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source: palm/trunk/SOURCE/basic_constants_and_equations_mod.f90 @ 4457

Last change on this file since 4457 was 4400, checked in by suehring, 5 years ago
Revision of the virtual-measurement module: data input from NetCDF file; removed binary output - instead parallel NetCDF output using the new data-output module; variable attributes added; further variables added that can be sampled, file connections added; Functions for coordinate transformation moved to basic_constants_and_equations; netcdf_data_input_mod: unused routines netcdf_data_input_att and netcdf_data_input_var removed; new routines to inquire fill values added; Preprocessing script (palm_cvd) to setup virtual-measurement input files provided; postprocessor combine_virtual_measurements deleted
Property svn:keywords set to `Id`
File size: 20.1 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 1997-2020 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: basic_constants_and_equations_mod.f90 4400 2020-02-10 20:32:41Z raasch $
27	! Move routine to transform coordinates from netcdf_interface_mod to
28	! basic_constants_and_equations_mod
29	!
30	! 4360 2020-01-07 11:25:50Z suehring
31	! Corrected "Former revisions" section
32	!
33	! 4088 2019-07-11 13:57:56Z Giersch
34	! Comment of barometric formula improved, function for ideal gas law revised
35	!
36	! 4084 2019-07-10 17:09:11Z knoop
37	! Changed precomputed fractions to be variable based
38	!
39	! 4055 2019-06-27 09:47:29Z suehring
40	! Added rgas_univ (universal gas constant) (E.C. Chan)
41	!
42	!
43	! 3655 2019-01-07 16:51:22Z knoop
44	! OpenACC port for SPEC
45	! 3361 2018-10-16 20:39:37Z knoop
46	! New module (introduced with modularization of bulk cloud physics model)
47	!
48	!
49	!
50	!
51	! Description:
52	! ------------
53	!> This module contains all basic (physical) constants
54	!> and
55	!> functions for the calculation of diagnostic quantities.
56	!------------------------------------------------------------------------------!
57	MODULE basic_constants_and_equations_mod
58
59
60	USE kinds
61
62	IMPLICIT NONE
63
64	REAL(wp), PARAMETER :: c_p = 1005.0_wp !< heat capacity of dry air (J kg-1 K-1)
65	REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K)
66	REAL(wp), PARAMETER :: g = 9.81_wp !< gravitational acceleration (m s-2)
67	REAL(wp), PARAMETER :: kappa = 0.4_wp !< von Karman constant
68	REAL(wp), PARAMETER :: l_m = 0.33E+06_wp !< latent heat of water melting (J kg-1)
69	REAL(wp), PARAMETER :: l_v = 2.5E+06_wp !< latent heat of water vaporization (J kg-1)
70	REAL(wp), PARAMETER :: l_s = l_m + l_v !< latent heat of water sublimation (J kg-1)
71	REAL(wp), PARAMETER :: molecular_weight_of_nacl = 0.05844_wp !< mol. m. NaCl (kg mol-1)
72	REAL(wp), PARAMETER :: molecular_weight_of_c3h4o4 = 0.10406_wp !< mol. m. malonic acid (kg mol-1)
73	REAL(wp), PARAMETER :: molecular_weight_of_nh4no3 = 0.08004_wp !< mol. m. ammonium sulfate (kg mol-1)
74	REAL(wp), PARAMETER :: molecular_weight_of_water = 0.01801528_wp !< mol. m. H2O (kg mol-1)
75	REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI
76	!$ACC DECLARE COPYIN(pi)
77	REAL(wp), PARAMETER :: rgas_univ = 8.31446261815324_wp !< universal gas constant (J K-1 mol-1)
78	REAL(wp), PARAMETER :: rho_l = 1.0E3_wp !< density of water (kg m-3)
79	REAL(wp), PARAMETER :: rho_nacl = 2165.0_wp !< density of NaCl (kg m-3)
80	REAL(wp), PARAMETER :: rho_c3h4o4 = 1600.0_wp !< density of malonic acid (kg m-3)
81	REAL(wp), PARAMETER :: rho_nh4no3 = 1720.0_wp !< density of ammonium sulfate (kg m-3)
82	REAL(wp), PARAMETER :: r_d = 287.0_wp !< sp. gas const. dry air (J kg-1 K-1)
83	REAL(wp), PARAMETER :: r_v = 461.51_wp !< sp. gas const. water vapor (J kg-1 K-1)
84	REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant
85	REAL(wp), PARAMETER :: solar_constant = 1368.0_wp !< solar constant at top of atmosphere
86	REAL(wp), PARAMETER :: vanthoff_nacl = 2.0_wp !< van't Hoff factor for NaCl
87	REAL(wp), PARAMETER :: vanthoff_c3h4o4 = 1.37_wp !< van't Hoff factor for malonic acid
88	REAL(wp), PARAMETER :: vanthoff_nh4no3 = 2.31_wp !< van't Hoff factor for ammonium sulfate
89
90	REAL(wp), PARAMETER :: p_0 = 100000.0_wp !< standard pressure reference state
91
92	REAL(wp), PARAMETER :: g_d_cp = g / c_p !< precomputed g / c_p
93	REAL(wp), PARAMETER :: lv_d_cp = l_v / c_p !< precomputed l_v / c_p
94	REAL(wp), PARAMETER :: lv_d_rd = l_v / r_d !< precomputed l_v / r_d
95	REAL(wp), PARAMETER :: rd_d_rv = r_d / r_v !< precomputed r_d / r_v
96	REAL(wp), PARAMETER :: rd_d_cp = r_d / c_p !< precomputed r_d / c_p
97	REAL(wp), PARAMETER :: cp_d_rd = c_p / r_d !< precomputed c_p / r_d
98
99	REAL(wp) :: molecular_weight_of_solute = molecular_weight_of_nacl !< mol. m. NaCl (kg mol-1)
100	REAL(wp) :: rho_s = rho_nacl !< density of NaCl (kg m-3)
101	REAL(wp) :: vanthoff = vanthoff_nacl !< van't Hoff factor for NaCl
102
103
104	SAVE
105
106	PRIVATE magnus_0d, &
107	magnus_1d, &
108	ideal_gas_law_rho_0d, &
109	ideal_gas_law_rho_1d, &
110	ideal_gas_law_rho_pt_0d, &
111	ideal_gas_law_rho_pt_1d, &
112	exner_function_0d, &
113	exner_function_1d, &
114	exner_function_invers_0d, &
115	exner_function_invers_1d, &
116	barometric_formula_0d, &
117	barometric_formula_1d
118
119
120	INTERFACE convert_utm_to_geographic
121	MODULE PROCEDURE convert_utm_to_geographic
122	END INTERFACE convert_utm_to_geographic
123
124	INTERFACE magnus
125	MODULE PROCEDURE magnus_0d
126	MODULE PROCEDURE magnus_1d
127	END INTERFACE magnus
128
129	INTERFACE ideal_gas_law_rho
130	MODULE PROCEDURE ideal_gas_law_rho_0d
131	MODULE PROCEDURE ideal_gas_law_rho_1d
132	END INTERFACE ideal_gas_law_rho
133
134	INTERFACE ideal_gas_law_rho_pt
135	MODULE PROCEDURE ideal_gas_law_rho_pt_0d
136	MODULE PROCEDURE ideal_gas_law_rho_pt_1d
137	END INTERFACE ideal_gas_law_rho_pt
138
139	INTERFACE exner_function
140	MODULE PROCEDURE exner_function_0d
141	MODULE PROCEDURE exner_function_1d
142	END INTERFACE exner_function
143
144	INTERFACE exner_function_invers
145	MODULE PROCEDURE exner_function_invers_0d
146	MODULE PROCEDURE exner_function_invers_1d
147	END INTERFACE exner_function_invers
148
149	INTERFACE barometric_formula
150	MODULE PROCEDURE barometric_formula_0d
151	MODULE PROCEDURE barometric_formula_1d
152	END INTERFACE barometric_formula
153	!
154	!-- Public routines
155	PUBLIC convert_utm_to_geographic
156
157	CONTAINS
158
159
160	!------------------------------------------------------------------------------!
161	! Description:
162	! ------------
163	!> Convert UTM coordinates into geographic latitude and longitude. Conversion
164	!> is based on the work of KrÃŒger (1912) DOI: 10.2312/GFZ.b103-krueger28
165	!> and Karney (2013) DOI: 10.1007/s00190-012-0578-z
166	!> Based on a JavaScript of the geodesy function library written by chrisveness
167	!> https://github.com/chrisveness/geodesy
168	!------------------------------------------------------------------------------!
169	SUBROUTINE convert_utm_to_geographic( crs, eutm, nutm, lon, lat )
170
171	INTEGER(iwp) :: j !< loop index
172
173	REAL(wp), INTENT(in) :: eutm !< easting (UTM)
174	REAL(wp), INTENT(out) :: lat !< geographic latitude in degree
175	REAL(wp), INTENT(out) :: lon !< geographic longitude in degree
176	REAL(wp), INTENT(in) :: nutm !< northing (UTM)
177
178	REAL(wp) :: a !< 2pia is the circumference of a meridian
179	REAL(wp) :: cos_eta_s !< cos(eta_s)
180	REAL(wp) :: delta_i !<
181	REAL(wp) :: delta_tau_i !<
182	REAL(wp) :: e !< eccentricity
183	REAL(wp) :: eta !<
184	REAL(wp) :: eta_s !<
185	REAL(wp) :: n !< 3rd flattening
186	REAL(wp) :: n2 !< n^2
187	REAL(wp) :: n3 !< n^3
188	REAL(wp) :: n4 !< n^4
189	REAL(wp) :: n5 !< n^5
190	REAL(wp) :: n6 !< n^6
191	REAL(wp) :: nu !<
192	REAL(wp) :: nu_s !<
193	REAL(wp) :: sin_eta_s !< sin(eta_s)
194	REAL(wp) :: sinh_nu_s !< sinush(nu_s)
195	REAL(wp) :: tau_i !<
196	REAL(wp) :: tau_i_s !<
197	REAL(wp) :: tau_s !<
198	REAL(wp) :: x !< adjusted easting
199	REAL(wp) :: y !< adjusted northing
200
201	REAL(wp), DIMENSION(6) :: beta !< 6th order KrÃŒger expressions
202
203	REAL(wp), DIMENSION(8), INTENT(in) :: crs !< coordinate reference system, consists of
204	!< (/semi_major_axis,
205	!< inverse_flattening,
206	!< longitude_of_prime_meridian,
207	!< longitude_of_central_meridian,
208	!< scale_factor_at_central_meridian,
209	!< latitude_of_projection_origin,
210	!< false_easting,
211	!< false_northing /)
212
213	x = eutm - crs(7) ! remove false easting
214	y = nutm - crs(8) ! remove false northing
215	!
216	!-- from Karney 2011 Eq 15-22, 36:
217	e = SQRT( 1.0_wp / crs(2) * ( 2.0_wp - 1.0_wp / crs(2) ) )
218	n = 1.0_wp / crs(2) / ( 2.0_wp - 1.0_wp / crs(2) )
219	n2 = n * n
220	n3 = n * n2
221	n4 = n * n3
222	n5 = n * n4
223	n6 = n * n5
224
225	a = crs(1) / ( 1.0_wp + n ) * ( 1.0_wp + 0.25_wp * n2 &
226	+ 0.015625_wp * n4 &
227	+ 3.90625E-3_wp * n6 )
228
229	nu = x / ( crs(5) * a )
230	eta = y / ( crs(5) * a )
231
232	!-- According to KrÃŒger (1912), eq. 26*
233	beta(1) = 0.5_wp * n &
234	- 2.0_wp / 3.0_wp * n2 &
235	+ 37.0_wp / 96.0_wp * n3 &
236	- 1.0_wp / 360.0_wp * n4 &
237	- 81.0_wp / 512.0_wp * n5 &
238	+ 96199.0_wp / 604800.0_wp * n6
239
240	beta(2) = 1.0_wp / 48.0_wp * n2 &
241	+ 1.0_wp / 15.0_wp * n3 &
242	- 437.0_wp / 1440.0_wp * n4 &
243	+ 46.0_wp / 105.0_wp * n5 &
244	- 1118711.0_wp / 3870720.0_wp * n6
245
246	beta(3) = 17.0_wp / 480.0_wp * n3 &
247	- 37.0_wp / 840.0_wp * n4 &
248	- 209.0_wp / 4480.0_wp * n5 &
249	+ 5569.0_wp / 90720.0_wp * n6
250
251	beta(4) = 4397.0_wp / 161280.0_wp * n4 &
252	- 11.0_wp / 504.0_wp * n5 &
253	- 830251.0_wp / 7257600.0_wp * n6
254
255	beta(5) = 4583.0_wp / 161280.0_wp * n5 &
256	- 108847.0_wp / 3991680.0_wp * n6
257
258	beta(6) = 20648693.0_wp / 638668800.0_wp * n6
259
260	eta_s = eta
261	nu_s = nu
262	DO j = 1, 6
263	eta_s = eta_s - beta(j) * SIN(2.0_wp * j * eta) * COSH(2.0_wp * j * nu)
264	nu_s = nu_s - beta(j) * COS(2.0_wp * j * eta) * SINH(2.0_wp * j * nu)
265	ENDDO
266
267	sinh_nu_s = SINH( nu_s )
268	sin_eta_s = SIN( eta_s )
269	cos_eta_s = COS( eta_s )
270
271	tau_s = sin_eta_s / SQRT( sinh_nu_s2 + cos_eta_s2 )
272
273	tau_i = tau_s
274	delta_tau_i = 1.0_wp
275
276	DO WHILE ( ABS( delta_tau_i ) > 1.0E-12_wp )
277
278	delta_i = SINH( e * ATANH( e * tau_i / SQRT( 1.0_wp + tau_i**2 ) ) )
279
280	tau_i_s = tau_i * SQRT( 1.0_wp + delta_i**2 ) &
281	- delta_i * SQRT( 1.0_wp + tau_i**2 )
282
283	delta_tau_i = ( tau_s - tau_i_s ) / SQRT( 1.0_wp + tau_i_s**2 ) &
284	* ( 1.0_wp + ( 1.0_wp - e*2 ) tau_i**2 ) &
285	/ ( ( 1.0_wp - e*2 ) SQRT( 1.0_wp + tau_i**2 ) )
286
287	tau_i = tau_i + delta_tau_i
288
289	ENDDO
290
291	lat = ATAN( tau_i ) / pi * 180.0_wp
292	lon = ATAN2( sinh_nu_s, cos_eta_s ) / pi * 180.0_wp + crs(4)
293
294	END SUBROUTINE convert_utm_to_geographic
295
296	!------------------------------------------------------------------------------!
297	! Description:
298	! ------------
299	!> This function computes the magnus formula (Press et al., 1992).
300	!> The magnus formula is needed to calculate the saturation vapor pressure
301	!------------------------------------------------------------------------------!
302	FUNCTION magnus_0d( t )
303
304	IMPLICIT NONE
305
306	REAL(wp), INTENT(IN) :: t !< temperature (K)
307
308	REAL(wp) :: magnus_0d
309	!
310	!-- Saturation vapor pressure for a specific temperature:
311	magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
312	( t - 29.65_wp ) )
313
314	END FUNCTION magnus_0d
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_1d( t )
323
324	IMPLICIT NONE
325
326	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
327
328	REAL(wp), DIMENSION(size(t)) :: magnus_1d
329	!
330	!-- Saturation vapor pressure for a specific temperature:
331	magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
332	( t - 29.65_wp ) )
333
334	END FUNCTION magnus_1d
335
336	!------------------------------------------------------------------------------!
337	! Description:
338	! ------------
339	!> Compute the ideal gas law for scalar arguments.
340	!------------------------------------------------------------------------------!
341	FUNCTION ideal_gas_law_rho_0d( p, t )
342
343	IMPLICIT NONE
344
345	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
346	REAL(wp), INTENT(IN) :: t !< temperature (K)
347
348	REAL(wp) :: ideal_gas_law_rho_0d
349	!
350	!-- compute density according to ideal gas law:
351	ideal_gas_law_rho_0d = p / (r_d * t)
352
353	END FUNCTION ideal_gas_law_rho_0d
354
355	!------------------------------------------------------------------------------!
356	! Description:
357	! ------------
358	!> Compute the ideal gas law for 1-D array arguments.
359	!------------------------------------------------------------------------------!
360	FUNCTION ideal_gas_law_rho_1d( p, t )
361
362	IMPLICIT NONE
363
364	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
365	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
366
367	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_1d
368	!
369	!-- compute density according to ideal gas law:
370	ideal_gas_law_rho_1d = p / (r_d * t)
371
372	END FUNCTION ideal_gas_law_rho_1d
373
374	!------------------------------------------------------------------------------!
375	! Description:
376	! ------------
377	!> Compute the ideal gas law for scalar arguments.
378	!------------------------------------------------------------------------------!
379	FUNCTION ideal_gas_law_rho_pt_0d( p, t )
380
381	IMPLICIT NONE
382
383	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
384	REAL(wp), INTENT(IN) :: t !< temperature (K)
385
386	REAL(wp) :: ideal_gas_law_rho_pt_0d
387	!
388	!-- compute density according to ideal gas law:
389	ideal_gas_law_rho_pt_0d = p / (r_d * exner_function(p) * t)
390
391	END FUNCTION ideal_gas_law_rho_pt_0d
392
393	!------------------------------------------------------------------------------!
394	! Description:
395	! ------------
396	!> Compute the ideal gas law for 1-D array arguments.
397	!------------------------------------------------------------------------------!
398	FUNCTION ideal_gas_law_rho_pt_1d( p, t )
399
400	IMPLICIT NONE
401
402	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
403	REAL(wp), INTENT(IN), DIMENSION(:) :: t !< temperature (K)
404
405	REAL(wp), DIMENSION(size(p)) :: ideal_gas_law_rho_pt_1d
406	!
407	!-- compute density according to ideal gas law:
408	ideal_gas_law_rho_pt_1d = p / (r_d * exner_function(p) * t)
409
410	END FUNCTION ideal_gas_law_rho_pt_1d
411
412	!------------------------------------------------------------------------------!
413	! Description:
414	! ------------
415	!> Compute the exner function for scalar arguments.
416	!------------------------------------------------------------------------------!
417	FUNCTION exner_function_0d( p )
418
419	IMPLICIT NONE
420
421	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
422
423	REAL(wp) :: exner_function_0d
424	!
425	!-- compute exner function:
426	exner_function_0d = ( p / p_0 )**( rd_d_cp )
427
428	END FUNCTION exner_function_0d
429
430	!------------------------------------------------------------------------------!
431	! Description:
432	! ------------
433	!> Compute the exner function for 1-D array arguments.
434	!------------------------------------------------------------------------------!
435	FUNCTION exner_function_1d( p )
436
437	IMPLICIT NONE
438
439	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
440
441	REAL(wp), DIMENSION(size(p)) :: exner_function_1d
442	!
443	!-- compute exner function:
444	exner_function_1d = ( p / p_0 )**( rd_d_cp )
445
446	END FUNCTION exner_function_1d
447
448	!------------------------------------------------------------------------------!
449	! Description:
450	! ------------
451	!> Compute the exner function for scalar arguments.
452	!------------------------------------------------------------------------------!
453	FUNCTION exner_function_invers_0d( p )
454
455	IMPLICIT NONE
456
457	REAL(wp), INTENT(IN) :: p !< pressure (Pa)
458
459	REAL(wp) :: exner_function_invers_0d
460	!
461	!-- compute exner function:
462	exner_function_invers_0d = ( p_0 / p )**( rd_d_cp )
463
464	END FUNCTION exner_function_invers_0d
465
466	!------------------------------------------------------------------------------!
467	! Description:
468	! ------------
469	!> Compute the exner function for 1-D array arguments.
470	!------------------------------------------------------------------------------!
471	FUNCTION exner_function_invers_1d( p )
472
473	IMPLICIT NONE
474
475	REAL(wp), INTENT(IN), DIMENSION(:) :: p !< pressure (Pa)
476
477	REAL(wp), DIMENSION(size(p)) :: exner_function_invers_1d
478	!
479	!-- compute exner function:
480	exner_function_invers_1d = ( p_0 / p )**( rd_d_cp )
481
482	END FUNCTION exner_function_invers_1d
483
484	!------------------------------------------------------------------------------!
485	! Description:
486	! ------------
487	!> Compute the barometric formula for scalar arguments. The calculation is
488	!> based on the assumption of a polytropic atmosphere and neutral
489	!> stratification, where the temperature lapse rate is g/cp.
490	!------------------------------------------------------------------------------!
491	FUNCTION barometric_formula_0d( z, t_0, p_0)
492
493	IMPLICIT NONE
494
495	REAL(wp), INTENT(IN) :: z !< height (m)
496	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
497	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
498
499	REAL(wp) :: barometric_formula_0d
500	!
501	!-- compute barometric formula:
502	barometric_formula_0d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
503
504	END FUNCTION barometric_formula_0d
505
506	!------------------------------------------------------------------------------!
507	! Description:
508	! ------------
509	!> Compute the barometric formula for 1-D array arguments. The calculation is
510	!> based on the assumption of a polytropic atmosphere and neutral
511	!> stratification, where the temperature lapse rate is g/cp.
512	!------------------------------------------------------------------------------!
513	FUNCTION barometric_formula_1d( z, t_0, p_0)
514
515	IMPLICIT NONE
516
517	REAL(wp), INTENT(IN), DIMENSION(:) :: z !< height (m)
518	REAL(wp), INTENT(IN) :: t_0 !< temperature reference state (K)
519	REAL(wp), INTENT(IN) :: p_0 !< surface pressure (Pa)
520
521	REAL(wp), DIMENSION(size(z)) :: barometric_formula_1d
522	!
523	!-- compute barometric formula:
524	barometric_formula_1d = p_0 * ( (t_0 - g_d_cp * z) / t_0 )**( cp_d_rd )
525
526	END FUNCTION barometric_formula_1d
527
528	END MODULE basic_constants_and_equations_mod

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