1 | !> @file basic_constants_and_equations_mod.f90 |
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2 | !--------------------------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General |
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6 | ! Public License as published by the Free Software Foundation, either version 3 of the License, or |
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7 | ! (at your option) any later version. |
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8 | ! |
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9 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the |
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10 | ! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General |
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11 | ! Public License for more details. |
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12 | ! |
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13 | ! You should have received a copy of the GNU General Public License along with PALM. If not, see |
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14 | ! <http://www.gnu.org/licenses/>. |
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15 | ! |
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16 | ! Copyright 1997-2020 Leibniz Universitaet Hannover |
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17 | !--------------------------------------------------------------------------------------------------! |
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18 | ! |
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19 | ! Current revisions: |
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20 | ! ----------------- |
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21 | ! |
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22 | ! |
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23 | ! Former revisions: |
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24 | ! ----------------- |
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25 | ! $Id: basic_constants_and_equations_mod.f90 4509 2020-04-26 15:57:55Z suehring $ |
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26 | ! file re-formatted to follow the PALM coding standard |
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27 | ! |
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28 | ! 4502 2020-04-17 16:14:16Z schwenkel |
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29 | ! Implementation of ice microphysics |
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30 | ! |
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31 | ! 4400 2020-02-10 20:32:41Z suehring |
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32 | ! Move routine to transform coordinates from netcdf_interface_mod to |
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33 | ! basic_constants_and_equations_mod |
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34 | ! |
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35 | ! 4360 2020-01-07 11:25:50Z suehring |
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36 | ! Corrected "Former revisions" section |
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37 | ! |
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38 | ! 4088 2019-07-11 13:57:56Z Giersch |
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39 | ! Comment of barometric formula improved, function for ideal gas law revised |
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40 | ! |
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41 | ! 4084 2019-07-10 17:09:11Z knoop |
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42 | ! Changed precomputed fractions to be variable based |
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43 | ! |
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44 | ! 4055 2019-06-27 09:47:29Z suehring |
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45 | ! Added rgas_univ (universal gas constant) (E.C. Chan) |
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46 | ! |
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47 | ! |
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48 | ! 3655 2019-01-07 16:51:22Z knoop |
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49 | ! OpenACC port for SPEC |
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50 | ! 3361 2018-10-16 20:39:37Z knoop |
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51 | ! New module (introduced with modularization of bulk cloud physics model) |
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52 | ! |
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53 | ! |
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54 | ! |
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55 | ! |
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56 | ! Description: |
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57 | ! ------------ |
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58 | !> This module contains all basic (physical) constants and functions for the calculation of |
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59 | !> diagnostic quantities. |
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60 | !- -----------------------------------------------------------------------------! |
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61 | MODULE basic_constants_and_equations_mod |
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62 | |
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63 | |
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64 | USE kinds |
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65 | |
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66 | IMPLICIT NONE |
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67 | |
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68 | |
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69 | REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1) |
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70 | REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K) |
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71 | REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2) |
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72 | REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant |
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73 | REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1) |
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74 | REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1) |
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75 | REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1) |
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76 | REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1) |
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77 | REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1) |
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78 | REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1) |
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79 | REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1) |
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80 | REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI |
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81 | !$ACC DECLARE COPYIN(pi) |
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82 | REAL(wp), PARAMETER :: rgas_univ = 8.31446261815324_wp !< universal gas constant (J K-1 mol-1) |
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83 | REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3) |
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84 | REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3) |
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85 | REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3) |
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86 | REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3) |
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87 | REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1) |
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88 | REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1) |
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89 | REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant |
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90 | REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere |
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91 | REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl |
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92 | REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid |
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93 | REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate |
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94 | |
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95 | REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state |
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96 | |
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97 | REAL(wp), PARAMETER :: cp_d_rd = c_p / r_d !< precomputed c_p / r_d |
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98 | REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p |
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99 | REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p |
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100 | REAL(wp), PARAMETER :: ls_d_cp = l_s / c_p !< precomputed l_s / c_p |
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101 | REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d |
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102 | REAL(wp), PARAMETER :: rd_d_rv = r_d / r_v !< precomputed r_d / r_v |
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103 | REAL(wp), PARAMETER :: rd_d_cp = r_d / c_p !< precomputed r_d / c_p |
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104 | |
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105 | REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1) |
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106 | REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3) |
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107 | REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl |
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108 | |
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109 | SAVE |
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110 | |
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111 | PRIVATE magnus_0d, & |
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112 | magnus_1d, & |
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113 | magnus_tl_0d, & |
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114 | magnus_tl_1d, & |
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115 | magnus_0d_ice, & |
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116 | magnus_1d_ice, & |
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117 | ideal_gas_law_rho_0d, & |
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118 | ideal_gas_law_rho_1d, & |
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119 | ideal_gas_law_rho_pt_0d, & |
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120 | ideal_gas_law_rho_pt_1d, & |
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121 | exner_function_0d, & |
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122 | exner_function_1d, & |
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123 | exner_function_invers_0d, & |
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124 | exner_function_invers_1d, & |
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125 | barometric_formula_0d, & |
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126 | barometric_formula_1d |
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127 | |
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128 | |
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129 | INTERFACE convert_utm_to_geographic |
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130 | MODULE PROCEDURE convert_utm_to_geographic |
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131 | END INTERFACE convert_utm_to_geographic |
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132 | |
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133 | INTERFACE magnus |
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134 | MODULE PROCEDURE magnus_0d |
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135 | MODULE PROCEDURE magnus_1d |
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136 | END INTERFACE magnus |
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137 | |
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138 | INTERFACE magnus_tl |
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139 | MODULE PROCEDURE magnus_tl_0d |
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140 | MODULE PROCEDURE magnus_tl_1d |
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141 | END INTERFACE magnus_tl |
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142 | |
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143 | INTERFACE magnus_ice |
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144 | MODULE PROCEDURE magnus_0d_ice |
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145 | MODULE PROCEDURE magnus_1d_ice |
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146 | END INTERFACE magnus_ice |
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147 | |
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148 | INTERFACE ideal_gas_law_rho |
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149 | MODULE PROCEDURE ideal_gas_law_rho_0d |
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150 | MODULE PROCEDURE ideal_gas_law_rho_1d |
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151 | END INTERFACE ideal_gas_law_rho |
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152 | |
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153 | INTERFACE ideal_gas_law_rho_pt |
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154 | MODULE PROCEDURE ideal_gas_law_rho_pt_0d |
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155 | MODULE PROCEDURE ideal_gas_law_rho_pt_1d |
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156 | END INTERFACE ideal_gas_law_rho_pt |
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157 | |
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158 | INTERFACE exner_function |
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159 | MODULE PROCEDURE exner_function_0d |
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160 | MODULE PROCEDURE exner_function_1d |
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161 | END INTERFACE exner_function |
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162 | |
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163 | INTERFACE exner_function_invers |
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164 | MODULE PROCEDURE exner_function_invers_0d |
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165 | MODULE PROCEDURE exner_function_invers_1d |
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166 | END INTERFACE exner_function_invers |
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167 | |
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168 | INTERFACE barometric_formula |
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169 | MODULE PROCEDURE barometric_formula_0d |
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170 | MODULE PROCEDURE barometric_formula_1d |
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171 | END INTERFACE barometric_formula |
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172 | ! |
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173 | !-- Public routines |
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174 | PUBLIC convert_utm_to_geographic |
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175 | |
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176 | CONTAINS |
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177 | |
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178 | |
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179 | !--------------------------------------------------------------------------------------------------! |
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180 | ! Description: |
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181 | ! ------------ |
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182 | !> Convert UTM coordinates into geographic latitude and longitude. Conversion is based on the work |
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183 | !> of KrÃŒger (1912) DOI: 10.2312/GFZ.b103-krueger28 and Karney (2013) DOI: 10.1007/s00190-012-0578-z |
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184 | !> Based on a JavaScript of the geodesy function library written by chrisveness |
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185 | !> https://github.com/chrisveness/geodesy |
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186 | !--------------------------------------------------------------------------------------------------! |
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187 | SUBROUTINE convert_utm_to_geographic( crs, eutm, nutm, lon, lat ) |
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188 | |
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189 | INTEGER(iwp) :: j !< loop index |
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190 | |
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191 | REAL(wp), INTENT(in) :: eutm !< easting (UTM) |
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192 | REAL(wp), INTENT(out) :: lat !< geographic latitude in degree |
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193 | REAL(wp), INTENT(out) :: lon !< geographic longitude in degree |
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194 | REAL(wp), INTENT(in) :: nutm !< northing (UTM) |
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195 | |
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196 | REAL(wp) :: a !< 2*pi*a is the circumference of a meridian |
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197 | REAL(wp) :: cos_eta_s !< cos(eta_s) |
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198 | REAL(wp) :: delta_i !< |
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199 | REAL(wp) :: delta_tau_i !< |
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200 | REAL(wp) :: e !< eccentricity |
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201 | REAL(wp) :: eta !< |
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202 | REAL(wp) :: eta_s !< |
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203 | REAL(wp) :: n !< 3rd flattening |
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204 | REAL(wp) :: n2 !< n^2 |
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205 | REAL(wp) :: n3 !< n^3 |
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206 | REAL(wp) :: n4 !< n^4 |
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207 | REAL(wp) :: n5 !< n^5 |
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208 | REAL(wp) :: n6 !< n^6 |
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209 | REAL(wp) :: nu !< |
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210 | REAL(wp) :: nu_s !< |
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211 | REAL(wp) :: sin_eta_s !< sin(eta_s) |
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212 | REAL(wp) :: sinh_nu_s !< sinush(nu_s) |
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213 | REAL(wp) :: tau_i !< |
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214 | REAL(wp) :: tau_i_s !< |
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215 | REAL(wp) :: tau_s !< |
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216 | REAL(wp) :: x !< adjusted easting |
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217 | REAL(wp) :: y !< adjusted northing |
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218 | |
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219 | REAL(wp), DIMENSION(6) :: beta !< 6th order KrÃŒger expressions |
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220 | |
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221 | REAL(wp), DIMENSION(8), INTENT(in) :: crs !< coordinate reference system, consists of |
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222 | !< (/semi_major_axis, |
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223 | !< inverse_flattening, |
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224 | !< longitude_of_prime_meridian, |
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225 | !< longitude_of_central_meridian, |
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226 | !< scale_factor_at_central_meridian, |
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227 | !< latitude_of_projection_origin, |
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228 | !< false_easting, |
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229 | !< false_northing /) |
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230 | |
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231 | x = eutm - crs(7) ! remove false easting |
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232 | y = nutm - crs(8) ! remove false northing |
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233 | ! |
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234 | !-- From Karney 2011 Eq 15-22, 36: |
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235 | e = SQRT( 1.0_wp / crs(2) * ( 2.0_wp - 1.0_wp / crs(2) ) ) |
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236 | n = 1.0_wp / crs(2) / ( 2.0_wp - 1.0_wp / crs(2) ) |
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237 | n2 = n * n |
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238 | n3 = n * n2 |
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239 | n4 = n * n3 |
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240 | n5 = n * n4 |
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241 | n6 = n * n5 |
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242 | |
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243 | a = crs(1) / ( 1.0_wp + n ) * ( 1.0_wp + 0.25_wp * n2 + 0.015625_wp * n4 + 3.90625E-3_wp * n6 ) |
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244 | |
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245 | nu = x / ( crs(5) * a ) |
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246 | eta = y / ( crs(5) * a ) |
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247 | |
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248 | !-- According to KrÃŒger (1912), eq. 26* |
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249 | beta(1) = 0.5_wp * n & |
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250 | - 2.0_wp / 3.0_wp * n2 & |
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251 | + 37.0_wp / 96.0_wp * n3 & |
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252 | - 1.0_wp / 360.0_wp * n4 & |
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253 | - 81.0_wp / 512.0_wp * n5 & |
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254 | + 96199.0_wp / 604800.0_wp * n6 |
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255 | |
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256 | beta(2) = 1.0_wp / 48.0_wp * n2 & |
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257 | + 1.0_wp / 15.0_wp * n3 & |
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258 | - 437.0_wp / 1440.0_wp * n4 & |
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259 | + 46.0_wp / 105.0_wp * n5 & |
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260 | - 1118711.0_wp / 3870720.0_wp * n6 |
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261 | |
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262 | beta(3) = 17.0_wp / 480.0_wp * n3 & |
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263 | - 37.0_wp / 840.0_wp * n4 & |
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264 | - 209.0_wp / 4480.0_wp * n5 & |
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265 | + 5569.0_wp / 90720.0_wp * n6 |
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266 | |
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267 | beta(4) = 4397.0_wp / 161280.0_wp * n4 & |
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268 | - 11.0_wp / 504.0_wp * n5 & |
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269 | - 830251.0_wp / 7257600.0_wp * n6 |
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270 | |
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271 | beta(5) = 4583.0_wp / 161280.0_wp * n5 & |
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272 | - 108847.0_wp / 3991680.0_wp * n6 |
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273 | |
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274 | beta(6) = 20648693.0_wp / 638668800.0_wp * n6 |
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275 | |
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276 | eta_s = eta |
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277 | nu_s = nu |
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278 | DO j = 1, 6 |
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279 | eta_s = eta_s - beta(j) * SIN(2.0_wp * j * eta) * COSH(2.0_wp * j * nu) |
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280 | nu_s = nu_s - beta(j) * COS(2.0_wp * j * eta) * SINH(2.0_wp * j * nu) |
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281 | ENDDO |
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282 | |
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283 | sinh_nu_s = SINH( nu_s ) |
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284 | sin_eta_s = SIN( eta_s ) |
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285 | cos_eta_s = COS( eta_s ) |
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286 | |
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287 | tau_s = sin_eta_s / SQRT( sinh_nu_s**2 + cos_eta_s**2 ) |
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288 | |
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289 | tau_i = tau_s |
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290 | delta_tau_i = 1.0_wp |
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291 | |
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292 | DO WHILE ( ABS( delta_tau_i ) > 1.0E-12_wp ) |
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293 | |
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294 | delta_i = SINH( e * ATANH( e * tau_i / SQRT( 1.0_wp + tau_i**2 ) ) ) |
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295 | |
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296 | tau_i_s = tau_i * SQRT( 1.0_wp + delta_i**2 ) - delta_i * SQRT( 1.0_wp + tau_i**2 ) |
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297 | |
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298 | delta_tau_i = ( tau_s - tau_i_s ) / SQRT( 1.0_wp + tau_i_s**2 ) & |
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299 | * ( 1.0_wp + ( 1.0_wp - e**2 ) * tau_i**2 ) & |
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300 | / ( ( 1.0_wp - e**2 ) * SQRT( 1.0_wp + tau_i**2 ) ) |
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301 | |
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302 | tau_i = tau_i + delta_tau_i |
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303 | |
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304 | ENDDO |
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305 | |
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306 | lat = ATAN( tau_i ) / pi * 180.0_wp |
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307 | lon = ATAN2( sinh_nu_s, cos_eta_s ) / pi * 180.0_wp + crs(4) |
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308 | |
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309 | END SUBROUTINE convert_utm_to_geographic |
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310 | |
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311 | !--------------------------------------------------------------------------------------------------! |
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312 | ! Description: |
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313 | ! ------------ |
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314 | !> This function computes the magnus formula (Press et al., 1992). |
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315 | !> The magnus formula is needed to calculate the saturation vapor pressure. |
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316 | !--------------------------------------------------------------------------------------------------! |
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317 | FUNCTION magnus_0d( t ) |
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318 | |
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319 | IMPLICIT NONE |
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320 | |
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321 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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322 | |
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323 | REAL(wp) :: magnus_0d |
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324 | |
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325 | ! |
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326 | !-- Saturation vapor pressure for a specific temperature: |
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327 | magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / ( t - 29.65_wp ) ) |
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328 | |
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329 | END FUNCTION magnus_0d |
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330 | |
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331 | !--------------------------------------------------------------------------------------------------! |
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332 | ! Description: |
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333 | ! ------------ |
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334 | !> This function computes the magnus formula (Press et al., 1992). |
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335 | !> The magnus formula is needed to calculate the saturation vapor pressure. |
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336 | !--------------------------------------------------------------------------------------------------! |
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337 | FUNCTION magnus_1d( t ) |
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338 | |
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339 | IMPLICIT NONE |
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340 | |
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341 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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342 | |
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343 | REAL(wp), DIMENSION(size(t)) :: magnus_1d |
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344 | |
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345 | ! |
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346 | !-- Saturation vapor pressure for a specific temperature: |
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347 | magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / ( t - 29.65_wp ) ) |
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348 | |
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349 | END FUNCTION magnus_1d |
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350 | |
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351 | !--------------------------------------------------------------------------------------------------! |
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352 | ! Description: |
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353 | ! ------------ |
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354 | !> This function computes the magnus formula (Press et al., 1992) using the (ice-) liquid water |
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355 | !> potential temperature. |
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356 | !> The magnus formula is needed to calculate the saturation vapor pressure over a plane liquid water |
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357 | !> surface. |
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358 | !--------------------------------------------------------------------------------------------------! |
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359 | FUNCTION magnus_tl_0d( t_l ) |
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360 | |
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361 | IMPLICIT NONE |
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362 | |
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363 | REAL(wp), INTENT(IN) :: t_l !< liquid water temperature (K) |
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364 | |
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365 | REAL(wp) :: magnus_tl_0d |
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366 | |
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367 | ! |
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368 | !-- Saturation vapor pressure for a specific temperature: |
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369 | magnus_tl_0d = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / ( t_l - 35.86_wp ) ) |
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370 | |
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371 | END FUNCTION magnus_tl_0d |
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372 | |
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373 | !--------------------------------------------------------------------------------------------------! |
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374 | ! Description: |
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375 | ! ------------ |
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376 | !> This function computes the magnus formula (Press et al., 1992) using the (ice-) liquid water |
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377 | !> potential temperature. |
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378 | !> The magnus formula is needed to calculate the saturation vapor pressure over a plane liquid water |
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379 | !> surface. |
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380 | !--------------------------------------------------------------------------------------------------! |
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381 | FUNCTION magnus_tl_1d( t_l ) |
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382 | |
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383 | IMPLICIT NONE |
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384 | |
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385 | REAL(wp), INTENT(IN), DIMENSION(:) :: t_l !< liquid water temperature (K) |
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386 | |
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387 | REAL(wp), DIMENSION(size(t_l)) :: magnus_tl_1d |
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388 | ! |
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389 | !-- Saturation vapor pressure for a specific temperature: |
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390 | magnus_tl_1d = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / ( t_l - 35.86_wp ) ) |
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391 | |
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392 | END FUNCTION magnus_tl_1d |
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393 | |
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394 | !--------------------------------------------------------------------------------------------------! |
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395 | ! Description: |
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396 | ! ------------ |
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397 | !> This function computes the magnus formula (Press et al., 1992). |
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398 | !> The magnus formula is needed to calculate the saturation vapor pressure over a plane ice surface. |
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399 | !--------------------------------------------------------------------------------------------------! |
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400 | FUNCTION magnus_0d_ice( t ) |
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401 | |
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402 | IMPLICIT NONE |
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403 | |
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404 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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405 | |
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406 | REAL(wp) :: magnus_0d_ice |
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407 | |
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408 | ! |
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409 | !-- Saturation vapor pressure for a specific temperature: |
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410 | magnus_0d_ice = 611.2_wp * EXP( 22.46_wp * ( t - degc_to_k ) / ( t - 0.53_wp ) ) |
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411 | |
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412 | END FUNCTION magnus_0d_ice |
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413 | |
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414 | !--------------------------------------------------------------------------------------------------! |
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415 | ! Description: |
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416 | ! ------------ |
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417 | !> This function computes the magnus formula (Press et al., 1992). |
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418 | !> The magnus formula is needed to calculate the saturation vapor pressure over a plane ice surface. |
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419 | !--------------------------------------------------------------------------------------------------! |
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420 | FUNCTION magnus_1d_ice( t ) |
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421 | |
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422 | IMPLICIT NONE |
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423 | |
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424 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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425 | |
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426 | REAL(wp), DIMENSION(size(t)) :: magnus_1d_ice |
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427 | |
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428 | ! |
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429 | !-- Saturation vapor pressure for a specific temperature: |
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430 | magnus_1d_ice = 611.2_wp * EXP( 22.46_wp * ( t - degc_to_k ) / ( t - 0.53_wp ) ) |
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431 | |
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432 | END FUNCTION magnus_1d_ice |
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433 | |
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434 | !--------------------------------------------------------------------------------------------------! |
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435 | ! Description: |
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436 | ! ------------ |
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437 | !> Compute the ideal gas law for scalar arguments. |
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438 | !--------------------------------------------------------------------------------------------------! |
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439 | FUNCTION ideal_gas_law_rho_0d( p, t ) |
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440 | |
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441 | IMPLICIT NONE |
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442 | |
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443 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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444 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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445 | |
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446 | REAL(wp) :: ideal_gas_law_rho_0d |
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447 | |
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448 | ! |
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449 | !-- Compute density according to ideal gas law: |
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450 | ideal_gas_law_rho_0d = p / (r_d * t) |
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451 | |
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452 | END FUNCTION ideal_gas_law_rho_0d |
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453 | |
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454 | !--------------------------------------------------------------------------------------------------! |
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455 | ! Description: |
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456 | ! ------------ |
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457 | !> Compute the ideal gas law for 1-D array arguments. |
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458 | !--------------------------------------------------------------------------------------------------! |
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459 | FUNCTION ideal_gas_law_rho_1d( p, t ) |
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460 | |
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461 | IMPLICIT NONE |
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462 | |
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463 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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464 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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465 | |
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466 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d |
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467 | |
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468 | ! |
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469 | !-- Compute density according to ideal gas law: |
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470 | ideal_gas_law_rho_1d = p / (r_d * t) |
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471 | |
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472 | END FUNCTION ideal_gas_law_rho_1d |
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473 | |
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474 | !--------------------------------------------------------------------------------------------------! |
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475 | ! Description: |
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476 | ! ------------ |
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477 | !> Compute the ideal gas law for scalar arguments. |
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478 | !--------------------------------------------------------------------------------------------------! |
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479 | FUNCTION ideal_gas_law_rho_pt_0d( p, t ) |
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480 | |
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481 | IMPLICIT NONE |
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482 | |
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483 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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484 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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485 | |
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486 | REAL(wp) :: ideal_gas_law_rho_pt_0d |
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487 | |
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488 | ! |
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489 | !-- Compute density according to ideal gas law: |
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490 | ideal_gas_law_rho_pt_0d = p / (r_d * exner_function(p) * t) |
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491 | |
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492 | END FUNCTION ideal_gas_law_rho_pt_0d |
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493 | |
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494 | !--------------------------------------------------------------------------------------------------! |
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495 | ! Description: |
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496 | ! ------------ |
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497 | !> Compute the ideal gas law for 1-D array arguments. |
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498 | !--------------------------------------------------------------------------------------------------! |
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499 | FUNCTION ideal_gas_law_rho_pt_1d( p, t ) |
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500 | |
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501 | IMPLICIT NONE |
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502 | |
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503 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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504 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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505 | |
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506 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d |
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507 | |
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508 | ! |
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509 | !-- Compute density according to ideal gas law: |
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510 | ideal_gas_law_rho_pt_1d = p / (r_d * exner_function(p) * t) |
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511 | |
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512 | END FUNCTION ideal_gas_law_rho_pt_1d |
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513 | |
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514 | !--------------------------------------------------------------------------------------------------! |
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515 | ! Description: |
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516 | ! ------------ |
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517 | !> Compute the exner function for scalar arguments. |
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518 | !--------------------------------------------------------------------------------------------------! |
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519 | FUNCTION exner_function_0d( p ) |
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520 | |
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521 | IMPLICIT NONE |
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522 | |
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523 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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524 | |
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525 | REAL(wp) :: exner_function_0d |
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526 | |
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527 | ! |
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528 | !-- Compute exner function: |
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529 | exner_function_0d = ( p / p_0 )**( rd_d_cp ) |
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530 | |
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531 | END FUNCTION exner_function_0d |
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532 | |
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533 | !--------------------------------------------------------------------------------------------------! |
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534 | ! Description: |
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535 | ! ------------ |
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536 | !> Compute the exner function for 1-D array arguments. |
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537 | !--------------------------------------------------------------------------------------------------! |
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538 | FUNCTION exner_function_1d( p ) |
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539 | |
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540 | IMPLICIT NONE |
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541 | |
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542 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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543 | |
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544 | REAL(wp), DIMENSION(size(p)) :: exner_function_1d |
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545 | |
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546 | ! |
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547 | !-- Compute exner function: |
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548 | exner_function_1d = ( p / p_0 )**( rd_d_cp ) |
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549 | |
---|
550 | END FUNCTION exner_function_1d |
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551 | |
---|
552 | !--------------------------------------------------------------------------------------------------! |
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553 | ! Description: |
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554 | ! ------------ |
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555 | !> Compute the exner function for scalar arguments. |
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556 | !--------------------------------------------------------------------------------------------------! |
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557 | FUNCTION exner_function_invers_0d( p ) |
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558 | |
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559 | IMPLICIT NONE |
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560 | |
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561 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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562 | |
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563 | REAL(wp) :: exner_function_invers_0d |
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564 | |
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565 | ! |
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566 | !-- Compute exner function: |
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567 | exner_function_invers_0d = ( p_0 / p )**( rd_d_cp ) |
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568 | |
---|
569 | END FUNCTION exner_function_invers_0d |
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570 | |
---|
571 | !--------------------------------------------------------------------------------------------------! |
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572 | ! Description: |
---|
573 | ! ------------ |
---|
574 | !> Compute the exner function for 1-D array arguments. |
---|
575 | !--------------------------------------------------------------------------------------------------! |
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576 | FUNCTION exner_function_invers_1d( p ) |
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577 | |
---|
578 | IMPLICIT NONE |
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579 | |
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580 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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581 | |
---|
582 | REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d |
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583 | |
---|
584 | ! |
---|
585 | !-- Compute exner function: |
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586 | exner_function_invers_1d = ( p_0 / p )**( rd_d_cp ) |
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587 | |
---|
588 | END FUNCTION exner_function_invers_1d |
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589 | |
---|
590 | !--------------------------------------------------------------------------------------------------! |
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591 | ! Description: |
---|
592 | ! ------------ |
---|
593 | !> Compute the barometric formula for scalar arguments. The calculation is based on the assumption |
---|
594 | !> of a polytropic atmosphere and neutral stratification, where the temperature lapse rate is g/cp. |
---|
595 | !--------------------------------------------------------------------------------------------------! |
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596 | FUNCTION barometric_formula_0d( z, t_0, p_0) |
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597 | |
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598 | IMPLICIT NONE |
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599 | |
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600 | REAL(wp), INTENT(IN) :: z !< height (m) |
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601 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
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602 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
---|
603 | |
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604 | REAL(wp) :: barometric_formula_0d |
---|
605 | |
---|
606 | ! |
---|
607 | !-- Compute barometric formula: |
---|
608 | barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
---|
609 | |
---|
610 | END FUNCTION barometric_formula_0d |
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611 | |
---|
612 | !--------------------------------------------------------------------------------------------------! |
---|
613 | ! Description: |
---|
614 | ! ------------ |
---|
615 | !> Compute the barometric formula for 1-D array arguments. The calculation is based on the |
---|
616 | !> assumption of a polytropic atmosphere and neutral stratification, where the temperature lapse |
---|
617 | !> rate is g/cp. |
---|
618 | !--------------------------------------------------------------------------------------------------! |
---|
619 | FUNCTION barometric_formula_1d( z, t_0, p_0) |
---|
620 | |
---|
621 | IMPLICIT NONE |
---|
622 | |
---|
623 | REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m) |
---|
624 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
---|
625 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
---|
626 | |
---|
627 | REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d |
---|
628 | |
---|
629 | ! |
---|
630 | !-- Compute barometric formula: |
---|
631 | barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
---|
632 | |
---|
633 | END FUNCTION barometric_formula_1d |
---|
634 | |
---|
635 | END MODULE basic_constants_and_equations_mod |
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