source: palm/trunk/SOURCE/basic_constants_and_equations_mod.f90 @ 3274

Last change on this file since 3274 was 3274, checked in by knoop, 3 years ago

Modularization of all bulk cloud physics code components

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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 1997-2018 Leibniz Universitaet Hannover
18!------------------------------------------------------------------------------!
19!
20! Current revisions:
21! -----------------
22!
23!
24! Former revisions:
25! -----------------
26! $Id: basic_constants_and_equations_mod.f90 3274 2018-09-24 15:42:55Z knoop $
27! New module (introduced with modularization of bulk cloud physics model)
28!
29!
30!
31!
32! Description:
33! ------------
34!> This module contains all basic (physical) constants
35!> and
36!> functions for the calculation of diagnostic quantities.
37!------------------------------------------------------------------------------!
38 MODULE basic_constants_and_equations_mod
39
40
41    USE kinds
42
43    IMPLICIT NONE
44
45    REAL(wp), PARAMETER ::  pi = 3.141592654_wp  !< PI
46
47    REAL(wp), PARAMETER ::  c_p = 1005.0_wp                           !< heat capacity of dry air (J kg-1 K-1)
48    REAL(wp), PARAMETER ::  g = 9.81_wp                               !< gravitational acceleration (m s-2)
49    REAL(wp), PARAMETER ::  kappa = 0.4_wp                            !< von Karman constant
50    REAL(wp), PARAMETER ::  l_m = 0.33E+06_wp                         !< latent heat of water melting (J kg-1)
51    REAL(wp), PARAMETER ::  l_v = 2.5E+06_wp                          !< latent heat of water vaporization (J kg-1)
52    REAL(wp), PARAMETER ::  l_s = l_m + l_v                           !< latent heat of water sublimation (J kg-1)
53    REAL(wp), PARAMETER ::  molecular_weight_of_nacl = 0.05844_wp     !< mol. m. NaCl (kg mol-1)
54    REAL(wp), PARAMETER ::  molecular_weight_of_c3h4o4 = 0.10406_wp   !< mol. m. malonic acid (kg mol-1)
55    REAL(wp), PARAMETER ::  molecular_weight_of_nh4no3 = 0.08004_wp   !< mol. m. ammonium sulfate (kg mol-1)
56    REAL(wp), PARAMETER ::  molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1)
57    REAL(wp), PARAMETER ::  rho_l = 1.0E3_wp                          !< density of water (kg m-3)
58    REAL(wp), PARAMETER ::  rho_nacl = 2165.0_wp                      !< density of NaCl (kg m-3)
59    REAL(wp), PARAMETER ::  rho_c3h4o4 = 1600.0_wp                    !< density of malonic acid (kg m-3)
60    REAL(wp), PARAMETER ::  rho_nh4no3 = 1720.0_wp                    !< density of ammonium sulfate (kg m-3)
61    REAL(wp), PARAMETER ::  r_d = 287.0_wp                            !< sp. gas const. dry air (J kg-1 K-1)
62    REAL(wp), PARAMETER ::  r_v = 461.51_wp                           !< sp. gas const. water vapor (J kg-1 K-1)
63    REAL(wp), PARAMETER ::  sigma_sb = 5.67E-08_wp                    !< Stefan-Boltzmann constant
64    REAL(wp), PARAMETER ::  solar_constant = 1368.0_wp                !< solar constant at top of atmosphere
65    REAL(wp), PARAMETER ::  vanthoff_nacl = 2.0_wp                    !< van't Hoff factor for NaCl
66    REAL(wp), PARAMETER ::  vanthoff_c3h4o4 = 1.37_wp                 !< van't Hoff factor for malonic acid
67    REAL(wp), PARAMETER ::  vanthoff_nh4no3 = 2.31_wp                 !< van't Hoff factor for ammonium sulfate
68
69    REAL(wp), PARAMETER ::  p_0 = 100000.0_wp                         !< standard pressure reference state
70
71    REAL(wp), PARAMETER ::  g_d_cp  = g   / c_p   !< precomputed g / c_p
72    REAL(wp), PARAMETER ::  lv_d_cp = l_v / c_p   !< precomputed l_v / c_p
73    REAL(wp), PARAMETER ::  lv_d_rd = l_v / r_d   !< precomputed l_v / r_d
74    REAL(wp), PARAMETER ::  rd_d_cp = 0.286_wp !r_d / c_p  !< precomputed r_d / c_p
75    REAL(wp), PARAMETER ::  cp_d_rd = 1.0_wp/0.286_wp !c_p / r_d  !< precomputed c_p / r_d
76
77    REAL(wp) ::  molecular_weight_of_solute = molecular_weight_of_nacl  !< mol. m. NaCl (kg mol-1)
78    REAL(wp) ::  rho_s = rho_nacl                                       !< density of NaCl (kg m-3)
79    REAL(wp) ::  vanthoff = vanthoff_nacl                               !< van't Hoff factor for NaCl
80
81
82    SAVE
83
84    PRIVATE magnus_0d, &
85            magnus_1d, &
86            ideal_gas_law_rho_0d, &
87            ideal_gas_law_rho_1d, &
88            ideal_gas_law_rho_pt_0d, &
89            ideal_gas_law_rho_pt_1d, &
90            exner_function_0d, &
91            exner_function_1d, &
92            exner_function_invers_0d, &
93            exner_function_invers_1d, &
94            barometric_formula_0d, &
95            barometric_formula_1d
96
97    INTERFACE magnus
98       MODULE PROCEDURE magnus_0d
99       MODULE PROCEDURE magnus_1d
100    END INTERFACE magnus
101
102    INTERFACE ideal_gas_law_rho
103       MODULE PROCEDURE ideal_gas_law_rho_0d
104       MODULE PROCEDURE ideal_gas_law_rho_1d
105    END INTERFACE ideal_gas_law_rho
106
107    INTERFACE ideal_gas_law_rho_pt
108       MODULE PROCEDURE ideal_gas_law_rho_pt_0d
109       MODULE PROCEDURE ideal_gas_law_rho_pt_1d
110    END INTERFACE ideal_gas_law_rho_pt
111
112    INTERFACE exner_function
113       MODULE PROCEDURE exner_function_0d
114       MODULE PROCEDURE exner_function_1d
115    END INTERFACE exner_function
116
117    INTERFACE exner_function_invers
118       MODULE PROCEDURE exner_function_invers_0d
119       MODULE PROCEDURE exner_function_invers_1d
120    END INTERFACE exner_function_invers
121
122    INTERFACE barometric_formula
123       MODULE PROCEDURE barometric_formula_0d
124       MODULE PROCEDURE barometric_formula_1d
125    END INTERFACE barometric_formula
126
127 CONTAINS
128
129!------------------------------------------------------------------------------!
130! Description:
131! ------------
132!> This function computes the magnus formula (Press et al., 1992).
133!> The magnus formula is needed to calculate the saturation vapor pressure
134!------------------------------------------------------------------------------!
135    FUNCTION magnus_0d( t )
136
137       IMPLICIT NONE
138
139       REAL(wp), INTENT(IN) ::  t  !< temperature (K)
140
141       REAL(wp) ::  magnus_0d
142!
143!--    Saturation vapor pressure for a specific temperature:
144       magnus_0d =  611.2_wp * EXP( 17.62_wp * ( t - 273.15_wp ) /             &
145                                                   ( t - 29.65_wp  ) )
146
147    END FUNCTION magnus_0d
148
149!------------------------------------------------------------------------------!
150! Description:
151! ------------
152!> This function computes the magnus formula (Press et al., 1992).
153!> The magnus formula is needed to calculate the saturation vapor pressure
154!------------------------------------------------------------------------------!
155    FUNCTION magnus_1d( t )
156
157       IMPLICIT NONE
158
159       REAL(wp), INTENT(IN), DIMENSION(:) ::  t  !< temperature (K)
160
161       REAL(wp), DIMENSION(size(t)) ::  magnus_1d
162!
163!--    Saturation vapor pressure for a specific temperature:
164       magnus_1d =  611.2_wp * EXP( 17.62_wp * ( t - 273.15_wp ) /             &
165                                               ( t - 29.65_wp  ) )
166
167    END FUNCTION magnus_1d
168
169!------------------------------------------------------------------------------!
170! Description:
171! ------------
172!> Compute the ideal gas law for scalar arguments.
173!------------------------------------------------------------------------------!
174    FUNCTION ideal_gas_law_rho_0d( p, t )
175
176       IMPLICIT NONE
177
178       REAL(wp), INTENT(IN) ::  p  !< pressure (Pa)
179       REAL(wp), INTENT(IN) ::  t  !< temperature (K)
180
181       REAL(wp) ::  ideal_gas_law_rho_0d
182!
183!--    compute density according to ideal gas law:
184       ideal_gas_law_rho_0d = p / (r_d * t)
185
186    END FUNCTION ideal_gas_law_rho_0d
187
188!------------------------------------------------------------------------------!
189! Description:
190! ------------
191!> Compute the ideal gas law for 1-D array arguments.
192!------------------------------------------------------------------------------!
193    FUNCTION ideal_gas_law_rho_1d( p, t )
194
195       IMPLICIT NONE
196
197       REAL(wp), INTENT(IN), DIMENSION(:) ::  p  !< pressure (Pa)
198       REAL(wp), INTENT(IN), DIMENSION(:) ::  t  !< temperature (K)
199
200       REAL(wp), DIMENSION(size(p)) ::  ideal_gas_law_rho_1d
201!
202!--    compute density according to ideal gas law:
203       ideal_gas_law_rho_1d = p / (r_d * t)
204
205    END FUNCTION ideal_gas_law_rho_1d
206
207!------------------------------------------------------------------------------!
208! Description:
209! ------------
210!> Compute the ideal gas law for scalar arguments.
211!------------------------------------------------------------------------------!
212    FUNCTION ideal_gas_law_rho_pt_0d( p, t )
213
214       IMPLICIT NONE
215
216       REAL(wp), INTENT(IN) ::  p  !< pressure (Pa)
217       REAL(wp), INTENT(IN) ::  t  !< temperature (K)
218
219       REAL(wp) ::  ideal_gas_law_rho_pt_0d
220!
221!--    compute density according to ideal gas law:
222       ideal_gas_law_rho_pt_0d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t)
223
224    END FUNCTION ideal_gas_law_rho_pt_0d
225
226!------------------------------------------------------------------------------!
227! Description:
228! ------------
229!> Compute the ideal gas law for 1-D array arguments.
230!------------------------------------------------------------------------------!
231    FUNCTION ideal_gas_law_rho_pt_1d( p, t )
232
233       IMPLICIT NONE
234
235       REAL(wp), INTENT(IN), DIMENSION(:) ::  p  !< pressure (Pa)
236       REAL(wp), INTENT(IN), DIMENSION(:) ::  t  !< temperature (K)
237
238       REAL(wp), DIMENSION(size(p)) ::  ideal_gas_law_rho_pt_1d
239!
240!--    compute density according to ideal gas law:
241       ideal_gas_law_rho_pt_1d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t)
242
243    END FUNCTION ideal_gas_law_rho_pt_1d
244
245!------------------------------------------------------------------------------!
246! Description:
247! ------------
248!> Compute the exner function for scalar arguments.
249!------------------------------------------------------------------------------!
250    FUNCTION exner_function_0d( p )
251
252       IMPLICIT NONE
253
254       REAL(wp), INTENT(IN) ::  p    !< pressure (Pa)
255
256       REAL(wp) ::  exner_function_0d
257!
258!--    compute exner function:
259       exner_function_0d = ( p / p_0 )**( rd_d_cp )
260
261    END FUNCTION exner_function_0d
262
263!------------------------------------------------------------------------------!
264! Description:
265! ------------
266!> Compute the exner function for 1-D array arguments.
267!------------------------------------------------------------------------------!
268    FUNCTION exner_function_1d( p )
269
270       IMPLICIT NONE
271
272       REAL(wp), INTENT(IN), DIMENSION(:) ::  p  !< pressure (Pa)
273
274       REAL(wp), DIMENSION(size(p)) ::  exner_function_1d
275!
276!--    compute exner function:
277       exner_function_1d = ( p / p_0 )**( rd_d_cp )
278
279    END FUNCTION exner_function_1d
280
281!------------------------------------------------------------------------------!
282! Description:
283! ------------
284!> Compute the exner function for scalar arguments.
285!------------------------------------------------------------------------------!
286    FUNCTION exner_function_invers_0d( p )
287
288       IMPLICIT NONE
289
290       REAL(wp), INTENT(IN) ::  p    !< pressure (Pa)
291
292       REAL(wp) ::  exner_function_invers_0d
293!
294!--    compute exner function:
295       exner_function_invers_0d = ( p_0 / p )**( rd_d_cp )
296
297    END FUNCTION exner_function_invers_0d
298
299!------------------------------------------------------------------------------!
300! Description:
301! ------------
302!> Compute the exner function for 1-D array arguments.
303!------------------------------------------------------------------------------!
304    FUNCTION exner_function_invers_1d( p )
305
306       IMPLICIT NONE
307
308       REAL(wp), INTENT(IN), DIMENSION(:) ::  p  !< pressure (Pa)
309
310       REAL(wp), DIMENSION(size(p)) ::  exner_function_invers_1d
311!
312!--    compute exner function:
313       exner_function_invers_1d = ( p_0 / p )**( rd_d_cp )
314
315    END FUNCTION exner_function_invers_1d
316
317!------------------------------------------------------------------------------!
318! Description:
319! ------------
320!> Compute the barometric formula for scalar arguments.
321!------------------------------------------------------------------------------!
322    FUNCTION barometric_formula_0d( z, t_0, p_0)
323
324       IMPLICIT NONE
325
326       REAL(wp), INTENT(IN) ::  z    !< height (m)
327       REAL(wp), INTENT(IN) ::  t_0  !< temperature reference state (K)
328       REAL(wp), INTENT(IN) ::  p_0  !< surface pressure (Pa)
329
330       REAL(wp) ::  barometric_formula_0d
331!
332!--    compute barometric formula:
333       barometric_formula_0d =  p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
334
335    END FUNCTION barometric_formula_0d
336
337!------------------------------------------------------------------------------!
338! Description:
339! ------------
340!> Compute the barometric formula for 1-D array arguments.
341!------------------------------------------------------------------------------!
342    FUNCTION barometric_formula_1d( z, t_0, p_0)
343
344       IMPLICIT NONE
345
346       REAL(wp), INTENT(IN), DIMENSION(:) ::  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), DIMENSION(size(z)) ::  barometric_formula_1d
351!
352!--    compute barometric formula:
353       barometric_formula_1d =  p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
354
355    END FUNCTION barometric_formula_1d
356
357 END MODULE basic_constants_and_equations_mod
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