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source: palm/trunk/SOURCE/basic_constants_and_equations_mod.f90 @ 4810

Last change on this file since 4810 was 4742, checked in by schwenkel, 4 years ago
Implement snow and graupel (bulk microphysics)
Property svn:keywords set to `Id`
File size: 25.7 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 terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2020 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: basic_constants_and_equations_mod.f90 4742 2020-10-14 15:11:02Z gronemeier $
26	! Implement snow and graupel (bulk microphysics)
27	!
28	! 4509 2020-04-26 15:57:55Z raasch
29	! file re-formatted to follow the PALM coding standard
30	!
31	! 4502 2020-04-17 16:14:16Z schwenkel
32	! Implementation of ice microphysics
33	!
34	! 4400 2020-02-10 20:32:41Z suehring
35	! Move routine to transform coordinates from netcdf_interface_mod to
36	! basic_constants_and_equations_mod
37	!
38	! 4360 2020-01-07 11:25:50Z suehring
39	! Corrected "Former revisions" section
40	!
41	! 4088 2019-07-11 13:57:56Z Giersch
42	! Comment of barometric formula improved, function for ideal gas law revised
43	!
44	! 4084 2019-07-10 17:09:11Z knoop
45	! Changed precomputed fractions to be variable based
46	!
47	! 4055 2019-06-27 09:47:29Z suehring
48	! Added rgas_univ (universal gas constant) (E.C. Chan)
49	!
50	!
51	! 3655 2019-01-07 16:51:22Z knoop
52	! OpenACC port for SPEC
53	! 3361 2018-10-16 20:39:37Z knoop
54	! New module (introduced with modularization of bulk cloud physics model)
55	!
56	!
57	!
58	!
59	! Description:
60	! ------------
61	!> This module contains all basic (physical) constants and functions for the calculation of
62	!> diagnostic quantities.
63	!- -----------------------------------------------------------------------------!
64	MODULE basic_constants_and_equations_mod
65
66
67	USE kinds
68
69	IMPLICIT NONE
70
71
72	REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1)
73	REAL(wp), PARAMETER :: c_w = 4185.0_wp !< heat capacity of water at 0Â°C (J kg-1 K-1)
74	REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K)
75	REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2)
76	REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant
77	REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1)
78	REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1)
79	REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1)
80	REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1)
81	REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1)
82	REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1)
83	REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1)
84	REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI
85	!$ACC DECLARE COPYIN(pi)
86	REAL(wp), PARAMETER :: rgas_univ = 8.31446261815324_wp !< universal gas constant (J K-1 mol-1)
87	REAL(wp), PARAMETER :: rho_i = 916.7_wp !> density of pure ice (kg m-3)
88	REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3)
89	REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3)
90	REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3)
91	REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3)
92	REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1)
93	REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1)
94	REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant
95	REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere
96	REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl
97	REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid
98	REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate
99
100	REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state
101
102	REAL(wp), PARAMETER :: cp_d_rd = c_p / r_d !< precomputed c_p / r_d
103	REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p
104	REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p
105	REAL(wp), PARAMETER :: ls_d_cp = l_s / c_p !< precomputed l_s / c_p
106	REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d
107	REAL(wp), PARAMETER :: rd_d_rv = r_d / r_v !< precomputed r_d / r_v
108	REAL(wp), PARAMETER :: rd_d_cp = r_d / c_p !< precomputed r_d / c_p
109
110	REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1)
111	REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3)
112	REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl
113
114	SAVE
115
116	PRIVATE magnus_0d, &
117	magnus_1d, &
118	magnus_tl_0d, &
119	magnus_tl_1d, &
120	magnus_0d_ice, &
121	magnus_1d_ice, &
122	ideal_gas_law_rho_0d, &
123	ideal_gas_law_rho_1d, &
124	ideal_gas_law_rho_pt_0d, &
125	ideal_gas_law_rho_pt_1d, &
126	exner_function_0d, &
127	exner_function_1d, &
128	exner_function_invers_0d, &
129	exner_function_invers_1d, &
130	barometric_formula_0d, &
131	barometric_formula_1d
132
133
134	INTERFACE convert_utm_to_geographic
135	MODULE PROCEDURE convert_utm_to_geographic
136	END INTERFACE convert_utm_to_geographic
137
138	INTERFACE magnus
139	MODULE PROCEDURE magnus_0d
140	MODULE PROCEDURE magnus_1d
141	END INTERFACE magnus
142
143	INTERFACE magnus_tl
144	MODULE PROCEDURE magnus_tl_0d
145	MODULE PROCEDURE magnus_tl_1d
146	END INTERFACE magnus_tl
147
148	INTERFACE magnus_ice
149	MODULE PROCEDURE magnus_0d_ice
150	MODULE PROCEDURE magnus_1d_ice
151	END INTERFACE magnus_ice
152
153	INTERFACE ideal_gas_law_rho
154	MODULE PROCEDURE ideal_gas_law_rho_0d
155	MODULE PROCEDURE ideal_gas_law_rho_1d
156	END INTERFACE ideal_gas_law_rho
157
158	INTERFACE ideal_gas_law_rho_pt
159	MODULE PROCEDURE ideal_gas_law_rho_pt_0d
160	MODULE PROCEDURE ideal_gas_law_rho_pt_1d
161	END INTERFACE ideal_gas_law_rho_pt
162
163	INTERFACE exner_function
164	MODULE PROCEDURE exner_function_0d
165	MODULE PROCEDURE exner_function_1d
166	END INTERFACE exner_function
167
168	INTERFACE exner_function_invers
169	MODULE PROCEDURE exner_function_invers_0d
170	MODULE PROCEDURE exner_function_invers_1d
171	END INTERFACE exner_function_invers
172
173	INTERFACE barometric_formula
174	MODULE PROCEDURE barometric_formula_0d
175	MODULE PROCEDURE barometric_formula_1d
176	END INTERFACE barometric_formula
177	!
178	!-- Public routines
179	PUBLIC convert_utm_to_geographic
180
181	CONTAINS
182
183
184	!--------------------------------------------------------------------------------------------------!
185	! Description:
186	! ------------
187	!> Convert UTM coordinates into geographic latitude and longitude. Conversion is based on the work
188	!> of KrÃŒger (1912) DOI: 10.2312/GFZ.b103-krueger28 and Karney (2013) DOI: 10.1007/s00190-012-0578-z
189	!> Based on a JavaScript of the geodesy function library written by chrisveness
190	!> https://github.com/chrisveness/geodesy
191	!--------------------------------------------------------------------------------------------------!
192	SUBROUTINE convert_utm_to_geographic( crs, eutm, nutm, lon, lat )
193
194	INTEGER(iwp) :: j !< loop index
195
196	REAL(wp), INTENT(in) :: eutm !< easting (UTM)
197	REAL(wp), INTENT(out) :: lat !< geographic latitude in degree
198	REAL(wp), INTENT(out) :: lon !< geographic longitude in degree
199	REAL(wp), INTENT(in) :: nutm !< northing (UTM)
200
201	REAL(wp) :: a !< 2pia is the circumference of a meridian
202	REAL(wp) :: cos_eta_s !< cos(eta_s)
203	REAL(wp) :: delta_i !<
204	REAL(wp) :: delta_tau_i !<
205	REAL(wp) :: e !< eccentricity
206	REAL(wp) :: eta !<
207	REAL(wp) :: eta_s !<
208	REAL(wp) :: n !< 3rd flattening
209	REAL(wp) :: n2 !< n^2
210	REAL(wp) :: n3 !< n^3
211	REAL(wp) :: n4 !< n^4
212	REAL(wp) :: n5 !< n^5
213	REAL(wp) :: n6 !< n^6
214	REAL(wp) :: nu !<
215	REAL(wp) :: nu_s !<
216	REAL(wp) :: sin_eta_s !< sin(eta_s)
217	REAL(wp) :: sinh_nu_s !< sinush(nu_s)
218	REAL(wp) :: tau_i !<
219	REAL(wp) :: tau_i_s !<
220	REAL(wp) :: tau_s !<
221	REAL(wp) :: x !< adjusted easting
222	REAL(wp) :: y !< adjusted northing
223
224	REAL(wp), DIMENSION(6) :: beta !< 6th order KrÃŒger expressions
225
226	REAL(wp), DIMENSION(8), INTENT(in) :: crs !< coordinate reference system, consists of
227	!< (/semi_major_axis,
228	!< inverse_flattening,
229	!< longitude_of_prime_meridian,
230	!< longitude_of_central_meridian,
231	!< scale_factor_at_central_meridian,
232	!< latitude_of_projection_origin,
233	!< false_easting,
234	!< false_northing /)
235
236	x = eutm - crs(7) ! remove false easting
237	y = nutm - crs(8) ! remove false northing
238	!
239	!-- From Karney 2011 Eq 15-22, 36:
240	e = SQRT( 1.0_wp / crs(2) * ( 2.0_wp - 1.0_wp / crs(2) ) )
241	n = 1.0_wp / crs(2) / ( 2.0_wp - 1.0_wp / crs(2) )
242	n2 = n * n
243	n3 = n * n2
244	n4 = n * n3
245	n5 = n * n4
246	n6 = n * n5
247
248	a = crs(1) / ( 1.0_wp + n ) * ( 1.0_wp + 0.25_wp * n2 + 0.015625_wp * n4 + 3.90625E-3_wp * n6 )
249
250	nu = x / ( crs(5) * a )
251	eta = y / ( crs(5) * a )
252
253	!-- According to KrÃŒger (1912), eq. 26*
254	beta(1) = 0.5_wp * n &
255	- 2.0_wp / 3.0_wp * n2 &
256	+ 37.0_wp / 96.0_wp * n3 &
257	- 1.0_wp / 360.0_wp * n4 &
258	- 81.0_wp / 512.0_wp * n5 &
259	+ 96199.0_wp / 604800.0_wp * n6
260
261	beta(2) = 1.0_wp / 48.0_wp * n2 &
262	+ 1.0_wp / 15.0_wp * n3 &
263	- 437.0_wp / 1440.0_wp * n4 &
264	+ 46.0_wp / 105.0_wp * n5 &
265	- 1118711.0_wp / 3870720.0_wp * n6
266
267	beta(3) = 17.0_wp / 480.0_wp * n3 &
268	- 37.0_wp / 840.0_wp * n4 &
269	- 209.0_wp / 4480.0_wp * n5 &
270	+ 5569.0_wp / 90720.0_wp * n6
271
272	beta(4) = 4397.0_wp / 161280.0_wp * n4 &
273	- 11.0_wp / 504.0_wp * n5 &
274	- 830251.0_wp / 7257600.0_wp * n6
275
276	beta(5) = 4583.0_wp / 161280.0_wp * n5 &
277	- 108847.0_wp / 3991680.0_wp * n6
278
279	beta(6) = 20648693.0_wp / 638668800.0_wp * n6
280
281	eta_s = eta
282	nu_s = nu
283	DO j = 1, 6
284	eta_s = eta_s - beta(j) * SIN(2.0_wp * j * eta) * COSH(2.0_wp * j * nu)
285	nu_s = nu_s - beta(j) * COS(2.0_wp * j * eta) * SINH(2.0_wp * j * nu)
286	ENDDO
287
288	sinh_nu_s = SINH( nu_s )
289	sin_eta_s = SIN( eta_s )
290	cos_eta_s = COS( eta_s )
291
292	tau_s = sin_eta_s / SQRT( sinh_nu_s2 + cos_eta_s2 )
293
294	tau_i = tau_s
295	delta_tau_i = 1.0_wp
296
297	DO WHILE ( ABS( delta_tau_i ) > 1.0E-12_wp )
298
299	delta_i = SINH( e * ATANH( e * tau_i / SQRT( 1.0_wp + tau_i**2 ) ) )
300
301	tau_i_s = tau_i * SQRT( 1.0_wp + delta_i*2 ) - delta_i SQRT( 1.0_wp + tau_i**2 )
302
303	delta_tau_i = ( tau_s - tau_i_s ) / SQRT( 1.0_wp + tau_i_s**2 ) &
304	* ( 1.0_wp + ( 1.0_wp - e*2 ) tau_i**2 ) &
305	/ ( ( 1.0_wp - e*2 ) SQRT( 1.0_wp + tau_i**2 ) )
306
307	tau_i = tau_i + delta_tau_i
308
309	ENDDO
310
311	lat = ATAN( tau_i ) / pi * 180.0_wp
312	lon = ATAN2( sinh_nu_s, cos_eta_s ) / pi * 180.0_wp + crs(4)
313
314	END SUBROUTINE convert_utm_to_geographic
315
316	!--------------------------------------------------------------------------------------------------!
317	! Description:
318	! ------------
319	!> This function computes the magnus formula (Press et al., 1992).
320	!> The magnus formula is needed to calculate the saturation vapor pressure.
321	!--------------------------------------------------------------------------------------------------!
322	FUNCTION magnus_0d( t )
323
324	IMPLICIT NONE
325
326	REAL(wp), INTENT(IN) :: t !< temperature (K)
327
328	REAL(wp) :: magnus_0d
329
330	!
331	!-- Saturation vapor pressure for a specific temperature:
332	magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / ( t - 29.65_wp ) )
333
334	END FUNCTION magnus_0d
335
336	!--------------------------------------------------------------------------------------------------!
337	! Description:
338	! ------------
339	!> This function computes the magnus formula (Press et al., 1992).
340	!> The magnus formula is needed to calculate the saturation vapor pressure.
341	!--------------------------------------------------------------------------------------------------!
342	FUNCTION magnus_1d( t )
343
344	IMPLICIT NONE
345
346	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
347
348	REAL(wp), DIMENSION(size(t)) :: magnus_1d
349
350	!
351	!-- Saturation vapor pressure for a specific temperature:
352	magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / ( t - 29.65_wp ) )
353
354	END FUNCTION magnus_1d
355
356	!--------------------------------------------------------------------------------------------------!
357	! Description:
358	! ------------
359	!> This function computes the magnus formula (Press et al., 1992) using the (ice-) liquid water
360	!> potential temperature.
361	!> The magnus formula is needed to calculate the saturation vapor pressure over a plane liquid water
362	!> surface.
363	!--------------------------------------------------------------------------------------------------!
364	FUNCTION magnus_tl_0d( t_l )
365
366	IMPLICIT NONE
367
368	REAL(wp), INTENT(IN) :: t_l !< liquid water temperature (K)
369
370	REAL(wp) :: magnus_tl_0d
371
372	!
373	!-- Saturation vapor pressure for a specific temperature:
374	magnus_tl_0d = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / ( t_l - 35.86_wp ) )
375
376	END FUNCTION magnus_tl_0d
377
378	!--------------------------------------------------------------------------------------------------!
379	! Description:
380	! ------------
381	!> This function computes the magnus formula (Press et al., 1992) using the (ice-) liquid water
382	!> potential temperature.
383	!> The magnus formula is needed to calculate the saturation vapor pressure over a plane liquid water
384	!> surface.
385	!--------------------------------------------------------------------------------------------------!
386	FUNCTION magnus_tl_1d( t_l )
387
388	IMPLICIT NONE
389
390	REAL(wp), INTENT(IN), DIMENSION(:) :: t_l !< liquid water temperature (K)
391
392	REAL(wp), DIMENSION(size(t_l)) :: magnus_tl_1d
393	!
394	!-- Saturation vapor pressure for a specific temperature:
395	magnus_tl_1d = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / ( t_l - 35.86_wp ) )
396
397	END FUNCTION magnus_tl_1d
398
399	!--------------------------------------------------------------------------------------------------!
400	! Description:
401	! ------------
402	!> This function computes the magnus formula (Press et al., 1992).
403	!> The magnus formula is needed to calculate the saturation vapor pressure over a plane ice surface.
404	!--------------------------------------------------------------------------------------------------!
405	FUNCTION magnus_0d_ice( t )
406
407	IMPLICIT NONE
408
409	REAL(wp), INTENT(IN) :: t !< temperature (K)
410
411	REAL(wp) :: magnus_0d_ice
412
413	!
414	!-- Saturation vapor pressure for a specific temperature:
415	!magnus_0d_ice = 611.2_wp * EXP( 22.46_wp * ( t - degc_to_k ) / ( t - 0.53_wp ) )
416	magnus_0d_ice = 610.78_wp * EXP( 21.875_wp * ( t - degc_to_k ) / ( t - 7.66_wp ) )
417
418
419	END FUNCTION magnus_0d_ice
420
421	!--------------------------------------------------------------------------------------------------!
422	! Description:
423	! ------------
424	!> This function computes the magnus formula (Press et al., 1992).
425	!> The magnus formula is needed to calculate the saturation vapor pressure over a plane ice surface.
426	!--------------------------------------------------------------------------------------------------!
427	FUNCTION magnus_1d_ice( t )
428
429	IMPLICIT NONE
430
431	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
432
433	REAL(wp), DIMENSION(size(t)) :: magnus_1d_ice
434
435	!
436	!-- Saturation vapor pressure for a specific temperature:
437	!magnus_1d_ice = 611.2_wp * EXP( 22.46_wp * ( t - degc_to_k ) / ( t - 0.53_wp ) )
438	magnus_1d_ice = 610.78_wp * EXP( 21.875_wp * ( t - degc_to_k ) / ( t - 7.66_wp ) )
439
440
441	END FUNCTION magnus_1d_ice
442
443	!--------------------------------------------------------------------------------------------------!
444	! Description:
445	! ------------
446	!> Compute the ideal gas law for scalar arguments.
447	!--------------------------------------------------------------------------------------------------!
448	FUNCTION ideal_gas_law_rho_0d( p, t )
449
450	IMPLICIT NONE
451
452	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
453	REAL(wp), INTENT(IN) :: t !< temperature (K)
454
455	REAL(wp) :: ideal_gas_law_rho_0d
456
457	!
458	!-- Compute density according to ideal gas law:
459	ideal_gas_law_rho_0d = p / (r_d * t)
460
461	END FUNCTION ideal_gas_law_rho_0d
462
463	!--------------------------------------------------------------------------------------------------!
464	! Description:
465	! ------------
466	!> Compute the ideal gas law for 1-D array arguments.
467	!--------------------------------------------------------------------------------------------------!
468	FUNCTION ideal_gas_law_rho_1d( p, t )
469
470	IMPLICIT NONE
471
472	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
473	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
474
475	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d
476
477	!
478	!-- Compute density according to ideal gas law:
479	ideal_gas_law_rho_1d = p / (r_d * t)
480
481	END FUNCTION ideal_gas_law_rho_1d
482
483	!--------------------------------------------------------------------------------------------------!
484	! Description:
485	! ------------
486	!> Compute the ideal gas law for scalar arguments.
487	!--------------------------------------------------------------------------------------------------!
488	FUNCTION ideal_gas_law_rho_pt_0d( p, t )
489
490	IMPLICIT NONE
491
492	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
493	REAL(wp), INTENT(IN) :: t !< temperature (K)
494
495	REAL(wp) :: ideal_gas_law_rho_pt_0d
496
497	!
498	!-- Compute density according to ideal gas law:
499	ideal_gas_law_rho_pt_0d = p / (r_d * exner_function(p) * t)
500
501	END FUNCTION ideal_gas_law_rho_pt_0d
502
503	!--------------------------------------------------------------------------------------------------!
504	! Description:
505	! ------------
506	!> Compute the ideal gas law for 1-D array arguments.
507	!--------------------------------------------------------------------------------------------------!
508	FUNCTION ideal_gas_law_rho_pt_1d( p, t )
509
510	IMPLICIT NONE
511
512	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
513	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
514
515	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d
516
517	!
518	!-- Compute density according to ideal gas law:
519	ideal_gas_law_rho_pt_1d = p / (r_d * exner_function(p) * t)
520
521	END FUNCTION ideal_gas_law_rho_pt_1d
522
523	!--------------------------------------------------------------------------------------------------!
524	! Description:
525	! ------------
526	!> Compute the exner function for scalar arguments.
527	!--------------------------------------------------------------------------------------------------!
528	FUNCTION exner_function_0d( p )
529
530	IMPLICIT NONE
531
532	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
533
534	REAL(wp) :: exner_function_0d
535
536	!
537	!-- Compute exner function:
538	exner_function_0d = ( p / p_0 )**( rd_d_cp )
539
540	END FUNCTION exner_function_0d
541
542	!--------------------------------------------------------------------------------------------------!
543	! Description:
544	! ------------
545	!> Compute the exner function for 1-D array arguments.
546	!--------------------------------------------------------------------------------------------------!
547	FUNCTION exner_function_1d( p )
548
549	IMPLICIT NONE
550
551	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
552
553	REAL(wp), DIMENSION(size(p)) :: exner_function_1d
554
555	!
556	!-- Compute exner function:
557	exner_function_1d = ( p / p_0 )**( rd_d_cp )
558
559	END FUNCTION exner_function_1d
560
561	!--------------------------------------------------------------------------------------------------!
562	! Description:
563	! ------------
564	!> Compute the exner function for scalar arguments.
565	!--------------------------------------------------------------------------------------------------!
566	FUNCTION exner_function_invers_0d( p )
567
568	IMPLICIT NONE
569
570	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
571
572	REAL(wp) :: exner_function_invers_0d
573
574	!
575	!-- Compute exner function:
576	exner_function_invers_0d = ( p_0 / p )**( rd_d_cp )
577
578	END FUNCTION exner_function_invers_0d
579
580	!--------------------------------------------------------------------------------------------------!
581	! Description:
582	! ------------
583	!> Compute the exner function for 1-D array arguments.
584	!--------------------------------------------------------------------------------------------------!
585	FUNCTION exner_function_invers_1d( p )
586
587	IMPLICIT NONE
588
589	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
590
591	REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d
592
593	!
594	!-- Compute exner function:
595	exner_function_invers_1d = ( p_0 / p )**( rd_d_cp )
596
597	END FUNCTION exner_function_invers_1d
598
599	!--------------------------------------------------------------------------------------------------!
600	! Description:
601	! ------------
602	!> Compute the barometric formula for scalar arguments. The calculation is based on the assumption
603	!> of a polytropic atmosphere and neutral stratification, where the temperature lapse rate is g/cp.
604	!--------------------------------------------------------------------------------------------------!
605	FUNCTION barometric_formula_0d( z, t_0, p_0)
606
607	IMPLICIT NONE
608
609	REAL(wp), INTENT(IN) :: z !< height (m)
610	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
611	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
612
613	REAL(wp) :: barometric_formula_0d
614
615	!
616	!-- Compute barometric formula:
617	barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
618
619	END FUNCTION barometric_formula_0d
620
621	!--------------------------------------------------------------------------------------------------!
622	! Description:
623	! ------------
624	!> Compute the barometric formula for 1-D array arguments. The calculation is based on the
625	!> assumption of a polytropic atmosphere and neutral stratification, where the temperature lapse
626	!> rate is g/cp.
627	!--------------------------------------------------------------------------------------------------!
628	FUNCTION barometric_formula_1d( z, t_0, p_0)
629
630	IMPLICIT NONE
631
632	REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m)
633	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
634	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
635
636	REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d
637
638	!
639	!-- Compute barometric formula:
640	barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
641
642	END FUNCTION barometric_formula_1d
643
644	END MODULE basic_constants_and_equations_mod

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