1 | !> @file diffusion_v.f90 |
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2 | !--------------------------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General |
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6 | ! Public License as published by the Free Software Foundation, either version 3 of the License, or |
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7 | ! (at your option) any later version. |
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8 | ! |
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9 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the |
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10 | ! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General |
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11 | ! Public License for more details. |
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12 | ! |
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13 | ! You should have received a copy of the GNU General Public License along with PALM. If not, see |
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14 | ! <http://www.gnu.org/licenses/>. |
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15 | ! |
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16 | ! Copyright 1997-2021 Leibniz Universitaet Hannover |
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17 | !--------------------------------------------------------------------------------------------------! |
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18 | ! |
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19 | ! Current revisions: |
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20 | ! ----------------- |
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21 | ! |
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22 | ! |
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23 | ! Former revisions: |
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24 | ! ----------------- |
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25 | ! $Id: diffusion_v.f90 4828 2021-01-05 11:21:41Z scharf $ |
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26 | ! Update ACC directives for downward facing USM and LSM surfaces |
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27 | ! |
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28 | ! 4671 2020-09-09 20:27:58Z pavelkrc |
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29 | ! Implementation of downward facing USM and LSM surfaces |
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30 | ! |
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31 | ! 4583 2020-06-29 12:36:47Z raasch |
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32 | ! file re-formatted to follow the PALM coding standard |
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33 | ! |
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34 | ! 4360 2020-01-07 11:25:50Z suehring |
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35 | ! Introduction of wall_flags_total_0, which currently sets bits based on static topography |
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36 | ! information used in wall_flags_static_0 |
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37 | ! |
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38 | ! 4329 2019-12-10 15:46:36Z motisi |
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39 | ! Renamed wall_flags_0 to wall_flags_static_0 |
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40 | ! |
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41 | ! 4182 2019-08-22 15:20:23Z scharf |
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42 | ! Corrected "Former revisions" section |
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43 | ! |
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44 | ! 3655 2019-01-07 16:51:22Z knoop |
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45 | ! OpenACC port for SPEC |
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46 | ! |
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47 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
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48 | ! Initial revision |
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49 | ! |
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50 | ! |
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51 | ! Description: |
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52 | ! ------------ |
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53 | !> Diffusion term of the v-component |
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54 | !--------------------------------------------------------------------------------------------------! |
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55 | MODULE diffusion_v_mod |
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56 | |
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57 | |
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58 | PRIVATE |
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59 | PUBLIC diffusion_v |
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60 | |
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61 | INTERFACE diffusion_v |
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62 | MODULE PROCEDURE diffusion_v |
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63 | MODULE PROCEDURE diffusion_v_ij |
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64 | END INTERFACE diffusion_v |
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65 | |
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66 | CONTAINS |
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67 | |
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68 | |
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69 | !--------------------------------------------------------------------------------------------------! |
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70 | ! Description: |
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71 | ! ------------ |
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72 | !> Call for all grid points |
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73 | !--------------------------------------------------------------------------------------------------! |
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74 | SUBROUTINE diffusion_v |
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75 | |
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76 | USE arrays_3d, & |
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77 | ONLY: ddzu, ddzw, drho_air, km, rho_air_zw, tend, u, v, w |
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78 | |
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79 | USE control_parameters, & |
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80 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
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81 | |
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82 | USE grid_variables, & |
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83 | ONLY: ddx, ddy, ddy2 |
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84 | |
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85 | USE indices, & |
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86 | ONLY: nxl, nxr, nyn, nysv, nzb, nzt, wall_flags_total_0 |
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87 | |
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88 | USE kinds |
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89 | |
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90 | USE surface_mod, & |
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91 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v |
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92 | |
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93 | IMPLICIT NONE |
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94 | |
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95 | INTEGER(iwp) :: i !< running index x direction |
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96 | INTEGER(iwp) :: j !< running index y direction |
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97 | INTEGER(iwp) :: k !< running index z direction |
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98 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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99 | INTEGER(iwp) :: m !< running index surface elements |
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100 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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101 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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102 | |
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103 | REAL(wp) :: flag !< flag to mask topography grid points |
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104 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid |
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105 | REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid |
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106 | REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto yv-zw grid |
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107 | REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto yv-zw grid |
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108 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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109 | REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point |
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110 | REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point |
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111 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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112 | |
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113 | !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) & |
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114 | !$ACC PRIVATE(surf_e, surf_s, flag, kmxm, kmxp, kmzm, kmzp) & |
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115 | !$ACC PRIVATE(mask_bottom, mask_east, mask_west, mask_top) & |
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116 | !$ACC PRESENT(wall_flags_total_0, km) & |
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117 | !$ACC PRESENT(u, v, w) & |
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118 | !$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) & |
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119 | !$ACC PRESENT(surf_def_h(0:2), surf_def_v(2:3)) & |
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120 | !$ACC PRESENT(surf_lsm_h(0:1), surf_lsm_v(2:3)) & |
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121 | !$ACC PRESENT(surf_usm_h(0:1), surf_usm_v(2:3)) & |
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122 | !$ACC PRESENT(tend) |
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123 | DO i = nxl, nxr |
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124 | DO j = nysv, nyn |
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125 | ! |
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126 | !-- Compute horizontal diffusion |
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127 | DO k = nzb+1, nzt |
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128 | |
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129 | ! |
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130 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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131 | !-- It is sufficient to masked only east- and west-facing surfaces, which need special |
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132 | !-- treatment for the v-component. |
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133 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) ) |
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134 | mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) ) |
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135 | mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) ) |
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136 | ! |
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137 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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138 | kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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139 | kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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140 | |
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141 | tend(k,j,i) = tend(k,j,i) + ( & |
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142 | mask_east * kmxp * ( & |
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143 | ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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144 | + ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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145 | ) & |
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146 | - mask_west * kmxm * ( & |
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147 | ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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148 | + ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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149 | ) & |
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150 | ) * ddx * flag & |
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151 | + 2.0_wp * ( & |
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152 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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153 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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154 | ) * ddy2 * flag |
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155 | |
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156 | ENDDO |
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157 | |
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158 | ! |
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159 | !-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note, |
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160 | !-- in the the flat case, loops won't be entered as start_index > end_index. Furtermore, |
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161 | !-- note, no vertical natural surfaces so far. |
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162 | !-- Default-type surfaces |
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163 | DO l = 2, 3 |
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164 | surf_s = surf_def_v(l)%start_index(j,i) |
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165 | surf_e = surf_def_v(l)%end_index(j,i) |
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166 | DO m = surf_s, surf_e |
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167 | k = surf_def_v(l)%k(m) |
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168 | tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx |
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169 | ENDDO |
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170 | ENDDO |
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171 | ! |
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172 | !-- Natural-type surfaces |
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173 | DO l = 2, 3 |
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174 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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175 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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176 | DO m = surf_s, surf_e |
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177 | k = surf_lsm_v(l)%k(m) |
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178 | tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx |
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179 | ENDDO |
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180 | ENDDO |
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181 | ! |
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182 | !-- Urban-type surfaces |
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183 | DO l = 2, 3 |
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184 | surf_s = surf_usm_v(l)%start_index(j,i) |
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185 | surf_e = surf_usm_v(l)%end_index(j,i) |
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186 | DO m = surf_s, surf_e |
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187 | k = surf_usm_v(l)%k(m) |
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188 | tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx |
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189 | ENDDO |
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190 | ENDDO |
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191 | ! |
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192 | !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid |
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193 | !-- diffusive fluxes are masked (flag 10) within this loop, and added further below, else, |
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194 | !-- simple gradient approach is applied. Model top is also mask if top-momentum flux is |
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195 | !-- given. |
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196 | DO k = nzb+1, nzt |
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197 | ! |
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198 | !-- Determine flags to mask topography below and above. Flag 2 is used to mask |
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199 | !-- topography in general, while flag 8 implies also information about |
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200 | !-- use_surface_fluxes. Flag 9 is used to control momentum flux at model top. |
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201 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) ) |
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202 | mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * & |
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203 | MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) ) |
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204 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) ) |
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205 | ! |
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206 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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207 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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208 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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209 | |
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210 | tend(k,j,i) = tend(k,j,i) & |
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211 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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212 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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213 | & ) * rho_air_zw(k) * mask_top & |
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214 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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215 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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216 | & ) * rho_air_zw(k-1) * mask_bottom & |
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217 | & ) * ddzw(k) * drho_air(k) * flag |
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218 | ENDDO |
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219 | |
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220 | ! |
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221 | !-- Vertical diffusion at the first grid point above the surface, if the momentum flux at |
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222 | !-- the bottom is given by the Prandtl law or if it is prescribed by the user. |
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223 | !-- Difference quotient of the momentum flux is not formed over half of the grid spacing |
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224 | !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the |
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225 | !-- values of the momentum flux becomes too large in this case. |
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226 | IF ( use_surface_fluxes ) THEN |
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227 | ! |
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228 | !-- Default-type surfaces, upward-facing |
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229 | surf_s = surf_def_h(0)%start_index(j,i) |
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230 | surf_e = surf_def_h(0)%end_index(j,i) |
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231 | DO m = surf_s, surf_e |
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232 | k = surf_def_h(0)%k(m) |
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233 | |
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234 | tend(k,j,i) = tend(k,j,i) & |
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235 | + ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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236 | ENDDO |
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237 | ! |
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238 | !-- Default-type surfaces, dowward-facing |
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239 | surf_s = surf_def_h(1)%start_index(j,i) |
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240 | surf_e = surf_def_h(1)%end_index(j,i) |
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241 | DO m = surf_s, surf_e |
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242 | k = surf_def_h(1)%k(m) |
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243 | |
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244 | tend(k,j,i) = tend(k,j,i) & |
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245 | + ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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246 | ENDDO |
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247 | ! |
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248 | !-- Natural-type surfaces, upward-facing |
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249 | surf_s = surf_lsm_h(0)%start_index(j,i) |
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250 | surf_e = surf_lsm_h(0)%end_index(j,i) |
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251 | DO m = surf_s, surf_e |
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252 | k = surf_lsm_h(0)%k(m) |
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253 | |
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254 | tend(k,j,i) = tend(k,j,i) & |
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255 | + ( - ( - surf_lsm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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256 | |
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257 | ENDDO |
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258 | ! |
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259 | !-- Natural-type surfaces, downward-facing |
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260 | surf_s = surf_lsm_h(1)%start_index(j,i) |
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261 | surf_e = surf_lsm_h(1)%end_index(j,i) |
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262 | DO m = surf_s, surf_e |
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263 | k = surf_lsm_h(1)%k(m) |
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264 | |
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265 | tend(k,j,i) = tend(k,j,i) & |
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266 | + ( - surf_lsm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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267 | |
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268 | ENDDO |
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269 | ! |
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270 | !-- Urban-type surfaces, upward-facing |
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271 | surf_s = surf_usm_h(0)%start_index(j,i) |
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272 | surf_e = surf_usm_h(0)%end_index(j,i) |
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273 | DO m = surf_s, surf_e |
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274 | k = surf_usm_h(0)%k(m) |
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275 | |
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276 | tend(k,j,i) = tend(k,j,i) & |
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277 | + ( - ( - surf_usm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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278 | |
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279 | ENDDO |
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280 | ! |
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281 | !-- Urban-type surfaces, downward-facing |
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282 | surf_s = surf_usm_h(1)%start_index(j,i) |
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283 | surf_e = surf_usm_h(1)%end_index(j,i) |
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284 | DO m = surf_s, surf_e |
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285 | k = surf_usm_h(1)%k(m) |
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286 | |
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287 | tend(k,j,i) = tend(k,j,i) & |
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288 | + ( - surf_usm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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289 | |
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290 | ENDDO |
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291 | ENDIF |
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292 | ! |
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293 | !-- Add momentum flux at model top |
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294 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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295 | surf_s = surf_def_h(2)%start_index(j,i) |
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296 | surf_e = surf_def_h(2)%end_index(j,i) |
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297 | DO m = surf_s, surf_e |
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298 | |
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299 | k = surf_def_h(2)%k(m) |
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300 | |
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301 | tend(k,j,i) = tend(k,j,i) & |
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302 | + ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k) |
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303 | ENDDO |
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304 | ENDIF |
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305 | |
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306 | ENDDO |
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307 | ENDDO |
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308 | |
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309 | END SUBROUTINE diffusion_v |
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310 | |
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311 | |
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312 | !--------------------------------------------------------------------------------------------------! |
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313 | ! Description: |
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314 | ! ------------ |
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315 | !> Call for grid point i,j |
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316 | !--------------------------------------------------------------------------------------------------! |
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317 | SUBROUTINE diffusion_v_ij( i, j ) |
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318 | |
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319 | USE arrays_3d, & |
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320 | ONLY: ddzu, ddzw, drho_air, km, tend, u, v, w, rho_air_zw |
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321 | |
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322 | USE control_parameters, & |
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323 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
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324 | |
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325 | USE grid_variables, & |
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326 | ONLY: ddx, ddy, ddy2 |
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327 | |
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328 | USE indices, & |
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329 | ONLY: nzb, nzt, wall_flags_total_0 |
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330 | |
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331 | USE kinds |
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332 | |
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333 | USE surface_mod, & |
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334 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v |
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335 | |
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336 | IMPLICIT NONE |
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337 | |
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338 | |
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339 | INTEGER(iwp) :: i !< running index x direction |
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340 | INTEGER(iwp) :: j !< running index y direction |
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341 | INTEGER(iwp) :: k !< running index z direction |
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342 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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343 | INTEGER(iwp) :: m !< running index surface elements |
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344 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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345 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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346 | |
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347 | REAL(wp) :: flag !< flag to mask topography grid points |
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348 | REAL(wp) :: kmxm !< diffusion coefficient on leftward side of the v-gridbox - interpolated onto xu-yv grid |
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349 | REAL(wp) :: kmxp !< diffusion coefficient on rightward side of the v-gridbox - interpolated onto xu-yv grid |
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350 | REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid |
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351 | REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid |
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352 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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353 | REAL(wp) :: mask_east !< flag to mask vertical surface south of the grid point |
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354 | REAL(wp) :: mask_west !< flag to mask vertical surface north of the grid point |
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355 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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356 | |
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357 | ! |
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358 | !-- Compute horizontal diffusion |
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359 | DO k = nzb+1, nzt |
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360 | ! |
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361 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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362 | !-- It is sufficient to masked only east- and west-facing surfaces, which need special |
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363 | !-- treatment for the v-component. |
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364 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) ) |
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365 | mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i+1), 2 ) ) |
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366 | mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i-1), 2 ) ) |
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367 | ! |
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368 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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369 | kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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370 | kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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371 | |
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372 | tend(k,j,i) = tend(k,j,i) + ( & |
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373 | mask_east * kmxp * ( & |
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374 | ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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375 | + ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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376 | ) & |
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377 | - mask_west * kmxm * ( & |
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378 | ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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379 | + ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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380 | ) & |
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381 | ) * ddx * flag & |
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382 | + 2.0_wp * ( & |
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383 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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384 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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385 | ) * ddy2 * flag |
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386 | ENDDO |
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387 | |
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388 | ! |
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389 | !-- Add horizontal momentum flux v'u' at east- (l=2) and west-facing (l=3) surfaces. Note, in the |
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390 | !-- the flat case, loops won't be entered as start_index > end_index. Furtermore, note, no |
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391 | !-- vertical natural surfaces so far. |
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392 | !-- Default-type surfaces |
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393 | DO l = 2, 3 |
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394 | surf_s = surf_def_v(l)%start_index(j,i) |
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395 | surf_e = surf_def_v(l)%end_index(j,i) |
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396 | DO m = surf_s, surf_e |
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397 | k = surf_def_v(l)%k(m) |
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398 | tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddx |
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399 | ENDDO |
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400 | ENDDO |
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401 | ! |
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402 | !-- Natural-type surfaces |
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403 | DO l = 2, 3 |
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404 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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405 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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406 | DO m = surf_s, surf_e |
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407 | k = surf_lsm_v(l)%k(m) |
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408 | tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddx |
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409 | ENDDO |
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410 | ENDDO |
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411 | ! |
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412 | !-- Urban-type surfaces |
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413 | DO l = 2, 3 |
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414 | surf_s = surf_usm_v(l)%start_index(j,i) |
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415 | surf_e = surf_usm_v(l)%end_index(j,i) |
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416 | DO m = surf_s, surf_e |
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417 | k = surf_usm_v(l)%k(m) |
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418 | tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddx |
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419 | ENDDO |
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420 | ENDDO |
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421 | ! |
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422 | !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid diffusive |
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423 | !-- fluxes are masked (flag 8) within this loop, and added further below, else, simple gradient |
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424 | !-- approach is applied. Model top is also mask if top-momentum flux is given. |
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425 | DO k = nzb+1, nzt |
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426 | ! |
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427 | !-- Determine flags to mask topography below and above. Flag 2 is used to mask topography in |
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428 | !-- general, while flag 10 implies also information about use_surface_fluxes. Flag 9 is used |
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429 | !-- to control momentum flux at model top. |
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430 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) ) |
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431 | mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * & |
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432 | MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) ) |
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433 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) ) |
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434 | ! |
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435 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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436 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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437 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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438 | |
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439 | tend(k,j,i) = tend(k,j,i) & |
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440 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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441 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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442 | & ) * rho_air_zw(k) * mask_top & |
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443 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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444 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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445 | & ) * rho_air_zw(k-1) * mask_bottom & |
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446 | & ) * ddzw(k) * drho_air(k) * flag |
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447 | ENDDO |
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448 | |
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449 | ! |
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450 | !-- Vertical diffusion at the first grid point above the surface, if the momentum flux at the |
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451 | !-- bottom is given by the Prandtl law or if it is prescribed by the user. |
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452 | !-- Difference quotient of the momentum flux is not formed over half of the grid spacing |
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453 | !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the values |
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454 | !-- of the momentum flux becomes too large in this case. |
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455 | IF ( use_surface_fluxes ) THEN |
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456 | ! |
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457 | !-- Default-type surfaces, upward-facing |
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458 | surf_s = surf_def_h(0)%start_index(j,i) |
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459 | surf_e = surf_def_h(0)%end_index(j,i) |
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460 | DO m = surf_s, surf_e |
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461 | k = surf_def_h(0)%k(m) |
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462 | |
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463 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_def_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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464 | ENDDO |
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465 | ! |
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466 | !-- Default-type surfaces, dowward-facing |
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467 | surf_s = surf_def_h(1)%start_index(j,i) |
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468 | surf_e = surf_def_h(1)%end_index(j,i) |
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469 | DO m = surf_s, surf_e |
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470 | k = surf_def_h(1)%k(m) |
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471 | |
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472 | tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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473 | ENDDO |
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474 | ! |
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475 | !-- Natural-type surfaces, upward-facing |
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476 | surf_s = surf_lsm_h(0)%start_index(j,i) |
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477 | surf_e = surf_lsm_h(0)%end_index(j,i) |
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478 | DO m = surf_s, surf_e |
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479 | k = surf_lsm_h(0)%k(m) |
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480 | |
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481 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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482 | |
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483 | ENDDO |
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484 | ! |
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485 | !-- Natural-type surfaces, downward-facing |
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486 | surf_s = surf_lsm_h(1)%start_index(j,i) |
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487 | surf_e = surf_lsm_h(1)%end_index(j,i) |
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488 | DO m = surf_s, surf_e |
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489 | k = surf_lsm_h(1)%k(m) |
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490 | |
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491 | tend(k,j,i) = tend(k,j,i) + ( - surf_lsm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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492 | |
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493 | ENDDO |
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494 | ! |
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495 | !-- Urban-type surfaces, upward-facing |
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496 | surf_s = surf_usm_h(0)%start_index(j,i) |
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497 | surf_e = surf_usm_h(0)%end_index(j,i) |
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498 | DO m = surf_s, surf_e |
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499 | k = surf_usm_h(0)%k(m) |
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500 | |
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501 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h(0)%vsws(m) ) ) * ddzw(k) * drho_air(k) |
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502 | |
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503 | ENDDO |
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504 | ! |
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505 | !-- Urban-type surfaces, downward-facing |
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506 | surf_s = surf_usm_h(1)%start_index(j,i) |
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507 | surf_e = surf_usm_h(1)%end_index(j,i) |
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508 | DO m = surf_s, surf_e |
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509 | k = surf_usm_h(1)%k(m) |
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510 | |
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511 | tend(k,j,i) = tend(k,j,i) + ( - surf_usm_h(1)%vsws(m) ) * ddzw(k) * drho_air(k) |
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512 | |
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513 | ENDDO |
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514 | ENDIF |
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515 | ! |
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516 | !-- Add momentum flux at model top |
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517 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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518 | surf_s = surf_def_h(2)%start_index(j,i) |
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519 | surf_e = surf_def_h(2)%end_index(j,i) |
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520 | DO m = surf_s, surf_e |
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521 | |
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522 | k = surf_def_h(2)%k(m) |
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523 | |
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524 | tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(2)%vsws(m) ) * ddzw(k) * drho_air(k) |
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525 | ENDDO |
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526 | ENDIF |
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527 | |
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528 | END SUBROUTINE diffusion_v_ij |
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529 | |
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530 | END MODULE diffusion_v_mod |
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