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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4337

Last change on this file since 4337 was 4335, checked in by suehring, 5 years ago
Plant canopy: implement fix for LAD on building edges also for the vectorl-optimized branch
Property svn:keywords set to `Id`
File size: 106.2 KB

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[2259]	1	!> @synthetic_turbulence_generator_mod.f90
	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[2259]	4	!
[2696]	5	! PALM is free software: you can redistribute it and/or modify it under the
[2259]	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
	9	!
[2696]	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
[2259]	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	!
[3885]	17	! Copyright 2017-2019 Leibniz Universitaet Hannover
[2259]	18	!------------------------------------------------------------------------------!
	19	!
	20	! Current revisions:
	21	! -----------------
	22	!
[3349]	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4335 2019-12-12 16:39:05Z Giersch $
[4335]	27	! Commentation of last commit
	28	!
	29	! 4332 2019-12-10 19:44:12Z suehring
[4332]	30	! Limit initial velocity seeds in restart runs, if not the seed calculation
	31	! may become unstable. Further, minor bugfix in initial velocity seed
	32	! calculation.
	33	!
	34	! 4329 2019-12-10 15:46:36Z motisi
[4329]	35	! Renamed wall_flags_0 to wall_flags_static_0
	36	!
	37	! 4309 2019-11-26 18:49:59Z suehring
[4309]	38	! Computation of velocity seeds optimized. This implies that random numbers
	39	! are computed now using the parallel random number generator. Random numbers
	40	! are now only computed and normalized locally, while distributed over all
	41	! mpi ranks afterwards, instead of computing random numbers on a global array.
	42	! Further, the number of calls for the time-consuming velocity-seed generation
	43	! is reduced - now the left and right, as well as the north and south boundary
	44	! share the same velocity-seed matrices.
	45	!
	46	! 4182 2019-08-22 15:20:23Z scharf
[4182]	47	! Corrected "Former revisions" section
	48	!
	49	! 4148 2019-08-08 11:26:00Z suehring
[4148]	50	! Remove unused variable
	51	!
	52	! 4144 2019-08-06 09:11:47Z raasch
[4144]	53	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	54	!
	55	! 4071 2019-07-03 20:02:00Z suehring
[4071]	56	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	57	! information is not read from file.
	58	!
	59	! 4022 2019-06-12 11:52:39Z suehring
[4022]	60	! Several bugfixes and improvements
	61	! - revise bias correction of the imposed perturbations (correction via volume
	62	! flow can create instabilities in case the mean volume flow is close to zero)
	63	! - introduce lower limits in calculation of coefficient matrix, else the
	64	! calculation may become numerically unstable
	65	! - impose perturbations every timestep, even though no new set of perturbations
	66	! is generated in case dt_stg_call /= dt_3d
	67	! - Implement a gradual decrease of Reynolds stress and length scales above
	68	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	69	! discontinuous decrease
	70	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	71	!
	72	! 3987 2019-05-22 09:52:13Z kanani
[3987]	73	! Introduce alternative switch for debug output during timestepping
	74	!
	75	! 3938 2019-04-29 16:06:25Z suehring
[3938]	76	! Remove unused variables
	77	!
	78	! 3937 2019-04-29 15:09:07Z suehring
[3937]	79	! Minor bugfix in case of a very early restart where mc_factor is sill not
	80	! present.
	81	! Some modification and fixing of potential bugs in the calculation of scaling
	82	! parameters used for synthetic turbulence parametrization.
	83	!
	84	! 3909 2019-04-17 09:13:25Z suehring
[3909]	85	! Minor bugfix for last commit
	86	!
	87	! 3900 2019-04-16 15:17:43Z suehring
[3900]	88	! Missing re-calculation of perturbation seeds in case of restarts
	89	!
	90	! 3891 2019-04-12 17:52:01Z suehring
[3891]	91	! Bugfix in initialization in case of restart runs.
	92	!
	93	! 3885 2019-04-11 11:29:34Z kanani
[3885]	94	! Changes related to global restructuring of location messages and introduction
	95	! of additional debug messages
	96	!
	97	!
[3775]	98	! removed unused variables
	99	!
	100	! 3719 2019-02-06 13:10:18Z kanani
[3719]	101	! Removed log_point measurement from stg_init, since this part is counted to
	102	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	103	! the subroutines in time_integration for better overview.
	104	!
[4182]	105	! 2259 2017-06-08 09:09:11Z gronemeier
	106	! Initial revision
[3044]	107	!
[4182]	108	! Authors:
	109	! --------
	110	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	111	!
	112	!
[2259]	113	! Description:
	114	! ------------
	115	!> The module generates turbulence at the inflow boundary based on a method by
	116	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	117	!> correction by Kim et al. (2013).
	118	!> The turbulence is correlated based on length scales in y- and z-direction and
	119	!> a time scale for each velocity component. The profiles of length and time
	120	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	121	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	122	!> within the boundary layer.
[2259]	123	!>
	124	!> @todo test restart
	125	!> enable cyclic_fill
	126	!> implement turbulence generation for e and pt
[2945]	127	!> @todo Input of height-constant length scales via namelist
[2259]	128	!> @note <Enter notes on the module>
	129	!> @bug Height information from input file is not used. Profiles from input
	130	!> must match with current PALM grid.
	131	!> In case of restart, velocity seeds differ from precursor run if a11,
	132	!> a22, or a33 are zero.
	133	!------------------------------------------------------------------------------!
	134	MODULE synthetic_turbulence_generator_mod
	135
	136
	137	USE arrays_3d, &
[4022]	138	ONLY: dzw, &
	139	ddzw, &
	140	drho_air, &
	141	mean_inflow_profiles, &
	142	q, &
[4071]	143	q_init, &
	144	pt, &
	145	pt_init, &
[4022]	146	u, &
	147	u_init, &
	148	v, &
	149	v_init, &
	150	w, &
	151	zu, &
	152	zw
[2259]	153
[3274]	154	USE basic_constants_and_equations_mod, &
[4022]	155	ONLY: g, &
	156	kappa, &
	157	pi
[2259]	158
	159	USE control_parameters, &
[4022]	160	ONLY: bc_lr, &
	161	bc_ns, &
	162	child_domain, &
	163	coupling_char, &
	164	debug_output_timestep, &
	165	dt_3d, &
	166	e_init, &
[4071]	167	humidity, &
[3885]	168	initializing_actions, &
[4022]	169	intermediate_timestep_count, &
	170	intermediate_timestep_count_max, &
	171	length, &
[3885]	172	message_string, &
[4022]	173	nesting_offline, &
[4071]	174	neutral, &
[3885]	175	num_mean_inflow_profiles, &
[4309]	176	random_generator, &
[4022]	177	rans_mode, &
	178	restart_string, &
	179	syn_turb_gen, &
	180	time_since_reference_point, &
	181	turbulent_inflow
	182
	183	USE grid_variables, &
	184	ONLY: ddx, &
	185	ddy, &
	186	dx, &
	187	dy
[2259]	188
	189	USE indices, &
[4022]	190	ONLY: nbgp, &
	191	nz, &
	192	nzb, &
	193	nzt, &
	194	nx, &
	195	nxl, &
	196	nxlu, &
	197	nxlg, &
	198	nxr, &
	199	nxrg, &
	200	ny, &
	201	nys, &
	202	nysv, &
	203	nyn, &
	204	nyng, &
	205	nysg, &
[4329]	206	wall_flags_static_0
[2259]	207
	208	USE kinds
	209
[2967]	210	#if defined( __parallel ) && !defined( __mpifh )
[2259]	211	USE MPI
[2841]	212	#endif
[2259]	213
[3347]	214	USE nesting_offl_mod, &
[4022]	215	ONLY: nesting_offl_calc_zi, &
	216	zi_ribulk
[3347]	217
[2259]	218	USE pegrid, &
[4022]	219	ONLY: comm1dx, &
	220	comm1dy, &
	221	comm2d, &
	222	ierr, &
	223	myidx, &
	224	myidy, &
	225	pdims
	226
	227	USE pmc_interface, &
	228	ONLY : rans_mode_parent
[4309]	229
	230	USE random_generator_parallel, &
	231	ONLY: random_dummy, &
	232	random_number_parallel, &
	233	random_seed_parallel, &
	234	seq_random_array
[2259]	235
	236	USE transpose_indices, &
[4022]	237	ONLY: nzb_x, &
	238	nzt_x
[2259]	239
	240
	241	IMPLICIT NONE
	242
[2967]	243	#if defined( __parallel ) && defined( __mpifh )
[2841]	244	INCLUDE "mpif.h"
	245	#endif
	246
[3182]	247
[3347]	248	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	249	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	250	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[2259]	251
[3038]	252	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	253	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	254	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	255	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[2938]	256	INTEGER(iwp) :: merg !< maximum length scale (in gp)
	257	INTEGER(iwp) :: mergp !< merg + nbgp
[3038]	258	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	259	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	260	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	261	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4309]	262	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	263	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	264	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	265	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[2259]	266
[4022]	267	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	268	!< required for bias correction of imposed perturbations
	269	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	270	!< required for bias correction of imposed perturbations
	271
[3347]	272	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	273	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	274	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	275	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
	276	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	277	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	278	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	279	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	280	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	281	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	282	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	283	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	284	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	285
[4022]	286	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	287	!< scales above the boundary layer
	288	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	289	!< one length scale above ABL top
	290	REAL(wp) :: d_l !< blend_coeff/length_scale
	291	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	292	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
	293	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
	294	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	295	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	296	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	297	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	298	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	299
[4022]	300	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	301
[4022]	302
[3347]	303	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	304	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	305	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	306	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	307	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	308	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	309
	310	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	311	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	312	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	313	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	314	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	315	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	316	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	317	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	318	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	319
[3347]	320	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	321	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	322	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	323	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	324	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	325	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	326	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	327	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	328	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	329	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	330	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	331	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	332	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	333	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	334	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	335	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	336	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	337	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	338	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	339	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	340	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	341
	342	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	343	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	344
	345	!
	346	!-- PALM interfaces:
[3347]	347	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	348	INTERFACE stg_adjust
	349	MODULE PROCEDURE stg_adjust
	350	END INTERFACE stg_adjust
	351	!
[2259]	352	!-- Input parameter checks to be done in check_parameters
	353	INTERFACE stg_check_parameters
	354	MODULE PROCEDURE stg_check_parameters
	355	END INTERFACE stg_check_parameters
	356
	357	!
	358	!-- Calculate filter functions
	359	INTERFACE stg_filter_func
	360	MODULE PROCEDURE stg_filter_func
	361	END INTERFACE stg_filter_func
	362
	363	!
[2938]	364	!-- Generate velocity seeds at south and north domain boundary
	365	INTERFACE stg_generate_seed_xz
	366	MODULE PROCEDURE stg_generate_seed_xz
	367	END INTERFACE stg_generate_seed_xz
	368	!
	369	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	370	INTERFACE stg_generate_seed_yz
	371	MODULE PROCEDURE stg_generate_seed_yz
	372	END INTERFACE stg_generate_seed_yz
	373
	374	!
	375	!-- Output of information to the header file
	376	INTERFACE stg_header
	377	MODULE PROCEDURE stg_header
	378	END INTERFACE stg_header
	379
	380	!
	381	!-- Initialization actions
	382	INTERFACE stg_init
	383	MODULE PROCEDURE stg_init
	384	END INTERFACE stg_init
	385
	386	!
	387	!-- Main procedure of synth. turb. gen.
	388	INTERFACE stg_main
	389	MODULE PROCEDURE stg_main
	390	END INTERFACE stg_main
	391
	392	!
	393	!-- Reading of NAMELIST parameters
	394	INTERFACE stg_parin
	395	MODULE PROCEDURE stg_parin
	396	END INTERFACE stg_parin
	397
	398	!
	399	!-- Reading of parameters for restart runs
[2894]	400	INTERFACE stg_rrd_global
	401	MODULE PROCEDURE stg_rrd_global
	402	END INTERFACE stg_rrd_global
[2259]	403
	404	!
	405	!-- Writing of binary output for restart runs
[2894]	406	INTERFACE stg_wrd_global
	407	MODULE PROCEDURE stg_wrd_global
	408	END INTERFACE stg_wrd_global
[2259]	409
	410	SAVE
	411
	412	PRIVATE
	413
	414	!
	415	!-- Public interfaces
[3347]	416	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	417	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	418
	419	!
	420	!-- Public variables
[3347]	421	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	422	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	423	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	424
	425
	426	CONTAINS
	427
	428
	429	!------------------------------------------------------------------------------!
	430	! Description:
	431	! ------------
	432	!> Check parameters routine for synthetic turbulence generator
	433	!------------------------------------------------------------------------------!
	434	SUBROUTINE stg_check_parameters
	435
	436	IMPLICIT NONE
	437
[3182]	438	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	439	nesting_offline ) THEN
[3376]	440	message_string = 'Synthetic turbulence generator is required ' // &
	441	'if offline nesting is applied and PALM operates ' // &
	442	'in LES mode.'
	443	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	444	ENDIF
	445
[3182]	446	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	447	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	448	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	449	'when nesting is applied and parent operates in ' // &
	450	'RANS-mode but current child in LES mode.'
[3376]	451	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	452	ENDIF
	453
[2776]	454	IF ( use_syn_turb_gen ) THEN
[2259]	455
[3579]	456	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	457	.NOT. rans_mode_parent ) THEN
	458	message_string = 'Using synthetic turbulence generator ' // &
	459	'is not allowed in LES-LES nesting.'
	460	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	461
	462	ENDIF
	463
	464	IF ( child_domain .AND. rans_mode .AND. &
	465	rans_mode_parent ) THEN
	466	message_string = 'Using synthetic turbulence generator ' // &
	467	'is not allowed in RANS-RANS nesting.'
	468	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	469
	470	ENDIF
	471
[3182]	472	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	473
[2938]	474	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	475	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	476	message_string = 'Using synthetic turbulence generator ' // &
[3579]	477	'requires %initializing_actions = ' // &
	478	'"set_constant_profiles" or "read_restart_data"' //&
	479	', if not offline nesting is applied.'
[2938]	480	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	481	ENDIF
	482
	483	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	484	message_string = 'Using synthetic turbulence generator ' // &
[3347]	485	'requires &bc_lr = "dirichlet/radiation", ' // &
	486	'if not offline nesting is applied.'
[2938]	487	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	488	ENDIF
	489	IF ( bc_ns /= 'cyclic' ) THEN
	490	message_string = 'Using synthetic turbulence generator ' // &
[3579]	491	'requires &bc_ns = "cyclic", ' // &
[3347]	492	'if not offline nesting is applied.'
[2938]	493	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	494	ENDIF
	495
[2259]	496	ENDIF
	497
	498	IF ( turbulent_inflow ) THEN
	499	message_string = 'Using synthetic turbulence generator ' // &
[2938]	500	'in combination &with turbulent_inflow = .T. '// &
	501	'is not allowed'
[2259]	502	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	503	ENDIF
[4309]	504	!
	505	!-- Synthetic turbulence generator requires the parallel random generator
	506	IF ( random_generator /= 'random-parallel' ) THEN
	507	message_string = 'Using synthetic turbulence generator ' // &
	508	'requires random_generator = random-parallel.'
	509	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	510	ENDIF
[2259]	511
	512	ENDIF
	513
	514	END SUBROUTINE stg_check_parameters
	515
	516
	517	!------------------------------------------------------------------------------!
	518	! Description:
	519	! ------------
	520	!> Header output for synthetic turbulence generator
	521	!------------------------------------------------------------------------------!
	522	SUBROUTINE stg_header ( io )
	523
	524
	525	IMPLICIT NONE
	526
	527	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	528
	529	!
	530	!-- Write synthetic turbulence generator Header
	531	WRITE( io, 1 )
[2776]	532	IF ( use_syn_turb_gen ) THEN
[2259]	533	WRITE( io, 2 )
	534	ELSE
	535	WRITE( io, 3 )
	536	ENDIF
[3347]	537
	538	IF ( parametrize_inflow_turbulence ) THEN
	539	WRITE( io, 4 ) dt_stg_adjust
	540	ELSE
	541	WRITE( io, 5 )
	542	ENDIF
[2259]	543
	544	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	545	' ------------------------------------------'/)
[3347]	546	2 FORMAT (' synthetic turbulence generator is switched on')
	547	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	548	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	549	5 FORMAT (' imposed turbulence is read from file' )
[2259]	550
	551	END SUBROUTINE stg_header
	552
	553
	554	!------------------------------------------------------------------------------!
	555	! Description:
	556	! ------------
	557	!> Initialization of the synthetic turbulence generator
	558	!------------------------------------------------------------------------------!
	559	SUBROUTINE stg_init
	560
	561	IMPLICIT NONE
	562
[3347]	563	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	564
[2669]	565	#if defined( __parallel )
[2259]	566	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	567	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	568	#endif
[2259]	569
[2938]	570	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	571	INTEGER(iwp) :: j !> loop index
	572	INTEGER(iwp) :: k !< index
	573	INTEGER(iwp) :: newtype !< dummy MPI type
	574	INTEGER(iwp) :: realsize !< size of REAL variables
[4309]	575
[4022]	576	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	577	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	578	!
	579	!-- Dummy variables used for reading profiles
	580	REAL(wp) :: d1 !< u profile
	581	REAL(wp) :: d2 !< v profile
	582	REAL(wp) :: d3 !< w profile
	583	REAL(wp) :: d5 !< e profile
	584	REAL(wp) :: luy !< length scale for u in y direction
	585	REAL(wp) :: luz !< length scale for u in z direction
	586	REAL(wp) :: lvy !< length scale for v in y direction
	587	REAL(wp) :: lvz !< length scale for v in z direction
	588	REAL(wp) :: lwy !< length scale for w in y direction
	589	REAL(wp) :: lwz !< length scale for w in z direction
[3038]	590	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[2259]	591	REAL(wp) :: zz !< height
	592
[2938]	593
[2259]	594	#if defined( __parallel )
	595	CALL MPI_BARRIER( comm2d, ierr )
	596	#endif
	597
[2669]	598	#if defined( __parallel )
[2259]	599	!
[2938]	600	!-- Determine processor decomposition of z-axis along x- and y-direction
	601	nnz = nz / pdims(1)
[2945]	602	nzb_x_stg = 1 + myidx * INT( nnz )
	603	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[2938]	604
[3038]	605	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[2945]	606	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[2938]	607
[3182]	608	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	609	.AND. .NOT. rans_mode ) ) THEN
[2938]	610	nnz = nz / pdims(2)
[2945]	611	nzb_y_stg = 1 + myidy * INT( nnz )
	612	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[2938]	613
[2945]	614	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[3038]	615	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
[2938]	616	ENDIF
	617
	618	!
[2259]	619	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	620	!-- velocity seeds
	621	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	622	extent = 1 * realsize
[2938]	623	!
[3038]	624	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	625	!-- layer
[2938]	626	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[2259]	627	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
	628	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	629	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	630	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
	631	CALL MPI_TYPE_FREE( newtype, ierr )
	632
[2938]	633	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	634	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
[2259]	635	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	636	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	637	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
	638	CALL MPI_TYPE_FREE( newtype, ierr )
	639
	640	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[2938]	641	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[2259]	642
[2938]	643	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	644	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[2259]	645
	646	DO j = 1, pdims(1)
[2938]	647	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2259]	648	ENDDO
[2938]	649	!
[3038]	650	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	651	!-- layer
[2938]	652	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
[3182]	653	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	654	.AND. .NOT. rans_mode ) ) THEN
[2945]	655	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
[2938]	656	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	657	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	658	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	659	CALL MPI_TYPE_FREE( newtype, ierr )
	660
	661	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	662	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
[2938]	663	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	664	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	665	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	666	CALL MPI_TYPE_FREE( newtype, ierr )
	667
	668	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	669	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	670
	671	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	672	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	673
	674	DO j = 1, pdims(2)
	675	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	676	ENDDO
	677
	678	ENDIF
	679
[2669]	680	#endif
[2259]	681	!
[4071]	682	!-- Allocate required arrays.
	683	!-- In case no offline nesting or self nesting is used, the arrary
	684	!-- mean_inflow profiles is required. Check if it is already allocated, else
	685	!-- allocate and initialize it appropriately. Note, in case turbulence and
	686	!-- inflow information is read from file, mean_inflow_profiles is already
	687	!-- allocated and initialized appropriately.
[3347]	688	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	689	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	690	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	691	mean_inflow_profiles = 0.0_wp
	692	mean_inflow_profiles(:,1) = u_init
	693	mean_inflow_profiles(:,2) = v_init
	694	!
	695	!-- Even though potential temperature and humidity are not perturbed,
	696	!-- they need to be initialized appropriately.
	697	IF ( .NOT. neutral ) &
	698	mean_inflow_profiles(:,4) = pt_init
	699	IF ( humidity ) &
	700	mean_inflow_profiles(:,6) = q_init
	701	ENDIF
[3347]	702	ENDIF
[2259]	703
[3347]	704	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	705	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	706	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	707	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	708	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	709	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	710	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	711	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	712
	713	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
	714	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
	715	dist_xz = 0.0_wp
	716	dist_yz = 0.0_wp
	717	!
[2259]	718	!-- Read inflow profile
	719	!-- Height levels of profiles in input profile is as follows:
	720	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	721	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	722	!-- WARNING: zz is not used at the moment
[2938]	723	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	724	EXIST = file_stg_exist )
[2259]	725
[2938]	726	IF ( file_stg_exist ) THEN
[2259]	727
[2938]	728	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	729	FORM='FORMATTED')
	730	!
	731	!-- Skip header
	732	READ( 90, * )
[2259]	733
[3182]	734	DO k = nzb+1, nzt+1
[2938]	735	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	736	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	737	d1, d2, d3, d5
	738
[2259]	739	!
[3182]	740	!-- Convert length scales from meter to number of grid points.
[2938]	741	nuy(k) = INT( luy * ddy )
[3182]	742	nuz(k) = INT( luz * ddzw(k) )
[2938]	743	nvy(k) = INT( lvy * ddy )
[3182]	744	nvz(k) = INT( lvz * ddzw(k) )
[2938]	745	nwy(k) = INT( lwy * ddy )
[3182]	746	nwz(k) = INT( lwz * ddzw(k) )
[2938]	747	!
	748	!-- Workaround, assume isotropic turbulence
	749	nwx(k) = nwy(k)
	750	nvx(k) = nvy(k)
	751	nux(k) = nuy(k)
	752	!
	753	!-- Save Mean inflow profiles
	754	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	755	mean_inflow_profiles(k,1) = d1
	756	mean_inflow_profiles(k,2) = d2
	757	! mean_inflow_profiles(k,4) = d4
	758	mean_inflow_profiles(k,5) = d5
	759	ENDIF
	760	ENDDO
[3182]	761	!
	762	!-- Set lenght scales at surface grid point
	763	nuy(nzb) = nuy(nzb+1)
	764	nuz(nzb) = nuz(nzb+1)
	765	nvy(nzb) = nvy(nzb+1)
	766	nvz(nzb) = nvz(nzb+1)
	767	nwy(nzb) = nwy(nzb+1)
	768	nwz(nzb) = nwz(nzb+1)
	769
[2938]	770	CLOSE( 90 )
[3347]	771	!
	772	!-- Calculate coefficient matrix from Reynolds stress tensor
	773	!-- (Lund rotation)
	774	CALL calc_coeff_matrix
	775	!
	776	!-- No information about turbulence and its length scales are available.
	777	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	778	!-- Set flag which indicates that turbulence is parametrized, which is done
	779	!-- later when energy-balance models are already initialized. This is
	780	!-- because the STG needs information about surface properties such as
	781	!-- roughness to build 'realistic' turbulence profiles.
[2938]	782	ELSE
[2259]	783	!
[4022]	784	!-- Define length scale for the imposed turbulence, which is defined as
	785	!-- 8 times the minimum grid spacing
	786	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
	787	!
	788	!-- Define constant to gradually decrease length scales and Reynolds stress
	789	!-- above ABL top. Assure that no zero length scales are used.
	790	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	791	!
[3347]	792	!-- Set flag indicating that turbulence is parametrized
	793	parametrize_inflow_turbulence = .TRUE.
	794	!
[4022]	795	!-- In case of dirichlet inflow boundary conditions only at one lateral
	796	!-- boundary, i.e. in the case no offline or self nesting is applied but
	797	!-- synthetic turbulence shall be parametrized nevertheless, the
	798	!-- boundary-layer depth need to determined first.
	799	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	800	CALL nesting_offl_calc_zi
	801	!
[3347]	802	!-- Determine boundary-layer depth, which is used to initialize lenght
	803	!-- scales
	804	CALL calc_scaling_variables
	805	!
	806	!-- Initialize lenght and time scales, which in turn are used
	807	!-- to initialize the filter functions.
	808	CALL calc_length_and_time_scale
[3891]	809	!
	810	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	811	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	812	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	813	!-- friction velocity and velocity scale.
	814	CALL parametrize_reynolds_stress
	815	!
	816	!-- Calculate coefficient matrix from Reynolds stress tensor
	817	!-- (Lund rotation)
	818	CALL calc_coeff_matrix
[3347]	819
[2938]	820	ENDIF
	821
[2259]	822	!
[3347]	823	!-- Assign initial profiles. Note, this is only required if turbulent
	824	!-- inflow from the left is desired, not in case of any of the
	825	!-- nesting (offline or self nesting) approaches.
[3182]	826	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	827	u_init = mean_inflow_profiles(:,1)
	828	v_init = mean_inflow_profiles(:,2)
	829	!pt_init = mean_inflow_profiles(:,4)
	830	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	831	ENDIF
[3347]	832
[2938]	833	!
[2259]	834	!-- Define the size of the filter functions and allocate them.
	835	merg = 0
	836
	837	! arrays must be large enough to cover the largest length scale
	838	DO k = nzb, nzt+1
[2938]	839	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	840	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	841	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[2259]	842	IF ( j > merg ) merg = j
	843	ENDDO
	844
	845	merg = 2 * merg
	846	mergp = merg + nbgp
	847
[2938]	848	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
	849	buy(-merg:merg,nzb:nzt+1), &
	850	buz(-merg:merg,nzb:nzt+1), &
	851	bvx(-merg:merg,nzb:nzt+1), &
	852	bvy(-merg:merg,nzb:nzt+1), &
	853	bvz(-merg:merg,nzb:nzt+1), &
	854	bwx(-merg:merg,nzb:nzt+1), &
	855	bwy(-merg:merg,nzb:nzt+1), &
	856	bwz(-merg:merg,nzb:nzt+1) )
[2259]	857
	858	!
[2938]	859	!-- Allocate velocity seeds for turbulence at xz-layer
	860	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
	861	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
	862	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
[2259]	863
[2938]	864	!
	865	!-- Allocate velocity seeds for turbulence at yz-layer
	866	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
	867	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
	868	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
[2259]	869
[2938]	870	fu_xz = 0.0_wp
	871	fuo_xz = 0.0_wp
	872	fv_xz = 0.0_wp
	873	fvo_xz = 0.0_wp
	874	fw_xz = 0.0_wp
	875	fwo_xz = 0.0_wp
	876
	877	fu_yz = 0.0_wp
	878	fuo_yz = 0.0_wp
	879	fv_yz = 0.0_wp
	880	fvo_yz = 0.0_wp
	881	fw_yz = 0.0_wp
	882	fwo_yz = 0.0_wp
	883
[2259]	884	!
	885	!-- Create filter functions
[2938]	886	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	887	CALL stg_filter_func( nuy, buy ) !filter uy
	888	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	889	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	890	CALL stg_filter_func( nvy, bvy ) !filter vy
	891	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	892	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	893	CALL stg_filter_func( nwy, bwy ) !filter wy
	894	CALL stg_filter_func( nwz, bwz ) !filter wz
	895
	896	#if defined( __parallel )
	897	CALL MPI_BARRIER( comm2d, ierr )
	898	#endif
	899
	900	!
[2938]	901	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	902	! time step.
	903	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	904	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	905	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	906	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	907
	908	IF ( myidx == id_stg_left ) i = -1
	909	IF ( myidx == id_stg_right ) i = nxr+1
	910
[2259]	911	DO j = nysg, nyng
	912	DO k = nzb, nzt+1
[4332]	913	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	914	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	915	ELSE
[4332]	916	fu_yz(k,j) = 10E-8_wp
[2259]	917	ENDIF
	918
[4332]	919	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	920	fv_yz(k,j) = ( v(k,j,i) - &
	921	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	922	ELSE
[4332]	923	fv_yz(k,j) = 10E-8_wp
[2259]	924	ENDIF
	925
[4332]	926	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	927	fw_yz(k,j) = ( w(k,j,i) - &
	928	a31(k) * fu_yz(k,j) - a32(k) * &
	929	fv_yz(k,j) ) / a33(k)
[2259]	930	ELSE
[4332]	931	fw_yz(k,j) = 10E-8_wp
[2259]	932	ENDIF
	933	ENDDO
	934	ENDDO
	935	ENDIF
[3900]	936
	937	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	938
	939	IF ( myidy == id_stg_south ) j = -1
	940	IF ( myidy == id_stg_north ) j = nyn+1
	941
	942	DO i = nxlg, nxrg
	943	DO k = nzb, nzt+1
[4335]	944	!
	945	!-- In case the correlation coefficients are very small, the
	946	!-- velocity seeds may become very large finally creating
	947	!-- numerical instabilities in the synthetic turbulence generator.
	948	!-- Empirically, a value of 10E-8 seems to be sufficient.
[4332]	949	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	950	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	951	ELSE
[4332]	952	fu_xz(k,i) = 10E-8_wp
[3900]	953	ENDIF
	954
[4332]	955	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	956	fv_xz(k,i) = ( v(k,j,i) - &
	957	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	958	ELSE
[4332]	959	fv_xz(k,i) = 10E-8_wp
[3900]	960	ENDIF
	961
[4332]	962	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	963	fw_xz(k,i) = ( w(k,j,i) - &
	964	a31(k) * fu_xz(k,i) - &
	965	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	966	ELSE
[4332]	967	fw_xz(k,i) = 10E-8_wp
[3900]	968	ENDIF
	969
	970	ENDDO
	971	ENDDO
	972	ENDIF
[2259]	973	ENDIF
[4022]	974	!
	975	!-- Count the number of non-topography grid points at the boundaries where
	976	!-- perturbations are imposed. This number is later used for bias corrections
	977	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	978	!-- due to the asymetry of u and v along x and y direction, respectively,
	979	!-- different cases must be distinguished.
	980	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	981	!
	982	!-- Number of grid points where perturbations are imposed on u
	983	IF ( myidx == id_stg_left ) i = nxl
	984	IF ( myidx == id_stg_right ) i = nxr+1
	985
	986	nr_non_topo_yz_l(1) = SUM( &
	987	MERGE( 1, 0, &
[4329]	988	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	989	!
	990	!-- Number of grid points where perturbations are imposed on v and w
	991	IF ( myidx == id_stg_left ) i = nxl-1
	992	IF ( myidx == id_stg_right ) i = nxr+1
	993
	994	nr_non_topo_yz_l(2) = SUM( &
	995	MERGE( 1, 0, &
[4329]	996	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	997	nr_non_topo_yz_l(3) = SUM( &
	998	MERGE( 1, 0, &
[4329]	999	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1000
	1001	#if defined( __parallel )
	1002	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	1003	MPI_SUM, comm1dy, ierr )
	1004	#else
	1005	nr_non_topo_yz = nr_non_topo_yz_l
	1006	#endif
	1007	ENDIF
	1008
	1009	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1010	!
	1011	!-- Number of grid points where perturbations are imposed on v
	1012	IF ( myidy == id_stg_south ) j = nys
	1013	IF ( myidy == id_stg_north ) j = nyn+1
	1014
	1015	nr_non_topo_xz_l(2) = SUM( &
	1016	MERGE( 1, 0, &
[4329]	1017	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1018	!
	1019	!-- Number of grid points where perturbations are imposed on u and w
	1020	IF ( myidy == id_stg_south ) j = nys-1
	1021	IF ( myidy == id_stg_north ) j = nyn+1
	1022
	1023	nr_non_topo_xz_l(1) = SUM( &
	1024	MERGE( 1, 0, &
[4329]	1025	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1026	nr_non_topo_xz_l(3) = SUM( &
	1027	MERGE( 1, 0, &
[4329]	1028	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1029
	1030	#if defined( __parallel )
	1031	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1032	MPI_SUM, comm1dx, ierr )
	1033	#else
	1034	nr_non_topo_xz = nr_non_topo_xz_l
	1035	#endif
	1036	ENDIF
[2259]	1037
[4022]	1038
[2259]	1039	END SUBROUTINE stg_init
	1040
	1041
	1042	!------------------------------------------------------------------------------!
	1043	! Description:
	1044	! ------------
	1045	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1046	!> (Xie and Castro, 2008)
	1047	!------------------------------------------------------------------------------!
	1048	SUBROUTINE stg_filter_func( nxx, bxx )
	1049
	1050
	1051	IMPLICIT NONE
	1052
	1053	INTEGER(iwp) :: k !< loop index
	1054	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1055	INTEGER(iwp) :: n_k2 !< n_k * 2
	1056	INTEGER(iwp) :: nf !< index for length scales
	1057
	1058	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1059	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1060
	1061	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
	1062
	1063	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
	1064
	1065
	1066	bxx = 0.0_wp
	1067
	1068	DO k = nzb, nzt+1
	1069	bdenom = 0.0_wp
	1070	n_k = nxx(k)
	1071	IF ( n_k /= 0 ) THEN
	1072	n_k2 = n_k * 2
	1073
	1074	!
	1075	!-- ( Eq.10 )^2
	1076	DO nf = -n_k2, n_k2
	1077	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1078	ENDDO
	1079
	1080	!
	1081	!-- ( Eq.9 )
	1082	bdenom = SQRT( bdenom )
	1083	DO nf = -n_k2, n_k2
	1084	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1085	ENDDO
	1086	ENDIF
	1087	ENDDO
	1088
[3347]	1089	END SUBROUTINE stg_filter_func
[2259]	1090
	1091
	1092	!------------------------------------------------------------------------------!
	1093	! Description:
	1094	! ------------
	1095	!> Parin for &stg_par for synthetic turbulence generator
	1096	!------------------------------------------------------------------------------!
	1097	SUBROUTINE stg_parin
	1098
	1099
	1100	IMPLICIT NONE
	1101
	1102	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1103
	1104
[3347]	1105	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
[2259]	1106
	1107	line = ' '
	1108
	1109	!
	1110	!-- Try to find stg package
	1111	REWIND ( 11 )
	1112	line = ' '
	1113	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1114	READ ( 11, '(A)', END=20 ) line
[2259]	1115	ENDDO
	1116	BACKSPACE ( 11 )
	1117
	1118	!
	1119	!-- Read namelist
[3246]	1120	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1121
	1122	!
	1123	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1124	!-- on
[2776]	1125	syn_turb_gen = .TRUE.
[3246]	1126	GOTO 20
[2259]	1127
[3246]	1128	10 BACKSPACE( 11 )
[3248]	1129	READ( 11 , '(A)') line
	1130	CALL parin_fail_message( 'stg_par', line )
[2563]	1131
[3246]	1132	20 CONTINUE
[2259]	1133
	1134	END SUBROUTINE stg_parin
	1135
	1136
	1137	!------------------------------------------------------------------------------!
	1138	! Description:
	1139	! ------------
[2894]	1140	!> This routine reads the respective restart data.
[2576]	1141	!------------------------------------------------------------------------------!
[2894]	1142	SUBROUTINE stg_rrd_global( found )
[2576]	1143
	1144
[2894]	1145	IMPLICIT NONE
[2576]	1146
[3044]	1147	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1148
	1149
[2894]	1150	found = .TRUE.
[2259]	1151
[3038]	1152
[2894]	1153	SELECT CASE ( restart_string(1:length) )
[4022]	1154
	1155	CASE ( 'time_stg_adjust' )
	1156	READ ( 13 ) time_stg_adjust
	1157
	1158	CASE ( 'time_stg_call' )
	1159	READ ( 13 ) time_stg_call
	1160
[2894]	1161	CASE ( 'use_syn_turb_gen' )
	1162	READ ( 13 ) use_syn_turb_gen
[2259]	1163
[2894]	1164	CASE DEFAULT
[2259]	1165
[3038]	1166	found = .FALSE.
[2259]	1167
[2894]	1168	END SELECT
[2259]	1169
	1170
[2894]	1171	END SUBROUTINE stg_rrd_global
[2259]	1172
	1173
	1174	!------------------------------------------------------------------------------!
	1175	! Description:
	1176	! ------------
	1177	!> This routine writes the respective restart data.
	1178	!------------------------------------------------------------------------------!
[2894]	1179	SUBROUTINE stg_wrd_global
[2259]	1180
	1181
	1182	IMPLICIT NONE
[4022]	1183
	1184	CALL wrd_write_string( 'time_stg_adjust' )
	1185	WRITE ( 14 ) time_stg_adjust
	1186
	1187	CALL wrd_write_string( 'time_stg_call' )
	1188	WRITE ( 14 ) time_stg_call
[2259]	1189
[2894]	1190	CALL wrd_write_string( 'use_syn_turb_gen' )
	1191	WRITE ( 14 ) use_syn_turb_gen
[2259]	1192
	1193
[2894]	1194	END SUBROUTINE stg_wrd_global
[2259]	1195
[2894]	1196
[2259]	1197	!------------------------------------------------------------------------------!
	1198	! Description:
	1199	! ------------
	1200	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1201	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1202	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1203	!> (Lund, 1998).
	1204	!------------------------------------------------------------------------------!
	1205	SUBROUTINE stg_main
	1206
	1207	IMPLICIT NONE
	1208
[2938]	1209	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1210	INTEGER(iwp) :: j !< loop index in y-direction
	1211	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1212
	1213	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1214
	1215	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1216
	1217	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1218
[3987]	1219	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1220	!
	1221	!-- Calculate time step which is needed for filter functions
[3775]	1222	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1223	!
[4022]	1224	!-- Check if synthetic turbulence generator needs to be called and new
	1225	!-- perturbations need to be created or if old disturbances can be imposed
	1226	!-- again.
	1227	IF ( time_stg_call >= dt_stg_call .AND. &
	1228	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1229	stg_call = .TRUE.
	1230	ELSE
	1231	stg_call = .FALSE.
	1232	ENDIF
	1233	!
[2259]	1234	!-- Initial value of fu, fv, fw
[3646]	1235	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1236	!
	1237	!-- Generate turbulence at the left and right boundary. Random numbers
	1238	!-- for the yz-planes at the left/right boundary are generated by the
	1239	!-- left-sided mpi ranks only. After random numbers are calculated, they
	1240	!-- are distributed to all other mpi ranks in the model, so that the
	1241	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
	1242	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
	1243	!-- that the left- and the right-sided lateral boundary have the same initial
	1244	!-- seeds.
	1245	!-- Note, in case of inflow from the right only, only turbulence at the left
	1246	!-- boundary is required.
	1247	IF ( .NOT. ( nesting_offline .OR. &
	1248	( child_domain .AND. rans_mode_parent &
	1249	.AND. .NOT. rans_mode ) ) ) THEN
[2938]	1250
[4309]	1251	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1252	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1253	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1254	ELSE
	1255	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
	1256	id_stg_left, id_stg_right )
	1257	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
	1258	id_stg_left, id_stg_right )
	1259	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
	1260	id_stg_left, id_stg_right )
[2938]	1261	!
[4309]	1262	!-- Generate turbulence at the south and north boundary. Random numbers
	1263	!-- for the xz-planes at the south/north boundary are generated by the
	1264	!-- south-sided mpi ranks only. Please see also comment above.
	1265	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
	1266	id_stg_south, id_stg_north )
	1267	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
	1268	id_stg_south, id_stg_north )
	1269	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
	1270	id_stg_south, id_stg_north )
[2938]	1271	ENDIF
[2259]	1272	velocity_seed_initialized = .TRUE.
	1273	ENDIF
	1274	!
[4309]	1275	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
	1276	!-- seeds are only required at the left boundary, while in case of offline
	1277	!-- nesting or RANS-LES nesting velocity seeds are required also at the
	1278	!-- right, south and north boundaries.
[4022]	1279	IF ( stg_call ) THEN
[4309]	1280	IF ( .NOT. ( nesting_offline .OR. &
	1281	( child_domain .AND. rans_mode_parent &
	1282	.AND. .NOT. rans_mode ) ) ) THEN
	1283	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1284	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1285	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1286
	1287	ELSE
	1288	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
	1289	id_stg_left, id_stg_right )
	1290	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
	1291	id_stg_left, id_stg_right )
	1292	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
	1293	id_stg_left, id_stg_right )
	1294
	1295	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
	1296	id_stg_south, id_stg_north )
	1297	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
	1298	id_stg_south, id_stg_north )
	1299	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
	1300	id_stg_south, id_stg_north )
[4022]	1301	ENDIF
[2938]	1302	ENDIF
[3347]	1303
[2938]	1304	!
[4309]	1305	!-- Turbulence generation at left and/or right boundary
[2938]	1306	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1307	!
[4022]	1308	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1309	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1310	!-- imposed
	1311	IF ( stg_call ) THEN
	1312
	1313	DO j = nysg, nyng
	1314	DO k = nzb, nzt + 1
	1315	!
	1316	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1317	IF ( tu(k) == 0.0_wp ) THEN
	1318	fu_yz(k,j) = fuo_yz(k,j)
	1319	ELSE
	1320	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1321	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1322	ENDIF
	1323
	1324	IF ( tv(k) == 0.0_wp ) THEN
	1325	fv_yz(k,j) = fvo_yz(k,j)
	1326	ELSE
	1327	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1328	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1329	ENDIF
	1330
	1331	IF ( tw(k) == 0.0_wp ) THEN
	1332	fw_yz(k,j) = fwo_yz(k,j)
	1333	ELSE
	1334	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1335	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1336	ENDIF
	1337	ENDDO
	1338	ENDDO
	1339
	1340	dist_yz(nzb,:,1) = 0.0_wp
	1341	dist_yz(nzb,:,2) = 0.0_wp
	1342	dist_yz(nzb,:,3) = 0.0_wp
	1343
	1344	IF ( myidx == id_stg_left ) i = nxl
	1345	IF ( myidx == id_stg_right ) i = nxr+1
	1346	DO j = nysg, nyng
	1347	DO k = nzb+1, nzt + 1
	1348	!
	1349	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1350	!-- Additional factors are added to improve the variance of v and w
	1351	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1352	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1353	BTEST( wall_flags_static_0(k,j,i), 1 ) )
[4022]	1354	ENDDO
	1355	ENDDO
[4309]	1356
[4022]	1357	IF ( myidx == id_stg_left ) i = nxl-1
	1358	IF ( myidx == id_stg_right ) i = nxr+1
	1359	DO j = nysg, nyng
	1360	DO k = nzb+1, nzt + 1
	1361	!
	1362	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1363	!-- Additional factors are added to improve the variance of v and w
	1364	!-- experimental test of 1.2
[3347]	1365	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1366	* 1.2_wp ) &
	1367	* ( a21(k) * fu_yz(k,j) &
[4022]	1368	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1369	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1370	BTEST( wall_flags_static_0(k,j,i), 2 ) )
[3347]	1371	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1372	* 1.3_wp ) &
	1373	* ( a31(k) * fu_yz(k,j) &
	1374	+ a32(k) * fv_yz(k,j) &
[4022]	1375	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1376	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1377	BTEST( wall_flags_static_0(k,j,i), 3 ) )
[4022]	1378	ENDDO
[2259]	1379	ENDDO
[4022]	1380	ENDIF
[2259]	1381	!
	1382	!-- Mass flux correction following Kim et al. (2013)
	1383	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1384	!-- inflow boundary. First, calculate mean value of the imposed
	1385	!-- perturbations at yz boundary.
	1386	!-- Note, this needs to be done only after the last RK3-substep, else
	1387	!-- the boundary values won't be accessed.
	1388	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1389	mc_factor_l = 0.0_wp
	1390	mc_factor = 0.0_wp
	1391	!
	1392	!-- Sum up the original volume flows (with and without perturbations).
	1393	!-- Note, for non-normal components (here v and w) it is actually no
	1394	!-- volume flow.
[2938]	1395	IF ( myidx == id_stg_left ) i = nxl
	1396	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1397
	1398	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1399	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1400	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1401
	1402	IF ( myidx == id_stg_left ) i = nxl-1
	1403	IF ( myidx == id_stg_right ) i = nxr+1
	1404
	1405	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1406	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1407	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1408	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1409	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1410	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1411
[2938]	1412	#if defined( __parallel )
	1413	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1414	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1415	#else
	1416	mc_factor = mc_factor_l
[2938]	1417	#endif
[4022]	1418	!
	1419	!-- Calculate correction factor and force zero mean perturbations.
	1420	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1421
	1422	IF ( myidx == id_stg_left ) i = nxl
	1423	IF ( myidx == id_stg_right ) i = nxr+1
	1424
	1425	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
	1426	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1427	BTEST( wall_flags_static_0(:,:,i), 1 ) )
[4022]	1428
	1429
	1430	IF ( myidx == id_stg_left ) i = nxl-1
	1431	IF ( myidx == id_stg_right ) i = nxr+1
	1432
	1433	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
	1434	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1435	BTEST( wall_flags_static_0(:,:,i), 2 ) )
[4022]	1436
	1437	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
	1438	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1439	BTEST( wall_flags_static_0(:,:,i), 3 ) )
[4022]	1440	!
[2938]	1441	!-- Add disturbances
	1442	IF ( myidx == id_stg_left ) THEN
[4022]	1443	!
	1444	!-- For the left boundary distinguish between mesoscale offline / self
	1445	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1446	!-- case turbulence is imposed on the mean inflow profiles.
	1447	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1448	!
	1449	!-- Add disturbance at the inflow
	1450	DO j = nysg, nyng
	1451	DO k = nzb, nzt+1
	1452	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1453	dist_yz(k,j,1) ) &
	1454	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1455	BTEST( wall_flags_static_0(k,j,0), 1 ) )
[4022]	1456	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1457	dist_yz(k,j,2) ) &
	1458	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1459	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
[4022]	1460	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1461	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1462	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
[4022]	1463	ENDDO
[2938]	1464	ENDDO
[4022]	1465	ELSE
	1466
	1467	DO j = nys, nyn
	1468	DO k = nzb+1, nzt
	1469	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1470	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1471	BTEST( wall_flags_static_0(k,j,0), 1 ) )
[4022]	1472	u(k,j,-1) = u(k,j,0)
	1473	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1474	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1475	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
[4022]	1476	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1477	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1478	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
[4022]	1479	ENDDO
	1480	ENDDO
	1481	ENDIF
[2938]	1482	ENDIF
	1483	IF ( myidx == id_stg_right ) THEN
[3186]	1484	DO j = nys, nyn
[3347]	1485	DO k = nzb+1, nzt
[3186]	1486	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1487	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1488	BTEST( wall_flags_static_0(k,j,nxr+1), 1 ) )
[3186]	1489	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1490	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1491	BTEST( wall_flags_static_0(k,j,nxr+1), 2 ) )
[3186]	1492	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1493	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1494	BTEST( wall_flags_static_0(k,j,nxr+1), 3 ) )
[2938]	1495	ENDDO
	1496	ENDDO
	1497	ENDIF
	1498	ENDIF
	1499	ENDIF
	1500	!
	1501	!-- Turbulence generation at north and south boundary
	1502	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1503	!
[4022]	1504	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1505	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1506	!-- imposed
	1507	IF ( stg_call ) THEN
	1508	DO i = nxlg, nxrg
	1509	DO k = nzb, nzt + 1
	1510	!
	1511	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1512	IF ( tu(k) == 0.0_wp ) THEN
	1513	fu_xz(k,i) = fuo_xz(k,i)
	1514	ELSE
	1515	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1516	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1517	ENDIF
	1518
	1519	IF ( tv(k) == 0.0_wp ) THEN
	1520	fv_xz(k,i) = fvo_xz(k,i)
	1521	ELSE
	1522	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1523	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1524	ENDIF
	1525
	1526	IF ( tw(k) == 0.0_wp ) THEN
	1527	fw_xz(k,i) = fwo_xz(k,i)
	1528	ELSE
	1529	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1530	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1531	ENDIF
	1532	ENDDO
	1533	ENDDO
	1534
	1535
	1536	dist_xz(nzb,:,1) = 0.0_wp
	1537	dist_xz(nzb,:,2) = 0.0_wp
	1538	dist_xz(nzb,:,3) = 0.0_wp
	1539
	1540	IF ( myidy == id_stg_south ) j = nys
	1541	IF ( myidy == id_stg_north ) j = nyn+1
	1542	DO i = nxlg, nxrg
	1543	DO k = nzb+1, nzt + 1
	1544	!
	1545	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1546	!-- Additional factors are added to improve the variance of v and w
	1547	!experimental test of 1.2
[3347]	1548	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1549	* 1.2_wp ) &
	1550	* ( a21(k) * fu_xz(k,i) &
[4022]	1551	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1552	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1553	BTEST( wall_flags_static_0(k,j,i), 2 ) )
[4022]	1554	ENDDO
	1555	ENDDO
	1556
	1557	IF ( myidy == id_stg_south ) j = nys-1
	1558	IF ( myidy == id_stg_north ) j = nyn+1
	1559	DO i = nxlg, nxrg
	1560	DO k = nzb+1, nzt + 1
	1561	!
	1562	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1563	!-- Additional factors are added to improve the variance of v and w
	1564	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1565	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1566	BTEST( wall_flags_static_0(k,j,i), 1 ) )
[4022]	1567
[3347]	1568	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1569	* 1.3_wp ) &
	1570	* ( a31(k) * fu_xz(k,i) &
	1571	+ a32(k) * fv_xz(k,i) &
[4022]	1572	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1573	MERGE( 1.0_wp, 0.0_wp, &
[4329]	1574	BTEST( wall_flags_static_0(k,j,i), 3 ) )
[4022]	1575	ENDDO
[2938]	1576	ENDDO
[4022]	1577	ENDIF
[3347]	1578
[2938]	1579	!
	1580	!-- Mass flux correction following Kim et al. (2013)
	1581	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1582	!-- inflow boundary. First, calculate mean value of the imposed
	1583	!-- perturbations at yz boundary.
	1584	!-- Note, this needs to be done only after the last RK3-substep, else
	1585	!-- the boundary values won't be accessed.
	1586	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1587	mc_factor_l = 0.0_wp
	1588	mc_factor = 0.0_wp
	1589
	1590	IF ( myidy == id_stg_south ) j = nys
	1591	IF ( myidy == id_stg_north ) j = nyn+1
	1592
	1593	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1594	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1595	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1596
	1597	IF ( myidy == id_stg_south ) j = nys-1
	1598	IF ( myidy == id_stg_north ) j = nyn+1
	1599
	1600	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1601	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1602	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1603	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1604	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1605	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1606
[2938]	1607	#if defined( __parallel )
[4022]	1608	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1609	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1610	#else
	1611	mc_factor = mc_factor_l
[2938]	1612	#endif
[4022]	1613
	1614	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1615
	1616	IF ( myidy == id_stg_south ) j = nys
	1617	IF ( myidy == id_stg_north ) j = nyn+1
	1618
	1619	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
	1620	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1621	BTEST( wall_flags_static_0(:,j,:), 2 ) )
[4022]	1622
	1623
	1624	IF ( myidy == id_stg_south ) j = nys-1
	1625	IF ( myidy == id_stg_north ) j = nyn+1
	1626
	1627	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
	1628	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1629	BTEST( wall_flags_static_0(:,j,:), 1 ) )
[4022]	1630
	1631	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
	1632	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1633	BTEST( wall_flags_static_0(:,j,:), 3 ) )
[4022]	1634	!
	1635	!-- Add disturbances
	1636	IF ( myidy == id_stg_south ) THEN
	1637	DO i = nxl, nxr
	1638	DO k = nzb+1, nzt
	1639	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1640	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1641	BTEST( wall_flags_static_0(k,-1,i), 1 ) )
[4022]	1642	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1643	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1644	BTEST( wall_flags_static_0(k,0,i), 2 ) )
[4022]	1645	v(k,-1,i) = v(k,0,i)
	1646	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1647	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1648	BTEST( wall_flags_static_0(k,-1,i), 3 ) )
[4022]	1649	ENDDO
[2938]	1650	ENDDO
[4022]	1651	ENDIF
	1652	IF ( myidy == id_stg_north ) THEN
	1653
	1654	DO i = nxl, nxr
	1655	DO k = nzb+1, nzt
	1656	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1657	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1658	BTEST( wall_flags_static_0(k,nyn+1,i), 1 ) )
[4022]	1659	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1660	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1661	BTEST( wall_flags_static_0(k,nyn+1,i), 2 ) )
[4022]	1662	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1663	* MERGE( 1.0_wp, 0.0_wp, &
[4329]	1664	BTEST( wall_flags_static_0(k,nyn+1,i), 3 ) )
[4022]	1665	ENDDO
[2938]	1666	ENDDO
[4022]	1667	ENDIF
[2938]	1668	ENDIF
[2259]	1669	ENDIF
[3347]	1670	!
	1671	!-- Finally, set time counter for calling STG to zero
[4022]	1672	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1673
[3987]	1674	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1675
[2259]	1676	END SUBROUTINE stg_main
	1677
	1678	!------------------------------------------------------------------------------!
	1679	! Description:
	1680	! ------------
	1681	!> Generate a set of random number rand_it wich is equal on each PE
	1682	!> and calculate the velocity seed f_n.
	1683	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1684	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1685	!> parts are collected to form the full array.
	1686	!------------------------------------------------------------------------------!
[4309]	1687	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
	1688
	1689	USE pegrid
[2259]	1690
	1691	IMPLICIT NONE
	1692
[4309]	1693	INTEGER(iwp) :: i !< grid index x-direction
	1694	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1695	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1696	INTEGER(iwp) :: j !< loop index in y-direction
	1697	INTEGER(iwp) :: jj !< loop index in y-direction
	1698	INTEGER(iwp) :: k !< loop index in z-direction
	1699	INTEGER(iwp) :: kk !< loop index in z-direction
	1700	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1701
	1702	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1703	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1704	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
	1705	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1706
	1707	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1708	REAL(wp) :: rand_av !< average of random number
	1709	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1710
[3347]	1711	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
	1712	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1713
[2938]	1714	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
[4309]	1715	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
	1716
	1717	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
	1718	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
[2259]	1719
	1720	!
[4309]	1721	!-- Generate random numbers using the parallel random generator.
[2259]	1722	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1723	!-- unit variance. Note, at the end the random number array must be defined
	1724	!-- globally in order to compute the correlation matrices. However,
	1725	!-- the calculation and normalization of random numbers is done locally,
	1726	!-- while the result is later distributed to all processes. Further,
	1727	!-- please note, a set of random numbers is only calculated for the
	1728	!-- left boundary, while the right boundary uses the same random numbers
	1729	!-- and thus also computes the same correlation matrix.
[2259]	1730	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
[4309]	1731	rand_it = 0.0_wp
[2259]	1732
	1733	rand_av = 0.0_wp
	1734	rand_sigma_inv = 0.0_wp
	1735	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
[4309]	1736	!
	1737	!-- Compute and normalize random numbers only on left-boundary ranks.
	1738	IF ( myidx == id_stg_left ) THEN
	1739	!
	1740	!-- Allocate array for local set of random numbers
	1741	ALLOCATE( rand_it_l(nzb:nzt+1,nys:nyn) )
	1742	rand_it_l = 0.0_wp
[2259]	1743
[4309]	1744	i = nxl
	1745	DO j = nys, nyn
	1746	!
	1747	!-- Put the random seeds at grid point j,i
	1748	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
	1749	DO k = nzb, nzt+1
	1750	CALL random_number_parallel( random_dummy )
	1751	rand_it_l(k,j) = random_dummy
	1752	rand_av = rand_av + rand_it_l(k,j)
	1753	ENDDO
	1754	!
	1755	!-- Get the new random seeds from last call at grid point j,i
	1756	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
[2259]	1757	ENDDO
[4309]	1758	#if defined( __parallel )
	1759	!
	1760	!-- Sum-up the local averages of the random numbers
	1761	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1762	MPI_SUM, comm1dy, ierr )
	1763	#endif
	1764	rand_av = rand_av * nyz_inv
	1765	!
	1766	!-- Obtain zero mean
	1767	rand_it_l = rand_it_l - rand_av
	1768	!
	1769	!-- Now, compute the variance
	1770	DO j = nys, nyn
	1771	DO k = nzb, nzt+1
	1772	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,j)**2
	1773	ENDDO
[2259]	1774	ENDDO
	1775
[4309]	1776	#if defined( __parallel )
[2259]	1777	!
[4309]	1778	!-- Sum-up the local quadratic averages of the random numbers
	1779	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1780	MPI_SUM, comm1dy, ierr )
	1781	#endif
	1782	!
	1783	!-- Compute standard deviation
	1784	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1785	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1786	ELSE
	1787	rand_sigma_inv = 1.0_wp
	1788	ENDIF
	1789	!
	1790	!-- Normalize with standard deviation to obtain unit variance
	1791	rand_it_l = rand_it_l * rand_sigma_inv
	1792	!
	1793	!-- Copy local random numbers on the global array
	1794	rand_it(nzb:nzt+1,nys:nyn) = rand_it_l(nzb:nzt+1,nys:nyn)
	1795	!
	1796	!-- Deallocate local array
	1797	DEALLOCATE( rand_it_l )
	1798	!
	1799	!-- Now, distribute the final set of random numbers to all mpi ranks located
	1800	!-- on the left boundary. Here, an allreduce with sum reduction is sufficient,
	1801	!-- or, in the non-parallel case, nothing need to be done at all.
	1802	#if defined( __parallel )
	1803	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
	1804	MPI_SUM, comm1dy, ierr )
	1805	#endif
	1806	ENDIF
	1807	!
	1808	!-- Finally, distribute the set of random numbers (defined on the leftmost-
	1809	!-- located mpi ranks) to all other mpi ranks. Here, a allreduce with sum
	1810	!-- option is sufficient, because rand_it is zero on all other mpi_ranks.
	1811	!-- Note, the reduce operation is only performed with communicator comm1dx,
	1812	!-- where only 1 rank within the communicator has non-zero random numbers.
	1813	#if defined( __parallel )
	1814	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
	1815	MPI_SUM, comm1dx, ierr )
	1816	#endif
	1817	!
	1818	!-- Periodic fill of random numbers in space
[2259]	1819	DO j = 0, ny
	1820	DO k = 1, mergp
	1821	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
	1822	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
	1823	ENDDO
	1824	ENDDO
	1825	DO j = 1, mergp
	1826	DO k = nzb-mergp, nzt+1+mergp
	1827	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
	1828	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
	1829	ENDDO
	1830	ENDDO
	1831
	1832	!
	1833	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	1834	n_y2 = n_y * 2
	1835	n_z2 = n_z * 2
	1836	f_n_l = 0.0_wp
	1837
	1838	DO j = nysg, nyng
[2938]	1839	DO k = nzb_x_stg, nzt_x_stg+1
[2259]	1840	DO jj = -n_y2(k), n_y2(k)
	1841	DO kk = -n_z2(k), n_z2(k)
	1842	f_n_l(k,j) = f_n_l(k,j) &
	1843	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1844	ENDDO
	1845	ENDDO
	1846	ENDDO
	1847	ENDDO
	1848
	1849	DEALLOCATE( rand_it )
	1850	!
	1851	!-- Gather velocity seeds of full subdomain
[2938]	1852	send_count = nzt_x_stg - nzb_x_stg + 1
	1853	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1854
	1855	#if defined( __parallel )
[4309]	1856	!
	1857	!-- Gather the velocity seed matrix on left boundary mpi ranks.
	1858	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
	1859	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
	1860	id_left, comm1dx, ierr )
	1861	!
	1862	!-- If required, gather the same velocity seed matrix on right boundary
	1863	!-- mpi ranks (in offline nesting for example).
	1864	IF ( PRESENT( id_right ) ) THEN
	1865	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
	1866	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz,&
	1867	id_right, comm1dx, ierr )
	1868	ENDIF
[2259]	1869	#else
[2938]	1870	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
[2259]	1871	#endif
	1872
	1873
	1874	END SUBROUTINE stg_generate_seed_yz
	1875
[2938]	1876
	1877	!------------------------------------------------------------------------------!
	1878	! Description:
	1879	! ------------
	1880	!> Generate a set of random number rand_it wich is equal on each PE
	1881	!> and calculate the velocity seed f_n.
	1882	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1883	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1884	!> parts are collected to form the full array.
	1885	!------------------------------------------------------------------------------!
[4309]	1886	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1887
	1888	IMPLICIT NONE
	1889
	1890	INTEGER(iwp) :: i !< loop index in x-direction
[4309]	1891	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1892	INTEGER(iwp) :: id_south !< core ids at respective boundaries
[2938]	1893	INTEGER(iwp) :: ii !< loop index in x-direction
[4309]	1894	INTEGER(iwp) :: j !< grid index y-direction
[2938]	1895	INTEGER(iwp) :: k !< loop index in z-direction
	1896	INTEGER(iwp) :: kk !< loop index in z-direction
	1897	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1898
	1899	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1900	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[3347]	1901	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
[2938]	1902	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1903
	1904	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1905	REAL(wp) :: rand_av !< average of random number
	1906	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1907
[3347]	1908	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
	1909	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1910
[2938]	1911	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
[4309]	1912	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
[2938]	1913
[4309]	1914	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
	1915	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
[2938]	1916
	1917	!
[4309]	1918	!-- Generate random numbers using the parallel random generator.
[2938]	1919	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1920	!-- unit variance. Note, at the end the random number array must be defined
	1921	!-- globally in order to compute the correlation matrices. However,
	1922	!-- the calculation and normalization of random numbers is done locally,
	1923	!-- while the result is later distributed to all processes. Further,
	1924	!-- please note, a set of random numbers is only calculated for the
	1925	!-- left boundary, while the right boundary uses the same random numbers
	1926	!-- and thus also computes the same correlation matrix.
[2938]	1927	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
[4309]	1928	rand_it = 0.0_wp
[2938]	1929
	1930	rand_av = 0.0_wp
	1931	rand_sigma_inv = 0.0_wp
	1932	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
[4309]	1933	!
	1934	!-- Compute and normalize random numbers only on south-boundary ranks.
	1935	IF ( myidy == id_stg_south ) THEN
	1936	!
	1937	!-- Allocate array for local set of random numbers
	1938	ALLOCATE( rand_it_l(nzb:nzt+1,nxl:nxr) )
	1939	rand_it_l = 0.0_wp
[2938]	1940
[4309]	1941	j = nys
	1942	DO i = nxl, nxr
	1943	!
	1944	!-- Put the random seeds at grid point j,i
	1945	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
	1946	DO k = nzb, nzt+1
	1947	CALL random_number_parallel( random_dummy )
	1948	rand_it_l(k,i) = random_dummy
	1949	rand_av = rand_av + rand_it_l(k,i)
	1950	ENDDO
	1951	!
	1952	!-- Get the new random seeds from last call at grid point j,i
	1953	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
[2938]	1954	ENDDO
[4309]	1955	#if defined( __parallel )
	1956	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1957	MPI_SUM, comm1dx, ierr )
	1958	#endif
	1959	rand_av = rand_av * nxz_inv
	1960	!
	1961	!-- Obtain zero mean
	1962	rand_it_l = rand_it_l - rand_av
	1963	!
	1964	!-- Now, compute the variance
	1965	DO i = nxl, nxr
	1966	DO k = nzb, nzt+1
	1967	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,i)**2
	1968	ENDDO
[2938]	1969	ENDDO
	1970
[4309]	1971	#if defined( __parallel )
	1972	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1973	MPI_SUM, comm1dx, ierr )
	1974	#endif
[2938]	1975	!
[4309]	1976	!-- Compute standard deviation
	1977	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1978	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	1979	ELSE
	1980	rand_sigma_inv = 1.0_wp
	1981	ENDIF
	1982	!
	1983	!-- Normalize with standard deviation to obtain unit variance
	1984	rand_it_l = rand_it_l * rand_sigma_inv
	1985	!
	1986	!-- Copy local random numbers on the global array
	1987	rand_it(nzb:nzt+1,nxl:nxr) = rand_it_l(nzb:nzt+1,nxl:nxr)
	1988	!
	1989	!-- Deallocate local array
	1990	DEALLOCATE( rand_it_l )
	1991	!
	1992	!-- Now, distribute the final set of random numbers to all mpi ranks located
	1993	!-- on the south boundary. Here, an allreduce with sum reduction is sufficient.
	1994	#if defined( __parallel )
	1995	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
	1996	MPI_SUM, comm1dx, ierr )
	1997	#endif
	1998	ENDIF
	1999	!
	2000	!-- Finally, distribute the set of random numbers (defined on the
	2001	!-- southmost-located mpi ranks) to all other mpi ranks. Here, a allreduce
	2002	!-- with sum option is sufficient, because rand_it is zero on all other
	2003	!-- mpi_ranks. Note, the reduce operation is only performed with communicator
	2004	!-- comm1dy, where only 1 rank within the communicator has non zero random numbers.
	2005	#if defined( __parallel )
	2006	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
	2007	MPI_SUM, comm1dy, ierr )
	2008	#endif
	2009	!
[2938]	2010	!-- Periodic fill of random number in space
	2011	DO i = 0, nx
	2012	DO k = 1, mergp
	2013	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
	2014	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
	2015	ENDDO
	2016	ENDDO
	2017	DO i = 1, mergp
	2018	DO k = nzb-mergp, nzt+1+mergp
	2019	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
	2020	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
	2021	ENDDO
	2022	ENDDO
	2023	!
	2024	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	2025	n_x2 = n_x * 2
	2026	n_z2 = n_z * 2
	2027	f_n_l = 0.0_wp
	2028
	2029	DO i = nxlg, nxrg
	2030	DO k = nzb_y_stg, nzt_y_stg+1
	2031	DO ii = -n_x2(k), n_x2(k)
	2032	DO kk = -n_z2(k), n_z2(k)
	2033	f_n_l(k,i) = f_n_l(k,i) &
	2034	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2035	ENDDO
	2036	ENDDO
	2037	ENDDO
	2038	ENDDO
	2039
	2040	DEALLOCATE( rand_it )
	2041
	2042	!
	2043	!-- Gather velocity seeds of full subdomain
	2044	send_count = nzt_y_stg - nzb_y_stg + 1
	2045	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
	2046
	2047	#if defined( __parallel )
[4309]	2048	!
	2049	!-- Gather the processed velocity seed on south boundary mpi ranks.
	2050	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
	2051	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
	2052	id_south, comm1dy, ierr )
	2053	!
	2054	!-- Gather the processed velocity seed on north boundary mpi ranks.
	2055	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
	2056	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
	2057	id_north, comm1dy, ierr )
[2938]	2058	#else
	2059	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
	2060	#endif
	2061
	2062	END SUBROUTINE stg_generate_seed_xz
	2063
[3347]	2064	!------------------------------------------------------------------------------!
	2065	! Description:
	2066	! ------------
	2067	!> Parametrization of the Reynolds stress tensor, following the parametrization
	2068	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	2069	!> dispserion modelling. Please note, the parametrization does not distinguish
	2070	!> between along-wind and cross-wind turbulence.
	2071	!------------------------------------------------------------------------------!
	2072	SUBROUTINE parametrize_reynolds_stress
	2073
	2074	IMPLICIT NONE
	2075
	2076	INTEGER(iwp) :: k !< loop index in z-direction
	2077
	2078	REAL(wp) :: zzi !< ratio of z/zi
	2079
	2080	DO k = nzb+1, nzt+1
	2081	!
[4022]	2082	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2083	!-- The function decreases to 1/10 after one length scale above the
	2084	!-- ABL top.
	2085	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2086	!
[4022]	2087	!-- Determine normalized height coordinate
	2088	zzi = zu(k) / zi_ribulk
[3347]	2089	!
[4022]	2090	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
	2091	!-- to the denominator, else the merge-function can crash if scale_l is
	2092	!-- zero.
	2093	r11(k) = scale_us*2 ( &
	2094	MERGE( 0.35_wp * ABS( &
	2095	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2096	)**( 2.0_wp / 3.0_wp ), &
	2097	0.0_wp, &
	2098	scale_l < 0.0_wp ) &
	2099	+ 5.0_wp - 4.0_wp * zzi &
	2100	) * blend
	2101
	2102	r22(k) = r11(k)
	2103	!
	2104	!-- w'w'
	2105	r33(k) = scale_wm*2 ( &
	2106	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2107	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2108	) * blend
	2109	!
	2110	!-- u'w' and v'w'. Assume isotropy.
	2111	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	2112	r32(k) = r31(k)
[3347]	2113	!
[4022]	2114	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	2115	!-- a similar profile as for u'w'.
	2116	r21(k) = r31(k)
[3347]	2117	ENDDO
	2118
	2119	!
	2120	!-- Set bottom boundary condition
	2121	r11(nzb) = r11(nzb+1)
	2122	r22(nzb) = r22(nzb+1)
	2123	r33(nzb) = r33(nzb+1)
	2124
	2125	r21(nzb) = r11(nzb+1)
	2126	r31(nzb) = r31(nzb+1)
	2127	r32(nzb) = r32(nzb+1)
	2128
	2129
	2130	END SUBROUTINE parametrize_reynolds_stress
	2131
	2132	!------------------------------------------------------------------------------!
	2133	! Description:
	2134	! ------------
	2135	!> Calculate the coefficient matrix from the Lund rotation.
	2136	!------------------------------------------------------------------------------!
	2137	SUBROUTINE calc_coeff_matrix
	2138
	2139	IMPLICIT NONE
	2140
	2141	INTEGER(iwp) :: k !< loop index in z-direction
	2142
	2143	!
	2144	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2145	DO k = nzb+1, nzt+1
[4022]	2146	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	2147	a11(k) = SQRT( r11(k) )
	2148	a21(k) = r21(k) / a11(k)
	2149	a31(k) = r31(k) / a11(k)
	2150	ELSE
	2151	a11(k) = 10E-8_wp
	2152	a21(k) = 10E-8_wp
	2153	a31(k) = 10E-8_wp
	2154	ENDIF
	2155	ENDDO
	2156	DO k = nzb+1, nzt+1
	2157	a22(k) = r22(k) - a21(k)**2
[4022]	2158	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2159	a22(k) = SQRT( a22(k) )
	2160	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	2161	ELSE
	2162	a22(k) = 10E-8_wp
	2163	a32(k) = 10E-8_wp
	2164	ENDIF
	2165	ENDDO
	2166	DO k = nzb+1, nzt+1
	2167	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2168	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2169	a33(k) = SQRT( a33(k) )
	2170	ELSE
	2171	a33(k) = 10E-8_wp
	2172	ENDIF
	2173	ENDDO
	2174	!
	2175	!-- Set bottom boundary condition
	2176	a11(nzb) = a11(nzb+1)
	2177	a22(nzb) = a22(nzb+1)
	2178	a21(nzb) = a21(nzb+1)
	2179	a33(nzb) = a33(nzb+1)
	2180	a31(nzb) = a31(nzb+1)
	2181	a32(nzb) = a32(nzb+1)
	2182
	2183	END SUBROUTINE calc_coeff_matrix
	2184
	2185	!------------------------------------------------------------------------------!
	2186	! Description:
	2187	! ------------
	2188	!> This routine controls the re-adjustment of the turbulence statistics used
	2189	!> for generating turbulence at the lateral boundaries.
	2190	!------------------------------------------------------------------------------!
	2191	SUBROUTINE stg_adjust
	2192
	2193	IMPLICIT NONE
	2194
[3987]	2195
	2196	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2197	!
[4022]	2198	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2199	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2200	!-- synthetic turbulence shall be parametrized nevertheless, the
	2201	!-- boundary-layer depth need to determined first.
	2202	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2203	CALL nesting_offl_calc_zi
	2204	!
	2205	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2206	!-- are calculated.
[3347]	2207	CALL calc_scaling_variables
	2208	!
	2209	!-- Set length and time scales depending on boundary-layer height
	2210	CALL calc_length_and_time_scale
	2211	!
	2212	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2213	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2214	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2215	!-- friction velocity and velocity scale.
	2216	CALL parametrize_reynolds_stress
	2217	!
	2218	!-- Calculate coefficient matrix from Reynolds stress tensor
	2219	!-- (Lund rotation)
	2220	CALL calc_coeff_matrix
	2221	!
	2222	!-- Determine filter functions on basis of updated length scales
	2223	CALL stg_filter_func( nux, bux ) !filter ux
	2224	CALL stg_filter_func( nuy, buy ) !filter uy
	2225	CALL stg_filter_func( nuz, buz ) !filter uz
	2226	CALL stg_filter_func( nvx, bvx ) !filter vx
	2227	CALL stg_filter_func( nvy, bvy ) !filter vy
	2228	CALL stg_filter_func( nvz, bvz ) !filter vz
	2229	CALL stg_filter_func( nwx, bwx ) !filter wx
	2230	CALL stg_filter_func( nwy, bwy ) !filter wy
	2231	CALL stg_filter_func( nwz, bwz ) !filter wz
	2232	!
	2233	!-- Reset time counter for controlling next adjustment to zero
	2234	time_stg_adjust = 0.0_wp
[3987]	2235
	2236	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2237
	2238	END SUBROUTINE stg_adjust
	2239
	2240
	2241	!------------------------------------------------------------------------------!
	2242	! Description:
	2243	! ------------
	2244	!> Calculates turbuluent length and time scales if these are not available
	2245	!> from measurements.
	2246	!------------------------------------------------------------------------------!
	2247	SUBROUTINE calc_length_and_time_scale
	2248
	2249	IMPLICIT NONE
	2250
	2251
[4022]	2252	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2253
[4022]	2254	REAL(wp) :: length_scale_dum !< effectively used length scale
	2255
[3347]	2256	!
	2257	!-- In initial call the boundary-layer depth can be zero. This case, set
	2258	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2259	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2260	!
	2261	!-- Set-up default turbulent length scales. From the numerical point of
	2262	!-- view the imposed perturbations should not be immediately dissipated
	2263	!-- by the numerics. The numerical dissipation, however, acts on scales
	2264	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2265	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2266	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2267	!-- imposing any perturbations) in order to save computational costs.
	2268	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2269	!-- using the length scales and the mean profiles of u- and v-component.
	2270	DO k = nzb+1, nzt+1
	2271	!
[4022]	2272	!-- Determine blending parameter. Within the boundary layer length scales
	2273	!-- are constant, while above lengths scales approach gradully zero,
	2274	!-- i.e. imposed turbulence is not correlated in space and time,
	2275	!-- just white noise, which saves computations power as the loops for the
	2276	!-- computation of the filter functions depend on the length scales.
	2277	!-- The value decreases to 1/10 after one length scale above the
	2278	!-- ABL top.
	2279	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2280	!
[4022]	2281	!-- Assume isotropic turbulence length scales
	2282	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2283	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2284	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2285	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2286	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2287	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2288	!
[4022]	2289	!-- Along the vertical direction limit the length scale further by the
	2290	!-- boundary-layer depth to assure that no length scales larger than
	2291	!-- the boundary-layer depth are used
	2292	length_scale_dum = MIN( length_scale, zi_ribulk )
	2293
	2294	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2295	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2296	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2297	!
[4022]	2298	!-- Limit time scales, else they become very larger for low wind speed,
	2299	!-- imposing long-living inflow perturbations which in turn propagate
	2300	!-- further into the model domain. Use u_init and v_init to calculate
	2301	!-- the time scales, which will be equal to the inflow profiles, both,
	2302	!-- in offline nesting mode or in dirichlet/radiation mode.
	2303	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2304	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2305	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2306	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2307	!
	2308	!-- Time scale of w-component is a mixture from u- and v-component.
	2309	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2310
[3347]	2311	ENDDO
	2312	!
	2313	!-- Set bottom boundary condition for the length and time scales
	2314	nux(nzb) = nux(nzb+1)
	2315	nuy(nzb) = nuy(nzb+1)
	2316	nuz(nzb) = nuz(nzb+1)
	2317	nvx(nzb) = nvx(nzb+1)
	2318	nvy(nzb) = nvy(nzb+1)
	2319	nvz(nzb) = nvz(nzb+1)
	2320	nwx(nzb) = nwx(nzb+1)
	2321	nwy(nzb) = nwy(nzb+1)
	2322	nwz(nzb) = nwz(nzb+1)
	2323
	2324	tu(nzb) = tu(nzb+1)
	2325	tv(nzb) = tv(nzb+1)
	2326	tw(nzb) = tw(nzb+1)
	2327
	2328
	2329	END SUBROUTINE calc_length_and_time_scale
	2330
	2331	!------------------------------------------------------------------------------!
	2332	! Description:
	2333	! ------------
	2334	!> Calculate scaling variables which are used for turbulence parametrization
	2335	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2336	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2337	!------------------------------------------------------------------------------!
	2338	SUBROUTINE calc_scaling_variables
	2339
	2340	USE surface_mod, &
[4148]	2341	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
[3347]	2342
	2343	IMPLICIT NONE
	2344
	2345	INTEGER(iwp) :: i !< loop index in x-direction
	2346	INTEGER(iwp) :: j !< loop index in y-direction
	2347	INTEGER(iwp) :: k !< loop index in z-direction
	2348	INTEGER(iwp) :: m !< surface element index
	2349
	2350	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2351	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2352	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2353	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2354	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2355	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2356	REAL(wp) :: w_convective !< convective velocity scale
	2357
	2358	!
[3937]	2359	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2360	!-- near-surface temperature in the model domain.
	2361	pt_surf_mean_l = 0.0_wp
	2362	shf_mean_l = 0.0_wp
	2363	scale_l_l = 0.0_wp
	2364	friction_vel_l = 0.0_wp
[3347]	2365	DO m = 1, surf_def_h(0)%ns
[3937]	2366	i = surf_def_h(0)%i(m)
	2367	j = surf_def_h(0)%j(m)
	2368	k = surf_def_h(0)%k(m)
	2369	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2370	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2371	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2372	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2373	ENDDO
	2374	DO m = 1, surf_lsm_h%ns
[3937]	2375	i = surf_lsm_h%i(m)
	2376	j = surf_lsm_h%j(m)
	2377	k = surf_lsm_h%k(m)
	2378	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2379	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2380	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2381	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2382	ENDDO
	2383	DO m = 1, surf_usm_h%ns
[3937]	2384	i = surf_usm_h%i(m)
	2385	j = surf_usm_h%j(m)
	2386	k = surf_usm_h%k(m)
	2387	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2388	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2389	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2390	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2391	ENDDO
	2392
	2393	#if defined( __parallel )
[3937]	2394	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2395	comm2d, ierr )
[3937]	2396	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2397	comm2d, ierr )
[3937]	2398	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2399	comm2d, ierr )
	2400	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2401	comm2d, ierr )
[3347]	2402	#else
[3937]	2403	scale_us = friction_vel_l
	2404	shf_mean = shf_mean_l
	2405	scale_l = scale_l_l
	2406	pt_surf_mean = pt_surf_mean_l
[3347]	2407	#endif
	2408
[3937]	2409	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2410	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2411	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2412	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2413	!
	2414	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2415	!-- is negative, set convective velocity scale to zero.
	2416	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2417	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2418	ELSE
	2419	w_convective = 0.0_wp
	2420	ENDIF
	2421	!
	2422	!-- Finally, in order to consider also neutral or stable stratification,
	2423	!-- compute momentum velocity scale from u* and convective velocity scale,
	2424	!-- according to Rotach et al. (1996).
	2425	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2426
	2427	END SUBROUTINE calc_scaling_variables
	2428
[2259]	2429	END MODULE synthetic_turbulence_generator_mod

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