1 | MODULE iceadv_umx |
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2 | !!============================================================================== |
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3 | !! *** MODULE iceadv_umx *** |
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4 | !! LIM sea-ice model : 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 | !!---------------------------------------------------------------------- |
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8 | #if defined key_lim3 |
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9 | !!---------------------------------------------------------------------- |
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10 | !! 'key_lim3' LIM 3.0 sea-ice model |
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11 | !!---------------------------------------------------------------------- |
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12 | !! ice_adv_umx : update the tracer trend with the 3D advection trends using a TVD scheme |
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13 | !! ultimate_x(_y): compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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14 | !! macho : ??? |
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15 | !! nonosc_2d : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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16 | !!---------------------------------------------------------------------- |
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17 | USE phycst ! physical constant |
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18 | USE dom_oce ! ocean domain |
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19 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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20 | USE ice ! sea-ice variables |
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21 | ! |
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22 | USE in_out_manager ! I/O manager |
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23 | USE lbclnk ! lateral boundary conditions -- MPP exchanges |
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24 | USE lib_mpp ! MPP library |
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25 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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26 | USE timing ! Timing |
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27 | |
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28 | IMPLICIT NONE |
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29 | PRIVATE |
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30 | |
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31 | PUBLIC ice_adv_umx ! routine called by iceadv.F90 |
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32 | |
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33 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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34 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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35 | |
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36 | !! * Substitutions |
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37 | # include "vectopt_loop_substitute.h90" |
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38 | !!---------------------------------------------------------------------- |
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39 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
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40 | !! $Id: iceadv_umx.F90 4499 2014-02-18 15:14:31Z timgraham $ |
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41 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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42 | !!---------------------------------------------------------------------- |
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43 | CONTAINS |
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44 | |
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45 | SUBROUTINE ice_adv_umx( kt, pu_ice, pv_ice, & |
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46 | & pato_i, pv_i, pv_s, psmv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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47 | !!---------------------------------------------------------------------- |
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48 | !! *** ROUTINE ice_adv_umx *** |
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49 | !! |
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50 | !! ** Purpose : Compute the now trend due to total advection of |
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51 | !! tracers and add it to the general trend of tracer equations |
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52 | !! using an "Ultimate-Macho" scheme |
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53 | !! |
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54 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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55 | !!---------------------------------------------------------------------- |
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56 | INTEGER , INTENT(in ) :: kt ! time step |
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57 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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58 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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59 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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60 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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61 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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62 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psmv_i ! salt content |
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63 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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64 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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65 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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66 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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67 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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68 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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69 | ! |
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70 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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71 | INTEGER :: initad ! number of sub-timestep for the advection |
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72 | REAL(wp) :: zcfl , zusnit, zdt ! - - |
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73 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zudy, zvdx, zcu_box, zcv_box |
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74 | !!---------------------------------------------------------------------- |
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75 | ! |
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76 | IF( kt == nit000 .AND. lwp ) THEN |
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77 | WRITE(numout,*) |
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78 | WRITE(numout,*) 'ice_adv_umx : Ultimate-MACHO advection scheme' |
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79 | WRITE(numout,*) '~~~~~~~~~~~' |
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80 | ENDIF |
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81 | ! |
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82 | ALLOCATE( zudy(jpi,jpj) , zvdx(jpi,jpj) , zcu_box(jpi,jpj) , zcv_box(jpi,jpj) ) |
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83 | ! |
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84 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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85 | zcfl = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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86 | zcfl = MAX( zcfl, MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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87 | IF( lk_mpp ) CALL mpp_max( zcfl ) |
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88 | |
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89 | IF( zcfl > 0.5 ) THEN ; initad = 2 ; zusnit = 0.5_wp |
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90 | ELSE ; initad = 1 ; zusnit = 1.0_wp |
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91 | ENDIF |
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92 | |
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93 | zdt = rdt_ice / REAL(initad) |
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94 | |
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95 | ! --- transport --- ! |
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96 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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97 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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98 | |
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99 | ! --- define velocity for advection: u*grad(H) --- ! |
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100 | DO jj = 2, jpjm1 |
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101 | DO ji = fs_2, fs_jpim1 |
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102 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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103 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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104 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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105 | ENDIF |
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106 | |
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107 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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108 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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109 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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110 | ENDIF |
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111 | END DO |
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112 | END DO |
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113 | |
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114 | !---------------! |
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115 | !== advection ==! |
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116 | !---------------! |
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117 | DO jt = 1, initad |
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118 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pato_i(:,:) ) ! Open water area |
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119 | DO jl = 1, jpl |
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120 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pa_i(:,:,jl) ) ! Ice area |
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121 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_i(:,:,jl) ) ! Ice volume |
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122 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, psmv_i(:,:,jl) ) ! Salt content |
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123 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, poa_i (:,:,jl) ) ! Age content |
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124 | DO jk = 1, nlay_i |
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125 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pe_i(:,:,jk,jl) ) ! Ice heat content |
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126 | END DO |
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127 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_s(:,:,jl) ) ! Snow volume |
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128 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pe_s(:,:,1,jl) ) ! Snow heat content |
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129 | IF ( nn_pnd_scheme > 0 ) THEN |
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130 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pa_ip(:,:,jl) ) ! Melt pond fraction |
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131 | CALL adv_umx( kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_ip(:,:,jl) ) ! Melt pond volume |
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132 | ENDIF |
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133 | END DO |
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134 | END DO |
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135 | ! |
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136 | DEALLOCATE( zudy, zvdx, zcu_box, zcv_box ) |
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137 | ! |
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138 | END SUBROUTINE ice_adv_umx |
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139 | |
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140 | SUBROUTINE adv_umx( kt, pdt, puc, pvc, pubox, pvbox, ptc ) |
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141 | !!---------------------------------------------------------------------- |
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142 | !! *** ROUTINE adv_umx *** |
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143 | !! |
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144 | !! ** Purpose : Compute the now trend due to total advection of |
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145 | !! tracers and add it to the general trend of tracer equations |
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146 | !! |
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147 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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148 | !! corrected flux (monotonic correction) |
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149 | !! note: - this advection scheme needs a leap-frog time scheme |
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150 | !! |
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151 | !! ** Action : - pt the after advective tracer |
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152 | !!---------------------------------------------------------------------- |
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153 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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154 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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155 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 |
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156 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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157 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ptc ! tracer content field |
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158 | ! |
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159 | INTEGER :: ji, jj ! dummy loop indices |
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160 | REAL(wp) :: ztra ! local scalar |
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161 | REAL(wp) :: zfp_ui, zfp_vj ! - - |
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162 | REAL(wp) :: zfm_ui, zfm_vj ! - - |
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163 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ups, zfu_ho, zt_u, zt_ups |
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164 | REAL(wp), DIMENSION(jpi,jpj) :: zfv_ups, zfv_ho, zt_v, ztrd |
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165 | !!---------------------------------------------------------------------- |
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166 | ! |
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167 | IF( nn_timing == 1 ) CALL timing_start('ice_adv_umx') |
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168 | ! |
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169 | ! upstream advection with initial mass fluxes & intermediate update |
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170 | ! -------------------------------------------------------------------- |
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171 | DO jj = 1, jpjm1 ! upstream tracer flux in the i and j direction |
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172 | DO ji = 1, fs_jpim1 ! vector opt. |
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173 | zfp_ui = puc(ji,jj) + ABS( puc(ji,jj) ) |
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174 | zfm_ui = puc(ji,jj) - ABS( puc(ji,jj) ) |
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175 | zfp_vj = pvc(ji,jj) + ABS( pvc(ji,jj) ) |
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176 | zfm_vj = pvc(ji,jj) - ABS( pvc(ji,jj) ) |
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177 | zfu_ups(ji,jj) = 0.5_wp * ( zfp_ui * ptc(ji,jj) + zfm_ui * ptc(ji+1,jj ) ) |
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178 | zfv_ups(ji,jj) = 0.5_wp * ( zfp_vj * ptc(ji,jj) + zfm_vj * ptc(ji ,jj+1) ) |
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179 | END DO |
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180 | END DO |
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181 | |
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182 | DO jj = 2, jpjm1 ! total intermediate advective trends |
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183 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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184 | ztra = - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj ) & |
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185 | & + zfv_ups(ji,jj) - zfv_ups(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
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186 | ! |
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187 | ztrd(ji,jj) = ztra ! upstream trend [ -div(uh) or -div(uhT) ] |
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188 | zt_ups (ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) ! guess after content field with monotonic scheme |
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189 | END DO |
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190 | END DO |
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191 | CALL lbc_lnk( zt_ups, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
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192 | |
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193 | ! High order (_ho) fluxes |
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194 | ! ----------------------- |
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195 | SELECT CASE( nn_limadv_ord ) |
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196 | CASE ( 20 ) ! centered second order |
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197 | DO jj = 2, jpjm1 |
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198 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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199 | zfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( ptc(ji,jj) + ptc(ji+1,jj) ) |
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200 | zfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( ptc(ji,jj) + ptc(ji,jj+1) ) |
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201 | END DO |
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202 | END DO |
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203 | ! |
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204 | CASE ( 1:5 ) ! 1st to 5th order ULTIMATE-MACHO scheme |
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205 | CALL macho( kt, nn_limadv_ord, pdt, ptc, puc, pvc, pubox, pvbox, zt_u, zt_v ) |
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206 | ! |
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207 | DO jj = 2, jpjm1 |
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208 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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209 | zfu_ho(ji,jj) = puc(ji,jj) * zt_u(ji,jj) |
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210 | zfv_ho(ji,jj) = pvc(ji,jj) * zt_v(ji,jj) |
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211 | END DO |
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212 | END DO |
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213 | ! |
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214 | END SELECT |
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215 | |
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216 | ! antidiffusive flux : high order minus low order |
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217 | ! -------------------------------------------------- |
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218 | DO jj = 2, jpjm1 |
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219 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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220 | zfu_ho(ji,jj) = zfu_ho(ji,jj) - zfu_ups(ji,jj) |
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221 | zfv_ho(ji,jj) = zfv_ho(ji,jj) - zfv_ups(ji,jj) |
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222 | END DO |
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223 | END DO |
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224 | CALL lbc_lnk_multi( zfu_ho, 'U', -1., zfv_ho, 'V', -1. ) ! Lateral bondary conditions |
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225 | |
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226 | ! monotonicity algorithm |
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227 | ! ------------------------- |
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228 | CALL nonosc_2d( ptc, zfu_ho, zfv_ho, zt_ups, pdt ) |
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229 | |
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230 | ! final trend with corrected fluxes |
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231 | ! ------------------------------------ |
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232 | DO jj = 2, jpjm1 |
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233 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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234 | ztra = ztrd(ji,jj) - ( zfu_ho(ji,jj) - zfu_ho(ji-1,jj ) & |
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235 | & + zfv_ho(ji,jj) - zfv_ho(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
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236 | ptc(ji,jj) = ptc(ji,jj) + pdt * ztra |
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237 | END DO |
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238 | END DO |
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239 | CALL lbc_lnk( ptc(:,:) , 'T', 1. ) |
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240 | ! |
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241 | IF( nn_timing == 1 ) CALL timing_stop('ice_adv_umx') |
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242 | ! |
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243 | END SUBROUTINE adv_umx |
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244 | |
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245 | |
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246 | SUBROUTINE macho( kt, k_order, pdt, ptc, puc, pvc, pubox, pvbox, pt_u, pt_v ) |
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247 | !!--------------------------------------------------------------------- |
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248 | !! *** ROUTINE ultimate_x *** |
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249 | !! |
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250 | !! ** Purpose : compute |
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251 | !! |
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252 | !! ** Method : ... ??? |
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253 | !! TIM = transient interpolation Modeling |
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254 | !! |
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255 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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256 | !!---------------------------------------------------------------------- |
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257 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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258 | INTEGER , INTENT(in ) :: k_order ! order of the ULTIMATE scheme |
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259 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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260 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer fields |
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261 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity components |
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262 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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263 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u, pt_v ! tracer at u- and v-points |
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264 | ! |
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265 | INTEGER :: ji, jj ! dummy loop indices |
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266 | REAL(wp) :: zc_box ! - - |
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267 | REAL(wp), DIMENSION(jpi,jpj) :: zzt |
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268 | !!---------------------------------------------------------------------- |
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269 | ! |
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270 | IF( nn_timing == 1 ) CALL timing_start('macho') |
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271 | ! |
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272 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == 0 ) THEN !== odd ice time step: adv_x then adv_y ==! |
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273 | ! |
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274 | ! !-- ultimate interpolation of pt at u-point --! |
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275 | CALL ultimate_x( k_order, pdt, ptc, puc, pt_u ) |
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276 | ! |
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277 | ! !-- advective form update in zzt --! |
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278 | DO jj = 2, jpjm1 |
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279 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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280 | zzt(ji,jj) = ptc(ji,jj) - pubox(ji,jj) * pdt * ( pt_u(ji,jj) - pt_u(ji-1,jj) ) * r1_e1t(ji,jj) & |
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281 | & - ptc (ji,jj) * pdt * ( puc (ji,jj) - puc (ji-1,jj) ) * r1_e1e2t(ji,jj) |
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282 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
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283 | END DO |
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284 | END DO |
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285 | CALL lbc_lnk( zzt, 'T', 1. ) |
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286 | ! |
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287 | ! !-- ultimate interpolation of pt at v-point --! |
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288 | CALL ultimate_y( k_order, pdt, zzt, pvc, pt_v ) |
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289 | ! |
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290 | ELSE !== even ice time step: adv_y then adv_x ==! |
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291 | ! |
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292 | ! !-- ultimate interpolation of pt at v-point --! |
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293 | CALL ultimate_y( k_order, pdt, ptc, pvc, pt_v ) |
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294 | ! |
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295 | ! !-- advective form update in zzt --! |
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296 | DO jj = 2, jpjm1 |
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297 | DO ji = fs_2, fs_jpim1 |
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298 | zzt(ji,jj) = ptc(ji,jj) - pvbox(ji,jj) * pdt * ( pt_v(ji,jj) - pt_v(ji,jj-1) ) * r1_e2t(ji,jj) & |
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299 | & - ptc (ji,jj) * pdt * ( pvc (ji,jj) - pvc (ji,jj-1) ) * r1_e1e2t(ji,jj) |
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300 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
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301 | END DO |
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302 | END DO |
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303 | CALL lbc_lnk( zzt, 'T', 1. ) |
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304 | ! |
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305 | ! !-- ultimate interpolation of pt at u-point --! |
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306 | CALL ultimate_x( k_order, pdt, zzt, puc, pt_u ) |
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307 | ! |
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308 | ENDIF |
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309 | ! |
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310 | IF( nn_timing == 1 ) CALL timing_stop('macho') |
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311 | ! |
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312 | END SUBROUTINE macho |
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313 | |
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314 | |
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315 | SUBROUTINE ultimate_x( k_order, pdt, pt, puc, pt_u ) |
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316 | !!--------------------------------------------------------------------- |
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317 | !! *** ROUTINE ultimate_x *** |
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318 | !! |
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319 | !! ** Purpose : compute |
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320 | !! |
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321 | !! ** Method : ... ??? |
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322 | !! TIM = transient interpolation Modeling |
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323 | !! |
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324 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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325 | !!---------------------------------------------------------------------- |
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326 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
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327 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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328 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc ! ice i-velocity component |
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329 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
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330 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u ! tracer at u-point |
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331 | ! |
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332 | INTEGER :: ji, jj ! dummy loop indices |
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333 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
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334 | REAL(wp), DIMENSION(jpi,jpj) :: ztu1, ztu2, ztu3, ztu4 |
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335 | !!---------------------------------------------------------------------- |
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336 | ! |
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337 | IF( nn_timing == 1 ) CALL timing_start('ultimate_x') |
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338 | ! |
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339 | ! !-- Laplacian in i-direction --! |
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340 | DO jj = 2, jpjm1 ! First derivative (gradient) |
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341 | DO ji = 1, fs_jpim1 |
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342 | ztu1(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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343 | END DO |
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344 | ! ! Second derivative (Laplacian) |
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345 | DO ji = fs_2, fs_jpim1 |
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346 | ztu2(ji,jj) = ( ztu1(ji,jj) - ztu1(ji-1,jj) ) * r1_e1t(ji,jj) |
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347 | END DO |
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348 | END DO |
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349 | CALL lbc_lnk( ztu2, 'T', 1. ) |
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350 | ! |
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351 | ! !-- BiLaplacian in i-direction --! |
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352 | DO jj = 2, jpjm1 ! Third derivative |
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353 | DO ji = 1, fs_jpim1 |
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354 | ztu3(ji,jj) = ( ztu2(ji+1,jj) - ztu2(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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355 | END DO |
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356 | ! ! Fourth derivative |
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357 | DO ji = fs_2, fs_jpim1 |
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358 | ztu4(ji,jj) = ( ztu3(ji,jj) - ztu3(ji-1,jj) ) * r1_e1t(ji,jj) |
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359 | END DO |
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360 | END DO |
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361 | CALL lbc_lnk( ztu4, 'T', 1. ) |
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362 | ! |
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363 | ! |
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364 | SELECT CASE (k_order ) |
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365 | ! |
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366 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
367 | ! |
---|
368 | DO jj = 1, jpj |
---|
369 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
370 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
371 | & - SIGN( 1._wp, puc(ji,jj) ) * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
372 | END DO |
---|
373 | END DO |
---|
374 | ! |
---|
375 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
376 | ! |
---|
377 | DO jj = 1, jpj |
---|
378 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
379 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
380 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
381 | & - zcu * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
382 | END DO |
---|
383 | END DO |
---|
384 | CALL lbc_lnk( pt_u(:,:) , 'U', 1. ) |
---|
385 | ! |
---|
386 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
387 | ! |
---|
388 | DO jj = 1, jpj |
---|
389 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
390 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
391 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
392 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
393 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
394 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
395 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
396 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
397 | END DO |
---|
398 | END DO |
---|
399 | ! |
---|
400 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
401 | ! |
---|
402 | DO jj = 1, jpj |
---|
403 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
404 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
405 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
406 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
407 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
408 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
409 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
410 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
411 | END DO |
---|
412 | END DO |
---|
413 | ! |
---|
414 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
415 | ! |
---|
416 | DO jj = 1, jpj |
---|
417 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
418 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
419 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
420 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
421 | zdx4 = zdx2 * zdx2 |
---|
422 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
423 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
424 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
425 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) & |
---|
426 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj) + ztu4(ji,jj) & |
---|
427 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj) - ztu4(ji,jj) ) ) ) |
---|
428 | END DO |
---|
429 | END DO |
---|
430 | ! |
---|
431 | END SELECT |
---|
432 | ! |
---|
433 | IF( nn_timing == 1 ) CALL timing_stop('ultimate_x') |
---|
434 | ! |
---|
435 | END SUBROUTINE ultimate_x |
---|
436 | |
---|
437 | |
---|
438 | SUBROUTINE ultimate_y( k_order, pdt, pt, pvc, pt_v ) |
---|
439 | !!--------------------------------------------------------------------- |
---|
440 | !! *** ROUTINE ultimate_y *** |
---|
441 | !! |
---|
442 | !! ** Purpose : compute |
---|
443 | !! |
---|
444 | !! ** Method : ... ??? |
---|
445 | !! TIM = transient interpolation Modeling |
---|
446 | !! |
---|
447 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
448 | !!---------------------------------------------------------------------- |
---|
449 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
---|
450 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
451 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pvc ! ice j-velocity component |
---|
452 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
453 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_v ! tracer at v-point |
---|
454 | ! |
---|
455 | INTEGER :: ji, jj ! dummy loop indices |
---|
456 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
457 | REAL(wp), DIMENSION(jpi,jpj) :: ztv1, ztv2, ztv3, ztv4 |
---|
458 | !!---------------------------------------------------------------------- |
---|
459 | ! |
---|
460 | IF( nn_timing == 1 ) CALL timing_start('ultimate_y') |
---|
461 | ! |
---|
462 | ! !-- Laplacian in j-direction --! |
---|
463 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
464 | DO ji = fs_2, fs_jpim1 |
---|
465 | ztv1(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
466 | END DO |
---|
467 | END DO |
---|
468 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
469 | DO ji = fs_2, fs_jpim1 |
---|
470 | ztv2(ji,jj) = ( ztv1(ji,jj) - ztv1(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
471 | END DO |
---|
472 | END DO |
---|
473 | CALL lbc_lnk( ztv2, 'T', 1. ) |
---|
474 | ! |
---|
475 | ! !-- BiLaplacian in j-direction --! |
---|
476 | DO jj = 1, jpjm1 ! First derivative |
---|
477 | DO ji = fs_2, fs_jpim1 |
---|
478 | ztv3(ji,jj) = ( ztv2(ji,jj+1) - ztv2(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
479 | END DO |
---|
480 | END DO |
---|
481 | DO jj = 2, jpjm1 ! Second derivative |
---|
482 | DO ji = fs_2, fs_jpim1 |
---|
483 | ztv4(ji,jj) = ( ztv3(ji,jj) - ztv3(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
484 | END DO |
---|
485 | END DO |
---|
486 | CALL lbc_lnk( ztv4, 'T', 1. ) |
---|
487 | ! |
---|
488 | ! |
---|
489 | SELECT CASE (k_order ) |
---|
490 | ! |
---|
491 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
492 | DO jj = 1, jpjm1 |
---|
493 | DO ji = 1, jpi |
---|
494 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
495 | & - SIGN( 1._wp, pvc(ji,jj) ) * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
496 | END DO |
---|
497 | END DO |
---|
498 | ! |
---|
499 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
500 | DO jj = 1, jpjm1 |
---|
501 | DO ji = 1, jpi |
---|
502 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
503 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
504 | & - zcv * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
505 | END DO |
---|
506 | END DO |
---|
507 | CALL lbc_lnk( pt_v(:,:) , 'V', 1. ) |
---|
508 | ! |
---|
509 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
510 | DO jj = 1, jpjm1 |
---|
511 | DO ji = 1, jpi |
---|
512 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
513 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
514 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
515 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
516 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
517 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
518 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
519 | END DO |
---|
520 | END DO |
---|
521 | ! |
---|
522 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
523 | DO jj = 1, jpjm1 |
---|
524 | DO ji = 1, jpi |
---|
525 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
526 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
527 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
528 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
529 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
530 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
531 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
532 | END DO |
---|
533 | END DO |
---|
534 | ! |
---|
535 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
536 | DO jj = 1, jpjm1 |
---|
537 | DO ji = 1, jpi |
---|
538 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
539 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
540 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
541 | zdy4 = zdy2 * zdy2 |
---|
542 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
543 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
544 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
545 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) & |
---|
546 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1) + ztv4(ji,jj) & |
---|
547 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1) - ztv4(ji,jj) ) ) ) |
---|
548 | END DO |
---|
549 | END DO |
---|
550 | ! |
---|
551 | END SELECT |
---|
552 | ! |
---|
553 | IF( nn_timing == 1 ) CALL timing_stop('ultimate_y') |
---|
554 | ! |
---|
555 | END SUBROUTINE ultimate_y |
---|
556 | |
---|
557 | |
---|
558 | SUBROUTINE nonosc_2d( pbef, paa, pbb, paft, pdt ) |
---|
559 | !!--------------------------------------------------------------------- |
---|
560 | !! *** ROUTINE nonosc *** |
---|
561 | !! |
---|
562 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
563 | !! scheme and the before field by a nonoscillatory algorithm |
---|
564 | !! |
---|
565 | !! ** Method : ... ??? |
---|
566 | !! warning : pbef and paft must be masked, but the boundaries |
---|
567 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
568 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
569 | !! in-space based differencing for fluid |
---|
570 | !!---------------------------------------------------------------------- |
---|
571 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
572 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pbef, paft ! before & after field |
---|
573 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: paa, pbb ! monotonic fluxes in the 2 directions |
---|
574 | ! |
---|
575 | INTEGER :: ji, jj ! dummy loop indices |
---|
576 | INTEGER :: ikm1 ! local integer |
---|
577 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zsml, z1_dt ! local scalars |
---|
578 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
579 | REAL(wp), DIMENSION(jpi,jpj) :: zbetup, zbetdo, zbup, zbdo, zmsk, zdiv |
---|
580 | !!---------------------------------------------------------------------- |
---|
581 | ! |
---|
582 | IF( nn_timing == 1 ) CALL timing_start('nonosc_2d') |
---|
583 | ! |
---|
584 | zbig = 1.e+40_wp |
---|
585 | zsml = 1.e-15_wp |
---|
586 | |
---|
587 | ! clem test |
---|
588 | DO jj = 2, jpjm1 |
---|
589 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
590 | zdiv(ji,jj) = - ( paa(ji,jj) - paa(ji-1,jj ) & |
---|
591 | & + pbb(ji,jj) - pbb(ji ,jj-1) ) |
---|
592 | END DO |
---|
593 | END DO |
---|
594 | CALL lbc_lnk( zdiv, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
---|
595 | |
---|
596 | ! Determine ice masks for before and after tracers |
---|
597 | WHERE( pbef(:,:) == 0._wp .AND. paft(:,:) == 0._wp .AND. zdiv(:,:) == 0._wp ) ; zmsk(:,:) = 0._wp |
---|
598 | ELSEWHERE ; zmsk(:,:) = 1._wp * tmask(:,:,1) |
---|
599 | END WHERE |
---|
600 | |
---|
601 | ! Search local extrema |
---|
602 | ! -------------------- |
---|
603 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
604 | ! zbup(:,:) = MAX( pbef(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ), & |
---|
605 | ! & paft(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ) ) |
---|
606 | ! zbdo(:,:) = MIN( pbef(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ), & |
---|
607 | ! & paft(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ) ) |
---|
608 | zbup(:,:) = MAX( pbef(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ), & |
---|
609 | & paft(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ) ) |
---|
610 | zbdo(:,:) = MIN( pbef(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ), & |
---|
611 | & paft(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ) ) |
---|
612 | |
---|
613 | z1_dt = 1._wp / pdt |
---|
614 | DO jj = 2, jpjm1 |
---|
615 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
616 | ! |
---|
617 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj ), zbup(ji+1,jj ), & ! search max/min in neighbourhood |
---|
618 | & zbup(ji ,jj-1), zbup(ji ,jj+1) ) |
---|
619 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj ), zbdo(ji+1,jj ), & |
---|
620 | & zbdo(ji ,jj-1), zbdo(ji ,jj+1) ) |
---|
621 | ! |
---|
622 | zpos = MAX( 0., paa(ji-1,jj ) ) - MIN( 0., paa(ji ,jj ) ) & ! positive/negative part of the flux |
---|
623 | & + MAX( 0., pbb(ji ,jj-1) ) - MIN( 0., pbb(ji ,jj ) ) |
---|
624 | zneg = MAX( 0., paa(ji ,jj ) ) - MIN( 0., paa(ji-1,jj ) ) & |
---|
625 | & + MAX( 0., pbb(ji ,jj ) ) - MIN( 0., pbb(ji ,jj-1) ) |
---|
626 | ! |
---|
627 | zbt = e1e2t(ji,jj) * z1_dt ! up & down beta terms |
---|
628 | zbetup(ji,jj) = ( zup - paft(ji,jj) ) / ( zpos + zsml ) * zbt |
---|
629 | zbetdo(ji,jj) = ( paft(ji,jj) - zdo ) / ( zneg + zsml ) * zbt |
---|
630 | END DO |
---|
631 | END DO |
---|
632 | CALL lbc_lnk_multi( zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
633 | |
---|
634 | ! monotonic flux in the i & j direction (paa & pbb) |
---|
635 | ! ------------------------------------- |
---|
636 | DO jj = 2, jpjm1 |
---|
637 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
638 | zau = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji+1,jj) ) |
---|
639 | zbu = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji+1,jj) ) |
---|
640 | zcu = 0.5 + SIGN( 0.5 , paa(ji,jj) ) |
---|
641 | ! |
---|
642 | zav = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji,jj+1) ) |
---|
643 | zbv = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji,jj+1) ) |
---|
644 | zcv = 0.5 + SIGN( 0.5 , pbb(ji,jj) ) |
---|
645 | ! |
---|
646 | paa(ji,jj) = paa(ji,jj) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
---|
647 | pbb(ji,jj) = pbb(ji,jj) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
---|
648 | ! |
---|
649 | END DO |
---|
650 | END DO |
---|
651 | CALL lbc_lnk_multi( paa, 'U', -1., pbb, 'V', -1. ) ! lateral boundary condition (changed sign) |
---|
652 | ! |
---|
653 | IF( nn_timing == 1 ) CALL timing_stop('nonosc_2d') |
---|
654 | ! |
---|
655 | END SUBROUTINE nonosc_2d |
---|
656 | |
---|
657 | #else |
---|
658 | !!---------------------------------------------------------------------- |
---|
659 | !! Default option Dummy module NO LIM 3.0 sea-ice model |
---|
660 | !!---------------------------------------------------------------------- |
---|
661 | #endif |
---|
662 | |
---|
663 | !!====================================================================== |
---|
664 | END MODULE iceadv_umx |
---|