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 par_ice ! LIM parameters |
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21 | USE dom_ice ! LIM domain |
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22 | USE limthd_lac ! LIM |
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23 | USE limvar ! LIM |
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24 | USE in_out_manager ! I/O manager |
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25 | USE lbclnk ! lateral boundary condition - MPP exchanges |
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26 | USE lib_mpp ! MPP library |
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27 | USE wrk_nemo ! work arrays |
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28 | USE prtctl ! Print control |
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29 | ! Check budget (Rousset) |
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30 | USE iom ! I/O manager |
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31 | USE lib_fortran ! glob_sum |
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32 | USE limdiahsb |
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33 | USE timing ! Timing |
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34 | USE limcons ! conservation tests |
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35 | |
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36 | IMPLICIT NONE |
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37 | PRIVATE |
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38 | |
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39 | PUBLIC lim_itd_me ! called by ice_stp |
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40 | PUBLIC lim_itd_me_icestrength |
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41 | PUBLIC lim_itd_me_init |
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42 | PUBLIC lim_itd_me_zapsmall |
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43 | PUBLIC lim_itd_me_alloc ! called by iceini.F90 |
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44 | |
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45 | REAL(wp) :: epsi20 = 1.e-20_wp ! constant values |
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46 | REAL(wp) :: epsi10 = 1.e-10_wp ! constant values |
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47 | REAL(wp) :: epsi06 = 1.e-06_wp ! constant values |
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48 | |
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49 | !----------------------------------------------------------------------- |
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50 | ! Variables shared among ridging subroutines |
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51 | !----------------------------------------------------------------------- |
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52 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
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53 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
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54 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/ |
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55 | ! ! closing associated w/ category n |
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56 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
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57 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
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58 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
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59 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! mean ridge thickness/thickness of ridging ice |
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60 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
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61 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
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62 | |
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63 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
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64 | REAL(wp), PARAMETER :: kraft = 2.0_wp ! rafting multipliyer |
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65 | REAL(wp), PARAMETER :: kamax = 1.0_wp ! max of ice area authorized (clem: scheme is not stable if kamax <= 0.99) |
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66 | |
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67 | REAL(wp) :: Cp ! |
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68 | ! |
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69 | !----------------------------------------------------------------------- |
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70 | ! Ridging diagnostic arrays for history files |
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71 | !----------------------------------------------------------------------- |
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72 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg1dt ! rate of fractional area loss by ridging ice (1/s) |
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73 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg2dt ! rate of fractional area gain by new ridges (1/s) |
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74 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dvirdgdt ! rate of ice volume ridged (m/s) |
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75 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: opening ! rate of opening due to divergence/shear (1/s) |
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76 | ! |
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77 | !!---------------------------------------------------------------------- |
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78 | !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) |
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79 | !! $Id$ |
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80 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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81 | !!---------------------------------------------------------------------- |
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82 | CONTAINS |
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83 | |
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84 | INTEGER FUNCTION lim_itd_me_alloc() |
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85 | !!---------------------------------------------------------------------! |
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86 | !! *** ROUTINE lim_itd_me_alloc *** |
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87 | !!---------------------------------------------------------------------! |
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88 | ALLOCATE( & |
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89 | !* Variables shared among ridging subroutines |
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90 | & asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , & |
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91 | & aksum(jpi,jpj) , & |
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92 | ! |
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93 | & hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
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94 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , & |
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95 | ! |
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96 | !* Ridging diagnostic arrays for history files |
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97 | & dardg1dt(jpi,jpj) , dardg2dt(jpi,jpj) , & |
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98 | & dvirdgdt(jpi,jpj) , opening(jpi,jpj) , STAT=lim_itd_me_alloc ) |
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99 | ! |
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100 | IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' ) |
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101 | ! |
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102 | END FUNCTION lim_itd_me_alloc |
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103 | |
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104 | |
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105 | SUBROUTINE lim_itd_me |
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106 | !!---------------------------------------------------------------------! |
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107 | !! *** ROUTINE lim_itd_me *** |
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108 | !! |
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109 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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110 | !! |
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111 | !! ** Method : Steps : |
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112 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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113 | !! Ridge preparation |
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114 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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115 | !! 3) Ridging iteration |
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116 | !! 4) Ridging diagnostics |
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117 | !! 5) Heat, salt and freshwater fluxes |
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118 | !! 6) Compute increments of tate variables and come back to old values |
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119 | !! |
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120 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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121 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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122 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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123 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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124 | !! Bitz et al., JGR, 2001 |
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125 | !! Amundrud and Melling, JGR 2005 |
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126 | !! Babko et al., JGR 2002 |
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127 | !! |
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128 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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129 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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130 | !!--------------------------------------------------------------------! |
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131 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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132 | INTEGER :: niter, nitermax = 20 ! local integer |
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133 | LOGICAL :: asum_error ! flag for asum .ne. 1 |
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134 | INTEGER :: iterate_ridging ! if true, repeat the ridging |
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135 | REAL(wp) :: w1, tmpfac ! local scalar |
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136 | CHARACTER (len = 15) :: fieldid |
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137 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s) |
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138 | ! (ridging ice area - area of new ridges) / dt |
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139 | REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s) |
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140 | REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear |
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141 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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142 | REAL(wp), POINTER, DIMENSION(:,:) :: msnow_mlt ! mass of snow added to ocean (kg m-2) |
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143 | REAL(wp), POINTER, DIMENSION(:,:) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
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144 | REAL(wp), POINTER, DIMENSION(:,:) :: vt_i_init, vt_i_final ! ice volume summed over categories |
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145 | ! |
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146 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
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147 | !!----------------------------------------------------------------------------- |
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148 | IF( nn_timing == 1 ) CALL timing_start('limitd_me') |
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149 | |
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150 | CALL wrk_alloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) |
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151 | |
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152 | IF(ln_ctl) THEN |
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153 | CALL prt_ctl(tab2d_1=ato_i , clinfo1=' lim_itd_me: ato_i : ', tab2d_2=at_i , clinfo2=' at_i : ') |
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154 | CALL prt_ctl(tab2d_1=divu_i, clinfo1=' lim_itd_me: divu_i : ', tab2d_2=delta_i, clinfo2=' delta_i : ') |
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155 | ENDIF |
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156 | |
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157 | IF( ln_limdyn ) THEN ! Start ridging and rafting ! |
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158 | |
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159 | ! conservation test |
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160 | 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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161 | |
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162 | !-----------------------------------------------------------------------------! |
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163 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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164 | !-----------------------------------------------------------------------------! |
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165 | Cp = 0.5 * grav * (rau0-rhoic) * rhoic / rau0 ! proport const for PE |
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166 | ! |
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167 | CALL lim_itd_me_ridgeprep ! prepare ridging |
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168 | ! |
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169 | IF( con_i) CALL lim_column_sum( jpl, v_i, vt_i_init ) ! conservation check |
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170 | |
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171 | DO jj = 1, jpj ! Initialize arrays. |
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172 | DO ji = 1, jpi |
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173 | msnow_mlt(ji,jj) = 0._wp |
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174 | esnow_mlt(ji,jj) = 0._wp |
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175 | dardg1dt (ji,jj) = 0._wp |
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176 | dardg2dt (ji,jj) = 0._wp |
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177 | dvirdgdt (ji,jj) = 0._wp |
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178 | opening (ji,jj) = 0._wp |
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179 | |
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180 | !-----------------------------------------------------------------------------! |
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181 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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182 | !-----------------------------------------------------------------------------! |
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183 | ! |
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184 | ! 2.1 closing_net |
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185 | !----------------- |
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186 | ! Compute the net rate of closing due to convergence |
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187 | ! and shear, based on Flato and Hibler (1995). |
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188 | ! |
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189 | ! The energy dissipation rate is equal to the net closing rate |
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190 | ! times the ice strength. |
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191 | ! |
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192 | ! NOTE: The NET closing rate is equal to the rate that open water |
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193 | ! area is removed, plus the rate at which ice area is removed by |
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194 | ! ridging, minus the rate at which area is added in new ridges. |
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195 | ! The GROSS closing rate is equal to the first two terms (open |
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196 | ! water closing and thin ice ridging) without the third term |
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197 | ! (thick, newly ridged ice). |
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198 | |
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199 | closing_net(ji,jj) = Cs * 0.5 * ( Delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) |
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200 | |
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201 | ! 2.2 divu_adv |
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202 | !-------------- |
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203 | ! Compute divu_adv, the divergence rate given by the transport/ |
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204 | ! advection scheme, which may not be equal to divu as computed |
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205 | ! from the velocity field. |
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206 | ! |
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207 | ! If divu_adv < 0, make sure the closing rate is large enough |
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208 | ! to give asum = 1.0 after ridging. |
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209 | |
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210 | divu_adv(ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
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211 | |
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212 | IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) |
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213 | |
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214 | ! 2.3 opning |
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215 | !------------ |
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216 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
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217 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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218 | END DO |
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219 | END DO |
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220 | |
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221 | !-----------------------------------------------------------------------------! |
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222 | ! 3) Ridging iteration |
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223 | !-----------------------------------------------------------------------------! |
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224 | niter = 1 ! iteration counter |
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225 | iterate_ridging = 1 |
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226 | |
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227 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
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228 | |
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229 | DO jj = 1, jpj |
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230 | DO ji = 1, jpi |
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231 | |
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232 | ! 3.2 closing_gross |
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233 | !-----------------------------------------------------------------------------! |
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234 | ! Based on the ITD of ridging and ridged ice, convert the net |
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235 | ! closing rate to a gross closing rate. |
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236 | ! NOTE: 0 < aksum <= 1 |
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237 | closing_gross(ji,jj) = closing_net(ji,jj) / aksum(ji,jj) |
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238 | |
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239 | ! correction to closing rate and opening if closing rate is excessive |
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240 | !--------------------------------------------------------------------- |
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241 | ! Reduce the closing rate if more than 100% of the open water |
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242 | ! would be removed. Reduce the opening rate proportionately. |
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243 | IF ( ato_i(ji,jj) .GT. epsi10 .AND. athorn(ji,jj,0) .GT. 0.0 ) THEN |
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244 | w1 = athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice |
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245 | IF ( w1 .GT. ato_i(ji,jj)) THEN |
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246 | tmpfac = ato_i(ji,jj) / w1 |
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247 | closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac |
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248 | opning(ji,jj) = opning(ji,jj) * tmpfac |
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249 | ENDIF !w1 |
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250 | ENDIF !at0i and athorn |
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251 | |
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252 | END DO ! ji |
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253 | END DO ! jj |
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254 | |
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255 | ! correction to closing rate / opening if excessive ice removal |
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256 | !--------------------------------------------------------------- |
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257 | ! Reduce the closing rate if more than 100% of any ice category |
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258 | ! would be removed. Reduce the opening rate proportionately. |
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259 | |
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260 | DO jl = 1, jpl |
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261 | DO jj = 1, jpj |
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262 | DO ji = 1, jpi |
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263 | IF ( a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0._wp )THEN |
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264 | w1 = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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265 | IF ( w1 > a_i(ji,jj,jl) ) THEN |
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266 | tmpfac = a_i(ji,jj,jl) / w1 |
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267 | closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac |
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268 | opning (ji,jj) = opning (ji,jj) * tmpfac |
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269 | ENDIF |
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270 | ENDIF |
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271 | END DO !ji |
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272 | END DO ! jj |
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273 | END DO !jl |
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274 | |
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275 | ! 3.3 Redistribute area, volume, and energy. |
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276 | !-----------------------------------------------------------------------------! |
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277 | |
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278 | CALL lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) |
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279 | |
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280 | ! 3.4 Compute total area of ice plus open water after ridging. |
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281 | !-----------------------------------------------------------------------------! |
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282 | |
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283 | CALL lim_itd_me_asumr |
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284 | |
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285 | ! 3.5 Do we keep on iterating ??? |
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286 | !-----------------------------------------------------------------------------! |
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287 | ! Check whether asum = 1. If not (because the closing and opening |
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288 | ! rates were reduced above), ridge again with new rates. |
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289 | |
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290 | iterate_ridging = 0 |
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291 | |
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292 | DO jj = 1, jpj |
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293 | DO ji = 1, jpi |
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294 | IF (ABS(asum(ji,jj) - kamax ) .LT. epsi10) THEN |
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295 | closing_net(ji,jj) = 0._wp |
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296 | opning (ji,jj) = 0._wp |
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297 | ELSE |
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298 | iterate_ridging = 1 |
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299 | divu_adv (ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice |
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300 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
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301 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
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302 | ENDIF |
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303 | END DO |
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304 | END DO |
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305 | |
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306 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
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307 | |
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308 | ! Repeat if necessary. |
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309 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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310 | ! iterated globally because of the boundary update in the |
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311 | ! smoothing. |
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312 | |
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313 | niter = niter + 1 |
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314 | |
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315 | IF( iterate_ridging == 1 ) THEN |
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316 | IF( niter > nitermax ) THEN |
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317 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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318 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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319 | ENDIF |
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320 | CALL lim_itd_me_ridgeprep |
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321 | ENDIF |
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322 | |
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323 | END DO !! on the do while over iter |
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324 | |
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325 | !-----------------------------------------------------------------------------! |
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326 | ! 4) Ridging diagnostics |
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327 | !-----------------------------------------------------------------------------! |
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328 | ! Convert ridging rate diagnostics to correct units. |
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329 | ! Update fresh water and heat fluxes due to snow melt. |
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330 | |
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331 | asum_error = .false. |
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332 | |
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333 | DO jj = 1, jpj |
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334 | DO ji = 1, jpi |
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335 | |
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336 | IF(ABS(asum(ji,jj) - kamax) > epsi10 ) asum_error = .true. |
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337 | |
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338 | dardg1dt(ji,jj) = dardg1dt(ji,jj) * r1_rdtice |
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339 | dardg2dt(ji,jj) = dardg2dt(ji,jj) * r1_rdtice |
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340 | dvirdgdt(ji,jj) = dvirdgdt(ji,jj) * r1_rdtice |
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341 | opening (ji,jj) = opening (ji,jj) * r1_rdtice |
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342 | |
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343 | !-----------------------------------------------------------------------------! |
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344 | ! 5) Heat, salt and freshwater fluxes |
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345 | !-----------------------------------------------------------------------------! |
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346 | wfx_snw(ji,jj) = wfx_snw(ji,jj) + msnow_mlt(ji,jj) * r1_rdtice ! fresh water source for ocean |
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347 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + esnow_mlt(ji,jj) * unit_fac / area(ji,jj) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
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348 | |
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349 | END DO |
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350 | END DO |
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351 | |
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352 | ! Check if there is a ridging error |
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353 | DO jj = 1, jpj |
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354 | DO ji = 1, jpi |
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355 | IF( ABS( asum(ji,jj) - kamax) > epsi10 ) THEN ! there is a bug |
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356 | WRITE(numout,*) ' ' |
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357 | WRITE(numout,*) ' ALERTE : Ridging error: total area = ', asum(ji,jj) |
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358 | WRITE(numout,*) ' limitd_me ' |
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359 | WRITE(numout,*) ' POINT : ', ji, jj |
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360 | WRITE(numout,*) ' jpl, a_i, athorn ' |
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361 | WRITE(numout,*) 0, ato_i(ji,jj), athorn(ji,jj,0) |
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362 | DO jl = 1, jpl |
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363 | WRITE(numout,*) jl, a_i(ji,jj,jl), athorn(ji,jj,jl) |
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364 | END DO |
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365 | ENDIF ! asum |
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366 | |
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367 | END DO !ji |
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368 | END DO !jj |
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369 | |
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370 | ! Conservation check |
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371 | IF ( con_i ) THEN |
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372 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
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373 | fieldid = ' v_i : limitd_me ' |
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374 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
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375 | ENDIF |
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376 | |
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377 | !-----------------------------------------------------------------------------! |
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378 | ! 6) Updating state variables and trend terms (done in limupdate) |
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379 | !-----------------------------------------------------------------------------! |
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380 | CALL lim_var_glo2eqv |
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381 | CALL lim_itd_me_zapsmall |
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382 | |
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383 | |
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384 | IF(ln_ctl) THEN ! Control print |
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385 | CALL prt_ctl_info(' ') |
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386 | CALL prt_ctl_info(' - Cell values : ') |
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387 | CALL prt_ctl_info(' ~~~~~~~~~~~~~ ') |
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388 | CALL prt_ctl(tab2d_1=area , clinfo1=' lim_itd_me : cell area :') |
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389 | CALL prt_ctl(tab2d_1=at_i , clinfo1=' lim_itd_me : at_i :') |
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390 | CALL prt_ctl(tab2d_1=vt_i , clinfo1=' lim_itd_me : vt_i :') |
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391 | CALL prt_ctl(tab2d_1=vt_s , clinfo1=' lim_itd_me : vt_s :') |
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392 | DO jl = 1, jpl |
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393 | CALL prt_ctl_info(' ') |
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394 | CALL prt_ctl_info(' - Category : ', ivar1=jl) |
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395 | CALL prt_ctl_info(' ~~~~~~~~~~') |
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396 | CALL prt_ctl(tab2d_1=a_i (:,:,jl) , clinfo1= ' lim_itd_me : a_i : ') |
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397 | CALL prt_ctl(tab2d_1=ht_i (:,:,jl) , clinfo1= ' lim_itd_me : ht_i : ') |
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398 | CALL prt_ctl(tab2d_1=ht_s (:,:,jl) , clinfo1= ' lim_itd_me : ht_s : ') |
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399 | CALL prt_ctl(tab2d_1=v_i (:,:,jl) , clinfo1= ' lim_itd_me : v_i : ') |
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400 | CALL prt_ctl(tab2d_1=v_s (:,:,jl) , clinfo1= ' lim_itd_me : v_s : ') |
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401 | CALL prt_ctl(tab2d_1=e_s (:,:,1,jl) , clinfo1= ' lim_itd_me : e_s : ') |
---|
402 | CALL prt_ctl(tab2d_1=t_su (:,:,jl) , clinfo1= ' lim_itd_me : t_su : ') |
---|
403 | CALL prt_ctl(tab2d_1=t_s (:,:,1,jl) , clinfo1= ' lim_itd_me : t_snow : ') |
---|
404 | CALL prt_ctl(tab2d_1=sm_i (:,:,jl) , clinfo1= ' lim_itd_me : sm_i : ') |
---|
405 | CALL prt_ctl(tab2d_1=smv_i (:,:,jl) , clinfo1= ' lim_itd_me : smv_i : ') |
---|
406 | DO jk = 1, nlay_i |
---|
407 | CALL prt_ctl_info(' ') |
---|
408 | CALL prt_ctl_info(' - Layer : ', ivar1=jk) |
---|
409 | CALL prt_ctl_info(' ~~~~~~~') |
---|
410 | CALL prt_ctl(tab2d_1=t_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : t_i : ') |
---|
411 | CALL prt_ctl(tab2d_1=e_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : e_i : ') |
---|
412 | END DO |
---|
413 | END DO |
---|
414 | ENDIF |
---|
415 | |
---|
416 | ! conservation test |
---|
417 | IF( ln_limdiahsb ) CALL lim_cons_hsm(1, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
---|
418 | |
---|
419 | ENDIF ! ln_limdyn=.true. |
---|
420 | ! |
---|
421 | CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) |
---|
422 | ! |
---|
423 | IF( nn_timing == 1 ) CALL timing_stop('limitd_me') |
---|
424 | END SUBROUTINE lim_itd_me |
---|
425 | |
---|
426 | |
---|
427 | SUBROUTINE lim_itd_me_icestrength( kstrngth ) |
---|
428 | !!---------------------------------------------------------------------- |
---|
429 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
430 | !! |
---|
431 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
---|
432 | !! |
---|
433 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
434 | !! dissipated per unit area removed from the ice pack under compression, |
---|
435 | !! and assumed proportional to the change in potential energy caused |
---|
436 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
437 | !! ice strength has to be smoothed |
---|
438 | !! |
---|
439 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
440 | !!---------------------------------------------------------------------- |
---|
441 | INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
442 | |
---|
443 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
444 | INTEGER :: ksmooth ! smoothing the resistance to deformation |
---|
445 | INTEGER :: numts_rm ! number of time steps for the P smoothing |
---|
446 | REAL(wp) :: hi, zw1, zp, zdummy, zzc, z1_3 ! local scalars |
---|
447 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
448 | !!---------------------------------------------------------------------- |
---|
449 | |
---|
450 | CALL wrk_alloc( jpi, jpj, zworka ) |
---|
451 | |
---|
452 | !------------------------------------------------------------------------------! |
---|
453 | ! 1) Initialize |
---|
454 | !------------------------------------------------------------------------------! |
---|
455 | strength(:,:) = 0._wp |
---|
456 | |
---|
457 | !------------------------------------------------------------------------------! |
---|
458 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
459 | !------------------------------------------------------------------------------! |
---|
460 | CALL lim_itd_me_ridgeprep |
---|
461 | |
---|
462 | !------------------------------------------------------------------------------! |
---|
463 | ! 3) Rothrock(1975)'s method |
---|
464 | !------------------------------------------------------------------------------! |
---|
465 | IF( kstrngth == 1 ) THEN |
---|
466 | z1_3 = 1._wp / 3._wp |
---|
467 | DO jl = 1, jpl |
---|
468 | DO jj= 1, jpj |
---|
469 | DO ji = 1, jpi |
---|
470 | ! |
---|
471 | IF( a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0._wp ) THEN |
---|
472 | hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
473 | !---------------------------- |
---|
474 | ! PE loss from deforming ice |
---|
475 | !---------------------------- |
---|
476 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * hi * hi |
---|
477 | |
---|
478 | !-------------------------- |
---|
479 | ! PE gain from rafting ice |
---|
480 | !-------------------------- |
---|
481 | strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * hi * hi |
---|
482 | |
---|
483 | !---------------------------- |
---|
484 | ! PE gain from ridging ice |
---|
485 | !---------------------------- |
---|
486 | strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl)/krdg(ji,jj,jl) & |
---|
487 | * z1_3 * (hrmax(ji,jj,jl)**3 - hrmin(ji,jj,jl)**3) / ( hrmax(ji,jj,jl)-hrmin(ji,jj,jl) ) |
---|
488 | !!gm Optimization: (a**3-b**3)/(a-b) = a*a+ab+b*b ==> less costly operations even if a**3 is replaced by a*a*a... |
---|
489 | ENDIF ! aicen > epsi10 |
---|
490 | ! |
---|
491 | END DO ! ji |
---|
492 | END DO !jj |
---|
493 | END DO !jl |
---|
494 | |
---|
495 | zzc = Cf * Cp ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and Cf accounts for frictional dissipation |
---|
496 | strength(:,:) = zzc * strength(:,:) / aksum(:,:) |
---|
497 | |
---|
498 | ksmooth = 1 |
---|
499 | |
---|
500 | !------------------------------------------------------------------------------! |
---|
501 | ! 4) Hibler (1979)' method |
---|
502 | !------------------------------------------------------------------------------! |
---|
503 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
504 | ! |
---|
505 | strength(:,:) = Pstar * vt_i(:,:) * EXP( - C_rhg * ( 1._wp - at_i(:,:) ) ) |
---|
506 | ! |
---|
507 | ksmooth = 1 |
---|
508 | ! |
---|
509 | ENDIF ! kstrngth |
---|
510 | |
---|
511 | ! |
---|
512 | !------------------------------------------------------------------------------! |
---|
513 | ! 5) Impact of brine volume |
---|
514 | !------------------------------------------------------------------------------! |
---|
515 | ! CAN BE REMOVED |
---|
516 | ! |
---|
517 | IF ( brinstren_swi == 1 ) THEN |
---|
518 | |
---|
519 | DO jj = 1, jpj |
---|
520 | DO ji = 1, jpi |
---|
521 | IF ( bv_i(ji,jj) .GT. 0.0 ) THEN |
---|
522 | zdummy = MIN ( bv_i(ji,jj), 0.10 ) * MIN( bv_i(ji,jj), 0.10 ) |
---|
523 | ELSE |
---|
524 | zdummy = 0.0 |
---|
525 | ENDIF |
---|
526 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bv_i(ji,jj),0.0))) |
---|
527 | END DO ! j |
---|
528 | END DO ! i |
---|
529 | |
---|
530 | ENDIF |
---|
531 | |
---|
532 | ! |
---|
533 | !------------------------------------------------------------------------------! |
---|
534 | ! 6) Smoothing ice strength |
---|
535 | !------------------------------------------------------------------------------! |
---|
536 | ! |
---|
537 | !------------------- |
---|
538 | ! Spatial smoothing |
---|
539 | !------------------- |
---|
540 | IF ( ksmooth == 1 ) THEN |
---|
541 | |
---|
542 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
543 | |
---|
544 | DO jj = 2, jpj - 1 |
---|
545 | DO ji = 2, jpi - 1 |
---|
546 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi10) THEN ! ice is |
---|
547 | ! present |
---|
548 | zworka(ji,jj) = 4.0 * strength(ji,jj) & |
---|
549 | & + strength(ji-1,jj) * tms(ji-1,jj) & |
---|
550 | & + strength(ji+1,jj) * tms(ji+1,jj) & |
---|
551 | & + strength(ji,jj-1) * tms(ji,jj-1) & |
---|
552 | & + strength(ji,jj+1) * tms(ji,jj+1) |
---|
553 | |
---|
554 | zw1 = 4.0 + tms(ji-1,jj) + tms(ji+1,jj) + tms(ji,jj-1) + tms(ji,jj+1) |
---|
555 | zworka(ji,jj) = zworka(ji,jj) / zw1 |
---|
556 | ELSE |
---|
557 | zworka(ji,jj) = 0._wp |
---|
558 | ENDIF |
---|
559 | END DO |
---|
560 | END DO |
---|
561 | |
---|
562 | DO jj = 2, jpj - 1 |
---|
563 | DO ji = 2, jpi - 1 |
---|
564 | strength(ji,jj) = zworka(ji,jj) |
---|
565 | END DO |
---|
566 | END DO |
---|
567 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
568 | |
---|
569 | ENDIF ! ksmooth |
---|
570 | |
---|
571 | !-------------------- |
---|
572 | ! Temporal smoothing |
---|
573 | !-------------------- |
---|
574 | IF ( numit == nit000 + nn_fsbc - 1 ) THEN |
---|
575 | strp1(:,:) = 0.0 |
---|
576 | strp2(:,:) = 0.0 |
---|
577 | ENDIF |
---|
578 | |
---|
579 | IF ( ksmooth == 2 ) THEN |
---|
580 | |
---|
581 | |
---|
582 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
583 | |
---|
584 | DO jj = 1, jpj - 1 |
---|
585 | DO ji = 1, jpi - 1 |
---|
586 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi10) THEN ! ice is present |
---|
587 | numts_rm = 1 ! number of time steps for the running mean |
---|
588 | IF ( strp1(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 |
---|
589 | IF ( strp2(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 |
---|
590 | zp = ( strength(ji,jj) + strp1(ji,jj) + strp2(ji,jj) ) / numts_rm |
---|
591 | strp2(ji,jj) = strp1(ji,jj) |
---|
592 | strp1(ji,jj) = strength(ji,jj) |
---|
593 | strength(ji,jj) = zp |
---|
594 | |
---|
595 | ENDIF |
---|
596 | END DO |
---|
597 | END DO |
---|
598 | |
---|
599 | ENDIF ! ksmooth |
---|
600 | |
---|
601 | CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions |
---|
602 | |
---|
603 | CALL wrk_dealloc( jpi, jpj, zworka ) |
---|
604 | ! |
---|
605 | END SUBROUTINE lim_itd_me_icestrength |
---|
606 | |
---|
607 | |
---|
608 | SUBROUTINE lim_itd_me_ridgeprep |
---|
609 | !!---------------------------------------------------------------------! |
---|
610 | !! *** ROUTINE lim_itd_me_ridgeprep *** |
---|
611 | !! |
---|
612 | !! ** Purpose : preparation for ridging and strength calculations |
---|
613 | !! |
---|
614 | !! ** Method : Compute the thickness distribution of the ice and open water |
---|
615 | !! participating in ridging and of the resulting ridges. |
---|
616 | !!---------------------------------------------------------------------! |
---|
617 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
618 | REAL(wp) :: Gstari, astari, hi, hrmean, zdummy ! local scalar |
---|
619 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
620 | REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n |
---|
621 | !------------------------------------------------------------------------------! |
---|
622 | |
---|
623 | CALL wrk_alloc( jpi,jpj, zworka ) |
---|
624 | CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
625 | |
---|
626 | Gstari = 1.0/Gstar |
---|
627 | astari = 1.0/astar |
---|
628 | aksum(:,:) = 0.0 |
---|
629 | athorn(:,:,:) = 0.0 |
---|
630 | aridge(:,:,:) = 0.0 |
---|
631 | araft (:,:,:) = 0.0 |
---|
632 | hrmin(:,:,:) = 0.0 |
---|
633 | hrmax(:,:,:) = 0.0 |
---|
634 | hraft(:,:,:) = 0.0 |
---|
635 | krdg (:,:,:) = 1.0 |
---|
636 | |
---|
637 | ! ! Zero out categories with very small areas |
---|
638 | CALL lim_itd_me_zapsmall |
---|
639 | |
---|
640 | !------------------------------------------------------------------------------! |
---|
641 | ! 1) Participation function |
---|
642 | !------------------------------------------------------------------------------! |
---|
643 | |
---|
644 | ! Compute total area of ice plus open water. |
---|
645 | CALL lim_itd_me_asumr |
---|
646 | ! This is in general not equal to one |
---|
647 | ! because of divergence during transport |
---|
648 | |
---|
649 | ! Compute cumulative thickness distribution function |
---|
650 | ! Compute the cumulative thickness distribution function Gsum, |
---|
651 | ! where Gsum(n) is the fractional area in categories 0 to n. |
---|
652 | ! initial value (in h = 0) equals open water area |
---|
653 | |
---|
654 | Gsum(:,:,-1) = 0._wp |
---|
655 | |
---|
656 | DO jj = 1, jpj |
---|
657 | DO ji = 1, jpi |
---|
658 | IF( ato_i(ji,jj) > epsi10 ) THEN ; Gsum(ji,jj,0) = ato_i(ji,jj) |
---|
659 | ELSE ; Gsum(ji,jj,0) = 0._wp |
---|
660 | ENDIF |
---|
661 | END DO |
---|
662 | END DO |
---|
663 | |
---|
664 | ! for each value of h, you have to add ice concentration then |
---|
665 | DO jl = 1, jpl |
---|
666 | DO jj = 1, jpj |
---|
667 | DO ji = 1, jpi |
---|
668 | IF( a_i(ji,jj,jl) .GT. epsi10 ) THEN ; Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) + a_i(ji,jj,jl) |
---|
669 | ELSE ; Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) |
---|
670 | ENDIF |
---|
671 | END DO |
---|
672 | END DO |
---|
673 | END DO |
---|
674 | |
---|
675 | ! Normalize the cumulative distribution to 1 |
---|
676 | zworka(:,:) = 1._wp / Gsum(:,:,jpl) |
---|
677 | DO jl = 0, jpl |
---|
678 | Gsum(:,:,jl) = Gsum(:,:,jl) * zworka(:,:) |
---|
679 | END DO |
---|
680 | |
---|
681 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
---|
682 | !-------------------------------------------------------------------------------------------------- |
---|
683 | ! Compute the participation function athorn; this is analogous to |
---|
684 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
---|
685 | ! area lost from category n due to ridging/closing |
---|
686 | ! athorn(n) = total area lost due to ridging/closing |
---|
687 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
---|
688 | ! |
---|
689 | ! The expressions for athorn are found by integrating b(h)g(h) between |
---|
690 | ! the category boundaries. |
---|
691 | !----------------------------------------------------------------- |
---|
692 | |
---|
693 | IF( partfun_swi == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) |
---|
694 | DO jl = 0, jpl |
---|
695 | DO jj = 1, jpj |
---|
696 | DO ji = 1, jpi |
---|
697 | IF( Gsum(ji,jj,jl) < Gstar) THEN |
---|
698 | athorn(ji,jj,jl) = Gstari * (Gsum(ji,jj,jl)-Gsum(ji,jj,jl-1)) * & |
---|
699 | (2.0 - (Gsum(ji,jj,jl-1)+Gsum(ji,jj,jl))*Gstari) |
---|
700 | ELSEIF (Gsum(ji,jj,jl-1) < Gstar) THEN |
---|
701 | athorn(ji,jj,jl) = Gstari * (Gstar-Gsum(ji,jj,jl-1)) * & |
---|
702 | (2.0 - (Gsum(ji,jj,jl-1)+Gstar)*Gstari) |
---|
703 | ELSE |
---|
704 | athorn(ji,jj,jl) = 0.0 |
---|
705 | ENDIF |
---|
706 | END DO ! ji |
---|
707 | END DO ! jj |
---|
708 | END DO ! jl |
---|
709 | |
---|
710 | ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
711 | ! |
---|
712 | zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array |
---|
713 | |
---|
714 | DO jl = -1, jpl |
---|
715 | Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy |
---|
716 | END DO !jl |
---|
717 | DO jl = 0, jpl |
---|
718 | athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) |
---|
719 | END DO |
---|
720 | ! |
---|
721 | ENDIF ! partfun_swi |
---|
722 | |
---|
723 | IF( raft_swi == 1 ) THEN ! Ridging and rafting ice participation functions |
---|
724 | ! |
---|
725 | DO jl = 1, jpl |
---|
726 | DO jj = 1, jpj |
---|
727 | DO ji = 1, jpi |
---|
728 | IF ( athorn(ji,jj,jl) .GT. 0._wp ) THEN |
---|
729 | !!gm TANH( -X ) = - TANH( X ) so can be computed only 1 time.... |
---|
730 | aridge(ji,jj,jl) = ( TANH ( Craft * ( ht_i(ji,jj,jl) - hparmeter ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) |
---|
731 | araft (ji,jj,jl) = ( TANH ( -Craft * ( ht_i(ji,jj,jl) - hparmeter ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) |
---|
732 | IF ( araft(ji,jj,jl) < epsi06 ) araft(ji,jj,jl) = 0._wp |
---|
733 | aridge(ji,jj,jl) = MAX( athorn(ji,jj,jl) - araft(ji,jj,jl), 0.0 ) |
---|
734 | ENDIF ! athorn |
---|
735 | END DO ! ji |
---|
736 | END DO ! jj |
---|
737 | END DO ! jl |
---|
738 | |
---|
739 | ELSE ! raft_swi = 0 |
---|
740 | ! |
---|
741 | DO jl = 1, jpl |
---|
742 | aridge(:,:,jl) = athorn(:,:,jl) |
---|
743 | END DO |
---|
744 | ! |
---|
745 | ENDIF |
---|
746 | |
---|
747 | IF ( raft_swi == 1 ) THEN |
---|
748 | |
---|
749 | IF( MAXVAL(aridge + araft - athorn(:,:,1:jpl)) .GT. epsi10 ) THEN |
---|
750 | DO jl = 1, jpl |
---|
751 | DO jj = 1, jpj |
---|
752 | DO ji = 1, jpi |
---|
753 | IF ( aridge(ji,jj,jl) + araft(ji,jj,jl) - athorn(ji,jj,jl) .GT. epsi10 ) THEN |
---|
754 | WRITE(numout,*) ' ALERTE 96 : wrong participation function ... ' |
---|
755 | WRITE(numout,*) ' ji, jj, jl : ', ji, jj, jl |
---|
756 | WRITE(numout,*) ' lat, lon : ', gphit(ji,jj), glamt(ji,jj) |
---|
757 | WRITE(numout,*) ' aridge : ', aridge(ji,jj,1:jpl) |
---|
758 | WRITE(numout,*) ' araft : ', araft(ji,jj,1:jpl) |
---|
759 | WRITE(numout,*) ' athorn : ', athorn(ji,jj,1:jpl) |
---|
760 | ENDIF |
---|
761 | END DO |
---|
762 | END DO |
---|
763 | END DO |
---|
764 | ENDIF |
---|
765 | |
---|
766 | ENDIF |
---|
767 | |
---|
768 | !----------------------------------------------------------------- |
---|
769 | ! 2) Transfer function |
---|
770 | !----------------------------------------------------------------- |
---|
771 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
772 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
773 | ! |
---|
774 | ! This parameterization is a modified version of Hibler (1980). |
---|
775 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
776 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
777 | ! |
---|
778 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
779 | ! (i.e., rafting) and for very thick ridging ice is |
---|
780 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
781 | ! |
---|
782 | ! The maximum ridging thickness, hrmax, is determined by |
---|
783 | ! hrmean and hrmin. |
---|
784 | ! |
---|
785 | ! These modifications have the effect of reducing the ice strength |
---|
786 | ! (relative to the Hibler formulation) when very thick ice is |
---|
787 | ! ridging. |
---|
788 | ! |
---|
789 | ! aksum = net area removed/ total area removed |
---|
790 | ! where total area removed = area of ice that ridges |
---|
791 | ! net area removed = total area removed - area of new ridges |
---|
792 | !----------------------------------------------------------------- |
---|
793 | |
---|
794 | ! Transfer function |
---|
795 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
796 | DO jj = 1, jpj |
---|
797 | DO ji = 1, jpi |
---|
798 | |
---|
799 | IF (a_i(ji,jj,jl) .GT. epsi10 .AND. athorn(ji,jj,jl) .GT. 0.0 ) THEN |
---|
800 | hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
801 | hrmean = MAX(SQRT(Hstar*hi), hi*krdgmin) |
---|
802 | hrmin(ji,jj,jl) = MIN(2.0*hi, 0.5*(hrmean + hi)) |
---|
803 | hrmax(ji,jj,jl) = 2.0*hrmean - hrmin(ji,jj,jl) |
---|
804 | hraft(ji,jj,jl) = kraft*hi |
---|
805 | krdg(ji,jj,jl) = hrmean / hi |
---|
806 | ELSE |
---|
807 | hraft(ji,jj,jl) = 0.0 |
---|
808 | hrmin(ji,jj,jl) = 0.0 |
---|
809 | hrmax(ji,jj,jl) = 0.0 |
---|
810 | krdg (ji,jj,jl) = 1.0 |
---|
811 | ENDIF |
---|
812 | |
---|
813 | END DO ! ji |
---|
814 | END DO ! jj |
---|
815 | END DO ! jl |
---|
816 | |
---|
817 | ! Normalization factor : aksum, ensures mass conservation |
---|
818 | aksum(:,:) = athorn(:,:,0) |
---|
819 | DO jl = 1, jpl |
---|
820 | aksum(:,:) = aksum(:,:) + aridge(:,:,jl) * ( 1._wp - 1._wp / krdg(:,:,jl) ) & |
---|
821 | & + araft (:,:,jl) * ( 1._wp - 1._wp / kraft ) |
---|
822 | END DO |
---|
823 | ! |
---|
824 | CALL wrk_dealloc( jpi,jpj, zworka ) |
---|
825 | CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
826 | ! |
---|
827 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
828 | |
---|
829 | |
---|
830 | SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) |
---|
831 | !!---------------------------------------------------------------------- |
---|
832 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
833 | !! |
---|
834 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
---|
835 | !! |
---|
836 | !! ** Method : Remove area, volume, and energy from each ridging category |
---|
837 | !! and add to thicker ice categories. |
---|
838 | !!---------------------------------------------------------------------- |
---|
839 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
---|
840 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges |
---|
841 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: msnow_mlt ! mass of snow added to ocean (kg m-2) |
---|
842 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
---|
843 | ! |
---|
844 | CHARACTER (len=80) :: fieldid ! field identifier |
---|
845 | LOGICAL, PARAMETER :: l_conservation_check = .true. ! if true, check conservation (useful for debugging) |
---|
846 | ! |
---|
847 | LOGICAL :: neg_ato_i ! flag for ato_i(i,j) < -puny |
---|
848 | LOGICAL :: large_afrac ! flag for afrac > 1 |
---|
849 | LOGICAL :: large_afrft ! flag for afrac > 1 |
---|
850 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
---|
851 | INTEGER :: ij ! horizontal index, combines i and j loops |
---|
852 | INTEGER :: icells ! number of cells with aicen > puny |
---|
853 | REAL(wp) :: zindb ! local scalar |
---|
854 | REAL(wp) :: hL, hR, farea, zdummy, zdummy0, ztmelts ! left and right limits of integration |
---|
855 | REAL(wp) :: zsstK ! SST in Kelvin |
---|
856 | |
---|
857 | INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices |
---|
858 | |
---|
859 | REAL(wp), POINTER, DIMENSION(:,:) :: vice_init, vice_final ! ice volume summed over categories |
---|
860 | REAL(wp), POINTER, DIMENSION(:,:) :: eice_init, eice_final ! ice energy summed over layers |
---|
861 | |
---|
862 | REAL(wp), POINTER, DIMENSION(:,:,:) :: aicen_init, vicen_init ! ice area & volume before ridging |
---|
863 | REAL(wp), POINTER, DIMENSION(:,:,:) :: vsnwn_init, esnwn_init ! snow volume & energy before ridging |
---|
864 | REAL(wp), POINTER, DIMENSION(:,:,:) :: smv_i_init, oa_i_init ! ice salinity & age before ridging |
---|
865 | |
---|
866 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: eicen_init ! ice energy before ridging |
---|
867 | |
---|
868 | REAL(wp), POINTER, DIMENSION(:,:) :: afrac , fvol ! fraction of category area ridged & new ridge volume going to n2 |
---|
869 | REAL(wp), POINTER, DIMENSION(:,:) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
---|
870 | REAL(wp), POINTER, DIMENSION(:,:) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
---|
871 | REAL(wp), POINTER, DIMENSION(:,:) :: oirdg1, oirdg2 ! areal age content of ridged & rifging ice |
---|
872 | REAL(wp), POINTER, DIMENSION(:,:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
---|
873 | |
---|
874 | REAL(wp), POINTER, DIMENSION(:,:) :: vrdg1 ! volume of ice ridged |
---|
875 | REAL(wp), POINTER, DIMENSION(:,:) :: vrdg2 ! volume of new ridges |
---|
876 | REAL(wp), POINTER, DIMENSION(:,:) :: vsw ! volume of seawater trapped into ridges |
---|
877 | REAL(wp), POINTER, DIMENSION(:,:) :: srdg1 ! sal*volume of ice ridged |
---|
878 | REAL(wp), POINTER, DIMENSION(:,:) :: srdg2 ! sal*volume of new ridges |
---|
879 | REAL(wp), POINTER, DIMENSION(:,:) :: smsw ! sal*volume of water trapped into ridges |
---|
880 | |
---|
881 | REAL(wp), POINTER, DIMENSION(:,:) :: afrft ! fraction of category area rafted |
---|
882 | REAL(wp), POINTER, DIMENSION(:,:) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
---|
883 | REAL(wp), POINTER, DIMENSION(:,:) :: virft , vsrft ! ice & snow volume of rafting ice |
---|
884 | REAL(wp), POINTER, DIMENSION(:,:) :: esrft , smrft ! snow energy & salinity of rafting ice |
---|
885 | REAL(wp), POINTER, DIMENSION(:,:) :: oirft1, oirft2 ! areal age content of rafted ice & rafting ice |
---|
886 | |
---|
887 | REAL(wp), POINTER, DIMENSION(:,:,:) :: eirft ! ice energy of rafting ice |
---|
888 | REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg1 ! enth*volume of ice ridged |
---|
889 | REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg2 ! enth*volume of new ridges |
---|
890 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ersw ! enth of water trapped into ridges |
---|
891 | !!---------------------------------------------------------------------- |
---|
892 | |
---|
893 | CALL wrk_alloc( (jpi+1)*(jpj+1), indxi, indxj ) |
---|
894 | CALL wrk_alloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) |
---|
895 | CALL wrk_alloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, oirdg1, oirdg2, dhr, dhr2 ) |
---|
896 | CALL wrk_alloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw ) |
---|
897 | CALL wrk_alloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
898 | CALL wrk_alloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnwn_init, esnwn_init, smv_i_init, oa_i_init ) |
---|
899 | CALL wrk_alloc( jpi, jpj, nlay_i+1, eirft, erdg1, erdg2, ersw ) |
---|
900 | CALL wrk_alloc( jpi, jpj, nlay_i+1, jpl, eicen_init ) |
---|
901 | |
---|
902 | ! Conservation check |
---|
903 | eice_init(:,:) = 0._wp |
---|
904 | |
---|
905 | IF( con_i ) THEN |
---|
906 | CALL lim_column_sum (jpl, v_i, vice_init ) |
---|
907 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_init ) |
---|
908 | DO ji = mi0(jiindx), mi1(jiindx) |
---|
909 | DO jj = mj0(jjindx), mj1(jjindx) |
---|
910 | WRITE(numout,*) ' vice_init : ', vice_init(ji,jj) |
---|
911 | WRITE(numout,*) ' eice_init : ', eice_init(ji,jj) |
---|
912 | END DO |
---|
913 | END DO |
---|
914 | ENDIF |
---|
915 | |
---|
916 | !------------------------------------------------------------------------------- |
---|
917 | ! 1) Compute change in open water area due to closing and opening. |
---|
918 | !------------------------------------------------------------------------------- |
---|
919 | |
---|
920 | neg_ato_i = .false. |
---|
921 | |
---|
922 | DO jj = 1, jpj |
---|
923 | DO ji = 1, jpi |
---|
924 | ato_i(ji,jj) = ato_i(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice & |
---|
925 | & + opning(ji,jj) * rdt_ice |
---|
926 | IF( ato_i(ji,jj) < -epsi10 ) THEN |
---|
927 | neg_ato_i = .TRUE. |
---|
928 | ELSEIF( ato_i(ji,jj) < 0._wp ) THEN ! roundoff error |
---|
929 | ato_i(ji,jj) = 0._wp |
---|
930 | ENDIF |
---|
931 | END DO !jj |
---|
932 | END DO !ji |
---|
933 | |
---|
934 | ! if negative open water area alert it |
---|
935 | IF( neg_ato_i ) THEN ! there is a bug |
---|
936 | DO jj = 1, jpj |
---|
937 | DO ji = 1, jpi |
---|
938 | IF( ato_i(ji,jj) < -epsi10 ) THEN |
---|
939 | WRITE(numout,*) '' |
---|
940 | WRITE(numout,*) 'Ridging error: ato_i < 0' |
---|
941 | WRITE(numout,*) 'ato_i : ', ato_i(ji,jj) |
---|
942 | ENDIF ! ato_i < -epsi10 |
---|
943 | END DO |
---|
944 | END DO |
---|
945 | ENDIF |
---|
946 | |
---|
947 | !----------------------------------------------------------------- |
---|
948 | ! 2) Save initial state variables |
---|
949 | !----------------------------------------------------------------- |
---|
950 | |
---|
951 | DO jl = 1, jpl |
---|
952 | aicen_init(:,:,jl) = a_i(:,:,jl) |
---|
953 | vicen_init(:,:,jl) = v_i(:,:,jl) |
---|
954 | vsnwn_init(:,:,jl) = v_s(:,:,jl) |
---|
955 | ! |
---|
956 | smv_i_init(:,:,jl) = smv_i(:,:,jl) |
---|
957 | oa_i_init (:,:,jl) = oa_i (:,:,jl) |
---|
958 | END DO !jl |
---|
959 | |
---|
960 | esnwn_init(:,:,:) = e_s(:,:,1,:) |
---|
961 | |
---|
962 | DO jl = 1, jpl |
---|
963 | DO jk = 1, nlay_i |
---|
964 | eicen_init(:,:,jk,jl) = e_i(:,:,jk,jl) |
---|
965 | END DO |
---|
966 | END DO |
---|
967 | |
---|
968 | ! |
---|
969 | !----------------------------------------------------------------- |
---|
970 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
971 | !----------------------------------------------------------------- |
---|
972 | ! Compute the area, volume, and energy of ice ridging in each |
---|
973 | ! category, along with the area of the resulting ridge. |
---|
974 | |
---|
975 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
976 | |
---|
977 | !------------------------------------------------ |
---|
978 | ! 3.1) Identify grid cells with nonzero ridging |
---|
979 | !------------------------------------------------ |
---|
980 | |
---|
981 | icells = 0 |
---|
982 | DO jj = 1, jpj |
---|
983 | DO ji = 1, jpi |
---|
984 | IF( aicen_init(ji,jj,jl1) > epsi10 .AND. athorn(ji,jj,jl1) > 0._wp & |
---|
985 | & .AND. closing_gross(ji,jj) > 0._wp ) THEN |
---|
986 | icells = icells + 1 |
---|
987 | indxi(icells) = ji |
---|
988 | indxj(icells) = jj |
---|
989 | ENDIF ! test on a_icen_init |
---|
990 | END DO ! ji |
---|
991 | END DO ! jj |
---|
992 | |
---|
993 | large_afrac = .false. |
---|
994 | large_afrft = .false. |
---|
995 | |
---|
996 | !CDIR NODEP |
---|
997 | DO ij = 1, icells |
---|
998 | ji = indxi(ij) |
---|
999 | jj = indxj(ij) |
---|
1000 | |
---|
1001 | !-------------------------------------------------------------------- |
---|
1002 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
1003 | !-------------------------------------------------------------------- |
---|
1004 | |
---|
1005 | ardg1(ji,jj) = aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
1006 | arft1(ji,jj) = araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
1007 | ardg2(ji,jj) = ardg1(ji,jj) / krdg(ji,jj,jl1) |
---|
1008 | arft2(ji,jj) = arft1(ji,jj) / kraft |
---|
1009 | |
---|
1010 | oirdg1(ji,jj)= aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
1011 | oirft1(ji,jj)= araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
1012 | oirdg2(ji,jj)= oirdg1(ji,jj) / krdg(ji,jj,jl1) |
---|
1013 | oirft2(ji,jj)= oirft1(ji,jj) / kraft |
---|
1014 | |
---|
1015 | !--------------------------------------------------------------- |
---|
1016 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
1017 | !--------------------------------------------------------------- |
---|
1018 | |
---|
1019 | afrac(ji,jj) = ardg1(ji,jj) / aicen_init(ji,jj,jl1) !ridging |
---|
1020 | afrft(ji,jj) = arft1(ji,jj) / aicen_init(ji,jj,jl1) !rafting |
---|
1021 | |
---|
1022 | IF (afrac(ji,jj) > kamax + epsi10) THEN !riging |
---|
1023 | large_afrac = .true. |
---|
1024 | ELSEIF (afrac(ji,jj) > kamax) THEN ! roundoff error |
---|
1025 | afrac(ji,jj) = kamax |
---|
1026 | ENDIF |
---|
1027 | IF (afrft(ji,jj) > kamax + epsi10) THEN !rafting |
---|
1028 | large_afrft = .true. |
---|
1029 | ELSEIF (afrft(ji,jj) > kamax) THEN ! roundoff error |
---|
1030 | afrft(ji,jj) = kamax |
---|
1031 | ENDIF |
---|
1032 | |
---|
1033 | !-------------------------------------------------------------------------- |
---|
1034 | ! 3.4) Subtract area, volume, and energy from ridging |
---|
1035 | ! / rafting category n1. |
---|
1036 | !-------------------------------------------------------------------------- |
---|
1037 | vrdg1(ji,jj) = vicen_init(ji,jj,jl1) * afrac(ji,jj) |
---|
1038 | vrdg2(ji,jj) = vrdg1(ji,jj) * ( 1. + ridge_por ) |
---|
1039 | vsw (ji,jj) = vrdg1(ji,jj) * ridge_por |
---|
1040 | |
---|
1041 | vsrdg(ji,jj) = vsnwn_init(ji,jj,jl1) * afrac(ji,jj) |
---|
1042 | esrdg(ji,jj) = esnwn_init(ji,jj,jl1) * afrac(ji,jj) |
---|
1043 | srdg1(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) |
---|
1044 | srdg2(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) !! MV HC 2014 this line seems useless |
---|
1045 | |
---|
1046 | ! rafting volumes, heat contents ... |
---|
1047 | virft(ji,jj) = vicen_init(ji,jj,jl1) * afrft(ji,jj) |
---|
1048 | vsrft(ji,jj) = vsnwn_init(ji,jj,jl1) * afrft(ji,jj) |
---|
1049 | esrft(ji,jj) = esnwn_init(ji,jj,jl1) * afrft(ji,jj) |
---|
1050 | smrft(ji,jj) = smv_i_init(ji,jj,jl1) * afrft(ji,jj) |
---|
1051 | |
---|
1052 | ! substract everything |
---|
1053 | a_i(ji,jj,jl1) = a_i(ji,jj,jl1) - ardg1(ji,jj) - arft1(ji,jj) |
---|
1054 | v_i(ji,jj,jl1) = v_i(ji,jj,jl1) - vrdg1(ji,jj) - virft(ji,jj) |
---|
1055 | v_s(ji,jj,jl1) = v_s(ji,jj,jl1) - vsrdg(ji,jj) - vsrft(ji,jj) |
---|
1056 | e_s(ji,jj,1,jl1) = e_s(ji,jj,1,jl1) - esrdg(ji,jj) - esrft(ji,jj) |
---|
1057 | oa_i(ji,jj,jl1) = oa_i(ji,jj,jl1) - oirdg1(ji,jj) - oirft1(ji,jj) |
---|
1058 | smv_i(ji,jj,jl1) = smv_i(ji,jj,jl1) - srdg1(ji,jj) - smrft(ji,jj) |
---|
1059 | |
---|
1060 | !----------------------------------------------------------------- |
---|
1061 | ! 3.5) Compute properties of new ridges |
---|
1062 | !----------------------------------------------------------------- |
---|
1063 | !------------- |
---|
1064 | ! Salinity |
---|
1065 | !------------- |
---|
1066 | smsw(ji,jj) = vsw(ji,jj) * sss_m(ji,jj) ! salt content of seawater frozen in voids !! MV HC2014 |
---|
1067 | srdg2(ji,jj) = srdg1(ji,jj) + smsw(ji,jj) ! salt content of new ridge |
---|
1068 | |
---|
1069 | !srdg2(ji,jj) = MIN( s_i_max * vrdg2(ji,jj) , zsrdg2 ) ! impose a maximum salinity |
---|
1070 | |
---|
1071 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ji,jj) * rhoic * r1_rdtice |
---|
1072 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ji,jj) * rhoic * r1_rdtice ! gurvan: increase in ice volume du to seawater frozen in voids |
---|
1073 | |
---|
1074 | !------------------------------------ |
---|
1075 | ! 3.6 Increment ridging diagnostics |
---|
1076 | !------------------------------------ |
---|
1077 | |
---|
1078 | ! jl1 looping 1-jpl |
---|
1079 | ! ij looping 1-icells |
---|
1080 | |
---|
1081 | dardg1dt (ji,jj) = dardg1dt(ji,jj) + ardg1(ji,jj) + arft1(ji,jj) |
---|
1082 | dardg2dt (ji,jj) = dardg2dt(ji,jj) + ardg2(ji,jj) + arft2(ji,jj) |
---|
1083 | opening (ji,jj) = opening (ji,jj) + opning(ji,jj) * rdt_ice |
---|
1084 | |
---|
1085 | IF( con_i ) vice_init(ji,jj) = vice_init(ji,jj) + vrdg2(ji,jj) - vrdg1(ji,jj) |
---|
1086 | |
---|
1087 | !------------------------------------------ |
---|
1088 | ! 3.7 Put the snow somewhere in the ocean |
---|
1089 | !------------------------------------------ |
---|
1090 | ! Place part of the snow lost by ridging into the ocean. |
---|
1091 | ! Note that esnow_mlt < 0; the ocean must cool to melt snow. |
---|
1092 | ! If the ocean temp = Tf already, new ice must grow. |
---|
1093 | ! During the next time step, thermo_rates will determine whether |
---|
1094 | ! the ocean cools or new ice grows. |
---|
1095 | ! jl1 looping 1-jpl |
---|
1096 | ! ij looping 1-icells |
---|
1097 | |
---|
1098 | msnow_mlt(ji,jj) = msnow_mlt(ji,jj) + rhosn*vsrdg(ji,jj)*(1.0-fsnowrdg) & ! rafting included |
---|
1099 | & + rhosn*vsrft(ji,jj)*(1.0-fsnowrft) |
---|
1100 | |
---|
1101 | ! in 1e-9 Joules (same as e_s) |
---|
1102 | esnow_mlt(ji,jj) = esnow_mlt(ji,jj) - esrdg(ji,jj)*(1.0-fsnowrdg) & !rafting included |
---|
1103 | & - esrft(ji,jj)*(1.0-fsnowrft) |
---|
1104 | |
---|
1105 | !----------------------------------------------------------------- |
---|
1106 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
1107 | ! in the n2 loop below |
---|
1108 | !----------------------------------------------------------------- |
---|
1109 | |
---|
1110 | ! jl1 looping 1-jpl |
---|
1111 | ! ij looping 1-icells |
---|
1112 | |
---|
1113 | dhr (ji,jj) = hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) |
---|
1114 | dhr2(ji,jj) = hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) |
---|
1115 | |
---|
1116 | END DO ! ij |
---|
1117 | |
---|
1118 | !-------------------------------------------------------------------- |
---|
1119 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
1120 | ! compute ridged ice enthalpy |
---|
1121 | !-------------------------------------------------------------------- |
---|
1122 | DO jk = 1, nlay_i |
---|
1123 | !CDIR NODEP |
---|
1124 | DO ij = 1, icells |
---|
1125 | ji = indxi(ij) |
---|
1126 | jj = indxj(ij) |
---|
1127 | ! heat content of ridged ice |
---|
1128 | erdg1(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrac(ji,jj) |
---|
1129 | eirft(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrft(ji,jj) |
---|
1130 | e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ji,jj,jk) - eirft(ji,jj,jk) |
---|
1131 | |
---|
1132 | |
---|
1133 | ! enthalpy of the trapped seawater (J/m2, >0) |
---|
1134 | ! clem: if sst>0, then ersw <0 (is that possible?) |
---|
1135 | zsstK = sst_m(ji,jj) + rt0 |
---|
1136 | ersw(ji,jj,jk) = - rhoic * vsw(ji,jj) * rcp * ( zsstK - rt0 ) / REAL( nlay_i ) |
---|
1137 | |
---|
1138 | ! heat flux to the ocean |
---|
1139 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ji,jj,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
---|
1140 | |
---|
1141 | ! Correct dimensions to avoid big values |
---|
1142 | ersw(ji,jj,jk) = ersw(ji,jj,jk) / unit_fac |
---|
1143 | |
---|
1144 | ! Mutliply by ice volume, and divide by number of layers to get heat content in 1.e9 J |
---|
1145 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
---|
1146 | !! MV HC 2014 |
---|
1147 | ersw (ji,jj,jk) = ersw(ji,jj,jk) * area(ji,jj) |
---|
1148 | |
---|
1149 | erdg2(ji,jj,jk) = erdg1(ji,jj,jk) + ersw(ji,jj,jk) |
---|
1150 | |
---|
1151 | END DO ! ij |
---|
1152 | END DO !jk |
---|
1153 | |
---|
1154 | |
---|
1155 | IF( con_i ) THEN |
---|
1156 | DO jk = 1, nlay_i |
---|
1157 | !CDIR NODEP |
---|
1158 | DO ij = 1, icells |
---|
1159 | ji = indxi(ij) |
---|
1160 | jj = indxj(ij) |
---|
1161 | eice_init(ji,jj) = eice_init(ji,jj) + erdg2(ji,jj,jk) - erdg1(ji,jj,jk) |
---|
1162 | END DO ! ij |
---|
1163 | END DO !jk |
---|
1164 | ENDIF |
---|
1165 | |
---|
1166 | IF( large_afrac ) THEN ! there is a bug |
---|
1167 | !CDIR NODEP |
---|
1168 | DO ij = 1, icells |
---|
1169 | ji = indxi(ij) |
---|
1170 | jj = indxj(ij) |
---|
1171 | IF( afrac(ji,jj) > kamax + epsi10 ) THEN |
---|
1172 | WRITE(numout,*) '' |
---|
1173 | WRITE(numout,*) ' ardg > a_i' |
---|
1174 | WRITE(numout,*) ' ardg, aicen_init : ', ardg1(ji,jj), aicen_init(ji,jj,jl1) |
---|
1175 | ENDIF |
---|
1176 | END DO |
---|
1177 | ENDIF |
---|
1178 | IF( large_afrft ) THEN ! there is a bug |
---|
1179 | !CDIR NODEP |
---|
1180 | DO ij = 1, icells |
---|
1181 | ji = indxi(ij) |
---|
1182 | jj = indxj(ij) |
---|
1183 | IF( afrft(ji,jj) > kamax + epsi10 ) THEN |
---|
1184 | WRITE(numout,*) '' |
---|
1185 | WRITE(numout,*) ' arft > a_i' |
---|
1186 | WRITE(numout,*) ' arft, aicen_init : ', arft1(ji,jj), aicen_init(ji,jj,jl1) |
---|
1187 | ENDIF |
---|
1188 | END DO |
---|
1189 | ENDIF |
---|
1190 | |
---|
1191 | !------------------------------------------------------------------------------- |
---|
1192 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
1193 | !------------------------------------------------------------------------------- |
---|
1194 | ! jl1 looping 1-jpl |
---|
1195 | DO jl2 = 1, jpl |
---|
1196 | ! over categories to which ridged ice is transferred |
---|
1197 | !CDIR NODEP |
---|
1198 | DO ij = 1, icells |
---|
1199 | ji = indxi(ij) |
---|
1200 | jj = indxj(ij) |
---|
1201 | |
---|
1202 | ! Compute the fraction of ridged ice area and volume going to |
---|
1203 | ! thickness category jl2. |
---|
1204 | ! Transfer area, volume, and energy accordingly. |
---|
1205 | |
---|
1206 | IF( hrmin(ji,jj,jl1) >= hi_max(jl2) .OR. & |
---|
1207 | hrmax(ji,jj,jl1) <= hi_max(jl2-1) ) THEN |
---|
1208 | hL = 0._wp |
---|
1209 | hR = 0._wp |
---|
1210 | ELSE |
---|
1211 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
---|
1212 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
---|
1213 | ENDIF |
---|
1214 | |
---|
1215 | ! fraction of ridged ice area and volume going to n2 |
---|
1216 | farea = ( hR - hL ) / dhr(ji,jj) |
---|
1217 | fvol(ji,jj) = ( hR*hR - hL*hL ) / dhr2(ji,jj) |
---|
1218 | |
---|
1219 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ardg2 (ji,jj) * farea |
---|
1220 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + vrdg2 (ji,jj) * fvol(ji,jj) |
---|
1221 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrdg (ji,jj) * fvol(ji,jj) * fsnowrdg |
---|
1222 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrdg (ji,jj) * fvol(ji,jj) * fsnowrdg |
---|
1223 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + srdg2 (ji,jj) * fvol(ji,jj) |
---|
1224 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirdg2(ji,jj) * farea |
---|
1225 | |
---|
1226 | END DO ! ij |
---|
1227 | |
---|
1228 | ! Transfer ice energy to category jl2 by ridging |
---|
1229 | DO jk = 1, nlay_i |
---|
1230 | !CDIR NODEP |
---|
1231 | DO ij = 1, icells |
---|
1232 | ji = indxi(ij) |
---|
1233 | jj = indxj(ij) |
---|
1234 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + fvol(ji,jj)*erdg2(ji,jj,jk) |
---|
1235 | END DO |
---|
1236 | END DO |
---|
1237 | ! |
---|
1238 | END DO ! jl2 (new ridges) |
---|
1239 | |
---|
1240 | DO jl2 = 1, jpl |
---|
1241 | |
---|
1242 | !CDIR NODEP |
---|
1243 | DO ij = 1, icells |
---|
1244 | ji = indxi(ij) |
---|
1245 | jj = indxj(ij) |
---|
1246 | ! Compute the fraction of rafted ice area and volume going to |
---|
1247 | ! thickness category jl2, transfer area, volume, and energy accordingly. |
---|
1248 | ! |
---|
1249 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. & |
---|
1250 | hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
1251 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + arft2 (ji,jj) |
---|
1252 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + virft (ji,jj) |
---|
1253 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrft (ji,jj) * fsnowrft |
---|
1254 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrft (ji,jj) * fsnowrft |
---|
1255 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + smrft (ji,jj) |
---|
1256 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirft2(ji,jj) |
---|
1257 | ENDIF ! hraft |
---|
1258 | ! |
---|
1259 | END DO ! ij |
---|
1260 | |
---|
1261 | ! Transfer rafted ice energy to category jl2 |
---|
1262 | DO jk = 1, nlay_i |
---|
1263 | !CDIR NODEP |
---|
1264 | DO ij = 1, icells |
---|
1265 | ji = indxi(ij) |
---|
1266 | jj = indxj(ij) |
---|
1267 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. & |
---|
1268 | hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
1269 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + eirft(ji,jj,jk) |
---|
1270 | ENDIF |
---|
1271 | END DO ! ij |
---|
1272 | END DO !jk |
---|
1273 | |
---|
1274 | END DO ! jl2 |
---|
1275 | |
---|
1276 | END DO ! jl1 (deforming categories) |
---|
1277 | |
---|
1278 | ! Conservation check |
---|
1279 | IF ( con_i ) THEN |
---|
1280 | CALL lim_column_sum (jpl, v_i, vice_final) |
---|
1281 | fieldid = ' v_i : limitd_me ' |
---|
1282 | CALL lim_cons_check (vice_init, vice_final, 1.0e-6, fieldid) |
---|
1283 | |
---|
1284 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_final ) |
---|
1285 | fieldid = ' e_i : limitd_me ' |
---|
1286 | CALL lim_cons_check (eice_init, eice_final, 1.0e-2, fieldid) |
---|
1287 | |
---|
1288 | DO ji = mi0(jiindx), mi1(jiindx) |
---|
1289 | DO jj = mj0(jjindx), mj1(jjindx) |
---|
1290 | WRITE(numout,*) ' vice_init : ', vice_init (ji,jj) |
---|
1291 | WRITE(numout,*) ' vice_final : ', vice_final(ji,jj) |
---|
1292 | WRITE(numout,*) ' eice_init : ', eice_init (ji,jj) |
---|
1293 | WRITE(numout,*) ' eice_final : ', eice_final(ji,jj) |
---|
1294 | END DO |
---|
1295 | END DO |
---|
1296 | ENDIF |
---|
1297 | ! |
---|
1298 | CALL wrk_dealloc( (jpi+1)*(jpj+1), indxi, indxj ) |
---|
1299 | CALL wrk_dealloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) |
---|
1300 | CALL wrk_dealloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, oirdg1, oirdg2, dhr, dhr2 ) |
---|
1301 | CALL wrk_dealloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw ) |
---|
1302 | CALL wrk_dealloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
1303 | CALL wrk_dealloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnwn_init, esnwn_init, smv_i_init, oa_i_init ) |
---|
1304 | CALL wrk_dealloc( jpi, jpj, nlay_i+1, eirft, erdg1, erdg2, ersw ) |
---|
1305 | CALL wrk_dealloc( jpi, jpj, nlay_i+1, jpl, eicen_init ) |
---|
1306 | ! |
---|
1307 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
1308 | |
---|
1309 | |
---|
1310 | SUBROUTINE lim_itd_me_asumr |
---|
1311 | !!----------------------------------------------------------------------------- |
---|
1312 | !! *** ROUTINE lim_itd_me_asumr *** |
---|
1313 | !! |
---|
1314 | !! ** Purpose : finds total fractional area |
---|
1315 | !! |
---|
1316 | !! ** Method : Find the total area of ice plus open water in each grid cell. |
---|
1317 | !! This is similar to the aggregate_area subroutine except that the |
---|
1318 | !! total area can be greater than 1, so the open water area is |
---|
1319 | !! included in the sum instead of being computed as a residual. |
---|
1320 | !!----------------------------------------------------------------------------- |
---|
1321 | INTEGER :: jl ! dummy loop index |
---|
1322 | !!----------------------------------------------------------------------------- |
---|
1323 | ! |
---|
1324 | asum(:,:) = ato_i(:,:) ! open water |
---|
1325 | DO jl = 1, jpl ! ice categories |
---|
1326 | asum(:,:) = asum(:,:) + a_i(:,:,jl) |
---|
1327 | END DO |
---|
1328 | ! |
---|
1329 | END SUBROUTINE lim_itd_me_asumr |
---|
1330 | |
---|
1331 | |
---|
1332 | SUBROUTINE lim_itd_me_init |
---|
1333 | !!------------------------------------------------------------------- |
---|
1334 | !! *** ROUTINE lim_itd_me_init *** |
---|
1335 | !! |
---|
1336 | !! ** Purpose : Physical constants and parameters linked |
---|
1337 | !! to the mechanical ice redistribution |
---|
1338 | !! |
---|
1339 | !! ** Method : Read the namiceitdme namelist |
---|
1340 | !! and check the parameters values |
---|
1341 | !! called at the first timestep (nit000) |
---|
1342 | !! |
---|
1343 | !! ** input : Namelist namiceitdme |
---|
1344 | !!------------------------------------------------------------------- |
---|
1345 | INTEGER :: ios ! Local integer output status for namelist read |
---|
1346 | NAMELIST/namiceitdme/ ridge_scheme_swi, Cs, Cf, fsnowrdg, fsnowrft, & |
---|
1347 | & Gstar, astar, Hstar, raft_swi, hparmeter, Craft, ridge_por, & |
---|
1348 | & partfun_swi, brinstren_swi |
---|
1349 | !!------------------------------------------------------------------- |
---|
1350 | ! |
---|
1351 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
---|
1352 | READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901) |
---|
1353 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp ) |
---|
1354 | |
---|
1355 | REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution |
---|
1356 | READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 ) |
---|
1357 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp ) |
---|
1358 | IF(lwm) WRITE ( numoni, namiceitdme ) |
---|
1359 | ! |
---|
1360 | IF (lwp) THEN ! control print |
---|
1361 | WRITE(numout,*) |
---|
1362 | WRITE(numout,*)' lim_itd_me_init : ice parameters for mechanical ice redistribution ' |
---|
1363 | WRITE(numout,*)' ~~~~~~~~~~~~~~~' |
---|
1364 | WRITE(numout,*)' Switch choosing the ice redistribution scheme ridge_scheme_swi', ridge_scheme_swi |
---|
1365 | WRITE(numout,*)' Fraction of shear energy contributing to ridging Cs ', Cs |
---|
1366 | WRITE(numout,*)' Ratio of ridging work to PotEner change in ridging Cf ', Cf |
---|
1367 | WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrdg ', fsnowrdg |
---|
1368 | WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrft ', fsnowrft |
---|
1369 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging Gstar ', Gstar |
---|
1370 | WRITE(numout,*)' Equivalent to G* for an exponential part function astar ', astar |
---|
1371 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness Hstar ', Hstar |
---|
1372 | WRITE(numout,*)' Rafting of ice sheets or not raft_swi ', raft_swi |
---|
1373 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) hparmeter ', hparmeter |
---|
1374 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient Craft ', Craft |
---|
1375 | WRITE(numout,*)' Initial porosity of ridges ridge_por ', ridge_por |
---|
1376 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential partfun_swi ', partfun_swi |
---|
1377 | WRITE(numout,*)' Switch for including brine volume in ice strength comp. brinstren_swi ', brinstren_swi |
---|
1378 | ENDIF |
---|
1379 | ! |
---|
1380 | END SUBROUTINE lim_itd_me_init |
---|
1381 | |
---|
1382 | |
---|
1383 | SUBROUTINE lim_itd_me_zapsmall |
---|
1384 | !!------------------------------------------------------------------- |
---|
1385 | !! *** ROUTINE lim_itd_me_zapsmall *** |
---|
1386 | !! |
---|
1387 | !! ** Purpose : Remove too small sea ice areas and correct salt fluxes |
---|
1388 | !! |
---|
1389 | !! history : |
---|
1390 | !! author: William H. Lipscomb, LANL |
---|
1391 | !! Nov 2003: Modified by Julie Schramm to conserve volume and energy |
---|
1392 | !! Sept 2004: Modified by William Lipscomb; replaced normalize_state with |
---|
1393 | !! additions to local freshwater, salt, and heat fluxes |
---|
1394 | !! 9.0, LIM3.0 - 02-2006 (M. Vancoppenolle) original code |
---|
1395 | !!------------------------------------------------------------------- |
---|
1396 | INTEGER :: ji, jj, jl, jk ! dummy loop indices |
---|
1397 | INTEGER :: icells ! number of cells with ice to zap |
---|
1398 | |
---|
1399 | REAL(wp), POINTER, DIMENSION(:,:) :: zmask ! 2D workspace |
---|
1400 | REAL(wp) :: zmask_glo, zsal, zvi, zvs, zei, zes |
---|
1401 | !!gm REAL(wp) :: xtmp ! temporary variable |
---|
1402 | !!------------------------------------------------------------------- |
---|
1403 | |
---|
1404 | CALL wrk_alloc( jpi, jpj, zmask ) |
---|
1405 | |
---|
1406 | ! to be sure that at_i is the sum of a_i(jl) |
---|
1407 | at_i(:,:) = SUM( a_i(:,:,:), dim=3 ) |
---|
1408 | |
---|
1409 | DO jl = 1, jpl |
---|
1410 | !----------------------------------------------------------------- |
---|
1411 | ! Count categories to be zapped. |
---|
1412 | !----------------------------------------------------------------- |
---|
1413 | icells = 0 |
---|
1414 | zmask(:,:) = 0._wp |
---|
1415 | DO jj = 1, jpj |
---|
1416 | DO ji = 1, jpi |
---|
1417 | IF( a_i(ji,jj,jl) <= epsi10 .OR. v_i(ji,jj,jl) <= epsi10 .OR. at_i(ji,jj) <= epsi10 ) THEN |
---|
1418 | zmask(ji,jj) = 1._wp |
---|
1419 | ENDIF |
---|
1420 | END DO |
---|
1421 | END DO |
---|
1422 | !zmask_glo = glob_sum(zmask) |
---|
1423 | !IF( ln_nicep .AND. lwp ) WRITE(numout,*) zmask_glo, ' cells of ice zapped in the ocean ' |
---|
1424 | |
---|
1425 | !----------------------------------------------------------------- |
---|
1426 | ! Zap ice energy and use ocean heat to melt ice |
---|
1427 | !----------------------------------------------------------------- |
---|
1428 | |
---|
1429 | DO jk = 1, nlay_i |
---|
1430 | DO jj = 1 , jpj |
---|
1431 | DO ji = 1 , jpi |
---|
1432 | zei = e_i(ji,jj,jk,jl) |
---|
1433 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1434 | t_i(ji,jj,jk,jl) = t_i(ji,jj,jk,jl) * ( 1._wp - zmask(ji,jj) ) + rtt * zmask(ji,jj) |
---|
1435 | ! update exchanges with ocean |
---|
1436 | hfx_res(ji,jj) = hfx_res(ji,jj) + ( e_i(ji,jj,jk,jl) - zei ) * unit_fac / area(ji,jj) * r1_rdtice ! W.m-2 <0 |
---|
1437 | END DO |
---|
1438 | END DO |
---|
1439 | END DO |
---|
1440 | |
---|
1441 | DO jj = 1 , jpj |
---|
1442 | DO ji = 1 , jpi |
---|
1443 | |
---|
1444 | zsal = smv_i(ji,jj,jl) |
---|
1445 | zvi = v_i(ji,jj,jl) |
---|
1446 | zvs = v_s(ji,jj,jl) |
---|
1447 | zes = e_s(ji,jj,1,jl) |
---|
1448 | !----------------------------------------------------------------- |
---|
1449 | ! Zap snow energy and use ocean heat to melt snow |
---|
1450 | !----------------------------------------------------------------- |
---|
1451 | ! xtmp = esnon(i,j,n) / dt ! < 0 |
---|
1452 | ! fhnet(i,j) = fhnet(i,j) + xtmp |
---|
1453 | ! fhnet_hist(i,j) = fhnet_hist(i,j) + xtmp |
---|
1454 | ! xtmp is greater than 0 |
---|
1455 | ! fluxes are positive to the ocean |
---|
1456 | ! here the flux has to be negative for the ocean |
---|
1457 | t_s(ji,jj,1,jl) = rtt * zmask(ji,jj) + t_s(ji,jj,1,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1458 | |
---|
1459 | !----------------------------------------------------------------- |
---|
1460 | ! zap ice and snow volume, add water and salt to ocean |
---|
1461 | !----------------------------------------------------------------- |
---|
1462 | ato_i(ji,jj) = a_i (ji,jj,jl) * zmask(ji,jj) + ato_i(ji,jj) |
---|
1463 | a_i (ji,jj,jl) = a_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1464 | v_i (ji,jj,jl) = v_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1465 | v_s (ji,jj,jl) = v_s (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1466 | t_su (ji,jj,jl) = t_su (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) + t_bo(ji,jj) * zmask(ji,jj) |
---|
1467 | oa_i (ji,jj,jl) = oa_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1468 | smv_i(ji,jj,jl) = smv_i(ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1469 | e_s(ji,jj,1,jl) = e_s(ji,jj,1,jl) * ( 1._wp - zmask(ji,jj) ) |
---|
1470 | ! additional condition |
---|
1471 | IF( v_s(ji,jj,jl) <= epsi10 ) THEN |
---|
1472 | v_s(ji,jj,jl) = 0._wp |
---|
1473 | e_s(ji,jj,1,jl) = 0._wp |
---|
1474 | ENDIF |
---|
1475 | ! update exchanges with ocean |
---|
1476 | sfx_res(ji,jj) = sfx_res(ji,jj) - ( smv_i(ji,jj,jl) - zsal ) * rhoic * r1_rdtice |
---|
1477 | wfx_res(ji,jj) = wfx_res(ji,jj) - ( v_i(ji,jj,jl) - zvi ) * rhoic * r1_rdtice |
---|
1478 | wfx_snw(ji,jj) = wfx_snw(ji,jj) - ( v_s(ji,jj,jl) - zvs ) * rhosn * r1_rdtice |
---|
1479 | hfx_res(ji,jj) = hfx_res(ji,jj) + ( e_s(ji,jj,1,jl) - zes ) * unit_fac / area(ji,jj) * r1_rdtice ! W.m-2 <0 |
---|
1480 | END DO |
---|
1481 | END DO |
---|
1482 | END DO ! jl |
---|
1483 | |
---|
1484 | ! to be sure that at_i is the sum of a_i(jl) |
---|
1485 | at_i(:,:) = SUM( a_i(:,:,:), dim=3 ) |
---|
1486 | ! |
---|
1487 | CALL wrk_dealloc( jpi, jpj, zmask ) |
---|
1488 | ! |
---|
1489 | END SUBROUTINE lim_itd_me_zapsmall |
---|
1490 | |
---|
1491 | #else |
---|
1492 | !!---------------------------------------------------------------------- |
---|
1493 | !! Default option Empty module NO LIM-3 sea-ice model |
---|
1494 | !!---------------------------------------------------------------------- |
---|
1495 | CONTAINS |
---|
1496 | SUBROUTINE lim_itd_me ! Empty routines |
---|
1497 | END SUBROUTINE lim_itd_me |
---|
1498 | SUBROUTINE lim_itd_me_icestrength |
---|
1499 | END SUBROUTINE lim_itd_me_icestrength |
---|
1500 | SUBROUTINE lim_itd_me_sort |
---|
1501 | END SUBROUTINE lim_itd_me_sort |
---|
1502 | SUBROUTINE lim_itd_me_init |
---|
1503 | END SUBROUTINE lim_itd_me_init |
---|
1504 | SUBROUTINE lim_itd_me_zapsmall |
---|
1505 | END SUBROUTINE lim_itd_me_zapsmall |
---|
1506 | #endif |
---|
1507 | !!====================================================================== |
---|
1508 | END MODULE limitd_me |
---|