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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4540

Last change on this file since 4540 was 4535, checked in by raasch, 4 years ago
bugfix for restart data format query
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1	!> @synthetic_turbulence_generator_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 2017-2020 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4535 2020-05-15 12:07:23Z raasch $
27	! bugfix for restart data format query
28	!
29	! 4495 2020-04-13 20:11:20Z raasch
30	! restart data handling with MPI-IO added
31	!
32	! 4481 2020-03-31 18:55:54Z maronga
33	! bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
34	!
35	! 4442 2020-03-04 19:21:13Z suehring
36	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
37	! (was accidantly changed).
38	!
39	! 4441 2020-03-04 19:20:35Z suehring
40	! Correct misplaced preprocessor directive
41	!
42	! 4438 2020-03-03 20:49:28Z suehring
43	! Performance optimizations in velocity-seed calculation:
44	! - random number array is only defined and computed locally (except for
45	! normalization to zero mean and unit variance)
46	! - parallel random number generator is applied independent on the 2D random
47	! numbers in other routines
48	! - option to decide wheter velocity seeds are computed locally without any
49	! further communication or are computed by all processes along the
50	! communicator
51	!
52	! 4346 2019-12-18 11:55:56Z motisi
53	! Introduction of wall_flags_total_0, which currently sets bits based on static
54	! topography information used in wall_flags_static_0
55	!
56	! 4335 2019-12-12 16:39:05Z suehring
57	! Commentation of last commit
58	!
59	! 4332 2019-12-10 19:44:12Z suehring
60	! Limit initial velocity seeds in restart runs, if not the seed calculation
61	! may become unstable. Further, minor bugfix in initial velocity seed
62	! calculation.
63	!
64	! 4329 2019-12-10 15:46:36Z motisi
65	! Renamed wall_flags_0 to wall_flags_static_0
66	!
67	! 4309 2019-11-26 18:49:59Z suehring
68	! Computation of velocity seeds optimized. This implies that random numbers
69	! are computed now using the parallel random number generator. Random numbers
70	! are now only computed and normalized locally, while distributed over all
71	! mpi ranks afterwards, instead of computing random numbers on a global array.
72	! Further, the number of calls for the time-consuming velocity-seed generation
73	! is reduced - now the left and right, as well as the north and south boundary
74	! share the same velocity-seed matrices.
75	!
76	! 4182 2019-08-22 15:20:23Z scharf
77	! Corrected "Former revisions" section
78	!
79	! 4148 2019-08-08 11:26:00Z suehring
80	! Remove unused variable
81	!
82	! 4144 2019-08-06 09:11:47Z raasch
83	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
84	!
85	! 4071 2019-07-03 20:02:00Z suehring
86	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
87	! information is not read from file.
88	!
89	! 4022 2019-06-12 11:52:39Z suehring
90	! Several bugfixes and improvements
91	! - revise bias correction of the imposed perturbations (correction via volume
92	! flow can create instabilities in case the mean volume flow is close to zero)
93	! - introduce lower limits in calculation of coefficient matrix, else the
94	! calculation may become numerically unstable
95	! - impose perturbations every timestep, even though no new set of perturbations
96	! is generated in case dt_stg_call /= dt_3d
97	! - Implement a gradual decrease of Reynolds stress and length scales above
98	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
99	! discontinuous decrease
100	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
101	!
102	! 3987 2019-05-22 09:52:13Z kanani
103	! Introduce alternative switch for debug output during timestepping
104	!
105	! 3938 2019-04-29 16:06:25Z suehring
106	! Remove unused variables
107	!
108	! 3937 2019-04-29 15:09:07Z suehring
109	! Minor bugfix in case of a very early restart where mc_factor is sill not
110	! present.
111	! Some modification and fixing of potential bugs in the calculation of scaling
112	! parameters used for synthetic turbulence parametrization.
113	!
114	! 3909 2019-04-17 09:13:25Z suehring
115	! Minor bugfix for last commit
116	!
117	! 3900 2019-04-16 15:17:43Z suehring
118	! Missing re-calculation of perturbation seeds in case of restarts
119	!
120	! 3891 2019-04-12 17:52:01Z suehring
121	! Bugfix in initialization in case of restart runs.
122	!
123	! 3885 2019-04-11 11:29:34Z kanani
124	! Changes related to global restructuring of location messages and introduction
125	! of additional debug messages
126	!
127	!
128	! removed unused variables
129	!
130	! 3719 2019-02-06 13:10:18Z kanani
131	! Removed log_point measurement from stg_init, since this part is counted to
132	! log_point(2) 'initialisation' already. Moved other log_points to calls of
133	! the subroutines in time_integration for better overview.
134	!
135	! 2259 2017-06-08 09:09:11Z gronemeier
136	! Initial revision
137	!
138	! Authors:
139	! --------
140	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
141	!
142	!
143	! Description:
144	! ------------
145	!> The module generates turbulence at the inflow boundary based on a method by
146	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
147	!> correction by Kim et al. (2013).
148	!> The turbulence is correlated based on length scales in y- and z-direction and
149	!> a time scale for each velocity component. The profiles of length and time
150	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
151	!> tensor can be either read from file STG_PROFILES, or will be parametrized
152	!> within the boundary layer.
153	!>
154	!> @todo test restart
155	!> enable cyclic_fill
156	!> implement turbulence generation for e and pt
157	!> @todo Input of height-constant length scales via namelist
158	!> @note <Enter notes on the module>
159	!> @bug Height information from input file is not used. Profiles from input
160	!> must match with current PALM grid.
161	!> In case of restart, velocity seeds differ from precursor run if a11,
162	!> a22, or a33 are zero.
163	!------------------------------------------------------------------------------!
164	MODULE synthetic_turbulence_generator_mod
165
166
167	USE arrays_3d, &
168	ONLY: dzw, &
169	ddzw, &
170	drho_air, &
171	mean_inflow_profiles, &
172	q, &
173	q_init, &
174	pt, &
175	pt_init, &
176	u, &
177	u_init, &
178	v, &
179	v_init, &
180	w, &
181	zu, &
182	zw
183
184	USE basic_constants_and_equations_mod, &
185	ONLY: g, &
186	kappa, &
187	pi
188
189	USE control_parameters, &
190	ONLY: bc_lr, &
191	bc_ns, &
192	child_domain, &
193	coupling_char, &
194	debug_output_timestep, &
195	dt_3d, &
196	e_init, &
197	humidity, &
198	initializing_actions, &
199	intermediate_timestep_count, &
200	intermediate_timestep_count_max, &
201	length, &
202	message_string, &
203	nesting_offline, &
204	neutral, &
205	num_mean_inflow_profiles, &
206	random_generator, &
207	rans_mode, &
208	restart_data_format_output, &
209	restart_string, &
210	syn_turb_gen, &
211	time_since_reference_point, &
212	turbulent_inflow
213
214	USE cpulog, &
215	ONLY: cpu_log, &
216	log_point_s
217
218	USE grid_variables, &
219	ONLY: ddx, &
220	ddy, &
221	dx, &
222	dy
223
224	USE indices, &
225	ONLY: nbgp, &
226	nz, &
227	nzb, &
228	nzt, &
229	nx, &
230	nxl, &
231	nxlu, &
232	nxr, &
233	ny, &
234	nys, &
235	nysv, &
236	nyn, &
237	wall_flags_total_0
238
239	USE kinds
240
241	#if defined( __parallel ) && !defined( __mpifh )
242	USE MPI
243	#endif
244
245	USE nesting_offl_mod, &
246	ONLY: nesting_offl_calc_zi, &
247	zi_ribulk
248
249	USE pegrid, &
250	ONLY: comm1dx, &
251	comm1dy, &
252	comm2d, &
253	ierr, &
254	myidx, &
255	myidy, &
256	pdims
257
258	USE pmc_interface, &
259	ONLY : rans_mode_parent
260
261	USE random_generator_parallel, &
262	ONLY: init_parallel_random_generator, &
263	random_dummy, &
264	random_number_parallel, &
265	random_seed_parallel
266
267	USE restart_data_mpi_io_mod, &
268	ONLY: rrd_mpi_io, &
269	wrd_mpi_io
270
271	USE transpose_indices, &
272	ONLY: nzb_x, &
273	nzt_x
274
275	USE surface_mod, &
276	ONLY: surf_def_h, &
277	surf_lsm_h, &
278	surf_usm_h
279
280	IMPLICIT NONE
281
282	#if defined( __parallel ) && defined( __mpifh )
283	INCLUDE "mpif.h"
284	#endif
285
286
287	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
288	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
289	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
290	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
291	!< is distributed over several processes
292
293	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
294	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
295	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
296	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
297	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
298	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
299	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
300	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
301	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
302	#if defined( __parallel )
303	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
304	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
305	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
306	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
307	#endif
308
309	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
310	!< required for bias correction of imposed perturbations
311	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
312	!< required for bias correction of imposed perturbations
313
314	#if defined( __parallel )
315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
318	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
319	#endif
320	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
329
330	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
331	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
332	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
333	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
334
335	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
336	!< scales above the boundary layer
337	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
338	!< one length scale above ABL top
339	REAL(wp) :: d_l !< blend_coeff/length_scale
340	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
341	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
342	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
343	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
344	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
345	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
346	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
347	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
348
349	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
350
351
352	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
353	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
354	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
355	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
356	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
357	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
358
359	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
360	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
361	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
362	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
363	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
364	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
365	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
366	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
367	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
368
369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
379	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
380	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
390
391	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
392	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
393
394	!
395	!-- PALM interfaces:
396	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
397	INTERFACE stg_adjust
398	MODULE PROCEDURE stg_adjust
399	END INTERFACE stg_adjust
400	!
401	!-- Input parameter checks to be done in check_parameters
402	INTERFACE stg_check_parameters
403	MODULE PROCEDURE stg_check_parameters
404	END INTERFACE stg_check_parameters
405
406	!
407	!-- Calculate filter functions
408	INTERFACE stg_filter_func
409	MODULE PROCEDURE stg_filter_func
410	END INTERFACE stg_filter_func
411
412	!
413	!-- Generate velocity seeds at south and north domain boundary
414	INTERFACE stg_generate_seed_xz
415	MODULE PROCEDURE stg_generate_seed_xz
416	END INTERFACE stg_generate_seed_xz
417	!
418	!-- Generate velocity seeds at left and/or right domain boundary
419	INTERFACE stg_generate_seed_yz
420	MODULE PROCEDURE stg_generate_seed_yz
421	END INTERFACE stg_generate_seed_yz
422
423	!
424	!-- Output of information to the header file
425	INTERFACE stg_header
426	MODULE PROCEDURE stg_header
427	END INTERFACE stg_header
428
429	!
430	!-- Initialization actions
431	INTERFACE stg_init
432	MODULE PROCEDURE stg_init
433	END INTERFACE stg_init
434
435	!
436	!-- Main procedure of synth. turb. gen.
437	INTERFACE stg_main
438	MODULE PROCEDURE stg_main
439	END INTERFACE stg_main
440
441	!
442	!-- Reading of NAMELIST parameters
443	INTERFACE stg_parin
444	MODULE PROCEDURE stg_parin
445	END INTERFACE stg_parin
446
447	!
448	!-- Reading of parameters for restart runs
449	INTERFACE stg_rrd_global
450	MODULE PROCEDURE stg_rrd_global_ftn
451	MODULE PROCEDURE stg_rrd_global_mpi
452	END INTERFACE stg_rrd_global
453
454	!
455	!-- Writing of binary output for restart runs
456	INTERFACE stg_wrd_global
457	MODULE PROCEDURE stg_wrd_global
458	END INTERFACE stg_wrd_global
459
460	SAVE
461
462	PRIVATE
463
464	!
465	!-- Public interfaces
466	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
467	stg_parin, stg_rrd_global, stg_wrd_global
468
469	!
470	!-- Public variables
471	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
472	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
473	time_stg_adjust, time_stg_call, use_syn_turb_gen
474
475
476	CONTAINS
477
478
479	!------------------------------------------------------------------------------!
480	! Description:
481	! ------------
482	!> Check parameters routine for synthetic turbulence generator
483	!------------------------------------------------------------------------------!
484	SUBROUTINE stg_check_parameters
485
486	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
487	nesting_offline ) THEN
488	message_string = 'Synthetic turbulence generator is required ' // &
489	'if offline nesting is applied and PALM operates ' // &
490	'in LES mode.'
491	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
492	ENDIF
493
494	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
495	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
496	message_string = 'Synthetic turbulence generator is required ' // &
497	'when nesting is applied and parent operates in ' // &
498	'RANS-mode but current child in LES mode.'
499	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
500	ENDIF
501
502	IF ( use_syn_turb_gen ) THEN
503
504	IF ( child_domain .AND. .NOT. rans_mode .AND. &
505	.NOT. rans_mode_parent ) THEN
506	message_string = 'Using synthetic turbulence generator ' // &
507	'is not allowed in LES-LES nesting.'
508	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
509
510	ENDIF
511
512	IF ( child_domain .AND. rans_mode .AND. &
513	rans_mode_parent ) THEN
514	message_string = 'Using synthetic turbulence generator ' // &
515	'is not allowed in RANS-RANS nesting.'
516	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
517
518	ENDIF
519
520	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
521
522	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
523	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
524	message_string = 'Using synthetic turbulence generator ' // &
525	'requires %initializing_actions = ' // &
526	'"set_constant_profiles" or "read_restart_data"' //&
527	', if not offline nesting is applied.'
528	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
529	ENDIF
530
531	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
532	message_string = 'Using synthetic turbulence generator ' // &
533	'requires &bc_lr = "dirichlet/radiation", ' // &
534	'if not offline nesting is applied.'
535	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
536	ENDIF
537	IF ( bc_ns /= 'cyclic' ) THEN
538	message_string = 'Using synthetic turbulence generator ' // &
539	'requires &bc_ns = "cyclic", ' // &
540	'if not offline nesting is applied.'
541	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
542	ENDIF
543
544	ENDIF
545
546	IF ( turbulent_inflow ) THEN
547	message_string = 'Using synthetic turbulence generator ' // &
548	'in combination &with turbulent_inflow = .T. '// &
549	'is not allowed'
550	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
551	ENDIF
552	!
553	!-- Synthetic turbulence generator requires the parallel random generator
554	IF ( random_generator /= 'random-parallel' ) THEN
555	message_string = 'Using synthetic turbulence generator ' // &
556	'requires random_generator = random-parallel.'
557	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
558	ENDIF
559
560	ENDIF
561
562	END SUBROUTINE stg_check_parameters
563
564
565	!------------------------------------------------------------------------------!
566	! Description:
567	! ------------
568	!> Header output for synthetic turbulence generator
569	!------------------------------------------------------------------------------!
570	SUBROUTINE stg_header ( io )
571
572	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
573
574	!
575	!-- Write synthetic turbulence generator Header
576	WRITE( io, 1 )
577	IF ( use_syn_turb_gen ) THEN
578	WRITE( io, 2 )
579	ELSE
580	WRITE( io, 3 )
581	ENDIF
582
583	IF ( parametrize_inflow_turbulence ) THEN
584	WRITE( io, 4 ) dt_stg_adjust
585	ELSE
586	WRITE( io, 5 )
587	ENDIF
588
589	1 FORMAT (//' Synthetic turbulence generator information:'/ &
590	' ------------------------------------------'/)
591	2 FORMAT (' synthetic turbulence generator is switched on')
592	3 FORMAT (' synthetic turbulence generator is switched off')
593	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
594	5 FORMAT (' imposed turbulence is read from file' )
595
596	END SUBROUTINE stg_header
597
598
599	!------------------------------------------------------------------------------!
600	! Description:
601	! ------------
602	!> Initialization of the synthetic turbulence generator
603	!------------------------------------------------------------------------------!
604	SUBROUTINE stg_init
605
606	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
607
608	#if defined( __parallel )
609	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
610	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
611	#endif
612
613	INTEGER(iwp) :: i !> grid index in x-direction
614	INTEGER(iwp) :: j !> loop index
615	INTEGER(iwp) :: k !< index
616	#if defined( __parallel )
617	INTEGER(iwp) :: newtype !< dummy MPI type
618	INTEGER(iwp) :: realsize !< size of REAL variables
619	#endif
620
621	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
622	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
623	!
624	!-- Dummy variables used for reading profiles
625	REAL(wp) :: d1 !< u profile
626	REAL(wp) :: d2 !< v profile
627	REAL(wp) :: d3 !< w profile
628	REAL(wp) :: d5 !< e profile
629	REAL(wp) :: luy !< length scale for u in y direction
630	REAL(wp) :: luz !< length scale for u in z direction
631	REAL(wp) :: lvy !< length scale for v in y direction
632	REAL(wp) :: lvz !< length scale for v in z direction
633	REAL(wp) :: lwy !< length scale for w in y direction
634	REAL(wp) :: lwz !< length scale for w in z direction
635	#if defined( __parallel )
636	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
637	#endif
638	REAL(wp) :: zz !< height
639
640
641	#if defined( __parallel )
642	CALL MPI_BARRIER( comm2d, ierr )
643	#endif
644	!
645	!-- Create mpi-datatypes for exchange in case of non-local but distributed
646	!-- computation of the velocity seeds. This option is useful in
647	!-- case large turbulent length scales are present, where the computational
648	!-- effort becomes large and need to be parallelized. For parameterized
649	!-- turbulence the length scales are small and computing the velocity seeds
650	!-- locally is faster (no overhead by communication).
651	IF ( .NOT. compute_velocity_seeds_local ) THEN
652	#if defined( __parallel )
653	!
654	!-- Determine processor decomposition of z-axis along x- and y-direction
655	nnz = nz / pdims(1)
656	nzb_x_stg = 1 + myidx * INT( nnz )
657	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
658
659	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
660	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
661
662	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
663	.AND. .NOT. rans_mode ) ) THEN
664	nnz = nz / pdims(2)
665	nzb_y_stg = 1 + myidy * INT( nnz )
666	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
667
668	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
669	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
670	ENDIF
671
672	!
673	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
674	!-- velocity seeds
675	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
676	extent = 1 * realsize
677	!
678	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
679	!-- layer
680	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
681	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
682	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
683	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
684	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
685	CALL MPI_TYPE_FREE( newtype, ierr )
686
687	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
688	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
689	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
690	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
691	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
692	CALL MPI_TYPE_FREE( newtype, ierr )
693
694	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
695	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
696
697	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
698	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
699
700	DO j = 1, pdims(1)
701	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
702	ENDDO
703	!
704	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
705	!-- layer
706	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
707	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
708	.AND. .NOT. rans_mode ) ) THEN
709	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
710	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
711	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
712	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
713	CALL MPI_TYPE_FREE( newtype, ierr )
714
715	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
716	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
717	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
718	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
719	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
720	CALL MPI_TYPE_FREE( newtype, ierr )
721
722	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
723	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
724
725	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
726	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
727
728	DO j = 1, pdims(2)
729	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
730	ENDDO
731
732	ENDIF
733	#endif
734	ENDIF
735	!
736	!-- Allocate required arrays.
737	!-- In case no offline nesting or self nesting is used, the arrary
738	!-- mean_inflow profiles is required. Check if it is already allocated, else
739	!-- allocate and initialize it appropriately. Note, in case turbulence and
740	!-- inflow information is read from file, mean_inflow_profiles is already
741	!-- allocated and initialized appropriately.
742	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
743	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
744	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
745	mean_inflow_profiles = 0.0_wp
746	mean_inflow_profiles(:,1) = u_init
747	mean_inflow_profiles(:,2) = v_init
748	!
749	!-- Even though potential temperature and humidity are not perturbed,
750	!-- they need to be initialized appropriately.
751	IF ( .NOT. neutral ) &
752	mean_inflow_profiles(:,4) = pt_init
753	IF ( humidity ) &
754	mean_inflow_profiles(:,6) = q_init
755	ENDIF
756	ENDIF
757
758	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
759	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
760	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
761	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
762	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
763	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
764	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
765	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
766
767	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
768	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
769	dist_xz = 0.0_wp
770	dist_yz = 0.0_wp
771	!
772	!-- Read inflow profile
773	!-- Height levels of profiles in input profile is as follows:
774	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
775	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
776	!-- WARNING: zz is not used at the moment
777	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
778	EXIST = file_stg_exist )
779
780	IF ( file_stg_exist ) THEN
781
782	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
783	FORM='FORMATTED')
784	!
785	!-- Skip header
786	READ( 90, * )
787
788	DO k = nzb+1, nzt+1
789	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
790	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
791	d1, d2, d3, d5
792
793	!
794	!-- Convert length scales from meter to number of grid points.
795	nuy(k) = INT( luy * ddy )
796	nuz(k) = INT( luz * ddzw(k) )
797	nvy(k) = INT( lvy * ddy )
798	nvz(k) = INT( lvz * ddzw(k) )
799	nwy(k) = INT( lwy * ddy )
800	nwz(k) = INT( lwz * ddzw(k) )
801	!
802	!-- Workaround, assume isotropic turbulence
803	nwx(k) = nwy(k)
804	nvx(k) = nvy(k)
805	nux(k) = nuy(k)
806	!
807	!-- Save Mean inflow profiles
808	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
809	mean_inflow_profiles(k,1) = d1
810	mean_inflow_profiles(k,2) = d2
811	! mean_inflow_profiles(k,4) = d4
812	mean_inflow_profiles(k,5) = d5
813	ENDIF
814	ENDDO
815	!
816	!-- Set lenght scales at surface grid point
817	nuy(nzb) = nuy(nzb+1)
818	nuz(nzb) = nuz(nzb+1)
819	nvy(nzb) = nvy(nzb+1)
820	nvz(nzb) = nvz(nzb+1)
821	nwy(nzb) = nwy(nzb+1)
822	nwz(nzb) = nwz(nzb+1)
823
824	CLOSE( 90 )
825	!
826	!-- Calculate coefficient matrix from Reynolds stress tensor
827	!-- (Lund rotation)
828	CALL calc_coeff_matrix
829	!
830	!-- No information about turbulence and its length scales are available.
831	!-- Instead, parametrize turbulence which is imposed at the boundaries.
832	!-- Set flag which indicates that turbulence is parametrized, which is done
833	!-- later when energy-balance models are already initialized. This is
834	!-- because the STG needs information about surface properties such as
835	!-- roughness to build 'realistic' turbulence profiles.
836	ELSE
837	!
838	!-- Define length scale for the imposed turbulence, which is defined as
839	!-- 8 times the minimum grid spacing
840	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
841	!
842	!-- Define constant to gradually decrease length scales and Reynolds stress
843	!-- above ABL top. Assure that no zero length scales are used.
844	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
845	!
846	!-- Set flag indicating that turbulence is parametrized
847	parametrize_inflow_turbulence = .TRUE.
848	!
849	!-- In case of dirichlet inflow boundary conditions only at one lateral
850	!-- boundary, i.e. in the case no offline or self nesting is applied but
851	!-- synthetic turbulence shall be parametrized nevertheless, the
852	!-- boundary-layer depth need to determined first.
853	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
854	CALL nesting_offl_calc_zi
855	!
856	!-- Determine boundary-layer depth, which is used to initialize lenght
857	!-- scales
858	CALL calc_scaling_variables
859	!
860	!-- Initialize lenght and time scales, which in turn are used
861	!-- to initialize the filter functions.
862	CALL calc_length_and_time_scale
863	!
864	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
865	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
866	!-- Rotach et al. (1996) and is based on boundary-layer depth,
867	!-- friction velocity and velocity scale.
868	CALL parametrize_reynolds_stress
869	!
870	!-- Calculate coefficient matrix from Reynolds stress tensor
871	!-- (Lund rotation)
872	CALL calc_coeff_matrix
873
874	ENDIF
875
876	!
877	!-- Assign initial profiles. Note, this is only required if turbulent
878	!-- inflow from the left is desired, not in case of any of the
879	!-- nesting (offline or self nesting) approaches.
880	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
881	u_init = mean_inflow_profiles(:,1)
882	v_init = mean_inflow_profiles(:,2)
883	!pt_init = mean_inflow_profiles(:,4)
884	e_init = MAXVAL( mean_inflow_profiles(:,5) )
885	ENDIF
886
887	!
888	!-- Define the size of the filter functions and allocate them.
889	mergp = 0
890
891	! arrays must be large enough to cover the largest length scale
892	DO k = nzb, nzt+1
893	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
894	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
895	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
896	IF ( j > mergp ) mergp = j
897	ENDDO
898
899	! mergp = 2 * mergp
900	! mergp = mergp
901
902	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
903	buy(-mergp:mergp,nzb:nzt+1), &
904	buz(-mergp:mergp,nzb:nzt+1), &
905	bvx(-mergp:mergp,nzb:nzt+1), &
906	bvy(-mergp:mergp,nzb:nzt+1), &
907	bvz(-mergp:mergp,nzb:nzt+1), &
908	bwx(-mergp:mergp,nzb:nzt+1), &
909	bwy(-mergp:mergp,nzb:nzt+1), &
910	bwz(-mergp:mergp,nzb:nzt+1) )
911
912	!
913	!-- Allocate velocity seeds for turbulence at xz-layer
914	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
915	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
916	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
917
918	!
919	!-- Allocate velocity seeds for turbulence at yz-layer
920	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
921	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
922	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
923
924	fu_xz = 0.0_wp
925	fuo_xz = 0.0_wp
926	fv_xz = 0.0_wp
927	fvo_xz = 0.0_wp
928	fw_xz = 0.0_wp
929	fwo_xz = 0.0_wp
930
931	fu_yz = 0.0_wp
932	fuo_yz = 0.0_wp
933	fv_yz = 0.0_wp
934	fvo_yz = 0.0_wp
935	fw_yz = 0.0_wp
936	fwo_yz = 0.0_wp
937
938	!
939	!-- Create filter functions
940	CALL stg_filter_func( nux, bux ) !filter ux
941	CALL stg_filter_func( nuy, buy ) !filter uy
942	CALL stg_filter_func( nuz, buz ) !filter uz
943	CALL stg_filter_func( nvx, bvx ) !filter vx
944	CALL stg_filter_func( nvy, bvy ) !filter vy
945	CALL stg_filter_func( nvz, bvz ) !filter vz
946	CALL stg_filter_func( nwx, bwx ) !filter wx
947	CALL stg_filter_func( nwy, bwy ) !filter wy
948	CALL stg_filter_func( nwz, bwz ) !filter wz
949
950	#if defined( __parallel )
951	CALL MPI_BARRIER( comm2d, ierr )
952	#endif
953
954	!
955	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
956	! time step.
957	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
958	! are 0 compared to the prerun. This is mostly for k=nzt+1.
959	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
960	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
961
962	IF ( myidx == id_stg_left ) i = -1
963	IF ( myidx == id_stg_right ) i = nxr+1
964
965	DO j = nys, nyn
966	DO k = nzb, nzt+1
967	IF ( a11(k) > 10E-8_wp ) THEN
968	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
969	ELSE
970	fu_yz(k,j) = 10E-8_wp
971	ENDIF
972
973	IF ( a22(k) > 10E-8_wp ) THEN
974	fv_yz(k,j) = ( v(k,j,i) - &
975	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
976	ELSE
977	fv_yz(k,j) = 10E-8_wp
978	ENDIF
979
980	IF ( a33(k) > 10E-8_wp ) THEN
981	fw_yz(k,j) = ( w(k,j,i) - &
982	a31(k) * fu_yz(k,j) - a32(k) * &
983	fv_yz(k,j) ) / a33(k)
984	ELSE
985	fw_yz(k,j) = 10E-8_wp
986	ENDIF
987	ENDDO
988	ENDDO
989	ENDIF
990
991	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
992
993	IF ( myidy == id_stg_south ) j = -1
994	IF ( myidy == id_stg_north ) j = nyn+1
995
996	DO i = nxl, nxr
997	DO k = nzb, nzt+1
998	!
999	!-- In case the correlation coefficients are very small, the
1000	!-- velocity seeds may become very large finally creating
1001	!-- numerical instabilities in the synthetic turbulence generator.
1002	!-- Empirically, a value of 10E-8 seems to be sufficient.
1003	IF ( a11(k) > 10E-8_wp ) THEN
1004	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1005	ELSE
1006	fu_xz(k,i) = 10E-8_wp
1007	ENDIF
1008
1009	IF ( a22(k) > 10E-8_wp ) THEN
1010	fv_xz(k,i) = ( v(k,j,i) - &
1011	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1012	ELSE
1013	fv_xz(k,i) = 10E-8_wp
1014	ENDIF
1015
1016	IF ( a33(k) > 10E-8_wp ) THEN
1017	fw_xz(k,i) = ( w(k,j,i) - &
1018	a31(k) * fu_xz(k,i) - &
1019	a32(k) * fv_xz(k,i) ) / a33(k)
1020	ELSE
1021	fw_xz(k,i) = 10E-8_wp
1022	ENDIF
1023
1024	ENDDO
1025	ENDDO
1026	ENDIF
1027	ENDIF
1028	!
1029	!-- Count the number of non-topography grid points at the boundaries where
1030	!-- perturbations are imposed. This number is later used for bias corrections
1031	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1032	!-- due to the asymetry of u and v along x and y direction, respectively,
1033	!-- different cases must be distinguished.
1034	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1035	!
1036	!-- Number of grid points where perturbations are imposed on u
1037	IF ( myidx == id_stg_left ) i = nxl
1038	IF ( myidx == id_stg_right ) i = nxr+1
1039
1040	nr_non_topo_yz_l(1) = SUM( &
1041	MERGE( 1, 0, &
1042	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1043	!
1044	!-- Number of grid points where perturbations are imposed on v and w
1045	IF ( myidx == id_stg_left ) i = nxl-1
1046	IF ( myidx == id_stg_right ) i = nxr+1
1047
1048	nr_non_topo_yz_l(2) = SUM( &
1049	MERGE( 1, 0, &
1050	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1051	nr_non_topo_yz_l(3) = SUM( &
1052	MERGE( 1, 0, &
1053	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1054
1055	#if defined( __parallel )
1056	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1057	MPI_SUM, comm1dy, ierr )
1058	#else
1059	nr_non_topo_yz = nr_non_topo_yz_l
1060	#endif
1061	ENDIF
1062
1063	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1064	!
1065	!-- Number of grid points where perturbations are imposed on v
1066	IF ( myidy == id_stg_south ) j = nys
1067	IF ( myidy == id_stg_north ) j = nyn+1
1068
1069	nr_non_topo_xz_l(2) = SUM( &
1070	MERGE( 1, 0, &
1071	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1072	!
1073	!-- Number of grid points where perturbations are imposed on u and w
1074	IF ( myidy == id_stg_south ) j = nys-1
1075	IF ( myidy == id_stg_north ) j = nyn+1
1076
1077	nr_non_topo_xz_l(1) = SUM( &
1078	MERGE( 1, 0, &
1079	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1080	nr_non_topo_xz_l(3) = SUM( &
1081	MERGE( 1, 0, &
1082	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1083
1084	#if defined( __parallel )
1085	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1086	MPI_SUM, comm1dx, ierr )
1087	#else
1088	nr_non_topo_xz = nr_non_topo_xz_l
1089	#endif
1090	ENDIF
1091	!
1092	!-- Initialize random number generator at xz- and yz-layers. Random numbers
1093	!-- are initialized at each core. In case there is only inflow from the left,
1094	!-- it is sufficient to generate only random numbers for the yz-layer, else
1095	!-- random numbers for the xz-layer are also required.
1096	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1097	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1098	id_rand_yz = 0
1099	seq_rand_yz = 0
1100
1101	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
1102	id_rand_yz, seq_rand_yz )
1103
1104	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1105	.AND. .NOT. rans_mode ) ) THEN
1106	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1107	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1108	id_rand_xz = 0
1109	seq_rand_xz = 0
1110
1111	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
1112	id_rand_xz, seq_rand_xz )
1113	ENDIF
1114
1115
1116
1117	END SUBROUTINE stg_init
1118
1119
1120	!------------------------------------------------------------------------------!
1121	! Description:
1122	! ------------
1123	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1124	!> (Xie and Castro, 2008)
1125	!------------------------------------------------------------------------------!
1126	SUBROUTINE stg_filter_func( nxx, bxx )
1127
1128	INTEGER(iwp) :: k !< loop index
1129	INTEGER(iwp) :: n_k !< length scale nXX in height k
1130	INTEGER(iwp) :: nf !< index for length scales
1131
1132	REAL(wp) :: bdenom !< denominator for filter functions bXX
1133	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1134
1135	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1136
1137	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1138
1139
1140	bxx = 0.0_wp
1141
1142	DO k = nzb, nzt+1
1143	bdenom = 0.0_wp
1144	n_k = nxx(k)
1145	IF ( n_k /= 0 ) THEN
1146
1147	!
1148	!-- ( Eq.10 )^2
1149	DO nf = -n_k, n_k
1150	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1151	ENDDO
1152
1153	!
1154	!-- ( Eq.9 )
1155	bdenom = SQRT( bdenom )
1156	DO nf = -n_k, n_k
1157	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1158	ENDDO
1159	ENDIF
1160	ENDDO
1161
1162	END SUBROUTINE stg_filter_func
1163
1164
1165	!------------------------------------------------------------------------------!
1166	! Description:
1167	! ------------
1168	!> Parin for &stg_par for synthetic turbulence generator
1169	!------------------------------------------------------------------------------!
1170	SUBROUTINE stg_parin
1171
1172	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1173
1174
1175	NAMELIST /stg_par/ dt_stg_adjust, &
1176	dt_stg_call, &
1177	use_syn_turb_gen, &
1178	compute_velocity_seeds_local
1179
1180	line = ' '
1181	!
1182	!-- Try to find stg package
1183	REWIND ( 11 )
1184	line = ' '
1185	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1186	READ ( 11, '(A)', END=20 ) line
1187	ENDDO
1188	BACKSPACE ( 11 )
1189
1190	!
1191	!-- Read namelist
1192	READ ( 11, stg_par, ERR = 10, END = 20 )
1193
1194	!
1195	!-- Set flag that indicates that the synthetic turbulence generator is switched
1196	!-- on
1197	syn_turb_gen = .TRUE.
1198	GOTO 20
1199
1200	10 BACKSPACE( 11 )
1201	READ( 11 , '(A)') line
1202	CALL parin_fail_message( 'stg_par', line )
1203
1204	20 CONTINUE
1205
1206	END SUBROUTINE stg_parin
1207
1208
1209	!------------------------------------------------------------------------------!
1210	! Description:
1211	! ------------
1212	!> Read module-specific global restart data (Fortran binary format).
1213	!------------------------------------------------------------------------------!
1214	SUBROUTINE stg_rrd_global_ftn( found )
1215
1216	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1217
1218	found = .TRUE.
1219
1220
1221	SELECT CASE ( restart_string(1:length) )
1222
1223	CASE ( 'time_stg_adjust' )
1224	READ ( 13 ) time_stg_adjust
1225
1226	CASE ( 'time_stg_call' )
1227	READ ( 13 ) time_stg_call
1228
1229	CASE ( 'use_syn_turb_gen' )
1230	READ ( 13 ) use_syn_turb_gen
1231
1232	CASE DEFAULT
1233
1234	found = .FALSE.
1235
1236	END SELECT
1237
1238
1239	END SUBROUTINE stg_rrd_global_ftn
1240
1241
1242	!------------------------------------------------------------------------------!
1243	! Description:
1244	! ------------
1245	!> Read module-specific global restart data (MPI-IO).
1246	!------------------------------------------------------------------------------!
1247	SUBROUTINE stg_rrd_global_mpi
1248
1249	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1250	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1251	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1252
1253	END SUBROUTINE stg_rrd_global_mpi
1254
1255
1256	!------------------------------------------------------------------------------!
1257	! Description:
1258	! ------------
1259	!> This routine writes the respective restart data.
1260	!------------------------------------------------------------------------------!
1261	SUBROUTINE stg_wrd_global
1262
1263	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1264
1265	CALL wrd_write_string( 'time_stg_adjust' )
1266	WRITE ( 14 ) time_stg_adjust
1267
1268	CALL wrd_write_string( 'time_stg_call' )
1269	WRITE ( 14 ) time_stg_call
1270
1271	CALL wrd_write_string( 'use_syn_turb_gen' )
1272	WRITE ( 14 ) use_syn_turb_gen
1273
1274	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1275
1276	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1277	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1278	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1279
1280	ENDIF
1281
1282	END SUBROUTINE stg_wrd_global
1283
1284
1285	!------------------------------------------------------------------------------!
1286	! Description:
1287	! ------------
1288	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1289	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1290	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1291	!> (Lund, 1998).
1292	!------------------------------------------------------------------------------!
1293	SUBROUTINE stg_main
1294
1295	USE exchange_horiz_mod, &
1296	ONLY: exchange_horiz
1297
1298	INTEGER(iwp) :: i !< grid index in x-direction
1299	INTEGER(iwp) :: j !< loop index in y-direction
1300	INTEGER(iwp) :: k !< loop index in z-direction
1301
1302	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1303
1304	REAL(wp) :: dt_stg !< wheighted subtimestep
1305
1306	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1307
1308	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1309	!
1310	!-- Calculate time step which is needed for filter functions
1311	dt_stg = MAX( dt_3d, dt_stg_call )
1312	!
1313	!-- Check if synthetic turbulence generator needs to be called and new
1314	!-- perturbations need to be created or if old disturbances can be imposed
1315	!-- again.
1316	IF ( time_stg_call >= dt_stg_call .AND. &
1317	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1318	stg_call = .TRUE.
1319	ELSE
1320	stg_call = .FALSE.
1321	ENDIF
1322	!
1323	!-- Initial value of fu, fv, fw
1324	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1325	!
1326	!-- Generate turbulence at the left and right boundary. Random numbers
1327	!-- for the yz-planes at the left/right boundary are generated by the
1328	!-- left-sided mpi ranks only. After random numbers are calculated, they
1329	!-- are distributed to all other mpi ranks in the model, so that the
1330	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1331	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1332	!-- that the left- and the right-sided lateral boundary have the same initial
1333	!-- seeds.
1334	!-- Note, in case of inflow from the right only, only turbulence at the left
1335	!-- boundary is required.
1336	IF ( .NOT. ( nesting_offline .OR. &
1337	( child_domain .AND. rans_mode_parent &
1338	.AND. .NOT. rans_mode ) ) ) THEN
1339	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1340	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1341	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1342	ELSE
1343	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1344	id_stg_left, id_stg_right )
1345	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1346	id_stg_left, id_stg_right )
1347	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1348	id_stg_left, id_stg_right )
1349	!
1350	!-- Generate turbulence at the south and north boundary. Random numbers
1351	!-- for the xz-planes at the south/north boundary are generated by the
1352	!-- south-sided mpi ranks only. Please see also comment above.
1353	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1354	id_stg_south, id_stg_north )
1355	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1356	id_stg_south, id_stg_north )
1357	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1358	id_stg_south, id_stg_north )
1359	ENDIF
1360	velocity_seed_initialized = .TRUE.
1361	ENDIF
1362	!
1363	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1364	!-- seeds are only required at the left boundary, while in case of offline
1365	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1366	!-- right, south and north boundaries.
1367	IF ( stg_call ) THEN
1368	IF ( .NOT. ( nesting_offline .OR. &
1369	( child_domain .AND. rans_mode_parent &
1370	.AND. .NOT. rans_mode ) ) ) THEN
1371	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1372	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1373	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1374
1375	ELSE
1376	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1377	id_stg_left, id_stg_right )
1378	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1379	id_stg_left, id_stg_right )
1380	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1381	id_stg_left, id_stg_right )
1382
1383	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1384	id_stg_south, id_stg_north )
1385	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1386	id_stg_south, id_stg_north )
1387	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1388	id_stg_south, id_stg_north )
1389	ENDIF
1390	ENDIF
1391
1392	!
1393	!-- Turbulence generation at left and/or right boundary
1394	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1395	!
1396	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1397	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1398	!-- imposed
1399	IF ( stg_call ) THEN
1400
1401	DO j = nys, nyn
1402	DO k = nzb, nzt + 1
1403	!
1404	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1405	IF ( tu(k) == 0.0_wp ) THEN
1406	fu_yz(k,j) = fuo_yz(k,j)
1407	ELSE
1408	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1409	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1410	ENDIF
1411
1412	IF ( tv(k) == 0.0_wp ) THEN
1413	fv_yz(k,j) = fvo_yz(k,j)
1414	ELSE
1415	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1416	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1417	ENDIF
1418
1419	IF ( tw(k) == 0.0_wp ) THEN
1420	fw_yz(k,j) = fwo_yz(k,j)
1421	ELSE
1422	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1423	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1424	ENDIF
1425	ENDDO
1426	ENDDO
1427
1428	dist_yz(nzb,:,1) = 0.0_wp
1429	dist_yz(nzb,:,2) = 0.0_wp
1430	dist_yz(nzb,:,3) = 0.0_wp
1431
1432	IF ( myidx == id_stg_left ) i = nxl
1433	IF ( myidx == id_stg_right ) i = nxr+1
1434	DO j = nys, nyn
1435	DO k = nzb+1, nzt + 1
1436	!
1437	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1438	!-- Additional factors are added to improve the variance of v and w
1439	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1440	MERGE( 1.0_wp, 0.0_wp, &
1441	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1442	ENDDO
1443	ENDDO
1444
1445	IF ( myidx == id_stg_left ) i = nxl-1
1446	IF ( myidx == id_stg_right ) i = nxr+1
1447	DO j = nys, nyn
1448	DO k = nzb+1, nzt + 1
1449	!
1450	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1451	!-- Additional factors are added to improve the variance of v and w
1452	!-- experimental test of 1.2
1453	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1454	* 1.2_wp ) &
1455	* ( a21(k) * fu_yz(k,j) &
1456	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1457	MERGE( 1.0_wp, 0.0_wp, &
1458	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1459	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1460	* 1.3_wp ) &
1461	* ( a31(k) * fu_yz(k,j) &
1462	+ a32(k) * fv_yz(k,j) &
1463	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1464	MERGE( 1.0_wp, 0.0_wp, &
1465	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1466	ENDDO
1467	ENDDO
1468	ENDIF
1469	!
1470	!-- Mass flux correction following Kim et al. (2013)
1471	!-- This correction factor insures that the mass flux is preserved at the
1472	!-- inflow boundary. First, calculate mean value of the imposed
1473	!-- perturbations at yz boundary.
1474	!-- Note, this needs to be done only after the last RK3-substep, else
1475	!-- the boundary values won't be accessed.
1476	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1477	mc_factor_l = 0.0_wp
1478	mc_factor = 0.0_wp
1479	!
1480	!-- Sum up the original volume flows (with and without perturbations).
1481	!-- Note, for non-normal components (here v and w) it is actually no
1482	!-- volume flow.
1483	IF ( myidx == id_stg_left ) i = nxl
1484	IF ( myidx == id_stg_right ) i = nxr+1
1485
1486	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1487	* MERGE( 1.0_wp, 0.0_wp, &
1488	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1489
1490	IF ( myidx == id_stg_left ) i = nxl-1
1491	IF ( myidx == id_stg_right ) i = nxr+1
1492
1493	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1494	* MERGE( 1.0_wp, 0.0_wp, &
1495	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1496	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1497	* MERGE( 1.0_wp, 0.0_wp, &
1498	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1499
1500	#if defined( __parallel )
1501	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1502	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1503	#else
1504	mc_factor = mc_factor_l
1505	#endif
1506	!
1507	!-- Calculate correction factor and force zero mean perturbations.
1508	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1509
1510	IF ( myidx == id_stg_left ) i = nxl
1511	IF ( myidx == id_stg_right ) i = nxr+1
1512
1513	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
1514	* MERGE( 1.0_wp, 0.0_wp, &
1515	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1516
1517
1518	IF ( myidx == id_stg_left ) i = nxl-1
1519	IF ( myidx == id_stg_right ) i = nxr+1
1520
1521	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
1522	* MERGE( 1.0_wp, 0.0_wp, &
1523	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1524
1525	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
1526	* MERGE( 1.0_wp, 0.0_wp, &
1527	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1528	!
1529	!-- Add disturbances
1530	IF ( myidx == id_stg_left ) THEN
1531	!
1532	!-- For the left boundary distinguish between mesoscale offline / self
1533	!-- nesting and turbulent inflow at the left boundary only. In the latter
1534	!-- case turbulence is imposed on the mean inflow profiles.
1535	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1536	!
1537	!-- Add disturbance at the inflow
1538	DO j = nys, nyn
1539	DO k = nzb, nzt+1
1540	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1541	dist_yz(k,j,1) ) &
1542	* MERGE( 1.0_wp, 0.0_wp, &
1543	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1544	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1545	dist_yz(k,j,2) ) &
1546	* MERGE( 1.0_wp, 0.0_wp, &
1547	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1548	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1549	* MERGE( 1.0_wp, 0.0_wp, &
1550	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1551	ENDDO
1552	ENDDO
1553	ELSE
1554
1555	DO j = nys, nyn
1556	DO k = nzb+1, nzt
1557	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1558	* MERGE( 1.0_wp, 0.0_wp, &
1559	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1560	u(k,j,-1) = u(k,j,0)
1561	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1562	* MERGE( 1.0_wp, 0.0_wp, &
1563	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1564	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1565	* MERGE( 1.0_wp, 0.0_wp, &
1566	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1567	ENDDO
1568	ENDDO
1569	ENDIF
1570	ENDIF
1571	IF ( myidx == id_stg_right ) THEN
1572	DO j = nys, nyn
1573	DO k = nzb+1, nzt
1574	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1575	* MERGE( 1.0_wp, 0.0_wp, &
1576	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1577	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1578	* MERGE( 1.0_wp, 0.0_wp, &
1579	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1580	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1581	* MERGE( 1.0_wp, 0.0_wp, &
1582	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1583	ENDDO
1584	ENDDO
1585	ENDIF
1586	ENDIF
1587	ENDIF
1588	!
1589	!-- Turbulence generation at north and south boundary
1590	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1591	!
1592	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1593	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1594	!-- imposed
1595	IF ( stg_call ) THEN
1596	DO i = nxl, nxr
1597	DO k = nzb, nzt + 1
1598	!
1599	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1600	IF ( tu(k) == 0.0_wp ) THEN
1601	fu_xz(k,i) = fuo_xz(k,i)
1602	ELSE
1603	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1604	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1605	ENDIF
1606
1607	IF ( tv(k) == 0.0_wp ) THEN
1608	fv_xz(k,i) = fvo_xz(k,i)
1609	ELSE
1610	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1611	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1612	ENDIF
1613
1614	IF ( tw(k) == 0.0_wp ) THEN
1615	fw_xz(k,i) = fwo_xz(k,i)
1616	ELSE
1617	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1618	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1619	ENDIF
1620	ENDDO
1621	ENDDO
1622
1623
1624	dist_xz(nzb,:,1) = 0.0_wp
1625	dist_xz(nzb,:,2) = 0.0_wp
1626	dist_xz(nzb,:,3) = 0.0_wp
1627
1628	IF ( myidy == id_stg_south ) j = nys
1629	IF ( myidy == id_stg_north ) j = nyn+1
1630	DO i = nxl, nxr
1631	DO k = nzb+1, nzt + 1
1632	!
1633	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1634	!-- Additional factors are added to improve the variance of v and w
1635	!experimental test of 1.2
1636	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1637	* 1.2_wp ) &
1638	* ( a21(k) * fu_xz(k,i) &
1639	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1640	MERGE( 1.0_wp, 0.0_wp, &
1641	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1642	ENDDO
1643	ENDDO
1644
1645	IF ( myidy == id_stg_south ) j = nys-1
1646	IF ( myidy == id_stg_north ) j = nyn+1
1647	DO i = nxl, nxr
1648	DO k = nzb+1, nzt + 1
1649	!
1650	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1651	!-- Additional factors are added to improve the variance of v and w
1652	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1653	MERGE( 1.0_wp, 0.0_wp, &
1654	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1655
1656	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1657	* 1.3_wp ) &
1658	* ( a31(k) * fu_xz(k,i) &
1659	+ a32(k) * fv_xz(k,i) &
1660	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1661	MERGE( 1.0_wp, 0.0_wp, &
1662	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1663	ENDDO
1664	ENDDO
1665	ENDIF
1666
1667	!
1668	!-- Mass flux correction following Kim et al. (2013)
1669	!-- This correction factor insures that the mass flux is preserved at the
1670	!-- inflow boundary. First, calculate mean value of the imposed
1671	!-- perturbations at yz boundary.
1672	!-- Note, this needs to be done only after the last RK3-substep, else
1673	!-- the boundary values won't be accessed.
1674	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1675	mc_factor_l = 0.0_wp
1676	mc_factor = 0.0_wp
1677
1678	IF ( myidy == id_stg_south ) j = nys
1679	IF ( myidy == id_stg_north ) j = nyn+1
1680
1681	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1682	* MERGE( 1.0_wp, 0.0_wp, &
1683	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1684
1685	IF ( myidy == id_stg_south ) j = nys-1
1686	IF ( myidy == id_stg_north ) j = nyn+1
1687
1688	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1689	* MERGE( 1.0_wp, 0.0_wp, &
1690	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1691	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1692	* MERGE( 1.0_wp, 0.0_wp, &
1693	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1694
1695	#if defined( __parallel )
1696	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1697	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1698	#else
1699	mc_factor = mc_factor_l
1700	#endif
1701
1702	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1703
1704	IF ( myidy == id_stg_south ) j = nys
1705	IF ( myidy == id_stg_north ) j = nyn+1
1706
1707	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
1708	* MERGE( 1.0_wp, 0.0_wp, &
1709	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1710
1711
1712	IF ( myidy == id_stg_south ) j = nys-1
1713	IF ( myidy == id_stg_north ) j = nyn+1
1714
1715	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
1716	* MERGE( 1.0_wp, 0.0_wp, &
1717	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1718
1719	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
1720	* MERGE( 1.0_wp, 0.0_wp, &
1721	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1722	!
1723	!-- Add disturbances
1724	IF ( myidy == id_stg_south ) THEN
1725	DO i = nxl, nxr
1726	DO k = nzb+1, nzt
1727	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1728	* MERGE( 1.0_wp, 0.0_wp, &
1729	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1730	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1731	* MERGE( 1.0_wp, 0.0_wp, &
1732	BTEST( wall_flags_total_0(k,0,i), 2 ) )
1733	v(k,-1,i) = v(k,0,i)
1734	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1735	* MERGE( 1.0_wp, 0.0_wp, &
1736	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1737	ENDDO
1738	ENDDO
1739	ENDIF
1740	IF ( myidy == id_stg_north ) THEN
1741
1742	DO i = nxl, nxr
1743	DO k = nzb+1, nzt
1744	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1745	* MERGE( 1.0_wp, 0.0_wp, &
1746	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1747	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1748	* MERGE( 1.0_wp, 0.0_wp, &
1749	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1750	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1751	* MERGE( 1.0_wp, 0.0_wp, &
1752	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1753	ENDDO
1754	ENDDO
1755	ENDIF
1756	ENDIF
1757	ENDIF
1758	!
1759	!-- Exchange ghost points.
1760	CALL exchange_horiz( u, nbgp )
1761	CALL exchange_horiz( v, nbgp )
1762	CALL exchange_horiz( w, nbgp )
1763	!
1764	!-- Finally, set time counter for calling STG to zero
1765	IF ( stg_call ) time_stg_call = 0.0_wp
1766
1767	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1768
1769	END SUBROUTINE stg_main
1770
1771	!------------------------------------------------------------------------------!
1772	! Description:
1773	! ------------
1774	!> Generate a set of random number rand_it wich is equal on each PE
1775	!> and calculate the velocity seed f_n.
1776	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1777	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1778	!> parts are collected to form the full array.
1779	!------------------------------------------------------------------------------!
1780	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1781
1782	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1783	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1784	INTEGER(iwp) :: j !< loop index in y-direction
1785	INTEGER(iwp) :: jj !< loop index in y-direction
1786	INTEGER(iwp) :: k !< loop index in z-direction
1787	INTEGER(iwp) :: kk !< loop index in z-direction
1788	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1789
1790	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1791	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1792
1793	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1794	REAL(wp) :: rand_av !< average of random number
1795	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1796
1797	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1798	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1799
1800	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1801	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1802
1803	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1804	!
1805	!-- Generate random numbers using the parallel random generator.
1806	!-- The set of random numbers are modified to have an average of 0 and
1807	!-- unit variance. Note, at the end the random number array must be defined
1808	!-- globally in order to compute the correlation matrices. However,
1809	!-- the calculation and normalization of random numbers is done locally,
1810	!-- while the result is later distributed to all processes. Further,
1811	!-- please note, a set of random numbers is only calculated for the
1812	!-- left boundary, while the right boundary uses the same random numbers
1813	!-- and thus also computes the same correlation matrix.
1814	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1815	rand_it = 0.0_wp
1816
1817	rand_av = 0.0_wp
1818	rand_sigma_inv = 0.0_wp
1819	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1820	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
1821	KIND=wp )
1822	!
1823	!-- Compute and normalize random numbers.
1824	DO j = nys - mergp, nyn + mergp
1825	!
1826	!-- Put the random seeds at grid point j
1827	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1828	DO k = nzb - mergp, nzt + 1 + mergp
1829	CALL random_number_parallel( random_dummy )
1830	rand_it(k,j) = random_dummy
1831	ENDDO
1832	!
1833	!-- Get the new random seeds from last call at grid point j
1834	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1835	ENDDO
1836	!
1837	!-- For normalization to zero mean, sum-up the global random numers.
1838	!-- To normalize the global set of random numbers,
1839	!-- the inner ghost layers mergp must not be summed-up, else
1840	!-- the random numbers on the ghost layers will be stronger weighted as they
1841	!-- also occur on the inner subdomains.
1842	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1843	MERGE( nyn, nyn + mergp, nyn /= ny )
1844	DO k = nzb - mergp, nzt + 1 + mergp
1845	rand_av = rand_av + rand_it(k,j)
1846	ENDDO
1847	ENDDO
1848
1849	#if defined( __parallel )
1850	!
1851	!-- Sum-up the local averages of the random numbers
1852	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1853	MPI_SUM, comm1dy, ierr )
1854	#endif
1855	rand_av = rand_av * nyz_inv
1856	!
1857	!-- Obtain zero mean
1858	rand_it= rand_it - rand_av
1859	!
1860	!-- Now, compute the variance
1861	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1862	MERGE( nyn, nyn + mergp, nyn /= ny )
1863	DO k = nzb - mergp, nzt + 1 + mergp
1864	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1865	ENDDO
1866	ENDDO
1867
1868	#if defined( __parallel )
1869	!
1870	!-- Sum-up the local quadratic averages of the random numbers
1871	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1872	MPI_SUM, comm1dy, ierr )
1873	#endif
1874	!
1875	!-- Compute standard deviation
1876	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1877	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1878	ELSE
1879	rand_sigma_inv = 1.0_wp
1880	ENDIF
1881	!
1882	!-- Normalize with standard deviation to obtain unit variance
1883	rand_it = rand_it * rand_sigma_inv
1884
1885	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1886	!
1887	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
1888	!-- are two options. In the first one, the computation of the seeds is
1889	!-- distributed to all processes along the communicator comm1dy and
1890	!-- gathered on the leftmost and, if necessary, on the rightmost process.
1891	!-- For huge length scales the computational effort can become quite huge
1892	!-- (it scales with the turbulent length scales), so that gain by parallelization
1893	!-- exceeds the costs by the subsequent communication.
1894	!-- In the second option, which performs better when the turbulent length scales
1895	!-- are parametrized and thus the loops are smaller, the seeds are computed
1896	!-- locally and no communication is necessary.
1897	IF ( compute_velocity_seeds_local ) THEN
1898
1899	f_n = 0.0_wp
1900	DO j = nys, nyn
1901	DO k = nzb, nzt+1
1902	DO jj = -n_y(k), n_y(k)
1903	DO kk = -n_z(k), n_z(k)
1904	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1905	ENDDO
1906	ENDDO
1907	ENDDO
1908	ENDDO
1909
1910	ELSE
1911
1912	f_n_l = 0.0_wp
1913	DO j = nys, nyn
1914	DO k = nzb_x_stg, nzt_x_stg+1
1915	DO jj = -n_y(k), n_y(k)
1916	DO kk = -n_z(k), n_z(k)
1917	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1918	ENDDO
1919	ENDDO
1920	ENDDO
1921	ENDDO
1922	!
1923	!-- Gather velocity seeds of full subdomain
1924	send_count = nzt_x_stg - nzb_x_stg + 1
1925	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1926
1927	#if defined( __parallel )
1928	!
1929	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1930	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1931	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1932	id_left, comm1dx, ierr )
1933	!
1934	!-- If required, gather the same velocity seed matrix on right boundary
1935	!-- mpi ranks (in offline nesting for example).
1936	IF ( PRESENT( id_right ) ) THEN
1937	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1938	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1939	id_right, comm1dx, ierr )
1940	ENDIF
1941	#else
1942	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1943	!
1944	!-- Next line required to avoid compile errors because of unused dummy arguments
1945	IF ( id_left == 0 ) id_right = 0
1946	#endif
1947
1948	ENDIF
1949
1950	DEALLOCATE( rand_it )
1951
1952	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1953
1954	END SUBROUTINE stg_generate_seed_yz
1955
1956
1957	!------------------------------------------------------------------------------!
1958	! Description:
1959	! ------------
1960	!> Generate a set of random number rand_it wich is equal on each PE
1961	!> and calculate the velocity seed f_n.
1962	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1963	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1964	!> parts are collected to form the full array.
1965	!------------------------------------------------------------------------------!
1966	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1967
1968	INTEGER(iwp) :: i !< loop index in x-direction
1969	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1970	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1971	INTEGER(iwp) :: ii !< loop index in x-direction
1972	INTEGER(iwp) :: k !< loop index in z-direction
1973	INTEGER(iwp) :: kk !< loop index in z-direction
1974	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1975
1976	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1977	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1978
1979	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1980	REAL(wp) :: rand_av !< average of random number
1981	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1982
1983	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1984	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1985
1986	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1987	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1988
1989	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1990
1991	!
1992	!-- Generate random numbers using the parallel random generator.
1993	!-- The set of random numbers are modified to have an average of 0 and
1994	!-- unit variance. Note, at the end the random number array must be defined
1995	!-- globally in order to compute the correlation matrices. However,
1996	!-- the calculation and normalization of random numbers is done locally,
1997	!-- while the result is later distributed to all processes. Further,
1998	!-- please note, a set of random numbers is only calculated for the
1999	!-- left boundary, while the right boundary uses the same random numbers
2000	!-- and thus also computes the same correlation matrix.
2001	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
2002	rand_it = 0.0_wp
2003
2004	rand_av = 0.0_wp
2005	rand_sigma_inv = 0.0_wp
2006	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
2007	* ( nx + mergp - ( 0 - mergp ) +1 ), &
2008	KIND=wp )
2009	!
2010	!-- Compute and normalize random numbers.
2011	DO i = nxl - mergp, nxr + mergp
2012	!
2013	!-- Put the random seeds at grid point ii
2014	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
2015	DO k = nzb - mergp, nzt + 1 + mergp
2016	CALL random_number_parallel( random_dummy )
2017	rand_it(k,i) = random_dummy
2018	ENDDO
2019	!
2020	!-- Get the new random seeds from last call at grid point ii
2021	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
2022	ENDDO
2023	!
2024	!-- For normalization to zero mean, sum-up the global random numers.
2025	!-- To normalize the global set of random numbers,
2026	!-- the inner ghost layers mergp must not be summed-up, else
2027	!-- the random numbers on the ghost layers will be stronger weighted as they
2028	!-- also occur on the inner subdomains.
2029	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
2030	MERGE( nxr, nxr + mergp, nxr /= nx )
2031	DO k = nzb - mergp, nzt + 1 + mergp
2032	rand_av = rand_av + rand_it(k,i)
2033	ENDDO
2034	ENDDO
2035
2036	#if defined( __parallel )
2037	!
2038	!-- Sum-up the local averages of the random numbers
2039	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
2040	MPI_SUM, comm1dx, ierr )
2041	#endif
2042	rand_av = rand_av * nxz_inv
2043	!
2044	!-- Obtain zero mean
2045	rand_it= rand_it - rand_av
2046	!
2047	!-- Now, compute the variance
2048	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
2049	MERGE( nxr, nxr + mergp, nxr /= nx )
2050	DO k = nzb - mergp, nzt + 1 + mergp
2051	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2052	ENDDO
2053	ENDDO
2054
2055	#if defined( __parallel )
2056	!
2057	!-- Sum-up the local quadratic averages of the random numbers
2058	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
2059	MPI_SUM, comm1dx, ierr )
2060	#endif
2061	!
2062	!-- Compute standard deviation
2063	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2064	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2065	ELSE
2066	rand_sigma_inv = 1.0_wp
2067	ENDIF
2068	!
2069	!-- Normalize with standard deviation to obtain unit variance
2070	rand_it = rand_it * rand_sigma_inv
2071
2072	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2073	!
2074	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
2075	!-- are two options. In the first one, the computation of the seeds is
2076	!-- distributed to all processes along the communicator comm1dx and
2077	!-- gathered on the southmost and, if necessary, on the northmost process.
2078	!-- For huge length scales the computational effort can become quite huge
2079	!-- (it scales with the turbulent length scales), so that gain by parallelization
2080	!-- exceeds the costs by the subsequent communication.
2081	!-- In the second option, which performs better when the turbulent length scales
2082	!-- are parametrized and thus the loops are smaller, the seeds are computed
2083	!-- locally and no communication is necessary.
2084	IF ( compute_velocity_seeds_local ) THEN
2085
2086	f_n = 0.0_wp
2087	DO i = nxl, nxr
2088	DO k = nzb, nzt+1
2089	DO ii = -n_x(k), n_x(k)
2090	DO kk = -n_z(k), n_z(k)
2091	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2092	ENDDO
2093	ENDDO
2094	ENDDO
2095	ENDDO
2096
2097	ELSE
2098
2099	f_n_l = 0.0_wp
2100	DO i = nxl, nxr
2101	DO k = nzb_y_stg, nzt_y_stg+1
2102	DO ii = -n_x(k), n_x(k)
2103	DO kk = -n_z(k), n_z(k)
2104	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2105	ENDDO
2106	ENDDO
2107	ENDDO
2108	ENDDO
2109	!
2110	!-- Gather velocity seeds of full subdomain
2111	send_count = nzt_y_stg - nzb_y_stg + 1
2112	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2113
2114	#if defined( __parallel )
2115	!
2116	!-- Gather the processed velocity seed on south boundary mpi ranks.
2117	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2118	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2119	id_south, comm1dy, ierr )
2120	!
2121	!-- Gather the processed velocity seed on north boundary mpi ranks.
2122	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2123	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2124	id_north, comm1dy, ierr )
2125	#else
2126	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2127	!
2128	!-- Next line required to avoid compile errors because of unused dummy arguments
2129	IF ( id_north == 0 ) id_south = 0
2130	#endif
2131
2132	ENDIF
2133
2134	DEALLOCATE( rand_it )
2135
2136	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2137
2138	END SUBROUTINE stg_generate_seed_xz
2139
2140	!------------------------------------------------------------------------------!
2141	! Description:
2142	! ------------
2143	!> Parametrization of the Reynolds stress tensor, following the parametrization
2144	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2145	!> dispserion modelling. Please note, the parametrization does not distinguish
2146	!> between along-wind and cross-wind turbulence.
2147	!------------------------------------------------------------------------------!
2148	SUBROUTINE parametrize_reynolds_stress
2149
2150	INTEGER(iwp) :: k !< loop index in z-direction
2151
2152	REAL(wp) :: zzi !< ratio of z/zi
2153
2154	DO k = nzb+1, nzt+1
2155	!
2156	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2157	!-- The function decreases to 1/10 after one length scale above the
2158	!-- ABL top.
2159	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2160	!
2161	!-- Determine normalized height coordinate
2162	zzi = zu(k) / zi_ribulk
2163	!
2164	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2165	!-- to the denominator, else the mergpe-function can crash if scale_l is
2166	!-- zero.
2167	r11(k) = scale_us*2 ( &
2168	MERGE( 0.35_wp * ABS( &
2169	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2170	)**( 2.0_wp / 3.0_wp ), &
2171	0.0_wp, &
2172	scale_l < 0.0_wp ) &
2173	+ 5.0_wp - 4.0_wp * zzi &
2174	) * blend
2175
2176	r22(k) = r11(k)
2177	!
2178	!-- w'w'
2179	r33(k) = scale_wm*2 ( &
2180	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2181	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2182	) * blend
2183	!
2184	!-- u'w' and v'w'. Assume isotropy.
2185	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2186	r32(k) = r31(k)
2187	!
2188	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2189	!-- a similar profile as for u'w'.
2190	r21(k) = r31(k)
2191	ENDDO
2192
2193	!
2194	!-- Set bottom boundary condition
2195	r11(nzb) = r11(nzb+1)
2196	r22(nzb) = r22(nzb+1)
2197	r33(nzb) = r33(nzb+1)
2198
2199	r21(nzb) = r11(nzb+1)
2200	r31(nzb) = r31(nzb+1)
2201	r32(nzb) = r32(nzb+1)
2202
2203
2204	END SUBROUTINE parametrize_reynolds_stress
2205
2206	!------------------------------------------------------------------------------!
2207	! Description:
2208	! ------------
2209	!> Calculate the coefficient matrix from the Lund rotation.
2210	!------------------------------------------------------------------------------!
2211	SUBROUTINE calc_coeff_matrix
2212
2213	INTEGER(iwp) :: k !< loop index in z-direction
2214
2215	!
2216	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2217	DO k = nzb+1, nzt+1
2218	IF ( r11(k) > 10E-6_wp ) THEN
2219	a11(k) = SQRT( r11(k) )
2220	a21(k) = r21(k) / a11(k)
2221	a31(k) = r31(k) / a11(k)
2222	ELSE
2223	a11(k) = 10E-8_wp
2224	a21(k) = 10E-8_wp
2225	a31(k) = 10E-8_wp
2226	ENDIF
2227	ENDDO
2228	DO k = nzb+1, nzt+1
2229	a22(k) = r22(k) - a21(k)**2
2230	IF ( a22(k) > 10E-6_wp ) THEN
2231	a22(k) = SQRT( a22(k) )
2232	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2233	ELSE
2234	a22(k) = 10E-8_wp
2235	a32(k) = 10E-8_wp
2236	ENDIF
2237	ENDDO
2238	DO k = nzb+1, nzt+1
2239	a33(k) = r33(k) - a31(k)2 - a32(k)2
2240	IF ( a33(k) > 10E-6_wp ) THEN
2241	a33(k) = SQRT( a33(k) )
2242	ELSE
2243	a33(k) = 10E-8_wp
2244	ENDIF
2245	ENDDO
2246	!
2247	!-- Set bottom boundary condition
2248	a11(nzb) = a11(nzb+1)
2249	a22(nzb) = a22(nzb+1)
2250	a21(nzb) = a21(nzb+1)
2251	a33(nzb) = a33(nzb+1)
2252	a31(nzb) = a31(nzb+1)
2253	a32(nzb) = a32(nzb+1)
2254
2255	END SUBROUTINE calc_coeff_matrix
2256
2257	!------------------------------------------------------------------------------!
2258	! Description:
2259	! ------------
2260	!> This routine controls the re-adjustment of the turbulence statistics used
2261	!> for generating turbulence at the lateral boundaries.
2262	!------------------------------------------------------------------------------!
2263	SUBROUTINE stg_adjust
2264
2265	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2266	!
2267	!-- In case of dirichlet inflow boundary conditions only at one lateral
2268	!-- boundary, i.e. in the case no offline or self nesting is applied but
2269	!-- synthetic turbulence shall be parametrized nevertheless, the
2270	!-- boundary-layer depth need to determined first.
2271	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2272	CALL nesting_offl_calc_zi
2273	!
2274	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2275	!-- are calculated.
2276	CALL calc_scaling_variables
2277	!
2278	!-- Set length and time scales depending on boundary-layer height
2279	CALL calc_length_and_time_scale
2280	!
2281	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2282	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2283	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2284	!-- friction velocity and velocity scale.
2285	CALL parametrize_reynolds_stress
2286	!
2287	!-- Calculate coefficient matrix from Reynolds stress tensor
2288	!-- (Lund rotation)
2289	CALL calc_coeff_matrix
2290	!
2291	!-- Determine filter functions on basis of updated length scales
2292	CALL stg_filter_func( nux, bux ) !filter ux
2293	CALL stg_filter_func( nuy, buy ) !filter uy
2294	CALL stg_filter_func( nuz, buz ) !filter uz
2295	CALL stg_filter_func( nvx, bvx ) !filter vx
2296	CALL stg_filter_func( nvy, bvy ) !filter vy
2297	CALL stg_filter_func( nvz, bvz ) !filter vz
2298	CALL stg_filter_func( nwx, bwx ) !filter wx
2299	CALL stg_filter_func( nwy, bwy ) !filter wy
2300	CALL stg_filter_func( nwz, bwz ) !filter wz
2301	!
2302	!-- Reset time counter for controlling next adjustment to zero
2303	time_stg_adjust = 0.0_wp
2304
2305	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2306
2307	END SUBROUTINE stg_adjust
2308
2309
2310	!------------------------------------------------------------------------------!
2311	! Description:
2312	! ------------
2313	!> Calculates turbuluent length and time scales if these are not available
2314	!> from measurements.
2315	!------------------------------------------------------------------------------!
2316	SUBROUTINE calc_length_and_time_scale
2317
2318	INTEGER(iwp) :: k !< loop index in z-direction
2319
2320	REAL(wp) :: length_scale_dum !< effectively used length scale
2321
2322	!
2323	!-- In initial call the boundary-layer depth can be zero. This case, set
2324	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2325	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2326	!
2327	!-- Set-up default turbulent length scales. From the numerical point of
2328	!-- view the imposed perturbations should not be immediately dissipated
2329	!-- by the numerics. The numerical dissipation, however, acts on scales
2330	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2331	!-- length scale to 8 time the grid spacing. Further, above the boundary
2332	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2333	!-- imposing any perturbations) in order to save computational costs.
2334	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2335	!-- using the length scales and the mean profiles of u- and v-component.
2336	DO k = nzb+1, nzt+1
2337	!
2338	!-- Determine blending parameter. Within the boundary layer length scales
2339	!-- are constant, while above lengths scales approach gradully zero,
2340	!-- i.e. imposed turbulence is not correlated in space and time,
2341	!-- just white noise, which saves computations power as the loops for the
2342	!-- computation of the filter functions depend on the length scales.
2343	!-- The value decreases to 1/10 after one length scale above the
2344	!-- ABL top.
2345	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2346	!
2347	!-- Assume isotropic turbulence length scales
2348	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2349	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2350	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2351	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2352	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2353	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2354	!
2355	!-- Along the vertical direction limit the length scale further by the
2356	!-- boundary-layer depth to assure that no length scales larger than
2357	!-- the boundary-layer depth are used
2358	length_scale_dum = MIN( length_scale, zi_ribulk )
2359
2360	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2361	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2362	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2363	!
2364	!-- Limit time scales, else they become very larger for low wind speed,
2365	!-- imposing long-living inflow perturbations which in turn propagate
2366	!-- further into the model domain. Use u_init and v_init to calculate
2367	!-- the time scales, which will be equal to the inflow profiles, both,
2368	!-- in offline nesting mode or in dirichlet/radiation mode.
2369	tu(k) = MIN( dt_stg_adjust, length_scale / &
2370	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2371	tv(k) = MIN( dt_stg_adjust, length_scale / &
2372	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2373	!
2374	!-- Time scale of w-component is a mixture from u- and v-component.
2375	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2376
2377	ENDDO
2378	!
2379	!-- Set bottom boundary condition for the length and time scales
2380	nux(nzb) = nux(nzb+1)
2381	nuy(nzb) = nuy(nzb+1)
2382	nuz(nzb) = nuz(nzb+1)
2383	nvx(nzb) = nvx(nzb+1)
2384	nvy(nzb) = nvy(nzb+1)
2385	nvz(nzb) = nvz(nzb+1)
2386	nwx(nzb) = nwx(nzb+1)
2387	nwy(nzb) = nwy(nzb+1)
2388	nwz(nzb) = nwz(nzb+1)
2389
2390	tu(nzb) = tu(nzb+1)
2391	tv(nzb) = tv(nzb+1)
2392	tw(nzb) = tw(nzb+1)
2393
2394
2395	END SUBROUTINE calc_length_and_time_scale
2396
2397	!------------------------------------------------------------------------------!
2398	! Description:
2399	! ------------
2400	!> Calculate scaling variables which are used for turbulence parametrization
2401	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2402	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2403	!------------------------------------------------------------------------------!
2404	SUBROUTINE calc_scaling_variables
2405
2406	INTEGER(iwp) :: i !< loop index in x-direction
2407	INTEGER(iwp) :: j !< loop index in y-direction
2408	INTEGER(iwp) :: k !< loop index in z-direction
2409	INTEGER(iwp) :: m !< surface element index
2410
2411	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2412	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2413	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2414	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2415	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2416	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2417	REAL(wp) :: w_convective !< convective velocity scale
2418
2419	!
2420	!-- Calculate mean friction velocity, velocity scale, heat flux and
2421	!-- near-surface temperature in the model domain.
2422	pt_surf_mean_l = 0.0_wp
2423	shf_mean_l = 0.0_wp
2424	scale_l_l = 0.0_wp
2425	friction_vel_l = 0.0_wp
2426	DO m = 1, surf_def_h(0)%ns
2427	i = surf_def_h(0)%i(m)
2428	j = surf_def_h(0)%j(m)
2429	k = surf_def_h(0)%k(m)
2430	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2431	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2432	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2433	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2434	ENDDO
2435	DO m = 1, surf_lsm_h%ns
2436	i = surf_lsm_h%i(m)
2437	j = surf_lsm_h%j(m)
2438	k = surf_lsm_h%k(m)
2439	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2440	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2441	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2442	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2443	ENDDO
2444	DO m = 1, surf_usm_h%ns
2445	i = surf_usm_h%i(m)
2446	j = surf_usm_h%j(m)
2447	k = surf_usm_h%k(m)
2448	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2449	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2450	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2451	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2452	ENDDO
2453
2454	#if defined( __parallel )
2455	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2456	comm2d, ierr )
2457	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2458	comm2d, ierr )
2459	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2460	comm2d, ierr )
2461	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2462	comm2d, ierr )
2463	#else
2464	scale_us = friction_vel_l
2465	shf_mean = shf_mean_l
2466	scale_l = scale_l_l
2467	pt_surf_mean = pt_surf_mean_l
2468	#endif
2469
2470	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2471	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2472	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2473	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2474	!
2475	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2476	!-- is negative, set convective velocity scale to zero.
2477	IF ( shf_mean > 0.0_wp ) THEN
2478	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2479	ELSE
2480	w_convective = 0.0_wp
2481	ENDIF
2482	!
2483	!-- Finally, in order to consider also neutral or stable stratification,
2484	!-- compute momentum velocity scale from u* and convective velocity scale,
2485	!-- according to Rotach et al. (1996).
2486	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2487
2488	END SUBROUTINE calc_scaling_variables
2489
2490	END MODULE synthetic_turbulence_generator_mod

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