1 | MODULE limthd_dh |
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2 | #if defined key_lim3 |
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3 | !!---------------------------------------------------------------------- |
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4 | !! 'key_lim3' LIM3 sea-ice model |
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5 | !!---------------------------------------------------------------------- |
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6 | !!====================================================================== |
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7 | !! *** MODULE limthd_dh *** |
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8 | !! thermodynamic growth and decay of the ice |
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9 | !!====================================================================== |
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10 | |
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11 | !!---------------------------------------------------------------------- |
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12 | !! lim_thd_dh : vertical accr./abl. and lateral ablation of sea ice |
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13 | !! * Modules used |
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14 | |
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15 | USE par_oce ! ocean parameters |
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16 | USE phycst ! physical constants (OCE directory) |
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17 | USE ice_oce ! ice variables |
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18 | USE sbc_oce ! Surface boundary condition: ocean fields |
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19 | USE thd_ice |
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20 | USE iceini |
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21 | USE limistate |
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22 | USE in_out_manager |
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23 | USE ice |
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24 | USE par_ice |
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25 | USE lib_mpp |
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26 | |
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27 | IMPLICIT NONE |
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28 | PRIVATE |
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29 | |
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30 | !! * Routine accessibility |
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31 | PUBLIC lim_thd_dh ! called by lim_thd |
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32 | |
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33 | !! * Module variables |
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34 | REAL(wp) :: & ! constant values |
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35 | epsi20 = 1e-20 , & |
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36 | epsi13 = 1e-13 , & |
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37 | epsi16 = 1e-16 , & |
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38 | zzero = 0.e0 , & |
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39 | zone = 1.e0 |
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40 | |
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41 | !!---------------------------------------------------------------------- |
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42 | !! LIM 3.0, UCL-LOCEAN-IPSL (2005) |
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43 | !! $Id$ |
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44 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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45 | !!---------------------------------------------------------------------- |
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46 | |
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47 | CONTAINS |
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48 | |
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49 | SUBROUTINE lim_thd_dh(kideb,kiut,jl) |
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50 | !!------------------------------------------------------------------ |
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51 | !! *** ROUTINE lim_thd_dh *** |
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52 | !!------------------------------------------------------------------ |
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53 | !! ** Purpose : |
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54 | !! This routine determines variations of ice and snow thicknesses. |
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55 | !! ** Method : |
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56 | !! Ice/Snow surface melting arises from imbalance in surface fluxes |
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57 | !! Bottom accretion/ablation arises from flux budget |
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58 | !! Snow thickness can increase by precipitation and decrease by |
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59 | !! sublimation |
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60 | !! If snow load excesses Archmiede limit, snow-ice is formed by |
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61 | !! the flooding of sea-water in the snow |
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62 | !! ** Steps |
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63 | !! 1) Compute available flux of heat for surface ablation |
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64 | !! 2) Compute snow and sea ice enthalpies |
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65 | !! 3) Surface ablation and sublimation |
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66 | !! 4) Bottom accretion/ablation |
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67 | !! 5) Case of Total ablation |
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68 | !! 6) Snow ice formation |
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69 | !! |
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70 | !! ** Arguments |
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71 | !! |
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72 | !! ** Inputs / Outputs |
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73 | !! |
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74 | !! ** External |
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75 | !! |
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76 | !! ** References : Bitz and Lipscomb, JGR 99 |
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77 | !! Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646 |
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78 | !! Vancoppenolle, Fichefet and Bitz, GRL 2005 |
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79 | !! Vancoppenolle et al., OM08 |
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80 | !! |
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81 | !! ** History : |
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82 | !! original code 01-04 (LIM) |
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83 | !! original routine |
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84 | !! (05-2003) M. Vancoppenolle, Louvain-La-Neuve, Belgium |
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85 | !! (06/07-2005) 3D version |
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86 | !! (03-2008) Clean code |
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87 | !! |
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88 | !!------------------------------------------------------------------ |
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89 | !! * Arguments |
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90 | INTEGER , INTENT (IN) :: & |
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91 | kideb , & !: Start point on which the the computation is applied |
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92 | kiut , & !: End point on which the the computation is applied |
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93 | jl !: Thickness cateogry number |
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94 | |
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95 | !! * Local variables |
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96 | INTEGER :: & |
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97 | ji , & !: space index |
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98 | jk , & !: ice layer index |
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99 | isnow , & !: switch for presence (1) or absence (0) of snow |
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100 | zji , & !: 2D corresponding indices to ji |
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101 | zjj , & |
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102 | isnowic , & !: snow ice formation not |
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103 | i_ice_switch , & !: ice thickness above a certain treshold or not |
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104 | iter |
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105 | |
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106 | REAL(wp) :: & |
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107 | zhsnew , & !: new snow thickness |
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108 | zihgnew , & !: switch for total ablation |
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109 | ztmelts , & !: melting point |
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110 | zhn , & |
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111 | zdhcf , & |
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112 | zdhbf , & |
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113 | zhni , & |
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114 | zhnfi , & |
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115 | zihg , & |
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116 | zdhnm , & |
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117 | zhnnew , & |
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118 | zeps = 1.0e-13, & |
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119 | zhisn , & |
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120 | zfracs , & !: fractionation coefficient for bottom salt |
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121 | !: entrapment |
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122 | zds , & !: increment of bottom ice salinity |
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123 | zcoeff , & !: dummy argument for snowfall partitioning |
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124 | !: over ice and leads |
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125 | zsm_snowice, & !: snow-ice salinity |
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126 | zswi1 , & !: switch for computation of bottom salinity |
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127 | zswi12 , & !: switch for computation of bottom salinity |
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128 | zswi2 , & !: switch for computation of bottom salinity |
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129 | zgrr , & !: bottom growth rate |
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130 | zihic , & !: |
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131 | ztform !: bottom formation temperature |
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132 | |
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133 | REAL(wp) , DIMENSION(jpij) :: & |
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134 | zh_i , & ! ice layer thickness |
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135 | zh_s , & ! snow layer thickness |
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136 | ztfs , & ! melting point |
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137 | zhsold , & ! old snow thickness |
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138 | zqprec , & !: energy of fallen snow |
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139 | zqfont_su , & ! incoming, remaining surface energy |
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140 | zqfont_bo ! incoming, bottom energy |
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141 | |
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142 | REAL(wp) , DIMENSION(jpij) :: & |
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143 | z_f_surf, & ! surface heat for ablation |
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144 | zhgnew ! new ice thickness |
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145 | |
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146 | REAL(wp), DIMENSION(jpij) :: & |
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147 | zdh_s_mel , & ! snow melt |
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148 | zdh_s_pre , & ! snow precipitation |
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149 | zdh_s_sub , & ! snow sublimation |
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150 | zfsalt_melt ! salt flux due to ice melt |
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151 | |
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152 | REAL(wp) , DIMENSION(jpij,jkmax) :: & |
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153 | zdeltah |
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154 | |
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155 | ! Pathological cases |
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156 | REAL(wp), DIMENSION(jpij) :: & |
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157 | zfdt_init , & !: total incoming heat for ice melt |
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158 | zfdt_final , & !: total remaing heat for ice melt |
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159 | zqt_i , & !: total ice heat content |
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160 | zqt_s , & !: total snow heat content |
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161 | zqt_dummy !: dummy heat content |
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162 | |
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163 | REAL(wp), DIMENSION(jpij,jkmax) :: & |
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164 | zqt_i_lay !: total ice heat content |
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165 | |
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166 | ! Heat conservation |
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167 | REAL(wp), DIMENSION(jpij) :: & |
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168 | zfbase, & |
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169 | zdq_i |
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170 | |
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171 | INTEGER, DIMENSION(jpij) :: & |
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172 | innermelt |
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173 | |
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174 | REAL(wp) :: & |
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175 | meance_dh |
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176 | |
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177 | INTEGER :: & |
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178 | num_iter_max, & |
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179 | numce_dh |
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180 | |
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181 | zfsalt_melt(:) = 0.0 |
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182 | ftotal_fin(:) = 0.0 |
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183 | zfdt_init(:) = 0.0 |
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184 | zfdt_final(:) = 0.0 |
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185 | |
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186 | DO ji = kideb, kiut |
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187 | old_ht_i_b(ji) = ht_i_b(ji) |
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188 | old_ht_s_b(ji) = ht_s_b(ji) |
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189 | END DO |
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190 | ! |
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191 | !------------------------------------------------------------------------------! |
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192 | ! 1) Calculate available heat for surface ablation ! |
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193 | !------------------------------------------------------------------------------! |
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194 | ! |
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195 | DO ji = kideb,kiut |
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196 | isnow = INT( 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_s_b(ji) ) ) ) |
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197 | ztfs(ji) = isnow * rtt + ( 1.0 - isnow ) * rtt |
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198 | z_f_surf(ji) = qnsr_ice_1d(ji) + ( 1.0 - i0(ji) ) * & |
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199 | qsr_ice_1d(ji) - fc_su(ji) |
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200 | z_f_surf(ji) = MAX( zzero , z_f_surf(ji) ) * & |
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201 | MAX( zzero , SIGN( zone , t_su_b(ji) - ztfs(ji) ) ) |
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202 | zfdt_init(ji) = ( z_f_surf(ji) + & |
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203 | MAX( fbif_1d(ji) + qlbbq_1d(ji) + fc_bo_i(ji),0.0 ) ) & |
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204 | * rdt_ice |
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205 | END DO ! ji |
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206 | |
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207 | zqfont_su(:) = 0.0 |
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208 | zqfont_bo(:) = 0.0 |
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209 | dsm_i_se_1d(:) = 0.0 |
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210 | dsm_i_si_1d(:) = 0.0 |
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211 | ! |
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212 | !------------------------------------------------------------------------------! |
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213 | ! 2) Computing layer thicknesses and snow and sea-ice enthalpies. ! |
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214 | !------------------------------------------------------------------------------! |
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215 | ! |
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216 | ! Layer thickness |
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217 | DO ji = kideb,kiut |
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218 | zh_i(ji) = ht_i_b(ji) / nlay_i |
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219 | zh_s(ji) = ht_s_b(ji) / nlay_s |
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220 | END DO |
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221 | |
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222 | ! Total enthalpy of the snow |
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223 | zqt_s(:) = 0.0 |
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224 | DO jk = 1, nlay_s |
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225 | DO ji = kideb,kiut |
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226 | zqt_s(ji) = zqt_s(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s |
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227 | END DO |
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228 | END DO |
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229 | |
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230 | ! Total enthalpy of the ice |
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231 | zqt_i(:) = 0.0 |
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232 | DO jk = 1, nlay_i |
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233 | DO ji = kideb,kiut |
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234 | zqt_i(ji) = zqt_i(ji) + q_i_b(ji,jk) * ht_i_b(ji) / nlay_i |
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235 | zqt_i_lay(ji,jk) = q_i_b(ji,jk) * ht_i_b(ji) / nlay_i |
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236 | END DO |
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237 | END DO |
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238 | ! |
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239 | !------------------------------------------------------------------------------| |
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240 | ! 3) Surface ablation and sublimation | |
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241 | !------------------------------------------------------------------------------| |
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242 | ! |
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243 | !------------------------- |
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244 | ! 3.1 Snow precips / melt |
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245 | !------------------------- |
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246 | ! Snow accumulation in one thermodynamic time step |
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247 | ! snowfall is partitionned between leads and ice |
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248 | ! if snow fall was uniform, a fraction (1-at_i) would fall into leads |
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249 | ! but because of the winds, more snow falls on leads than on sea ice |
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250 | ! and a greater fraction (1-at_i)^beta of the total mass of snow |
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251 | ! (beta < 1) falls in leads. |
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252 | ! In reality, beta depends on wind speed, |
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253 | ! and should decrease with increasing wind speed but here, it is |
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254 | ! considered as a constant. an average value is 0.66 |
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255 | ! Martin Vancoppenolle, December 2006 |
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256 | |
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257 | ! Snow fall |
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258 | DO ji = kideb, kiut |
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259 | zcoeff = ( 1.0 - ( 1.0 - at_i_b(ji) )**betas ) / at_i_b(ji) |
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260 | zdh_s_pre(ji) = zcoeff * sprecip_1d(ji) * rdt_ice / rhosn |
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261 | END DO |
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262 | zdh_s_mel(:) = 0.0 |
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263 | |
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264 | ! Melt of fallen snow |
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265 | DO ji = kideb, kiut |
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266 | ! tatm_ice is now in K |
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267 | zqprec(ji) = rhosn * ( cpic * ( rtt - tatm_ice_1d(ji) ) + lfus ) |
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268 | zqfont_su(ji) = z_f_surf(ji) * rdt_ice |
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269 | zdeltah(ji,1) = MIN( 0.0 , - zqfont_su(ji) / MAX( zqprec(ji) , epsi13 ) ) |
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270 | zqfont_su(ji) = MAX( 0.0 , - zdh_s_pre(ji) - zdeltah(ji,1) ) * & |
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271 | zqprec(ji) |
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272 | zdeltah(ji,1) = MAX( - zdh_s_pre(ji) , zdeltah(ji,1) ) |
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273 | zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,1) |
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274 | ! heat conservation |
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275 | qt_s_in(ji,jl) = qt_s_in(ji,jl) + zqprec(ji) * zdh_s_pre(ji) |
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276 | zqt_s(ji) = zqt_s(ji) + zqprec(ji) * zdh_s_pre(ji) |
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277 | zqt_s(ji) = MAX ( zqt_s(ji) - zqfont_su(ji) , 0.0 ) |
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278 | END DO |
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279 | |
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280 | |
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281 | ! Snow melt due to surface heat imbalance |
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282 | DO jk = 1, nlay_s |
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283 | DO ji = kideb, kiut |
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284 | zdeltah(ji,jk) = - zqfont_su(ji) / q_s_b(ji,jk) |
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285 | zqfont_su(ji) = MAX( 0.0 , - zh_s(ji) - zdeltah(ji,jk) ) * & |
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286 | q_s_b(ji,jk) |
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287 | zdeltah(ji,jk) = MAX( zdeltah(ji,jk) , - zh_s(ji) ) |
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288 | zdh_s_mel(ji) = zdh_s_mel(ji) + zdeltah(ji,jk) !resulting melt of snow |
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289 | END DO |
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290 | END DO |
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291 | |
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292 | ! Apply snow melt to snow depth |
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293 | DO ji = kideb, kiut |
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294 | dh_s_tot(ji) = zdh_s_mel(ji) + zdh_s_pre(ji) |
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295 | ! Old and new snow depths |
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296 | zhsold(ji) = ht_s_b(ji) |
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297 | zhsnew = ht_s_b(ji) + dh_s_tot(ji) |
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298 | ! If snow is still present zhn = 1, else zhn = 0 |
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299 | zhn = 1.0 - MAX( zzero , SIGN( zone , - zhsnew ) ) |
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300 | ht_s_b(ji) = MAX( zzero , zhsnew ) |
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301 | ! Volume and mass variations of snow |
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302 | dvsbq_1d(ji) = a_i_b(ji) * ( ht_s_b(ji) - zhsold(ji) & |
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303 | - zdh_s_mel(ji) ) |
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304 | dvsbq_1d(ji) = MIN( zzero, dvsbq_1d(ji) ) |
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305 | rdmsnif_1d(ji) = rhosn*dvsbq_1d(ji) |
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306 | END DO ! ji |
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307 | |
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308 | !-------------------------- |
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309 | ! 3.2 Surface ice ablation |
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310 | !-------------------------- |
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311 | DO ji = kideb, kiut |
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312 | dh_i_surf(ji) = 0.0 |
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313 | ! For heat conservation test |
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314 | z_f_surf(ji) = zqfont_su(ji) / rdt_ice ! heat conservation test |
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315 | zdq_i(ji) = 0.0 |
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316 | END DO ! ji |
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317 | |
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318 | DO jk = 1, nlay_i |
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319 | DO ji = kideb, kiut |
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320 | ! melt of layer jk |
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321 | zdeltah(ji,jk) = - zqfont_su(ji) / q_i_b(ji,jk) |
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322 | ! recompute heat available |
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323 | zqfont_su(ji) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * & |
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324 | q_i_b(ji,jk) |
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325 | ! melt of layer jk cannot be higher than its thickness |
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326 | zdeltah(ji,jk) = MAX( zdeltah(ji,jk) , - zh_i(ji) ) |
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327 | ! update surface melt |
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328 | dh_i_surf(ji) = dh_i_surf(ji) + zdeltah(ji,jk) |
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329 | ! for energy conservation |
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330 | zdq_i(ji) = zdq_i(ji) + zdeltah(ji,jk) * & |
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331 | q_i_b(ji,jk) / rdt_ice |
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332 | ! contribution to ice-ocean salt flux |
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333 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
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334 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
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335 | zfsalt_melt(ji) = zfsalt_melt(ji) + & |
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336 | ( sss_m(zji,zjj) - sm_i_b(ji) ) * & |
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337 | a_i_b(ji) * & |
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338 | MIN( zdeltah(ji,jk) , 0.0 ) * rhoic / rdt_ice |
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339 | END DO ! ji |
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340 | END DO ! jk |
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341 | |
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342 | !------------------- |
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343 | ! Conservation test |
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344 | !------------------- |
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345 | IF ( con_i ) THEN |
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346 | numce_dh = 0 |
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347 | meance_dh = 0.0 |
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348 | DO ji = kideb, kiut |
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349 | |
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350 | IF ( ( z_f_surf(ji) + zdq_i(ji) ) .GE. 1.0e-3 ) THEN |
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351 | numce_dh = numce_dh + 1 |
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352 | meance_dh = meance_dh + z_f_surf(ji) + zdq_i(ji) |
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353 | ENDIF |
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354 | |
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355 | IF ( z_f_surf(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN! |
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356 | WRITE(numout,*) ' ALERTE heat loss for surface melt ' |
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357 | WRITE(numout,*) ' zji, zjj, jl :', zji, zjj, jl |
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358 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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359 | WRITE(numout,*) ' z_f_surf : ', z_f_surf(ji) |
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360 | WRITE(numout,*) ' zdq_i : ', zdq_i(ji) |
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361 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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362 | WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji) |
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363 | WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji) |
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364 | WRITE(numout,*) ' qlbbq_1d: ', qlbbq_1d(ji) |
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365 | WRITE(numout,*) ' s_i_new : ', s_i_new(ji) |
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366 | WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj) |
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367 | ENDIF |
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368 | |
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369 | END DO ! ji |
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370 | |
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371 | IF ( numce_dh .GT. 0 ) meance_dh = meance_dh / numce_dh |
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372 | WRITE(numout,*) ' Error report - Category : ', jl |
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373 | WRITE(numout,*) ' ~~~~~~~~~~~~ ' |
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374 | WRITE(numout,*) ' Number of points where there is sur. me. error : ', numce_dh |
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375 | WRITE(numout,*) ' Mean basal growth error on error points : ', meance_dh |
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376 | |
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377 | ENDIF ! con_i |
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378 | |
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379 | !---------------------- |
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380 | ! 3.3 Snow sublimation |
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381 | !---------------------- |
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382 | |
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383 | DO ji = kideb, kiut |
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384 | ! if qla is positive (upwards), heat goes to the atmosphere, therefore |
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385 | ! snow sublimates, if qla is negative (downwards), snow condensates |
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386 | zdh_s_sub(ji) = - parsub * qla_ice_1d(ji) / ( rhosn * lsub ) * rdt_ice |
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387 | dh_s_tot(ji) = dh_s_tot(ji) + zdh_s_sub(ji) |
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388 | zdhcf = ht_s_b(ji) + zdh_s_sub(ji) |
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389 | ht_s_b(ji) = MAX( zzero , zdhcf ) |
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390 | ! we recompute dh_s_tot |
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391 | dh_s_tot(ji) = ht_s_b(ji) - zhsold(ji) |
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392 | qt_s_in(ji,jl) = qt_s_in(ji,jl) + zdh_s_sub(ji)*q_s_b(ji,1) |
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393 | END DO !ji |
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394 | |
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395 | zqt_dummy(:) = 0.0 |
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396 | DO jk = 1, nlay_s |
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397 | DO ji = kideb,kiut |
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398 | q_s_b(ji,jk) = rhosn * ( cpic * ( rtt - t_s_b(ji,jk) ) + lfus ) |
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399 | ! heat conservation |
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400 | zqt_dummy(ji) = zqt_dummy(ji) + q_s_b(ji,jk) * ht_s_b(ji) / nlay_s |
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401 | END DO |
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402 | END DO |
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403 | |
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404 | DO jk = 1, nlay_s !n |
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405 | DO ji = kideb, kiut !n |
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406 | ! In case of disparition of the snow, we have to update the snow |
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407 | ! temperatures |
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408 | zhisn = MAX( zzero , SIGN( zone, - ht_s_b(ji) ) ) |
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409 | t_s_b(ji,jk) = ( 1.0 - zhisn ) * t_s_b(ji,jk) + zhisn * rtt |
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410 | q_s_b(ji,jk) = ( 1.0 - zhisn ) * q_s_b(ji,jk) |
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411 | END DO |
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412 | END DO |
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413 | |
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414 | ! |
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415 | !------------------------------------------------------------------------------! |
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416 | ! 4) Basal growth / melt ! |
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417 | !------------------------------------------------------------------------------! |
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418 | ! |
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419 | ! Ice basal growth / melt is given by the ratio of heat budget over basal |
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420 | ! ice heat content. Basal heat budget is given by the difference between |
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421 | ! the inner conductive flux (fc_bo_i), from the open water heat flux |
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422 | ! (qlbbqb) and the turbulent ocean flux (fbif). |
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423 | ! fc_bo_i is positive downwards. fbif and qlbbq are positive to the ice |
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424 | |
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425 | !----------------------------------------------------- |
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426 | ! 4.1 Basal growth - (a) salinity not varying in time |
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427 | !----------------------------------------------------- |
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428 | IF ( ( num_sal .NE. 2 ) .AND. ( num_sal .NE. 4 ) ) THEN |
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429 | DO ji = kideb, kiut |
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430 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN |
---|
431 | s_i_new(ji) = sm_i_b(ji) |
---|
432 | ! Melting point in K |
---|
433 | ztmelts = - tmut * s_i_new(ji) + rtt |
---|
434 | ! New ice heat content (Bitz and Lipscomb, 1999) |
---|
435 | ztform = t_i_b(ji,nlay_i) ! t_bo_b crashes in the |
---|
436 | ! Baltic |
---|
437 | q_i_b(ji,nlay_i+1) = rhoic * & |
---|
438 | ( cpic * ( ztmelts - ztform ) & |
---|
439 | + lfus * ( 1.0 - ( ztmelts - rtt ) / & |
---|
440 | ( ztform - rtt ) ) & |
---|
441 | - rcp * ( ztmelts-rtt ) ) |
---|
442 | ! Basal growth rate = - F*dt / q |
---|
443 | dh_i_bott(ji) = - rdt_ice*( fc_bo_i(ji) + fbif_1d(ji) + & |
---|
444 | qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1) |
---|
445 | ENDIF ! heat budget |
---|
446 | END DO ! ji |
---|
447 | ENDIF ! num_sal |
---|
448 | |
---|
449 | !------------------------------------------------- |
---|
450 | ! 4.1 Basal growth - (b) salinity varying in time |
---|
451 | !------------------------------------------------- |
---|
452 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
453 | ! the growth rate (dh_i_bott) is function of the new ice |
---|
454 | ! heat content (q_i_b(nlay_i+1)). q_i_b depends on the new ice |
---|
455 | ! salinity (snewice). snewice depends on dh_i_bott |
---|
456 | ! it converges quickly, so, no problem |
---|
457 | ! See Vancoppenolle et al., OM08 for more info on this |
---|
458 | |
---|
459 | ! Initial value (tested 1D, can be anything between 1 and 20) |
---|
460 | num_iter_max = 4 |
---|
461 | s_i_new(:) = 4.0 |
---|
462 | |
---|
463 | ! Iterative procedure |
---|
464 | DO iter = 1, num_iter_max |
---|
465 | DO ji = kideb, kiut |
---|
466 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN |
---|
467 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
468 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
469 | ! Melting point in K |
---|
470 | ztmelts = - tmut * s_i_new(ji) + rtt |
---|
471 | ! New ice heat content (Bitz and Lipscomb, 1999) |
---|
472 | q_i_b(ji,nlay_i+1) = rhoic * & |
---|
473 | ( cpic * ( ztmelts - t_bo_b(ji) ) & |
---|
474 | + lfus * ( 1.0 - ( ztmelts - rtt ) / & |
---|
475 | ( t_bo_b(ji) - rtt ) ) & |
---|
476 | - rcp * ( ztmelts-rtt ) ) |
---|
477 | ! Bottom growth rate = - F*dt / q |
---|
478 | dh_i_bott(ji) = - rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) & |
---|
479 | + qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1) |
---|
480 | ! New ice salinity ( Cox and Weeks, JGR, 1988 ) |
---|
481 | ! zswi2 (1) if dh_i_bott/rdt .GT. 3.6e-7 |
---|
482 | ! zswi12 (1) if dh_i_bott/rdt .LT. 3.6e-7 and .GT. 2.0e-8 |
---|
483 | ! zswi1 (1) if dh_i_bott/rdt .LT. 2.0e-8 |
---|
484 | zgrr = MIN( 1.0e-3, MAX ( dh_i_bott(ji) / rdt_ice , zeps ) ) |
---|
485 | zswi2 = MAX( zzero , SIGN( zone , zgrr - 3.6e-7 ) ) |
---|
486 | zswi12 = MAX( zzero , SIGN( zone , zgrr - 2.0e-8 ) ) * ( 1.0 - zswi2 ) |
---|
487 | zswi1 = 1. - zswi2 * zswi12 |
---|
488 | zfracs = zswi1 * 0.12 + & |
---|
489 | zswi12 * ( 0.8925 + 0.0568 * LOG( 100.0 * zgrr ) ) + & |
---|
490 | zswi2 * 0.26 / & |
---|
491 | ( 0.26 + 0.74 * EXP ( - 724300.0 * zgrr ) ) |
---|
492 | zds = zfracs*sss_m(zji,zjj) - s_i_new(ji) |
---|
493 | s_i_new(ji) = zfracs * sss_m(zji,zjj) |
---|
494 | ENDIF ! fc_bo_i |
---|
495 | END DO ! ji |
---|
496 | END DO ! iter |
---|
497 | |
---|
498 | ! Final values |
---|
499 | DO ji = kideb, kiut |
---|
500 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .LT. 0.0 ) THEN |
---|
501 | ! New ice salinity must not exceed 15 psu |
---|
502 | s_i_new(ji) = MIN( s_i_new(ji), s_i_max ) |
---|
503 | ! Metling point in K |
---|
504 | ztmelts = - tmut * s_i_new(ji) + rtt |
---|
505 | ! New ice heat content (Bitz and Lipscomb, 1999) |
---|
506 | q_i_b(ji,nlay_i+1) = rhoic * & |
---|
507 | ( cpic * ( ztmelts - t_bo_b(ji) ) & |
---|
508 | + lfus * ( 1.0 - ( ztmelts - rtt ) / & |
---|
509 | ( t_bo_b(ji) - rtt ) ) & |
---|
510 | - rcp * ( ztmelts-rtt ) ) |
---|
511 | ! Basal growth rate = - F*dt / q |
---|
512 | dh_i_bott(ji) = - rdt_ice*( fc_bo_i(ji) + fbif_1d(ji) + & |
---|
513 | qlbbq_1d(ji) ) / q_i_b(ji,nlay_i+1) |
---|
514 | ! Salinity update |
---|
515 | ! entrapment during bottom growth |
---|
516 | dsm_i_se_1d(ji) = ( s_i_new(ji)*dh_i_bott(ji) + & |
---|
517 | sm_i_b(ji)*ht_i_b(ji) ) / & |
---|
518 | MAX( ht_i_b(ji) + dh_i_bott(ji) ,zeps ) & |
---|
519 | - sm_i_b(ji) |
---|
520 | ENDIF ! heat budget |
---|
521 | END DO ! ji |
---|
522 | ENDIF ! num_sal |
---|
523 | |
---|
524 | !---------------- |
---|
525 | ! 4.2 Basal melt |
---|
526 | !---------------- |
---|
527 | meance_dh = 0.0 |
---|
528 | numce_dh = 0 |
---|
529 | innermelt(:) = 0 |
---|
530 | |
---|
531 | DO ji = kideb, kiut |
---|
532 | ! heat convergence at the surface > 0 |
---|
533 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .GE. 0.0 ) THEN |
---|
534 | |
---|
535 | s_i_new(ji) = s_i_b(ji,nlay_i) |
---|
536 | zqfont_bo(ji) = rdt_ice * ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) |
---|
537 | |
---|
538 | zfbase(ji) = zqfont_bo(ji) / rdt_ice ! heat conservation test |
---|
539 | zdq_i(ji) = 0.0 |
---|
540 | |
---|
541 | dh_i_bott(ji) = 0.0 |
---|
542 | ENDIF |
---|
543 | END DO |
---|
544 | |
---|
545 | DO jk = nlay_i, 1, -1 |
---|
546 | DO ji = kideb, kiut |
---|
547 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .GE. 0.0 ) THEN |
---|
548 | ztmelts = - tmut * s_i_b(ji,jk) + rtt |
---|
549 | IF ( t_i_b(ji,jk) .GE. ztmelts ) THEN |
---|
550 | zdeltah(ji,jk) = - zh_i(ji) |
---|
551 | dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(ji,jk) |
---|
552 | innermelt(ji) = 1 |
---|
553 | ELSE ! normal ablation |
---|
554 | zdeltah(ji,jk) = - zqfont_bo(ji) / q_i_b(ji,jk) |
---|
555 | zqfont_bo(ji) = MAX( 0.0 , - zh_i(ji) - zdeltah(ji,jk) ) * & |
---|
556 | q_i_b(ji,jk) |
---|
557 | zdeltah(ji,jk) = MAX(zdeltah(ji,jk), - zh_i(ji) ) |
---|
558 | dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(ji,jk) |
---|
559 | zdq_i(ji) = zdq_i(ji) + zdeltah(ji,jk) * & |
---|
560 | q_i_b(ji,jk) / rdt_ice |
---|
561 | ! contribution to salt flux |
---|
562 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
563 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
564 | zfsalt_melt(ji) = zfsalt_melt(ji) + & |
---|
565 | ( sss_m(zji,zjj) - sm_i_b(ji) ) * & |
---|
566 | a_i_b(ji) * & |
---|
567 | MIN( zdeltah(ji,jk) , 0.0 ) * rhoic / rdt_ice |
---|
568 | ENDIF |
---|
569 | ENDIF |
---|
570 | END DO ! ji |
---|
571 | END DO ! jk |
---|
572 | |
---|
573 | !------------------- |
---|
574 | ! Conservation test |
---|
575 | !------------------- |
---|
576 | IF ( con_i ) THEN |
---|
577 | DO ji = kideb, kiut |
---|
578 | IF ( ( fc_bo_i(ji) + fbif_1d(ji) + qlbbq_1d(ji) ) .GE. 0.0 ) THEN |
---|
579 | IF ( ( zfbase(ji) + zdq_i(ji) ) .GE. 1.0e-3 ) THEN |
---|
580 | numce_dh = numce_dh + 1 |
---|
581 | meance_dh = meance_dh + zfbase(ji) + zdq_i(ji) |
---|
582 | ENDIF |
---|
583 | IF ( zfbase(ji) + zdq_i(ji) .GE. 1.0e-3 ) THEN |
---|
584 | WRITE(numout,*) ' ALERTE heat loss for basal melt ' |
---|
585 | WRITE(numout,*) ' zji, zjj, jl :', zji, zjj, jl |
---|
586 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
---|
587 | WRITE(numout,*) ' zfbase : ', zfbase(ji) |
---|
588 | WRITE(numout,*) ' zdq_i : ', zdq_i(ji) |
---|
589 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
---|
590 | WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji) |
---|
591 | WRITE(numout,*) ' fbif_1d : ', fbif_1d(ji) |
---|
592 | WRITE(numout,*) ' qlbbq_1d: ', qlbbq_1d(ji) |
---|
593 | WRITE(numout,*) ' s_i_new : ', s_i_new(ji) |
---|
594 | WRITE(numout,*) ' sss_m : ', sss_m(zji,zjj) |
---|
595 | WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji) |
---|
596 | WRITE(numout,*) ' innermelt : ', innermelt(ji) |
---|
597 | ENDIF |
---|
598 | ENDIF ! heat convergence at the surface |
---|
599 | END DO ! ji |
---|
600 | |
---|
601 | IF ( numce_dh .GT. 0 ) meance_dh = meance_dh / numce_dh |
---|
602 | WRITE(numout,*) ' Number of points where there is bas. me. error : ', numce_dh |
---|
603 | WRITE(numout,*) ' Mean basal melt error on error points : ', meance_dh |
---|
604 | WRITE(numout,*) ' Remaining bottom heat : ', zqfont_bo(jiindex_1d) |
---|
605 | |
---|
606 | ENDIF ! con_i |
---|
607 | |
---|
608 | ! |
---|
609 | !------------------------------------------------------------------------------! |
---|
610 | ! 5) Pathological cases ! |
---|
611 | !------------------------------------------------------------------------------! |
---|
612 | ! |
---|
613 | !---------------------------------------------- |
---|
614 | ! 5.1 Excessive ablation in a 1-category model |
---|
615 | !---------------------------------------------- |
---|
616 | |
---|
617 | DO ji = kideb, kiut |
---|
618 | ! in a 1-category sea ice model, bottom ablation must not exceed hmelt (-0.15) |
---|
619 | zdhbf = dh_i_bott(ji) |
---|
620 | IF (jpl.EQ.1) zdhbf = MAX( hmelt , dh_i_bott(ji) ) |
---|
621 | ! excessive energy is sent to lateral ablation |
---|
622 | fsup(ji) = rhoic*lfus * at_i_b(ji) / MAX( ( 1.0 - at_i_b(ji) ),epsi13) & |
---|
623 | * ( zdhbf - dh_i_bott(ji) ) / rdt_ice |
---|
624 | |
---|
625 | dh_i_bott(ji) = zdhbf |
---|
626 | !since ice volume is only used for outputs, we keep it global for all categories |
---|
627 | dvbbq_1d(ji) = a_i_b(ji)*dh_i_bott(ji) |
---|
628 | !new ice thickness |
---|
629 | zhgnew(ji) = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji) |
---|
630 | |
---|
631 | ! diagnostic ( bottom ice growth ) |
---|
632 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
633 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
634 | diag_bot_gr(zji,zjj) = diag_bot_gr(zji,zjj) + MAX(dh_i_bott(ji),0.0)*a_i_b(ji) & |
---|
635 | / rdt_ice |
---|
636 | diag_sur_me(zji,zjj) = diag_sur_me(zji,zjj) + MIN(dh_i_surf(ji),0.0)*a_i_b(ji) & |
---|
637 | / rdt_ice |
---|
638 | diag_bot_me(zji,zjj) = diag_bot_me(zji,zjj) + MIN(dh_i_bott(ji),0.0)*a_i_b(ji) & |
---|
639 | / rdt_ice |
---|
640 | END DO |
---|
641 | |
---|
642 | !----------------------------------- |
---|
643 | ! 5.2 More than available ice melts |
---|
644 | !----------------------------------- |
---|
645 | ! then heat applied minus heat content at previous time step |
---|
646 | ! should equal heat remaining |
---|
647 | ! |
---|
648 | DO ji = kideb, kiut |
---|
649 | ! Adapt the remaining energy if too much ice melts |
---|
650 | !-------------------------------------------------- |
---|
651 | zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice |
---|
652 | ! 0 if no more ice |
---|
653 | zhgnew(ji) = zihgnew * zhgnew(ji) ! ice thickness is put to 0 |
---|
654 | ! remaining heat |
---|
655 | zfdt_final(ji) = ( 1.0 - zihgnew ) * ( zqfont_su(ji) + zqfont_bo(ji) ) |
---|
656 | |
---|
657 | ! If snow remains, energy is used to melt snow |
---|
658 | zhni = ht_s_b(ji) ! snow depth at previous time step |
---|
659 | zihg = MAX( zzero , SIGN ( zone , - ht_s_b(ji) ) ) ! 0 if snow |
---|
660 | |
---|
661 | ! energy of melting of remaining snow |
---|
662 | zqt_s(ji) = ( 1. - zihg) * zqt_s(ji) / MAX( zhni, zeps ) |
---|
663 | zdhnm = - ( 1. - zihg ) * ( 1. - zihgnew ) * ( zfdt_final(ji) / & |
---|
664 | MAX( zqt_s(ji) , zeps ) ) |
---|
665 | zhnfi = zhni + zdhnm |
---|
666 | zfdt_final(ji) = MAX ( zfdt_final(ji) + zqt_s(ji) * zdhnm , 0.0 ) |
---|
667 | ht_s_b(ji) = MAX( zzero , zhnfi ) |
---|
668 | zqt_s(ji) = zqt_s(ji) * ht_s_b(ji) |
---|
669 | |
---|
670 | ! Mass variations of ice and snow |
---|
671 | !--------------------------------- |
---|
672 | rdmicif_1d(ji) = rdmicif_1d(ji) + a_i_b(ji) * & |
---|
673 | (zhgnew(ji)-ht_i_b(ji))*rhoic ! good |
---|
674 | |
---|
675 | rdmsnif_1d(ji) = rdmsnif_1d(ji) + a_i_b(ji) * & |
---|
676 | (ht_s_b(ji)-zhni)*rhosn ! good too |
---|
677 | |
---|
678 | ! Remaining heat to the ocean |
---|
679 | !--------------------------------- |
---|
680 | ! focea is in W.m-2 * dt |
---|
681 | focea(ji) = - zfdt_final(ji) / rdt_ice |
---|
682 | |
---|
683 | END DO |
---|
684 | |
---|
685 | ftotal_fin (:) = zfdt_final(:) / rdt_ice |
---|
686 | |
---|
687 | !--------------------------- |
---|
688 | ! Salt flux and heat fluxes |
---|
689 | !--------------------------- |
---|
690 | DO ji = kideb, kiut |
---|
691 | zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) !1 if ice |
---|
692 | |
---|
693 | ! Salt flux |
---|
694 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
695 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
696 | IF ( num_sal .NE. 4 ) & |
---|
697 | fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) + & |
---|
698 | (1.0 - zihgnew) * rdmicif_1d(ji) * & |
---|
699 | ( sss_m(zji,zjj) - sm_i_b(ji) ) / rdt_ice |
---|
700 | ! new lines |
---|
701 | IF ( num_sal .EQ. 4 ) & |
---|
702 | fseqv_1d(ji) = fseqv_1d(ji) + zihgnew * zfsalt_melt(ji) + & |
---|
703 | (1.0 - zihgnew) * rdmicif_1d(ji) * & |
---|
704 | ( sss_m(zji,zjj) - bulk_sal ) / rdt_ice |
---|
705 | ! Heat flux |
---|
706 | ! excessive bottom ablation energy (fsup) - 0 except if jpl = 1 |
---|
707 | ! excessive total ablation energy (focea) sent to the ocean |
---|
708 | qfvbq_1d(ji) = qfvbq_1d(ji) + & |
---|
709 | fsup(ji) + ( 1.0 - zihgnew ) * & |
---|
710 | focea(ji) * a_i_b(ji) * rdt_ice |
---|
711 | |
---|
712 | zihic = 1.0 - MAX( zzero , SIGN( zone , -ht_i_b(ji) ) ) |
---|
713 | ! equals 0 if ht_i = 0, 1 if ht_i gt 0 |
---|
714 | fscbq_1d(ji) = a_i_b(ji) * fstbif_1d(ji) |
---|
715 | qldif_1d(ji) = qldif_1d(ji) & |
---|
716 | + fsup(ji) + ( 1.0 - zihgnew ) * focea(ji) * a_i_b(ji) & |
---|
717 | * rdt_ice & |
---|
718 | + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice |
---|
719 | END DO ! ji |
---|
720 | |
---|
721 | !------------------------------------------- |
---|
722 | ! Correct temperature, energy and thickness |
---|
723 | !------------------------------------------- |
---|
724 | DO ji = kideb, kiut |
---|
725 | zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) |
---|
726 | t_su_b(ji) = zihgnew * t_su_b(ji) + ( 1.0 - zihgnew ) * rtt |
---|
727 | END DO ! ji |
---|
728 | |
---|
729 | DO jk = 1, nlay_i |
---|
730 | DO ji = kideb, kiut |
---|
731 | zihgnew = 1.0 - MAX( zzero , SIGN( zone , - zhgnew(ji) ) ) |
---|
732 | t_i_b(ji,jk) = zihgnew * t_i_b(ji,jk) + ( 1.0 - zihgnew ) * rtt |
---|
733 | q_i_b(ji,jk) = zihgnew * q_i_b(ji,jk) |
---|
734 | END DO |
---|
735 | END DO ! ji |
---|
736 | |
---|
737 | DO ji = kideb, kiut |
---|
738 | ht_i_b(ji) = zhgnew(ji) |
---|
739 | END DO ! ji |
---|
740 | ! |
---|
741 | !------------------------------------------------------------------------------| |
---|
742 | ! 6) Snow-Ice formation | |
---|
743 | !------------------------------------------------------------------------------| |
---|
744 | ! |
---|
745 | ! When snow load excesses Archimede's limit, snow-ice interface goes down |
---|
746 | ! under sea-level, flooding of seawater transforms snow into ice |
---|
747 | ! dh_snowice is positive for the ice |
---|
748 | DO ji = kideb, kiut |
---|
749 | |
---|
750 | dh_snowice(ji) = MAX(zzero,(rhosn*ht_s_b(ji)+(rhoic-rau0) & |
---|
751 | * ht_i_b(ji))/(rhosn+rau0-rhoic)) |
---|
752 | zhgnew(ji) = MAX(zhgnew(ji),zhgnew(ji)+dh_snowice(ji)) |
---|
753 | zhnnew = MIN(ht_s_b(ji),ht_s_b(ji)-dh_snowice(ji)) |
---|
754 | |
---|
755 | ! Changes in ice volume and ice mass. |
---|
756 | dvnbq_1d(ji) = a_i_b(ji) * (zhgnew(ji)-ht_i_b(ji)) |
---|
757 | dmgwi_1d(ji) = dmgwi_1d(ji) + a_i_b(ji) & |
---|
758 | *(ht_s_b(ji)-zhnnew)*rhosn |
---|
759 | |
---|
760 | rdmicif_1d(ji) = rdmicif_1d(ji) + a_i_b(ji) & |
---|
761 | * ( zhgnew(ji) - ht_i_b(ji) )*rhoic |
---|
762 | rdmsnif_1d(ji) = rdmsnif_1d(ji) + a_i_b(ji) & |
---|
763 | * ( zhnnew - ht_s_b(ji) )*rhosn |
---|
764 | |
---|
765 | ! Equivalent salt flux (1) Snow-ice formation component |
---|
766 | ! ----------------------------------------------------- |
---|
767 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
768 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
769 | |
---|
770 | zsm_snowice = ( rhoic - rhosn ) / rhoic * & |
---|
771 | sss_m(zji,zjj) |
---|
772 | |
---|
773 | IF ( num_sal .NE. 2 ) zsm_snowice = sm_i_b(ji) |
---|
774 | |
---|
775 | IF ( num_sal .NE. 4 ) & |
---|
776 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
777 | ( sss_m(zji,zjj) - zsm_snowice ) * & |
---|
778 | a_i_b(ji) * & |
---|
779 | ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice |
---|
780 | ! new lines |
---|
781 | IF ( num_sal .EQ. 4 ) & |
---|
782 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
783 | ( sss_m(zji,zjj) - bulk_sal ) * & |
---|
784 | a_i_b(ji) * & |
---|
785 | ( zhgnew(ji) - ht_i_b(ji) ) * rhoic / rdt_ice |
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786 | |
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787 | ! entrapment during snow ice formation |
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788 | i_ice_switch = 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_i_b(ji) + 1.0e-6 ) ) |
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789 | isnowic = 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - dh_snowice(ji) ) ) * & |
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790 | i_ice_switch |
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791 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
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792 | dsm_i_si_1d(ji) = ( zsm_snowice*dh_snowice(ji) & |
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793 | + sm_i_b(ji) * ht_i_b(ji) & |
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794 | / MAX( ht_i_b(ji) + dh_snowice(ji), zeps) & |
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795 | - sm_i_b(ji) ) * isnowic |
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796 | |
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797 | ! Actualize new snow and ice thickness. |
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798 | ht_s_b(ji) = zhnnew |
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799 | ht_i_b(ji) = zhgnew(ji) |
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800 | |
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801 | ! Total ablation ! new lines added to debug |
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802 | IF( ht_i_b(ji).LE.0.0 ) a_i_b(ji) = 0.0 |
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803 | |
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804 | ! diagnostic ( snow ice growth ) |
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805 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
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806 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
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807 | diag_sni_gr(zji,zjj) = diag_sni_gr(zji,zjj) + dh_snowice(ji)*a_i_b(ji) / & |
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808 | rdt_ice |
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809 | |
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810 | END DO !ji |
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811 | |
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812 | END SUBROUTINE lim_thd_dh |
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813 | #else |
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814 | !!====================================================================== |
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815 | !! *** MODULE limthd_dh *** |
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816 | !! no sea ice model |
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817 | !!====================================================================== |
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818 | CONTAINS |
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819 | SUBROUTINE lim_thd_dh ! Empty routine |
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820 | END SUBROUTINE lim_thd_dh |
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821 | #endif |
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822 | END MODULE limthd_dh |
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