1 | MODULE icedyn_adv_umx |
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2 | !!============================================================================== |
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3 | !! *** MODULE icedyn_adv_umx *** |
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4 | !! sea-ice : advection using the ULTIMATE-MACHO scheme |
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5 | !!============================================================================== |
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6 | !! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code |
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7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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8 | !!---------------------------------------------------------------------- |
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9 | #if defined key_si3 |
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10 | !!---------------------------------------------------------------------- |
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11 | !! 'key_si3' SI3 sea-ice model |
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12 | !!---------------------------------------------------------------------- |
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13 | !! ice_dyn_adv_umx : update the tracer fields |
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14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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15 | !! macho : compute the fluxes |
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16 | !! nonosc_ice : limit the fluxes using a non-oscillatory algorithm |
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17 | !!---------------------------------------------------------------------- |
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18 | USE phycst ! physical constant |
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19 | USE dom_oce ! ocean domain |
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20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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21 | USE ice ! sea-ice variables |
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22 | USE icevar ! sea-ice: operations |
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23 | ! |
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24 | USE in_out_manager ! I/O manager |
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25 | USE iom ! I/O manager library |
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26 | USE lib_mpp ! MPP library |
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27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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29 | |
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30 | IMPLICIT NONE |
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31 | PRIVATE |
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32 | |
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33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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34 | ! |
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35 | INTEGER, PARAMETER :: np_advS = 1 ! advection for S and T: dVS/dt = -div( uVS ) => np_advS = 1 |
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36 | ! or dVS/dt = -div( uA * uHS / u ) => np_advS = 2 |
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37 | ! or dVS/dt = -div( uV * uS / u ) => np_advS = 3 |
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38 | INTEGER, PARAMETER :: np_limiter = 1 ! limiter: 1 = nonosc |
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39 | ! 2 = superbee |
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40 | ! 3 = h3 |
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41 | LOGICAL :: ll_upsxy = .TRUE. ! alternate directions for upstream |
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42 | LOGICAL :: ll_hoxy = .TRUE. ! alternate directions for high order |
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43 | LOGICAL :: ll_neg = .TRUE. ! if T interpolated at u/v points is negative or v_i < 1.e-6 |
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44 | ! then interpolate T at u/v points using the upstream scheme |
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45 | LOGICAL :: ll_prelim = .FALSE. ! prelimiter from: Zalesak(1979) eq. 14 => not well defined in 2D |
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46 | ! |
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47 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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48 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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49 | ! |
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50 | INTEGER, ALLOCATABLE, DIMENSION(:,:,:) :: imsk_small, jmsk_small |
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51 | ! |
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52 | !! * Substitutions |
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53 | # include "do_loop_substitute.h90" |
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54 | !!---------------------------------------------------------------------- |
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55 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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56 | !! $Id$ |
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57 | !! Software governed by the CeCILL licence (./LICENSE) |
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58 | !!---------------------------------------------------------------------- |
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59 | CONTAINS |
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60 | |
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61 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, & |
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62 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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63 | !!---------------------------------------------------------------------- |
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64 | !! *** ROUTINE ice_dyn_adv_umx *** |
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65 | !! |
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66 | !! ** Purpose : Compute the now trend due to total advection of |
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67 | !! tracers and add it to the general trend of tracer equations |
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68 | !! using an "Ultimate-Macho" scheme |
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69 | !! |
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70 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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71 | !!---------------------------------------------------------------------- |
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72 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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73 | INTEGER , INTENT(in ) :: kt ! time step |
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74 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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75 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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76 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness |
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77 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness |
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78 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness |
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79 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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80 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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81 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond concentration |
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86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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87 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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88 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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89 | ! |
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90 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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91 | INTEGER :: icycle ! number of sub-timestep for the advection |
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92 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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93 | REAL(wp) :: zdt, zvi_cen |
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94 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication |
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95 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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96 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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97 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zu_cat, zv_cat |
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98 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups |
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99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai , z1_aip, zhvar |
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100 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max |
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101 | ! |
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102 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs |
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103 | !!---------------------------------------------------------------------- |
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104 | ! |
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105 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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106 | ! |
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107 | ! --- Record max of the surrounding 9-pts ice thick. (for call Hbig) --- ! |
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108 | DO jl = 1, jpl |
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109 | DO_2D( 0, 0, 0, 0 ) |
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110 | zhip_max(ji,jj,jl) = MAX( epsi20, ph_ip(ji,jj,jl), ph_ip(ji+1,jj ,jl), ph_ip(ji ,jj+1,jl), & |
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111 | & ph_ip(ji-1,jj ,jl), ph_ip(ji ,jj-1,jl), & |
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112 | & ph_ip(ji+1,jj+1,jl), ph_ip(ji-1,jj-1,jl), & |
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113 | & ph_ip(ji+1,jj-1,jl), ph_ip(ji-1,jj+1,jl) ) |
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114 | zhi_max (ji,jj,jl) = MAX( epsi20, ph_i (ji,jj,jl), ph_i (ji+1,jj ,jl), ph_i (ji ,jj+1,jl), & |
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115 | & ph_i (ji-1,jj ,jl), ph_i (ji ,jj-1,jl), & |
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116 | & ph_i (ji+1,jj+1,jl), ph_i (ji-1,jj-1,jl), & |
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117 | & ph_i (ji+1,jj-1,jl), ph_i (ji-1,jj+1,jl) ) |
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118 | zhs_max (ji,jj,jl) = MAX( epsi20, ph_s (ji,jj,jl), ph_s (ji+1,jj ,jl), ph_s (ji ,jj+1,jl), & |
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119 | & ph_s (ji-1,jj ,jl), ph_s (ji ,jj-1,jl), & |
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120 | & ph_s (ji+1,jj+1,jl), ph_s (ji-1,jj-1,jl), & |
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121 | & ph_s (ji+1,jj-1,jl), ph_s (ji-1,jj+1,jl) ) |
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122 | END_2D |
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123 | END DO |
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124 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max, 'T', 1.0_wp, zhs_max, 'T', 1.0_wp, zhip_max, 'T', 1.0_wp ) |
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125 | ! |
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126 | ! |
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127 | ! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- ! |
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128 | ! Note: the advection split is applied at the next time-step in order to avoid blocking global comm. |
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129 | ! this should not affect too much the stability |
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130 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rDt_ice * r1_e1u(:,:) ) |
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131 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rDt_ice * r1_e2v(:,:) ) ) |
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132 | |
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133 | ! non-blocking global communication send zcflnow and receive zcflprv |
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134 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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135 | |
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136 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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137 | ELSE ; icycle = 1 |
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138 | ENDIF |
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139 | zdt = rDt_ice / REAL(icycle) |
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140 | |
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141 | ! --- transport --- ! |
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142 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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143 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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144 | ! |
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145 | ! setup transport for each ice cat |
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146 | DO jl = 1, jpl |
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147 | zu_cat(:,:,jl) = zudy(:,:) |
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148 | zv_cat(:,:,jl) = zvdx(:,:) |
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149 | END DO |
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150 | ! |
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151 | ! --- define velocity for advection: u*grad(H) --- ! |
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152 | DO_2D( 0, 0, 0, 0 ) |
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153 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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154 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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155 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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156 | ENDIF |
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157 | |
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158 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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159 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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160 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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161 | ENDIF |
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162 | END_2D |
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163 | |
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164 | !---------------! |
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165 | !== advection ==! |
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166 | !---------------! |
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167 | DO jt = 1, icycle |
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168 | |
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169 | ! record at_i before advection (for open water) |
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170 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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171 | |
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172 | ! inverse of A and Ap |
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173 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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174 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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175 | END WHERE |
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176 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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177 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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178 | END WHERE |
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179 | ! |
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180 | ! setup a mask where advection will be upstream |
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181 | IF( ll_neg ) THEN |
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182 | IF( .NOT. ALLOCATED(imsk_small) ) ALLOCATE( imsk_small(jpi,jpj,jpl) ) |
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183 | IF( .NOT. ALLOCATED(jmsk_small) ) ALLOCATE( jmsk_small(jpi,jpj,jpl) ) |
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184 | DO jl = 1, jpl |
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185 | DO_2D( 1, 0, 1, 0 ) |
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186 | zvi_cen = 0.5_wp * ( pv_i(ji+1,jj,jl) + pv_i(ji,jj,jl) ) |
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187 | IF( zvi_cen < epsi06) THEN ; imsk_small(ji,jj,jl) = 0 |
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188 | ELSE ; imsk_small(ji,jj,jl) = 1 ; ENDIF |
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189 | zvi_cen = 0.5_wp * ( pv_i(ji,jj+1,jl) + pv_i(ji,jj,jl) ) |
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190 | IF( zvi_cen < epsi06) THEN ; jmsk_small(ji,jj,jl) = 0 |
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191 | ELSE ; jmsk_small(ji,jj,jl) = 1 ; ENDIF |
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192 | END_2D |
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193 | END DO |
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194 | ENDIF |
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195 | ! |
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196 | ! ----------------------- ! |
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197 | ! ==> start advection <== ! |
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198 | ! ----------------------- ! |
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199 | ! |
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200 | !== Ice area ==! |
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201 | zamsk = 1._wp |
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202 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zu_cat , zv_cat , zcu_box, zcv_box, & |
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203 | & pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho ) |
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204 | ! |
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205 | ! ! --------------------------------- ! |
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206 | IF( np_advS == 1 ) THEN ! -- advection form: -div( uVS ) -- ! |
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207 | ! ! --------------------------------- ! |
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208 | zamsk = 0._wp |
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209 | !== Ice volume ==! |
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210 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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211 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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212 | & zhvar, pv_i, zua_ups, zva_ups ) |
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213 | !== Snw volume ==! |
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214 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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215 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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216 | & zhvar, pv_s, zua_ups, zva_ups ) |
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217 | ! |
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218 | zamsk = 1._wp |
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219 | !== Salt content ==! |
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220 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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221 | & psv_i, psv_i ) |
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222 | !== Ice heat content ==! |
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223 | DO jk = 1, nlay_i |
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224 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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225 | & pe_i(:,:,jk,:), pe_i(:,:,jk,:) ) |
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226 | END DO |
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227 | !== Snw heat content ==! |
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228 | DO jk = 1, nlay_s |
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229 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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230 | & pe_s(:,:,jk,:), pe_s(:,:,jk,:) ) |
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231 | END DO |
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232 | ! |
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233 | ! ! ------------------------------------------ ! |
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234 | ELSEIF( np_advS == 2 ) THEN ! -- advection form: -div( uA * uHS / u ) -- ! |
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235 | ! ! ------------------------------------------ ! |
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236 | zamsk = 0._wp |
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237 | !== Ice volume ==! |
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238 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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239 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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240 | & zhvar, pv_i, zua_ups, zva_ups ) |
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241 | !== Snw volume ==! |
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242 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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243 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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244 | & zhvar, pv_s, zua_ups, zva_ups ) |
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245 | !== Salt content ==! |
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246 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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247 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
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248 | & zhvar, psv_i, zua_ups, zva_ups ) |
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249 | !== Ice heat content ==! |
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250 | DO jk = 1, nlay_i |
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251 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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252 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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253 | & zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups ) |
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254 | END DO |
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255 | !== Snw heat content ==! |
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256 | DO jk = 1, nlay_s |
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257 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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258 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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259 | & zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups ) |
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260 | END DO |
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261 | ! |
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262 | ! ! ----------------------------------------- ! |
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263 | ELSEIF( np_advS == 3 ) THEN ! -- advection form: -div( uV * uS / u ) -- ! |
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264 | ! ! ----------------------------------------- ! |
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265 | zamsk = 0._wp |
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266 | ! |
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267 | ALLOCATE( zuv_ho (jpi,jpj,jpl), zvv_ho (jpi,jpj,jpl), & |
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268 | & zuv_ups(jpi,jpj,jpl), zvv_ups(jpi,jpj,jpl), z1_vi(jpi,jpj,jpl), z1_vs(jpi,jpj,jpl) ) |
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269 | ! |
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270 | ! inverse of Vi |
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271 | WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:) |
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272 | ELSEWHERE ; z1_vi(:,:,:) = 0. |
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273 | END WHERE |
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274 | ! inverse of Vs |
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275 | WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:) |
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276 | ELSEWHERE ; z1_vs(:,:,:) = 0. |
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277 | END WHERE |
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278 | ! |
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279 | ! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays) |
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280 | ! |
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281 | !== Ice volume ==! |
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282 | zuv_ups = zua_ups |
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283 | zvv_ups = zva_ups |
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284 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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285 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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286 | & zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
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287 | !== Salt content ==! |
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288 | zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:) |
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289 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, & |
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290 | & zhvar, psv_i, zuv_ups, zvv_ups ) |
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291 | !== Ice heat content ==! |
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292 | DO jk = 1, nlay_i |
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293 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:) |
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294 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
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295 | & zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups ) |
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296 | END DO |
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297 | !== Snow volume ==! |
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298 | zuv_ups = zua_ups |
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299 | zvv_ups = zva_ups |
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300 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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301 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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302 | & zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
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303 | !== Snw heat content ==! |
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304 | DO jk = 1, nlay_s |
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305 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:) |
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306 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
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307 | & zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups ) |
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308 | END DO |
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309 | ! |
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310 | DEALLOCATE( zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs ) |
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311 | ! |
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312 | ENDIF |
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313 | ! |
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314 | !== Ice age ==! |
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315 | zamsk = 1._wp |
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316 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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317 | & poa_i, poa_i ) |
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318 | ! |
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319 | !== melt ponds ==! |
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320 | IF ( ln_pnd_H12 ) THEN |
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321 | ! concentration |
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322 | zamsk = 1._wp |
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323 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat , zv_cat , zcu_box, zcv_box, & |
---|
324 | & pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho ) |
---|
325 | ! volume |
---|
326 | zamsk = 0._wp |
---|
327 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
---|
328 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
329 | & zhvar, pv_ip, zua_ups, zva_ups ) |
---|
330 | ENDIF |
---|
331 | ! |
---|
332 | !== Open water area ==! |
---|
333 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
334 | DO_2D( 0, 0, 0, 0 ) |
---|
335 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & |
---|
336 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
---|
337 | END_2D |
---|
338 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i, 'T', 1.0_wp ) |
---|
339 | ! |
---|
340 | ! |
---|
341 | ! --- Ensure non-negative fields and in-bound thicknesses --- ! |
---|
342 | ! Remove negative values (conservation is ensured) |
---|
343 | ! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20) |
---|
344 | CALL ice_var_zapneg( zdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
345 | ! |
---|
346 | ! --- Make sure ice thickness is not too big --- ! |
---|
347 | ! (because ice thickness can be too large where ice concentration is very small) |
---|
348 | CALL Hbig( zdt, zhi_max, zhs_max, zhip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
---|
349 | ! |
---|
350 | ! --- Ensure snow load is not too big --- ! |
---|
351 | CALL Hsnow( zdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
352 | ! |
---|
353 | END DO |
---|
354 | ! |
---|
355 | END SUBROUTINE ice_dyn_adv_umx |
---|
356 | |
---|
357 | |
---|
358 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, & |
---|
359 | & pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho ) |
---|
360 | !!---------------------------------------------------------------------- |
---|
361 | !! *** ROUTINE adv_umx *** |
---|
362 | !! |
---|
363 | !! ** Purpose : Compute the now trend due to total advection of |
---|
364 | !! tracers and add it to the general trend of tracer equations |
---|
365 | !! |
---|
366 | !! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc |
---|
367 | !! - calculate tracer H at u and v points (Ultimate) |
---|
368 | !! - calculate the high order fluxes using alterning directions (Macho) |
---|
369 | !! - apply a limiter on the fluxes (nonosc_ice) |
---|
370 | !! - convert this tracer flux to a "volume" flux (uH -> uV) |
---|
371 | !! - apply a limiter a second time on the volumes fluxes (nonosc_ice) |
---|
372 | !! - calculate the high order solution for V |
---|
373 | !! |
---|
374 | !! ** Action : solve 3 equations => a) dA/dt = -div(uA) |
---|
375 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
---|
376 | !! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S) |
---|
377 | !! |
---|
378 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H. |
---|
379 | !! - then we convert this flux to a "volume" flux this way => uH * uA / u |
---|
380 | !! where uA is the flux from eq. a) |
---|
381 | !! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur) |
---|
382 | !! - at last we estimate dV/dt = -div(uH * uA / u) |
---|
383 | !! |
---|
384 | !! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u) |
---|
385 | !! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u) |
---|
386 | !! |
---|
387 | !! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc. |
---|
388 | !! - At the ice edge, Ultimate scheme can lead to: |
---|
389 | !! 1) negative interpolated tracers at u-v points |
---|
390 | !! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward |
---|
391 | !! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
---|
392 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
---|
393 | !! Solution for 2): we set it to 0 in this case |
---|
394 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
---|
395 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
---|
396 | !! work on H (and not V). It is partly related to the multi-category approach |
---|
397 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
---|
398 | !! concentration is small). Since we do not limit S and T, large values can occur at the edge but it does not really matter |
---|
399 | !! since sv_i and e_i are still good. |
---|
400 | !!---------------------------------------------------------------------- |
---|
401 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
402 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
403 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
404 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
405 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
406 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
---|
407 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
---|
408 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
409 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
---|
410 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
---|
411 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes |
---|
412 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
---|
413 | ! |
---|
414 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
415 | REAL(wp) :: ztra ! local scalar |
---|
416 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
---|
417 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
---|
418 | !!---------------------------------------------------------------------- |
---|
419 | ! |
---|
420 | ! Upstream (_ups) fluxes |
---|
421 | ! ----------------------- |
---|
422 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
---|
423 | |
---|
424 | ! High order (_ho) fluxes |
---|
425 | ! ----------------------- |
---|
426 | SELECT CASE( kn_umx ) |
---|
427 | ! |
---|
428 | CASE ( 20 ) !== centered second order ==! |
---|
429 | ! |
---|
430 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
431 | ! |
---|
432 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
433 | ! |
---|
434 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
435 | ! |
---|
436 | END SELECT |
---|
437 | ! |
---|
438 | ! --ho --ho |
---|
439 | ! new fluxes = u*H * u*a / u |
---|
440 | ! ---------------------------- |
---|
441 | IF( pamsk == 0._wp ) THEN |
---|
442 | DO jl = 1, jpl |
---|
443 | DO_2D( 1, 0, 1, 0 ) |
---|
444 | IF( ABS( pu(ji,jj) ) > epsi10 ) THEN |
---|
445 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj) |
---|
446 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj) |
---|
447 | ELSE |
---|
448 | zfu_ho (ji,jj,jl) = 0._wp |
---|
449 | zfu_ups(ji,jj,jl) = 0._wp |
---|
450 | ENDIF |
---|
451 | ! |
---|
452 | IF( ABS( pv(ji,jj) ) > epsi10 ) THEN |
---|
453 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj) |
---|
454 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj) |
---|
455 | ELSE |
---|
456 | zfv_ho (ji,jj,jl) = 0._wp |
---|
457 | zfv_ups(ji,jj,jl) = 0._wp |
---|
458 | ENDIF |
---|
459 | END_2D |
---|
460 | END DO |
---|
461 | |
---|
462 | ! the new "volume" fluxes must also be "flux corrected" |
---|
463 | ! thus we calculate the upstream solution and apply a limiter again |
---|
464 | DO jl = 1, jpl |
---|
465 | DO_2D( 0, 0, 0, 0 ) |
---|
466 | ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) ) |
---|
467 | ! |
---|
468 | zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
469 | END_2D |
---|
470 | END DO |
---|
471 | CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1.0_wp ) |
---|
472 | ! |
---|
473 | IF ( np_limiter == 1 ) THEN |
---|
474 | CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
475 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
476 | CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho ) |
---|
477 | CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho ) |
---|
478 | ENDIF |
---|
479 | ! |
---|
480 | ENDIF |
---|
481 | ! --ho --ups |
---|
482 | ! in case of advection of A: output u*a and u*a |
---|
483 | ! ----------------------------------------------- |
---|
484 | IF( PRESENT( pua_ho ) ) THEN |
---|
485 | DO jl = 1, jpl |
---|
486 | DO_2D( 1, 0, 1, 0 ) |
---|
487 | pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) ; pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) |
---|
488 | pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) ; pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) |
---|
489 | END_2D |
---|
490 | END DO |
---|
491 | ENDIF |
---|
492 | ! |
---|
493 | ! final trend with corrected fluxes |
---|
494 | ! --------------------------------- |
---|
495 | DO jl = 1, jpl |
---|
496 | DO_2D( 0, 0, 0, 0 ) |
---|
497 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
498 | ! |
---|
499 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
500 | END_2D |
---|
501 | END DO |
---|
502 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1.0_wp ) |
---|
503 | ! |
---|
504 | END SUBROUTINE adv_umx |
---|
505 | |
---|
506 | |
---|
507 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
508 | !!--------------------------------------------------------------------- |
---|
509 | !! *** ROUTINE upstream *** |
---|
510 | !! |
---|
511 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
512 | !!---------------------------------------------------------------------- |
---|
513 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
514 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
515 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
516 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
517 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
518 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
519 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
520 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
521 | ! |
---|
522 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
523 | REAL(wp) :: ztra ! local scalar |
---|
524 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
525 | !!---------------------------------------------------------------------- |
---|
526 | |
---|
527 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
528 | ! |
---|
529 | DO jl = 1, jpl |
---|
530 | DO_2D( 1, 0, 1, 0 ) |
---|
531 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
532 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
533 | END_2D |
---|
534 | END DO |
---|
535 | ! |
---|
536 | ELSE !** alternate directions **! |
---|
537 | ! |
---|
538 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
539 | ! |
---|
540 | DO jl = 1, jpl !-- flux in x-direction |
---|
541 | DO_2D( 1, 0, 1, 0 ) |
---|
542 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
543 | END_2D |
---|
544 | END DO |
---|
545 | ! |
---|
546 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
547 | DO_2D( 0, 0, 0, 0 ) |
---|
548 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
549 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
550 | ! |
---|
551 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
552 | END_2D |
---|
553 | END DO |
---|
554 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
555 | ! |
---|
556 | DO jl = 1, jpl !-- flux in y-direction |
---|
557 | DO_2D( 1, 0, 1, 0 ) |
---|
558 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl) |
---|
559 | END_2D |
---|
560 | END DO |
---|
561 | ! |
---|
562 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
563 | ! |
---|
564 | DO jl = 1, jpl !-- flux in y-direction |
---|
565 | DO_2D( 1, 0, 1, 0 ) |
---|
566 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
567 | END_2D |
---|
568 | END DO |
---|
569 | ! |
---|
570 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
571 | DO_2D( 0, 0, 0, 0 ) |
---|
572 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
573 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
574 | ! |
---|
575 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
576 | END_2D |
---|
577 | END DO |
---|
578 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
579 | ! |
---|
580 | DO jl = 1, jpl !-- flux in x-direction |
---|
581 | DO_2D( 1, 0, 1, 0 ) |
---|
582 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl) |
---|
583 | END_2D |
---|
584 | END DO |
---|
585 | ! |
---|
586 | ENDIF |
---|
587 | |
---|
588 | ENDIF |
---|
589 | ! |
---|
590 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
591 | DO_2D( 0, 0, 0, 0 ) |
---|
592 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
593 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
594 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
595 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
596 | ! |
---|
597 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
598 | END_2D |
---|
599 | END DO |
---|
600 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1.0_wp ) |
---|
601 | |
---|
602 | END SUBROUTINE upstream |
---|
603 | |
---|
604 | |
---|
605 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
606 | !!--------------------------------------------------------------------- |
---|
607 | !! *** ROUTINE cen2 *** |
---|
608 | !! |
---|
609 | !! ** Purpose : compute the high order fluxes using a centered |
---|
610 | !! second order scheme |
---|
611 | !!---------------------------------------------------------------------- |
---|
612 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
613 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
614 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
615 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
616 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
617 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
618 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
619 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
620 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
621 | ! |
---|
622 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
623 | REAL(wp) :: ztra ! local scalar |
---|
624 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
625 | !!---------------------------------------------------------------------- |
---|
626 | ! |
---|
627 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
628 | ! |
---|
629 | DO jl = 1, jpl |
---|
630 | DO_2D( 1, 0, 1, 0 ) |
---|
631 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
632 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
633 | END_2D |
---|
634 | END DO |
---|
635 | ! |
---|
636 | IF ( np_limiter == 1 ) THEN |
---|
637 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
638 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
639 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
640 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
641 | ENDIF |
---|
642 | ! |
---|
643 | ELSE !** alternate directions **! |
---|
644 | ! |
---|
645 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
646 | ! |
---|
647 | DO jl = 1, jpl !-- flux in x-direction |
---|
648 | DO_2D( 1, 0, 1, 0 ) |
---|
649 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
650 | END_2D |
---|
651 | END DO |
---|
652 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
653 | |
---|
654 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
655 | DO_2D( 0, 0, 0, 0 ) |
---|
656 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
657 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
658 | ! |
---|
659 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
660 | END_2D |
---|
661 | END DO |
---|
662 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
663 | |
---|
664 | DO jl = 1, jpl !-- flux in y-direction |
---|
665 | DO_2D( 1, 0, 1, 0 ) |
---|
666 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
667 | END_2D |
---|
668 | END DO |
---|
669 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
670 | |
---|
671 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
672 | ! |
---|
673 | DO jl = 1, jpl !-- flux in y-direction |
---|
674 | DO_2D( 1, 0, 1, 0 ) |
---|
675 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
676 | END_2D |
---|
677 | END DO |
---|
678 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
679 | ! |
---|
680 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
681 | DO_2D( 0, 0, 0, 0 ) |
---|
682 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
683 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
684 | ! |
---|
685 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
686 | END_2D |
---|
687 | END DO |
---|
688 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
689 | ! |
---|
690 | DO jl = 1, jpl !-- flux in x-direction |
---|
691 | DO_2D( 1, 0, 1, 0 ) |
---|
692 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
693 | END_2D |
---|
694 | END DO |
---|
695 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
696 | |
---|
697 | ENDIF |
---|
698 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
699 | |
---|
700 | ENDIF |
---|
701 | |
---|
702 | END SUBROUTINE cen2 |
---|
703 | |
---|
704 | |
---|
705 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
706 | !!--------------------------------------------------------------------- |
---|
707 | !! *** ROUTINE macho *** |
---|
708 | !! |
---|
709 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
710 | !! |
---|
711 | !! ** Method : ... |
---|
712 | !! |
---|
713 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
714 | !!---------------------------------------------------------------------- |
---|
715 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
716 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
717 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
718 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
719 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
720 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
721 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
722 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
723 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
724 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
725 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
726 | ! |
---|
727 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
728 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
729 | !!---------------------------------------------------------------------- |
---|
730 | ! |
---|
731 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
732 | ! |
---|
733 | ! !-- ultimate interpolation of pt at u-point --! |
---|
734 | CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
735 | ! !-- limiter in x --! |
---|
736 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
737 | ! !-- advective form update in zpt --! |
---|
738 | DO jl = 1, jpl |
---|
739 | DO_2D( 0, 0, 0, 0 ) |
---|
740 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) & |
---|
741 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
742 | & * pamsk & |
---|
743 | & ) * pdt ) * tmask(ji,jj,1) |
---|
744 | END_2D |
---|
745 | END DO |
---|
746 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
747 | ! |
---|
748 | ! !-- ultimate interpolation of pt at v-point --! |
---|
749 | IF( ll_hoxy ) THEN |
---|
750 | CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
751 | ELSE |
---|
752 | CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
753 | ENDIF |
---|
754 | ! !-- limiter in y --! |
---|
755 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
756 | ! |
---|
757 | ! |
---|
758 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
759 | ! |
---|
760 | ! !-- ultimate interpolation of pt at v-point --! |
---|
761 | CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
762 | ! !-- limiter in y --! |
---|
763 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
764 | ! !-- advective form update in zpt --! |
---|
765 | DO jl = 1, jpl |
---|
766 | DO_2D( 0, 0, 0, 0 ) |
---|
767 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) & |
---|
768 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
769 | & * pamsk & |
---|
770 | & ) * pdt ) * tmask(ji,jj,1) |
---|
771 | END_2D |
---|
772 | END DO |
---|
773 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
774 | ! |
---|
775 | ! !-- ultimate interpolation of pt at u-point --! |
---|
776 | IF( ll_hoxy ) THEN |
---|
777 | CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
778 | ELSE |
---|
779 | CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
780 | ENDIF |
---|
781 | ! !-- limiter in x --! |
---|
782 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
783 | ! |
---|
784 | ENDIF |
---|
785 | |
---|
786 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
787 | ! |
---|
788 | END SUBROUTINE macho |
---|
789 | |
---|
790 | |
---|
791 | SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
792 | !!--------------------------------------------------------------------- |
---|
793 | !! *** ROUTINE ultimate_x *** |
---|
794 | !! |
---|
795 | !! ** Purpose : compute tracer at u-points |
---|
796 | !! |
---|
797 | !! ** Method : ... |
---|
798 | !! |
---|
799 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
800 | !!---------------------------------------------------------------------- |
---|
801 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
802 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
803 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
804 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
805 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
806 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
807 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
808 | ! |
---|
809 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
810 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
811 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
812 | !!---------------------------------------------------------------------- |
---|
813 | ! |
---|
814 | ! !-- Laplacian in i-direction --! |
---|
815 | DO jl = 1, jpl |
---|
816 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
817 | DO ji = 1, jpim1 |
---|
818 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
819 | END DO |
---|
820 | ! ! Second derivative (Laplacian) |
---|
821 | DO ji = 2, jpim1 |
---|
822 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
823 | END DO |
---|
824 | END DO |
---|
825 | END DO |
---|
826 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1.0_wp ) |
---|
827 | ! |
---|
828 | ! !-- BiLaplacian in i-direction --! |
---|
829 | DO jl = 1, jpl |
---|
830 | DO jj = 2, jpjm1 ! Third derivative |
---|
831 | DO ji = 1, jpim1 |
---|
832 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
833 | END DO |
---|
834 | ! ! Fourth derivative |
---|
835 | DO ji = 2, jpim1 |
---|
836 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
837 | END DO |
---|
838 | END DO |
---|
839 | END DO |
---|
840 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1.0_wp ) |
---|
841 | ! |
---|
842 | ! |
---|
843 | SELECT CASE (kn_umx ) |
---|
844 | ! |
---|
845 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
846 | ! |
---|
847 | DO jl = 1, jpl |
---|
848 | DO_2D( 1, 0, 1, 0 ) |
---|
849 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
850 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
851 | END_2D |
---|
852 | END DO |
---|
853 | ! |
---|
854 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
855 | ! |
---|
856 | DO jl = 1, jpl |
---|
857 | DO_2D( 1, 0, 1, 0 ) |
---|
858 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
859 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
860 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
861 | END_2D |
---|
862 | END DO |
---|
863 | ! |
---|
864 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
865 | ! |
---|
866 | DO jl = 1, jpl |
---|
867 | DO_2D( 1, 0, 1, 0 ) |
---|
868 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
869 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
870 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
871 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
872 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
873 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
874 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
875 | END_2D |
---|
876 | END DO |
---|
877 | ! |
---|
878 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
879 | ! |
---|
880 | DO jl = 1, jpl |
---|
881 | DO_2D( 1, 0, 1, 0 ) |
---|
882 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
883 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
884 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
885 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
886 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
887 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
888 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
889 | END_2D |
---|
890 | END DO |
---|
891 | ! |
---|
892 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
893 | ! |
---|
894 | DO jl = 1, jpl |
---|
895 | DO_2D( 1, 0, 1, 0 ) |
---|
896 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
897 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
898 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
899 | zdx4 = zdx2 * zdx2 |
---|
900 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
901 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
902 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
903 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
904 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
905 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
906 | END_2D |
---|
907 | END DO |
---|
908 | ! |
---|
909 | END SELECT |
---|
910 | ! |
---|
911 | ! if pt at u-point is negative then use the upstream value |
---|
912 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
913 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
914 | IF( ll_neg ) THEN |
---|
915 | DO jl = 1, jpl |
---|
916 | DO_2D( 1, 0, 1, 0 ) |
---|
917 | IF( pt_u(ji,jj,jl) < 0._wp .OR. ( imsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
918 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
919 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
920 | ENDIF |
---|
921 | END_2D |
---|
922 | END DO |
---|
923 | ENDIF |
---|
924 | ! !-- High order flux in i-direction --! |
---|
925 | DO jl = 1, jpl |
---|
926 | DO_2D( 1, 0, 1, 0 ) |
---|
927 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
928 | END_2D |
---|
929 | END DO |
---|
930 | ! |
---|
931 | END SUBROUTINE ultimate_x |
---|
932 | |
---|
933 | |
---|
934 | SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
935 | !!--------------------------------------------------------------------- |
---|
936 | !! *** ROUTINE ultimate_y *** |
---|
937 | !! |
---|
938 | !! ** Purpose : compute tracer at v-points |
---|
939 | !! |
---|
940 | !! ** Method : ... |
---|
941 | !! |
---|
942 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
943 | !!---------------------------------------------------------------------- |
---|
944 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
945 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
946 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
947 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
948 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
949 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
950 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
951 | ! |
---|
952 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
953 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
954 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
955 | !!---------------------------------------------------------------------- |
---|
956 | ! |
---|
957 | ! !-- Laplacian in j-direction --! |
---|
958 | DO jl = 1, jpl |
---|
959 | DO_2D( 1, 0, 0, 0 ) |
---|
960 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
961 | END_2D |
---|
962 | DO_2D( 0, 0, 0, 0 ) |
---|
963 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
964 | END_2D |
---|
965 | END DO |
---|
966 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1.0_wp ) |
---|
967 | ! |
---|
968 | ! !-- BiLaplacian in j-direction --! |
---|
969 | DO jl = 1, jpl |
---|
970 | DO_2D( 1, 0, 0, 0 ) |
---|
971 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
972 | END_2D |
---|
973 | DO_2D( 0, 0, 0, 0 ) |
---|
974 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
975 | END_2D |
---|
976 | END DO |
---|
977 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1.0_wp ) |
---|
978 | ! |
---|
979 | ! |
---|
980 | SELECT CASE (kn_umx ) |
---|
981 | ! |
---|
982 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
983 | DO jl = 1, jpl |
---|
984 | DO_2D( 1, 0, 1, 0 ) |
---|
985 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
986 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
987 | END_2D |
---|
988 | END DO |
---|
989 | ! |
---|
990 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
991 | DO jl = 1, jpl |
---|
992 | DO_2D( 1, 0, 1, 0 ) |
---|
993 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
994 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
995 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
996 | END_2D |
---|
997 | END DO |
---|
998 | ! |
---|
999 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
1000 | DO jl = 1, jpl |
---|
1001 | DO_2D( 1, 0, 1, 0 ) |
---|
1002 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
1003 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
1004 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
1005 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
1006 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
1007 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
1008 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
1009 | END_2D |
---|
1010 | END DO |
---|
1011 | ! |
---|
1012 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
1013 | DO jl = 1, jpl |
---|
1014 | DO_2D( 1, 0, 1, 0 ) |
---|
1015 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
1016 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
1017 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
1018 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
1019 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
1020 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
1021 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
1022 | END_2D |
---|
1023 | END DO |
---|
1024 | ! |
---|
1025 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
1026 | DO jl = 1, jpl |
---|
1027 | DO_2D( 1, 0, 1, 0 ) |
---|
1028 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
1029 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
1030 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
1031 | zdy4 = zdy2 * zdy2 |
---|
1032 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
1033 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
1034 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
1035 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
1036 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
1037 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
1038 | END_2D |
---|
1039 | END DO |
---|
1040 | ! |
---|
1041 | END SELECT |
---|
1042 | ! |
---|
1043 | ! if pt at v-point is negative then use the upstream value |
---|
1044 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
1045 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
1046 | IF( ll_neg ) THEN |
---|
1047 | DO jl = 1, jpl |
---|
1048 | DO_2D( 1, 0, 1, 0 ) |
---|
1049 | IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
1050 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
1051 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
1052 | ENDIF |
---|
1053 | END_2D |
---|
1054 | END DO |
---|
1055 | ENDIF |
---|
1056 | ! !-- High order flux in j-direction --! |
---|
1057 | DO jl = 1, jpl |
---|
1058 | DO_2D( 1, 0, 1, 0 ) |
---|
1059 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
1060 | END_2D |
---|
1061 | END DO |
---|
1062 | ! |
---|
1063 | END SUBROUTINE ultimate_y |
---|
1064 | |
---|
1065 | |
---|
1066 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
1067 | !!--------------------------------------------------------------------- |
---|
1068 | !! *** ROUTINE nonosc_ice *** |
---|
1069 | !! |
---|
1070 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
1071 | !! scheme and the before field by a non-oscillatory algorithm |
---|
1072 | !! |
---|
1073 | !! ** Method : ... |
---|
1074 | !!---------------------------------------------------------------------- |
---|
1075 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
1076 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1077 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
1078 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
1079 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
1080 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
1081 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
1082 | ! |
---|
1083 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
1084 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
1085 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
1086 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
1087 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
1088 | !!---------------------------------------------------------------------- |
---|
1089 | zbig = 1.e+40_wp |
---|
1090 | |
---|
1091 | ! antidiffusive flux : high order minus low order |
---|
1092 | ! -------------------------------------------------- |
---|
1093 | DO jl = 1, jpl |
---|
1094 | DO_2D( 1, 0, 1, 0 ) |
---|
1095 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
1096 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
1097 | END_2D |
---|
1098 | END DO |
---|
1099 | |
---|
1100 | ! extreme case where pfu_ho has to be zero |
---|
1101 | ! ---------------------------------------- |
---|
1102 | ! pfu_ho |
---|
1103 | ! * ---> |
---|
1104 | ! | | * | | |
---|
1105 | ! | | | * | |
---|
1106 | ! | | | | * |
---|
1107 | ! t_ups : i-1 i i+1 i+2 |
---|
1108 | IF( ll_prelim ) THEN |
---|
1109 | |
---|
1110 | DO jl = 1, jpl |
---|
1111 | DO_2D( 0, 0, 0, 0 ) |
---|
1112 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
1113 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
1114 | END_2D |
---|
1115 | END DO |
---|
1116 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1.0_wp, ztj_ups, 'T', 1.0_wp ) |
---|
1117 | |
---|
1118 | DO jl = 1, jpl |
---|
1119 | DO_2D( 0, 0, 0, 0 ) |
---|
1120 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
1121 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
1122 | ! |
---|
1123 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
1124 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
1125 | pfu_ho(ji,jj,jl)=0._wp |
---|
1126 | pfv_ho(ji,jj,jl)=0._wp |
---|
1127 | ENDIF |
---|
1128 | ! |
---|
1129 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
1130 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
1131 | pfu_ho(ji,jj,jl)=0._wp |
---|
1132 | pfv_ho(ji,jj,jl)=0._wp |
---|
1133 | ENDIF |
---|
1134 | ! |
---|
1135 | ENDIF |
---|
1136 | END_2D |
---|
1137 | END DO |
---|
1138 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp, pfv_ho, 'V', -1.0_wp ) ! lateral boundary cond. |
---|
1139 | |
---|
1140 | ENDIF |
---|
1141 | |
---|
1142 | ! Search local extrema |
---|
1143 | ! -------------------- |
---|
1144 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
1145 | z1_dt = 1._wp / pdt |
---|
1146 | DO jl = 1, jpl |
---|
1147 | |
---|
1148 | DO_2D( 1, 1, 1, 1 ) |
---|
1149 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
1150 | zbup(ji,jj) = -zbig |
---|
1151 | zbdo(ji,jj) = zbig |
---|
1152 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
1153 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
1154 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
1155 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
1156 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
1157 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
1158 | ELSE |
---|
1159 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
1160 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
1161 | ENDIF |
---|
1162 | END_2D |
---|
1163 | |
---|
1164 | DO_2D( 0, 0, 0, 0 ) |
---|
1165 | ! |
---|
1166 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood |
---|
1167 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
1168 | ! |
---|
1169 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
1170 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
1171 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
1172 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
1173 | ! |
---|
1174 | zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
1175 | & ) * ( 1. - pamsk ) |
---|
1176 | zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
1177 | & ) * ( 1. - pamsk ) |
---|
1178 | ! |
---|
1179 | ! ! up & down beta terms |
---|
1180 | ! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!) |
---|
1181 | IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
1182 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
1183 | ENDIF |
---|
1184 | ! |
---|
1185 | IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
1186 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
1187 | ENDIF |
---|
1188 | ! |
---|
1189 | ! if all the points are outside ice cover |
---|
1190 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
1191 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
1192 | ! |
---|
1193 | END_2D |
---|
1194 | END DO |
---|
1195 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1.0_wp, zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign) |
---|
1196 | |
---|
1197 | |
---|
1198 | ! monotonic flux in the y direction |
---|
1199 | ! --------------------------------- |
---|
1200 | DO jl = 1, jpl |
---|
1201 | DO_2D( 1, 0, 1, 0 ) |
---|
1202 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
1203 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
1204 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
1205 | ! |
---|
1206 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
1207 | ! |
---|
1208 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
1209 | ! |
---|
1210 | END_2D |
---|
1211 | |
---|
1212 | DO_2D( 1, 0, 1, 0 ) |
---|
1213 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
1214 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
1215 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
1216 | ! |
---|
1217 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
1218 | ! |
---|
1219 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
1220 | ! |
---|
1221 | END_2D |
---|
1222 | |
---|
1223 | END DO |
---|
1224 | ! |
---|
1225 | END SUBROUTINE nonosc_ice |
---|
1226 | |
---|
1227 | |
---|
1228 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
1229 | !!--------------------------------------------------------------------- |
---|
1230 | !! *** ROUTINE limiter_x *** |
---|
1231 | !! |
---|
1232 | !! ** Purpose : compute flux limiter |
---|
1233 | !!---------------------------------------------------------------------- |
---|
1234 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1235 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
1236 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
1237 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
1238 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
1239 | ! |
---|
1240 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
1241 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
1242 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
1243 | !!---------------------------------------------------------------------- |
---|
1244 | ! |
---|
1245 | DO jl = 1, jpl |
---|
1246 | DO_2D( 0, 0, 0, 0 ) |
---|
1247 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
1248 | END_2D |
---|
1249 | END DO |
---|
1250 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.0_wp) ! lateral boundary cond. |
---|
1251 | |
---|
1252 | DO jl = 1, jpl |
---|
1253 | DO_2D( 0, 0, 0, 0 ) |
---|
1254 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
1255 | |
---|
1256 | Rjm = zslpx(ji-1,jj,jl) |
---|
1257 | Rj = zslpx(ji ,jj,jl) |
---|
1258 | Rjp = zslpx(ji+1,jj,jl) |
---|
1259 | |
---|
1260 | IF( np_limiter == 3 ) THEN |
---|
1261 | |
---|
1262 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
1263 | ELSE ; Rr = Rjp |
---|
1264 | ENDIF |
---|
1265 | |
---|
1266 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
1267 | IF( Rj > 0. ) THEN |
---|
1268 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
1269 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
1270 | ELSE |
---|
1271 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
1272 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
1273 | ENDIF |
---|
1274 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
1275 | |
---|
1276 | ELSEIF( np_limiter == 2 ) THEN |
---|
1277 | IF( Rj /= 0. ) THEN |
---|
1278 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
1279 | ELSE ; Cr = Rjp / Rj |
---|
1280 | ENDIF |
---|
1281 | ELSE |
---|
1282 | Cr = 0. |
---|
1283 | ENDIF |
---|
1284 | |
---|
1285 | ! -- superbee -- |
---|
1286 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
1287 | ! -- van albada 2 -- |
---|
1288 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
1289 | ! -- sweby (with beta=1) -- |
---|
1290 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
1291 | ! -- van Leer -- |
---|
1292 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
1293 | ! -- ospre -- |
---|
1294 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
1295 | ! -- koren -- |
---|
1296 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
1297 | ! -- charm -- |
---|
1298 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
1299 | !ELSE ; zpsi = 0. |
---|
1300 | !ENDIF |
---|
1301 | ! -- van albada 1 -- |
---|
1302 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
1303 | ! -- smart -- |
---|
1304 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
1305 | ! -- umist -- |
---|
1306 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
1307 | |
---|
1308 | ! high order flux corrected by the limiter |
---|
1309 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
1310 | |
---|
1311 | ENDIF |
---|
1312 | END_2D |
---|
1313 | END DO |
---|
1314 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp) ! lateral boundary cond. |
---|
1315 | ! |
---|
1316 | END SUBROUTINE limiter_x |
---|
1317 | |
---|
1318 | |
---|
1319 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
1320 | !!--------------------------------------------------------------------- |
---|
1321 | !! *** ROUTINE limiter_y *** |
---|
1322 | !! |
---|
1323 | !! ** Purpose : compute flux limiter |
---|
1324 | !!---------------------------------------------------------------------- |
---|
1325 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1326 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
1327 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
1328 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
1329 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
1330 | ! |
---|
1331 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
1332 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
1333 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
1334 | !!---------------------------------------------------------------------- |
---|
1335 | ! |
---|
1336 | DO jl = 1, jpl |
---|
1337 | DO_2D( 0, 0, 0, 0 ) |
---|
1338 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
1339 | END_2D |
---|
1340 | END DO |
---|
1341 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.0_wp) ! lateral boundary cond. |
---|
1342 | |
---|
1343 | DO jl = 1, jpl |
---|
1344 | DO_2D( 0, 0, 0, 0 ) |
---|
1345 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
1346 | |
---|
1347 | Rjm = zslpy(ji,jj-1,jl) |
---|
1348 | Rj = zslpy(ji,jj ,jl) |
---|
1349 | Rjp = zslpy(ji,jj+1,jl) |
---|
1350 | |
---|
1351 | IF( np_limiter == 3 ) THEN |
---|
1352 | |
---|
1353 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
1354 | ELSE ; Rr = Rjp |
---|
1355 | ENDIF |
---|
1356 | |
---|
1357 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
1358 | IF( Rj > 0. ) THEN |
---|
1359 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
1360 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
1361 | ELSE |
---|
1362 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
1363 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
1364 | ENDIF |
---|
1365 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
1366 | |
---|
1367 | ELSEIF( np_limiter == 2 ) THEN |
---|
1368 | |
---|
1369 | IF( Rj /= 0. ) THEN |
---|
1370 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
1371 | ELSE ; Cr = Rjp / Rj |
---|
1372 | ENDIF |
---|
1373 | ELSE |
---|
1374 | Cr = 0. |
---|
1375 | ENDIF |
---|
1376 | |
---|
1377 | ! -- superbee -- |
---|
1378 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
1379 | ! -- van albada 2 -- |
---|
1380 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
1381 | ! -- sweby (with beta=1) -- |
---|
1382 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
1383 | ! -- van Leer -- |
---|
1384 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
1385 | ! -- ospre -- |
---|
1386 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
1387 | ! -- koren -- |
---|
1388 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
1389 | ! -- charm -- |
---|
1390 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
1391 | !ELSE ; zpsi = 0. |
---|
1392 | !ENDIF |
---|
1393 | ! -- van albada 1 -- |
---|
1394 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
1395 | ! -- smart -- |
---|
1396 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
1397 | ! -- umist -- |
---|
1398 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
1399 | |
---|
1400 | ! high order flux corrected by the limiter |
---|
1401 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
1402 | |
---|
1403 | ENDIF |
---|
1404 | END_2D |
---|
1405 | END DO |
---|
1406 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.0_wp) ! lateral boundary cond. |
---|
1407 | ! |
---|
1408 | END SUBROUTINE limiter_y |
---|
1409 | |
---|
1410 | |
---|
1411 | SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
---|
1412 | !!------------------------------------------------------------------- |
---|
1413 | !! *** ROUTINE Hbig *** |
---|
1414 | !! |
---|
1415 | !! ** Purpose : Thickness correction in case advection scheme creates |
---|
1416 | !! abnormally tick ice or snow |
---|
1417 | !! |
---|
1418 | !! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points |
---|
1419 | !! (before advection) and reduce it by adapting ice concentration |
---|
1420 | !! 2- check whether snow thickness is larger than the surrounding 9-points |
---|
1421 | !! (before advection) and reduce it by sending the excess in the ocean |
---|
1422 | !! |
---|
1423 | !! ** input : Max thickness of the surrounding 9-points |
---|
1424 | !!------------------------------------------------------------------- |
---|
1425 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1426 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max ! max ice thick from surrounding 9-pts |
---|
1427 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip, pv_ip |
---|
1428 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
1429 | ! |
---|
1430 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
1431 | REAL(wp) :: z1_dt, zhip, zhi, zhs, zfra |
---|
1432 | !!------------------------------------------------------------------- |
---|
1433 | ! |
---|
1434 | z1_dt = 1._wp / pdt |
---|
1435 | ! |
---|
1436 | DO jl = 1, jpl |
---|
1437 | |
---|
1438 | DO_2D( 1, 1, 1, 1 ) |
---|
1439 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
1440 | ! |
---|
1441 | ! ! -- check h_ip -- ! |
---|
1442 | ! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip |
---|
1443 | IF( ln_pnd_H12 .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN |
---|
1444 | zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) ) |
---|
1445 | IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN |
---|
1446 | pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl) |
---|
1447 | ENDIF |
---|
1448 | ENDIF |
---|
1449 | ! |
---|
1450 | ! ! -- check h_i -- ! |
---|
1451 | ! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i |
---|
1452 | zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
1453 | IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
1454 | pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m) |
---|
1455 | ENDIF |
---|
1456 | ! |
---|
1457 | ! ! -- check h_s -- ! |
---|
1458 | ! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean |
---|
1459 | zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
1460 | IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
1461 | zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 ) |
---|
1462 | ! |
---|
1463 | wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt |
---|
1464 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
1465 | ! |
---|
1466 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
1467 | pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl) |
---|
1468 | ENDIF |
---|
1469 | ! |
---|
1470 | ENDIF |
---|
1471 | END_2D |
---|
1472 | END DO |
---|
1473 | ! |
---|
1474 | END SUBROUTINE Hbig |
---|
1475 | |
---|
1476 | |
---|
1477 | SUBROUTINE Hsnow( pdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
1478 | !!------------------------------------------------------------------- |
---|
1479 | !! *** ROUTINE Hsnow *** |
---|
1480 | !! |
---|
1481 | !! ** Purpose : 1- Check snow load after advection |
---|
1482 | !! 2- Correct pond concentration to avoid a_ip > a_i |
---|
1483 | !! |
---|
1484 | !! ** Method : If snow load makes snow-ice interface to deplet below the ocean surface |
---|
1485 | !! then put the snow excess in the ocean |
---|
1486 | !! |
---|
1487 | !! ** Notes : This correction is crucial because of the call to routine icecor afterwards |
---|
1488 | !! which imposes a mini of ice thick. (rn_himin). This imposed mini can artificially |
---|
1489 | !! make the snow very thick (if concentration decreases drastically) |
---|
1490 | !! This behavior has been seen in Ultimate-Macho and supposedly it can also be true for Prather |
---|
1491 | !!------------------------------------------------------------------- |
---|
1492 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1493 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip |
---|
1494 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
1495 | ! |
---|
1496 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
1497 | REAL(wp) :: z1_dt, zvs_excess, zfra |
---|
1498 | !!------------------------------------------------------------------- |
---|
1499 | ! |
---|
1500 | z1_dt = 1._wp / pdt |
---|
1501 | ! |
---|
1502 | ! -- check snow load -- ! |
---|
1503 | DO jl = 1, jpl |
---|
1504 | DO_2D( 1, 1, 1, 1 ) |
---|
1505 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
1506 | ! |
---|
1507 | zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rho0-rhoi) * r1_rhos ) |
---|
1508 | ! |
---|
1509 | IF( zvs_excess > 0._wp ) THEN ! snow-ice interface deplets below the ocean surface |
---|
1510 | ! put snow excess in the ocean |
---|
1511 | zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 ) |
---|
1512 | wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt |
---|
1513 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
1514 | ! correct snow volume and heat content |
---|
1515 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
1516 | pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess |
---|
1517 | ENDIF |
---|
1518 | ! |
---|
1519 | ENDIF |
---|
1520 | END_2D |
---|
1521 | END DO |
---|
1522 | ! |
---|
1523 | !-- correct pond concentration to avoid a_ip > a_i -- ! |
---|
1524 | WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:) |
---|
1525 | ! |
---|
1526 | END SUBROUTINE Hsnow |
---|
1527 | |
---|
1528 | |
---|
1529 | #else |
---|
1530 | !!---------------------------------------------------------------------- |
---|
1531 | !! Default option Dummy module NO SI3 sea-ice model |
---|
1532 | !!---------------------------------------------------------------------- |
---|
1533 | #endif |
---|
1534 | |
---|
1535 | !!====================================================================== |
---|
1536 | END MODULE icedyn_adv_umx |
---|