1 | MODULE limthd_zdf |
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2 | !!====================================================================== |
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3 | !! *** MODULE limthd_zdf *** |
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4 | !! thermodynamic growth and decay of the ice |
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5 | !!====================================================================== |
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6 | #if defined key_ice_lim |
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7 | !!---------------------------------------------------------------------- |
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8 | !! 'key_ice_lim' LIM sea-ice model |
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9 | !!---------------------------------------------------------------------- |
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10 | !! lim_thd_zdf : vertical accr./abl. and lateral ablation of sea ice |
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11 | !!---------------------------------------------------------------------- |
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12 | !! * Modules used |
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13 | USE par_oce ! ocean parameters |
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14 | USE phycst ! ??? |
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15 | USE ice_oce ! ice variables |
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16 | USE thd_ice |
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17 | USE iceini |
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18 | USE limistate |
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19 | USE in_out_manager |
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20 | |
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21 | IMPLICIT NONE |
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22 | PRIVATE |
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23 | |
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24 | !! * Routine accessibility |
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25 | PUBLIC lim_thd_zdf ! called by lim_thd |
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26 | |
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27 | !! * Module variables |
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28 | REAL(wp) :: & ! constant values |
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29 | epsi20 = 1.e-20 , & |
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30 | epsi13 = 1.e-13 , & |
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31 | zzero = 0.e0 , & |
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32 | zone = 1.e0 |
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33 | !!---------------------------------------------------------------------- |
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34 | !! LIM 2.0 , UCL-LODYC-IPSL (2003) |
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35 | !!---------------------------------------------------------------------- |
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36 | CONTAINS |
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37 | |
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38 | SUBROUTINE lim_thd_zdf( kideb , kiut ) |
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39 | !!------------------------------------------------------------------ |
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40 | !! *** ROUTINE lim_thd_zdf *** |
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41 | !! |
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42 | !! ** Purpose : This routine determines the time evolution of snow |
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43 | !! and sea-ice thicknesses, concentration and heat content |
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44 | !! due to the vertical and lateral thermodynamic accretion- |
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45 | !! ablation processes. One only treats the case of lat. abl. |
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46 | !! For lateral accretion, see routine lim_lat_accr |
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47 | !! |
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48 | !! ** Method : The representation of vertical growth and decay of |
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49 | !! the sea-ice model is based upon the diffusion of heat |
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50 | !! through the external and internal boundaries of a |
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51 | !! three-layer system (two layers of ice and one layer and |
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52 | !! one layer of snow, if present, on top of the ice). |
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53 | !! |
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54 | !! ** Action : - Calculation of some intermediates variables |
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55 | !! - Calculation of surface temperature |
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56 | !! - Calculation of available heat for surface ablation |
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57 | !! - Calculation of the changes in internal temperature |
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58 | !! of the three-layer system, due to vertical diffusion |
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59 | !! processes |
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60 | !! - Performs surface ablation and bottom accretion-ablation |
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61 | !! - Performs snow-ice formation |
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62 | !! - Performs lateral ablation |
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63 | !! |
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64 | !! References : |
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65 | !! Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646 |
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66 | !! Fichefet T. and M. Maqueda 1999, Clim. Dyn, 15(4), 251-268 |
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67 | !! |
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68 | !! History : |
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69 | !! original : 01-04 (LIM) |
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70 | !! addition : 02-08 (C. Ethe, G. Madec) |
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71 | !!------------------------------------------------------------------ |
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72 | !! * Arguments |
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73 | INTEGER , INTENT (in) :: & |
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74 | kideb , & ! Start point on which the the computation is applied |
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75 | kiut ! End point on which the the computation is applied |
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76 | |
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77 | !! * Local variables |
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78 | INTEGER :: ji ! dummy loop indices |
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79 | |
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80 | REAL(wp) , DIMENSION(jpij,2) :: & |
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81 | zqcmlt ! energy due to surface( /1 ) and bottom melting( /2 ) |
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82 | |
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83 | REAL(wp), DIMENSION(jpij) :: & |
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84 | ztsmlt & ! snow/ice surface melting temperature |
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85 | ,ztbif & ! int. temp. at the mid-point of the 1st layer of the snow/ice sys. |
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86 | ,zksn & ! effective conductivity of snow |
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87 | ,zkic & ! effective conductivity of ice |
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88 | ,zksndh & ! thermal cond. at the mid-point of the 1st layer of the snow/ice sys. |
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89 | , zfcsu & ! conductive heat flux at the surface of the snow/ice system |
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90 | , zfcsudt & ! = zfcsu * dt |
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91 | , zi0 & ! frac. of the net SW rad. which is not absorbed at the surface |
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92 | , z1mi0 & ! fraction of the net SW radiation absorbed at the surface |
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93 | , zqmax & ! maximum energy stored in brine pockets |
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94 | , zrcpdt & ! h_su*rho_su*cp_su/dt(h_su being the thick. of surf. layer) |
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95 | , zts_old & ! previous surface temperature |
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96 | , zidsn , z1midsn , zidsnic ! tempory variables |
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97 | |
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98 | REAL(wp), DIMENSION(jpij) :: & |
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99 | zfnet & ! net heat flux at the top surface( incl. conductive heat flux) |
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100 | , zsprecip & ! snow accumulation |
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101 | , zhsnw_old & ! previous snow thickness |
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102 | , zdhictop & ! change in ice thickness due to top surf ablation/accretion |
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103 | , zdhicbot & ! change in ice thickness due to bottom surf abl/acc |
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104 | , zqsup & ! energy transmitted to ocean (coming from top surf abl/acc) |
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105 | , zqocea & ! energy transmitted to ocean (coming from bottom sur abl/acc) |
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106 | , zfrl_old & ! previous sea/ice fraction |
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107 | , zfrld_1d & ! new sea/ice fraction |
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108 | , zep ! internal temperature of the 2nd layer of the snow/ice system |
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109 | |
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110 | REAL(wp), DIMENSION(3) :: & |
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111 | zplediag & ! principle diagonal, subdiag. and supdiag. of the |
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112 | , zsubdiag & ! tri-diagonal matrix coming from the computation |
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113 | , zsupdiag & ! of the temperatures inside the snow-ice system |
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114 | , zsmbr ! second member |
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115 | |
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116 | REAL(wp) :: & |
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117 | zhsu & ! thickness of surface layer |
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118 | , zhe & ! effective thickness for compu. of equ. thermal conductivity |
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119 | , zheshth & ! = zhe / thth |
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120 | , zghe & ! correction factor of the thermal conductivity |
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121 | , zumsb & ! parameter for numerical method to solve heat-diffusion eq. |
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122 | , zkhsn & ! conductivity at the snow layer |
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123 | , zkhic & ! conductivity at the ice layers |
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124 | , zkint & ! equivalent conductivity at the snow-ice interface |
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125 | , zkhsnint & ! = zkint*dt / (hsn*rhosn*cpsn) |
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126 | , zkhicint & ! = 2*zkint*dt / (hic*rhoic*cpic) |
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127 | , zpiv1 , zpiv2 & ! tempory scalars used to solve the tri-diagonal system |
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128 | , zb2 , zd2 , zb3 , zd3 & |
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129 | , ztint ! equivalent temperature at the snow-ice interface |
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130 | |
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131 | REAL(wp) :: & |
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132 | zexp & ! exponential function of the ice thickness |
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133 | , zfsab & ! part of solar radiation stored in brine pockets |
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134 | , zfts & ! value of energy balance function when the temp. equal surf. temp. |
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135 | , zdfts & ! value of derivative of ztfs when the temp. equal surf. temp. |
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136 | , zdts & ! surface temperature increment |
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137 | , zqsnw_mlt & ! energy needed to melt snow |
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138 | , zdhsmlt & ! change in snow thickness due to melt |
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139 | , zhsn & ! snow thickness (previous+accumulation-melt) |
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140 | , zqsn_mlt_rem & ! remaining heat coming from snow melting |
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141 | , zqice_top_mlt & ! energy used to melt ice at top surface |
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142 | , zdhssub & ! change in snow thick. due to sublimation or evaporation |
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143 | , zdhisub & ! change in ice thick. due to sublimation or evaporation |
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144 | , zdhsn & ! snow ice thickness increment |
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145 | , zdtsn & ! snow internal temp. increment |
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146 | , zdtic & ! ice internal temp. increment |
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147 | , zqnes ! conductive energy due to ice melting in the first ice layer |
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148 | |
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149 | REAL(wp) :: & |
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150 | ztbot & ! temperature at the bottom surface |
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151 | , zfcbot & ! conductive heat flux at bottom surface |
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152 | , zqice_bot & ! energy used for bottom melting/growing |
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153 | , zqice_bot_mlt & ! energy used for bottom melting |
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154 | , zqstbif_bot & ! part of energy stored in brine pockets used for bottom melting |
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155 | , zqstbif_old & ! tempory var. for zqstbif_bot |
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156 | , zdhicmlt & ! change in ice thickness due to bottom melting |
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157 | , zdhicm & ! change in ice thickness var. |
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158 | , zdhsnm & ! change in snow thickness var. |
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159 | , zhsnfi & ! snow thickness var. |
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160 | , zc1, zpc1, zc2, zpc2, zp1, zp2 & ! tempory variables |
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161 | , ztb2, ztb3 |
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162 | |
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163 | REAL(wp) :: & |
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164 | zdrmh & ! change in snow/ice thick. after snow-ice formation |
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165 | , zhicnew & ! new ice thickness |
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166 | , zhsnnew & ! new snow thickness |
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167 | , zquot , ztneq & ! tempory temp. variables |
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168 | , zqice, zqicetot & ! total heat inside the snow/ice system |
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169 | , zdfrl & ! change in ice concentration |
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170 | , zdvsnvol & ! change in snow volume |
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171 | , zdrfrl1, zdrfrl2 & ! tempory scalars |
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172 | , zihsn, zidhb, zihic, zihe, zihq, ziexp, ziqf, zihnf, zibmlt, ziqr, zihgnew, zind |
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173 | !!---------------------------------------------------------------------- |
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174 | |
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175 | !----------------------------------------------------------------------- |
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176 | ! 1. Boundaries conditions for snow/ice system internal temperature |
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177 | ! - If tbif_1d(ji,1) > rt0_snow, tbif_1d(ji,1) = rt0_snow |
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178 | ! - If tbif_1d(ji,2/3) > rt0_ice, tbif_1d(ji,2/3) = rt0_ice |
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179 | ! Computation of energies due to surface and bottom melting |
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180 | !----------------------------------------------------------------------- |
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181 | |
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182 | |
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183 | DO ji = kideb , kiut |
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184 | zihsn = MAX( zzero , SIGN( zone , hsndif - h_snow_1d(ji) ) ) |
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185 | zihic = MAX( zzero , SIGN( zone , hicdif - h_ice_1d(ji) ) ) |
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186 | !--computation of energy due to surface melting |
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187 | zqcmlt(ji,1) = ( MAX ( zzero , & |
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188 | & rcpsn * h_snow_1d(ji) * ( tbif_1d(ji,1) - rt0_snow ) ) ) * ( 1.0 - zihsn ) |
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189 | !--computation of energy due to bottom melting |
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190 | zqcmlt(ji,2) = ( MAX( zzero , & |
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191 | & rcpic * ( tbif_1d(ji,2) - rt0_ice ) * ( h_ice_1d(ji) / 2. ) ) & |
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192 | & + MAX( zzero , & |
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193 | & rcpic * ( tbif_1d(ji,3) - rt0_ice ) * ( h_ice_1d(ji) / 2. ) ) & |
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194 | & ) * ( 1.0 - zihic ) |
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195 | !--limitation of snow/ice system internal temperature |
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196 | tbif_1d(ji,1) = MIN( rt0_snow, tbif_1d(ji,1) ) |
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197 | tbif_1d(ji,2) = MIN( rt0_ice , tbif_1d(ji,2) ) |
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198 | tbif_1d(ji,3) = MIN( rt0_ice , tbif_1d(ji,3) ) |
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199 | END DO |
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200 | |
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201 | |
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202 | !------------------------------------------- |
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203 | ! 2. Calculate some intermediate variables. |
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204 | !------------------------------------------- |
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205 | |
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206 | ! initialisation of the thickness of surface layer |
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207 | zhsu = hnzst |
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208 | |
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209 | DO ji = kideb , kiut |
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210 | zind = MAX( zzero , SIGN( zone , zhsu - h_snow_1d(ji) ) ) |
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211 | zihsn = MAX( zzero , SIGN( zone , hsndif - h_snow_1d(ji) ) ) |
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212 | zihsn = MAX( zihsn , zind ) |
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213 | zihic = MAX( zzero , sign( zone , hicdif - h_ice_1d(ji) ) ) |
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214 | ! 2.1. Computation of surface melting temperature |
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215 | !---------------------------------------------------- |
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216 | zind = MAX( zzero , SIGN( zone , -h_snow_1d(ji) ) ) |
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217 | ztsmlt(ji) = ( 1.0 - zind ) * rt0_snow + zind * rt0_ice |
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218 | ! |
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219 | ! 2.2. Effective conductivity of snow and ice |
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220 | !----------------------------------------------- |
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221 | |
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222 | !---computation of the correction factor on the thermal conductivity |
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223 | !-- (Morales Maqueda, 1995 ; Fichefet and Morales Maqueda, 1997) |
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224 | zhe = ( rcdsn / ( rcdsn + rcdic ) ) * h_ice_1d(ji) & |
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225 | & + ( rcdic / ( rcdsn + rcdic ) ) * h_snow_1d(ji) |
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226 | zihe = MAX( zzero , SIGN( zone , 2.0 * zhe - thth ) ) |
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227 | zheshth = zhe / thth |
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228 | zghe = ( 1.0 - zihe ) * zheshth * ( 2.0 - zheshth ) & |
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229 | & + zihe * 0.5 * ( 1.5 + LOG( 2.0 * zheshth ) ) |
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230 | #if defined key_lim_cp3 |
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231 | zghe = 1.0 |
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232 | #endif |
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233 | |
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234 | !---effective conductivities |
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235 | zksn(ji) = zghe * rcdsn |
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236 | zkic(ji) = zghe * rcdic |
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237 | |
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238 | ! |
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239 | ! 2.3. Computation of the conductive heat flux from the snow/ice |
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240 | ! system interior toward the top surface |
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241 | !------------------------------------------------------------------ |
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242 | |
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243 | !---Thermal conductivity at the mid-point of the first snow/ice system layer |
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244 | zksndh(ji) = ( ( 1.0 - zihsn ) * 2.0 * zksn(ji) + zihsn * 4.0 * zkic(ji) ) & |
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245 | & / ( ( 1.0 - zihsn ) * h_snow_1d(ji) & |
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246 | & + zihsn * ( ( 1.0 + 3.0 * zihic ) * h_ice_1d(ji) & |
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247 | & + 4.0 * zkic(ji)/zksn(ji) * h_snow_1d(ji) ) ) |
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248 | |
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249 | !---internal temperature at the mid-point of the first snow/ice system layer |
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250 | ztbif(ji) = ( 1.0 - zihsn ) * tbif_1d(ji,1) & |
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251 | & + zihsn * ( ( 1.0 - zihic ) * tbif_1d(ji,2) & |
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252 | & + zihic * tfu_1d(ji) ) |
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253 | !---conductive heat flux |
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254 | zfcsu(ji) = zksndh(ji) * ( ztbif(ji) - sist_1d(ji) ) |
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255 | |
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256 | END DO |
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257 | |
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258 | !-------------------------------------------------------------------- |
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259 | ! 3. Calculate : |
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260 | ! - fstbif_1d, part of solar radiation absorbing inside the ice |
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261 | ! assuming an exponential absorption (Grenfell and Maykut, 1977) |
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262 | ! - zqmax, maximum energy stored in brine pockets |
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263 | ! - qstbif_1d, total energy stored in brine pockets (updating) |
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264 | !------------------------------------------------------------------- |
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265 | |
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266 | |
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267 | DO ji = kideb , kiut |
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268 | zihsn = MAX( zzero , SIGN (zone , -h_snow_1d(ji) ) ) |
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269 | zihic = MAX( zzero , 1.0 - ( h_ice_1d(ji) / zhsu ) ) |
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270 | zind = MAX( zzero , SIGN (zone , hicdif - h_ice_1d(ji) ) ) |
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271 | !--Computation of the fraction of the net shortwave radiation which |
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272 | !--penetrates inside the ice cover ( See Forcat) |
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273 | zi0(ji) = zihsn * ( fr1_i0_1d(ji) + zihic * fr2_i0_1d(ji) ) |
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274 | zexp = MIN( zone , EXP( -1.5 * ( h_ice_1d(ji) - zhsu ) ) ) |
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275 | fstbif_1d(ji) = zi0(ji) * qsr_ice_1d(ji) * zexp |
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276 | !--Computation of maximum energy stored in brine pockets zqmax and update |
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277 | !--the total energy stored in brine pockets, if less than zqmax |
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278 | zqmax(ji) = MAX( zzero , 0.5 * xlic * ( h_ice_1d(ji) - hicmin ) ) |
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279 | zfsab = zi0(ji) * qsr_ice_1d(ji) * ( 1.0 - zexp ) |
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280 | zihq = ( 1.0 - zind ) * MAX(zzero, SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) & |
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281 | & + zind * zone |
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282 | qstbif_1d(ji) = ( qstbif_1d(ji) + ( 1.0 - zihq ) * zfsab * rdt_ice ) * swiqst |
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283 | !--fraction of shortwave radiation absorbed at surface |
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284 | ziexp = zihq * zexp + ( 1.0 - zihq ) * ( swiqst + ( 1.0 - swiqst ) * zexp ) |
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285 | z1mi0(ji) = 1.0 - zi0(ji) * ziexp |
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286 | END DO |
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287 | |
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288 | |
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289 | !-------------------------------------------------------------------------------- |
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290 | ! 4. Computation of the surface temperature : determined by considering the |
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291 | ! budget of a thin layer of thick. zhsu at the top surface (H. Grenier, 1995) |
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292 | ! and based on a surface energy balance : |
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293 | ! hsu * rcp * dT/dt = Fsr + Fnsr(T) + Fcs(T), |
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294 | ! where - Fsr is the net absorbed solar radiation, |
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295 | ! - Fnsr is the total non solar radiation (incoming and outgoing long-wave, |
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296 | ! sensible and latent heat fluxes) |
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297 | ! - Fcs the conductive heat flux at the top of surface |
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298 | !------------------------------------------------------------------------------ |
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299 | |
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300 | ! 4.1. Computation of intermediate values |
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301 | !--------------------------------------------- |
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302 | DO ji = kideb, kiut |
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303 | zrcpdt(ji) = ( rcpsn * MIN( h_snow_1d(ji) , zhsu ) & |
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304 | & + rcpic * MAX( zhsu - h_snow_1d(ji) , zzero ) ) / rdt_ice |
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305 | zts_old(ji) = sist_1d(ji) |
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306 | END DO |
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307 | |
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308 | ! 4.2. Computation of surface temperature by expanding the eq. of energy balance |
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309 | ! with Ts = Tp + DT. One obtain , F(Tp) + DT * DF(Tp) = 0 |
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310 | ! where - F(Tp) = Fsr + Fnsr(Tp) + Fcs(Tp) |
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311 | ! - DF(Tp)= (dFnsr(Tp)/dT) + (dFcs(Tp)/dT) - hsu*rcp/dt |
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312 | !--------------------------------------------------------------------------------- |
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313 | |
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314 | DO ji = kideb, kiut |
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315 | !---computation of the derivative of energy balance function |
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316 | #if defined key_coupled |
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317 | # if defined key_lim_cp2 |
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318 | zdfts = zksndh(ji) & ! contribution of the conductive heat flux |
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319 | & + zrcpdt(ji) & ! contribution of hsu * rcp / dt |
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320 | & - dqns_ice_1d(ji) ! contribution of the total non solar radiation |
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321 | # else |
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322 | zdfts = zksndh(ji) & ! contribution of the conductive heat flux |
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323 | & + zrcpdt(ji) ! contribution of hsu * rcp / dt |
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324 | # endif |
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325 | |
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326 | #else |
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327 | zdfts = zksndh(ji) & ! contribution of the conductive heat flux |
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328 | & + zrcpdt(ji) & ! contribution of hsu * rcp / dt |
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329 | & - dqns_ice_1d (ji) ! contribution of the total non solar radiation |
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330 | #endif |
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331 | !---computation of the energy balance function |
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332 | zfts = - z1mi0 (ji) * qsr_ice_1d(ji) & ! net absorbed solar radiation |
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333 | & - qnsr_ice_1d(ji) & ! total non solar radiation |
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334 | & - zfcsu (ji) ! conductive heat flux from the surface |
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335 | !---computation of surface temperature increment |
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336 | zdts = -zfts / zdfts |
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337 | #if defined key_lim_cp3 |
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338 | zdts = zdts / 3.0 |
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339 | #endif |
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340 | !---computation of the new surface temperature |
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341 | sist_1d(ji) = sist_1d(ji) + zdts |
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342 | |
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343 | END DO |
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344 | |
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345 | !---------------------------------------------------------------------------- |
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346 | ! 5. Boundary condition at the top surface |
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347 | !-- IF Tsb < Tmelt, Fnet = Fcs (the net heat flux equal the conductive heat flux) |
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348 | ! Otherwise Tsb = Tmelt and Qnet(Tmelt) > 0 |
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349 | ! Fnet(Tmelt) is therefore the net surface flux needed for melting |
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350 | !---------------------------------------------------------------------------- |
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351 | |
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352 | |
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353 | ! 5.1. Limitation of surface temperature and update total non solar fluxes, |
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354 | ! latent heat flux and conductive flux at the top surface |
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355 | !---------------------------------------------------------------------- |
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356 | |
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357 | DO ji = kideb, kiut |
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358 | sist_1d(ji) = MIN( ztsmlt(ji) , sist_1d(ji) ) |
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359 | #if defined key_coupled |
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360 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) - ( emic * stefan * sist_1d(ji) * sist_1d(ji) * sist_1d(ji) * sist_1d(ji) ) |
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361 | #else |
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362 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) + dqns_ice_1d(ji) * ( sist_1d(ji) - zts_old(ji) ) |
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363 | qla_ice_1d (ji) = qla_ice_1d (ji) + dqla_ice_1d(ji) * ( sist_1d(ji) - zts_old(ji) ) |
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364 | #endif |
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365 | zfcsu(ji) = zksndh(ji) * ( ztbif(ji) - sist_1d(ji) ) |
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366 | END DO |
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367 | |
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368 | |
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369 | |
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370 | ! 5.2. Calculate available heat for surface ablation. |
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371 | !--------------------------------------------------------------------- |
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372 | |
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373 | DO ji = kideb, kiut |
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374 | zfnet(ji) = qnsr_ice_1d(ji) + z1mi0(ji) * qsr_ice_1d(ji) + zfcsu(ji) |
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375 | zfnet(ji) = MAX( zzero , zfnet(ji) ) |
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376 | zfnet(ji) = zfnet(ji) * MAX( zzero , SIGN( zone , sist_1d(ji) - ztsmlt(ji) ) ) |
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377 | END DO |
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378 | |
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379 | !------------------------------------------------------------------------- |
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380 | ! 6. Calculate changes in internal temperature due to vertical diffusion |
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381 | ! processes. The evolution of this temperature is governed by the one- |
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382 | ! dimensionnal heat-diffusion equation. |
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383 | ! Given the temperature tbif(1/2/3), at time m we solve a set |
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384 | ! of finite difference equations to obtain new tempe. Each tempe is coupled |
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385 | ! to the temp. immediatly above and below by heat conduction terms. Thus |
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386 | ! we have a set of equations of the form A * T = B, where A is a tridiagonal |
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387 | ! matrix, T a vector whose components are the unknown new temp. |
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388 | !------------------------------------------------------------------------- |
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389 | |
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390 | !--parameter for the numerical methode use to solve the heat-diffusion equation |
---|
391 | !- implicit, explicit or Crank-Nicholson |
---|
392 | zumsb = 1.0 - sbeta |
---|
393 | DO ji = kideb, kiut |
---|
394 | zidsn(ji) = MAX ( zzero, SIGN( zone, hsndif - h_snow_1d(ji) ) ) |
---|
395 | z1midsn(ji) = 1.0 - zidsn(ji) |
---|
396 | zihic = MAX ( zzero, SIGN( zone, hicdif - h_ice_1d(ji) ) ) |
---|
397 | zidsnic(ji) = zidsn(ji) * zihic |
---|
398 | zfcsudt(ji) = zfcsu(ji) * rdt_ice |
---|
399 | END DO |
---|
400 | |
---|
401 | DO ji = kideb, kiut |
---|
402 | |
---|
403 | ! 6.1 Calculate intermediate variables. |
---|
404 | !---------------------------------------- |
---|
405 | |
---|
406 | !--conductivity at the snow surface |
---|
407 | zkhsn = 2.0 * zksn(ji) * rdt_ice / rcpsn |
---|
408 | !--conductivity at the ice surface |
---|
409 | zkhic = 4.0 * zkic(ji) * rdt_ice / MAX( h_ice_1d(ji) * h_ice_1d(ji) * rcpic , epsi20 ) |
---|
410 | !--conductivity at the snow/ice interface |
---|
411 | zkint = 4.0 * zksn(ji) * zkic(ji) & |
---|
412 | & / ( zksn(ji) * h_ice_1d(ji) + 2.0 * zkic(ji) * h_snow_1d(ji) * z1midsn(ji)) |
---|
413 | zkhsnint = zkint * rdt_ice / rcpsn |
---|
414 | zkhicint = zkint * 2.0 * rdt_ice / MAX( h_ice_1d(ji) * rcpic , epsi20 ) |
---|
415 | |
---|
416 | ! 6.2. Fulfill the linear system matrix. |
---|
417 | !----------------------------------------- |
---|
418 | !$$$ zplediag(1) = 1 + sbeta * z1midsn(ji) * ( zkhsn + zkhsnint ) |
---|
419 | zplediag(1) = zidsn(ji) + z1midsn(ji) * h_snow_1d(ji) & |
---|
420 | & + sbeta * z1midsn(ji) * zkhsnint |
---|
421 | zplediag(2) = 1 + sbeta * ( z1midsn(ji) * zkhicint + zkhic ) |
---|
422 | zplediag(3) = 1 + 3.0 * sbeta * zkhic |
---|
423 | |
---|
424 | zsubdiag(1) = 0.e0 |
---|
425 | zsubdiag(2) = -1.e0 * z1midsn(ji) * sbeta * zkhicint |
---|
426 | zsubdiag(3) = -1.e0 * sbeta * zkhic |
---|
427 | |
---|
428 | zsupdiag(1) = -1.e0 * z1midsn(ji) * sbeta * zkhsnint |
---|
429 | zsupdiag(2) = zsubdiag(3) |
---|
430 | zsupdiag(3) = 0.e0 |
---|
431 | |
---|
432 | ! 6.3. Fulfill the idependent term vector. |
---|
433 | !------------------------------------------- |
---|
434 | |
---|
435 | !$$$ zsmbr(1) = zidsn(ji) * sist_1d(ji) + z1midsn(ji) * & |
---|
436 | !$$$ & ( tbif_1d(ji,1) + zkhsn * sist_1d(ji) |
---|
437 | !$$$ & - zumsb * ( zkhsn * tbif_1d(ji,1) |
---|
438 | !$$$ & + zkhsnint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) ) ) |
---|
439 | zsmbr(1) = zidsn(ji) * sist_1d(ji) + z1midsn(ji) * & |
---|
440 | & ( h_snow_1d(ji) * tbif_1d(ji,1) - ( zfcsudt(ji) / rcpsn ) & |
---|
441 | & - zumsb * zkhsnint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) ) |
---|
442 | |
---|
443 | zsmbr(2) = tbif_1d(ji,2) & |
---|
444 | & - zidsn(ji) * ( 1.0 - zidsnic(ji) ) & |
---|
445 | & * ( zfcsudt(ji) / MAX( h_ice_1d(ji) * rcpic , epsi20 ) ) & |
---|
446 | & + zumsb * ( zkhicint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) & |
---|
447 | & - zkhic * ( tbif_1d(ji,2) - tbif_1d(ji,3) ) ) |
---|
448 | |
---|
449 | zsmbr(3) = tbif_1d(ji,3) & |
---|
450 | & + zkhic * ( 2.0 * tfu_1d(ji) & |
---|
451 | & + zumsb * ( tbif_1d(ji,2) - 3.0 * tbif_1d(ji,3) ) ) |
---|
452 | |
---|
453 | ! 6.4. Solve the system (Gauss elimination method). |
---|
454 | !---------------------------------------------------- |
---|
455 | |
---|
456 | zpiv1 = zsubdiag(2) / zplediag(1) |
---|
457 | zb2 = zplediag(2) - zpiv1 * zsupdiag(1) |
---|
458 | zd2 = zsmbr(2) - zpiv1 * zsmbr(1) |
---|
459 | |
---|
460 | zpiv2 = zsubdiag(3) / zb2 |
---|
461 | zb3 = zplediag(3) - zpiv2 * zsupdiag(2) |
---|
462 | zd3 = zsmbr(3) - zpiv2 * zd2 |
---|
463 | |
---|
464 | tbif_1d(ji,3) = zd3 / zb3 |
---|
465 | tbif_1d(ji,2) = ( zd2 - zsupdiag(2) * tbif_1d(ji,3) ) / zb2 |
---|
466 | tbif_1d(ji,1) = ( zsmbr(1) - zsupdiag(1) * tbif_1d(ji,2) ) / zplediag(1) |
---|
467 | |
---|
468 | !--- taking into account the particular case of zidsnic(ji) = 1 |
---|
469 | ztint = ( zkic(ji) * h_snow_1d(ji) * tfu_1d (ji) & |
---|
470 | & + zksn(ji) * h_ice_1d(ji) * sist_1d(ji) ) & |
---|
471 | & / ( zkic(ji) * h_snow_1d(ji) + zksn(ji) * h_ice_1d(ji) ) |
---|
472 | |
---|
473 | tbif_1d(ji,1) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,1) & |
---|
474 | & + zidsnic(ji) * ( ztint + sist_1d(ji) ) / 2.0 |
---|
475 | tbif_1d(ji,2) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,2) & |
---|
476 | & + zidsnic(ji) * ( 3.0 * ztint + tfu_1d(ji) ) / 4.0 |
---|
477 | tbif_1d(ji,3) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,3) & |
---|
478 | & + zidsnic(ji) * ( ztint + 3.0 * tfu_1d(ji) ) / 4.0 |
---|
479 | END DO |
---|
480 | |
---|
481 | !---------------------------------------------------------------------- |
---|
482 | ! 9. Take into account surface ablation and bottom accretion-ablation.| |
---|
483 | !---------------------------------------------------------------------- |
---|
484 | |
---|
485 | !---Snow accumulation in one thermodynamic time step |
---|
486 | zsprecip(kideb:kiut) = sprecip_1d(kideb:kiut) * rdt_ice / rhosn |
---|
487 | |
---|
488 | |
---|
489 | DO ji = kideb, kiut |
---|
490 | |
---|
491 | ! 9.1. Surface ablation and update of snow thickness and qstbif_1d |
---|
492 | !-------------------------------------------------------------------- |
---|
493 | |
---|
494 | !-------------------------------------------------------------------------- |
---|
495 | !-- Melting snow processes : |
---|
496 | !-- Melt at the upper surface is computed from the difference between |
---|
497 | !-- the net heat flux (including the conductive heat flux) at the upper |
---|
498 | !-- surface and the pre-existing energy due to surface melting |
---|
499 | !------------------------------------------------------------------------------ |
---|
500 | |
---|
501 | !-- store the snow thickness |
---|
502 | zhsnw_old(ji) = h_snow_1d(ji) |
---|
503 | !--computation of the energy needed to melt snow |
---|
504 | zqsnw_mlt = zfnet(ji) * rdt_ice - zqcmlt(ji,1) |
---|
505 | !--change in snow thickness due to melt |
---|
506 | zdhsmlt = - zqsnw_mlt / xlsn |
---|
507 | |
---|
508 | !-- compute new snow thickness, taking into account the part of snow accumulation |
---|
509 | ! (as snow precipitation) and the part of snow lost due to melt |
---|
510 | zhsn = h_snow_1d(ji) + zsprecip(ji) + zdhsmlt |
---|
511 | h_snow_1d(ji) = MAX( zzero , zhsn ) |
---|
512 | !-- compute the volume of snow lost after surface melting and the associated mass |
---|
513 | dvsbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * ( h_snow_1d(ji) - zhsnw_old(ji) - zsprecip(ji) ) |
---|
514 | dvsbq_1d(ji) = MIN( zzero , dvsbq_1d(ji) ) |
---|
515 | rdmsnif_1d(ji) = rhosn * dvsbq_1d(ji) |
---|
516 | !-- If the snow is completely melted the remaining heat is used to melt ice |
---|
517 | zqsn_mlt_rem = MAX( zzero , -zhsn ) * xlsn |
---|
518 | zqice_top_mlt = zqsn_mlt_rem |
---|
519 | zqstbif_old = qstbif_1d(ji) |
---|
520 | |
---|
521 | !-------------------------------------------------------------------------- |
---|
522 | !-- Melting ice processes at the top surface : |
---|
523 | !-- The energy used to melt ice, zqice_top_mlt, is taken from the energy |
---|
524 | !-- stored in brine pockets qstbif_1d and the remaining energy coming |
---|
525 | !-- from the melting snow process zqsn_mlt_rem. |
---|
526 | !-- If qstbif_1d > zqsn_mlt_rem then, one uses only a zqsn_mlt_rem part |
---|
527 | !-- of qstbif_1d to melt ice, |
---|
528 | !-- zqice_top_mlt = zqice_top_mlt + zqsn_mlt_rem |
---|
529 | !-- qstbif_1d = qstbif_1d - zqsn_mlt_rem |
---|
530 | !-- Otherwise one uses all qstbif_1d to melt ice |
---|
531 | !-- zqice_top_mlt = zqice_top_mlt + qstbif_1d |
---|
532 | !-- qstbif_1d = 0 |
---|
533 | !------------------------------------------------------ |
---|
534 | |
---|
535 | ziqf = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqsn_mlt_rem ) ) |
---|
536 | zqice_top_mlt = ziqf * ( zqice_top_mlt + zqsn_mlt_rem ) & |
---|
537 | & + ( 1.0 - ziqf ) * ( zqice_top_mlt + qstbif_1d(ji) ) |
---|
538 | |
---|
539 | qstbif_1d(ji) = ziqf * ( qstbif_1d(ji) - zqsn_mlt_rem ) & |
---|
540 | & + ( 1.0 - ziqf ) * ( qstbif_1d(ji) - qstbif_1d(ji) ) |
---|
541 | |
---|
542 | !-- The contribution of the energy stored in brine pockets qstbif_1d to melt |
---|
543 | !-- ice is taking into account only when qstbif_1d is less than zqmax. |
---|
544 | !-- Otherwise, only the remaining energy coming from the melting snow |
---|
545 | !-- process is used |
---|
546 | zihq = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) |
---|
547 | |
---|
548 | zqice_top_mlt = zihq * zqice_top_mlt & |
---|
549 | & + ( 1.0 - zihq ) * zqsn_mlt_rem |
---|
550 | |
---|
551 | qstbif_1d(ji) = zihq * qstbif_1d(ji) & |
---|
552 | & + ( 1.0 - zihq ) * zqstbif_old |
---|
553 | |
---|
554 | !--change in ice thickness due to melt at the top surface |
---|
555 | zdhictop(ji) = -zqice_top_mlt / xlic |
---|
556 | !--compute the volume formed after surface melting |
---|
557 | dvsbq_1d(ji) = zdhictop(ji) * ( 1.0 - frld_1d(ji) ) |
---|
558 | |
---|
559 | !------------------------------------------------------------------------- |
---|
560 | !-- A small variation at the surface also occurs because of sublimation |
---|
561 | !-- associated with the latent flux. If qla_ice_1d is negative, snow condensates at |
---|
562 | ! the surface. Otherwise, snow evaporates |
---|
563 | !----------------------------------------------------------------------- |
---|
564 | !----change in snow and ice thicknesses due to sublimation or evaporation |
---|
565 | zdhssub = parsub * ( qla_ice_1d(ji) / ( rhosn * xsn ) ) * rdt_ice |
---|
566 | zhsn = h_snow_1d(ji) - zdhssub |
---|
567 | zdhisub = MAX( zzero , -zhsn ) * rhosn/rhoic |
---|
568 | zdhictop(ji) = zdhictop(ji) - zdhisub |
---|
569 | h_snow_1d(ji) = MAX( zzero , zhsn ) |
---|
570 | !------------------------------------------------- |
---|
571 | !-- Update Internal temperature and qstbif_1d. |
---|
572 | !------------------------------------------- |
---|
573 | zihsn = MAX( zzero , SIGN( zone, -h_snow_1d(ji) ) ) |
---|
574 | tbif_1d(ji,1) = ( 1.0 - zihsn ) * tbif_1d(ji,1) + zihsn * tfu_1d(ji) |
---|
575 | !--change in snow internal temperature if snow has increased |
---|
576 | zihnf = MAX( zzero , SIGN( zone , h_snow_1d(ji) - zhsnw_old(ji) ) ) |
---|
577 | zdhsn = 1.0 - zhsnw_old(ji) / MAX( h_snow_1d(ji) , epsi20 ) |
---|
578 | zdtsn = zdhsn * ( sist_1d(ji) - tbif_1d(ji,1) ) |
---|
579 | tbif_1d(ji,1) = tbif_1d(ji,1) + z1midsn(ji) * zihnf * zdtsn |
---|
580 | !--energy created due to ice melting in the first ice layer |
---|
581 | zqnes = ( rt0_ice - tbif_1d(ji,2) ) * rcpic * ( h_ice_1d(ji) / 2. ) |
---|
582 | !--change in first ice layer internal temperature |
---|
583 | ziqr = MAX( zzero , SIGN( zone , qstbif_1d(ji) - zqnes ) ) |
---|
584 | zdtic = qstbif_1d(ji) / ( rcpic * ( h_ice_1d(ji) / 2. ) ) |
---|
585 | tbif_1d(ji,2) = ziqr * rt0_ice + ( 1 - ziqr ) * ( tbif_1d(ji,2) + zdtic ) |
---|
586 | !--update qstbif_1d |
---|
587 | qstbif_1d(ji) = ziqr * ( qstbif_1d(ji) - zqnes ) * swiqst |
---|
588 | |
---|
589 | |
---|
590 | !-- 9.2. Calculate bottom accretion-ablation and update qstbif_1d. |
---|
591 | ! Growth and melting at bottom ice surface are governed by |
---|
592 | ! -xlic * Dh = (Fcb - Fbot ) * Dt |
---|
593 | ! where Fbot is the net downward heat flux from ice to the ocean |
---|
594 | ! and Fcb is the conductive heat flux at the bottom surface |
---|
595 | !--------------------------------------------------------------------------- |
---|
596 | ztbot = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,3) + zidsnic(ji) * sist_1d(ji) |
---|
597 | !---computes conductive heat flux at bottom surface |
---|
598 | zfcbot = 4.0 * zkic(ji) * ( tfu_1d(ji) - ztbot ) & |
---|
599 | & / ( h_ice_1d(ji) + zidsnic(ji) * ( 3. * h_ice_1d(ji) & |
---|
600 | & + 4.0 * zkic(ji)/zksn(ji) * h_snow_1d(ji) ) ) |
---|
601 | !---computation of net energy needed for bottom melting/growing |
---|
602 | zqice_bot = ( zfcbot - ( fbif_1d(ji) + qlbbq_1d(ji) ) ) * rdt_ice |
---|
603 | zqstbif_bot = qstbif_1d(ji) |
---|
604 | !---switch to know if bottom surface melts ( = 1 ) or grows ( = 0 )occurs |
---|
605 | zibmlt = MAX( zzero , SIGN( zone , -zqice_bot ) ) |
---|
606 | !--particular case of melting (in the same way as the top surface) |
---|
607 | zqice_bot_mlt = zqice_bot |
---|
608 | zqstbif_old = zqstbif_bot |
---|
609 | |
---|
610 | ziqf = MAX ( zzero , SIGN( zone , qstbif_1d(ji) + zqice_bot_mlt ) ) |
---|
611 | zqice_bot_mlt = ziqf * ( zqice_bot_mlt + zqice_bot_mlt ) & |
---|
612 | & + ( 1.0 - ziqf ) * ( zqice_bot_mlt + qstbif_1d(ji) ) |
---|
613 | qstbif_1d(ji) = ziqf * ( qstbif_1d(ji) + zqice_bot_mlt ) & |
---|
614 | & + ( 1.0 - ziqf ) * ( qstbif_1d(ji) - qstbif_1d(ji) ) |
---|
615 | !-- The contribution of the energy stored in brine pockets qstbif_1d to melt |
---|
616 | !-- ice is taking into account only when qstbif_1d is less than zqmax. |
---|
617 | zihq = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) |
---|
618 | zqice_bot_mlt = zihq * zqice_bot_mlt & |
---|
619 | & + ( 1.0 - zihq ) * zqice_bot |
---|
620 | qstbif_1d(ji) = zihq * qstbif_1d(ji) & |
---|
621 | & + ( 1.0 - zihq ) * zqstbif_old |
---|
622 | |
---|
623 | !---treatment of the case of melting/growing |
---|
624 | zqice_bot = zibmlt * ( zqice_bot_mlt - zqcmlt(ji,2) ) & |
---|
625 | & + ( 1.0 - zibmlt ) * ( zqice_bot - zqcmlt(ji,2) ) |
---|
626 | qstbif_1d(ji) = zibmlt * qstbif_1d(ji) & |
---|
627 | & + ( 1.0 - zibmlt ) * zqstbif_bot |
---|
628 | |
---|
629 | !--computes change in ice thickness due to melt or growth |
---|
630 | zdhicbot(ji) = zqice_bot / xlic |
---|
631 | !--limitation of bottom melting if so : hmelt maximum melting at bottom |
---|
632 | zdhicmlt = MAX( hmelt , zdhicbot(ji) ) |
---|
633 | !--energy after bottom melting/growing |
---|
634 | zqsup(ji) = ( 1.0 - frld_1d(ji) ) * xlic * ( zdhicmlt - zdhicbot(ji) ) |
---|
635 | !-- compute the new thickness and the newly formed volume after bottom melting/growing |
---|
636 | zdhicbot(ji) = zdhicmlt |
---|
637 | dvbbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * zdhicbot(ji) |
---|
638 | |
---|
639 | |
---|
640 | ! 9.3. Updating ice thickness after top surface ablation |
---|
641 | ! and bottom surface accretion/ablation |
---|
642 | !--------------------------------------------------------------- |
---|
643 | zhicnew = h_ice_1d(ji) + zdhictop(ji) + zdhicbot(ji) |
---|
644 | |
---|
645 | ! |
---|
646 | ! 9.4. Case of total ablation (ice is gone but snow may be left) |
---|
647 | !------------------------------------------------------------------- |
---|
648 | zhsn = h_snow_1d(ji) |
---|
649 | zihgnew = 1.0 - MAX( zzero , SIGN( zone , -zhicnew ) ) |
---|
650 | zihsn = MAX( zzero , SIGN( zone , -zhsn ) ) |
---|
651 | !---convert |
---|
652 | zdhicm = ( 1.0 - zihgnew ) * ( zhicnew - qstbif_1d(ji) / xlic ) |
---|
653 | zdhsnm = ( 1.0 - zihsn ) * zdhicm * rhoic / rhosn |
---|
654 | !---updating new ice thickness and computing the newly formed ice mass |
---|
655 | zhicnew = zihgnew * zhicnew |
---|
656 | rdmicif_1d(ji) = rdmicif_1d(ji) + ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d(ji) ) * rhoic |
---|
657 | !---updating new snow thickness and computing the newly formed snow mass |
---|
658 | zhsnfi = zhsn + zdhsnm |
---|
659 | h_snow_1d(ji) = MAX( zzero , zhsnfi ) |
---|
660 | rdmsnif_1d(ji) = rdmsnif_1d(ji) + ( 1.0 - frld_1d(ji) ) * ( h_snow_1d(ji) - zhsn ) * rhosn |
---|
661 | !--remaining energy in case of total ablation |
---|
662 | zqocea(ji) = - ( zihsn * xlic * zdhicm + xlsn * ( zhsnfi - h_snow_1d(ji) ) ) * ( 1.0 - frld_1d(ji) ) |
---|
663 | qstbif_1d(ji) = zihgnew * qstbif_1d(ji) |
---|
664 | |
---|
665 | ! |
---|
666 | ! 9.5. Update internal temperature and ice thickness. |
---|
667 | !------------------------------------------------------- |
---|
668 | ! |
---|
669 | sist_1d(ji) = zihgnew * sist_1d(ji) + ( 1.0 - zihgnew ) * tfu_1d(ji) |
---|
670 | zidhb = MAX( zzero , SIGN( zone , - zdhicbot(ji) ) ) |
---|
671 | zc1 = - zhicnew * 0.5 |
---|
672 | zpc1 = MIN( 0.5 * zone , - h_ice_1d(ji) * 0.5 - zdhictop(ji) ) |
---|
673 | zc2 = - zhicnew |
---|
674 | zpc2 = zidhb * zc2 + ( 1.0 - zidhb ) * ( - h_ice_1d(ji) - zdhictop(ji) ) |
---|
675 | zp1 = MAX( zpc1 , zc1 ) |
---|
676 | zp2 = MAX( zpc2 , zc1 ) |
---|
677 | zep(ji) = tbif_1d(ji,2) |
---|
678 | ztb2 = 2.0 * ( - zp1 * tbif_1d(ji,2) & |
---|
679 | & + ( zp1 - zp2 ) * tbif_1d(ji,3) & |
---|
680 | & + ( zp2 - zc1 ) * tfu_1d(ji) ) / MAX( zhicnew , epsi20 ) |
---|
681 | tbif_1d(ji,2) = zihgnew * ztb2 + ( 1.0 - zihgnew ) * tfu_1d(ji) |
---|
682 | !--- |
---|
683 | zp1 = MIN( zpc1 , zc1 ) |
---|
684 | zp2 = MIN( zpc2 , zc1 ) |
---|
685 | zp1 = MAX( zc2 , zp1 ) |
---|
686 | ztb3 = 2.0 * ( ( 1.0 - zidhb ) * ( ( zc1 - zp2 ) * tbif_1d(ji,3) & |
---|
687 | & + ( zp2 - zc2 ) * tfu_1d(ji) ) & |
---|
688 | & + zidhb * ( ( zc1 - zp1 ) * zep(ji) & |
---|
689 | & + ( zp1 - zc2 ) * tbif_1d(ji,3)) ) / MAX( zhicnew , epsi20 ) |
---|
690 | tbif_1d(ji,3) = zihgnew * ztb3 + ( 1.0 - zihgnew ) * tfu_1d(ji) |
---|
691 | h_ice_1d(ji) = zhicnew |
---|
692 | END DO |
---|
693 | |
---|
694 | |
---|
695 | !---------------------------------------------------------------------------- |
---|
696 | ! 10. Surface accretion. |
---|
697 | ! The change of ice thickness after snow/ice formation is such that |
---|
698 | ! the interface between snow and ice is located at the same height |
---|
699 | ! as the ocean surface. It is given by (Fichefet and Morales Maqueda 1999) |
---|
700 | ! D(h_ice) = (- D(hsn)/alph) = [rhosn*hsn - (rau0 - rhoic)*hic] |
---|
701 | ! / [alph*rhosn+rau0 - rhoic] |
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702 | !---------------------------------------------------------------------------- |
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703 | ! |
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704 | DO ji = kideb , kiut |
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705 | |
---|
706 | !-- Computation of the change of ice thickness after snow-ice formation |
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707 | zdrmh = ( rhosn * h_snow_1d(ji) + ( rhoic - rau0 ) * h_ice_1d(ji) ) & |
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708 | & / ( alphs * rhosn + rau0 - rhoic ) |
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709 | zdrmh = MAX( zzero , zdrmh ) |
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710 | |
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711 | !--New ice and snow thicknesses Fichefet and Morales Maqueda (1999) |
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712 | zhicnew = MAX( h_ice_1d(ji) , h_ice_1d(ji) + zdrmh ) |
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713 | zhsnnew = MIN( h_snow_1d(ji) , h_snow_1d(ji) - alphs * zdrmh ) |
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714 | !---Compute new ice temperatures. snow temperature remains unchanged |
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715 | ! Lepparanta (1983): |
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716 | zihic = 1.0 - MAX( zzero , SIGN( zone , -zhicnew ) ) |
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717 | zquot = ( 1.0 - zihic ) & |
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718 | & + zihic * MIN( zone , h_ice_1d(ji) / MAX( zhicnew , epsi20 ) ) |
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719 | ztneq = alphs * cnscg * tbif_1d(ji,1) & |
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720 | & + ( 1.0 - alphs * ( rhosn/rhoic ) ) * tfu_1d(ji) |
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721 | zep(ji) = tbif_1d(ji,2) |
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722 | tbif_1d(ji,2) = ztneq - zquot * zquot * ( ztneq - tbif_1d(ji,2) ) |
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723 | tbif_1d(ji,3) = 2.0 * ztneq & |
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724 | & + zquot * ( tbif_1d(ji,3) + zep(ji) - 2.0 * ztneq ) - tbif_1d(ji,2) |
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725 | |
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726 | !--- Lepparanta (1983) (latent heat released during white ice formation |
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727 | ! goes to the ocean -for lateral ablation-) |
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728 | qldif_1d(ji) = qldif_1d(ji) + zdrmh * ( 1.0 - alphs * ( rhosn/rhoic ) ) * xlic * ( 1.0 - frld_1d(ji) ) |
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729 | !-- Changes in ice volume and ice mass Lepparanta (1983): |
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730 | dvnbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d(ji) ) |
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731 | dmgwi_1d(ji) = dmgwi_1d(ji) + ( 1.0 -frld_1d(ji) ) * ( h_snow_1d(ji) - zhsnnew ) * rhosn |
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732 | ! case of natural freshwater flux |
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733 | #if defined key_lim_fdd |
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734 | rdmicif_1d(ji) = rdmicif_1d(ji) + ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d(ji) ) * rhoic |
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735 | rdmsnif_1d(ji) = rdmsnif_1d(ji) + ( 1.0 - frld_1d(ji) ) * ( zhsnnew - h_snow_1d(ji) ) * rhosn |
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736 | |
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737 | #else |
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738 | rdmicif_1d(ji) = rdmicif_1d(ji) + ( 1.0 - frld_1d(ji) ) * ( ( zhicnew - h_ice_1d(ji) ) * rhoic & |
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739 | & + ( zhsnnew - h_snow_1d(ji) ) * rhosn ) |
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740 | #endif |
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741 | |
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742 | !--- Actualize new snow and ice thickness. |
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743 | |
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744 | h_snow_1d(ji) = zhsnnew |
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745 | h_ice_1d(ji) = zhicnew |
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746 | |
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747 | END DO |
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748 | |
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749 | !---------------------------------------------------- |
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750 | ! 11. Lateral ablation (Changes in sea/ice fraction) |
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751 | !---------------------------------------------------- |
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752 | DO ji = kideb , kiut |
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753 | zfrl_old(ji) = frld_1d(ji) |
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754 | zihic = 1.0 - MAX( zzero , SIGN( zone , -h_ice_1d(ji) ) ) |
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755 | zihsn = 1.0 - MAX( zzero , SIGN( zone , -h_snow_1d(ji) ) ) |
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756 | !--In the case of total ablation (all the ice ice has melted) frld = 1 |
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757 | frld_1d(ji) = ( 1.0 - zihic ) + zihic * zfrl_old(ji) |
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758 | !--Part of solar radiation absorbing inside the ice and going |
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759 | !--through the ocean |
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760 | fscbq_1d(ji) = ( 1.0 - zfrl_old(ji) ) * ( 1.0 - thcm_1d(ji) ) * fstbif_1d(ji) |
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761 | !--Total remaining energy after bottom melting/growing |
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762 | qfvbq_1d(ji) = zqsup(ji) + ( 1.0 - zihic ) * zqocea(ji) |
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763 | !--Updating of total heat from the ocean |
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764 | qldif_1d(ji) = qldif_1d(ji) + qfvbq_1d(ji) + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice |
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765 | !--Computation of total heat inside the snow/ice system |
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766 | zqice = h_snow_1d(ji) * xlsn + h_ice_1d(ji) * xlic |
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767 | zqicetot = ( 1.0 - frld_1d(ji) ) * zqice |
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768 | !--The concentration of ice is reduced (frld increases) if the heat |
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769 | !--exchange between ice and ocean is positive |
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770 | ziqf = MAX( zzero , SIGN( zone , zqicetot - qldif_1d(ji) ) ) |
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771 | zdfrl = qldif_1d(ji) / MAX( epsi20 , zqice ) |
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772 | frld_1d(ji) = ( 1.0 - ziqf ) & |
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773 | & + ziqf * ( frld_1d(ji) + MAX( zzero , zdfrl ) ) |
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774 | fltbif_1d(ji) = ( ( 1.0 - zfrl_old(ji) ) * qstbif_1d(ji) - zqicetot ) / rdt_ice |
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775 | !-- Opening of leads: Hakkinen & Mellor, 1992. |
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776 | zdfrl = - ( zdhictop(ji) + zdhicbot(ji) ) * hakspl * ( 1.0 - zfrl_old(ji) ) & |
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777 | & / MAX( epsi13 , h_ice_1d(ji) + h_snow_1d(ji) * rhosn/rhoic ) |
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778 | zfrld_1d(ji) = frld_1d(ji) + MAX( zzero , zdfrl ) |
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779 | !--Limitation of sea-ice fraction <= 1 |
---|
780 | zfrld_1d(ji) = ziqf * MIN( 0.99 * zone , zfrld_1d(ji) ) + ( 1 - ziqf ) |
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781 | !---Update surface and internal temperature and snow/ice thicknesses. |
---|
782 | sist_1d(ji) = sist_1d(ji) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - sist_1d(ji) ) |
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783 | tbif_1d(ji,1) = tbif_1d(ji,1) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,1) ) |
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784 | tbif_1d(ji,2) = tbif_1d(ji,2) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,2) ) |
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785 | tbif_1d(ji,3) = tbif_1d(ji,3) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,3) ) |
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786 | !--variation of ice volume and ice mass |
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787 | dvlbq_1d(ji) = zihic * ( zfrl_old(ji) - frld_1d(ji) ) * h_ice_1d(ji) |
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788 | rdmicif_1d(ji) = rdmicif_1d(ji) + dvlbq_1d(ji) * rhoic |
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789 | !--variation of snow volume and snow mass |
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790 | zdvsnvol = zihsn * ( zfrl_old(ji) - frld_1d(ji) ) * h_snow_1d(ji) |
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791 | rdmsnif_1d(ji) = rdmsnif_1d(ji) + zdvsnvol * rhosn |
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792 | h_snow_1d(ji) = ziqf * h_snow_1d(ji) |
---|
793 | |
---|
794 | zdrfrl1 = ziqf * ( 1.0 - frld_1d(ji) ) / MAX( epsi20 , 1.0 - zfrld_1d(ji) ) |
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795 | zdrfrl2 = ziqf * ( 1.0 - zfrl_old(ji) ) / MAX( epsi20 , 1.0 - zfrld_1d(ji) ) |
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796 | |
---|
797 | h_snow_1d (ji) = zdrfrl1 * h_snow_1d(ji) |
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798 | h_ice_1d (ji) = zdrfrl1 * h_ice_1d(ji) |
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799 | qstbif_1d(ji) = zdrfrl2 * qstbif_1d(ji) |
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800 | frld_1d(ji) = zfrld_1d(ji) |
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801 | |
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802 | END DO |
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803 | |
---|
804 | END SUBROUTINE lim_thd_zdf |
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805 | #else |
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806 | !!====================================================================== |
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807 | !! *** MODULE limthd_zdf *** |
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808 | !! no sea ice model |
---|
809 | !!====================================================================== |
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810 | CONTAINS |
---|
811 | SUBROUTINE lim_thd_zdf ! Empty routine |
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812 | END SUBROUTINE lim_thd_zdf |
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813 | #endif |
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814 | END MODULE limthd_zdf |
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