| 1 | !> @file basic_constants_and_equations_mod.f90 |
|---|
| 2 | !------------------------------------------------------------------------------! |
|---|
| 3 | ! This file is part of the PALM model system. |
|---|
| 4 | ! |
|---|
| 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
|---|
| 6 | ! terms of the GNU General Public License as published by the Free Software |
|---|
| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
|---|
| 8 | ! version. |
|---|
| 9 | ! |
|---|
| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
|---|
| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
|---|
| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
|---|
| 13 | ! |
|---|
| 14 | ! You should have received a copy of the GNU General Public License along with |
|---|
| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
|---|
| 16 | ! |
|---|
| 17 | ! Copyright 1997-2019 Leibniz Universitaet Hannover |
|---|
| 18 | !------------------------------------------------------------------------------! |
|---|
| 19 | ! |
|---|
| 20 | ! Current revisions: |
|---|
| 21 | ! ----------------- |
|---|
| 22 | ! |
|---|
| 23 | ! |
|---|
| 24 | ! Former revisions: |
|---|
| 25 | ! ----------------- |
|---|
| 26 | ! $Id: basic_constants_and_equations_mod.f90 4182 2019-08-22 15:20:23Z suehring $ |
|---|
| 27 | ! Corrected "Former revisions" section |
|---|
| 28 | ! |
|---|
| 29 | ! 4088 2019-07-11 13:57:56Z Giersch |
|---|
| 30 | ! Comment of barometric formula improved, function for ideal gas law revised |
|---|
| 31 | ! |
|---|
| 32 | ! 4084 2019-07-10 17:09:11Z knoop |
|---|
| 33 | ! Changed precomputed fractions to be variable based |
|---|
| 34 | ! |
|---|
| 35 | ! 4055 2019-06-27 09:47:29Z suehring |
|---|
| 36 | ! Added rgas_univ (universal gas constant) (E.C. Chan) |
|---|
| 37 | ! |
|---|
| 38 | ! |
|---|
| 39 | ! 3655 2019-01-07 16:51:22Z knoop |
|---|
| 40 | ! OpenACC port for SPEC |
|---|
| 41 | ! 3361 2018-10-16 20:39:37Z knoop |
|---|
| 42 | ! New module (introduced with modularization of bulk cloud physics model) |
|---|
| 43 | ! |
|---|
| 44 | ! |
|---|
| 45 | ! |
|---|
| 46 | ! |
|---|
| 47 | ! Description: |
|---|
| 48 | ! ------------ |
|---|
| 49 | !> This module contains all basic (physical) constants |
|---|
| 50 | !> and |
|---|
| 51 | !> functions for the calculation of diagnostic quantities. |
|---|
| 52 | !------------------------------------------------------------------------------! |
|---|
| 53 | MODULE basic_constants_and_equations_mod |
|---|
| 54 | |
|---|
| 55 | |
|---|
| 56 | USE kinds |
|---|
| 57 | |
|---|
| 58 | IMPLICIT NONE |
|---|
| 59 | |
|---|
| 60 | REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1) |
|---|
| 61 | REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K) |
|---|
| 62 | REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2) |
|---|
| 63 | REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant |
|---|
| 64 | REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1) |
|---|
| 65 | REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1) |
|---|
| 66 | REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1) |
|---|
| 67 | REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1) |
|---|
| 68 | REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1) |
|---|
| 69 | REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1) |
|---|
| 70 | REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1) |
|---|
| 71 | REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI |
|---|
| 72 | !$ACC DECLARE COPYIN(pi) |
|---|
| 73 | REAL(wp), PARAMETER :: rgas_univ = 8.31446261815324_wp !< universal gas constant (J K-1 mol-1) |
|---|
| 74 | REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3) |
|---|
| 75 | REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3) |
|---|
| 76 | REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3) |
|---|
| 77 | REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3) |
|---|
| 78 | REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1) |
|---|
| 79 | REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1) |
|---|
| 80 | REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant |
|---|
| 81 | REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere |
|---|
| 82 | REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl |
|---|
| 83 | REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid |
|---|
| 84 | REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate |
|---|
| 85 | |
|---|
| 86 | REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state |
|---|
| 87 | |
|---|
| 88 | REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p |
|---|
| 89 | REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p |
|---|
| 90 | REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d |
|---|
| 91 | REAL(wp), PARAMETER :: rd_d_rv = r_d / r_v !< precomputed r_d / r_v |
|---|
| 92 | REAL(wp), PARAMETER :: rd_d_cp = r_d / c_p !< precomputed r_d / c_p |
|---|
| 93 | REAL(wp), PARAMETER :: cp_d_rd = c_p / r_d !< precomputed c_p / r_d |
|---|
| 94 | |
|---|
| 95 | REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1) |
|---|
| 96 | REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3) |
|---|
| 97 | REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl |
|---|
| 98 | |
|---|
| 99 | |
|---|
| 100 | SAVE |
|---|
| 101 | |
|---|
| 102 | PRIVATE magnus_0d, & |
|---|
| 103 | magnus_1d, & |
|---|
| 104 | ideal_gas_law_rho_0d, & |
|---|
| 105 | ideal_gas_law_rho_1d, & |
|---|
| 106 | ideal_gas_law_rho_pt_0d, & |
|---|
| 107 | ideal_gas_law_rho_pt_1d, & |
|---|
| 108 | exner_function_0d, & |
|---|
| 109 | exner_function_1d, & |
|---|
| 110 | exner_function_invers_0d, & |
|---|
| 111 | exner_function_invers_1d, & |
|---|
| 112 | barometric_formula_0d, & |
|---|
| 113 | barometric_formula_1d |
|---|
| 114 | |
|---|
| 115 | INTERFACE magnus |
|---|
| 116 | MODULE PROCEDURE magnus_0d |
|---|
| 117 | MODULE PROCEDURE magnus_1d |
|---|
| 118 | END INTERFACE magnus |
|---|
| 119 | |
|---|
| 120 | INTERFACE ideal_gas_law_rho |
|---|
| 121 | MODULE PROCEDURE ideal_gas_law_rho_0d |
|---|
| 122 | MODULE PROCEDURE ideal_gas_law_rho_1d |
|---|
| 123 | END INTERFACE ideal_gas_law_rho |
|---|
| 124 | |
|---|
| 125 | INTERFACE ideal_gas_law_rho_pt |
|---|
| 126 | MODULE PROCEDURE ideal_gas_law_rho_pt_0d |
|---|
| 127 | MODULE PROCEDURE ideal_gas_law_rho_pt_1d |
|---|
| 128 | END INTERFACE ideal_gas_law_rho_pt |
|---|
| 129 | |
|---|
| 130 | INTERFACE exner_function |
|---|
| 131 | MODULE PROCEDURE exner_function_0d |
|---|
| 132 | MODULE PROCEDURE exner_function_1d |
|---|
| 133 | END INTERFACE exner_function |
|---|
| 134 | |
|---|
| 135 | INTERFACE exner_function_invers |
|---|
| 136 | MODULE PROCEDURE exner_function_invers_0d |
|---|
| 137 | MODULE PROCEDURE exner_function_invers_1d |
|---|
| 138 | END INTERFACE exner_function_invers |
|---|
| 139 | |
|---|
| 140 | INTERFACE barometric_formula |
|---|
| 141 | MODULE PROCEDURE barometric_formula_0d |
|---|
| 142 | MODULE PROCEDURE barometric_formula_1d |
|---|
| 143 | END INTERFACE barometric_formula |
|---|
| 144 | |
|---|
| 145 | CONTAINS |
|---|
| 146 | |
|---|
| 147 | !------------------------------------------------------------------------------! |
|---|
| 148 | ! Description: |
|---|
| 149 | ! ------------ |
|---|
| 150 | !> This function computes the magnus formula (Press et al., 1992). |
|---|
| 151 | !> The magnus formula is needed to calculate the saturation vapor pressure |
|---|
| 152 | !------------------------------------------------------------------------------! |
|---|
| 153 | FUNCTION magnus_0d( t ) |
|---|
| 154 | |
|---|
| 155 | IMPLICIT NONE |
|---|
| 156 | |
|---|
| 157 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
|---|
| 158 | |
|---|
| 159 | REAL(wp) :: magnus_0d |
|---|
| 160 | ! |
|---|
| 161 | !-- Saturation vapor pressure for a specific temperature: |
|---|
| 162 | magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / & |
|---|
| 163 | ( t - 29.65_wp ) ) |
|---|
| 164 | |
|---|
| 165 | END FUNCTION magnus_0d |
|---|
| 166 | |
|---|
| 167 | !------------------------------------------------------------------------------! |
|---|
| 168 | ! Description: |
|---|
| 169 | ! ------------ |
|---|
| 170 | !> This function computes the magnus formula (Press et al., 1992). |
|---|
| 171 | !> The magnus formula is needed to calculate the saturation vapor pressure |
|---|
| 172 | !------------------------------------------------------------------------------! |
|---|
| 173 | FUNCTION magnus_1d( t ) |
|---|
| 174 | |
|---|
| 175 | IMPLICIT NONE |
|---|
| 176 | |
|---|
| 177 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
|---|
| 178 | |
|---|
| 179 | REAL(wp), DIMENSION(size(t)) :: magnus_1d |
|---|
| 180 | ! |
|---|
| 181 | !-- Saturation vapor pressure for a specific temperature: |
|---|
| 182 | magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / & |
|---|
| 183 | ( t - 29.65_wp ) ) |
|---|
| 184 | |
|---|
| 185 | END FUNCTION magnus_1d |
|---|
| 186 | |
|---|
| 187 | !------------------------------------------------------------------------------! |
|---|
| 188 | ! Description: |
|---|
| 189 | ! ------------ |
|---|
| 190 | !> Compute the ideal gas law for scalar arguments. |
|---|
| 191 | !------------------------------------------------------------------------------! |
|---|
| 192 | FUNCTION ideal_gas_law_rho_0d( p, t ) |
|---|
| 193 | |
|---|
| 194 | IMPLICIT NONE |
|---|
| 195 | |
|---|
| 196 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
|---|
| 197 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
|---|
| 198 | |
|---|
| 199 | REAL(wp) :: ideal_gas_law_rho_0d |
|---|
| 200 | ! |
|---|
| 201 | !-- compute density according to ideal gas law: |
|---|
| 202 | ideal_gas_law_rho_0d = p / (r_d * t) |
|---|
| 203 | |
|---|
| 204 | END FUNCTION ideal_gas_law_rho_0d |
|---|
| 205 | |
|---|
| 206 | !------------------------------------------------------------------------------! |
|---|
| 207 | ! Description: |
|---|
| 208 | ! ------------ |
|---|
| 209 | !> Compute the ideal gas law for 1-D array arguments. |
|---|
| 210 | !------------------------------------------------------------------------------! |
|---|
| 211 | FUNCTION ideal_gas_law_rho_1d( p, t ) |
|---|
| 212 | |
|---|
| 213 | IMPLICIT NONE |
|---|
| 214 | |
|---|
| 215 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
|---|
| 216 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
|---|
| 217 | |
|---|
| 218 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d |
|---|
| 219 | ! |
|---|
| 220 | !-- compute density according to ideal gas law: |
|---|
| 221 | ideal_gas_law_rho_1d = p / (r_d * t) |
|---|
| 222 | |
|---|
| 223 | END FUNCTION ideal_gas_law_rho_1d |
|---|
| 224 | |
|---|
| 225 | !------------------------------------------------------------------------------! |
|---|
| 226 | ! Description: |
|---|
| 227 | ! ------------ |
|---|
| 228 | !> Compute the ideal gas law for scalar arguments. |
|---|
| 229 | !------------------------------------------------------------------------------! |
|---|
| 230 | FUNCTION ideal_gas_law_rho_pt_0d( p, t ) |
|---|
| 231 | |
|---|
| 232 | IMPLICIT NONE |
|---|
| 233 | |
|---|
| 234 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
|---|
| 235 | REAL(wp), INTENT(IN) :: t !< temperature (K) |
|---|
| 236 | |
|---|
| 237 | REAL(wp) :: ideal_gas_law_rho_pt_0d |
|---|
| 238 | ! |
|---|
| 239 | !-- compute density according to ideal gas law: |
|---|
| 240 | ideal_gas_law_rho_pt_0d = p / (r_d * exner_function(p) * t) |
|---|
| 241 | |
|---|
| 242 | END FUNCTION ideal_gas_law_rho_pt_0d |
|---|
| 243 | |
|---|
| 244 | !------------------------------------------------------------------------------! |
|---|
| 245 | ! Description: |
|---|
| 246 | ! ------------ |
|---|
| 247 | !> Compute the ideal gas law for 1-D array arguments. |
|---|
| 248 | !------------------------------------------------------------------------------! |
|---|
| 249 | FUNCTION ideal_gas_law_rho_pt_1d( p, t ) |
|---|
| 250 | |
|---|
| 251 | IMPLICIT NONE |
|---|
| 252 | |
|---|
| 253 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
|---|
| 254 | REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K) |
|---|
| 255 | |
|---|
| 256 | REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d |
|---|
| 257 | ! |
|---|
| 258 | !-- compute density according to ideal gas law: |
|---|
| 259 | ideal_gas_law_rho_pt_1d = p / (r_d * exner_function(p) * t) |
|---|
| 260 | |
|---|
| 261 | END FUNCTION ideal_gas_law_rho_pt_1d |
|---|
| 262 | |
|---|
| 263 | !------------------------------------------------------------------------------! |
|---|
| 264 | ! Description: |
|---|
| 265 | ! ------------ |
|---|
| 266 | !> Compute the exner function for scalar arguments. |
|---|
| 267 | !------------------------------------------------------------------------------! |
|---|
| 268 | FUNCTION exner_function_0d( p ) |
|---|
| 269 | |
|---|
| 270 | IMPLICIT NONE |
|---|
| 271 | |
|---|
| 272 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
|---|
| 273 | |
|---|
| 274 | REAL(wp) :: exner_function_0d |
|---|
| 275 | ! |
|---|
| 276 | !-- compute exner function: |
|---|
| 277 | exner_function_0d = ( p / p_0 )**( rd_d_cp ) |
|---|
| 278 | |
|---|
| 279 | END FUNCTION exner_function_0d |
|---|
| 280 | |
|---|
| 281 | !------------------------------------------------------------------------------! |
|---|
| 282 | ! Description: |
|---|
| 283 | ! ------------ |
|---|
| 284 | !> Compute the exner function for 1-D array arguments. |
|---|
| 285 | !------------------------------------------------------------------------------! |
|---|
| 286 | FUNCTION exner_function_1d( p ) |
|---|
| 287 | |
|---|
| 288 | IMPLICIT NONE |
|---|
| 289 | |
|---|
| 290 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
|---|
| 291 | |
|---|
| 292 | REAL(wp), DIMENSION(size(p)) :: exner_function_1d |
|---|
| 293 | ! |
|---|
| 294 | !-- compute exner function: |
|---|
| 295 | exner_function_1d = ( p / p_0 )**( rd_d_cp ) |
|---|
| 296 | |
|---|
| 297 | END FUNCTION exner_function_1d |
|---|
| 298 | |
|---|
| 299 | !------------------------------------------------------------------------------! |
|---|
| 300 | ! Description: |
|---|
| 301 | ! ------------ |
|---|
| 302 | !> Compute the exner function for scalar arguments. |
|---|
| 303 | !------------------------------------------------------------------------------! |
|---|
| 304 | FUNCTION exner_function_invers_0d( p ) |
|---|
| 305 | |
|---|
| 306 | IMPLICIT NONE |
|---|
| 307 | |
|---|
| 308 | REAL(wp), INTENT(IN) :: p !< pressure (Pa) |
|---|
| 309 | |
|---|
| 310 | REAL(wp) :: exner_function_invers_0d |
|---|
| 311 | ! |
|---|
| 312 | !-- compute exner function: |
|---|
| 313 | exner_function_invers_0d = ( p_0 / p )**( rd_d_cp ) |
|---|
| 314 | |
|---|
| 315 | END FUNCTION exner_function_invers_0d |
|---|
| 316 | |
|---|
| 317 | !------------------------------------------------------------------------------! |
|---|
| 318 | ! Description: |
|---|
| 319 | ! ------------ |
|---|
| 320 | !> Compute the exner function for 1-D array arguments. |
|---|
| 321 | !------------------------------------------------------------------------------! |
|---|
| 322 | FUNCTION exner_function_invers_1d( p ) |
|---|
| 323 | |
|---|
| 324 | IMPLICIT NONE |
|---|
| 325 | |
|---|
| 326 | REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa) |
|---|
| 327 | |
|---|
| 328 | REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d |
|---|
| 329 | ! |
|---|
| 330 | !-- compute exner function: |
|---|
| 331 | exner_function_invers_1d = ( p_0 / p )**( rd_d_cp ) |
|---|
| 332 | |
|---|
| 333 | END FUNCTION exner_function_invers_1d |
|---|
| 334 | |
|---|
| 335 | !------------------------------------------------------------------------------! |
|---|
| 336 | ! Description: |
|---|
| 337 | ! ------------ |
|---|
| 338 | !> Compute the barometric formula for scalar arguments. The calculation is |
|---|
| 339 | !> based on the assumption of a polytropic atmosphere and neutral |
|---|
| 340 | !> stratification, where the temperature lapse rate is g/cp. |
|---|
| 341 | !------------------------------------------------------------------------------! |
|---|
| 342 | FUNCTION barometric_formula_0d( z, t_0, p_0) |
|---|
| 343 | |
|---|
| 344 | IMPLICIT NONE |
|---|
| 345 | |
|---|
| 346 | REAL(wp), INTENT(IN) :: z !< height (m) |
|---|
| 347 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
|---|
| 348 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
|---|
| 349 | |
|---|
| 350 | REAL(wp) :: barometric_formula_0d |
|---|
| 351 | ! |
|---|
| 352 | !-- compute barometric formula: |
|---|
| 353 | barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
|---|
| 354 | |
|---|
| 355 | END FUNCTION barometric_formula_0d |
|---|
| 356 | |
|---|
| 357 | !------------------------------------------------------------------------------! |
|---|
| 358 | ! Description: |
|---|
| 359 | ! ------------ |
|---|
| 360 | !> Compute the barometric formula for 1-D array arguments. The calculation is |
|---|
| 361 | !> based on the assumption of a polytropic atmosphere and neutral |
|---|
| 362 | !> stratification, where the temperature lapse rate is g/cp. |
|---|
| 363 | !------------------------------------------------------------------------------! |
|---|
| 364 | FUNCTION barometric_formula_1d( z, t_0, p_0) |
|---|
| 365 | |
|---|
| 366 | IMPLICIT NONE |
|---|
| 367 | |
|---|
| 368 | REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m) |
|---|
| 369 | REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K) |
|---|
| 370 | REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa) |
|---|
| 371 | |
|---|
| 372 | REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d |
|---|
| 373 | ! |
|---|
| 374 | !-- compute barometric formula: |
|---|
| 375 | barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd ) |
|---|
| 376 | |
|---|
| 377 | END FUNCTION barometric_formula_1d |
|---|
| 378 | |
|---|
| 379 | END MODULE basic_constants_and_equations_mod |
|---|
