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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4438

Last change on this file since 4438 was 4438, checked in by suehring, 4 years ago
Synthetic turbulence: performance optimizations - random numbers only defined and computed locally, option to compute velocity seeds locally without need of global communication; paralell random number generator: new routine to initialize 1D random number arrays; virtual measurements: CPU-log points added
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File size: 108.5 KB

Rev	Line
[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 4438 2020-03-03 20:49:28Z suehring $
[4438]	27	! Performance optimizations in velocity-seed calculation:
	28	! - random number array is only defined and computed locally (except for
	29	! normalization to zero mean and unit variance)
	30	! - parallel random number generator is applied independent on the 2D random
	31	! numbers in other routines
	32	! - option to decide wheter velocity seeds are computed locally without any
	33	! further communication or are computed by all processes along the
	34	! communicator
	35	!
	36	! 4346 2019-12-18 11:55:56Z motisi
[4346]	37	! Introduction of wall_flags_total_0, which currently sets bits based on static
	38	! topography information used in wall_flags_static_0
	39	!
	40	! 4335 2019-12-12 16:39:05Z suehring
[4335]	41	! Commentation of last commit
	42	!
	43	! 4332 2019-12-10 19:44:12Z suehring
[4332]	44	! Limit initial velocity seeds in restart runs, if not the seed calculation
	45	! may become unstable. Further, minor bugfix in initial velocity seed
	46	! calculation.
	47	!
	48	! 4329 2019-12-10 15:46:36Z motisi
[4329]	49	! Renamed wall_flags_0 to wall_flags_static_0
	50	!
	51	! 4309 2019-11-26 18:49:59Z suehring
[4309]	52	! Computation of velocity seeds optimized. This implies that random numbers
	53	! are computed now using the parallel random number generator. Random numbers
	54	! are now only computed and normalized locally, while distributed over all
	55	! mpi ranks afterwards, instead of computing random numbers on a global array.
	56	! Further, the number of calls for the time-consuming velocity-seed generation
	57	! is reduced - now the left and right, as well as the north and south boundary
	58	! share the same velocity-seed matrices.
	59	!
	60	! 4182 2019-08-22 15:20:23Z scharf
[4182]	61	! Corrected "Former revisions" section
	62	!
	63	! 4148 2019-08-08 11:26:00Z suehring
[4148]	64	! Remove unused variable
	65	!
	66	! 4144 2019-08-06 09:11:47Z raasch
[4144]	67	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	68	!
	69	! 4071 2019-07-03 20:02:00Z suehring
[4071]	70	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	71	! information is not read from file.
	72	!
	73	! 4022 2019-06-12 11:52:39Z suehring
[4022]	74	! Several bugfixes and improvements
	75	! - revise bias correction of the imposed perturbations (correction via volume
	76	! flow can create instabilities in case the mean volume flow is close to zero)
	77	! - introduce lower limits in calculation of coefficient matrix, else the
	78	! calculation may become numerically unstable
	79	! - impose perturbations every timestep, even though no new set of perturbations
	80	! is generated in case dt_stg_call /= dt_3d
	81	! - Implement a gradual decrease of Reynolds stress and length scales above
	82	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	83	! discontinuous decrease
	84	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	85	!
	86	! 3987 2019-05-22 09:52:13Z kanani
[3987]	87	! Introduce alternative switch for debug output during timestepping
	88	!
	89	! 3938 2019-04-29 16:06:25Z suehring
[3938]	90	! Remove unused variables
	91	!
	92	! 3937 2019-04-29 15:09:07Z suehring
[3937]	93	! Minor bugfix in case of a very early restart where mc_factor is sill not
	94	! present.
	95	! Some modification and fixing of potential bugs in the calculation of scaling
	96	! parameters used for synthetic turbulence parametrization.
	97	!
	98	! 3909 2019-04-17 09:13:25Z suehring
[3909]	99	! Minor bugfix for last commit
	100	!
	101	! 3900 2019-04-16 15:17:43Z suehring
[3900]	102	! Missing re-calculation of perturbation seeds in case of restarts
	103	!
	104	! 3891 2019-04-12 17:52:01Z suehring
[3891]	105	! Bugfix in initialization in case of restart runs.
	106	!
	107	! 3885 2019-04-11 11:29:34Z kanani
[3885]	108	! Changes related to global restructuring of location messages and introduction
	109	! of additional debug messages
	110	!
	111	!
[3775]	112	! removed unused variables
	113	!
	114	! 3719 2019-02-06 13:10:18Z kanani
[3719]	115	! Removed log_point measurement from stg_init, since this part is counted to
	116	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	117	! the subroutines in time_integration for better overview.
	118	!
[4182]	119	! 2259 2017-06-08 09:09:11Z gronemeier
	120	! Initial revision
[3044]	121	!
[4182]	122	! Authors:
	123	! --------
	124	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	125	!
	126	!
[2259]	127	! Description:
	128	! ------------
	129	!> The module generates turbulence at the inflow boundary based on a method by
	130	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	131	!> correction by Kim et al. (2013).
	132	!> The turbulence is correlated based on length scales in y- and z-direction and
	133	!> a time scale for each velocity component. The profiles of length and time
	134	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	135	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	136	!> within the boundary layer.
[2259]	137	!>
	138	!> @todo test restart
	139	!> enable cyclic_fill
	140	!> implement turbulence generation for e and pt
[2945]	141	!> @todo Input of height-constant length scales via namelist
[2259]	142	!> @note <Enter notes on the module>
	143	!> @bug Height information from input file is not used. Profiles from input
	144	!> must match with current PALM grid.
	145	!> In case of restart, velocity seeds differ from precursor run if a11,
	146	!> a22, or a33 are zero.
	147	!------------------------------------------------------------------------------!
	148	MODULE synthetic_turbulence_generator_mod
	149
	150
	151	USE arrays_3d, &
[4022]	152	ONLY: dzw, &
	153	ddzw, &
	154	drho_air, &
	155	mean_inflow_profiles, &
	156	q, &
[4071]	157	q_init, &
	158	pt, &
	159	pt_init, &
[4022]	160	u, &
	161	u_init, &
	162	v, &
	163	v_init, &
	164	w, &
	165	zu, &
	166	zw
[2259]	167
[3274]	168	USE basic_constants_and_equations_mod, &
[4022]	169	ONLY: g, &
	170	kappa, &
	171	pi
[2259]	172
	173	USE control_parameters, &
[4022]	174	ONLY: bc_lr, &
	175	bc_ns, &
	176	child_domain, &
	177	coupling_char, &
	178	debug_output_timestep, &
	179	dt_3d, &
	180	e_init, &
[4071]	181	humidity, &
[3885]	182	initializing_actions, &
[4022]	183	intermediate_timestep_count, &
	184	intermediate_timestep_count_max, &
	185	length, &
[3885]	186	message_string, &
[4022]	187	nesting_offline, &
[4071]	188	neutral, &
[3885]	189	num_mean_inflow_profiles, &
[4309]	190	random_generator, &
[4022]	191	rans_mode, &
	192	restart_string, &
	193	syn_turb_gen, &
	194	time_since_reference_point, &
	195	turbulent_inflow
[4438]	196
	197	USE cpulog, &
	198	ONLY: cpu_log, &
	199	log_point_s
	200
[4022]	201	USE grid_variables, &
	202	ONLY: ddx, &
	203	ddy, &
	204	dx, &
	205	dy
[2259]	206
	207	USE indices, &
[4022]	208	ONLY: nbgp, &
	209	nz, &
	210	nzb, &
	211	nzt, &
	212	nx, &
	213	nxl, &
	214	nxlu, &
	215	nxr, &
	216	ny, &
	217	nys, &
	218	nysv, &
	219	nyn, &
[4346]	220	wall_flags_total_0
[2259]	221
	222	USE kinds
	223
[2967]	224	#if defined( __parallel ) && !defined( __mpifh )
[2259]	225	USE MPI
[2841]	226	#endif
[2259]	227
[3347]	228	USE nesting_offl_mod, &
[4022]	229	ONLY: nesting_offl_calc_zi, &
	230	zi_ribulk
[3347]	231
[2259]	232	USE pegrid, &
[4022]	233	ONLY: comm1dx, &
	234	comm1dy, &
	235	comm2d, &
	236	ierr, &
	237	myidx, &
	238	myidy, &
	239	pdims
[4438]	240
[4022]	241	USE pmc_interface, &
	242	ONLY : rans_mode_parent
[4438]	243
	244	USE random_generator_parallel, &
	245	ONLY: init_parallel_random_generator, &
	246	random_dummy, &
[4309]	247	random_number_parallel, &
[4438]	248	random_seed_parallel
[2259]	249
	250	USE transpose_indices, &
[4022]	251	ONLY: nzb_x, &
	252	nzt_x
[2259]	253
[4438]	254	USE surface_mod, &
	255	ONLY: surf_def_h, &
	256	surf_lsm_h, &
	257	surf_usm_h
[2259]	258
	259	IMPLICIT NONE
	260
[2967]	261	#if defined( __parallel ) && defined( __mpifh )
[2841]	262	INCLUDE "mpif.h"
	263	#endif
	264
[3182]	265
[3347]	266	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	267	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	268	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[4438]	269	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
	270	!< is distributed over several processes
[2259]	271
[3038]	272	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	273	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	274	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	275	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4438]	276	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
[3038]	277	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	278	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	279	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	280	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4309]	281	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	282	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	283	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	284	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[2259]	285
[4022]	286	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	287	!< required for bias correction of imposed perturbations
	288	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	289	!< required for bias correction of imposed perturbations
	290
[3347]	291	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	292	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	293	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	294	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
	295	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	296	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	297	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	298	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	299	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	300	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	301	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	302	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	303	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	304
[4438]	305	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	306	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	307	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	308	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
	309
[4022]	310	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	311	!< scales above the boundary layer
	312	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	313	!< one length scale above ABL top
	314	REAL(wp) :: d_l !< blend_coeff/length_scale
	315	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	316	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
[4438]	317	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
[3347]	318	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	319	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	320	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	321	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	322	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	323
[4022]	324	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	325
[4022]	326
[3347]	327	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	328	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	329	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	330	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	331	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	332	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	333
	334	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	335	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	336	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	337	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	338	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	339	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	340	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	341	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	342	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	343
[3347]	344	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	345	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	346	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	347	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	348	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	349	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	350	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	351	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	352	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	353	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	354	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	355	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	356	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	357	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	365
	366	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	367	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	368
	369	!
	370	!-- PALM interfaces:
[3347]	371	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	372	INTERFACE stg_adjust
	373	MODULE PROCEDURE stg_adjust
	374	END INTERFACE stg_adjust
	375	!
[2259]	376	!-- Input parameter checks to be done in check_parameters
	377	INTERFACE stg_check_parameters
	378	MODULE PROCEDURE stg_check_parameters
	379	END INTERFACE stg_check_parameters
	380
	381	!
	382	!-- Calculate filter functions
	383	INTERFACE stg_filter_func
	384	MODULE PROCEDURE stg_filter_func
	385	END INTERFACE stg_filter_func
	386
	387	!
[2938]	388	!-- Generate velocity seeds at south and north domain boundary
	389	INTERFACE stg_generate_seed_xz
	390	MODULE PROCEDURE stg_generate_seed_xz
	391	END INTERFACE stg_generate_seed_xz
	392	!
	393	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	394	INTERFACE stg_generate_seed_yz
	395	MODULE PROCEDURE stg_generate_seed_yz
	396	END INTERFACE stg_generate_seed_yz
	397
	398	!
	399	!-- Output of information to the header file
	400	INTERFACE stg_header
	401	MODULE PROCEDURE stg_header
	402	END INTERFACE stg_header
	403
	404	!
	405	!-- Initialization actions
	406	INTERFACE stg_init
	407	MODULE PROCEDURE stg_init
	408	END INTERFACE stg_init
	409
	410	!
	411	!-- Main procedure of synth. turb. gen.
	412	INTERFACE stg_main
	413	MODULE PROCEDURE stg_main
	414	END INTERFACE stg_main
	415
	416	!
	417	!-- Reading of NAMELIST parameters
	418	INTERFACE stg_parin
	419	MODULE PROCEDURE stg_parin
	420	END INTERFACE stg_parin
	421
	422	!
	423	!-- Reading of parameters for restart runs
[2894]	424	INTERFACE stg_rrd_global
	425	MODULE PROCEDURE stg_rrd_global
	426	END INTERFACE stg_rrd_global
[2259]	427
	428	!
	429	!-- Writing of binary output for restart runs
[2894]	430	INTERFACE stg_wrd_global
	431	MODULE PROCEDURE stg_wrd_global
	432	END INTERFACE stg_wrd_global
[2259]	433
	434	SAVE
	435
	436	PRIVATE
	437
	438	!
	439	!-- Public interfaces
[3347]	440	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	441	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	442
	443	!
	444	!-- Public variables
[3347]	445	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	446	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	447	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	448
	449
	450	CONTAINS
	451
	452
	453	!------------------------------------------------------------------------------!
	454	! Description:
	455	! ------------
	456	!> Check parameters routine for synthetic turbulence generator
	457	!------------------------------------------------------------------------------!
	458	SUBROUTINE stg_check_parameters
	459
[3182]	460	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	461	nesting_offline ) THEN
[3376]	462	message_string = 'Synthetic turbulence generator is required ' // &
	463	'if offline nesting is applied and PALM operates ' // &
	464	'in LES mode.'
	465	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	466	ENDIF
	467
[3182]	468	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	469	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	470	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	471	'when nesting is applied and parent operates in ' // &
	472	'RANS-mode but current child in LES mode.'
[3376]	473	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	474	ENDIF
	475
[2776]	476	IF ( use_syn_turb_gen ) THEN
[2259]	477
[3579]	478	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	479	.NOT. rans_mode_parent ) THEN
	480	message_string = 'Using synthetic turbulence generator ' // &
	481	'is not allowed in LES-LES nesting.'
	482	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	483
	484	ENDIF
	485
	486	IF ( child_domain .AND. rans_mode .AND. &
	487	rans_mode_parent ) THEN
	488	message_string = 'Using synthetic turbulence generator ' // &
	489	'is not allowed in RANS-RANS nesting.'
	490	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	491
	492	ENDIF
	493
[3182]	494	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	495
[2938]	496	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	497	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	498	message_string = 'Using synthetic turbulence generator ' // &
[3579]	499	'requires %initializing_actions = ' // &
	500	'"set_constant_profiles" or "read_restart_data"' //&
	501	', if not offline nesting is applied.'
[2938]	502	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	503	ENDIF
	504
	505	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	506	message_string = 'Using synthetic turbulence generator ' // &
[3347]	507	'requires &bc_lr = "dirichlet/radiation", ' // &
	508	'if not offline nesting is applied.'
[2938]	509	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	510	ENDIF
	511	IF ( bc_ns /= 'cyclic' ) THEN
	512	message_string = 'Using synthetic turbulence generator ' // &
[3579]	513	'requires &bc_ns = "cyclic", ' // &
[3347]	514	'if not offline nesting is applied.'
[2938]	515	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	516	ENDIF
	517
[2259]	518	ENDIF
	519
	520	IF ( turbulent_inflow ) THEN
	521	message_string = 'Using synthetic turbulence generator ' // &
[2938]	522	'in combination &with turbulent_inflow = .T. '// &
	523	'is not allowed'
[2259]	524	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	525	ENDIF
[4309]	526	!
	527	!-- Synthetic turbulence generator requires the parallel random generator
	528	IF ( random_generator /= 'random-parallel' ) THEN
	529	message_string = 'Using synthetic turbulence generator ' // &
	530	'requires random_generator = random-parallel.'
	531	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	532	ENDIF
[2259]	533
	534	ENDIF
	535
	536	END SUBROUTINE stg_check_parameters
	537
	538
	539	!------------------------------------------------------------------------------!
	540	! Description:
	541	! ------------
	542	!> Header output for synthetic turbulence generator
	543	!------------------------------------------------------------------------------!
	544	SUBROUTINE stg_header ( io )
	545
	546	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	547
	548	!
	549	!-- Write synthetic turbulence generator Header
	550	WRITE( io, 1 )
[2776]	551	IF ( use_syn_turb_gen ) THEN
[2259]	552	WRITE( io, 2 )
	553	ELSE
	554	WRITE( io, 3 )
	555	ENDIF
[3347]	556
	557	IF ( parametrize_inflow_turbulence ) THEN
	558	WRITE( io, 4 ) dt_stg_adjust
	559	ELSE
	560	WRITE( io, 5 )
	561	ENDIF
[2259]	562
	563	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	564	' ------------------------------------------'/)
[3347]	565	2 FORMAT (' synthetic turbulence generator is switched on')
	566	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	567	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	568	5 FORMAT (' imposed turbulence is read from file' )
[2259]	569
	570	END SUBROUTINE stg_header
	571
	572
	573	!------------------------------------------------------------------------------!
	574	! Description:
	575	! ------------
	576	!> Initialization of the synthetic turbulence generator
	577	!------------------------------------------------------------------------------!
	578	SUBROUTINE stg_init
	579
[3347]	580	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	581
[2669]	582	#if defined( __parallel )
[2259]	583	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	584	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	585	#endif
[2259]	586
[2938]	587	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	588	INTEGER(iwp) :: j !> loop index
	589	INTEGER(iwp) :: k !< index
	590	INTEGER(iwp) :: newtype !< dummy MPI type
	591	INTEGER(iwp) :: realsize !< size of REAL variables
[4309]	592
[4022]	593	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	594	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	595	!
	596	!-- Dummy variables used for reading profiles
	597	REAL(wp) :: d1 !< u profile
	598	REAL(wp) :: d2 !< v profile
	599	REAL(wp) :: d3 !< w profile
	600	REAL(wp) :: d5 !< e profile
	601	REAL(wp) :: luy !< length scale for u in y direction
	602	REAL(wp) :: luz !< length scale for u in z direction
	603	REAL(wp) :: lvy !< length scale for v in y direction
	604	REAL(wp) :: lvz !< length scale for v in z direction
	605	REAL(wp) :: lwy !< length scale for w in y direction
	606	REAL(wp) :: lwz !< length scale for w in z direction
[3038]	607	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[2259]	608	REAL(wp) :: zz !< height
	609
[2938]	610
[2259]	611	#if defined( __parallel )
	612	CALL MPI_BARRIER( comm2d, ierr )
	613	#endif
[4438]	614	!
	615	!-- Create mpi-datatypes for exchange in case of non-local but distributed
	616	!-- computation of the velocity seeds. This option is useful in
	617	!-- case large turbulent length scales are presentm, where the computational
	618	!-- effort becomes large and need to be parallelized. For parametrized
	619	!-- turbulence the length scales are small and computing the velocity seeds
	620	!-- locally is faster (no overhead by communication).
	621	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	622	#if defined( __parallel )
[4438]	623	!
	624	!-- Determine processor decomposition of z-axis along x- and y-direction
	625	nnz = nz / pdims(1)
	626	nzb_x_stg = 1 + myidx * INT( nnz )
	627	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
	628
	629	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
	630	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
	631
	632	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	633	.AND. .NOT. rans_mode ) ) THEN
	634	nnz = nz / pdims(2)
	635	nzb_y_stg = 1 + myidy * INT( nnz )
	636	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
	637
	638	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
	639	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	640	ENDIF
	641
	642	!
	643	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	644	!-- velocity seeds
	645	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	646	extent = 1 * realsize
	647	!
	648	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	649	!-- layer
	650	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
	651	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
	652	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	653	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	654	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	655	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	656
	657	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	658	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
	659	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	660	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	661	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	662	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	663
[2938]	664	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	665	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
	666
	667	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	668	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
	669
	670	DO j = 1, pdims(1)
	671	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	672	ENDDO
[4438]	673	!
	674	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	675	!-- layer
	676	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	677	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	678	.AND. .NOT. rans_mode ) ) THEN
	679	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	680	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	681	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	682	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	683	CALL MPI_TYPE_FREE( newtype, ierr )
	684
	685	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	686	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	687	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	688	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	689	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	690	CALL MPI_TYPE_FREE( newtype, ierr )
	691
	692	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	693	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	694
	695	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	696	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	697
	698	DO j = 1, pdims(2)
	699	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	700	ENDDO
	701
	702	ENDIF
[2938]	703	ENDIF
	704
[2669]	705	#endif
[2259]	706	!
[4071]	707	!-- Allocate required arrays.
	708	!-- In case no offline nesting or self nesting is used, the arrary
	709	!-- mean_inflow profiles is required. Check if it is already allocated, else
	710	!-- allocate and initialize it appropriately. Note, in case turbulence and
	711	!-- inflow information is read from file, mean_inflow_profiles is already
	712	!-- allocated and initialized appropriately.
[3347]	713	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	714	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	715	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	716	mean_inflow_profiles = 0.0_wp
	717	mean_inflow_profiles(:,1) = u_init
	718	mean_inflow_profiles(:,2) = v_init
	719	!
	720	!-- Even though potential temperature and humidity are not perturbed,
	721	!-- they need to be initialized appropriately.
	722	IF ( .NOT. neutral ) &
	723	mean_inflow_profiles(:,4) = pt_init
	724	IF ( humidity ) &
	725	mean_inflow_profiles(:,6) = q_init
	726	ENDIF
[3347]	727	ENDIF
[2259]	728
[3347]	729	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	730	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	731	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	732	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	733	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	734	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	735	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	736	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	737
[4438]	738	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	739	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	740	dist_xz = 0.0_wp
	741	dist_yz = 0.0_wp
	742	!
[2259]	743	!-- Read inflow profile
	744	!-- Height levels of profiles in input profile is as follows:
	745	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	746	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	747	!-- WARNING: zz is not used at the moment
[2938]	748	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	749	EXIST = file_stg_exist )
[2259]	750
[2938]	751	IF ( file_stg_exist ) THEN
[2259]	752
[2938]	753	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	754	FORM='FORMATTED')
	755	!
	756	!-- Skip header
	757	READ( 90, * )
[2259]	758
[3182]	759	DO k = nzb+1, nzt+1
[2938]	760	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	761	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	762	d1, d2, d3, d5
	763
[2259]	764	!
[3182]	765	!-- Convert length scales from meter to number of grid points.
[2938]	766	nuy(k) = INT( luy * ddy )
[3182]	767	nuz(k) = INT( luz * ddzw(k) )
[2938]	768	nvy(k) = INT( lvy * ddy )
[3182]	769	nvz(k) = INT( lvz * ddzw(k) )
[2938]	770	nwy(k) = INT( lwy * ddy )
[3182]	771	nwz(k) = INT( lwz * ddzw(k) )
[2938]	772	!
	773	!-- Workaround, assume isotropic turbulence
	774	nwx(k) = nwy(k)
	775	nvx(k) = nvy(k)
	776	nux(k) = nuy(k)
	777	!
	778	!-- Save Mean inflow profiles
	779	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	780	mean_inflow_profiles(k,1) = d1
	781	mean_inflow_profiles(k,2) = d2
	782	! mean_inflow_profiles(k,4) = d4
	783	mean_inflow_profiles(k,5) = d5
	784	ENDIF
	785	ENDDO
[3182]	786	!
	787	!-- Set lenght scales at surface grid point
	788	nuy(nzb) = nuy(nzb+1)
	789	nuz(nzb) = nuz(nzb+1)
	790	nvy(nzb) = nvy(nzb+1)
	791	nvz(nzb) = nvz(nzb+1)
	792	nwy(nzb) = nwy(nzb+1)
	793	nwz(nzb) = nwz(nzb+1)
	794
[2938]	795	CLOSE( 90 )
[3347]	796	!
	797	!-- Calculate coefficient matrix from Reynolds stress tensor
	798	!-- (Lund rotation)
	799	CALL calc_coeff_matrix
	800	!
	801	!-- No information about turbulence and its length scales are available.
	802	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	803	!-- Set flag which indicates that turbulence is parametrized, which is done
	804	!-- later when energy-balance models are already initialized. This is
	805	!-- because the STG needs information about surface properties such as
	806	!-- roughness to build 'realistic' turbulence profiles.
[2938]	807	ELSE
[2259]	808	!
[4022]	809	!-- Define length scale for the imposed turbulence, which is defined as
	810	!-- 8 times the minimum grid spacing
[4438]	811	length_scale = 30.0_wp * MIN( dx, dy, MINVAL( dzw ) ) !8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
[4022]	812	!
	813	!-- Define constant to gradually decrease length scales and Reynolds stress
	814	!-- above ABL top. Assure that no zero length scales are used.
	815	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	816	!
[3347]	817	!-- Set flag indicating that turbulence is parametrized
	818	parametrize_inflow_turbulence = .TRUE.
	819	!
[4022]	820	!-- In case of dirichlet inflow boundary conditions only at one lateral
	821	!-- boundary, i.e. in the case no offline or self nesting is applied but
	822	!-- synthetic turbulence shall be parametrized nevertheless, the
	823	!-- boundary-layer depth need to determined first.
	824	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	825	CALL nesting_offl_calc_zi
	826	!
[3347]	827	!-- Determine boundary-layer depth, which is used to initialize lenght
	828	!-- scales
	829	CALL calc_scaling_variables
	830	!
	831	!-- Initialize lenght and time scales, which in turn are used
	832	!-- to initialize the filter functions.
	833	CALL calc_length_and_time_scale
[3891]	834	!
	835	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	836	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	837	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	838	!-- friction velocity and velocity scale.
	839	CALL parametrize_reynolds_stress
	840	!
	841	!-- Calculate coefficient matrix from Reynolds stress tensor
	842	!-- (Lund rotation)
	843	CALL calc_coeff_matrix
[3347]	844
[2938]	845	ENDIF
	846
[2259]	847	!
[3347]	848	!-- Assign initial profiles. Note, this is only required if turbulent
	849	!-- inflow from the left is desired, not in case of any of the
	850	!-- nesting (offline or self nesting) approaches.
[3182]	851	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	852	u_init = mean_inflow_profiles(:,1)
	853	v_init = mean_inflow_profiles(:,2)
	854	!pt_init = mean_inflow_profiles(:,4)
	855	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	856	ENDIF
[3347]	857
[2938]	858	!
[2259]	859	!-- Define the size of the filter functions and allocate them.
[4438]	860	mergp = 0
[2259]	861
	862	! arrays must be large enough to cover the largest length scale
	863	DO k = nzb, nzt+1
[2938]	864	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	865	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	866	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[4438]	867	IF ( j > mergp ) mergp = j
[2259]	868	ENDDO
	869
[4438]	870	! mergp = 2 * mergp
	871	! mergp = mergp
[2259]	872
[4438]	873	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
	874	buy(-mergp:mergp,nzb:nzt+1), &
	875	buz(-mergp:mergp,nzb:nzt+1), &
	876	bvx(-mergp:mergp,nzb:nzt+1), &
	877	bvy(-mergp:mergp,nzb:nzt+1), &
	878	bvz(-mergp:mergp,nzb:nzt+1), &
	879	bwx(-mergp:mergp,nzb:nzt+1), &
	880	bwy(-mergp:mergp,nzb:nzt+1), &
	881	bwz(-mergp:mergp,nzb:nzt+1) )
[2259]	882
	883	!
[2938]	884	!-- Allocate velocity seeds for turbulence at xz-layer
[4438]	885	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	886	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	887	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	888
[2938]	889	!
	890	!-- Allocate velocity seeds for turbulence at yz-layer
[4438]	891	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	892	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	893	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	894
[2938]	895	fu_xz = 0.0_wp
	896	fuo_xz = 0.0_wp
	897	fv_xz = 0.0_wp
	898	fvo_xz = 0.0_wp
	899	fw_xz = 0.0_wp
	900	fwo_xz = 0.0_wp
	901
	902	fu_yz = 0.0_wp
	903	fuo_yz = 0.0_wp
	904	fv_yz = 0.0_wp
	905	fvo_yz = 0.0_wp
	906	fw_yz = 0.0_wp
	907	fwo_yz = 0.0_wp
	908
[2259]	909	!
	910	!-- Create filter functions
[2938]	911	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	912	CALL stg_filter_func( nuy, buy ) !filter uy
	913	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	914	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	915	CALL stg_filter_func( nvy, bvy ) !filter vy
	916	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	917	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	918	CALL stg_filter_func( nwy, bwy ) !filter wy
	919	CALL stg_filter_func( nwz, bwz ) !filter wz
	920
	921	#if defined( __parallel )
	922	CALL MPI_BARRIER( comm2d, ierr )
	923	#endif
	924
	925	!
[2938]	926	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	927	! time step.
	928	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	929	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	930	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	931	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	932
	933	IF ( myidx == id_stg_left ) i = -1
	934	IF ( myidx == id_stg_right ) i = nxr+1
	935
[4438]	936	DO j = nys, nyn
[2259]	937	DO k = nzb, nzt+1
[4332]	938	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	939	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	940	ELSE
[4332]	941	fu_yz(k,j) = 10E-8_wp
[2259]	942	ENDIF
	943
[4332]	944	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	945	fv_yz(k,j) = ( v(k,j,i) - &
	946	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	947	ELSE
[4332]	948	fv_yz(k,j) = 10E-8_wp
[2259]	949	ENDIF
	950
[4332]	951	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	952	fw_yz(k,j) = ( w(k,j,i) - &
	953	a31(k) * fu_yz(k,j) - a32(k) * &
	954	fv_yz(k,j) ) / a33(k)
[2259]	955	ELSE
[4332]	956	fw_yz(k,j) = 10E-8_wp
[2259]	957	ENDIF
	958	ENDDO
	959	ENDDO
	960	ENDIF
[3900]	961
	962	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	963
	964	IF ( myidy == id_stg_south ) j = -1
	965	IF ( myidy == id_stg_north ) j = nyn+1
	966
[4438]	967	DO i = nxl, nxr
[3900]	968	DO k = nzb, nzt+1
[4335]	969	!
	970	!-- In case the correlation coefficients are very small, the
	971	!-- velocity seeds may become very large finally creating
	972	!-- numerical instabilities in the synthetic turbulence generator.
	973	!-- Empirically, a value of 10E-8 seems to be sufficient.
[4332]	974	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	975	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	976	ELSE
[4332]	977	fu_xz(k,i) = 10E-8_wp
[3900]	978	ENDIF
	979
[4332]	980	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	981	fv_xz(k,i) = ( v(k,j,i) - &
	982	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	983	ELSE
[4332]	984	fv_xz(k,i) = 10E-8_wp
[3900]	985	ENDIF
	986
[4332]	987	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	988	fw_xz(k,i) = ( w(k,j,i) - &
	989	a31(k) * fu_xz(k,i) - &
	990	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	991	ELSE
[4332]	992	fw_xz(k,i) = 10E-8_wp
[3900]	993	ENDIF
	994
	995	ENDDO
	996	ENDDO
	997	ENDIF
[2259]	998	ENDIF
[4022]	999	!
	1000	!-- Count the number of non-topography grid points at the boundaries where
	1001	!-- perturbations are imposed. This number is later used for bias corrections
	1002	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	1003	!-- due to the asymetry of u and v along x and y direction, respectively,
	1004	!-- different cases must be distinguished.
	1005	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1006	!
	1007	!-- Number of grid points where perturbations are imposed on u
	1008	IF ( myidx == id_stg_left ) i = nxl
	1009	IF ( myidx == id_stg_right ) i = nxr+1
	1010
	1011	nr_non_topo_yz_l(1) = SUM( &
	1012	MERGE( 1, 0, &
[4346]	1013	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1014	!
	1015	!-- Number of grid points where perturbations are imposed on v and w
	1016	IF ( myidx == id_stg_left ) i = nxl-1
	1017	IF ( myidx == id_stg_right ) i = nxr+1
	1018
	1019	nr_non_topo_yz_l(2) = SUM( &
	1020	MERGE( 1, 0, &
[4346]	1021	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1022	nr_non_topo_yz_l(3) = SUM( &
	1023	MERGE( 1, 0, &
[4346]	1024	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1025
	1026	#if defined( __parallel )
	1027	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	1028	MPI_SUM, comm1dy, ierr )
	1029	#else
	1030	nr_non_topo_yz = nr_non_topo_yz_l
	1031	#endif
	1032	ENDIF
	1033
	1034	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1035	!
	1036	!-- Number of grid points where perturbations are imposed on v
	1037	IF ( myidy == id_stg_south ) j = nys
	1038	IF ( myidy == id_stg_north ) j = nyn+1
	1039
	1040	nr_non_topo_xz_l(2) = SUM( &
	1041	MERGE( 1, 0, &
[4346]	1042	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1043	!
	1044	!-- Number of grid points where perturbations are imposed on u and w
	1045	IF ( myidy == id_stg_south ) j = nys-1
	1046	IF ( myidy == id_stg_north ) j = nyn+1
	1047
	1048	nr_non_topo_xz_l(1) = SUM( &
	1049	MERGE( 1, 0, &
[4346]	1050	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1051	nr_non_topo_xz_l(3) = SUM( &
	1052	MERGE( 1, 0, &
[4346]	1053	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1054
	1055	#if defined( __parallel )
	1056	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1057	MPI_SUM, comm1dx, ierr )
	1058	#else
	1059	nr_non_topo_xz = nr_non_topo_xz_l
	1060	#endif
	1061	ENDIF
[4438]	1062	!
	1063	!-- Initialize random number generator at xz- and yz-layers. Random numbers
	1064	!-- are initialized at each core. In case there is only inflow from the left,
	1065	!-- it is sufficient to generate only random numbers for the yz-layer, else
	1066	!-- random numbers for the xz-layer are also required.
	1067	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
	1068	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
	1069	id_rand_yz = 0
	1070	seq_rand_yz = 0
[2259]	1071
[4438]	1072	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
	1073	id_rand_yz, seq_rand_yz )
[4022]	1074
[4438]	1075	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1076	.AND. .NOT. rans_mode ) ) THEN
	1077	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
	1078	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
	1079	id_rand_xz = 0
	1080	seq_rand_xz = 0
	1081
	1082	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
	1083	id_rand_xz, seq_rand_xz )
	1084	ENDIF
	1085
	1086
	1087
[2259]	1088	END SUBROUTINE stg_init
	1089
	1090
	1091	!------------------------------------------------------------------------------!
	1092	! Description:
	1093	! ------------
	1094	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1095	!> (Xie and Castro, 2008)
	1096	!------------------------------------------------------------------------------!
	1097	SUBROUTINE stg_filter_func( nxx, bxx )
	1098
	1099	INTEGER(iwp) :: k !< loop index
	1100	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1101	INTEGER(iwp) :: nf !< index for length scales
	1102
	1103	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1104	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1105
[4438]	1106	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
[2259]	1107
[4438]	1108	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1109
	1110
	1111	bxx = 0.0_wp
	1112
	1113	DO k = nzb, nzt+1
	1114	bdenom = 0.0_wp
	1115	n_k = nxx(k)
	1116	IF ( n_k /= 0 ) THEN
	1117
	1118	!
	1119	!-- ( Eq.10 )^2
[4438]	1120	DO nf = -n_k, n_k
[2259]	1121	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1122	ENDDO
	1123
	1124	!
	1125	!-- ( Eq.9 )
	1126	bdenom = SQRT( bdenom )
[4438]	1127	DO nf = -n_k, n_k
[2259]	1128	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1129	ENDDO
	1130	ENDIF
	1131	ENDDO
	1132
[3347]	1133	END SUBROUTINE stg_filter_func
[2259]	1134
	1135
	1136	!------------------------------------------------------------------------------!
	1137	! Description:
	1138	! ------------
	1139	!> Parin for &stg_par for synthetic turbulence generator
	1140	!------------------------------------------------------------------------------!
	1141	SUBROUTINE stg_parin
	1142
	1143	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1144
	1145
[4438]	1146	NAMELIST /stg_par/ dt_stg_adjust, &
	1147	dt_stg_call, &
	1148	use_syn_turb_gen, &
	1149	compute_velocity_seeds_local
[2259]	1150
	1151	line = ' '
	1152	!
	1153	!-- Try to find stg package
	1154	REWIND ( 11 )
	1155	line = ' '
	1156	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1157	READ ( 11, '(A)', END=20 ) line
[2259]	1158	ENDDO
	1159	BACKSPACE ( 11 )
	1160
	1161	!
	1162	!-- Read namelist
[3246]	1163	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1164
	1165	!
	1166	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1167	!-- on
[2776]	1168	syn_turb_gen = .TRUE.
[3246]	1169	GOTO 20
[2259]	1170
[3246]	1171	10 BACKSPACE( 11 )
[3248]	1172	READ( 11 , '(A)') line
	1173	CALL parin_fail_message( 'stg_par', line )
[2563]	1174
[3246]	1175	20 CONTINUE
[2259]	1176
	1177	END SUBROUTINE stg_parin
	1178
	1179
	1180	!------------------------------------------------------------------------------!
	1181	! Description:
	1182	! ------------
[2894]	1183	!> This routine reads the respective restart data.
[2576]	1184	!------------------------------------------------------------------------------!
[2894]	1185	SUBROUTINE stg_rrd_global( found )
[2576]	1186
[3044]	1187	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1188
[2894]	1189	found = .TRUE.
[2259]	1190
[3038]	1191
[2894]	1192	SELECT CASE ( restart_string(1:length) )
[4022]	1193
	1194	CASE ( 'time_stg_adjust' )
	1195	READ ( 13 ) time_stg_adjust
	1196
	1197	CASE ( 'time_stg_call' )
	1198	READ ( 13 ) time_stg_call
	1199
[2894]	1200	CASE ( 'use_syn_turb_gen' )
	1201	READ ( 13 ) use_syn_turb_gen
[2259]	1202
[2894]	1203	CASE DEFAULT
[2259]	1204
[3038]	1205	found = .FALSE.
[2259]	1206
[2894]	1207	END SELECT
[2259]	1208
	1209
[2894]	1210	END SUBROUTINE stg_rrd_global
[2259]	1211
	1212
	1213	!------------------------------------------------------------------------------!
	1214	! Description:
	1215	! ------------
	1216	!> This routine writes the respective restart data.
	1217	!------------------------------------------------------------------------------!
[2894]	1218	SUBROUTINE stg_wrd_global
[2259]	1219
[4022]	1220	CALL wrd_write_string( 'time_stg_adjust' )
	1221	WRITE ( 14 ) time_stg_adjust
	1222
	1223	CALL wrd_write_string( 'time_stg_call' )
	1224	WRITE ( 14 ) time_stg_call
[2259]	1225
[2894]	1226	CALL wrd_write_string( 'use_syn_turb_gen' )
	1227	WRITE ( 14 ) use_syn_turb_gen
[2259]	1228
	1229
[2894]	1230	END SUBROUTINE stg_wrd_global
[2259]	1231
[2894]	1232
[2259]	1233	!------------------------------------------------------------------------------!
	1234	! Description:
	1235	! ------------
	1236	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1237	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1238	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1239	!> (Lund, 1998).
	1240	!------------------------------------------------------------------------------!
	1241	SUBROUTINE stg_main
	1242
[2938]	1243	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1244	INTEGER(iwp) :: j !< loop index in y-direction
	1245	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1246
	1247	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1248
	1249	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1250
	1251	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1252
[3987]	1253	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1254	!
	1255	!-- Calculate time step which is needed for filter functions
[3775]	1256	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1257	!
[4022]	1258	!-- Check if synthetic turbulence generator needs to be called and new
	1259	!-- perturbations need to be created or if old disturbances can be imposed
	1260	!-- again.
	1261	IF ( time_stg_call >= dt_stg_call .AND. &
	1262	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1263	stg_call = .TRUE.
	1264	ELSE
	1265	stg_call = .FALSE.
	1266	ENDIF
	1267	!
[2259]	1268	!-- Initial value of fu, fv, fw
[3646]	1269	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1270	!
	1271	!-- Generate turbulence at the left and right boundary. Random numbers
	1272	!-- for the yz-planes at the left/right boundary are generated by the
	1273	!-- left-sided mpi ranks only. After random numbers are calculated, they
	1274	!-- are distributed to all other mpi ranks in the model, so that the
	1275	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
	1276	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
	1277	!-- that the left- and the right-sided lateral boundary have the same initial
	1278	!-- seeds.
	1279	!-- Note, in case of inflow from the right only, only turbulence at the left
	1280	!-- boundary is required.
	1281	IF ( .NOT. ( nesting_offline .OR. &
	1282	( child_domain .AND. rans_mode_parent &
	1283	.AND. .NOT. rans_mode ) ) ) THEN
	1284	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1285	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1286	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1287	ELSE
	1288	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
	1289	id_stg_left, id_stg_right )
	1290	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
	1291	id_stg_left, id_stg_right )
	1292	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
	1293	id_stg_left, id_stg_right )
[2938]	1294	!
[4309]	1295	!-- Generate turbulence at the south and north boundary. Random numbers
	1296	!-- for the xz-planes at the south/north boundary are generated by the
	1297	!-- south-sided mpi ranks only. Please see also comment above.
	1298	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
	1299	id_stg_south, id_stg_north )
	1300	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
	1301	id_stg_south, id_stg_north )
	1302	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
	1303	id_stg_south, id_stg_north )
[2938]	1304	ENDIF
[2259]	1305	velocity_seed_initialized = .TRUE.
	1306	ENDIF
	1307	!
[4309]	1308	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
	1309	!-- seeds are only required at the left boundary, while in case of offline
	1310	!-- nesting or RANS-LES nesting velocity seeds are required also at the
	1311	!-- right, south and north boundaries.
[4022]	1312	IF ( stg_call ) THEN
[4309]	1313	IF ( .NOT. ( nesting_offline .OR. &
	1314	( child_domain .AND. rans_mode_parent &
	1315	.AND. .NOT. rans_mode ) ) ) THEN
	1316	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1317	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1318	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1319
	1320	ELSE
	1321	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
	1322	id_stg_left, id_stg_right )
	1323	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
	1324	id_stg_left, id_stg_right )
	1325	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
	1326	id_stg_left, id_stg_right )
	1327
	1328	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
	1329	id_stg_south, id_stg_north )
	1330	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
	1331	id_stg_south, id_stg_north )
	1332	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
	1333	id_stg_south, id_stg_north )
[4022]	1334	ENDIF
[2938]	1335	ENDIF
[3347]	1336
[2938]	1337	!
[4309]	1338	!-- Turbulence generation at left and/or right boundary
[2938]	1339	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1340	!
[4022]	1341	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1342	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1343	!-- imposed
	1344	IF ( stg_call ) THEN
	1345
[4438]	1346	DO j = nys, nyn
[4022]	1347	DO k = nzb, nzt + 1
	1348	!
	1349	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1350	IF ( tu(k) == 0.0_wp ) THEN
	1351	fu_yz(k,j) = fuo_yz(k,j)
	1352	ELSE
	1353	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1354	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1355	ENDIF
	1356
	1357	IF ( tv(k) == 0.0_wp ) THEN
	1358	fv_yz(k,j) = fvo_yz(k,j)
	1359	ELSE
	1360	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1361	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1362	ENDIF
	1363
	1364	IF ( tw(k) == 0.0_wp ) THEN
	1365	fw_yz(k,j) = fwo_yz(k,j)
	1366	ELSE
	1367	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1368	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1369	ENDIF
	1370	ENDDO
	1371	ENDDO
	1372
	1373	dist_yz(nzb,:,1) = 0.0_wp
	1374	dist_yz(nzb,:,2) = 0.0_wp
	1375	dist_yz(nzb,:,3) = 0.0_wp
	1376
	1377	IF ( myidx == id_stg_left ) i = nxl
	1378	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1379	DO j = nys, nyn
[4022]	1380	DO k = nzb+1, nzt + 1
	1381	!
	1382	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1383	!-- Additional factors are added to improve the variance of v and w
	1384	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1385	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1386	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1387	ENDDO
	1388	ENDDO
[4309]	1389
[4022]	1390	IF ( myidx == id_stg_left ) i = nxl-1
	1391	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1392	DO j = nys, nyn
[4022]	1393	DO k = nzb+1, nzt + 1
	1394	!
	1395	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1396	!-- Additional factors are added to improve the variance of v and w
	1397	!-- experimental test of 1.2
[3347]	1398	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1399	* 1.2_wp ) &
	1400	* ( a21(k) * fu_yz(k,j) &
[4022]	1401	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1402	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1403	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[3347]	1404	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1405	* 1.3_wp ) &
	1406	* ( a31(k) * fu_yz(k,j) &
	1407	+ a32(k) * fv_yz(k,j) &
[4022]	1408	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1409	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1410	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1411	ENDDO
[2259]	1412	ENDDO
[4022]	1413	ENDIF
[2259]	1414	!
	1415	!-- Mass flux correction following Kim et al. (2013)
	1416	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1417	!-- inflow boundary. First, calculate mean value of the imposed
	1418	!-- perturbations at yz boundary.
	1419	!-- Note, this needs to be done only after the last RK3-substep, else
	1420	!-- the boundary values won't be accessed.
	1421	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1422	mc_factor_l = 0.0_wp
	1423	mc_factor = 0.0_wp
	1424	!
	1425	!-- Sum up the original volume flows (with and without perturbations).
	1426	!-- Note, for non-normal components (here v and w) it is actually no
	1427	!-- volume flow.
[2938]	1428	IF ( myidx == id_stg_left ) i = nxl
	1429	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1430
	1431	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1432	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1433	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1434
	1435	IF ( myidx == id_stg_left ) i = nxl-1
	1436	IF ( myidx == id_stg_right ) i = nxr+1
	1437
	1438	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1439	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1440	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1441	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1442	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1443	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1444
[2938]	1445	#if defined( __parallel )
	1446	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1447	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1448	#else
	1449	mc_factor = mc_factor_l
[2938]	1450	#endif
[4022]	1451	!
	1452	!-- Calculate correction factor and force zero mean perturbations.
	1453	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1454
	1455	IF ( myidx == id_stg_left ) i = nxl
	1456	IF ( myidx == id_stg_right ) i = nxr+1
	1457
[4438]	1458	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
[4022]	1459	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1460	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4022]	1461
	1462
	1463	IF ( myidx == id_stg_left ) i = nxl-1
	1464	IF ( myidx == id_stg_right ) i = nxr+1
	1465
[4438]	1466	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
[4022]	1467	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1468	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4022]	1469
[4438]	1470	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
[4022]	1471	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1472	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4022]	1473	!
[2938]	1474	!-- Add disturbances
	1475	IF ( myidx == id_stg_left ) THEN
[4022]	1476	!
	1477	!-- For the left boundary distinguish between mesoscale offline / self
	1478	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1479	!-- case turbulence is imposed on the mean inflow profiles.
	1480	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1481	!
	1482	!-- Add disturbance at the inflow
[4438]	1483	DO j = nys, nyn
[4022]	1484	DO k = nzb, nzt+1
	1485	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1486	dist_yz(k,j,1) ) &
	1487	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1488	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1489	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1490	dist_yz(k,j,2) ) &
	1491	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1492	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1493	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1494	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1495	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1496	ENDDO
[2938]	1497	ENDDO
[4022]	1498	ELSE
	1499
	1500	DO j = nys, nyn
	1501	DO k = nzb+1, nzt
	1502	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1503	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1504	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1505	u(k,j,-1) = u(k,j,0)
	1506	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1507	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1508	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1509	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1510	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1511	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1512	ENDDO
	1513	ENDDO
	1514	ENDIF
[2938]	1515	ENDIF
	1516	IF ( myidx == id_stg_right ) THEN
[3186]	1517	DO j = nys, nyn
[3347]	1518	DO k = nzb+1, nzt
[3186]	1519	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1520	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1521	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
[3186]	1522	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1523	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1524	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
[3186]	1525	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1526	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1527	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1528	ENDDO
	1529	ENDDO
	1530	ENDIF
	1531	ENDIF
	1532	ENDIF
	1533	!
	1534	!-- Turbulence generation at north and south boundary
	1535	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1536	!
[4022]	1537	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1538	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1539	!-- imposed
	1540	IF ( stg_call ) THEN
[4438]	1541	DO i = nxl, nxr
[4022]	1542	DO k = nzb, nzt + 1
	1543	!
	1544	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1545	IF ( tu(k) == 0.0_wp ) THEN
	1546	fu_xz(k,i) = fuo_xz(k,i)
	1547	ELSE
	1548	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1549	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1550	ENDIF
	1551
	1552	IF ( tv(k) == 0.0_wp ) THEN
	1553	fv_xz(k,i) = fvo_xz(k,i)
	1554	ELSE
	1555	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1556	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1557	ENDIF
	1558
	1559	IF ( tw(k) == 0.0_wp ) THEN
	1560	fw_xz(k,i) = fwo_xz(k,i)
	1561	ELSE
	1562	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1563	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1564	ENDIF
	1565	ENDDO
	1566	ENDDO
	1567
	1568
	1569	dist_xz(nzb,:,1) = 0.0_wp
	1570	dist_xz(nzb,:,2) = 0.0_wp
	1571	dist_xz(nzb,:,3) = 0.0_wp
	1572
	1573	IF ( myidy == id_stg_south ) j = nys
	1574	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1575	DO i = nxl, nxr
[4022]	1576	DO k = nzb+1, nzt + 1
	1577	!
	1578	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1579	!-- Additional factors are added to improve the variance of v and w
	1580	!experimental test of 1.2
[3347]	1581	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1582	* 1.2_wp ) &
	1583	* ( a21(k) * fu_xz(k,i) &
[4022]	1584	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1585	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1586	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1587	ENDDO
	1588	ENDDO
	1589
	1590	IF ( myidy == id_stg_south ) j = nys-1
	1591	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1592	DO i = nxl, nxr
[4022]	1593	DO k = nzb+1, nzt + 1
	1594	!
	1595	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1596	!-- Additional factors are added to improve the variance of v and w
	1597	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1598	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1599	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1600
[3347]	1601	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1602	* 1.3_wp ) &
	1603	* ( a31(k) * fu_xz(k,i) &
	1604	+ a32(k) * fv_xz(k,i) &
[4022]	1605	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1606	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1607	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1608	ENDDO
[2938]	1609	ENDDO
[4022]	1610	ENDIF
[3347]	1611
[2938]	1612	!
	1613	!-- Mass flux correction following Kim et al. (2013)
	1614	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1615	!-- inflow boundary. First, calculate mean value of the imposed
	1616	!-- perturbations at yz boundary.
	1617	!-- Note, this needs to be done only after the last RK3-substep, else
	1618	!-- the boundary values won't be accessed.
	1619	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1620	mc_factor_l = 0.0_wp
	1621	mc_factor = 0.0_wp
	1622
	1623	IF ( myidy == id_stg_south ) j = nys
	1624	IF ( myidy == id_stg_north ) j = nyn+1
	1625
	1626	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1627	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1628	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1629
	1630	IF ( myidy == id_stg_south ) j = nys-1
	1631	IF ( myidy == id_stg_north ) j = nyn+1
	1632
	1633	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1634	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1635	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1636	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1637	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1638	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1639
[2938]	1640	#if defined( __parallel )
[4022]	1641	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1642	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1643	#else
	1644	mc_factor = mc_factor_l
[2938]	1645	#endif
[4022]	1646
	1647	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1648
	1649	IF ( myidy == id_stg_south ) j = nys
	1650	IF ( myidy == id_stg_north ) j = nyn+1
	1651
[4438]	1652	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
[4022]	1653	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1654	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4022]	1655
	1656
	1657	IF ( myidy == id_stg_south ) j = nys-1
	1658	IF ( myidy == id_stg_north ) j = nyn+1
	1659
[4438]	1660	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
[4022]	1661	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1662	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4022]	1663
[4438]	1664	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
[4022]	1665	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1666	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4022]	1667	!
	1668	!-- Add disturbances
	1669	IF ( myidy == id_stg_south ) THEN
	1670	DO i = nxl, nxr
	1671	DO k = nzb+1, nzt
	1672	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1673	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1674	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
[4022]	1675	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1676	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1677	BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1678	v(k,-1,i) = v(k,0,i)
	1679	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1680	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1681	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1682	ENDDO
[2938]	1683	ENDDO
[4022]	1684	ENDIF
	1685	IF ( myidy == id_stg_north ) THEN
	1686
	1687	DO i = nxl, nxr
	1688	DO k = nzb+1, nzt
	1689	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1690	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1691	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
[4022]	1692	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1693	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1694	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
[4022]	1695	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1696	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1697	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1698	ENDDO
[2938]	1699	ENDDO
[4022]	1700	ENDIF
[2938]	1701	ENDIF
[2259]	1702	ENDIF
[3347]	1703	!
[4438]	1704	!-- Exchange ghost points.
	1705	CALL exchange_horiz( u, nbgp )
	1706	CALL exchange_horiz( v, nbgp )
	1707	CALL exchange_horiz( w, nbgp )
	1708	!
[3347]	1709	!-- Finally, set time counter for calling STG to zero
[4022]	1710	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1711
[3987]	1712	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1713
[2259]	1714	END SUBROUTINE stg_main
	1715
	1716	!------------------------------------------------------------------------------!
	1717	! Description:
	1718	! ------------
	1719	!> Generate a set of random number rand_it wich is equal on each PE
	1720	!> and calculate the velocity seed f_n.
	1721	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1722	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1723	!> parts are collected to form the full array.
	1724	!------------------------------------------------------------------------------!
[4309]	1725	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1726
[4309]	1727	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1728	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1729	INTEGER(iwp) :: j !< loop index in y-direction
	1730	INTEGER(iwp) :: jj !< loop index in y-direction
	1731	INTEGER(iwp) :: k !< loop index in z-direction
	1732	INTEGER(iwp) :: kk !< loop index in z-direction
	1733	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1734
	1735	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1736	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1737
	1738	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1739	REAL(wp) :: rand_av !< average of random number
	1740	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1741
[4438]	1742	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
	1743	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1744
[4438]	1745	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1746	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
[4309]	1747
	1748	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1749	!
[4309]	1750	!-- Generate random numbers using the parallel random generator.
[2259]	1751	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1752	!-- unit variance. Note, at the end the random number array must be defined
	1753	!-- globally in order to compute the correlation matrices. However,
	1754	!-- the calculation and normalization of random numbers is done locally,
	1755	!-- while the result is later distributed to all processes. Further,
	1756	!-- please note, a set of random numbers is only calculated for the
	1757	!-- left boundary, while the right boundary uses the same random numbers
	1758	!-- and thus also computes the same correlation matrix.
[4438]	1759	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
	1760	rand_it = 0.0_wp
[2259]	1761
	1762	rand_av = 0.0_wp
	1763	rand_sigma_inv = 0.0_wp
[4438]	1764	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1765	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
	1766	KIND=wp )
[4309]	1767	!
[4438]	1768	!-- Compute and normalize random numbers.
	1769	DO j = nys - mergp, nyn + mergp
[4309]	1770	!
[4438]	1771	!-- Put the random seeds at grid point j
	1772	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
	1773	DO k = nzb - mergp, nzt + 1 + mergp
	1774	CALL random_number_parallel( random_dummy )
	1775	rand_it(k,j) = random_dummy
	1776	ENDDO
[4309]	1777	!
[4438]	1778	!-- Get the new random seeds from last call at grid point j
	1779	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1780	ENDDO
[4309]	1781	!
[4438]	1782	!-- For normalization to zero mean, sum-up the global random numers.
	1783	!-- To normalize the global set of random numbers,
	1784	!-- the inner ghost layers mergp must not be summed-up, else
	1785	!-- the random numbers on the ghost layers will be stronger weighted as they
	1786	!-- also occur on the inner subdomains.
	1787	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1788	MERGE( nyn, nyn + mergp, nyn /= ny )
	1789	DO k = nzb - mergp, nzt + 1 + mergp
	1790	rand_av = rand_av + rand_it(k,j)
[2259]	1791	ENDDO
[4438]	1792	ENDDO
	1793
[4309]	1794	#if defined( __parallel )
	1795	!
[4438]	1796	!-- Sum-up the local averages of the random numbers
	1797	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1798	MPI_SUM, comm1dy, ierr )
[4309]	1799	#endif
[4438]	1800	rand_av = rand_av * nyz_inv
[4309]	1801	!
[4438]	1802	!-- Obtain zero mean
	1803	rand_it= rand_it - rand_av
[4309]	1804	!
[4438]	1805	!-- Now, compute the variance
	1806	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1807	MERGE( nyn, nyn + mergp, nyn /= ny )
	1808	DO k = nzb - mergp, nzt + 1 + mergp
	1809	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1810	ENDDO
[4438]	1811	ENDDO
[2259]	1812
[4309]	1813	#if defined( __parallel )
[2259]	1814	!
[4438]	1815	!-- Sum-up the local quadratic averages of the random numbers
	1816	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1817	MPI_SUM, comm1dy, ierr )
[4309]	1818	#endif
	1819	!
[4438]	1820	!-- Compute standard deviation
	1821	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1822	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1823	ELSE
	1824	rand_sigma_inv = 1.0_wp
[4309]	1825	ENDIF
	1826	!
[4438]	1827	!-- Normalize with standard deviation to obtain unit variance
	1828	rand_it = rand_it * rand_sigma_inv
	1829
	1830	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1831	!
[4438]	1832	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	1833	!-- are two options. In the first one, the computation of the seeds is
	1834	!-- distributed to all processes along the communicator comm1dy and
	1835	!-- gathered on the leftmost and, if necessary, on the rightmost process.
	1836	!-- For huge length scales the computational effort can become quite huge
	1837	!-- (it scales with the turbulent length scales), so that gain by parallelization
	1838	!-- exceeds the costs by the subsequent communication.
	1839	!-- In the second option, which performs better when the turbulent length scales
	1840	!-- are parametrized and thus the loops are smaller, the seeds are computed
	1841	!-- locally and no communication is necessary.
	1842	IF ( compute_velocity_seeds_local ) THEN
	1843
	1844	f_n = 0.0_wp
	1845	DO j = nys, nyn
	1846	DO k = nzb, nzt+1
	1847	DO jj = -n_y(k), n_y(k)
	1848	DO kk = -n_z(k), n_z(k)
	1849	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1850	ENDDO
	1851	ENDDO
	1852	ENDDO
[2259]	1853	ENDDO
	1854
[4438]	1855	ELSE
[2259]	1856
[4438]	1857	f_n_l = 0.0_wp
	1858	DO j = nys, nyn
	1859	DO k = nzb_x_stg, nzt_x_stg+1
	1860	DO jj = -n_y(k), n_y(k)
	1861	DO kk = -n_z(k), n_z(k)
	1862	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1863	ENDDO
[2259]	1864	ENDDO
	1865	ENDDO
	1866	ENDDO
	1867	!
[4438]	1868	!-- Gather velocity seeds of full subdomain
	1869	send_count = nzt_x_stg - nzb_x_stg + 1
	1870	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1871
	1872	#if defined( __parallel )
[4309]	1873	!
[4438]	1874	!-- Gather the velocity seed matrix on left boundary mpi ranks.
	1875	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1876	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1877	id_left, comm1dx, ierr )
[4309]	1878	!
[4438]	1879	!-- If required, gather the same velocity seed matrix on right boundary
	1880	!-- mpi ranks (in offline nesting for example).
	1881	IF ( PRESENT( id_right ) ) THEN
	1882	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1883	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1884	id_right, comm1dx, ierr )
	1885	ENDIF
[2259]	1886	#else
[4438]	1887	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[2259]	1888	#endif
	1889
[4438]	1890	ENDIF
[2259]	1891
[4438]	1892	DEALLOCATE( rand_it )
	1893
	1894	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1895
[2259]	1896	END SUBROUTINE stg_generate_seed_yz
	1897
[2938]	1898
	1899	!------------------------------------------------------------------------------!
	1900	! Description:
	1901	! ------------
	1902	!> Generate a set of random number rand_it wich is equal on each PE
	1903	!> and calculate the velocity seed f_n.
	1904	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1905	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1906	!> parts are collected to form the full array.
	1907	!------------------------------------------------------------------------------!
[4309]	1908	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1909
	1910	INTEGER(iwp) :: i !< loop index in x-direction
[4309]	1911	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1912	INTEGER(iwp) :: id_south !< core ids at respective boundaries
[2938]	1913	INTEGER(iwp) :: ii !< loop index in x-direction
	1914	INTEGER(iwp) :: k !< loop index in z-direction
	1915	INTEGER(iwp) :: kk !< loop index in z-direction
	1916	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1917
	1918	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1919	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1920
	1921	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1922	REAL(wp) :: rand_av !< average of random number
	1923	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1924
[4438]	1925	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
	1926	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1927
[4438]	1928	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1929	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1930
[4309]	1931	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1932
	1933	!
[4309]	1934	!-- Generate random numbers using the parallel random generator.
[2938]	1935	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1936	!-- unit variance. Note, at the end the random number array must be defined
	1937	!-- globally in order to compute the correlation matrices. However,
	1938	!-- the calculation and normalization of random numbers is done locally,
	1939	!-- while the result is later distributed to all processes. Further,
	1940	!-- please note, a set of random numbers is only calculated for the
	1941	!-- left boundary, while the right boundary uses the same random numbers
	1942	!-- and thus also computes the same correlation matrix.
[4438]	1943	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
	1944	rand_it = 0.0_wp
[2938]	1945
	1946	rand_av = 0.0_wp
	1947	rand_sigma_inv = 0.0_wp
[4438]	1948	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1949	* ( nx + mergp - ( 0 - mergp ) +1 ), &
	1950	KIND=wp )
[4309]	1951	!
[4438]	1952	!-- Compute and normalize random numbers.
	1953	DO i = nxl - mergp, nxr + mergp
[4309]	1954	!
[4438]	1955	!-- Put the random seeds at grid point ii
	1956	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
	1957	DO k = nzb - mergp, nzt + 1 + mergp
	1958	CALL random_number_parallel( random_dummy )
	1959	rand_it(k,i) = random_dummy
	1960	ENDDO
[4309]	1961	!
[4438]	1962	!-- Get the new random seeds from last call at grid point ii
	1963	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1964	ENDDO
[4309]	1965	!
[4438]	1966	!-- For normalization to zero mean, sum-up the global random numers.
	1967	!-- To normalize the global set of random numbers,
	1968	!-- the inner ghost layers mergp must not be summed-up, else
	1969	!-- the random numbers on the ghost layers will be stronger weighted as they
	1970	!-- also occur on the inner subdomains.
	1971	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	1972	MERGE( nxr, nxr + mergp, nxr /= nx )
	1973	DO k = nzb - mergp, nzt + 1 + mergp
	1974	rand_av = rand_av + rand_it(k,i)
[2938]	1975	ENDDO
[4438]	1976	ENDDO
	1977
[4309]	1978	#if defined( __parallel )
[4438]	1979	!
	1980	!-- Sum-up the local averages of the random numbers
	1981	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1982	MPI_SUM, comm1dx, ierr )
[4309]	1983	#endif
[4438]	1984	rand_av = rand_av * nxz_inv
[4309]	1985	!
[4438]	1986	!-- Obtain zero mean
	1987	rand_it= rand_it - rand_av
[4309]	1988	!
[4438]	1989	!-- Now, compute the variance
	1990	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	1991	MERGE( nxr, nxr + mergp, nxr /= nx )
	1992	DO k = nzb - mergp, nzt + 1 + mergp
	1993	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	1994	ENDDO
[4438]	1995	ENDDO
[2938]	1996
[4309]	1997	#if defined( __parallel )
[4438]	1998	!
	1999	!-- Sum-up the local quadratic averages of the random numbers
	2000	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	2001	MPI_SUM, comm1dx, ierr )
[4309]	2002	#endif
[2938]	2003	!
[4438]	2004	!-- Compute standard deviation
	2005	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	2006	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	2007	ELSE
	2008	rand_sigma_inv = 1.0_wp
[4309]	2009	ENDIF
	2010	!
[4438]	2011	!-- Normalize with standard deviation to obtain unit variance
	2012	rand_it = rand_it * rand_sigma_inv
	2013
	2014	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2015	!
[4438]	2016	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	2017	!-- are two options. In the first one, the computation of the seeds is
	2018	!-- distributed to all processes along the communicator comm1dx and
	2019	!-- gathered on the southmost and, if necessary, on the northmost process.
	2020	!-- For huge length scales the computational effort can become quite huge
	2021	!-- (it scales with the turbulent length scales), so that gain by parallelization
	2022	!-- exceeds the costs by the subsequent communication.
	2023	!-- In the second option, which performs better when the turbulent length scales
	2024	!-- are parametrized and thus the loops are smaller, the seeds are computed
	2025	!-- locally and no communication is necessary.
	2026	IF ( compute_velocity_seeds_local ) THEN
[2938]	2027
[4438]	2028	f_n = 0.0_wp
	2029	DO i = nxl, nxr
	2030	DO k = nzb, nzt+1
	2031	DO ii = -n_x(k), n_x(k)
	2032	DO kk = -n_z(k), n_z(k)
	2033	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2034	ENDDO
[2938]	2035	ENDDO
	2036	ENDDO
	2037	ENDDO
	2038
[4438]	2039	ELSE
[2938]	2040
[4438]	2041	f_n_l = 0.0_wp
	2042	DO i = nxl, nxr
	2043	DO k = nzb_y_stg, nzt_y_stg+1
	2044	DO ii = -n_x(k), n_x(k)
	2045	DO kk = -n_z(k), n_z(k)
	2046	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2047	ENDDO
	2048	ENDDO
	2049	ENDDO
	2050	ENDDO
[2938]	2051	!
[4438]	2052	!-- Gather velocity seeds of full subdomain
	2053	send_count = nzt_y_stg - nzb_y_stg + 1
	2054	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2055
	2056	#if defined( __parallel )
[4309]	2057	!
[4438]	2058	!-- Gather the processed velocity seed on south boundary mpi ranks.
	2059	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2060	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2061	id_south, comm1dy, ierr )
[4309]	2062	!
[4438]	2063	!-- Gather the processed velocity seed on north boundary mpi ranks.
	2064	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2065	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2066	id_north, comm1dy, ierr )
[2938]	2067	#else
[4438]	2068	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[2938]	2069	#endif
	2070
[4438]	2071	ENDIF
	2072
	2073	DEALLOCATE( rand_it )
	2074
	2075	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2076
[2938]	2077	END SUBROUTINE stg_generate_seed_xz
	2078
[3347]	2079	!------------------------------------------------------------------------------!
	2080	! Description:
	2081	! ------------
	2082	!> Parametrization of the Reynolds stress tensor, following the parametrization
	2083	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	2084	!> dispserion modelling. Please note, the parametrization does not distinguish
	2085	!> between along-wind and cross-wind turbulence.
	2086	!------------------------------------------------------------------------------!
	2087	SUBROUTINE parametrize_reynolds_stress
	2088
	2089	INTEGER(iwp) :: k !< loop index in z-direction
	2090
	2091	REAL(wp) :: zzi !< ratio of z/zi
	2092
	2093	DO k = nzb+1, nzt+1
	2094	!
[4022]	2095	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2096	!-- The function decreases to 1/10 after one length scale above the
	2097	!-- ABL top.
	2098	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2099	!
[4022]	2100	!-- Determine normalized height coordinate
	2101	zzi = zu(k) / zi_ribulk
[3347]	2102	!
[4022]	2103	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
[4438]	2104	!-- to the denominator, else the mergpe-function can crash if scale_l is
[4022]	2105	!-- zero.
	2106	r11(k) = scale_us*2 ( &
	2107	MERGE( 0.35_wp * ABS( &
	2108	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2109	)**( 2.0_wp / 3.0_wp ), &
	2110	0.0_wp, &
	2111	scale_l < 0.0_wp ) &
	2112	+ 5.0_wp - 4.0_wp * zzi &
	2113	) * blend
	2114
	2115	r22(k) = r11(k)
	2116	!
	2117	!-- w'w'
	2118	r33(k) = scale_wm*2 ( &
	2119	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2120	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2121	) * blend
	2122	!
	2123	!-- u'w' and v'w'. Assume isotropy.
	2124	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	2125	r32(k) = r31(k)
[3347]	2126	!
[4022]	2127	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	2128	!-- a similar profile as for u'w'.
	2129	r21(k) = r31(k)
[3347]	2130	ENDDO
	2131
	2132	!
	2133	!-- Set bottom boundary condition
	2134	r11(nzb) = r11(nzb+1)
	2135	r22(nzb) = r22(nzb+1)
	2136	r33(nzb) = r33(nzb+1)
	2137
	2138	r21(nzb) = r11(nzb+1)
	2139	r31(nzb) = r31(nzb+1)
	2140	r32(nzb) = r32(nzb+1)
	2141
	2142
	2143	END SUBROUTINE parametrize_reynolds_stress
	2144
	2145	!------------------------------------------------------------------------------!
	2146	! Description:
	2147	! ------------
	2148	!> Calculate the coefficient matrix from the Lund rotation.
	2149	!------------------------------------------------------------------------------!
	2150	SUBROUTINE calc_coeff_matrix
	2151
	2152	INTEGER(iwp) :: k !< loop index in z-direction
	2153
	2154	!
	2155	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2156	DO k = nzb+1, nzt+1
[4022]	2157	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	2158	a11(k) = SQRT( r11(k) )
	2159	a21(k) = r21(k) / a11(k)
	2160	a31(k) = r31(k) / a11(k)
	2161	ELSE
	2162	a11(k) = 10E-8_wp
	2163	a21(k) = 10E-8_wp
	2164	a31(k) = 10E-8_wp
	2165	ENDIF
	2166	ENDDO
	2167	DO k = nzb+1, nzt+1
	2168	a22(k) = r22(k) - a21(k)**2
[4022]	2169	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2170	a22(k) = SQRT( a22(k) )
	2171	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	2172	ELSE
	2173	a22(k) = 10E-8_wp
	2174	a32(k) = 10E-8_wp
	2175	ENDIF
	2176	ENDDO
	2177	DO k = nzb+1, nzt+1
	2178	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2179	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2180	a33(k) = SQRT( a33(k) )
	2181	ELSE
	2182	a33(k) = 10E-8_wp
	2183	ENDIF
	2184	ENDDO
	2185	!
	2186	!-- Set bottom boundary condition
	2187	a11(nzb) = a11(nzb+1)
	2188	a22(nzb) = a22(nzb+1)
	2189	a21(nzb) = a21(nzb+1)
	2190	a33(nzb) = a33(nzb+1)
	2191	a31(nzb) = a31(nzb+1)
	2192	a32(nzb) = a32(nzb+1)
	2193
	2194	END SUBROUTINE calc_coeff_matrix
	2195
	2196	!------------------------------------------------------------------------------!
	2197	! Description:
	2198	! ------------
	2199	!> This routine controls the re-adjustment of the turbulence statistics used
	2200	!> for generating turbulence at the lateral boundaries.
	2201	!------------------------------------------------------------------------------!
	2202	SUBROUTINE stg_adjust
	2203
[3987]	2204	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2205	!
[4022]	2206	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2207	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2208	!-- synthetic turbulence shall be parametrized nevertheless, the
	2209	!-- boundary-layer depth need to determined first.
	2210	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2211	CALL nesting_offl_calc_zi
	2212	!
	2213	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2214	!-- are calculated.
[3347]	2215	CALL calc_scaling_variables
	2216	!
	2217	!-- Set length and time scales depending on boundary-layer height
	2218	CALL calc_length_and_time_scale
	2219	!
	2220	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2221	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2222	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2223	!-- friction velocity and velocity scale.
	2224	CALL parametrize_reynolds_stress
	2225	!
	2226	!-- Calculate coefficient matrix from Reynolds stress tensor
	2227	!-- (Lund rotation)
	2228	CALL calc_coeff_matrix
	2229	!
	2230	!-- Determine filter functions on basis of updated length scales
	2231	CALL stg_filter_func( nux, bux ) !filter ux
	2232	CALL stg_filter_func( nuy, buy ) !filter uy
	2233	CALL stg_filter_func( nuz, buz ) !filter uz
	2234	CALL stg_filter_func( nvx, bvx ) !filter vx
	2235	CALL stg_filter_func( nvy, bvy ) !filter vy
	2236	CALL stg_filter_func( nvz, bvz ) !filter vz
	2237	CALL stg_filter_func( nwx, bwx ) !filter wx
	2238	CALL stg_filter_func( nwy, bwy ) !filter wy
	2239	CALL stg_filter_func( nwz, bwz ) !filter wz
	2240	!
	2241	!-- Reset time counter for controlling next adjustment to zero
	2242	time_stg_adjust = 0.0_wp
[3987]	2243
	2244	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2245
	2246	END SUBROUTINE stg_adjust
	2247
	2248
	2249	!------------------------------------------------------------------------------!
	2250	! Description:
	2251	! ------------
	2252	!> Calculates turbuluent length and time scales if these are not available
	2253	!> from measurements.
	2254	!------------------------------------------------------------------------------!
	2255	SUBROUTINE calc_length_and_time_scale
	2256
[4022]	2257	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2258
[4022]	2259	REAL(wp) :: length_scale_dum !< effectively used length scale
	2260
[3347]	2261	!
	2262	!-- In initial call the boundary-layer depth can be zero. This case, set
	2263	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2264	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2265	!
	2266	!-- Set-up default turbulent length scales. From the numerical point of
	2267	!-- view the imposed perturbations should not be immediately dissipated
	2268	!-- by the numerics. The numerical dissipation, however, acts on scales
	2269	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2270	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2271	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2272	!-- imposing any perturbations) in order to save computational costs.
	2273	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2274	!-- using the length scales and the mean profiles of u- and v-component.
	2275	DO k = nzb+1, nzt+1
	2276	!
[4022]	2277	!-- Determine blending parameter. Within the boundary layer length scales
	2278	!-- are constant, while above lengths scales approach gradully zero,
	2279	!-- i.e. imposed turbulence is not correlated in space and time,
	2280	!-- just white noise, which saves computations power as the loops for the
	2281	!-- computation of the filter functions depend on the length scales.
	2282	!-- The value decreases to 1/10 after one length scale above the
	2283	!-- ABL top.
	2284	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2285	!
[4022]	2286	!-- Assume isotropic turbulence length scales
	2287	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2288	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2289	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2290	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2291	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2292	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2293	!
[4022]	2294	!-- Along the vertical direction limit the length scale further by the
	2295	!-- boundary-layer depth to assure that no length scales larger than
	2296	!-- the boundary-layer depth are used
	2297	length_scale_dum = MIN( length_scale, zi_ribulk )
	2298
	2299	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2300	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2301	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2302	!
[4022]	2303	!-- Limit time scales, else they become very larger for low wind speed,
	2304	!-- imposing long-living inflow perturbations which in turn propagate
	2305	!-- further into the model domain. Use u_init and v_init to calculate
	2306	!-- the time scales, which will be equal to the inflow profiles, both,
	2307	!-- in offline nesting mode or in dirichlet/radiation mode.
	2308	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2309	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2310	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2311	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2312	!
	2313	!-- Time scale of w-component is a mixture from u- and v-component.
	2314	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2315
[3347]	2316	ENDDO
	2317	!
	2318	!-- Set bottom boundary condition for the length and time scales
	2319	nux(nzb) = nux(nzb+1)
	2320	nuy(nzb) = nuy(nzb+1)
	2321	nuz(nzb) = nuz(nzb+1)
	2322	nvx(nzb) = nvx(nzb+1)
	2323	nvy(nzb) = nvy(nzb+1)
	2324	nvz(nzb) = nvz(nzb+1)
	2325	nwx(nzb) = nwx(nzb+1)
	2326	nwy(nzb) = nwy(nzb+1)
	2327	nwz(nzb) = nwz(nzb+1)
	2328
	2329	tu(nzb) = tu(nzb+1)
	2330	tv(nzb) = tv(nzb+1)
	2331	tw(nzb) = tw(nzb+1)
	2332
	2333
	2334	END SUBROUTINE calc_length_and_time_scale
	2335
	2336	!------------------------------------------------------------------------------!
	2337	! Description:
	2338	! ------------
	2339	!> Calculate scaling variables which are used for turbulence parametrization
	2340	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2341	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2342	!------------------------------------------------------------------------------!
	2343	SUBROUTINE calc_scaling_variables
	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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