1 | SUBROUTINE init_1d_model |
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2 | |
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3 | !--------------------------------------------------------------------------------! |
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4 | ! This file is part of PALM. |
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5 | ! |
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6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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8 | ! either version 3 of the License, or (at your option) any later 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 1997-2014 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 | ! ONLY-attribute added to USE-statements, |
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23 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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24 | ! kinds are defined in new module kinds, |
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25 | ! old module precision_kind is removed, |
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26 | ! revision history before 2012 removed, |
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27 | ! comment fields (!:) to be used for variable explanations added to |
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28 | ! all variable declaration statements |
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29 | ! |
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30 | ! Former revisions: |
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31 | ! ----------------- |
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32 | ! $Id: init_1d_model.f90 1320 2014-03-20 08:40:49Z raasch $ |
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33 | ! |
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34 | ! 1036 2012-10-22 13:43:42Z raasch |
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35 | ! code put under GPL (PALM 3.9) |
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36 | ! |
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37 | ! 1015 2012-09-27 09:23:24Z raasch |
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38 | ! adjustment of mixing length to the Prandtl mixing length at first grid point |
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39 | ! above ground removed |
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40 | ! |
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41 | ! 1001 2012-09-13 14:08:46Z raasch |
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42 | ! all actions concerning leapfrog scheme removed |
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43 | ! |
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44 | ! 996 2012-09-07 10:41:47Z raasch |
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45 | ! little reformatting |
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46 | ! |
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47 | ! 978 2012-08-09 08:28:32Z fricke |
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48 | ! roughness length for scalar quantities z0h1d added |
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49 | ! |
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50 | ! Revision 1.1 1998/03/09 16:22:10 raasch |
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51 | ! Initial revision |
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52 | ! |
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53 | ! |
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54 | ! Description: |
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55 | ! ------------ |
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56 | ! 1D-model to initialize the 3D-arrays. |
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57 | ! The temperature profile is set as steady and a corresponding steady solution |
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58 | ! of the wind profile is being computed. |
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59 | ! All subroutines required can be found within this file. |
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60 | !------------------------------------------------------------------------------! |
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61 | |
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62 | USE arrays_3d, & |
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63 | ONLY: l_grid, ug, u_init, vg, v_init, zu |
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64 | |
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65 | USE indices, & |
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66 | ONLY: nzb, nzt |
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67 | |
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68 | USE kinds |
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69 | |
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70 | USE model_1d, & |
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71 | ONLY: e1d, e1d_p, kh1d, km1d, l1d, l_black, qs1d, rif1d, & |
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72 | simulated_time_1d, te_e, te_em, te_u, te_um, te_v, te_vm, ts1d, & |
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73 | u1d, u1d_p, us1d, usws1d, v1d, v1d_p, vsws1d, z01d, z0h1d |
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74 | |
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75 | USE control_parameters, & |
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76 | ONLY: constant_diffusion, f, humidity, kappa, km_constant, & |
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77 | mixing_length_1d, passive_scalar, prandtl_layer, & |
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78 | prandtl_number, roughness_length, simulated_time_chr, & |
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79 | z0h_factor |
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80 | |
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81 | IMPLICIT NONE |
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82 | |
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83 | CHARACTER (LEN=9) :: time_to_string !: |
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84 | |
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85 | INTEGER(iwp) :: k !: |
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86 | |
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87 | REAL(wp) :: lambda !: |
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88 | |
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89 | ! |
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90 | !-- Allocate required 1D-arrays |
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91 | ALLOCATE( e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), & |
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92 | kh1d(nzb:nzt+1), km1d(nzb:nzt+1), & |
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93 | l_black(nzb:nzt+1), l1d(nzb:nzt+1), & |
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94 | rif1d(nzb:nzt+1), te_e(nzb:nzt+1), & |
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95 | te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), & |
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96 | te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), & |
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97 | u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), & |
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98 | v1d_p(nzb:nzt+1) ) |
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99 | |
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100 | ! |
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101 | !-- Initialize arrays |
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102 | IF ( constant_diffusion ) THEN |
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103 | km1d = km_constant |
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104 | kh1d = km_constant / prandtl_number |
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105 | ELSE |
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106 | e1d = 0.0; e1d_p = 0.0 |
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107 | kh1d = 0.0; km1d = 0.0 |
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108 | rif1d = 0.0 |
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109 | ! |
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110 | !-- Compute the mixing length |
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111 | l_black(nzb) = 0.0 |
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112 | |
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113 | IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN |
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114 | ! |
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115 | !-- Blackadar mixing length |
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116 | IF ( f /= 0.0 ) THEN |
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117 | lambda = 2.7E-4 * SQRT( ug(nzt+1)**2 + vg(nzt+1)**2 ) / & |
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118 | ABS( f ) + 1E-10 |
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119 | ELSE |
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120 | lambda = 30.0 |
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121 | ENDIF |
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122 | |
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123 | DO k = nzb+1, nzt+1 |
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124 | l_black(k) = kappa * zu(k) / ( 1.0 + kappa * zu(k) / lambda ) |
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125 | ENDDO |
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126 | |
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127 | ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN |
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128 | ! |
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129 | !-- Use the same mixing length as in 3D model |
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130 | l_black(1:nzt) = l_grid |
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131 | l_black(nzt+1) = l_black(nzt) |
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132 | |
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133 | ENDIF |
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134 | ENDIF |
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135 | l1d = l_black |
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136 | u1d = u_init |
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137 | u1d_p = u_init |
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138 | v1d = v_init |
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139 | v1d_p = v_init |
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140 | |
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141 | ! |
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142 | !-- Set initial horizontal velocities at the lowest grid levels to a very small |
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143 | !-- value in order to avoid too small time steps caused by the diffusion limit |
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144 | !-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!) |
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145 | u1d(0:1) = 0.1 |
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146 | u1d_p(0:1) = 0.1 |
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147 | v1d(0:1) = 0.1 |
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148 | v1d_p(0:1) = 0.1 |
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149 | |
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150 | ! |
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151 | !-- For u*, theta* and the momentum fluxes plausible values are set |
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152 | IF ( prandtl_layer ) THEN |
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153 | us1d = 0.1 ! without initial friction the flow would not change |
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154 | ELSE |
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155 | e1d(nzb+1) = 1.0 |
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156 | km1d(nzb+1) = 1.0 |
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157 | us1d = 0.0 |
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158 | ENDIF |
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159 | ts1d = 0.0 |
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160 | usws1d = 0.0 |
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161 | vsws1d = 0.0 |
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162 | z01d = roughness_length |
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163 | z0h1d = z0h_factor * z01d |
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164 | IF ( humidity .OR. passive_scalar ) qs1d = 0.0 |
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165 | |
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166 | ! |
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167 | !-- Tendencies must be preset in order to avoid runtime errors within the |
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168 | !-- first Runge-Kutta step |
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169 | te_em = 0.0 |
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170 | te_um = 0.0 |
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171 | te_vm = 0.0 |
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172 | |
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173 | ! |
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174 | !-- Set start time in hh:mm:ss - format |
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175 | simulated_time_chr = time_to_string( simulated_time_1d ) |
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176 | |
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177 | ! |
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178 | !-- Integrate the 1D-model equations using the leap-frog scheme |
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179 | CALL time_integration_1d |
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180 | |
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181 | |
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182 | END SUBROUTINE init_1d_model |
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183 | |
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184 | |
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185 | |
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186 | SUBROUTINE time_integration_1d |
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187 | |
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188 | !------------------------------------------------------------------------------! |
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189 | ! Description: |
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190 | ! ------------ |
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191 | ! Leap-frog time differencing scheme for the 1D-model. |
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192 | !------------------------------------------------------------------------------! |
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193 | |
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194 | USE arrays_3d, & |
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195 | ONLY: dd2zu, ddzu, ddzw, l_grid, pt_init, q_init, ug, vg, zu |
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196 | |
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197 | USE control_parameters, & |
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198 | ONLY: constant_diffusion, dissipation_1d, humidity, & |
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199 | intermediate_timestep_count, intermediate_timestep_count_max, & |
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200 | f, g, ibc_e_b, kappa, mixing_length_1d, passive_scalar, & |
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201 | prandtl_layer, rif_max, rif_min, simulated_time_chr, & |
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202 | timestep_scheme, tsc |
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203 | |
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204 | USE indices, & |
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205 | ONLY: nzb, nzb_diff, nzt |
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206 | |
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207 | USE kinds |
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208 | |
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209 | USE model_1d, & |
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210 | ONLY: current_timestep_number_1d, damp_level_ind_1d, dt_1d, & |
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211 | dt_pr_1d, dt_run_control_1d, e1d, e1d_p, end_time_1d, & |
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212 | kh1d, km1d, l1d, l_black, qs1d, rif1d, simulated_time_1d, & |
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213 | stop_dt_1d, te_e, te_em, te_u, te_um, te_v, te_vm, time_pr_1d, & |
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214 | ts1d, time_run_control_1d, u1d, u1d_p, us1d, usws1d, v1d, & |
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215 | v1d_p, vsws1d, z01d, z0h1d |
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216 | |
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217 | USE pegrid |
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218 | |
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219 | IMPLICIT NONE |
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220 | |
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221 | CHARACTER (LEN=9) :: time_to_string !: |
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222 | |
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223 | INTEGER(iwp) :: k !: |
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224 | |
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225 | REAL(wp) :: a !: |
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226 | REAL(wp) :: b !: |
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227 | REAL(wp) :: dissipation !: |
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228 | REAL(wp) :: dpt_dz !: |
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229 | REAL(wp) :: flux !: |
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230 | REAL(wp) :: kmzm !: |
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231 | REAL(wp) :: kmzp !: |
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232 | REAL(wp) :: l_stable !: |
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233 | REAL(wp) :: pt_0 !: |
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234 | REAL(wp) :: uv_total !: |
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235 | |
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236 | ! |
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237 | !-- Determine the time step at the start of a 1D-simulation and |
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238 | !-- determine and printout quantities used for run control |
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239 | CALL timestep_1d |
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240 | CALL run_control_1d |
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241 | |
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242 | ! |
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243 | !-- Start of time loop |
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244 | DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d ) |
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245 | |
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246 | ! |
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247 | !-- Depending on the timestep scheme, carry out one or more intermediate |
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248 | !-- timesteps |
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249 | |
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250 | intermediate_timestep_count = 0 |
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251 | DO WHILE ( intermediate_timestep_count < & |
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252 | intermediate_timestep_count_max ) |
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253 | |
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254 | intermediate_timestep_count = intermediate_timestep_count + 1 |
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255 | |
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256 | CALL timestep_scheme_steering |
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257 | |
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258 | ! |
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259 | !-- Compute all tendency terms. If a Prandtl-layer is simulated, k starts |
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260 | !-- at nzb+2. |
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261 | DO k = nzb_diff, nzt |
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262 | |
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263 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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264 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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265 | ! |
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266 | !-- u-component |
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267 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
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268 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) & |
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269 | - kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) & |
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270 | ) * ddzw(k) |
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271 | ! |
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272 | !-- v-component |
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273 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
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274 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) & |
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275 | - kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) & |
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276 | ) * ddzw(k) |
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277 | ENDDO |
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278 | IF ( .NOT. constant_diffusion ) THEN |
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279 | DO k = nzb_diff, nzt |
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280 | ! |
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281 | !-- TKE |
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282 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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283 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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284 | IF ( .NOT. humidity ) THEN |
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285 | pt_0 = pt_init(k) |
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286 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
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287 | ELSE |
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288 | pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) ) |
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289 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
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290 | 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) & |
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291 | ) * dd2zu(k) |
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292 | ENDIF |
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293 | |
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294 | IF ( dissipation_1d == 'detering' ) THEN |
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295 | ! |
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296 | !-- According to Detering, c_e=0.064 |
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297 | dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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298 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
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299 | dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) & |
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300 | * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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301 | ENDIF |
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302 | |
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303 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
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304 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
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305 | ) & |
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306 | - g / pt_0 * kh1d(k) * flux & |
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307 | + ( & |
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308 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
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309 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
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310 | ) * ddzw(k) & |
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311 | - dissipation |
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312 | ENDDO |
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313 | ENDIF |
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314 | |
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315 | ! |
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316 | !-- Tendency terms at the top of the Prandtl-layer. |
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317 | !-- Finite differences of the momentum fluxes are computed using half the |
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318 | !-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy |
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319 | IF ( prandtl_layer ) THEN |
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320 | |
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321 | k = nzb+1 |
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322 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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323 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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324 | IF ( .NOT. humidity ) THEN |
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325 | pt_0 = pt_init(k) |
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326 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
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327 | ELSE |
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328 | pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) ) |
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329 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
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330 | 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) & |
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331 | ) * dd2zu(k) |
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332 | ENDIF |
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333 | |
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334 | IF ( dissipation_1d == 'detering' ) THEN |
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335 | ! |
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336 | !-- According to Detering, c_e=0.064 |
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337 | dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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338 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
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339 | dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) & |
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340 | * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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341 | ENDIF |
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342 | |
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343 | ! |
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344 | !-- u-component |
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345 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
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346 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d & |
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347 | ) * 2.0 * ddzw(k) |
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348 | ! |
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349 | !-- v-component |
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350 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
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351 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d & |
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352 | ) * 2.0 * ddzw(k) |
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353 | ! |
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354 | !-- TKE |
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355 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
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356 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
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357 | ) & |
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358 | - g / pt_0 * kh1d(k) * flux & |
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359 | + ( & |
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360 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
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361 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
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362 | ) * ddzw(k) & |
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363 | - dissipation |
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364 | ENDIF |
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365 | |
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366 | ! |
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367 | !-- Prognostic equations for all 1D variables |
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368 | DO k = nzb+1, nzt |
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369 | |
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370 | u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + & |
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371 | tsc(3) * te_um(k) ) |
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372 | v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + & |
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373 | tsc(3) * te_vm(k) ) |
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374 | |
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375 | ENDDO |
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376 | IF ( .NOT. constant_diffusion ) THEN |
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377 | DO k = nzb+1, nzt |
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378 | |
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379 | e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + & |
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380 | tsc(3) * te_em(k) ) |
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381 | |
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382 | ENDDO |
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383 | ! |
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384 | !-- Eliminate negative TKE values, which can result from the |
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385 | !-- integration due to numerical inaccuracies. In such cases the TKE |
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386 | !-- value is reduced to 10 percent of its old value. |
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387 | WHERE ( e1d_p < 0.0 ) e1d_p = 0.1 * e1d |
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388 | ENDIF |
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389 | |
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390 | ! |
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391 | !-- Calculate tendencies for the next Runge-Kutta step |
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392 | IF ( timestep_scheme(1:5) == 'runge' ) THEN |
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393 | IF ( intermediate_timestep_count == 1 ) THEN |
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394 | |
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395 | DO k = nzb+1, nzt |
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396 | te_um(k) = te_u(k) |
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397 | te_vm(k) = te_v(k) |
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398 | ENDDO |
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399 | |
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400 | IF ( .NOT. constant_diffusion ) THEN |
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401 | DO k = nzb+1, nzt |
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402 | te_em(k) = te_e(k) |
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403 | ENDDO |
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404 | ENDIF |
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405 | |
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406 | ELSEIF ( intermediate_timestep_count < & |
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407 | intermediate_timestep_count_max ) THEN |
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408 | |
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409 | DO k = nzb+1, nzt |
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410 | te_um(k) = -9.5625 * te_u(k) + 5.3125 * te_um(k) |
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411 | te_vm(k) = -9.5625 * te_v(k) + 5.3125 * te_vm(k) |
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412 | ENDDO |
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413 | |
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414 | IF ( .NOT. constant_diffusion ) THEN |
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415 | DO k = nzb+1, nzt |
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416 | te_em(k) = -9.5625 * te_e(k) + 5.3125 * te_em(k) |
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417 | ENDDO |
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418 | ENDIF |
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419 | |
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420 | ENDIF |
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421 | ENDIF |
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422 | |
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423 | |
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424 | ! |
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425 | !-- Boundary conditions for the prognostic variables. |
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426 | !-- At the top boundary (nzt+1) u,v and e keep their initial values |
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427 | !-- (ug(nzt+1), vg(nzt+1), 0), at the bottom boundary the mirror |
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428 | !-- boundary condition applies to u and v. |
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429 | !-- The boundary condition for e is set further below ( (u*/cm)**2 ). |
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430 | ! u1d_p(nzb) = -u1d_p(nzb+1) |
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431 | ! v1d_p(nzb) = -v1d_p(nzb+1) |
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432 | |
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433 | u1d_p(nzb) = 0.0 |
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434 | v1d_p(nzb) = 0.0 |
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435 | |
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436 | ! |
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437 | !-- Swap the time levels in preparation for the next time step. |
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438 | u1d = u1d_p |
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439 | v1d = v1d_p |
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440 | IF ( .NOT. constant_diffusion ) THEN |
---|
441 | e1d = e1d_p |
---|
442 | ENDIF |
---|
443 | |
---|
444 | ! |
---|
445 | !-- Compute diffusion quantities |
---|
446 | IF ( .NOT. constant_diffusion ) THEN |
---|
447 | |
---|
448 | ! |
---|
449 | !-- First compute the vertical fluxes in the Prandtl-layer |
---|
450 | IF ( prandtl_layer ) THEN |
---|
451 | ! |
---|
452 | !-- Compute theta* using Rif numbers of the previous time step |
---|
453 | IF ( rif1d(1) >= 0.0 ) THEN |
---|
454 | ! |
---|
455 | !-- Stable stratification |
---|
456 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
457 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
458 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
459 | ) |
---|
460 | ELSE |
---|
461 | ! |
---|
462 | !-- Unstable stratification |
---|
463 | a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) |
---|
464 | b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d ) |
---|
465 | ! |
---|
466 | !-- In the borderline case the formula for stable stratification |
---|
467 | !-- must be applied, because otherwise a zero division would |
---|
468 | !-- occur in the argument of the logarithm. |
---|
469 | IF ( a == 0.0 .OR. b == 0.0 ) THEN |
---|
470 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
471 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
472 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
473 | ) |
---|
474 | ELSE |
---|
475 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
476 | LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) ) |
---|
477 | ENDIF |
---|
478 | ENDIF |
---|
479 | |
---|
480 | ENDIF ! prandtl_layer |
---|
481 | |
---|
482 | ! |
---|
483 | !-- Compute the Richardson-flux numbers, |
---|
484 | !-- first at the top of the Prandtl-layer using u* of the previous |
---|
485 | !-- time step (+1E-30, if u* = 0), then in the remaining area. There |
---|
486 | !-- the rif-numbers of the previous time step are used. |
---|
487 | |
---|
488 | IF ( prandtl_layer ) THEN |
---|
489 | IF ( .NOT. humidity ) THEN |
---|
490 | pt_0 = pt_init(nzb+1) |
---|
491 | flux = ts1d |
---|
492 | ELSE |
---|
493 | pt_0 = pt_init(nzb+1) * ( 1.0 + 0.61 * q_init(nzb+1) ) |
---|
494 | flux = ts1d + 0.61 * pt_init(k) * qs1d |
---|
495 | ENDIF |
---|
496 | rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / & |
---|
497 | ( pt_0 * ( us1d**2 + 1E-30 ) ) |
---|
498 | ENDIF |
---|
499 | |
---|
500 | DO k = nzb_diff, nzt |
---|
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 + 0.61 * q_init(k) ) |
---|
506 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) & |
---|
507 | + 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) )& |
---|
508 | ) * dd2zu(k) |
---|
509 | ENDIF |
---|
510 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
511 | rif1d(k) = g / pt_0 * flux / & |
---|
512 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
513 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
514 | + 1E-30 & |
---|
515 | ) |
---|
516 | ELSE |
---|
517 | rif1d(k) = g / pt_0 * flux / & |
---|
518 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
519 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
520 | + 1E-30 & |
---|
521 | ) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
522 | ENDIF |
---|
523 | ENDDO |
---|
524 | ! |
---|
525 | !-- Richardson-numbers must remain restricted to a realistic value |
---|
526 | !-- range. It is exceeded excessively for very small velocities |
---|
527 | !-- (u,v --> 0). |
---|
528 | WHERE ( rif1d < rif_min ) rif1d = rif_min |
---|
529 | WHERE ( rif1d > rif_max ) rif1d = rif_max |
---|
530 | |
---|
531 | ! |
---|
532 | !-- Compute u* from the absolute velocity value |
---|
533 | IF ( prandtl_layer ) THEN |
---|
534 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
535 | |
---|
536 | IF ( rif1d(nzb+1) >= 0.0 ) THEN |
---|
537 | ! |
---|
538 | !-- Stable stratification |
---|
539 | us1d = kappa * uv_total / ( & |
---|
540 | LOG( zu(nzb+1) / z01d ) + 5.0 * rif1d(nzb+1) * & |
---|
541 | ( zu(nzb+1) - z01d ) / zu(nzb+1) & |
---|
542 | ) |
---|
543 | ELSE |
---|
544 | ! |
---|
545 | !-- Unstable stratification |
---|
546 | a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) ) |
---|
547 | b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) & |
---|
548 | * z01d ) ) |
---|
549 | ! |
---|
550 | !-- In the borderline case the formula for stable stratification |
---|
551 | !-- must be applied, because otherwise a zero division would |
---|
552 | !-- occur in the argument of the logarithm. |
---|
553 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
---|
554 | us1d = kappa * uv_total / ( & |
---|
555 | LOG( zu(nzb+1) / z01d ) + & |
---|
556 | 5.0 * rif1d(nzb+1) * ( zu(nzb+1) - z01d ) / & |
---|
557 | zu(nzb+1) ) |
---|
558 | ELSE |
---|
559 | us1d = kappa * uv_total / ( & |
---|
560 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) +& |
---|
561 | 2.0 * ( ATAN( b ) - ATAN( a ) ) & |
---|
562 | ) |
---|
563 | ENDIF |
---|
564 | ENDIF |
---|
565 | |
---|
566 | ! |
---|
567 | !-- Compute the momentum fluxes for the diffusion terms |
---|
568 | usws1d = - u1d(nzb+1) / uv_total * us1d**2 |
---|
569 | vsws1d = - v1d(nzb+1) / uv_total * us1d**2 |
---|
570 | |
---|
571 | ! |
---|
572 | !-- Boundary condition for the turbulent kinetic energy at the top |
---|
573 | !-- of the Prandtl-layer. c_m = 0.4 according to Detering. |
---|
574 | !-- Additional Neumann condition de/dz = 0 at nzb is set to ensure |
---|
575 | !-- compatibility with the 3D model. |
---|
576 | IF ( ibc_e_b == 2 ) THEN |
---|
577 | e1d(nzb+1) = ( us1d / 0.1 )**2 |
---|
578 | ! e1d(nzb+1) = ( us1d / 0.4 )**2 !not used so far, see also |
---|
579 | !prandtl_fluxes |
---|
580 | ENDIF |
---|
581 | e1d(nzb) = e1d(nzb+1) |
---|
582 | |
---|
583 | IF ( humidity .OR. passive_scalar ) THEN |
---|
584 | ! |
---|
585 | !-- Compute q* |
---|
586 | IF ( rif1d(1) >= 0.0 ) THEN |
---|
587 | ! |
---|
588 | !-- Stable stratification |
---|
589 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
590 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
591 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
592 | ) |
---|
593 | ELSE |
---|
594 | ! |
---|
595 | !-- Unstable stratification |
---|
596 | a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) |
---|
597 | b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d ) |
---|
598 | ! |
---|
599 | !-- In the borderline case the formula for stable stratification |
---|
600 | !-- must be applied, because otherwise a zero division would |
---|
601 | !-- occur in the argument of the logarithm. |
---|
602 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
---|
603 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
604 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
605 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
606 | ) |
---|
607 | ELSE |
---|
608 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
609 | LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) ) |
---|
610 | ENDIF |
---|
611 | ENDIF |
---|
612 | ELSE |
---|
613 | qs1d = 0.0 |
---|
614 | ENDIF |
---|
615 | |
---|
616 | ENDIF ! prandtl_layer |
---|
617 | |
---|
618 | ! |
---|
619 | !-- Compute the diabatic mixing length |
---|
620 | IF ( mixing_length_1d == 'blackadar' ) THEN |
---|
621 | DO k = nzb+1, nzt |
---|
622 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
623 | l1d(k) = l_black(k) / ( 1.0 + 5.0 * rif1d(k) ) |
---|
624 | ELSE |
---|
625 | l1d(k) = l_black(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
626 | ENDIF |
---|
627 | l1d(k) = l_black(k) |
---|
628 | ENDDO |
---|
629 | |
---|
630 | ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN |
---|
631 | DO k = nzb+1, nzt |
---|
632 | dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
633 | IF ( dpt_dz > 0.0 ) THEN |
---|
634 | l_stable = 0.76 * SQRT( e1d(k) ) / & |
---|
635 | SQRT( g / pt_init(k) * dpt_dz ) + 1E-5 |
---|
636 | ELSE |
---|
637 | l_stable = l_grid(k) |
---|
638 | ENDIF |
---|
639 | l1d(k) = MIN( l_grid(k), l_stable ) |
---|
640 | ENDDO |
---|
641 | ENDIF |
---|
642 | |
---|
643 | ! |
---|
644 | !-- Compute the diffusion coefficients for momentum via the |
---|
645 | !-- corresponding Prandtl-layer relationship and according to |
---|
646 | !-- Prandtl-Kolmogorov, respectively. The unstable stratification is |
---|
647 | !-- computed via the adiabatic mixing length, for the unstability has |
---|
648 | !-- already been taken account of via the TKE (cf. also Diss.). |
---|
649 | IF ( prandtl_layer ) THEN |
---|
650 | IF ( rif1d(nzb+1) >= 0.0 ) THEN |
---|
651 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) / & |
---|
652 | ( 1.0 + 5.0 * rif1d(nzb+1) ) |
---|
653 | ELSE |
---|
654 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) * & |
---|
655 | ( 1.0 - 16.0 * rif1d(nzb+1) )**0.25 |
---|
656 | ENDIF |
---|
657 | ENDIF |
---|
658 | DO k = nzb_diff, nzt |
---|
659 | ! km1d(k) = 0.4 * SQRT( e1d(k) ) !changed: adjustment to 3D-model |
---|
660 | km1d(k) = 0.1 * SQRT( e1d(k) ) |
---|
661 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
662 | km1d(k) = km1d(k) * l1d(k) |
---|
663 | ELSE |
---|
664 | km1d(k) = km1d(k) * l_black(k) |
---|
665 | ENDIF |
---|
666 | ENDDO |
---|
667 | |
---|
668 | ! |
---|
669 | !-- Add damping layer |
---|
670 | DO k = damp_level_ind_1d+1, nzt+1 |
---|
671 | km1d(k) = 1.1 * km1d(k-1) |
---|
672 | km1d(k) = MIN( km1d(k), 10.0 ) |
---|
673 | ENDDO |
---|
674 | |
---|
675 | ! |
---|
676 | !-- Compute the diffusion coefficient for heat via the relationship |
---|
677 | !-- kh = phim / phih * km |
---|
678 | DO k = nzb+1, nzt |
---|
679 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
680 | kh1d(k) = km1d(k) |
---|
681 | ELSE |
---|
682 | kh1d(k) = km1d(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
683 | ENDIF |
---|
684 | ENDDO |
---|
685 | |
---|
686 | ENDIF ! .NOT. constant_diffusion |
---|
687 | |
---|
688 | ENDDO ! intermediate step loop |
---|
689 | |
---|
690 | ! |
---|
691 | !-- Increment simulated time and output times |
---|
692 | current_timestep_number_1d = current_timestep_number_1d + 1 |
---|
693 | simulated_time_1d = simulated_time_1d + dt_1d |
---|
694 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
695 | time_pr_1d = time_pr_1d + dt_1d |
---|
696 | time_run_control_1d = time_run_control_1d + dt_1d |
---|
697 | |
---|
698 | ! |
---|
699 | !-- Determine and print out quantities for run control |
---|
700 | IF ( time_run_control_1d >= dt_run_control_1d ) THEN |
---|
701 | CALL run_control_1d |
---|
702 | time_run_control_1d = time_run_control_1d - dt_run_control_1d |
---|
703 | ENDIF |
---|
704 | |
---|
705 | ! |
---|
706 | !-- Profile output on file |
---|
707 | IF ( time_pr_1d >= dt_pr_1d ) THEN |
---|
708 | CALL print_1d_model |
---|
709 | time_pr_1d = time_pr_1d - dt_pr_1d |
---|
710 | ENDIF |
---|
711 | |
---|
712 | ! |
---|
713 | !-- Determine size of next time step |
---|
714 | CALL timestep_1d |
---|
715 | |
---|
716 | ENDDO ! time loop |
---|
717 | |
---|
718 | |
---|
719 | END SUBROUTINE time_integration_1d |
---|
720 | |
---|
721 | |
---|
722 | SUBROUTINE run_control_1d |
---|
723 | |
---|
724 | !------------------------------------------------------------------------------! |
---|
725 | ! Description: |
---|
726 | ! ------------ |
---|
727 | ! Compute and print out quantities for run control of the 1D model. |
---|
728 | !------------------------------------------------------------------------------! |
---|
729 | |
---|
730 | USE constants, & |
---|
731 | ONLY: pi |
---|
732 | |
---|
733 | USE indices, & |
---|
734 | ONLY: nzb, nzt |
---|
735 | |
---|
736 | USE kinds |
---|
737 | |
---|
738 | USE model_1d, & |
---|
739 | ONLY: current_timestep_number_1d, dt_1d, run_control_header_1d, u1d, & |
---|
740 | us1d, v1d |
---|
741 | |
---|
742 | USE pegrid |
---|
743 | |
---|
744 | USE control_parameters, & |
---|
745 | ONLY: simulated_time_chr |
---|
746 | |
---|
747 | IMPLICIT NONE |
---|
748 | |
---|
749 | INTEGER(iwp) :: k !: |
---|
750 | |
---|
751 | REAL(wp) :: alpha |
---|
752 | REAL(wp) :: energy |
---|
753 | REAL(wp) :: umax |
---|
754 | REAL(wp) :: uv_total |
---|
755 | REAL(wp) :: vmax |
---|
756 | |
---|
757 | ! |
---|
758 | !-- Output |
---|
759 | IF ( myid == 0 ) THEN |
---|
760 | ! |
---|
761 | !-- If necessary, write header |
---|
762 | IF ( .NOT. run_control_header_1d ) THEN |
---|
763 | CALL check_open( 15 ) |
---|
764 | WRITE ( 15, 100 ) |
---|
765 | run_control_header_1d = .TRUE. |
---|
766 | ENDIF |
---|
767 | |
---|
768 | ! |
---|
769 | !-- Compute control quantities |
---|
770 | !-- grid level nzp is excluded due to mirror boundary condition |
---|
771 | umax = 0.0; vmax = 0.0; energy = 0.0 |
---|
772 | DO k = nzb+1, nzt+1 |
---|
773 | umax = MAX( ABS( umax ), ABS( u1d(k) ) ) |
---|
774 | vmax = MAX( ABS( vmax ), ABS( v1d(k) ) ) |
---|
775 | energy = energy + 0.5 * ( u1d(k)**2 + v1d(k)**2 ) |
---|
776 | ENDDO |
---|
777 | energy = energy / REAL( nzt - nzb + 1 ) |
---|
778 | |
---|
779 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
780 | IF ( ABS( v1d(nzb+1) ) .LT. 1.0E-5 ) THEN |
---|
781 | alpha = ACOS( SIGN( 1.0 , u1d(nzb+1) ) ) |
---|
782 | ELSE |
---|
783 | alpha = ACOS( u1d(nzb+1) / uv_total ) |
---|
784 | IF ( v1d(nzb+1) <= 0.0 ) alpha = 2.0 * pi - alpha |
---|
785 | ENDIF |
---|
786 | alpha = alpha / ( 2.0 * pi ) * 360.0 |
---|
787 | |
---|
788 | WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, & |
---|
789 | dt_1d, umax, vmax, us1d, alpha, energy |
---|
790 | ! |
---|
791 | !-- Write buffer contents to disc immediately |
---|
792 | CALL local_flush( 15 ) |
---|
793 | |
---|
794 | ENDIF |
---|
795 | |
---|
796 | ! |
---|
797 | !-- formats |
---|
798 | 100 FORMAT (///'1D-Zeitschrittkontrollausgaben:'/ & |
---|
799 | &'------------------------------'// & |
---|
800 | &'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ & |
---|
801 | &'-------------------------------------------------------------') |
---|
802 | 101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,2X,F5.3,2X,F5.1,2X,F7.2) |
---|
803 | |
---|
804 | |
---|
805 | END SUBROUTINE run_control_1d |
---|
806 | |
---|
807 | |
---|
808 | |
---|
809 | SUBROUTINE timestep_1d |
---|
810 | |
---|
811 | !------------------------------------------------------------------------------! |
---|
812 | ! Description: |
---|
813 | ! ------------ |
---|
814 | ! Compute the time step w.r.t. the diffusion criterion |
---|
815 | !------------------------------------------------------------------------------! |
---|
816 | |
---|
817 | USE arrays_3d, & |
---|
818 | ONLY: dzu, zu |
---|
819 | |
---|
820 | USE indices, & |
---|
821 | ONLY: nzb, nzt |
---|
822 | |
---|
823 | USE kinds |
---|
824 | |
---|
825 | USE model_1d, & |
---|
826 | ONLY: dt_1d, dt_max_1d, km1d, old_dt_1d, stop_dt_1d |
---|
827 | |
---|
828 | USE pegrid |
---|
829 | |
---|
830 | USE control_parameters, & |
---|
831 | ONLY: message_string |
---|
832 | |
---|
833 | IMPLICIT NONE |
---|
834 | |
---|
835 | INTEGER(iwp) :: k !: |
---|
836 | |
---|
837 | REAL(wp) :: div !: |
---|
838 | REAL(wp) :: dt_diff !: |
---|
839 | REAL(wp) :: fac !: |
---|
840 | REAL(wp) :: value !: |
---|
841 | |
---|
842 | |
---|
843 | ! |
---|
844 | !-- Compute the currently feasible time step according to the diffusion |
---|
845 | !-- criterion. At nzb+1 the half grid length is used. |
---|
846 | fac = 0.35 |
---|
847 | dt_diff = dt_max_1d |
---|
848 | DO k = nzb+2, nzt |
---|
849 | value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20 ) |
---|
850 | dt_diff = MIN( value, dt_diff ) |
---|
851 | ENDDO |
---|
852 | value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20 ) |
---|
853 | dt_1d = MIN( value, dt_diff ) |
---|
854 | |
---|
855 | ! |
---|
856 | !-- Set flag when the time step becomes too small |
---|
857 | IF ( dt_1d < ( 0.00001 * dt_max_1d ) ) THEN |
---|
858 | stop_dt_1d = .TRUE. |
---|
859 | |
---|
860 | WRITE( message_string, * ) 'timestep has exceeded the lower limit &', & |
---|
861 | 'dt_1d = ',dt_1d,' s simulation stopped!' |
---|
862 | CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 ) |
---|
863 | |
---|
864 | ENDIF |
---|
865 | |
---|
866 | ! |
---|
867 | !-- A more or less simple new time step value is obtained taking only the |
---|
868 | !-- first two significant digits |
---|
869 | div = 1000.0 |
---|
870 | DO WHILE ( dt_1d < div ) |
---|
871 | div = div / 10.0 |
---|
872 | ENDDO |
---|
873 | dt_1d = NINT( dt_1d * 100.0 / div ) * div / 100.0 |
---|
874 | |
---|
875 | old_dt_1d = dt_1d |
---|
876 | |
---|
877 | |
---|
878 | END SUBROUTINE timestep_1d |
---|
879 | |
---|
880 | |
---|
881 | |
---|
882 | SUBROUTINE print_1d_model |
---|
883 | |
---|
884 | !------------------------------------------------------------------------------! |
---|
885 | ! Description: |
---|
886 | ! ------------ |
---|
887 | ! List output of profiles from the 1D-model |
---|
888 | !------------------------------------------------------------------------------! |
---|
889 | |
---|
890 | USE arrays_3d, & |
---|
891 | ONLY: pt_init, zu |
---|
892 | |
---|
893 | USE indices, & |
---|
894 | ONLY: nzb, nzt |
---|
895 | |
---|
896 | USE kinds |
---|
897 | |
---|
898 | USE model_1d, & |
---|
899 | ONLY: e1d, kh1d, km1d, l1d, rif1d, u1d, v1d |
---|
900 | |
---|
901 | USE pegrid |
---|
902 | |
---|
903 | USE control_parameters, & |
---|
904 | ONLY: run_description_header, simulated_time_chr |
---|
905 | |
---|
906 | IMPLICIT NONE |
---|
907 | |
---|
908 | |
---|
909 | INTEGER(iwp) :: k !: |
---|
910 | |
---|
911 | |
---|
912 | IF ( myid == 0 ) THEN |
---|
913 | ! |
---|
914 | !-- Open list output file for profiles from the 1D-model |
---|
915 | CALL check_open( 17 ) |
---|
916 | |
---|
917 | ! |
---|
918 | !-- Write Header |
---|
919 | WRITE ( 17, 100 ) TRIM( run_description_header ), & |
---|
920 | TRIM( simulated_time_chr ) |
---|
921 | WRITE ( 17, 101 ) |
---|
922 | |
---|
923 | ! |
---|
924 | !-- Write the values |
---|
925 | WRITE ( 17, 102 ) |
---|
926 | WRITE ( 17, 101 ) |
---|
927 | DO k = nzt+1, nzb, -1 |
---|
928 | WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), & |
---|
929 | rif1d(k), km1d(k), kh1d(k), l1d(k), zu(k), k |
---|
930 | ENDDO |
---|
931 | WRITE ( 17, 101 ) |
---|
932 | WRITE ( 17, 102 ) |
---|
933 | WRITE ( 17, 101 ) |
---|
934 | |
---|
935 | ! |
---|
936 | !-- Write buffer contents to disc immediately |
---|
937 | CALL local_flush( 17 ) |
---|
938 | |
---|
939 | ENDIF |
---|
940 | |
---|
941 | ! |
---|
942 | !-- Formats |
---|
943 | 100 FORMAT (//1X,A/1X,10('-')/' 1d-model profiles'/ & |
---|
944 | ' Time: ',A) |
---|
945 | 101 FORMAT (1X,79('-')) |
---|
946 | 102 FORMAT (' k zu u v pt e rif Km Kh ', & |
---|
947 | 'l zu k') |
---|
948 | 103 FORMAT (1X,I4,1X,F7.1,1X,F6.2,1X,F6.2,1X,F6.2,1X,F6.2,1X,F5.2,1X,F5.2, & |
---|
949 | 1X,F5.2,1X,F6.2,1X,F7.1,2X,I4) |
---|
950 | |
---|
951 | |
---|
952 | END SUBROUTINE print_1d_model |
---|