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 |
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6 | ! terms of the GNU General Public License as published by the Free Software |
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7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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8 | ! version. |
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9 | ! |
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10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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13 | ! |
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14 | ! You should have received a copy of the GNU General Public License along with |
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15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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16 | ! |
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17 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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18 | !------------------------------------------------------------------------------! |
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19 | ! |
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20 | ! Current revisions: |
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21 | ! ----------------- |
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22 | ! |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: diffusion_u.f90 2718 2018-01-02 08:49:38Z kanani $ |
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27 | ! Corrected "Former revisions" section |
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28 | ! |
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29 | ! 2696 2017-12-14 17:12:51Z kanani |
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30 | ! Change in file header (GPL part) |
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31 | ! |
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32 | ! 2638 2017-11-23 12:44:23Z raasch |
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33 | ! bugfix for constant top momentumflux |
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34 | ! |
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35 | ! 2233 2017-05-30 18:08:54Z suehring |
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36 | ! |
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37 | ! 2232 2017-05-30 17:47:52Z suehring |
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38 | ! Adjustments to new topography and surface concept |
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39 | ! |
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40 | ! 2118 2017-01-17 16:38:49Z raasch |
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41 | ! OpenACC version of subroutine removed |
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42 | ! |
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43 | ! 2037 2016-10-26 11:15:40Z knoop |
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44 | ! Anelastic approximation implemented |
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45 | ! |
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46 | ! 2000 2016-08-20 18:09:15Z knoop |
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47 | ! Forced header and separation lines into 80 columns |
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48 | ! |
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49 | ! 1873 2016-04-18 14:50:06Z maronga |
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50 | ! Module renamed (removed _mod) |
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51 | ! |
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52 | ! 1850 2016-04-08 13:29:27Z maronga |
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53 | ! Module renamed |
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54 | ! |
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55 | ! 1740 2016-01-13 08:19:40Z raasch |
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56 | ! unnecessary calculations of kmzm and kmzp in wall bounded parts removed |
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57 | ! |
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58 | ! 1691 2015-10-26 16:17:44Z maronga |
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59 | ! Formatting corrections. |
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60 | ! |
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61 | ! 1682 2015-10-07 23:56:08Z knoop |
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62 | ! Code annotations made doxygen readable |
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63 | ! |
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64 | ! 1340 2014-03-25 19:45:13Z kanani |
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65 | ! REAL constants defined as wp-kind |
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66 | ! |
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67 | ! 1320 2014-03-20 08:40:49Z raasch |
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68 | ! ONLY-attribute added to USE-statements, |
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69 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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70 | ! kinds are defined in new module kinds, |
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71 | ! revision history before 2012 removed, |
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72 | ! comment fields (!:) to be used for variable explanations added to |
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73 | ! all variable declaration statements |
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74 | ! |
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75 | ! 1257 2013-11-08 15:18:40Z raasch |
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76 | ! openacc loop and loop vector clauses removed, declare create moved after |
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77 | ! the FORTRAN declaration statement |
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78 | ! |
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79 | ! 1128 2013-04-12 06:19:32Z raasch |
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80 | ! loop index bounds in accelerator version replaced by i_left, i_right, j_south, |
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81 | ! j_north |
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82 | ! |
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83 | ! 1036 2012-10-22 13:43:42Z raasch |
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84 | ! code put under GPL (PALM 3.9) |
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85 | ! |
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86 | ! 1015 2012-09-27 09:23:24Z raasch |
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87 | ! accelerator version (*_acc) added |
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88 | ! |
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89 | ! 1001 2012-09-13 14:08:46Z raasch |
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90 | ! arrays comunicated by module instead of parameter list |
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91 | ! |
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92 | ! 978 2012-08-09 08:28:32Z fricke |
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93 | ! outflow damping layer removed |
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94 | ! kmym_x/_y and kmyp_x/_y change to kmym and kmyp |
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95 | ! |
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96 | ! Revision 1.1 1997/09/12 06:23:51 raasch |
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97 | ! Initial revision |
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98 | ! |
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99 | ! |
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100 | ! Description: |
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101 | ! ------------ |
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102 | !> Diffusion term of the u-component |
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103 | !> @todo additional damping (needed for non-cyclic bc) causes bad vectorization |
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104 | !> and slows down the speed on NEC about 5-10% |
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105 | !------------------------------------------------------------------------------! |
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106 | MODULE diffusion_u_mod |
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107 | |
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108 | |
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109 | PRIVATE |
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110 | PUBLIC diffusion_u |
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111 | |
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112 | INTERFACE diffusion_u |
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113 | MODULE PROCEDURE diffusion_u |
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114 | MODULE PROCEDURE diffusion_u_ij |
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115 | END INTERFACE diffusion_u |
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116 | |
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117 | CONTAINS |
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118 | |
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119 | |
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120 | !------------------------------------------------------------------------------! |
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121 | ! Description: |
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122 | ! ------------ |
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123 | !> Call for all grid points |
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124 | !------------------------------------------------------------------------------! |
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125 | SUBROUTINE diffusion_u |
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126 | |
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127 | USE arrays_3d, & |
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128 | ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw |
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129 | |
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130 | USE control_parameters, & |
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131 | ONLY: constant_top_momentumflux, use_surface_fluxes, & |
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132 | use_top_fluxes |
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133 | |
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134 | USE grid_variables, & |
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135 | ONLY: ddx, ddx2, ddy |
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136 | |
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137 | USE indices, & |
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138 | ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzt, wall_flags_0 |
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139 | |
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140 | USE kinds |
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141 | |
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142 | USE surface_mod, & |
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143 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, & |
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144 | surf_usm_v |
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145 | |
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146 | IMPLICIT NONE |
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147 | |
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148 | INTEGER(iwp) :: i !< running index x direction |
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149 | INTEGER(iwp) :: j !< running index y direction |
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150 | INTEGER(iwp) :: k !< running index z direction |
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151 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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152 | INTEGER(iwp) :: m !< running index surface elements |
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153 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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154 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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155 | |
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156 | REAL(wp) :: flag !< flag to mask topography grid points |
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157 | REAL(wp) :: kmym !< |
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158 | REAL(wp) :: kmyp !< |
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159 | REAL(wp) :: kmzm !< |
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160 | REAL(wp) :: kmzp !< |
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161 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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162 | REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point |
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163 | REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point |
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164 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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165 | |
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166 | |
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167 | |
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168 | DO i = nxlu, nxr |
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169 | DO j = nys, nyn |
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170 | ! |
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171 | !-- Compute horizontal diffusion |
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172 | DO k = nzb+1, nzt |
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173 | ! |
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174 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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175 | !-- It is sufficient to masked only north- and south-facing surfaces, which |
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176 | !-- need special treatment for the u-component. |
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177 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) ) |
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178 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) ) |
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179 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) ) |
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180 | ! |
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181 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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182 | kmyp = 0.25_wp * & |
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183 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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184 | kmym = 0.25_wp * & |
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185 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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186 | |
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187 | tend(k,j,i) = tend(k,j,i) & |
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188 | + 2.0_wp * ( & |
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189 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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190 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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191 | ) * ddx2 * flag & |
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192 | + ( mask_north * ( & |
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193 | kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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194 | + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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195 | ) & |
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196 | - mask_south * ( & |
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197 | kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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198 | + kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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199 | ) & |
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200 | ) * ddy * flag |
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201 | ENDDO |
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202 | ! |
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203 | !-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) |
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204 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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205 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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206 | !-- so far. |
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207 | !-- Default-type surfaces |
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208 | DO l = 0, 1 |
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209 | surf_s = surf_def_v(l)%start_index(j,i) |
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210 | surf_e = surf_def_v(l)%end_index(j,i) |
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211 | DO m = surf_s, surf_e |
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212 | k = surf_def_v(l)%k(m) |
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213 | tend(k,j,i) = tend(k,j,i) + & |
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214 | surf_def_v(l)%mom_flux_uv(m) * ddy |
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215 | ENDDO |
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216 | ENDDO |
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217 | ! |
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218 | !-- Natural-type surfaces |
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219 | DO l = 0, 1 |
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220 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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221 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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222 | DO m = surf_s, surf_e |
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223 | k = surf_lsm_v(l)%k(m) |
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224 | tend(k,j,i) = tend(k,j,i) + & |
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225 | surf_lsm_v(l)%mom_flux_uv(m) * ddy |
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226 | ENDDO |
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227 | ENDDO |
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228 | ! |
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229 | !-- Urban-type surfaces |
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230 | DO l = 0, 1 |
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231 | surf_s = surf_usm_v(l)%start_index(j,i) |
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232 | surf_e = surf_usm_v(l)%end_index(j,i) |
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233 | DO m = surf_s, surf_e |
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234 | k = surf_usm_v(l)%k(m) |
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235 | tend(k,j,i) = tend(k,j,i) + & |
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236 | surf_usm_v(l)%mom_flux_uv(m) * ddy |
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237 | ENDDO |
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238 | ENDDO |
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239 | |
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240 | ! |
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241 | !-- Compute vertical diffusion. In case of simulating a surface layer, |
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242 | !-- respective grid diffusive fluxes are masked (flag 8) within this |
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243 | !-- loop, and added further below, else, simple gradient approach is |
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244 | !-- applied. Model top is also mask if top-momentum flux is given. |
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245 | DO k = nzb+1, nzt |
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246 | ! |
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247 | !-- Determine flags to mask topography below and above. Flag 1 is |
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248 | !-- used to mask topography in general, and flag 8 implies |
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249 | !-- information about use_surface_fluxes. Flag 9 is used to control |
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250 | !-- momentum flux at model top. |
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251 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, & |
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252 | BTEST( wall_flags_0(k-1,j,i), 8 ) ) |
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253 | mask_top = MERGE( 1.0_wp, 0.0_wp, & |
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254 | BTEST( wall_flags_0(k+1,j,i), 8 ) ) * & |
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255 | MERGE( 1.0_wp, 0.0_wp, & |
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256 | BTEST( wall_flags_0(k+1,j,i), 9 ) ) |
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257 | flag = MERGE( 1.0_wp, 0.0_wp, & |
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258 | BTEST( wall_flags_0(k,j,i), 1 ) ) |
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259 | ! |
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260 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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261 | kmzp = 0.25_wp * & |
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262 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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263 | kmzm = 0.25_wp * & |
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264 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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265 | |
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266 | tend(k,j,i) = tend(k,j,i) & |
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267 | + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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268 | + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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269 | ) * rho_air_zw(k) * mask_top & |
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270 | - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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271 | + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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272 | ) * rho_air_zw(k-1) * mask_bottom & |
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273 | ) * ddzw(k) * drho_air(k) * flag |
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274 | ENDDO |
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275 | |
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276 | ! |
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277 | !-- Vertical diffusion at the first grid point above the surface, |
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278 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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279 | !-- if it is prescribed by the user. |
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280 | !-- Difference quotient of the momentum flux is not formed over half |
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281 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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282 | !-- with other (LES) models showed that the values of the momentum |
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283 | !-- flux becomes too large in this case. |
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284 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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285 | !-- because the vertical velocity is assumed to be zero at the surface. |
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286 | IF ( use_surface_fluxes ) THEN |
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287 | ! |
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288 | !-- Default-type surfaces, upward-facing |
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289 | surf_s = surf_def_h(0)%start_index(j,i) |
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290 | surf_e = surf_def_h(0)%end_index(j,i) |
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291 | DO m = surf_s, surf_e |
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292 | |
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293 | k = surf_def_h(0)%k(m) |
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294 | |
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295 | tend(k,j,i) = tend(k,j,i) & |
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296 | + ( - ( - surf_def_h(0)%usws(m) ) & |
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297 | ) * ddzw(k) * drho_air(k) |
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298 | ENDDO |
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299 | ! |
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300 | !-- Default-type surfaces, dowward-facing |
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301 | surf_s = surf_def_h(1)%start_index(j,i) |
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302 | surf_e = surf_def_h(1)%end_index(j,i) |
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303 | DO m = surf_s, surf_e |
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304 | |
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305 | k = surf_def_h(1)%k(m) |
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306 | |
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307 | tend(k,j,i) = tend(k,j,i) & |
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308 | + ( - surf_def_h(1)%usws(m) & |
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309 | ) * ddzw(k) * drho_air(k) |
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310 | ENDDO |
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311 | ! |
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312 | !-- Natural-type surfaces, upward-facing |
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313 | surf_s = surf_lsm_h%start_index(j,i) |
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314 | surf_e = surf_lsm_h%end_index(j,i) |
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315 | DO m = surf_s, surf_e |
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316 | |
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317 | k = surf_lsm_h%k(m) |
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318 | |
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319 | tend(k,j,i) = tend(k,j,i) & |
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320 | + ( - ( - surf_lsm_h%usws(m) ) & |
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321 | ) * ddzw(k) * drho_air(k) |
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322 | ENDDO |
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323 | ! |
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324 | !-- Urban-type surfaces, upward-facing |
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325 | surf_s = surf_usm_h%start_index(j,i) |
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326 | surf_e = surf_usm_h%end_index(j,i) |
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327 | DO m = surf_s, surf_e |
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328 | |
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329 | k = surf_usm_h%k(m) |
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330 | |
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331 | tend(k,j,i) = tend(k,j,i) & |
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332 | + ( - ( - surf_usm_h%usws(m) ) & |
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333 | ) * ddzw(k) * drho_air(k) |
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334 | ENDDO |
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335 | |
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336 | ENDIF |
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337 | ! |
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338 | !-- Add momentum flux at model top |
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339 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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340 | surf_s = surf_def_h(2)%start_index(j,i) |
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341 | surf_e = surf_def_h(2)%end_index(j,i) |
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342 | DO m = surf_s, surf_e |
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343 | |
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344 | k = surf_def_h(2)%k(m) |
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345 | |
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346 | tend(k,j,i) = tend(k,j,i) & |
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347 | + ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k) |
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348 | ENDDO |
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349 | ENDIF |
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350 | |
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351 | ENDDO |
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352 | ENDDO |
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353 | |
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354 | END SUBROUTINE diffusion_u |
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355 | |
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356 | |
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357 | !------------------------------------------------------------------------------! |
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358 | ! Description: |
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359 | ! ------------ |
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360 | !> Call for grid point i,j |
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361 | !------------------------------------------------------------------------------! |
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362 | SUBROUTINE diffusion_u_ij( i, j ) |
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363 | |
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364 | USE arrays_3d, & |
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365 | ONLY: ddzu, ddzw, km, tend, u, v, w, drho_air, rho_air_zw |
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366 | |
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367 | USE control_parameters, & |
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368 | ONLY: constant_top_momentumflux, use_surface_fluxes, & |
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369 | use_top_fluxes |
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370 | |
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371 | USE grid_variables, & |
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372 | ONLY: ddx, ddx2, ddy |
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373 | |
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374 | USE indices, & |
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375 | ONLY: nzb, nzt, wall_flags_0 |
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376 | |
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377 | USE kinds |
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378 | |
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379 | USE surface_mod, & |
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380 | ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, & |
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381 | surf_usm_v |
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382 | |
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383 | IMPLICIT NONE |
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384 | |
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385 | INTEGER(iwp) :: i !< running index x direction |
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386 | INTEGER(iwp) :: j !< running index y direction |
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387 | INTEGER(iwp) :: k !< running index z direction |
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388 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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389 | INTEGER(iwp) :: m !< running index surface elements |
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390 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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391 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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392 | |
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393 | REAL(wp) :: flag !< flag to mask topography grid points |
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394 | REAL(wp) :: kmym !< |
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395 | REAL(wp) :: kmyp !< |
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396 | REAL(wp) :: kmzm !< |
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397 | REAL(wp) :: kmzp !< |
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398 | REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface |
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399 | REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point |
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400 | REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point |
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401 | REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface |
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402 | ! |
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403 | !-- Compute horizontal diffusion |
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404 | DO k = nzb+1, nzt |
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405 | ! |
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406 | !-- Predetermine flag to mask topography and wall-bounded grid points. |
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407 | !-- It is sufficient to masked only north- and south-facing surfaces, which |
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408 | !-- need special treatment for the u-component. |
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409 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 1 ) ) |
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410 | mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j-1,i), 1 ) ) |
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411 | mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j+1,i), 1 ) ) |
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412 | ! |
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413 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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414 | 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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415 | 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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416 | |
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417 | tend(k,j,i) = tend(k,j,i) & |
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418 | + 2.0_wp * ( & |
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419 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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420 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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421 | ) * ddx2 * flag & |
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422 | + ( & |
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423 | mask_north * kmyp * ( ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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424 | + ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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425 | ) & |
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426 | - mask_south * kmym * ( ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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427 | + ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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428 | ) & |
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429 | ) * ddy * flag |
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430 | ENDDO |
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431 | |
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432 | ! |
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433 | !-- Add horizontal momentum flux u'v' at north- (l=0) and south-facing (l=1) |
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434 | !-- surfaces. Note, in the the flat case, loops won't be entered as |
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435 | !-- start_index > end_index. Furtermore, note, no vertical natural surfaces |
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436 | !-- so far. |
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437 | !-- Default-type surfaces |
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438 | DO l = 0, 1 |
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439 | surf_s = surf_def_v(l)%start_index(j,i) |
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440 | surf_e = surf_def_v(l)%end_index(j,i) |
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441 | DO m = surf_s, surf_e |
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442 | k = surf_def_v(l)%k(m) |
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443 | tend(k,j,i) = tend(k,j,i) + surf_def_v(l)%mom_flux_uv(m) * ddy |
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444 | ENDDO |
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445 | ENDDO |
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446 | ! |
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447 | !-- Natural-type surfaces |
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448 | DO l = 0, 1 |
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449 | surf_s = surf_lsm_v(l)%start_index(j,i) |
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450 | surf_e = surf_lsm_v(l)%end_index(j,i) |
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451 | DO m = surf_s, surf_e |
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452 | k = surf_lsm_v(l)%k(m) |
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453 | tend(k,j,i) = tend(k,j,i) + surf_lsm_v(l)%mom_flux_uv(m) * ddy |
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454 | ENDDO |
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455 | ENDDO |
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456 | ! |
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457 | !-- Urban-type surfaces |
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458 | DO l = 0, 1 |
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459 | surf_s = surf_usm_v(l)%start_index(j,i) |
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460 | surf_e = surf_usm_v(l)%end_index(j,i) |
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461 | DO m = surf_s, surf_e |
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462 | k = surf_usm_v(l)%k(m) |
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463 | tend(k,j,i) = tend(k,j,i) + surf_usm_v(l)%mom_flux_uv(m) * ddy |
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464 | ENDDO |
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465 | ENDDO |
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466 | ! |
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467 | !-- Compute vertical diffusion. In case of simulating a surface layer, |
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468 | !-- respective grid diffusive fluxes are masked (flag 8) within this |
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469 | !-- loop, and added further below, else, simple gradient approach is |
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470 | !-- applied. Model top is also mask if top-momentum flux is given. |
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471 | DO k = nzb+1, nzt |
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472 | ! |
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473 | !-- Determine flags to mask topography below and above. Flag 1 is |
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474 | !-- used to mask topography in general, and flag 8 implies |
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475 | !-- information about use_surface_fluxes. Flag 9 is used to control |
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476 | !-- momentum flux at model top. |
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477 | mask_bottom = MERGE( 1.0_wp, 0.0_wp, & |
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478 | BTEST( wall_flags_0(k-1,j,i), 8 ) ) |
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479 | mask_top = MERGE( 1.0_wp, 0.0_wp, & |
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480 | BTEST( wall_flags_0(k+1,j,i), 8 ) ) * & |
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481 | MERGE( 1.0_wp, 0.0_wp, & |
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482 | BTEST( wall_flags_0(k+1,j,i), 9 ) ) |
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483 | flag = MERGE( 1.0_wp, 0.0_wp, & |
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484 | BTEST( wall_flags_0(k,j,i), 1 ) ) |
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485 | ! |
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486 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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487 | 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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488 | 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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489 | |
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490 | tend(k,j,i) = tend(k,j,i) & |
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491 | + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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492 | + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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493 | ) * rho_air_zw(k) * mask_top & |
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494 | - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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495 | + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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496 | ) * rho_air_zw(k-1) * mask_bottom & |
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497 | ) * ddzw(k) * drho_air(k) * flag |
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498 | ENDDO |
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499 | |
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500 | ! |
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501 | !-- Vertical diffusion at the first surface grid points, if the |
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502 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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503 | !-- prescribed by the user. |
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504 | !-- Difference quotient of the momentum flux is not formed over half of |
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505 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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506 | !-- other (LES) models showed that the values of the momentum flux becomes |
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507 | !-- too large in this case. |
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508 | IF ( use_surface_fluxes ) THEN |
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509 | ! |
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510 | !-- Default-type surfaces, upward-facing |
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511 | surf_s = surf_def_h(0)%start_index(j,i) |
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512 | surf_e = surf_def_h(0)%end_index(j,i) |
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513 | DO m = surf_s, surf_e |
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514 | |
---|
515 | k = surf_def_h(0)%k(m) |
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516 | |
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517 | tend(k,j,i) = tend(k,j,i) & |
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518 | + ( - ( - surf_def_h(0)%usws(m) ) & |
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519 | ) * ddzw(k) * drho_air(k) |
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520 | ENDDO |
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521 | ! |
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522 | !-- Default-type surfaces, dowward-facing (except for model-top fluxes) |
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523 | surf_s = surf_def_h(1)%start_index(j,i) |
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524 | surf_e = surf_def_h(1)%end_index(j,i) |
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525 | DO m = surf_s, surf_e |
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526 | |
---|
527 | k = surf_def_h(1)%k(m) |
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528 | |
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529 | tend(k,j,i) = tend(k,j,i) & |
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530 | + ( - surf_def_h(1)%usws(m) & |
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531 | ) * ddzw(k) * drho_air(k) |
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532 | ENDDO |
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533 | ! |
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534 | !-- Natural-type surfaces, upward-facing |
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535 | surf_s = surf_lsm_h%start_index(j,i) |
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536 | surf_e = surf_lsm_h%end_index(j,i) |
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537 | DO m = surf_s, surf_e |
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538 | |
---|
539 | k = surf_lsm_h%k(m) |
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540 | |
---|
541 | tend(k,j,i) = tend(k,j,i) & |
---|
542 | + ( - ( - surf_lsm_h%usws(m) ) & |
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543 | ) * ddzw(k) * drho_air(k) |
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544 | ENDDO |
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545 | ! |
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546 | !-- Urban-type surfaces, upward-facing |
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547 | surf_s = surf_usm_h%start_index(j,i) |
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548 | surf_e = surf_usm_h%end_index(j,i) |
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549 | DO m = surf_s, surf_e |
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550 | |
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551 | k = surf_usm_h%k(m) |
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552 | |
---|
553 | tend(k,j,i) = tend(k,j,i) & |
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554 | + ( - ( - surf_usm_h%usws(m) ) & |
---|
555 | ) * ddzw(k) * drho_air(k) |
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556 | ENDDO |
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557 | |
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558 | ENDIF |
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559 | ! |
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560 | !-- Add momentum flux at model top |
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561 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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562 | surf_s = surf_def_h(2)%start_index(j,i) |
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563 | surf_e = surf_def_h(2)%end_index(j,i) |
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564 | DO m = surf_s, surf_e |
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565 | |
---|
566 | k = surf_def_h(2)%k(m) |
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567 | |
---|
568 | tend(k,j,i) = tend(k,j,i) & |
---|
569 | + ( - surf_def_h(2)%usws(m) ) * ddzw(k) * drho_air(k) |
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570 | ENDDO |
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571 | ENDIF |
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572 | |
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573 | |
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574 | END SUBROUTINE diffusion_u_ij |
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575 | |
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576 | END MODULE diffusion_u_mod |
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