[825] | 1 | MODULE limthd_lac |
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[834] | 2 | !!---------------------------------------------------------------------- |
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| 3 | !! 'key_lim3' LIM3 sea-ice model |
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| 4 | !!---------------------------------------------------------------------- |
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[825] | 5 | !!====================================================================== |
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| 6 | !! *** MODULE limthd_lac *** |
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| 7 | !! lateral thermodynamic growth of the ice |
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| 8 | !!====================================================================== |
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[888] | 9 | #if defined key_lim3 |
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[825] | 10 | !!---------------------------------------------------------------------- |
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| 11 | !! lim_lat_acr : lateral accretion of ice |
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| 12 | !! * Modules used |
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| 13 | USE par_oce ! ocean parameters |
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| 14 | USE dom_oce |
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| 15 | USE in_out_manager |
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| 16 | USE phycst |
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[888] | 17 | USE sbc_oce ! Surface boundary condition: ocean fields |
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| 18 | USE sbc_ice ! Surface boundary condition: ice fields |
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[825] | 19 | USE thd_ice |
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| 20 | USE dom_ice |
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| 21 | USE par_ice |
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| 22 | USE ice |
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| 23 | USE iceini |
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| 24 | USE limtab |
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| 25 | USE limcons |
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[921] | 26 | |
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[825] | 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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| 30 | !! * Routine accessibility |
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| 31 | PUBLIC lim_thd_lac ! called by lim_thd |
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| 32 | |
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| 33 | !! * Module variables |
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| 34 | REAL(wp) :: & ! constant values |
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| 35 | epsi20 = 1.e-20 , & |
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| 36 | epsi13 = 1.e-13 , & |
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| 37 | epsi11 = 1.e-13 , & |
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| 38 | epsi03 = 1.e-03 , & |
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| 39 | epsi06 = 1.e-06 , & |
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| 40 | zeps = 1.e-10 , & |
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| 41 | zzero = 0.e0 , & |
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| 42 | zone = 1.e0 |
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| 43 | |
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| 44 | !!---------------------------------------------------------------------- |
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[834] | 45 | !! LIM 3.0, UCL-ASTR-LOCEAN-IPSL (2008) |
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[1156] | 46 | !! $Id$ |
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[888] | 47 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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[825] | 48 | !!---------------------------------------------------------------------- |
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| 49 | |
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| 50 | CONTAINS |
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[921] | 51 | |
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[825] | 52 | SUBROUTINE lim_thd_lac |
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| 53 | !!------------------------------------------------------------------- |
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| 54 | !! *** ROUTINE lim_thd_lac *** |
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| 55 | !! |
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| 56 | !! ** Purpose : Computation of the evolution of the ice thickness and |
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| 57 | !! concentration as a function of the heat balance in the leads. |
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| 58 | !! It is only used for lateral accretion |
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| 59 | !! |
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| 60 | !! ** Method : Ice is formed in the open water when ocean lose heat |
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| 61 | !! (heat budget of open water Bl is negative) . |
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| 62 | !! Computation of the increase of 1-A (ice concentration) fol- |
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| 63 | !! lowing the law : |
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| 64 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
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| 65 | !! where - h0 is the thickness of ice created in the lead |
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| 66 | !! - a is a minimum fraction for leads |
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| 67 | !! - F is a monotonic non-increasing function defined as: |
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| 68 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
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| 69 | !! - exld is the exponent closure rate (=2 default val.) |
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| 70 | !! |
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| 71 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
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| 72 | !! content in brine pockets |
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| 73 | !! - Updating ice internal temperature |
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| 74 | !! - Computation of variation of ice volume and mass |
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| 75 | !! - Computation of frldb after lateral accretion and |
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| 76 | !! update ht_s_b, ht_i_b and tbif_1d(:,:) |
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| 77 | !! |
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| 78 | !! ** References : Not available yet |
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| 79 | !! |
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| 80 | !! History : |
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| 81 | !! 3.0 ! 12-05 (M. Vancoppenolle) Thorough rewrite of the routine |
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| 82 | !! Salinity variations in sea ice, |
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| 83 | !! Multi-layer code |
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[834] | 84 | !! 3.1 ! 01-06 (M. Vancoppenolle) ITD |
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[825] | 85 | !! 3.2 ! 04-07 (M. Vancoppenolle) Mass and energy conservation tested |
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| 86 | !!------------------------------------------------------------------------ |
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| 87 | !! * Arguments |
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| 88 | !! * Local variables |
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| 89 | INTEGER :: & |
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| 90 | ji,jj,jk,jl,jm , & !: dummy loop indices |
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| 91 | layer , & !: layer index |
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| 92 | nbpac !: nb of pts for lateral accretion |
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| 93 | |
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| 94 | INTEGER :: & |
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| 95 | zji , & !: ji of dummy test point |
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| 96 | zjj , & !: jj of dummy test point |
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| 97 | iter !: iteration for frazil ice computation |
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| 98 | |
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| 99 | INTEGER, DIMENSION(jpij) :: & |
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| 100 | zcatac , & !: indexes of categories where new ice grows |
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| 101 | zswinew !: switch for new ice or not |
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| 102 | |
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| 103 | REAL(wp), DIMENSION(jpij) :: & |
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| 104 | zv_newice , & !: volume of accreted ice |
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| 105 | za_newice , & !: fractional area of accreted ice |
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| 106 | zh_newice , & !: thickness of accreted ice |
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| 107 | ze_newice , & !: heat content of accreted ice |
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| 108 | zs_newice , & !: salinity of accreted ice |
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| 109 | zo_newice , & !: age of accreted ice |
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| 110 | zdv_res , & !: residual volume in case of excessive heat budget |
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| 111 | zda_res , & !: residual area in case of excessive heat budget |
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| 112 | zat_i_ac , & !: total ice fraction |
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| 113 | zat_i_lev , & !: total ice fraction for level ice only (type 1) |
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| 114 | zdh_frazb , & !: accretion of frazil ice at the ice bottom |
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| 115 | zvrel_ac !: relative ice / frazil velocity (1D vector) |
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| 116 | |
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| 117 | REAL(wp), DIMENSION(jpij,jpl) :: & |
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| 118 | zhice_old , & !: previous ice thickness |
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| 119 | zdummy , & !: dummy thickness of new ice |
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| 120 | zdhicbot , & !: thickness of new ice which is accreted vertically |
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| 121 | zv_old , & !: old volume of ice in category jl |
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| 122 | za_old , & !: old area of ice in category jl |
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| 123 | za_i_ac , & !: 1-D version of a_i |
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| 124 | zv_i_ac , & !: 1-D version of v_i |
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| 125 | zoa_i_ac , & !: 1-D version of oa_i |
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| 126 | zsmv_i_ac !: 1-D version of smv_i |
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| 127 | |
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| 128 | REAL(wp), DIMENSION(jpij,jkmax,jpl) :: & |
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| 129 | ze_i_ac !: 1-D version of e_i |
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| 130 | |
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| 131 | REAL(wp), DIMENSION(jpij) :: & |
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| 132 | zqbgow , & !: heat budget of the open water (negative) |
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| 133 | zdhex !: excessively thick accreted sea ice (hlead-hice) |
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| 134 | |
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| 135 | REAL(wp) :: & |
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| 136 | ztmelts , & !: melting point of an ice layer |
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| 137 | zdv , & !: increase in ice volume in each category |
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| 138 | zfrazb !: fraction of frazil ice accreted at the ice bottom |
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| 139 | |
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| 140 | ! Redistribution of energy after bottom accretion |
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| 141 | REAL(wp) :: & !: Energy redistribution |
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| 142 | zqold , & !: old ice enthalpy |
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| 143 | zweight , & !: weight of redistribution |
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| 144 | zeps6 , & !: epsilon value |
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| 145 | zalphai , & !: factor describing how old and new layers overlap each other [m] |
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| 146 | zindb |
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[921] | 147 | |
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[825] | 148 | REAL(wp), DIMENSION(jpij,jkmax+1,jpl) :: & |
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| 149 | zqm0 , & !: old layer-system heat content |
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| 150 | zthick0 !: old ice thickness |
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| 151 | |
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| 152 | ! Frazil ice collection thickness |
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| 153 | LOGICAL :: & !: iterate frazil ice collection thickness |
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| 154 | iterate_frazil |
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| 155 | |
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| 156 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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| 157 | zvrel !: relative ice / frazil velocity |
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| 158 | |
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| 159 | REAL(wp) :: & |
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| 160 | zgamafr , & !: mult. coeff. between frazil vel. and wind speed |
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| 161 | ztenagm , & !: square root of wind stress |
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| 162 | zvfrx , & !: x-component of frazil velocity |
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| 163 | zvfry , & !: y-component of frazil velocity |
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| 164 | zvgx , & !: x-component of ice velocity |
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| 165 | zvgy , & !: y-component of ice velocity |
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| 166 | ztaux , & !: x-component of wind stress |
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| 167 | ztauy , & !: y-component of wind stress |
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| 168 | ztwogp , & !: dummy factor including reduced gravity |
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| 169 | zvrel2 , & !: square of the relative ice-frazil velocity |
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| 170 | zf , & !: F for Newton-Raphson procedure |
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| 171 | zfp , & !: dF for Newton-Raphson procedure |
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| 172 | zhicol_new , & !: updated collection thickness |
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| 173 | zsqcd , & !: 1 / square root of ( airdensity * drag ) |
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| 174 | zhicrit !: minimum thickness of frazil ice |
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| 175 | |
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| 176 | ! Variables for energy conservation |
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| 177 | REAL (wp), DIMENSION(jpi,jpj) :: & ! |
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| 178 | vt_i_init, vt_i_final, & ! ice volume summed over categories |
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| 179 | vt_s_init, vt_s_final, & ! snow volume summed over categories |
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| 180 | et_i_init, et_i_final, & ! ice energy summed over categories |
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[888] | 181 | et_s_init ! snow energy summed over categories |
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[825] | 182 | |
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| 183 | REAL(wp) :: & |
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[834] | 184 | zde ! :increment of energy in category jl |
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[825] | 185 | |
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| 186 | CHARACTER (len = 15) :: fieldid |
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| 187 | |
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| 188 | !!-----------------------------------------------------------------------! |
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[921] | 189 | |
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[825] | 190 | et_i_init(:,:) = 0.0 |
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| 191 | et_s_init(:,:) = 0.0 |
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| 192 | vt_i_init(:,:) = 0.0 |
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| 193 | vt_s_init(:,:) = 0.0 |
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| 194 | zeps6 = 1.0e-6 |
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| 195 | |
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[921] | 196 | !------------------------------------------------------------------------------! |
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| 197 | ! 1) Conservation check and changes in each ice category |
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| 198 | !------------------------------------------------------------------------------! |
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[834] | 199 | IF ( con_i ) THEN |
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| 200 | CALL lim_column_sum (jpl, v_i, vt_i_init) |
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| 201 | CALL lim_column_sum (jpl, v_s, vt_s_init) |
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| 202 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, et_i_init) |
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| 203 | CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
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| 204 | ENDIF |
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[825] | 205 | |
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[921] | 206 | !------------------------------------------------------------------------------| |
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| 207 | ! 2) Convert units for ice internal energy |
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| 208 | !------------------------------------------------------------------------------| |
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[825] | 209 | DO jl = 1, jpl |
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[921] | 210 | DO jk = 1, nlay_i |
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| 211 | DO jj = 1, jpj |
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| 212 | DO ji = 1, jpi |
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| 213 | !Energy of melting q(S,T) [J.m-3] |
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| 214 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / & |
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| 215 | MAX( area(ji,jj) * v_i(ji,jj,jl) , zeps ) * & |
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| 216 | nlay_i |
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| 217 | zindb = 1.0-MAX(0.0,SIGN(1.0,-v_i(ji,jj,jl))) !0 if no ice and 1 if yes |
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| 218 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl)*unit_fac*zindb |
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| 219 | END DO |
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[825] | 220 | END DO |
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[921] | 221 | END DO |
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[825] | 222 | END DO |
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| 223 | |
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[921] | 224 | !------------------------------------------------------------------------------! |
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| 225 | ! 3) Collection thickness of ice formed in leads and polynyas |
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| 226 | !------------------------------------------------------------------------------! |
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[865] | 227 | ! hicol is the thickness of new ice formed in open water |
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| 228 | ! hicol can be either prescribed (frazswi = 0) |
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| 229 | ! or computed (frazswi = 1) |
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[825] | 230 | ! Frazil ice forms in open water, is transported by wind |
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| 231 | ! accumulates at the edge of the consolidated ice edge |
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| 232 | ! where it forms aggregates of a specific thickness called |
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| 233 | ! collection thickness. |
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| 234 | |
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[865] | 235 | ! Note : the following algorithm currently breaks vectorization |
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| 236 | ! |
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| 237 | |
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[825] | 238 | zvrel(:,:) = 0.0 |
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| 239 | |
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| 240 | ! Default new ice thickness |
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| 241 | DO jj = 1, jpj |
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| 242 | DO ji = 1, jpi |
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| 243 | hicol(ji,jj) = hiccrit(1) |
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| 244 | END DO |
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| 245 | END DO |
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| 246 | |
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| 247 | IF (fraz_swi.eq.1.0) THEN |
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| 248 | |
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[921] | 249 | !-------------------- |
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| 250 | ! Physical constants |
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| 251 | !-------------------- |
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| 252 | hicol(:,:) = 0.0 |
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[825] | 253 | |
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[921] | 254 | zhicrit = 0.04 ! frazil ice thickness |
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| 255 | ztwogp = 2. * rau0 / ( grav * 0.3 * ( rau0 - rhoic ) ) ! reduced grav |
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| 256 | zsqcd = 1.0 / SQRT( 1.3 * cai ) ! 1/SQRT(airdensity*drag) |
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| 257 | zgamafr = 0.03 |
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[825] | 258 | |
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[921] | 259 | DO jj = 1, jpj |
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| 260 | DO ji = 1, jpi |
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[825] | 261 | |
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[921] | 262 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
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| 263 | !------------- |
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| 264 | ! Wind stress |
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| 265 | !------------- |
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| 266 | ! C-grid wind stress components |
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[1469] | 267 | ztaux = ( utau_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
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| 268 | & + utau_ice(ji ,jj ) * tmu(ji ,jj ) ) / 2.0 |
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| 269 | ztauy = ( vtau_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
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| 270 | & + vtau_ice(ji ,jj ) * tmv(ji ,jj ) ) / 2.0 |
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[921] | 271 | ! Square root of wind stress |
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| 272 | ztenagm = SQRT( SQRT( ztaux * ztaux + ztauy * ztauy ) ) |
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[825] | 273 | |
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[921] | 274 | !--------------------- |
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| 275 | ! Frazil ice velocity |
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| 276 | !--------------------- |
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| 277 | zvfrx = zgamafr * zsqcd * ztaux / MAX(ztenagm,zeps) |
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| 278 | zvfry = zgamafr * zsqcd * ztauy / MAX(ztenagm,zeps) |
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[825] | 279 | |
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[921] | 280 | !------------------- |
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| 281 | ! Pack ice velocity |
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| 282 | !------------------- |
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| 283 | ! C-grid ice velocity |
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| 284 | zindb = MAX(0.0, SIGN(1.0, at_i(ji,jj) )) |
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| 285 | zvgx = zindb * ( u_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
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| 286 | + u_ice(ji,jj ) * tmu(ji ,jj ) ) / 2.0 |
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| 287 | zvgy = zindb * ( v_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
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| 288 | + v_ice(ji,jj ) * tmv(ji ,jj ) ) / 2.0 |
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[825] | 289 | |
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[921] | 290 | !----------------------------------- |
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| 291 | ! Relative frazil/pack ice velocity |
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| 292 | !----------------------------------- |
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| 293 | ! absolute relative velocity |
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| 294 | zvrel2 = MAX( ( zvfrx - zvgx ) * ( zvfrx - zvgx ) + & |
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| 295 | ( zvfry - zvgy ) * ( zvfry - zvgy ) & |
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| 296 | , 0.15 * 0.15 ) |
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| 297 | zvrel(ji,jj) = SQRT(zvrel2) |
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[825] | 298 | |
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[921] | 299 | !--------------------- |
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| 300 | ! Iterative procedure |
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| 301 | !--------------------- |
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| 302 | hicol(ji,jj) = zhicrit + 0.1 |
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| 303 | hicol(ji,jj) = zhicrit + hicol(ji,jj) / & |
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| 304 | ( hicol(ji,jj) * hicol(ji,jj) - & |
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| 305 | zhicrit * zhicrit ) * ztwogp * zvrel2 |
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[825] | 306 | |
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[921] | 307 | iter = 1 |
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| 308 | iterate_frazil = .true. |
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[825] | 309 | |
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[921] | 310 | DO WHILE ( iter .LT. 100 .AND. iterate_frazil ) |
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| 311 | zf = ( hicol(ji,jj) - zhicrit ) * ( hicol(ji,jj)**2 - zhicrit**2 ) & |
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| 312 | - hicol(ji,jj) * zhicrit * ztwogp * zvrel2 |
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| 313 | zfp = ( hicol(ji,jj) - zhicrit ) * ( 3.0*hicol(ji,jj) + zhicrit ) & |
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| 314 | - zhicrit * ztwogp * zvrel2 |
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| 315 | zhicol_new = hicol(ji,jj) - zf/zfp |
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| 316 | hicol(ji,jj) = zhicol_new |
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[825] | 317 | |
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[921] | 318 | iter = iter + 1 |
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[825] | 319 | |
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[921] | 320 | END DO ! do while |
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[825] | 321 | |
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[921] | 322 | ENDIF ! end of selection of pixels where ice forms |
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[825] | 323 | |
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[921] | 324 | END DO ! loop on ji ends |
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| 325 | END DO ! loop on jj ends |
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[825] | 326 | |
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| 327 | ENDIF ! End of computation of frazil ice collection thickness |
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| 328 | |
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[921] | 329 | !------------------------------------------------------------------------------! |
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| 330 | ! 4) Identify grid points where new ice forms |
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| 331 | !------------------------------------------------------------------------------! |
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[825] | 332 | |
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| 333 | !------------------------------------- |
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| 334 | ! Select points for new ice formation |
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| 335 | !------------------------------------- |
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| 336 | ! This occurs if open water energy budget is negative |
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| 337 | nbpac = 0 |
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| 338 | DO jj = 1, jpj |
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| 339 | DO ji = 1, jpi |
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| 340 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
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| 341 | nbpac = nbpac + 1 |
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| 342 | npac( nbpac ) = (jj - 1) * jpi + ji |
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[888] | 343 | IF ( (ji.eq.jiindx).AND.(jj.eq.jjindx) ) THEN |
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[825] | 344 | jiindex_1d = nbpac |
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| 345 | ENDIF |
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| 346 | ENDIF |
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| 347 | END DO |
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| 348 | END DO |
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| 349 | |
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[921] | 350 | IF( ln_nicep ) THEN |
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[825] | 351 | WRITE(numout,*) 'lim_thd_lac : nbpac = ', nbpac |
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| 352 | ENDIF |
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| 353 | |
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| 354 | !------------------------------ |
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| 355 | ! Move from 2-D to 1-D vectors |
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| 356 | !------------------------------ |
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| 357 | ! If ocean gains heat do nothing |
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| 358 | ! 0therwise compute new ice formation |
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| 359 | |
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| 360 | IF ( nbpac > 0 ) THEN |
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| 361 | |
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[921] | 362 | CALL tab_2d_1d( nbpac, zat_i_ac (1:nbpac) , at_i , & |
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| 363 | jpi, jpj, npac(1:nbpac) ) |
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| 364 | DO jl = 1, jpl |
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| 365 | CALL tab_2d_1d( nbpac, za_i_ac(1:nbpac,jl) , a_i(:,:,jl) , & |
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| 366 | jpi, jpj, npac(1:nbpac) ) |
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| 367 | CALL tab_2d_1d( nbpac, zv_i_ac(1:nbpac,jl) , v_i(:,:,jl) , & |
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| 368 | jpi, jpj, npac(1:nbpac) ) |
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| 369 | CALL tab_2d_1d( nbpac, zoa_i_ac(1:nbpac,jl) , oa_i(:,:,jl) , & |
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| 370 | jpi, jpj, npac(1:nbpac) ) |
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| 371 | CALL tab_2d_1d( nbpac, zsmv_i_ac(1:nbpac,jl), smv_i(:,:,jl), & |
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| 372 | jpi, jpj, npac(1:nbpac) ) |
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| 373 | DO jk = 1, nlay_i |
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| 374 | CALL tab_2d_1d( nbpac, ze_i_ac(1:nbpac,jk,jl), e_i(:,:,jk,jl) , & |
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| 375 | jpi, jpj, npac(1:nbpac) ) |
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| 376 | END DO ! jk |
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| 377 | END DO ! jl |
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[825] | 378 | |
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[921] | 379 | CALL tab_2d_1d( nbpac, qldif_1d (1:nbpac) , qldif , & |
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| 380 | jpi, jpj, npac(1:nbpac) ) |
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| 381 | CALL tab_2d_1d( nbpac, qcmif_1d (1:nbpac) , qcmif , & |
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| 382 | jpi, jpj, npac(1:nbpac) ) |
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| 383 | CALL tab_2d_1d( nbpac, t_bo_b (1:nbpac) , t_bo , & |
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| 384 | jpi, jpj, npac(1:nbpac) ) |
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| 385 | CALL tab_2d_1d( nbpac, fseqv_1d (1:nbpac) , fseqv , & |
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| 386 | jpi, jpj, npac(1:nbpac) ) |
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| 387 | CALL tab_2d_1d( nbpac, hicol_b (1:nbpac) , hicol , & |
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| 388 | jpi, jpj, npac(1:nbpac) ) |
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| 389 | CALL tab_2d_1d( nbpac, zvrel_ac (1:nbpac) , zvrel , & |
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| 390 | jpi, jpj, npac(1:nbpac) ) |
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[834] | 391 | |
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[921] | 392 | !------------------------------------------------------------------------------! |
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| 393 | ! 5) Compute thickness, salinity, enthalpy, age, area and volume of new ice |
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| 394 | !------------------------------------------------------------------------------! |
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[825] | 395 | |
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[921] | 396 | !---------------------- |
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| 397 | ! Thickness of new ice |
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| 398 | !---------------------- |
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| 399 | DO ji = 1, nbpac |
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| 400 | zh_newice(ji) = hiccrit(1) |
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| 401 | END DO |
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| 402 | IF ( fraz_swi .EQ. 1.0 ) zh_newice(:) = hicol_b(:) |
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[825] | 403 | |
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[921] | 404 | !---------------------- |
---|
| 405 | ! Salinity of new ice |
---|
| 406 | !---------------------- |
---|
[825] | 407 | |
---|
[921] | 408 | IF ( num_sal .EQ. 1 ) THEN |
---|
| 409 | zs_newice(:) = bulk_sal |
---|
| 410 | ENDIF ! num_sal |
---|
[825] | 411 | |
---|
[921] | 412 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
[825] | 413 | |
---|
[921] | 414 | DO ji = 1, nbpac |
---|
| 415 | zs_newice(ji) = MIN( 4.606 + 0.91 / zh_newice(ji) , s_i_max ) |
---|
| 416 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
| 417 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
| 418 | zs_newice(ji) = MIN( 0.5*sss_m(zji,zjj) , zs_newice(ji) ) |
---|
| 419 | END DO ! jl |
---|
[825] | 420 | |
---|
[921] | 421 | ENDIF ! num_sal |
---|
[825] | 422 | |
---|
[921] | 423 | IF ( num_sal .EQ. 3 ) THEN |
---|
| 424 | zs_newice(:) = 2.3 |
---|
| 425 | ENDIF ! num_sal |
---|
[825] | 426 | |
---|
[921] | 427 | !------------------------- |
---|
| 428 | ! Heat content of new ice |
---|
| 429 | !------------------------- |
---|
| 430 | ! We assume that new ice is formed at the seawater freezing point |
---|
| 431 | DO ji = 1, nbpac |
---|
| 432 | ztmelts = - tmut * zs_newice(ji) + rtt ! Melting point (K) |
---|
| 433 | ze_newice(ji) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) & |
---|
| 434 | + lfus * ( 1.0 - ( ztmelts - rtt ) & |
---|
| 435 | / ( t_bo_b(ji) - rtt ) ) & |
---|
| 436 | - rcp * ( ztmelts-rtt ) ) |
---|
| 437 | ze_newice(ji) = MAX( ze_newice(ji) , 0.0 ) + & |
---|
| 438 | MAX( 0.0 , SIGN( 1.0 , - ze_newice(ji) ) ) & |
---|
| 439 | * rhoic * lfus |
---|
| 440 | END DO ! ji |
---|
| 441 | !---------------- |
---|
| 442 | ! Age of new ice |
---|
| 443 | !---------------- |
---|
| 444 | DO ji = 1, nbpac |
---|
| 445 | zo_newice(ji) = 0.0 |
---|
| 446 | END DO ! ji |
---|
[825] | 447 | |
---|
[921] | 448 | !-------------------------- |
---|
| 449 | ! Open water energy budget |
---|
| 450 | !-------------------------- |
---|
| 451 | DO ji = 1, nbpac |
---|
| 452 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) !<0 |
---|
| 453 | END DO ! ji |
---|
[825] | 454 | |
---|
[921] | 455 | !------------------- |
---|
| 456 | ! Volume of new ice |
---|
| 457 | !------------------- |
---|
| 458 | DO ji = 1, nbpac |
---|
| 459 | zv_newice(ji) = - zqbgow(ji) / ze_newice(ji) |
---|
[825] | 460 | |
---|
[921] | 461 | ! A fraction zfrazb of frazil ice is accreted at the ice bottom |
---|
| 462 | zfrazb = ( TANH ( Cfrazb * ( zvrel_ac(ji) - vfrazb ) ) & |
---|
| 463 | + 1.0 ) / 2.0 * maxfrazb |
---|
| 464 | zdh_frazb(ji) = zfrazb*zv_newice(ji) |
---|
| 465 | zv_newice(ji) = ( 1.0 - zfrazb ) * zv_newice(ji) |
---|
| 466 | END DO |
---|
[865] | 467 | |
---|
[921] | 468 | !--------------------------------- |
---|
| 469 | ! Salt flux due to new ice growth |
---|
| 470 | !--------------------------------- |
---|
| 471 | IF ( ( num_sal .EQ. 4 ) ) THEN |
---|
| 472 | DO ji = 1, nbpac |
---|
| 473 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
| 474 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
| 475 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
| 476 | ( sss_m(zji,zjj) - bulk_sal ) * rhoic * & |
---|
| 477 | zv_newice(ji) / rdt_ice |
---|
| 478 | END DO |
---|
| 479 | ELSE |
---|
| 480 | DO ji = 1, nbpac |
---|
| 481 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
| 482 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
| 483 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
| 484 | ( sss_m(zji,zjj) - zs_newice(ji) ) * rhoic * & |
---|
| 485 | zv_newice(ji) / rdt_ice |
---|
| 486 | END DO ! ji |
---|
| 487 | ENDIF |
---|
[825] | 488 | |
---|
[921] | 489 | !------------------------------------ |
---|
| 490 | ! Diags for energy conservation test |
---|
| 491 | !------------------------------------ |
---|
| 492 | DO ji = 1, nbpac |
---|
| 493 | ! Volume |
---|
| 494 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
| 495 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
| 496 | vt_i_init(zji,zjj) = vt_i_init(zji,zjj) + zv_newice(ji) |
---|
| 497 | ! Energy |
---|
| 498 | zde = ze_newice(ji) / unit_fac |
---|
| 499 | zde = zde * area(zji,zjj) * zv_newice(ji) |
---|
| 500 | et_i_init(zji,zjj) = et_i_init(zji,zjj) + zde |
---|
| 501 | END DO |
---|
[825] | 502 | |
---|
[921] | 503 | ! keep new ice volume in memory |
---|
| 504 | CALL tab_1d_2d( nbpac, v_newice , npac(1:nbpac), zv_newice(1:nbpac) , & |
---|
| 505 | jpi, jpj ) |
---|
[825] | 506 | |
---|
[921] | 507 | !----------------- |
---|
| 508 | ! Area of new ice |
---|
| 509 | !----------------- |
---|
| 510 | DO ji = 1, nbpac |
---|
| 511 | za_newice(ji) = zv_newice(ji) / zh_newice(ji) |
---|
| 512 | ! diagnostic |
---|
| 513 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
| 514 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
| 515 | diag_lat_gr(zji,zjj) = zv_newice(ji) / rdt_ice |
---|
| 516 | END DO !ji |
---|
[825] | 517 | |
---|
[921] | 518 | !------------------------------------------------------------------------------! |
---|
| 519 | ! 6) Redistribute new ice area and volume into ice categories ! |
---|
| 520 | !------------------------------------------------------------------------------! |
---|
[825] | 521 | |
---|
[921] | 522 | !----------------------------------------- |
---|
| 523 | ! Keep old ice areas and volume in memory |
---|
| 524 | !----------------------------------------- |
---|
| 525 | zv_old(:,:) = zv_i_ac(:,:) |
---|
| 526 | za_old(:,:) = za_i_ac(:,:) |
---|
[825] | 527 | |
---|
[921] | 528 | !------------------------------------------- |
---|
| 529 | ! Compute excessive new ice area and volume |
---|
| 530 | !------------------------------------------- |
---|
| 531 | ! If lateral ice growth gives an ice concentration gt 1, then |
---|
| 532 | ! we keep the excessive volume in memory and attribute it later |
---|
| 533 | ! to bottom accretion |
---|
| 534 | DO ji = 1, nbpac |
---|
| 535 | ! vectorize |
---|
| 536 | IF ( za_newice(ji) .GT. ( 1.0 - zat_i_ac(ji) ) ) THEN |
---|
| 537 | zda_res(ji) = za_newice(ji) - (1.0 - zat_i_ac(ji) ) |
---|
| 538 | zdv_res(ji) = zda_res(ji) * zh_newice(ji) |
---|
| 539 | za_newice(ji) = za_newice(ji) - zda_res(ji) |
---|
| 540 | zv_newice(ji) = zv_newice(ji) - zdv_res(ji) |
---|
| 541 | ELSE |
---|
| 542 | zda_res(ji) = 0.0 |
---|
| 543 | zdv_res(ji) = 0.0 |
---|
| 544 | ENDIF |
---|
| 545 | END DO ! ji |
---|
[825] | 546 | |
---|
[921] | 547 | !------------------------------------------------ |
---|
| 548 | ! Laterally redistribute new ice volume and area |
---|
| 549 | !------------------------------------------------ |
---|
| 550 | zat_i_ac(:) = 0.0 |
---|
[825] | 551 | |
---|
[921] | 552 | DO jl = 1, jpl |
---|
| 553 | DO ji = 1, nbpac |
---|
| 554 | ! vectorize |
---|
| 555 | IF ( ( hi_max(jl-1) .LT. zh_newice(ji) ) & |
---|
| 556 | .AND. ( zh_newice(ji) .LE. hi_max(jl) ) ) THEN |
---|
| 557 | za_i_ac(ji,jl) = za_i_ac(ji,jl) + za_newice(ji) |
---|
| 558 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + zv_newice(ji) |
---|
| 559 | zat_i_ac(ji) = zat_i_ac(ji) + za_i_ac(ji,jl) |
---|
| 560 | zcatac(ji) = jl |
---|
| 561 | ENDIF |
---|
| 562 | END DO ! ji |
---|
| 563 | END DO ! jl |
---|
[825] | 564 | |
---|
[921] | 565 | !---------------------------------- |
---|
| 566 | ! Heat content - lateral accretion |
---|
| 567 | !---------------------------------- |
---|
| 568 | DO ji = 1, nbpac |
---|
| 569 | jl = zcatac(ji) ! categroy in which new ice is put |
---|
| 570 | ! zindb = 0 if no ice and 1 if yes |
---|
| 571 | zindb = 1.0 - MAX ( 0.0 , SIGN ( 1.0 , -za_old(ji,jl) ) ) |
---|
| 572 | ! old ice thickness |
---|
| 573 | zhice_old(ji,jl) = zv_old(ji,jl) & |
---|
| 574 | / MAX ( za_old(ji,jl) , zeps ) * zindb |
---|
| 575 | ! difference in thickness |
---|
| 576 | zdhex(ji) = MAX( 0.0, zh_newice(ji) - zhice_old(ji,jl) ) |
---|
| 577 | ! is ice totally new in category jl ? |
---|
| 578 | zswinew(ji) = MAX( 0.0, SIGN( 1.0 , - za_old(ji,jl) + epsi11 ) ) |
---|
| 579 | END DO |
---|
[825] | 580 | |
---|
[921] | 581 | DO jk = 1, nlay_i |
---|
| 582 | DO ji = 1, nbpac |
---|
| 583 | jl = zcatac(ji) |
---|
| 584 | zqold = ze_i_ac(ji,jk,jl) ! [ J.m-3 ] |
---|
| 585 | zalphai = MIN( zhice_old(ji,jl) * jk / nlay_i , & |
---|
| 586 | zh_newice(ji) ) & |
---|
| 587 | - MIN( zhice_old(ji,jl) * ( jk - 1 ) & |
---|
| 588 | / nlay_i , zh_newice(ji) ) |
---|
| 589 | ze_i_ac(ji,jk,jl) = & |
---|
| 590 | zswinew(ji) * ze_newice(ji) & |
---|
| 591 | + ( 1.0 - zswinew(ji) ) * & |
---|
| 592 | ( za_old(ji,jl) * zqold * zhice_old(ji,jl) / nlay_i & |
---|
| 593 | + za_newice(ji) * ze_newice(ji) * zalphai & |
---|
| 594 | + za_newice(ji) * ze_newice(ji) * zdhex(ji) / nlay_i ) / & |
---|
| 595 | ( ( zv_i_ac(ji,jl) ) / nlay_i ) |
---|
[825] | 596 | |
---|
[921] | 597 | END DO !ji |
---|
| 598 | END DO !jl |
---|
[825] | 599 | |
---|
[921] | 600 | !----------------------------------------------- |
---|
| 601 | ! Add excessive volume of new ice at the bottom |
---|
| 602 | !----------------------------------------------- |
---|
| 603 | ! If the ice concentration exceeds 1, the remaining volume of new ice |
---|
| 604 | ! is equally redistributed among all ice categories in which there is |
---|
| 605 | ! ice |
---|
[825] | 606 | |
---|
[921] | 607 | ! Fraction of level ice |
---|
| 608 | jm = 1 |
---|
| 609 | zat_i_lev(:) = 0.0 |
---|
[825] | 610 | |
---|
[921] | 611 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 612 | DO ji = 1, nbpac |
---|
| 613 | zat_i_lev(ji) = zat_i_lev(ji) + za_i_ac(ji,jl) |
---|
| 614 | END DO |
---|
| 615 | END DO |
---|
[825] | 616 | |
---|
[921] | 617 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
| 618 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 619 | DO ji = 1, nbpac |
---|
| 620 | zindb = MAX( 0.0, SIGN( 1.0, zdv_res(ji) ) ) |
---|
| 621 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + & |
---|
| 622 | zindb * zdv_res(ji) * za_i_ac(ji,jl) / & |
---|
| 623 | MAX( zat_i_lev(ji) , epsi06 ) |
---|
| 624 | END DO ! ji |
---|
| 625 | END DO ! jl |
---|
| 626 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
[825] | 627 | |
---|
[921] | 628 | !--------------------------------- |
---|
| 629 | ! Heat content - bottom accretion |
---|
| 630 | !--------------------------------- |
---|
| 631 | jm = 1 |
---|
| 632 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 633 | DO ji = 1, nbpac |
---|
| 634 | ! zindb = 0 if no ice and 1 if yes |
---|
| 635 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
| 636 | , - za_i_ac(ji,jl ) ) ) |
---|
| 637 | zhice_old(ji,jl) = zv_i_ac(ji,jl) / & |
---|
| 638 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
| 639 | zdhicbot(ji,jl) = zdv_res(ji) / MAX( za_i_ac(ji,jl) , zeps ) & |
---|
| 640 | * zindb & |
---|
| 641 | + zindb * zdh_frazb(ji) ! frazil ice |
---|
| 642 | ! may coalesce |
---|
| 643 | ! thickness of residual ice |
---|
| 644 | zdummy(ji,jl) = zv_i_ac(ji,jl)/MAX(za_i_ac(ji,jl),zeps)*zindb |
---|
| 645 | END DO !ji |
---|
| 646 | END DO !jl |
---|
[825] | 647 | |
---|
[921] | 648 | ! old layers thicknesses and enthalpies |
---|
| 649 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 650 | DO jk = 1, nlay_i |
---|
| 651 | DO ji = 1, nbpac |
---|
| 652 | zthick0(ji,jk,jl)= zhice_old(ji,jl) / nlay_i |
---|
| 653 | zqm0 (ji,jk,jl)= ze_i_ac(ji,jk,jl) * zthick0(ji,jk,jl) |
---|
| 654 | END DO !ji |
---|
| 655 | END DO !jk |
---|
| 656 | END DO !jl |
---|
| 657 | |
---|
| 658 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 659 | DO ji = 1, nbpac |
---|
| 660 | zthick0(ji,nlay_i+1,jl) = zdhicbot(ji,jl) |
---|
| 661 | zqm0 (ji,nlay_i+1,jl) = ze_newice(ji)*zdhicbot(ji,jl) |
---|
| 662 | END DO ! ji |
---|
| 663 | END DO ! jl |
---|
| 664 | |
---|
| 665 | ! Redistributing energy on the new grid |
---|
| 666 | ze_i_ac(:,:,:) = 0.0 |
---|
| 667 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 668 | DO jk = 1, nlay_i |
---|
| 669 | DO layer = 1, nlay_i + 1 |
---|
| 670 | DO ji = 1, nbpac |
---|
| 671 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , & |
---|
| 672 | - za_i_ac(ji,jl ) ) ) |
---|
| 673 | ! Redistributing energy on the new grid |
---|
| 674 | zweight = MAX ( & |
---|
| 675 | MIN( zhice_old(ji,jl) * layer , zdummy(ji,jl) * jk ) - & |
---|
| 676 | MAX( zhice_old(ji,jl) * ( layer - 1 ) , zdummy(ji,jl) * & |
---|
[825] | 677 | ( jk - 1 ) ) , 0.0 ) & |
---|
[921] | 678 | / ( MAX(nlay_i * zthick0(ji,layer,jl),zeps) ) * zindb |
---|
| 679 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) + & |
---|
| 680 | zweight * zqm0(ji,layer,jl) |
---|
| 681 | END DO ! ji |
---|
| 682 | END DO ! layer |
---|
| 683 | END DO ! jk |
---|
| 684 | END DO ! jl |
---|
[825] | 685 | |
---|
[921] | 686 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
| 687 | DO jk = 1, nlay_i |
---|
| 688 | DO ji = 1, nbpac |
---|
| 689 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
| 690 | , - zv_i_ac(ji,jl) ) ) !0 if no ice |
---|
| 691 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) / & |
---|
| 692 | MAX( zv_i_ac(ji,jl) , zeps) & |
---|
| 693 | * za_i_ac(ji,jl) * nlay_i * zindb |
---|
| 694 | END DO |
---|
| 695 | END DO |
---|
| 696 | END DO |
---|
[825] | 697 | |
---|
[921] | 698 | !------------ |
---|
| 699 | ! Update age |
---|
| 700 | !------------ |
---|
| 701 | DO jl = 1, jpl |
---|
| 702 | DO ji = 1, nbpac |
---|
| 703 | !--ice age |
---|
| 704 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
| 705 | za_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
| 706 | zoa_i_ac(ji,jl) = za_old(ji,jl) * zoa_i_ac(ji,jl) / & |
---|
| 707 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
| 708 | END DO ! ji |
---|
| 709 | END DO ! jl |
---|
[825] | 710 | |
---|
[921] | 711 | !----------------- |
---|
| 712 | ! Update salinity |
---|
| 713 | !----------------- |
---|
| 714 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
[825] | 715 | |
---|
[921] | 716 | DO jl = 1, jpl |
---|
| 717 | DO ji = 1, nbpac |
---|
| 718 | !zindb = 0 if no ice and 1 if yes |
---|
| 719 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
| 720 | zv_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
| 721 | zdv = zv_i_ac(ji,jl) - zv_old(ji,jl) |
---|
| 722 | zsmv_i_ac(ji,jl) = ( zsmv_i_ac(ji,jl) + zdv * zs_newice(ji) ) * & |
---|
| 723 | zindb |
---|
| 724 | END DO ! ji |
---|
| 725 | END DO ! jl |
---|
[825] | 726 | |
---|
[921] | 727 | ENDIF ! num_sal |
---|
[825] | 728 | |
---|
| 729 | |
---|
[921] | 730 | !------------------------------------------------------------------------------! |
---|
| 731 | ! 8) Change 2D vectors to 1D vectors |
---|
| 732 | !------------------------------------------------------------------------------! |
---|
[825] | 733 | |
---|
[921] | 734 | DO jl = 1, jpl |
---|
| 735 | CALL tab_1d_2d( nbpac, a_i(:,:,jl) , npac(1:nbpac) , & |
---|
| 736 | za_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
| 737 | CALL tab_1d_2d( nbpac, v_i(:,:,jl) , npac(1:nbpac) , & |
---|
| 738 | zv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
| 739 | CALL tab_1d_2d( nbpac, oa_i(:,:,jl), npac(1:nbpac) , & |
---|
| 740 | zoa_i_ac(1:nbpac,jl), jpi, jpj ) |
---|
| 741 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
| 742 | CALL tab_1d_2d( nbpac, smv_i(:,:,jl) , npac(1:nbpac) , & |
---|
| 743 | zsmv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
| 744 | DO jk = 1, nlay_i |
---|
| 745 | CALL tab_1d_2d( nbpac, e_i(:,:,jk,jl) , npac(1:nbpac), & |
---|
| 746 | ze_i_ac(1:nbpac,jk,jl), jpi, jpj ) |
---|
| 747 | END DO ! jk |
---|
| 748 | END DO !jl |
---|
| 749 | CALL tab_1d_2d( nbpac, fseqv , npac(1:nbpac), fseqv_1d (1:nbpac) , & |
---|
| 750 | jpi, jpj ) |
---|
[825] | 751 | |
---|
[921] | 752 | ENDIF ! nbpac > 0 |
---|
[825] | 753 | |
---|
[921] | 754 | !------------------------------------------------------------------------------! |
---|
| 755 | ! 9) Change units for e_i |
---|
| 756 | !------------------------------------------------------------------------------! |
---|
| 757 | |
---|
[825] | 758 | DO jl = 1, jpl |
---|
| 759 | DO jk = 1, nlay_i |
---|
| 760 | DO jj = 1, jpj |
---|
| 761 | DO ji = 1, jpi |
---|
| 762 | ! Correct dimensions to avoid big values |
---|
| 763 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / unit_fac |
---|
| 764 | |
---|
| 765 | ! Mutliply by ice volume, and divide by number |
---|
| 766 | ! of layers to get heat content in 10^9 Joules |
---|
| 767 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * & |
---|
[921] | 768 | area(ji,jj) * v_i(ji,jj,jl) / & |
---|
| 769 | nlay_i |
---|
[825] | 770 | END DO |
---|
| 771 | END DO |
---|
| 772 | END DO |
---|
| 773 | END DO |
---|
| 774 | |
---|
[921] | 775 | !------------------------------------------------------------------------------| |
---|
| 776 | ! 10) Conservation check and changes in each ice category |
---|
| 777 | !------------------------------------------------------------------------------| |
---|
| 778 | |
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[834] | 779 | IF ( con_i ) THEN |
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[921] | 780 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
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| 781 | fieldid = 'v_i, limthd_lac' |
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| 782 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
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[825] | 783 | |
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[921] | 784 | CALL lim_column_sum_energy(jpl, nlay_i, e_i, et_i_final) |
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| 785 | fieldid = 'e_i, limthd_lac' |
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| 786 | CALL lim_cons_check (et_i_final, et_i_final, 1.0e-3, fieldid) |
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[825] | 787 | |
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[921] | 788 | CALL lim_column_sum (jpl, v_s, vt_s_final) |
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| 789 | fieldid = 'v_s, limthd_lac' |
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| 790 | CALL lim_cons_check (vt_s_init, vt_s_final, 1.0e-6, fieldid) |
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[825] | 791 | |
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[921] | 792 | ! CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
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| 793 | ! fieldid = 'e_s, limthd_lac' |
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| 794 | ! CALL lim_cons_check (et_s_init, et_s_final, 1.0e-3, fieldid) |
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[825] | 795 | |
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[921] | 796 | IF( ln_nicep ) THEN |
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| 797 | WRITE(numout,*) ' vt_i_init : ', vt_i_init(jiindx,jjindx) |
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| 798 | WRITE(numout,*) ' vt_i_final: ', vt_i_final(jiindx,jjindx) |
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| 799 | WRITE(numout,*) ' et_i_init : ', et_i_init(jiindx,jjindx) |
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| 800 | WRITE(numout,*) ' et_i_final: ', et_i_final(jiindx,jjindx) |
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| 801 | ENDIF |
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| 802 | |
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[834] | 803 | ENDIF |
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| 804 | |
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[825] | 805 | END SUBROUTINE lim_thd_lac |
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| 806 | |
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| 807 | #else |
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| 808 | !!====================================================================== |
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| 809 | !! *** MODULE limthd_lac *** |
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| 810 | !! no sea ice model |
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| 811 | !!====================================================================== |
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| 812 | CONTAINS |
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| 813 | SUBROUTINE lim_thd_lac ! Empty routine |
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| 814 | END SUBROUTINE lim_thd_lac |
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| 815 | #endif |
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| 816 | END MODULE limthd_lac |
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