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 | !! ice_thd_zdf : select the appropriate routine for vertical heat diffusion calculation |
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18 | !! ice_thd_zdf_BL99 : |
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19 | !! ice_thd_enmelt : |
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20 | !! ice_thd_zdf_init : |
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21 | !!---------------------------------------------------------------------- |
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22 | USE dom_oce ! ocean space and time domain |
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23 | USE phycst ! physical constants (ocean directory) |
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24 | USE ice ! sea-ice: variables |
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25 | USE ice1D ! sea-ice: thermodynamics variables |
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26 | ! |
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27 | USE in_out_manager ! I/O manager |
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28 | USE lib_mpp ! MPP library |
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29 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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30 | |
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31 | IMPLICIT NONE |
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32 | PRIVATE |
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33 | |
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34 | PUBLIC ice_thd_zdf ! called by icethd |
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35 | PUBLIC ice_thd_zdf_init ! called by icestp |
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36 | |
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37 | !!** namelist (namthd_zdf) ** |
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38 | LOGICAL :: ln_zdf_BL99 ! Heat diffusion follows Bitz and Lipscomb (1999) |
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39 | LOGICAL :: ln_cndi_U64 ! thermal conductivity: Untersteiner (1964) |
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40 | LOGICAL :: ln_cndi_P07 ! thermal conductivity: Pringle et al (2007) |
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41 | REAL(wp) :: rn_kappa_i ! coef. for the extinction of radiation Grenfell et al. (2006) [1/m] |
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42 | REAL(wp), PUBLIC :: rn_cnd_s ! thermal conductivity of the snow [W/m/K] |
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43 | |
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44 | INTEGER :: nice_zdf ! Choice of the type of vertical heat diffusion formulation |
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45 | ! ! associated indices: |
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46 | INTEGER, PARAMETER :: np_BL99 = 1 ! Bitz and Lipscomb (1999) |
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47 | |
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48 | INTEGER, PARAMETER :: np_zdf_jules_OFF = 0 ! compute all temperatures from qsr and qns |
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49 | INTEGER, PARAMETER :: np_zdf_jules_SND = 1 ! compute conductive heat flux and surface temperature from qsr and qns |
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50 | INTEGER, PARAMETER :: np_zdf_jules_RCV = 2 ! compute snow and inner ice temperatures from qcnd |
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51 | |
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52 | !!---------------------------------------------------------------------- |
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53 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
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54 | !! $Id: icethd_zdf.F90 8420 2017-08-08 12:18:46Z clem $ |
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55 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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56 | !!---------------------------------------------------------------------- |
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57 | CONTAINS |
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58 | |
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59 | SUBROUTINE ice_thd_zdf |
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60 | !!------------------------------------------------------------------- |
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61 | !! *** ROUTINE ice_thd_zdf *** |
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62 | !! |
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63 | !! ** Purpose : select the appropriate routine for the computation |
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64 | !! of vertical diffusion |
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65 | !!------------------------------------------------------------------- |
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66 | |
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67 | SELECT CASE ( nice_zdf ) ! Choose the vertical heat diffusion solver |
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68 | ! |
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69 | ! !------------- |
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70 | CASE( np_BL99 ) ! BL99 solver |
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71 | ! !------------- |
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72 | SELECT CASE( nice_jules ) |
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73 | CASE( np_jules_OFF ) ; CALL ice_thd_zdf_BL99 ( np_zdf_jules_OFF ) ! No Jules coupler |
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74 | CASE( np_jules_EMULE ) ; CALL ice_thd_zdf_BL99 ( np_zdf_jules_SND ) ! Jules coupler is emulated (send/recieve) |
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75 | CALL ice_thd_zdf_BL99 ( np_zdf_jules_RCV ) |
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76 | CASE( np_jules_ACTIVE ) ; CALL ice_thd_zdf_BL99 ( np_zdf_jules_RCV ) ! Jules coupler is active (receive only) |
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77 | END SELECT |
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78 | END SELECT |
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79 | |
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80 | END SUBROUTINE ice_thd_zdf |
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81 | |
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82 | |
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83 | SUBROUTINE ice_thd_zdf_BL99( k_jules ) |
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84 | !!------------------------------------------------------------------- |
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85 | !! *** ROUTINE ice_thd_zdf_BL99 *** |
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86 | !! |
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87 | !! ** Purpose : computes the time evolution of snow and sea-ice temperature |
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88 | !! profiles, using the original Bitz and Lipscomb (1999) algorithm |
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89 | !! |
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90 | !! ** Method : solves the heat equation diffusion with a Neumann boundary |
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91 | !! condition at the surface and a Dirichlet one at the bottom. |
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92 | !! Solar radiation is partially absorbed into the ice. |
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93 | !! The specific heat and thermal conductivities depend on ice |
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94 | !! salinity and temperature to take into account brine pocket |
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95 | !! melting. The numerical scheme is an iterative Crank-Nicolson |
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96 | !! on a non-uniform multilayer grid in the ice and snow system. |
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97 | !! |
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98 | !! The successive steps of this routine are |
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99 | !! 1. initialization of ice-snow layers thicknesses |
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100 | !! 2. Internal absorbed and transmitted radiation |
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101 | !! Then iterative procedure begins |
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102 | !! 3. Thermal conductivity |
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103 | !! 4. Kappa factors |
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104 | !! 5. specific heat in the ice |
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105 | !! 6. eta factors |
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106 | !! 7. surface flux computation |
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107 | !! 8. tridiagonal system terms |
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108 | !! 9. solving the tridiagonal system with Gauss elimination |
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109 | !! Iterative procedure ends according to a criterion on evolution |
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110 | !! of temperature |
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111 | !! 10. Fluxes at the interfaces |
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112 | !! |
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113 | !! ** Inputs / Ouputs : (global commons) |
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114 | !! surface temperature : t_su_1d |
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115 | !! ice/snow temperatures : t_i_1d, t_s_1d |
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116 | !! ice salinities : sz_i_1d |
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117 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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118 | !! total ice/snow thickness : h_i_1d, h_s_1d |
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119 | !!------------------------------------------------------------------- |
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120 | INTEGER, INTENT(in) :: k_jules ! Jules coupling (0=OFF, 1=RECEIVE, 2=SEND) |
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121 | ! |
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122 | INTEGER :: ji, jk ! spatial loop index |
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123 | INTEGER :: jm ! current reference number of equation |
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124 | INTEGER :: jm_mint, jm_maxt |
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125 | INTEGER :: iconv ! number of iterations in iterative procedure |
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126 | INTEGER :: iconv_max = 50 ! max number of iterations in iterative procedure |
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127 | ! |
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128 | INTEGER, DIMENSION(jpij) :: jm_min ! reference number of top equation |
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129 | INTEGER, DIMENSION(jpij) :: jm_max ! reference number of bottom equation |
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130 | ! |
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131 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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132 | REAL(wp) :: zg1 = 2._wp ! |
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133 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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134 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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135 | REAL(wp) :: zraext_s = 10._wp ! extinction coefficient of radiation in the snow |
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136 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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137 | REAL(wp) :: ztsu_err = 1.e-5_wp ! range around which t_su is considered at 0C |
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138 | REAL(wp) :: zdti_bnd = 1.e-4_wp ! maximal authorized error on temperature |
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139 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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140 | REAL(wp) :: zdti_max ! current maximal error on temperature |
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141 | REAL(wp) :: zcpi ! Ice specific heat |
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142 | REAL(wp) :: zhfx_err, zdq ! diag errors on heat |
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143 | REAL(wp) :: zfac ! dummy factor |
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144 | ! |
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145 | REAL(wp), DIMENSION(jpij) :: isnow ! switch for presence (1) or absence (0) of snow |
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146 | REAL(wp), DIMENSION(jpij) :: ztsub ! surface temperature at previous iteration |
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147 | REAL(wp), DIMENSION(jpij) :: zh_i, z1_h_i ! ice layer thickness |
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148 | REAL(wp), DIMENSION(jpij) :: zh_s, z1_h_s ! snow layer thickness |
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149 | REAL(wp), DIMENSION(jpij) :: zqns_ice_b ! solar radiation absorbed at the surface |
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150 | REAL(wp), DIMENSION(jpij) :: zfnet ! surface flux function |
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151 | REAL(wp), DIMENSION(jpij) :: zdqns_ice_b ! derivative of the surface flux function |
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152 | ! |
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153 | REAL(wp), DIMENSION(jpij ) :: ztsuold ! Old surface temperature in the ice |
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154 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztiold ! Old temperature in the ice |
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155 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsold ! Old temperature in the snow |
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156 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztib ! Temporary temperature in the ice to check the convergence |
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157 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsb ! Temporary temperature in the snow to check the convergence |
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158 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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159 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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160 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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161 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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162 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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163 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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164 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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165 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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166 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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167 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindterm ! 'Ind'ependent term |
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168 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindtbis ! Temporary 'ind'ependent term |
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169 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zdiagbis ! Temporary 'dia'gonal term |
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170 | REAL(wp), DIMENSION(jpij,nlay_i+3,3) :: ztrid ! Tridiagonal system terms |
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171 | REAL(wp), DIMENSION(jpij) :: zq_ini ! diag errors on heat |
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172 | REAL(wp), DIMENSION(jpij) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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173 | ! |
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174 | REAL(wp) :: zfr1, zfr2, zfrqsr_tr_i ! dummy factor |
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175 | ! |
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176 | ! Mono-category |
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177 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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178 | REAL(wp) :: zhe ! dummy factor |
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179 | REAL(wp) :: zcnd_i ! mean sea ice thermal conductivity |
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180 | !!------------------------------------------------------------------ |
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181 | |
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182 | ! --- diag error on heat diffusion - PART 1 --- ! |
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183 | DO ji = 1, npti |
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184 | zq_ini(ji) = ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
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185 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
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186 | END DO |
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187 | |
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188 | !------------------ |
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189 | ! 1) Initialization |
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190 | !------------------ |
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191 | DO ji = 1, npti |
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192 | isnow(ji)= 1._wp - MAX( 0._wp , SIGN(1._wp, - h_s_1d(ji) ) ) ! is there snow or not |
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193 | ! layer thickness |
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194 | zh_i(ji) = h_i_1d(ji) * r1_nlay_i |
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195 | zh_s(ji) = h_s_1d(ji) * r1_nlay_s |
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196 | END DO |
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197 | ! |
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198 | WHERE( zh_i(1:npti) >= epsi10 ) ; z1_h_i(1:npti) = 1._wp / zh_i(1:npti) |
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199 | ELSEWHERE ; z1_h_i(1:npti) = 0._wp |
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200 | END WHERE |
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201 | ! |
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202 | WHERE( zh_s(1:npti) >= epsi10 ) ; z1_h_s(1:npti) = 1._wp / zh_s(1:npti) |
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203 | ELSEWHERE ; z1_h_s(1:npti) = 0._wp |
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204 | END WHERE |
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205 | ! |
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206 | ! Store initial temperatures and non solar heat fluxes |
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207 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN ! OFF or SND mode |
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208 | ! |
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209 | ztsub (1:npti) = t_su_1d(1:npti) ! surface temperature at iteration n-1 |
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210 | ztsuold(1:npti) = t_su_1d(1:npti) ! surface temperature initial value |
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211 | zdqns_ice_b(1:npti) = dqns_ice_1d(1:npti) ! derivative of incoming nonsolar flux |
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212 | zqns_ice_b (1:npti) = qns_ice_1d(1:npti) ! store previous qns_ice_1d value |
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213 | ! |
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214 | t_su_1d(1:npti) = MIN( t_su_1d(1:npti), rt0 - ztsu_err ) ! required to leave the choice between melting or not |
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215 | ! |
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216 | ENDIF |
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217 | ! |
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218 | ztsold (1:npti,:) = t_s_1d(1:npti,:) ! Old snow temperature |
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219 | ztiold (1:npti,:) = t_i_1d(1:npti,:) ! Old ice temperature |
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220 | |
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221 | !------------- |
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222 | ! 2) Radiation |
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223 | !------------- |
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224 | ! --- Transmission/absorption of solar radiation in the ice --- ! |
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225 | ! zfr1 = ( 0.18 * ( 1.0 - 0.81 ) + 0.35 * 0.81 ) ! standard value |
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226 | ! zfr2 = ( 0.82 * ( 1.0 - 0.81 ) + 0.65 * 0.81 ) ! zfr2 such that zfr1 + zfr2 to equal 1 |
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227 | ! |
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228 | ! DO ji = 1, npti |
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229 | ! |
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230 | ! zfac = MAX( 0._wp , 1._wp - ( h_i_1d(ji) * 10._wp ) ) |
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231 | ! |
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232 | ! zfrqsr_tr_i = zfr1 + zfac * zfr2 ! below 10 cm, linearly increase zfrqsr_tr_i until 1 at zero thickness |
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233 | ! IF ( h_s_1d(ji) >= 0.0_wp ) zfrqsr_tr_i = 0._wp ! snow fully opaque |
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234 | ! |
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235 | ! qsr_ice_tr_1d(ji) = zfrqsr_tr_i * qsr_ice_1d(ji) ! transmitted solar radiation |
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236 | ! |
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237 | ! zfsw(ji) = qsr_ice_1d(ji) - qsr_ice_tr_1d(ji) |
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238 | ! zftrice(ji) = qsr_ice_tr_1d(ji) |
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239 | ! i0(ji) = zfrqsr_tr_i |
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240 | ! |
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241 | ! END DO |
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242 | |
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243 | zradtr_s(1:npti,0) = qsr_ice_tr_1d(1:npti) |
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244 | DO jk = 1, nlay_s |
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245 | DO ji = 1, npti |
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246 | ! ! radiation transmitted below the layer-th snow layer |
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247 | zradtr_s(ji,jk) = zradtr_s(ji,0) * EXP( - zraext_s * zh_s(ji) * REAL(jk) ) |
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248 | ! ! radiation absorbed by the layer-th snow layer |
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249 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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250 | END DO |
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251 | END DO |
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252 | ! |
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253 | zradtr_i(1:npti,0) = zradtr_s(1:npti,nlay_s) * isnow(1:npti) + qsr_ice_tr_1d(1:npti) * ( 1._wp - isnow(1:npti) ) |
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254 | DO jk = 1, nlay_i |
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255 | DO ji = 1, npti |
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256 | ! ! radiation transmitted below the layer-th ice layer |
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257 | zradtr_i(ji,jk) = zradtr_i(ji,0) * EXP( - rn_kappa_i * zh_i(ji) * REAL(jk) ) |
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258 | ! ! radiation absorbed by the layer-th ice layer |
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259 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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260 | END DO |
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261 | END DO |
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262 | ! |
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263 | ftr_ice_1d(1:npti) = zradtr_i(1:npti,nlay_i) ! record radiation transmitted below the ice |
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264 | ! |
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265 | iconv = 0 ! number of iterations |
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266 | zdti_max = 1000._wp ! maximal value of error on all points |
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267 | ! !============================! |
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268 | DO WHILE ( zdti_max > zdti_bnd .AND. iconv < iconv_max ) ! Iterative procedure begins ! |
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269 | ! !============================! |
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270 | iconv = iconv + 1 |
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271 | ! |
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272 | ztib(1:npti,:) = t_i_1d(1:npti,:) |
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273 | ztsb(1:npti,:) = t_s_1d(1:npti,:) |
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274 | ! |
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275 | !-------------------------------- |
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276 | ! 3) Sea ice thermal conductivity |
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277 | !-------------------------------- |
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278 | IF( ln_cndi_U64 ) THEN !-- Untersteiner (1964) formula: k = k0 + beta.S/T |
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279 | ! |
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280 | DO ji = 1, npti |
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281 | ztcond_i(ji,0) = rcdic + zbeta * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) |
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282 | ztcond_i(ji,nlay_i) = rcdic + zbeta * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) |
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283 | END DO |
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284 | DO jk = 1, nlay_i-1 |
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285 | DO ji = 1, npti |
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286 | ztcond_i(ji,jk) = rcdic + zbeta * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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287 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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288 | END DO |
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289 | END DO |
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290 | ! |
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291 | ELSEIF( ln_cndi_P07 ) THEN !-- Pringle et al formula: k = k0 + beta1.S/T - beta2.T |
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292 | ! |
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293 | DO ji = 1, npti |
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294 | ztcond_i(ji,0) = rcdic + 0.09_wp * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) & |
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295 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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296 | ztcond_i(ji,nlay_i) = rcdic + 0.09_wp * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) & |
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297 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
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298 | END DO |
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299 | DO jk = 1, nlay_i-1 |
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300 | DO ji = 1, npti |
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301 | ztcond_i(ji,jk) = rcdic + 0.09_wp * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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302 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) & |
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303 | & - 0.011_wp * ( 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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304 | END DO |
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305 | END DO |
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306 | ! |
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307 | ENDIF |
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308 | ztcond_i(1:npti,:) = MAX( zkimin, ztcond_i(1:npti,:) ) |
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309 | ! |
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310 | !--- G(he) : enhancement of thermal conductivity in mono-category case |
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311 | ! Computation of effective thermal conductivity G(h) |
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312 | ! Used in mono-category case only to simulate an ITD implicitly |
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313 | ! Fichefet and Morales Maqueda, JGR 1997 |
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314 | zghe(1:npti) = 1._wp |
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315 | ! |
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316 | SELECT CASE ( nn_monocat ) |
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317 | ! |
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318 | CASE ( 1 , 3 ) |
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319 | ! |
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320 | zepsilon = 0.1_wp |
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321 | DO ji = 1, npti |
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322 | zcnd_i = SUM( ztcond_i(ji,:) ) / REAL( nlay_i+1, wp ) ! Mean sea ice thermal conductivity |
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323 | zhe = ( rn_cnd_s * h_i_1d(ji) + zcnd_i * h_s_1d(ji) ) / ( rn_cnd_s + zcnd_i ) ! Effective thickness he (zhe) |
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324 | IF( zhe >= zepsilon * 0.5_wp * EXP(1._wp) ) THEN |
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325 | zghe(ji) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) ) ! G(he) |
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326 | ENDIF |
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327 | END DO |
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328 | ! |
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329 | END SELECT |
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330 | ! |
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331 | !----------------- |
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332 | ! 4) kappa factors |
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333 | !----------------- |
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334 | !--- Snow |
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335 | DO jk = 0, nlay_s-1 |
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336 | DO ji = 1, npti |
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337 | zkappa_s(ji,jk) = zghe(ji) * rn_cnd_s * z1_h_s(ji) |
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338 | END DO |
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339 | END DO |
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340 | DO ji = 1, npti ! Snow-ice interface |
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341 | zfac = 0.5_wp * ( ztcond_i(ji,0) * zh_s(ji) + rn_cnd_s * zh_i(ji) ) |
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342 | IF( zfac > epsi10 ) THEN |
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343 | zkappa_s(ji,nlay_s) = zghe(ji) * rn_cnd_s * ztcond_i(ji,0) / zfac |
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344 | ELSE |
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345 | zkappa_s(ji,nlay_s) = 0._wp |
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346 | ENDIF |
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347 | END DO |
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348 | |
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349 | !--- Ice |
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350 | DO jk = 0, nlay_i |
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351 | DO ji = 1, npti |
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352 | zkappa_i(ji,jk) = zghe(ji) * ztcond_i(ji,jk) * z1_h_i(ji) |
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353 | END DO |
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354 | END DO |
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355 | DO ji = 1, npti ! Snow-ice interface |
---|
356 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s) * isnow(ji) + zkappa_i(ji,0) * ( 1._wp - isnow(ji) ) |
---|
357 | END DO |
---|
358 | ! |
---|
359 | !-------------------------------------- |
---|
360 | ! 5) Sea ice specific heat, eta factors |
---|
361 | !-------------------------------------- |
---|
362 | DO jk = 1, nlay_i |
---|
363 | DO ji = 1, npti |
---|
364 | zcpi = cpic + zgamma * sz_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztiold(ji,jk) - rt0 ), epsi10 ) |
---|
365 | zeta_i(ji,jk) = rdt_ice * r1_rhoic * z1_h_i(ji) / MAX( epsi10, zcpi ) |
---|
366 | END DO |
---|
367 | END DO |
---|
368 | |
---|
369 | DO jk = 1, nlay_s |
---|
370 | DO ji = 1, npti |
---|
371 | zeta_s(ji,jk) = rdt_ice * r1_rhosn * r1_cpic * z1_h_s(ji) |
---|
372 | END DO |
---|
373 | END DO |
---|
374 | |
---|
375 | ! |
---|
376 | !----------------------------------------! |
---|
377 | ! ! |
---|
378 | ! JULES IF (OFF or SND MODE) ! |
---|
379 | ! ! |
---|
380 | !----------------------------------------! |
---|
381 | ! |
---|
382 | |
---|
383 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN ! OFF or SND mode |
---|
384 | |
---|
385 | ! |
---|
386 | ! In OFF mode the original BL99 temperature computation is used |
---|
387 | ! (with qsr_ice, qns_ice and dqns_ice as inputs) |
---|
388 | ! |
---|
389 | ! In SND mode, the computation is required to compute the conduction fluxes |
---|
390 | ! |
---|
391 | |
---|
392 | !---------------------------- |
---|
393 | ! 6) surface flux computation |
---|
394 | !---------------------------- |
---|
395 | |
---|
396 | DO ji = 1, npti |
---|
397 | ! update of the non solar flux according to the update in T_su |
---|
398 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsub(ji) ) |
---|
399 | END DO |
---|
400 | |
---|
401 | DO ji = 1, npti |
---|
402 | zfnet(ji) = qsr_ice_1d(ji) - qsr_ice_tr_1d(ji) + qns_ice_1d(ji) ! net heat flux = net solar - transmitted solar + non solar |
---|
403 | END DO |
---|
404 | ! |
---|
405 | !---------------------------- |
---|
406 | ! 7) tridiagonal system terms |
---|
407 | !---------------------------- |
---|
408 | !!layer denotes the number of the layer in the snow or in the ice |
---|
409 | !!jm denotes the reference number of the equation in the tridiagonal |
---|
410 | !!system, terms of tridiagonal system are indexed as following : |
---|
411 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
412 | |
---|
413 | !!ice interior terms (top equation has the same form as the others) |
---|
414 | ztrid (1:npti,:,:) = 0._wp |
---|
415 | zindterm(1:npti,:) = 0._wp |
---|
416 | zindtbis(1:npti,:) = 0._wp |
---|
417 | zdiagbis(1:npti,:) = 0._wp |
---|
418 | |
---|
419 | DO jm = nlay_s + 2, nlay_s + nlay_i |
---|
420 | DO ji = 1, npti |
---|
421 | jk = jm - nlay_s - 1 |
---|
422 | ztrid(ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
423 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
424 | ztrid(ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
425 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
426 | END DO |
---|
427 | END DO |
---|
428 | |
---|
429 | jm = nlay_s + nlay_i + 1 |
---|
430 | DO ji = 1, npti |
---|
431 | !!ice bottom term |
---|
432 | ztrid(ji,jm,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
433 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
---|
434 | ztrid(ji,jm,3) = 0.0 |
---|
435 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
436 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
437 | END DO |
---|
438 | |
---|
439 | |
---|
440 | DO ji = 1, npti |
---|
441 | ! !---------------------! |
---|
442 | IF ( h_s_1d(ji) > 0.0 ) THEN ! snow-covered cells ! |
---|
443 | ! !---------------------! |
---|
444 | ! snow interior terms (bottom equation has the same form as the others) |
---|
445 | DO jm = 3, nlay_s + 1 |
---|
446 | jk = jm - 1 |
---|
447 | ztrid(ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
448 | ztrid(ji,jm,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
449 | ztrid(ji,jm,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
---|
450 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
451 | END DO |
---|
452 | |
---|
453 | ! case of only one layer in the ice (ice equation is altered) |
---|
454 | IF ( nlay_i == 1 ) THEN |
---|
455 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
456 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
---|
457 | ENDIF |
---|
458 | |
---|
459 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
460 | |
---|
461 | jm_min(ji) = 1 |
---|
462 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
463 | |
---|
464 | ! surface equation |
---|
465 | ztrid(ji,1,1) = 0.0 |
---|
466 | ztrid(ji,1,2) = zdqns_ice_b(ji) - zg1s * zkappa_s(ji,0) |
---|
467 | ztrid(ji,1,3) = zg1s * zkappa_s(ji,0) |
---|
468 | zindterm(ji,1) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
---|
469 | |
---|
470 | ! first layer of snow equation |
---|
471 | ztrid(ji,2,1) = - zkappa_s(ji,0) * zg1s * zeta_s(ji,1) |
---|
472 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
473 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
474 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
---|
475 | |
---|
476 | ELSE !-- case 2 : surface is melting |
---|
477 | ! |
---|
478 | jm_min(ji) = 2 |
---|
479 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
480 | |
---|
481 | ! first layer of snow equation |
---|
482 | ztrid(ji,2,1) = 0.0 |
---|
483 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
484 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
485 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
486 | & ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
---|
487 | ENDIF |
---|
488 | ! !---------------------! |
---|
489 | ELSE ! cells without snow ! |
---|
490 | ! !---------------------! |
---|
491 | ! |
---|
492 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
493 | ! |
---|
494 | jm_min(ji) = nlay_s + 1 |
---|
495 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
496 | |
---|
497 | ! surface equation |
---|
498 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
499 | ztrid(ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0)*zg1 |
---|
500 | ztrid(ji,jm_min(ji),3) = zkappa_i(ji,0)*zg1 |
---|
501 | zindterm(ji,jm_min(ji)) = zdqns_ice_b(ji)*t_su_1d(ji) - zfnet(ji) |
---|
502 | |
---|
503 | ! first layer of ice equation |
---|
504 | ztrid(ji,jm_min(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
505 | ztrid(ji,jm_min(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
506 | ztrid(ji,jm_min(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
507 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
---|
508 | |
---|
509 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
510 | IF ( nlay_i == 1 ) THEN |
---|
511 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
512 | ztrid(ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * 2.0 |
---|
513 | ztrid(ji,jm_min(ji),3) = zkappa_i(ji,0) * 2.0 |
---|
514 | ztrid(ji,jm_min(ji)+1,1) = -zkappa_i(ji,0) * 2.0 * zeta_i(ji,1) |
---|
515 | ztrid(ji,jm_min(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
516 | ztrid(ji,jm_min(ji)+1,3) = 0.0 |
---|
517 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
518 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) |
---|
519 | ENDIF |
---|
520 | |
---|
521 | ELSE !-- case 2 : surface is melting |
---|
522 | |
---|
523 | jm_min(ji) = nlay_s + 2 |
---|
524 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
525 | |
---|
526 | ! first layer of ice equation |
---|
527 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
528 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
529 | ztrid(ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
530 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
531 | & ( zradab_i(ji,1) + zkappa_i(ji,0) * zg1 * t_su_1d(ji) ) |
---|
532 | |
---|
533 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
534 | IF ( nlay_i == 1 ) THEN |
---|
535 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
536 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
537 | ztrid(ji,jm_min(ji),3) = 0.0 |
---|
538 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
---|
539 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2.0 |
---|
540 | ENDIF |
---|
541 | |
---|
542 | ENDIF |
---|
543 | ENDIF |
---|
544 | ! |
---|
545 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
---|
546 | zdiagbis(ji,jm_min(ji)) = ztrid(ji,jm_min(ji),2) |
---|
547 | ! |
---|
548 | END DO |
---|
549 | ! |
---|
550 | !------------------------------ |
---|
551 | ! 8) tridiagonal system solving |
---|
552 | !------------------------------ |
---|
553 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
554 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
---|
555 | jm_maxt = 0 |
---|
556 | jm_mint = nlay_i+5 |
---|
557 | DO ji = 1, npti |
---|
558 | jm_mint = MIN(jm_min(ji),jm_mint) |
---|
559 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
---|
560 | END DO |
---|
561 | |
---|
562 | DO jk = jm_mint+1, jm_maxt |
---|
563 | DO ji = 1, npti |
---|
564 | jm = min(max(jm_min(ji)+1,jk),jm_max(ji)) |
---|
565 | zdiagbis(ji,jm) = ztrid(ji,jm,2) - ztrid(ji,jm,1) * ztrid(ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
566 | zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
---|
567 | END DO |
---|
568 | END DO |
---|
569 | |
---|
570 | DO ji = 1, npti |
---|
571 | ! ice temperatures |
---|
572 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
---|
573 | END DO |
---|
574 | |
---|
575 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
576 | DO ji = 1, npti |
---|
577 | jk = jm - nlay_s - 1 |
---|
578 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
579 | END DO |
---|
580 | END DO |
---|
581 | |
---|
582 | DO ji = 1, npti |
---|
583 | ! snow temperatures |
---|
584 | IF( h_s_1d(ji) > 0._wp ) THEN |
---|
585 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
---|
586 | & / zdiagbis(ji,nlay_s+1) |
---|
587 | ENDIF |
---|
588 | ! surface temperature |
---|
589 | ztsub(ji) = t_su_1d(ji) |
---|
590 | IF( t_su_1d(ji) < rt0 ) THEN |
---|
591 | t_su_1d(ji) = ( zindtbis(ji,jm_min(ji)) - ztrid(ji,jm_min(ji),3) * & |
---|
592 | & ( isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) ) ) / zdiagbis(ji,jm_min(ji)) |
---|
593 | ENDIF |
---|
594 | END DO |
---|
595 | ! |
---|
596 | !-------------------------------------------------------------- |
---|
597 | ! 9) Has the scheme converged ?, end of the iterative procedure |
---|
598 | !-------------------------------------------------------------- |
---|
599 | ! check that nowhere it has started to melt |
---|
600 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
---|
601 | zdti_max = 0._wp |
---|
602 | DO ji = 1, npti |
---|
603 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , rt0 - 100._wp ) |
---|
604 | zdti_max = MAX( zdti_max, ABS( t_su_1d(ji) - ztsub(ji) ) ) |
---|
605 | END DO |
---|
606 | |
---|
607 | DO jk = 1, nlay_s |
---|
608 | DO ji = 1, npti |
---|
609 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
---|
610 | zdti_max = MAX( zdti_max, ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
---|
611 | END DO |
---|
612 | END DO |
---|
613 | |
---|
614 | DO jk = 1, nlay_i |
---|
615 | DO ji = 1, npti |
---|
616 | ztmelt_i = -tmut * sz_i_1d(ji,jk) + rt0 |
---|
617 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), rt0 - 100._wp ) |
---|
618 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
---|
619 | END DO |
---|
620 | END DO |
---|
621 | |
---|
622 | ! Compute spatial maximum over all errors |
---|
623 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
624 | IF( lk_mpp ) CALL mpp_max( zdti_max, kcom=ncomm_ice ) |
---|
625 | ! |
---|
626 | !----------------------------------------! |
---|
627 | ! ! |
---|
628 | ! JULES IF (RCV MODE) ! |
---|
629 | ! ! |
---|
630 | !----------------------------------------! |
---|
631 | ! |
---|
632 | |
---|
633 | ELSE IF ( k_jules == np_zdf_jules_RCV ) THEN ! RCV mode |
---|
634 | |
---|
635 | ! |
---|
636 | ! In RCV mode, we use a modified BL99 solver |
---|
637 | ! with conduction flux (qcn_ice) as forcing term |
---|
638 | ! |
---|
639 | !---------------------------- |
---|
640 | ! 7) tridiagonal system terms |
---|
641 | !---------------------------- |
---|
642 | !!layer denotes the number of the layer in the snow or in the ice |
---|
643 | !!jm denotes the reference number of the equation in the tridiagonal |
---|
644 | !!system, terms of tridiagonal system are indexed as following : |
---|
645 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
646 | |
---|
647 | !!ice interior terms (top equation has the same form as the others) |
---|
648 | ztrid (1:npti,:,:) = 0._wp |
---|
649 | zindterm(1:npti,:) = 0._wp |
---|
650 | zindtbis(1:npti,:) = 0._wp |
---|
651 | zdiagbis(1:npti,:) = 0._wp |
---|
652 | |
---|
653 | DO jm = nlay_s + 2, nlay_s + nlay_i |
---|
654 | DO ji = 1, npti |
---|
655 | jk = jm - nlay_s - 1 |
---|
656 | ztrid(ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
657 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
658 | ztrid(ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
659 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
660 | END DO |
---|
661 | ENDDO |
---|
662 | |
---|
663 | jm = nlay_s + nlay_i + 1 |
---|
664 | DO ji = 1, npti |
---|
665 | !!ice bottom term |
---|
666 | ztrid(ji,jm,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
667 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
---|
668 | ztrid(ji,jm,3) = 0.0 |
---|
669 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
670 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
671 | ENDDO |
---|
672 | |
---|
673 | |
---|
674 | DO ji = 1, npti |
---|
675 | ! !---------------------! |
---|
676 | IF ( h_s_1d(ji) > 0.0 ) THEN ! snow-covered cells ! |
---|
677 | ! !---------------------! |
---|
678 | ! snow interior terms (bottom equation has the same form as the others) |
---|
679 | DO jm = 3, nlay_s + 1 |
---|
680 | jk = jm - 1 |
---|
681 | ztrid(ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
682 | ztrid(ji,jm,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
683 | ztrid(ji,jm,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
---|
684 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
685 | END DO |
---|
686 | |
---|
687 | ! case of only one layer in the ice (ice equation is altered) |
---|
688 | IF ( nlay_i == 1 ) THEN |
---|
689 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
690 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
---|
691 | ENDIF |
---|
692 | |
---|
693 | jm_min(ji) = 2 |
---|
694 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
695 | |
---|
696 | ! first layer of snow equation |
---|
697 | ztrid(ji,2,1) = 0.0 |
---|
698 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * zkappa_s(ji,1) |
---|
699 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
700 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
701 | & ( zradab_s(ji,1) + qcn_ice_1d(ji) ) |
---|
702 | |
---|
703 | ! !---------------------! |
---|
704 | ELSE ! cells without snow ! |
---|
705 | ! !---------------------! |
---|
706 | |
---|
707 | jm_min(ji) = nlay_s + 2 |
---|
708 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
709 | |
---|
710 | ! first layer of ice equation |
---|
711 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
712 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * zkappa_i(ji,1) |
---|
713 | ztrid(ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
714 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
715 | & ( zradab_i(ji,1) + qcn_ice_1d(ji) ) |
---|
716 | |
---|
717 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
718 | IF ( nlay_i == 1 ) THEN |
---|
719 | ztrid(ji,jm_min(ji),1) = 0.0 |
---|
720 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * zkappa_i(ji,1) |
---|
721 | ztrid(ji,jm_min(ji),3) = 0.0 |
---|
722 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) & |
---|
723 | & + qcn_ice_1d(ji) ) |
---|
724 | |
---|
725 | ENDIF |
---|
726 | |
---|
727 | ENDIF |
---|
728 | ! |
---|
729 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
---|
730 | zdiagbis(ji,jm_min(ji)) = ztrid(ji,jm_min(ji),2) |
---|
731 | ! |
---|
732 | END DO |
---|
733 | ! |
---|
734 | !------------------------------ |
---|
735 | ! 8) tridiagonal system solving |
---|
736 | !------------------------------ |
---|
737 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
738 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
---|
739 | jm_maxt = 0 |
---|
740 | jm_mint = nlay_i+5 |
---|
741 | DO ji = 1, npti |
---|
742 | jm_mint = MIN(jm_min(ji),jm_mint) |
---|
743 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
---|
744 | END DO |
---|
745 | |
---|
746 | DO jk = jm_mint+1, jm_maxt |
---|
747 | DO ji = 1, npti |
---|
748 | jm = min(max(jm_min(ji)+1,jk),jm_max(ji)) |
---|
749 | zdiagbis(ji,jm) = ztrid(ji,jm,2) - ztrid(ji,jm,1) * ztrid(ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
750 | zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
---|
751 | END DO |
---|
752 | END DO |
---|
753 | |
---|
754 | DO ji = 1, npti |
---|
755 | ! ice temperatures |
---|
756 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
---|
757 | END DO |
---|
758 | |
---|
759 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
760 | DO ji = 1, npti |
---|
761 | jk = jm - nlay_s - 1 |
---|
762 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
763 | END DO |
---|
764 | END DO |
---|
765 | |
---|
766 | DO ji = 1, npti |
---|
767 | ! snow temperatures |
---|
768 | IF( h_s_1d(ji) > 0._wp ) THEN |
---|
769 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
---|
770 | & / zdiagbis(ji,nlay_s+1) |
---|
771 | ENDIF |
---|
772 | END DO |
---|
773 | ! |
---|
774 | !-------------------------------------------------------------- |
---|
775 | ! 9) Has the scheme converged ?, end of the iterative procedure |
---|
776 | !-------------------------------------------------------------- |
---|
777 | ! check that nowhere it has started to melt |
---|
778 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
---|
779 | zdti_max = 0._wp |
---|
780 | |
---|
781 | DO jk = 1, nlay_s |
---|
782 | DO ji = 1, npti |
---|
783 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
---|
784 | zdti_max = MAX( zdti_max, ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
---|
785 | END DO |
---|
786 | END DO |
---|
787 | |
---|
788 | DO jk = 1, nlay_i |
---|
789 | DO ji = 1, npti |
---|
790 | ztmelt_i = -tmut * sz_i_1d(ji,jk) + rt0 |
---|
791 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), rt0 - 100._wp ) |
---|
792 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
---|
793 | END DO |
---|
794 | END DO |
---|
795 | |
---|
796 | ! Compute spatial maximum over all errors |
---|
797 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
798 | IF( lk_mpp ) CALL mpp_max( zdti_max, kcom=ncomm_ice ) |
---|
799 | |
---|
800 | ENDIF ! k_jules |
---|
801 | |
---|
802 | END DO ! End of the do while iterative procedure |
---|
803 | |
---|
804 | IF( ln_icectl .AND. lwp ) THEN |
---|
805 | WRITE(numout,*) ' zdti_max : ', zdti_max |
---|
806 | WRITE(numout,*) ' iconv : ', iconv |
---|
807 | ENDIF |
---|
808 | |
---|
809 | ! |
---|
810 | !----------------------------- |
---|
811 | ! 10) Fluxes at the interfaces |
---|
812 | !----------------------------- |
---|
813 | ! |
---|
814 | ! --- update conduction fluxes |
---|
815 | ! |
---|
816 | DO ji = 1, npti |
---|
817 | ! ! surface ice conduction flux |
---|
818 | fc_su(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * (t_s_1d(ji,1) - t_su_1d(ji)) & |
---|
819 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_1d(ji,1) - t_su_1d(ji)) |
---|
820 | ! ! bottom ice conduction flux |
---|
821 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_1d(ji) - t_i_1d(ji,nlay_i)) ) |
---|
822 | END DO |
---|
823 | |
---|
824 | ! |
---|
825 | ! --- Diagnose the heat loss due to changing non-solar / conduction flux --- ! |
---|
826 | ! |
---|
827 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN ! OFF or SND mode |
---|
828 | DO ji = 1, npti |
---|
829 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
---|
830 | END DO |
---|
831 | ELSE ! RCV mode |
---|
832 | DO ji = 1, npti |
---|
833 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( fc_su(ji) - qcn_ice_1d(ji) ) * a_i_1d(ji) |
---|
834 | END DO |
---|
835 | ENDIF |
---|
836 | |
---|
837 | ! |
---|
838 | ! --- Diagnose the heat loss due to non-fully converged temperature solution (should not be above 10-4 W-m2) --- ! |
---|
839 | ! |
---|
840 | |
---|
841 | IF ( ( k_jules == np_zdf_jules_OFF ) .OR. ( k_jules == np_zdf_jules_RCV ) ) THEN ! OFF |
---|
842 | |
---|
843 | CALL ice_thd_enmelt |
---|
844 | |
---|
845 | ! zhfx_err = correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
---|
846 | DO ji = 1, npti |
---|
847 | zdq = - zq_ini(ji) + ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
---|
848 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
---|
849 | |
---|
850 | IF ( ( k_jules == np_zdf_jules_OFF ) ) THEN |
---|
851 | |
---|
852 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
---|
853 | 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) |
---|
854 | ELSE ! case T_su = 0degC |
---|
855 | zhfx_err = ( fc_su(ji) + qsr_ice_tr_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
---|
856 | ENDIF |
---|
857 | |
---|
858 | ELSE ! RCV CASE |
---|
859 | |
---|
860 | zhfx_err = ( fc_su(ji) + qsr_ice_tr_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
---|
861 | |
---|
862 | ENDIF |
---|
863 | ! |
---|
864 | ! total heat sink to be sent to the ocean |
---|
865 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err |
---|
866 | ! |
---|
867 | ! hfx_dif = Heat flux diagnostic of sensible heat used to warm/cool ice in W.m-2 |
---|
868 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zdq * r1_rdtice * a_i_1d(ji) |
---|
869 | ! |
---|
870 | END DO |
---|
871 | ! |
---|
872 | ! --- SIMIP diagnostics |
---|
873 | ! |
---|
874 | DO ji = 1, npti |
---|
875 | !--- Conduction fluxes (positive downwards) |
---|
876 | diag_fc_bo_1d(ji) = diag_fc_bo_1d(ji) + fc_bo_i(ji) * a_i_1d(ji) / at_i_1d(ji) |
---|
877 | diag_fc_su_1d(ji) = diag_fc_su_1d(ji) + fc_su(ji) * a_i_1d(ji) / at_i_1d(ji) |
---|
878 | |
---|
879 | !--- Snow-ice interfacial temperature (diagnostic SIMIP) |
---|
880 | zfac = rn_cnd_s * zh_i(ji) + ztcond_i(ji,1) * zh_s(ji) |
---|
881 | IF( zh_s(ji) >= 1.e-3 .AND. zfac > epsi10 ) THEN |
---|
882 | t_si_1d(ji) = ( rn_cnd_s * zh_i(ji) * t_s_1d(ji,1) + & |
---|
883 | & ztcond_i(ji,1) * zh_s(ji) * t_i_1d(ji,1) ) / zfac |
---|
884 | ELSE |
---|
885 | t_si_1d(ji) = t_su_1d(ji) |
---|
886 | ENDIF |
---|
887 | END DO |
---|
888 | ! |
---|
889 | ENDIF |
---|
890 | ! |
---|
891 | !--------------------------------------------------------------------------------------- |
---|
892 | ! 11) Jules coupling: reset inner snow and ice temperatures, update conduction fluxes |
---|
893 | !--------------------------------------------------------------------------------------- |
---|
894 | ! |
---|
895 | IF ( k_jules == np_zdf_jules_SND ) THEN ! --- Jules coupling in "SND" mode |
---|
896 | ! |
---|
897 | ! Restore temperatures to their initial values |
---|
898 | t_s_1d(1:npti,:) = ztsold (1:npti,:) |
---|
899 | t_i_1d(1:npti,:) = ztiold (1:npti,:) |
---|
900 | qcn_ice_1d(1:npti) = fc_su(1:npti) |
---|
901 | ! |
---|
902 | ENDIF |
---|
903 | ! |
---|
904 | END SUBROUTINE ice_thd_zdf_BL99 |
---|
905 | |
---|
906 | |
---|
907 | SUBROUTINE ice_thd_enmelt |
---|
908 | !!------------------------------------------------------------------- |
---|
909 | !! *** ROUTINE ice_thd_enmelt *** |
---|
910 | !! |
---|
911 | !! ** Purpose : Computes sea ice energy of melting q_i (J.m-3) from temperature |
---|
912 | !! |
---|
913 | !! ** Method : Formula (Bitz and Lipscomb, 1999) |
---|
914 | !!------------------------------------------------------------------- |
---|
915 | INTEGER :: ji, jk ! dummy loop indices |
---|
916 | REAL(wp) :: ztmelts ! local scalar |
---|
917 | !!------------------------------------------------------------------- |
---|
918 | ! |
---|
919 | DO jk = 1, nlay_i ! Sea ice energy of melting |
---|
920 | DO ji = 1, npti |
---|
921 | ztmelts = - tmut * sz_i_1d(ji,jk) |
---|
922 | t_i_1d(ji,jk) = MIN( t_i_1d(ji,jk), ztmelts + rt0 ) ! Force t_i_1d to be lower than melting point |
---|
923 | ! (sometimes dif scheme produces abnormally high temperatures) |
---|
924 | e_i_1d(ji,jk) = rhoic * ( cpic * ( ztmelts - ( t_i_1d(ji,jk) - rt0 ) ) & |
---|
925 | & + lfus * ( 1._wp - ztmelts / ( t_i_1d(ji,jk) - rt0 ) ) & |
---|
926 | & - rcp * ztmelts ) |
---|
927 | END DO |
---|
928 | END DO |
---|
929 | DO jk = 1, nlay_s ! Snow energy of melting |
---|
930 | DO ji = 1, npti |
---|
931 | e_s_1d(ji,jk) = rhosn * ( cpic * ( rt0 - t_s_1d(ji,jk) ) + lfus ) |
---|
932 | END DO |
---|
933 | END DO |
---|
934 | ! |
---|
935 | END SUBROUTINE ice_thd_enmelt |
---|
936 | |
---|
937 | |
---|
938 | SUBROUTINE ice_thd_zdf_init |
---|
939 | !!----------------------------------------------------------------------- |
---|
940 | !! *** ROUTINE ice_thd_zdf_init *** |
---|
941 | !! |
---|
942 | !! ** Purpose : Physical constants and parameters associated with |
---|
943 | !! ice thermodynamics |
---|
944 | !! |
---|
945 | !! ** Method : Read the namthd_zdf namelist and check the parameters |
---|
946 | !! called at the first timestep (nit000) |
---|
947 | !! |
---|
948 | !! ** input : Namelist namthd_zdf |
---|
949 | !!------------------------------------------------------------------- |
---|
950 | INTEGER :: ios, ioptio ! Local integer |
---|
951 | !! |
---|
952 | NAMELIST/namthd_zdf/ ln_zdf_BL99, ln_cndi_U64, ln_cndi_P07, rn_cnd_s, rn_kappa_i |
---|
953 | !!------------------------------------------------------------------- |
---|
954 | ! |
---|
955 | REWIND( numnam_ice_ref ) ! Namelist namthd_zdf in reference namelist : Ice thermodynamics |
---|
956 | READ ( numnam_ice_ref, namthd_zdf, IOSTAT = ios, ERR = 901) |
---|
957 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in reference namelist', lwp ) |
---|
958 | |
---|
959 | REWIND( numnam_ice_cfg ) ! Namelist namthd_zdf in configuration namelist : Ice thermodynamics |
---|
960 | READ ( numnam_ice_cfg, namthd_zdf, IOSTAT = ios, ERR = 902 ) |
---|
961 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in configuration namelist', lwp ) |
---|
962 | IF(lwm) WRITE ( numoni, namthd_zdf ) |
---|
963 | ! |
---|
964 | ! |
---|
965 | IF(lwp) THEN ! control print |
---|
966 | WRITE(numout,*) 'ice_thd_zdf_init: Ice vertical heat diffusion' |
---|
967 | WRITE(numout,*) '~~~~~~~~~~~~~~~~' |
---|
968 | WRITE(numout,*) ' Namelist namthd_zdf:' |
---|
969 | WRITE(numout,*) ' Bitz and Lipscomb (1999) formulation ln_zdf_BL99 = ', ln_zdf_BL99 |
---|
970 | WRITE(numout,*) ' thermal conductivity in the ice (Untersteiner 1964) ln_cndi_U64 = ', ln_cndi_U64 |
---|
971 | WRITE(numout,*) ' thermal conductivity in the ice (Pringle et al 2007) ln_cndi_P07 = ', ln_cndi_P07 |
---|
972 | WRITE(numout,*) ' thermal conductivity in the snow rn_cnd_s = ', rn_cnd_s |
---|
973 | WRITE(numout,*) ' extinction radiation parameter in sea ice rn_kappa_i = ', rn_kappa_i |
---|
974 | ENDIF |
---|
975 | |
---|
976 | ! |
---|
977 | IF ( ( ln_cndi_U64 .AND. ln_cndi_P07 ) .OR. ( .NOT.ln_cndi_U64 .AND. .NOT.ln_cndi_P07 ) ) THEN |
---|
978 | CALL ctl_stop( 'ice_thd_zdf_init: choose one and only one formulation for thermal conduction (ln_cndi_U64 or ln_cndi_P07)' ) |
---|
979 | ENDIF |
---|
980 | |
---|
981 | ! !== set the choice of ice vertical thermodynamic formulation ==! |
---|
982 | ioptio = 0 |
---|
983 | ! !--- BL99 thermo dynamics (linear liquidus + constant thermal properties) |
---|
984 | IF( ln_zdf_BL99 ) THEN ; ioptio = ioptio + 1 ; nice_zdf = np_BL99 ; ENDIF |
---|
985 | IF( ioptio /= 1 ) CALL ctl_stop( 'ice_thd_init: one and only one ice thermo option has to be defined ' ) |
---|
986 | ! |
---|
987 | END SUBROUTINE ice_thd_zdf_init |
---|
988 | |
---|
989 | #else |
---|
990 | !!---------------------------------------------------------------------- |
---|
991 | !! Default option Dummy Module No ESIM sea-ice model |
---|
992 | !!---------------------------------------------------------------------- |
---|
993 | #endif |
---|
994 | |
---|
995 | !!====================================================================== |
---|
996 | END MODULE icethd_zdf |
---|