1 | MODULE limitd_me |
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2 | !!====================================================================== |
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3 | !! *** MODULE limitd_me *** |
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4 | !! LIM-3 : Mechanical impact on ice thickness distribution |
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5 | !!====================================================================== |
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6 | !! History : LIM ! 2006-02 (M. Vancoppenolle) Original code |
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7 | !! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in smsw & sfx_dyn |
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8 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
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9 | !!---------------------------------------------------------------------- |
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10 | #if defined key_lim3 |
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11 | !!---------------------------------------------------------------------- |
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12 | !! 'key_lim3' LIM-3 sea-ice model |
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13 | !!---------------------------------------------------------------------- |
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14 | USE par_oce ! ocean parameters |
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15 | USE dom_oce ! ocean domain |
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16 | USE phycst ! physical constants (ocean directory) |
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17 | USE sbc_oce ! surface boundary condition: ocean fields |
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18 | USE thd_ice ! LIM thermodynamics |
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19 | USE ice ! LIM variables |
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20 | USE limvar ! LIM |
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21 | USE lbclnk ! lateral boundary condition - MPP exchanges |
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22 | USE lib_mpp ! MPP library |
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23 | USE wrk_nemo ! work arrays |
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24 | USE prtctl ! Print control |
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25 | |
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26 | USE in_out_manager ! I/O manager |
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27 | USE iom ! I/O manager |
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28 | USE lib_fortran ! glob_sum |
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29 | USE limdiahsb |
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30 | USE timing ! Timing |
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31 | USE limcons ! conservation tests |
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32 | |
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33 | IMPLICIT NONE |
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34 | PRIVATE |
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35 | |
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36 | PUBLIC lim_itd_me ! called by ice_stp |
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37 | PUBLIC lim_itd_me_icestrength |
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38 | PUBLIC lim_itd_me_init |
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39 | PUBLIC lim_itd_me_alloc ! called by sbc_lim_init |
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40 | |
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41 | !----------------------------------------------------------------------- |
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42 | ! Variables shared among ridging subroutines |
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43 | !----------------------------------------------------------------------- |
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44 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
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45 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
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46 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/closing associated w/ category n |
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47 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
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48 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
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49 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
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50 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! thickness of ridging ice / mean ridge thickness |
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51 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
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52 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
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53 | |
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54 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
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55 | REAL(wp), PARAMETER :: kraft = 0.5_wp ! rafting multipliyer |
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56 | |
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57 | REAL(wp) :: Cp ! |
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58 | ! |
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59 | ! |
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60 | !!---------------------------------------------------------------------- |
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61 | !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) |
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62 | !! $Id$ |
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63 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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64 | !!---------------------------------------------------------------------- |
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65 | CONTAINS |
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66 | |
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67 | INTEGER FUNCTION lim_itd_me_alloc() |
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68 | !!---------------------------------------------------------------------! |
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69 | !! *** ROUTINE lim_itd_me_alloc *** |
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70 | !!---------------------------------------------------------------------! |
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71 | ALLOCATE( & |
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72 | !* Variables shared among ridging subroutines |
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73 | & asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , aksum (jpi,jpj) , & |
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74 | & hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
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75 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , STAT=lim_itd_me_alloc ) |
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76 | ! |
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77 | IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' ) |
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78 | ! |
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79 | END FUNCTION lim_itd_me_alloc |
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80 | |
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81 | |
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82 | SUBROUTINE lim_itd_me |
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83 | !!---------------------------------------------------------------------! |
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84 | !! *** ROUTINE lim_itd_me *** |
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85 | !! |
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86 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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87 | !! |
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88 | !! ** Method : Steps : |
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89 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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90 | !! Ridge preparation |
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91 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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92 | !! 3) Ridging iteration |
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93 | !! 4) Ridging diagnostics |
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94 | !! 5) Heat, salt and freshwater fluxes |
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95 | !! 6) Compute increments of tate variables and come back to old values |
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96 | !! |
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97 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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98 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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99 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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100 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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101 | !! Bitz et al., JGR, 2001 |
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102 | !! Amundrud and Melling, JGR 2005 |
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103 | !! Babko et al., JGR 2002 |
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104 | !! |
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105 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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106 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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107 | !!--------------------------------------------------------------------! |
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108 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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109 | INTEGER :: niter ! local integer |
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110 | INTEGER :: iterate_ridging ! if true, repeat the ridging |
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111 | REAL(wp) :: za, zfac ! local scalar |
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112 | CHARACTER (len = 15) :: fieldid |
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113 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s) |
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114 | ! (ridging ice area - area of new ridges) / dt |
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115 | REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s) |
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116 | REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear |
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117 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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118 | ! |
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119 | INTEGER, PARAMETER :: nitermax = 20 |
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120 | ! |
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121 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
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122 | !!----------------------------------------------------------------------------- |
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123 | IF( nn_timing == 1 ) CALL timing_start('limitd_me') |
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124 | |
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125 | CALL wrk_alloc( jpi,jpj, closing_net, divu_adv, opning, closing_gross ) |
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126 | |
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127 | IF(ln_ctl) THEN |
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128 | CALL prt_ctl(tab2d_1=ato_i , clinfo1=' lim_itd_me: ato_i : ', tab2d_2=at_i , clinfo2=' at_i : ') |
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129 | CALL prt_ctl(tab2d_1=divu_i, clinfo1=' lim_itd_me: divu_i : ', tab2d_2=delta_i, clinfo2=' delta_i : ') |
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130 | ENDIF |
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131 | |
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132 | ! conservation test |
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133 | IF( ln_limdiahsb ) CALL lim_cons_hsm(0, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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134 | |
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135 | !-----------------------------------------------------------------------------! |
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136 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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137 | !-----------------------------------------------------------------------------! |
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138 | Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
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139 | ! |
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140 | CALL lim_itd_me_ridgeprep ! prepare ridging |
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141 | ! |
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142 | |
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143 | DO jj = 1, jpj ! Initialize arrays. |
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144 | DO ji = 1, jpi |
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145 | |
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146 | !-----------------------------------------------------------------------------! |
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147 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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148 | !-----------------------------------------------------------------------------! |
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149 | ! |
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150 | ! 2.1 closing_net |
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151 | !----------------- |
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152 | ! Compute the net rate of closing due to convergence |
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153 | ! and shear, based on Flato and Hibler (1995). |
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154 | ! |
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155 | ! The energy dissipation rate is equal to the net closing rate |
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156 | ! times the ice strength. |
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157 | ! |
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158 | ! NOTE: The NET closing rate is equal to the rate that open water |
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159 | ! area is removed, plus the rate at which ice area is removed by |
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160 | ! ridging, minus the rate at which area is added in new ridges. |
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161 | ! The GROSS closing rate is equal to the first two terms (open |
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162 | ! water closing and thin ice ridging) without the third term |
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163 | ! (thick, newly ridged ice). |
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164 | |
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165 | closing_net(ji,jj) = rn_cs * 0.5 * ( delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) |
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166 | |
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167 | ! 2.2 divu_adv |
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168 | !-------------- |
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169 | ! Compute divu_adv, the divergence rate given by the transport/ |
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170 | ! advection scheme, which may not be equal to divu as computed |
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171 | ! from the velocity field. |
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172 | ! |
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173 | ! If divu_adv < 0, make sure the closing rate is large enough |
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174 | ! to give asum = 1.0 after ridging. |
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175 | |
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176 | divu_adv(ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
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177 | |
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178 | IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) |
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179 | |
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180 | ! 2.3 opning |
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181 | !------------ |
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182 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
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183 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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184 | END DO |
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185 | END DO |
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186 | |
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187 | !-----------------------------------------------------------------------------! |
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188 | ! 3) Ridging iteration |
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189 | !-----------------------------------------------------------------------------! |
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190 | niter = 1 ! iteration counter |
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191 | iterate_ridging = 1 |
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192 | |
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193 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
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194 | |
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195 | ! 3.2 closing_gross |
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196 | !-----------------------------------------------------------------------------! |
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197 | ! Based on the ITD of ridging and ridged ice, convert the net |
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198 | ! closing rate to a gross closing rate. |
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199 | ! NOTE: 0 < aksum <= 1 |
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200 | closing_gross(:,:) = closing_net(:,:) / aksum(:,:) |
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201 | |
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202 | ! correction to closing rate and opening if closing rate is excessive |
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203 | !--------------------------------------------------------------------- |
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204 | ! Reduce the closing rate if more than 100% of the open water |
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205 | ! would be removed. Reduce the opening rate proportionately. |
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206 | DO jj = 1, jpj |
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207 | DO ji = 1, jpi |
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208 | za = ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice |
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209 | IF ( za < 0._wp .AND. za > - ato_i(ji,jj) ) THEN ! would lead to negative ato_i |
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210 | zfac = - ato_i(ji,jj) / za |
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211 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) - ato_i(ji,jj) * r1_rdtice |
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212 | ELSEIF( za > 0._wp .AND. za > ( asum(ji,jj) - ato_i(ji,jj) ) ) THEN ! would lead to ato_i > asum |
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213 | zfac = ( asum(ji,jj) - ato_i(ji,jj) ) / za |
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214 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) + ( asum(ji,jj) - ato_i(ji,jj) ) * r1_rdtice |
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215 | ENDIF |
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216 | END DO |
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217 | END DO |
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218 | |
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219 | ! correction to closing rate / opening if excessive ice removal |
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220 | !--------------------------------------------------------------- |
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221 | ! Reduce the closing rate if more than 100% of any ice category |
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222 | ! would be removed. Reduce the opening rate proportionately. |
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223 | DO jl = 1, jpl |
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224 | DO jj = 1, jpj |
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225 | DO ji = 1, jpi |
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226 | za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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227 | IF( za > a_i(ji,jj,jl) ) THEN |
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228 | zfac = a_i(ji,jj,jl) / za |
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229 | closing_gross(ji,jj) = closing_gross(ji,jj) * zfac |
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230 | ENDIF |
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231 | END DO |
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232 | END DO |
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233 | END DO |
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234 | |
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235 | ! 3.3 Redistribute area, volume, and energy. |
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236 | !-----------------------------------------------------------------------------! |
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237 | |
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238 | CALL lim_itd_me_ridgeshift( opning, closing_gross ) |
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239 | |
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240 | |
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241 | ! 3.4 Compute total area of ice plus open water after ridging. |
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242 | !-----------------------------------------------------------------------------! |
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243 | ! This is in general not equal to one because of divergence during transport |
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244 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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245 | |
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246 | ! 3.5 Do we keep on iterating ??? |
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247 | !-----------------------------------------------------------------------------! |
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248 | ! Check whether asum = 1. If not (because the closing and opening |
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249 | ! rates were reduced above), ridge again with new rates. |
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250 | |
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251 | iterate_ridging = 0 |
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252 | DO jj = 1, jpj |
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253 | DO ji = 1, jpi |
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254 | IF( ABS( asum(ji,jj) - 1._wp ) < epsi10 ) THEN |
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255 | closing_net(ji,jj) = 0._wp |
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256 | opning (ji,jj) = 0._wp |
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257 | ato_i (ji,jj) = MAX( 0._wp, 1._wp - SUM( a_i(ji,jj,:) ) ) |
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258 | ELSE |
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259 | iterate_ridging = 1 |
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260 | divu_adv (ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice |
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261 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
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262 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
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263 | ENDIF |
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264 | END DO |
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265 | END DO |
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266 | |
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267 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
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268 | |
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269 | ! Repeat if necessary. |
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270 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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271 | ! iterated globally because of the boundary update in the |
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272 | ! smoothing. |
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273 | |
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274 | niter = niter + 1 |
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275 | |
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276 | IF( iterate_ridging == 1 ) THEN |
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277 | CALL lim_itd_me_ridgeprep |
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278 | IF( niter > nitermax ) THEN |
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279 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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280 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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281 | ENDIF |
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282 | ENDIF |
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283 | |
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284 | END DO !! on the do while over iter |
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285 | |
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286 | CALL lim_var_agg( 1 ) |
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287 | |
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288 | !-----------------------------------------------------------------------------! |
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289 | ! control prints |
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290 | !-----------------------------------------------------------------------------! |
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291 | IF(ln_ctl) THEN |
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292 | CALL lim_var_glo2eqv |
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293 | |
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294 | CALL prt_ctl_info(' ') |
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295 | CALL prt_ctl_info(' - Cell values : ') |
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296 | CALL prt_ctl_info(' ~~~~~~~~~~~~~ ') |
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297 | CALL prt_ctl(tab2d_1=e12t , clinfo1=' lim_itd_me : cell area :') |
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298 | CALL prt_ctl(tab2d_1=at_i , clinfo1=' lim_itd_me : at_i :') |
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299 | CALL prt_ctl(tab2d_1=vt_i , clinfo1=' lim_itd_me : vt_i :') |
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300 | CALL prt_ctl(tab2d_1=vt_s , clinfo1=' lim_itd_me : vt_s :') |
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301 | DO jl = 1, jpl |
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302 | CALL prt_ctl_info(' ') |
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303 | CALL prt_ctl_info(' - Category : ', ivar1=jl) |
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304 | CALL prt_ctl_info(' ~~~~~~~~~~') |
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305 | CALL prt_ctl(tab2d_1=a_i (:,:,jl) , clinfo1= ' lim_itd_me : a_i : ') |
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306 | CALL prt_ctl(tab2d_1=ht_i (:,:,jl) , clinfo1= ' lim_itd_me : ht_i : ') |
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307 | CALL prt_ctl(tab2d_1=ht_s (:,:,jl) , clinfo1= ' lim_itd_me : ht_s : ') |
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308 | CALL prt_ctl(tab2d_1=v_i (:,:,jl) , clinfo1= ' lim_itd_me : v_i : ') |
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309 | CALL prt_ctl(tab2d_1=v_s (:,:,jl) , clinfo1= ' lim_itd_me : v_s : ') |
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310 | CALL prt_ctl(tab2d_1=e_s (:,:,1,jl) , clinfo1= ' lim_itd_me : e_s : ') |
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311 | CALL prt_ctl(tab2d_1=t_su (:,:,jl) , clinfo1= ' lim_itd_me : t_su : ') |
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312 | CALL prt_ctl(tab2d_1=t_s (:,:,1,jl) , clinfo1= ' lim_itd_me : t_snow : ') |
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313 | CALL prt_ctl(tab2d_1=sm_i (:,:,jl) , clinfo1= ' lim_itd_me : sm_i : ') |
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314 | CALL prt_ctl(tab2d_1=smv_i (:,:,jl) , clinfo1= ' lim_itd_me : smv_i : ') |
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315 | DO jk = 1, nlay_i |
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316 | CALL prt_ctl_info(' ') |
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317 | CALL prt_ctl_info(' - Layer : ', ivar1=jk) |
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318 | CALL prt_ctl_info(' ~~~~~~~') |
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319 | CALL prt_ctl(tab2d_1=t_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : t_i : ') |
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320 | CALL prt_ctl(tab2d_1=e_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : e_i : ') |
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321 | END DO |
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322 | END DO |
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323 | ENDIF |
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324 | |
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325 | ! conservation test |
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326 | IF( ln_limdiahsb ) CALL lim_cons_hsm(1, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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327 | |
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328 | CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross ) |
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329 | ! |
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330 | IF( nn_timing == 1 ) CALL timing_stop('limitd_me') |
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331 | END SUBROUTINE lim_itd_me |
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332 | |
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333 | SUBROUTINE lim_itd_me_ridgeprep |
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334 | !!---------------------------------------------------------------------! |
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335 | !! *** ROUTINE lim_itd_me_ridgeprep *** |
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336 | !! |
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337 | !! ** Purpose : preparation for ridging and strength calculations |
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338 | !! |
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339 | !! ** Method : Compute the thickness distribution of the ice and open water |
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340 | !! participating in ridging and of the resulting ridges. |
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341 | !!---------------------------------------------------------------------! |
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342 | INTEGER :: ji,jj, jl ! dummy loop indices |
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343 | REAL(wp) :: Gstari, astari, hrmean, zdummy ! local scalar |
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344 | REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n |
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345 | !------------------------------------------------------------------------------! |
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346 | |
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347 | CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
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348 | |
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349 | Gstari = 1.0/rn_gstar |
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350 | astari = 1.0/rn_astar |
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351 | aksum(:,:) = 0.0 |
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352 | athorn(:,:,:) = 0.0 |
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353 | aridge(:,:,:) = 0.0 |
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354 | araft (:,:,:) = 0.0 |
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355 | |
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356 | ! Zero out categories with very small areas |
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357 | CALL lim_var_zapsmall |
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358 | |
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359 | ! Ice thickness needed for rafting |
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360 | DO jl = 1, jpl |
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361 | DO jj = 1, jpj |
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362 | DO ji = 1, jpi |
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363 | rswitch = MAX( 0._wp , SIGN( 1._wp, a_i(ji,jj,jl) - epsi20 ) ) |
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364 | ht_i(ji,jj,jl) = v_i (ji,jj,jl) / MAX( a_i(ji,jj,jl) , epsi20 ) * rswitch |
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365 | END DO |
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366 | END DO |
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367 | END DO |
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368 | |
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369 | !------------------------------------------------------------------------------! |
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370 | ! 1) Participation function |
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371 | !------------------------------------------------------------------------------! |
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372 | |
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373 | ! Compute total area of ice plus open water. |
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374 | ! This is in general not equal to one because of divergence during transport |
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375 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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376 | |
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377 | ! Compute cumulative thickness distribution function |
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378 | ! Compute the cumulative thickness distribution function Gsum, |
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379 | ! where Gsum(n) is the fractional area in categories 0 to n. |
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380 | ! initial value (in h = 0) equals open water area |
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381 | Gsum(:,:,-1) = 0._wp |
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382 | Gsum(:,:,0 ) = ato_i(:,:) |
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383 | ! for each value of h, you have to add ice concentration then |
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384 | DO jl = 1, jpl |
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385 | Gsum(:,:,jl) = Gsum(:,:,jl-1) + a_i(:,:,jl) |
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386 | END DO |
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387 | |
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388 | ! Normalize the cumulative distribution to 1 |
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389 | DO jl = 0, jpl |
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390 | Gsum(:,:,jl) = Gsum(:,:,jl) / asum(:,:) |
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391 | END DO |
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392 | |
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393 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
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394 | !-------------------------------------------------------------------------------------------------- |
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395 | ! Compute the participation function athorn; this is analogous to |
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396 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
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397 | ! area lost from category n due to ridging/closing |
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398 | ! athorn(n) = total area lost due to ridging/closing |
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399 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
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400 | ! |
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401 | ! The expressions for athorn are found by integrating b(h)g(h) between |
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402 | ! the category boundaries. |
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403 | ! athorn is always >= 0 and SUM(athorn(0:jpl))=1 |
---|
404 | !----------------------------------------------------------------- |
---|
405 | |
---|
406 | IF( nn_partfun == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) |
---|
407 | DO jl = 0, jpl |
---|
408 | DO jj = 1, jpj |
---|
409 | DO ji = 1, jpi |
---|
410 | IF ( Gsum(ji,jj,jl) < rn_gstar ) THEN |
---|
411 | athorn(ji,jj,jl) = Gstari * ( Gsum(ji,jj,jl) - Gsum(ji,jj,jl-1) ) * & |
---|
412 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + Gsum(ji,jj,jl) ) * Gstari ) |
---|
413 | ELSEIF( Gsum(ji,jj,jl-1) < rn_gstar ) THEN |
---|
414 | athorn(ji,jj,jl) = Gstari * ( rn_gstar - Gsum(ji,jj,jl-1) ) * & |
---|
415 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + rn_gstar ) * Gstari ) |
---|
416 | ELSE |
---|
417 | athorn(ji,jj,jl) = 0._wp |
---|
418 | ENDIF |
---|
419 | END DO |
---|
420 | END DO |
---|
421 | END DO |
---|
422 | |
---|
423 | ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
424 | ! |
---|
425 | zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array |
---|
426 | DO jl = -1, jpl |
---|
427 | Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy |
---|
428 | END DO |
---|
429 | DO jl = 0, jpl |
---|
430 | athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) |
---|
431 | END DO |
---|
432 | ! |
---|
433 | ENDIF |
---|
434 | |
---|
435 | ! --- Ridging and rafting participation concentrations --- ! |
---|
436 | IF( ln_rafting .AND. ln_ridging ) THEN |
---|
437 | ! |
---|
438 | DO jl = 1, jpl |
---|
439 | DO jj = 1, jpj |
---|
440 | DO ji = 1, jpi |
---|
441 | zdummy = TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) |
---|
442 | aridge(ji,jj,jl) = ( 1._wp + zdummy ) * 0.5_wp * athorn(ji,jj,jl) |
---|
443 | araft (ji,jj,jl) = athorn(ji,jj,jl) - aridge(ji,jj,jl) |
---|
444 | END DO |
---|
445 | END DO |
---|
446 | END DO |
---|
447 | ! |
---|
448 | ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN |
---|
449 | ! |
---|
450 | DO jl = 1, jpl |
---|
451 | aridge(:,:,jl) = athorn(:,:,jl) |
---|
452 | END DO |
---|
453 | ! |
---|
454 | ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN |
---|
455 | ! |
---|
456 | DO jl = 1, jpl |
---|
457 | araft(:,:,jl) = athorn(:,:,jl) |
---|
458 | END DO |
---|
459 | ! |
---|
460 | ENDIF |
---|
461 | |
---|
462 | !----------------------------------------------------------------- |
---|
463 | ! 2) Transfer function |
---|
464 | !----------------------------------------------------------------- |
---|
465 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
466 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
467 | ! |
---|
468 | ! This parameterization is a modified version of Hibler (1980). |
---|
469 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
470 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
471 | ! |
---|
472 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
473 | ! (i.e., rafting) and for very thick ridging ice is |
---|
474 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
475 | ! |
---|
476 | ! The maximum ridging thickness, hrmax, is determined by |
---|
477 | ! hrmean and hrmin. |
---|
478 | ! |
---|
479 | ! These modifications have the effect of reducing the ice strength |
---|
480 | ! (relative to the Hibler formulation) when very thick ice is |
---|
481 | ! ridging. |
---|
482 | ! |
---|
483 | ! aksum = net area removed/ total area removed |
---|
484 | ! where total area removed = area of ice that ridges |
---|
485 | ! net area removed = total area removed - area of new ridges |
---|
486 | !----------------------------------------------------------------- |
---|
487 | |
---|
488 | aksum(:,:) = athorn(:,:,0) |
---|
489 | ! Transfer function |
---|
490 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
491 | DO jj = 1, jpj |
---|
492 | DO ji = 1, jpi |
---|
493 | |
---|
494 | IF( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
495 | hrmean = MAX( SQRT( rn_hstar * ht_i(ji,jj,jl) ), ht_i(ji,jj,jl) * krdgmin ) |
---|
496 | hrmin(ji,jj,jl) = MIN( 2._wp * ht_i(ji,jj,jl), 0.5_wp * ( hrmean + ht_i(ji,jj,jl) ) ) |
---|
497 | hrmax(ji,jj,jl) = 2._wp * hrmean - hrmin(ji,jj,jl) |
---|
498 | hraft(ji,jj,jl) = ht_i(ji,jj,jl) / kraft |
---|
499 | krdg(ji,jj,jl) = ht_i(ji,jj,jl) / MAX( hrmean, epsi20 ) |
---|
500 | |
---|
501 | ! Normalization factor : aksum, ensures mass conservation |
---|
502 | aksum(ji,jj) = aksum(ji,jj) + aridge(ji,jj,jl) * ( 1._wp - krdg(ji,jj,jl) ) & |
---|
503 | & + araft (ji,jj,jl) * ( 1._wp - kraft ) |
---|
504 | |
---|
505 | ELSE |
---|
506 | hrmin(ji,jj,jl) = 0._wp |
---|
507 | hrmax(ji,jj,jl) = 0._wp |
---|
508 | hraft(ji,jj,jl) = 0._wp |
---|
509 | krdg (ji,jj,jl) = 1._wp |
---|
510 | ENDIF |
---|
511 | |
---|
512 | END DO |
---|
513 | END DO |
---|
514 | END DO |
---|
515 | ! |
---|
516 | CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
517 | ! |
---|
518 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
519 | |
---|
520 | |
---|
521 | SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross ) |
---|
522 | !!---------------------------------------------------------------------- |
---|
523 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
524 | !! |
---|
525 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
---|
526 | !! |
---|
527 | !! ** Method : Remove area, volume, and energy from each ridging category |
---|
528 | !! and add to thicker ice categories. |
---|
529 | !!---------------------------------------------------------------------- |
---|
530 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
---|
531 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges |
---|
532 | ! |
---|
533 | CHARACTER (len=80) :: fieldid ! field identifier |
---|
534 | ! |
---|
535 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
---|
536 | INTEGER :: ij ! horizontal index, combines i and j loops |
---|
537 | INTEGER :: icells ! number of cells with a_i > puny |
---|
538 | REAL(wp) :: hL, hR, farea ! left and right limits of integration |
---|
539 | |
---|
540 | INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices |
---|
541 | REAL(wp), POINTER, DIMENSION(:) :: zswitch, fvol ! new ridge volume going to n2 |
---|
542 | |
---|
543 | REAL(wp), POINTER, DIMENSION(:) :: afrac ! fraction of category area ridged |
---|
544 | REAL(wp), POINTER, DIMENSION(:) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
---|
545 | REAL(wp), POINTER, DIMENSION(:) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
---|
546 | REAL(wp), POINTER, DIMENSION(:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
---|
547 | |
---|
548 | REAL(wp), POINTER, DIMENSION(:) :: vrdg1 ! volume of ice ridged |
---|
549 | REAL(wp), POINTER, DIMENSION(:) :: vrdg2 ! volume of new ridges |
---|
550 | REAL(wp), POINTER, DIMENSION(:) :: vsw ! volume of seawater trapped into ridges |
---|
551 | REAL(wp), POINTER, DIMENSION(:) :: srdg1 ! sal*volume of ice ridged |
---|
552 | REAL(wp), POINTER, DIMENSION(:) :: srdg2 ! sal*volume of new ridges |
---|
553 | REAL(wp), POINTER, DIMENSION(:) :: smsw ! sal*volume of water trapped into ridges |
---|
554 | REAL(wp), POINTER, DIMENSION(:) :: oirdg1, oirdg2 ! ice age of ice ridged |
---|
555 | |
---|
556 | REAL(wp), POINTER, DIMENSION(:) :: afrft ! fraction of category area rafted |
---|
557 | REAL(wp), POINTER, DIMENSION(:) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
---|
558 | REAL(wp), POINTER, DIMENSION(:) :: virft , vsrft ! ice & snow volume of rafting ice |
---|
559 | REAL(wp), POINTER, DIMENSION(:) :: esrft , smrft ! snow energy & salinity of rafting ice |
---|
560 | REAL(wp), POINTER, DIMENSION(:) :: oirft1, oirft2 ! ice age of ice rafted |
---|
561 | |
---|
562 | REAL(wp), POINTER, DIMENSION(:,:) :: eirft ! ice energy of rafting ice |
---|
563 | REAL(wp), POINTER, DIMENSION(:,:) :: erdg1 ! enth*volume of ice ridged |
---|
564 | REAL(wp), POINTER, DIMENSION(:,:) :: erdg2 ! enth*volume of new ridges |
---|
565 | REAL(wp), POINTER, DIMENSION(:,:) :: ersw ! enth of water trapped into ridges |
---|
566 | !!---------------------------------------------------------------------- |
---|
567 | |
---|
568 | CALL wrk_alloc( jpij, indxi, indxj ) |
---|
569 | CALL wrk_alloc( jpij, zswitch, fvol ) |
---|
570 | CALL wrk_alloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
571 | CALL wrk_alloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
572 | CALL wrk_alloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
573 | CALL wrk_alloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
574 | |
---|
575 | !------------------------------------------------------------------------------- |
---|
576 | ! 1) Compute change in open water area due to closing and opening. |
---|
577 | !------------------------------------------------------------------------------- |
---|
578 | DO jj = 1, jpj |
---|
579 | DO ji = 1, jpi |
---|
580 | ato_i(ji,jj) = MAX( 0._wp, ato_i(ji,jj) + & |
---|
581 | & ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice ) |
---|
582 | END DO |
---|
583 | END DO |
---|
584 | |
---|
585 | !----------------------------------------------------------------- |
---|
586 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
587 | !----------------------------------------------------------------- |
---|
588 | ! Compute the area, volume, and energy of ice ridging in each |
---|
589 | ! category, along with the area of the resulting ridge. |
---|
590 | |
---|
591 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
592 | |
---|
593 | !------------------------------------------------ |
---|
594 | ! 3.1) Identify grid cells with nonzero ridging |
---|
595 | !------------------------------------------------ |
---|
596 | icells = 0 |
---|
597 | DO jj = 1, jpj |
---|
598 | DO ji = 1, jpi |
---|
599 | IF( athorn(ji,jj,jl1) > 0._wp .AND. closing_gross(ji,jj) > 0._wp ) THEN |
---|
600 | icells = icells + 1 |
---|
601 | indxi(icells) = ji |
---|
602 | indxj(icells) = jj |
---|
603 | ENDIF |
---|
604 | END DO |
---|
605 | END DO |
---|
606 | |
---|
607 | DO ij = 1, icells |
---|
608 | ji = indxi(ij) ; jj = indxj(ij) |
---|
609 | |
---|
610 | !-------------------------------------------------------------------- |
---|
611 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
612 | !-------------------------------------------------------------------- |
---|
613 | ardg1(ij) = aridge(ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
614 | arft1(ij) = araft (ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
615 | |
---|
616 | !--------------------------------------------------------------- |
---|
617 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
618 | !--------------------------------------------------------------- |
---|
619 | afrac(ij) = ardg1(ij) / a_i(ji,jj,jl1) !ridging |
---|
620 | afrft(ij) = arft1(ij) / a_i(ji,jj,jl1) !rafting |
---|
621 | ardg2(ij) = ardg1(ij) * krdg(ji,jj,jl1) |
---|
622 | arft2(ij) = arft1(ij) * kraft |
---|
623 | |
---|
624 | !-------------------------------------------------------------------------- |
---|
625 | ! 3.4) Subtract area, volume, and energy from ridging |
---|
626 | ! / rafting category n1. |
---|
627 | !-------------------------------------------------------------------------- |
---|
628 | vrdg1(ij) = v_i(ji,jj,jl1) * afrac(ij) |
---|
629 | vrdg2(ij) = vrdg1(ij) * ( 1. + rn_por_rdg ) |
---|
630 | vsw (ij) = vrdg1(ij) * rn_por_rdg |
---|
631 | |
---|
632 | vsrdg (ij) = v_s (ji,jj, jl1) * afrac(ij) |
---|
633 | esrdg (ij) = e_s (ji,jj,1,jl1) * afrac(ij) |
---|
634 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
---|
635 | oirdg1(ij) = oa_i (ji,jj, jl1) * afrac(ij) |
---|
636 | oirdg2(ij) = oa_i (ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
---|
637 | |
---|
638 | ! rafting volumes, heat contents ... |
---|
639 | virft (ij) = v_i (ji,jj, jl1) * afrft(ij) |
---|
640 | vsrft (ij) = v_s (ji,jj, jl1) * afrft(ij) |
---|
641 | esrft (ij) = e_s (ji,jj,1,jl1) * afrft(ij) |
---|
642 | smrft (ij) = smv_i(ji,jj, jl1) * afrft(ij) |
---|
643 | oirft1(ij) = oa_i (ji,jj, jl1) * afrft(ij) |
---|
644 | oirft2(ij) = oa_i (ji,jj, jl1) * afrft(ij) * kraft |
---|
645 | |
---|
646 | !----------------------------------------------------------------- |
---|
647 | ! 3.5) Compute properties of new ridges |
---|
648 | !----------------------------------------------------------------- |
---|
649 | smsw(ij) = vsw(ij) * sss_m(ji,jj) ! salt content of seawater frozen in voids |
---|
650 | srdg2(ij) = srdg1(ij) + smsw(ij) ! salt content of new ridge |
---|
651 | |
---|
652 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ij) * rhoic * r1_rdtice |
---|
653 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ij) * rhoic * r1_rdtice ! increase in ice volume due to seawater frozen in voids |
---|
654 | |
---|
655 | ! virtual salt flux to keep salinity constant |
---|
656 | IF( nn_icesal == 1 .OR. nn_icesal == 3 ) THEN |
---|
657 | srdg2(ij) = srdg2(ij) - vsw(ij) * ( sss_m(ji,jj) - sm_i(ji,jj,jl1) ) ! ridge salinity = sm_i |
---|
658 | sfx_bri(ji,jj) = sfx_bri(ji,jj) + sss_m(ji,jj) * vsw(ij) * rhoic * r1_rdtice & ! put back sss_m into the ocean |
---|
659 | & - sm_i(ji,jj,jl1) * vsw(ij) * rhoic * r1_rdtice ! and get sm_i from the ocean |
---|
660 | ENDIF |
---|
661 | |
---|
662 | !------------------------------------------ |
---|
663 | ! 3.7 Put the snow somewhere in the ocean |
---|
664 | !------------------------------------------ |
---|
665 | ! Place part of the snow lost by ridging into the ocean. |
---|
666 | ! Note that esrdg > 0; the ocean must cool to melt snow. |
---|
667 | ! If the ocean temp = Tf already, new ice must grow. |
---|
668 | ! During the next time step, thermo_rates will determine whether |
---|
669 | ! the ocean cools or new ice grows. |
---|
670 | wfx_snw(ji,jj) = wfx_snw(ji,jj) + ( rhosn * vsrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
671 | & + rhosn * vsrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! fresh water source for ocean |
---|
672 | |
---|
673 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ( - esrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
674 | & - esrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
---|
675 | |
---|
676 | !----------------------------------------------------------------- |
---|
677 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
678 | ! in the n2 loop below |
---|
679 | !----------------------------------------------------------------- |
---|
680 | dhr (ij) = 1._wp / ( hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) ) |
---|
681 | dhr2(ij) = 1._wp / ( hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) ) |
---|
682 | |
---|
683 | |
---|
684 | ! update jl1 (removing ridged/rafted area) |
---|
685 | a_i (ji,jj, jl1) = a_i (ji,jj, jl1) - ardg1 (ij) - arft1 (ij) |
---|
686 | v_i (ji,jj, jl1) = v_i (ji,jj, jl1) - vrdg1 (ij) - virft (ij) |
---|
687 | v_s (ji,jj, jl1) = v_s (ji,jj, jl1) - vsrdg (ij) - vsrft (ij) |
---|
688 | e_s (ji,jj,1,jl1) = e_s (ji,jj,1,jl1) - esrdg (ij) - esrft (ij) |
---|
689 | smv_i(ji,jj, jl1) = smv_i(ji,jj, jl1) - srdg1 (ij) - smrft (ij) |
---|
690 | oa_i (ji,jj, jl1) = oa_i (ji,jj, jl1) - oirdg1(ij) - oirft1(ij) |
---|
691 | |
---|
692 | END DO |
---|
693 | |
---|
694 | !-------------------------------------------------------------------- |
---|
695 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
696 | ! compute ridged ice enthalpy |
---|
697 | !-------------------------------------------------------------------- |
---|
698 | DO jk = 1, nlay_i |
---|
699 | DO ij = 1, icells |
---|
700 | ji = indxi(ij) ; jj = indxj(ij) |
---|
701 | ! heat content of ridged ice |
---|
702 | erdg1(ij,jk) = e_i(ji,jj,jk,jl1) * afrac(ij) |
---|
703 | eirft(ij,jk) = e_i(ji,jj,jk,jl1) * afrft(ij) |
---|
704 | |
---|
705 | ! enthalpy of the trapped seawater (J/m2, >0) |
---|
706 | ! clem: if sst>0, then ersw <0 (is that possible?) |
---|
707 | ersw(ij,jk) = - rhoic * vsw(ij) * rcp * sst_m(ji,jj) * r1_nlay_i |
---|
708 | |
---|
709 | ! heat flux to the ocean |
---|
710 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ij,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
---|
711 | |
---|
712 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
---|
713 | erdg2(ij,jk) = erdg1(ij,jk) + ersw(ij,jk) |
---|
714 | |
---|
715 | ! update jl1 |
---|
716 | e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ij,jk) - eirft(ij,jk) |
---|
717 | |
---|
718 | END DO |
---|
719 | END DO |
---|
720 | |
---|
721 | !------------------------------------------------------------------------------- |
---|
722 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
723 | !------------------------------------------------------------------------------- |
---|
724 | DO jl2 = 1, jpl |
---|
725 | ! over categories to which ridged/rafted ice is transferred |
---|
726 | DO ij = 1, icells |
---|
727 | ji = indxi(ij) ; jj = indxj(ij) |
---|
728 | |
---|
729 | ! Compute the fraction of ridged ice area and volume going to thickness category jl2. |
---|
730 | IF( hrmin(ji,jj,jl1) <= hi_max(jl2) .AND. hrmax(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
731 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
---|
732 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
---|
733 | farea = ( hR - hL ) * dhr(ij) |
---|
734 | fvol(ij) = ( hR * hR - hL * hL ) * dhr2(ij) |
---|
735 | ELSE |
---|
736 | farea = 0._wp |
---|
737 | fvol(ij) = 0._wp |
---|
738 | ENDIF |
---|
739 | |
---|
740 | ! Compute the fraction of rafted ice area and volume going to thickness category jl2 |
---|
741 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
742 | zswitch(ij) = 1._wp |
---|
743 | ELSE |
---|
744 | zswitch(ij) = 0._wp |
---|
745 | ENDIF |
---|
746 | |
---|
747 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ( ardg2 (ij) * farea + arft2 (ij) * zswitch(ij) ) |
---|
748 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + ( oirdg2(ij) * farea + oirft2(ij) * zswitch(ij) ) |
---|
749 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + ( vrdg2 (ij) * fvol(ij) + virft (ij) * zswitch(ij) ) |
---|
750 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + ( srdg2 (ij) * fvol(ij) + smrft (ij) * zswitch(ij) ) |
---|
751 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + ( vsrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
752 | & vsrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
753 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + ( esrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
754 | & esrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
755 | |
---|
756 | END DO |
---|
757 | |
---|
758 | ! Transfer ice energy to category jl2 by ridging |
---|
759 | DO jk = 1, nlay_i |
---|
760 | DO ij = 1, icells |
---|
761 | ji = indxi(ij) ; jj = indxj(ij) |
---|
762 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + erdg2(ij,jk) * fvol(ij) + eirft(ij,jk) * zswitch(ij) |
---|
763 | END DO |
---|
764 | END DO |
---|
765 | ! |
---|
766 | END DO ! jl2 |
---|
767 | |
---|
768 | END DO ! jl1 (deforming categories) |
---|
769 | |
---|
770 | ! |
---|
771 | CALL wrk_dealloc( jpij, indxi, indxj ) |
---|
772 | CALL wrk_dealloc( jpij, zswitch, fvol ) |
---|
773 | CALL wrk_dealloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
774 | CALL wrk_dealloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
775 | CALL wrk_dealloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
776 | CALL wrk_dealloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
777 | ! |
---|
778 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
779 | |
---|
780 | SUBROUTINE lim_itd_me_icestrength( kstrngth ) |
---|
781 | !!---------------------------------------------------------------------- |
---|
782 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
783 | !! |
---|
784 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
---|
785 | !! |
---|
786 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
787 | !! dissipated per unit area removed from the ice pack under compression, |
---|
788 | !! and assumed proportional to the change in potential energy caused |
---|
789 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
790 | !! ice strength has to be smoothed |
---|
791 | !! |
---|
792 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
793 | !!---------------------------------------------------------------------- |
---|
794 | INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
795 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
796 | INTEGER :: ksmooth ! smoothing the resistance to deformation |
---|
797 | INTEGER :: numts_rm ! number of time steps for the P smoothing |
---|
798 | REAL(wp) :: zp, z1_3 ! local scalars |
---|
799 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
800 | REAL(wp), POINTER, DIMENSION(:,:) :: zstrp1, zstrp2 ! strength at previous time steps |
---|
801 | !!---------------------------------------------------------------------- |
---|
802 | |
---|
803 | CALL wrk_alloc( jpi,jpj, zworka, zstrp1, zstrp2 ) |
---|
804 | |
---|
805 | !------------------------------------------------------------------------------! |
---|
806 | ! 1) Initialize |
---|
807 | !------------------------------------------------------------------------------! |
---|
808 | strength(:,:) = 0._wp |
---|
809 | |
---|
810 | !------------------------------------------------------------------------------! |
---|
811 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
812 | !------------------------------------------------------------------------------! |
---|
813 | CALL lim_itd_me_ridgeprep |
---|
814 | |
---|
815 | !------------------------------------------------------------------------------! |
---|
816 | ! 3) Rothrock(1975)'s method |
---|
817 | !------------------------------------------------------------------------------! |
---|
818 | IF( kstrngth == 1 ) THEN |
---|
819 | z1_3 = 1._wp / 3._wp |
---|
820 | DO jl = 1, jpl |
---|
821 | DO jj= 1, jpj |
---|
822 | DO ji = 1, jpi |
---|
823 | ! |
---|
824 | IF( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
825 | !---------------------------- |
---|
826 | ! PE loss from deforming ice |
---|
827 | !---------------------------- |
---|
828 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
829 | |
---|
830 | !-------------------------- |
---|
831 | ! PE gain from rafting ice |
---|
832 | !-------------------------- |
---|
833 | strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
834 | |
---|
835 | !---------------------------- |
---|
836 | ! PE gain from ridging ice |
---|
837 | !---------------------------- |
---|
838 | strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl) * krdg(ji,jj,jl) * z1_3 * & |
---|
839 | & ( hrmax(ji,jj,jl) * hrmax(ji,jj,jl) + & |
---|
840 | & hrmin(ji,jj,jl) * hrmin(ji,jj,jl) + & |
---|
841 | & hrmax(ji,jj,jl) * hrmin(ji,jj,jl) ) |
---|
842 | !!(a**3-b**3)/(a-b) = a*a+ab+b*b |
---|
843 | ENDIF |
---|
844 | ! |
---|
845 | END DO |
---|
846 | END DO |
---|
847 | END DO |
---|
848 | |
---|
849 | strength(:,:) = rn_pe_rdg * Cp * strength(:,:) / aksum(:,:) * tmask(:,:,1) |
---|
850 | ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and rn_pe_rdg accounts for frictional dissipation |
---|
851 | ksmooth = 1 |
---|
852 | |
---|
853 | !------------------------------------------------------------------------------! |
---|
854 | ! 4) Hibler (1979)' method |
---|
855 | !------------------------------------------------------------------------------! |
---|
856 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
857 | ! |
---|
858 | strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) * tmask(:,:,1) |
---|
859 | ! |
---|
860 | ksmooth = 1 |
---|
861 | ! |
---|
862 | ENDIF ! kstrngth |
---|
863 | ! |
---|
864 | !------------------------------------------------------------------------------! |
---|
865 | ! 5) Impact of brine volume |
---|
866 | !------------------------------------------------------------------------------! |
---|
867 | ! CAN BE REMOVED |
---|
868 | IF( ln_icestr_bvf ) THEN |
---|
869 | DO jj = 1, jpj |
---|
870 | DO ji = 1, jpi |
---|
871 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bvm_i(ji,jj),0.0))) |
---|
872 | END DO |
---|
873 | END DO |
---|
874 | ENDIF |
---|
875 | ! |
---|
876 | !------------------------------------------------------------------------------! |
---|
877 | ! 6) Smoothing ice strength |
---|
878 | !------------------------------------------------------------------------------! |
---|
879 | ! |
---|
880 | !------------------- |
---|
881 | ! Spatial smoothing |
---|
882 | !------------------- |
---|
883 | IF ( ksmooth == 1 ) THEN |
---|
884 | |
---|
885 | DO jj = 2, jpjm1 |
---|
886 | DO ji = 2, jpim1 |
---|
887 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
888 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
---|
889 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
---|
890 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
---|
891 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
---|
892 | ELSE |
---|
893 | zworka(ji,jj) = 0._wp |
---|
894 | ENDIF |
---|
895 | END DO |
---|
896 | END DO |
---|
897 | |
---|
898 | DO jj = 2, jpjm1 |
---|
899 | DO ji = 2, jpim1 |
---|
900 | strength(ji,jj) = zworka(ji,jj) |
---|
901 | END DO |
---|
902 | END DO |
---|
903 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
904 | |
---|
905 | ENDIF |
---|
906 | |
---|
907 | !-------------------- |
---|
908 | ! Temporal smoothing |
---|
909 | !-------------------- |
---|
910 | IF ( ksmooth == 2 ) THEN |
---|
911 | |
---|
912 | IF ( numit == nit000 + nn_fsbc - 1 ) THEN |
---|
913 | zstrp1(:,:) = 0._wp |
---|
914 | zstrp2(:,:) = 0._wp |
---|
915 | ENDIF |
---|
916 | |
---|
917 | DO jj = 2, jpjm1 |
---|
918 | DO ji = 2, jpim1 |
---|
919 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
920 | numts_rm = 1 ! number of time steps for the running mean |
---|
921 | IF ( zstrp1(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
922 | IF ( zstrp2(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
923 | zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / numts_rm |
---|
924 | zstrp2(ji,jj) = zstrp1(ji,jj) |
---|
925 | zstrp1(ji,jj) = strength(ji,jj) |
---|
926 | strength(ji,jj) = zp |
---|
927 | ENDIF |
---|
928 | END DO |
---|
929 | END DO |
---|
930 | |
---|
931 | CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions |
---|
932 | |
---|
933 | ENDIF ! ksmooth |
---|
934 | |
---|
935 | CALL wrk_dealloc( jpi,jpj, zworka, zstrp1, zstrp2 ) |
---|
936 | ! |
---|
937 | END SUBROUTINE lim_itd_me_icestrength |
---|
938 | |
---|
939 | SUBROUTINE lim_itd_me_init |
---|
940 | !!------------------------------------------------------------------- |
---|
941 | !! *** ROUTINE lim_itd_me_init *** |
---|
942 | !! |
---|
943 | !! ** Purpose : Physical constants and parameters linked |
---|
944 | !! to the mechanical ice redistribution |
---|
945 | !! |
---|
946 | !! ** Method : Read the namiceitdme namelist |
---|
947 | !! and check the parameters values |
---|
948 | !! called at the first timestep (nit000) |
---|
949 | !! |
---|
950 | !! ** input : Namelist namiceitdme |
---|
951 | !!------------------------------------------------------------------- |
---|
952 | INTEGER :: ios ! Local integer output status for namelist read |
---|
953 | NAMELIST/namiceitdme/ rn_cs, nn_partfun, rn_gstar, rn_astar, & |
---|
954 | & ln_ridging, rn_hstar, rn_por_rdg, rn_fsnowrdg, ln_rafting, rn_hraft, rn_craft, rn_fsnowrft |
---|
955 | !!------------------------------------------------------------------- |
---|
956 | ! |
---|
957 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
---|
958 | READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901) |
---|
959 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp ) |
---|
960 | |
---|
961 | REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution |
---|
962 | READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 ) |
---|
963 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp ) |
---|
964 | IF(lwm) WRITE ( numoni, namiceitdme ) |
---|
965 | ! |
---|
966 | IF (lwp) THEN ! control print |
---|
967 | WRITE(numout,*) |
---|
968 | WRITE(numout,*)'lim_itd_me_init : ice parameters for mechanical ice redistribution ' |
---|
969 | WRITE(numout,*)'~~~~~~~~~~~~~~~' |
---|
970 | WRITE(numout,*)' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs |
---|
971 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential nn_partfun = ', nn_partfun |
---|
972 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging rn_gstar = ', rn_gstar |
---|
973 | WRITE(numout,*)' Equivalent to G* for an exponential part function rn_astar = ', rn_astar |
---|
974 | WRITE(numout,*)' Ridging of ice sheets or not ln_ridging = ', ln_ridging |
---|
975 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness rn_hstar = ', rn_hstar |
---|
976 | WRITE(numout,*)' Initial porosity of ridges rn_por_rdg = ', rn_por_rdg |
---|
977 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrdg = ', rn_fsnowrdg |
---|
978 | WRITE(numout,*)' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
---|
979 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
---|
980 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
---|
981 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrft = ', rn_fsnowrft |
---|
982 | ENDIF |
---|
983 | ! |
---|
984 | END SUBROUTINE lim_itd_me_init |
---|
985 | |
---|
986 | #else |
---|
987 | !!---------------------------------------------------------------------- |
---|
988 | !! Default option Empty module NO LIM-3 sea-ice model |
---|
989 | !!---------------------------------------------------------------------- |
---|
990 | CONTAINS |
---|
991 | SUBROUTINE lim_itd_me ! Empty routines |
---|
992 | END SUBROUTINE lim_itd_me |
---|
993 | SUBROUTINE lim_itd_me_icestrength |
---|
994 | END SUBROUTINE lim_itd_me_icestrength |
---|
995 | SUBROUTINE lim_itd_me_init |
---|
996 | END SUBROUTINE lim_itd_me_init |
---|
997 | #endif |
---|
998 | !!====================================================================== |
---|
999 | END MODULE limitd_me |
---|