1 | !> @file model_1d_mod.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 1997-2019 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: model_1d_mod.f90 3655 2019-01-07 16:51:22Z hellstea $ |
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27 | ! Modularization of all bulk cloud physics code components |
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28 | ! |
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29 | ! 3135 2018-07-16 14:43:04Z gronemeier |
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30 | ! Bugfix: add +1 to c_3 according to Sogachev et al. (2012) |
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31 | ! |
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32 | ! 3126 2018-07-13 15:13:54Z gronemeier |
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33 | ! Bugfix: define c_0 = 0.03^0.25 = 0.416179145 |
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34 | ! |
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35 | ! 3083 2018-06-19 14:03:12Z gronemeier |
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36 | ! Bugfixes: |
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37 | ! - preset te_diss and te_e to avoid runtime errors |
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38 | ! - implementation of buoyancy term to dissipation |
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39 | ! according to Sogachev et al. (2012) |
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40 | ! - where diss_p < 0 set diss_p = 0.1 diss |
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41 | ! - calculate progn eq(diss) starting from nzb+1 |
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42 | ! Changes: |
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43 | ! - add sig_e to TKE equation |
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44 | ! - adjust prognostic equation of diss |
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45 | ! - set model constants according to Koblitz (2013) |
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46 | ! - renamed c_m to c_0 |
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47 | ! - rename l_black into l1d_init |
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48 | ! - calculate l_grid within init_1d_model and save it as l1d_init |
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49 | ! - calculate l1d according to DE85 if dissipation is a prognostic value |
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50 | ! - made annotations doxygen-readable |
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51 | ! |
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52 | ! 3049 2018-05-29 13:52:36Z Giersch |
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53 | ! Error messages revised |
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54 | ! |
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55 | ! 3045 2018-05-28 07:55:41Z Giersch |
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56 | ! Error message revised |
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57 | ! |
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58 | ! 2965 2018-04-13 07:37:25Z scharf |
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59 | ! adjusted format string for 1D run control output |
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60 | ! |
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61 | ! 2918 2018-03-21 15:52:14Z gronemeier |
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62 | ! - rename l_black into l1d_init |
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63 | ! - calculate l_grid within init_1d_model and save it as l1d_init |
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64 | ! |
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65 | ! 2718 2018-01-02 08:49:38Z maronga |
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66 | ! Corrected "Former revisions" section |
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67 | ! |
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68 | ! 2696 2017-12-14 17:12:51Z kanani |
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69 | ! Change in file header (GPL part) |
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70 | ! implement TKE-e closure |
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71 | ! modification of dissipation production according to Detering and Etling |
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72 | ! reduced factor for timestep criterion to 0.125 and first dt to 1s (TG) |
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73 | ! |
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74 | ! 2339 2017-08-07 13:55:26Z gronemeier |
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75 | ! corrected timestamp in header |
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76 | ! |
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77 | ! 2338 2017-08-07 12:15:38Z gronemeier |
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78 | ! renamed init_1d_model to model_1d_mod and and formatted it as a module; |
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79 | ! reformatted output of profiles |
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80 | ! |
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81 | ! 2337 2017-08-07 08:59:53Z gronemeier |
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82 | ! revised calculation of mixing length |
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83 | ! removed rounding of time step |
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84 | ! corrected calculation of virtual potential temperature |
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85 | ! |
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86 | ! 2334 2017-08-04 11:57:04Z gronemeier |
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87 | ! set c_m = 0.4 according to Detering and Etling (1985) |
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88 | ! |
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89 | ! 2299 2017-06-29 10:14:38Z maronga |
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90 | ! Removed german text |
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91 | ! |
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92 | ! 2101 2017-01-05 16:42:31Z suehring |
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93 | ! |
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94 | ! 2059 2016-11-10 14:20:40Z maronga |
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95 | ! Corrected min/max values of Rif. |
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96 | ! |
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97 | ! 2000 2016-08-20 18:09:15Z knoop |
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98 | ! Forced header and separation lines into 80 columns |
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99 | ! |
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100 | ! 1960 2016-07-12 16:34:24Z suehring |
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101 | ! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively |
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102 | ! not used. |
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103 | ! Formatting adjustment |
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104 | ! |
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105 | ! 1808 2016-04-05 19:44:00Z raasch |
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106 | ! routine local_flush replaced by FORTRAN statement |
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107 | ! |
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108 | ! 1709 2015-11-04 14:47:01Z maronga |
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109 | ! Set initial time step to 10 s to avoid instability of the 1d model for small |
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110 | ! grid spacings |
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111 | ! |
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112 | ! 1697 2015-10-28 17:14:10Z raasch |
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113 | ! small E- and F-FORMAT changes to avoid informative compiler messages about |
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114 | ! insufficient field width |
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115 | ! |
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116 | ! 1691 2015-10-26 16:17:44Z maronga |
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117 | ! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta. |
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118 | ! |
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119 | ! 1682 2015-10-07 23:56:08Z knoop |
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120 | ! Code annotations made doxygen readable |
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121 | ! |
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122 | ! 1353 2014-04-08 15:21:23Z heinze |
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123 | ! REAL constants provided with KIND-attribute |
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124 | ! |
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125 | ! 1346 2014-03-27 13:18:20Z heinze |
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126 | ! Bugfix: REAL constants provided with KIND-attribute especially in call of |
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127 | ! intrinsic function like MAX, MIN, SIGN |
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128 | ! |
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129 | ! 1322 2014-03-20 16:38:49Z raasch |
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130 | ! REAL functions provided with KIND-attribute |
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131 | ! |
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132 | ! 1320 2014-03-20 08:40:49Z raasch |
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133 | ! ONLY-attribute added to USE-statements, |
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134 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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135 | ! kinds are defined in new module kinds, |
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136 | ! revision history before 2012 removed, |
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137 | ! comment fields (!:) to be used for variable explanations added to |
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138 | ! all variable declaration statements |
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139 | ! |
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140 | ! 1036 2012-10-22 13:43:42Z raasch |
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141 | ! code put under GPL (PALM 3.9) |
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142 | ! |
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143 | ! 1015 2012-09-27 09:23:24Z raasch |
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144 | ! adjustment of mixing length to the Prandtl mixing length at first grid point |
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145 | ! above ground removed |
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146 | ! |
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147 | ! 1001 2012-09-13 14:08:46Z raasch |
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148 | ! all actions concerning leapfrog scheme removed |
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149 | ! |
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150 | ! 996 2012-09-07 10:41:47Z raasch |
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151 | ! little reformatting |
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152 | ! |
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153 | ! 978 2012-08-09 08:28:32Z fricke |
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154 | ! roughness length for scalar quantities z0h1d added |
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155 | ! |
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156 | ! Revision 1.1 1998/03/09 16:22:10 raasch |
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157 | ! Initial revision |
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158 | ! |
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159 | ! |
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160 | ! Description: |
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161 | ! ------------ |
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162 | !> 1D-model to initialize the 3D-arrays. |
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163 | !> The temperature profile is set as steady and a corresponding steady solution |
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164 | !> of the wind profile is being computed. |
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165 | !> All subroutines required can be found within this file. |
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166 | !> |
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167 | !> @todo harmonize code with new surface_layer_fluxes module |
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168 | !> @bug 1D model crashes when using small grid spacings in the order of 1 m |
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169 | !> @fixme option "as_in_3d_model" seems to be an inappropriate option because |
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170 | !> the 1D model uses different turbulence closure approaches at least if |
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171 | !> the 3D model is set to LES-mode. |
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172 | !------------------------------------------------------------------------------! |
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173 | MODULE model_1d_mod |
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174 | |
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175 | USE arrays_3d, & |
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176 | ONLY: dd2zu, ddzu, ddzw, dzu, dzw, pt_init, q_init, ug, u_init, & |
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177 | vg, v_init, zu |
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178 | |
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179 | USE basic_constants_and_equations_mod, & |
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180 | ONLY: g, kappa, pi |
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181 | |
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182 | USE control_parameters, & |
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183 | ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, & |
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184 | humidity, ibc_e_b, intermediate_timestep_count, & |
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185 | intermediate_timestep_count_max, km_constant, & |
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186 | message_string, mixing_length_1d, prandtl_number, & |
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187 | roughness_length, run_description_header, simulated_time_chr, & |
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188 | timestep_scheme, tsc, z0h_factor |
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189 | |
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190 | USE indices, & |
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191 | ONLY: nzb, nzb_diff, nzt |
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192 | |
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193 | USE kinds |
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194 | |
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195 | USE pegrid, & |
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196 | ONLY: myid |
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197 | |
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198 | |
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199 | IMPLICIT NONE |
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200 | |
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201 | INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model) |
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202 | INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model) |
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203 | |
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204 | LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model) |
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205 | LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model) |
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206 | |
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207 | REAL(wp) :: alpha_buoyancy !< model constant according to Koblitz (2013) |
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208 | REAL(wp) :: c_0 = 0.416179145_wp !< = 0.03^0.25; model constant according to Koblitz (2013) |
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209 | REAL(wp) :: c_1 = 1.52_wp !< model constant according to Koblitz (2013) |
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210 | REAL(wp) :: c_2 = 1.83_wp !< model constant according to Koblitz (2013) |
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211 | REAL(wp) :: c_3 !< model constant |
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212 | REAL(wp) :: c_mu !< model constant |
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213 | REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter |
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214 | REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model) |
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215 | REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model) |
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216 | REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter |
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217 | REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter |
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218 | REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter |
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219 | REAL(wp) :: lambda !< maximum mixing length |
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220 | REAL(wp) :: qs1d !< characteristic humidity scale (1d-model) |
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221 | REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model) |
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222 | REAL(wp) :: sig_diss = 2.95_wp !< model constant according to Koblitz (2013) |
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223 | REAL(wp) :: sig_e = 2.95_wp !< model constant according to Koblitz (2013) |
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224 | REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model) |
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225 | REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model) |
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226 | REAL(wp) :: ts1d !< characteristic temperature scale (1d-model) |
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227 | REAL(wp) :: us1d !< friction velocity (1d-model) |
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228 | REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model) |
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229 | REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model) |
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230 | REAL(wp) :: z01d !< roughness length for momentum (1d-model) |
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231 | REAL(wp) :: z0h1d !< roughness length for scalars (1d-model) |
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232 | |
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233 | REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d !< tke dissipation rate (1d-model) |
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234 | REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d_p !< prognostic value of tke dissipation rate (1d-model) |
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235 | REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model) |
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236 | REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model) |
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237 | REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model) |
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238 | REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model) |
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239 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model) |
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240 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_init !< initial mixing length (1d-model) |
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241 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model) |
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242 | REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model) |
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243 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_diss !< tendency of diss (1d-model) |
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244 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_dissm !< weighted tendency of diss for previous sub-timestep (1d-model) |
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245 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model) |
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246 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model) |
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247 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model) |
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248 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model) |
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249 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model) |
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250 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model) |
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251 | REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model) |
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252 | REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model) |
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253 | REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model) |
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254 | REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model) |
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255 | |
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256 | ! |
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257 | !-- Initialize 1D model |
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258 | INTERFACE init_1d_model |
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259 | MODULE PROCEDURE init_1d_model |
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260 | END INTERFACE init_1d_model |
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261 | |
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262 | ! |
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263 | !-- Print profiles |
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264 | INTERFACE print_1d_model |
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265 | MODULE PROCEDURE print_1d_model |
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266 | END INTERFACE print_1d_model |
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267 | |
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268 | ! |
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269 | !-- Print run control information |
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270 | INTERFACE run_control_1d |
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271 | MODULE PROCEDURE run_control_1d |
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272 | END INTERFACE run_control_1d |
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273 | |
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274 | ! |
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275 | !-- Main procedure |
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276 | INTERFACE time_integration_1d |
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277 | MODULE PROCEDURE time_integration_1d |
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278 | END INTERFACE time_integration_1d |
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279 | |
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280 | ! |
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281 | !-- Calculate time step |
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282 | INTERFACE timestep_1d |
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283 | MODULE PROCEDURE timestep_1d |
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284 | END INTERFACE timestep_1d |
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285 | |
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286 | SAVE |
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287 | |
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288 | PRIVATE |
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289 | ! |
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290 | !-- Public interfaces |
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291 | PUBLIC init_1d_model |
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292 | |
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293 | ! |
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294 | !-- Public variables |
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295 | PUBLIC damp_level_1d, damp_level_ind_1d, diss1d, dt_pr_1d, & |
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296 | dt_run_control_1d, e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, & |
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297 | us1d, usws1d, v1d, vsws1d |
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298 | |
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299 | |
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300 | CONTAINS |
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301 | |
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302 | SUBROUTINE init_1d_model |
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303 | |
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304 | USE grid_variables, & |
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305 | ONLY: dx, dy |
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306 | |
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307 | IMPLICIT NONE |
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308 | |
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309 | CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string |
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310 | |
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311 | INTEGER(iwp) :: k !< loop index |
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312 | |
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313 | ! |
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314 | !-- Allocate required 1D-arrays |
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315 | ALLOCATE( diss1d(nzb:nzt+1), diss1d_p(nzb:nzt+1), & |
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316 | e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), & |
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317 | km1d(nzb:nzt+1), l1d(nzb:nzt+1), l1d_init(nzb:nzt+1), & |
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318 | l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_diss(nzb:nzt+1), & |
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319 | te_dissm(nzb:nzt+1), te_e(nzb:nzt+1), & |
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320 | te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), & |
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321 | te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), & |
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322 | u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) ) |
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323 | |
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324 | ! |
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325 | !-- Initialize arrays |
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326 | IF ( constant_diffusion ) THEN |
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327 | km1d = km_constant |
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328 | kh1d = km_constant / prandtl_number |
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329 | ELSE |
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330 | diss1d = 0.0_wp; diss1d_p = 0.0_wp |
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331 | e1d = 0.0_wp; e1d_p = 0.0_wp |
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332 | kh1d = 0.0_wp; km1d = 0.0_wp |
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333 | rif1d = 0.0_wp |
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334 | ! |
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335 | !-- Compute the mixing length |
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336 | l1d_init(nzb) = 0.0_wp |
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337 | |
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338 | IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN |
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339 | ! |
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340 | !-- Blackadar mixing length |
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341 | IF ( f /= 0.0_wp ) THEN |
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342 | lambda = 2.7E-4_wp * SQRT( ug(nzt+1)**2 + vg(nzt+1)**2 ) / & |
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343 | ABS( f ) + 1E-10_wp |
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344 | ELSE |
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345 | lambda = 30.0_wp |
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346 | ENDIF |
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347 | |
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348 | DO k = nzb+1, nzt+1 |
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349 | l1d_init(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda ) |
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350 | ENDDO |
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351 | |
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352 | ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN |
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353 | ! |
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354 | !-- Use the same mixing length as in 3D model (LES-mode) |
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355 | !> @todo rename (delete?) this option |
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356 | !> As the mixing length is different between RANS and LES mode, it |
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357 | !> must be distinguished here between these modes. For RANS mode, |
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358 | !> the mixing length is calculated accoding to Blackadar, which is |
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359 | !> the other option at this point. |
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360 | !> Maybe delete this option entirely (not appropriate in LES case) |
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361 | !> 2018-03-20, gronemeier |
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362 | DO k = nzb+1, nzt |
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363 | l1d_init(k) = ( dx * dy * dzw(k) )**0.33333333333333_wp |
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364 | ENDDO |
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365 | l1d_init(nzt+1) = l1d_init(nzt) |
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366 | |
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367 | ENDIF |
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368 | ENDIF |
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369 | l1d = l1d_init |
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370 | l1d_diss = l1d_init |
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371 | u1d = u_init |
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372 | u1d_p = u_init |
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373 | v1d = v_init |
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374 | v1d_p = v_init |
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375 | |
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376 | ! |
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377 | !-- Set initial horizontal velocities at the lowest grid levels to a very small |
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378 | !-- value in order to avoid too small time steps caused by the diffusion limit |
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379 | !-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!) |
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380 | u1d(0:1) = 0.1_wp |
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381 | u1d_p(0:1) = 0.1_wp |
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382 | v1d(0:1) = 0.1_wp |
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383 | v1d_p(0:1) = 0.1_wp |
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384 | |
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385 | ! |
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386 | !-- For u*, theta* and the momentum fluxes plausible values are set |
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387 | IF ( constant_flux_layer ) THEN |
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388 | us1d = 0.1_wp ! without initial friction the flow would not change |
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389 | ELSE |
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390 | diss1d(nzb+1) = 0.001_wp |
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391 | e1d(nzb+1) = 1.0_wp |
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392 | km1d(nzb+1) = 1.0_wp |
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393 | us1d = 0.0_wp |
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394 | ENDIF |
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395 | ts1d = 0.0_wp |
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396 | usws1d = 0.0_wp |
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397 | vsws1d = 0.0_wp |
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398 | z01d = roughness_length |
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399 | z0h1d = z0h_factor * z01d |
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400 | IF ( humidity ) qs1d = 0.0_wp |
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401 | |
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402 | ! |
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403 | !-- Tendencies must be preset in order to avoid runtime errors |
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404 | te_diss = 0.0_wp |
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405 | te_dissm = 0.0_wp |
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406 | te_e = 0.0_wp |
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407 | te_em = 0.0_wp |
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408 | te_um = 0.0_wp |
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409 | te_vm = 0.0_wp |
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410 | |
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411 | ! |
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412 | !-- Set model constant |
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413 | IF ( dissipation_1d == 'as_in_3d_model' ) c_0 = 0.1_wp |
---|
414 | c_mu = c_0**4 |
---|
415 | |
---|
416 | ! |
---|
417 | !-- Set start time in hh:mm:ss - format |
---|
418 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
419 | |
---|
420 | ! |
---|
421 | !-- Integrate the 1D-model equations using the Runge-Kutta scheme |
---|
422 | CALL time_integration_1d |
---|
423 | |
---|
424 | |
---|
425 | END SUBROUTINE init_1d_model |
---|
426 | |
---|
427 | |
---|
428 | |
---|
429 | !------------------------------------------------------------------------------! |
---|
430 | ! Description: |
---|
431 | ! ------------ |
---|
432 | !> Runge-Kutta time differencing scheme for the 1D-model. |
---|
433 | !------------------------------------------------------------------------------! |
---|
434 | |
---|
435 | SUBROUTINE time_integration_1d |
---|
436 | |
---|
437 | IMPLICIT NONE |
---|
438 | |
---|
439 | CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string |
---|
440 | |
---|
441 | INTEGER(iwp) :: k !< loop index |
---|
442 | |
---|
443 | REAL(wp) :: a !< auxiliary variable |
---|
444 | REAL(wp) :: b !< auxiliary variable |
---|
445 | REAL(wp) :: dpt_dz !< vertical temperature gradient |
---|
446 | REAL(wp) :: flux !< vertical temperature gradient |
---|
447 | REAL(wp) :: kmzm !< Km(z-dz/2) |
---|
448 | REAL(wp) :: kmzp !< Km(z+dz/2) |
---|
449 | REAL(wp) :: l_stable !< mixing length for stable case |
---|
450 | REAL(wp) :: pt_0 !< reference temperature |
---|
451 | REAL(wp) :: uv_total !< horizontal wind speed |
---|
452 | |
---|
453 | ! |
---|
454 | !-- Determine the time step at the start of a 1D-simulation and |
---|
455 | !-- determine and printout quantities used for run control |
---|
456 | dt_1d = 0.01_wp |
---|
457 | CALL run_control_1d |
---|
458 | |
---|
459 | ! |
---|
460 | !-- Start of time loop |
---|
461 | DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d ) |
---|
462 | |
---|
463 | ! |
---|
464 | !-- Depending on the timestep scheme, carry out one or more intermediate |
---|
465 | !-- timesteps |
---|
466 | |
---|
467 | intermediate_timestep_count = 0 |
---|
468 | DO WHILE ( intermediate_timestep_count < & |
---|
469 | intermediate_timestep_count_max ) |
---|
470 | |
---|
471 | intermediate_timestep_count = intermediate_timestep_count + 1 |
---|
472 | |
---|
473 | CALL timestep_scheme_steering |
---|
474 | |
---|
475 | ! |
---|
476 | !-- Compute all tendency terms. If a constant-flux layer is simulated, |
---|
477 | !-- k starts at nzb+2. |
---|
478 | DO k = nzb_diff, nzt |
---|
479 | |
---|
480 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
481 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
482 | ! |
---|
483 | !-- u-component |
---|
484 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
---|
485 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) & |
---|
486 | - kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) & |
---|
487 | ) * ddzw(k) |
---|
488 | ! |
---|
489 | !-- v-component |
---|
490 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
---|
491 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) & |
---|
492 | - kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) & |
---|
493 | ) * ddzw(k) |
---|
494 | ENDDO |
---|
495 | IF ( .NOT. constant_diffusion ) THEN |
---|
496 | DO k = nzb_diff, nzt |
---|
497 | ! |
---|
498 | !-- TKE and dissipation rate |
---|
499 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
500 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
501 | IF ( .NOT. humidity ) THEN |
---|
502 | pt_0 = pt_init(k) |
---|
503 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
---|
504 | ELSE |
---|
505 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
506 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
---|
507 | 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & |
---|
508 | pt_init(k-1) * q_init(k-1) ) & |
---|
509 | ) * dd2zu(k) |
---|
510 | ENDIF |
---|
511 | |
---|
512 | ! |
---|
513 | !-- Calculate dissipation rate if no prognostic equation is used for |
---|
514 | !-- dissipation rate |
---|
515 | IF ( dissipation_1d == 'detering' ) THEN |
---|
516 | diss1d(k) = c_0**3 * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
517 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
---|
518 | diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) & |
---|
519 | ) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
520 | ENDIF |
---|
521 | ! |
---|
522 | !-- TKE |
---|
523 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
---|
524 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
---|
525 | ) & |
---|
526 | - g / pt_0 * kh1d(k) * flux & |
---|
527 | + ( & |
---|
528 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
---|
529 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
---|
530 | ) * ddzw(k) / sig_e & |
---|
531 | - diss1d(k) |
---|
532 | |
---|
533 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
534 | ! |
---|
535 | !-- dissipation rate |
---|
536 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
537 | alpha_buoyancy = 1.0_wp - l1d(k) / lambda |
---|
538 | ELSE |
---|
539 | alpha_buoyancy = 1.0_wp - ( 1.0_wp + ( c_2 - 1.0_wp ) & |
---|
540 | / ( c_2 - c_1 ) ) & |
---|
541 | * l1d(k) / lambda |
---|
542 | ENDIF |
---|
543 | c_3 = ( c_1 - c_2 ) * alpha_buoyancy + 1.0_wp |
---|
544 | te_diss(k) = ( km1d(k) * & |
---|
545 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
546 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
547 | ) * ( c_1 + (c_2 - c_1) * l1d(k) / lambda ) & |
---|
548 | - g / pt_0 * kh1d(k) * flux * c_3 & |
---|
549 | - c_2 * diss1d(k) & |
---|
550 | ) * diss1d(k) / ( e1d(k) + 1.0E-20_wp ) & |
---|
551 | + ( kmzp * ( diss1d(k+1) - diss1d(k) ) & |
---|
552 | * ddzu(k+1) & |
---|
553 | - kmzm * ( diss1d(k) - diss1d(k-1) ) & |
---|
554 | * ddzu(k) & |
---|
555 | ) * ddzw(k) / sig_diss |
---|
556 | |
---|
557 | ENDIF |
---|
558 | |
---|
559 | ENDDO |
---|
560 | ENDIF |
---|
561 | |
---|
562 | ! |
---|
563 | !-- Tendency terms at the top of the constant-flux layer. |
---|
564 | !-- Finite differences of the momentum fluxes are computed using half the |
---|
565 | !-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy |
---|
566 | IF ( constant_flux_layer ) THEN |
---|
567 | |
---|
568 | k = nzb+1 |
---|
569 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
570 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
571 | IF ( .NOT. humidity ) THEN |
---|
572 | pt_0 = pt_init(k) |
---|
573 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
---|
574 | ELSE |
---|
575 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
576 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
---|
577 | 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & |
---|
578 | pt_init(k-1) * q_init(k-1) ) & |
---|
579 | ) * dd2zu(k) |
---|
580 | ENDIF |
---|
581 | |
---|
582 | ! |
---|
583 | !-- Calculate dissipation rate if no prognostic equation is used for |
---|
584 | !-- dissipation rate |
---|
585 | IF ( dissipation_1d == 'detering' ) THEN |
---|
586 | diss1d(k) = c_0**3 * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
587 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
---|
588 | diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) ) & |
---|
589 | * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
590 | ENDIF |
---|
591 | |
---|
592 | ! |
---|
593 | !-- u-component |
---|
594 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
---|
595 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d & |
---|
596 | ) * 2.0_wp * ddzw(k) |
---|
597 | ! |
---|
598 | !-- v-component |
---|
599 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
---|
600 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d & |
---|
601 | ) * 2.0_wp * ddzw(k) |
---|
602 | ! |
---|
603 | !-- TKE |
---|
604 | IF ( .NOT. dissipation_1d == 'prognostic' ) THEN |
---|
605 | !> @query why integrate over 2dz |
---|
606 | !> Why is it allowed to integrate over two delta-z for e |
---|
607 | !> while for u and v it is not? |
---|
608 | !> 2018-04-23, gronemeier |
---|
609 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
---|
610 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
---|
611 | ) & |
---|
612 | - g / pt_0 * kh1d(k) * flux & |
---|
613 | + ( & |
---|
614 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
---|
615 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
---|
616 | ) * ddzw(k) / sig_e & |
---|
617 | - diss1d(k) |
---|
618 | ENDIF |
---|
619 | |
---|
620 | ENDIF |
---|
621 | |
---|
622 | ! |
---|
623 | !-- Prognostic equations for all 1D variables |
---|
624 | DO k = nzb+1, nzt |
---|
625 | |
---|
626 | u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + & |
---|
627 | tsc(3) * te_um(k) ) |
---|
628 | v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + & |
---|
629 | tsc(3) * te_vm(k) ) |
---|
630 | |
---|
631 | ENDDO |
---|
632 | IF ( .NOT. constant_diffusion ) THEN |
---|
633 | |
---|
634 | DO k = nzb+1, nzt |
---|
635 | e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + & |
---|
636 | tsc(3) * te_em(k) ) |
---|
637 | ENDDO |
---|
638 | |
---|
639 | ! |
---|
640 | !-- Eliminate negative TKE values, which can result from the |
---|
641 | !-- integration due to numerical inaccuracies. In such cases the TKE |
---|
642 | !-- value is reduced to 10 percent of its old value. |
---|
643 | WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d |
---|
644 | |
---|
645 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
646 | DO k = nzb+1, nzt |
---|
647 | diss1d_p(k) = diss1d(k) + dt_1d * ( tsc(2) * te_diss(k) + & |
---|
648 | tsc(3) * te_dissm(k) ) |
---|
649 | ENDDO |
---|
650 | WHERE ( diss1d_p < 0.0_wp ) diss1d_p = 0.1_wp * diss1d |
---|
651 | ENDIF |
---|
652 | ENDIF |
---|
653 | |
---|
654 | ! |
---|
655 | !-- Calculate tendencies for the next Runge-Kutta step |
---|
656 | IF ( timestep_scheme(1:5) == 'runge' ) THEN |
---|
657 | IF ( intermediate_timestep_count == 1 ) THEN |
---|
658 | |
---|
659 | DO k = nzb+1, nzt |
---|
660 | te_um(k) = te_u(k) |
---|
661 | te_vm(k) = te_v(k) |
---|
662 | ENDDO |
---|
663 | |
---|
664 | IF ( .NOT. constant_diffusion ) THEN |
---|
665 | DO k = nzb+1, nzt |
---|
666 | te_em(k) = te_e(k) |
---|
667 | ENDDO |
---|
668 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
669 | DO k = nzb+1, nzt |
---|
670 | te_dissm(k) = te_diss(k) |
---|
671 | ENDDO |
---|
672 | ENDIF |
---|
673 | ENDIF |
---|
674 | |
---|
675 | ELSEIF ( intermediate_timestep_count < & |
---|
676 | intermediate_timestep_count_max ) THEN |
---|
677 | |
---|
678 | DO k = nzb+1, nzt |
---|
679 | te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k) |
---|
680 | te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k) |
---|
681 | ENDDO |
---|
682 | |
---|
683 | IF ( .NOT. constant_diffusion ) THEN |
---|
684 | DO k = nzb+1, nzt |
---|
685 | te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k) |
---|
686 | ENDDO |
---|
687 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
688 | DO k = nzb+1, nzt |
---|
689 | te_dissm(k) = -9.5625_wp * te_diss(k) & |
---|
690 | + 5.3125_wp * te_dissm(k) |
---|
691 | ENDDO |
---|
692 | ENDIF |
---|
693 | ENDIF |
---|
694 | |
---|
695 | ENDIF |
---|
696 | ENDIF |
---|
697 | |
---|
698 | ! |
---|
699 | !-- Boundary conditions for the prognostic variables. |
---|
700 | !-- At the top boundary (nzt+1) u, v, e, and diss keep their initial |
---|
701 | !-- values (ug(nzt+1), vg(nzt+1), 0, 0). |
---|
702 | !-- At the bottom boundary, Dirichlet condition is used for u and v (0) |
---|
703 | !-- and Neumann condition for e and diss (e(nzb)=e(nzb+1)). |
---|
704 | u1d_p(nzb) = 0.0_wp |
---|
705 | v1d_p(nzb) = 0.0_wp |
---|
706 | |
---|
707 | ! |
---|
708 | !-- Swap the time levels in preparation for the next time step. |
---|
709 | u1d = u1d_p |
---|
710 | v1d = v1d_p |
---|
711 | IF ( .NOT. constant_diffusion ) THEN |
---|
712 | e1d = e1d_p |
---|
713 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
714 | diss1d = diss1d_p |
---|
715 | ENDIF |
---|
716 | ENDIF |
---|
717 | |
---|
718 | ! |
---|
719 | !-- Compute diffusion quantities |
---|
720 | IF ( .NOT. constant_diffusion ) THEN |
---|
721 | |
---|
722 | ! |
---|
723 | !-- First compute the vertical fluxes in the constant-flux layer |
---|
724 | IF ( constant_flux_layer ) THEN |
---|
725 | ! |
---|
726 | !-- Compute theta* using Rif numbers of the previous time step |
---|
727 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
728 | ! |
---|
729 | !-- Stable stratification |
---|
730 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
731 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
732 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
733 | ) |
---|
734 | ELSE |
---|
735 | ! |
---|
736 | !-- Unstable stratification |
---|
737 | a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) |
---|
738 | b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
739 | zu(nzb+1) * z0h1d ) |
---|
740 | |
---|
741 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
742 | LOG( (a-1.0_wp) / (a+1.0_wp) * & |
---|
743 | (b+1.0_wp) / (b-1.0_wp) ) |
---|
744 | ENDIF |
---|
745 | |
---|
746 | ENDIF ! constant_flux_layer |
---|
747 | !> @todo combine if clauses |
---|
748 | !> The previous and following if clauses can be combined into a |
---|
749 | !> single clause |
---|
750 | !> 2018-04-23, gronemeier |
---|
751 | ! |
---|
752 | !-- Compute the Richardson-flux numbers, |
---|
753 | !-- first at the top of the constant-flux layer using u* of the |
---|
754 | !-- previous time step (+1E-30, if u* = 0), then in the remaining area. |
---|
755 | !-- There the rif-numbers of the previous time step are used. |
---|
756 | |
---|
757 | IF ( constant_flux_layer ) THEN |
---|
758 | IF ( .NOT. humidity ) THEN |
---|
759 | pt_0 = pt_init(nzb+1) |
---|
760 | flux = ts1d |
---|
761 | ELSE |
---|
762 | pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) ) |
---|
763 | flux = ts1d + 0.61_wp * pt_init(k) * qs1d |
---|
764 | ENDIF |
---|
765 | rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / & |
---|
766 | ( pt_0 * ( us1d**2 + 1E-30_wp ) ) |
---|
767 | ENDIF |
---|
768 | |
---|
769 | DO k = nzb_diff, nzt |
---|
770 | IF ( .NOT. humidity ) THEN |
---|
771 | pt_0 = pt_init(k) |
---|
772 | flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
773 | ELSE |
---|
774 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
775 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) & |
---|
776 | + 0.61_wp & |
---|
777 | * ( pt_init(k+1) * q_init(k+1) & |
---|
778 | - pt_init(k-1) * q_init(k-1) ) & |
---|
779 | ) * dd2zu(k) |
---|
780 | ENDIF |
---|
781 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
782 | rif1d(k) = g / pt_0 * flux / & |
---|
783 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
784 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
785 | + 1E-30_wp & |
---|
786 | ) |
---|
787 | ELSE |
---|
788 | rif1d(k) = g / pt_0 * flux / & |
---|
789 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
790 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
791 | + 1E-30_wp & |
---|
792 | ) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp |
---|
793 | ENDIF |
---|
794 | ENDDO |
---|
795 | ! |
---|
796 | !-- Richardson-numbers must remain restricted to a realistic value |
---|
797 | !-- range. It is exceeded excessively for very small velocities |
---|
798 | !-- (u,v --> 0). |
---|
799 | WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp |
---|
800 | WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp |
---|
801 | |
---|
802 | ! |
---|
803 | !-- Compute u* from the absolute velocity value |
---|
804 | IF ( constant_flux_layer ) THEN |
---|
805 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
806 | |
---|
807 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
808 | ! |
---|
809 | !-- Stable stratification |
---|
810 | us1d = kappa * uv_total / ( & |
---|
811 | LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
812 | ( zu(nzb+1) - z01d ) / zu(nzb+1) & |
---|
813 | ) |
---|
814 | ELSE |
---|
815 | ! |
---|
816 | !-- Unstable stratification |
---|
817 | a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) ) |
---|
818 | b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
819 | zu(nzb+1) * z01d ) ) |
---|
820 | us1d = kappa * uv_total / ( & |
---|
821 | LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / & |
---|
822 | (1.0_wp+a) ) + & |
---|
823 | 2.0_wp * ( ATAN( b ) - ATAN( a ) ) & |
---|
824 | ) |
---|
825 | ENDIF |
---|
826 | |
---|
827 | ! |
---|
828 | !-- Compute the momentum fluxes for the diffusion terms |
---|
829 | usws1d = - u1d(nzb+1) / uv_total * us1d**2 |
---|
830 | vsws1d = - v1d(nzb+1) / uv_total * us1d**2 |
---|
831 | |
---|
832 | ! |
---|
833 | !-- Boundary condition for the turbulent kinetic energy and |
---|
834 | !-- dissipation rate at the top of the constant-flux layer. |
---|
835 | !-- Additional Neumann condition de/dz = 0 at nzb is set to ensure |
---|
836 | !-- compatibility with the 3D model. |
---|
837 | IF ( ibc_e_b == 2 ) THEN |
---|
838 | e1d(nzb+1) = ( us1d / c_0 )**2 |
---|
839 | ENDIF |
---|
840 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
841 | e1d(nzb+1) = ( us1d / c_0 )**2 |
---|
842 | diss1d(nzb+1) = us1d**3 / ( kappa * zu(nzb+1) ) |
---|
843 | diss1d(nzb) = diss1d(nzb+1) |
---|
844 | ENDIF |
---|
845 | e1d(nzb) = e1d(nzb+1) |
---|
846 | |
---|
847 | IF ( humidity ) THEN |
---|
848 | ! |
---|
849 | !-- Compute q* |
---|
850 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
851 | ! |
---|
852 | !-- Stable stratification |
---|
853 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
854 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
855 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
856 | ) |
---|
857 | ELSE |
---|
858 | ! |
---|
859 | !-- Unstable stratification |
---|
860 | a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) |
---|
861 | b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
862 | zu(nzb+1) * z0h1d ) |
---|
863 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
864 | LOG( (a-1.0_wp) / (a+1.0_wp) * & |
---|
865 | (b+1.0_wp) / (b-1.0_wp) ) |
---|
866 | ENDIF |
---|
867 | ELSE |
---|
868 | qs1d = 0.0_wp |
---|
869 | ENDIF |
---|
870 | |
---|
871 | ENDIF ! constant_flux_layer |
---|
872 | |
---|
873 | ! |
---|
874 | !-- Compute the diabatic mixing length. The unstable stratification |
---|
875 | !-- must not be considered for l1d (km1d) as it is already considered |
---|
876 | !-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be |
---|
877 | !-- too large. |
---|
878 | IF ( dissipation_1d /= 'prognostic' ) THEN |
---|
879 | IF ( mixing_length_1d == 'blackadar' ) THEN |
---|
880 | DO k = nzb+1, nzt |
---|
881 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
882 | l1d(k) = l1d_init(k) / ( 1.0_wp + 5.0_wp * rif1d(k) ) |
---|
883 | l1d_diss(k) = l1d(k) |
---|
884 | ELSE |
---|
885 | l1d(k) = l1d_init(k) |
---|
886 | l1d_diss(k) = l1d_init(k) * & |
---|
887 | SQRT( 1.0_wp - 16.0_wp * rif1d(k) ) |
---|
888 | ENDIF |
---|
889 | ENDDO |
---|
890 | ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN |
---|
891 | DO k = nzb+1, nzt |
---|
892 | dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
893 | IF ( dpt_dz > 0.0_wp ) THEN |
---|
894 | l_stable = 0.76_wp * SQRT( e1d(k) ) & |
---|
895 | / SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp |
---|
896 | ELSE |
---|
897 | l_stable = l1d_init(k) |
---|
898 | ENDIF |
---|
899 | l1d(k) = MIN( l1d_init(k), l_stable ) |
---|
900 | l1d_diss(k) = l1d(k) |
---|
901 | ENDDO |
---|
902 | ENDIF |
---|
903 | ELSE |
---|
904 | DO k = nzb+1, nzt |
---|
905 | l1d(k) = c_0**3 * e1d(k) * SQRT( e1d(k) ) & |
---|
906 | / ( diss1d(k) + 1.0E-30_wp ) |
---|
907 | ENDDO |
---|
908 | ENDIF |
---|
909 | |
---|
910 | ! |
---|
911 | !-- Compute the diffusion coefficients for momentum via the |
---|
912 | !-- corresponding Prandtl-layer relationship and according to |
---|
913 | !-- Prandtl-Kolmogorov, respectively |
---|
914 | IF ( constant_flux_layer ) THEN |
---|
915 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
916 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) / & |
---|
917 | ( 1.0_wp + 5.0_wp * rif1d(nzb+1) ) |
---|
918 | ELSE |
---|
919 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) * & |
---|
920 | ( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp |
---|
921 | ENDIF |
---|
922 | ENDIF |
---|
923 | |
---|
924 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
925 | DO k = nzb_diff, nzt |
---|
926 | km1d(k) = c_mu * e1d(k)**2 / ( diss1d(k) + 1.0E-30_wp ) |
---|
927 | ENDDO |
---|
928 | ELSE |
---|
929 | DO k = nzb_diff, nzt |
---|
930 | km1d(k) = c_0 * SQRT( e1d(k) ) * l1d(k) |
---|
931 | ENDDO |
---|
932 | ENDIF |
---|
933 | |
---|
934 | ! |
---|
935 | !-- Add damping layer |
---|
936 | DO k = damp_level_ind_1d+1, nzt+1 |
---|
937 | km1d(k) = 1.1_wp * km1d(k-1) |
---|
938 | km1d(k) = MIN( km1d(k), 10.0_wp ) |
---|
939 | ENDDO |
---|
940 | |
---|
941 | ! |
---|
942 | !-- Compute the diffusion coefficient for heat via the relationship |
---|
943 | !-- kh = phim / phih * km |
---|
944 | DO k = nzb+1, nzt |
---|
945 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
946 | kh1d(k) = km1d(k) |
---|
947 | ELSE |
---|
948 | kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp |
---|
949 | ENDIF |
---|
950 | ENDDO |
---|
951 | |
---|
952 | ENDIF ! .NOT. constant_diffusion |
---|
953 | |
---|
954 | ENDDO ! intermediate step loop |
---|
955 | |
---|
956 | ! |
---|
957 | !-- Increment simulated time and output times |
---|
958 | current_timestep_number_1d = current_timestep_number_1d + 1 |
---|
959 | simulated_time_1d = simulated_time_1d + dt_1d |
---|
960 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
961 | time_pr_1d = time_pr_1d + dt_1d |
---|
962 | time_run_control_1d = time_run_control_1d + dt_1d |
---|
963 | |
---|
964 | ! |
---|
965 | !-- Determine and print out quantities for run control |
---|
966 | IF ( time_run_control_1d >= dt_run_control_1d ) THEN |
---|
967 | CALL run_control_1d |
---|
968 | time_run_control_1d = time_run_control_1d - dt_run_control_1d |
---|
969 | ENDIF |
---|
970 | |
---|
971 | ! |
---|
972 | !-- Profile output on file |
---|
973 | IF ( time_pr_1d >= dt_pr_1d ) THEN |
---|
974 | CALL print_1d_model |
---|
975 | time_pr_1d = time_pr_1d - dt_pr_1d |
---|
976 | ENDIF |
---|
977 | |
---|
978 | ! |
---|
979 | !-- Determine size of next time step |
---|
980 | CALL timestep_1d |
---|
981 | |
---|
982 | ENDDO ! time loop |
---|
983 | |
---|
984 | |
---|
985 | END SUBROUTINE time_integration_1d |
---|
986 | |
---|
987 | |
---|
988 | !------------------------------------------------------------------------------! |
---|
989 | ! Description: |
---|
990 | ! ------------ |
---|
991 | !> Compute and print out quantities for run control of the 1D model. |
---|
992 | !------------------------------------------------------------------------------! |
---|
993 | |
---|
994 | SUBROUTINE run_control_1d |
---|
995 | |
---|
996 | |
---|
997 | IMPLICIT NONE |
---|
998 | |
---|
999 | INTEGER(iwp) :: k !< loop index |
---|
1000 | |
---|
1001 | REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer |
---|
1002 | REAL(wp) :: energy !< kinetic energy |
---|
1003 | REAL(wp) :: umax !< maximum of u |
---|
1004 | REAL(wp) :: uv_total !< horizontal wind speed |
---|
1005 | REAL(wp) :: vmax !< maximum of v |
---|
1006 | |
---|
1007 | ! |
---|
1008 | !-- Output |
---|
1009 | IF ( myid == 0 ) THEN |
---|
1010 | ! |
---|
1011 | !-- If necessary, write header |
---|
1012 | IF ( .NOT. run_control_header_1d ) THEN |
---|
1013 | CALL check_open( 15 ) |
---|
1014 | WRITE ( 15, 100 ) |
---|
1015 | run_control_header_1d = .TRUE. |
---|
1016 | ENDIF |
---|
1017 | |
---|
1018 | ! |
---|
1019 | !-- Compute control quantities |
---|
1020 | !-- grid level nzp is excluded due to mirror boundary condition |
---|
1021 | umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp |
---|
1022 | DO k = nzb+1, nzt+1 |
---|
1023 | umax = MAX( ABS( umax ), ABS( u1d(k) ) ) |
---|
1024 | vmax = MAX( ABS( vmax ), ABS( v1d(k) ) ) |
---|
1025 | energy = energy + 0.5_wp * ( u1d(k)**2 + v1d(k)**2 ) |
---|
1026 | ENDDO |
---|
1027 | energy = energy / REAL( nzt - nzb + 1, KIND=wp ) |
---|
1028 | |
---|
1029 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
1030 | IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN |
---|
1031 | alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) ) |
---|
1032 | ELSE |
---|
1033 | alpha = ACOS( u1d(nzb+1) / uv_total ) |
---|
1034 | IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha |
---|
1035 | ENDIF |
---|
1036 | alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp |
---|
1037 | |
---|
1038 | WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, & |
---|
1039 | dt_1d, umax, vmax, us1d, alpha, energy |
---|
1040 | ! |
---|
1041 | !-- Write buffer contents to disc immediately |
---|
1042 | FLUSH( 15 ) |
---|
1043 | |
---|
1044 | ENDIF |
---|
1045 | |
---|
1046 | ! |
---|
1047 | !-- formats |
---|
1048 | 100 FORMAT (///'1D run control output:'/ & |
---|
1049 | &'------------------------------'// & |
---|
1050 | &'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ & |
---|
1051 | &'-------------------------------------------------------------') |
---|
1052 | 101 FORMAT (I7,1X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2) |
---|
1053 | |
---|
1054 | |
---|
1055 | END SUBROUTINE run_control_1d |
---|
1056 | |
---|
1057 | |
---|
1058 | |
---|
1059 | !------------------------------------------------------------------------------! |
---|
1060 | ! Description: |
---|
1061 | ! ------------ |
---|
1062 | !> Compute the time step w.r.t. the diffusion criterion |
---|
1063 | !------------------------------------------------------------------------------! |
---|
1064 | |
---|
1065 | SUBROUTINE timestep_1d |
---|
1066 | |
---|
1067 | IMPLICIT NONE |
---|
1068 | |
---|
1069 | INTEGER(iwp) :: k !< loop index |
---|
1070 | |
---|
1071 | REAL(wp) :: dt_diff !< time step accorind to diffusion criterion |
---|
1072 | REAL(wp) :: dt_old !< previous time step |
---|
1073 | REAL(wp) :: fac !< factor of criterion |
---|
1074 | REAL(wp) :: value !< auxiliary variable |
---|
1075 | |
---|
1076 | ! |
---|
1077 | !-- Save previous time step |
---|
1078 | dt_old = dt_1d |
---|
1079 | |
---|
1080 | ! |
---|
1081 | !-- Compute the currently feasible time step according to the diffusion |
---|
1082 | !-- criterion. At nzb+1 the half grid length is used. |
---|
1083 | fac = 0.125 |
---|
1084 | dt_diff = dt_max_1d |
---|
1085 | DO k = nzb+2, nzt |
---|
1086 | value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp ) |
---|
1087 | dt_diff = MIN( value, dt_diff ) |
---|
1088 | ENDDO |
---|
1089 | value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp ) |
---|
1090 | dt_1d = MIN( value, dt_diff ) |
---|
1091 | |
---|
1092 | ! |
---|
1093 | !-- Limit the new time step to a maximum of 10 times the previous time step |
---|
1094 | dt_1d = MIN( dt_old * 10.0_wp, dt_1d ) |
---|
1095 | |
---|
1096 | ! |
---|
1097 | !-- Set flag when the time step becomes too small |
---|
1098 | IF ( dt_1d < ( 1.0E-15_wp * dt_max_1d ) ) THEN |
---|
1099 | stop_dt_1d = .TRUE. |
---|
1100 | |
---|
1101 | WRITE( message_string, * ) 'timestep has exceeded the lower limit&', & |
---|
1102 | 'dt_1d = ',dt_1d,' s simulation stopped!' |
---|
1103 | CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 ) |
---|
1104 | |
---|
1105 | ENDIF |
---|
1106 | |
---|
1107 | END SUBROUTINE timestep_1d |
---|
1108 | |
---|
1109 | |
---|
1110 | |
---|
1111 | !------------------------------------------------------------------------------! |
---|
1112 | ! Description: |
---|
1113 | ! ------------ |
---|
1114 | !> List output of profiles from the 1D-model |
---|
1115 | !------------------------------------------------------------------------------! |
---|
1116 | |
---|
1117 | SUBROUTINE print_1d_model |
---|
1118 | |
---|
1119 | IMPLICIT NONE |
---|
1120 | |
---|
1121 | INTEGER(iwp) :: k !< loop parameter |
---|
1122 | |
---|
1123 | LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header |
---|
1124 | |
---|
1125 | |
---|
1126 | IF ( myid == 0 ) THEN |
---|
1127 | ! |
---|
1128 | !-- Open list output file for profiles from the 1D-model |
---|
1129 | CALL check_open( 17 ) |
---|
1130 | |
---|
1131 | ! |
---|
1132 | !-- Write Header |
---|
1133 | IF ( write_first ) THEN |
---|
1134 | WRITE ( 17, 100 ) TRIM( run_description_header ) |
---|
1135 | write_first = .FALSE. |
---|
1136 | ENDIF |
---|
1137 | |
---|
1138 | ! |
---|
1139 | !-- Write the values |
---|
1140 | WRITE ( 17, 104 ) TRIM( simulated_time_chr ) |
---|
1141 | WRITE ( 17, 101 ) |
---|
1142 | WRITE ( 17, 102 ) |
---|
1143 | WRITE ( 17, 101 ) |
---|
1144 | DO k = nzt+1, nzb, -1 |
---|
1145 | WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), & |
---|
1146 | rif1d(k), km1d(k), kh1d(k), l1d(k), diss1d(k) |
---|
1147 | ENDDO |
---|
1148 | WRITE ( 17, 101 ) |
---|
1149 | WRITE ( 17, 102 ) |
---|
1150 | WRITE ( 17, 101 ) |
---|
1151 | |
---|
1152 | ! |
---|
1153 | !-- Write buffer contents to disc immediately |
---|
1154 | FLUSH( 17 ) |
---|
1155 | |
---|
1156 | ENDIF |
---|
1157 | |
---|
1158 | ! |
---|
1159 | !-- Formats |
---|
1160 | 100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles') |
---|
1161 | 104 FORMAT (//'# Time: ',A) |
---|
1162 | 101 FORMAT ('#',111('-')) |
---|
1163 | 102 FORMAT ('# k zu u v pt e ', & |
---|
1164 | 'rif Km Kh l diss ') |
---|
1165 | 103 FORMAT (1X,I4,1X,F7.1,9(1X,E10.3)) |
---|
1166 | |
---|
1167 | |
---|
1168 | END SUBROUTINE print_1d_model |
---|
1169 | |
---|
1170 | |
---|
1171 | END MODULE |
---|