| 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 |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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| 18 | !------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ----------------- |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: basic_constants_and_equations_mod.f90 3361 2018-10-16 20:39:37Z raasch $ |
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| 27 | ! New module (introduced with modularization of bulk cloud physics model) |
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| 28 | ! |
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| 29 | ! |
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| 30 | ! |
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| 31 | ! |
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| 32 | ! Description: |
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| 33 | ! ------------ |
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| 34 | !> This module contains all basic (physical) constants |
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| 35 | !> and |
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| 36 | !> functions for the calculation of diagnostic quantities. |
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| 37 | !------------------------------------------------------------------------------! |
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| 38 | MODULE basic_constants_and_equations_mod |
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| 39 | |
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| 40 | |
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| 41 | USE kinds |
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| 42 | |
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| 43 | IMPLICIT NONE |
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| 44 | |
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| 45 | REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI |
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| 46 | |
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| 47 | REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1) |
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| 48 | REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2) |
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| 49 | REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant |
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| 50 | REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1) |
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| 51 | REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1) |
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| 52 | REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1) |
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| 53 | REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1) |
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| 54 | REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1) |
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| 55 | REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1) |
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| 56 | REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1) |
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| 57 | REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3) |
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| 58 | REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3) |
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| 59 | REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3) |
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| 60 | REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3) |
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| 61 | REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1) |
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| 62 | REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1) |
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| 63 | REAL(wp), PARAMETER :: sigma_sb = 5.67E-08_wp !< Stefan-Boltzmann constant |
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| 64 | REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere |
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| 65 | REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl |
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| 66 | REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid |
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| 67 | REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate |
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| 68 | |
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| 69 | REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state |
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| 70 | |
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| 71 | REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p |
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| 72 | REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p |
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| 73 | REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d |
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| 74 | REAL(wp), PARAMETER :: rd_d_rv = 0.622_wp !r_d / r_v !< precomputed r_d / r_v |
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| 75 | REAL(wp), PARAMETER :: rd_d_cp = 0.286_wp !r_d / c_p !< precomputed r_d / c_p |
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| 76 | REAL(wp), PARAMETER :: cp_d_rd = 1.0_wp/0.286_wp !c_p / r_d !< precomputed c_p / r_d |
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| 77 | |
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| 78 | REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1) |
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| 79 | REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3) |
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| 80 | REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl |
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| 81 | |
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| 82 | |
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| 83 | SAVE |
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| 84 | |
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| 85 | PRIVATE magnus_0d, & |
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| 86 | magnus_1d, & |
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| 87 | ideal_gas_law_rho_0d, & |
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| 88 | ideal_gas_law_rho_1d, & |
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| 89 | ideal_gas_law_rho_pt_0d, & |
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| 90 | ideal_gas_law_rho_pt_1d, & |
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| 91 | exner_function_0d, & |
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| 92 | exner_function_1d, & |
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| 93 | exner_function_invers_0d, & |
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| 94 | exner_function_invers_1d, & |
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| 95 | barometric_formula_0d, & |
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| 96 | barometric_formula_1d |
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| 97 | |
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| 98 | INTERFACE magnus |
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| 99 | MODULE PROCEDURE magnus_0d |
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| 100 | MODULE PROCEDURE magnus_1d |
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| 101 | END INTERFACE magnus |
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| 102 | |
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| 103 | INTERFACE ideal_gas_law_rho |
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| 104 | MODULE PROCEDURE ideal_gas_law_rho_0d |
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| 105 | MODULE PROCEDURE ideal_gas_law_rho_1d |
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| 106 | END INTERFACE ideal_gas_law_rho |
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| 107 | |
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| 108 | INTERFACE ideal_gas_law_rho_pt |
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| 109 | MODULE PROCEDURE ideal_gas_law_rho_pt_0d |
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| 110 | MODULE PROCEDURE ideal_gas_law_rho_pt_1d |
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| 111 | END INTERFACE ideal_gas_law_rho_pt |
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| 112 | |
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| 113 | INTERFACE exner_function |
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| 114 | MODULE PROCEDURE exner_function_0d |
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| 115 | MODULE PROCEDURE exner_function_1d |
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| 116 | END INTERFACE exner_function |
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| 117 | |
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| 118 | INTERFACE exner_function_invers |
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| 119 | MODULE PROCEDURE exner_function_invers_0d |
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| 120 | MODULE PROCEDURE exner_function_invers_1d |
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| 121 | END INTERFACE exner_function_invers |
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| 122 | |
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| 123 | INTERFACE barometric_formula |
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| 124 | MODULE PROCEDURE barometric_formula_0d |
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| 125 | MODULE PROCEDURE barometric_formula_1d |
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| 126 | END INTERFACE barometric_formula |
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| 127 | |
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| 128 | CONTAINS |
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| 129 | |
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| 130 | !------------------------------------------------------------------------------! |
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| 131 | ! Description: |
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| 132 | ! ------------ |
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| 133 | !> This function computes the magnus formula (Press et al., 1992). |
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| 134 | !> The magnus formula is needed to calculate the saturation vapor pressure |
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| 135 | !------------------------------------------------------------------------------! |
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| 136 | FUNCTION magnus_0d( t ) |
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| 137 | |
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| 138 | IMPLICIT NONE |
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| 139 | |
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| 140 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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| 141 | |
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| 142 | REAL(wp) :: magnus_0d |
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| 143 | ! |
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| 144 | !-- Saturation vapor pressure for a specific temperature: |
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| 145 | magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - 273.15_wp ) / & |
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| 146 | ( t - 29.65_wp ) ) |
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| 147 | |
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| 148 | END FUNCTION magnus_0d |
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| 149 | |
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| 150 | !------------------------------------------------------------------------------! |
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| 151 | ! Description: |
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| 152 | ! ------------ |
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| 153 | !> This function computes the magnus formula (Press et al., 1992). |
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| 154 | !> The magnus formula is needed to calculate the saturation vapor pressure |
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| 155 | !------------------------------------------------------------------------------! |
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| 156 | FUNCTION magnus_1d( t ) |
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| 157 | |
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| 158 | IMPLICIT NONE |
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| 159 | |
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| 160 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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| 161 | |
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| 162 | REAL(wp), DIMENSION(size(t)) :: magnus_1d |
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| 163 | ! |
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| 164 | !-- Saturation vapor pressure for a specific temperature: |
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| 165 | magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - 273.15_wp ) / & |
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| 166 | ( t - 29.65_wp ) ) |
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| 167 | |
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| 168 | END FUNCTION magnus_1d |
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| 169 | |
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| 170 | !------------------------------------------------------------------------------! |
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| 171 | ! Description: |
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| 172 | ! ------------ |
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| 173 | !> Compute the ideal gas law for scalar arguments. |
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| 174 | !------------------------------------------------------------------------------! |
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| 175 | FUNCTION ideal_gas_law_rho_0d( p, t ) |
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| 176 | |
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| 177 | IMPLICIT NONE |
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| 178 | |
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| 179 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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| 180 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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| 181 | |
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| 182 | REAL(wp) :: ideal_gas_law_rho_0d |
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| 183 | ! |
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| 184 | !-- compute density according to ideal gas law: |
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| 185 | ideal_gas_law_rho_0d = p / (r_d * t) |
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| 186 | |
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| 187 | END FUNCTION ideal_gas_law_rho_0d |
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| 188 | |
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| 189 | !------------------------------------------------------------------------------! |
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| 190 | ! Description: |
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| 191 | ! ------------ |
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| 192 | !> Compute the ideal gas law for 1-D array arguments. |
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| 193 | !------------------------------------------------------------------------------! |
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| 194 | FUNCTION ideal_gas_law_rho_1d( p, t ) |
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| 195 | |
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| 196 | IMPLICIT NONE |
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| 197 | |
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| 198 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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| 199 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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| 200 | |
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| 201 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d |
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| 202 | ! |
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| 203 | !-- compute density according to ideal gas law: |
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| 204 | ideal_gas_law_rho_1d = p / (r_d * t) |
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| 205 | |
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| 206 | END FUNCTION ideal_gas_law_rho_1d |
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| 207 | |
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| 208 | !------------------------------------------------------------------------------! |
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| 209 | ! Description: |
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| 210 | ! ------------ |
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| 211 | !> Compute the ideal gas law for scalar arguments. |
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| 212 | !------------------------------------------------------------------------------! |
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| 213 | FUNCTION ideal_gas_law_rho_pt_0d( p, t ) |
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| 214 | |
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| 215 | IMPLICIT NONE |
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| 216 | |
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| 217 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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| 218 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
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| 219 | |
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| 220 | REAL(wp) :: ideal_gas_law_rho_pt_0d |
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| 221 | ! |
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| 222 | !-- compute density according to ideal gas law: |
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| 223 | ideal_gas_law_rho_pt_0d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t) |
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| 224 | |
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| 225 | END FUNCTION ideal_gas_law_rho_pt_0d |
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| 226 | |
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| 227 | !------------------------------------------------------------------------------! |
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| 228 | ! Description: |
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| 229 | ! ------------ |
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| 230 | !> Compute the ideal gas law for 1-D array arguments. |
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| 231 | !------------------------------------------------------------------------------! |
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| 232 | FUNCTION ideal_gas_law_rho_pt_1d( p, t ) |
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| 233 | |
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| 234 | IMPLICIT NONE |
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| 235 | |
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| 236 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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| 237 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
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| 238 | |
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| 239 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d |
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| 240 | ! |
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| 241 | !-- compute density according to ideal gas law: |
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| 242 | ideal_gas_law_rho_pt_1d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t) |
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| 243 | |
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| 244 | END FUNCTION ideal_gas_law_rho_pt_1d |
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| 245 | |
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| 246 | !------------------------------------------------------------------------------! |
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| 247 | ! Description: |
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| 248 | ! ------------ |
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| 249 | !> Compute the exner function for scalar arguments. |
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| 250 | !------------------------------------------------------------------------------! |
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| 251 | FUNCTION exner_function_0d( p ) |
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| 252 | |
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| 253 | IMPLICIT NONE |
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| 254 | |
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| 255 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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| 256 | |
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| 257 | REAL(wp) :: exner_function_0d |
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| 258 | ! |
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| 259 | !-- compute exner function: |
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| 260 | exner_function_0d = ( p / p_0 )**( rd_d_cp ) |
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| 261 | |
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| 262 | END FUNCTION exner_function_0d |
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| 263 | |
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| 264 | !------------------------------------------------------------------------------! |
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| 265 | ! Description: |
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| 266 | ! ------------ |
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| 267 | !> Compute the exner function for 1-D array arguments. |
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| 268 | !------------------------------------------------------------------------------! |
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| 269 | FUNCTION exner_function_1d( p ) |
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| 270 | |
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| 271 | IMPLICIT NONE |
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| 272 | |
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| 273 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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| 274 | |
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| 275 | REAL(wp), DIMENSION(size(p)) :: exner_function_1d |
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| 276 | ! |
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| 277 | !-- compute exner function: |
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| 278 | exner_function_1d = ( p / p_0 )**( rd_d_cp ) |
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| 279 | |
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| 280 | END FUNCTION exner_function_1d |
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| 281 | |
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| 282 | !------------------------------------------------------------------------------! |
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| 283 | ! Description: |
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| 284 | ! ------------ |
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| 285 | !> Compute the exner function for scalar arguments. |
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| 286 | !------------------------------------------------------------------------------! |
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| 287 | FUNCTION exner_function_invers_0d( p ) |
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| 288 | |
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| 289 | IMPLICIT NONE |
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| 290 | |
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| 291 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
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| 292 | |
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| 293 | REAL(wp) :: exner_function_invers_0d |
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| 294 | ! |
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| 295 | !-- compute exner function: |
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| 296 | exner_function_invers_0d = ( p_0 / p )**( rd_d_cp ) |
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| 297 | |
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| 298 | END FUNCTION exner_function_invers_0d |
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| 299 | |
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| 300 | !------------------------------------------------------------------------------! |
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| 301 | ! Description: |
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| 302 | ! ------------ |
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| 303 | !> Compute the exner function for 1-D array arguments. |
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| 304 | !------------------------------------------------------------------------------! |
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| 305 | FUNCTION exner_function_invers_1d( p ) |
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| 306 | |
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| 307 | IMPLICIT NONE |
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| 308 | |
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| 309 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
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| 310 | |
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| 311 | REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d |
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| 312 | ! |
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| 313 | !-- compute exner function: |
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| 314 | exner_function_invers_1d = ( p_0 / p )**( rd_d_cp ) |
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| 315 | |
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| 316 | END FUNCTION exner_function_invers_1d |
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| 317 | |
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| 318 | !------------------------------------------------------------------------------! |
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| 319 | ! Description: |
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| 320 | ! ------------ |
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| 321 | !> Compute the barometric formula for scalar arguments. |
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| 322 | !------------------------------------------------------------------------------! |
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| 323 | FUNCTION barometric_formula_0d( z, t_0, p_0) |
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| 324 | |
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| 325 | IMPLICIT NONE |
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| 326 | |
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| 327 | REAL(wp), INTENT(IN) :: z !< height (m) |
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| 328 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
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| 329 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
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| 330 | |
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| 331 | REAL(wp) :: barometric_formula_0d |
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| 332 | ! |
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| 333 | !-- compute barometric formula: |
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| 334 | barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
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| 335 | |
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| 336 | END FUNCTION barometric_formula_0d |
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| 337 | |
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| 338 | !------------------------------------------------------------------------------! |
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| 339 | ! Description: |
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| 340 | ! ------------ |
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| 341 | !> Compute the barometric formula for 1-D array arguments. |
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| 342 | !------------------------------------------------------------------------------! |
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| 343 | FUNCTION barometric_formula_1d( z, t_0, p_0) |
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| 344 | |
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| 345 | IMPLICIT NONE |
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| 346 | |
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| 347 | REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m) |
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| 348 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
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| 349 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
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| 350 | |
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| 351 | REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d |
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| 352 | ! |
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| 353 | !-- compute barometric formula: |
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| 354 | barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
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| 355 | |
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| 356 | END FUNCTION barometric_formula_1d |
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| 357 | |
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| 358 | END MODULE basic_constants_and_equations_mod |
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