1 | MODULE limrhg |
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2 | !!====================================================================== |
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3 | !! *** MODULE limrhg *** |
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4 | !! Ice rheology : sea ice rheology |
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5 | !!====================================================================== |
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6 | !! History : - ! 2007-03 (M.A. Morales Maqueda, S. Bouillon) Original code |
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7 | !! 3.0 ! 2008-03 (M. Vancoppenolle) LIM3 |
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8 | !! - ! 2008-11 (M. Vancoppenolle, S. Bouillon, Y. Aksenov) add surface tilt in ice rheolohy |
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9 | !! 3.3 ! 2009-05 (G.Garric) addition of the lim2_evp cas |
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10 | !! 3.4 ! 2011-01 (A. Porter) dynamical allocation |
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11 | !! 3.5 ! 2012-08 (R. Benshila) AGRIF |
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12 | !! 3.6 ! 2016-06 (C. Rousset) Rewriting (conserves energy) |
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13 | !!---------------------------------------------------------------------- |
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14 | #if defined key_lim3 || ( defined key_lim2 && ! defined key_lim2_vp ) |
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15 | !!---------------------------------------------------------------------- |
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16 | !! 'key_lim3' OR LIM-3 sea-ice model |
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17 | !! 'key_lim2' AND NOT 'key_lim2_vp' EVP LIM-2 sea-ice model |
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18 | !!---------------------------------------------------------------------- |
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19 | !! lim_rhg : computes ice velocities |
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20 | !!---------------------------------------------------------------------- |
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21 | USE phycst ! Physical constant |
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22 | USE oce , ONLY : snwice_mass, snwice_mass_b |
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23 | USE par_oce ! Ocean parameters |
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24 | USE dom_oce ! Ocean domain |
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25 | USE sbc_oce ! Surface boundary condition: ocean fields |
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26 | USE sbc_ice ! Surface boundary condition: ice fields |
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27 | #if defined key_lim3 |
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28 | USE ice ! LIM-3: ice variables |
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29 | USE dom_ice ! LIM-3: ice domain |
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30 | USE limitd_me ! LIM-3: |
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31 | #else |
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32 | USE ice_2 ! LIM-2: ice variables |
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33 | USE dom_ice_2 ! LIM-2: ice domain |
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34 | #endif |
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35 | USE lbclnk ! Lateral Boundary Condition / MPP link |
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36 | USE lib_mpp ! MPP library |
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37 | USE wrk_nemo ! work arrays |
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38 | USE in_out_manager ! I/O manager |
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39 | USE prtctl ! Print control |
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40 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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41 | #if defined key_agrif && defined key_lim2 |
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42 | USE agrif_lim2_interp |
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43 | #endif |
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44 | #if defined key_bdy |
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45 | USE bdyice_lim |
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46 | #endif |
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47 | |
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48 | IMPLICIT NONE |
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49 | PRIVATE |
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50 | |
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51 | PUBLIC lim_rhg ! routine called by lim_dyn (or lim_dyn_2) |
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52 | |
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53 | !! * Substitutions |
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54 | # include "vectopt_loop_substitute.h90" |
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55 | !!---------------------------------------------------------------------- |
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56 | !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) |
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57 | !! $Id$ |
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58 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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59 | !!---------------------------------------------------------------------- |
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60 | CONTAINS |
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61 | |
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62 | SUBROUTINE lim_rhg( k_j1, k_jpj ) |
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63 | !!------------------------------------------------------------------- |
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64 | !! *** SUBROUTINE lim_rhg *** |
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65 | !! EVP-C-grid |
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66 | !! |
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67 | !! ** purpose : determines sea ice drift from wind stress, ice-ocean |
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68 | !! stress and sea-surface slope. Ice-ice interaction is described by |
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69 | !! a non-linear elasto-viscous-plastic (EVP) law including shear |
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70 | !! strength and a bulk rheology (Hunke and Dukowicz, 2002). |
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71 | !! |
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72 | !! The points in the C-grid look like this, dear reader |
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73 | !! |
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74 | !! (ji,jj) |
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75 | !! | |
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76 | !! | |
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77 | !! (ji-1,jj) | (ji,jj) |
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78 | !! --------- |
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79 | !! | | |
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80 | !! | (ji,jj) |------(ji,jj) |
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81 | !! | | |
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82 | !! --------- |
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83 | !! (ji-1,jj-1) (ji,jj-1) |
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84 | !! |
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85 | !! ** Inputs : - wind forcing (stress), oceanic currents |
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86 | !! ice total volume (vt_i) per unit area |
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87 | !! snow total volume (vt_s) per unit area |
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88 | !! |
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89 | !! ** Action : - compute u_ice, v_ice : the components of the |
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90 | !! sea-ice velocity vector |
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91 | !! - compute delta_i, shear_i, divu_i, which are inputs |
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92 | !! of the ice thickness distribution |
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93 | !! |
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94 | !! ** Steps : 1) Compute ice snow mass, ice strength |
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95 | !! 2) Compute wind, oceanic stresses, mass terms and |
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96 | !! coriolis terms of the momentum equation |
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97 | !! 3) Solve the momentum equation (iterative procedure) |
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98 | !! 4) Recompute invariants of the strain rate tensor |
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99 | !! which are inputs of the ITD, store stress |
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100 | !! for the next time step |
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101 | !! 5) Control prints of residual (convergence) |
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102 | !! and charge ellipse. |
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103 | !! The user should make sure that the parameters |
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104 | !! nn_nevp, elastic time scale and rn_creepl maintain stress state |
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105 | !! on the charge ellipse for plastic flow |
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106 | !! e.g. in the Canadian Archipelago |
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107 | !! |
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108 | !! ** Notes : Boundary condition for ice is chosen no-slip |
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109 | !! but can be adjusted with param rn_shlat |
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110 | !! |
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111 | !! References : Hunke and Dukowicz, JPO97 |
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112 | !! Bouillon et al., Ocean Modelling 2009 |
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113 | !!------------------------------------------------------------------- |
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114 | INTEGER, INTENT(in) :: k_j1 ! southern j-index for ice computation |
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115 | INTEGER, INTENT(in) :: k_jpj ! northern j-index for ice computation |
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116 | !! |
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117 | INTEGER :: ji, jj ! dummy loop indices |
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118 | INTEGER :: jter ! local integers |
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119 | CHARACTER (len=50) :: charout |
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120 | |
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121 | REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling |
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122 | REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity |
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123 | REAL(wp) :: zbeta, zalph1, z1_alph1, zalph2, z1_alph2 ! alpha and beta from Bouillon 2009 and 2013 |
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124 | REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV ! ice/snow mass |
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125 | REAL(wp) :: zdelta, zp_delf, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars |
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126 | REAL(wp) :: zTauO, zTauE, zCor ! temporary scalars |
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127 | |
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128 | REAL(wp) :: zsig1, zsig2 ! internal ice stress |
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129 | REAL(wp) :: zresm ! Maximal error on ice velocity |
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130 | REAL(wp) :: zintb, zintn ! dummy argument |
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131 | |
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132 | REAL(wp), POINTER, DIMENSION(:,:) :: zpresh ! temporary array for ice strength |
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133 | REAL(wp), POINTER, DIMENSION(:,:) :: z1_e1t0, z1_e2t0 ! scale factors |
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134 | REAL(wp), POINTER, DIMENSION(:,:) :: zp_delt ! P/delta at T points |
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135 | ! |
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136 | REAL(wp), POINTER, DIMENSION(:,:) :: zaU , zaV ! ice fraction on U/V points |
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137 | REAL(wp), POINTER, DIMENSION(:,:) :: zmU_t, zmV_t ! ice/snow mass/dt on U/V points |
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138 | REAL(wp), POINTER, DIMENSION(:,:) :: zmf ! coriolis parameter at T points |
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139 | REAL(wp), POINTER, DIMENSION(:,:) :: zTauU_ia , ztauV_ia ! ice-atm. stress at U-V points |
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140 | REAL(wp), POINTER, DIMENSION(:,:) :: zspgU , zspgV ! surface pressure gradient at U/V points |
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141 | REAL(wp), POINTER, DIMENSION(:,:) :: v_oceU, u_oceV, v_iceU, u_iceV ! ocean/ice u/v component on V/U points |
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142 | REAL(wp), POINTER, DIMENSION(:,:) :: zfU , zfV ! internal stresses |
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143 | |
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144 | REAL(wp), POINTER, DIMENSION(:,:) :: zds ! shear |
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145 | REAL(wp), POINTER, DIMENSION(:,:) :: zs1, zs2, zs12 ! stress tensor components |
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146 | REAL(wp), POINTER, DIMENSION(:,:) :: zu_ice, zv_ice, zresr ! check convergence |
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147 | REAL(wp), POINTER, DIMENSION(:,:) :: zpice ! array used for the calculation of ice surface slope: |
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148 | ! ocean surface (ssh_m) if ice is not embedded |
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149 | ! ice top surface if ice is embedded |
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150 | REAL(wp), POINTER, DIMENSION(:,:) :: zswitchU, zswitchV ! dummy arrays |
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151 | REAL(wp), POINTER, DIMENSION(:,:) :: zmaskU, zmaskV ! mask for ice presence |
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152 | REAL(wp), POINTER, DIMENSION(:,:) :: zfmask, zwf ! mask at F points for the ice |
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153 | |
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154 | REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter |
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155 | REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity equals ocean velocity |
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156 | REAL(wp), PARAMETER :: zshlat = 2._wp ! boundary condition for sea-ice velocity (2=no slip ; 0=free slip) |
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157 | !!------------------------------------------------------------------- |
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158 | |
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159 | CALL wrk_alloc( jpi,jpj, zpresh, z1_e1t0, z1_e2t0, zp_delt ) |
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160 | CALL wrk_alloc( jpi,jpj, zaU, zaV, zmU_t, zmV_t, zmf, zTauU_ia, ztauV_ia ) |
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161 | CALL wrk_alloc( jpi,jpj, zspgU, zspgV, v_oceU, u_oceV, v_iceU, u_iceV, zfU, zfV ) |
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162 | CALL wrk_alloc( jpi,jpj, zds, zs1, zs2, zs12, zu_ice, zv_ice, zresr, zpice ) |
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163 | CALL wrk_alloc( jpi,jpj, zswitchU, zswitchV, zmaskU, zmaskV, zfmask, zwf ) |
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164 | |
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165 | #if defined key_lim2 && ! defined key_lim2_vp |
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166 | # if defined key_agrif |
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167 | USE ice_2, vt_s => hsnm |
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168 | USE ice_2, vt_i => hicm |
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169 | # else |
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170 | vt_s => hsnm |
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171 | vt_i => hicm |
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172 | # endif |
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173 | at_i(:,:) = 1. - frld(:,:) |
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174 | #endif |
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175 | #if defined key_agrif && defined key_lim2 |
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176 | CALL agrif_rhg_lim2_load ! First interpolation of coarse values |
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177 | #endif |
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178 | ! |
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179 | !------------------------------------------------------------------------------! |
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180 | ! 0) mask at F points for the ice (on the whole domain, not only k_j1,k_jpj) |
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181 | !------------------------------------------------------------------------------! |
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182 | ! ocean/land mask |
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183 | DO jj = 1, jpjm1 |
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184 | DO ji = 1, jpim1 ! NO vector opt. |
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185 | zfmask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1) |
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186 | END DO |
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187 | END DO |
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188 | CALL lbc_lnk( zfmask, 'F', 1._wp ) |
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189 | |
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190 | ! Lateral boundary conditions on velocity (modify zfmask) |
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191 | zwf(:,:) = zfmask(:,:) |
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192 | DO jj = 2, jpjm1 |
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193 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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194 | IF( zfmask(ji,jj) == 0._wp ) THEN |
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195 | zfmask(ji,jj) = zshlat * MIN( 1._wp , MAX( zwf(ji+1,jj), zwf(ji,jj+1), zwf(ji-1,jj), zwf(ji,jj-1) ) ) |
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196 | ENDIF |
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197 | END DO |
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198 | END DO |
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199 | DO jj = 2, jpjm1 |
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200 | IF( zfmask(1,jj) == 0._wp ) THEN |
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201 | zfmask(1 ,jj) = zshlat * MIN( 1._wp , MAX( zwf(2,jj), zwf(1,jj+1), zwf(1,jj-1) ) ) |
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202 | ENDIF |
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203 | IF( zfmask(jpi,jj) == 0._wp ) THEN |
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204 | zfmask(jpi,jj) = zshlat * MIN( 1._wp , MAX( zwf(jpi,jj+1), zwf(jpim1,jj), zwf(jpi,jj-1) ) ) |
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205 | ENDIF |
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206 | END DO |
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207 | DO ji = 2, jpim1 |
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208 | IF( zfmask(ji,1) == 0._wp ) THEN |
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209 | zfmask(ji,1 ) = zshlat * MIN( 1._wp , MAX( zwf(ji+1,1), zwf(ji,2), zwf(ji-1,1) ) ) |
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210 | ENDIF |
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211 | IF( zfmask(ji,jpj) == 0._wp ) THEN |
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212 | zfmask(ji,jpj) = zshlat * MIN( 1._wp , MAX( zwf(ji+1,jpj), zwf(ji-1,jpj), zwf(ji,jpjm1) ) ) |
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213 | ENDIF |
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214 | END DO |
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215 | CALL lbc_lnk( zfmask, 'F', 1._wp ) |
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216 | |
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217 | !------------------------------------------------------------------------------! |
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218 | ! 1) define some variables and initialize arrays |
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219 | !------------------------------------------------------------------------------! |
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220 | ! ecc2: square of yield ellipse eccenticrity |
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221 | ecc2 = rn_ecc * rn_ecc |
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222 | z1_ecc2 = 1._wp / ecc2 |
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223 | |
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224 | ! Time step for subcycling |
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225 | zdtevp = rdt_ice / REAL( nn_nevp ) |
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226 | z1_dtevp = 1._wp / zdtevp |
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227 | |
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228 | ! alpha parameters (Bouillon 2009) |
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229 | #if defined key_lim3 |
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230 | zalph1 = ( 2._wp * rn_relast * rdt_ice ) * z1_dtevp |
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231 | #else |
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232 | zalph1 = ( 2._wp * telast ) * z1_dtevp |
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233 | #endif |
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234 | zalph2 = zalph1 * z1_ecc2 |
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235 | |
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236 | z1_alph1 = 1._wp / ( zalph1 + 1._wp ) |
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237 | z1_alph2 = 1._wp / ( zalph2 + 1._wp ) |
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238 | |
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239 | ! Initialise stress tensor |
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240 | zs1 (:,:) = stress1_i (:,:) |
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241 | zs2 (:,:) = stress2_i (:,:) |
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242 | zs12(:,:) = stress12_i(:,:) |
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243 | |
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244 | ! Ice strength |
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245 | #if defined key_lim3 |
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246 | CALL lim_itd_me_icestrength( nn_icestr ) |
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247 | zpresh(:,:) = tmask(:,:,1) * strength(:,:) |
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248 | #else |
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249 | zpresh(:,:) = tmask(:,:,1) * pstar * vt_i(:,:) * EXP( -c_rhg * (1. - at_i(:,:) ) ) |
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250 | #endif |
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251 | |
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252 | ! scale factors |
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253 | DO jj = k_j1+1, k_jpj-1 |
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254 | DO ji = fs_2, fs_jpim1 |
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255 | z1_e1t0(ji,jj) = 1._wp / ( e1t(ji+1,jj ) + e1t(ji,jj ) ) |
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256 | z1_e2t0(ji,jj) = 1._wp / ( e2t(ji ,jj+1) + e2t(ji,jj ) ) |
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257 | END DO |
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258 | END DO |
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259 | |
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260 | ! |
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261 | !------------------------------------------------------------------------------! |
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262 | ! 2) Wind / ocean stress, mass terms, coriolis terms |
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263 | !------------------------------------------------------------------------------! |
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264 | |
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265 | IF( nn_ice_embd == 2 ) THEN !== embedded sea ice: compute representative ice top surface ==! |
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266 | ! |
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267 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[n/nn_fsbc], n=0,nn_fsbc-1} |
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268 | ! = (1/nn_fsbc)^2 * {SUM[n], n=0,nn_fsbc-1} |
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269 | zintn = REAL( nn_fsbc - 1 ) / REAL( nn_fsbc ) * 0.5_wp |
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270 | ! |
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271 | ! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[1-n/nn_fsbc], n=0,nn_fsbc-1} |
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272 | ! = (1/nn_fsbc)^2 * (nn_fsbc^2 - {SUM[n], n=0,nn_fsbc-1}) |
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273 | zintb = REAL( nn_fsbc + 1 ) / REAL( nn_fsbc ) * 0.5_wp |
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274 | ! |
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275 | zpice(:,:) = ssh_m(:,:) + ( zintn * snwice_mass(:,:) + zintb * snwice_mass_b(:,:) ) * r1_rau0 |
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276 | ! |
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277 | ELSE !== non-embedded sea ice: use ocean surface for slope calculation ==! |
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278 | zpice(:,:) = ssh_m(:,:) |
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279 | ENDIF |
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280 | |
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281 | DO jj = k_j1+1, k_jpj-1 |
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282 | DO ji = fs_2, fs_jpim1 |
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283 | |
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284 | ! ice fraction at U-V points |
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285 | zaU(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e12t(ji,jj) + at_i(ji+1,jj) * e12t(ji+1,jj) ) * r1_e12u(ji,jj) * umask(ji,jj,1) |
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286 | zaV(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e12t(ji,jj) + at_i(ji,jj+1) * e12t(ji,jj+1) ) * r1_e12v(ji,jj) * vmask(ji,jj,1) |
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287 | |
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288 | ! Ice/snow mass at U-V points |
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289 | zm1 = ( rhosn * vt_s(ji ,jj ) + rhoic * vt_i(ji ,jj ) ) |
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290 | zm2 = ( rhosn * vt_s(ji+1,jj ) + rhoic * vt_i(ji+1,jj ) ) |
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291 | zm3 = ( rhosn * vt_s(ji ,jj+1) + rhoic * vt_i(ji ,jj+1) ) |
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292 | zmassU = 0.5_wp * ( zm1 * e12t(ji,jj) + zm2 * e12t(ji+1,jj) ) * r1_e12u(ji,jj) * umask(ji,jj,1) |
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293 | zmassV = 0.5_wp * ( zm1 * e12t(ji,jj) + zm3 * e12t(ji,jj+1) ) * r1_e12v(ji,jj) * vmask(ji,jj,1) |
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294 | |
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295 | ! Ocean currents at U-V points |
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296 | v_oceU(ji,jj) = 0.5_wp * ( ( v_oce(ji ,jj) + v_oce(ji ,jj-1) ) * e1t(ji+1,jj) & |
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297 | & + ( v_oce(ji+1,jj) + v_oce(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
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298 | |
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299 | u_oceV(ji,jj) = 0.5_wp * ( ( u_oce(ji,jj ) + u_oce(ji-1,jj ) ) * e2t(ji,jj+1) & |
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300 | & + ( u_oce(ji,jj+1) + u_oce(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
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301 | |
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302 | ! Coriolis at T points (m*f) |
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303 | zmf(ji,jj) = zm1 * fcor(ji,jj) |
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304 | |
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305 | ! m/dt |
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306 | zmU_t(ji,jj) = zmassU * z1_dtevp |
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307 | zmV_t(ji,jj) = zmassV * z1_dtevp |
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308 | |
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309 | ! Drag ice-atm. |
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310 | zTauU_ia(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj) |
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311 | zTauV_ia(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj) |
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312 | |
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313 | ! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points |
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314 | zspgU(ji,jj) = - zmassU * grav * ( zpice(ji+1,jj) - zpice(ji,jj) ) * r1_e1u(ji,jj) |
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315 | zspgV(ji,jj) = - zmassV * grav * ( zpice(ji,jj+1) - zpice(ji,jj) ) * r1_e2v(ji,jj) |
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316 | |
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317 | ! masks |
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318 | zmaskU(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice |
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319 | zmaskV(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice |
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320 | |
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321 | ! switches |
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322 | zswitchU(ji,jj) = MAX( 0._wp, SIGN( 1._wp, zmassU - zmmin ) ) ! 0 if ice mass < zmmin |
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323 | zswitchV(ji,jj) = MAX( 0._wp, SIGN( 1._wp, zmassV - zmmin ) ) ! 0 if ice mass < zmmin |
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324 | |
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325 | END DO |
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326 | END DO |
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327 | CALL lbc_lnk( zmf, 'T', 1. ) |
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328 | ! |
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329 | !------------------------------------------------------------------------------! |
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330 | ! 3) Solution of the momentum equation, iterative procedure |
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331 | !------------------------------------------------------------------------------! |
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332 | ! |
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333 | ! !----------------------! |
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334 | DO jter = 1 , nn_nevp ! loop over jter ! |
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335 | ! !----------------------! |
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336 | IF(ln_ctl) THEN ! Convergence test |
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337 | DO jj = k_j1, k_jpj-1 |
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338 | zu_ice(:,jj) = u_ice(:,jj) ! velocity at previous time step |
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339 | zv_ice(:,jj) = v_ice(:,jj) |
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340 | END DO |
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341 | ENDIF |
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342 | |
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343 | ! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- ! |
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344 | DO jj = k_j1, k_jpj-1 ! loops start at 1 since there is no boundary condition (lbc_lnk) at i=1 and j=1 for F points |
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345 | DO ji = 1, jpim1 |
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346 | |
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347 | ! shear at F points |
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348 | zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) & |
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349 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
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350 | & ) * r1_e12f(ji,jj) * zfmask(ji,jj) |
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351 | |
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352 | END DO |
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353 | END DO |
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354 | CALL lbc_lnk( zds, 'F', 1. ) |
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355 | |
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356 | DO jj = k_j1+1, k_jpj-1 |
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357 | DO ji = 2, jpim1 ! no vector loop |
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358 | |
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359 | ! shear**2 at T points (doc eq. A16) |
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360 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e12f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e12f(ji-1,jj ) & |
---|
361 | & + zds(ji,jj-1) * zds(ji,jj-1) * e12f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e12f(ji-1,jj-1) & |
---|
362 | & ) * 0.25_wp * r1_e12t(ji,jj) |
---|
363 | |
---|
364 | ! divergence at T points |
---|
365 | zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
---|
366 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
---|
367 | & ) * r1_e12t(ji,jj) |
---|
368 | zdiv2 = zdiv * zdiv |
---|
369 | |
---|
370 | ! tension at T points |
---|
371 | zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
---|
372 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
---|
373 | & ) * r1_e12t(ji,jj) |
---|
374 | zdt2 = zdt * zdt |
---|
375 | |
---|
376 | ! delta at T points |
---|
377 | zdelta = SQRT( zdiv2 + ( zdt2 + zds2 ) * usecc2 ) |
---|
378 | |
---|
379 | ! P/delta at T points |
---|
380 | zp_delt(ji,jj) = zpresh(ji,jj) / ( zdelta + rn_creepl ) |
---|
381 | |
---|
382 | ! stress at T points |
---|
383 | zs1(ji,jj) = ( zs1(ji,jj) * zalph1 + zp_delt(ji,jj) * ( zdiv - zdelta ) ) * z1_alph1 |
---|
384 | zs2(ji,jj) = ( zs2(ji,jj) * zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 ) ) * z1_alph2 |
---|
385 | |
---|
386 | END DO |
---|
387 | END DO |
---|
388 | CALL lbc_lnk( zp_delt, 'T', 1. ) |
---|
389 | |
---|
390 | DO jj = k_j1, k_jpj-1 |
---|
391 | DO ji = 1, jpim1 |
---|
392 | |
---|
393 | ! P/delta at F points |
---|
394 | zp_delf = 0.25_wp * ( zp_delt(ji,jj) + zp_delt(ji+1,jj) + zp_delt(ji,jj+1) + zp_delt(ji+1,jj+1) ) |
---|
395 | |
---|
396 | ! stress at F points |
---|
397 | zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 ) * 0.5_wp ) * z1_alph2 |
---|
398 | |
---|
399 | END DO |
---|
400 | END DO |
---|
401 | CALL lbc_lnk_multi( zs1, 'T', 1., zs2, 'T', 1., zs12, 'F', 1. ) |
---|
402 | |
---|
403 | ! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- ! |
---|
404 | DO jj = k_j1+1, k_jpj-1 |
---|
405 | DO ji = fs_2, fs_jpim1 |
---|
406 | |
---|
407 | ! U points |
---|
408 | zfU(ji,jj) = 0.5_wp * ( ( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) & |
---|
409 | & + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) & |
---|
410 | & ) * r1_e2u(ji,jj) & |
---|
411 | & + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) & |
---|
412 | & ) * 2._wp * r1_e1u(ji,jj) & |
---|
413 | & ) * r1_e12u(ji,jj) |
---|
414 | |
---|
415 | ! V points |
---|
416 | zfV(ji,jj) = 0.5_wp * ( ( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) & |
---|
417 | & - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) & |
---|
418 | & ) * r1_e1v(ji,jj) & |
---|
419 | & + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) & |
---|
420 | & ) * 2._wp * r1_e2v(ji,jj) & |
---|
421 | & ) * r1_e12v(ji,jj) |
---|
422 | |
---|
423 | ! u_ice at V point |
---|
424 | u_iceV(ji,jj) = 0.5_wp * ( ( u_ice(ji,jj ) + u_ice(ji-1,jj ) ) * e2t(ji,jj+1) & |
---|
425 | & + ( u_ice(ji,jj+1) + u_ice(ji-1,jj+1) ) * e2t(ji,jj ) ) * z1_e2t0(ji,jj) * vmask(ji,jj,1) |
---|
426 | |
---|
427 | ! v_ice at U point |
---|
428 | v_iceU(ji,jj) = 0.5_wp * ( ( v_ice(ji ,jj) + v_ice(ji ,jj-1) ) * e1t(ji+1,jj) & |
---|
429 | & + ( v_ice(ji+1,jj) + v_ice(ji+1,jj-1) ) * e1t(ji ,jj) ) * z1_e1t0(ji,jj) * umask(ji,jj,1) |
---|
430 | |
---|
431 | END DO |
---|
432 | END DO |
---|
433 | ! |
---|
434 | ! --- Computation of ice velocity --- ! |
---|
435 | ! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta are chosen wisely and large nn_nevp |
---|
436 | ! Bouillon et al. 2009 (eq 34-35) => stable |
---|
437 | IF( MOD(jter,2) .EQ. 0 ) THEN ! even iterations |
---|
438 | |
---|
439 | DO jj = k_j1+1, k_jpj-1 |
---|
440 | DO ji = fs_2, fs_jpim1 |
---|
441 | |
---|
442 | ! tau_io/(v_oce - v_ice) |
---|
443 | zTauO = zaV(ji,jj) * rhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
---|
444 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
---|
445 | |
---|
446 | ! Coriolis at V-points (energy conserving formulation) |
---|
447 | zCor = - 0.25_wp * r1_e2v(ji,jj) * & |
---|
448 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
---|
449 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
---|
450 | |
---|
451 | ! Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
---|
452 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCor + zspgV(ji,jj) + zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
---|
453 | |
---|
454 | ! ice velocity using implicit formulation (cf Madec doc & Bouillon 2009) |
---|
455 | v_ice(ji,jj) = ( ( zmV_t(ji,jj) * v_ice(ji,jj) + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
---|
456 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO ) * zswitchV(ji,jj) & ! m/dt + tau_io(only ice part) |
---|
457 | & + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
---|
458 | & ) * zmaskV(ji,jj) |
---|
459 | END DO |
---|
460 | END DO |
---|
461 | CALL lbc_lnk( v_ice, 'V', -1. ) |
---|
462 | |
---|
463 | #if defined key_agrif && defined key_lim2 |
---|
464 | CALL agrif_rhg_lim2( jter, nn_nevp, 'V' ) |
---|
465 | #endif |
---|
466 | #if defined key_bdy |
---|
467 | CALL bdy_ice_lim_dyn( 'V' ) |
---|
468 | #endif |
---|
469 | |
---|
470 | DO jj = k_j1+1, k_jpj-1 |
---|
471 | DO ji = fs_2, fs_jpim1 |
---|
472 | |
---|
473 | ! tau_io/(u_oce - u_ice) |
---|
474 | zTauO = zaU(ji,jj) * rhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
---|
475 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
---|
476 | |
---|
477 | ! Coriolis at U-points (energy conserving formulation) |
---|
478 | zCor = 0.25_wp * r1_e1u(ji,jj) * & |
---|
479 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
---|
480 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
---|
481 | |
---|
482 | ! Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
---|
483 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCor + zspgU(ji,jj) + zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
---|
484 | |
---|
485 | ! ice velocity using implicit formulation (cf Madec doc & Bouillon 2009) |
---|
486 | u_ice(ji,jj) = ( ( zmU_t(ji,jj) * u_ice(ji,jj) + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
---|
487 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO ) * zswitchU(ji,jj) & ! m/dt + tau_io(only ice part) |
---|
488 | & + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
---|
489 | & ) * zmaskU(ji,jj) |
---|
490 | END DO |
---|
491 | END DO |
---|
492 | CALL lbc_lnk( u_ice, 'U', -1. ) |
---|
493 | |
---|
494 | #if defined key_agrif && defined key_lim2 |
---|
495 | CALL agrif_rhg_lim2( jter, nn_nevp, 'U' ) |
---|
496 | #endif |
---|
497 | #if defined key_bdy |
---|
498 | CALL bdy_ice_lim_dyn( 'U' ) |
---|
499 | #endif |
---|
500 | |
---|
501 | ELSE ! odd iterations |
---|
502 | |
---|
503 | DO jj = k_j1+1, k_jpj-1 |
---|
504 | DO ji = fs_2, fs_jpim1 |
---|
505 | |
---|
506 | ! tau_io/(u_oce - u_ice) |
---|
507 | zTauO = zaU(ji,jj) * rhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) & |
---|
508 | & + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) ) |
---|
509 | |
---|
510 | ! Coriolis at U-points (energy conserving formulation) |
---|
511 | zCor = 0.25_wp * r1_e1u(ji,jj) * & |
---|
512 | & ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) & |
---|
513 | & + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) ) |
---|
514 | |
---|
515 | ! Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
---|
516 | zTauE = zfU(ji,jj) + zTauU_ia(ji,jj) + zCor + zspgU(ji,jj) + zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) ) |
---|
517 | |
---|
518 | ! ice velocity using implicit formulation (cf Madec doc & Bouillon 2009) |
---|
519 | u_ice(ji,jj) = ( ( zmU_t(ji,jj) * u_ice(ji,jj) + zTauE + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
---|
520 | & ) / MAX( zepsi, zmU_t(ji,jj) + zTauO ) * zswitchU(ji,jj) & ! m/dt + tau_io(only ice part) |
---|
521 | & + u_oce(ji,jj) * ( 1._wp - zswitchU(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
---|
522 | & ) * zmaskU(ji,jj) |
---|
523 | END DO |
---|
524 | END DO |
---|
525 | CALL lbc_lnk( u_ice, 'U', -1. ) |
---|
526 | |
---|
527 | #if defined key_agrif && defined key_lim2 |
---|
528 | CALL agrif_rhg_lim2( jter, nn_nevp, 'U' ) |
---|
529 | #endif |
---|
530 | #if defined key_bdy |
---|
531 | CALL bdy_ice_lim_dyn( 'U' ) |
---|
532 | #endif |
---|
533 | |
---|
534 | DO jj = k_j1+1, k_jpj-1 |
---|
535 | DO ji = fs_2, fs_jpim1 |
---|
536 | |
---|
537 | ! tau_io/(v_oce - v_ice) |
---|
538 | zTauO = zaV(ji,jj) * rhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) & |
---|
539 | & + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) ) |
---|
540 | |
---|
541 | ! Coriolis at V-points (energy conserving formulation) |
---|
542 | zCor = - 0.25_wp * r1_e2v(ji,jj) * & |
---|
543 | & ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) & |
---|
544 | & + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) ) |
---|
545 | |
---|
546 | ! Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io |
---|
547 | zTauE = zfV(ji,jj) + zTauV_ia(ji,jj) + zCor + zspgV(ji,jj) + zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) ) |
---|
548 | |
---|
549 | ! ice velocity using implicit formulation (cf Madec doc & Bouillon 2009) |
---|
550 | v_ice(ji,jj) = ( ( zmV_t(ji,jj) * v_ice(ji,jj) + zTauE + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part) |
---|
551 | & ) / MAX( zepsi, zmV_t(ji,jj) + zTauO ) * zswitchV(ji,jj) & ! m/dt + tau_io(only ice part) |
---|
552 | & + v_oce(ji,jj) * ( 1._wp - zswitchV(ji,jj) ) & ! v_ice = v_oce if mass < zmmin |
---|
553 | & ) * zmaskV(ji,jj) |
---|
554 | END DO |
---|
555 | END DO |
---|
556 | CALL lbc_lnk( v_ice, 'V', -1. ) |
---|
557 | |
---|
558 | #if defined key_agrif && defined key_lim2 |
---|
559 | CALL agrif_rhg_lim2( jter, nn_nevp, 'V' ) |
---|
560 | #endif |
---|
561 | #if defined key_bdy |
---|
562 | CALL bdy_ice_lim_dyn( 'V' ) |
---|
563 | #endif |
---|
564 | |
---|
565 | ENDIF |
---|
566 | |
---|
567 | IF(ln_ctl) THEN ! Convergence test |
---|
568 | DO jj = k_j1+1, k_jpj-1 |
---|
569 | zresr(:,jj) = MAX( ABS( u_ice(:,jj) - zu_ice(:,jj) ), ABS( v_ice(:,jj) - zv_ice(:,jj) ) ) |
---|
570 | END DO |
---|
571 | zresm = MAXVAL( zresr( 1:jpi, k_j1+1:k_jpj-1 ) ) |
---|
572 | IF( lk_mpp ) CALL mpp_max( zresm ) ! max over the global domain |
---|
573 | ENDIF |
---|
574 | ! |
---|
575 | ! ! ==================== ! |
---|
576 | END DO ! end loop over jter ! |
---|
577 | ! ! ==================== ! |
---|
578 | ! |
---|
579 | !------------------------------------------------------------------------------! |
---|
580 | ! 4) Recompute delta, shear and div (inputs for mechanical redistribution) |
---|
581 | !------------------------------------------------------------------------------! |
---|
582 | DO jj = k_j1, k_jpj-1 |
---|
583 | DO ji = 1, jpim1 |
---|
584 | |
---|
585 | ! shear at F points |
---|
586 | zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) & |
---|
587 | & + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) & |
---|
588 | & ) * r1_e12f(ji,jj) * zfmask(ji,jj) |
---|
589 | |
---|
590 | END DO |
---|
591 | END DO |
---|
592 | CALL lbc_lnk( zds, 'F', 1. ) |
---|
593 | |
---|
594 | DO jj = k_j1+1, k_jpj-1 |
---|
595 | DO ji = 2, jpim1 ! no vector loop |
---|
596 | |
---|
597 | ! tension**2 at T points |
---|
598 | zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) & |
---|
599 | & - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) & |
---|
600 | & ) * r1_e12t(ji,jj) |
---|
601 | zdt2 = zdt * zdt |
---|
602 | |
---|
603 | ! shear**2 at T points (doc eq. A16) |
---|
604 | zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e12f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e12f(ji-1,jj ) & |
---|
605 | & + zds(ji,jj-1) * zds(ji,jj-1) * e12f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e12f(ji-1,jj-1) & |
---|
606 | & ) * 0.25_wp * r1_e12t(ji,jj) |
---|
607 | |
---|
608 | ! shear at T points |
---|
609 | shear_i(ji,jj) = SQRT( zdt2 + zds2 ) |
---|
610 | |
---|
611 | ! divergence at T points |
---|
612 | divu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) & |
---|
613 | & + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) & |
---|
614 | & ) * r1_e12t(ji,jj) |
---|
615 | |
---|
616 | ! delta at T points |
---|
617 | zdelta = SQRT( divu_i(ji,jj) * divu_i(ji,jj) + ( zdt2 + zds2 ) * usecc2 ) |
---|
618 | rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zdelta ) ) ! 0 if delta=0 |
---|
619 | delta_i(ji,jj) = zdelta + rn_creepl * rswitch |
---|
620 | |
---|
621 | END DO |
---|
622 | END DO |
---|
623 | CALL lbc_lnk_multi( shear_i, 'T', 1., divu_i, 'T', 1., delta_i, 'T', 1. ) |
---|
624 | |
---|
625 | ! --- Store the stress tensor for the next time step --- ! |
---|
626 | stress1_i (:,:) = zs1 (:,:) |
---|
627 | stress2_i (:,:) = zs2 (:,:) |
---|
628 | stress12_i(:,:) = zs12(:,:) |
---|
629 | |
---|
630 | ! |
---|
631 | !------------------------------------------------------------------------------! |
---|
632 | ! 5) Control prints of residual and charge ellipse |
---|
633 | !------------------------------------------------------------------------------! |
---|
634 | ! |
---|
635 | ! print the residual for convergence |
---|
636 | IF(ln_ctl) THEN |
---|
637 | WRITE(charout,FMT="('lim_rhg : res =',D23.16, ' iter =',I4)") zresm, jter |
---|
638 | CALL prt_ctl_info(charout) |
---|
639 | CALL prt_ctl(tab2d_1=u_ice, clinfo1=' lim_rhg : u_ice :', tab2d_2=v_ice, clinfo2=' v_ice :') |
---|
640 | ENDIF |
---|
641 | |
---|
642 | ! print charge ellipse |
---|
643 | ! This can be desactivated once the user is sure that the stress state |
---|
644 | ! lie on the charge ellipse. See Bouillon et al. 08 for more details |
---|
645 | IF(ln_ctl) THEN |
---|
646 | CALL prt_ctl_info('lim_rhg : numit :',ivar1=numit) |
---|
647 | CALL prt_ctl_info('lim_rhg : nwrite :',ivar1=nwrite) |
---|
648 | CALL prt_ctl_info('lim_rhg : MOD :',ivar1=MOD(numit,nwrite)) |
---|
649 | IF( MOD(numit,nwrite) .EQ. 0 ) THEN |
---|
650 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 1000, numit, 0, 0, ' ch. ell. ' |
---|
651 | CALL prt_ctl_info(charout) |
---|
652 | DO jj = k_j1+1, k_jpj-1 |
---|
653 | DO ji = 2, jpim1 |
---|
654 | IF (zpresh(ji,jj) > 1.0) THEN |
---|
655 | zsig1 = ( zs1(ji,jj) + (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
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656 | zsig2 = ( zs1(ji,jj) - (zs2(ji,jj)**2 + 4*zs12(ji,jj)**2 )**0.5 ) / ( 2*zpresh(ji,jj) ) |
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657 | WRITE(charout,FMT="('lim_rhg :', I4, I4, D23.16, D23.16, D23.16, D23.16, A10)") |
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658 | CALL prt_ctl_info(charout) |
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659 | ENDIF |
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660 | END DO |
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661 | END DO |
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662 | WRITE(charout,FMT="('lim_rhg :', I4, I6, I1, I1, A10)") 2000, numit, 0, 0, ' ch. ell. ' |
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663 | CALL prt_ctl_info(charout) |
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664 | ENDIF |
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665 | ENDIF |
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666 | ! |
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667 | CALL wrk_dealloc( jpi,jpj, zpresh, z1_e1t0, z1_e2t0, zp_delt ) |
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668 | CALL wrk_dealloc( jpi,jpj, zaU, zaV, zmU_t, zmV_t, zmf, zTauU_ia, ztauV_ia ) |
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669 | CALL wrk_dealloc( jpi,jpj, zspgU, zspgV, v_oceU, u_oceV, v_iceU, u_iceV, zfU, zfV ) |
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670 | CALL wrk_dealloc( jpi,jpj, zds, zs1, zs2, zs12, zu_ice, zv_ice, zresr, zpice ) |
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671 | CALL wrk_dealloc( jpi,jpj, zswitchU, zswitchV, zmaskU, zmaskV, zfmask, zwf ) |
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672 | |
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673 | END SUBROUTINE lim_rhg |
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674 | |
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675 | #else |
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676 | !!---------------------------------------------------------------------- |
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677 | !! Default option Dummy module NO LIM sea-ice model |
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678 | !!---------------------------------------------------------------------- |
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679 | CONTAINS |
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680 | SUBROUTINE lim_rhg( k1 , k2 ) ! Dummy routine |
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681 | WRITE(*,*) 'lim_rhg: You should not have seen this print! error?', k1, k2 |
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682 | END SUBROUTINE lim_rhg |
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683 | #endif |
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684 | |
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685 | !!============================================================================== |
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686 | END MODULE limrhg |
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