.251520e-11 * zh ) * zh ) * zstl |
---|
1965 | |
---|
1966 | zbetatl = ( ( -3.*0.415613e-09 * zt & |
---|
1967 | & +2.*0.555579e-07 ) * zt & |
---|
1968 | & - 0.301985e-05 & |
---|
1969 | & + 0.788212e-08 * zs & |
---|
1970 | & + ( -2.*0.213127e-11 * zt & |
---|
1971 | & - 0.175379e-14 * zh & |
---|
1972 | & + 0.192867e-09 ) * zh ) * zttl & |
---|
1973 | & + ( 2.*0.515032e-08 * zs & |
---|
1974 | & + 0.788212e-08 * zt & |
---|
1975 | & - 0.356603e-06 & |
---|
1976 | & + ( - 0.602281e-15 * zh & |
---|
1977 | & + 0.408195e-10 ) * zh ) * zstl |
---|
1978 | |
---|
1979 | pn2_tl(ji,jj,jk) = zgde3w * tmask(ji,jj,jk) * ( & |
---|
1980 | & zbeta * ( zalbet & |
---|
1981 | & * ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) & |
---|
1982 | & + zalbettl & |
---|
1983 | & * ( ptem (ji,jj,jk-1) - ptem (ji,jj,jk) ) & |
---|
1984 | & - ( psal_tl(ji,jj,jk-1) - psal_tl(ji,jj,jk) ) ) & |
---|
1985 | & + zbetatl * ( zalbet & |
---|
1986 | & * ( ptem (ji,jj,jk-1) - ptem (ji,jj,jk) ) & |
---|
1987 | & - ( psal (ji,jj,jk-1) - psal (ji,jj,jk) ) ) ) |
---|
1988 | #if defined key_zdfddm |
---|
1989 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) |
---|
1990 | zdstl = ( psal_tl(ji,jj,jk-1) - psal_tl(ji,jj,jk) ) |
---|
1991 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
1992 | zds = 1.e-20 |
---|
1993 | rrau_tl(ji,jj,jk) = zalbettl * & |
---|
1994 | & ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds & |
---|
1995 | & + zalbet * & |
---|
1996 | & ( ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) / zds ) |
---|
1997 | ELSE |
---|
1998 | rrau_tl(ji,jj,jk) = zalbettl * & |
---|
1999 | & ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds & |
---|
2000 | & + zalbet * & |
---|
2001 | & ( ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) / zds & |
---|
2002 | & - ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) * zdstl/ zds**2 ) |
---|
2003 | ENDIF |
---|
2004 | #endif |
---|
2005 | END DO |
---|
2006 | END DO |
---|
2007 | ! ! =============== |
---|
2008 | END DO ! End of slab |
---|
2009 | ! ! =============== |
---|
2010 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
2011 | |
---|
2012 | ! ! =============== |
---|
2013 | DO jk = 2, jpkm1 ! Horizontal slab |
---|
2014 | ! ! =============== |
---|
2015 | DO jj = 1, jpj |
---|
2016 | DO ji = 1, jpi |
---|
2017 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
---|
2018 | pn2_tl(ji,jj,jk) = zgde3w * ralpha * & |
---|
2019 | & ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) |
---|
2020 | END DO |
---|
2021 | END DO |
---|
2022 | ! ! =============== |
---|
2023 | END DO ! End of slab |
---|
2024 | ! ! =============== |
---|
2025 | |
---|
2026 | |
---|
2027 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
2028 | |
---|
2029 | ! ! =============== |
---|
2030 | DO jk = 2, jpkm1 ! Horizontal slab |
---|
2031 | ! ! =============== |
---|
2032 | DO jj = 1, jpj |
---|
2033 | DO ji = 1, jpi |
---|
2034 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
---|
2035 | pn2_tl(ji,jj,jk) = zgde3w * ( & |
---|
2036 | & ralpha * ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) & |
---|
2037 | & - rbeta * ( psal_tl(ji,jj,jk-1) - psal_tl(ji,jj,jk) ) ) |
---|
2038 | END DO |
---|
2039 | END DO |
---|
2040 | #if defined key_zdfddm |
---|
2041 | zalbet = ralpha / rbeta |
---|
2042 | DO jj = 1, jpj |
---|
2043 | DO ji = 1, jpi |
---|
2044 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) |
---|
2045 | zdstl = psal_tl(ji,jj,jk-1) - psal_tl(ji,jj,jk) |
---|
2046 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
2047 | zds = 1.e-20 |
---|
2048 | rrau_tl(ji,jj,jk) = zalbet * & |
---|
2049 | & ( ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) / zds ) |
---|
2050 | ELSE |
---|
2051 | rrau_tl(ji,jj,jk) = zalbet * & |
---|
2052 | & ( ( ptem_tl(ji,jj,jk-1) - ptem_tl(ji,jj,jk) ) / zds & |
---|
2053 | & - ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) * zdstl / zds**2 ) |
---|
2054 | ENDIF |
---|
2055 | rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds |
---|
2056 | END DO |
---|
2057 | END DO |
---|
2058 | #endif |
---|
2059 | ! =============== |
---|
2060 | END DO ! End of slab |
---|
2061 | ! =============== |
---|
2062 | |
---|
2063 | CASE DEFAULT |
---|
2064 | |
---|
2065 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
2066 | CALL ctl_stop( ctmp1 ) |
---|
2067 | |
---|
2068 | END SELECT |
---|
2069 | |
---|
2070 | |
---|
2071 | |
---|
2072 | |
---|
2073 | END SUBROUTINE eos_bn2_tan |
---|
2074 | SUBROUTINE eos_bn2_adj ( ptem, psal, ptem_ad, psal_ad, pn2_ad ) |
---|
2075 | !!---------------------------------------------------------------------- |
---|
2076 | !! *** ROUTINE eos_bn2_adj *** |
---|
2077 | !! |
---|
2078 | !! ** Purpose of the direct routine: Compute the local |
---|
2079 | !! Brunt-Vaisala frequency at the time-step of the input arguments |
---|
2080 | !! |
---|
2081 | !! ** Method of the direct routine: |
---|
2082 | !! * neos = 0 : UNESCO sea water properties |
---|
2083 | !! The brunt-vaisala frequency is computed using the polynomial |
---|
2084 | !! polynomial expression of McDougall (1987): |
---|
2085 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
---|
2086 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
---|
2087 | !! computed and used in zdfddm module : |
---|
2088 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
---|
2089 | !! * neos = 1 : linear equation of state (temperature only) |
---|
2090 | !! N^2 = grav * ralpha * dk[ t ]/e3w |
---|
2091 | !! * neos = 2 : linear equation of state (temperature & salinity) |
---|
2092 | !! N^2 = grav * (ralpha * dk[ t ] - rbeta * dk[ s ] ) / e3w |
---|
2093 | !! The use of potential density to compute N^2 introduces e r r o r |
---|
2094 | !! in the sign of N^2 at great depths. We recommand the use of |
---|
2095 | !! neos = 0, except for academical studies. |
---|
2096 | !! Macro-tasked on horizontal slab (jk-loop) |
---|
2097 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
---|
2098 | !! and is never used at this level. |
---|
2099 | !! |
---|
2100 | !! ** Action : - pn2 : the brunt-vaisala frequency |
---|
2101 | !! |
---|
2102 | !! References : |
---|
2103 | !! McDougall, T. J., J. Phys. Oceanogr., 17, 1950-1964, 1987. |
---|
2104 | !! |
---|
2105 | !! History: |
---|
2106 | !! ! 08-07 (A. Vidard) First version |
---|
2107 | !!---------------------------------------------------------------------- |
---|
2108 | !! * Arguments |
---|
2109 | |
---|
2110 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
2111 | ptem, & ! potential temperature |
---|
2112 | psal ! salinity |
---|
2113 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
2114 | ptem_ad, & ! adjoint potential temperature |
---|
2115 | psal_ad ! adjoint salinity |
---|
2116 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
2117 | pn2_ad ! adjoint Brunt-Vaisala frequency |
---|
2118 | |
---|
2119 | !! * Local declarations |
---|
2120 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
2121 | REAL(wp) :: & |
---|
2122 | zgde3w, zt, zs, zh, & ! temporary scalars |
---|
2123 | zalbet, zbeta ! " " |
---|
2124 | REAL(wp) :: & |
---|
2125 | ztad, zsad, & ! temporary scalars |
---|
2126 | zalbetad, zbetaad ! " " |
---|
2127 | #if defined key_zdfddm |
---|
2128 | REAL(wp) :: zds, zdsad ! temporary scalars |
---|
2129 | #endif |
---|
2130 | ! pn2_tl : first and last levels |
---|
2131 | ! --------------------------- |
---|
2132 | ! bn^2=0. at jk=1 and jpk set in inidtr.F : no computation |
---|
2133 | |
---|
2134 | |
---|
2135 | ! pn2_tl : interior points only (2=< jk =< jpkm1 ) |
---|
2136 | ! -------------------------- |
---|
2137 | zalbetad = 0.0_wp |
---|
2138 | zbetaad = 0.0_wp |
---|
2139 | ztad = 0.0_wp |
---|
2140 | zsad = 0.0_wp |
---|
2141 | #if defined key_zdfddm |
---|
2142 | zdsad = 0.0_wp |
---|
2143 | #endif |
---|
2144 | |
---|
2145 | SELECT CASE ( neos ) |
---|
2146 | |
---|
2147 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
2148 | ! ! =============== |
---|
2149 | DO jk = jpkm1, 2, -1 ! Horizontal slab |
---|
2150 | ! ! =============== |
---|
2151 | DO jj = jpj, 1, -1 |
---|
2152 | DO ji = jpi, 1, -1 |
---|
2153 | zgde3w = grav / fse3w(ji,jj,jk) |
---|
2154 | zt = 0.5 * ( ptem(ji,jj,jk) + ptem(ji,jj,jk-1) ) ! potential temperature at w-point |
---|
2155 | zs = 0.5 * ( psal(ji,jj,jk) + psal(ji,jj,jk-1) ) - 35.0 ! salinity anomaly (s-35) at w-point |
---|
2156 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
---|
2157 | |
---|
2158 | zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta |
---|
2159 | & - 0.203814e-03 ) * zt & |
---|
2160 | & + 0.170907e-01 ) * zt & |
---|
2161 | & + 0.665157e-01 & |
---|
2162 | & + ( - 0.678662e-05 * zs & |
---|
2163 | & - 0.846960e-04 * zt + 0.378110e-02 ) * zs & |
---|
2164 | & + ( ( - 0.302285e-13 * zh & |
---|
2165 | & - 0.251520e-11 * zs & |
---|
2166 | & + 0.512857e-12 * zt * zt ) * zh & |
---|
2167 | & - 0.164759e-06 * zs & |
---|
2168 | & +( 0.791325e-08 * zt - 0.933746e-06 ) * zt & |
---|
2169 | & + 0.380374e-04 ) * zh |
---|
2170 | |
---|
2171 | zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta |
---|
2172 | & - 0.301985e-05 ) * zt & |
---|
2173 | & + 0.785567e-03 & |
---|
2174 | & + ( 0.515032e-08 * zs & |
---|
2175 | & + 0.788212e-08 * zt - 0.356603e-06 ) * zs & |
---|
2176 | & +( ( 0.121551e-17 * zh & |
---|
2177 | & - 0.602281e-15 * zs & |
---|
2178 | & - 0.175379e-14 * zt + 0.176621e-12 ) * zh & |
---|
2179 | & + 0.408195e-10 * zs & |
---|
2180 | & + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt & |
---|
2181 | & - 0.121555e-07 ) * zh |
---|
2182 | |
---|
2183 | |
---|
2184 | #if defined key_zdfddm |
---|
2185 | |
---|
2186 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) |
---|
2187 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
2188 | zds = 1.e-20 |
---|
2189 | zdsad = 0.0_wp |
---|
2190 | ELSE |
---|
2191 | zdsad = rrau_ad(ji,jj,jk) * zalbet *( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds**2 |
---|
2192 | ENDIF |
---|
2193 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) + rrau_ad(ji,jj,jk) * zalbet / zds |
---|
2194 | ptem_ad(ji,jj,jk ) = ptem_ad(ji,jj,jk ) - rrau_ad(ji,jj,jk) * zalbet / zds |
---|
2195 | zalbetad = zalbetad + rrau_ad(ji,jj,jk) * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds |
---|
2196 | rrau_ad(ji,jj,jk) = 0._wp |
---|
2197 | |
---|
2198 | psal_ad(ji,jj,jk-1) = psal_ad(ji,jj,jk-1) + zdsad |
---|
2199 | psal_ad(ji,jj,jk ) = psal_ad(ji,jj,jk ) - zdsad |
---|
2200 | zdsad = 0._wp |
---|
2201 | #endif |
---|
2202 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) + zalbet*zbeta*zgde3w*tmask(ji,jj,jk)*pn2_ad(ji,jj,jk) |
---|
2203 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk ) - zalbet*zbeta*zgde3w*tmask(ji,jj,jk)*pn2_ad(ji,jj,jk) |
---|
2204 | zalbetad = zalbetad + zbeta*zgde3w*tmask(ji,jj,jk)*( ptem (ji,jj,jk-1) - ptem (ji,jj,jk) ) *pn2_ad(ji,jj,jk) |
---|
2205 | psal_ad(ji,jj,jk-1) = psal_ad(ji,jj,jk-1) - zbeta*tmask(ji,jj,jk)*zgde3w*pn2_ad(ji,jj,jk) |
---|
2206 | psal_ad(ji,jj,jk ) = psal_ad(ji,jj,jk ) + zbeta*tmask(ji,jj,jk)*zgde3w*pn2_ad(ji,jj,jk) |
---|
2207 | zbetaad = zbetaad & |
---|
2208 | & + zgde3w *tmask(ji,jj,jk)* ( zalbet * ( ptem (ji,jj,jk-1) - ptem (ji,jj,jk) ) & |
---|
2209 | & - ( psal (ji,jj,jk-1) - psal (ji,jj,jk) ) )*pn2_ad(ji,jj,jk) |
---|
2210 | |
---|
2211 | pn2_ad(ji,jj,jk) = 0.0_wp |
---|
2212 | |
---|
2213 | ztad = ztad + ( ( -3.*0.415613e-09 * zt & |
---|
2214 | & +2.*0.555579e-07 ) * zt & |
---|
2215 | & - 0.301985e-05 & |
---|
2216 | & + 0.788212e-08 * zs & |
---|
2217 | & + ( -2.*0.213127e-11 * zt & |
---|
2218 | & - 0.175379e-14 * zh & |
---|
2219 | & + 0.192867e-09 ) * zh ) *zbetaad |
---|
2220 | |
---|
2221 | zsad = zsad + ( 2.*0.515032e-08 * zs & |
---|
2222 | & + 0.788212e-08 * zt & |
---|
2223 | & - 0.356603e-06 & |
---|
2224 | & + ( - 0.602281e-15 * zh & |
---|
2225 | & + 0.408195e-10 ) * zh ) * zbetaad |
---|
2226 | |
---|
2227 | zbetaad = 0.0_wp |
---|
2228 | |
---|
2229 | ztad = ztad + ( ( ( -4.*0.255019e-07 * zt &! ratio alpha/beta |
---|
2230 | & +3.*0.298357e-05 ) * zt & |
---|
2231 | & -2.*0.203814e-03 ) * zt & |
---|
2232 | & + 0.170907e-01 & |
---|
2233 | & - 0.846960e-04 * zs & |
---|
2234 | & - ( 0.933746e-06 & |
---|
2235 | & - ( 2.*0.791325e-08 & |
---|
2236 | & +2.*0.512857e-12 * zh ) * zt ) * zh & |
---|
2237 | & ) *zalbetad |
---|
2238 | |
---|
2239 | zsad = zsad + ( - 2.*0.678662e-05 * zs & |
---|
2240 | & - 0.846960e-04 * zt & |
---|
2241 | & + 0.378110e-02 & |
---|
2242 | & + ( - 0.164759e-06 & |
---|
2243 | & - 0.251520e-11 * zh ) * zh & |
---|
2244 | & ) *zalbetad |
---|
2245 | |
---|
2246 | zalbetad = 0.0_wp |
---|
2247 | |
---|
2248 | |
---|
2249 | psal_ad(ji,jj,jk) = psal_ad(ji,jj,jk) + 0.5 * zsad |
---|
2250 | psal_ad(ji,jj,jk-1) = psal_ad(ji,jj,jk-1) + 0.5 * zsad |
---|
2251 | zsad = 0.0_wp |
---|
2252 | |
---|
2253 | ptem_ad(ji,jj,jk) = ptem_ad(ji,jj,jk) + 0.5 * ztad |
---|
2254 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) + 0.5 * ztad |
---|
2255 | ztad = 0.0_wp |
---|
2256 | |
---|
2257 | END DO |
---|
2258 | END DO |
---|
2259 | ! ! =============== |
---|
2260 | END DO ! End of slab |
---|
2261 | ! ! =============== |
---|
2262 | CASE ( 1 ) ! Linear formulation function of temperature only |
---|
2263 | |
---|
2264 | ! ! =============== |
---|
2265 | DO jk = jpkm1, 2, -1 ! Horizontal slab |
---|
2266 | ! ! =============== |
---|
2267 | DO jj = jpj, 1, -1 |
---|
2268 | DO ji = jpi, 1, -1 |
---|
2269 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
---|
2270 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) + zgde3w * ralpha * pn2_ad(ji,jj,jk) |
---|
2271 | ptem_ad(ji,jj,jk ) = ptem_ad(ji,jj,jk ) - zgde3w * ralpha * pn2_ad(ji,jj,jk) |
---|
2272 | |
---|
2273 | pn2_ad(ji,jj,jk) = 0.0_wp |
---|
2274 | END DO |
---|
2275 | END DO |
---|
2276 | ! ! =============== |
---|
2277 | END DO ! End of slab |
---|
2278 | ! ! =============== |
---|
2279 | |
---|
2280 | |
---|
2281 | CASE ( 2 ) ! Linear formulation function of temperature and salinity |
---|
2282 | |
---|
2283 | ! ! =============== |
---|
2284 | DO jk = jpkm1, 2, -1 ! Horizontal slab |
---|
2285 | ! ! =============== |
---|
2286 | #if defined key_zdfddm |
---|
2287 | zalbet = ralpha / rbeta |
---|
2288 | DO jj = jpj, 1, -1 |
---|
2289 | DO ji = jpi, 1, -1 |
---|
2290 | zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) |
---|
2291 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
2292 | zds = 1.e-20 |
---|
2293 | zdsad = 0.0_wp |
---|
2294 | ELSE |
---|
2295 | zdsad = zdsad - rrau_ad(ji,jj,jk) * zalbet & |
---|
2296 | & * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds**2 |
---|
2297 | ENDIF |
---|
2298 | rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds |
---|
2299 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) & |
---|
2300 | & + rrau_ad(ji,jj,jk) * zalbet / zds |
---|
2301 | ptem_ad(ji,jj,jk ) = ptem_ad(ji,jj,jk ) & |
---|
2302 | & - rrau_ad(ji,jj,jk) * zalbet / zds |
---|
2303 | rrau_ad(ji,jj,jk) = 0._wp |
---|
2304 | |
---|
2305 | psal_ad(ji,jj,jk-1) = psal_ad(ji,jj,jk-1) + zdsad |
---|
2306 | psal_ad(ji,jj,jk ) = psal_ad(ji,jj,jk ) - zdsad |
---|
2307 | zdsad = 0._wp |
---|
2308 | END DO |
---|
2309 | END DO |
---|
2310 | #endif |
---|
2311 | DO jj = jpj, 1, -1 |
---|
2312 | DO ji = jpi, 1, -1 |
---|
2313 | zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) |
---|
2314 | ptem_ad(ji,jj,jk-1) = ptem_ad(ji,jj,jk-1) + zgde3w * ralpha * pn2_ad(ji,jj,jk) |
---|
2315 | ptem_ad(ji,jj,jk ) = ptem_ad(ji,jj,jk ) - zgde3w * ralpha * pn2_ad(ji,jj,jk) |
---|
2316 | psal_ad(ji,jj,jk-1) = psal_ad(ji,jj,jk-1) - zgde3w * rbeta * pn2_ad(ji,jj,jk) |
---|
2317 | psal_ad(ji,jj,jk ) = psal_ad(ji,jj,jk ) + zgde3w * rbeta * pn2_ad(ji,jj,jk) |
---|
2318 | pn2_ad(ji,jj,jk) = 0.0_wp |
---|
2319 | END DO |
---|
2320 | END DO |
---|
2321 | ! =============== |
---|
2322 | END DO ! End of slab |
---|
2323 | ! =============== |
---|
2324 | |
---|
2325 | CASE DEFAULT |
---|
2326 | |
---|
2327 | WRITE(ctmp1,*) ' bad flag value for neos = ', neos |
---|
2328 | CALL ctl_stop( ctmp1 ) |
---|
2329 | |
---|
2330 | END SELECT |
---|
2331 | |
---|
2332 | END SUBROUTINE eos_bn2_adj |
---|
2333 | |
---|
2334 | #if defined key_tam |
---|
2335 | SUBROUTINE eos_insitu_adj_tst( kumadt ) |
---|
2336 | !!----------------------------------------------------------------------- |
---|
2337 | !! |
---|
2338 | !! *** ROUTINE eos_adj_tst *** |
---|
2339 | !! |
---|
2340 | !! ** Purpose : Test the adjoint routine. |
---|
2341 | !! |
---|
2342 | !! ** Method : Verify the scalar product |
---|
2343 | !! |
---|
2344 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
2345 | !! |
---|
2346 | !! where L = tangent routine |
---|
2347 | !! L^T = adjoint routine |
---|
2348 | !! W = diagonal matrix of scale factors |
---|
2349 | !! dx = input perturbation (random field) |
---|
2350 | !! dy = L dx |
---|
2351 | !! |
---|
2352 | !! |
---|
2353 | !! History : |
---|
2354 | !! ! 08-07 (A. Vidard) |
---|
2355 | !!----------------------------------------------------------------------- |
---|
2356 | !! * Modules used |
---|
2357 | |
---|
2358 | !! * Arguments |
---|
2359 | INTEGER, INTENT(IN) :: & |
---|
2360 | & kumadt ! Output unit |
---|
2361 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2362 | ztem, & ! potential temperature |
---|
2363 | zsal ! salinity |
---|
2364 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2365 | & zt_adout, & ! potential temperature |
---|
2366 | & zs_adout ! salinity |
---|
2367 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2368 | & zrd_adin ! anomaly density |
---|
2369 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2370 | & zt_tlin, & ! potential temperature |
---|
2371 | & zs_tlin ! salinity |
---|
2372 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2373 | & znt, & ! potential temperature |
---|
2374 | & zns ! salinity |
---|
2375 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2376 | & zrd_tlout ! anomaly density |
---|
2377 | REAL(KIND=wp) :: & |
---|
2378 | & zsp1, & ! scalar product involving the tangent routine |
---|
2379 | & zsp2, & ! scalar product involving the adjoint routine |
---|
2380 | & zsp2_1, & ! scalar product involving the adjoint routine |
---|
2381 | & zsp2_2 ! scalar product involving the adjoint routine |
---|
2382 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
2383 | & iseed_2d ! 2D seed for the random number generator |
---|
2384 | INTEGER :: & |
---|
2385 | & ji, & |
---|
2386 | & jj, & |
---|
2387 | & jk |
---|
2388 | CHARACTER(LEN=14) :: cl_name |
---|
2389 | |
---|
2390 | ALLOCATE( & |
---|
2391 | & ztem( jpi, jpj, jpk ), & |
---|
2392 | & zsal( jpi, jpj, jpk ), & |
---|
2393 | & znt( jpi, jpj, jpk ), & |
---|
2394 | & zns( jpi, jpj, jpk ), & |
---|
2395 | & zt_adout( jpi, jpj, jpk ), & |
---|
2396 | & zs_adout( jpi, jpj, jpk ), & |
---|
2397 | & zrd_adin( jpi, jpj, jpk ), & |
---|
2398 | & zs_tlin( jpi, jpj, jpk ), & |
---|
2399 | & zt_tlin( jpi, jpj, jpk ), & |
---|
2400 | & zrd_tlout(jpi, jpj, jpk ) ) |
---|
2401 | ! Initialize the reference state |
---|
2402 | ztem(:,:,:) = tn(:,:,:) |
---|
2403 | zsal(:,:,:) = sn(:,:,:) |
---|
2404 | |
---|
2405 | |
---|
2406 | !============================================================= |
---|
2407 | ! 1) dx = ( T ) and dy = ( T ) |
---|
2408 | !============================================================= |
---|
2409 | |
---|
2410 | !-------------------------------------------------------------------- |
---|
2411 | ! Reset the tangent and adjoint variables |
---|
2412 | !-------------------------------------------------------------------- |
---|
2413 | zt_tlin(:,:,:) = 0.0_wp |
---|
2414 | zs_tlin(:,:,:) = 0.0_wp |
---|
2415 | zrd_tlout(:,:,:) = 0.0_wp |
---|
2416 | zt_adout(:,:,:) = 0.0_wp |
---|
2417 | zs_adout(:,:,:) = 0.0_wp |
---|
2418 | zrd_adin(:,:,:) = 0.0_wp |
---|
2419 | |
---|
2420 | !-------------------------------------------------------------------- |
---|
2421 | ! Initialize the tangent input with random noise: dx |
---|
2422 | !-------------------------------------------------------------------- |
---|
2423 | DO jj = 1, jpj |
---|
2424 | DO ji = 1, jpi |
---|
2425 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2426 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2427 | END DO |
---|
2428 | END DO |
---|
2429 | CALL grid_random( iseed_2d, znt, 'T', 0.0_wp, stdt ) |
---|
2430 | DO jj = 1, jpj |
---|
2431 | DO ji = 1, jpi |
---|
2432 | iseed_2d(ji,jj) = - ( 395703 + & |
---|
2433 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2434 | END DO |
---|
2435 | END DO |
---|
2436 | CALL grid_random( iseed_2d, zns, 'T', 0.0_wp, stds ) |
---|
2437 | |
---|
2438 | DO jk = 1, jpk |
---|
2439 | DO jj = nldj, nlej |
---|
2440 | DO ji = nldi, nlei |
---|
2441 | zt_tlin(ji,jj,jk) = znt(ji,jj,jk) |
---|
2442 | zs_tlin(ji,jj,jk) = zns(ji,jj,jk) |
---|
2443 | END DO |
---|
2444 | END DO |
---|
2445 | END DO |
---|
2446 | |
---|
2447 | CALL eos_insitu_tan(ztem, zsal, zt_tlin, zs_tlin, zrd_tlout) |
---|
2448 | |
---|
2449 | DO jk = 1, jpk |
---|
2450 | DO jj = nldj, nlej |
---|
2451 | DO ji = nldi, nlei |
---|
2452 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
---|
2453 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
2454 | & * tmask(ji,jj,jk) |
---|
2455 | END DO |
---|
2456 | END DO |
---|
2457 | END DO |
---|
2458 | |
---|
2459 | !-------------------------------------------------------------------- |
---|
2460 | ! Compute the scalar product: ( L dx )^T W dy |
---|
2461 | !-------------------------------------------------------------------- |
---|
2462 | |
---|
2463 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
---|
2464 | |
---|
2465 | !-------------------------------------------------------------------- |
---|
2466 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
2467 | !-------------------------------------------------------------------- |
---|
2468 | |
---|
2469 | CALL eos_insitu_adj(ztem, zsal, zt_adout, zs_adout, zrd_adin) |
---|
2470 | |
---|
2471 | zsp2_1 = DOT_PRODUCT( zt_tlin, zt_adout ) |
---|
2472 | zsp2_2 = DOT_PRODUCT( zs_tlin, zs_adout ) |
---|
2473 | zsp2 = zsp2_1 + zsp2_2 |
---|
2474 | |
---|
2475 | ! Compare the scalar products |
---|
2476 | |
---|
2477 | ! Compare the scalar products |
---|
2478 | ! 14 char:'12345678901234' |
---|
2479 | cl_name = 'eos_adj insitu' |
---|
2480 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
2481 | ! Deallocate memory |
---|
2482 | |
---|
2483 | DEALLOCATE( & |
---|
2484 | & ztem, & |
---|
2485 | & zsal, & |
---|
2486 | & zt_adout, & |
---|
2487 | & zs_adout, & |
---|
2488 | & zrd_adin, & |
---|
2489 | & zt_tlin, & |
---|
2490 | & zs_tlin, & |
---|
2491 | & zrd_tlout, & |
---|
2492 | & znt, & |
---|
2493 | & zns & |
---|
2494 | & ) |
---|
2495 | |
---|
2496 | |
---|
2497 | END SUBROUTINE eos_insitu_adj_tst |
---|
2498 | SUBROUTINE eos_insitu_pot_adj_tst( kumadt ) |
---|
2499 | !!----------------------------------------------------------------------- |
---|
2500 | !! |
---|
2501 | !! *** ROUTINE eos_adj_tst *** |
---|
2502 | !! |
---|
2503 | !! ** Purpose : Test the adjoint routine. |
---|
2504 | !! |
---|
2505 | !! ** Method : Verify the scalar product |
---|
2506 | !! |
---|
2507 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
2508 | !! |
---|
2509 | !! where L = tangent routine |
---|
2510 | !! L^T = adjoint routine |
---|
2511 | !! W = diagonal matrix of scale factors |
---|
2512 | !! dx = input perturbation (random field) |
---|
2513 | !! dy = L dx |
---|
2514 | !! |
---|
2515 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
2516 | !! |
---|
2517 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
2518 | !! |
---|
2519 | !! History : |
---|
2520 | !! ! 08-07 (A. Vidard) |
---|
2521 | !!----------------------------------------------------------------------- |
---|
2522 | !! * Modules used |
---|
2523 | |
---|
2524 | !! * Arguments |
---|
2525 | INTEGER, INTENT(IN) :: & |
---|
2526 | & kumadt ! Output unit |
---|
2527 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2528 | ztem, & ! potential temperature |
---|
2529 | zsal ! salinity |
---|
2530 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2531 | & zt_adout, & ! potential temperature |
---|
2532 | & zs_adout ! salinity |
---|
2533 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2534 | & zrd_adin ! anomaly density |
---|
2535 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2536 | & zrhop_adin ! volume mass |
---|
2537 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2538 | & zt_tlin, & ! potential temperature |
---|
2539 | & zs_tlin ! salinity |
---|
2540 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2541 | & znt, & ! potential temperature |
---|
2542 | & zns ! salinity |
---|
2543 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2544 | & zrd_tlout ! anomaly density |
---|
2545 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2546 | & zrhop_tlout ! volume mass |
---|
2547 | REAL(KIND=wp) :: & |
---|
2548 | & zsp1, & ! scalar product involving the tangent routine |
---|
2549 | & zsp2, & ! scalar product involving the adjoint routine |
---|
2550 | & zsp2_1, & ! scalar product involving the adjoint routine |
---|
2551 | & zsp2_2 ! scalar product involving the adjoint routine |
---|
2552 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
2553 | & iseed_2d ! 2D seed for the random number generator |
---|
2554 | INTEGER :: & |
---|
2555 | & ji, & |
---|
2556 | & jj, & |
---|
2557 | & jk |
---|
2558 | CHARACTER(LEN=14) :: cl_name |
---|
2559 | |
---|
2560 | ! Allocate memory |
---|
2561 | ALLOCATE( & |
---|
2562 | & ztem( jpi, jpj, jpk ), & |
---|
2563 | & zsal( jpi, jpj, jpk ), & |
---|
2564 | & zt_adout( jpi, jpj, jpk ), & |
---|
2565 | & zs_adout( jpi, jpj, jpk ), & |
---|
2566 | & zrhop_adin( jpi, jpj, jpk ), & |
---|
2567 | & zrd_adin( jpi, jpj, jpk ), & |
---|
2568 | & zs_tlin( jpi, jpj, jpk ), & |
---|
2569 | & zt_tlin( jpi, jpj, jpk ), & |
---|
2570 | & zns( jpi, jpj, jpk ), & |
---|
2571 | & znt( jpi, jpj, jpk ), & |
---|
2572 | & zrd_tlout(jpi, jpj, jpk ), & |
---|
2573 | & zrhop_tlout(jpi, jpj, jpk ) ) |
---|
2574 | ! Initialize random field standard deviationsthe reference state |
---|
2575 | ztem = tn |
---|
2576 | zsal = sn |
---|
2577 | |
---|
2578 | !============================================= |
---|
2579 | ! testing of eos_insitu_pot |
---|
2580 | !============================================= |
---|
2581 | |
---|
2582 | !============================================================= |
---|
2583 | ! 1) dx = ( T ) and dy = ( T ) |
---|
2584 | !============================================================= |
---|
2585 | |
---|
2586 | !-------------------------------------------------------------------- |
---|
2587 | ! Reset the tangent and adjoint variables |
---|
2588 | !-------------------------------------------------------------------- |
---|
2589 | zt_tlin(:,:,:) = 0.0_wp |
---|
2590 | zs_tlin(:,:,:) = 0.0_wp |
---|
2591 | zrd_tlout(:,:,:) = 0.0_wp |
---|
2592 | zrhop_tlout(:,:,:) = 0.0_wp |
---|
2593 | zt_adout(:,:,:) = 0.0_wp |
---|
2594 | zs_adout(:,:,:) = 0.0_wp |
---|
2595 | zrhop_adin(:,:,:) = 0.0_wp |
---|
2596 | zrd_adin(:,:,:) = 0.0_wp |
---|
2597 | |
---|
2598 | !-------------------------------------------------------------------- |
---|
2599 | ! Initialize the tangent input with random noise: dx |
---|
2600 | !-------------------------------------------------------------------- |
---|
2601 | DO jj = 1, jpj |
---|
2602 | DO ji = 1, jpi |
---|
2603 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2604 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2605 | END DO |
---|
2606 | END DO |
---|
2607 | CALL grid_random( iseed_2d, znt, 'T', 0.0_wp, stdt ) |
---|
2608 | DO jj = 1, jpj |
---|
2609 | DO ji = 1, jpi |
---|
2610 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2611 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2612 | END DO |
---|
2613 | END DO |
---|
2614 | CALL grid_random( iseed_2d, zns, 'T', 0.0_wp, stds ) |
---|
2615 | DO jk = 1, jpk |
---|
2616 | DO jj = nldj, nlej |
---|
2617 | DO ji = nldi, nlei |
---|
2618 | zt_tlin(ji,jj,jk) = znt(ji,jj,jk) |
---|
2619 | zs_tlin(ji,jj,jk) = zns(ji,jj,jk) |
---|
2620 | END DO |
---|
2621 | END DO |
---|
2622 | END DO |
---|
2623 | !-------------------------------------------------------------------- |
---|
2624 | ! Call the tangent routine: dy = L dx |
---|
2625 | !-------------------------------------------------------------------- |
---|
2626 | |
---|
2627 | call eos_insitu_pot_tan ( ztem, zsal, zt_tlin, zs_tlin, zrd_tlout, zrhop_tlout ) |
---|
2628 | |
---|
2629 | !-------------------------------------------------------------------- |
---|
2630 | ! Initialize the adjoint variables: dy^* = W dy |
---|
2631 | !-------------------------------------------------------------------- |
---|
2632 | DO jk = 1, jpk |
---|
2633 | DO jj = nldj, nlej |
---|
2634 | DO ji = nldi, nlei |
---|
2635 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
---|
2636 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
2637 | & * tmask(ji,jj,jk) |
---|
2638 | zrhop_adin(ji,jj,jk) = zrhop_tlout(ji,jj,jk) & |
---|
2639 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
2640 | & * tmask(ji,jj,jk) |
---|
2641 | END DO |
---|
2642 | END DO |
---|
2643 | END DO |
---|
2644 | |
---|
2645 | !-------------------------------------------------------------------- |
---|
2646 | ! Compute the scalar product: ( L dx )^T W dy |
---|
2647 | !-------------------------------------------------------------------- |
---|
2648 | |
---|
2649 | zsp1 = DOT_PRODUCT( zrd_tlout , zrd_adin ) & |
---|
2650 | & + DOT_PRODUCT( zrhop_tlout, zrhop_adin ) |
---|
2651 | !-------------------------------------------------------------------- |
---|
2652 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
2653 | !-------------------------------------------------------------------- |
---|
2654 | |
---|
2655 | CALL eos_insitu_pot_adj( ztem, zsal, zt_adout, zs_adout, zrd_adin, zrhop_adin ) |
---|
2656 | !-------------------------------------------------------------------- |
---|
2657 | ! Compute the scalar product: dx^T L^T W dy |
---|
2658 | !-------------------------------------------------------------------- |
---|
2659 | |
---|
2660 | zsp2_1 = DOT_PRODUCT( zt_tlin, zt_adout ) |
---|
2661 | zsp2_2 = DOT_PRODUCT( zs_tlin, zs_adout ) |
---|
2662 | zsp2 = zsp2_1 + zsp2_2 |
---|
2663 | ! Compare the scalar products |
---|
2664 | |
---|
2665 | ! 14 char:'12345678901234' |
---|
2666 | cl_name = 'eos_adj pot ' |
---|
2667 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
2668 | ! Deallocate memory |
---|
2669 | DEALLOCATE( & |
---|
2670 | & ztem, & |
---|
2671 | & zsal, & |
---|
2672 | & zt_adout, & |
---|
2673 | & zs_adout, & |
---|
2674 | & zrd_adin, & |
---|
2675 | & zrhop_adin, & |
---|
2676 | & zt_tlin, & |
---|
2677 | & zs_tlin, & |
---|
2678 | & zrd_tlout, & |
---|
2679 | & zrhop_tlout,& |
---|
2680 | & zns, znt ) |
---|
2681 | |
---|
2682 | END SUBROUTINE eos_insitu_pot_adj_tst |
---|
2683 | SUBROUTINE eos_insitu_2d_adj_tst( kumadt ) |
---|
2684 | !!----------------------------------------------------------------------- |
---|
2685 | !! |
---|
2686 | !! *** ROUTINE eos_adj_tst *** |
---|
2687 | !! |
---|
2688 | !! ** Purpose : Test the adjoint routine. |
---|
2689 | !! |
---|
2690 | !! ** Method : Verify the scalar product |
---|
2691 | !! |
---|
2692 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
2693 | !! |
---|
2694 | !! where L = tangent routine |
---|
2695 | !! L^T = adjoint routine |
---|
2696 | !! W = diagonal matrix of scale factors |
---|
2697 | !! dx = input perturbation (random field) |
---|
2698 | !! dy = L dx |
---|
2699 | !! |
---|
2700 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
2701 | !! |
---|
2702 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
2703 | !! |
---|
2704 | !! History : |
---|
2705 | !! ! 08-07 (A. Vidard) |
---|
2706 | !!----------------------------------------------------------------------- |
---|
2707 | !! * Modules used |
---|
2708 | |
---|
2709 | !! * Arguments |
---|
2710 | INTEGER, INTENT(IN) :: & |
---|
2711 | & kumadt ! Output unit |
---|
2712 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2713 | zdep ! depth |
---|
2714 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2715 | ztem, & ! potential temperature |
---|
2716 | zsal ! salinity |
---|
2717 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2718 | & zt_adout, & ! potential temperature |
---|
2719 | & zs_adout ! salinity |
---|
2720 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2721 | & zrd_adin ! anomaly density |
---|
2722 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2723 | & zt_tlin, & ! potential temperature |
---|
2724 | & zs_tlin ! salinity |
---|
2725 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2726 | & znt, & ! potential temperature |
---|
2727 | & zns ! salinity |
---|
2728 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
2729 | & zrd_tlout ! anomaly density |
---|
2730 | REAL(KIND=wp) :: & |
---|
2731 | & zsp1, & ! scalar product involving the tangent routine |
---|
2732 | & zsp2, & ! scalar product involving the adjoint routine |
---|
2733 | & zsp2_1, & ! scalar product involving the adjoint routine |
---|
2734 | & zsp2_2 ! scalar product involving the adjoint routine |
---|
2735 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
2736 | & iseed_2d ! 2D seed for the random number generator |
---|
2737 | INTEGER :: & |
---|
2738 | & ji, & |
---|
2739 | & jj |
---|
2740 | CHARACTER(LEN=14) :: cl_name |
---|
2741 | |
---|
2742 | ! Allocate memory |
---|
2743 | |
---|
2744 | ALLOCATE( & |
---|
2745 | & zdep( jpi, jpj ), & |
---|
2746 | & ztem( jpi, jpj ), & |
---|
2747 | & zsal( jpi, jpj ), & |
---|
2748 | & znt( jpi, jpj ), & |
---|
2749 | & zns( jpi, jpj ), & |
---|
2750 | & zt_adout( jpi, jpj ), & |
---|
2751 | & zs_adout( jpi, jpj ), & |
---|
2752 | & zrd_adin( jpi, jpj ), & |
---|
2753 | & zs_tlin( jpi, jpj ), & |
---|
2754 | & zt_tlin( jpi, jpj ), & |
---|
2755 | & zrd_tlout(jpi, jpj ) ) |
---|
2756 | ! Initialize the reference state |
---|
2757 | ztem(:,:) = tn(:,:,2) |
---|
2758 | zsal(:,:) = sn(:,:,2) |
---|
2759 | zdep(:,:) = fsdept(:,:,2) |
---|
2760 | |
---|
2761 | |
---|
2762 | !============================================================= |
---|
2763 | ! 1) dx = ( T ) and dy = ( T ) |
---|
2764 | !============================================================= |
---|
2765 | |
---|
2766 | !-------------------------------------------------------------------- |
---|
2767 | ! Reset the tangent and adjoint variables |
---|
2768 | !-------------------------------------------------------------------- |
---|
2769 | zt_tlin(:,:) = 0.0_wp |
---|
2770 | zs_tlin(:,:) = 0.0_wp |
---|
2771 | zrd_tlout(:,:) = 0.0_wp |
---|
2772 | zt_adout(:,:) = 0.0_wp |
---|
2773 | zs_adout(:,:) = 0.0_wp |
---|
2774 | zrd_adin(:,:) = 0.0_wp |
---|
2775 | |
---|
2776 | !-------------------------------------------------------------------- |
---|
2777 | ! Initialize the tangent input with random noise: dx |
---|
2778 | !-------------------------------------------------------------------- |
---|
2779 | DO jj = 1, jpj |
---|
2780 | DO ji = 1, jpi |
---|
2781 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2782 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2783 | END DO |
---|
2784 | END DO |
---|
2785 | CALL grid_random( iseed_2d, znt, 'T', 0.0_wp, stdt ) |
---|
2786 | DO jj = 1, jpj |
---|
2787 | DO ji = 1, jpi |
---|
2788 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2789 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2790 | END DO |
---|
2791 | END DO |
---|
2792 | CALL grid_random( iseed_2d, zns, 'T', 0.0_wp, stds ) |
---|
2793 | DO jj = nldj, nlej |
---|
2794 | DO ji = nldi, nlei |
---|
2795 | zt_tlin(ji,jj) = znt(ji,jj) |
---|
2796 | zs_tlin(ji,jj) = zns(ji,jj) |
---|
2797 | END DO |
---|
2798 | END DO |
---|
2799 | |
---|
2800 | CALL eos_insitu_2d_tan(ztem, zsal, zdep, zt_tlin, zs_tlin, zrd_tlout) |
---|
2801 | |
---|
2802 | DO jj = nldj, nlej |
---|
2803 | DO ji = nldi, nlei |
---|
2804 | zrd_adin(ji,jj) = zrd_tlout(ji,jj) & |
---|
2805 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,2)& |
---|
2806 | & * tmask(ji,jj,2) |
---|
2807 | END DO |
---|
2808 | END DO |
---|
2809 | |
---|
2810 | !-------------------------------------------------------------------- |
---|
2811 | ! Compute the scalar product: ( L dx )^T W dy |
---|
2812 | !-------------------------------------------------------------------- |
---|
2813 | |
---|
2814 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
---|
2815 | |
---|
2816 | !-------------------------------------------------------------------- |
---|
2817 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
2818 | !-------------------------------------------------------------------- |
---|
2819 | |
---|
2820 | CALL eos_insitu_2d_adj(ztem, zsal, zdep, zt_adout, zs_adout, zrd_adin) |
---|
2821 | |
---|
2822 | zsp2_1 = DOT_PRODUCT( zt_tlin, zt_adout ) |
---|
2823 | zsp2_2 = DOT_PRODUCT( zs_tlin, zs_adout ) |
---|
2824 | zsp2 = zsp2_1 + zsp2_2 |
---|
2825 | |
---|
2826 | ! Compare the scalar products |
---|
2827 | |
---|
2828 | ! 14 char:'12345678901234' |
---|
2829 | cl_name = 'eos_adj 2d ' |
---|
2830 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
2831 | |
---|
2832 | ! Deallocate memory |
---|
2833 | |
---|
2834 | DEALLOCATE( & |
---|
2835 | & zdep, & |
---|
2836 | & ztem, & |
---|
2837 | & zsal, & |
---|
2838 | & zt_adout, & |
---|
2839 | & zs_adout, & |
---|
2840 | & zrd_adin, & |
---|
2841 | & zt_tlin, & |
---|
2842 | & zs_tlin, & |
---|
2843 | & zrd_tlout, & |
---|
2844 | & zns, znt ) |
---|
2845 | |
---|
2846 | |
---|
2847 | END SUBROUTINE eos_insitu_2d_adj_tst |
---|
2848 | |
---|
2849 | SUBROUTINE eos_adj_tst( kumadt ) |
---|
2850 | !!----------------------------------------------------------------------- |
---|
2851 | !! |
---|
2852 | !! *** ROUTINE eos_adj_tst *** |
---|
2853 | !! |
---|
2854 | !! ** Purpose : Test the adjoint routine. |
---|
2855 | !! |
---|
2856 | !! History : |
---|
2857 | !! ! 08-07 (A. Vidard) |
---|
2858 | !!----------------------------------------------------------------------- |
---|
2859 | !! * Arguments |
---|
2860 | INTEGER, INTENT(IN) :: & |
---|
2861 | & kumadt ! Output unit |
---|
2862 | |
---|
2863 | CALL eos_insitu_adj_tst( kumadt ) |
---|
2864 | |
---|
2865 | CALL eos_insitu_pot_adj_tst( kumadt ) |
---|
2866 | |
---|
2867 | CALL eos_insitu_2d_adj_tst( kumadt ) |
---|
2868 | |
---|
2869 | END SUBROUTINE eos_adj_tst |
---|
2870 | SUBROUTINE bn2_adj_tst( kumadt ) |
---|
2871 | !!----------------------------------------------------------------------- |
---|
2872 | !! |
---|
2873 | !! *** ROUTINE bn2_adj_tst *** |
---|
2874 | !! |
---|
2875 | !! ** Purpose : Test the adjoint routine. |
---|
2876 | !! |
---|
2877 | !! ** Method : Verify the scalar product |
---|
2878 | !! |
---|
2879 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
2880 | !! |
---|
2881 | !! where L = tangent routine |
---|
2882 | !! L^T = adjoint routine |
---|
2883 | !! W = diagonal matrix of scale factors |
---|
2884 | !! dx = input perturbation (random field) |
---|
2885 | !! dy = L dx |
---|
2886 | !! |
---|
2887 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
2888 | !! |
---|
2889 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
2890 | !! |
---|
2891 | !! History : |
---|
2892 | !! ! 08-07 (A. Vidard) |
---|
2893 | !!----------------------------------------------------------------------- |
---|
2894 | !! * Modules used |
---|
2895 | |
---|
2896 | !! * Arguments |
---|
2897 | INTEGER, INTENT(IN) :: & |
---|
2898 | & kumadt ! Output unit |
---|
2899 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2900 | ztem, & ! potential temperature |
---|
2901 | zsal ! salinity |
---|
2902 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2903 | & zt_adout, & ! potential temperature |
---|
2904 | & zs_adout ! salinity |
---|
2905 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2906 | & zrd_adin, & ! potential density (surface referenced) |
---|
2907 | & zrd_adout ! potential density (surface referenced) |
---|
2908 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2909 | & zt_tlin, & ! potential temperature |
---|
2910 | & zs_tlin, & ! salinity |
---|
2911 | & zt_tlout, & ! potential temperature |
---|
2912 | & zs_tlout ! salinity |
---|
2913 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2914 | & zrd_tlout ! potential density (surface referenced) |
---|
2915 | REAL(KIND=wp) :: & |
---|
2916 | & zsp1, & ! scalar product involving the tangent routine |
---|
2917 | & zsp2, & ! scalar product involving the adjoint routine |
---|
2918 | & zsp2_1, & ! scalar product involving the adjoint routine |
---|
2919 | & zsp2_2 ! scalar product involving the adjoint routine |
---|
2920 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
2921 | & znt, & ! potential temperature |
---|
2922 | & zns ! salinity |
---|
2923 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
2924 | & iseed_2d ! 2D seed for the random number generator |
---|
2925 | INTEGER :: & |
---|
2926 | & iseed, & |
---|
2927 | & ji, & |
---|
2928 | & jj, & |
---|
2929 | & jk |
---|
2930 | CHARACTER(LEN=14) :: cl_name |
---|
2931 | |
---|
2932 | ! Allocate memory |
---|
2933 | ALLOCATE( & |
---|
2934 | & ztem( jpi, jpj, jpk ), & |
---|
2935 | & zsal( jpi, jpj, jpk ), & |
---|
2936 | & zt_adout( jpi, jpj, jpk ), & |
---|
2937 | & zs_adout( jpi, jpj, jpk ), & |
---|
2938 | & zrd_adin( jpi, jpj, jpk ), & |
---|
2939 | & zrd_adout(jpi, jpj, jpk ), & |
---|
2940 | & zs_tlin( jpi, jpj, jpk ), & |
---|
2941 | & zt_tlin( jpi, jpj, jpk ), & |
---|
2942 | & zns( jpi, jpj, jpk ), & |
---|
2943 | & znt( jpi, jpj, jpk ), & |
---|
2944 | & zt_tlout( jpi, jpj, jpk ), & |
---|
2945 | & zs_tlout( jpi, jpj, jpk ), & |
---|
2946 | & zrd_tlout(jpi, jpj, jpk ) ) |
---|
2947 | ! Initialize random field standard deviationsthe reference state |
---|
2948 | ztem = tn |
---|
2949 | zsal = sn |
---|
2950 | |
---|
2951 | !============================================================= |
---|
2952 | ! 1) dx = ( T ) and dy = ( T ) |
---|
2953 | !============================================================= |
---|
2954 | |
---|
2955 | !-------------------------------------------------------------------- |
---|
2956 | ! Reset the tangent and adjoint variables |
---|
2957 | !-------------------------------------------------------------------- |
---|
2958 | zt_tlin(:,:,:) = 0.0_wp |
---|
2959 | zs_tlin(:,:,:) = 0.0_wp |
---|
2960 | zt_tlout(:,:,:) = 0.0_wp |
---|
2961 | zs_tlout(:,:,:) = 0.0_wp |
---|
2962 | zrd_tlout(:,:,:) = 0.0_wp |
---|
2963 | zt_adout(:,:,:) = 0.0_wp |
---|
2964 | zs_adout(:,:,:) = 0.0_wp |
---|
2965 | zrd_adin(:,:,:) = 0.0_wp |
---|
2966 | zrd_adout(:,:,:) = 0.0_wp |
---|
2967 | |
---|
2968 | !-------------------------------------------------------------------- |
---|
2969 | ! Initialize the tangent input with random noise: dx |
---|
2970 | !-------------------------------------------------------------------- |
---|
2971 | DO jj = 1, jpj |
---|
2972 | DO ji = 1, jpi |
---|
2973 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2974 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2975 | END DO |
---|
2976 | END DO |
---|
2977 | CALL grid_random( iseed_2d, znt, 'T', 0.0_wp, stdt ) |
---|
2978 | DO jj = 1, jpj |
---|
2979 | DO ji = 1, jpi |
---|
2980 | iseed_2d(ji,jj) = - ( 456953 + & |
---|
2981 | & mig(ji) + ( mjg(jj) - 1 ) * jpiglo ) |
---|
2982 | END DO |
---|
2983 | END DO |
---|
2984 | CALL grid_random( iseed_2d, zns, 'T', 0.0_wp, stds ) |
---|
2985 | DO jk = 1, jpk |
---|
2986 | DO jj = nldj, nlej |
---|
2987 | DO ji = nldi, nlei |
---|
2988 | zt_tlin(ji,jj,jk) = znt(ji,jj,jk) |
---|
2989 | zs_tlin(ji,jj,jk) = zns(ji,jj,jk) |
---|
2990 | END DO |
---|
2991 | END DO |
---|
2992 | END DO |
---|
2993 | !-------------------------------------------------------------------- |
---|
2994 | ! Call the tangent routine: dy = L dx |
---|
2995 | !-------------------------------------------------------------------- |
---|
2996 | zt_tlout(:,:,:) = zt_tlin |
---|
2997 | zs_tlout(:,:,:) = zs_tlin |
---|
2998 | |
---|
2999 | CALL eos_bn2_tan( ztem, zsal, zt_tlout, zs_tlout, zrd_tlout ) |
---|
3000 | !-------------------------------------------------------------------- |
---|
3001 | ! Initialize the adjoint variables: dy^* = W dy |
---|
3002 | !-------------------------------------------------------------------- |
---|
3003 | DO jk = 1, jpk |
---|
3004 | DO jj = nldj, nlej |
---|
3005 | DO ji = nldi, nlei |
---|
3006 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
---|
3007 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
---|
3008 | & * tmask(ji,jj,jk) |
---|
3009 | END DO |
---|
3010 | END DO |
---|
3011 | END DO |
---|
3012 | |
---|
3013 | !-------------------------------------------------------------------- |
---|
3014 | ! Compute the scalar product: ( L dx )^T W dy |
---|
3015 | !-------------------------------------------------------------------- |
---|
3016 | |
---|
3017 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
---|
3018 | |
---|
3019 | !-------------------------------------------------------------------- |
---|
3020 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
3021 | !-------------------------------------------------------------------- |
---|
3022 | |
---|
3023 | zrd_adout(:,:,:) = zrd_adin(:,:,:) |
---|
3024 | |
---|
3025 | CALL eos_bn2_adj( ztem, zsal, zt_adout, zs_adout, zrd_adout ) |
---|
3026 | |
---|
3027 | !-------------------------------------------------------------------- |
---|
3028 | ! Compute the scalar product: dx^T L^T W dy |
---|
3029 | !-------------------------------------------------------------------- |
---|
3030 | |
---|
3031 | zsp2_1 = DOT_PRODUCT( zt_tlin, zt_adout ) |
---|
3032 | zsp2_2 = DOT_PRODUCT( zs_tlin, zs_adout ) |
---|
3033 | zsp2 = zsp2_1 + zsp2_2 |
---|
3034 | |
---|
3035 | ! Compare the scalar products |
---|
3036 | |
---|
3037 | ! 14 char:'12345678901234' |
---|
3038 | cl_name = 'bn2_adj ' |
---|
3039 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
3040 | |
---|
3041 | ! Deallocate memory |
---|
3042 | |
---|
3043 | DEALLOCATE( & |
---|
3044 | & ztem, & |
---|
3045 | & zsal, & |
---|
3046 | & zt_adout, & |
---|
3047 | & zs_adout, & |
---|
3048 | & zrd_adin, & |
---|
3049 | & zrd_adout, & |
---|
3050 | & zt_tlin, & |
---|
3051 | & zs_tlin, & |
---|
3052 | & zt_tlout, & |
---|
3053 | & zs_tlout, & |
---|
3054 | & zrd_tlout, & |
---|
3055 | & zns, znt ) |
---|
3056 | |
---|
3057 | |
---|
3058 | END SUBROUTINE bn2_adj_tst |
---|
3059 | |
---|
3060 | SUBROUTINE eos_insitu_tlm_tst( kumadt ) |
---|
3061 | !!----------------------------------------------------------------------- |
---|
3062 | !! |
---|
3063 | !! *** ROUTINE eos_insitu_tlm_tst *** |
---|
3064 | !! |
---|
3065 | !! ** Purpose : Test the tangent routine. |
---|
3066 | !! |
---|
3067 | !! ** Method : Verify the tangent with Taylor expansion |
---|
3068 | !! |
---|
3069 | !! M(x+hdx) = M(x) + L(hdx) + O(h^2) |
---|
3070 | !! |
---|
3071 | !! where L = tangent routine |
---|
3072 | !! M = direct routine |
---|
3073 | !! dx = input perturbation (random field) |
---|
3074 | !! h = ration on perturbation |
---|
3075 | !! |
---|
3076 | !! In the tangent test we verify that: |
---|
3077 | !! M(x+h*dx) - M(x) |
---|
3078 | !! g(h) = ------------------ ---> 1 as h ---> 0 |
---|
3079 | !! L(h*dx) |
---|
3080 | !! and |
---|
3081 | !! g(h) - 1 |
---|
3082 | !! f(h) = ---------- ---> k (costant) as h ---> 0 |
---|
3083 | !! p |
---|
3084 | !! |
---|
3085 | !! History : |
---|
3086 | !! ! 09-08 (A. Vigilant) |
---|
3087 | !!----------------------------------------------------------------------- |
---|
3088 | !! * Modules used |
---|
3089 | USE eosbn2, ONLY: & ! horizontal & vertical advective trend |
---|
3090 | & eos |
---|
3091 | USE tamtrj ! writing out state trajectory |
---|
3092 | USE par_tlm, ONLY: & |
---|
3093 | & cur_loop, & |
---|
3094 | & h_ratio |
---|
3095 | USE istate_mod |
---|
3096 | USE gridrandom, ONLY: & |
---|
3097 | & grid_rd_sd |
---|
3098 | USE trj_tam |
---|
3099 | USE oce , ONLY: & ! ocean dynamics and tracers variables |
---|
3100 | & tn, sn, rhd, rhop |
---|
3101 | USE opatam_tst_ini, ONLY: & |
---|
3102 | & tlm_namrd |
---|
3103 | USE in_out_manager, ONLY: & ! I/O manager |
---|
3104 | & nitend, & |
---|
3105 | & nit000 |
---|
3106 | USE tamctl, ONLY: & ! Control parameters |
---|
3107 | & numtan, numtan_sc |
---|
3108 | !! * Arguments |
---|
3109 | INTEGER, INTENT(IN) :: & |
---|
3110 | & kumadt ! Output unit |
---|
3111 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
3112 | & zrd_out, & ! |
---|
3113 | & zt_tlin , & ! |
---|
3114 | & zs_tlin , & |
---|
3115 | & zrd_tl , & |
---|
3116 | & zrd_wop, & |
---|
3117 | & z3r |
---|
3118 | REAL(KIND=wp) :: & |
---|
3119 | & zsp1, & |
---|
3120 | & zsp2, & |
---|
3121 | & zsp3, & |
---|
3122 | & zzsp, & |
---|
3123 | & gamma, & |
---|
3124 | & zgsp1, & |
---|
3125 | & zgsp2, & |
---|
3126 | & zgsp3, & |
---|
3127 | & zgsp4, & |
---|
3128 | & zgsp5, & |
---|
3129 | & zgsp6, & |
---|
3130 | & zgsp7 |
---|
3131 | INTEGER :: & |
---|
3132 | & ji, & |
---|
3133 | & jj, & |
---|
3134 | & jk |
---|
3135 | CHARACTER(LEN=14) :: cl_name |
---|
3136 | CHARACTER (LEN=128) :: file_out_sc, file_wop, file_out |
---|
3137 | CHARACTER (LEN=90) :: FMT |
---|
3138 | REAL(KIND=wp), DIMENSION(100):: & |
---|
3139 | & zscrd, zscerrrd |
---|
3140 | INTEGER, DIMENSION(100):: & |
---|
3141 | & iiposrd, ijposrd, ikposrd |
---|
3142 | INTEGER:: & |
---|
3143 | & ii, numsctlm, & |
---|
3144 | & numtlm, & |
---|
3145 | & isamp=40,jsamp=40, ksamp=10 |
---|
3146 | REAL(KIND=wp), DIMENSION(jpi,jpj,jpk) :: & |
---|
3147 | & zerrrd |
---|
3148 | ALLOCATE( & |
---|
3149 | & zrd_out( jpi, jpj, jpk ), & |
---|
3150 | & zrd_tl( jpi, jpj, jpk ), & |
---|
3151 | & zs_tlin( jpi, jpj, jpk ), & |
---|
3152 | & zt_tlin( jpi, jpj, jpk ), & |
---|
3153 | & zrd_wop( jpi, jpj, jpk ), & |
---|
3154 | & z3r ( jpi, jpj, jpk ) ) |
---|
3155 | |
---|
3156 | !-------------------------------------------------------------------- |
---|
3157 | ! Reset the tangent and adjoint variables |
---|
3158 | !-------------------------------------------------------------------- |
---|
3159 | zt_tlin( :,:,:) = 0.0_wp |
---|
3160 | zs_tlin( :,:,:) = 0.0_wp |
---|
3161 | zrd_out( :,:,:) = 0.0_wp |
---|
3162 | zrd_tl ( :,:,:) = 0.0_wp |
---|
3163 | zrd_wop( :,:,:) = 0.0_wp |
---|
3164 | zscerrrd(:) = 0.0_wp |
---|
3165 | zscrd(:) = 0.0_wp |
---|
3166 | |
---|
3167 | !-------------------------------------------------------------------- |
---|
3168 | ! Output filename Xn=F(X0) |
---|
3169 | !-------------------------------------------------------------------- |
---|
3170 | file_wop='trj_wop_eos_insitu' |
---|
3171 | CALL tlm_namrd |
---|
3172 | gamma = h_ratio |
---|
3173 | !-------------------------------------------------------------------- |
---|
3174 | ! Initialize the tangent input with random noise: dx |
---|
3175 | !-------------------------------------------------------------------- |
---|
3176 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3177 | CALL grid_rd_sd( 596035, z3r, 'T', 0.0_wp, stdt) |
---|
3178 | DO jk = 1, jpk |
---|
3179 | DO jj = nldj, nlej |
---|
3180 | DO ji = nldi, nlei |
---|
3181 | zt_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
3182 | END DO |
---|
3183 | END DO |
---|
3184 | END DO |
---|
3185 | CALL grid_rd_sd( 371836, z3r, 'S', 0.0_wp, stds) |
---|
3186 | DO jk = 1, jpk |
---|
3187 | DO jj = nldj, nlej |
---|
3188 | DO ji = nldi, nlei |
---|
3189 | zs_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
3190 | END DO |
---|
3191 | END DO |
---|
3192 | END DO |
---|
3193 | ENDIF |
---|
3194 | |
---|
3195 | !-------------------------------------------------------------------- |
---|
3196 | ! Complete Init for Direct |
---|
3197 | !------------------------------------------------------------------- |
---|
3198 | CALL istate_p |
---|
3199 | |
---|
3200 | ! *** initialize the reference trajectory |
---|
3201 | ! ------------ |
---|
3202 | CALL trj_rea( nit000-1, 1 ) |
---|
3203 | CALL trj_rea( nit000, 1 ) |
---|
3204 | |
---|
3205 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3206 | zt_tlin(:,:,:) = gamma * zt_tlin(:,:,:) |
---|
3207 | tn(:,:,:) = tn(:,:,:) + zt_tlin(:,:,:) |
---|
3208 | |
---|
3209 | zs_tlin(:,:,:) = gamma * zs_tlin(:,:,:) |
---|
3210 | sn(:,:,:) = sn(:,:,:) + zs_tlin(:,:,:) |
---|
3211 | ENDIF |
---|
3212 | !-------------------------------------------------------------------- |
---|
3213 | ! Compute the direct model F(X0,t=n) = Xn |
---|
3214 | !-------------------------------------------------------------------- |
---|
3215 | CALL eos(tn, sn, zrd_out) |
---|
3216 | rhd(:,:,:)= zrd_out(:,:,:) |
---|
3217 | IF ( cur_loop .EQ. 0) CALL trj_wri_spl(file_wop) |
---|
3218 | !-------------------------------------------------------------------- |
---|
3219 | ! Compute the Tangent |
---|
3220 | !-------------------------------------------------------------------- |
---|
3221 | IF ( cur_loop .NE. 0) THEN |
---|
3222 | !-------------------------------------------------------------------- |
---|
3223 | ! Storing data |
---|
3224 | !-------------------------------------------------------------------- |
---|
3225 | !-------------------------------------------------------------------- |
---|
3226 | ! Initialize the tangent variables: dy^* = W dy |
---|
3227 | !-------------------------------------------------------------------- |
---|
3228 | CALL trj_rea( nit000-1, 1 ) |
---|
3229 | CALL trj_rea( nit000, 1 ) |
---|
3230 | !----------------------------------------------------------------------- |
---|
3231 | ! Initialization of the dynamics and tracer fields for the tangent |
---|
3232 | !----------------------------------------------------------------------- |
---|
3233 | CALL eos_insitu_tan(tn, sn, zt_tlin, zs_tlin, zrd_tl) |
---|
3234 | !-------------------------------------------------------------------- |
---|
3235 | ! Compute the scalar product: ( L(t0,tn) gamma dx0 ) ) |
---|
3236 | !-------------------------------------------------------------------- |
---|
3237 | zsp2 = DOT_PRODUCT( zrd_tl, zrd_tl ) |
---|
3238 | !-------------------------------------------------------------------- |
---|
3239 | ! Storing data |
---|
3240 | !-------------------------------------------------------------------- |
---|
3241 | CALL trj_rd_spl(file_wop) |
---|
3242 | zrd_wop (:,:,:) = rhd (:,:,:) |
---|
3243 | |
---|
3244 | !-------------------------------------------------------------------- |
---|
3245 | ! Compute the Linearization Error |
---|
3246 | ! Nn = M( X0+gamma.dX0, t0,tn) - M(X0, t0,tn) |
---|
3247 | ! and |
---|
3248 | ! Compute the Linearization Error |
---|
3249 | ! En = Nn -TL(gamma.dX0, t0,tn) |
---|
3250 | !-------------------------------------------------------------------- |
---|
3251 | ! Warning: Here we re-use local variables z()_out and z()_wop |
---|
3252 | ii=0 |
---|
3253 | DO jk = 1, jpk |
---|
3254 | DO jj = 1, jpj |
---|
3255 | DO ji = 1, jpi |
---|
3256 | zrd_out (ji,jj,jk) = zrd_out (ji,jj,jk) - zrd_wop (ji,jj,jk) |
---|
3257 | zrd_wop (ji,jj,jk) = zrd_out (ji,jj,jk) - zrd_tl (ji,jj,jk) |
---|
3258 | IF ( zrd_tl(ji,jj,jk) .NE. 0.0_wp ) & |
---|
3259 | & zerrrd(ji,jj,jk) = zrd_out(ji,jj,jk)/zrd_tl(ji,jj,jk) |
---|
3260 | IF( (MOD(ji, isamp) .EQ. 0) .AND. & |
---|
3261 | & (MOD(jj, jsamp) .EQ. 0) .AND. & |
---|
3262 | & (MOD(jk, ksamp) .EQ. 0) ) THEN |
---|
3263 | ii = ii+1 |
---|
3264 | iiposrd(ii) = ji |
---|
3265 | ijposrd(ii) = jj |
---|
3266 | ikposrd(ii) = jk |
---|
3267 | IF ( INT(tmask(ji,jj,jk)) .NE. 0) THEN |
---|
3268 | zscrd (ii) = zrd_wop(ji,jj,jk) |
---|
3269 | zscerrrd (ii) = ( zerrrd(ji,jj,jk) - 1.0_wp ) / gamma |
---|
3270 | ENDIF |
---|
3271 | ENDIF |
---|
3272 | END DO |
---|
3273 | END DO |
---|
3274 | END DO |
---|
3275 | |
---|
3276 | zsp1 = DOT_PRODUCT( zrd_out, zrd_out ) |
---|
3277 | zsp3 = DOT_PRODUCT( zrd_wop, zrd_wop ) |
---|
3278 | |
---|
3279 | !-------------------------------------------------------------------- |
---|
3280 | ! Print the linearization error En - norme 2 |
---|
3281 | !-------------------------------------------------------------------- |
---|
3282 | ! 14 char:'12345678901234' |
---|
3283 | cl_name = 'eos_insitu:En ' |
---|
3284 | zzsp = SQRT(zsp3) |
---|
3285 | zgsp5 = zzsp |
---|
3286 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3287 | !-------------------------------------------------------------------- |
---|
3288 | ! Compute TLM norm2 |
---|
3289 | !-------------------------------------------------------------------- |
---|
3290 | zzsp = SQRT(zsp2) |
---|
3291 | zgsp4 = zzsp |
---|
3292 | cl_name = 'eos_insitu:Ln2' |
---|
3293 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3294 | !-------------------------------------------------------------------- |
---|
3295 | ! Print the linearization error Nn - norme 2 |
---|
3296 | !-------------------------------------------------------------------- |
---|
3297 | zzsp = SQRT(zsp1) |
---|
3298 | cl_name = 'eosins:Mhdx-Mx' |
---|
3299 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3300 | |
---|
3301 | zgsp3 = SQRT( zsp3/zsp2 ) |
---|
3302 | zgsp7 = zgsp3/gamma |
---|
3303 | zgsp1 = zzsp |
---|
3304 | zgsp2 = zgsp1 / zgsp4 |
---|
3305 | zgsp6 = (zgsp2 - 1.0_wp)/gamma |
---|
3306 | |
---|
3307 | FMT = "(A8,2X,I4.4,2X,E6.1,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13)" |
---|
3308 | WRITE(numtan,FMT) 'eosinsit', cur_loop, h_ratio, zgsp1, zgsp2, zgsp3, zgsp4, zgsp5, zgsp6, zgsp7 |
---|
3309 | |
---|
3310 | !-------------------------------------------------------------------- |
---|
3311 | ! Unitary calculus |
---|
3312 | !-------------------------------------------------------------------- |
---|
3313 | FMT = "(A8,2X,A8,2X,I4.4,2X,E6.1,2X,I4.4,2X,I4.4,2X,I4.4,2X,E20.13,1X)" |
---|
3314 | cl_name = 'eosinsit' |
---|
3315 | IF(lwp) THEN |
---|
3316 | DO ii=1, 100, 1 |
---|
3317 | IF ( zscrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscrd ', & |
---|
3318 | & cur_loop, h_ratio, iiposrd(ii), ijposrd(ii), ikposrd(ii), zscrd(ii) |
---|
3319 | ENDDO |
---|
3320 | DO ii=1, 100, 1 |
---|
3321 | IF ( zscerrrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscerrrd', & |
---|
3322 | & cur_loop, h_ratio, iiposrd(ii), ijposrd(ii), ikposrd(ii), zscerrrd(ii) |
---|
3323 | ENDDO |
---|
3324 | ! write separator |
---|
3325 | WRITE(numtan_sc,"(A4)") '====' |
---|
3326 | ENDIF |
---|
3327 | |
---|
3328 | ENDIF |
---|
3329 | |
---|
3330 | DEALLOCATE( & |
---|
3331 | & zrd_out, zrd_tl, zrd_wop, & |
---|
3332 | & zt_tlin, zs_tlin, z3r & |
---|
3333 | & ) |
---|
3334 | END SUBROUTINE eos_insitu_tlm_tst |
---|
3335 | |
---|
3336 | SUBROUTINE eos_insitu_pot_tlm_tst( kumadt ) |
---|
3337 | !!----------------------------------------------------------------------- |
---|
3338 | !! |
---|
3339 | !! *** ROUTINE eos_insitu_pot_tlm_tst *** |
---|
3340 | !! |
---|
3341 | !! ** Purpose : Test the tangent routine. |
---|
3342 | !! |
---|
3343 | !! ** Method : Verify the tangent with Taylor expansion |
---|
3344 | !! |
---|
3345 | !! M(x+hdx) = M(x) + L(hdx) + O(h^2) |
---|
3346 | !! |
---|
3347 | !! where L = tangent routine |
---|
3348 | !! M = direct routine |
---|
3349 | !! dx = input perturbation (random field) |
---|
3350 | !! h = ration on perturbation |
---|
3351 | !! |
---|
3352 | !! In the tangent test we verify that: |
---|
3353 | !! M(x+h*dx) - M(x) |
---|
3354 | !! g(h) = ------------------ ---> 1 as h ---> 0 |
---|
3355 | !! L(h*dx) |
---|
3356 | !! and |
---|
3357 | !! g(h) - 1 |
---|
3358 | !! f(h) = ---------- ---> k (costant) as h ---> 0 |
---|
3359 | !! p |
---|
3360 | !! |
---|
3361 | !! History : |
---|
3362 | !! ! 09-08 (A. Vigilant) |
---|
3363 | !!----------------------------------------------------------------------- |
---|
3364 | !! * Modules used |
---|
3365 | USE eosbn2, ONLY: & ! horizontal & vertical advective trend |
---|
3366 | & eos |
---|
3367 | USE tamtrj ! writing out state trajectory |
---|
3368 | USE par_tlm, ONLY: & |
---|
3369 | & cur_loop, & |
---|
3370 | & h_ratio |
---|
3371 | USE istate_mod |
---|
3372 | USE gridrandom, ONLY: & |
---|
3373 | & grid_rd_sd |
---|
3374 | USE trj_tam |
---|
3375 | USE oce , ONLY: & ! ocean dynamics and tracers variables |
---|
3376 | & tn, sn, rhd, rhop |
---|
3377 | USE opatam_tst_ini, ONLY: & |
---|
3378 | & tlm_namrd |
---|
3379 | USE in_out_manager, ONLY: & ! I/O manager |
---|
3380 | & nitend, & |
---|
3381 | & nit000 |
---|
3382 | USE tamctl, ONLY: & ! Control parameters |
---|
3383 | & numtan, numtan_sc |
---|
3384 | !! * Arguments |
---|
3385 | INTEGER, INTENT(IN) :: & |
---|
3386 | & kumadt ! Output unit |
---|
3387 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
3388 | & zrd_out, & ! |
---|
3389 | & zrh_out, & |
---|
3390 | & zt_tlin , & ! |
---|
3391 | & zs_tlin , & |
---|
3392 | & zrh_tl , & |
---|
3393 | & zrd_tl , & |
---|
3394 | & zrd_wop , & |
---|
3395 | & zrh_wop , & |
---|
3396 | & z3r |
---|
3397 | REAL(KIND=wp) :: & |
---|
3398 | & zsp1, & |
---|
3399 | & zsp2, & |
---|
3400 | & zsp3, & |
---|
3401 | & zsp1_Rd, Zsp1_Rh, & |
---|
3402 | & zsp2_Rd, zsp2_Rh, & |
---|
3403 | & zsp3_Rd, zsp3_Rh, & |
---|
3404 | & zzsp, & |
---|
3405 | & gamma, & |
---|
3406 | & zgsp1, & |
---|
3407 | & zgsp2, & |
---|
3408 | & zgsp3, & |
---|
3409 | & zgsp4, & |
---|
3410 | & zgsp5, & |
---|
3411 | & zgsp6, & |
---|
3412 | & zgsp7 |
---|
3413 | INTEGER :: & |
---|
3414 | & ji, & |
---|
3415 | & jj, & |
---|
3416 | & jk |
---|
3417 | CHARACTER(LEN=14) :: cl_name |
---|
3418 | CHARACTER (LEN=128) :: file_out, file_wop |
---|
3419 | CHARACTER (LEN=90) :: FMT |
---|
3420 | REAL(KIND=wp), DIMENSION(100):: & |
---|
3421 | & zscrd, zscerrrd, & |
---|
3422 | & zscrh, zscerrrh |
---|
3423 | INTEGER, DIMENSION(100):: & |
---|
3424 | & iiposrd, ijposrd, ikposrd, & |
---|
3425 | & iiposrh, ijposrh, ikposrh |
---|
3426 | INTEGER:: & |
---|
3427 | & ii, numsctlm, & |
---|
3428 | & isamp=40,jsamp=40, ksamp=10 |
---|
3429 | REAL(KIND=wp), DIMENSION(jpi,jpj,jpk) :: & |
---|
3430 | & zerrrd, zerrrh |
---|
3431 | ALLOCATE( & |
---|
3432 | & zrd_out( jpi, jpj, jpk ), & |
---|
3433 | & zrh_out( jpi, jpj, jpk ), & |
---|
3434 | & zrd_tl( jpi, jpj, jpk ), & |
---|
3435 | & zrh_tl( jpi, jpj, jpk ), & |
---|
3436 | & zs_tlin( jpi, jpj, jpk ), & |
---|
3437 | & zt_tlin( jpi, jpj, jpk ), & |
---|
3438 | & zrd_wop( jpi, jpj, jpk ), & |
---|
3439 | & zrh_wop( jpi, jpj, jpk ), & |
---|
3440 | & z3r ( jpi, jpj, jpk ) ) |
---|
3441 | |
---|
3442 | !-------------------------------------------------------------------- |
---|
3443 | ! Reset the tangent and adjoint variables |
---|
3444 | !-------------------------------------------------------------------- |
---|
3445 | zt_tlin( :,:,:) = 0.0_wp |
---|
3446 | zs_tlin( :,:,:) = 0.0_wp |
---|
3447 | zrd_out( :,:,:) = 0.0_wp |
---|
3448 | zrh_out( :,:,:) = 0.0_wp |
---|
3449 | zrd_tl ( :,:,:) = 0.0_wp |
---|
3450 | zrh_tl ( :,:,:) = 0.0_wp |
---|
3451 | zrd_wop( :,:,:) = 0.0_wp |
---|
3452 | zrh_wop( :,:,:) = 0.0_wp |
---|
3453 | zscerrrd( :) = 0.0_wp |
---|
3454 | zscerrrh( :) = 0.0_wp |
---|
3455 | zscrd(:) = 0.0_wp |
---|
3456 | zscrh(:) = 0.0_wp |
---|
3457 | |
---|
3458 | !-------------------------------------------------------------------- |
---|
3459 | ! Output filename Xn=F(X0) |
---|
3460 | !-------------------------------------------------------------------- |
---|
3461 | file_wop='trj_wop_eos_pot' |
---|
3462 | CALL tlm_namrd |
---|
3463 | gamma = h_ratio |
---|
3464 | !-------------------------------------------------------------------- |
---|
3465 | ! Initialize the tangent input with random noise: dx |
---|
3466 | !-------------------------------------------------------------------- |
---|
3467 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3468 | CALL grid_rd_sd( 596035, z3r, 'T', 0.0_wp, stdt) |
---|
3469 | DO jk = 1, jpk |
---|
3470 | DO jj = nldj, nlej |
---|
3471 | DO ji = nldi, nlei |
---|
3472 | zt_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
3473 | END DO |
---|
3474 | END DO |
---|
3475 | END DO |
---|
3476 | CALL grid_rd_sd( 371836, z3r, 'S', 0.0_wp, stds) |
---|
3477 | DO jk = 1, jpk |
---|
3478 | DO jj = nldj, nlej |
---|
3479 | DO ji = nldi, nlei |
---|
3480 | zs_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
3481 | END DO |
---|
3482 | END DO |
---|
3483 | END DO |
---|
3484 | ENDIF |
---|
3485 | !-------------------------------------------------------------------- |
---|
3486 | ! Complete Init for Direct |
---|
3487 | !------------------------------------------------------------------- |
---|
3488 | CALL istate_p |
---|
3489 | |
---|
3490 | ! *** initialize the reference trajectory |
---|
3491 | ! ------------ |
---|
3492 | CALL trj_rea( nit000-1, 1 ) |
---|
3493 | CALL trj_rea( nit000, 1 ) |
---|
3494 | |
---|
3495 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3496 | zt_tlin(:,:,:) = gamma * zt_tlin(:,:,:) |
---|
3497 | tn(:,:,:) = tn(:,:,:) + zt_tlin(:,:,:) |
---|
3498 | |
---|
3499 | zs_tlin(:,:,:) = gamma * zs_tlin(:,:,:) |
---|
3500 | sn(:,:,:) = sn(:,:,:) + zs_tlin(:,:,:) |
---|
3501 | ENDIF |
---|
3502 | !-------------------------------------------------------------------- |
---|
3503 | ! Compute the direct model F(X0,t=n) = Xn |
---|
3504 | !-------------------------------------------------------------------- |
---|
3505 | CALL eos(tn, sn, zrd_out, zrh_out) |
---|
3506 | rhd (:,:,:) = zrd_out(:,:,:) |
---|
3507 | rhop(:,:,:) = zrh_out(:,:,:) |
---|
3508 | IF ( cur_loop .EQ. 0) CALL trj_wri_spl(file_wop) |
---|
3509 | !-------------------------------------------------------------------- |
---|
3510 | ! Compute the Tangent |
---|
3511 | !-------------------------------------------------------------------- |
---|
3512 | IF ( cur_loop .NE. 0) THEN |
---|
3513 | !-------------------------------------------------------------------- |
---|
3514 | ! Storing data |
---|
3515 | !-------------------------------------------------------------------- |
---|
3516 | !-------------------------------------------------------------------- |
---|
3517 | ! Initialize the tangent variables: dy^* = W dy |
---|
3518 | !-------------------------------------------------------------------- |
---|
3519 | CALL trj_rea( nit000-1, 1 ) |
---|
3520 | CALL trj_rea( nit000, 1 ) |
---|
3521 | !----------------------------------------------------------------------- |
---|
3522 | ! Initialization of the dynamics and tracer fields for the tangent |
---|
3523 | !----------------------------------------------------------------------- |
---|
3524 | CALL eos_insitu_pot_tan(tn, sn, zt_tlin, zs_tlin, zrd_tl, zrh_tl) |
---|
3525 | !-------------------------------------------------------------------- |
---|
3526 | ! Compute the scalar product: ( L(t0,tn) gamma dx0 ) ) |
---|
3527 | !-------------------------------------------------------------------- |
---|
3528 | |
---|
3529 | zsp2_Rd = DOT_PRODUCT( zrd_tl, zrd_tl ) |
---|
3530 | zsp2_Rh = DOT_PRODUCT( zrh_tl, zrh_tl ) |
---|
3531 | zsp2 = zsp2_Rd + zsp2_Rh |
---|
3532 | !-------------------------------------------------------------------- |
---|
3533 | ! Storing data |
---|
3534 | !-------------------------------------------------------------------- |
---|
3535 | CALL trj_rd_spl(file_wop) |
---|
3536 | zrd_wop (:,:,:) = rhd (:,:,:) |
---|
3537 | zrh_wop (:,:,:) = rhop (:,:,:) |
---|
3538 | |
---|
3539 | !-------------------------------------------------------------------- |
---|
3540 | ! Compute the Linearization Error |
---|
3541 | ! Nn = M( X0+gamma.dX0, t0,tn) - M(X0, t0,tn) |
---|
3542 | ! and |
---|
3543 | ! Compute the Linearization Error |
---|
3544 | ! En = Nn -TL(gamma.dX0, t0,tn) |
---|
3545 | !-------------------------------------------------------------------- |
---|
3546 | ! Warning: Here we re-use local variables z()_out and z()_wop |
---|
3547 | ii=0 |
---|
3548 | DO jk = 1, jpk |
---|
3549 | DO jj = 1, jpj |
---|
3550 | DO ji = 1, jpi |
---|
3551 | zrd_out (ji,jj,jk) = zrd_out (ji,jj,jk) - zrd_wop (ji,jj,jk) |
---|
3552 | zrd_wop (ji,jj,jk) = zrd_out (ji,jj,jk) - zrd_tl (ji,jj,jk) |
---|
3553 | IF ( zrd_tl(ji,jj,jk) .NE. 0.0_wp ) & |
---|
3554 | & zerrrd(ji,jj,jk) = zrd_out(ji,jj,jk)/zrd_tl(ji,jj,jk) |
---|
3555 | IF( (MOD(ji, isamp) .EQ. 0) .AND. & |
---|
3556 | & (MOD(jj, jsamp) .EQ. 0) .AND. & |
---|
3557 | & (MOD(jk, ksamp) .EQ. 0) ) THEN |
---|
3558 | ii = ii+1 |
---|
3559 | iiposrd(ii) = ji |
---|
3560 | ijposrd(ii) = jj |
---|
3561 | ikposrd(ii) = jk |
---|
3562 | IF ( INT(tmask(ji,jj,jk)) .NE. 0) THEN |
---|
3563 | zscrd (ii) = zrd_wop(ji,jj,jk) |
---|
3564 | zscerrrd (ii) = ( zerrrd( ji,jj,jk) - 1.0_wp ) / gamma |
---|
3565 | ENDIF |
---|
3566 | ENDIF |
---|
3567 | END DO |
---|
3568 | END DO |
---|
3569 | END DO |
---|
3570 | ii=0 |
---|
3571 | DO jk = 1, jpk |
---|
3572 | DO jj = 1, jpj |
---|
3573 | DO ji = 1, jpi |
---|
3574 | zrh_out (ji,jj,jk) = zrh_out (ji,jj,jk) - zrh_wop (ji,jj,jk) |
---|
3575 | zrh_wop (ji,jj,jk) = zrh_out (ji,jj,jk) - zrh_tl (ji,jj,jk) |
---|
3576 | IF ( zrh_tl(ji,jj,jk) .NE. 0.0_wp ) & |
---|
3577 | & zerrrh(ji,jj,jk) = zrh_out(ji,jj,jk)/zrh_tl(ji,jj,jk) |
---|
3578 | IF( (MOD(ji, isamp) .EQ. 0) .AND. & |
---|
3579 | & (MOD(jj, jsamp) .EQ. 0) .AND. & |
---|
3580 | & (MOD(jk, ksamp) .EQ. 0) ) THEN |
---|
3581 | ii = ii+1 |
---|
3582 | iiposrh(ii) = ji |
---|
3583 | ijposrh(ii) = jj |
---|
3584 | ikposrh(ii) = jk |
---|
3585 | IF ( INT(tmask(ji,jj,jk)) .NE. 0) THEN |
---|
3586 | zscrh (ii) = zrh_wop(ji,jj,jk) |
---|
3587 | zscerrrh (ii) = ( zerrrh( ji,jj,jk) - 1.0_wp ) /gamma |
---|
3588 | ENDIF |
---|
3589 | ENDIF |
---|
3590 | END DO |
---|
3591 | END DO |
---|
3592 | END DO |
---|
3593 | zsp1_Rd = DOT_PRODUCT( zrd_out, zrd_out ) |
---|
3594 | zsp1_Rh = DOT_PRODUCT( zrh_out, zrh_out ) |
---|
3595 | zsp1 = zsp1_Rd + zsp1_Rh |
---|
3596 | |
---|
3597 | zsp3_Rd = DOT_PRODUCT( zrd_wop, zrd_wop ) |
---|
3598 | zsp3_Rh = DOT_PRODUCT( zrh_wop, zrh_wop ) |
---|
3599 | zsp3 = zsp3_Rd + zsp3_Rh |
---|
3600 | !-------------------------------------------------------------------- |
---|
3601 | ! Print the linearization error En - norme 2 |
---|
3602 | !-------------------------------------------------------------------- |
---|
3603 | ! 14 char:'12345678901234' |
---|
3604 | cl_name = 'eos_pot:En ' |
---|
3605 | zzsp = SQRT(zsp3) |
---|
3606 | zgsp5 = zzsp |
---|
3607 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3608 | !-------------------------------------------------------------------- |
---|
3609 | ! Compute TLM norm2 |
---|
3610 | !-------------------------------------------------------------------- |
---|
3611 | zzsp = SQRT(zsp2) |
---|
3612 | zgsp4 = zzsp |
---|
3613 | cl_name = 'eos_pot:Ln2' |
---|
3614 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3615 | !-------------------------------------------------------------------- |
---|
3616 | ! Print the linearization error Nn - norme 2 |
---|
3617 | !-------------------------------------------------------------------- |
---|
3618 | zzsp = SQRT(zsp1) |
---|
3619 | cl_name = 'eospot:Mhdx-Mx' |
---|
3620 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3621 | |
---|
3622 | zgsp3 = SQRT( zsp3/zsp2 ) |
---|
3623 | zgsp7 = zgsp3/gamma |
---|
3624 | zgsp1 = zzsp |
---|
3625 | zgsp2 = zgsp1 / zgsp4 |
---|
3626 | zgsp6 = (zgsp2 - 1.0_wp)/gamma |
---|
3627 | |
---|
3628 | FMT = "(A8,2X,I4.4,2X,E6.1,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13)" |
---|
3629 | WRITE(numtan,FMT) 'eosinsp ', cur_loop, h_ratio, zgsp1, zgsp2, zgsp3, zgsp4, zgsp5, zgsp6, zgsp7 |
---|
3630 | !-------------------------------------------------------------------- |
---|
3631 | ! Unitary calculus |
---|
3632 | !-------------------------------------------------------------------- |
---|
3633 | FMT = "(A8,2X,A8,2X,I4.4,2X,E6.1,2X,I4.4,2X,I4.4,2X,I4.4,2X,E20.13,1X)" |
---|
3634 | cl_name = 'eosinsp ' |
---|
3635 | IF(lwp) THEN |
---|
3636 | DO ii=1, 100, 1 |
---|
3637 | IF ( zscrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscrd ', & |
---|
3638 | & cur_loop, h_ratio, iiposrd(ii), ijposrd(ii), ikposrd(ii), zscrd(ii) |
---|
3639 | ENDDO |
---|
3640 | DO ii=1, 100, 1 |
---|
3641 | IF ( zscrh(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscrh ', & |
---|
3642 | & cur_loop, h_ratio, iiposrh(ii), ijposrh(ii), ikposrh(ii), zscrh(ii) |
---|
3643 | ENDDO |
---|
3644 | DO ii=1, 100, 1 |
---|
3645 | IF ( zscerrrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscerrrd', & |
---|
3646 | & cur_loop, h_ratio, iiposrd(ii), ijposrd(ii), ikposrd(ii), zscerrrd(ii) |
---|
3647 | ENDDO |
---|
3648 | DO ii=1, 100, 1 |
---|
3649 | IF ( zscerrrh(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscerrrh', & |
---|
3650 | & cur_loop, h_ratio, iiposrh(ii), ijposrh(ii), ikposrh(ii), zscerrrh(ii) |
---|
3651 | ENDDO |
---|
3652 | ! write separator |
---|
3653 | WRITE(numtan_sc,"(A4)") '====' |
---|
3654 | ENDIF |
---|
3655 | ENDIF |
---|
3656 | |
---|
3657 | DEALLOCATE( & |
---|
3658 | & zrd_out, zrd_tl, zrd_wop, & |
---|
3659 | & zrh_out, zrh_tl, zrh_wop, & |
---|
3660 | & zt_tlin, zs_tlin, z3r & |
---|
3661 | & ) |
---|
3662 | END SUBROUTINE eos_insitu_pot_tlm_tst |
---|
3663 | |
---|
3664 | SUBROUTINE eos_insitu_2d_tlm_tst( kumadt ) |
---|
3665 | !!----------------------------------------------------------------------- |
---|
3666 | !! |
---|
3667 | !! *** ROUTINE eos_insitu_2d_tlm_tst *** |
---|
3668 | !! |
---|
3669 | !! ** Purpose : Test the tangent routine. |
---|
3670 | !! |
---|
3671 | !! ** Method : Verify the tangent with Taylor expansion |
---|
3672 | !! |
---|
3673 | !! M(x+hdx) = M(x) + L(hdx) + O(h^2) |
---|
3674 | !! |
---|
3675 | !! where L = tangent routine |
---|
3676 | !! M = direct routine |
---|
3677 | !! dx = input perturbation (random field) |
---|
3678 | !! h = ration on perturbation |
---|
3679 | !! |
---|
3680 | !! In the tangent test we verify that: |
---|
3681 | !! M(x+h*dx) - M(x) |
---|
3682 | !! g(h) = ------------------ ---> 1 as h ---> 0 |
---|
3683 | !! L(h*dx) |
---|
3684 | !! and |
---|
3685 | !! g(h) - 1 |
---|
3686 | !! f(h) = ---------- ---> k (costant) as h ---> 0 |
---|
3687 | !! p |
---|
3688 | !! |
---|
3689 | !! History : |
---|
3690 | !! ! 09-08 (A. Vigilant) |
---|
3691 | !!----------------------------------------------------------------------- |
---|
3692 | !! * Modules used |
---|
3693 | USE eosbn2, ONLY: & ! horizontal & vertical advective trend |
---|
3694 | & eos |
---|
3695 | USE tamtrj ! writing out state trajectory |
---|
3696 | USE par_tlm, ONLY: & |
---|
3697 | & cur_loop, & |
---|
3698 | & h_ratio |
---|
3699 | USE istate_mod |
---|
3700 | USE gridrandom, ONLY: & |
---|
3701 | & grid_rd_sd |
---|
3702 | USE trj_tam |
---|
3703 | USE oce , ONLY: & ! ocean dynamics and tracers variables |
---|
3704 | & tn, sn, rhd, rhop |
---|
3705 | USE opatam_tst_ini, ONLY: & |
---|
3706 | & tlm_namrd |
---|
3707 | USE in_out_manager, ONLY: & ! I/O manager |
---|
3708 | & nitend, & |
---|
3709 | & nit000 |
---|
3710 | USE tamctl, ONLY: & ! Control parameters |
---|
3711 | & numtan, numtan_sc |
---|
3712 | !! * Arguments |
---|
3713 | INTEGER, INTENT(IN) :: & |
---|
3714 | & kumadt ! Output unit |
---|
3715 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
3716 | & zdep, & ! depth |
---|
3717 | & ztem, & ! potential temperature |
---|
3718 | & zsal ! salinity |
---|
3719 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
3720 | & zrd_out, & ! |
---|
3721 | & zt_tlin , & ! |
---|
3722 | & zs_tlin , & |
---|
3723 | & zrd_tl , & |
---|
3724 | & zrd_wop , & |
---|
3725 | & z2r |
---|
3726 | REAL(KIND=wp) :: & |
---|
3727 | & zsp1, & |
---|
3728 | & zsp2, & |
---|
3729 | & zsp3, & |
---|
3730 | & zzsp, & |
---|
3731 | & gamma, & |
---|
3732 | & zgsp1, & |
---|
3733 | & zgsp2, & |
---|
3734 | & zgsp3, & |
---|
3735 | & zgsp4, & |
---|
3736 | & zgsp5, & |
---|
3737 | & zgsp6, & |
---|
3738 | & zgsp7 |
---|
3739 | INTEGER :: & |
---|
3740 | & ji, & |
---|
3741 | & jj |
---|
3742 | CHARACTER(LEN=14) :: cl_name |
---|
3743 | CHARACTER (LEN=128) :: file_out, file_wop |
---|
3744 | CHARACTER (LEN=90) :: FMT |
---|
3745 | REAL(KIND=wp), DIMENSION(100):: & |
---|
3746 | & zscrd, zscerrrd |
---|
3747 | INTEGER, DIMENSION(100):: & |
---|
3748 | & iiposrd, ijposrd |
---|
3749 | INTEGER:: & |
---|
3750 | & ii, numsctlm, & |
---|
3751 | & isamp=40,jsamp=40 |
---|
3752 | REAL(KIND=wp), DIMENSION(jpi,jpj) :: & |
---|
3753 | & zerrrd |
---|
3754 | ALLOCATE( & |
---|
3755 | & ztem ( jpi, jpj ), & |
---|
3756 | & zsal ( jpi, jpj ), & |
---|
3757 | & zdep ( jpi, jpj ), & |
---|
3758 | & zrd_out( jpi, jpj ), & |
---|
3759 | & zrd_tl( jpi, jpj ), & |
---|
3760 | & zs_tlin( jpi, jpj ), & |
---|
3761 | & zt_tlin( jpi, jpj ), & |
---|
3762 | & zrd_wop( jpi, jpj ), & |
---|
3763 | & z2r ( jpi, jpj ) ) |
---|
3764 | |
---|
3765 | !-------------------------------------------------------------------- |
---|
3766 | ! Reset the tangent and adjoint variables |
---|
3767 | !-------------------------------------------------------------------- |
---|
3768 | ztem ( :,:) = 0.0_wp |
---|
3769 | zsal ( :,:) = 0.0_wp |
---|
3770 | zt_tlin( :,:) = 0.0_wp |
---|
3771 | zs_tlin( :,:) = 0.0_wp |
---|
3772 | zrd_out( :,:) = 0.0_wp |
---|
3773 | zrd_tl ( :,:) = 0.0_wp |
---|
3774 | zrd_wop( :,:) = 0.0_wp |
---|
3775 | zscerrrd( :) = 0.0_wp |
---|
3776 | zscrd(:) = 0.0_wp |
---|
3777 | |
---|
3778 | !-------------------------------------------------------------------- |
---|
3779 | ! Output filename Xn=F(X0) |
---|
3780 | !-------------------------------------------------------------------- |
---|
3781 | file_wop='trj_wop_eos_2d' |
---|
3782 | |
---|
3783 | CALL tlm_namrd |
---|
3784 | gamma = h_ratio |
---|
3785 | !-------------------------------------------------------------------- |
---|
3786 | ! Initialize the tangent input with random noise: dx |
---|
3787 | !-------------------------------------------------------------------- |
---|
3788 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3789 | CALL grid_rd_sd( 596035, z2r, 'T', 0.0_wp, stdt) |
---|
3790 | DO jj = nldj, nlej |
---|
3791 | DO ji = nldi, nlei |
---|
3792 | zt_tlin(ji,jj) = z2r(ji,jj) |
---|
3793 | END DO |
---|
3794 | END DO |
---|
3795 | CALL grid_rd_sd( 371836, z2r, 'S', 0.0_wp, stds) |
---|
3796 | DO jj = nldj, nlej |
---|
3797 | DO ji = nldi, nlei |
---|
3798 | zs_tlin(ji,jj) = z2r(ji,jj) |
---|
3799 | END DO |
---|
3800 | END DO |
---|
3801 | ENDIF |
---|
3802 | |
---|
3803 | !-------------------------------------------------------------------- |
---|
3804 | ! Complete Init for Direct |
---|
3805 | !------------------------------------------------------------------- |
---|
3806 | CALL istate_p |
---|
3807 | ! *** initialize the reference trajectory |
---|
3808 | ! ------------ |
---|
3809 | CALL trj_rea( nit000-1, 1 ) |
---|
3810 | CALL trj_rea( nit000, 1 ) |
---|
3811 | ! Initialize the reference state |
---|
3812 | ztem(:,:) = tn(:,:,2) |
---|
3813 | zsal(:,:) = sn(:,:,2) |
---|
3814 | zdep(:,:) = fsdept(:,:,2) |
---|
3815 | |
---|
3816 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
3817 | zt_tlin(:,:) = gamma * zt_tlin(:,:) |
---|
3818 | ztem(:,:) = ztem(:,:) + zt_tlin(:,:) |
---|
3819 | |
---|
3820 | zs_tlin(:,:) = gamma * zs_tlin(:,:) |
---|
3821 | zsal(:,:) = zsal(:,:) + zs_tlin(:,:) |
---|
3822 | ENDIF |
---|
3823 | !-------------------------------------------------------------------- |
---|
3824 | ! Compute the direct model F(X0,t=n) = Xn |
---|
3825 | !-------------------------------------------------------------------- |
---|
3826 | CALL eos(ztem, zsal, zdep, zrd_out) |
---|
3827 | rhd (:,:,2) = zrd_out(:,:) |
---|
3828 | IF ( cur_loop .EQ. 0) CALL trj_wri_spl(file_wop) |
---|
3829 | !-------------------------------------------------------------------- |
---|
3830 | ! Compute the Tangent |
---|
3831 | !-------------------------------------------------------------------- |
---|
3832 | IF ( cur_loop .NE. 0) THEN |
---|
3833 | !-------------------------------------------------------------------- |
---|
3834 | ! Storing data |
---|
3835 | !-------------------------------------------------------------------- |
---|
3836 | !-------------------------------------------------------------------- |
---|
3837 | ! Initialize the tangent variables: dy^* = W dy |
---|
3838 | !-------------------------------------------------------------------- |
---|
3839 | CALL trj_rea( nit000-1, 1 ) |
---|
3840 | CALL trj_rea( nit000, 1 ) |
---|
3841 | ztem(:,:) = tn(:,:,2) |
---|
3842 | zsal(:,:) = sn(:,:,2) |
---|
3843 | !----------------------------------------------------------------------- |
---|
3844 | ! Initialization of the dynamics and tracer fields for the tangent |
---|
3845 | !----------------------------------------------------------------------- |
---|
3846 | CALL eos_insitu_2d_tan(ztem, zsal, zdep, zt_tlin, zs_tlin, zrd_tl) |
---|
3847 | !-------------------------------------------------------------------- |
---|
3848 | ! Compute the scalar product: ( L(t0,tn) gamma dx0 ) ) |
---|
3849 | !-------------------------------------------------------------------- |
---|
3850 | zsp2 = DOT_PRODUCT( zrd_tl, zrd_tl ) |
---|
3851 | !-------------------------------------------------------------------- |
---|
3852 | ! Storing data |
---|
3853 | !-------------------------------------------------------------------- |
---|
3854 | CALL trj_rd_spl(file_wop) |
---|
3855 | zrd_wop (:,:) = rhd (:,:,2) |
---|
3856 | !-------------------------------------------------------------------- |
---|
3857 | ! Compute the Linearization Error |
---|
3858 | ! Nn = M( X0+gamma.dX0, t0,tn) - M(X0, t0,tn) |
---|
3859 | ! and |
---|
3860 | ! Compute the Linearization Error |
---|
3861 | ! En = Nn -TL(gamma.dX0, t0,tn) |
---|
3862 | !-------------------------------------------------------------------- |
---|
3863 | ! Warning: Here we re-use local variables z()_out and z()_wop |
---|
3864 | ii=0 |
---|
3865 | DO jj = 1, jpj |
---|
3866 | DO ji = 1, jpi |
---|
3867 | zrd_out (ji,jj) = zrd_out (ji,jj) - zrd_wop (ji,jj) |
---|
3868 | zrd_wop (ji,jj) = zrd_out (ji,jj) - zrd_tl (ji,jj) |
---|
3869 | IF ( zrd_tl(ji,jj) .NE. 0.0_wp ) & |
---|
3870 | & zerrrd(ji,jj) = zrd_out(ji,jj)/zrd_tl(ji,jj) |
---|
3871 | IF( (MOD(ji, isamp) .EQ. 0) .AND. & |
---|
3872 | & (MOD(jj, jsamp) .EQ. 0) ) THEN |
---|
3873 | ii = ii+1 |
---|
3874 | iiposrd(ii) = ji |
---|
3875 | ijposrd(ii) = jj |
---|
3876 | IF ( INT(tmask(ji,jj,2)) .NE. 0) THEN |
---|
3877 | zscrd (ii) = zrd_wop(ji,jj) |
---|
3878 | zscerrrd (ii) = ( zerrrd( ji,jj) - 1.0_wp ) / gamma |
---|
3879 | ENDIF |
---|
3880 | ENDIF |
---|
3881 | END DO |
---|
3882 | END DO |
---|
3883 | |
---|
3884 | zsp1 = DOT_PRODUCT( zrd_out, zrd_out ) |
---|
3885 | |
---|
3886 | zsp3 = DOT_PRODUCT( zrd_wop, zrd_wop ) |
---|
3887 | !-------------------------------------------------------------------- |
---|
3888 | ! Print the linearization error En - norme 2 |
---|
3889 | !-------------------------------------------------------------------- |
---|
3890 | ! 14 char:'12345678901234' |
---|
3891 | cl_name = 'eos_2d:En ' |
---|
3892 | zzsp = SQRT(zsp3) |
---|
3893 | zgsp5 = zzsp |
---|
3894 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3895 | !-------------------------------------------------------------------- |
---|
3896 | ! Compute TLM norm2 |
---|
3897 | !-------------------------------------------------------------------- |
---|
3898 | zzsp = SQRT(zsp2) |
---|
3899 | zgsp4 = zzsp |
---|
3900 | cl_name = 'eos_2d:Ln2' |
---|
3901 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3902 | !-------------------------------------------------------------------- |
---|
3903 | ! Print the linearization error Nn - norme 2 |
---|
3904 | !-------------------------------------------------------------------- |
---|
3905 | zzsp = SQRT(zsp1) |
---|
3906 | cl_name = 'eos_2d:Mhdx-Mx' |
---|
3907 | CALL prntst_tlm( cl_name, kumadt, zzsp, h_ratio ) |
---|
3908 | |
---|
3909 | zgsp3 = SQRT( zsp3/zsp2 ) |
---|
3910 | zgsp7 = zgsp3/gamma |
---|
3911 | zgsp1 = zzsp |
---|
3912 | zgsp2 = zgsp1 / zgsp4 |
---|
3913 | zgsp6 = (zgsp2 - 1.0_wp)/gamma |
---|
3914 | |
---|
3915 | FMT = "(A8,2X,I4.4,2X,E6.1,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13,2X,E20.13)" |
---|
3916 | WRITE(numtan,FMT) 'eosins2d', cur_loop, h_ratio, zgsp1, zgsp2, zgsp3, zgsp4, zgsp5, zgsp6, zgsp7 |
---|
3917 | !-------------------------------------------------------------------- |
---|
3918 | ! Unitary calculus |
---|
3919 | !-------------------------------------------------------------------- |
---|
3920 | FMT = "(A8,2X,A8,2X,I4.4,2X,E6.1,2X,I4.4,2X,I4.4,2X,I4.4,2X,E20.13,1X)" |
---|
3921 | cl_name = 'eosins2d' |
---|
3922 | IF(lwp) THEN |
---|
3923 | DO ii=1, 100, 1 |
---|
3924 | IF ( zscrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscrd ', & |
---|
3925 | & cur_loop, h_ratio, ii, iiposrd(ii), ijposrd(ii), zscrd(ii) |
---|
3926 | ENDDO |
---|
3927 | DO ii=1, 100, 1 |
---|
3928 | IF ( zscerrrd(ii) .NE. 0.0_wp ) WRITE(numtan_sc,FMT) cl_name, 'zscerrrd', & |
---|
3929 | & cur_loop, h_ratio, ii, iiposrd(ii), ijposrd(ii), zscerrrd(ii) |
---|
3930 | ENDDO |
---|
3931 | ! write separator |
---|
3932 | WRITE(numtan_sc,"(A4)") '====' |
---|
3933 | ENDIF |
---|
3934 | |
---|
3935 | ENDIF |
---|
3936 | |
---|
3937 | DEALLOCATE( & |
---|
3938 | & zrd_out, zrd_tl, zrd_wop, & |
---|
3939 | & ztem, zsal, zdep, & |
---|
3940 | & zt_tlin, zs_tlin, z2r & |
---|
3941 | & ) |
---|
3942 | END SUBROUTINE eos_insitu_2d_tlm_tst |
---|
3943 | |
---|
3944 | |
---|
3945 | SUBROUTINE bn2_tlm_tst( kumadt ) |
---|
3946 | !!----------------------------------------------------------------------- |
---|
3947 | !! |
---|
3948 | !! *** ROUTINE bn2_tlm_tst *** |
---|
3949 | !! |
---|
3950 | !! ** Purpose : Test the tangent routine. |
---|
3951 | !! |
---|
3952 | !! ** Method : Verify the tangent with Taylor expansion |
---|
3953 | !! |
---|
3954 | !! M(x+hdx) = M(x) + L(hdx) + O(h^2) |
---|
3955 | !! |
---|
3956 | !! where L = tangent routine |
---|
3957 | !! M = direct routine |
---|
3958 | !! dx = input perturbation (random field) |
---|
3959 | !! h = ration on perturbation |
---|
3960 | !! |
---|
3961 | !! In the tangent test we verify that: |
---|
3962 | !! M(x+h*dx) - M(x) |
---|
3963 | !! g(h) = ------------------ ---> 1 as h ---> 0 |
---|
3964 | !! L(h*dx) |
---|
3965 | !! and |
---|
3966 | !! g(h) - 1 |
---|
3967 | !! f(h) = ---------- ---> k (costant) as h ---> 0 |
---|
3968 | !! p |
---|
3969 | !! |
---|
3970 | !! History : |
---|
3971 | !! ! 09-12 (A. Vigilant) |
---|
3972 | !!----------------------------------------------------------------------- |
---|
3973 | !! * Modules used |
---|
3974 | USE eosbn2, ONLY: & ! horizontal & vertical advective trend |
---|
3975 | & bn2 |
---|
3976 | USE tamtrj ! writing out state trajectory |
---|
3977 | USE par_tlm, ONLY: & |
---|
3978 | & cur_loop, & |
---|
3979 | & h_ratio |
---|
3980 | USE istate_mod |
---|
3981 | USE wzvmod ! vertical velocity |
---|
3982 | USE gridrandom, ONLY: & |
---|
3983 | & grid_rd_sd |
---|
3984 | USE trj_tam |
---|
3985 | USE oce , ONLY: & ! ocean dynamics and tracers variables |
---|
3986 | & tn, sn, rn2 |
---|
3987 | USE oce_tam , ONLY: & |
---|
3988 | & tn_tl, & |
---|
3989 | & sn_tl, & |
---|
3990 | & rn2_tl |
---|
3991 | USE in_out_manager, ONLY: & ! I/O manager & |
---|
3992 | & nit000 |
---|
3993 | USE opatam_tst_ini, ONLY: & |
---|
3994 | & tlm_namrd |
---|
3995 | USE tamctl, ONLY: & ! Control parameters |
---|
3996 | & numtan, numtan_sc |
---|
3997 | !! * Arguments |
---|
3998 | INTEGER, INTENT(IN) :: & |
---|
3999 | & kumadt ! Output unit |
---|
4000 | !! * Local declarations |
---|
4001 | INTEGER :: & |
---|
4002 | & ji, & ! dummy loop indices |
---|
4003 | & jj, & |
---|
4004 | & jk |
---|
4005 | REAL(KIND=wp) :: & |
---|
4006 | & zsp1, & ! scalar product involving the tangent routine |
---|
4007 | & zsp2, & ! scalar product involving the tangent routine |
---|
4008 | & zsp3, & ! scalar product involving the tangent routine |
---|
4009 | & zzsp, & ! scalar product involving the tangent routine |
---|
4010 | & gamma, & |
---|
4011 | & zgsp1, & |
---|
4012 | & zgsp2, & |
---|
4013 | & zgsp3, & |
---|
4014 | & zgsp4, & |
---|
4015 | & zgsp5, & |
---|
4016 | & zgsp6, & |
---|
4017 | & zgsp7 |
---|
4018 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
4019 | & ztn_tlin, & ! potential temperature |
---|
4020 | & zsn_tlin, & ! salinity |
---|
4021 | & zrn2_out, & ! Brunt-Vaisala frequency [s-1] Direct output |
---|
4022 | & zrn2_wop, & ! Brunt-Vaisala frequency [s-1] Direct output w/o perturbation |
---|
4023 | & z3r |
---|
4024 | CHARACTER(LEN=14) :: cl_name |
---|
4025 | CHARACTER (LEN=128) :: file_out, file_wop |
---|
4026 | CHARACTER (LEN=90) :: FMT |
---|
4027 | REAL(KIND=wp), DIMENSION(100):: & |
---|
4028 | & zscrn2, & |
---|
4029 | & zscerrrn2 |
---|
4030 | INTEGER, DIMENSION(100):: & |
---|
4031 | & iiposrn2,ijposrn2, ikposrn2 |
---|
4032 | INTEGER:: & |
---|
4033 | & ii, & |
---|
4034 | & isamp=40, & |
---|
4035 | & jsamp=40, & |
---|
4036 | & ksamp=10, & |
---|
4037 | & numsctlm |
---|
4038 | REAL(KIND=wp), DIMENSION(jpi,jpj,jpk) :: & |
---|
4039 | & zerrrn2 |
---|
4040 | |
---|
4041 | ! Allocate memory |
---|
4042 | ALLOCATE( & |
---|
4043 | & zsn_tlin( jpi, jpj, jpk ), & |
---|
4044 | & ztn_tlin( jpi, jpj, jpk ), & |
---|
4045 | & zrn2_out( jpi, jpj, jpk ), & |
---|
4046 | & zrn2_wop( jpi, jpj, jpk ), & |
---|
4047 | & z3r( jpi, jpj, jpk ) ) |
---|
4048 | |
---|
4049 | |
---|
4050 | !-------------------------------------------------------------------- |
---|
4051 | ! Output filename Xn=F(X0) |
---|
4052 | !-------------------------------------------------------------------- |
---|
4053 | file_wop='trj_wop_bn2' |
---|
4054 | |
---|
4055 | CALL tlm_namrd |
---|
4056 | gamma = h_ratio |
---|
4057 | !-------------------------------------------------------------------- |
---|
4058 | ! Initialize the tangent input with random noise: dx |
---|
4059 | !-------------------------------------------------------------------- |
---|
4060 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
4061 | CALL grid_rd_sd( 264940, z3r, 'T', 0.0_wp, stdt) |
---|
4062 | DO jk = 1, jpk |
---|
4063 | DO jj = nldj, nlej |
---|
4064 | DO ji = nldi, nlei |
---|
4065 | ztn_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
4066 | END DO |
---|
4067 | END DO |
---|
4068 | END DO |
---|
4069 | CALL grid_rd_sd( 618304, z3r, 'T', 0.0_wp, stds) |
---|
4070 | DO jk = 1, jpk |
---|
4071 | DO jj = nldj, nlej |
---|
4072 | DO ji = nldi, nlei |
---|
4073 | zsn_tlin(ji,jj,jk) = z3r(ji,jj,jk) |
---|
4074 | END DO |
---|
4075 | END DO |
---|
4076 | END DO |
---|
4077 | ENDIF |
---|
4078 | !-------------------------------------------------------------------- |
---|
4079 | ! Complete Init for Direct |
---|
4080 | !------------------------------------------------------------------- |
---|
4081 | CALL istate_p |
---|
4082 | |
---|
4083 | ! *** initialize the reference trajectory |
---|
4084 | ! ------------ |
---|
4085 | CALL trj_rea( nit000-1, 1 ) |
---|
4086 | |
---|
4087 | IF (( cur_loop .NE. 0) .OR. ( gamma .NE. 0.0_wp) )THEN |
---|
4088 | |
---|
4089 | ztn_tlin(:,:,:) = gamma * ztn_tlin(:,:,:) |
---|
4090 | tn(:,:,:) = tn(:,:,:) + ztn_tlin(:,:,:) |
---|
4091 | |
---|
4092 | zsn_tlin(:,:,:) = gamma * zsn_tlin(:,:,:) |
---|
4093 | sn(:,:,:) = sn(:,:,:) + zsn_tlin(:,:,:) |
---|
4094 | |
---|
4095 | ENDIF |
---|
4096 | |
---|
4097 | !-------------------------------------------------------------------- |
---|
4098 | ! Compute the direct model F(X0,t=n) = Xn |
---|
4099 | !-------------------------------------------------------------------- |
---|
4100 | CALL bn2(tn, sn, rn2) |
---|
4101 | IF ( cur_loop .EQ. 0) CALL trj_wri_spl(file_wop) |
---|
4102 | !-------------------------------------------------------------------- |
---|
4103 | ! Compute the Tangent |
---|
4104 | !-------------------------------------------------------------------- |
---|
4105 | IF ( cur_loop .NE. 0) THEN |
---|
4106 | !-------------------------------------------------------------------- |
---|
4107 | ! Storing data |
---|
4108 | !-------------------------------------------------------------------- |
---|
4109 | zrn2_out (:,:,:) = rn2 (:,:,:) |
---|
4110 | |
---|
4111 | !-------------------------------------------------------------------- |
---|
4112 | ! Initialize the tangent variables: dy^* = W dy |
---|
4113 | !-------------------------------------------------------------------- |
---|
4114 | CALL trj_rea( nit000-1, 1 ) |
---|
4115 | tn_tl (:,:,:) = ztn_tlin (:,:,:) |
---|
4116 | sn_tl (:,:,:) = zsn_tlin (:,:,:) |
---|
4117 | |
---|
4118 | !----------------------------------------------------------------------- |
---|
4119 | ! Initialization of the dynamics and tracer fields for the tangent |
---|
4120 | !----------------------------------------------------------------------- |
---|
4121 | CALL bn2_tan(tn, sn, ztn_tlin, zsn_tlin, rn2_tl) |
---|
4122 | |
---|
4123 | !-------------------------------------------------------------------- |
---|
4124 | ! Compute the scalar product: ( L(t0,tn) gamma dx0 ) ) |
---|
4125 | !-------------------------------------------------------------------- |
---|
4126 | zsp2 = DOT_PRODUCT( rn2_tl, rn2_tl ) |
---|
4127 | |
---|
4128 | !-------------------------------------------------------------------- |
---|
4129 | ! Storing data |
---|
4130 | !-------------------------------------------------------------------- |
---|
4131 | CALL trj_rd_spl(file_wop) |
---|
4132 | zrn2_wop (:,:,:) = rn2 (:,:,:) |
---|
4133 | |
---|
4134 | !-------------------------------------------------------------------- |
---|
4135 | ! Compute the Linearization Error |
---|
4136 | ! Nn = M( X0+gamma.dX0, t0,tn) - M(X0, t0,tn) |
---|
4137 | ! and |
---|
4138 | ! Compute the Linearization Error |
---|
4139 | ! En = Nn -TL(gamma.dX0, t0,tn) |
---|
4140 | !-------------------------------------------------------------------- |
---|
4141 | ! Warning: Here we re-use local variables z()_out and z()_wop |
---|
4142 | ii=0 |
---|
4143 | DO jk = 1, jpk |
---|
4144 | DO jj = 1, jpj |
---|
4145 | DO ji = 1, jpi |
---|
4146 | zrn2_out (ji,jj,jk) = zrn2_out (ji,jj,jk) - zrn2_wop (ji,jj,jk) |
---|
4147 | zrn2_wop (ji,jj,jk) = zrn2_out (ji,jj,jk) - rn2_tl (ji,jj,jk) |
---|
4148 | IF ( rn2_tl(ji,jj,jk) .NE. 0.0_wp ) & |
---|
4149 | & zerrrn2(ji,jj,jk) = zrn2_out(ji,jj,jk)/rn2_tl(ji,jj,jk) |
---|
4150 | IF( (MOD(ji, isamp) .EQ. 0) .AND. & |
---|
4151 | & (MOD(jj, jsamp) .EQ. 0) .AND. & |
---|
4152 | & (MOD(jk, ksamp) .EQ. 0) ) THEN |
---|
4153 | ii = ii+1 |
---|
4154 | iiposrn2(ii) = ji |
---|
4155 | ijposrn2(ii) = jj |
---|
4156 | ikposrn2(ii) = jk |
---|
4157 | IF ( INT(tmask(ji,jj,jk)) .NE. 0) THEN |
---|
4158 | zscrn2 (ii) = zrn2_wop(ji,jj,jk) |
---|
4159 | zscerrrn2 (ii) = ( zerrrn2(ji,jj,jk) - 1.0_wp ) / gamma |
---|
4160 | ENDIF |
---|
4161 | ENDIF |
---|
4162 | END DO |
---|
4163 | END DO |
---|
4164 | END DO |
---|
4165 | |
---|
4166 | zsp1 = DOT_PRODUCT( zrn2_out, zrn2_out ) |
---|
4167 | |
---|
4168 | zsp3 = DOT_PRODUCT( zrn2_wop, zrn2_wop ) |
---|
4169 | |
---|
4170 | !-------------------------------------------------------------------- |
---|
4171 | ! Print the linearization error En - norme 2 |
---|
4172 | !-------------------------------------------------------------------- |
---|
4173 | ! 14 char:'12345678901234' |
---|
4174 | cl_name = 'eosbn2_tam:En ' |
---|
4175 | zzsp = SQRT(zsp3) |
---|
4176 |
---|