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source: palm/trunk/SOURCE/model_1d_mod.f90 @ 2939

Last change on this file since 2939 was 2918, checked in by gronemeier, 7 years ago
moved initialization of mixing length to turbulence_closure_mod; consider walls in calculation of ml in rans-mode
Property svn:keywords set to `Id`
File size: 42.1 KB

Rev	Line
[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	!
[2299]	23	!
[1961]	24	! Former revisions:
	25	! -----------------
	26	! $Id: model_1d_mod.f90 2918 2018-03-21 15:52:14Z suehring $
[2918]	27	! - rename l_black into l1d_init
	28	! - calculate l_grid within init_1d_model and save it as l1d_init
	29	!
	30	! 2718 2018-01-02 08:49:38Z maronga
[2716]	31	! Corrected "Former revisions" section
	32	!
	33	! 2696 2017-12-14 17:12:51Z kanani
	34	! Change in file header (GPL part)
[2696]	35	! implement TKE-e closure
	36	! modification of dissipation production according to Detering and Etling
	37	! reduced factor for timestep criterion to 0.125 and first dt to 1s (TG)
	38	!
	39	! 2339 2017-08-07 13:55:26Z gronemeier
[2339]	40	! corrected timestamp in header
	41	!
	42	! 2338 2017-08-07 12:15:38Z gronemeier
[2338]	43	! renamed init_1d_model to model_1d_mod and and formatted it as a module;
	44	! reformatted output of profiles
	45	!
[2339]	46	! 2337 2017-08-07 08:59:53Z gronemeier
[2337]	47	! revised calculation of mixing length
	48	! removed rounding of time step
	49	! corrected calculation of virtual potential temperature
	50	!
	51	! 2334 2017-08-04 11:57:04Z gronemeier
[2334]	52	! set c_m = 0.4 according to Detering and Etling (1985)
	53	!
	54	! 2299 2017-06-29 10:14:38Z maronga
[2299]	55	! Removed german text
[1961]	56	!
[2299]	57	! 2101 2017-01-05 16:42:31Z suehring
	58	!
[2060]	59	! 2059 2016-11-10 14:20:40Z maronga
	60	! Corrected min/max values of Rif.
	61	!
[2001]	62	! 2000 2016-08-20 18:09:15Z knoop
	63	! Forced header and separation lines into 80 columns
	64	!
[1961]	65	! 1960 2016-07-12 16:34:24Z suehring
[1960]	66	! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively
	67	! not used.
	68	! Formatting adjustment
[1809]	69	!
	70	! 1808 2016-04-05 19:44:00Z raasch
	71	! routine local_flush replaced by FORTRAN statement
	72	!
[1710]	73	! 1709 2015-11-04 14:47:01Z maronga
	74	! Set initial time step to 10 s to avoid instability of the 1d model for small
	75	! grid spacings
	76	!
[1698]	77	! 1697 2015-10-28 17:14:10Z raasch
	78	! small E- and F-FORMAT changes to avoid informative compiler messages about
	79	! insufficient field width
	80	!
[1692]	81	! 1691 2015-10-26 16:17:44Z maronga
	82	! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta.
	83	!
[1683]	84	! 1682 2015-10-07 23:56:08Z knoop
	85	! Code annotations made doxygen readable
	86	!
[1354]	87	! 1353 2014-04-08 15:21:23Z heinze
	88	! REAL constants provided with KIND-attribute
	89	!
[1347]	90	! 1346 2014-03-27 13:18:20Z heinze
	91	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	92	! intrinsic function like MAX, MIN, SIGN
	93	!
[1323]	94	! 1322 2014-03-20 16:38:49Z raasch
	95	! REAL functions provided with KIND-attribute
	96	!
[1321]	97	! 1320 2014-03-20 08:40:49Z raasch
[1320]	98	! ONLY-attribute added to USE-statements,
	99	! kind-parameters added to all INTEGER and REAL declaration statements,
	100	! kinds are defined in new module kinds,
	101	! revision history before 2012 removed,
	102	! comment fields (!:) to be used for variable explanations added to
	103	! all variable declaration statements
[1321]	104	!
[1037]	105	! 1036 2012-10-22 13:43:42Z raasch
	106	! code put under GPL (PALM 3.9)
	107	!
[1017]	108	! 1015 2012-09-27 09:23:24Z raasch
	109	! adjustment of mixing length to the Prandtl mixing length at first grid point
	110	! above ground removed
	111	!
[1002]	112	! 1001 2012-09-13 14:08:46Z raasch
	113	! all actions concerning leapfrog scheme removed
	114	!
[997]	115	! 996 2012-09-07 10:41:47Z raasch
	116	! little reformatting
	117	!
[979]	118	! 978 2012-08-09 08:28:32Z fricke
	119	! roughness length for scalar quantities z0h1d added
	120	!
[1]	121	! Revision 1.1 1998/03/09 16:22:10 raasch
	122	! Initial revision
	123	!
	124	!
	125	! Description:
	126	! ------------
[1682]	127	!> 1D-model to initialize the 3D-arrays.
	128	!> The temperature profile is set as steady and a corresponding steady solution
	129	!> of the wind profile is being computed.
	130	!> All subroutines required can be found within this file.
[1691]	131	!>
	132	!> @todo harmonize code with new surface_layer_fluxes module
[1709]	133	!> @bug 1D model crashes when using small grid spacings in the order of 1 m
[2918]	134	!> @fixme option "as_in_3d_model" seems to eb an inappropriate option because
	135	!> the 1D model uses different turbulence closure approaches at least if
	136	!> the 3D model is set to LES-mode.
[1]	137	!------------------------------------------------------------------------------!
[2338]	138	MODULE model_1d_mod
[1]	139
[1320]	140	USE arrays_3d, &
[2918]	141	ONLY: dd2zu, ddzu, ddzw, dzu, dzw, pt_init, q_init, ug, u_init, &
[2338]	142	vg, v_init, zu
[1320]	143
[2338]	144	USE control_parameters, &
	145	ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, g, &
	146	humidity, ibc_e_b, intermediate_timestep_count, &
	147	intermediate_timestep_count_max, kappa, km_constant, &
	148	message_string, mixing_length_1d, prandtl_number, &
[2696]	149	roughness_length, run_description_header, simulated_time_chr, &
	150	timestep_scheme, tsc, z0h_factor
[2338]	151
[1320]	152	USE indices, &
[2338]	153	ONLY: nzb, nzb_diff, nzt
[1320]	154
	155	USE kinds
[1]	156
[2338]	157	USE pegrid
	158
	159
[1]	160	IMPLICIT NONE
	161
[2338]	162	INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model)
[2696]	163	INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model)
[2338]	164
	165	LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model)
	166	LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model)
	167
[2696]	168	REAL(wp) :: c_1 = 1.44_wp !< model constant
	169	REAL(wp) :: c_2 = 1.92_wp !< model constant
	170	REAL(wp) :: c_3 = 1.44_wp !< model constant
	171	REAL(wp) :: c_h = 0.0015_wp !< model constant according to Detering and Etling (1985)
[2338]	172	REAL(wp) :: c_m = 0.4_wp !< model constant, 0.4 according to Detering and Etling (1985)
[2696]	173	REAL(wp) :: c_mu = 0.09_wp !< model constant
	174	REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter
[2338]	175	REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model)
	176	REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model)
[2696]	177	REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter
	178	REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter
	179	REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter
[2338]	180	REAL(wp) :: qs1d !< characteristic humidity scale (1d-model)
	181	REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model)
[2696]	182	REAL(wp) :: sig_diss = 1.3_wp !< model constant
[2338]	183	REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model)
	184	REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model)
	185	REAL(wp) :: ts1d !< characteristic temperature scale (1d-model)
[2696]	186	REAL(wp) :: us1d !< friction velocity (1d-model)
	187	REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model)
	188	REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model)
[2338]	189	REAL(wp) :: z01d !< roughness length for momentum (1d-model)
	190	REAL(wp) :: z0h1d !< roughness length for scalars (1d-model)
	191
	192
[2696]	193	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d !< tke dissipation rate (1d-model)
	194	REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d_p !< prognostic value of tke dissipation rate (1d-model)
	195	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model)
[2338]	196	REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model)
[2696]	197	REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model)
	198	REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model)
	199	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model)
[2918]	200	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_init !< initial mixing length (1d-model)
[2338]	201	REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model)
[2696]	202	REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model)
	203	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_diss !< tendency of diss (1d-model)
	204	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_dissm !< weighted tendency of diss for previous sub-timestep (1d-model)
[2338]	205	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model)
	206	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model)
	207	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model)
	208	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model)
	209	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model)
	210	REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model)
[2696]	211	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model)
[2338]	212	REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model)
[2696]	213	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model)
[2338]	214	REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model)
	215
	216	!
	217	!-- Initialize 1D model
	218	INTERFACE init_1d_model
	219	MODULE PROCEDURE init_1d_model
	220	END INTERFACE init_1d_model
	221
	222	!
	223	!-- Print profiles
	224	INTERFACE print_1d_model
	225	MODULE PROCEDURE print_1d_model
	226	END INTERFACE print_1d_model
	227
	228	!
	229	!-- Print run control information
	230	INTERFACE run_control_1d
	231	MODULE PROCEDURE run_control_1d
	232	END INTERFACE run_control_1d
	233
	234	!
	235	!-- Main procedure
	236	INTERFACE time_integration_1d
	237	MODULE PROCEDURE time_integration_1d
	238	END INTERFACE time_integration_1d
	239
	240	!
	241	!-- Calculate time step
	242	INTERFACE timestep_1d
	243	MODULE PROCEDURE timestep_1d
	244	END INTERFACE timestep_1d
	245
	246	SAVE
	247
	248	PRIVATE
	249	!
	250	!-- Public interfaces
	251	PUBLIC init_1d_model
	252
	253	!
	254	!-- Public variables
[2696]	255	PUBLIC damp_level_1d, damp_level_ind_1d, diss1d, dt_pr_1d, &
	256	dt_run_control_1d, e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, &
	257	us1d, usws1d, v1d, vsws1d
[2338]	258
	259
	260	CONTAINS
	261
	262	SUBROUTINE init_1d_model
	263
[2918]	264	USE grid_variables, &
	265	ONLY: dx, dy
	266
[2338]	267	IMPLICIT NONE
	268
[2696]	269	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	270
	271	INTEGER(iwp) :: k !< loop index
[1320]	272
[2696]	273	REAL(wp) :: lambda !< maximum mixing length
[1]	274
	275	!
	276	!-- Allocate required 1D-arrays
[2696]	277	ALLOCATE( diss1d(nzb:nzt+1), diss1d_p(nzb:nzt+1), &
	278	e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), &
[2918]	279	km1d(nzb:nzt+1), l1d(nzb:nzt+1), l1d_init(nzb:nzt+1), &
[2696]	280	l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_diss(nzb:nzt+1), &
	281	te_dissm(nzb:nzt+1), te_e(nzb:nzt+1), &
[2338]	282	te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), &
	283	te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), &
	284	u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) )
[1]	285
	286	!
	287	!-- Initialize arrays
	288	IF ( constant_diffusion ) THEN
[1001]	289	km1d = km_constant
	290	kh1d = km_constant / prandtl_number
[1]	291	ELSE
[2696]	292	diss1d = 0.0_wp; diss1d_p = 0.0_wp
[1353]	293	e1d = 0.0_wp; e1d_p = 0.0_wp
	294	kh1d = 0.0_wp; km1d = 0.0_wp
	295	rif1d = 0.0_wp
[1]	296	!
	297	!-- Compute the mixing length
[2918]	298	l1d_init(nzb) = 0.0_wp
[1]	299
	300	IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN
	301	!
	302	!-- Blackadar mixing length
[1353]	303	IF ( f /= 0.0_wp ) THEN
	304	lambda = 2.7E-4_wp * SQRT( ug(nzt+1)2 + vg(nzt+1)2 ) / &
	305	ABS( f ) + 1E-10_wp
[1]	306	ELSE
[1353]	307	lambda = 30.0_wp
[1]	308	ENDIF
	309
	310	DO k = nzb+1, nzt+1
[2918]	311	l1d_init(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda )
[1]	312	ENDDO
	313
	314	ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN
	315	!
[2918]	316	!-- Use the same mixing length as in 3D model (LES-mode)
	317	!### TODO: rename (delete?) this option
	318	!### As the mixing length is different between RANS and LES mode, it
	319	!### must be distinguished here between these modes. For RANS mode,
	320	!### the mixing length is calculated accoding to Blackadar, which is
	321	!### the other option at this point.
	322	!### Maybe delete this option entirely (not appropriate in LES case)
	323	!### 2018-03-20, gronemeier
	324	DO k = nzb+1, nzt
	325	l1d_init(k) = ( dx * dy * dzw(k) )**0.33333333333333_wp
	326	ENDDO
	327	l1d_init(nzt+1) = l1d_init(nzt)
[1]	328
	329	ENDIF
	330	ENDIF
[2918]	331	l1d = l1d_init
	332	l1d_diss = l1d_init
[2337]	333	u1d = u_init
	334	u1d_p = u_init
	335	v1d = v_init
	336	v1d_p = v_init
[1]	337
	338	!
	339	!-- Set initial horizontal velocities at the lowest grid levels to a very small
	340	!-- value in order to avoid too small time steps caused by the diffusion limit
	341	!-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!)
[1353]	342	u1d(0:1) = 0.1_wp
	343	u1d_p(0:1) = 0.1_wp
	344	v1d(0:1) = 0.1_wp
	345	v1d_p(0:1) = 0.1_wp
[1]	346
	347	!
	348	!-- For u, theta and the momentum fluxes plausible values are set
[1691]	349	IF ( constant_flux_layer ) THEN
[1353]	350	us1d = 0.1_wp ! without initial friction the flow would not change
[1]	351	ELSE
[2696]	352	diss1d(nzb+1) = 1.0_wp
[1353]	353	e1d(nzb+1) = 1.0_wp
	354	km1d(nzb+1) = 1.0_wp
	355	us1d = 0.0_wp
[1]	356	ENDIF
[1353]	357	ts1d = 0.0_wp
	358	usws1d = 0.0_wp
	359	vsws1d = 0.0_wp
[996]	360	z01d = roughness_length
[978]	361	z0h1d = z0h_factor * z01d
[1960]	362	IF ( humidity ) qs1d = 0.0_wp
[1]	363
	364	!
[46]	365	!-- Tendencies must be preset in order to avoid runtime errors within the
	366	!-- first Runge-Kutta step
[2696]	367	te_dissm = 0.0_wp
[1353]	368	te_em = 0.0_wp
	369	te_um = 0.0_wp
	370	te_vm = 0.0_wp
[46]	371
	372	!
[2338]	373	!-- Set model constant
	374	IF ( dissipation_1d == 'as_in_3d_model' ) c_m = 0.1_wp
	375
	376	!
[1]	377	!-- Set start time in hh:mm:ss - format
	378	simulated_time_chr = time_to_string( simulated_time_1d )
	379
	380	!
[2337]	381	!-- Integrate the 1D-model equations using the Runge-Kutta scheme
[1]	382	CALL time_integration_1d
	383
	384
	385	END SUBROUTINE init_1d_model
	386
	387
	388
	389	!------------------------------------------------------------------------------!
	390	! Description:
	391	! ------------
[2338]	392	!> Runge-Kutta time differencing scheme for the 1D-model.
[1]	393	!------------------------------------------------------------------------------!
[1682]	394
	395	SUBROUTINE time_integration_1d
[1]	396
	397	IMPLICIT NONE
	398
[2696]	399	CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string
	400
[2338]	401	INTEGER(iwp) :: k !< loop index
[2696]	402
[2338]	403	REAL(wp) :: a !< auxiliary variable
	404	REAL(wp) :: b !< auxiliary variable
	405	REAL(wp) :: dpt_dz !< vertical temperature gradient
	406	REAL(wp) :: flux !< vertical temperature gradient
	407	REAL(wp) :: kmzm !< Km(z-dz/2)
	408	REAL(wp) :: kmzp !< Km(z+dz/2)
	409	REAL(wp) :: l_stable !< mixing length for stable case
	410	REAL(wp) :: pt_0 !< reference temperature
	411	REAL(wp) :: uv_total !< horizontal wind speed
[1]	412
	413	!
	414	!-- Determine the time step at the start of a 1D-simulation and
	415	!-- determine and printout quantities used for run control
[2696]	416	dt_1d = 1.0_wp
[1]	417	CALL run_control_1d
	418
	419	!
	420	!-- Start of time loop
	421	DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d )
	422
	423	!
	424	!-- Depending on the timestep scheme, carry out one or more intermediate
	425	!-- timesteps
	426
	427	intermediate_timestep_count = 0
	428	DO WHILE ( intermediate_timestep_count < &
	429	intermediate_timestep_count_max )
	430
	431	intermediate_timestep_count = intermediate_timestep_count + 1
	432
	433	CALL timestep_scheme_steering
	434
	435	!
[2696]	436	!-- Compute all tendency terms. If a constant-flux layer is simulated,
	437	!-- k starts at nzb+2.
[1]	438	DO k = nzb_diff, nzt
	439
[1353]	440	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	441	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[1]	442	!
	443	!-- u-component
	444	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
[1001]	445	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) &
	446	- kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) &
	447	) * ddzw(k)
[1]	448	!
	449	!-- v-component
[1001]	450	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	451	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) &
	452	- kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) &
	453	) * ddzw(k)
[1]	454	ENDDO
	455	IF ( .NOT. constant_diffusion ) THEN
	456	DO k = nzb_diff, nzt
	457	!
[2696]	458	!-- TKE and dissipation rate
[1353]	459	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	460	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	461	IF ( .NOT. humidity ) THEN
[1]	462	pt_0 = pt_init(k)
	463	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	464	ELSE
[1353]	465	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	466	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	467	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	468	pt_init(k-1) * q_init(k-1) ) &
	469	) * dd2zu(k)
[1]	470	ENDIF
	471
[2696]	472	!
	473	!-- Calculate dissipation rate if no prognostic equation is used for
	474	!-- dissipation rate
[1]	475	IF ( dissipation_1d == 'detering' ) THEN
[2696]	476	diss1d(k) = c_m*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	477	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	478	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) &
[2696]	479	) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	480	ENDIF
[2696]	481	!
	482	!-- TKE
[1]	483	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	484	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	485	) &
	486	- g / pt_0 * kh1d(k) * flux &
	487	+ ( &
[1001]	488	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	489	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[1]	490	) * ddzw(k) &
[2696]	491	- diss1d(k)
	492
	493	IF ( dissipation_1d == 'prognostic' ) THEN
	494	!
	495	!-- dissipation rate
	496	te_diss(k) = km1d(k) * &
	497	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	498	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	499	) * c_1 * c_mu*0.75 / c_h f / us1d &
	500	* SQRT(e1d(k)) &
	501	- g / pt_0 * kh1d(k) * flux * c_3 &
	502	* diss1d(k) / ( e1d(k) + 1.0E-20_wp ) &
	503	+ ( kmzp * ( diss1d(k+1) - diss1d(k) ) &
	504	* ddzu(k+1) &
	505	- kmzm * ( diss1d(k) - diss1d(k-1) ) &
	506	* ddzu(k) &
	507	) * ddzw(k) / sig_diss &
	508	- c_2 * diss1d(k)**2 / ( e1d(k) + 1.0E-20_wp )
	509
	510	ENDIF
	511
[1]	512	ENDDO
	513	ENDIF
	514
	515	!
[2696]	516	!-- Tendency terms at the top of the constant-flux layer.
[1]	517	!-- Finite differences of the momentum fluxes are computed using half the
	518	!-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy
[1691]	519	IF ( constant_flux_layer ) THEN
[1]	520
	521	k = nzb+1
[1353]	522	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	523	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	524	IF ( .NOT. humidity ) THEN
[1]	525	pt_0 = pt_init(k)
	526	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	527	ELSE
[1353]	528	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	529	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
[2337]	530	0.61_wp * ( pt_init(k+1) * q_init(k+1) - &
	531	pt_init(k-1) * q_init(k-1) ) &
[1]	532	) * dd2zu(k)
	533	ENDIF
	534
[2696]	535	!
	536	!-- Calculate dissipation rate if no prognostic equation is used for
	537	!-- dissipation rate
[1]	538	IF ( dissipation_1d == 'detering' ) THEN
[2696]	539	diss1d(k) = c_m*3 e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	540	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[2918]	541	diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) ) &
[2696]	542	* e1d(k) * SQRT( e1d(k) ) / l1d_diss(k)
[1]	543	ENDIF
	544
	545	!
	546	!-- u-component
[1001]	547	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
	548	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d &
[1353]	549	) * 2.0_wp * ddzw(k)
[1]	550	!
	551	!-- v-component
[1001]	552	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	553	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d &
[1353]	554	) * 2.0_wp * ddzw(k)
[1]	555	!
	556	!-- TKE
[2696]	557	IF ( .NOT. dissipation_1d == 'prognostic' ) THEN
	558	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	559	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	560	) &
	561	- g / pt_0 * kh1d(k) * flux &
	562	+ ( &
	563	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	564	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
	565	) * ddzw(k) &
	566	- diss1d(k)
	567	ENDIF
	568
[1]	569	ENDIF
	570
	571	!
	572	!-- Prognostic equations for all 1D variables
	573	DO k = nzb+1, nzt
	574
[1001]	575	u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + &
	576	tsc(3) * te_um(k) )
	577	v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + &
	578	tsc(3) * te_vm(k) )
[1]	579
	580	ENDDO
	581	IF ( .NOT. constant_diffusion ) THEN
[2696]	582
[1]	583	DO k = nzb+1, nzt
[1001]	584	e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + &
	585	tsc(3) * te_em(k) )
[2696]	586	ENDDO
[1]	587
[2696]	588	IF ( dissipation_1d == 'prognostic' ) THEN
	589	DO k = nzb_diff, nzt
	590	diss1d_p(k) = diss1d(k) + dt_1d * ( tsc(2) * te_diss(k) + &
	591	tsc(3) * te_dissm(k) )
	592	ENDDO
	593	ENDIF
[1]	594	!
	595	!-- Eliminate negative TKE values, which can result from the
	596	!-- integration due to numerical inaccuracies. In such cases the TKE
	597	!-- value is reduced to 10 percent of its old value.
[1353]	598	WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d
[1]	599	ENDIF
	600
	601	!
	602	!-- Calculate tendencies for the next Runge-Kutta step
	603	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	604	IF ( intermediate_timestep_count == 1 ) THEN
	605
	606	DO k = nzb+1, nzt
	607	te_um(k) = te_u(k)
	608	te_vm(k) = te_v(k)
	609	ENDDO
	610
	611	IF ( .NOT. constant_diffusion ) THEN
	612	DO k = nzb+1, nzt
	613	te_em(k) = te_e(k)
	614	ENDDO
[2696]	615	IF ( dissipation_1d == 'prognostic' ) THEN
	616	DO k = nzb+1, nzt
	617	te_dissm(k) = te_diss(k)
	618	ENDDO
	619	ENDIF
[1]	620	ENDIF
	621
	622	ELSEIF ( intermediate_timestep_count < &
	623	intermediate_timestep_count_max ) THEN
	624
	625	DO k = nzb+1, nzt
[1353]	626	te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k)
	627	te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k)
[1]	628	ENDDO
	629
	630	IF ( .NOT. constant_diffusion ) THEN
	631	DO k = nzb+1, nzt
[1353]	632	te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k)
[1]	633	ENDDO
[2696]	634	IF ( dissipation_1d == 'prognostic' ) THEN
	635	DO k = nzb+1, nzt
	636	te_dissm(k) = -9.5625_wp * te_diss(k) + 5.3125_wp * te_dissm(k)
	637	ENDDO
	638	ENDIF
[1]	639	ENDIF
	640
	641	ENDIF
	642	ENDIF
	643
	644
	645	!
	646	!-- Boundary conditions for the prognostic variables.
[2696]	647	!-- At the top boundary (nzt+1) u, v, e, and diss keep their initial
	648	!-- values (ug(nzt+1), vg(nzt+1), 0, 0).
[2334]	649	!-- At the bottom boundary, Dirichlet condition is used for u and v (0)
[2696]	650	!-- and Neumann condition for e and diss (e(nzb)=e(nzb+1)).
[1353]	651	u1d_p(nzb) = 0.0_wp
	652	v1d_p(nzb) = 0.0_wp
[667]	653
[1]	654	!
	655	!-- Swap the time levels in preparation for the next time step.
	656	u1d = u1d_p
	657	v1d = v1d_p
	658	IF ( .NOT. constant_diffusion ) THEN
	659	e1d = e1d_p
[2696]	660	IF ( dissipation_1d == 'prognostic' ) THEN
	661	diss1d = diss1d_p
	662	ENDIF
[1]	663	ENDIF
	664
	665	!
	666	!-- Compute diffusion quantities
	667	IF ( .NOT. constant_diffusion ) THEN
	668
	669	!
[2696]	670	!-- First compute the vertical fluxes in the constant-flux layer
[1691]	671	IF ( constant_flux_layer ) THEN
[1]	672	!
	673	!-- Compute theta* using Rif numbers of the previous time step
[2334]	674	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	675	!
	676	!-- Stable stratification
[1353]	677	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	678	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	679	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	680	)
	681	ELSE
	682	!
	683	!-- Unstable stratification
[1353]	684	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	685	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	686	zu(nzb+1) * z0h1d )
[2337]	687
	688	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	689	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	690	(b+1.0_wp) / (b-1.0_wp) )
[1]	691	ENDIF
	692
[1691]	693	ENDIF ! constant_flux_layer
[1]	694
	695	!
	696	!-- Compute the Richardson-flux numbers,
[2696]	697	!-- first at the top of the constant-flux layer using u* of the
	698	!-- previous time step (+1E-30, if u* = 0), then in the remaining area.
	699	!-- There the rif-numbers of the previous time step are used.
[1]	700
[1691]	701	IF ( constant_flux_layer ) THEN
[75]	702	IF ( .NOT. humidity ) THEN
[1]	703	pt_0 = pt_init(nzb+1)
	704	flux = ts1d
	705	ELSE
[1353]	706	pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) )
	707	flux = ts1d + 0.61_wp * pt_init(k) * qs1d
[1]	708	ENDIF
	709	rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / &
[1353]	710	( pt_0 * ( us1d**2 + 1E-30_wp ) )
[1]	711	ENDIF
	712
	713	DO k = nzb_diff, nzt
[75]	714	IF ( .NOT. humidity ) THEN
[1]	715	pt_0 = pt_init(k)
	716	flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	717	ELSE
[1353]	718	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
[1]	719	flux = ( ( pt_init(k+1) - pt_init(k-1) ) &
[2337]	720	+ 0.61_wp &
	721	* ( pt_init(k+1) * q_init(k+1) &
	722	- pt_init(k-1) * q_init(k-1) ) &
[1]	723	) * dd2zu(k)
	724	ENDIF
[1353]	725	IF ( rif1d(k) >= 0.0_wp ) THEN
	726	rif1d(k) = g / pt_0 * flux / &
	727	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	728	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	729	+ 1E-30_wp &
[1]	730	)
	731	ELSE
[1353]	732	rif1d(k) = g / pt_0 * flux / &
	733	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	734	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	735	+ 1E-30_wp &
	736	) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	737	ENDIF
	738	ENDDO
	739	!
	740	!-- Richardson-numbers must remain restricted to a realistic value
	741	!-- range. It is exceeded excessively for very small velocities
	742	!-- (u,v --> 0).
[2059]	743	WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp
	744	WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp
[1]	745
	746	!
	747	!-- Compute u* from the absolute velocity value
[1691]	748	IF ( constant_flux_layer ) THEN
[1]	749	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
	750
[1353]	751	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	752	!
	753	!-- Stable stratification
	754	us1d = kappa * uv_total / ( &
[1353]	755	LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * &
[1]	756	( zu(nzb+1) - z01d ) / zu(nzb+1) &
	757	)
	758	ELSE
	759	!
	760	!-- Unstable stratification
[1353]	761	a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) )
	762	b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	763	zu(nzb+1) * z01d ) )
[2337]	764	us1d = kappa * uv_total / ( &
	765	LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / &
	766	(1.0_wp+a) ) + &
	767	2.0_wp * ( ATAN( b ) - ATAN( a ) ) &
	768	)
[1]	769	ENDIF
	770
	771	!
	772	!-- Compute the momentum fluxes for the diffusion terms
	773	usws1d = - u1d(nzb+1) / uv_total * us1d**2
	774	vsws1d = - v1d(nzb+1) / uv_total * us1d**2
	775
	776	!
[2696]	777	!-- Boundary condition for the turbulent kinetic energy and
	778	!-- dissipation rate at the top of the constant-flux layer.
[1]	779	!-- Additional Neumann condition de/dz = 0 at nzb is set to ensure
	780	!-- compatibility with the 3D model.
	781	IF ( ibc_e_b == 2 ) THEN
[2334]	782	e1d(nzb+1) = ( us1d / c_m )**2
[1]	783	ENDIF
[2696]	784	IF ( dissipation_1d == 'prognostic' ) THEN
	785	e1d(nzb+1) = us1d**2 / SQRT( c_mu )
	786	diss1d(nzb+1) = us1d*3 / ( kappa zu(nzb+1) )
	787	diss1d(nzb) = diss1d(nzb+1)
	788	ENDIF
[1]	789	e1d(nzb) = e1d(nzb+1)
	790
[1960]	791	IF ( humidity ) THEN
[1]	792	!
	793	!-- Compute q*
[2334]	794	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	795	!
[1960]	796	!-- Stable stratification
	797	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
[1353]	798	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	799	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	800	)
[1960]	801	ELSE
[1]	802	!
[1960]	803	!-- Unstable stratification
	804	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	805	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	806	zu(nzb+1) * z0h1d )
[2337]	807	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
	808	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	809	(b+1.0_wp) / (b-1.0_wp) )
	810	ENDIF
[1]	811	ELSE
[1353]	812	qs1d = 0.0_wp
[2337]	813	ENDIF
[1]	814
[1691]	815	ENDIF ! constant_flux_layer
[1]	816
	817	!
[2337]	818	!-- Compute the diabatic mixing length. The unstable stratification
	819	!-- must not be considered for l1d (km1d) as it is already considered
	820	!-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be
	821	!-- too large.
[1]	822	IF ( mixing_length_1d == 'blackadar' ) THEN
	823	DO k = nzb+1, nzt
[1353]	824	IF ( rif1d(k) >= 0.0_wp ) THEN
[2918]	825	l1d(k) = l1d_init(k) / ( 1.0_wp + 5.0_wp * rif1d(k) )
[2337]	826	l1d_diss(k) = l1d(k)
[1]	827	ELSE
[2918]	828	l1d(k) = l1d_init(k)
	829	l1d_diss(k) = l1d_init(k) * &
[2337]	830	SQRT( 1.0_wp - 16.0_wp * rif1d(k) )
[1]	831	ENDIF
	832	ENDDO
	833	ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN
	834	DO k = nzb+1, nzt
	835	dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
[1353]	836	IF ( dpt_dz > 0.0_wp ) THEN
	837	l_stable = 0.76_wp * SQRT( e1d(k) ) / &
	838	SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp
[1]	839	ELSE
[2918]	840	l_stable = l1d_init(k)
[1]	841	ENDIF
[2918]	842	l1d(k) = MIN( l1d_init(k), l_stable )
[2337]	843	l1d_diss(k) = l1d(k)
[1]	844	ENDDO
	845	ENDIF
	846
	847	!
	848	!-- Compute the diffusion coefficients for momentum via the
	849	!-- corresponding Prandtl-layer relationship and according to
[2337]	850	!-- Prandtl-Kolmogorov, respectively
[1691]	851	IF ( constant_flux_layer ) THEN
[1353]	852	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
	853	km1d(nzb+1) = us1d * kappa * zu(nzb+1) / &
	854	( 1.0_wp + 5.0_wp * rif1d(nzb+1) )
[1]	855	ELSE
[1353]	856	km1d(nzb+1) = us1d * kappa * zu(nzb+1) * &
	857	( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp
[1]	858	ENDIF
	859	ENDIF
[2696]	860	IF ( dissipation_1d == 'prognostic' ) THEN
	861	DO k = nzb_diff, nzt
	862	km1d(k) = c_mu * e1d(k)**2 / ( diss1d(k) + 1.0E-30_wp )
	863	ENDDO
	864	ELSE
	865	DO k = nzb_diff, nzt
	866	km1d(k) = c_m * SQRT( e1d(k) ) * l1d(k)
	867	ENDDO
	868	ENDIF
[1]	869
	870	!
	871	!-- Add damping layer
	872	DO k = damp_level_ind_1d+1, nzt+1
[1353]	873	km1d(k) = 1.1_wp * km1d(k-1)
[1346]	874	km1d(k) = MIN( km1d(k), 10.0_wp )
[1]	875	ENDDO
	876
	877	!
	878	!-- Compute the diffusion coefficient for heat via the relationship
	879	!-- kh = phim / phih * km
	880	DO k = nzb+1, nzt
[1353]	881	IF ( rif1d(k) >= 0.0_wp ) THEN
[1]	882	kh1d(k) = km1d(k)
	883	ELSE
[1353]	884	kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	885	ENDIF
	886	ENDDO
	887
	888	ENDIF ! .NOT. constant_diffusion
	889
	890	ENDDO ! intermediate step loop
	891
	892	!
	893	!-- Increment simulated time and output times
	894	current_timestep_number_1d = current_timestep_number_1d + 1
	895	simulated_time_1d = simulated_time_1d + dt_1d
	896	simulated_time_chr = time_to_string( simulated_time_1d )
	897	time_pr_1d = time_pr_1d + dt_1d
	898	time_run_control_1d = time_run_control_1d + dt_1d
	899
	900	!
	901	!-- Determine and print out quantities for run control
	902	IF ( time_run_control_1d >= dt_run_control_1d ) THEN
	903	CALL run_control_1d
	904	time_run_control_1d = time_run_control_1d - dt_run_control_1d
	905	ENDIF
	906
	907	!
	908	!-- Profile output on file
	909	IF ( time_pr_1d >= dt_pr_1d ) THEN
	910	CALL print_1d_model
	911	time_pr_1d = time_pr_1d - dt_pr_1d
	912	ENDIF
	913
	914	!
	915	!-- Determine size of next time step
	916	CALL timestep_1d
	917
	918	ENDDO ! time loop
	919
	920
	921	END SUBROUTINE time_integration_1d
	922
	923
	924	!------------------------------------------------------------------------------!
	925	! Description:
	926	! ------------
[1682]	927	!> Compute and print out quantities for run control of the 1D model.
[1]	928	!------------------------------------------------------------------------------!
[1682]	929
	930	SUBROUTINE run_control_1d
[1]	931
[1682]	932
[1320]	933	USE constants, &
	934	ONLY: pi
[1]	935
	936	IMPLICIT NONE
	937
[2338]	938	INTEGER(iwp) :: k !< loop index
[1320]	939
[2338]	940	REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer
	941	REAL(wp) :: energy !< kinetic energy
	942	REAL(wp) :: umax !< maximum of u
	943	REAL(wp) :: uv_total !< horizontal wind speed
	944	REAL(wp) :: vmax !< maximum of v
[1]	945
	946	!
	947	!-- Output
	948	IF ( myid == 0 ) THEN
	949	!
	950	!-- If necessary, write header
	951	IF ( .NOT. run_control_header_1d ) THEN
[184]	952	CALL check_open( 15 )
[1]	953	WRITE ( 15, 100 )
	954	run_control_header_1d = .TRUE.
	955	ENDIF
	956
	957	!
	958	!-- Compute control quantities
	959	!-- grid level nzp is excluded due to mirror boundary condition
[1353]	960	umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp
[1]	961	DO k = nzb+1, nzt+1
	962	umax = MAX( ABS( umax ), ABS( u1d(k) ) )
	963	vmax = MAX( ABS( vmax ), ABS( v1d(k) ) )
[1353]	964	energy = energy + 0.5_wp * ( u1d(k)2 + v1d(k)2 )
[1]	965	ENDDO
[1322]	966	energy = energy / REAL( nzt - nzb + 1, KIND=wp )
[1]	967
	968	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
[1691]	969	IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN
[1346]	970	alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) )
[1]	971	ELSE
	972	alpha = ACOS( u1d(nzb+1) / uv_total )
[1353]	973	IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha
[1]	974	ENDIF
[1353]	975	alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp
[1]	976
	977	WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, &
	978	dt_1d, umax, vmax, us1d, alpha, energy
	979	!
	980	!-- Write buffer contents to disc immediately
[1808]	981	FLUSH( 15 )
[1]	982
	983	ENDIF
	984
	985	!
	986	!-- formats
[2299]	987	100 FORMAT (///'1D run control output:'/ &
[1]	988	&'------------------------------'// &
	989	&'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ &
	990	&'-------------------------------------------------------------')
[1697]	991	101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2)
[1]	992
	993
	994	END SUBROUTINE run_control_1d
	995
	996
	997
	998	!------------------------------------------------------------------------------!
	999	! Description:
	1000	! ------------
[1682]	1001	!> Compute the time step w.r.t. the diffusion criterion
[1]	1002	!------------------------------------------------------------------------------!
[1682]	1003
	1004	SUBROUTINE timestep_1d
[1]	1005
	1006	IMPLICIT NONE
	1007
[2338]	1008	INTEGER(iwp) :: k !< loop index
[1]	1009
[2338]	1010	REAL(wp) :: dt_diff !< time step accorind to diffusion criterion
	1011	REAL(wp) :: fac !< factor of criterion
	1012	REAL(wp) :: value !< auxiliary variable
[1]	1013
	1014	!
	1015	!-- Compute the currently feasible time step according to the diffusion
	1016	!-- criterion. At nzb+1 the half grid length is used.
[2696]	1017	fac = 0.125 !0.35_wp !### changed from 0.35
[1]	1018	dt_diff = dt_max_1d
	1019	DO k = nzb+2, nzt
[1353]	1020	value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp )
[1]	1021	dt_diff = MIN( value, dt_diff )
	1022	ENDDO
[1353]	1023	value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp )
[1]	1024	dt_1d = MIN( value, dt_diff )
	1025
	1026	!
	1027	!-- Set flag when the time step becomes too small
[1353]	1028	IF ( dt_1d < ( 0.00001_wp * dt_max_1d ) ) THEN
[1]	1029	stop_dt_1d = .TRUE.
[254]	1030
	1031	WRITE( message_string, * ) 'timestep has exceeded the lower limit &', &
	1032	'dt_1d = ',dt_1d,' s simulation stopped!'
	1033	CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 )
	1034
[1]	1035	ENDIF
	1036
	1037	END SUBROUTINE timestep_1d
	1038
	1039
	1040
	1041	!------------------------------------------------------------------------------!
	1042	! Description:
	1043	! ------------
[1682]	1044	!> List output of profiles from the 1D-model
[1]	1045	!------------------------------------------------------------------------------!
[1682]	1046
	1047	SUBROUTINE print_1d_model
[1]	1048
	1049	IMPLICIT NONE
	1050
[2338]	1051	INTEGER(iwp) :: k !< loop parameter
[1]	1052
[2338]	1053	LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header
[1]	1054
	1055
	1056	IF ( myid == 0 ) THEN
	1057	!
	1058	!-- Open list output file for profiles from the 1D-model
	1059	CALL check_open( 17 )
	1060
	1061	!
	1062	!-- Write Header
[2338]	1063	IF ( write_first ) THEN
	1064	WRITE ( 17, 100 ) TRIM( run_description_header )
	1065	write_first = .FALSE.
	1066	ENDIF
[1]	1067
	1068	!
	1069	!-- Write the values
[2338]	1070	WRITE ( 17, 104 ) TRIM( simulated_time_chr )
	1071	WRITE ( 17, 101 )
[1]	1072	WRITE ( 17, 102 )
	1073	WRITE ( 17, 101 )
	1074	DO k = nzt+1, nzb, -1
	1075	WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), &
[2696]	1076	rif1d(k), km1d(k), kh1d(k), l1d(k), diss1d(k)
[1]	1077	ENDDO
	1078	WRITE ( 17, 101 )
	1079	WRITE ( 17, 102 )
	1080	WRITE ( 17, 101 )
	1081
	1082	!
	1083	!-- Write buffer contents to disc immediately
[1808]	1084	FLUSH( 17 )
[1]	1085
	1086	ENDIF
	1087
	1088	!
	1089	!-- Formats
[2338]	1090	100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles')
	1091	104 FORMAT (//'# Time: ',A)
[2696]	1092	101 FORMAT ('#',111('-'))
	1093	102 FORMAT ('# k zu u v pt e ', &
	1094	'rif Km Kh l diss ')
	1095	103 FORMAT (1X,I4,1X,F7.1,9(1X,E10.3))
[1]	1096
	1097
	1098	END SUBROUTINE print_1d_model
[2338]	1099
	1100
	1101	END MODULE

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