1 | !> @file diffusion_u.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_u.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 06:23:51 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 u-component |
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54 | !> @todo additional damping (needed for non-cyclic bc) causes bad vectorization and slows down the |
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55 | ! speed on NEC about 5-10% |
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56 | !--------------------------------------------------------------------------------------------------! |
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57 | MODULE diffusion_u_mod |
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58 | |
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59 | |
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60 | PRIVATE |
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61 | PUBLIC diffusion_u |
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62 | |
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63 | INTERFACE diffusion_u |
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64 | MODULE PROCEDURE diffusion_u |
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65 | MODULE PROCEDURE diffusion_u_ij |
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66 | END INTERFACE diffusion_u |
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67 | |
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68 | CONTAINS |
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69 | |
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70 | |
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71 | !--------------------------------------------------------------------------------------------------! |
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72 | ! Description: |
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73 | ! ------------ |
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74 | !> Call for all grid points |
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75 | !--------------------------------------------------------------------------------------------------! |
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76 | SUBROUTINE diffusion_u |
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77 | |
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78 | USE arrays_3d, & |
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79 | ONLY: ddzu, ddzw, drho_air, km, rho_air_zw, tend, u, v, w |
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80 | |
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81 | USE control_parameters, & |
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82 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
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83 | |
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84 | USE grid_variables, & |
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85 | ONLY: ddx, ddx2, ddy |
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86 | |
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87 | USE indices, & |
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88 | ONLY: nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_total_0 |
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89 | |
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90 | USE kinds |
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91 | |
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92 | USE surface_mod, & |
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93 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v |
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94 | |
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95 | IMPLICIT NONE |
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96 | |
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97 | INTEGER(iwp) :: i !< running index x direction |
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98 | INTEGER(iwp) :: j !< running index y direction |
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99 | INTEGER(iwp) :: k !< running index z direction |
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100 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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101 | INTEGER(iwp) :: m !< running index surface elements |
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102 | INTEGER(iwp) :: surf_e !< end index of surface elements at (j,i)-gridpoint |
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103 | INTEGER(iwp) :: surf_s !< start index of surface elements at (j,i)-gridpoint |
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104 | |
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105 | REAL(wp) :: flag !< flag to mask topography grid points |
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106 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid |
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107 | REAL(wp) :: kmyp !< diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid |
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108 | REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid |
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109 | REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid |
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110 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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111 | REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point |
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112 | REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point |
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113 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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114 | |
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115 | |
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116 | |
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117 | !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, l, m) & |
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118 | !$ACC PRIVATE(surf_e, surf_s, flag, kmym, kmyp, kmzm, kmzp) & |
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119 | !$ACC PRIVATE(mask_bottom, mask_north, mask_south, mask_top) & |
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120 | !$ACC PRESENT(wall_flags_total_0, km) & |
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121 | !$ACC PRESENT(u, v, w) & |
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122 | !$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) & |
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123 | !$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:1)) & |
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124 | !$ACC PRESENT(surf_lsm_h(0:1), surf_lsm_v(0:1)) & |
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125 | !$ACC PRESENT(surf_usm_h(0:1), surf_usm_v(0:1)) & |
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126 | !$ACC PRESENT(tend) |
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127 | DO i = nxlu, nxr |
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128 | DO j = nys, nyn |
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129 | ! |
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130 | !-- Compute horizontal diffusion |
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131 | DO k = nzb+1, nzt |
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132 | ! |
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133 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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134 | !-- It is sufficient to masked only north- and south-facing surfaces, which need special |
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135 | !-- treatment for the u-component. |
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136 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) ) |
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137 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) ) |
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138 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) ) |
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139 | ! |
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140 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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141 | kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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142 | kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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143 | |
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144 | tend(k,j,i) = tend(k,j,i) & |
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145 | + 2.0_wp * ( & |
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146 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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147 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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148 | ) * ddx2 * flag & |
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149 | + ( mask_north * ( & |
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150 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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151 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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152 | ) & |
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153 | - mask_south * ( & |
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154 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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155 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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156 | ) & |
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157 | ) * ddy * flag |
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158 | ENDDO |
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159 | ! |
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160 | !-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) surfaces. |
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161 | !-- Note, in the the flat case, loops won't be entered as start_index > end_index. |
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162 | !-- Furtermore, note, no vertical natural surfaces so far. |
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163 | !-- Default-type surfaces |
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164 | DO l = 0, 1 |
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165 | surf_s = surf_def_v(l)%start_index(j,i) |
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166 | surf_e = surf_def_v(l)%end_index(j,i) |
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167 | DO m = surf_s, surf_e |
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168 | k = surf_def_v(l)%k(m) |
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169 | tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy |
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170 | ENDDO |
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171 | ENDDO |
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172 | ! |
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173 | !-- Natural-type surfaces |
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174 | DO l = 0, 1 |
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175 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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176 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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177 | DO m = surf_s, surf_e |
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178 | k = surf_lsm_v(l)%k(m) |
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179 | tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy |
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180 | ENDDO |
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181 | ENDDO |
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182 | ! |
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183 | !-- Urban-type surfaces |
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184 | DO l = 0, 1 |
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185 | surf_s = surf_usm_v(l)%start_index(j,i) |
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186 | surf_e = surf_usm_v(l)%end_index(j,i) |
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187 | DO m = surf_s, surf_e |
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188 | k = surf_usm_v(l)%k(m) |
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189 | tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy |
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190 | ENDDO |
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191 | ENDDO |
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192 | |
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193 | ! |
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194 | !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid |
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195 | !-- diffusive fluxes are masked (flag 8) within this loop, and added further below, else, |
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196 | !-- simple gradient approach is applied. Model top is also mask if top-momentum flux is |
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197 | !-- given. |
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198 | DO k = nzb+1, nzt |
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199 | ! |
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200 | !-- Determine flags to mask topography below and above. Flag 1 is used to mask |
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201 | !-- topography in general, and flag 8 implies information about use_surface_fluxes. |
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202 | !-- Flag 9 is used to control momentum flux at model top. |
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203 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) ) |
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204 | mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * & |
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205 | MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) ) |
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206 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) ) |
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207 | ! |
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208 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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209 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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210 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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211 | |
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212 | tend(k,j,i) = tend(k,j,i) & |
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213 | + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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214 | + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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215 | ) * rho_air_zw(k) * mask_top & |
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216 | - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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217 | + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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218 | ) * rho_air_zw(k-1) * mask_bottom & |
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219 | ) * ddzw(k) * drho_air(k) * flag |
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220 | ENDDO |
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221 | |
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222 | ! |
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223 | !-- Vertical diffusion at the first grid point above the surface, if the momentum flux at |
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224 | !-- the bottom is given by the Prandtl law or if it is prescribed by the user. |
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225 | !-- Difference quotient of the momentum flux is not formed over half of the grid spacing |
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226 | !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the |
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227 | !-- values of the momentum flux becomes too large in this case. |
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228 | !-- The term containing w(k-1,..) (see above equation) is removed here because the vertical |
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229 | !-- velocity is assumed to be zero at the surface. |
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230 | IF ( use_surface_fluxes ) THEN |
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231 | ! |
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232 | !-- Default-type surfaces, upward-facing |
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233 | surf_s = surf_def_h(0)%start_index(j,i) |
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234 | surf_e = surf_def_h(0)%end_index(j,i) |
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235 | DO m = surf_s, surf_e |
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236 | |
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237 | k = surf_def_h(0)%k(m) |
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238 | |
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239 | tend(k,j,i) = tend(k,j,i) & |
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240 | + ( - ( - surf_def_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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241 | ENDDO |
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242 | ! |
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243 | !-- Default-type surfaces, dowward-facing |
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244 | surf_s = surf_def_h(1)%start_index(j,i) |
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245 | surf_e = surf_def_h(1)%end_index(j,i) |
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246 | DO m = surf_s, surf_e |
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247 | |
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248 | k = surf_def_h(1)%k(m) |
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249 | |
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250 | tend(k,j,i) = tend(k,j,i) & |
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251 | + ( - surf_def_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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252 | ENDDO |
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253 | ! |
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254 | !-- Natural-type surfaces, upward-facing |
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255 | surf_s = surf_lsm_h(0)%start_index(j,i) |
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256 | surf_e = surf_lsm_h(0)%end_index(j,i) |
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257 | DO m = surf_s, surf_e |
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258 | |
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259 | k = surf_lsm_h(0)%k(m) |
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260 | |
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261 | tend(k,j,i) = tend(k,j,i) & |
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262 | + ( - ( - surf_lsm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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263 | ENDDO |
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264 | ! |
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265 | !-- Natural-type surfaces, downward-facing |
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266 | surf_s = surf_lsm_h(1)%start_index(j,i) |
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267 | surf_e = surf_lsm_h(1)%end_index(j,i) |
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268 | DO m = surf_s, surf_e |
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269 | |
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270 | k = surf_lsm_h(1)%k(m) |
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271 | |
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272 | tend(k,j,i) = tend(k,j,i) & |
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273 | + ( - surf_lsm_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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274 | ENDDO |
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275 | ! |
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276 | !-- Urban-type surfaces, upward-facing |
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277 | surf_s = surf_usm_h(0)%start_index(j,i) |
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278 | surf_e = surf_usm_h(0)%end_index(j,i) |
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279 | DO m = surf_s, surf_e |
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280 | |
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281 | k = surf_usm_h(0)%k(m) |
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282 | |
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283 | tend(k,j,i) = tend(k,j,i) & |
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284 | + ( - ( - surf_usm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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285 | ENDDO |
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286 | ! |
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287 | !-- Urban-type surfaces, downward-facing |
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288 | surf_s = surf_usm_h(1)%start_index(j,i) |
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289 | surf_e = surf_usm_h(1)%end_index(j,i) |
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290 | DO m = surf_s, surf_e |
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291 | |
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292 | k = surf_usm_h(1)%k(m) |
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293 | |
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294 | tend(k,j,i) = tend(k,j,i) & |
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295 | + ( - surf_usm_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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296 | ENDDO |
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297 | |
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298 | ENDIF |
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299 | ! |
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300 | !-- Add momentum flux at model top |
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301 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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302 | surf_s = surf_def_h(2)%start_index(j,i) |
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303 | surf_e = surf_def_h(2)%end_index(j,i) |
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304 | DO m = surf_s, surf_e |
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305 | |
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306 | k = surf_def_h(2)%k(m) |
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307 | |
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308 | tend(k,j,i) = tend(k,j,i) & |
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309 | + ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k) |
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310 | ENDDO |
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311 | ENDIF |
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312 | |
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313 | ENDDO |
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314 | ENDDO |
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315 | |
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316 | END SUBROUTINE diffusion_u |
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317 | |
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318 | |
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319 | !--------------------------------------------------------------------------------------------------! |
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320 | ! Description: |
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321 | ! ------------ |
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322 | !> Call for grid point i,j |
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323 | !--------------------------------------------------------------------------------------------------! |
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324 | SUBROUTINE diffusion_u_ij( i, j ) |
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325 | |
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326 | USE arrays_3d, & |
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327 | ONLY: ddzu, ddzw, drho_air, km, tend, u, v, w, rho_air_zw |
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328 | |
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329 | USE control_parameters, & |
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330 | ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes |
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331 | |
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332 | USE grid_variables, & |
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333 | ONLY: ddx, ddx2, ddy |
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334 | |
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335 | USE indices, & |
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336 | ONLY: nzb, nzt, wall_flags_total_0 |
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337 | |
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338 | USE kinds |
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339 | |
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340 | USE surface_mod, & |
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341 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v |
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342 | |
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343 | IMPLICIT NONE |
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344 | |
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345 | INTEGER(iwp) :: i !< running index x direction |
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346 | INTEGER(iwp) :: j !< running index y direction |
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347 | INTEGER(iwp) :: k !< running index z direction |
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348 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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349 | INTEGER(iwp) :: m !< running index surface elements |
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350 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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351 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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352 | |
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353 | REAL(wp) :: flag !< flag to mask topography grid points |
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354 | REAL(wp) :: kmym !< diffusion coefficient on southward side of the u-gridbox - interpolated onto xu-yv grid |
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355 | REAL(wp) :: kmyp !<diffusion coefficient on northward side of the u-gridbox - interpolated onto xu-yv grid |
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356 | REAL(wp) :: kmzm !< diffusion coefficient on bottom of the gridbox - interpolated onto xu-zw grid |
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357 | REAL(wp) :: kmzp !< diffusion coefficient on top of the gridbox - interpolated onto xu-zw grid |
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358 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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359 | REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point |
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360 | REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point |
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361 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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362 | ! |
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363 | !-- Compute horizontal diffusion |
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364 | DO k = nzb+1, nzt |
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365 | ! |
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366 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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367 | !-- It is sufficient to masked only north- and south-facing surfaces, which need special |
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368 | !-- treatment for the u-component. |
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369 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) ) |
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370 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j-1,i), 1 ) ) |
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371 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j+1,i), 1 ) ) |
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372 | ! |
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373 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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374 | kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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375 | kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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376 | |
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377 | tend(k,j,i) = tend(k,j,i) & |
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378 | + 2.0_wp * ( & |
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379 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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380 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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381 | ) * ddx2 * flag & |
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382 | + ( & |
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383 | mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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384 | + ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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385 | ) & |
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386 | - mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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387 | + ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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388 | ) & |
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389 | ) * ddy * flag |
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390 | ENDDO |
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391 | |
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392 | ! |
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393 | !-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) surfaces. Note, in |
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394 | !-- the the flat case, loops won't be entered as start_index > end_index. Furtermore, note, no |
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395 | !-- vertical natural surfaces so far. |
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396 | !-- Default-type surfaces |
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397 | DO l = 0, 1 |
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398 | surf_s = surf_def_v(l)%start_index(j,i) |
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399 | surf_e = surf_def_v(l)%end_index(j,i) |
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400 | DO m = surf_s, surf_e |
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401 | k = surf_def_v(l)%k(m) |
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402 | tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy |
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403 | ENDDO |
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404 | ENDDO |
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405 | ! |
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406 | !-- Natural-type surfaces |
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407 | DO l = 0, 1 |
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408 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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409 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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410 | DO m = surf_s, surf_e |
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411 | k = surf_lsm_v(l)%k(m) |
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412 | tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy |
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413 | ENDDO |
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414 | ENDDO |
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415 | ! |
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416 | !-- Urban-type surfaces |
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417 | DO l = 0, 1 |
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418 | surf_s = surf_usm_v(l)%start_index(j,i) |
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419 | surf_e = surf_usm_v(l)%end_index(j,i) |
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420 | DO m = surf_s, surf_e |
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421 | k = surf_usm_v(l)%k(m) |
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422 | tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy |
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423 | ENDDO |
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424 | ENDDO |
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425 | ! |
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426 | !-- Compute vertical diffusion. In case of simulating a surface layer, respective grid diffusive |
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427 | !-- fluxes are masked (flag 8) within this loop, and added further below, else, simple gradient |
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428 | !-- approach is applied. Model top is also mask if top-momentum flux is given. |
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429 | DO k = nzb+1, nzt |
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430 | ! |
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431 | !-- Determine flags to mask topography below and above. Flag 1 is used to mask topography in |
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432 | !-- general, and flag 8 implies information about use_surface_fluxes. Flag 9 is used to |
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433 | !-- control momentum flux at model top. |
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434 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k-1,j,i), 8 ) ) |
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435 | mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 8 ) ) * & |
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436 | MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k+1,j,i), 9 ) ) |
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437 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) ) |
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438 | ! |
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439 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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440 | kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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441 | kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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442 | |
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443 | tend(k,j,i) = tend(k,j,i) & |
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444 | + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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445 | + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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446 | ) * rho_air_zw(k) * mask_top & |
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447 | - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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448 | + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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449 | ) * rho_air_zw(k-1) * mask_bottom & |
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450 | ) * ddzw(k) * drho_air(k) * flag |
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451 | ENDDO |
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452 | |
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453 | ! |
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454 | !-- Vertical diffusion at the first surface grid points, if the momentum flux at the bottom is |
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455 | !-- given by the Prandtl law or if it is prescribed by the user. |
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456 | !-- Difference quotient of the momentum flux is not formed over half of the grid spacing |
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457 | !-- (2.0*ddzw(k)) any more, since the comparison with other (LES) models showed that the values |
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458 | !-- of the momentum flux becomes too large in this case. |
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459 | IF ( use_surface_fluxes ) THEN |
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460 | ! |
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461 | !-- Default-type surfaces, upward-facing |
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462 | surf_s = surf_def_h(0)%start_index(j,i) |
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463 | surf_e = surf_def_h(0)%end_index(j,i) |
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464 | DO m = surf_s, surf_e |
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465 | |
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466 | k = surf_def_h(0)%k(m) |
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467 | |
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468 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_def_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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469 | ENDDO |
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470 | ! |
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471 | !-- Default-type surfaces, dowward-facing (except for model-top fluxes) |
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472 | surf_s = surf_def_h(1)%start_index(j,i) |
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473 | surf_e = surf_def_h(1)%end_index(j,i) |
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474 | DO m = surf_s, surf_e |
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475 | |
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476 | k = surf_def_h(1)%k(m) |
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477 | |
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478 | tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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479 | ENDDO |
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480 | ! |
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481 | !-- Natural-type surfaces, upward-facing |
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482 | surf_s = surf_lsm_h(0)%start_index(j,i) |
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483 | surf_e = surf_lsm_h(0)%end_index(j,i) |
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484 | DO m = surf_s, surf_e |
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485 | |
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486 | k = surf_lsm_h(0)%k(m) |
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487 | |
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488 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_lsm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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489 | ENDDO |
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490 | ! |
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491 | !-- Natural-type surfaces, downward-facing |
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492 | surf_s = surf_lsm_h(1)%start_index(j,i) |
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493 | surf_e = surf_lsm_h(1)%end_index(j,i) |
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494 | DO m = surf_s, surf_e |
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495 | |
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496 | k = surf_lsm_h(1)%k(m) |
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497 | |
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498 | tend(k,j,i) = tend(k,j,i) + ( - surf_lsm_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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499 | ENDDO |
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500 | ! |
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501 | !-- Urban-type surfaces, upward-facing |
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502 | surf_s = surf_usm_h(0)%start_index(j,i) |
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503 | surf_e = surf_usm_h(0)%end_index(j,i) |
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504 | DO m = surf_s, surf_e |
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505 | |
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506 | k = surf_usm_h(0)%k(m) |
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507 | |
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508 | tend(k,j,i) = tend(k,j,i) + ( - ( - surf_usm_h(0)%usws(m) ) ) * ddzw(k) * drho_air(k) |
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509 | ENDDO |
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510 | ! |
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511 | !-- Urban-type surfaces, downward-facing |
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512 | surf_s = surf_usm_h(1)%start_index(j,i) |
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513 | surf_e = surf_usm_h(1)%end_index(j,i) |
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514 | DO m = surf_s, surf_e |
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515 | |
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516 | k = surf_usm_h(1)%k(m) |
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517 | |
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518 | tend(k,j,i) = tend(k,j,i) + ( - surf_usm_h(1)%usws(m) ) * ddzw(k) * drho_air(k) |
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519 | ENDDO |
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520 | |
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521 | ENDIF |
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522 | ! |
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523 | !-- Add momentum flux at model top |
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524 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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525 | surf_s = surf_def_h(2)%start_index(j,i) |
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526 | surf_e = surf_def_h(2)%end_index(j,i) |
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527 | DO m = surf_s, surf_e |
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528 | |
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529 | k = surf_def_h(2)%k(m) |
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530 | |
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531 | tend(k,j,i) = tend(k,j,i) + ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k) |
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532 | ENDDO |
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533 | ENDIF |
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534 | |
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535 | |
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536 | END SUBROUTINE diffusion_u_ij |
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537 | |
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538 | END MODULE diffusion_u_mod |
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