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 1997-2012 Leibniz University 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: init_1d_model.f90 1037 2012-10-22 14:10:22Z witha $ |
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27 | ! |
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28 | ! 1036 2012-10-22 13:43:42Z raasch |
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29 | ! code put under GPL (PALM 3.9) |
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30 | ! |
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31 | ! 1015 2012-09-27 09:23:24Z raasch |
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32 | ! adjustment of mixing length to the Prandtl mixing length at first grid point |
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33 | ! above ground removed |
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34 | ! |
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35 | ! 1001 2012-09-13 14:08:46Z raasch |
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36 | ! all actions concerning leapfrog scheme removed |
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37 | ! |
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38 | ! 996 2012-09-07 10:41:47Z raasch |
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39 | ! little reformatting |
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40 | ! |
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41 | ! 978 2012-08-09 08:28:32Z fricke |
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42 | ! roughness length for scalar quantities z0h1d added |
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43 | ! |
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44 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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45 | ! replaced mirror boundary conditions for u and v at the ground |
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46 | ! by dirichlet boundary conditions |
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47 | ! |
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48 | ! 254 2009-03-05 15:33:42Z heinze |
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49 | ! Output of messages replaced by message handling routine. |
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50 | ! |
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51 | ! 184 2008-08-04 15:53:39Z letzel |
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52 | ! provisional solution for run_control_1d output: add 'CALL check_open( 15 )' |
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53 | ! |
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54 | ! 135 2007-11-22 12:24:23Z raasch |
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55 | ! Bugfix: absolute value of f must be used when calculating the Blackadar |
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56 | ! mixing length |
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57 | ! |
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58 | ! 82 2007-04-16 15:40:52Z raasch |
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59 | ! Preprocessor strings for different linux clusters changed to "lc", |
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60 | ! routine local_flush is used for buffer flushing |
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61 | ! |
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62 | ! 75 2007-03-22 09:54:05Z raasch |
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63 | ! Bugfix: preset of tendencies te_em, te_um, te_vm, |
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64 | ! moisture renamed humidity |
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65 | ! |
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66 | ! RCS Log replace by Id keyword, revision history cleaned up |
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67 | ! |
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68 | ! Revision 1.21 2006/06/02 15:19:57 raasch |
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69 | ! cpp-directives extended for lctit |
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70 | ! |
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71 | ! Revision 1.1 1998/03/09 16:22:10 raasch |
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72 | ! Initial revision |
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73 | ! |
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74 | ! |
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75 | ! Description: |
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76 | ! ------------ |
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77 | ! 1D-model to initialize the 3D-arrays. |
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78 | ! The temperature profile is set as steady and a corresponding steady solution |
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79 | ! of the wind profile is being computed. |
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80 | ! All subroutines required can be found within this file. |
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81 | !------------------------------------------------------------------------------! |
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82 | |
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83 | USE arrays_3d |
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84 | USE indices |
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85 | USE model_1d |
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86 | USE control_parameters |
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87 | |
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88 | IMPLICIT NONE |
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89 | |
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90 | CHARACTER (LEN=9) :: time_to_string |
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91 | INTEGER :: k |
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92 | REAL :: lambda |
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93 | |
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94 | ! |
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95 | !-- Allocate required 1D-arrays |
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96 | ALLOCATE( e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), & |
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97 | kh1d(nzb:nzt+1), km1d(nzb:nzt+1), & |
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98 | l_black(nzb:nzt+1), l1d(nzb:nzt+1), & |
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99 | rif1d(nzb:nzt+1), te_e(nzb:nzt+1), & |
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100 | te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), & |
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101 | te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), & |
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102 | u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), & |
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103 | v1d_p(nzb:nzt+1) ) |
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104 | |
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105 | ! |
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106 | !-- Initialize arrays |
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107 | IF ( constant_diffusion ) THEN |
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108 | km1d = km_constant |
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109 | kh1d = km_constant / prandtl_number |
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110 | ELSE |
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111 | e1d = 0.0; e1d_p = 0.0 |
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112 | kh1d = 0.0; km1d = 0.0 |
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113 | rif1d = 0.0 |
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114 | ! |
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115 | !-- Compute the mixing length |
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116 | l_black(nzb) = 0.0 |
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117 | |
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118 | IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN |
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119 | ! |
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120 | !-- Blackadar mixing length |
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121 | IF ( f /= 0.0 ) THEN |
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122 | lambda = 2.7E-4 * SQRT( ug(nzt+1)**2 + vg(nzt+1)**2 ) / & |
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123 | ABS( f ) + 1E-10 |
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124 | ELSE |
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125 | lambda = 30.0 |
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126 | ENDIF |
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127 | |
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128 | DO k = nzb+1, nzt+1 |
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129 | l_black(k) = kappa * zu(k) / ( 1.0 + kappa * zu(k) / lambda ) |
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130 | ENDDO |
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131 | |
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132 | ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN |
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133 | ! |
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134 | !-- Use the same mixing length as in 3D model |
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135 | l_black(1:nzt) = l_grid |
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136 | l_black(nzt+1) = l_black(nzt) |
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137 | |
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138 | ENDIF |
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139 | ENDIF |
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140 | l1d = l_black |
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141 | u1d = u_init |
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142 | u1d_p = u_init |
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143 | v1d = v_init |
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144 | v1d_p = v_init |
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145 | |
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146 | ! |
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147 | !-- Set initial horizontal velocities at the lowest grid levels to a very small |
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148 | !-- value in order to avoid too small time steps caused by the diffusion limit |
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149 | !-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!) |
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150 | u1d(0:1) = 0.1 |
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151 | u1d_p(0:1) = 0.1 |
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152 | v1d(0:1) = 0.1 |
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153 | v1d_p(0:1) = 0.1 |
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154 | |
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155 | ! |
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156 | !-- For u*, theta* and the momentum fluxes plausible values are set |
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157 | IF ( prandtl_layer ) THEN |
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158 | us1d = 0.1 ! without initial friction the flow would not change |
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159 | ELSE |
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160 | e1d(nzb+1) = 1.0 |
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161 | km1d(nzb+1) = 1.0 |
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162 | us1d = 0.0 |
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163 | ENDIF |
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164 | ts1d = 0.0 |
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165 | usws1d = 0.0 |
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166 | vsws1d = 0.0 |
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167 | z01d = roughness_length |
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168 | z0h1d = z0h_factor * z01d |
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169 | IF ( humidity .OR. passive_scalar ) qs1d = 0.0 |
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170 | |
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171 | ! |
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172 | !-- Tendencies must be preset in order to avoid runtime errors within the |
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173 | !-- first Runge-Kutta step |
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174 | te_em = 0.0 |
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175 | te_um = 0.0 |
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176 | te_vm = 0.0 |
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177 | |
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178 | ! |
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179 | !-- Set start time in hh:mm:ss - format |
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180 | simulated_time_chr = time_to_string( simulated_time_1d ) |
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181 | |
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182 | ! |
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183 | !-- Integrate the 1D-model equations using the leap-frog scheme |
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184 | CALL time_integration_1d |
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185 | |
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186 | |
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187 | END SUBROUTINE init_1d_model |
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188 | |
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189 | |
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190 | |
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191 | SUBROUTINE time_integration_1d |
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192 | |
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193 | !------------------------------------------------------------------------------! |
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194 | ! Description: |
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195 | ! ------------ |
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196 | ! Leap-frog time differencing scheme for the 1D-model. |
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197 | !------------------------------------------------------------------------------! |
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198 | |
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199 | USE arrays_3d |
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200 | USE control_parameters |
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201 | USE indices |
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202 | USE model_1d |
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203 | USE pegrid |
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204 | |
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205 | IMPLICIT NONE |
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206 | |
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207 | CHARACTER (LEN=9) :: time_to_string |
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208 | INTEGER :: k |
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209 | REAL :: a, b, dissipation, dpt_dz, flux, kmzm, kmzp, l_stable, pt_0, & |
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210 | uv_total |
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211 | |
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212 | ! |
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213 | !-- Determine the time step at the start of a 1D-simulation and |
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214 | !-- determine and printout quantities used for run control |
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215 | CALL timestep_1d |
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216 | CALL run_control_1d |
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217 | |
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218 | ! |
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219 | !-- Start of time loop |
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220 | DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d ) |
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221 | |
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222 | ! |
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223 | !-- Depending on the timestep scheme, carry out one or more intermediate |
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224 | !-- timesteps |
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225 | |
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226 | intermediate_timestep_count = 0 |
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227 | DO WHILE ( intermediate_timestep_count < & |
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228 | intermediate_timestep_count_max ) |
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229 | |
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230 | intermediate_timestep_count = intermediate_timestep_count + 1 |
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231 | |
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232 | CALL timestep_scheme_steering |
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233 | |
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234 | ! |
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235 | !-- Compute all tendency terms. If a Prandtl-layer is simulated, k starts |
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236 | !-- at nzb+2. |
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237 | DO k = nzb_diff, nzt |
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238 | |
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239 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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240 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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241 | ! |
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242 | !-- u-component |
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243 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
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244 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) & |
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245 | - kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) & |
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246 | ) * ddzw(k) |
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247 | ! |
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248 | !-- v-component |
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249 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
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250 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) & |
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251 | - kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) & |
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252 | ) * ddzw(k) |
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253 | ENDDO |
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254 | IF ( .NOT. constant_diffusion ) THEN |
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255 | DO k = nzb_diff, nzt |
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256 | ! |
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257 | !-- TKE |
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258 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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259 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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260 | IF ( .NOT. humidity ) THEN |
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261 | pt_0 = pt_init(k) |
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262 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
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263 | ELSE |
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264 | pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) ) |
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265 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
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266 | 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) & |
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267 | ) * dd2zu(k) |
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268 | ENDIF |
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269 | |
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270 | IF ( dissipation_1d == 'detering' ) THEN |
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271 | ! |
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272 | !-- According to Detering, c_e=0.064 |
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273 | dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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274 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
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275 | dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) & |
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276 | * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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277 | ENDIF |
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278 | |
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279 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
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280 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
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281 | ) & |
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282 | - g / pt_0 * kh1d(k) * flux & |
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283 | + ( & |
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284 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
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285 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
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286 | ) * ddzw(k) & |
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287 | - dissipation |
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288 | ENDDO |
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289 | ENDIF |
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290 | |
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291 | ! |
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292 | !-- Tendency terms at the top of the Prandtl-layer. |
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293 | !-- Finite differences of the momentum fluxes are computed using half the |
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294 | !-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy |
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295 | IF ( prandtl_layer ) THEN |
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296 | |
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297 | k = nzb+1 |
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298 | kmzm = 0.5 * ( km1d(k-1) + km1d(k) ) |
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299 | kmzp = 0.5 * ( km1d(k) + km1d(k+1) ) |
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300 | IF ( .NOT. humidity ) THEN |
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301 | pt_0 = pt_init(k) |
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302 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
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303 | ELSE |
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304 | pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) ) |
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305 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
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306 | 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) & |
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307 | ) * dd2zu(k) |
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308 | ENDIF |
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309 | |
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310 | IF ( dissipation_1d == 'detering' ) THEN |
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311 | ! |
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312 | !-- According to Detering, c_e=0.064 |
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313 | dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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314 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
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315 | dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) & |
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316 | * e1d(k) * SQRT( e1d(k) ) / l1d(k) |
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317 | ENDIF |
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318 | |
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319 | ! |
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320 | !-- u-component |
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321 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
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322 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d & |
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323 | ) * 2.0 * ddzw(k) |
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324 | ! |
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325 | !-- v-component |
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326 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
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327 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d & |
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328 | ) * 2.0 * ddzw(k) |
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329 | ! |
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330 | !-- TKE |
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331 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
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332 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
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333 | ) & |
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334 | - g / pt_0 * kh1d(k) * flux & |
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335 | + ( & |
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336 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
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337 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
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338 | ) * ddzw(k) & |
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339 | - dissipation |
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340 | ENDIF |
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341 | |
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342 | ! |
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343 | !-- Prognostic equations for all 1D variables |
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344 | DO k = nzb+1, nzt |
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345 | |
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346 | u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + & |
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347 | tsc(3) * te_um(k) ) |
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348 | v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + & |
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349 | tsc(3) * te_vm(k) ) |
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350 | |
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351 | ENDDO |
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352 | IF ( .NOT. constant_diffusion ) THEN |
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353 | DO k = nzb+1, nzt |
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354 | |
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355 | e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + & |
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356 | tsc(3) * te_em(k) ) |
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357 | |
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358 | ENDDO |
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359 | ! |
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360 | !-- Eliminate negative TKE values, which can result from the |
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361 | !-- integration due to numerical inaccuracies. In such cases the TKE |
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362 | !-- value is reduced to 10 percent of its old value. |
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363 | WHERE ( e1d_p < 0.0 ) e1d_p = 0.1 * e1d |
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364 | ENDIF |
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365 | |
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366 | ! |
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367 | !-- Calculate tendencies for the next Runge-Kutta step |
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368 | IF ( timestep_scheme(1:5) == 'runge' ) THEN |
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369 | IF ( intermediate_timestep_count == 1 ) THEN |
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370 | |
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371 | DO k = nzb+1, nzt |
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372 | te_um(k) = te_u(k) |
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373 | te_vm(k) = te_v(k) |
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374 | ENDDO |
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375 | |
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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 | te_em(k) = te_e(k) |
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379 | ENDDO |
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380 | ENDIF |
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381 | |
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382 | ELSEIF ( intermediate_timestep_count < & |
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383 | intermediate_timestep_count_max ) THEN |
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384 | |
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385 | DO k = nzb+1, nzt |
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386 | te_um(k) = -9.5625 * te_u(k) + 5.3125 * te_um(k) |
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387 | te_vm(k) = -9.5625 * te_v(k) + 5.3125 * te_vm(k) |
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388 | ENDDO |
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389 | |
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390 | IF ( .NOT. constant_diffusion ) THEN |
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391 | DO k = nzb+1, nzt |
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392 | te_em(k) = -9.5625 * te_e(k) + 5.3125 * te_em(k) |
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393 | ENDDO |
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394 | ENDIF |
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395 | |
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396 | ENDIF |
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397 | ENDIF |
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398 | |
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399 | |
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400 | ! |
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401 | !-- Boundary conditions for the prognostic variables. |
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402 | !-- At the top boundary (nzt+1) u,v and e keep their initial values |
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403 | !-- (ug(nzt+1), vg(nzt+1), 0), at the bottom boundary the mirror |
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404 | !-- boundary condition applies to u and v. |
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405 | !-- The boundary condition for e is set further below ( (u*/cm)**2 ). |
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406 | ! u1d_p(nzb) = -u1d_p(nzb+1) |
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407 | ! v1d_p(nzb) = -v1d_p(nzb+1) |
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408 | |
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409 | u1d_p(nzb) = 0.0 |
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410 | v1d_p(nzb) = 0.0 |
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411 | |
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412 | ! |
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413 | !-- Swap the time levels in preparation for the next time step. |
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414 | u1d = u1d_p |
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415 | v1d = v1d_p |
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416 | IF ( .NOT. constant_diffusion ) THEN |
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417 | e1d = e1d_p |
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418 | ENDIF |
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419 | |
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420 | ! |
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421 | !-- Compute diffusion quantities |
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422 | IF ( .NOT. constant_diffusion ) THEN |
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423 | |
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424 | ! |
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425 | !-- First compute the vertical fluxes in the Prandtl-layer |
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426 | IF ( prandtl_layer ) THEN |
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427 | ! |
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428 | !-- Compute theta* using Rif numbers of the previous time step |
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429 | IF ( rif1d(1) >= 0.0 ) THEN |
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430 | ! |
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431 | !-- Stable stratification |
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432 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
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433 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
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434 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
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435 | ) |
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436 | ELSE |
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437 | ! |
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438 | !-- Unstable stratification |
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439 | a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) |
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440 | b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d ) |
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441 | ! |
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442 | !-- In the borderline case the formula for stable stratification |
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443 | !-- must be applied, because otherwise a zero division would |
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444 | !-- occur in the argument of the logarithm. |
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445 | IF ( a == 0.0 .OR. b == 0.0 ) THEN |
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446 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
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447 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
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448 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
449 | ) |
---|
450 | ELSE |
---|
451 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
452 | LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) ) |
---|
453 | ENDIF |
---|
454 | ENDIF |
---|
455 | |
---|
456 | ENDIF ! prandtl_layer |
---|
457 | |
---|
458 | ! |
---|
459 | !-- Compute the Richardson-flux numbers, |
---|
460 | !-- first at the top of the Prandtl-layer using u* of the previous |
---|
461 | !-- time step (+1E-30, if u* = 0), then in the remaining area. There |
---|
462 | !-- the rif-numbers of the previous time step are used. |
---|
463 | |
---|
464 | IF ( prandtl_layer ) THEN |
---|
465 | IF ( .NOT. humidity ) THEN |
---|
466 | pt_0 = pt_init(nzb+1) |
---|
467 | flux = ts1d |
---|
468 | ELSE |
---|
469 | pt_0 = pt_init(nzb+1) * ( 1.0 + 0.61 * q_init(nzb+1) ) |
---|
470 | flux = ts1d + 0.61 * pt_init(k) * qs1d |
---|
471 | ENDIF |
---|
472 | rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / & |
---|
473 | ( pt_0 * ( us1d**2 + 1E-30 ) ) |
---|
474 | ENDIF |
---|
475 | |
---|
476 | DO k = nzb_diff, nzt |
---|
477 | IF ( .NOT. humidity ) THEN |
---|
478 | pt_0 = pt_init(k) |
---|
479 | flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
480 | ELSE |
---|
481 | pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) ) |
---|
482 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) & |
---|
483 | + 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) )& |
---|
484 | ) * dd2zu(k) |
---|
485 | ENDIF |
---|
486 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
487 | rif1d(k) = g / pt_0 * flux / & |
---|
488 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
489 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
490 | + 1E-30 & |
---|
491 | ) |
---|
492 | ELSE |
---|
493 | rif1d(k) = g / pt_0 * flux / & |
---|
494 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
495 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
496 | + 1E-30 & |
---|
497 | ) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
498 | ENDIF |
---|
499 | ENDDO |
---|
500 | ! |
---|
501 | !-- Richardson-numbers must remain restricted to a realistic value |
---|
502 | !-- range. It is exceeded excessively for very small velocities |
---|
503 | !-- (u,v --> 0). |
---|
504 | WHERE ( rif1d < rif_min ) rif1d = rif_min |
---|
505 | WHERE ( rif1d > rif_max ) rif1d = rif_max |
---|
506 | |
---|
507 | ! |
---|
508 | !-- Compute u* from the absolute velocity value |
---|
509 | IF ( prandtl_layer ) THEN |
---|
510 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
511 | |
---|
512 | IF ( rif1d(nzb+1) >= 0.0 ) THEN |
---|
513 | ! |
---|
514 | !-- Stable stratification |
---|
515 | us1d = kappa * uv_total / ( & |
---|
516 | LOG( zu(nzb+1) / z01d ) + 5.0 * rif1d(nzb+1) * & |
---|
517 | ( zu(nzb+1) - z01d ) / zu(nzb+1) & |
---|
518 | ) |
---|
519 | ELSE |
---|
520 | ! |
---|
521 | !-- Unstable stratification |
---|
522 | a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) ) |
---|
523 | b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) & |
---|
524 | * z01d ) ) |
---|
525 | ! |
---|
526 | !-- In the borderline case the formula for stable stratification |
---|
527 | !-- must be applied, because otherwise a zero division would |
---|
528 | !-- occur in the argument of the logarithm. |
---|
529 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
---|
530 | us1d = kappa * uv_total / ( & |
---|
531 | LOG( zu(nzb+1) / z01d ) + & |
---|
532 | 5.0 * rif1d(nzb+1) * ( zu(nzb+1) - z01d ) / & |
---|
533 | zu(nzb+1) ) |
---|
534 | ELSE |
---|
535 | us1d = kappa * uv_total / ( & |
---|
536 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) +& |
---|
537 | 2.0 * ( ATAN( b ) - ATAN( a ) ) & |
---|
538 | ) |
---|
539 | ENDIF |
---|
540 | ENDIF |
---|
541 | |
---|
542 | ! |
---|
543 | !-- Compute the momentum fluxes for the diffusion terms |
---|
544 | usws1d = - u1d(nzb+1) / uv_total * us1d**2 |
---|
545 | vsws1d = - v1d(nzb+1) / uv_total * us1d**2 |
---|
546 | |
---|
547 | ! |
---|
548 | !-- Boundary condition for the turbulent kinetic energy at the top |
---|
549 | !-- of the Prandtl-layer. c_m = 0.4 according to Detering. |
---|
550 | !-- Additional Neumann condition de/dz = 0 at nzb is set to ensure |
---|
551 | !-- compatibility with the 3D model. |
---|
552 | IF ( ibc_e_b == 2 ) THEN |
---|
553 | e1d(nzb+1) = ( us1d / 0.1 )**2 |
---|
554 | ! e1d(nzb+1) = ( us1d / 0.4 )**2 !not used so far, see also |
---|
555 | !prandtl_fluxes |
---|
556 | ENDIF |
---|
557 | e1d(nzb) = e1d(nzb+1) |
---|
558 | |
---|
559 | IF ( humidity .OR. passive_scalar ) THEN |
---|
560 | ! |
---|
561 | !-- Compute q* |
---|
562 | IF ( rif1d(1) >= 0.0 ) THEN |
---|
563 | ! |
---|
564 | !-- Stable stratification |
---|
565 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
566 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
567 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
568 | ) |
---|
569 | ELSE |
---|
570 | ! |
---|
571 | !-- Unstable stratification |
---|
572 | a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) |
---|
573 | b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d ) |
---|
574 | ! |
---|
575 | !-- In the borderline case the formula for stable stratification |
---|
576 | !-- must be applied, because otherwise a zero division would |
---|
577 | !-- occur in the argument of the logarithm. |
---|
578 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
---|
579 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
580 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * & |
---|
581 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
582 | ) |
---|
583 | ELSE |
---|
584 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
585 | LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) ) |
---|
586 | ENDIF |
---|
587 | ENDIF |
---|
588 | ELSE |
---|
589 | qs1d = 0.0 |
---|
590 | ENDIF |
---|
591 | |
---|
592 | ENDIF ! prandtl_layer |
---|
593 | |
---|
594 | ! |
---|
595 | !-- Compute the diabatic mixing length |
---|
596 | IF ( mixing_length_1d == 'blackadar' ) THEN |
---|
597 | DO k = nzb+1, nzt |
---|
598 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
599 | l1d(k) = l_black(k) / ( 1.0 + 5.0 * rif1d(k) ) |
---|
600 | ELSE |
---|
601 | l1d(k) = l_black(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
602 | ENDIF |
---|
603 | l1d(k) = l_black(k) |
---|
604 | ENDDO |
---|
605 | |
---|
606 | ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN |
---|
607 | DO k = nzb+1, nzt |
---|
608 | dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
609 | IF ( dpt_dz > 0.0 ) THEN |
---|
610 | l_stable = 0.76 * SQRT( e1d(k) ) / & |
---|
611 | SQRT( g / pt_init(k) * dpt_dz ) + 1E-5 |
---|
612 | ELSE |
---|
613 | l_stable = l_grid(k) |
---|
614 | ENDIF |
---|
615 | l1d(k) = MIN( l_grid(k), l_stable ) |
---|
616 | ENDDO |
---|
617 | ENDIF |
---|
618 | |
---|
619 | ! |
---|
620 | !-- Compute the diffusion coefficients for momentum via the |
---|
621 | !-- corresponding Prandtl-layer relationship and according to |
---|
622 | !-- Prandtl-Kolmogorov, respectively. The unstable stratification is |
---|
623 | !-- computed via the adiabatic mixing length, for the unstability has |
---|
624 | !-- already been taken account of via the TKE (cf. also Diss.). |
---|
625 | IF ( prandtl_layer ) THEN |
---|
626 | IF ( rif1d(nzb+1) >= 0.0 ) THEN |
---|
627 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) / & |
---|
628 | ( 1.0 + 5.0 * rif1d(nzb+1) ) |
---|
629 | ELSE |
---|
630 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) * & |
---|
631 | ( 1.0 - 16.0 * rif1d(nzb+1) )**0.25 |
---|
632 | ENDIF |
---|
633 | ENDIF |
---|
634 | DO k = nzb_diff, nzt |
---|
635 | ! km1d(k) = 0.4 * SQRT( e1d(k) ) !changed: adjustment to 3D-model |
---|
636 | km1d(k) = 0.1 * SQRT( e1d(k) ) |
---|
637 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
638 | km1d(k) = km1d(k) * l1d(k) |
---|
639 | ELSE |
---|
640 | km1d(k) = km1d(k) * l_black(k) |
---|
641 | ENDIF |
---|
642 | ENDDO |
---|
643 | |
---|
644 | ! |
---|
645 | !-- Add damping layer |
---|
646 | DO k = damp_level_ind_1d+1, nzt+1 |
---|
647 | km1d(k) = 1.1 * km1d(k-1) |
---|
648 | km1d(k) = MIN( km1d(k), 10.0 ) |
---|
649 | ENDDO |
---|
650 | |
---|
651 | ! |
---|
652 | !-- Compute the diffusion coefficient for heat via the relationship |
---|
653 | !-- kh = phim / phih * km |
---|
654 | DO k = nzb+1, nzt |
---|
655 | IF ( rif1d(k) >= 0.0 ) THEN |
---|
656 | kh1d(k) = km1d(k) |
---|
657 | ELSE |
---|
658 | kh1d(k) = km1d(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25 |
---|
659 | ENDIF |
---|
660 | ENDDO |
---|
661 | |
---|
662 | ENDIF ! .NOT. constant_diffusion |
---|
663 | |
---|
664 | ENDDO ! intermediate step loop |
---|
665 | |
---|
666 | ! |
---|
667 | !-- Increment simulated time and output times |
---|
668 | current_timestep_number_1d = current_timestep_number_1d + 1 |
---|
669 | simulated_time_1d = simulated_time_1d + dt_1d |
---|
670 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
671 | time_pr_1d = time_pr_1d + dt_1d |
---|
672 | time_run_control_1d = time_run_control_1d + dt_1d |
---|
673 | |
---|
674 | ! |
---|
675 | !-- Determine and print out quantities for run control |
---|
676 | IF ( time_run_control_1d >= dt_run_control_1d ) THEN |
---|
677 | CALL run_control_1d |
---|
678 | time_run_control_1d = time_run_control_1d - dt_run_control_1d |
---|
679 | ENDIF |
---|
680 | |
---|
681 | ! |
---|
682 | !-- Profile output on file |
---|
683 | IF ( time_pr_1d >= dt_pr_1d ) THEN |
---|
684 | CALL print_1d_model |
---|
685 | time_pr_1d = time_pr_1d - dt_pr_1d |
---|
686 | ENDIF |
---|
687 | |
---|
688 | ! |
---|
689 | !-- Determine size of next time step |
---|
690 | CALL timestep_1d |
---|
691 | |
---|
692 | ENDDO ! time loop |
---|
693 | |
---|
694 | |
---|
695 | END SUBROUTINE time_integration_1d |
---|
696 | |
---|
697 | |
---|
698 | SUBROUTINE run_control_1d |
---|
699 | |
---|
700 | !------------------------------------------------------------------------------! |
---|
701 | ! Description: |
---|
702 | ! ------------ |
---|
703 | ! Compute and print out quantities for run control of the 1D model. |
---|
704 | !------------------------------------------------------------------------------! |
---|
705 | |
---|
706 | USE constants |
---|
707 | USE indices |
---|
708 | USE model_1d |
---|
709 | USE pegrid |
---|
710 | USE control_parameters |
---|
711 | |
---|
712 | IMPLICIT NONE |
---|
713 | |
---|
714 | INTEGER :: k |
---|
715 | REAL :: alpha, energy, umax, uv_total, vmax |
---|
716 | |
---|
717 | ! |
---|
718 | !-- Output |
---|
719 | IF ( myid == 0 ) THEN |
---|
720 | ! |
---|
721 | !-- If necessary, write header |
---|
722 | IF ( .NOT. run_control_header_1d ) THEN |
---|
723 | CALL check_open( 15 ) |
---|
724 | WRITE ( 15, 100 ) |
---|
725 | run_control_header_1d = .TRUE. |
---|
726 | ENDIF |
---|
727 | |
---|
728 | ! |
---|
729 | !-- Compute control quantities |
---|
730 | !-- grid level nzp is excluded due to mirror boundary condition |
---|
731 | umax = 0.0; vmax = 0.0; energy = 0.0 |
---|
732 | DO k = nzb+1, nzt+1 |
---|
733 | umax = MAX( ABS( umax ), ABS( u1d(k) ) ) |
---|
734 | vmax = MAX( ABS( vmax ), ABS( v1d(k) ) ) |
---|
735 | energy = energy + 0.5 * ( u1d(k)**2 + v1d(k)**2 ) |
---|
736 | ENDDO |
---|
737 | energy = energy / REAL( nzt - nzb + 1 ) |
---|
738 | |
---|
739 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
740 | IF ( ABS( v1d(nzb+1) ) .LT. 1.0E-5 ) THEN |
---|
741 | alpha = ACOS( SIGN( 1.0 , u1d(nzb+1) ) ) |
---|
742 | ELSE |
---|
743 | alpha = ACOS( u1d(nzb+1) / uv_total ) |
---|
744 | IF ( v1d(nzb+1) <= 0.0 ) alpha = 2.0 * pi - alpha |
---|
745 | ENDIF |
---|
746 | alpha = alpha / ( 2.0 * pi ) * 360.0 |
---|
747 | |
---|
748 | WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, & |
---|
749 | dt_1d, umax, vmax, us1d, alpha, energy |
---|
750 | ! |
---|
751 | !-- Write buffer contents to disc immediately |
---|
752 | CALL local_flush( 15 ) |
---|
753 | |
---|
754 | ENDIF |
---|
755 | |
---|
756 | ! |
---|
757 | !-- formats |
---|
758 | 100 FORMAT (///'1D-Zeitschrittkontrollausgaben:'/ & |
---|
759 | &'------------------------------'// & |
---|
760 | &'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ & |
---|
761 | &'-------------------------------------------------------------') |
---|
762 | 101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,2X,F5.3,2X,F5.1,2X,F7.2) |
---|
763 | |
---|
764 | |
---|
765 | END SUBROUTINE run_control_1d |
---|
766 | |
---|
767 | |
---|
768 | |
---|
769 | SUBROUTINE timestep_1d |
---|
770 | |
---|
771 | !------------------------------------------------------------------------------! |
---|
772 | ! Description: |
---|
773 | ! ------------ |
---|
774 | ! Compute the time step w.r.t. the diffusion criterion |
---|
775 | !------------------------------------------------------------------------------! |
---|
776 | |
---|
777 | USE arrays_3d |
---|
778 | USE indices |
---|
779 | USE model_1d |
---|
780 | USE pegrid |
---|
781 | USE control_parameters |
---|
782 | |
---|
783 | IMPLICIT NONE |
---|
784 | |
---|
785 | INTEGER :: k |
---|
786 | REAL :: div, dt_diff, fac, value |
---|
787 | |
---|
788 | |
---|
789 | ! |
---|
790 | !-- Compute the currently feasible time step according to the diffusion |
---|
791 | !-- criterion. At nzb+1 the half grid length is used. |
---|
792 | fac = 0.35 |
---|
793 | dt_diff = dt_max_1d |
---|
794 | DO k = nzb+2, nzt |
---|
795 | value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20 ) |
---|
796 | dt_diff = MIN( value, dt_diff ) |
---|
797 | ENDDO |
---|
798 | value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20 ) |
---|
799 | dt_1d = MIN( value, dt_diff ) |
---|
800 | |
---|
801 | ! |
---|
802 | !-- Set flag when the time step becomes too small |
---|
803 | IF ( dt_1d < ( 0.00001 * dt_max_1d ) ) THEN |
---|
804 | stop_dt_1d = .TRUE. |
---|
805 | |
---|
806 | WRITE( message_string, * ) 'timestep has exceeded the lower limit &', & |
---|
807 | 'dt_1d = ',dt_1d,' s simulation stopped!' |
---|
808 | CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 ) |
---|
809 | |
---|
810 | ENDIF |
---|
811 | |
---|
812 | ! |
---|
813 | !-- A more or less simple new time step value is obtained taking only the |
---|
814 | !-- first two significant digits |
---|
815 | div = 1000.0 |
---|
816 | DO WHILE ( dt_1d < div ) |
---|
817 | div = div / 10.0 |
---|
818 | ENDDO |
---|
819 | dt_1d = NINT( dt_1d * 100.0 / div ) * div / 100.0 |
---|
820 | |
---|
821 | old_dt_1d = dt_1d |
---|
822 | |
---|
823 | |
---|
824 | END SUBROUTINE timestep_1d |
---|
825 | |
---|
826 | |
---|
827 | |
---|
828 | SUBROUTINE print_1d_model |
---|
829 | |
---|
830 | !------------------------------------------------------------------------------! |
---|
831 | ! Description: |
---|
832 | ! ------------ |
---|
833 | ! List output of profiles from the 1D-model |
---|
834 | !------------------------------------------------------------------------------! |
---|
835 | |
---|
836 | USE arrays_3d |
---|
837 | USE indices |
---|
838 | USE model_1d |
---|
839 | USE pegrid |
---|
840 | USE control_parameters |
---|
841 | |
---|
842 | IMPLICIT NONE |
---|
843 | |
---|
844 | |
---|
845 | INTEGER :: k |
---|
846 | |
---|
847 | |
---|
848 | IF ( myid == 0 ) THEN |
---|
849 | ! |
---|
850 | !-- Open list output file for profiles from the 1D-model |
---|
851 | CALL check_open( 17 ) |
---|
852 | |
---|
853 | ! |
---|
854 | !-- Write Header |
---|
855 | WRITE ( 17, 100 ) TRIM( run_description_header ), & |
---|
856 | TRIM( simulated_time_chr ) |
---|
857 | WRITE ( 17, 101 ) |
---|
858 | |
---|
859 | ! |
---|
860 | !-- Write the values |
---|
861 | WRITE ( 17, 102 ) |
---|
862 | WRITE ( 17, 101 ) |
---|
863 | DO k = nzt+1, nzb, -1 |
---|
864 | WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), & |
---|
865 | rif1d(k), km1d(k), kh1d(k), l1d(k), zu(k), k |
---|
866 | ENDDO |
---|
867 | WRITE ( 17, 101 ) |
---|
868 | WRITE ( 17, 102 ) |
---|
869 | WRITE ( 17, 101 ) |
---|
870 | |
---|
871 | ! |
---|
872 | !-- Write buffer contents to disc immediately |
---|
873 | CALL local_flush( 17 ) |
---|
874 | |
---|
875 | ENDIF |
---|
876 | |
---|
877 | ! |
---|
878 | !-- Formats |
---|
879 | 100 FORMAT (//1X,A/1X,10('-')/' 1d-model profiles'/ & |
---|
880 | ' Time: ',A) |
---|
881 | 101 FORMAT (1X,79('-')) |
---|
882 | 102 FORMAT (' k zu u v pt e rif Km Kh ', & |
---|
883 | 'l zu k') |
---|
884 | 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, & |
---|
885 | 1X,F5.2,1X,F6.2,1X,F7.1,2X,I4) |
---|
886 | |
---|
887 | |
---|
888 | END SUBROUTINE print_1d_model |
---|