1 | MODULE icethd_zdf |
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2 | !!====================================================================== |
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3 | !! *** MODULE icethd_zdf *** |
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4 | !! sea-ice: vertical heat diffusion in sea ice (computation of temperatures) |
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5 | !!====================================================================== |
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6 | !! History : LIM ! 02-2003 (M. Vancoppenolle) original 1D code |
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7 | !! ! 06-2005 (M. Vancoppenolle) 3d version |
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8 | !! ! 11-2006 (X Fettweis) Vectorization by Xavier |
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9 | !! ! 04-2007 (M. Vancoppenolle) Energy conservation |
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10 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
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11 | !! - ! 2012-05 (C. Rousset) add penetration solar flux |
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12 | !!---------------------------------------------------------------------- |
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13 | #if defined key_lim3 |
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14 | !!---------------------------------------------------------------------- |
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15 | !! 'key_lim3' ESIM sea-ice model |
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16 | !!---------------------------------------------------------------------- |
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17 | USE dom_oce ! ocean space and time domain |
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18 | USE phycst ! physical constants (ocean directory) |
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19 | USE ice ! sea-ice: variables |
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20 | USE ice1D ! sea-ice: thermodynamics variables |
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21 | ! |
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22 | USE in_out_manager ! I/O manager |
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23 | USE lib_mpp ! MPP library |
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24 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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25 | |
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26 | IMPLICIT NONE |
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27 | PRIVATE |
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28 | |
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29 | PUBLIC ice_thd_zdf ! called by icethd |
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30 | PUBLIC ice_thd_zdf_init ! called by icestp |
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31 | |
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32 | !!** namelist (namthd_zdf) ** |
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33 | LOGICAL :: ln_zdf_Beer ! Heat diffusion follows a Beer Law |
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34 | LOGICAL :: ln_cndi_U64 ! thermal conductivity: Untersteiner (1964) |
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35 | LOGICAL :: ln_cndi_P07 ! thermal conductivity: Pringle et al (2007) |
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36 | REAL(wp) :: rn_cnd_s ! thermal conductivity of the snow [W/m/K] |
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37 | REAL(wp) :: rn_kappa_i ! coef. for the extinction of radiation Grenfell et al. (2006) [1/m] |
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38 | LOGICAL :: ln_dqns_i ! change non-solar surface flux with changing surface temperature (T) or not (F) |
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39 | |
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40 | !!---------------------------------------------------------------------- |
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41 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
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42 | !! $Id: icethd_zdf.F90 8420 2017-08-08 12:18:46Z clem $ |
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43 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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44 | !!---------------------------------------------------------------------- |
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45 | CONTAINS |
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46 | |
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47 | SUBROUTINE ice_thd_zdf |
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48 | !!------------------------------------------------------------------- |
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49 | !! *** ROUTINE ice_thd_zdf *** |
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50 | !! ** Purpose : |
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51 | !! This routine determines the time evolution of snow and sea-ice |
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52 | !! temperature profiles. |
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53 | !! ** Method : |
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54 | !! This is done by solving the heat equation diffusion with |
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55 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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56 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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57 | !! The specific heat and thermal conductivities depend on ice salinity |
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58 | !! and temperature to take into account brine pocket melting. The |
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59 | !! numerical |
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60 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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61 | !! in the ice and snow system. |
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62 | !! |
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63 | !! The successive steps of this routine are |
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64 | !! 1. initialization of ice-snow layers thicknesses |
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65 | !! 2. Internal absorbed and transmitted radiation |
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66 | !! Then iterative procedure begins |
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67 | !! 3. Thermal conductivity |
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68 | !! 4. Kappa factors |
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69 | !! 5. specific heat in the ice |
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70 | !! 6. eta factors |
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71 | !! 7. surface flux computation |
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72 | !! 8. tridiagonal system terms |
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73 | !! 9. solving the tridiagonal system with Gauss elimination |
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74 | !! Iterative procedure ends according to a criterion on evolution |
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75 | !! of temperature |
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76 | !! 10. Fluxes at the interfaces |
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77 | !! |
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78 | !! ** Inputs / Ouputs : (global commons) |
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79 | !! surface temperature : t_su_1d |
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80 | !! ice/snow temperatures : t_i_1d, t_s_1d |
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81 | !! ice salinities : s_i_1d |
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82 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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83 | !! total ice/snow thickness : ht_i_1d, ht_s_1d |
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84 | !!------------------------------------------------------------------- |
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85 | INTEGER :: ji, jk ! spatial loop index |
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86 | INTEGER :: numeq ! current reference number of equation |
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87 | INTEGER :: minnumeqmin, maxnumeqmax |
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88 | INTEGER :: iconv ! number of iterations in iterative procedure |
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89 | INTEGER :: iconv_max = 50 ! max number of iterations in iterative procedure |
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90 | |
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91 | INTEGER, DIMENSION(jpij) :: numeqmin ! reference number of top equation |
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92 | INTEGER, DIMENSION(jpij) :: numeqmax ! reference number of bottom equation |
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93 | |
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94 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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95 | REAL(wp) :: zg1 = 2._wp ! |
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96 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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97 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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98 | REAL(wp) :: zraext_s = 10._wp ! extinction coefficient of radiation in the snow |
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99 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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100 | REAL(wp) :: ztsu_err = 1.e-5_wp ! range around which t_su is considered at 0C |
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101 | REAL(wp) :: zdti_bnd = 1.e-4_wp ! maximal authorized error on temperature |
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102 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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103 | REAL(wp) :: z1_hsu |
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104 | REAL(wp) :: zdti_max ! current maximal error on temperature |
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105 | REAL(wp) :: zcpi ! Ice specific heat |
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106 | REAL(wp) :: zhfx_err, zdq ! diag errors on heat |
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107 | REAL(wp) :: zfac ! dummy factor |
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108 | |
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109 | REAL(wp), DIMENSION(jpij) :: isnow ! switch for presence (1) or absence (0) of snow |
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110 | REAL(wp), DIMENSION(jpij) :: ztsub ! surface temperature at previous iteration |
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111 | REAL(wp), DIMENSION(jpij) :: zh_i, z1_h_i ! ice layer thickness |
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112 | REAL(wp), DIMENSION(jpij) :: zh_s, z1_h_s ! snow layer thickness |
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113 | REAL(wp), DIMENSION(jpij) :: zfsw ! solar radiation absorbed at the surface |
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114 | REAL(wp), DIMENSION(jpij) :: zqns_ice_b ! solar radiation absorbed at the surface |
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115 | REAL(wp), DIMENSION(jpij) :: zf ! surface flux function |
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116 | REAL(wp), DIMENSION(jpij) :: zdqns_ice_b ! derivative of the surface flux function |
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117 | REAL(wp), DIMENSION(jpij) :: zftrice ! solar radiation transmitted through the ice |
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118 | |
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119 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztiold ! Old temperature in the ice |
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120 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsold ! Old temperature in the snow |
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121 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztib ! Temporary temperature in the ice to check the convergence |
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122 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsb ! Temporary temperature in the snow to check the convergence |
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123 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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124 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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125 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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126 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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127 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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128 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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129 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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130 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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131 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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132 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindterm ! 'Ind'ependent term |
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133 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindtbis ! Temporary 'ind'ependent term |
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134 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zdiagbis ! Temporary 'dia'gonal term |
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135 | REAL(wp), DIMENSION(jpij,nlay_i+3,3) :: ztrid ! Tridiagonal system terms |
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136 | REAL(wp), DIMENSION(jpij) :: zq_ini ! diag errors on heat |
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137 | REAL(wp), DIMENSION(jpij) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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138 | |
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139 | ! Mono-category |
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140 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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141 | REAL(wp) :: zhe ! dummy factor |
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142 | REAL(wp) :: zcnd_i ! mean sea ice thermal conductivity |
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143 | !!------------------------------------------------------------------ |
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144 | |
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145 | ! --- diag error on heat diffusion - PART 1 --- ! |
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146 | DO ji = 1, nidx |
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147 | zq_ini(ji) = ( SUM( e_i_1d(ji,1:nlay_i) ) * ht_i_1d(ji) * r1_nlay_i + & |
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148 | & SUM( e_s_1d(ji,1:nlay_s) ) * ht_s_1d(ji) * r1_nlay_s ) |
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149 | END DO |
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150 | |
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151 | !------------------ |
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152 | ! 1) Initialization |
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153 | !------------------ |
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154 | DO ji = 1, nidx |
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155 | isnow(ji)= 1._wp - MAX( 0._wp , SIGN(1._wp, - ht_s_1d(ji) ) ) ! is there snow or not |
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156 | ! layer thickness |
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157 | zh_i(ji) = ht_i_1d(ji) * r1_nlay_i |
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158 | zh_s(ji) = ht_s_1d(ji) * r1_nlay_s |
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159 | END DO |
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160 | ! |
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161 | WHERE( zh_i(1:nidx) >= epsi10 ) ; z1_h_i(1:nidx) = 1._wp / zh_i(1:nidx) |
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162 | ELSEWHERE ; z1_h_i(1:nidx) = 0._wp |
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163 | END WHERE |
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164 | |
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165 | WHERE( zh_s(1:nidx) >= epsi10 ) ; z1_h_s(1:nidx) = 1._wp / zh_s(1:nidx) |
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166 | ELSEWHERE ; z1_h_s(1:nidx) = 0._wp |
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167 | END WHERE |
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168 | ! |
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169 | ! temperatures |
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170 | ztsub (1:nidx) = t_su_1d(1:nidx) ! temperature at the previous iteration |
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171 | ztsold (1:nidx,:) = t_s_1d(1:nidx,:) ! Old snow temperature |
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172 | ztiold (1:nidx,:) = t_i_1d(1:nidx,:) ! Old ice temperature |
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173 | t_su_1d(1:nidx) = MIN( t_su_1d(1:nidx), rt0 - ztsu_err ) ! necessary |
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174 | ! |
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175 | !------------- |
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176 | ! 2) Radiation |
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177 | !------------- |
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178 | ! |
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179 | z1_hsu = 1._wp / 0.1_wp ! threshold for the computation of i0 |
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180 | DO ji = 1, nidx |
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181 | ! --- Computation of i0 --- ! |
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182 | ! i0 describes the fraction of solar radiation which does not contribute |
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183 | ! to the surface energy budget but rather penetrates inside the ice. |
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184 | ! We assume that no radiation is transmitted through the snow |
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185 | ! If there is no no snow |
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186 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
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187 | ! zftrice = io.qsr_ice is below the surface |
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188 | ! ftr_ice = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
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189 | ! fr1_i0_1d = i0 for a thin ice cover, fr1_i0_2d = i0 for a thick ice cover |
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190 | zfac = MAX( 0._wp , 1._wp - ( ht_i_1d(ji) * z1_hsu ) ) |
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191 | i0(ji) = ( 1._wp - isnow(ji) ) * ( fr1_i0_1d(ji) + zfac * fr2_i0_1d(ji) ) |
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192 | |
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193 | ! --- Solar radiation absorbed / transmitted at the surface --- ! |
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194 | ! Derivative of the non solar flux |
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195 | zfsw (ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) ! Shortwave radiation absorbed at surface |
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196 | zftrice(ji) = qsr_ice_1d(ji) * i0(ji) ! Solar radiation transmitted below the surface layer |
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197 | zdqns_ice_b(ji) = dqns_ice_1d(ji) ! derivative of incoming nonsolar flux |
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198 | zqns_ice_b (ji) = qns_ice_1d(ji) ! store previous qns_ice_1d value |
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199 | END DO |
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200 | |
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201 | ! --- Transmission/absorption of solar radiation in the ice --- ! |
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202 | zradtr_s(1:nidx,0) = zftrice(1:nidx) |
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203 | DO jk = 1, nlay_s |
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204 | DO ji = 1, nidx |
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205 | ! ! radiation transmitted below the layer-th snow layer |
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206 | zradtr_s(ji,jk) = zradtr_s(ji,0) * EXP( - zraext_s * zh_s(ji) * REAL(jk) ) |
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207 | ! ! radiation absorbed by the layer-th snow layer |
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208 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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209 | END DO |
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210 | END DO |
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211 | |
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212 | zradtr_i(1:nidx,0) = zradtr_s(1:nidx,nlay_s) * isnow(1:nidx) + zftrice(1:nidx) * ( 1._wp - isnow(1:nidx) ) |
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213 | DO jk = 1, nlay_i |
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214 | DO ji = 1, nidx |
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215 | ! ! radiation transmitted below the layer-th ice layer |
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216 | zradtr_i(ji,jk) = zradtr_i(ji,0) * EXP( - rn_kappa_i * zh_i(ji) * REAL(jk) ) |
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217 | ! ! radiation absorbed by the layer-th ice layer |
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218 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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219 | END DO |
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220 | END DO |
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221 | |
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222 | ftr_ice_1d(1:nidx) = zradtr_i(1:nidx,nlay_i) ! record radiation transmitted below the ice |
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223 | ! |
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224 | iconv = 0 ! number of iterations |
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225 | zdti_max = 1000._wp ! maximal value of error on all points |
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226 | ! !----------------------------! |
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227 | DO WHILE ( zdti_max > zdti_bnd .AND. iconv < iconv_max ) ! Iterative procedure begins ! |
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228 | ! !----------------------------! |
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229 | ! |
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230 | iconv = iconv + 1 |
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231 | ! |
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232 | ztib(1:nidx,:) = t_i_1d(1:nidx,:) |
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233 | ztsb(1:nidx,:) = t_s_1d(1:nidx,:) |
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234 | ! |
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235 | !-------------------------------- |
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236 | ! 3) Sea ice thermal conductivity |
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237 | !-------------------------------- |
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238 | IF( ln_cndi_U64 ) THEN !-- Untersteiner (1964) formula: k = k0 + beta.S/T |
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239 | ! |
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240 | DO ji = 1, nidx |
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241 | ztcond_i(ji,0) = rcdic + zbeta * s_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) |
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242 | ztcond_i(ji,nlay_i) = rcdic + zbeta * s_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) |
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243 | END DO |
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244 | DO jk = 1, nlay_i-1 |
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245 | DO ji = 1, nidx |
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246 | ztcond_i(ji,jk) = rcdic + zbeta * 0.5_wp * ( s_i_1d(ji,jk) + s_i_1d(ji,jk+1) ) / & |
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247 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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248 | END DO |
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249 | END DO |
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250 | ! |
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251 | ELSEIF( ln_cndi_P07 ) THEN !-- Pringle et al formula: k = k0 + beta1.S/T - beta2.T |
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252 | ! |
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253 | DO ji = 1, nidx |
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254 | ztcond_i(ji,0) = rcdic + 0.09_wp * s_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) & |
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255 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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256 | ztcond_i(ji,nlay_i) = rcdic + 0.09_wp * s_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) & |
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257 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
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258 | END DO |
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259 | DO jk = 1, nlay_i-1 |
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260 | DO ji = 1, nidx |
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261 | ztcond_i(ji,jk) = rcdic + 0.09_wp * 0.5_wp * ( s_i_1d(ji,jk) + s_i_1d(ji,jk+1) ) / & |
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262 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) & |
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263 | & - 0.011_wp * ( 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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264 | END DO |
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265 | END DO |
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266 | ! |
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267 | ENDIF |
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268 | ztcond_i(1:nidx,:) = MAX( zkimin, ztcond_i(1:nidx,:) ) |
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269 | ! |
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270 | !--- G(he) : enhancement of thermal conductivity in mono-category case |
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271 | ! Computation of effective thermal conductivity G(h) |
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272 | ! Used in mono-category case only to simulate an ITD implicitly |
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273 | ! Fichefet and Morales Maqueda, JGR 1997 |
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274 | |
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275 | zghe(1:nidx) = 1._wp |
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276 | |
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277 | SELECT CASE ( nn_monocat ) |
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278 | |
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279 | CASE ( 1 , 3 ) |
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280 | |
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281 | zepsilon = 0.1_wp |
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282 | DO ji = 1, nidx |
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283 | |
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284 | ! Mean sea ice thermal conductivity |
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285 | zcnd_i = SUM( ztcond_i(ji,:) ) / REAL( nlay_i+1, wp ) |
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286 | |
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287 | ! Effective thickness he (zhe) |
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288 | zhe = ( rn_cnd_s * ht_i_1d(ji) + zcnd_i * ht_s_1d(ji) ) / ( rn_cnd_s + zcnd_i ) |
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289 | |
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290 | ! G(he) |
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291 | IF( zhe >= zepsilon * 0.5_wp * EXP(1._wp) ) THEN |
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292 | zghe(ji) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) ) |
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293 | ENDIF |
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294 | |
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295 | END DO |
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296 | |
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297 | END SELECT |
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298 | ! |
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299 | !----------------- |
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300 | ! 4) kappa factors |
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301 | !----------------- |
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302 | !--- Snow |
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303 | DO jk = 0, nlay_s-1 |
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304 | DO ji = 1, nidx |
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305 | zkappa_s(ji,jk) = zghe(ji) * rn_cnd_s * z1_h_s(ji) |
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306 | END DO |
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307 | END DO |
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308 | DO ji = 1, nidx ! Snow-ice interface |
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309 | zfac = 0.5_wp * ( ztcond_i(ji,0) * zh_s(ji) + rn_cnd_s * zh_i(ji) ) |
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310 | IF( zfac > epsi10 ) THEN |
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311 | zkappa_s(ji,nlay_s) = zghe(ji) * rn_cnd_s * ztcond_i(ji,0) / zfac |
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312 | ELSE |
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313 | zkappa_s(ji,nlay_s) = 0._wp |
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314 | ENDIF |
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315 | END DO |
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316 | |
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317 | !--- Ice |
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318 | DO jk = 0, nlay_i |
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319 | DO ji = 1, nidx |
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320 | zkappa_i(ji,jk) = zghe(ji) * ztcond_i(ji,jk) * z1_h_i(ji) |
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321 | END DO |
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322 | END DO |
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323 | DO ji = 1, nidx ! Snow-ice interface |
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324 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s) * isnow(ji) + zkappa_i(ji,0) * ( 1._wp - isnow(ji) ) |
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325 | END DO |
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326 | ! |
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327 | !-------------------------------------- |
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328 | ! 5) Sea ice specific heat, eta factors |
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329 | !-------------------------------------- |
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330 | DO jk = 1, nlay_i |
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331 | DO ji = 1, nidx |
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332 | zcpi = cpic + zgamma * s_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztiold(ji,jk) - rt0 ), epsi10 ) |
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333 | zeta_i(ji,jk) = rdt_ice * r1_rhoic * z1_h_i(ji) / MAX( epsi10, zcpi ) |
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334 | END DO |
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335 | END DO |
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336 | |
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337 | DO jk = 1, nlay_s |
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338 | DO ji = 1, nidx |
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339 | zeta_s(ji,jk) = rdt_ice * r1_rhosn * r1_cpic * z1_h_s(ji) |
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340 | END DO |
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341 | END DO |
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342 | ! |
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343 | !---------------------------- |
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344 | ! 6) surface flux computation |
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345 | !---------------------------- |
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346 | IF ( ln_dqns_i ) THEN |
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347 | DO ji = 1, nidx |
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348 | ! update of the non solar flux according to the update in T_su |
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349 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsub(ji) ) |
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350 | END DO |
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351 | ENDIF |
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352 | |
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353 | DO ji = 1, nidx |
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354 | zf(ji) = zfsw(ji) + qns_ice_1d(ji) ! incoming = net absorbed solar radiation + non solar total flux (LWup, LWdw, SH, LH) |
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355 | END DO |
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356 | ! |
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357 | !---------------------------- |
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358 | ! 7) tridiagonal system terms |
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359 | !---------------------------- |
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360 | !!layer denotes the number of the layer in the snow or in the ice |
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361 | !!numeq denotes the reference number of the equation in the tridiagonal |
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362 | !!system, terms of tridiagonal system are indexed as following : |
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363 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
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364 | |
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365 | !!ice interior terms (top equation has the same form as the others) |
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366 | |
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367 | DO numeq=1,nlay_i+3 |
---|
368 | DO ji = 1, nidx |
---|
369 | ztrid(ji,numeq,1) = 0. |
---|
370 | ztrid(ji,numeq,2) = 0. |
---|
371 | ztrid(ji,numeq,3) = 0. |
---|
372 | zindterm(ji,numeq)= 0. |
---|
373 | zindtbis(ji,numeq)= 0. |
---|
374 | zdiagbis(ji,numeq)= 0. |
---|
375 | ENDDO |
---|
376 | ENDDO |
---|
377 | |
---|
378 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
379 | DO ji = 1, nidx |
---|
380 | jk = numeq - nlay_s - 1 |
---|
381 | ztrid(ji,numeq,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
382 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
383 | ztrid(ji,numeq,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
384 | zindterm(ji,numeq) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
385 | END DO |
---|
386 | ENDDO |
---|
387 | |
---|
388 | numeq = nlay_s + nlay_i + 1 |
---|
389 | DO ji = 1, nidx |
---|
390 | !!ice bottom term |
---|
391 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
392 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
---|
393 | ztrid(ji,numeq,3) = 0.0 |
---|
394 | zindterm(ji,numeq) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
395 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
396 | ENDDO |
---|
397 | |
---|
398 | |
---|
399 | DO ji = 1, nidx |
---|
400 | ! !---------------------! |
---|
401 | IF ( ht_s_1d(ji) > 0.0 ) THEN ! snow-covered cells ! |
---|
402 | ! !---------------------! |
---|
403 | ! |
---|
404 | !!snow interior terms (bottom equation has the same form as the others) |
---|
405 | DO numeq = 3, nlay_s + 1 |
---|
406 | jk = numeq - 1 |
---|
407 | ztrid(ji,numeq,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
408 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
409 | ztrid(ji,numeq,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
---|
410 | zindterm(ji,numeq) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
411 | END DO |
---|
412 | |
---|
413 | !!case of only one layer in the ice (ice equation is altered) |
---|
414 | IF ( nlay_i == 1 ) THEN |
---|
415 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
416 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
---|
417 | ENDIF |
---|
418 | |
---|
419 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
420 | |
---|
421 | numeqmin(ji) = 1 |
---|
422 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
423 | |
---|
424 | !!surface equation |
---|
425 | ztrid(ji,1,1) = 0.0 |
---|
426 | ztrid(ji,1,2) = zdqns_ice_b(ji) - zg1s * zkappa_s(ji,0) |
---|
427 | ztrid(ji,1,3) = zg1s * zkappa_s(ji,0) |
---|
428 | zindterm(ji,1) = zdqns_ice_b(ji) * t_su_1d(ji) - zf(ji) |
---|
429 | |
---|
430 | !!first layer of snow equation |
---|
431 | ztrid(ji,2,1) = - zkappa_s(ji,0) * zg1s * zeta_s(ji,1) |
---|
432 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
433 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
434 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
---|
435 | |
---|
436 | ELSE !-- case 2 : surface is melting |
---|
437 | ! |
---|
438 | numeqmin(ji) = 2 |
---|
439 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
440 | |
---|
441 | !!first layer of snow equation |
---|
442 | ztrid(ji,2,1) = 0.0 |
---|
443 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
444 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
445 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
446 | & ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
---|
447 | ENDIF |
---|
448 | ! !---------------------! |
---|
449 | ELSE ! cells without snow ! |
---|
450 | ! !---------------------! |
---|
451 | ! |
---|
452 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
453 | ! |
---|
454 | numeqmin(ji) = nlay_s + 1 |
---|
455 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
456 | |
---|
457 | !!surface equation |
---|
458 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
459 | ztrid(ji,numeqmin(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0)*zg1 |
---|
460 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
461 | zindterm(ji,numeqmin(ji)) = zdqns_ice_b(ji)*t_su_1d(ji) - zf(ji) |
---|
462 | |
---|
463 | !!first layer of ice equation |
---|
464 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
465 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
466 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
467 | zindterm(ji,numeqmin(ji)+1)= ztiold(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
---|
468 | |
---|
469 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
470 | |
---|
471 | IF ( nlay_i == 1 ) THEN |
---|
472 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
473 | ztrid(ji,numeqmin(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * 2.0 |
---|
474 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0) * 2.0 |
---|
475 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0) * 2.0 * zeta_i(ji,1) |
---|
476 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
477 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
478 | |
---|
479 | zindterm(ji,numeqmin(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
480 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) |
---|
481 | ENDIF |
---|
482 | |
---|
483 | ELSE !-- case 2 : surface is melting |
---|
484 | |
---|
485 | numeqmin(ji) = nlay_s + 2 |
---|
486 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
487 | |
---|
488 | !!first layer of ice equation |
---|
489 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
490 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
491 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
492 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
493 | & ( zradab_i(ji,1) + zkappa_i(ji,0) * zg1 * t_su_1d(ji) ) |
---|
494 | |
---|
495 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
496 | IF ( nlay_i == 1 ) THEN |
---|
497 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
498 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
499 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
500 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
---|
501 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2.0 |
---|
502 | ENDIF |
---|
503 | |
---|
504 | ENDIF |
---|
505 | ENDIF |
---|
506 | |
---|
507 | END DO |
---|
508 | ! |
---|
509 | !------------------------------ |
---|
510 | ! 8) tridiagonal system solving |
---|
511 | !------------------------------ |
---|
512 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
513 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984. |
---|
514 | |
---|
515 | maxnumeqmax = 0 |
---|
516 | minnumeqmin = nlay_i+5 |
---|
517 | |
---|
518 | DO ji = 1, nidx |
---|
519 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
520 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
521 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
522 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
523 | END DO |
---|
524 | |
---|
525 | DO jk = minnumeqmin+1, maxnumeqmax |
---|
526 | DO ji = 1, nidx |
---|
527 | numeq = min(max(numeqmin(ji)+1,jk),numeqmax(ji)) |
---|
528 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1) * ztrid(ji,numeq-1,3) / zdiagbis(ji,numeq-1) |
---|
529 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1) * zindtbis(ji,numeq-1) / zdiagbis(ji,numeq-1) |
---|
530 | END DO |
---|
531 | END DO |
---|
532 | |
---|
533 | DO ji = 1, nidx |
---|
534 | ! ice temperatures |
---|
535 | t_i_1d(ji,nlay_i) = zindtbis(ji,numeqmax(ji)) / zdiagbis(ji,numeqmax(ji)) |
---|
536 | END DO |
---|
537 | |
---|
538 | DO numeq = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
539 | DO ji = 1, nidx |
---|
540 | jk = numeq - nlay_s - 1 |
---|
541 | t_i_1d(ji,jk) = ( zindtbis(ji,numeq) - ztrid(ji,numeq,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,numeq) |
---|
542 | END DO |
---|
543 | END DO |
---|
544 | |
---|
545 | DO ji = 1, nidx |
---|
546 | ! snow temperatures |
---|
547 | IF( ht_s_1d(ji) > 0._wp ) THEN |
---|
548 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
---|
549 | & / zdiagbis(ji,nlay_s+1) |
---|
550 | ENDIF |
---|
551 | ! surface temperature |
---|
552 | ztsub(ji) = t_su_1d(ji) |
---|
553 | IF( t_su_1d(ji) < rt0 ) THEN |
---|
554 | t_su_1d(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3) * & |
---|
555 | & ( isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) ) ) / zdiagbis(ji,numeqmin(ji)) |
---|
556 | ENDIF |
---|
557 | END DO |
---|
558 | ! |
---|
559 | !-------------------------------------------------------------- |
---|
560 | ! 9) Has the scheme converged ?, end of the iterative procedure |
---|
561 | !-------------------------------------------------------------- |
---|
562 | ! check that nowhere it has started to melt |
---|
563 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
---|
564 | zdti_max = 0._wp |
---|
565 | DO ji = 1, nidx |
---|
566 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , rt0 - 100._wp ) |
---|
567 | zdti_max = MAX( zdti_max, ABS( t_su_1d(ji) - ztsub(ji) ) ) |
---|
568 | END DO |
---|
569 | |
---|
570 | DO jk = 1, nlay_s |
---|
571 | DO ji = 1, nidx |
---|
572 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
---|
573 | zdti_max = MAX( zdti_max, ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
---|
574 | END DO |
---|
575 | END DO |
---|
576 | |
---|
577 | DO jk = 1, nlay_i |
---|
578 | DO ji = 1, nidx |
---|
579 | ztmelt_i = -tmut * s_i_1d(ji,jk) + rt0 |
---|
580 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), rt0 - 100._wp ) |
---|
581 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
---|
582 | END DO |
---|
583 | END DO |
---|
584 | |
---|
585 | ! Compute spatial maximum over all errors |
---|
586 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
587 | IF( lk_mpp ) CALL mpp_max( zdti_max, kcom=ncomm_ice ) |
---|
588 | |
---|
589 | END DO ! End of the do while iterative procedure |
---|
590 | |
---|
591 | IF( ln_icectl .AND. lwp ) THEN |
---|
592 | WRITE(numout,*) ' zdti_max : ', zdti_max |
---|
593 | WRITE(numout,*) ' iconv : ', iconv |
---|
594 | ENDIF |
---|
595 | ! |
---|
596 | !----------------------------- |
---|
597 | ! 10) Fluxes at the interfaces |
---|
598 | !----------------------------- |
---|
599 | DO ji = 1, nidx |
---|
600 | ! ! surface ice conduction flux |
---|
601 | fc_su(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * (t_s_1d(ji,1) - t_su_1d(ji)) & |
---|
602 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_1d(ji,1) - t_su_1d(ji)) |
---|
603 | ! ! bottom ice conduction flux |
---|
604 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_1d(ji) - t_i_1d(ji,nlay_i)) ) |
---|
605 | END DO |
---|
606 | |
---|
607 | ! --- computes sea ice energy of melting compulsory for icethd_dh --- ! |
---|
608 | CALL ice_thd_enmelt |
---|
609 | |
---|
610 | ! --- diagnose the change in non-solar flux due to surface temperature change --- ! |
---|
611 | IF ( ln_dqns_i ) THEN |
---|
612 | DO ji = 1, nidx |
---|
613 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
---|
614 | END DO |
---|
615 | END IF |
---|
616 | |
---|
617 | ! --- diag conservation imbalance on heat diffusion - PART 2 --- ! |
---|
618 | ! hfx_dif = Heat flux used to warm/cool ice in W.m-2 |
---|
619 | ! zhfx_err = correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
---|
620 | DO ji = 1, nidx |
---|
621 | zdq = - zq_ini(ji) + ( SUM( e_i_1d(ji,1:nlay_i) ) * ht_i_1d(ji) * r1_nlay_i + & |
---|
622 | & SUM( e_s_1d(ji,1:nlay_s) ) * ht_s_1d(ji) * r1_nlay_s ) |
---|
623 | |
---|
624 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
---|
625 | zhfx_err = ( qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
---|
626 | ELSE ! case T_su = 0degC |
---|
627 | zhfx_err = ( fc_su(ji) + i0(ji) * qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
---|
628 | ENDIF |
---|
629 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zdq * r1_rdtice * a_i_1d(ji) |
---|
630 | |
---|
631 | ! total heat that is sent to the ocean (i.e. not used in the heat diffusion equation) |
---|
632 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err |
---|
633 | |
---|
634 | END DO |
---|
635 | |
---|
636 | ! --- Diagnostics SIMIP --- ! |
---|
637 | DO ji = 1, nidx |
---|
638 | !--- Conduction fluxes (positive downwards) |
---|
639 | diag_fc_bo_1d(ji) = diag_fc_bo_1d(ji) + fc_bo_i(ji) * a_i_1d(ji) / at_i_1d(ji) |
---|
640 | diag_fc_su_1d(ji) = diag_fc_su_1d(ji) + fc_su(ji) * a_i_1d(ji) / at_i_1d(ji) |
---|
641 | |
---|
642 | !--- Snow-ice interfacial temperature (diagnostic SIMIP) |
---|
643 | zfac = rn_cnd_s * zh_i(ji) + ztcond_i(ji,1) * zh_s(ji) |
---|
644 | IF( zh_s(ji) >= 1.e-3 .AND. zfac > epsi10 ) THEN |
---|
645 | t_si_1d(ji) = ( rn_cnd_s * zh_i(ji) * t_s_1d(ji,1) + & |
---|
646 | & ztcond_i(ji,1) * zh_s(ji) * t_i_1d(ji,1) ) / zfac |
---|
647 | ELSE |
---|
648 | t_si_1d(ji) = t_su_1d(ji) |
---|
649 | ENDIF |
---|
650 | END DO |
---|
651 | ! |
---|
652 | END SUBROUTINE ice_thd_zdf |
---|
653 | |
---|
654 | |
---|
655 | SUBROUTINE ice_thd_enmelt |
---|
656 | !!------------------------------------------------------------------- |
---|
657 | !! *** ROUTINE ice_thd_enmelt *** |
---|
658 | !! |
---|
659 | !! ** Purpose : Computes sea ice energy of melting q_i (J.m-3) from temperature |
---|
660 | !! |
---|
661 | !! ** Method : Formula (Bitz and Lipscomb, 1999) |
---|
662 | !!------------------------------------------------------------------- |
---|
663 | INTEGER :: ji, jk ! dummy loop indices |
---|
664 | REAL(wp) :: ztmelts ! local scalar |
---|
665 | !!------------------------------------------------------------------- |
---|
666 | ! |
---|
667 | DO jk = 1, nlay_i ! Sea ice energy of melting |
---|
668 | DO ji = 1, nidx |
---|
669 | ztmelts = - tmut * s_i_1d(ji,jk) |
---|
670 | t_i_1d(ji,jk) = MIN( t_i_1d(ji,jk), ztmelts + rt0 ) ! Force t_i_1d to be lower than melting point |
---|
671 | ! (sometimes dif scheme produces abnormally high temperatures) |
---|
672 | e_i_1d(ji,jk) = rhoic * ( cpic * ( ztmelts - ( t_i_1d(ji,jk) - rt0 ) ) & |
---|
673 | & + lfus * ( 1._wp - ztmelts / ( t_i_1d(ji,jk) - rt0 ) ) & |
---|
674 | & - rcp * ztmelts ) |
---|
675 | END DO |
---|
676 | END DO |
---|
677 | DO jk = 1, nlay_s ! Snow energy of melting |
---|
678 | DO ji = 1, nidx |
---|
679 | e_s_1d(ji,jk) = rhosn * ( cpic * ( rt0 - t_s_1d(ji,jk) ) + lfus ) |
---|
680 | END DO |
---|
681 | END DO |
---|
682 | ! |
---|
683 | END SUBROUTINE ice_thd_enmelt |
---|
684 | |
---|
685 | |
---|
686 | SUBROUTINE ice_thd_zdf_init |
---|
687 | !!----------------------------------------------------------------------- |
---|
688 | !! *** ROUTINE ice_thd_zdf_init *** |
---|
689 | !! |
---|
690 | !! ** Purpose : Physical constants and parameters associated with |
---|
691 | !! ice thermodynamics |
---|
692 | !! |
---|
693 | !! ** Method : Read the namthd_zdf namelist and check the parameters |
---|
694 | !! called at the first timestep (nit000) |
---|
695 | !! |
---|
696 | !! ** input : Namelist namthd_zdf |
---|
697 | !!------------------------------------------------------------------- |
---|
698 | INTEGER :: ios ! Local integer output status for namelist read |
---|
699 | !! |
---|
700 | NAMELIST/namthd_zdf/ ln_zdf_Beer, ln_cndi_U64, ln_cndi_P07, rn_cnd_s, rn_kappa_i, ln_dqns_i |
---|
701 | !!------------------------------------------------------------------- |
---|
702 | ! |
---|
703 | REWIND( numnam_ice_ref ) ! Namelist namthd_zdf in reference namelist : Ice thermodynamics |
---|
704 | READ ( numnam_ice_ref, namthd_zdf, IOSTAT = ios, ERR = 901) |
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705 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in reference namelist', lwp ) |
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706 | |
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707 | REWIND( numnam_ice_cfg ) ! Namelist namthd_zdf in configuration namelist : Ice thermodynamics |
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708 | READ ( numnam_ice_cfg, namthd_zdf, IOSTAT = ios, ERR = 902 ) |
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709 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in configuration namelist', lwp ) |
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710 | IF(lwm) WRITE ( numoni, namthd_zdf ) |
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711 | ! |
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712 | ! |
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713 | IF(lwp) THEN ! control print |
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714 | WRITE(numout,*) 'ice_thd_zdf_init: Ice vertical heat diffusion' |
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715 | WRITE(numout,*) '~~~~~~~~~~~~~~~~' |
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716 | WRITE(numout,*) ' Namelist namthd_zdf:' |
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717 | WRITE(numout,*) ' Diffusion follows a Beer Law ln_zdf_Beer = ', ln_zdf_Beer |
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718 | WRITE(numout,*) ' thermal conductivity in the ice (Untersteiner 1964) ln_cndi_U64 = ', ln_cndi_U64 |
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719 | WRITE(numout,*) ' thermal conductivity in the ice (Pringle et al 2007) ln_cndi_P07 = ', ln_cndi_P07 |
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720 | WRITE(numout,*) ' thermal conductivity in the snow rn_cnd_s = ', rn_cnd_s |
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721 | WRITE(numout,*) ' extinction radiation parameter in sea ice rn_kappa_i = ', rn_kappa_i |
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722 | WRITE(numout,*) ' change the surface non-solar flux with Tsu or not ln_dqns_i = ', ln_dqns_i |
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723 | ENDIF |
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724 | ! |
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725 | IF ( ( ln_cndi_U64 .AND. ln_cndi_P07 ) .OR. ( .NOT.ln_cndi_U64 .AND. .NOT.ln_cndi_P07 ) ) THEN |
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726 | CALL ctl_stop( 'ice_thd_zdf_init: choose one and only one formulation for thermal conduction (ln_cndi_U64 or ln_cndi_P07)' ) |
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727 | ENDIF |
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728 | ! |
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729 | END SUBROUTINE ice_thd_zdf_init |
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730 | |
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731 | #else |
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732 | !!---------------------------------------------------------------------- |
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733 | !! Default option Dummy Module No ESIM sea-ice model |
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734 | !!---------------------------------------------------------------------- |
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735 | #endif |
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736 | |
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737 | !!====================================================================== |
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738 | END MODULE icethd_zdf |
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