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source: palm/trunk/SOURCE/model_1d_mod.f90 @ 3083

Last change on this file since 3083 was 3083, checked in by gronemeier, 6 years ago
merge with branch rans
Property svn:keywords set to `Id`
File size: 44.6 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 3083 2018-06-19 14:03:12Z gronemeier $
[3083]	27	! Bugfixes:
	28	! - preset te_diss and te_e to avoid runtime errors
	29	! - implementation of buoyancy term to dissipation
	30	! according to Sogachev et al. (2012)
	31	! - where diss_p < 0 set diss_p = 0.1 diss
	32	! - calculate progn eq(diss) starting from nzb+1
	33	! Changes:
	34	! - add sig_e to TKE equation
	35	! - adjust prognostic equation of diss
	36	! - set model constants according to Koblitz (2013)
	37	! - renamed c_m to c_0
	38	! - rename l_black into l1d_init
	39	! - calculate l_grid within init_1d_model and save it as l1d_init
	40	! - calculate l1d according to DE85 if dissipation is a prognostic value
	41	! - made annotations doxygen-readable
	42	!
	43	! 3049 2018-05-29 13:52:36Z Giersch
[3049]	44	! Error messages revised
	45	!
	46	! 3045 2018-05-28 07:55:41Z Giersch
[3045]	47	! Error message revised
	48	!
	49	! 2965 2018-04-13 07:37:25Z scharf
[2965]	50	! adjusted format string for 1D run control output
	51	!
	52	! 2918 2018-03-21 15:52:14Z gronemeier
[2918]	53	! - rename l_black into l1d_init
	54	! - calculate l_grid within init_1d_model and save it as l1d_init
	55	!
	56	! 2718 2018-01-02 08:49:38Z maronga
[2716]	57	! Corrected "Former revisions" section
	58	!
	59	! 2696 2017-12-14 17:12:51Z kanani
	60	! Change in file header (GPL part)
[2696]	61	! implement TKE-e closure
	62	! modification of dissipation production according to Detering and Etling
	63	! reduced factor for timestep criterion to 0.125 and first dt to 1s (TG)
	64	!
	65	! 2339 2017-08-07 13:55:26Z gronemeier
[2339]	66	! corrected timestamp in header
	67	!
	68	! 2338 2017-08-07 12:15:38Z gronemeier
[2338]	69	! renamed init_1d_model to model_1d_mod and and formatted it as a module;
	70	! reformatted output of profiles
	71	!
[2339]	72	! 2337 2017-08-07 08:59:53Z gronemeier
[2337]	73	! revised calculation of mixing length
	74	! removed rounding of time step
	75	! corrected calculation of virtual potential temperature
	76	!
	77	! 2334 2017-08-04 11:57:04Z gronemeier
[2334]	78	! set c_m = 0.4 according to Detering and Etling (1985)
	79	!
	80	! 2299 2017-06-29 10:14:38Z maronga
[2299]	81	! Removed german text
[1961]	82	!
[2299]	83	! 2101 2017-01-05 16:42:31Z suehring
	84	!
[2060]	85	! 2059 2016-11-10 14:20:40Z maronga
	86	! Corrected min/max values of Rif.
	87	!
[2001]	88	! 2000 2016-08-20 18:09:15Z knoop
	89	! Forced header and separation lines into 80 columns
	90	!
[1961]	91	! 1960 2016-07-12 16:34:24Z suehring
[1960]	92	! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively
	93	! not used.
	94	! Formatting adjustment
[1809]	95	!
	96	! 1808 2016-04-05 19:44:00Z raasch
	97	! routine local_flush replaced by FORTRAN statement
	98	!
[1710]	99	! 1709 2015-11-04 14:47:01Z maronga
	100	! Set initial time step to 10 s to avoid instability of the 1d model for small
	101	! grid spacings
	102	!
[1698]	103	! 1697 2015-10-28 17:14:10Z raasch
	104	! small E- and F-FORMAT changes to avoid informative compiler messages about
	105	! insufficient field width
	106	!
[1692]	107	! 1691 2015-10-26 16:17:44Z maronga
	108	! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta.
	109	!
[1683]	110	! 1682 2015-10-07 23:56:08Z knoop
	111	! Code annotations made doxygen readable
	112	!
[1354]	113	! 1353 2014-04-08 15:21:23Z heinze
	114	! REAL constants provided with KIND-attribute
	115	!
[1347]	116	! 1346 2014-03-27 13:18:20Z heinze
	117	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	118	! intrinsic function like MAX, MIN, SIGN
	119	!
[1323]	120	! 1322 2014-03-20 16:38:49Z raasch
	121	! REAL functions provided with KIND-attribute
	122	!
[1321]	123	! 1320 2014-03-20 08:40:49Z raasch
[1320]	124	! ONLY-attribute added to USE-statements,
	125	! kind-parameters added to all INTEGER and REAL declaration statements,
	126	! kinds are defined in new module kinds,
	127	! revision history before 2012 removed,
	128	! comment fields (!:) to be used for variable explanations added to
	129	! all variable declaration statements
[1321]	130	!
[1037]	131	! 1036 2012-10-22 13:43:42Z raasch
	132	! code put under GPL (PALM 3.9)
	133	!
[1017]	134	! 1015 2012-09-27 09:23:24Z raasch
	135	! adjustment of mixing length to the Prandtl mixing length at first grid point
	136	! above ground removed
	137	!
[1002]	138	! 1001 2012-09-13 14:08:46Z raasch
	139	! all actions concerning leapfrog scheme removed
	140	!
[997]	141	! 996 2012-09-07 10:41:47Z raasch
	142	! little reformatting
	143	!
[979]	144	! 978 2012-08-09 08:28:32Z fricke
	145	! roughness length for scalar quantities z0h1d added
	146	!
[1]	147	! Revision 1.1 1998/03/09 16:22:10 raasch
	148	! Initial revision
	149	!
	150	!
	151	! Description:
	152	! ------------
[1682]	153	!> 1D-model to initialize the 3D-arrays.
	154	!> The temperature profile is set as steady and a corresponding steady solution
	155	!> of the wind profile is being computed.
	156	!> All subroutines required can be found within this file.
[1691]	157	!>
	158	!> @todo harmonize code with new surface_layer_fluxes module
[1709]	159	!> @bug 1D model crashes when using small grid spacings in the order of 1 m
[2965]	160	!> @fixme option "as_in_3d_model" seems to be an inappropriate option because
[2918]	161	!> the 1D model uses different turbulence closure approaches at least if
	162	!> the 3D model is set to LES-mode.
[1]	163	!------------------------------------------------------------------------------!
[2338]	164	MODULE model_1d_mod
[1]	165
[1320]	166	USE arrays_3d, &
[2918]	167	ONLY: dd2zu, ddzu, ddzw, dzu, dzw, pt_init, q_init, ug, u_init, &
[2338]	168	vg, v_init, zu
[1320]	169
[2338]	170	USE control_parameters, &
	171	ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, g, &
	172	humidity, ibc_e_b, intermediate_timestep_count, &
	173	intermediate_timestep_count_max, kappa, km_constant, &
	174	message_string, mixing_length_1d, prandtl_number, &
[2696]	175	roughness_length, run_description_header, simulated_time_chr, &
	176	timestep_scheme, tsc, z0h_factor
[2338]	177
[1320]	178	USE indices, &
[2338]	179	ONLY: nzb, nzb_diff, nzt
[1320]	180
	181	USE kinds
[1]	182
[3083]	183	USE pegrid, &
	184	ONLY: myid
[2338]	185
	186
[1]	187	IMPLICIT NONE
	188
[2338]	189	INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model)
[2696]	190	INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model)
[2338]	191
	192	LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model)
	193	LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model)
	194
[3083]	195	REAL(wp) :: alpha_buoyancy !< model constant according to Koblitz (2013)
	196	REAL(wp) :: c_0 = 0.03_wp**0.25_wp !< model constant according to Koblitz (2013)
	197	REAL(wp) :: c_1 = 1.52_wp !< model constant according to Koblitz (2013)
	198	REAL(wp) :: c_2 = 1.83_wp !< model constant according to Koblitz (2013)
	199	REAL(wp) :: c_3 !< model constant
	200	REAL(wp) :: c_mu !< model constant
[2696]	201	REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter
[2338]	202	REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model)
	203	REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model)
[2696]	204	REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter
	205	REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter
	206	REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter
[3083]	207	REAL(wp) :: lambda !< maximum mixing length
[2338]	208	REAL(wp) :: qs1d !< characteristic humidity scale (1d-model)
	209	REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model)
[3083]	210	REAL(wp) :: sig_diss = 2.95_wp !< model constant according to Koblitz (2013)
	211	REAL(wp) :: sig_e = 2.95_wp !< model constant according to Koblitz (2013)
[2338]	212	REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model)
	213	REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model)
	214	REAL(wp) :: ts1d !< characteristic temperature scale (1d-model)
[2696]	215	REAL(wp) :: us1d !< friction velocity (1d-model)
	216	REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model)
	217	REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model)
[2338]	218	REAL(wp) :: z01d !< roughness length for momentum (1d-model)
	219	REAL(wp) :: z0h1d !< roughness length for scalars (1d-model)
	220
[2696]	221	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d !< tke dissipation rate (1d-model)
	222	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d_p !< prognostic value of tke dissipation rate (1d-model)
	223	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model)
[2338]	224	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model)
[2696]	225	REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model)
	226	REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model)
	227	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model)
[2918]	228	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_init !< initial mixing length (1d-model)
[2338]	229	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model)
[2696]	230	REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model)
	231	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_diss !< tendency of diss (1d-model)
	232	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_dissm !< weighted tendency of diss for previous sub-timestep (1d-model)
[2338]	233	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model)
	234	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model)
	235	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model)
	236	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model)
	237	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model)
	238	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model)
[2696]	239	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model)
[2338]	240	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model)
[2696]	241	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model)
[2338]	242	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model)
	243
	244	!
	245	!-- Initialize 1D model
	246	INTERFACE init_1d_model
	247	MODULE PROCEDURE init_1d_model
	248	END INTERFACE init_1d_model
	249
	250	!
	251	!-- Print profiles
	252	INTERFACE print_1d_model
	253	MODULE PROCEDURE print_1d_model
	254	END INTERFACE print_1d_model
	255
	256	!
	257	!-- Print run control information
	258	INTERFACE run_control_1d
	259	MODULE PROCEDURE run_control_1d
	260	END INTERFACE run_control_1d
	261
	262	!
	263	!-- Main procedure
	264	INTERFACE time_integration_1d
	265	MODULE PROCEDURE time_integration_1d
	266	END INTERFACE time_integration_1d
	267
	268	!
	269	!-- Calculate time step
	270	INTERFACE timestep_1d
	271	MODULE PROCEDURE timestep_1d
	272	END INTERFACE timestep_1d
	273
	274	SAVE
	275
	276	PRIVATE
	277	!
	278	!-- Public interfaces
	279	PUBLIC init_1d_model
	280
	281	!
	282	!-- Public variables
[2696]	283	PUBLIC damp_level_1d, damp_level_ind_1d, diss1d, dt_pr_1d, &
	284	dt_run_control_1d, e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, &
	285	us1d, usws1d, v1d, vsws1d
[2338]	286
	287
	288	CONTAINS
	289
	290	SUBROUTINE init_1d_model
	291
[2918]	292	USE grid_variables, &
	293	ONLY: dx, dy
	294
[2338]	295	IMPLICIT NONE
	296
[2696]	297	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	298
	299	INTEGER(iwp) :: k !< loop index
[1]	300
	301	!
	302	!-- Allocate required 1D-arrays
[2696]	303	ALLOCATE( diss1d(nzb:nzt+1), diss1d_p(nzb:nzt+1), &
	304	e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), &
[2918]	305	km1d(nzb:nzt+1), l1d(nzb:nzt+1), l1d_init(nzb:nzt+1), &
[2696]	306	l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_diss(nzb:nzt+1), &
	307	te_dissm(nzb:nzt+1), te_e(nzb:nzt+1), &
[2338]	308	te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), &
	309	te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), &
	310	u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) )
[1]	311
	312	!
	313	!-- Initialize arrays
	314	IF ( constant_diffusion ) THEN
[1001]	315	km1d = km_constant
	316	kh1d = km_constant / prandtl_number
[1]	317	ELSE
[2696]	318	diss1d = 0.0_wp; diss1d_p = 0.0_wp
[1353]	319	e1d = 0.0_wp; e1d_p = 0.0_wp
	320	kh1d = 0.0_wp; km1d = 0.0_wp
	321	rif1d = 0.0_wp
[1]	322	!
	323	!-- Compute the mixing length
[2918]	324	l1d_init(nzb) = 0.0_wp
[1]	325
	326	IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN
	327	!
	328	!-- Blackadar mixing length
[1353]	329	IF ( f /= 0.0_wp ) THEN
	330	lambda = 2.7E-4_wp * SQRT( ug(nzt+1)2 + vg(nzt+1)2 ) / &
	331	ABS( f ) + 1E-10_wp
[1]	332	ELSE
[1353]	333	lambda = 30.0_wp
[1]	334	ENDIF
	335
	336	DO k = nzb+1, nzt+1
[2918]	337	l1d_init(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda )
[1]	338	ENDDO
	339
	340	ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN
	341	!
[2918]	342	!-- Use the same mixing length as in 3D model (LES-mode)
[3083]	343	!> @todo rename (delete?) this option
	344	!> As the mixing length is different between RANS and LES mode, it
	345	!> must be distinguished here between these modes. For RANS mode,
	346	!> the mixing length is calculated accoding to Blackadar, which is
	347	!> the other option at this point.
	348	!> Maybe delete this option entirely (not appropriate in LES case)
	349	!> 2018-03-20, gronemeier
[2918]	350	DO k = nzb+1, nzt
	351	l1d_init(k) = ( dx * dy * dzw(k) )**0.33333333333333_wp
	352	ENDDO
	353	l1d_init(nzt+1) = l1d_init(nzt)
[1]	354
	355	ENDIF
	356	ENDIF
[2918]	357	l1d = l1d_init
	358	l1d_diss = l1d_init
[2337]	359	u1d = u_init
	360	u1d_p = u_init
	361	v1d = v_init
	362	v1d_p = v_init
[1]	363
	364	!
	365	!-- Set initial horizontal velocities at the lowest grid levels to a very small
	366	!-- value in order to avoid too small time steps caused by the diffusion limit
	367	!-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!)
[1353]	368	u1d(0:1) = 0.1_wp
	369	u1d_p(0:1) = 0.1_wp
	370	v1d(0:1) = 0.1_wp
	371	v1d_p(0:1) = 0.1_wp
[1]	372
	373	!
	374	!-- For u, theta and the momentum fluxes plausible values are set
[1691]	375	IF ( constant_flux_layer ) THEN
[1353]	376	us1d = 0.1_wp ! without initial friction the flow would not change
[1]	377	ELSE
[3083]	378	diss1d(nzb+1) = 0.001_wp
[1353]	379	e1d(nzb+1) = 1.0_wp
	380	km1d(nzb+1) = 1.0_wp
	381	us1d = 0.0_wp
[1]	382	ENDIF
[1353]	383	ts1d = 0.0_wp
	384	usws1d = 0.0_wp
	385	vsws1d = 0.0_wp
[996]	386	z01d = roughness_length
[978]	387	z0h1d = z0h_factor * z01d
[1960]	388	IF ( humidity ) qs1d = 0.0_wp
[1]	389
	390	!
[3083]	391	!-- Tendencies must be preset in order to avoid runtime errors
	392	te_diss = 0.0_wp
[2696]	393	te_dissm = 0.0_wp
[3083]	394	te_e = 0.0_wp
[1353]	395	te_em = 0.0_wp
	396	te_um = 0.0_wp
	397	te_vm = 0.0_wp
[46]	398
	399	!
[2338]	400	!-- Set model constant
[3083]	401	IF ( dissipation_1d == 'as_in_3d_model' ) c_0 = 0.1_wp
	402	c_mu = c_0**4
[2338]	403
	404	!
[1]	405	!-- Set start time in hh:mm:ss - format
	406	simulated_time_chr = time_to_string( simulated_time_1d )
	407
	408	!
[2337]	409	!-- Integrate the 1D-model equations using the Runge-Kutta scheme
[1]	410	CALL time_integration_1d
	411
	412
	413	END SUBROUTINE init_1d_model
	414
	415
	416
	417	!------------------------------------------------------------------------------!
	418	! Description:
	419	! ------------
[2338]	420	!> Runge-Kutta time differencing scheme for the 1D-model.
[1]	421	!------------------------------------------------------------------------------!
[1682]	422
	423	SUBROUTINE time_integration_1d
[1]	424
	425	IMPLICIT NONE
	426
[2696]	427	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	428
[2338]	429	INTEGER(iwp) :: k !< loop index
[2696]	430
[2338]	431	REAL(wp) :: a !< auxiliary variable
	432	REAL(wp) :: b !< auxiliary variable
	433	REAL(wp) :: dpt_dz !< vertical temperature gradient
	434	REAL(wp) :: flux !< vertical temperature gradient
	435	REAL(wp) :: kmzm !< Km(z-dz/2)
	436	REAL(wp) :: kmzp !< Km(z+dz/2)
	437	REAL(wp) :: l_stable !< mixing length for stable case
	438	REAL(wp) :: pt_0 !< reference temperature
	439	REAL(wp) :: uv_total !< horizontal wind speed
[1]	440
	441	!
	442	!-- Determine the time step at the start of a 1D-simulation and
	443	!-- determine and printout quantities used for run control
[3083]	444	dt_1d = 0.01_wp
[1]	445	CALL run_control_1d
	446
	447	!
	448	!-- Start of time loop
	449	DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d )
	450
	451	!
	452	!-- Depending on the timestep scheme, carry out one or more intermediate
	453	!-- timesteps
	454
	455	intermediate_timestep_count = 0
	456	DO WHILE ( intermediate_timestep_count < &
	457	intermediate_timestep_count_max )
	458
	459	intermediate_timestep_count = intermediate_timestep_count + 1
	460
	461	CALL timestep_scheme_steering
	462
	463	!
[2696]	464	!-- Compute all tendency terms. If a constant-flux layer is simulated,
	465	!-- k starts at nzb+2.
[1]	466	DO k = nzb_diff, nzt
	467
[1353]	468	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	469	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[1]	470	!
	471	!-- u-component
	472	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
[1001]	473	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) &
	474	- kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) &
	475	) * ddzw(k)
[1]	476	!
	477	!-- v-component
[1001]	478	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	479	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) &
	480	- kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) &
	481	) * ddzw(k)
[1]	482	ENDDO
	483	IF ( .NOT. constant_diffusion ) THEN
	484	DO k = nzb_diff, nzt
	485	!
[2696]	486	!-- TKE and dissipation rate
[1353]	487	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	488	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	489	IF ( .NOT. humidity ) THEN
[1]	490	pt_0 = pt_init(k)
	491	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	492	ELSE
[1353]	493	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	494	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	495	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	496	pt_init(k-1) * q_init(k-1) ) &
	497	) * dd2zu(k)
[1]	498	ENDIF
	499
[2696]	500	!
	501	!-- Calculate dissipation rate if no prognostic equation is used for
	502	!-- dissipation rate
[1]	503	IF ( dissipation_1d == 'detering' ) THEN
[3083]	504	diss1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	505	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	506	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) &
[2696]	507	) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	508	ENDIF
[2696]	509	!
	510	!-- TKE
[1]	511	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	512	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	513	) &
	514	- g / pt_0 * kh1d(k) * flux &
	515	+ ( &
[1001]	516	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	517	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[3083]	518	) * ddzw(k) / sig_e &
[2696]	519	- diss1d(k)
	520
	521	IF ( dissipation_1d == 'prognostic' ) THEN
	522	!
	523	!-- dissipation rate
[3083]	524	IF ( rif1d(k) >= 0.0_wp ) THEN
	525	alpha_buoyancy = 1.0_wp - l1d(k) / lambda
	526	ELSE
	527	alpha_buoyancy = 1.0_wp - ( 1.0_wp + ( c_2 - 1.0_wp ) &
	528	/ ( c_2 - c_1 ) ) &
	529	* l1d(k) / lambda
	530	ENDIF
	531	c_3 = ( c_1 - c_2 ) * alpha_buoyancy
	532	te_diss(k) = ( km1d(k) * &
[2696]	533	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	534	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
[3083]	535	) * ( c_1 + (c_2 - c_1) * l1d(k) / lambda ) &
[2696]	536	- g / pt_0 * kh1d(k) * flux * c_3 &
[3083]	537	- c_2 * diss1d(k) &
	538	) * diss1d(k) / ( e1d(k) + 1.0E-20_wp ) &
	539	+ ( kmzp * ( diss1d(k+1) - diss1d(k) ) &
[2696]	540	* ddzu(k+1) &
	541	- kmzm * ( diss1d(k) - diss1d(k-1) ) &
	542	* ddzu(k) &
[3083]	543	) * ddzw(k) / sig_diss
[2696]	544
	545	ENDIF
	546
[1]	547	ENDDO
	548	ENDIF
	549
	550	!
[2696]	551	!-- Tendency terms at the top of the constant-flux layer.
[1]	552	!-- Finite differences of the momentum fluxes are computed using half the
	553	!-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy
[1691]	554	IF ( constant_flux_layer ) THEN
[1]	555
	556	k = nzb+1
[1353]	557	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	558	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	559	IF ( .NOT. humidity ) THEN
[1]	560	pt_0 = pt_init(k)
	561	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	562	ELSE
[1353]	563	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	564	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	565	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	566	pt_init(k-1) * q_init(k-1) ) &
[1]	567	) * dd2zu(k)
	568	ENDIF
	569
[2696]	570	!
	571	!-- Calculate dissipation rate if no prognostic equation is used for
	572	!-- dissipation rate
[1]	573	IF ( dissipation_1d == 'detering' ) THEN
[3083]	574	diss1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	575	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	576	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) ) &
[2696]	577	* e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	578	ENDIF
	579
	580	!
	581	!-- u-component
[1001]	582	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
	583	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d &
[1353]	584	) * 2.0_wp * ddzw(k)
[1]	585	!
	586	!-- v-component
[1001]	587	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	588	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d &
[1353]	589	) * 2.0_wp * ddzw(k)
[1]	590	!
	591	!-- TKE
[2696]	592	IF ( .NOT. dissipation_1d == 'prognostic' ) THEN
[3083]	593	!> @query why integrate over 2dz
	594	!> Why is it allowed to integrate over two delta-z for e
	595	!> while for u and v it is not?
	596	!> 2018-04-23, gronemeier
[2696]	597	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	598	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	599	) &
	600	- g / pt_0 * kh1d(k) * flux &
	601	+ ( &
	602	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	603	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[3083]	604	) * ddzw(k) / sig_e &
[2696]	605	- diss1d(k)
	606	ENDIF
	607
[1]	608	ENDIF
	609
	610	!
	611	!-- Prognostic equations for all 1D variables
	612	DO k = nzb+1, nzt
	613
[1001]	614	u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + &
	615	tsc(3) * te_um(k) )
	616	v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + &
	617	tsc(3) * te_vm(k) )
[1]	618
	619	ENDDO
	620	IF ( .NOT. constant_diffusion ) THEN
[2696]	621
[1]	622	DO k = nzb+1, nzt
[1001]	623	e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + &
	624	tsc(3) * te_em(k) )
[2696]	625	ENDDO
[1]	626
	627	!
	628	!-- Eliminate negative TKE values, which can result from the
	629	!-- integration due to numerical inaccuracies. In such cases the TKE
	630	!-- value is reduced to 10 percent of its old value.
[1353]	631	WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d
[3083]	632
	633	IF ( dissipation_1d == 'prognostic' ) THEN
	634	DO k = nzb+1, nzt
	635	diss1d_p(k) = diss1d(k) + dt_1d * ( tsc(2) * te_diss(k) + &
	636	tsc(3) * te_dissm(k) )
	637	ENDDO
	638	WHERE ( diss1d_p < 0.0_wp ) diss1d_p = 0.1_wp * diss1d
	639	ENDIF
[1]	640	ENDIF
	641
	642	!
	643	!-- Calculate tendencies for the next Runge-Kutta step
	644	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	645	IF ( intermediate_timestep_count == 1 ) THEN
	646
	647	DO k = nzb+1, nzt
	648	te_um(k) = te_u(k)
	649	te_vm(k) = te_v(k)
	650	ENDDO
	651
	652	IF ( .NOT. constant_diffusion ) THEN
	653	DO k = nzb+1, nzt
	654	te_em(k) = te_e(k)
	655	ENDDO
[2696]	656	IF ( dissipation_1d == 'prognostic' ) THEN
	657	DO k = nzb+1, nzt
	658	te_dissm(k) = te_diss(k)
	659	ENDDO
	660	ENDIF
[1]	661	ENDIF
	662
	663	ELSEIF ( intermediate_timestep_count < &
	664	intermediate_timestep_count_max ) THEN
	665
	666	DO k = nzb+1, nzt
[1353]	667	te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k)
	668	te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k)
[1]	669	ENDDO
	670
	671	IF ( .NOT. constant_diffusion ) THEN
	672	DO k = nzb+1, nzt
[1353]	673	te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k)
[1]	674	ENDDO
[2696]	675	IF ( dissipation_1d == 'prognostic' ) THEN
	676	DO k = nzb+1, nzt
[3083]	677	te_dissm(k) = -9.5625_wp * te_diss(k) &
	678	+ 5.3125_wp * te_dissm(k)
[2696]	679	ENDDO
	680	ENDIF
[1]	681	ENDIF
	682
	683	ENDIF
	684	ENDIF
	685
	686	!
	687	!-- Boundary conditions for the prognostic variables.
[2696]	688	!-- At the top boundary (nzt+1) u, v, e, and diss keep their initial
	689	!-- values (ug(nzt+1), vg(nzt+1), 0, 0).
[2334]	690	!-- At the bottom boundary, Dirichlet condition is used for u and v (0)
[2696]	691	!-- and Neumann condition for e and diss (e(nzb)=e(nzb+1)).
[1353]	692	u1d_p(nzb) = 0.0_wp
	693	v1d_p(nzb) = 0.0_wp
[667]	694
[1]	695	!
	696	!-- Swap the time levels in preparation for the next time step.
	697	u1d = u1d_p
	698	v1d = v1d_p
	699	IF ( .NOT. constant_diffusion ) THEN
	700	e1d = e1d_p
[2696]	701	IF ( dissipation_1d == 'prognostic' ) THEN
	702	diss1d = diss1d_p
	703	ENDIF
[1]	704	ENDIF
	705
	706	!
	707	!-- Compute diffusion quantities
	708	IF ( .NOT. constant_diffusion ) THEN
	709
	710	!
[2696]	711	!-- First compute the vertical fluxes in the constant-flux layer
[1691]	712	IF ( constant_flux_layer ) THEN
[1]	713	!
	714	!-- Compute theta* using Rif numbers of the previous time step
[2334]	715	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	716	!
	717	!-- Stable stratification
[1353]	718	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	719	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	720	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	721	)
	722	ELSE
	723	!
	724	!-- Unstable stratification
[1353]	725	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	726	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	727	zu(nzb+1) * z0h1d )
[2337]	728
	729	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	730	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	731	(b+1.0_wp) / (b-1.0_wp) )
[1]	732	ENDIF
	733
[1691]	734	ENDIF ! constant_flux_layer
[3083]	735	!> @todo combine if clauses
	736	!> The previous and following if clauses can be combined into a
	737	!> single clause
	738	!> 2018-04-23, gronemeier
[1]	739	!
	740	!-- Compute the Richardson-flux numbers,
[2696]	741	!-- first at the top of the constant-flux layer using u* of the
	742	!-- previous time step (+1E-30, if u* = 0), then in the remaining area.
	743	!-- There the rif-numbers of the previous time step are used.
[1]	744
[1691]	745	IF ( constant_flux_layer ) THEN
[75]	746	IF ( .NOT. humidity ) THEN
[1]	747	pt_0 = pt_init(nzb+1)
	748	flux = ts1d
	749	ELSE
[1353]	750	pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) )
	751	flux = ts1d + 0.61_wp * pt_init(k) * qs1d
[1]	752	ENDIF
	753	rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / &
[1353]	754	( pt_0 * ( us1d**2 + 1E-30_wp ) )
[1]	755	ENDIF
	756
	757	DO k = nzb_diff, nzt
[75]	758	IF ( .NOT. humidity ) THEN
[1]	759	pt_0 = pt_init(k)
	760	flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	761	ELSE
[1353]	762	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
[1]	763	flux = ( ( pt_init(k+1) - pt_init(k-1) ) &
[2337]	764	+ 0.61_wp &
	765	* ( pt_init(k+1) * q_init(k+1) &
	766	- pt_init(k-1) * q_init(k-1) ) &
[1]	767	) * dd2zu(k)
	768	ENDIF
[1353]	769	IF ( rif1d(k) >= 0.0_wp ) THEN
	770	rif1d(k) = g / pt_0 * flux / &
	771	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	772	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	773	+ 1E-30_wp &
[1]	774	)
	775	ELSE
[1353]	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 &
	780	) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	781	ENDIF
	782	ENDDO
	783	!
	784	!-- Richardson-numbers must remain restricted to a realistic value
	785	!-- range. It is exceeded excessively for very small velocities
	786	!-- (u,v --> 0).
[2059]	787	WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp
	788	WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp
[1]	789
	790	!
	791	!-- Compute u* from the absolute velocity value
[1691]	792	IF ( constant_flux_layer ) THEN
[1]	793	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
	794
[1353]	795	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	796	!
	797	!-- Stable stratification
	798	us1d = kappa * uv_total / ( &
[1353]	799	LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * &
[1]	800	( zu(nzb+1) - z01d ) / zu(nzb+1) &
	801	)
	802	ELSE
	803	!
	804	!-- Unstable stratification
[1353]	805	a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) )
	806	b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	807	zu(nzb+1) * z01d ) )
[2337]	808	us1d = kappa * uv_total / ( &
	809	LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / &
	810	(1.0_wp+a) ) + &
	811	2.0_wp * ( ATAN( b ) - ATAN( a ) ) &
	812	)
[1]	813	ENDIF
	814
	815	!
	816	!-- Compute the momentum fluxes for the diffusion terms
	817	usws1d = - u1d(nzb+1) / uv_total * us1d**2
	818	vsws1d = - v1d(nzb+1) / uv_total * us1d**2
	819
	820	!
[2696]	821	!-- Boundary condition for the turbulent kinetic energy and
	822	!-- dissipation rate at the top of the constant-flux layer.
[1]	823	!-- Additional Neumann condition de/dz = 0 at nzb is set to ensure
	824	!-- compatibility with the 3D model.
	825	IF ( ibc_e_b == 2 ) THEN
[3083]	826	e1d(nzb+1) = ( us1d / c_0 )**2
[1]	827	ENDIF
[2696]	828	IF ( dissipation_1d == 'prognostic' ) THEN
[3083]	829	e1d(nzb+1) = ( us1d / c_0 )**2
[2696]	830	diss1d(nzb+1) = us1d*3 / ( kappa zu(nzb+1) )
	831	diss1d(nzb) = diss1d(nzb+1)
	832	ENDIF
[1]	833	e1d(nzb) = e1d(nzb+1)
	834
[1960]	835	IF ( humidity ) THEN
[1]	836	!
	837	!-- Compute q*
[2334]	838	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	839	!
[1960]	840	!-- Stable stratification
	841	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
[1353]	842	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	843	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	844	)
[1960]	845	ELSE
[1]	846	!
[1960]	847	!-- Unstable stratification
	848	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	849	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	850	zu(nzb+1) * z0h1d )
[2337]	851	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
	852	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	853	(b+1.0_wp) / (b-1.0_wp) )
	854	ENDIF
[1]	855	ELSE
[1353]	856	qs1d = 0.0_wp
[2337]	857	ENDIF
[1]	858
[1691]	859	ENDIF ! constant_flux_layer
[1]	860
	861	!
[2337]	862	!-- Compute the diabatic mixing length. The unstable stratification
	863	!-- must not be considered for l1d (km1d) as it is already considered
	864	!-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be
	865	!-- too large.
[3083]	866	IF ( dissipation_1d /= 'prognostic' ) THEN
	867	IF ( mixing_length_1d == 'blackadar' ) THEN
	868	DO k = nzb+1, nzt
	869	IF ( rif1d(k) >= 0.0_wp ) THEN
	870	l1d(k) = l1d_init(k) / ( 1.0_wp + 5.0_wp * rif1d(k) )
	871	l1d_diss(k) = l1d(k)
	872	ELSE
	873	l1d(k) = l1d_init(k)
	874	l1d_diss(k) = l1d_init(k) * &
	875	SQRT( 1.0_wp - 16.0_wp * rif1d(k) )
	876	ENDIF
	877	ENDDO
	878	ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN
	879	DO k = nzb+1, nzt
	880	dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	881	IF ( dpt_dz > 0.0_wp ) THEN
	882	l_stable = 0.76_wp * SQRT( e1d(k) ) &
	883	/ SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp
	884	ELSE
	885	l_stable = l1d_init(k)
	886	ENDIF
	887	l1d(k) = MIN( l1d_init(k), l_stable )
[2337]	888	l1d_diss(k) = l1d(k)
[3083]	889	ENDDO
	890	ENDIF
	891	ELSE
[1]	892	DO k = nzb+1, nzt
[3083]	893	l1d(k) = c_0*3 e1d(k) * SQRT( e1d(k) ) &
	894	/ ( diss1d(k) + 1.0E-30_wp )
[1]	895	ENDDO
	896	ENDIF
	897
	898	!
	899	!-- Compute the diffusion coefficients for momentum via the
	900	!-- corresponding Prandtl-layer relationship and according to
[2337]	901	!-- Prandtl-Kolmogorov, respectively
[1691]	902	IF ( constant_flux_layer ) THEN
[1353]	903	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
	904	km1d(nzb+1) = us1d * kappa * zu(nzb+1) / &
	905	( 1.0_wp + 5.0_wp * rif1d(nzb+1) )
[1]	906	ELSE
[1353]	907	km1d(nzb+1) = us1d * kappa * zu(nzb+1) * &
	908	( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp
[1]	909	ENDIF
	910	ENDIF
[3083]	911
[2696]	912	IF ( dissipation_1d == 'prognostic' ) THEN
	913	DO k = nzb_diff, nzt
	914	km1d(k) = c_mu * e1d(k)**2 / ( diss1d(k) + 1.0E-30_wp )
	915	ENDDO
	916	ELSE
	917	DO k = nzb_diff, nzt
[3083]	918	km1d(k) = c_0 * SQRT( e1d(k) ) * l1d(k)
[2696]	919	ENDDO
	920	ENDIF
[1]	921
	922	!
	923	!-- Add damping layer
	924	DO k = damp_level_ind_1d+1, nzt+1
[1353]	925	km1d(k) = 1.1_wp * km1d(k-1)
[1346]	926	km1d(k) = MIN( km1d(k), 10.0_wp )
[1]	927	ENDDO
	928
	929	!
	930	!-- Compute the diffusion coefficient for heat via the relationship
	931	!-- kh = phim / phih * km
	932	DO k = nzb+1, nzt
[1353]	933	IF ( rif1d(k) >= 0.0_wp ) THEN
[1]	934	kh1d(k) = km1d(k)
	935	ELSE
[1353]	936	kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	937	ENDIF
	938	ENDDO
	939
	940	ENDIF ! .NOT. constant_diffusion
	941
	942	ENDDO ! intermediate step loop
	943
	944	!
	945	!-- Increment simulated time and output times
	946	current_timestep_number_1d = current_timestep_number_1d + 1
	947	simulated_time_1d = simulated_time_1d + dt_1d
	948	simulated_time_chr = time_to_string( simulated_time_1d )
	949	time_pr_1d = time_pr_1d + dt_1d
	950	time_run_control_1d = time_run_control_1d + dt_1d
	951
	952	!
	953	!-- Determine and print out quantities for run control
	954	IF ( time_run_control_1d >= dt_run_control_1d ) THEN
	955	CALL run_control_1d
	956	time_run_control_1d = time_run_control_1d - dt_run_control_1d
	957	ENDIF
	958
	959	!
	960	!-- Profile output on file
	961	IF ( time_pr_1d >= dt_pr_1d ) THEN
	962	CALL print_1d_model
	963	time_pr_1d = time_pr_1d - dt_pr_1d
	964	ENDIF
	965
	966	!
	967	!-- Determine size of next time step
	968	CALL timestep_1d
	969
	970	ENDDO ! time loop
	971
	972
	973	END SUBROUTINE time_integration_1d
	974
	975
	976	!------------------------------------------------------------------------------!
	977	! Description:
	978	! ------------
[1682]	979	!> Compute and print out quantities for run control of the 1D model.
[1]	980	!------------------------------------------------------------------------------!
[1682]	981
	982	SUBROUTINE run_control_1d
[1]	983
[1682]	984
[1320]	985	USE constants, &
	986	ONLY: pi
[1]	987
	988	IMPLICIT NONE
	989
[2338]	990	INTEGER(iwp) :: k !< loop index
[1320]	991
[2338]	992	REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer
	993	REAL(wp) :: energy !< kinetic energy
	994	REAL(wp) :: umax !< maximum of u
	995	REAL(wp) :: uv_total !< horizontal wind speed
	996	REAL(wp) :: vmax !< maximum of v
[1]	997
	998	!
	999	!-- Output
	1000	IF ( myid == 0 ) THEN
	1001	!
	1002	!-- If necessary, write header
	1003	IF ( .NOT. run_control_header_1d ) THEN
[184]	1004	CALL check_open( 15 )
[1]	1005	WRITE ( 15, 100 )
	1006	run_control_header_1d = .TRUE.
	1007	ENDIF
	1008
	1009	!
	1010	!-- Compute control quantities
	1011	!-- grid level nzp is excluded due to mirror boundary condition
[1353]	1012	umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp
[1]	1013	DO k = nzb+1, nzt+1
	1014	umax = MAX( ABS( umax ), ABS( u1d(k) ) )
	1015	vmax = MAX( ABS( vmax ), ABS( v1d(k) ) )
[1353]	1016	energy = energy + 0.5_wp * ( u1d(k)2 + v1d(k)2 )
[1]	1017	ENDDO
[1322]	1018	energy = energy / REAL( nzt - nzb + 1, KIND=wp )
[1]	1019
	1020	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
[1691]	1021	IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN
[1346]	1022	alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) )
[1]	1023	ELSE
	1024	alpha = ACOS( u1d(nzb+1) / uv_total )
[1353]	1025	IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha
[1]	1026	ENDIF
[1353]	1027	alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp
[1]	1028
	1029	WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, &
	1030	dt_1d, umax, vmax, us1d, alpha, energy
	1031	!
	1032	!-- Write buffer contents to disc immediately
[1808]	1033	FLUSH( 15 )
[1]	1034
	1035	ENDIF
	1036
	1037	!
	1038	!-- formats
[2299]	1039	100 FORMAT (///'1D run control output:'/ &
[1]	1040	&'------------------------------'// &
[2965]	1041	&'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ &
[1]	1042	&'-------------------------------------------------------------')
[2965]	1043	101 FORMAT (I7,1X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2)
[1]	1044
	1045
	1046	END SUBROUTINE run_control_1d
	1047
	1048
	1049
	1050	!------------------------------------------------------------------------------!
	1051	! Description:
	1052	! ------------
[1682]	1053	!> Compute the time step w.r.t. the diffusion criterion
[1]	1054	!------------------------------------------------------------------------------!
[1682]	1055
	1056	SUBROUTINE timestep_1d
[1]	1057
	1058	IMPLICIT NONE
	1059
[2338]	1060	INTEGER(iwp) :: k !< loop index
[1]	1061
[2338]	1062	REAL(wp) :: dt_diff !< time step accorind to diffusion criterion
[3083]	1063	REAL(wp) :: dt_old !< previous time step
[2338]	1064	REAL(wp) :: fac !< factor of criterion
	1065	REAL(wp) :: value !< auxiliary variable
[1]	1066
	1067	!
[3083]	1068	!-- Save previous time step
	1069	dt_old = dt_1d
	1070
	1071	!
[1]	1072	!-- Compute the currently feasible time step according to the diffusion
	1073	!-- criterion. At nzb+1 the half grid length is used.
[3083]	1074	fac = 0.125
[1]	1075	dt_diff = dt_max_1d
	1076	DO k = nzb+2, nzt
[1353]	1077	value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp )
[1]	1078	dt_diff = MIN( value, dt_diff )
	1079	ENDDO
[1353]	1080	value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp )
[1]	1081	dt_1d = MIN( value, dt_diff )
	1082
	1083	!
[3083]	1084	!-- Limit the new time step to a maximum of 10 times the previous time step
	1085	dt_1d = MIN( dt_old * 10.0_wp, dt_1d )
	1086
	1087	!
[1]	1088	!-- Set flag when the time step becomes too small
[3083]	1089	IF ( dt_1d < ( 1.0E-15_wp * dt_max_1d ) ) THEN
[1]	1090	stop_dt_1d = .TRUE.
[254]	1091
[3046]	1092	WRITE( message_string, * ) 'timestep has exceeded the lower limit&', &
[254]	1093	'dt_1d = ',dt_1d,' s simulation stopped!'
	1094	CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 )
	1095
[1]	1096	ENDIF
	1097
	1098	END SUBROUTINE timestep_1d
	1099
	1100
	1101
	1102	!------------------------------------------------------------------------------!
	1103	! Description:
	1104	! ------------
[1682]	1105	!> List output of profiles from the 1D-model
[1]	1106	!------------------------------------------------------------------------------!
[1682]	1107
	1108	SUBROUTINE print_1d_model
[1]	1109
	1110	IMPLICIT NONE
	1111
[2338]	1112	INTEGER(iwp) :: k !< loop parameter
[1]	1113
[2338]	1114	LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header
[1]	1115
	1116
	1117	IF ( myid == 0 ) THEN
	1118	!
	1119	!-- Open list output file for profiles from the 1D-model
	1120	CALL check_open( 17 )
	1121
	1122	!
	1123	!-- Write Header
[2338]	1124	IF ( write_first ) THEN
	1125	WRITE ( 17, 100 ) TRIM( run_description_header )
	1126	write_first = .FALSE.
	1127	ENDIF
[1]	1128
	1129	!
	1130	!-- Write the values
[2338]	1131	WRITE ( 17, 104 ) TRIM( simulated_time_chr )
	1132	WRITE ( 17, 101 )
[1]	1133	WRITE ( 17, 102 )
	1134	WRITE ( 17, 101 )
	1135	DO k = nzt+1, nzb, -1
	1136	WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), &
[2696]	1137	rif1d(k), km1d(k), kh1d(k), l1d(k), diss1d(k)
[1]	1138	ENDDO
	1139	WRITE ( 17, 101 )
	1140	WRITE ( 17, 102 )
	1141	WRITE ( 17, 101 )
	1142
	1143	!
	1144	!-- Write buffer contents to disc immediately
[1808]	1145	FLUSH( 17 )
[1]	1146
	1147	ENDIF
	1148
	1149	!
	1150	!-- Formats
[2338]	1151	100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles')
	1152	104 FORMAT (//'# Time: ',A)
[2696]	1153	101 FORMAT ('#',111('-'))
	1154	102 FORMAT ('# k zu u v pt e ', &
	1155	'rif Km Kh l diss ')
	1156	103 FORMAT (1X,I4,1X,F7.1,9(1X,E10.3))
[1]	1157
	1158
	1159	END SUBROUTINE print_1d_model
[2338]	1160
	1161
[3045]	1162	END MODULE

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