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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4641

Last change on this file since 4641 was 4640, checked in by suehring, 4 years ago
synthetic turbulence generator: to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit Obukhov length (term is not valid for near neutral conditions); to avoid unrealistically large perturbations, change computation of r21 so that this resembles the vertical transport of horizontal momentum
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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 terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2020 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4640 2020-08-11 16:28:32Z suehring $
27	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
28	! Obukhov length (term is not valid for near neutral conditions)
29	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
30	! the vertical transport of horizontal momentum
31	!
32	! 4629 2020-07-29 09:37:56Z raasch
33	! support for MPI Fortran77 interface (mpif.h) removed
34	!
35	! 4603 2020-07-14 16:08:30Z suehring
36	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
37	! initialized properly
38	!
39	! 4566 2020-06-16 10:11:51Z suehring
40	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
41	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
42	! - change default value of time interval to adjust turbulence parametrization
43	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
44	!
45	! 4562 2020-06-12 08:38:47Z raasch
46	! Parts of r4559 re-formatted
47	!
48	! 4559 2020-06-11 08:51:48Z raasch
49	! File re-formatted to follow the PALM coding standard
50	!
51	! 4535 2020-05-15 12:07:23Z raasch
52	! Bugfix for restart data format query
53	!
54	! 4495 2020-04-13 20:11:20Z raasch
55	! Restart data handling with MPI-IO added
56	!
57	! 4481 2020-03-31 18:55:54Z maronga
58	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
59	!
60	! 4442 2020-03-04 19:21:13Z suehring
61	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
62	! (was accidantly changed).
63	!
64	! 4441 2020-03-04 19:20:35Z suehring
65	! Correct misplaced preprocessor directive
66	!
67	! 4438 2020-03-03 20:49:28Z suehring
68	! Performance optimizations in velocity-seed calculation:
69	! - Random number array is only defined and computed locally (except for normalization to zero mean
70	! and unit variance)
71	! - Parallel random number generator is applied independent on the 2D random numbers in other
72	! routines
73	! - Option to decide wheter velocity seeds are computed locally without any further communication
74	! or are computed by all processes along the communicator
75	!
76	! 4346 2019-12-18 11:55:56Z motisi
77	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
78	! information used in wall_flags_static_0
79	!
80	! 4335 2019-12-12 16:39:05Z suehring
81	! Commentation of last commit
82	!
83	! 4332 2019-12-10 19:44:12Z suehring
84	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
85	! Further, minor bugfix in initial velocity seed calculation.
86	!
87	! 4329 2019-12-10 15:46:36Z motisi
88	! Renamed wall_flags_0 to wall_flags_static_0
89	!
90	! 4309 2019-11-26 18:49:59Z suehring
91	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
92	! the parallel random number generator. Random numbers are now only computed and normalized locally,
93	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
94	! array.
95	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
96	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
97	!
98	! 4182 2019-08-22 15:20:23Z scharf
99	! Corrected "Former revisions" section
100	!
101	! 4148 2019-08-08 11:26:00Z suehring
102	! Remove unused variable
103	!
104	! 4144 2019-08-06 09:11:47Z raasch
105	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
106	!
107	! 4071 2019-07-03 20:02:00Z suehring
108	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
109	! file.
110	!
111	! 4022 2019-06-12 11:52:39Z suehring
112	! Several bugfixes and improvements
113	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
114	! instabilities in case the mean volume flow is close to zero)
115	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
116	! numerically unstable
117	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
118	! case dt_stg_call /= dt_3d
119	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
120	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
121	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
122	!
123	! 3987 2019-05-22 09:52:13Z kanani
124	! Introduce alternative switch for debug output during timestepping
125	!
126	! 3938 2019-04-29 16:06:25Z suehring
127	! Remove unused variables
128	!
129	! 3937 2019-04-29 15:09:07Z suehring
130	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
131	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
132	! synthetic turbulence parametrization.
133	!
134	! 3909 2019-04-17 09:13:25Z suehring
135	! Minor bugfix for last commit
136	!
137	! 3900 2019-04-16 15:17:43Z suehring
138	! Missing re-calculation of perturbation seeds in case of restarts
139	!
140	! 3891 2019-04-12 17:52:01Z suehring
141	! Bugfix in initialization in case of restart runs.
142	!
143	! 3885 2019-04-11 11:29:34Z kanani
144	! Changes related to global restructuring of location messages and introduction of additional debug
145	! messages
146	!
147	!
148	! Removed unused variables
149	!
150	! 3719 2019-02-06 13:10:18Z kanani
151	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
152	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
153	! for better overview.
154	!
155	! 2259 2017-06-08 09:09:11Z gronemeier
156	! Initial revision
157	!
158	! Authors:
159	! --------
160	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
161	!
162	!
163	! Description:
164	! ------------
165	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
166	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
167	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
168	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
169	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
170	!> parametrized within the boundary layer.
171	!>
172	!> @todo Enable cyclic_fill
173	!> Implement turbulence generation for e and pt
174	!> @note <Enter notes on the module>
175	!> @bug Height information from input file is not used. Profiles from input must match with current
176	!> PALM grid.
177	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
178	!--------------------------------------------------------------------------------------------------!
179	MODULE synthetic_turbulence_generator_mod
180
181
182	USE arrays_3d, &
183	ONLY: dzw, &
184	ddzw, &
185	drho_air, &
186	mean_inflow_profiles, &
187	pt, &
188	pt_init, &
189	q, &
190	q_init, &
191	u, &
192	u_init, &
193	v, &
194	v_init, &
195	w, &
196	zu, &
197	zw
198
199	USE basic_constants_and_equations_mod, &
200	ONLY: g, &
201	kappa, &
202	pi
203
204	USE control_parameters, &
205	ONLY: bc_lr, &
206	bc_ns, &
207	child_domain, &
208	coupling_char, &
209	debug_output_timestep, &
210	dt_3d, &
211	e_init, &
212	humidity, &
213	initializing_actions, &
214	intermediate_timestep_count, &
215	intermediate_timestep_count_max, &
216	length, &
217	message_string, &
218	nesting_offline, &
219	neutral, &
220	num_mean_inflow_profiles, &
221	random_generator, &
222	rans_mode, &
223	restart_data_format_output, &
224	restart_string, &
225	syn_turb_gen, &
226	time_since_reference_point, &
227	turbulent_inflow
228
229	USE cpulog, &
230	ONLY: cpu_log, &
231	log_point_s
232
233	USE grid_variables, &
234	ONLY: ddx, &
235	ddy, &
236	dx, &
237	dy
238
239	USE indices, &
240	ONLY: nbgp, &
241	nz, &
242	nzb, &
243	nzt, &
244	nx, &
245	nxl, &
246	nxlu, &
247	nxr, &
248	ny, &
249	nys, &
250	nysv, &
251	nyn, &
252	wall_flags_total_0
253
254	USE kinds
255
256	#if defined( __parallel )
257	USE MPI
258	#endif
259
260	USE nesting_offl_mod, &
261	ONLY: nesting_offl_calc_zi, &
262	zi_ribulk
263
264	USE pegrid, &
265	ONLY: comm1dx, &
266	comm1dy, &
267	comm2d, &
268	ierr, &
269	myidx, &
270	myidy, &
271	pdims
272
273	USE pmc_interface, &
274	ONLY : rans_mode_parent
275
276	USE random_generator_parallel, &
277	ONLY: init_parallel_random_generator, &
278	random_dummy, &
279	random_number_parallel, &
280	random_seed_parallel
281
282	USE restart_data_mpi_io_mod, &
283	ONLY: rrd_mpi_io, &
284	wrd_mpi_io
285
286	USE transpose_indices, &
287	ONLY: nzb_x, &
288	nzt_x
289
290	USE surface_mod, &
291	ONLY: surf_def_h, &
292	surf_lsm_h, &
293	surf_usm_h
294
295	IMPLICIT NONE
296
297	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
298	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
299	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
300	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
301	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
302	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
303	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
304	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
305	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
306	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
307	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
308	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
309	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
310	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
311	#if defined( __parallel )
312	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
313	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
314	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
315	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
316	#endif
317
318	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
319	!< required for bias correction of imposed perturbations
320	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
321	!< required for bias correction of imposed perturbations
322
323	#if defined( __parallel )
324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
328	#endif
329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
330	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
331	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
333	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
334	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
335	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
336	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
337	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
338
339	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
340	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
341	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
342	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
343
344
345	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
346	!< no time correlation to the timestep before should be considered
347	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
348	!< or if computation is distributed over several processes
349	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
350	!< (.FALSE.) or if it parametrized
351	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
352	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
353
354
355	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
356	!< scales above the boundary layer
357	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
358	!< one length scale above ABL top
359	REAL(wp) :: d_l !< blend_coeff/length_scale
360	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
361	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
362	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
363	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
364	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
365	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
366	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
367	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
368
369	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
370
371
372	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
373	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
374	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
375	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
376	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
377	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
378
379	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
380	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
381	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
382	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
383	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
384	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
385	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
386	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
387	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
388
389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
410
411	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
412	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
413
414	!
415	!-- PALM interfaces:
416	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
417	INTERFACE stg_adjust
418	MODULE PROCEDURE stg_adjust
419	END INTERFACE stg_adjust
420	!
421	!-- Input parameter checks to be done in check_parameters
422	INTERFACE stg_check_parameters
423	MODULE PROCEDURE stg_check_parameters
424	END INTERFACE stg_check_parameters
425
426	!
427	!-- Calculate filter functions
428	INTERFACE stg_filter_func
429	MODULE PROCEDURE stg_filter_func
430	END INTERFACE stg_filter_func
431
432	!
433	!-- Generate velocity seeds at south and north domain boundary
434	INTERFACE stg_generate_seed_xz
435	MODULE PROCEDURE stg_generate_seed_xz
436	END INTERFACE stg_generate_seed_xz
437	!
438	!-- Generate velocity seeds at left and/or right domain boundary
439	INTERFACE stg_generate_seed_yz
440	MODULE PROCEDURE stg_generate_seed_yz
441	END INTERFACE stg_generate_seed_yz
442
443	!
444	!-- Output of information to the header file
445	INTERFACE stg_header
446	MODULE PROCEDURE stg_header
447	END INTERFACE stg_header
448
449	!
450	!-- Initialization actions
451	INTERFACE stg_init
452	MODULE PROCEDURE stg_init
453	END INTERFACE stg_init
454
455	!
456	!-- Main procedure of synth. turb. gen.
457	INTERFACE stg_main
458	MODULE PROCEDURE stg_main
459	END INTERFACE stg_main
460
461	!
462	!-- Reading of NAMELIST parameters
463	INTERFACE stg_parin
464	MODULE PROCEDURE stg_parin
465	END INTERFACE stg_parin
466
467	!
468	!-- Reading of parameters for restart runs
469	INTERFACE stg_rrd_global
470	MODULE PROCEDURE stg_rrd_global_ftn
471	MODULE PROCEDURE stg_rrd_global_mpi
472	END INTERFACE stg_rrd_global
473
474	!
475	!-- Writing of binary output for restart runs
476	INTERFACE stg_wrd_global
477	MODULE PROCEDURE stg_wrd_global
478	END INTERFACE stg_wrd_global
479
480	SAVE
481
482	PRIVATE
483
484	!
485	!-- Public interfaces
486	PUBLIC stg_adjust, &
487	stg_check_parameters, &
488	stg_header, &
489	stg_init, &
490	stg_main, &
491	stg_parin, &
492	stg_rrd_global, &
493	stg_wrd_global
494
495	!
496	!-- Public variables
497	PUBLIC dt_stg_call, &
498	dt_stg_adjust, &
499	id_stg_left, &
500	id_stg_north, &
501	id_stg_right, &
502	id_stg_south, &
503	parametrize_inflow_turbulence, &
504	time_stg_adjust, &
505	time_stg_call, &
506	use_syn_turb_gen
507
508
509	CONTAINS
510
511
512	!--------------------------------------------------------------------------------------------------!
513	! Description:
514	! ------------
515	!> Check parameters routine for synthetic turbulence generator
516	!--------------------------------------------------------------------------------------------------!
517	SUBROUTINE stg_check_parameters
518
519	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
520	nesting_offline ) THEN
521	message_string = 'Synthetic turbulence generator is required ' // &
522	'if offline nesting is applied and PALM operates in LES mode.'
523	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
524	ENDIF
525
526	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
527	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
528	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
529	'and parent operates in RANS-mode but current child in LES mode.'
530	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
531	ENDIF
532
533	IF ( use_syn_turb_gen ) THEN
534
535	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
536	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
537	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
538
539	ENDIF
540
541	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
542	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
543	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
544
545	ENDIF
546
547	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
548
549	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
550	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
551	message_string = 'Using synthetic turbulence generator requires ' // &
552	'%initializing_actions = "set_constant_profiles" or ' // &
553	' "read_restart_data", if not offline nesting is applied.'
554	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
555	ENDIF
556
557	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
558	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
559	' "dirichlet/radiation", if not offline nesting is applied.'
560	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
561	ENDIF
562	IF ( bc_ns /= 'cyclic' ) THEN
563	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
564	' "cyclic", if not offline nesting is applied.'
565	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
566	ENDIF
567
568	ENDIF
569
570	IF ( turbulent_inflow ) THEN
571	message_string = 'Using synthetic turbulence generator in combination ' // &
572	'&with turbulent_inflow = .T. is not allowed'
573	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
574	ENDIF
575	!
576	!-- Synthetic turbulence generator requires the parallel random generator
577	IF ( random_generator /= 'random-parallel' ) THEN
578	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
579	'random-parallel.'
580	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
581	ENDIF
582
583	ENDIF
584
585	END SUBROUTINE stg_check_parameters
586
587
588	!--------------------------------------------------------------------------------------------------!
589	! Description:
590	! ------------
591	!> Header output for synthetic turbulence generator
592	!--------------------------------------------------------------------------------------------------!
593	SUBROUTINE stg_header ( io )
594
595	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
596
597	!
598	!-- Write synthetic turbulence generator Header
599	WRITE( io, 1 )
600	IF ( use_syn_turb_gen ) THEN
601	WRITE( io, 2 )
602	ELSE
603	WRITE( io, 3 )
604	ENDIF
605
606	IF ( parametrize_inflow_turbulence ) THEN
607	WRITE( io, 4 ) dt_stg_adjust
608	ELSE
609	WRITE( io, 5 )
610	ENDIF
611
612	1 FORMAT (//' Synthetic turbulence generator information:'/ &
613	' ------------------------------------------'/)
614	2 FORMAT (' synthetic turbulence generator is switched on')
615	3 FORMAT (' synthetic turbulence generator is switched off')
616	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
617	5 FORMAT (' imposed turbulence is read from file' )
618
619	END SUBROUTINE stg_header
620
621
622	!--------------------------------------------------------------------------------------------------!
623	! Description:
624	! ------------
625	!> Initialization of the synthetic turbulence generator
626	!--------------------------------------------------------------------------------------------------!
627	SUBROUTINE stg_init
628
629	#if defined( __parallel )
630	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
631	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
632	#endif
633
634	INTEGER(iwp) :: i !> grid index in x-direction
635	INTEGER(iwp) :: j !> loop index
636	INTEGER(iwp) :: k !< index
637	#if defined( __parallel )
638	INTEGER(iwp) :: newtype !< dummy MPI type
639	INTEGER(iwp) :: realsize !< size of REAL variables
640	#endif
641
642	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
643	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
644
645
646	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
647
648	!
649	!-- Dummy variables used for reading profiles
650	REAL(wp) :: d1 !< u profile
651	REAL(wp) :: d2 !< v profile
652	REAL(wp) :: d3 !< w profile
653	REAL(wp) :: d5 !< e profile
654	REAL(wp) :: luy !< length scale for u in y direction
655	REAL(wp) :: luz !< length scale for u in z direction
656	REAL(wp) :: lvy !< length scale for v in y direction
657	REAL(wp) :: lvz !< length scale for v in z direction
658	REAL(wp) :: lwy !< length scale for w in y direction
659	REAL(wp) :: lwz !< length scale for w in z direction
660	#if defined( __parallel )
661	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
662	#endif
663	REAL(wp) :: zz !< height
664
665
666	#if defined( __parallel )
667	CALL MPI_BARRIER( comm2d, ierr )
668	#endif
669	!
670	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
671	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
672	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
673	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
674	!-- communication).
675	IF ( .NOT. compute_velocity_seeds_local ) THEN
676	#if defined( __parallel )
677	!
678	!-- Determine processor decomposition of z-axis along x- and y-direction
679	nnz = nz / pdims(1)
680	nzb_x_stg = 1 + myidx * INT( nnz )
681	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
682
683	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
684	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
685
686	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
687	.AND. .NOT. rans_mode ) ) THEN
688	nnz = nz / pdims(2)
689	nzb_y_stg = 1 + myidy * INT( nnz )
690	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
691
692	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
693	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
694	ENDIF
695
696	!
697	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
698	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
699	extent = 1 * realsize
700	!
701	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
702	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
703	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
704	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
705	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
706	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
707	CALL MPI_TYPE_FREE( newtype, ierr )
708
709	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
710	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
711	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
712	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
713	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
714	CALL MPI_TYPE_FREE( newtype, ierr )
715
716	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
717	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
718
719	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
720	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
721
722	DO j = 1, pdims(1)
723	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
724	ENDDO
725	!
726	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
727	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
728	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
729	.AND. .NOT. rans_mode ) ) THEN
730	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
731	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
732	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
733	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
734	CALL MPI_TYPE_FREE( newtype, ierr )
735
736	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
737	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
738	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
739	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
740	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
741	CALL MPI_TYPE_FREE( newtype, ierr )
742
743	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
744	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
745
746	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
747	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
748
749	DO j = 1, pdims(2)
750	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
751	ENDDO
752
753	ENDIF
754	#endif
755	ENDIF
756	!
757	!-- Allocate required arrays.
758	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
759	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
760	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
761	!-- and initialized appropriately.
762	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
763	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
764	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
765	mean_inflow_profiles = 0.0_wp
766	mean_inflow_profiles(:,1) = u_init
767	mean_inflow_profiles(:,2) = v_init
768	!
769	!-- Even though potential temperature and humidity are not perturbed, they need to be
770	!-- initialized appropriately.
771	IF ( .NOT. neutral ) &
772	mean_inflow_profiles(:,4) = pt_init
773	IF ( humidity ) &
774	mean_inflow_profiles(:,6) = q_init
775	ENDIF
776	ENDIF
777	!
778	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
779	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
780	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
781	u_init = mean_inflow_profiles(:,1)
782	v_init = mean_inflow_profiles(:,2)
783	e_init = MAXVAL( mean_inflow_profiles(:,5) )
784	ENDIF
785
786	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
787	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
788	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
789	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
790	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
791	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
792	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
793	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
794
795	r11 = 0.0_wp
796	r21 = 0.0_wp
797	r22 = 0.0_wp
798	r31 = 0.0_wp
799	r32 = 0.0_wp
800	r33 = 0.0_wp
801	tu = 0.0_wp
802	tv = 0.0_wp
803	tw = 0.0_wp
804
805	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
806	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
807	dist_xz = 0.0_wp
808	dist_yz = 0.0_wp
809	!
810	!-- Read inflow profile
811	!-- Height levels of profiles in input profile is as follows:
812	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
813	!-- WARNING: zz is not used at the moment
814	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
815
816	IF ( file_stg_exist ) THEN
817
818	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
819	!
820	!-- Skip header
821	READ( 90, * )
822
823	DO k = nzb, nzt
824	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
825	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
826
827	!
828	!-- Convert length scales from meter to number of grid points.
829	IF ( k /= nzb ) THEN
830	nuz(k) = INT( luz * ddzw(k) )
831	nvz(k) = INT( lvz * ddzw(k) )
832	nwz(k) = INT( lwz * ddzw(k) )
833	ELSE
834	nuz(k) = INT( luz * ddzw(k+1) )
835	nvz(k) = INT( lvz * ddzw(k+1) )
836	nwz(k) = INT( lwz * ddzw(k+1) )
837	ENDIF
838
839	nuy(k) = INT( luy * ddy )
840	nvy(k) = INT( lvy * ddy )
841	nwy(k) = INT( lwy * ddy )
842	!
843	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
844	!-- y-direction.
845	nwx(k) = nwy(k)
846	nvx(k) = nvy(k)
847	nux(k) = nuy(k)
848	!
849	!-- Save Mean inflow profiles
850	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
851	mean_inflow_profiles(k,1) = d1
852	mean_inflow_profiles(k,2) = d2
853	! mean_inflow_profiles(k,4) = d4
854	mean_inflow_profiles(k,5) = d5
855	ENDIF
856	ENDDO
857	!
858	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
859	!-- simply overwritten.
860	nwx(nzb) = nwy(nzb+1)
861	nvx(nzb) = nvy(nzb+1)
862	nux(nzb) = nuy(nzb+1)
863	nuy(nzb) = nuy(nzb+1)
864	nuz(nzb) = nuz(nzb+1)
865	nvy(nzb) = nvy(nzb+1)
866	nvz(nzb) = nvz(nzb+1)
867	nwy(nzb) = nwy(nzb+1)
868	nwz(nzb) = nwz(nzb+1)
869
870	nwx(nzt+1) = nwy(nzt)
871	nvx(nzt+1) = nvy(nzt)
872	nux(nzt+1) = nuy(nzt)
873	nuy(nzt+1) = nuy(nzt)
874	nuz(nzt+1) = nuz(nzt)
875	nvy(nzt+1) = nvy(nzt)
876	nvz(nzt+1) = nvz(nzt)
877	nwy(nzt+1) = nwy(nzt)
878	nwz(nzt+1) = nwz(nzt)
879
880	CLOSE( 90 )
881	!
882	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
883	CALL calc_coeff_matrix
884	!
885	!-- No information about turbulence and its length scales are available. Instead, parametrize
886	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
887	!-- parametrized, which is done later when energy-balance models are already initialized. This is
888	!-- because the STG needs information about surface properties such as roughness to build
889	!-- 'realistic' turbulence profiles.
890	ELSE
891	!
892	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
893	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
894	!
895	!-- Set flag indicating that turbulence is parametrized
896	parametrize_inflow_turbulence = .TRUE.
897	!
898	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
899	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
900	!-- nevertheless, the boundary-layer depth needs to be determined first.
901	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
902	CALL nesting_offl_calc_zi
903	!
904	!-- Determine boundary-layer depth, which is used to initialize lenght scales
905	CALL calc_scaling_variables
906	!
907	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
908	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
909	!-- friction velocity and velocity scale.
910	CALL parametrize_turbulence
911	!
912	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
913	CALL calc_coeff_matrix
914
915	ENDIF
916	!
917	!-- Initial filter functions
918	CALL stg_setup_filter_function
919	!
920	!-- Allocate velocity seeds for turbulence at xz-layer
921	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
922	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
923	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
924
925	!
926	!-- Allocate velocity seeds for turbulence at yz-layer
927	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
928	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
929	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
930
931	fu_xz = 0.0_wp
932	fuo_xz = 0.0_wp
933	fv_xz = 0.0_wp
934	fvo_xz = 0.0_wp
935	fw_xz = 0.0_wp
936	fwo_xz = 0.0_wp
937
938	fu_yz = 0.0_wp
939	fuo_yz = 0.0_wp
940	fv_yz = 0.0_wp
941	fvo_yz = 0.0_wp
942	fw_yz = 0.0_wp
943	fwo_yz = 0.0_wp
944
945	#if defined( __parallel )
946	CALL MPI_BARRIER( comm2d, ierr )
947	#endif
948
949	!
950	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
951	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
952	!-- This is mostly for k=nzt+1.
953	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
954	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
955
956	IF ( myidx == id_stg_left ) i = -1
957	IF ( myidx == id_stg_right ) i = nxr+1
958
959	DO j = nys, nyn
960	DO k = nzb, nzt+1
961	IF ( a11(k) > 10E-8_wp ) THEN
962	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
963	ELSE
964	fu_yz(k,j) = 10E-8_wp
965	ENDIF
966
967	IF ( a22(k) > 10E-8_wp ) THEN
968	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
969	ELSE
970	fv_yz(k,j) = 10E-8_wp
971	ENDIF
972
973	IF ( a33(k) > 10E-8_wp ) THEN
974	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
975	ELSE
976	fw_yz(k,j) = 10E-8_wp
977	ENDIF
978	ENDDO
979	ENDDO
980	ENDIF
981
982	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
983
984	IF ( myidy == id_stg_south ) j = -1
985	IF ( myidy == id_stg_north ) j = nyn+1
986
987	DO i = nxl, nxr
988	DO k = nzb, nzt+1
989	!
990	!-- In case the correlation coefficients are very small, the velocity seeds may become
991	!-- very large finally creating numerical instabilities in the synthetic turbulence
992	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
993	IF ( a11(k) > 10E-8_wp ) THEN
994	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
995	ELSE
996	fu_xz(k,i) = 10E-8_wp
997	ENDIF
998
999	IF ( a22(k) > 10E-8_wp ) THEN
1000	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1001	ELSE
1002	fv_xz(k,i) = 10E-8_wp
1003	ENDIF
1004
1005	IF ( a33(k) > 10E-8_wp ) THEN
1006	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1007	ELSE
1008	fw_xz(k,i) = 10E-8_wp
1009	ENDIF
1010
1011	ENDDO
1012	ENDDO
1013	ENDIF
1014	ENDIF
1015	!
1016	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1017	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1018	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1019	!-- different cases must be distinguished.
1020	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1021	!
1022	!-- Number of grid points where perturbations are imposed on u
1023	IF ( myidx == id_stg_left ) i = nxl
1024	IF ( myidx == id_stg_right ) i = nxr+1
1025
1026	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1027	!
1028	!-- Number of grid points where perturbations are imposed on v and w
1029	IF ( myidx == id_stg_left ) i = nxl-1
1030	IF ( myidx == id_stg_right ) i = nxr+1
1031
1032	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1033	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1034
1035	#if defined( __parallel )
1036	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1037	#else
1038	nr_non_topo_yz = nr_non_topo_yz_l
1039	#endif
1040	ENDIF
1041
1042	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1043	!
1044	!-- Number of grid points where perturbations are imposed on v
1045	IF ( myidy == id_stg_south ) j = nys
1046	IF ( myidy == id_stg_north ) j = nyn+1
1047
1048	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1049	!
1050	!-- Number of grid points where perturbations are imposed on u and w
1051	IF ( myidy == id_stg_south ) j = nys-1
1052	IF ( myidy == id_stg_north ) j = nyn+1
1053
1054	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1055	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1056
1057	#if defined( __parallel )
1058	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1059	#else
1060	nr_non_topo_xz = nr_non_topo_xz_l
1061	#endif
1062	ENDIF
1063	!
1064	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1065	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1066	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1067	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1068	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1069	id_rand_yz = 0
1070	seq_rand_yz = 0
1071
1072	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1073
1074	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1075	.AND. .NOT. rans_mode ) ) THEN
1076	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1077	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1078	id_rand_xz = 0
1079	seq_rand_xz = 0
1080
1081	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1082	ENDIF
1083
1084	END SUBROUTINE stg_init
1085
1086
1087	!--------------------------------------------------------------------------------------------------!
1088	! Description:
1089	! ------------
1090	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1091	!--------------------------------------------------------------------------------------------------!
1092	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1093
1094	INTEGER(iwp) :: k !< loop index
1095	INTEGER(iwp) :: mergp !< passed length scale in grid points
1096	INTEGER(iwp) :: n_k !< length scale nXX in height k
1097	INTEGER(iwp) :: nf !< index for length scales
1098
1099	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1100
1101	REAL(wp) :: bdenom !< denominator for filter functions bXX
1102	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1103
1104	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1105
1106
1107	bxx = 0.0_wp
1108
1109	DO k = nzb, nzt+1
1110	bdenom = 0.0_wp
1111	n_k = nxx(k)
1112	IF ( n_k /= 0 ) THEN
1113
1114	!
1115	!-- ( Eq.10 )^2
1116	DO nf = -n_k, n_k
1117	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1118	ENDDO
1119
1120	!
1121	!-- ( Eq.9 )
1122	bdenom = SQRT( bdenom )
1123	DO nf = -n_k, n_k
1124	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1125	ENDDO
1126	ENDIF
1127	ENDDO
1128
1129	END SUBROUTINE stg_filter_func
1130
1131
1132	!------------------------------------------------------------------------------!
1133	! Description:
1134	! ------------
1135	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1136	!> (Xie and Castro, 2008)
1137	!------------------------------------------------------------------------------!
1138	SUBROUTINE stg_setup_filter_function
1139
1140	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1141	INTEGER(iwp) :: k !< loop index along vertical direction
1142	!
1143	!-- Define the size of the filter functions and allocate them.
1144	mergp_x = 0
1145	mergp_y = 0
1146	mergp_z = 0
1147
1148	DO k = nzb, nzt+1
1149	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1150	IF ( j > mergp_x ) mergp_x = j
1151	ENDDO
1152	DO k = nzb, nzt+1
1153	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1154	IF ( j > mergp_y ) mergp_y = j
1155	ENDDO
1156	DO k = nzb, nzt+1
1157	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1158	IF ( j > mergp_z ) mergp_z = j
1159	ENDDO
1160
1161	mergp_xy = MAX( mergp_x, mergp_y )
1162
1163	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1164	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1165	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1166	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1167	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1168	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1169	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1170	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1171	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1172
1173	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1174	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1175	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1176	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1177	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1178	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1179	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1180	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1181	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1182	!
1183	!-- Create filter functions
1184	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1185	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1186	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1187	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1188	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1189	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1190	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1191	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1192	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1193
1194	END SUBROUTINE stg_setup_filter_function
1195
1196	!--------------------------------------------------------------------------------------------------!
1197	! Description:
1198	! ------------
1199	!> Parin for &stg_par for synthetic turbulence generator
1200	!--------------------------------------------------------------------------------------------------!
1201	SUBROUTINE stg_parin
1202
1203	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1204
1205
1206	NAMELIST /stg_par/ dt_stg_adjust, &
1207	dt_stg_call, &
1208	use_syn_turb_gen, &
1209	compute_velocity_seeds_local
1210
1211	line = ' '
1212	!
1213	!-- Try to find stg package
1214	REWIND ( 11 )
1215	line = ' '
1216	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1217	READ ( 11, '(A)', END = 20 ) line
1218	ENDDO
1219	BACKSPACE ( 11 )
1220
1221	!
1222	!-- Read namelist
1223	READ ( 11, stg_par, ERR = 10, END = 20 )
1224
1225	!
1226	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1227	syn_turb_gen = .TRUE.
1228	GOTO 20
1229
1230	10 BACKSPACE( 11 )
1231	READ( 11 , '(A)') line
1232	CALL parin_fail_message( 'stg_par', line )
1233
1234	20 CONTINUE
1235
1236	END SUBROUTINE stg_parin
1237
1238
1239	!--------------------------------------------------------------------------------------------------!
1240	! Description:
1241	! ------------
1242	!> Read module-specific global restart data (Fortran binary format).
1243	!--------------------------------------------------------------------------------------------------!
1244	SUBROUTINE stg_rrd_global_ftn( found )
1245
1246	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1247
1248	found = .TRUE.
1249
1250
1251	SELECT CASE ( restart_string(1:length) )
1252
1253	CASE ( 'time_stg_adjust' )
1254	READ ( 13 ) time_stg_adjust
1255
1256	CASE ( 'time_stg_call' )
1257	READ ( 13 ) time_stg_call
1258
1259	CASE ( 'use_syn_turb_gen' )
1260	READ ( 13 ) use_syn_turb_gen
1261
1262	CASE DEFAULT
1263
1264	found = .FALSE.
1265
1266	END SELECT
1267
1268
1269	END SUBROUTINE stg_rrd_global_ftn
1270
1271
1272	!--------------------------------------------------------------------------------------------------!
1273	! Description:
1274	! ------------
1275	!> Read module-specific global restart data (MPI-IO).
1276	!--------------------------------------------------------------------------------------------------!
1277	SUBROUTINE stg_rrd_global_mpi
1278
1279	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1280	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1281	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1282
1283	END SUBROUTINE stg_rrd_global_mpi
1284
1285
1286	!--------------------------------------------------------------------------------------------------!
1287	! Description:
1288	! ------------
1289	!> This routine writes the respective restart data.
1290	!--------------------------------------------------------------------------------------------------!
1291	SUBROUTINE stg_wrd_global
1292
1293	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1294
1295	CALL wrd_write_string( 'time_stg_adjust' )
1296	WRITE ( 14 ) time_stg_adjust
1297
1298	CALL wrd_write_string( 'time_stg_call' )
1299	WRITE ( 14 ) time_stg_call
1300
1301	CALL wrd_write_string( 'use_syn_turb_gen' )
1302	WRITE ( 14 ) use_syn_turb_gen
1303
1304	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1305
1306	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1307	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1308	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1309
1310	ENDIF
1311
1312	END SUBROUTINE stg_wrd_global
1313
1314
1315	!--------------------------------------------------------------------------------------------------!
1316	! Description:
1317	! ------------
1318	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1319	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1320	!> (2013), and using a Lund rotation (Lund, 1998).
1321	!--------------------------------------------------------------------------------------------------!
1322	SUBROUTINE stg_main
1323
1324	USE exchange_horiz_mod, &
1325	ONLY: exchange_horiz
1326
1327	INTEGER(iwp) :: i !< grid index in x-direction
1328	INTEGER(iwp) :: j !< loop index in y-direction
1329	INTEGER(iwp) :: k !< loop index in z-direction
1330
1331	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1332
1333	REAL(wp) :: dt_stg !< time interval the STG is called
1334
1335	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1336
1337	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1338	!
1339	!-- Calculate time step which is needed for filter functions
1340	dt_stg = MAX( dt_3d, dt_stg_call )
1341	!
1342	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1343	!-- created or if old disturbances can be imposed again.
1344	IF ( time_stg_call >= dt_stg_call .AND. &
1345	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1346	stg_call = .TRUE.
1347	ELSE
1348	stg_call = .FALSE.
1349	ENDIF
1350	!
1351	!-- Initial value of fu, fv, fw
1352	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1353	!
1354	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1355	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1356	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1357	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1358	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1359	!-- have the same initial seeds.
1360	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1361	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1362	.AND. .NOT. rans_mode ) ) ) THEN
1363	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1364	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1365	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1366	ELSE
1367	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1368	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1369	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1370	!
1371	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1372	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1373	!-- comment above.
1374	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1375	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1376	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1377	ENDIF
1378	velocity_seed_initialized = .TRUE.
1379	ENDIF
1380	!
1381	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1382	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1383	!-- seeds are required also at the right, south and north boundaries.
1384	IF ( stg_call ) THEN
1385	IF ( .NOT. ( nesting_offline .OR. &
1386	( child_domain .AND. rans_mode_parent &
1387	.AND. .NOT. rans_mode ) ) ) THEN
1388	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1389	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1390	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1391
1392	ELSE
1393	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1394	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1395	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1396
1397	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1398	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1399	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1400	ENDIF
1401	ENDIF
1402
1403	!
1404	!-- Turbulence generation at left and/or right boundary
1405	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1406	!
1407	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1408	!-- exceeded. Else the old set of perturbations is imposed
1409	IF ( stg_call ) THEN
1410
1411	DO j = nys, nyn
1412	DO k = nzb, nzt + 1
1413	!
1414	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1415	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1416	fu_yz(k,j) = fuo_yz(k,j)
1417	ELSE
1418	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1419	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1420	ENDIF
1421
1422	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1423	fv_yz(k,j) = fvo_yz(k,j)
1424	ELSE
1425	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1426	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1427	ENDIF
1428
1429	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1430	fw_yz(k,j) = fwo_yz(k,j)
1431	ELSE
1432	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1433	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1434	ENDIF
1435	ENDDO
1436	ENDDO
1437
1438	dist_yz(nzb,:,1) = 0.0_wp
1439	dist_yz(nzb,:,2) = 0.0_wp
1440	dist_yz(nzb,:,3) = 0.0_wp
1441
1442	IF ( myidx == id_stg_left ) i = nxl
1443	IF ( myidx == id_stg_right ) i = nxr+1
1444	DO j = nys, nyn
1445	DO k = nzb+1, nzt + 1
1446	!
1447	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1448	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1449	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1450
1451	ENDDO
1452	ENDDO
1453
1454	IF ( myidx == id_stg_left ) i = nxl-1
1455	IF ( myidx == id_stg_right ) i = nxr+1
1456	DO j = nys, nyn
1457	DO k = nzb+1, nzt + 1
1458	!
1459	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1460	!-- Additional factors are added to improve the variance of v and w experimental test
1461	!-- of 1.2
1462	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1463	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1464	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1465	a33(k) * fw_yz(k,j) ) * &
1466	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1467
1468	ENDDO
1469	ENDDO
1470	ENDIF
1471	!
1472	!-- Mass flux correction following Kim et al. (2013)
1473	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1474	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1475	!-- only after the last RK3-substep, else 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 volume flow.
1482	IF ( myidx == id_stg_left ) i = nxl
1483	IF ( myidx == id_stg_right ) i = nxr+1
1484
1485	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1486	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1487
1488	IF ( myidx == id_stg_left ) i = nxl-1
1489	IF ( myidx == id_stg_right ) i = nxr+1
1490
1491	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1492	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1493	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1494	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1495
1496	#if defined( __parallel )
1497	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1498	#else
1499	mc_factor = mc_factor_l
1500	#endif
1501	!
1502	!-- Calculate correction factor and force zero mean perturbations.
1503	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1504
1505	IF ( myidx == id_stg_left ) i = nxl
1506	IF ( myidx == id_stg_right ) i = nxr+1
1507
1508	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1509	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1510
1511
1512	IF ( myidx == id_stg_left ) i = nxl-1
1513	IF ( myidx == id_stg_right ) i = nxr+1
1514
1515	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1516	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1517
1518	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1519	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1520	!
1521	!-- Add disturbances
1522	IF ( myidx == id_stg_left ) THEN
1523	!
1524	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1525	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1526	!-- the mean inflow profiles.
1527	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1528	!
1529	!-- Add disturbance at the inflow
1530	DO j = nys, nyn
1531	DO k = nzb, nzt+1
1532	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1533	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1534	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1535	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1536	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1537	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1538	ENDDO
1539	ENDDO
1540	ELSE
1541
1542	DO j = nys, nyn
1543	DO k = nzb+1, nzt
1544	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1545	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1546	u(k,j,-1) = u(k,j,0)
1547	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1548	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1549	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1550	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1551	ENDDO
1552	ENDDO
1553	ENDIF
1554	ENDIF
1555	IF ( myidx == id_stg_right ) THEN
1556	DO j = nys, nyn
1557	DO k = nzb+1, nzt
1558	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1559	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1560	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1561	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1562	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1563	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1564	ENDDO
1565	ENDDO
1566	ENDIF
1567	ENDIF
1568	ENDIF
1569	!
1570	!-- Turbulence generation at north and south boundary
1571	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1572	!
1573	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1574	!-- exceeded. Else the old set of perturbations is imposed
1575	IF ( stg_call ) THEN
1576	DO i = nxl, nxr
1577	DO k = nzb, nzt + 1
1578	!
1579	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1580	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1581	fu_xz(k,i) = fuo_xz(k,i)
1582	ELSE
1583	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1584	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1585	ENDIF
1586
1587	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1588	fv_xz(k,i) = fvo_xz(k,i)
1589	ELSE
1590	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1591	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1592	ENDIF
1593
1594	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1595	fw_xz(k,i) = fwo_xz(k,i)
1596	ELSE
1597	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1598	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1599	ENDIF
1600	ENDDO
1601	ENDDO
1602
1603
1604	dist_xz(nzb,:,1) = 0.0_wp
1605	dist_xz(nzb,:,2) = 0.0_wp
1606	dist_xz(nzb,:,3) = 0.0_wp
1607
1608	IF ( myidy == id_stg_south ) j = nys
1609	IF ( myidy == id_stg_north ) j = nyn+1
1610	DO i = nxl, nxr
1611	DO k = nzb+1, nzt + 1
1612	!
1613	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1614	!-- Additional factors are added to improve the variance of v and w
1615	!experimental test of 1.2
1616	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1617	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1618	ENDDO
1619	ENDDO
1620
1621	IF ( myidy == id_stg_south ) j = nys-1
1622	IF ( myidy == id_stg_north ) j = nyn+1
1623	DO i = nxl, nxr
1624	DO k = nzb+1, nzt + 1
1625	!
1626	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1627	!-- Additional factors are added to improve the variance of v and w
1628	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1629	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1630
1631	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1632	a33(k) * fw_xz(k,i) ) * &
1633	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1634	ENDDO
1635	ENDDO
1636	ENDIF
1637
1638	!
1639	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1640	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1641	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1642	!-- else the boundary values won't be accessed.
1643	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1644	mc_factor_l = 0.0_wp
1645	mc_factor = 0.0_wp
1646
1647	IF ( myidy == id_stg_south ) j = nys
1648	IF ( myidy == id_stg_north ) j = nyn+1
1649
1650	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1651	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1652
1653	IF ( myidy == id_stg_south ) j = nys-1
1654	IF ( myidy == id_stg_north ) j = nyn+1
1655
1656	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1657	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1658	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1659	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1660
1661	#if defined( __parallel )
1662	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1663	#else
1664	mc_factor = mc_factor_l
1665	#endif
1666
1667	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1668
1669	IF ( myidy == id_stg_south ) j = nys
1670	IF ( myidy == id_stg_north ) j = nyn+1
1671
1672	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1673	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1674
1675
1676	IF ( myidy == id_stg_south ) j = nys-1
1677	IF ( myidy == id_stg_north ) j = nyn+1
1678
1679	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1680	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1681
1682	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1683	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1684	!
1685	!-- Add disturbances
1686	IF ( myidy == id_stg_south ) THEN
1687	DO i = nxl, nxr
1688	DO k = nzb+1, nzt
1689	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1690	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1691	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1692	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1693	v(k,-1,i) = v(k,0,i)
1694	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1695	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1696	ENDDO
1697	ENDDO
1698	ENDIF
1699	IF ( myidy == id_stg_north ) THEN
1700
1701	DO i = nxl, nxr
1702	DO k = nzb+1, nzt
1703	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1704	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1705	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1706	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1707	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1708	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1709	ENDDO
1710	ENDDO
1711	ENDIF
1712	ENDIF
1713	ENDIF
1714	!
1715	!-- Exchange ghost points.
1716	CALL exchange_horiz( u, nbgp )
1717	CALL exchange_horiz( v, nbgp )
1718	CALL exchange_horiz( w, nbgp )
1719	!
1720	!-- Finally, set time counter for calling STG to zero
1721	IF ( stg_call ) time_stg_call = 0.0_wp
1722	!
1723	!-- Set adjustment step to False to indicate that time correlation can be
1724	!-- switched-on again.
1725	adjustment_step = .FALSE.
1726
1727	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1728
1729	END SUBROUTINE stg_main
1730
1731	!--------------------------------------------------------------------------------------------------!
1732	! Description:
1733	! ------------
1734	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1735	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1736	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1737	!> array.
1738	!--------------------------------------------------------------------------------------------------!
1739	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1740
1741	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1742	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1743	INTEGER(iwp) :: j !< loop index in y-direction
1744	INTEGER(iwp) :: jj !< loop index in y-direction
1745	INTEGER(iwp) :: k !< loop index in z-direction
1746	INTEGER(iwp) :: kk !< loop index in z-direction
1747	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1748
1749	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1750	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1751
1752	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1753	REAL(wp) :: rand_av !< average of random number
1754	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1755
1756	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1757	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1758
1759	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1760	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1761
1762	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1763	!
1764	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1765	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1766	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1767	!-- and normalization of random numbers is done locally, while the result is later distributed to
1768	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1769	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1770	!-- correlation matrix.
1771	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1772	rand_it = 0.0_wp
1773
1774	rand_av = 0.0_wp
1775	rand_sigma_inv = 0.0_wp
1776	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1777	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1778	!
1779	!-- Compute and normalize random numbers.
1780	DO j = nys - mergp_y, nyn + mergp_y
1781	!
1782	!-- Put the random seeds at grid point j
1783	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1784	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1785	CALL random_number_parallel( random_dummy )
1786	rand_it(k,j) = random_dummy
1787	ENDDO
1788	!
1789	!-- Get the new random seeds from last call at grid point j
1790	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1791	ENDDO
1792	!
1793	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1794	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1795	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1796	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1797	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1798	rand_av = rand_av + rand_it(k,j)
1799	ENDDO
1800	ENDDO
1801
1802	#if defined( __parallel )
1803	!
1804	!-- Sum-up the local averages of the random numbers
1805	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1806	#endif
1807	rand_av = rand_av * nyz_inv
1808	!
1809	!-- Obtain zero mean
1810	rand_it= rand_it - rand_av
1811	!
1812	!-- Now, compute the variance
1813	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1814	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1815	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1816	ENDDO
1817	ENDDO
1818
1819	#if defined( __parallel )
1820	!
1821	!-- Sum-up the local quadratic averages of the random numbers
1822	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1823	#endif
1824	!
1825	!-- Compute standard deviation
1826	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1827	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1828	ELSE
1829	rand_sigma_inv = 1.0_wp
1830	ENDIF
1831	!
1832	!-- Normalize with standard deviation to obtain unit variance
1833	rand_it = rand_it * rand_sigma_inv
1834
1835	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1836	!
1837	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1838	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1839	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1840	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1841	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1842	!-- communication. In the second option, which performs better when the turbulent length scales
1843	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1844	!-- communication is necessary.
1845	IF ( compute_velocity_seeds_local ) THEN
1846
1847	f_n = 0.0_wp
1848	DO j = nys, nyn
1849	DO k = nzb, nzt+1
1850	DO jj = -n_y(k), n_y(k)
1851	DO kk = -n_z(k), n_z(k)
1852	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1853	ENDDO
1854	ENDDO
1855	ENDDO
1856	ENDDO
1857
1858	ELSE
1859
1860	f_n_l = 0.0_wp
1861	DO j = nys, nyn
1862	DO k = nzb_x_stg, nzt_x_stg+1
1863	DO jj = -n_y(k), n_y(k)
1864	DO kk = -n_z(k), n_z(k)
1865	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1866	ENDDO
1867	ENDDO
1868	ENDDO
1869	ENDDO
1870	!
1871	!-- Gather velocity seeds of full subdomain
1872	send_count = nzt_x_stg - nzb_x_stg + 1
1873	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1874
1875	#if defined( __parallel )
1876	!
1877	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1878	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1879	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1880	!
1881	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1882	!-- nesting for example).
1883	IF ( PRESENT( id_right ) ) THEN
1884	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1885	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1886	ENDIF
1887	#else
1888	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1889	!
1890	!-- Next line required to avoid compile errors because of unused dummy arguments
1891	IF ( id_left == 0 ) id_right = 0
1892	#endif
1893
1894	ENDIF
1895
1896	DEALLOCATE( rand_it )
1897
1898	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1899
1900	END SUBROUTINE stg_generate_seed_yz
1901
1902
1903	!--------------------------------------------------------------------------------------------------!
1904	! Description:
1905	! ------------
1906	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1907	!> f_n.
1908	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1909	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1910	!> full array.
1911	!--------------------------------------------------------------------------------------------------!
1912	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1913
1914	INTEGER(iwp) :: i !< loop index in x-direction
1915	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1916	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1917	INTEGER(iwp) :: ii !< loop index in x-direction
1918	INTEGER(iwp) :: k !< loop index in z-direction
1919	INTEGER(iwp) :: kk !< loop index in z-direction
1920	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1921
1922	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1923	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1924
1925	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1926	REAL(wp) :: rand_av !< average of random number
1927	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1928
1929	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1930	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1931
1932	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1933	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1934
1935	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1936
1937	!
1938	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1939	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1940	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1941	!-- and normalization of random numbers is done locally, while the result is later distributed to
1942	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1943	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1944	!-- correlation matrix.
1945	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1946	rand_it = 0.0_wp
1947
1948	rand_av = 0.0_wp
1949	rand_sigma_inv = 0.0_wp
1950	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1951	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1952	!
1953	!-- Compute and normalize random numbers.
1954	DO i = nxl - mergp_x, nxr + mergp_x
1955	!
1956	!-- Put the random seeds at grid point ii
1957	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1958	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1959	CALL random_number_parallel( random_dummy )
1960	rand_it(k,i) = random_dummy
1961	ENDDO
1962	!
1963	!-- Get the new random seeds from last call at grid point ii
1964	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1965	ENDDO
1966	!
1967	!-- For normalization to zero mean, sum-up the global random numers.
1968	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1969	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1970	!-- also occur on the inner subdomains.
1971	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1972	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1973	rand_av = rand_av + rand_it(k,i)
1974	ENDDO
1975	ENDDO
1976
1977	#if defined( __parallel )
1978	!
1979	!-- Sum-up the local averages of the random numbers
1980	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1981	#endif
1982	rand_av = rand_av * nxz_inv
1983	!
1984	!-- Obtain zero mean
1985	rand_it= rand_it - rand_av
1986	!
1987	!-- Now, compute the variance
1988	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1989	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1990	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1991	ENDDO
1992	ENDDO
1993
1994	#if defined( __parallel )
1995	!
1996	!-- Sum-up the local quadratic averages of the random numbers
1997	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1998	#endif
1999	!
2000	!-- Compute standard deviation
2001	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2002	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2003	ELSE
2004	rand_sigma_inv = 1.0_wp
2005	ENDIF
2006	!
2007	!-- Normalize with standard deviation to obtain unit variance
2008	rand_it = rand_it * rand_sigma_inv
2009
2010	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2011	!
2012	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2013	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2014	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2015	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2016	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2017	!-- In the second option, which performs better when the turbulent length scales are parametrized
2018	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2019	IF ( compute_velocity_seeds_local ) THEN
2020
2021	f_n = 0.0_wp
2022	DO i = nxl, nxr
2023	DO k = nzb, nzt+1
2024	DO ii = -n_x(k), n_x(k)
2025	DO kk = -n_z(k), n_z(k)
2026	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2027	ENDDO
2028	ENDDO
2029	ENDDO
2030	ENDDO
2031
2032	ELSE
2033
2034	f_n_l = 0.0_wp
2035	DO i = nxl, nxr
2036	DO k = nzb_y_stg, nzt_y_stg+1
2037	DO ii = -n_x(k), n_x(k)
2038	DO kk = -n_z(k), n_z(k)
2039	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2040	ENDDO
2041	ENDDO
2042	ENDDO
2043	ENDDO
2044	!
2045	!-- Gather velocity seeds of full subdomain
2046	send_count = nzt_y_stg - nzb_y_stg + 1
2047	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2048
2049	#if defined( __parallel )
2050	!
2051	!-- Gather the processed velocity seed on south boundary mpi ranks.
2052	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2053	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2054	!
2055	!-- Gather the processed velocity seed on north boundary mpi ranks.
2056	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2057	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2058	#else
2059	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2060	!
2061	!-- Next line required to avoid compile errors because of unused dummy arguments
2062	IF ( id_north == 0 ) id_south = 0
2063	#endif
2064
2065	ENDIF
2066
2067	DEALLOCATE( rand_it )
2068
2069	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2070
2071	END SUBROUTINE stg_generate_seed_xz
2072
2073	!--------------------------------------------------------------------------------------------------!
2074	! Description:
2075	! ------------
2076	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2077	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2078	!> which is applied in state-of-the-art dispserion modelling.
2079	!--------------------------------------------------------------------------------------------------!
2080	SUBROUTINE parametrize_turbulence
2081
2082	INTEGER(iwp) :: k !< loop index in z-direction
2083
2084	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2085	REAL(wp) :: d_zi !< inverse boundary-layer depth
2086	REAL(wp) :: length_scale_lon !< length scale in flow direction
2087	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2088	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2089	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2090	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2091	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2092	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2093	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2094	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2095	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2096	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2097	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2098	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2099	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2100	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2101	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2102	REAL(wp) :: zzi !< ratio of z/zi
2103
2104	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2105	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2106	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2107
2108	!
2109	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2110	!-- criterion according to Heinze et al. (2017).
2111	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2112	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2113	k_zi = MIN( k_zi, nzt )
2114	!
2115	!-- Calculate angle between flow direction and x-axis.
2116	DO k = nzb+1, nzt + 1
2117	IF ( u_init(k) /= 0.0_wp ) THEN
2118	phi(k) = ATAN( v_init(k) / u_init(k) )
2119	ELSE
2120	phi(k) = 0.5 * pi
2121	ENDIF
2122	!
2123	!-- Pre-calculate sine and cosine.
2124	cos_phi(k) = COS( phi(k) )
2125	sin_phi(k) = SIN( phi(k) )
2126	ENDDO
2127	!
2128	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2129	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2130	!-- coincide with the grid axis. Hence, components are rotated after computation.
2131	d_zi = 1.0_wp / zi_ribulk
2132	DO k = nzb+1, k_zi
2133
2134	corr_term_uh = MERGE( 0.35_wp * ABS( &
2135	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2136	)**( 2.0_wp / 3.0_wp ), &
2137	0.0_wp, &
2138	scale_l < -5.0_wp )
2139	!
2140	!-- Determine normalized height coordinate
2141	zzi = zu(k) * d_zi
2142	!
2143	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2144	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2145	!-- variances cannot become negative, take the absolute values.
2146	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2147	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2148
2149	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2150	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2151	!
2152	!-- w'w'
2153	r33(k) = scale_wm*2 ( &
2154	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2155	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2156	)
2157	!
2158	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2159	!-- these are projected along the x- and y-direction. Note, it is assumed that
2160	!-- the flux within the boundary points opposite to the vertical gradient.
2161	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2162	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2163
2164	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2165	- ( u_init(k+1) - u_init(k-1) ) )
2166	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2167	- ( v_init(k+1) - v_init(k-1) ) )
2168	!
2169	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2170	!-- for the vertical transport.
2171	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2172	!
2173	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2174	!-- limited to the adjustment time scales.
2175	tu(k) = MIN( dt_stg_adjust, &
2176	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2177
2178	tv(k) = tu(k)
2179	tw(k) = tu(k)
2180
2181	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2182	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2183	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2184	!
2185	!-- Assume isotropic turbulence length scales
2186	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2187	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2188	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2189	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2190	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2191	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2192	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2193	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2194	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2195
2196	ENDDO
2197	!
2198	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2199	!-- reduced to zero by a blending function.
2200	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2201	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2202	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2203
2204	time_scale_zi = tu(k_zi)
2205	r11_zi = r11(k_zi)
2206	r22_zi = r22(k_zi)
2207	r33_zi = r33(k_zi)
2208	r31_zi = r31(k_zi)
2209	r32_zi = r32(k_zi)
2210
2211	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2212
2213	DO k = k_zi+1, nzt+1
2214	!
2215	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2216	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2217	!
2218	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2219	!-- the mergpe-function can crash if scale_l is zero.
2220	r11(k) = r11_zi * blend
2221	r22(k) = r22_zi * blend
2222	r33(k) = r33_zi * blend
2223	r31(k) = r31_zi * blend
2224	r32(k) = r32_zi * blend
2225	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2226
2227	!
2228	!-- Compute turbulent time scales according to Brost et al. (1982).
2229	!-- Note, time scales are limited to the adjustment time scales.
2230	tu(k) = time_scale_zi * blend
2231	tv(k) = time_scale_zi * blend
2232	tw(k) = time_scale_zi * blend
2233
2234	length_scale_lon = length_scale_lon_zi * blend
2235	length_scale_lat = length_scale_lat_zi * blend
2236	length_scale_vert = length_scale_vert_zi * blend
2237	!
2238	!-- Assume isotropic turbulence length scales
2239	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2240	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2241	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2242	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2243	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2244	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2245	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2246	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2247	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2248	ENDDO
2249	!
2250	!-- Set bottom boundary condition for reynolds stresses
2251	r11(nzb) = r11(nzb+1)
2252	r22(nzb) = r22(nzb+1)
2253	r33(nzb) = r33(nzb+1)
2254
2255	r21(nzb) = r11(nzb+1)
2256	r31(nzb) = r31(nzb+1)
2257	r32(nzb) = r32(nzb+1)
2258
2259	!
2260	!-- Set bottom boundary condition for the length and time scales
2261	nux(nzb) = nux(nzb+1)
2262	nuy(nzb) = nuy(nzb+1)
2263	nuz(nzb) = nuz(nzb+1)
2264	nvx(nzb) = nvx(nzb+1)
2265	nvy(nzb) = nvy(nzb+1)
2266	nvz(nzb) = nvz(nzb+1)
2267	nwx(nzb) = nwx(nzb+1)
2268	nwy(nzb) = nwy(nzb+1)
2269	nwz(nzb) = nwz(nzb+1)
2270
2271	tu(nzb) = tu(nzb+1)
2272	tv(nzb) = tv(nzb+1)
2273	tw(nzb) = tw(nzb+1)
2274
2275	adjustment_step = .TRUE.
2276
2277	END SUBROUTINE parametrize_turbulence
2278
2279	!--------------------------------------------------------------------------------------------------!
2280	! Description:
2281	! ------------
2282	!> Calculate the coefficient matrix from the Lund rotation.
2283	!--------------------------------------------------------------------------------------------------!
2284	SUBROUTINE calc_coeff_matrix
2285
2286	INTEGER(iwp) :: k !< loop index in z-direction
2287
2288	!
2289	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2290	DO k = nzb+1, nzt+1
2291	IF ( r11(k) > 10E-6_wp ) THEN
2292	a11(k) = SQRT( r11(k) )
2293	a21(k) = r21(k) / a11(k)
2294	a31(k) = r31(k) / a11(k)
2295	ELSE
2296	a11(k) = 10E-8_wp
2297	a21(k) = 10E-8_wp
2298	a31(k) = 10E-8_wp
2299	ENDIF
2300	ENDDO
2301	DO k = nzb+1, nzt+1
2302	a22(k) = r22(k) - a21(k)**2
2303	IF ( a22(k) > 10E-6_wp ) THEN
2304	a22(k) = SQRT( a22(k) )
2305	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2306	ELSE
2307	a22(k) = 10E-8_wp
2308	a32(k) = 10E-8_wp
2309	ENDIF
2310	ENDDO
2311	DO k = nzb+1, nzt+1
2312	a33(k) = r33(k) - a31(k)2 - a32(k)2
2313	IF ( a33(k) > 10E-6_wp ) THEN
2314	a33(k) = SQRT( a33(k) )
2315	ELSE
2316	a33(k) = 10E-8_wp
2317	ENDIF
2318	ENDDO
2319	!
2320	!-- Set bottom boundary condition
2321	a11(nzb) = a11(nzb+1)
2322	a22(nzb) = a22(nzb+1)
2323	a21(nzb) = a21(nzb+1)
2324	a33(nzb) = a33(nzb+1)
2325	a31(nzb) = a31(nzb+1)
2326	a32(nzb) = a32(nzb+1)
2327
2328	END SUBROUTINE calc_coeff_matrix
2329
2330	!--------------------------------------------------------------------------------------------------!
2331	! Description:
2332	! ------------
2333	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2334	!> turbulence at the lateral boundaries.
2335	!--------------------------------------------------------------------------------------------------!
2336	SUBROUTINE stg_adjust
2337
2338	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2339	!
2340	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2341	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2342	!-- nevertheless, the boundary-layer depth need to determined first.
2343	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2344	CALL nesting_offl_calc_zi
2345	!
2346	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2347	CALL calc_scaling_variables
2348	!
2349	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2350	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2351	!-- velocity and velocity scale.
2352	CALL parametrize_turbulence
2353	!
2354	!-- Calculate coefficient matrix from Reynolds stress tensor
2355	!-- (Lund rotation)
2356	CALL calc_coeff_matrix
2357	!
2358	!-- Setup filter functions according to updated length scales.
2359	CALL stg_setup_filter_function
2360	!
2361	!-- Reset time counter for controlling next adjustment to zero
2362	time_stg_adjust = 0.0_wp
2363
2364	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2365
2366	END SUBROUTINE stg_adjust
2367
2368
2369	!--------------------------------------------------------------------------------------------------!
2370	! Description:
2371	! ------------
2372	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2373	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2374	!> scale, and Obukhov length.
2375	!--------------------------------------------------------------------------------------------------!
2376	SUBROUTINE calc_scaling_variables
2377
2378	INTEGER(iwp) :: i !< loop index in x-direction
2379	INTEGER(iwp) :: j !< loop index in y-direction
2380	INTEGER(iwp) :: k !< loop index in z-direction
2381	INTEGER(iwp) :: m !< surface element index
2382
2383	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2384	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2385	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2386	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2387	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2388	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2389	REAL(wp) :: w_convective !< convective velocity scale
2390
2391	!
2392	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2393	!-- model domain.
2394	pt_surf_mean_l = 0.0_wp
2395	shf_mean_l = 0.0_wp
2396	scale_l_l = 0.0_wp
2397	friction_vel_l = 0.0_wp
2398	DO m = 1, surf_def_h(0)%ns
2399	i = surf_def_h(0)%i(m)
2400	j = surf_def_h(0)%j(m)
2401	k = surf_def_h(0)%k(m)
2402	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2403	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2404	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2405	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2406	ENDDO
2407	DO m = 1, surf_lsm_h%ns
2408	i = surf_lsm_h%i(m)
2409	j = surf_lsm_h%j(m)
2410	k = surf_lsm_h%k(m)
2411	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2412	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2413	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2414	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2415	ENDDO
2416	DO m = 1, surf_usm_h%ns
2417	i = surf_usm_h%i(m)
2418	j = surf_usm_h%j(m)
2419	k = surf_usm_h%k(m)
2420	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2421	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2422	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2423	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2424	ENDDO
2425
2426	#if defined( __parallel )
2427	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2428	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2429	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2430	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2431	#else
2432	scale_us = friction_vel_l
2433	shf_mean = shf_mean_l
2434	scale_l = scale_l_l
2435	pt_surf_mean = pt_surf_mean_l
2436	#endif
2437
2438	scale_us = scale_us * d_nxy
2439	shf_mean = shf_mean * d_nxy
2440	scale_l = scale_l * d_nxy
2441	pt_surf_mean = pt_surf_mean * d_nxy
2442	!
2443	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2444	!-- convective velocity scale to zero.
2445	IF ( shf_mean > 0.0_wp ) THEN
2446	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2447	ELSE
2448	w_convective = 0.0_wp
2449	ENDIF
2450	!
2451	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2452	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2453	!-- value of friction velocity for the reynolds-stress parametrization.
2454	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2455	!
2456	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2457	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2458	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2459
2460	END SUBROUTINE calc_scaling_variables
2461
2462	END MODULE synthetic_turbulence_generator_mod

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