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source: palm/trunk/SOURCE/basic_constants_and_equations_mod.f90 @ 4448

Last change on this file since 4448 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

Rev	Line
[3274]	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	!
[4360]	17	! Copyright 1997-2020 Leibniz Universitaet Hannover
[3274]	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 moh.hefny $
[4400]	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
[4182]	31	! Corrected "Former revisions" section
	32	!
	33	! 4088 2019-07-11 13:57:56Z Giersch
[4088]	34	! Comment of barometric formula improved, function for ideal gas law revised
	35	!
	36	! 4084 2019-07-10 17:09:11Z knoop
[4084]	37	! Changed precomputed fractions to be variable based
	38	!
	39	! 4055 2019-06-27 09:47:29Z suehring
[4055]	40	! Added rgas_univ (universal gas constant) (E.C. Chan)
	41	!
	42	!
	43	! 3655 2019-01-07 16:51:22Z knoop
[3634]	44	! OpenACC port for SPEC
[4182]	45	! 3361 2018-10-16 20:39:37Z knoop
	46	! New module (introduced with modularization of bulk cloud physics model)
	47	!
[3634]	48	!
[3274]	49	!
[4182]	50	!
[3274]	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)
[3449]	65	REAL(wp), PARAMETER :: degc_to_k = 273.15_wp !< temperature (in K) of 0 deg C (K)
[3274]	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)
[3449]	75	REAL(wp), PARAMETER :: pi = 3.141592654_wp !< PI
[3634]	76	!$ACC DECLARE COPYIN(pi)
[4055]	77	REAL(wp), PARAMETER :: rgas_univ = 8.31446261815324_wp !< universal gas constant (J K-1 mol-1)
[3274]	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)
[3449]	84	REAL(wp), PARAMETER :: sigma_sb = 5.67037E-08_wp !< Stefan-Boltzmann constant
[3274]	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
[4084]	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
[3274]	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
[4400]	119
	120	INTERFACE convert_utm_to_geographic
	121	MODULE PROCEDURE convert_utm_to_geographic
	122	END INTERFACE convert_utm_to_geographic
	123
[3274]	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
[4400]	153	!
	154	!-- Public routines
	155	PUBLIC convert_utm_to_geographic
[3274]	156
	157	CONTAINS
	158
[4400]	159
[3274]	160	!------------------------------------------------------------------------------!
	161	! Description:
	162	! ------------
[4400]	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	! ------------
[3274]	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:
[3449]	311	magnus_0d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
[4400]	312	( t - 29.65_wp ) )
[3274]	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:
[3449]	331	magnus_1d = 611.2_wp * EXP( 17.62_wp * ( t - degc_to_k ) / &
[3274]	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:
[4088]	389	ideal_gas_law_rho_pt_0d = p / (r_d * exner_function(p) * t)
[3274]	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:
[4088]	408	ideal_gas_law_rho_pt_1d = p / (r_d * exner_function(p) * t)
[3274]	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	! ------------
[4088]	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.
[3274]	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	! ------------
[4088]	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.
[3274]	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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