1 | SUBROUTINE ice_th_dh(nlay_s,nlay_i,kideb,kiut) |
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2 | !!------------------------------------------------------------------ |
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3 | !! *** ROUTINE ice_th_dh *** |
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4 | !! ** Purpose : |
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5 | !! This routine determines variations of ice and snow thicknesses. |
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6 | !! ** Method : |
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7 | !! Ice/Snow surface melting arises from imbalance in surface fluxes |
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8 | !! Bottom accretion/ablation arises from flux budget |
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9 | !! Snow thickness can increase by precipitation and decrease by |
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10 | !! sublimation |
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11 | !! If snow load excesses Archmiede limit, snow-ice is formed by |
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12 | !! the flooding of sea-water in the snow |
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13 | !! ** Steps |
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14 | !! 1) Compute available flux of heat for surface ablation |
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15 | !! 2) Compute snow and sea ice enthalpies |
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16 | !! 3) Surface ablation and sublimation |
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17 | !! 4) Bottom accretion/ablation |
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18 | !! 5) Case of Total ablation |
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19 | !! 6) Snow ice formation |
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20 | !! |
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21 | !! ** Inputs / Outputs |
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22 | !! |
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23 | !! ** External |
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24 | !! |
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25 | !! ** References : Bitz and Lipscomb, JGR 99 |
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26 | !! Fichefet T. and M. Maqueda 1997, |
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27 | !! J. Geophys. Res., 102(C6), 12609-12646 |
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28 | !! Vancoppenolle, Fichefet and Bitz, GRL 2005 |
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29 | !! Vancoppenolle et al., OM08 |
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30 | !! |
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31 | !! ** History : |
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32 | !! original code 01-04 (LIM) |
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33 | !! original routine |
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34 | !! (05-2003) M. Vancoppenolle, Louvain-La-Neuve, Belgium |
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35 | !! (05-2008) BIO-LIM |
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36 | !! |
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37 | !!------------------------------------------------------------------ |
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38 | !! * Arguments |
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39 | !!------------------------------------------------------------------ |
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40 | |
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41 | USE lib_fortran |
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42 | |
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43 | INCLUDE 'type.com' |
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44 | INCLUDE 'para.com' |
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45 | INCLUDE 'const.com' |
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46 | INCLUDE 'ice.com' |
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47 | INCLUDE 'thermo.com' |
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48 | |
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49 | ! Local Variables |
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50 | DIMENSION zrchu1(nbpt), zrchu2(nbpt), zqsat(nbpt), z_f_surf(nbpt) |
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51 | DIMENSION zdeltah(maxnlay) |
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52 | LOGICAL l_write |
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53 | |
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54 | zqt_s_ini = 0.0 |
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55 | zqt_s_fin = 0.0 |
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56 | zdqt_s = 0.0 |
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57 | zqt_i_ini = 0.0 |
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58 | zqt_i_fin = 0.0 |
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59 | zdqt_i = 0.0 |
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60 | s_i_max = 15.0 |
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61 | |
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62 | ! Local Constants |
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63 | zeps = 1.0e-20 |
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64 | l_write = .TRUE. |
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65 | |
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66 | IF ( l_write ) THEN |
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67 | WRITE(numout,*) ' ** ice_th_dh : ' |
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68 | WRITE(numout,*) ' ~~~~~~~~~~~~~~ ' |
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69 | WRITE(numout,*) |
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70 | ENDIF |
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71 | ! |
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72 | !------------------------------------------------------------------------------| |
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73 | ! 1) Calculate available heat for surface ablation |
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74 | !------------------------------------------------------------------------------| |
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75 | ! |
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76 | DO 20 ji = kideb, kiut |
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77 | |
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78 | z_f_surf(ji) = fratsb(ji) + fleb(ji) + fcsb(ji) - fc_su(ji) |
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79 | & + ab(ji)*fsolgb(ji) |
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80 | z_f_surf(ji) = MAX(c_zero,z_f_surf(ji)) |
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81 | z_f_surf(ji) = z_f_surf(ji)*MAX(c_zero, |
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82 | & SIGN(one,t_su_b(ji)-tfs(ji))) |
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83 | |
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84 | IF ( l_write ) THEN |
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85 | WRITE(numout,*) ' Available heat for surface ablation ... ' |
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86 | WRITE(numout,*) |
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87 | WRITE(numout,*) ' z_f_surf : ', z_f_surf(ji) |
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88 | WRITE(numout,*) ' fratsb : ', fratsb(ji) |
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89 | WRITE(numout,*) ' fleb : ', fleb(ji) |
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90 | WRITE(numout,*) ' fcsb : ', fcsb(ji) |
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91 | WRITE(numout,*) ' fc_su : ', fc_su(ji) |
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92 | WRITE(numout,*) ' ab : ', ab(ji) |
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93 | WRITE(numout,*) ' fsolgb : ', fsolgb(ji) |
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94 | WRITE(numout,*) |
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95 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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96 | WRITE(numout,*) ' ht_s_b : ', ht_s_b(ji) |
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97 | WRITE(numout,*) ' t_su_b : ', t_su_b(ji) |
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98 | WRITE(numout,*) |
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99 | ENDIF |
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100 | |
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101 | 20 CONTINUE |
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102 | |
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103 | ! |
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104 | !------------------------------------------------------------------------------| |
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105 | ! 2) Snowfall and surface melt | |
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106 | !------------------------------------------------------------------------------| |
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107 | ! |
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108 | DO 40 ji = kideb, kiut |
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109 | |
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110 | ! total snow heat content for conservation |
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111 | zqt_s_ini = q_s_b(ji,1) * ht_s_b(ji) |
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112 | |
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113 | IF ( l_write ) THEN |
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114 | WRITE(numout,*) ' Surface ablation and sublimation ... ' |
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115 | WRITE(numout,*) |
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116 | WRITE(numout,*) ' zqt_s_ini : ', zqt_s_ini / ddtb |
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117 | WRITE(numout,*) ' ht_s_b : ', ht_s_b(ji) |
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118 | WRITE(numout,*) ' q_s_b(1) : ', q_s_b(ji,1) |
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119 | WRITE(numout,*) |
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120 | ENDIF |
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121 | |
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122 | !---------- |
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123 | ! Snowfall |
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124 | !---------- |
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125 | dh_s_prec(ji) = hnpbqb(ji) |
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126 | dh_s_melt(ji) = 0.0 |
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127 | zqprec = rhon * ( cpg * ( tpw - tabqb(ji) ) + lfus ) |
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128 | |
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129 | ! Conservation update |
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130 | zqt_s_ini = zqt_s_ini + zqprec*hnpbqb(ji) |
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131 | fprec = - zqprec * hnpbqb(ji) / ddtb |
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132 | |
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133 | IF ( l_write ) THEN |
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134 | WRITE(numout,*) ' snow falls! ' |
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135 | WRITE(numout,*) ' dh_s_prec : ', dh_s_prec(ji) |
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136 | WRITE(numout,*) ' flux of h : ', |
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137 | & zqprec*hnpbqb(ji) / ddtb |
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138 | WRITE(numout,*) ' zqt_s_ini : ', zqt_s_ini / ddtb |
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139 | WRITE(numout,*) |
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140 | ENDIF |
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141 | |
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142 | !----------- |
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143 | ! Snow melt |
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144 | !----------- |
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145 | ! Energy available for surface melt |
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146 | zqfont_su = ( z_f_surf(ji) + f_s_im(ji) ) * ddtb |
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147 | IF ( l_write ) THEN |
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148 | WRITE(numout,*) ' snow melts! ' |
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149 | WRITE(numout,*) ' z_f_surf(ji) : ', z_f_surf(ji) |
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150 | WRITE(numout,*) ' f_s_im : ', f_s_im(ji) |
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151 | WRITE(numout,*) ' zqfont_su : ', zqfont_su |
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152 | ENDIF |
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153 | |
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154 | ! Melt of fallen snow |
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155 | zdeltah(1) = MIN( 0.0 , - zqfont_su / |
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156 | & MAX( zqprec , zeps ) ) |
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157 | zqfont_su = MAX( 0.0 , - dh_s_prec(ji) - zdeltah(1) ) * |
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158 | & zqprec |
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159 | zdeltah(1) = MAX( - dh_s_prec(ji), zdeltah(1) ) |
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160 | dh_s_melt(ji) = dh_s_melt(ji) + zdeltah(1) |
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161 | |
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162 | ! Melt / evaporation of snow |
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163 | zswi_evap = 0 |
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164 | WRITE(numout,*) ' ln_evap : ', ln_evap |
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165 | WRITE(numout,*) ' tdewb : ', tdewb(ji) |
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166 | IF ( ln_evap .AND. ( qsfcb(ji) .GT. qabqb(ji) ) .AND. |
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167 | & tdewb(ji) .LT. 1. ) zswi_evap = 1 |
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168 | |
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169 | DO layer = 1, nlay_s ! in case of melting of more than 1 layer |
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170 | zlvap = zswi_evap * rhon * ( lvap + cpg * ( tabqb(ji) - tpw ) ) ! MV new evaporation |
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171 | |
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172 | ! zdeltah(layer) = - zqfont_su / q_s_b(ji,layer) |
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173 | zdeltah(layer) = - zqfont_su / ( q_s_b(ji,layer) + zlvap ) |
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174 | zqfont_su = MAX( c_zero, - deltaz_s_phy(layer) - |
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175 | & zdeltah(layer) ) * |
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176 | ! & q_s_b(ji,layer) !MV new evaporation |
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177 | & ( q_s_b(ji,layer) + zlvap ) |
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178 | zdeltah(layer) = MAX( zdeltah(layer), - deltaz_s_phy(layer) ) |
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179 | dh_s_melt(ji) = dh_s_melt(ji) + zdeltah(layer) !resulting melt of snow |
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180 | END DO |
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181 | |
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182 | dh_s_tot(ji) = dh_s_melt(ji) + dh_s_prec(ji) |
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183 | |
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184 | ! old and new snow thicknesses |
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185 | hsold = ht_s_b(ji) |
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186 | hsnew = ht_s_b(ji) + dh_s_tot(ji) |
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187 | |
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188 | ! if snow is still present zhn = 1, else zhn = 0 |
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189 | zhn = 1.0 - MAX( c_zero , SIGN( one , - hsnew ) ) |
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190 | ht_s_b(ji) = MAX( c_zero , hsnew ) |
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191 | |
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192 | !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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193 | ! Conservation test for snow |
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194 | zqt_s_fin = q_s_b(ji,1) * ht_s_b(ji) |
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195 | zdqt_s = zqt_s_fin - zqt_s_ini |
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196 | |
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197 | WRITE(numout,*) |
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198 | WRITE(numout,*) ' Conservation in snow... ' |
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199 | WRITE(numout,*) ' dh_s_melt : ', dh_s_melt(ji) |
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200 | WRITE(numout,*) ' dh_s_prec : ', dh_s_prec(ji) |
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201 | WRITE(numout,*) ' ht_s_b : ', ht_s_b(ji) |
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202 | WRITE(numout,*) ' zqt_s_ini : ', zqt_s_ini / ddtb |
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203 | WRITE(numout,*) ' zqt_s_fin : ', zqt_s_fin / ddtb |
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204 | WRITE(numout,*) ' zdqt_s : ', zdqt_s / ddtb |
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205 | WRITE(numout,*) ' z_f_surf : ', - z_f_surf(ji) |
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206 | IF ( zqt_s_fin.GT.0.0 ) THEN |
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207 | cons_err = ABS(zdqt_s / ddtb + z_f_surf(ji) ) |
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208 | ELSE |
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209 | cons_err = ABS(zqt_s_ini / ddtb + zdqt_s / ddtb ) |
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210 | ENDIF |
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211 | WRITE(numout,*) ' Cons error, snow : ', cons_err |
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212 | WRITE(numout,*) |
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213 | !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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214 | |
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215 | !------------------ |
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216 | ! Ice surface melt |
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217 | !------------------ |
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218 | IF ( l_write ) WRITE(numout,*) ' ice melts! ' |
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219 | |
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220 | zzf_surf = zqfont_su / ddtb |
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221 | zdqt_i = 0.0 |
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222 | dh_i_surf(ji) = 0.0 |
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223 | DO layer = 1, nlay_i |
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224 | zdeltah(layer) = - zqfont_su / q_i_b(ji,layer) |
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225 | zqfont_su = MAX( c_zero , - deltaz_i_phy(layer) |
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226 | & - zdeltah(layer) ) * q_i_b(ji,layer) |
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227 | zdeltah(layer) = MAX( zdeltah(layer) , - deltaz_i_phy(layer) ) |
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228 | dh_i_surf(ji) = dh_i_surf(ji) + zdeltah(layer) !resulting melt of ice |
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229 | zdqt_i = zdqt_i + zdeltah(layer) * q_i_b(ji,layer) |
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230 | & / ddtb |
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231 | END DO |
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232 | |
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233 | cons_err = ABS( zzf_surf + zdqt_i ) |
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234 | |
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235 | IF ( l_write ) THEN |
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236 | WRITE(numout,*) ' Conservation in sea ice, surface ' |
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237 | WRITE(numout,*) ' dh_i_surf: ', dh_i_surf(ji) |
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238 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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239 | WRITE(numout,*) ' zzf_surf : ', zzf_surf |
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240 | WRITE(numout,*) ' zdqt_i : ', zdqt_i |
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241 | WRITE(numout,*) ' Cons error, ice : ', cons_err |
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242 | WRITE(numout,*) |
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243 | ENDIF |
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244 | |
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245 | ! |
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246 | !------------------------------------------------------------------------------| |
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247 | ! 3) Sublimation at the surface | |
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248 | !------------------------------------------------------------------------------| |
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249 | ! |
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250 | !------------------ |
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251 | ! Snow sublimation |
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252 | !------------------ |
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253 | |
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254 | !------------------ |
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255 | ! Ice sublimation |
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256 | !------------------ |
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257 | |
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258 | !------------------- |
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259 | ! Snow condensation |
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260 | !------------------- |
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261 | |
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262 | ! THIS IS DEFINITELY WRONG SINCE LATENT HEAT IS ALREADY COUNTED TO |
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263 | ! remove heat from the snow pack |
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264 | ! ! 4.3) Snow/ice sublimation |
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265 | ! ! |
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266 | ! ! If fleb is negative, snow condensates at the surface. |
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267 | ! ! |
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268 | dh_s_subl(ji) = + parsub*fleb(ji)/(rhon*lsub)*ddtb |
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269 | dh_s_tot(ji) = dh_s_tot(ji) + dh_s_subl(ji) |
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270 | zdhcf = ht_s_b(ji) + dh_s_subl(ji) |
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271 | ht_s_b(ji) = MAX(c_zero,zdhcf) |
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272 | dh_s_tot(ji) = ht_s_b(ji) - hsold |
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273 | dh_i_subl(ji) = - MAX(c_zero,-zdhcf)*rhon/rhog |
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274 | |
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275 | dh_i_surf(ji) = dh_i_surf(ji) + dh_i_subl(ji) |
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276 | |
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277 | hsnew = ht_s_b(ji) |
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278 | |
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279 | IF ( ht_s_b(ji) .LE. 0.0 ) THEN |
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280 | dh_s_tot(ji) = MAX( 0.0 , dh_s_tot(ji) ) |
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281 | ENDIF |
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282 | |
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283 | IF ( l_write ) THEN |
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284 | WRITE(numout,*) ' Snow sublimation ... ' |
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285 | WRITE(numout,*) ' ' |
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286 | WRITE(numout,*) ' parsub : ', parsub |
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287 | WRITE(numout,*) ' dh_s_subl : ', dh_s_subl(ji) |
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288 | WRITE(numout,*) ' dh_i_subl : ', dh_i_subl(ji) |
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289 | ENDIF |
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290 | |
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291 | 40 CONTINUE |
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292 | ! |
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293 | !------------------------------------------------------------------------------| |
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294 | ! 4) Basal growth and melt | |
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295 | !------------------------------------------------------------------------------| |
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296 | ! |
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297 | DO 50 ji = kideb, kiut |
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298 | |
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299 | IF ( l_write ) THEN |
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300 | WRITE(numout,*) ' Basal growth and melt ... ' |
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301 | WRITE(numout,*) |
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302 | WRITE(numout,*) ' fbbqb : ', fbbqb(ji) |
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303 | WRITE(numout,*) ' fc_bo_i : ', fc_bo_i(ji) |
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304 | WRITE(numout,*) |
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305 | ENDIF |
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306 | |
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307 | ! formation / melting of ice at the base is determined by the balance of |
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308 | ! the conductive heat flux in the ice (fc_bo_i), and the heat fluxes |
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309 | ! from the ocean (fbbqb). Conductive heat flux is positive |
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310 | ! downwards and fbbq is positive to the ice, i.e., upwards. |
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311 | ! Melt/formation rate is modulated by the enthalpy of the bottom ice layer. |
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312 | ! accretion of ice at the base |
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313 | |
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314 | !-------------- |
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315 | ! Basal growth |
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316 | !-------------- |
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317 | IF ( ( fc_bo_i(ji) + fbbqb(ji) ) .LT. 0.0 ) THEN |
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318 | |
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319 | s_i_new = rn_e_newice * s_w ! New ice salinity (g/kg) |
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320 | |
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321 | ztmelts = - tmut * s_i_new + tpw ! Melting point in K |
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322 | |
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323 | ! New ice heat content (Bitz and Lipscomb, 1999) |
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324 | ! should be zdE instead |
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325 | q_i_b(ji,nlay_i+1) = rhog*( cpg*(tmelts-t_bo_b(ji)) |
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326 | & + lfus*( 1.0-(tmelts-tpw) |
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327 | & / (t_bo_b(ji) - tpw) ) |
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328 | & - cpw*(tmelts-tpw) ) |
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329 | |
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330 | zE1 = - cpw * ( t_bo_b(ji) - tpw ) ! specific enthalpy of sea water <0 |
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331 | zE2 = - q_i_b(ji,nlay_i+1) / rhog ! specific enthalpy of new sea ice <0 |
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332 | |
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333 | WRITE(numout,*) ' zE1 : ', zE1 |
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334 | WRITE(numout,*) ' zE2 : ', zE2 |
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335 | |
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336 | zdE = zE2 - zE1 ! <0 |
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337 | |
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338 | WRITE(numout,*) ' zdE : ', zdE |
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339 | |
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340 | dh_i_bott(ji) = ddtb*(fc_bo_i(ji) + fbbqb(ji) ) |
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341 | & / ( zdE * rhog ) |
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342 | |
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343 | ! salt flux due to initial salt entrapment (keep ?) |
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344 | fsbp = s_w * ( 1. - rn_e_newice ) * dh_i_bott(ji) / ddtb * |
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345 | & rhog / 1000. |
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346 | |
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347 | IF ( l_write ) WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji) |
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348 | |
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349 | ENDIF |
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350 | |
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351 | !----------------- |
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352 | ! Basal melt |
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353 | !----------------- |
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354 | IF ( ( fc_bo_i(ji) + fbbqb(ji) ) .GE. 0.0 ) THEN |
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355 | |
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356 | IF ( l_write ) WRITE(numout,*) ' Energy available for |
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357 | & basal melt : ', |
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358 | & fc_bo_i(ji) + fbbqb(ji) |
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359 | |
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360 | zqfont_bo = ddtb * ( fc_bo_i(ji) + fbbqb(ji) ) |
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361 | zzf_base = zqfont_bo / ddtb |
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362 | zdqt_i = 0.0 |
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363 | |
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364 | IF ( l_write ) WRITE(numout,*) ' zqfont_bo : ', zqfont_bo |
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365 | |
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366 | dh_i_bott(ji) = 0.0 |
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367 | DO layer = nlay_i, 1, -1 |
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368 | zdeltah(layer) = - zqfont_bo / q_i_b(ji,layer) |
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369 | zqfont_bo = MAX ( 0.0 , - deltaz_i_phy(layer) - |
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370 | & zdeltah(layer) ) |
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371 | & * q_i_b(ji,layer) |
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372 | dh_i_bott(ji) = dh_i_bott(ji) + zdeltah(layer) |
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373 | zdqt_i = zdqt_i + zdeltah(layer) * |
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374 | & q_i_b(ji,layer) / ddtb |
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375 | END DO |
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376 | |
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377 | IF ( l_write ) WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji) |
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378 | |
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379 | cons_err = ABS( zzf_base + zdqt_i ) |
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380 | |
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381 | IF ( l_write ) THEN |
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382 | WRITE(numout,*) ' Conservation in sea ice, base ' |
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383 | WRITE(numout,*) ' dh_i_bott: ', dh_i_bott(ji) |
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384 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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385 | WRITE(numout,*) ' zzf_base : ', zzf_base |
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386 | WRITE(numout,*) ' zdqt_i : ', zdqt_i |
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387 | ! WRITE(numout,*) ' Conservation error ice surface : ', |
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388 | ! & cons_err |
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389 | ! WRITE(numout,*) |
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390 | ENDIF |
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391 | |
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392 | ENDIF |
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393 | |
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394 | ! It can be than an internal temperature is greater than melt point |
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395 | ! then, see lim3 for correction |
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396 | |
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397 | ! new ice thickness |
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398 | zhgnew = ht_i_b(ji) + dh_i_surf(ji) + dh_i_bott(ji) |
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399 | old_ht_i_b(ji) = ht_i_b(ji) |
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400 | |
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401 | ht_i_b(ji) = zhgnew |
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402 | |
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403 | 50 CONTINUE |
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404 | |
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405 | ! |
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406 | !------------------------------------------------------------------------------| |
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407 | ! 5) Formation of snow-ice | |
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408 | !------------------------------------------------------------------------------| |
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409 | ! |
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410 | ! When snow load excesses Archimede's limit, snow-ice interface goes down |
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411 | ! under sea-level, flooding of seawater transforms snow into ice |
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412 | ! dh_snowice is positive for the ice |
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413 | |
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414 | DO 70 ji = kideb, kiut |
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415 | |
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416 | dh_snowice(ji) = MAX( c_zero , ( rhon * ht_s_b(ji) + (rhog -rho0 ) |
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417 | & * ht_i_b(ji)) / ( rhon + rho0 - rhog ) ) |
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418 | |
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419 | zhgnew = MAX( zhgnew , zhgnew + dh_snowice(ji) ) |
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420 | zhnnew = MIN( ht_s_b(ji) , ht_s_b(ji) - dh_snowice(ji) ) |
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421 | |
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422 | ht_s_b(ji) = zhnnew |
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423 | ht_i_b(ji) = zhgnew |
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424 | |
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425 | IF ( l_write ) THEN |
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426 | WRITE(numout,*) ' dh_snowice : ', dh_snowice(ji) |
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427 | WRITE(numout,*) |
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428 | WRITE(numout,*) ' At the end of the routine ... ' |
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429 | WRITE(numout,*) ' ht_s_b : ', ht_s_b(ji) |
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430 | WRITE(numout,*) ' ht_i_b : ', ht_i_b(ji) |
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431 | ENDIF |
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432 | |
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433 | ! give a minimum snow depth |
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434 | zhsnmin = 1.0e-10 |
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435 | isnow = 0 |
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436 | IF ( ht_s_b(ji) .GT. zhsnmin ) isnow = 1 |
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437 | ht_s_b(ji) = isnow * ht_s_b(ji) |
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438 | |
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439 | !--- Remove --- |
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440 | WRITE(numout,*) ' dh_i_bott : ', dh_i_bott(ji) |
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441 | WRITE(numout,*) ' dh_i_surf : ', dh_i_surf(ji) |
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442 | WRITE(numout,*) ' dh_i_snowice : ', dh_snowice(ji) |
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443 | WRITE(numout,*) ' dh_s_melt : ', dh_s_melt(ji) |
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444 | !--- Remove --- |
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445 | |
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446 | 70 CONTINUE |
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447 | |
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448 | RETURN |
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449 | |
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450 | !------------------------------------------------------------------------------| |
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451 | ! Fin de la subroutine ice_th_dh |
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452 | END SUBROUTINE |
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