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source: palm/trunk/SOURCE/basic_constants_and_equations_mod.f90 @ 3550

Last change on this file since 3550 was 3449, checked in by suehring, 6 years ago
Branch resler -r 3439 re-integrated into current trunk: RTM 3.0, transpiration of plant canopy, output fixes in USM
Property svn:keywords set to `Id`
File size: 13.6 KB

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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 3449 2018-10-29 19:36:56Z gronemeier $
27	! +degc_to_k
28	!
29	! 3361 2018-10-16 20:39:37Z knoop
30	! New module (introduced with modularization of bulk cloud physics model)
31	!
32	!
33	!
34	!
35	! Description:
36	! ------------
37	!> This module contains all basic (physical) constants
38	!> and
39	!> functions for the calculation of diagnostic quantities.
40	!------------------------------------------------------------------------------!
41	MODULE basic_constants_and_equations_mod
42
43
44	USE kinds
45
46	IMPLICIT NONE
47
48	REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1)
49	REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K)
50	REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2)
51	REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant
52	REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1)
53	REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1)
54	REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1)
55	REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1)
56	REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1)
57	REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1)
58	REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1)
59	REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI
60	REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3)
61	REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3)
62	REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3)
63	REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3)
64	REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1)
65	REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1)
66	REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant
67	REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere
68	REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl
69	REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid
70	REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate
71
72	REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state
73
74	REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p
75	REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p
76	REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d
77	REAL(wp), PARAMETER :: rd_d_rv = 0.622_wp !r_d / r_v !< precomputed r_d / r_v
78	REAL(wp), PARAMETER :: rd_d_cp = 0.286_wp !r_d / c_p !< precomputed r_d / c_p
79	REAL(wp), PARAMETER :: cp_d_rd = 1.0_wp/0.286_wp !c_p / r_d !< precomputed c_p / r_d
80
81	REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1)
82	REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3)
83	REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl
84
85
86	SAVE
87
88	PRIVATE magnus_0d, &
89	magnus_1d, &
90	ideal_gas_law_rho_0d, &
91	ideal_gas_law_rho_1d, &
92	ideal_gas_law_rho_pt_0d, &
93	ideal_gas_law_rho_pt_1d, &
94	exner_function_0d, &
95	exner_function_1d, &
96	exner_function_invers_0d, &
97	exner_function_invers_1d, &
98	barometric_formula_0d, &
99	barometric_formula_1d
100
101	INTERFACE magnus
102	MODULE PROCEDURE magnus_0d
103	MODULE PROCEDURE magnus_1d
104	END INTERFACE magnus
105
106	INTERFACE ideal_gas_law_rho
107	MODULE PROCEDURE ideal_gas_law_rho_0d
108	MODULE PROCEDURE ideal_gas_law_rho_1d
109	END INTERFACE ideal_gas_law_rho
110
111	INTERFACE ideal_gas_law_rho_pt
112	MODULE PROCEDURE ideal_gas_law_rho_pt_0d
113	MODULE PROCEDURE ideal_gas_law_rho_pt_1d
114	END INTERFACE ideal_gas_law_rho_pt
115
116	INTERFACE exner_function
117	MODULE PROCEDURE exner_function_0d
118	MODULE PROCEDURE exner_function_1d
119	END INTERFACE exner_function
120
121	INTERFACE exner_function_invers
122	MODULE PROCEDURE exner_function_invers_0d
123	MODULE PROCEDURE exner_function_invers_1d
124	END INTERFACE exner_function_invers
125
126	INTERFACE barometric_formula
127	MODULE PROCEDURE barometric_formula_0d
128	MODULE PROCEDURE barometric_formula_1d
129	END INTERFACE barometric_formula
130
131	CONTAINS
132
133	!------------------------------------------------------------------------------!
134	! Description:
135	! ------------
136	!> This function computes the magnus formula (Press et al., 1992).
137	!> The magnus formula is needed to calculate the saturation vapor pressure
138	!------------------------------------------------------------------------------!
139	FUNCTION magnus_0d( t )
140
141	IMPLICIT NONE
142
143	REAL(wp), INTENT(IN) :: t !< temperature (K)
144
145	REAL(wp) :: magnus_0d
146	!
147	!-- Saturation vapor pressure for a specific temperature:
148	magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
149	( t - 29.65_wp ) )
150
151	END FUNCTION magnus_0d
152
153	!------------------------------------------------------------------------------!
154	! Description:
155	! ------------
156	!> This function computes the magnus formula (Press et al., 1992).
157	!> The magnus formula is needed to calculate the saturation vapor pressure
158	!------------------------------------------------------------------------------!
159	FUNCTION magnus_1d( t )
160
161	IMPLICIT NONE
162
163	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
164
165	REAL(wp), DIMENSION(size(t)) :: magnus_1d
166	!
167	!-- Saturation vapor pressure for a specific temperature:
168	magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
169	( t - 29.65_wp ) )
170
171	END FUNCTION magnus_1d
172
173	!------------------------------------------------------------------------------!
174	! Description:
175	! ------------
176	!> Compute the ideal gas law for scalar arguments.
177	!------------------------------------------------------------------------------!
178	FUNCTION ideal_gas_law_rho_0d( p, t )
179
180	IMPLICIT NONE
181
182	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
183	REAL(wp), INTENT(IN) :: t !< temperature (K)
184
185	REAL(wp) :: ideal_gas_law_rho_0d
186	!
187	!-- compute density according to ideal gas law:
188	ideal_gas_law_rho_0d = p / (r_d * t)
189
190	END FUNCTION ideal_gas_law_rho_0d
191
192	!------------------------------------------------------------------------------!
193	! Description:
194	! ------------
195	!> Compute the ideal gas law for 1-D array arguments.
196	!------------------------------------------------------------------------------!
197	FUNCTION ideal_gas_law_rho_1d( p, t )
198
199	IMPLICIT NONE
200
201	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
202	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
203
204	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d
205	!
206	!-- compute density according to ideal gas law:
207	ideal_gas_law_rho_1d = p / (r_d * t)
208
209	END FUNCTION ideal_gas_law_rho_1d
210
211	!------------------------------------------------------------------------------!
212	! Description:
213	! ------------
214	!> Compute the ideal gas law for scalar arguments.
215	!------------------------------------------------------------------------------!
216	FUNCTION ideal_gas_law_rho_pt_0d( p, t )
217
218	IMPLICIT NONE
219
220	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
221	REAL(wp), INTENT(IN) :: t !< temperature (K)
222
223	REAL(wp) :: ideal_gas_law_rho_pt_0d
224	!
225	!-- compute density according to ideal gas law:
226	ideal_gas_law_rho_pt_0d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t)
227
228	END FUNCTION ideal_gas_law_rho_pt_0d
229
230	!------------------------------------------------------------------------------!
231	! Description:
232	! ------------
233	!> Compute the ideal gas law for 1-D array arguments.
234	!------------------------------------------------------------------------------!
235	FUNCTION ideal_gas_law_rho_pt_1d( p, t )
236
237	IMPLICIT NONE
238
239	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
240	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
241
242	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d
243	!
244	!-- compute density according to ideal gas law:
245	ideal_gas_law_rho_pt_1d = p / (r_d * (1.0_wp / exner_function_invers(p)) * t)
246
247	END FUNCTION ideal_gas_law_rho_pt_1d
248
249	!------------------------------------------------------------------------------!
250	! Description:
251	! ------------
252	!> Compute the exner function for scalar arguments.
253	!------------------------------------------------------------------------------!
254	FUNCTION exner_function_0d( p )
255
256	IMPLICIT NONE
257
258	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
259
260	REAL(wp) :: exner_function_0d
261	!
262	!-- compute exner function:
263	exner_function_0d = ( p / p_0 )**( rd_d_cp )
264
265	END FUNCTION exner_function_0d
266
267	!------------------------------------------------------------------------------!
268	! Description:
269	! ------------
270	!> Compute the exner function for 1-D array arguments.
271	!------------------------------------------------------------------------------!
272	FUNCTION exner_function_1d( p )
273
274	IMPLICIT NONE
275
276	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
277
278	REAL(wp), DIMENSION(size(p)) :: exner_function_1d
279	!
280	!-- compute exner function:
281	exner_function_1d = ( p / p_0 )**( rd_d_cp )
282
283	END FUNCTION exner_function_1d
284
285	!------------------------------------------------------------------------------!
286	! Description:
287	! ------------
288	!> Compute the exner function for scalar arguments.
289	!------------------------------------------------------------------------------!
290	FUNCTION exner_function_invers_0d( p )
291
292	IMPLICIT NONE
293
294	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
295
296	REAL(wp) :: exner_function_invers_0d
297	!
298	!-- compute exner function:
299	exner_function_invers_0d = ( p_0 / p )**( rd_d_cp )
300
301	END FUNCTION exner_function_invers_0d
302
303	!------------------------------------------------------------------------------!
304	! Description:
305	! ------------
306	!> Compute the exner function for 1-D array arguments.
307	!------------------------------------------------------------------------------!
308	FUNCTION exner_function_invers_1d( p )
309
310	IMPLICIT NONE
311
312	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
313
314	REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d
315	!
316	!-- compute exner function:
317	exner_function_invers_1d = ( p_0 / p )**( rd_d_cp )
318
319	END FUNCTION exner_function_invers_1d
320
321	!------------------------------------------------------------------------------!
322	! Description:
323	! ------------
324	!> Compute the barometric formula for scalar arguments.
325	!------------------------------------------------------------------------------!
326	FUNCTION barometric_formula_0d( z, t_0, p_0)
327
328	IMPLICIT NONE
329
330	REAL(wp), INTENT(IN) :: z !< height (m)
331	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
332	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
333
334	REAL(wp) :: barometric_formula_0d
335	!
336	!-- compute barometric formula:
337	barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
338
339	END FUNCTION barometric_formula_0d
340
341	!------------------------------------------------------------------------------!
342	! Description:
343	! ------------
344	!> Compute the barometric formula for 1-D array arguments.
345	!------------------------------------------------------------------------------!
346	FUNCTION barometric_formula_1d( z, t_0, p_0)
347
348	IMPLICIT NONE
349
350	REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m)
351	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
352	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
353
354	REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d
355	!
356	!-- compute barometric formula:
357	barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
358
359	END FUNCTION barometric_formula_1d
360
361	END MODULE basic_constants_and_equations_mod

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