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source: palm/trunk/SOURCE/model_1d_mod.f90 @ 3137

Last change on this file since 3137 was 3135, checked in by gronemeier, 6 years ago
Bugfix: add +1 to c_3 according to Sogachev et al. (2012)
Property svn:keywords set to `Id`
File size: 44.8 KB

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[2338]	1	!> @file model_1d_mod.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[2000]	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.
[1036]	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	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[254]	20	! Current revisions:
[1]	21	! -----------------
[1961]	22	!
[3049]	23	!
[1961]	24	! Former revisions:
	25	! -----------------
	26	! $Id: model_1d_mod.f90 3135 2018-07-16 14:43:04Z maronga $
[3135]	27	! Bugfix: add +1 to c_3 according to Sogachev et al. (2012)
	28	!
	29	! 3126 2018-07-13 15:13:54Z gronemeier
[3126]	30	! Bugfix: define c_0 = 0.03^0.25 = 0.416179145
	31	!
	32	! 3083 2018-06-19 14:03:12Z gronemeier
[3083]	33	! Bugfixes:
	34	! - preset te_diss and te_e to avoid runtime errors
	35	! - implementation of buoyancy term to dissipation
	36	! according to Sogachev et al. (2012)
	37	! - where diss_p < 0 set diss_p = 0.1 diss
	38	! - calculate progn eq(diss) starting from nzb+1
	39	! Changes:
	40	! - add sig_e to TKE equation
	41	! - adjust prognostic equation of diss
	42	! - set model constants according to Koblitz (2013)
	43	! - renamed c_m to c_0
	44	! - rename l_black into l1d_init
	45	! - calculate l_grid within init_1d_model and save it as l1d_init
	46	! - calculate l1d according to DE85 if dissipation is a prognostic value
	47	! - made annotations doxygen-readable
	48	!
	49	! 3049 2018-05-29 13:52:36Z Giersch
[3049]	50	! Error messages revised
	51	!
	52	! 3045 2018-05-28 07:55:41Z Giersch
[3045]	53	! Error message revised
	54	!
	55	! 2965 2018-04-13 07:37:25Z scharf
[2965]	56	! adjusted format string for 1D run control output
	57	!
	58	! 2918 2018-03-21 15:52:14Z gronemeier
[2918]	59	! - rename l_black into l1d_init
	60	! - calculate l_grid within init_1d_model and save it as l1d_init
	61	!
	62	! 2718 2018-01-02 08:49:38Z maronga
[2716]	63	! Corrected "Former revisions" section
	64	!
	65	! 2696 2017-12-14 17:12:51Z kanani
	66	! Change in file header (GPL part)
[2696]	67	! implement TKE-e closure
	68	! modification of dissipation production according to Detering and Etling
	69	! reduced factor for timestep criterion to 0.125 and first dt to 1s (TG)
	70	!
	71	! 2339 2017-08-07 13:55:26Z gronemeier
[2339]	72	! corrected timestamp in header
	73	!
	74	! 2338 2017-08-07 12:15:38Z gronemeier
[2338]	75	! renamed init_1d_model to model_1d_mod and and formatted it as a module;
	76	! reformatted output of profiles
	77	!
[2339]	78	! 2337 2017-08-07 08:59:53Z gronemeier
[2337]	79	! revised calculation of mixing length
	80	! removed rounding of time step
	81	! corrected calculation of virtual potential temperature
	82	!
	83	! 2334 2017-08-04 11:57:04Z gronemeier
[2334]	84	! set c_m = 0.4 according to Detering and Etling (1985)
	85	!
	86	! 2299 2017-06-29 10:14:38Z maronga
[2299]	87	! Removed german text
[1961]	88	!
[2299]	89	! 2101 2017-01-05 16:42:31Z suehring
	90	!
[2060]	91	! 2059 2016-11-10 14:20:40Z maronga
	92	! Corrected min/max values of Rif.
	93	!
[2001]	94	! 2000 2016-08-20 18:09:15Z knoop
	95	! Forced header and separation lines into 80 columns
	96	!
[1961]	97	! 1960 2016-07-12 16:34:24Z suehring
[1960]	98	! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively
	99	! not used.
	100	! Formatting adjustment
[1809]	101	!
	102	! 1808 2016-04-05 19:44:00Z raasch
	103	! routine local_flush replaced by FORTRAN statement
	104	!
[1710]	105	! 1709 2015-11-04 14:47:01Z maronga
	106	! Set initial time step to 10 s to avoid instability of the 1d model for small
	107	! grid spacings
	108	!
[1698]	109	! 1697 2015-10-28 17:14:10Z raasch
	110	! small E- and F-FORMAT changes to avoid informative compiler messages about
	111	! insufficient field width
	112	!
[1692]	113	! 1691 2015-10-26 16:17:44Z maronga
	114	! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta.
	115	!
[1683]	116	! 1682 2015-10-07 23:56:08Z knoop
	117	! Code annotations made doxygen readable
	118	!
[1354]	119	! 1353 2014-04-08 15:21:23Z heinze
	120	! REAL constants provided with KIND-attribute
	121	!
[1347]	122	! 1346 2014-03-27 13:18:20Z heinze
	123	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	124	! intrinsic function like MAX, MIN, SIGN
	125	!
[1323]	126	! 1322 2014-03-20 16:38:49Z raasch
	127	! REAL functions provided with KIND-attribute
	128	!
[1321]	129	! 1320 2014-03-20 08:40:49Z raasch
[1320]	130	! ONLY-attribute added to USE-statements,
	131	! kind-parameters added to all INTEGER and REAL declaration statements,
	132	! kinds are defined in new module kinds,
	133	! revision history before 2012 removed,
	134	! comment fields (!:) to be used for variable explanations added to
	135	! all variable declaration statements
[1321]	136	!
[1037]	137	! 1036 2012-10-22 13:43:42Z raasch
	138	! code put under GPL (PALM 3.9)
	139	!
[1017]	140	! 1015 2012-09-27 09:23:24Z raasch
	141	! adjustment of mixing length to the Prandtl mixing length at first grid point
	142	! above ground removed
	143	!
[1002]	144	! 1001 2012-09-13 14:08:46Z raasch
	145	! all actions concerning leapfrog scheme removed
	146	!
[997]	147	! 996 2012-09-07 10:41:47Z raasch
	148	! little reformatting
	149	!
[979]	150	! 978 2012-08-09 08:28:32Z fricke
	151	! roughness length for scalar quantities z0h1d added
	152	!
[1]	153	! Revision 1.1 1998/03/09 16:22:10 raasch
	154	! Initial revision
	155	!
	156	!
	157	! Description:
	158	! ------------
[1682]	159	!> 1D-model to initialize the 3D-arrays.
	160	!> The temperature profile is set as steady and a corresponding steady solution
	161	!> of the wind profile is being computed.
	162	!> All subroutines required can be found within this file.
[1691]	163	!>
	164	!> @todo harmonize code with new surface_layer_fluxes module
[1709]	165	!> @bug 1D model crashes when using small grid spacings in the order of 1 m
[2965]	166	!> @fixme option "as_in_3d_model" seems to be an inappropriate option because
[2918]	167	!> the 1D model uses different turbulence closure approaches at least if
	168	!> the 3D model is set to LES-mode.
[1]	169	!------------------------------------------------------------------------------!
[2338]	170	MODULE model_1d_mod
[1]	171
[1320]	172	USE arrays_3d, &
[2918]	173	ONLY: dd2zu, ddzu, ddzw, dzu, dzw, pt_init, q_init, ug, u_init, &
[2338]	174	vg, v_init, zu
[1320]	175
[2338]	176	USE control_parameters, &
	177	ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, g, &
	178	humidity, ibc_e_b, intermediate_timestep_count, &
	179	intermediate_timestep_count_max, kappa, km_constant, &
	180	message_string, mixing_length_1d, prandtl_number, &
[2696]	181	roughness_length, run_description_header, simulated_time_chr, &
	182	timestep_scheme, tsc, z0h_factor
[2338]	183
[1320]	184	USE indices, &
[2338]	185	ONLY: nzb, nzb_diff, nzt
[1320]	186
	187	USE kinds
[1]	188
[3083]	189	USE pegrid, &
	190	ONLY: myid
[2338]	191
	192
[1]	193	IMPLICIT NONE
	194
[2338]	195	INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model)
[2696]	196	INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model)
[2338]	197
	198	LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model)
	199	LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model)
	200
[3083]	201	REAL(wp) :: alpha_buoyancy !< model constant according to Koblitz (2013)
[3126]	202	REAL(wp) :: c_0 = 0.416179145_wp !< = 0.03^0.25; model constant according to Koblitz (2013)
[3083]	203	REAL(wp) :: c_1 = 1.52_wp !< model constant according to Koblitz (2013)
	204	REAL(wp) :: c_2 = 1.83_wp !< model constant according to Koblitz (2013)
	205	REAL(wp) :: c_3 !< model constant
	206	REAL(wp) :: c_mu !< model constant
[2696]	207	REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter
[2338]	208	REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model)
	209	REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model)
[2696]	210	REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter
	211	REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter
	212	REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter
[3083]	213	REAL(wp) :: lambda !< maximum mixing length
[2338]	214	REAL(wp) :: qs1d !< characteristic humidity scale (1d-model)
	215	REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model)
[3083]	216	REAL(wp) :: sig_diss = 2.95_wp !< model constant according to Koblitz (2013)
	217	REAL(wp) :: sig_e = 2.95_wp !< model constant according to Koblitz (2013)
[2338]	218	REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model)
	219	REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model)
	220	REAL(wp) :: ts1d !< characteristic temperature scale (1d-model)
[2696]	221	REAL(wp) :: us1d !< friction velocity (1d-model)
	222	REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model)
	223	REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model)
[2338]	224	REAL(wp) :: z01d !< roughness length for momentum (1d-model)
	225	REAL(wp) :: z0h1d !< roughness length for scalars (1d-model)
	226
[2696]	227	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d !< tke dissipation rate (1d-model)
	228	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d_p !< prognostic value of tke dissipation rate (1d-model)
	229	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model)
[2338]	230	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model)
[2696]	231	REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model)
	232	REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model)
	233	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model)
[2918]	234	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_init !< initial mixing length (1d-model)
[2338]	235	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model)
[2696]	236	REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model)
	237	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_diss !< tendency of diss (1d-model)
	238	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_dissm !< weighted tendency of diss for previous sub-timestep (1d-model)
[2338]	239	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model)
	240	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model)
	241	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model)
	242	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model)
	243	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model)
	244	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model)
[2696]	245	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model)
[2338]	246	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model)
[2696]	247	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model)
[2338]	248	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model)
	249
	250	!
	251	!-- Initialize 1D model
	252	INTERFACE init_1d_model
	253	MODULE PROCEDURE init_1d_model
	254	END INTERFACE init_1d_model
	255
	256	!
	257	!-- Print profiles
	258	INTERFACE print_1d_model
	259	MODULE PROCEDURE print_1d_model
	260	END INTERFACE print_1d_model
	261
	262	!
	263	!-- Print run control information
	264	INTERFACE run_control_1d
	265	MODULE PROCEDURE run_control_1d
	266	END INTERFACE run_control_1d
	267
	268	!
	269	!-- Main procedure
	270	INTERFACE time_integration_1d
	271	MODULE PROCEDURE time_integration_1d
	272	END INTERFACE time_integration_1d
	273
	274	!
	275	!-- Calculate time step
	276	INTERFACE timestep_1d
	277	MODULE PROCEDURE timestep_1d
	278	END INTERFACE timestep_1d
	279
	280	SAVE
	281
	282	PRIVATE
	283	!
	284	!-- Public interfaces
	285	PUBLIC init_1d_model
	286
	287	!
	288	!-- Public variables
[2696]	289	PUBLIC damp_level_1d, damp_level_ind_1d, diss1d, dt_pr_1d, &
	290	dt_run_control_1d, e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, &
	291	us1d, usws1d, v1d, vsws1d
[2338]	292
	293
	294	CONTAINS
	295
	296	SUBROUTINE init_1d_model
	297
[2918]	298	USE grid_variables, &
	299	ONLY: dx, dy
	300
[2338]	301	IMPLICIT NONE
	302
[2696]	303	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	304
	305	INTEGER(iwp) :: k !< loop index
[1]	306
	307	!
	308	!-- Allocate required 1D-arrays
[2696]	309	ALLOCATE( diss1d(nzb:nzt+1), diss1d_p(nzb:nzt+1), &
	310	e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), &
[2918]	311	km1d(nzb:nzt+1), l1d(nzb:nzt+1), l1d_init(nzb:nzt+1), &
[2696]	312	l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_diss(nzb:nzt+1), &
	313	te_dissm(nzb:nzt+1), te_e(nzb:nzt+1), &
[2338]	314	te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), &
	315	te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), &
	316	u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) )
[1]	317
	318	!
	319	!-- Initialize arrays
	320	IF ( constant_diffusion ) THEN
[1001]	321	km1d = km_constant
	322	kh1d = km_constant / prandtl_number
[1]	323	ELSE
[2696]	324	diss1d = 0.0_wp; diss1d_p = 0.0_wp
[1353]	325	e1d = 0.0_wp; e1d_p = 0.0_wp
	326	kh1d = 0.0_wp; km1d = 0.0_wp
	327	rif1d = 0.0_wp
[1]	328	!
	329	!-- Compute the mixing length
[2918]	330	l1d_init(nzb) = 0.0_wp
[1]	331
	332	IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN
	333	!
	334	!-- Blackadar mixing length
[1353]	335	IF ( f /= 0.0_wp ) THEN
	336	lambda = 2.7E-4_wp * SQRT( ug(nzt+1)2 + vg(nzt+1)2 ) / &
	337	ABS( f ) + 1E-10_wp
[1]	338	ELSE
[1353]	339	lambda = 30.0_wp
[1]	340	ENDIF
	341
	342	DO k = nzb+1, nzt+1
[2918]	343	l1d_init(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda )
[1]	344	ENDDO
	345
	346	ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN
	347	!
[2918]	348	!-- Use the same mixing length as in 3D model (LES-mode)
[3083]	349	!> @todo rename (delete?) this option
	350	!> As the mixing length is different between RANS and LES mode, it
	351	!> must be distinguished here between these modes. For RANS mode,
	352	!> the mixing length is calculated accoding to Blackadar, which is
	353	!> the other option at this point.
	354	!> Maybe delete this option entirely (not appropriate in LES case)
	355	!> 2018-03-20, gronemeier
[2918]	356	DO k = nzb+1, nzt
	357	l1d_init(k) = ( dx * dy * dzw(k) )**0.33333333333333_wp
	358	ENDDO
	359	l1d_init(nzt+1) = l1d_init(nzt)
[1]	360
	361	ENDIF
	362	ENDIF
[2918]	363	l1d = l1d_init
	364	l1d_diss = l1d_init
[2337]	365	u1d = u_init
	366	u1d_p = u_init
	367	v1d = v_init
	368	v1d_p = v_init
[1]	369
	370	!
	371	!-- Set initial horizontal velocities at the lowest grid levels to a very small
	372	!-- value in order to avoid too small time steps caused by the diffusion limit
	373	!-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!)
[1353]	374	u1d(0:1) = 0.1_wp
	375	u1d_p(0:1) = 0.1_wp
	376	v1d(0:1) = 0.1_wp
	377	v1d_p(0:1) = 0.1_wp
[1]	378
	379	!
	380	!-- For u, theta and the momentum fluxes plausible values are set
[1691]	381	IF ( constant_flux_layer ) THEN
[1353]	382	us1d = 0.1_wp ! without initial friction the flow would not change
[1]	383	ELSE
[3083]	384	diss1d(nzb+1) = 0.001_wp
[1353]	385	e1d(nzb+1) = 1.0_wp
	386	km1d(nzb+1) = 1.0_wp
	387	us1d = 0.0_wp
[1]	388	ENDIF
[1353]	389	ts1d = 0.0_wp
	390	usws1d = 0.0_wp
	391	vsws1d = 0.0_wp
[996]	392	z01d = roughness_length
[978]	393	z0h1d = z0h_factor * z01d
[1960]	394	IF ( humidity ) qs1d = 0.0_wp
[1]	395
	396	!
[3083]	397	!-- Tendencies must be preset in order to avoid runtime errors
	398	te_diss = 0.0_wp
[2696]	399	te_dissm = 0.0_wp
[3083]	400	te_e = 0.0_wp
[1353]	401	te_em = 0.0_wp
	402	te_um = 0.0_wp
	403	te_vm = 0.0_wp
[46]	404
	405	!
[2338]	406	!-- Set model constant
[3083]	407	IF ( dissipation_1d == 'as_in_3d_model' ) c_0 = 0.1_wp
	408	c_mu = c_0**4
[2338]	409
	410	!
[1]	411	!-- Set start time in hh:mm:ss - format
	412	simulated_time_chr = time_to_string( simulated_time_1d )
	413
	414	!
[2337]	415	!-- Integrate the 1D-model equations using the Runge-Kutta scheme
[1]	416	CALL time_integration_1d
	417
	418
	419	END SUBROUTINE init_1d_model
	420
	421
	422
	423	!------------------------------------------------------------------------------!
	424	! Description:
	425	! ------------
[2338]	426	!> Runge-Kutta time differencing scheme for the 1D-model.
[1]	427	!------------------------------------------------------------------------------!
[1682]	428
	429	SUBROUTINE time_integration_1d
[1]	430
	431	IMPLICIT NONE
	432
[2696]	433	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	434
[2338]	435	INTEGER(iwp) :: k !< loop index
[2696]	436
[2338]	437	REAL(wp) :: a !< auxiliary variable
	438	REAL(wp) :: b !< auxiliary variable
	439	REAL(wp) :: dpt_dz !< vertical temperature gradient
	440	REAL(wp) :: flux !< vertical temperature gradient
	441	REAL(wp) :: kmzm !< Km(z-dz/2)
	442	REAL(wp) :: kmzp !< Km(z+dz/2)
	443	REAL(wp) :: l_stable !< mixing length for stable case
	444	REAL(wp) :: pt_0 !< reference temperature
	445	REAL(wp) :: uv_total !< horizontal wind speed
[1]	446
	447	!
	448	!-- Determine the time step at the start of a 1D-simulation and
	449	!-- determine and printout quantities used for run control
[3083]	450	dt_1d = 0.01_wp
[1]	451	CALL run_control_1d
	452
	453	!
	454	!-- Start of time loop
	455	DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d )
	456
	457	!
	458	!-- Depending on the timestep scheme, carry out one or more intermediate
	459	!-- timesteps
	460
	461	intermediate_timestep_count = 0
	462	DO WHILE ( intermediate_timestep_count < &
	463	intermediate_timestep_count_max )
	464
	465	intermediate_timestep_count = intermediate_timestep_count + 1
	466
	467	CALL timestep_scheme_steering
	468
	469	!
[2696]	470	!-- Compute all tendency terms. If a constant-flux layer is simulated,
	471	!-- k starts at nzb+2.
[1]	472	DO k = nzb_diff, nzt
	473
[1353]	474	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	475	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[1]	476	!
	477	!-- u-component
	478	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
[1001]	479	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) &
	480	- kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) &
	481	) * ddzw(k)
[1]	482	!
	483	!-- v-component
[1001]	484	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	485	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) &
	486	- kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) &
	487	) * ddzw(k)
[1]	488	ENDDO
	489	IF ( .NOT. constant_diffusion ) THEN
	490	DO k = nzb_diff, nzt
	491	!
[2696]	492	!-- TKE and dissipation rate
[1353]	493	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	494	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	495	IF ( .NOT. humidity ) THEN
[1]	496	pt_0 = pt_init(k)
	497	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	498	ELSE
[1353]	499	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	500	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	501	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	502	pt_init(k-1) * q_init(k-1) ) &
	503	) * dd2zu(k)
[1]	504	ENDIF
	505
[2696]	506	!
	507	!-- Calculate dissipation rate if no prognostic equation is used for
	508	!-- dissipation rate
[1]	509	IF ( dissipation_1d == 'detering' ) THEN
[3083]	510	diss1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	511	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	512	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) &
[2696]	513	) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	514	ENDIF
[2696]	515	!
	516	!-- TKE
[1]	517	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	518	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	519	) &
	520	- g / pt_0 * kh1d(k) * flux &
	521	+ ( &
[1001]	522	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	523	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[3083]	524	) * ddzw(k) / sig_e &
[2696]	525	- diss1d(k)
	526
	527	IF ( dissipation_1d == 'prognostic' ) THEN
	528	!
	529	!-- dissipation rate
[3083]	530	IF ( rif1d(k) >= 0.0_wp ) THEN
	531	alpha_buoyancy = 1.0_wp - l1d(k) / lambda
	532	ELSE
	533	alpha_buoyancy = 1.0_wp - ( 1.0_wp + ( c_2 - 1.0_wp ) &
	534	/ ( c_2 - c_1 ) ) &
	535	* l1d(k) / lambda
	536	ENDIF
[3135]	537	c_3 = ( c_1 - c_2 ) * alpha_buoyancy + 1.0_wp
[3083]	538	te_diss(k) = ( km1d(k) * &
[2696]	539	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	540	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
[3083]	541	) * ( c_1 + (c_2 - c_1) * l1d(k) / lambda ) &
[2696]	542	- g / pt_0 * kh1d(k) * flux * c_3 &
[3083]	543	- c_2 * diss1d(k) &
	544	) * diss1d(k) / ( e1d(k) + 1.0E-20_wp ) &
	545	+ ( kmzp * ( diss1d(k+1) - diss1d(k) ) &
[2696]	546	* ddzu(k+1) &
	547	- kmzm * ( diss1d(k) - diss1d(k-1) ) &
	548	* ddzu(k) &
[3083]	549	) * ddzw(k) / sig_diss
[2696]	550
	551	ENDIF
	552
[1]	553	ENDDO
	554	ENDIF
	555
	556	!
[2696]	557	!-- Tendency terms at the top of the constant-flux layer.
[1]	558	!-- Finite differences of the momentum fluxes are computed using half the
	559	!-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy
[1691]	560	IF ( constant_flux_layer ) THEN
[1]	561
	562	k = nzb+1
[1353]	563	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	564	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	565	IF ( .NOT. humidity ) THEN
[1]	566	pt_0 = pt_init(k)
	567	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	568	ELSE
[1353]	569	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	570	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	571	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	572	pt_init(k-1) * q_init(k-1) ) &
[1]	573	) * dd2zu(k)
	574	ENDIF
	575
[2696]	576	!
	577	!-- Calculate dissipation rate if no prognostic equation is used for
	578	!-- dissipation rate
[1]	579	IF ( dissipation_1d == 'detering' ) THEN
[3083]	580	diss1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	581	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	582	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) ) &
[2696]	583	* e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	584	ENDIF
	585
	586	!
	587	!-- u-component
[1001]	588	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
	589	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d &
[1353]	590	) * 2.0_wp * ddzw(k)
[1]	591	!
	592	!-- v-component
[1001]	593	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	594	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d &
[1353]	595	) * 2.0_wp * ddzw(k)
[1]	596	!
	597	!-- TKE
[2696]	598	IF ( .NOT. dissipation_1d == 'prognostic' ) THEN
[3083]	599	!> @query why integrate over 2dz
	600	!> Why is it allowed to integrate over two delta-z for e
	601	!> while for u and v it is not?
	602	!> 2018-04-23, gronemeier
[2696]	603	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	604	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	605	) &
	606	- g / pt_0 * kh1d(k) * flux &
	607	+ ( &
	608	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	609	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[3083]	610	) * ddzw(k) / sig_e &
[2696]	611	- diss1d(k)
	612	ENDIF
	613
[1]	614	ENDIF
	615
	616	!
	617	!-- Prognostic equations for all 1D variables
	618	DO k = nzb+1, nzt
	619
[1001]	620	u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + &
	621	tsc(3) * te_um(k) )
	622	v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + &
	623	tsc(3) * te_vm(k) )
[1]	624
	625	ENDDO
	626	IF ( .NOT. constant_diffusion ) THEN
[2696]	627
[1]	628	DO k = nzb+1, nzt
[1001]	629	e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + &
	630	tsc(3) * te_em(k) )
[2696]	631	ENDDO
[1]	632
	633	!
	634	!-- Eliminate negative TKE values, which can result from the
	635	!-- integration due to numerical inaccuracies. In such cases the TKE
	636	!-- value is reduced to 10 percent of its old value.
[1353]	637	WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d
[3083]	638
	639	IF ( dissipation_1d == 'prognostic' ) THEN
	640	DO k = nzb+1, nzt
	641	diss1d_p(k) = diss1d(k) + dt_1d * ( tsc(2) * te_diss(k) + &
	642	tsc(3) * te_dissm(k) )
	643	ENDDO
	644	WHERE ( diss1d_p < 0.0_wp ) diss1d_p = 0.1_wp * diss1d
	645	ENDIF
[1]	646	ENDIF
	647
	648	!
	649	!-- Calculate tendencies for the next Runge-Kutta step
	650	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	651	IF ( intermediate_timestep_count == 1 ) THEN
	652
	653	DO k = nzb+1, nzt
	654	te_um(k) = te_u(k)
	655	te_vm(k) = te_v(k)
	656	ENDDO
	657
	658	IF ( .NOT. constant_diffusion ) THEN
	659	DO k = nzb+1, nzt
	660	te_em(k) = te_e(k)
	661	ENDDO
[2696]	662	IF ( dissipation_1d == 'prognostic' ) THEN
	663	DO k = nzb+1, nzt
	664	te_dissm(k) = te_diss(k)
	665	ENDDO
	666	ENDIF
[1]	667	ENDIF
	668
	669	ELSEIF ( intermediate_timestep_count < &
	670	intermediate_timestep_count_max ) THEN
	671
	672	DO k = nzb+1, nzt
[1353]	673	te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k)
	674	te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k)
[1]	675	ENDDO
	676
	677	IF ( .NOT. constant_diffusion ) THEN
	678	DO k = nzb+1, nzt
[1353]	679	te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k)
[1]	680	ENDDO
[2696]	681	IF ( dissipation_1d == 'prognostic' ) THEN
	682	DO k = nzb+1, nzt
[3083]	683	te_dissm(k) = -9.5625_wp * te_diss(k) &
	684	+ 5.3125_wp * te_dissm(k)
[2696]	685	ENDDO
	686	ENDIF
[1]	687	ENDIF
	688
	689	ENDIF
	690	ENDIF
	691
	692	!
	693	!-- Boundary conditions for the prognostic variables.
[2696]	694	!-- At the top boundary (nzt+1) u, v, e, and diss keep their initial
	695	!-- values (ug(nzt+1), vg(nzt+1), 0, 0).
[2334]	696	!-- At the bottom boundary, Dirichlet condition is used for u and v (0)
[2696]	697	!-- and Neumann condition for e and diss (e(nzb)=e(nzb+1)).
[1353]	698	u1d_p(nzb) = 0.0_wp
	699	v1d_p(nzb) = 0.0_wp
[667]	700
[1]	701	!
	702	!-- Swap the time levels in preparation for the next time step.
	703	u1d = u1d_p
	704	v1d = v1d_p
	705	IF ( .NOT. constant_diffusion ) THEN
	706	e1d = e1d_p
[2696]	707	IF ( dissipation_1d == 'prognostic' ) THEN
	708	diss1d = diss1d_p
	709	ENDIF
[1]	710	ENDIF
	711
	712	!
	713	!-- Compute diffusion quantities
	714	IF ( .NOT. constant_diffusion ) THEN
	715
	716	!
[2696]	717	!-- First compute the vertical fluxes in the constant-flux layer
[1691]	718	IF ( constant_flux_layer ) THEN
[1]	719	!
	720	!-- Compute theta* using Rif numbers of the previous time step
[2334]	721	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	722	!
	723	!-- Stable stratification
[1353]	724	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	725	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	726	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	727	)
	728	ELSE
	729	!
	730	!-- Unstable stratification
[1353]	731	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	732	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	733	zu(nzb+1) * z0h1d )
[2337]	734
	735	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	736	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	737	(b+1.0_wp) / (b-1.0_wp) )
[1]	738	ENDIF
	739
[1691]	740	ENDIF ! constant_flux_layer
[3083]	741	!> @todo combine if clauses
	742	!> The previous and following if clauses can be combined into a
	743	!> single clause
	744	!> 2018-04-23, gronemeier
[1]	745	!
	746	!-- Compute the Richardson-flux numbers,
[2696]	747	!-- first at the top of the constant-flux layer using u* of the
	748	!-- previous time step (+1E-30, if u* = 0), then in the remaining area.
	749	!-- There the rif-numbers of the previous time step are used.
[1]	750
[1691]	751	IF ( constant_flux_layer ) THEN
[75]	752	IF ( .NOT. humidity ) THEN
[1]	753	pt_0 = pt_init(nzb+1)
	754	flux = ts1d
	755	ELSE
[1353]	756	pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) )
	757	flux = ts1d + 0.61_wp * pt_init(k) * qs1d
[1]	758	ENDIF
	759	rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / &
[1353]	760	( pt_0 * ( us1d**2 + 1E-30_wp ) )
[1]	761	ENDIF
	762
	763	DO k = nzb_diff, nzt
[75]	764	IF ( .NOT. humidity ) THEN
[1]	765	pt_0 = pt_init(k)
	766	flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	767	ELSE
[1353]	768	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
[1]	769	flux = ( ( pt_init(k+1) - pt_init(k-1) ) &
[2337]	770	+ 0.61_wp &
	771	* ( pt_init(k+1) * q_init(k+1) &
	772	- pt_init(k-1) * q_init(k-1) ) &
[1]	773	) * dd2zu(k)
	774	ENDIF
[1353]	775	IF ( rif1d(k) >= 0.0_wp ) THEN
	776	rif1d(k) = g / pt_0 * flux / &
	777	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	778	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	779	+ 1E-30_wp &
[1]	780	)
	781	ELSE
[1353]	782	rif1d(k) = g / pt_0 * flux / &
	783	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	784	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	785	+ 1E-30_wp &
	786	) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	787	ENDIF
	788	ENDDO
	789	!
	790	!-- Richardson-numbers must remain restricted to a realistic value
	791	!-- range. It is exceeded excessively for very small velocities
	792	!-- (u,v --> 0).
[2059]	793	WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp
	794	WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp
[1]	795
	796	!
	797	!-- Compute u* from the absolute velocity value
[1691]	798	IF ( constant_flux_layer ) THEN
[1]	799	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
	800
[1353]	801	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	802	!
	803	!-- Stable stratification
	804	us1d = kappa * uv_total / ( &
[1353]	805	LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * &
[1]	806	( zu(nzb+1) - z01d ) / zu(nzb+1) &
	807	)
	808	ELSE
	809	!
	810	!-- Unstable stratification
[1353]	811	a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) )
	812	b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	813	zu(nzb+1) * z01d ) )
[2337]	814	us1d = kappa * uv_total / ( &
	815	LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / &
	816	(1.0_wp+a) ) + &
	817	2.0_wp * ( ATAN( b ) - ATAN( a ) ) &
	818	)
[1]	819	ENDIF
	820
	821	!
	822	!-- Compute the momentum fluxes for the diffusion terms
	823	usws1d = - u1d(nzb+1) / uv_total * us1d**2
	824	vsws1d = - v1d(nzb+1) / uv_total * us1d**2
	825
	826	!
[2696]	827	!-- Boundary condition for the turbulent kinetic energy and
	828	!-- dissipation rate at the top of the constant-flux layer.
[1]	829	!-- Additional Neumann condition de/dz = 0 at nzb is set to ensure
	830	!-- compatibility with the 3D model.
	831	IF ( ibc_e_b == 2 ) THEN
[3083]	832	e1d(nzb+1) = ( us1d / c_0 )**2
[1]	833	ENDIF
[2696]	834	IF ( dissipation_1d == 'prognostic' ) THEN
[3083]	835	e1d(nzb+1) = ( us1d / c_0 )**2
[2696]	836	diss1d(nzb+1) = us1d*3 / ( kappa zu(nzb+1) )
	837	diss1d(nzb) = diss1d(nzb+1)
	838	ENDIF
[1]	839	e1d(nzb) = e1d(nzb+1)
	840
[1960]	841	IF ( humidity ) THEN
[1]	842	!
	843	!-- Compute q*
[2334]	844	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	845	!
[1960]	846	!-- Stable stratification
	847	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
[1353]	848	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	849	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	850	)
[1960]	851	ELSE
[1]	852	!
[1960]	853	!-- Unstable stratification
	854	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	855	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	856	zu(nzb+1) * z0h1d )
[2337]	857	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
	858	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	859	(b+1.0_wp) / (b-1.0_wp) )
	860	ENDIF
[1]	861	ELSE
[1353]	862	qs1d = 0.0_wp
[2337]	863	ENDIF
[1]	864
[1691]	865	ENDIF ! constant_flux_layer
[1]	866
	867	!
[2337]	868	!-- Compute the diabatic mixing length. The unstable stratification
	869	!-- must not be considered for l1d (km1d) as it is already considered
	870	!-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be
	871	!-- too large.
[3083]	872	IF ( dissipation_1d /= 'prognostic' ) THEN
	873	IF ( mixing_length_1d == 'blackadar' ) THEN
	874	DO k = nzb+1, nzt
	875	IF ( rif1d(k) >= 0.0_wp ) THEN
	876	l1d(k) = l1d_init(k) / ( 1.0_wp + 5.0_wp * rif1d(k) )
	877	l1d_diss(k) = l1d(k)
	878	ELSE
	879	l1d(k) = l1d_init(k)
	880	l1d_diss(k) = l1d_init(k) * &
	881	SQRT( 1.0_wp - 16.0_wp * rif1d(k) )
	882	ENDIF
	883	ENDDO
	884	ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN
	885	DO k = nzb+1, nzt
	886	dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	887	IF ( dpt_dz > 0.0_wp ) THEN
	888	l_stable = 0.76_wp * SQRT( e1d(k) ) &
	889	/ SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp
	890	ELSE
	891	l_stable = l1d_init(k)
	892	ENDIF
	893	l1d(k) = MIN( l1d_init(k), l_stable )
[2337]	894	l1d_diss(k) = l1d(k)
[3083]	895	ENDDO
	896	ENDIF
	897	ELSE
[1]	898	DO k = nzb+1, nzt
[3083]	899	l1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) &
	900	/ ( diss1d(k) + 1.0E-30_wp )
[1]	901	ENDDO
	902	ENDIF
	903
	904	!
	905	!-- Compute the diffusion coefficients for momentum via the
	906	!-- corresponding Prandtl-layer relationship and according to
[2337]	907	!-- Prandtl-Kolmogorov, respectively
[1691]	908	IF ( constant_flux_layer ) THEN
[1353]	909	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
	910	km1d(nzb+1) = us1d * kappa * zu(nzb+1) / &
	911	( 1.0_wp + 5.0_wp * rif1d(nzb+1) )
[1]	912	ELSE
[1353]	913	km1d(nzb+1) = us1d * kappa * zu(nzb+1) * &
	914	( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp
[1]	915	ENDIF
	916	ENDIF
[3083]	917
[2696]	918	IF ( dissipation_1d == 'prognostic' ) THEN
	919	DO k = nzb_diff, nzt
	920	km1d(k) = c_mu * e1d(k)**2 / ( diss1d(k) + 1.0E-30_wp )
	921	ENDDO
	922	ELSE
	923	DO k = nzb_diff, nzt
[3083]	924	km1d(k) = c_0 * SQRT( e1d(k) ) * l1d(k)
[2696]	925	ENDDO
	926	ENDIF
[1]	927
	928	!
	929	!-- Add damping layer
	930	DO k = damp_level_ind_1d+1, nzt+1
[1353]	931	km1d(k) = 1.1_wp * km1d(k-1)
[1346]	932	km1d(k) = MIN( km1d(k), 10.0_wp )
[1]	933	ENDDO
	934
	935	!
	936	!-- Compute the diffusion coefficient for heat via the relationship
	937	!-- kh = phim / phih * km
	938	DO k = nzb+1, nzt
[1353]	939	IF ( rif1d(k) >= 0.0_wp ) THEN
[1]	940	kh1d(k) = km1d(k)
	941	ELSE
[1353]	942	kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	943	ENDIF
	944	ENDDO
	945
	946	ENDIF ! .NOT. constant_diffusion
	947
	948	ENDDO ! intermediate step loop
	949
	950	!
	951	!-- Increment simulated time and output times
	952	current_timestep_number_1d = current_timestep_number_1d + 1
	953	simulated_time_1d = simulated_time_1d + dt_1d
	954	simulated_time_chr = time_to_string( simulated_time_1d )
	955	time_pr_1d = time_pr_1d + dt_1d
	956	time_run_control_1d = time_run_control_1d + dt_1d
	957
	958	!
	959	!-- Determine and print out quantities for run control
	960	IF ( time_run_control_1d >= dt_run_control_1d ) THEN
	961	CALL run_control_1d
	962	time_run_control_1d = time_run_control_1d - dt_run_control_1d
	963	ENDIF
	964
	965	!
	966	!-- Profile output on file
	967	IF ( time_pr_1d >= dt_pr_1d ) THEN
	968	CALL print_1d_model
	969	time_pr_1d = time_pr_1d - dt_pr_1d
	970	ENDIF
	971
	972	!
	973	!-- Determine size of next time step
	974	CALL timestep_1d
	975
	976	ENDDO ! time loop
	977
	978
	979	END SUBROUTINE time_integration_1d
	980
	981
	982	!------------------------------------------------------------------------------!
	983	! Description:
	984	! ------------
[1682]	985	!> Compute and print out quantities for run control of the 1D model.
[1]	986	!------------------------------------------------------------------------------!
[1682]	987
	988	SUBROUTINE run_control_1d
[1]	989
[1682]	990
[1320]	991	USE constants, &
	992	ONLY: pi
[1]	993
	994	IMPLICIT NONE
	995
[2338]	996	INTEGER(iwp) :: k !< loop index
[1320]	997
[2338]	998	REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer
	999	REAL(wp) :: energy !< kinetic energy
	1000	REAL(wp) :: umax !< maximum of u
	1001	REAL(wp) :: uv_total !< horizontal wind speed
	1002	REAL(wp) :: vmax !< maximum of v
[1]	1003
	1004	!
	1005	!-- Output
	1006	IF ( myid == 0 ) THEN
	1007	!
	1008	!-- If necessary, write header
	1009	IF ( .NOT. run_control_header_1d ) THEN
[184]	1010	CALL check_open( 15 )
[1]	1011	WRITE ( 15, 100 )
	1012	run_control_header_1d = .TRUE.
	1013	ENDIF
	1014
	1015	!
	1016	!-- Compute control quantities
	1017	!-- grid level nzp is excluded due to mirror boundary condition
[1353]	1018	umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp
[1]	1019	DO k = nzb+1, nzt+1
	1020	umax = MAX( ABS( umax ), ABS( u1d(k) ) )
	1021	vmax = MAX( ABS( vmax ), ABS( v1d(k) ) )
[1353]	1022	energy = energy + 0.5_wp * ( u1d(k)2 + v1d(k)2 )
[1]	1023	ENDDO
[1322]	1024	energy = energy / REAL( nzt - nzb + 1, KIND=wp )
[1]	1025
	1026	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
[1691]	1027	IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN
[1346]	1028	alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) )
[1]	1029	ELSE
	1030	alpha = ACOS( u1d(nzb+1) / uv_total )
[1353]	1031	IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha
[1]	1032	ENDIF
[1353]	1033	alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp
[1]	1034
	1035	WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, &
	1036	dt_1d, umax, vmax, us1d, alpha, energy
	1037	!
	1038	!-- Write buffer contents to disc immediately
[1808]	1039	FLUSH( 15 )
[1]	1040
	1041	ENDIF
	1042
	1043	!
	1044	!-- formats
[2299]	1045	100 FORMAT (///'1D run control output:'/ &
[1]	1046	&'------------------------------'// &
[2965]	1047	&'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ &
[1]	1048	&'-------------------------------------------------------------')
[2965]	1049	101 FORMAT (I7,1X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2)
[1]	1050
	1051
	1052	END SUBROUTINE run_control_1d
	1053
	1054
	1055
	1056	!------------------------------------------------------------------------------!
	1057	! Description:
	1058	! ------------
[1682]	1059	!> Compute the time step w.r.t. the diffusion criterion
[1]	1060	!------------------------------------------------------------------------------!
[1682]	1061
	1062	SUBROUTINE timestep_1d
[1]	1063
	1064	IMPLICIT NONE
	1065
[2338]	1066	INTEGER(iwp) :: k !< loop index
[1]	1067
[2338]	1068	REAL(wp) :: dt_diff !< time step accorind to diffusion criterion
[3083]	1069	REAL(wp) :: dt_old !< previous time step
[2338]	1070	REAL(wp) :: fac !< factor of criterion
	1071	REAL(wp) :: value !< auxiliary variable
[1]	1072
	1073	!
[3083]	1074	!-- Save previous time step
	1075	dt_old = dt_1d
	1076
	1077	!
[1]	1078	!-- Compute the currently feasible time step according to the diffusion
	1079	!-- criterion. At nzb+1 the half grid length is used.
[3083]	1080	fac = 0.125
[1]	1081	dt_diff = dt_max_1d
	1082	DO k = nzb+2, nzt
[1353]	1083	value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp )
[1]	1084	dt_diff = MIN( value, dt_diff )
	1085	ENDDO
[1353]	1086	value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp )
[1]	1087	dt_1d = MIN( value, dt_diff )
	1088
	1089	!
[3083]	1090	!-- Limit the new time step to a maximum of 10 times the previous time step
	1091	dt_1d = MIN( dt_old * 10.0_wp, dt_1d )
	1092
	1093	!
[1]	1094	!-- Set flag when the time step becomes too small
[3083]	1095	IF ( dt_1d < ( 1.0E-15_wp * dt_max_1d ) ) THEN
[1]	1096	stop_dt_1d = .TRUE.
[254]	1097
[3046]	1098	WRITE( message_string, * ) 'timestep has exceeded the lower limit&', &
[254]	1099	'dt_1d = ',dt_1d,' s simulation stopped!'
	1100	CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 )
	1101
[1]	1102	ENDIF
	1103
	1104	END SUBROUTINE timestep_1d
	1105
	1106
	1107
	1108	!------------------------------------------------------------------------------!
	1109	! Description:
	1110	! ------------
[1682]	1111	!> List output of profiles from the 1D-model
[1]	1112	!------------------------------------------------------------------------------!
[1682]	1113
	1114	SUBROUTINE print_1d_model
[1]	1115
	1116	IMPLICIT NONE
	1117
[2338]	1118	INTEGER(iwp) :: k !< loop parameter
[1]	1119
[2338]	1120	LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header
[1]	1121
	1122
	1123	IF ( myid == 0 ) THEN
	1124	!
	1125	!-- Open list output file for profiles from the 1D-model
	1126	CALL check_open( 17 )
	1127
	1128	!
	1129	!-- Write Header
[2338]	1130	IF ( write_first ) THEN
	1131	WRITE ( 17, 100 ) TRIM( run_description_header )
	1132	write_first = .FALSE.
	1133	ENDIF
[1]	1134
	1135	!
	1136	!-- Write the values
[2338]	1137	WRITE ( 17, 104 ) TRIM( simulated_time_chr )
	1138	WRITE ( 17, 101 )
[1]	1139	WRITE ( 17, 102 )
	1140	WRITE ( 17, 101 )
	1141	DO k = nzt+1, nzb, -1
	1142	WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), &
[2696]	1143	rif1d(k), km1d(k), kh1d(k), l1d(k), diss1d(k)
[1]	1144	ENDDO
	1145	WRITE ( 17, 101 )
	1146	WRITE ( 17, 102 )
	1147	WRITE ( 17, 101 )
	1148
	1149	!
	1150	!-- Write buffer contents to disc immediately
[1808]	1151	FLUSH( 17 )
[1]	1152
	1153	ENDIF
	1154
	1155	!
	1156	!-- Formats
[2338]	1157	100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles')
	1158	104 FORMAT (//'# Time: ',A)
[2696]	1159	101 FORMAT ('#',111('-'))
	1160	102 FORMAT ('# k zu u v pt e ', &
	1161	'rif Km Kh l diss ')
	1162	103 FORMAT (1X,I4,1X,F7.1,9(1X,E10.3))
[1]	1163
	1164
	1165	END SUBROUTINE print_1d_model
[2338]	1166
	1167
[3045]	1168	END MODULE

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