1 | MODULE limthd_lac |
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2 | !!---------------------------------------------------------------------- |
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3 | !! 'key_lim3' LIM3 sea-ice model |
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4 | !!---------------------------------------------------------------------- |
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5 | !!====================================================================== |
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6 | !! *** MODULE limthd_lac *** |
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7 | !! lateral thermodynamic growth of the ice |
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8 | !!====================================================================== |
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9 | #if defined key_lim3 |
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10 | !!---------------------------------------------------------------------- |
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11 | !! lim_lat_acr : lateral accretion of ice |
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12 | !! * Modules used |
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13 | USE par_oce ! ocean parameters |
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14 | USE dom_oce |
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15 | USE in_out_manager |
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16 | USE phycst |
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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 sbc_ice ! Surface boundary condition: ice fields |
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20 | USE thd_ice |
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21 | USE dom_ice |
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22 | USE par_ice |
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23 | USE ice |
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24 | USE iceini |
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25 | USE limtab |
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26 | USE limcons |
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27 | |
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28 | IMPLICIT NONE |
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29 | PRIVATE |
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30 | |
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31 | !! * Routine accessibility |
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32 | PUBLIC lim_thd_lac ! called by lim_thd |
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33 | |
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34 | !! * Module variables |
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35 | REAL(wp) :: & ! constant values |
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36 | epsi20 = 1.e-20 , & |
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37 | epsi13 = 1.e-13 , & |
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38 | epsi11 = 1.e-13 , & |
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39 | epsi03 = 1.e-03 , & |
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40 | epsi06 = 1.e-06 , & |
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41 | zeps = 1.e-10 , & |
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42 | zzero = 0.e0 , & |
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43 | zone = 1.e0 |
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44 | |
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45 | !!---------------------------------------------------------------------- |
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46 | !! LIM 3.0, UCL-ASTR-LOCEAN-IPSL (2008) |
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47 | !! $Id$ |
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48 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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49 | !!---------------------------------------------------------------------- |
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50 | |
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51 | CONTAINS |
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52 | |
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53 | SUBROUTINE lim_thd_lac |
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54 | !!------------------------------------------------------------------- |
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55 | !! *** ROUTINE lim_thd_lac *** |
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56 | !! |
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57 | !! ** Purpose : Computation of the evolution of the ice thickness and |
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58 | !! concentration as a function of the heat balance in the leads. |
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59 | !! It is only used for lateral accretion |
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60 | !! |
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61 | !! ** Method : Ice is formed in the open water when ocean lose heat |
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62 | !! (heat budget of open water Bl is negative) . |
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63 | !! Computation of the increase of 1-A (ice concentration) fol- |
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64 | !! lowing the law : |
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65 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
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66 | !! where - h0 is the thickness of ice created in the lead |
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67 | !! - a is a minimum fraction for leads |
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68 | !! - F is a monotonic non-increasing function defined as: |
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69 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
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70 | !! - exld is the exponent closure rate (=2 default val.) |
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71 | !! |
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72 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
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73 | !! content in brine pockets |
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74 | !! - Updating ice internal temperature |
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75 | !! - Computation of variation of ice volume and mass |
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76 | !! - Computation of frldb after lateral accretion and |
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77 | !! update ht_s_b, ht_i_b and tbif_1d(:,:) |
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78 | !! |
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79 | !! ** References : Not available yet |
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80 | !! |
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81 | !! History : |
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82 | !! 3.0 ! 12-05 (M. Vancoppenolle) Thorough rewrite of the routine |
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83 | !! Salinity variations in sea ice, |
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84 | !! Multi-layer code |
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85 | !! 3.1 ! 01-06 (M. Vancoppenolle) ITD |
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86 | !! 3.2 ! 04-07 (M. Vancoppenolle) Mass and energy conservation tested |
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87 | !!------------------------------------------------------------------------ |
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88 | !! * Arguments |
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89 | !! * Local variables |
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90 | INTEGER :: & |
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91 | ji,jj,jk,jl,jm , & !: dummy loop indices |
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92 | layer , & !: layer index |
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93 | nbpac !: nb of pts for lateral accretion |
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94 | |
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95 | INTEGER :: & |
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96 | zji , & !: ji of dummy test point |
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97 | zjj , & !: jj of dummy test point |
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98 | iter !: iteration for frazil ice computation |
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99 | |
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100 | INTEGER, DIMENSION(jpij) :: & |
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101 | zcatac , & !: indexes of categories where new ice grows |
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102 | zswinew !: switch for new ice or not |
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103 | |
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104 | REAL(wp), DIMENSION(jpij) :: & |
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105 | zv_newice , & !: volume of accreted ice |
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106 | za_newice , & !: fractional area of accreted ice |
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107 | zh_newice , & !: thickness of accreted ice |
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108 | ze_newice , & !: heat content of accreted ice |
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109 | zs_newice , & !: salinity of accreted ice |
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110 | zo_newice , & !: age of accreted ice |
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111 | zdv_res , & !: residual volume in case of excessive heat budget |
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112 | zda_res , & !: residual area in case of excessive heat budget |
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113 | zat_i_ac , & !: total ice fraction |
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114 | zat_i_lev , & !: total ice fraction for level ice only (type 1) |
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115 | zdh_frazb , & !: accretion of frazil ice at the ice bottom |
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116 | zvrel_ac !: relative ice / frazil velocity (1D vector) |
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117 | |
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118 | REAL(wp), DIMENSION(jpij,jpl) :: & |
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119 | zhice_old , & !: previous ice thickness |
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120 | zdummy , & !: dummy thickness of new ice |
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121 | zdhicbot , & !: thickness of new ice which is accreted vertically |
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122 | zv_old , & !: old volume of ice in category jl |
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123 | za_old , & !: old area of ice in category jl |
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124 | za_i_ac , & !: 1-D version of a_i |
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125 | zv_i_ac , & !: 1-D version of v_i |
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126 | zoa_i_ac , & !: 1-D version of oa_i |
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127 | zsmv_i_ac !: 1-D version of smv_i |
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128 | |
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129 | REAL(wp), DIMENSION(jpij,jkmax,jpl) :: & |
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130 | ze_i_ac !: 1-D version of e_i |
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131 | |
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132 | REAL(wp), DIMENSION(jpij) :: & |
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133 | zqbgow , & !: heat budget of the open water (negative) |
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134 | zdhex !: excessively thick accreted sea ice (hlead-hice) |
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135 | |
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136 | REAL(wp) :: & |
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137 | ztmelts , & !: melting point of an ice layer |
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138 | zdv , & !: increase in ice volume in each category |
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139 | zfrazb !: fraction of frazil ice accreted at the ice bottom |
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140 | |
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141 | ! Redistribution of energy after bottom accretion |
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142 | REAL(wp) :: & !: Energy redistribution |
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143 | zqold , & !: old ice enthalpy |
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144 | zweight , & !: weight of redistribution |
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145 | zeps6 , & !: epsilon value |
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146 | zalphai , & !: factor describing how old and new layers overlap each other [m] |
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147 | zindb |
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148 | |
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149 | REAL(wp), DIMENSION(jpij,jkmax+1,jpl) :: & |
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150 | zqm0 , & !: old layer-system heat content |
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151 | zthick0 !: old ice thickness |
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152 | |
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153 | ! Frazil ice collection thickness |
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154 | LOGICAL :: & !: iterate frazil ice collection thickness |
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155 | iterate_frazil |
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156 | |
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157 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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158 | zvrel !: relative ice / frazil velocity |
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159 | |
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160 | REAL(wp) :: & |
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161 | zgamafr , & !: mult. coeff. between frazil vel. and wind speed |
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162 | ztenagm , & !: square root of wind stress |
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163 | zvfrx , & !: x-component of frazil velocity |
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164 | zvfry , & !: y-component of frazil velocity |
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165 | zvgx , & !: x-component of ice velocity |
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166 | zvgy , & !: y-component of ice velocity |
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167 | ztaux , & !: x-component of wind stress |
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168 | ztauy , & !: y-component of wind stress |
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169 | ztwogp , & !: dummy factor including reduced gravity |
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170 | zvrel2 , & !: square of the relative ice-frazil velocity |
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171 | zf , & !: F for Newton-Raphson procedure |
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172 | zfp , & !: dF for Newton-Raphson procedure |
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173 | zhicol_new , & !: updated collection thickness |
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174 | zsqcd , & !: 1 / square root of ( airdensity * drag ) |
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175 | zhicrit !: minimum thickness of frazil ice |
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176 | |
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177 | ! Variables for energy conservation |
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178 | REAL (wp), DIMENSION(jpi,jpj) :: & ! |
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179 | vt_i_init, vt_i_final, & ! ice volume summed over categories |
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180 | vt_s_init, vt_s_final, & ! snow volume summed over categories |
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181 | et_i_init, et_i_final, & ! ice energy summed over categories |
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182 | et_s_init ! snow energy summed over categories |
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183 | |
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184 | REAL(wp) :: & |
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185 | zde ! :increment of energy in category jl |
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186 | |
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187 | CHARACTER (len = 15) :: fieldid |
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188 | |
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189 | !!-----------------------------------------------------------------------! |
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190 | |
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191 | et_i_init(:,:) = 0.0 |
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192 | et_s_init(:,:) = 0.0 |
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193 | vt_i_init(:,:) = 0.0 |
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194 | vt_s_init(:,:) = 0.0 |
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195 | zeps6 = 1.0e-6 |
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196 | |
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197 | !------------------------------------------------------------------------------! |
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198 | ! 1) Conservation check and changes in each ice category |
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199 | !------------------------------------------------------------------------------! |
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200 | IF ( con_i ) THEN |
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201 | CALL lim_column_sum (jpl, v_i, vt_i_init) |
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202 | CALL lim_column_sum (jpl, v_s, vt_s_init) |
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203 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, et_i_init) |
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204 | CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
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205 | ENDIF |
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206 | |
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207 | !------------------------------------------------------------------------------| |
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208 | ! 2) Convert units for ice internal energy |
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209 | !------------------------------------------------------------------------------| |
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210 | DO jl = 1, jpl |
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211 | DO jk = 1, nlay_i |
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212 | DO jj = 1, jpj |
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213 | DO ji = 1, jpi |
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214 | !Energy of melting q(S,T) [J.m-3] |
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215 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / & |
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216 | MAX( area(ji,jj) * v_i(ji,jj,jl) , zeps ) * & |
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217 | nlay_i |
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218 | zindb = 1.0-MAX(0.0,SIGN(1.0,-v_i(ji,jj,jl))) !0 if no ice and 1 if yes |
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219 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl)*unit_fac*zindb |
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220 | END DO |
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221 | END DO |
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222 | END DO |
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223 | END DO |
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224 | |
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225 | !------------------------------------------------------------------------------! |
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226 | ! 3) Collection thickness of ice formed in leads and polynyas |
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227 | !------------------------------------------------------------------------------! |
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228 | ! hicol is the thickness of new ice formed in open water |
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229 | ! hicol can be either prescribed (frazswi = 0) |
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230 | ! or computed (frazswi = 1) |
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231 | ! Frazil ice forms in open water, is transported by wind |
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232 | ! accumulates at the edge of the consolidated ice edge |
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233 | ! where it forms aggregates of a specific thickness called |
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234 | ! collection thickness. |
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235 | |
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236 | ! Note : the following algorithm currently breaks vectorization |
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237 | ! |
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238 | |
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239 | zvrel(:,:) = 0.0 |
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240 | |
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241 | ! Default new ice thickness |
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242 | DO jj = 1, jpj |
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243 | DO ji = 1, jpi |
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244 | hicol(ji,jj) = hiccrit(1) |
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245 | END DO |
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246 | END DO |
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247 | |
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248 | IF (fraz_swi.eq.1.0) THEN |
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249 | |
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250 | !-------------------- |
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251 | ! Physical constants |
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252 | !-------------------- |
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253 | hicol(:,:) = 0.0 |
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254 | |
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255 | zhicrit = 0.04 ! frazil ice thickness |
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256 | ztwogp = 2. * rau0 / ( grav * 0.3 * ( rau0 - rhoic ) ) ! reduced grav |
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257 | zsqcd = 1.0 / SQRT( 1.3 * cai ) ! 1/SQRT(airdensity*drag) |
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258 | zgamafr = 0.03 |
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259 | |
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260 | DO jj = 1, jpj |
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261 | DO ji = 1, jpi |
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262 | |
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263 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
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264 | !------------- |
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265 | ! Wind stress |
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266 | !------------- |
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267 | ! C-grid wind stress components |
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268 | ztaux = ( utaui_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
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269 | + utaui_ice(ji ,jj ) * tmu(ji ,jj ) ) / 2.0 |
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270 | ztauy = ( vtaui_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
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271 | + vtaui_ice(ji ,jj ) * tmv(ji ,jj ) ) / 2.0 |
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272 | ! Square root of wind stress |
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273 | ztenagm = SQRT( SQRT( ztaux * ztaux + ztauy * ztauy ) ) |
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274 | |
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275 | !--------------------- |
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276 | ! Frazil ice velocity |
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277 | !--------------------- |
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278 | zvfrx = zgamafr * zsqcd * ztaux / MAX(ztenagm,zeps) |
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279 | zvfry = zgamafr * zsqcd * ztauy / MAX(ztenagm,zeps) |
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280 | |
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281 | !------------------- |
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282 | ! Pack ice velocity |
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283 | !------------------- |
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284 | ! C-grid ice velocity |
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285 | zindb = MAX(0.0, SIGN(1.0, at_i(ji,jj) )) |
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286 | zvgx = zindb * ( u_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
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287 | + u_ice(ji,jj ) * tmu(ji ,jj ) ) / 2.0 |
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288 | zvgy = zindb * ( v_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
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289 | + v_ice(ji,jj ) * tmv(ji ,jj ) ) / 2.0 |
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290 | |
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291 | !----------------------------------- |
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292 | ! Relative frazil/pack ice velocity |
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293 | !----------------------------------- |
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294 | ! absolute relative velocity |
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295 | zvrel2 = MAX( ( zvfrx - zvgx ) * ( zvfrx - zvgx ) + & |
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296 | ( zvfry - zvgy ) * ( zvfry - zvgy ) & |
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297 | , 0.15 * 0.15 ) |
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298 | zvrel(ji,jj) = SQRT(zvrel2) |
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299 | |
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300 | !--------------------- |
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301 | ! Iterative procedure |
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302 | !--------------------- |
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303 | hicol(ji,jj) = zhicrit + 0.1 |
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304 | hicol(ji,jj) = zhicrit + hicol(ji,jj) / & |
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305 | ( hicol(ji,jj) * hicol(ji,jj) - & |
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306 | zhicrit * zhicrit ) * ztwogp * zvrel2 |
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307 | |
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308 | iter = 1 |
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309 | iterate_frazil = .true. |
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310 | |
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311 | DO WHILE ( iter .LT. 100 .AND. iterate_frazil ) |
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312 | zf = ( hicol(ji,jj) - zhicrit ) * ( hicol(ji,jj)**2 - zhicrit**2 ) & |
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313 | - hicol(ji,jj) * zhicrit * ztwogp * zvrel2 |
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314 | zfp = ( hicol(ji,jj) - zhicrit ) * ( 3.0*hicol(ji,jj) + zhicrit ) & |
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315 | - zhicrit * ztwogp * zvrel2 |
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316 | zhicol_new = hicol(ji,jj) - zf/zfp |
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317 | hicol(ji,jj) = zhicol_new |
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318 | |
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319 | iter = iter + 1 |
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320 | |
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321 | END DO ! do while |
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322 | |
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323 | ENDIF ! end of selection of pixels where ice forms |
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324 | |
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325 | END DO ! loop on ji ends |
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326 | END DO ! loop on jj ends |
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327 | |
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328 | ENDIF ! End of computation of frazil ice collection thickness |
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329 | |
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330 | !------------------------------------------------------------------------------! |
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331 | ! 4) Identify grid points where new ice forms |
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332 | !------------------------------------------------------------------------------! |
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333 | |
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334 | !------------------------------------- |
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335 | ! Select points for new ice formation |
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336 | !------------------------------------- |
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337 | ! This occurs if open water energy budget is negative |
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338 | nbpac = 0 |
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339 | DO jj = 1, jpj |
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340 | DO ji = 1, jpi |
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341 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
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342 | nbpac = nbpac + 1 |
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343 | npac( nbpac ) = (jj - 1) * jpi + ji |
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344 | IF ( (ji.eq.jiindx).AND.(jj.eq.jjindx) ) THEN |
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345 | jiindex_1d = nbpac |
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346 | ENDIF |
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347 | ENDIF |
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348 | END DO |
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349 | END DO |
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350 | |
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351 | IF( ln_nicep ) THEN |
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352 | WRITE(numout,*) 'lim_thd_lac : nbpac = ', nbpac |
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353 | ENDIF |
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354 | |
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355 | !------------------------------ |
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356 | ! Move from 2-D to 1-D vectors |
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357 | !------------------------------ |
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358 | ! If ocean gains heat do nothing |
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359 | ! 0therwise compute new ice formation |
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360 | |
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361 | IF ( nbpac > 0 ) THEN |
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362 | |
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363 | CALL tab_2d_1d( nbpac, zat_i_ac (1:nbpac) , at_i , & |
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364 | jpi, jpj, npac(1:nbpac) ) |
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365 | DO jl = 1, jpl |
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366 | CALL tab_2d_1d( nbpac, za_i_ac(1:nbpac,jl) , a_i(:,:,jl) , & |
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367 | jpi, jpj, npac(1:nbpac) ) |
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368 | CALL tab_2d_1d( nbpac, zv_i_ac(1:nbpac,jl) , v_i(:,:,jl) , & |
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369 | jpi, jpj, npac(1:nbpac) ) |
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370 | CALL tab_2d_1d( nbpac, zoa_i_ac(1:nbpac,jl) , oa_i(:,:,jl) , & |
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371 | jpi, jpj, npac(1:nbpac) ) |
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372 | CALL tab_2d_1d( nbpac, zsmv_i_ac(1:nbpac,jl), smv_i(:,:,jl), & |
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373 | jpi, jpj, npac(1:nbpac) ) |
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374 | DO jk = 1, nlay_i |
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375 | CALL tab_2d_1d( nbpac, ze_i_ac(1:nbpac,jk,jl), e_i(:,:,jk,jl) , & |
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376 | jpi, jpj, npac(1:nbpac) ) |
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377 | END DO ! jk |
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378 | END DO ! jl |
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379 | |
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380 | CALL tab_2d_1d( nbpac, qldif_1d (1:nbpac) , qldif , & |
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381 | jpi, jpj, npac(1:nbpac) ) |
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382 | CALL tab_2d_1d( nbpac, qcmif_1d (1:nbpac) , qcmif , & |
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383 | jpi, jpj, npac(1:nbpac) ) |
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384 | CALL tab_2d_1d( nbpac, t_bo_b (1:nbpac) , t_bo , & |
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385 | jpi, jpj, npac(1:nbpac) ) |
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386 | CALL tab_2d_1d( nbpac, fseqv_1d (1:nbpac) , fseqv , & |
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387 | jpi, jpj, npac(1:nbpac) ) |
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388 | CALL tab_2d_1d( nbpac, hicol_b (1:nbpac) , hicol , & |
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389 | jpi, jpj, npac(1:nbpac) ) |
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390 | CALL tab_2d_1d( nbpac, zvrel_ac (1:nbpac) , zvrel , & |
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391 | jpi, jpj, npac(1:nbpac) ) |
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392 | |
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393 | !------------------------------------------------------------------------------! |
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394 | ! 5) Compute thickness, salinity, enthalpy, age, area and volume of new ice |
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395 | !------------------------------------------------------------------------------! |
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396 | |
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397 | !---------------------- |
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398 | ! Thickness of new ice |
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399 | !---------------------- |
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400 | DO ji = 1, nbpac |
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401 | zh_newice(ji) = hiccrit(1) |
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402 | END DO |
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403 | IF ( fraz_swi .EQ. 1.0 ) zh_newice(:) = hicol_b(:) |
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404 | |
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405 | !---------------------- |
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406 | ! Salinity of new ice |
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407 | !---------------------- |
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408 | |
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409 | IF ( num_sal .EQ. 1 ) THEN |
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410 | zs_newice(:) = bulk_sal |
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411 | ENDIF ! num_sal |
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412 | |
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413 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
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414 | |
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415 | DO ji = 1, nbpac |
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416 | zs_newice(ji) = MIN( 4.606 + 0.91 / zh_newice(ji) , s_i_max ) |
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417 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
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418 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
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419 | zs_newice(ji) = MIN( 0.5*sss_m(zji,zjj) , zs_newice(ji) ) |
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420 | END DO ! jl |
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421 | |
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422 | ENDIF ! num_sal |
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423 | |
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424 | IF ( num_sal .EQ. 3 ) THEN |
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425 | zs_newice(:) = 2.3 |
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426 | ENDIF ! num_sal |
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427 | |
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428 | !------------------------- |
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429 | ! Heat content of new ice |
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430 | !------------------------- |
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431 | ! We assume that new ice is formed at the seawater freezing point |
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432 | DO ji = 1, nbpac |
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433 | ztmelts = - tmut * zs_newice(ji) + rtt ! Melting point (K) |
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434 | ze_newice(ji) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) & |
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435 | + lfus * ( 1.0 - ( ztmelts - rtt ) & |
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436 | / ( t_bo_b(ji) - rtt ) ) & |
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437 | - rcp * ( ztmelts-rtt ) ) |
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438 | ze_newice(ji) = MAX( ze_newice(ji) , 0.0 ) + & |
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439 | MAX( 0.0 , SIGN( 1.0 , - ze_newice(ji) ) ) & |
---|
440 | * rhoic * lfus |
---|
441 | END DO ! ji |
---|
442 | !---------------- |
---|
443 | ! Age of new ice |
---|
444 | !---------------- |
---|
445 | DO ji = 1, nbpac |
---|
446 | zo_newice(ji) = 0.0 |
---|
447 | END DO ! ji |
---|
448 | |
---|
449 | !-------------------------- |
---|
450 | ! Open water energy budget |
---|
451 | !-------------------------- |
---|
452 | DO ji = 1, nbpac |
---|
453 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) !<0 |
---|
454 | END DO ! ji |
---|
455 | |
---|
456 | !------------------- |
---|
457 | ! Volume of new ice |
---|
458 | !------------------- |
---|
459 | DO ji = 1, nbpac |
---|
460 | zv_newice(ji) = - zqbgow(ji) / ze_newice(ji) |
---|
461 | |
---|
462 | ! A fraction zfrazb of frazil ice is accreted at the ice bottom |
---|
463 | zfrazb = ( TANH ( Cfrazb * ( zvrel_ac(ji) - vfrazb ) ) & |
---|
464 | + 1.0 ) / 2.0 * maxfrazb |
---|
465 | zdh_frazb(ji) = zfrazb*zv_newice(ji) |
---|
466 | zv_newice(ji) = ( 1.0 - zfrazb ) * zv_newice(ji) |
---|
467 | END DO |
---|
468 | |
---|
469 | !--------------------------------- |
---|
470 | ! Salt flux due to new ice growth |
---|
471 | !--------------------------------- |
---|
472 | IF ( ( num_sal .EQ. 4 ) ) THEN |
---|
473 | DO ji = 1, nbpac |
---|
474 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
475 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
476 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
477 | ( sss_m(zji,zjj) - bulk_sal ) * rhoic * & |
---|
478 | zv_newice(ji) / rdt_ice |
---|
479 | END DO |
---|
480 | ELSE |
---|
481 | DO ji = 1, nbpac |
---|
482 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
483 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
484 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
485 | ( sss_m(zji,zjj) - zs_newice(ji) ) * rhoic * & |
---|
486 | zv_newice(ji) / rdt_ice |
---|
487 | END DO ! ji |
---|
488 | ENDIF |
---|
489 | |
---|
490 | !------------------------------------ |
---|
491 | ! Diags for energy conservation test |
---|
492 | !------------------------------------ |
---|
493 | DO ji = 1, nbpac |
---|
494 | ! Volume |
---|
495 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
496 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
497 | vt_i_init(zji,zjj) = vt_i_init(zji,zjj) + zv_newice(ji) |
---|
498 | ! Energy |
---|
499 | zde = ze_newice(ji) / unit_fac |
---|
500 | zde = zde * area(zji,zjj) * zv_newice(ji) |
---|
501 | et_i_init(zji,zjj) = et_i_init(zji,zjj) + zde |
---|
502 | END DO |
---|
503 | |
---|
504 | ! keep new ice volume in memory |
---|
505 | CALL tab_1d_2d( nbpac, v_newice , npac(1:nbpac), zv_newice(1:nbpac) , & |
---|
506 | jpi, jpj ) |
---|
507 | |
---|
508 | !----------------- |
---|
509 | ! Area of new ice |
---|
510 | !----------------- |
---|
511 | DO ji = 1, nbpac |
---|
512 | za_newice(ji) = zv_newice(ji) / zh_newice(ji) |
---|
513 | ! diagnostic |
---|
514 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
515 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
516 | diag_lat_gr(zji,zjj) = zv_newice(ji) / rdt_ice |
---|
517 | END DO !ji |
---|
518 | |
---|
519 | !------------------------------------------------------------------------------! |
---|
520 | ! 6) Redistribute new ice area and volume into ice categories ! |
---|
521 | !------------------------------------------------------------------------------! |
---|
522 | |
---|
523 | !----------------------------------------- |
---|
524 | ! Keep old ice areas and volume in memory |
---|
525 | !----------------------------------------- |
---|
526 | zv_old(:,:) = zv_i_ac(:,:) |
---|
527 | za_old(:,:) = za_i_ac(:,:) |
---|
528 | |
---|
529 | !------------------------------------------- |
---|
530 | ! Compute excessive new ice area and volume |
---|
531 | !------------------------------------------- |
---|
532 | ! If lateral ice growth gives an ice concentration gt 1, then |
---|
533 | ! we keep the excessive volume in memory and attribute it later |
---|
534 | ! to bottom accretion |
---|
535 | DO ji = 1, nbpac |
---|
536 | ! vectorize |
---|
537 | IF ( za_newice(ji) .GT. ( 1.0 - zat_i_ac(ji) ) ) THEN |
---|
538 | zda_res(ji) = za_newice(ji) - (1.0 - zat_i_ac(ji) ) |
---|
539 | zdv_res(ji) = zda_res(ji) * zh_newice(ji) |
---|
540 | za_newice(ji) = za_newice(ji) - zda_res(ji) |
---|
541 | zv_newice(ji) = zv_newice(ji) - zdv_res(ji) |
---|
542 | ELSE |
---|
543 | zda_res(ji) = 0.0 |
---|
544 | zdv_res(ji) = 0.0 |
---|
545 | ENDIF |
---|
546 | END DO ! ji |
---|
547 | |
---|
548 | !------------------------------------------------ |
---|
549 | ! Laterally redistribute new ice volume and area |
---|
550 | !------------------------------------------------ |
---|
551 | zat_i_ac(:) = 0.0 |
---|
552 | |
---|
553 | DO jl = 1, jpl |
---|
554 | DO ji = 1, nbpac |
---|
555 | ! vectorize |
---|
556 | IF ( ( hi_max(jl-1) .LT. zh_newice(ji) ) & |
---|
557 | .AND. ( zh_newice(ji) .LE. hi_max(jl) ) ) THEN |
---|
558 | za_i_ac(ji,jl) = za_i_ac(ji,jl) + za_newice(ji) |
---|
559 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + zv_newice(ji) |
---|
560 | zat_i_ac(ji) = zat_i_ac(ji) + za_i_ac(ji,jl) |
---|
561 | zcatac(ji) = jl |
---|
562 | ENDIF |
---|
563 | END DO ! ji |
---|
564 | END DO ! jl |
---|
565 | |
---|
566 | !---------------------------------- |
---|
567 | ! Heat content - lateral accretion |
---|
568 | !---------------------------------- |
---|
569 | DO ji = 1, nbpac |
---|
570 | jl = zcatac(ji) ! categroy in which new ice is put |
---|
571 | ! zindb = 0 if no ice and 1 if yes |
---|
572 | zindb = 1.0 - MAX ( 0.0 , SIGN ( 1.0 , -za_old(ji,jl) ) ) |
---|
573 | ! old ice thickness |
---|
574 | zhice_old(ji,jl) = zv_old(ji,jl) & |
---|
575 | / MAX ( za_old(ji,jl) , zeps ) * zindb |
---|
576 | ! difference in thickness |
---|
577 | zdhex(ji) = MAX( 0.0, zh_newice(ji) - zhice_old(ji,jl) ) |
---|
578 | ! is ice totally new in category jl ? |
---|
579 | zswinew(ji) = MAX( 0.0, SIGN( 1.0 , - za_old(ji,jl) + epsi11 ) ) |
---|
580 | END DO |
---|
581 | |
---|
582 | DO jk = 1, nlay_i |
---|
583 | DO ji = 1, nbpac |
---|
584 | jl = zcatac(ji) |
---|
585 | zqold = ze_i_ac(ji,jk,jl) ! [ J.m-3 ] |
---|
586 | zalphai = MIN( zhice_old(ji,jl) * jk / nlay_i , & |
---|
587 | zh_newice(ji) ) & |
---|
588 | - MIN( zhice_old(ji,jl) * ( jk - 1 ) & |
---|
589 | / nlay_i , zh_newice(ji) ) |
---|
590 | ze_i_ac(ji,jk,jl) = & |
---|
591 | zswinew(ji) * ze_newice(ji) & |
---|
592 | + ( 1.0 - zswinew(ji) ) * & |
---|
593 | ( za_old(ji,jl) * zqold * zhice_old(ji,jl) / nlay_i & |
---|
594 | + za_newice(ji) * ze_newice(ji) * zalphai & |
---|
595 | + za_newice(ji) * ze_newice(ji) * zdhex(ji) / nlay_i ) / & |
---|
596 | ( ( zv_i_ac(ji,jl) ) / nlay_i ) |
---|
597 | |
---|
598 | END DO !ji |
---|
599 | END DO !jl |
---|
600 | |
---|
601 | !----------------------------------------------- |
---|
602 | ! Add excessive volume of new ice at the bottom |
---|
603 | !----------------------------------------------- |
---|
604 | ! If the ice concentration exceeds 1, the remaining volume of new ice |
---|
605 | ! is equally redistributed among all ice categories in which there is |
---|
606 | ! ice |
---|
607 | |
---|
608 | ! Fraction of level ice |
---|
609 | jm = 1 |
---|
610 | zat_i_lev(:) = 0.0 |
---|
611 | |
---|
612 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
613 | DO ji = 1, nbpac |
---|
614 | zat_i_lev(ji) = zat_i_lev(ji) + za_i_ac(ji,jl) |
---|
615 | END DO |
---|
616 | END DO |
---|
617 | |
---|
618 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
619 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
620 | DO ji = 1, nbpac |
---|
621 | zindb = MAX( 0.0, SIGN( 1.0, zdv_res(ji) ) ) |
---|
622 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + & |
---|
623 | zindb * zdv_res(ji) * za_i_ac(ji,jl) / & |
---|
624 | MAX( zat_i_lev(ji) , epsi06 ) |
---|
625 | END DO ! ji |
---|
626 | END DO ! jl |
---|
627 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
628 | |
---|
629 | !--------------------------------- |
---|
630 | ! Heat content - bottom accretion |
---|
631 | !--------------------------------- |
---|
632 | jm = 1 |
---|
633 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
634 | DO ji = 1, nbpac |
---|
635 | ! zindb = 0 if no ice and 1 if yes |
---|
636 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
637 | , - za_i_ac(ji,jl ) ) ) |
---|
638 | zhice_old(ji,jl) = zv_i_ac(ji,jl) / & |
---|
639 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
640 | zdhicbot(ji,jl) = zdv_res(ji) / MAX( za_i_ac(ji,jl) , zeps ) & |
---|
641 | * zindb & |
---|
642 | + zindb * zdh_frazb(ji) ! frazil ice |
---|
643 | ! may coalesce |
---|
644 | ! thickness of residual ice |
---|
645 | zdummy(ji,jl) = zv_i_ac(ji,jl)/MAX(za_i_ac(ji,jl),zeps)*zindb |
---|
646 | END DO !ji |
---|
647 | END DO !jl |
---|
648 | |
---|
649 | ! old layers thicknesses and enthalpies |
---|
650 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
651 | DO jk = 1, nlay_i |
---|
652 | DO ji = 1, nbpac |
---|
653 | zthick0(ji,jk,jl)= zhice_old(ji,jl) / nlay_i |
---|
654 | zqm0 (ji,jk,jl)= ze_i_ac(ji,jk,jl) * zthick0(ji,jk,jl) |
---|
655 | END DO !ji |
---|
656 | END DO !jk |
---|
657 | END DO !jl |
---|
658 | |
---|
659 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
660 | DO ji = 1, nbpac |
---|
661 | zthick0(ji,nlay_i+1,jl) = zdhicbot(ji,jl) |
---|
662 | zqm0 (ji,nlay_i+1,jl) = ze_newice(ji)*zdhicbot(ji,jl) |
---|
663 | END DO ! ji |
---|
664 | END DO ! jl |
---|
665 | |
---|
666 | ! Redistributing energy on the new grid |
---|
667 | ze_i_ac(:,:,:) = 0.0 |
---|
668 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
669 | DO jk = 1, nlay_i |
---|
670 | DO layer = 1, nlay_i + 1 |
---|
671 | DO ji = 1, nbpac |
---|
672 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , & |
---|
673 | - za_i_ac(ji,jl ) ) ) |
---|
674 | ! Redistributing energy on the new grid |
---|
675 | zweight = MAX ( & |
---|
676 | MIN( zhice_old(ji,jl) * layer , zdummy(ji,jl) * jk ) - & |
---|
677 | MAX( zhice_old(ji,jl) * ( layer - 1 ) , zdummy(ji,jl) * & |
---|
678 | ( jk - 1 ) ) , 0.0 ) & |
---|
679 | / ( MAX(nlay_i * zthick0(ji,layer,jl),zeps) ) * zindb |
---|
680 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) + & |
---|
681 | zweight * zqm0(ji,layer,jl) |
---|
682 | END DO ! ji |
---|
683 | END DO ! layer |
---|
684 | END DO ! jk |
---|
685 | END DO ! jl |
---|
686 | |
---|
687 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
688 | DO jk = 1, nlay_i |
---|
689 | DO ji = 1, nbpac |
---|
690 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
691 | , - zv_i_ac(ji,jl) ) ) !0 if no ice |
---|
692 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) / & |
---|
693 | MAX( zv_i_ac(ji,jl) , zeps) & |
---|
694 | * za_i_ac(ji,jl) * nlay_i * zindb |
---|
695 | END DO |
---|
696 | END DO |
---|
697 | END DO |
---|
698 | |
---|
699 | !------------ |
---|
700 | ! Update age |
---|
701 | !------------ |
---|
702 | DO jl = 1, jpl |
---|
703 | DO ji = 1, nbpac |
---|
704 | !--ice age |
---|
705 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
706 | za_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
707 | zoa_i_ac(ji,jl) = za_old(ji,jl) * zoa_i_ac(ji,jl) / & |
---|
708 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
709 | END DO ! ji |
---|
710 | END DO ! jl |
---|
711 | |
---|
712 | !----------------- |
---|
713 | ! Update salinity |
---|
714 | !----------------- |
---|
715 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
716 | |
---|
717 | DO jl = 1, jpl |
---|
718 | DO ji = 1, nbpac |
---|
719 | !zindb = 0 if no ice and 1 if yes |
---|
720 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
721 | zv_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
722 | zdv = zv_i_ac(ji,jl) - zv_old(ji,jl) |
---|
723 | zsmv_i_ac(ji,jl) = ( zsmv_i_ac(ji,jl) + zdv * zs_newice(ji) ) * & |
---|
724 | zindb |
---|
725 | END DO ! ji |
---|
726 | END DO ! jl |
---|
727 | |
---|
728 | ENDIF ! num_sal |
---|
729 | |
---|
730 | |
---|
731 | !------------------------------------------------------------------------------! |
---|
732 | ! 8) Change 2D vectors to 1D vectors |
---|
733 | !------------------------------------------------------------------------------! |
---|
734 | |
---|
735 | DO jl = 1, jpl |
---|
736 | CALL tab_1d_2d( nbpac, a_i(:,:,jl) , npac(1:nbpac) , & |
---|
737 | za_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
738 | CALL tab_1d_2d( nbpac, v_i(:,:,jl) , npac(1:nbpac) , & |
---|
739 | zv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
740 | CALL tab_1d_2d( nbpac, oa_i(:,:,jl), npac(1:nbpac) , & |
---|
741 | zoa_i_ac(1:nbpac,jl), jpi, jpj ) |
---|
742 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
743 | CALL tab_1d_2d( nbpac, smv_i(:,:,jl) , npac(1:nbpac) , & |
---|
744 | zsmv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
745 | DO jk = 1, nlay_i |
---|
746 | CALL tab_1d_2d( nbpac, e_i(:,:,jk,jl) , npac(1:nbpac), & |
---|
747 | ze_i_ac(1:nbpac,jk,jl), jpi, jpj ) |
---|
748 | END DO ! jk |
---|
749 | END DO !jl |
---|
750 | CALL tab_1d_2d( nbpac, fseqv , npac(1:nbpac), fseqv_1d (1:nbpac) , & |
---|
751 | jpi, jpj ) |
---|
752 | |
---|
753 | ENDIF ! nbpac > 0 |
---|
754 | |
---|
755 | !------------------------------------------------------------------------------! |
---|
756 | ! 9) Change units for e_i |
---|
757 | !------------------------------------------------------------------------------! |
---|
758 | |
---|
759 | DO jl = 1, jpl |
---|
760 | DO jk = 1, nlay_i |
---|
761 | DO jj = 1, jpj |
---|
762 | DO ji = 1, jpi |
---|
763 | ! Correct dimensions to avoid big values |
---|
764 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / unit_fac |
---|
765 | |
---|
766 | ! Mutliply by ice volume, and divide by number |
---|
767 | ! of layers to get heat content in 10^9 Joules |
---|
768 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * & |
---|
769 | area(ji,jj) * v_i(ji,jj,jl) / & |
---|
770 | nlay_i |
---|
771 | END DO |
---|
772 | END DO |
---|
773 | END DO |
---|
774 | END DO |
---|
775 | |
---|
776 | !------------------------------------------------------------------------------| |
---|
777 | ! 10) Conservation check and changes in each ice category |
---|
778 | !------------------------------------------------------------------------------| |
---|
779 | |
---|
780 | IF ( con_i ) THEN |
---|
781 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
---|
782 | fieldid = 'v_i, limthd_lac' |
---|
783 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
---|
784 | |
---|
785 | CALL lim_column_sum_energy(jpl, nlay_i, e_i, et_i_final) |
---|
786 | fieldid = 'e_i, limthd_lac' |
---|
787 | CALL lim_cons_check (et_i_final, et_i_final, 1.0e-3, fieldid) |
---|
788 | |
---|
789 | CALL lim_column_sum (jpl, v_s, vt_s_final) |
---|
790 | fieldid = 'v_s, limthd_lac' |
---|
791 | CALL lim_cons_check (vt_s_init, vt_s_final, 1.0e-6, fieldid) |
---|
792 | |
---|
793 | ! CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
---|
794 | ! fieldid = 'e_s, limthd_lac' |
---|
795 | ! CALL lim_cons_check (et_s_init, et_s_final, 1.0e-3, fieldid) |
---|
796 | |
---|
797 | IF( ln_nicep ) THEN |
---|
798 | WRITE(numout,*) ' vt_i_init : ', vt_i_init(jiindx,jjindx) |
---|
799 | WRITE(numout,*) ' vt_i_final: ', vt_i_final(jiindx,jjindx) |
---|
800 | WRITE(numout,*) ' et_i_init : ', et_i_init(jiindx,jjindx) |
---|
801 | WRITE(numout,*) ' et_i_final: ', et_i_final(jiindx,jjindx) |
---|
802 | ENDIF |
---|
803 | |
---|
804 | ENDIF |
---|
805 | |
---|
806 | END SUBROUTINE lim_thd_lac |
---|
807 | |
---|
808 | #else |
---|
809 | !!====================================================================== |
---|
810 | !! *** MODULE limthd_lac *** |
---|
811 | !! no sea ice model |
---|
812 | !!====================================================================== |
---|
813 | CONTAINS |
---|
814 | SUBROUTINE lim_thd_lac ! Empty routine |
---|
815 | END SUBROUTINE lim_thd_lac |
---|
816 | #endif |
---|
817 | END MODULE limthd_lac |
---|