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Last change on this file since 4619 was 4603, checked in by suehring, 4 years ago
Synthetic turbulence generator: Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not initialized properly
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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 4603 2020-07-14 16:08:30Z raasch $
27	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
28	! initialized properly
29	!
30	! 4566 2020-06-16 10:11:51Z suehring
31	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
32	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
33	! - change default value of time interval to adjust turbulence parametrization
34	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
35	!
36	! 4562 2020-06-12 08:38:47Z raasch
37	! Parts of r4559 re-formatted
38	!
39	! 4559 2020-06-11 08:51:48Z raasch
40	! File re-formatted to follow the PALM coding standard
41	!
42	! 4535 2020-05-15 12:07:23Z raasch
43	! Bugfix for restart data format query
44	!
45	! 4495 2020-04-13 20:11:20Z raasch
46	! Restart data handling with MPI-IO added
47	!
48	! 4481 2020-03-31 18:55:54Z maronga
49	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
50	!
51	! 4442 2020-03-04 19:21:13Z suehring
52	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
53	! (was accidantly changed).
54	!
55	! 4441 2020-03-04 19:20:35Z suehring
56	! Correct misplaced preprocessor directive
57	!
58	! 4438 2020-03-03 20:49:28Z suehring
59	! Performance optimizations in velocity-seed calculation:
60	! - Random number array is only defined and computed locally (except for normalization to zero mean
61	! and unit variance)
62	! - Parallel random number generator is applied independent on the 2D random numbers in other
63	! routines
64	! - Option to decide wheter velocity seeds are computed locally without any further communication
65	! or are computed by all processes along the communicator
66	!
67	! 4346 2019-12-18 11:55:56Z motisi
68	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
69	! information used in wall_flags_static_0
70	!
71	! 4335 2019-12-12 16:39:05Z suehring
72	! Commentation of last commit
73	!
74	! 4332 2019-12-10 19:44:12Z suehring
75	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
76	! Further, minor bugfix in initial velocity seed calculation.
77	!
78	! 4329 2019-12-10 15:46:36Z motisi
79	! Renamed wall_flags_0 to wall_flags_static_0
80	!
81	! 4309 2019-11-26 18:49:59Z suehring
82	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
83	! the parallel random number generator. Random numbers are now only computed and normalized locally,
84	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
85	! array.
86	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
87	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
88	!
89	! 4182 2019-08-22 15:20:23Z scharf
90	! Corrected "Former revisions" section
91	!
92	! 4148 2019-08-08 11:26:00Z suehring
93	! Remove unused variable
94	!
95	! 4144 2019-08-06 09:11:47Z raasch
96	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
97	!
98	! 4071 2019-07-03 20:02:00Z suehring
99	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
100	! file.
101	!
102	! 4022 2019-06-12 11:52:39Z suehring
103	! Several bugfixes and improvements
104	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
105	! instabilities in case the mean volume flow is close to zero)
106	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
107	! numerically unstable
108	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
109	! case dt_stg_call /= dt_3d
110	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
111	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
112	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
113	!
114	! 3987 2019-05-22 09:52:13Z kanani
115	! Introduce alternative switch for debug output during timestepping
116	!
117	! 3938 2019-04-29 16:06:25Z suehring
118	! Remove unused variables
119	!
120	! 3937 2019-04-29 15:09:07Z suehring
121	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
122	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
123	! synthetic turbulence parametrization.
124	!
125	! 3909 2019-04-17 09:13:25Z suehring
126	! Minor bugfix for last commit
127	!
128	! 3900 2019-04-16 15:17:43Z suehring
129	! Missing re-calculation of perturbation seeds in case of restarts
130	!
131	! 3891 2019-04-12 17:52:01Z suehring
132	! Bugfix in initialization in case of restart runs.
133	!
134	! 3885 2019-04-11 11:29:34Z kanani
135	! Changes related to global restructuring of location messages and introduction of additional debug
136	! messages
137	!
138	!
139	! Removed unused variables
140	!
141	! 3719 2019-02-06 13:10:18Z kanani
142	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
143	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
144	! for better overview.
145	!
146	! 2259 2017-06-08 09:09:11Z gronemeier
147	! Initial revision
148	!
149	! Authors:
150	! --------
151	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
152	!
153	!
154	! Description:
155	! ------------
156	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
157	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
158	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
159	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
160	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
161	!> parametrized within the boundary layer.
162	!>
163	!> @todo Enable cyclic_fill
164	!> Implement turbulence generation for e and pt
165	!> @note <Enter notes on the module>
166	!> @bug Height information from input file is not used. Profiles from input must match with current
167	!> PALM grid.
168	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
169	!--------------------------------------------------------------------------------------------------!
170	MODULE synthetic_turbulence_generator_mod
171
172
173	USE arrays_3d, &
174	ONLY: dzw, &
175	ddzw, &
176	drho_air, &
177	mean_inflow_profiles, &
178	pt, &
179	pt_init, &
180	q, &
181	q_init, &
182	u, &
183	u_init, &
184	v, &
185	v_init, &
186	w, &
187	zu, &
188	zw
189
190	USE basic_constants_and_equations_mod, &
191	ONLY: g, &
192	kappa, &
193	pi
194
195	USE control_parameters, &
196	ONLY: bc_lr, &
197	bc_ns, &
198	child_domain, &
199	coupling_char, &
200	debug_output_timestep, &
201	dt_3d, &
202	e_init, &
203	humidity, &
204	initializing_actions, &
205	intermediate_timestep_count, &
206	intermediate_timestep_count_max, &
207	length, &
208	message_string, &
209	nesting_offline, &
210	neutral, &
211	num_mean_inflow_profiles, &
212	random_generator, &
213	rans_mode, &
214	restart_data_format_output, &
215	restart_string, &
216	syn_turb_gen, &
217	time_since_reference_point, &
218	turbulent_inflow
219
220	USE cpulog, &
221	ONLY: cpu_log, &
222	log_point_s
223
224	USE grid_variables, &
225	ONLY: ddx, &
226	ddy, &
227	dx, &
228	dy
229
230	USE indices, &
231	ONLY: nbgp, &
232	nz, &
233	nzb, &
234	nzt, &
235	nx, &
236	nxl, &
237	nxlu, &
238	nxr, &
239	ny, &
240	nys, &
241	nysv, &
242	nyn, &
243	wall_flags_total_0
244
245	USE kinds
246
247	#if defined( __parallel ) && !defined( __mpifh )
248	USE MPI
249	#endif
250
251	USE nesting_offl_mod, &
252	ONLY: nesting_offl_calc_zi, &
253	zi_ribulk
254
255	USE pegrid, &
256	ONLY: comm1dx, &
257	comm1dy, &
258	comm2d, &
259	ierr, &
260	myidx, &
261	myidy, &
262	pdims
263
264	USE pmc_interface, &
265	ONLY : rans_mode_parent
266
267	USE random_generator_parallel, &
268	ONLY: init_parallel_random_generator, &
269	random_dummy, &
270	random_number_parallel, &
271	random_seed_parallel
272
273	USE restart_data_mpi_io_mod, &
274	ONLY: rrd_mpi_io, &
275	wrd_mpi_io
276
277	USE transpose_indices, &
278	ONLY: nzb_x, &
279	nzt_x
280
281	USE surface_mod, &
282	ONLY: surf_def_h, &
283	surf_lsm_h, &
284	surf_usm_h
285
286	IMPLICIT NONE
287
288	#if defined( __parallel ) && defined( __mpifh )
289	INCLUDE "mpif.h"
290	#endif
291
292
293	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
294	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
295	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
296	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
297	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
298	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
299	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
300	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
301	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
302	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
303	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
304	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
305	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
306	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
307	#if defined( __parallel )
308	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
309	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
310	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
311	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
312	#endif
313
314	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
315	!< required for bias correction of imposed perturbations
316	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
317	!< required for bias correction of imposed perturbations
318
319	#if defined( __parallel )
320	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
324	#endif
325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
330	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
331	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
333	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
334
335	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
336	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
337	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
338	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
339
340
341	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
342	!< no time correlation to the timestep before should be considered
343	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
344	!< or if computation is distributed over several processes
345	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
346	!< (.FALSE.) or if it parametrized
347	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
348	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
349
350
351	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
352	!< scales above the boundary layer
353	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
354	!< one length scale above ABL top
355	REAL(wp) :: d_l !< blend_coeff/length_scale
356	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
357	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
358	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
359	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
360	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
361	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
362	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
363	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
364
365	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
366
367
368	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
369	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
370	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
371	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
372	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
373	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
374
375	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
376	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
377	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
378	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
379	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
380	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
381	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
382	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
383	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
384
385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
406
407	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
408	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
409
410	!
411	!-- PALM interfaces:
412	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
413	INTERFACE stg_adjust
414	MODULE PROCEDURE stg_adjust
415	END INTERFACE stg_adjust
416	!
417	!-- Input parameter checks to be done in check_parameters
418	INTERFACE stg_check_parameters
419	MODULE PROCEDURE stg_check_parameters
420	END INTERFACE stg_check_parameters
421
422	!
423	!-- Calculate filter functions
424	INTERFACE stg_filter_func
425	MODULE PROCEDURE stg_filter_func
426	END INTERFACE stg_filter_func
427
428	!
429	!-- Generate velocity seeds at south and north domain boundary
430	INTERFACE stg_generate_seed_xz
431	MODULE PROCEDURE stg_generate_seed_xz
432	END INTERFACE stg_generate_seed_xz
433	!
434	!-- Generate velocity seeds at left and/or right domain boundary
435	INTERFACE stg_generate_seed_yz
436	MODULE PROCEDURE stg_generate_seed_yz
437	END INTERFACE stg_generate_seed_yz
438
439	!
440	!-- Output of information to the header file
441	INTERFACE stg_header
442	MODULE PROCEDURE stg_header
443	END INTERFACE stg_header
444
445	!
446	!-- Initialization actions
447	INTERFACE stg_init
448	MODULE PROCEDURE stg_init
449	END INTERFACE stg_init
450
451	!
452	!-- Main procedure of synth. turb. gen.
453	INTERFACE stg_main
454	MODULE PROCEDURE stg_main
455	END INTERFACE stg_main
456
457	!
458	!-- Reading of NAMELIST parameters
459	INTERFACE stg_parin
460	MODULE PROCEDURE stg_parin
461	END INTERFACE stg_parin
462
463	!
464	!-- Reading of parameters for restart runs
465	INTERFACE stg_rrd_global
466	MODULE PROCEDURE stg_rrd_global_ftn
467	MODULE PROCEDURE stg_rrd_global_mpi
468	END INTERFACE stg_rrd_global
469
470	!
471	!-- Writing of binary output for restart runs
472	INTERFACE stg_wrd_global
473	MODULE PROCEDURE stg_wrd_global
474	END INTERFACE stg_wrd_global
475
476	SAVE
477
478	PRIVATE
479
480	!
481	!-- Public interfaces
482	PUBLIC stg_adjust, &
483	stg_check_parameters, &
484	stg_header, &
485	stg_init, &
486	stg_main, &
487	stg_parin, &
488	stg_rrd_global, &
489	stg_wrd_global
490
491	!
492	!-- Public variables
493	PUBLIC dt_stg_call, &
494	dt_stg_adjust, &
495	id_stg_left, &
496	id_stg_north, &
497	id_stg_right, &
498	id_stg_south, &
499	parametrize_inflow_turbulence, &
500	time_stg_adjust, &
501	time_stg_call, &
502	use_syn_turb_gen
503
504
505	CONTAINS
506
507
508	!--------------------------------------------------------------------------------------------------!
509	! Description:
510	! ------------
511	!> Check parameters routine for synthetic turbulence generator
512	!--------------------------------------------------------------------------------------------------!
513	SUBROUTINE stg_check_parameters
514
515	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
516	nesting_offline ) THEN
517	message_string = 'Synthetic turbulence generator is required ' // &
518	'if offline nesting is applied and PALM operates in LES mode.'
519	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
520	ENDIF
521
522	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
523	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
524	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
525	'and parent operates in RANS-mode but current child in LES mode.'
526	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
527	ENDIF
528
529	IF ( use_syn_turb_gen ) THEN
530
531	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
532	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
533	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
534
535	ENDIF
536
537	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
538	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
539	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
540
541	ENDIF
542
543	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
544
545	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
546	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
547	message_string = 'Using synthetic turbulence generator requires ' // &
548	'%initializing_actions = "set_constant_profiles" or ' // &
549	' "read_restart_data", if not offline nesting is applied.'
550	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
551	ENDIF
552
553	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
554	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
555	' "dirichlet/radiation", if not offline nesting is applied.'
556	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
557	ENDIF
558	IF ( bc_ns /= 'cyclic' ) THEN
559	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
560	' "cyclic", if not offline nesting is applied.'
561	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
562	ENDIF
563
564	ENDIF
565
566	IF ( turbulent_inflow ) THEN
567	message_string = 'Using synthetic turbulence generator in combination ' // &
568	'&with turbulent_inflow = .T. is not allowed'
569	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
570	ENDIF
571	!
572	!-- Synthetic turbulence generator requires the parallel random generator
573	IF ( random_generator /= 'random-parallel' ) THEN
574	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
575	'random-parallel.'
576	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
577	ENDIF
578
579	ENDIF
580
581	END SUBROUTINE stg_check_parameters
582
583
584	!--------------------------------------------------------------------------------------------------!
585	! Description:
586	! ------------
587	!> Header output for synthetic turbulence generator
588	!--------------------------------------------------------------------------------------------------!
589	SUBROUTINE stg_header ( io )
590
591	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
592
593	!
594	!-- Write synthetic turbulence generator Header
595	WRITE( io, 1 )
596	IF ( use_syn_turb_gen ) THEN
597	WRITE( io, 2 )
598	ELSE
599	WRITE( io, 3 )
600	ENDIF
601
602	IF ( parametrize_inflow_turbulence ) THEN
603	WRITE( io, 4 ) dt_stg_adjust
604	ELSE
605	WRITE( io, 5 )
606	ENDIF
607
608	1 FORMAT (//' Synthetic turbulence generator information:'/ &
609	' ------------------------------------------'/)
610	2 FORMAT (' synthetic turbulence generator is switched on')
611	3 FORMAT (' synthetic turbulence generator is switched off')
612	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
613	5 FORMAT (' imposed turbulence is read from file' )
614
615	END SUBROUTINE stg_header
616
617
618	!--------------------------------------------------------------------------------------------------!
619	! Description:
620	! ------------
621	!> Initialization of the synthetic turbulence generator
622	!--------------------------------------------------------------------------------------------------!
623	SUBROUTINE stg_init
624
625	#if defined( __parallel )
626	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
627	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
628	#endif
629
630	INTEGER(iwp) :: i !> grid index in x-direction
631	INTEGER(iwp) :: j !> loop index
632	INTEGER(iwp) :: k !< index
633	#if defined( __parallel )
634	INTEGER(iwp) :: newtype !< dummy MPI type
635	INTEGER(iwp) :: realsize !< size of REAL variables
636	#endif
637
638	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
639	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
640
641
642	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
643
644	!
645	!-- Dummy variables used for reading profiles
646	REAL(wp) :: d1 !< u profile
647	REAL(wp) :: d2 !< v profile
648	REAL(wp) :: d3 !< w profile
649	REAL(wp) :: d5 !< e profile
650	REAL(wp) :: luy !< length scale for u in y direction
651	REAL(wp) :: luz !< length scale for u in z direction
652	REAL(wp) :: lvy !< length scale for v in y direction
653	REAL(wp) :: lvz !< length scale for v in z direction
654	REAL(wp) :: lwy !< length scale for w in y direction
655	REAL(wp) :: lwz !< length scale for w in z direction
656	#if defined( __parallel )
657	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
658	#endif
659	REAL(wp) :: zz !< height
660
661
662	#if defined( __parallel )
663	CALL MPI_BARRIER( comm2d, ierr )
664	#endif
665	!
666	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
667	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
668	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
669	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
670	!-- communication).
671	IF ( .NOT. compute_velocity_seeds_local ) THEN
672	#if defined( __parallel )
673	!
674	!-- Determine processor decomposition of z-axis along x- and y-direction
675	nnz = nz / pdims(1)
676	nzb_x_stg = 1 + myidx * INT( nnz )
677	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
678
679	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
680	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
681
682	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
683	.AND. .NOT. rans_mode ) ) THEN
684	nnz = nz / pdims(2)
685	nzb_y_stg = 1 + myidy * INT( nnz )
686	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
687
688	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
689	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
690	ENDIF
691
692	!
693	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
694	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
695	extent = 1 * realsize
696	!
697	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
698	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
699	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
700	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
701	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
702	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
703	CALL MPI_TYPE_FREE( newtype, ierr )
704
705	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
706	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
707	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
708	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
709	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
710	CALL MPI_TYPE_FREE( newtype, ierr )
711
712	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
713	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
714
715	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
716	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
717
718	DO j = 1, pdims(1)
719	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
720	ENDDO
721	!
722	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
723	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
724	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
725	.AND. .NOT. rans_mode ) ) THEN
726	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
727	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
728	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
729	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
730	CALL MPI_TYPE_FREE( newtype, ierr )
731
732	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
733	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
734	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
735	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
736	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
737	CALL MPI_TYPE_FREE( newtype, ierr )
738
739	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
740	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
741
742	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
743	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
744
745	DO j = 1, pdims(2)
746	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
747	ENDDO
748
749	ENDIF
750	#endif
751	ENDIF
752	!
753	!-- Allocate required arrays.
754	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
755	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
756	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
757	!-- and initialized appropriately.
758	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
759	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
760	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
761	mean_inflow_profiles = 0.0_wp
762	mean_inflow_profiles(:,1) = u_init
763	mean_inflow_profiles(:,2) = v_init
764	!
765	!-- Even though potential temperature and humidity are not perturbed, they need to be
766	!-- initialized appropriately.
767	IF ( .NOT. neutral ) &
768	mean_inflow_profiles(:,4) = pt_init
769	IF ( humidity ) &
770	mean_inflow_profiles(:,6) = q_init
771	ENDIF
772	ENDIF
773	!
774	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
775	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
776	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
777	u_init = mean_inflow_profiles(:,1)
778	v_init = mean_inflow_profiles(:,2)
779	e_init = MAXVAL( mean_inflow_profiles(:,5) )
780	ENDIF
781
782	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
783	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
784	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
785	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
786	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
787	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
788	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
789	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
790
791	r11 = 0.0_wp
792	r21 = 0.0_wp
793	r22 = 0.0_wp
794	r31 = 0.0_wp
795	r32 = 0.0_wp
796	r33 = 0.0_wp
797	tu = 0.0_wp
798	tv = 0.0_wp
799	tw = 0.0_wp
800
801	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
802	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
803	dist_xz = 0.0_wp
804	dist_yz = 0.0_wp
805	!
806	!-- Read inflow profile
807	!-- Height levels of profiles in input profile is as follows:
808	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
809	!-- WARNING: zz is not used at the moment
810	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
811
812	IF ( file_stg_exist ) THEN
813
814	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
815	!
816	!-- Skip header
817	READ( 90, * )
818
819	DO k = nzb, nzt
820	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
821	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
822
823	!
824	!-- Convert length scales from meter to number of grid points.
825	IF ( k /= nzb ) THEN
826	nuz(k) = INT( luz * ddzw(k) )
827	nvz(k) = INT( lvz * ddzw(k) )
828	nwz(k) = INT( lwz * ddzw(k) )
829	ELSE
830	nuz(k) = INT( luz * ddzw(k+1) )
831	nvz(k) = INT( lvz * ddzw(k+1) )
832	nwz(k) = INT( lwz * ddzw(k+1) )
833	ENDIF
834
835	nuy(k) = INT( luy * ddy )
836	nvy(k) = INT( lvy * ddy )
837	nwy(k) = INT( lwy * ddy )
838	!
839	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
840	!-- y-direction.
841	nwx(k) = nwy(k)
842	nvx(k) = nvy(k)
843	nux(k) = nuy(k)
844	!
845	!-- Save Mean inflow profiles
846	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
847	mean_inflow_profiles(k,1) = d1
848	mean_inflow_profiles(k,2) = d2
849	! mean_inflow_profiles(k,4) = d4
850	mean_inflow_profiles(k,5) = d5
851	ENDIF
852	ENDDO
853	!
854	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
855	!-- simply overwritten.
856	nwx(nzb) = nwy(nzb+1)
857	nvx(nzb) = nvy(nzb+1)
858	nux(nzb) = nuy(nzb+1)
859	nuy(nzb) = nuy(nzb+1)
860	nuz(nzb) = nuz(nzb+1)
861	nvy(nzb) = nvy(nzb+1)
862	nvz(nzb) = nvz(nzb+1)
863	nwy(nzb) = nwy(nzb+1)
864	nwz(nzb) = nwz(nzb+1)
865
866	nwx(nzt+1) = nwy(nzt)
867	nvx(nzt+1) = nvy(nzt)
868	nux(nzt+1) = nuy(nzt)
869	nuy(nzt+1) = nuy(nzt)
870	nuz(nzt+1) = nuz(nzt)
871	nvy(nzt+1) = nvy(nzt)
872	nvz(nzt+1) = nvz(nzt)
873	nwy(nzt+1) = nwy(nzt)
874	nwz(nzt+1) = nwz(nzt)
875
876	CLOSE( 90 )
877	!
878	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
879	CALL calc_coeff_matrix
880	!
881	!-- No information about turbulence and its length scales are available. Instead, parametrize
882	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
883	!-- parametrized, which is done later when energy-balance models are already initialized. This is
884	!-- because the STG needs information about surface properties such as roughness to build
885	!-- 'realistic' turbulence profiles.
886	ELSE
887	!
888	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
889	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
890	!
891	!-- Set flag indicating that turbulence is parametrized
892	parametrize_inflow_turbulence = .TRUE.
893	!
894	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
895	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
896	!-- nevertheless, the boundary-layer depth needs to be determined first.
897	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
898	CALL nesting_offl_calc_zi
899	!
900	!-- Determine boundary-layer depth, which is used to initialize lenght scales
901	CALL calc_scaling_variables
902	!
903	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
904	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
905	!-- friction velocity and velocity scale.
906	CALL parametrize_turbulence
907	!
908	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
909	CALL calc_coeff_matrix
910
911	ENDIF
912	!
913	!-- Initial filter functions
914	CALL stg_setup_filter_function
915	!
916	!-- Allocate velocity seeds for turbulence at xz-layer
917	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
918	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
919	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
920
921	!
922	!-- Allocate velocity seeds for turbulence at yz-layer
923	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
924	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
925	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
926
927	fu_xz = 0.0_wp
928	fuo_xz = 0.0_wp
929	fv_xz = 0.0_wp
930	fvo_xz = 0.0_wp
931	fw_xz = 0.0_wp
932	fwo_xz = 0.0_wp
933
934	fu_yz = 0.0_wp
935	fuo_yz = 0.0_wp
936	fv_yz = 0.0_wp
937	fvo_yz = 0.0_wp
938	fw_yz = 0.0_wp
939	fwo_yz = 0.0_wp
940
941	#if defined( __parallel )
942	CALL MPI_BARRIER( comm2d, ierr )
943	#endif
944
945	!
946	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
947	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
948	!-- This is mostly for k=nzt+1.
949	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
950	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
951
952	IF ( myidx == id_stg_left ) i = -1
953	IF ( myidx == id_stg_right ) i = nxr+1
954
955	DO j = nys, nyn
956	DO k = nzb, nzt+1
957	IF ( a11(k) > 10E-8_wp ) THEN
958	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
959	ELSE
960	fu_yz(k,j) = 10E-8_wp
961	ENDIF
962
963	IF ( a22(k) > 10E-8_wp ) THEN
964	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
965	ELSE
966	fv_yz(k,j) = 10E-8_wp
967	ENDIF
968
969	IF ( a33(k) > 10E-8_wp ) THEN
970	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
971	ELSE
972	fw_yz(k,j) = 10E-8_wp
973	ENDIF
974	ENDDO
975	ENDDO
976	ENDIF
977
978	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
979
980	IF ( myidy == id_stg_south ) j = -1
981	IF ( myidy == id_stg_north ) j = nyn+1
982
983	DO i = nxl, nxr
984	DO k = nzb, nzt+1
985	!
986	!-- In case the correlation coefficients are very small, the velocity seeds may become
987	!-- very large finally creating numerical instabilities in the synthetic turbulence
988	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
989	IF ( a11(k) > 10E-8_wp ) THEN
990	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
991	ELSE
992	fu_xz(k,i) = 10E-8_wp
993	ENDIF
994
995	IF ( a22(k) > 10E-8_wp ) THEN
996	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
997	ELSE
998	fv_xz(k,i) = 10E-8_wp
999	ENDIF
1000
1001	IF ( a33(k) > 10E-8_wp ) THEN
1002	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1003	ELSE
1004	fw_xz(k,i) = 10E-8_wp
1005	ENDIF
1006
1007	ENDDO
1008	ENDDO
1009	ENDIF
1010	ENDIF
1011	!
1012	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1013	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1014	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1015	!-- different cases must be distinguished.
1016	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1017	!
1018	!-- Number of grid points where perturbations are imposed on u
1019	IF ( myidx == id_stg_left ) i = nxl
1020	IF ( myidx == id_stg_right ) i = nxr+1
1021
1022	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1023	!
1024	!-- Number of grid points where perturbations are imposed on v and w
1025	IF ( myidx == id_stg_left ) i = nxl-1
1026	IF ( myidx == id_stg_right ) i = nxr+1
1027
1028	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1029	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1030
1031	#if defined( __parallel )
1032	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1033	#else
1034	nr_non_topo_yz = nr_non_topo_yz_l
1035	#endif
1036	ENDIF
1037
1038	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1039	!
1040	!-- Number of grid points where perturbations are imposed on v
1041	IF ( myidy == id_stg_south ) j = nys
1042	IF ( myidy == id_stg_north ) j = nyn+1
1043
1044	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1045	!
1046	!-- Number of grid points where perturbations are imposed on u and w
1047	IF ( myidy == id_stg_south ) j = nys-1
1048	IF ( myidy == id_stg_north ) j = nyn+1
1049
1050	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1051	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1052
1053	#if defined( __parallel )
1054	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1055	#else
1056	nr_non_topo_xz = nr_non_topo_xz_l
1057	#endif
1058	ENDIF
1059	!
1060	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1061	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1062	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1063	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1064	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1065	id_rand_yz = 0
1066	seq_rand_yz = 0
1067
1068	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1069
1070	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1071	.AND. .NOT. rans_mode ) ) THEN
1072	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1073	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1074	id_rand_xz = 0
1075	seq_rand_xz = 0
1076
1077	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1078	ENDIF
1079
1080	END SUBROUTINE stg_init
1081
1082
1083	!--------------------------------------------------------------------------------------------------!
1084	! Description:
1085	! ------------
1086	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1087	!--------------------------------------------------------------------------------------------------!
1088	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1089
1090	INTEGER(iwp) :: k !< loop index
1091	INTEGER(iwp) :: mergp !< passed length scale in grid points
1092	INTEGER(iwp) :: n_k !< length scale nXX in height k
1093	INTEGER(iwp) :: nf !< index for length scales
1094
1095	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1096
1097	REAL(wp) :: bdenom !< denominator for filter functions bXX
1098	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1099
1100	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1101
1102
1103	bxx = 0.0_wp
1104
1105	DO k = nzb, nzt+1
1106	bdenom = 0.0_wp
1107	n_k = nxx(k)
1108	IF ( n_k /= 0 ) THEN
1109
1110	!
1111	!-- ( Eq.10 )^2
1112	DO nf = -n_k, n_k
1113	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1114	ENDDO
1115
1116	!
1117	!-- ( Eq.9 )
1118	bdenom = SQRT( bdenom )
1119	DO nf = -n_k, n_k
1120	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1121	ENDDO
1122	ENDIF
1123	ENDDO
1124
1125	END SUBROUTINE stg_filter_func
1126
1127
1128	!------------------------------------------------------------------------------!
1129	! Description:
1130	! ------------
1131	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1132	!> (Xie and Castro, 2008)
1133	!------------------------------------------------------------------------------!
1134	SUBROUTINE stg_setup_filter_function
1135
1136	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1137	INTEGER(iwp) :: k !< loop index along vertical direction
1138	!
1139	!-- Define the size of the filter functions and allocate them.
1140	mergp_x = 0
1141	mergp_y = 0
1142	mergp_z = 0
1143
1144	DO k = nzb, nzt+1
1145	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1146	IF ( j > mergp_x ) mergp_x = j
1147	ENDDO
1148	DO k = nzb, nzt+1
1149	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1150	IF ( j > mergp_y ) mergp_y = j
1151	ENDDO
1152	DO k = nzb, nzt+1
1153	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1154	IF ( j > mergp_z ) mergp_z = j
1155	ENDDO
1156
1157	mergp_xy = MAX( mergp_x, mergp_y )
1158
1159	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1160	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1161	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1162	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1163	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1164	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1165	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1166	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1167	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1168
1169	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1170	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1171	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1172	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1173	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1174	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1175	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1176	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1177	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1178	!
1179	!-- Create filter functions
1180	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1181	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1182	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1183	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1184	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1185	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1186	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1187	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1188	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1189
1190	END SUBROUTINE stg_setup_filter_function
1191
1192	!--------------------------------------------------------------------------------------------------!
1193	! Description:
1194	! ------------
1195	!> Parin for &stg_par for synthetic turbulence generator
1196	!--------------------------------------------------------------------------------------------------!
1197	SUBROUTINE stg_parin
1198
1199	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1200
1201
1202	NAMELIST /stg_par/ dt_stg_adjust, &
1203	dt_stg_call, &
1204	use_syn_turb_gen, &
1205	compute_velocity_seeds_local
1206
1207	line = ' '
1208	!
1209	!-- Try to find stg package
1210	REWIND ( 11 )
1211	line = ' '
1212	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1213	READ ( 11, '(A)', END = 20 ) line
1214	ENDDO
1215	BACKSPACE ( 11 )
1216
1217	!
1218	!-- Read namelist
1219	READ ( 11, stg_par, ERR = 10, END = 20 )
1220
1221	!
1222	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1223	syn_turb_gen = .TRUE.
1224	GOTO 20
1225
1226	10 BACKSPACE( 11 )
1227	READ( 11 , '(A)') line
1228	CALL parin_fail_message( 'stg_par', line )
1229
1230	20 CONTINUE
1231
1232	END SUBROUTINE stg_parin
1233
1234
1235	!--------------------------------------------------------------------------------------------------!
1236	! Description:
1237	! ------------
1238	!> Read module-specific global restart data (Fortran binary format).
1239	!--------------------------------------------------------------------------------------------------!
1240	SUBROUTINE stg_rrd_global_ftn( found )
1241
1242	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1243
1244	found = .TRUE.
1245
1246
1247	SELECT CASE ( restart_string(1:length) )
1248
1249	CASE ( 'time_stg_adjust' )
1250	READ ( 13 ) time_stg_adjust
1251
1252	CASE ( 'time_stg_call' )
1253	READ ( 13 ) time_stg_call
1254
1255	CASE ( 'use_syn_turb_gen' )
1256	READ ( 13 ) use_syn_turb_gen
1257
1258	CASE DEFAULT
1259
1260	found = .FALSE.
1261
1262	END SELECT
1263
1264
1265	END SUBROUTINE stg_rrd_global_ftn
1266
1267
1268	!--------------------------------------------------------------------------------------------------!
1269	! Description:
1270	! ------------
1271	!> Read module-specific global restart data (MPI-IO).
1272	!--------------------------------------------------------------------------------------------------!
1273	SUBROUTINE stg_rrd_global_mpi
1274
1275	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1276	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1277	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1278
1279	END SUBROUTINE stg_rrd_global_mpi
1280
1281
1282	!--------------------------------------------------------------------------------------------------!
1283	! Description:
1284	! ------------
1285	!> This routine writes the respective restart data.
1286	!--------------------------------------------------------------------------------------------------!
1287	SUBROUTINE stg_wrd_global
1288
1289	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1290
1291	CALL wrd_write_string( 'time_stg_adjust' )
1292	WRITE ( 14 ) time_stg_adjust
1293
1294	CALL wrd_write_string( 'time_stg_call' )
1295	WRITE ( 14 ) time_stg_call
1296
1297	CALL wrd_write_string( 'use_syn_turb_gen' )
1298	WRITE ( 14 ) use_syn_turb_gen
1299
1300	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1301
1302	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1303	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1304	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1305
1306	ENDIF
1307
1308	END SUBROUTINE stg_wrd_global
1309
1310
1311	!--------------------------------------------------------------------------------------------------!
1312	! Description:
1313	! ------------
1314	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1315	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1316	!> (2013), and using a Lund rotation (Lund, 1998).
1317	!--------------------------------------------------------------------------------------------------!
1318	SUBROUTINE stg_main
1319
1320	USE exchange_horiz_mod, &
1321	ONLY: exchange_horiz
1322
1323	INTEGER(iwp) :: i !< grid index in x-direction
1324	INTEGER(iwp) :: j !< loop index in y-direction
1325	INTEGER(iwp) :: k !< loop index in z-direction
1326
1327	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1328
1329	REAL(wp) :: dt_stg !< time interval the STG is called
1330
1331	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1332
1333	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1334	!
1335	!-- Calculate time step which is needed for filter functions
1336	dt_stg = MAX( dt_3d, dt_stg_call )
1337	!
1338	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1339	!-- created or if old disturbances can be imposed again.
1340	IF ( time_stg_call >= dt_stg_call .AND. &
1341	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1342	stg_call = .TRUE.
1343	ELSE
1344	stg_call = .FALSE.
1345	ENDIF
1346	!
1347	!-- Initial value of fu, fv, fw
1348	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1349	!
1350	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1351	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1352	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1353	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1354	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1355	!-- have the same initial seeds.
1356	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1357	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1358	.AND. .NOT. rans_mode ) ) ) THEN
1359	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1360	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1361	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1362	ELSE
1363	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1364	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1365	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1366	!
1367	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1368	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1369	!-- comment above.
1370	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1371	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1372	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1373	ENDIF
1374	velocity_seed_initialized = .TRUE.
1375	ENDIF
1376	!
1377	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1378	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1379	!-- seeds are required also at the right, south and north boundaries.
1380	IF ( stg_call ) THEN
1381	IF ( .NOT. ( nesting_offline .OR. &
1382	( child_domain .AND. rans_mode_parent &
1383	.AND. .NOT. rans_mode ) ) ) THEN
1384	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1385	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1386	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1387
1388	ELSE
1389	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1390	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1391	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1392
1393	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1394	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1395	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1396	ENDIF
1397	ENDIF
1398
1399	!
1400	!-- Turbulence generation at left and/or right boundary
1401	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1402	!
1403	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1404	!-- exceeded. Else the old set of perturbations is imposed
1405	IF ( stg_call ) THEN
1406
1407	DO j = nys, nyn
1408	DO k = nzb, nzt + 1
1409	!
1410	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1411	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1412	fu_yz(k,j) = fuo_yz(k,j)
1413	ELSE
1414	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1415	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1416	ENDIF
1417
1418	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1419	fv_yz(k,j) = fvo_yz(k,j)
1420	ELSE
1421	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1422	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1423	ENDIF
1424
1425	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1426	fw_yz(k,j) = fwo_yz(k,j)
1427	ELSE
1428	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1429	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1430	ENDIF
1431	ENDDO
1432	ENDDO
1433
1434	dist_yz(nzb,:,1) = 0.0_wp
1435	dist_yz(nzb,:,2) = 0.0_wp
1436	dist_yz(nzb,:,3) = 0.0_wp
1437
1438	IF ( myidx == id_stg_left ) i = nxl
1439	IF ( myidx == id_stg_right ) i = nxr+1
1440	DO j = nys, nyn
1441	DO k = nzb+1, nzt + 1
1442	!
1443	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1444	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1445	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1446
1447	ENDDO
1448	ENDDO
1449
1450	IF ( myidx == id_stg_left ) i = nxl-1
1451	IF ( myidx == id_stg_right ) i = nxr+1
1452	DO j = nys, nyn
1453	DO k = nzb+1, nzt + 1
1454	!
1455	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1456	!-- Additional factors are added to improve the variance of v and w experimental test
1457	!-- of 1.2
1458	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1459	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1460	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1461	a33(k) * fw_yz(k,j) ) * &
1462	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1463
1464	ENDDO
1465	ENDDO
1466	ENDIF
1467	!
1468	!-- Mass flux correction following Kim et al. (2013)
1469	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1470	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1471	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1472	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1473	mc_factor_l = 0.0_wp
1474	mc_factor = 0.0_wp
1475	!
1476	!-- Sum up the original volume flows (with and without perturbations).
1477	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1478	IF ( myidx == id_stg_left ) i = nxl
1479	IF ( myidx == id_stg_right ) i = nxr+1
1480
1481	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1482	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1483
1484	IF ( myidx == id_stg_left ) i = nxl-1
1485	IF ( myidx == id_stg_right ) i = nxr+1
1486
1487	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1488	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1489	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1490	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1491
1492	#if defined( __parallel )
1493	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1494	#else
1495	mc_factor = mc_factor_l
1496	#endif
1497	!
1498	!-- Calculate correction factor and force zero mean perturbations.
1499	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1500
1501	IF ( myidx == id_stg_left ) i = nxl
1502	IF ( myidx == id_stg_right ) i = nxr+1
1503
1504	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1505	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1506
1507
1508	IF ( myidx == id_stg_left ) i = nxl-1
1509	IF ( myidx == id_stg_right ) i = nxr+1
1510
1511	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1512	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1513
1514	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1515	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1516	!
1517	!-- Add disturbances
1518	IF ( myidx == id_stg_left ) THEN
1519	!
1520	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1521	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1522	!-- the mean inflow profiles.
1523	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1524	!
1525	!-- Add disturbance at the inflow
1526	DO j = nys, nyn
1527	DO k = nzb, nzt+1
1528	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1529	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1530	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1531	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1532	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1533	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1534	ENDDO
1535	ENDDO
1536	ELSE
1537
1538	DO j = nys, nyn
1539	DO k = nzb+1, nzt
1540	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1541	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1542	u(k,j,-1) = u(k,j,0)
1543	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1544	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1545	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1546	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1547	ENDDO
1548	ENDDO
1549	ENDIF
1550	ENDIF
1551	IF ( myidx == id_stg_right ) THEN
1552	DO j = nys, nyn
1553	DO k = nzb+1, nzt
1554	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1556	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1557	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1558	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1559	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1560	ENDDO
1561	ENDDO
1562	ENDIF
1563	ENDIF
1564	ENDIF
1565	!
1566	!-- Turbulence generation at north and south boundary
1567	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1568	!
1569	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1570	!-- exceeded. Else the old set of perturbations is imposed
1571	IF ( stg_call ) THEN
1572	DO i = nxl, nxr
1573	DO k = nzb, nzt + 1
1574	!
1575	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1576	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1577	fu_xz(k,i) = fuo_xz(k,i)
1578	ELSE
1579	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1580	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1581	ENDIF
1582
1583	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1584	fv_xz(k,i) = fvo_xz(k,i)
1585	ELSE
1586	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1587	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1588	ENDIF
1589
1590	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1591	fw_xz(k,i) = fwo_xz(k,i)
1592	ELSE
1593	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1594	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1595	ENDIF
1596	ENDDO
1597	ENDDO
1598
1599
1600	dist_xz(nzb,:,1) = 0.0_wp
1601	dist_xz(nzb,:,2) = 0.0_wp
1602	dist_xz(nzb,:,3) = 0.0_wp
1603
1604	IF ( myidy == id_stg_south ) j = nys
1605	IF ( myidy == id_stg_north ) j = nyn+1
1606	DO i = nxl, nxr
1607	DO k = nzb+1, nzt + 1
1608	!
1609	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1610	!-- Additional factors are added to improve the variance of v and w
1611	!experimental test of 1.2
1612	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1613	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1614	ENDDO
1615	ENDDO
1616
1617	IF ( myidy == id_stg_south ) j = nys-1
1618	IF ( myidy == id_stg_north ) j = nyn+1
1619	DO i = nxl, nxr
1620	DO k = nzb+1, nzt + 1
1621	!
1622	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1623	!-- Additional factors are added to improve the variance of v and w
1624	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1625	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1626
1627	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1628	a33(k) * fw_xz(k,i) ) * &
1629	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1630	ENDDO
1631	ENDDO
1632	ENDIF
1633
1634	!
1635	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1636	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1637	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1638	!-- else the boundary values won't be accessed.
1639	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1640	mc_factor_l = 0.0_wp
1641	mc_factor = 0.0_wp
1642
1643	IF ( myidy == id_stg_south ) j = nys
1644	IF ( myidy == id_stg_north ) j = nyn+1
1645
1646	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1647	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1648
1649	IF ( myidy == id_stg_south ) j = nys-1
1650	IF ( myidy == id_stg_north ) j = nyn+1
1651
1652	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1653	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1654	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1655	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1656
1657	#if defined( __parallel )
1658	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1659	#else
1660	mc_factor = mc_factor_l
1661	#endif
1662
1663	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1664
1665	IF ( myidy == id_stg_south ) j = nys
1666	IF ( myidy == id_stg_north ) j = nyn+1
1667
1668	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1669	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1670
1671
1672	IF ( myidy == id_stg_south ) j = nys-1
1673	IF ( myidy == id_stg_north ) j = nyn+1
1674
1675	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1676	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1677
1678	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1679	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1680	!
1681	!-- Add disturbances
1682	IF ( myidy == id_stg_south ) THEN
1683	DO i = nxl, nxr
1684	DO k = nzb+1, nzt
1685	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1686	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1687	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1688	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1689	v(k,-1,i) = v(k,0,i)
1690	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1691	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1692	ENDDO
1693	ENDDO
1694	ENDIF
1695	IF ( myidy == id_stg_north ) THEN
1696
1697	DO i = nxl, nxr
1698	DO k = nzb+1, nzt
1699	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1700	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1701	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1702	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1703	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1704	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1705	ENDDO
1706	ENDDO
1707	ENDIF
1708	ENDIF
1709	ENDIF
1710	!
1711	!-- Exchange ghost points.
1712	CALL exchange_horiz( u, nbgp )
1713	CALL exchange_horiz( v, nbgp )
1714	CALL exchange_horiz( w, nbgp )
1715	!
1716	!-- Finally, set time counter for calling STG to zero
1717	IF ( stg_call ) time_stg_call = 0.0_wp
1718	!
1719	!-- Set adjustment step to False to indicate that time correlation can be
1720	!-- switched-on again.
1721	adjustment_step = .FALSE.
1722
1723	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1724
1725	END SUBROUTINE stg_main
1726
1727	!--------------------------------------------------------------------------------------------------!
1728	! Description:
1729	! ------------
1730	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1731	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1732	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1733	!> array.
1734	!--------------------------------------------------------------------------------------------------!
1735	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1736
1737	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1738	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1739	INTEGER(iwp) :: j !< loop index in y-direction
1740	INTEGER(iwp) :: jj !< loop index in y-direction
1741	INTEGER(iwp) :: k !< loop index in z-direction
1742	INTEGER(iwp) :: kk !< loop index in z-direction
1743	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1744
1745	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1746	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1747
1748	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1749	REAL(wp) :: rand_av !< average of random number
1750	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1751
1752	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1753	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1754
1755	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1756	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1757
1758	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1759	!
1760	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1761	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1762	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1763	!-- and normalization of random numbers is done locally, while the result is later distributed to
1764	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1765	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1766	!-- correlation matrix.
1767	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1768	rand_it = 0.0_wp
1769
1770	rand_av = 0.0_wp
1771	rand_sigma_inv = 0.0_wp
1772	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1773	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1774	!
1775	!-- Compute and normalize random numbers.
1776	DO j = nys - mergp_y, nyn + mergp_y
1777	!
1778	!-- Put the random seeds at grid point j
1779	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1780	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1781	CALL random_number_parallel( random_dummy )
1782	rand_it(k,j) = random_dummy
1783	ENDDO
1784	!
1785	!-- Get the new random seeds from last call at grid point j
1786	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1787	ENDDO
1788	!
1789	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1790	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1791	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1792	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1793	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1794	rand_av = rand_av + rand_it(k,j)
1795	ENDDO
1796	ENDDO
1797
1798	#if defined( __parallel )
1799	!
1800	!-- Sum-up the local averages of the random numbers
1801	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1802	#endif
1803	rand_av = rand_av * nyz_inv
1804	!
1805	!-- Obtain zero mean
1806	rand_it= rand_it - rand_av
1807	!
1808	!-- Now, compute the variance
1809	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1810	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1811	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1812	ENDDO
1813	ENDDO
1814
1815	#if defined( __parallel )
1816	!
1817	!-- Sum-up the local quadratic averages of the random numbers
1818	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1819	#endif
1820	!
1821	!-- Compute standard deviation
1822	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1823	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1824	ELSE
1825	rand_sigma_inv = 1.0_wp
1826	ENDIF
1827	!
1828	!-- Normalize with standard deviation to obtain unit variance
1829	rand_it = rand_it * rand_sigma_inv
1830
1831	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1832	!
1833	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1834	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1835	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1836	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1837	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1838	!-- communication. In the second option, which performs better when the turbulent length scales
1839	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1840	!-- communication is necessary.
1841	IF ( compute_velocity_seeds_local ) THEN
1842
1843	f_n = 0.0_wp
1844	DO j = nys, nyn
1845	DO k = nzb, nzt+1
1846	DO jj = -n_y(k), n_y(k)
1847	DO kk = -n_z(k), n_z(k)
1848	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1849	ENDDO
1850	ENDDO
1851	ENDDO
1852	ENDDO
1853
1854	ELSE
1855
1856	f_n_l = 0.0_wp
1857	DO j = nys, nyn
1858	DO k = nzb_x_stg, nzt_x_stg+1
1859	DO jj = -n_y(k), n_y(k)
1860	DO kk = -n_z(k), n_z(k)
1861	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1862	ENDDO
1863	ENDDO
1864	ENDDO
1865	ENDDO
1866	!
1867	!-- Gather velocity seeds of full subdomain
1868	send_count = nzt_x_stg - nzb_x_stg + 1
1869	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1870
1871	#if defined( __parallel )
1872	!
1873	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1874	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1875	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1876	!
1877	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1878	!-- nesting for example).
1879	IF ( PRESENT( id_right ) ) THEN
1880	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1881	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1882	ENDIF
1883	#else
1884	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1885	!
1886	!-- Next line required to avoid compile errors because of unused dummy arguments
1887	IF ( id_left == 0 ) id_right = 0
1888	#endif
1889
1890	ENDIF
1891
1892	DEALLOCATE( rand_it )
1893
1894	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1895
1896	END SUBROUTINE stg_generate_seed_yz
1897
1898
1899	!--------------------------------------------------------------------------------------------------!
1900	! Description:
1901	! ------------
1902	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1903	!> f_n.
1904	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1905	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1906	!> full array.
1907	!--------------------------------------------------------------------------------------------------!
1908	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1909
1910	INTEGER(iwp) :: i !< loop index in x-direction
1911	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1912	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1913	INTEGER(iwp) :: ii !< loop index in x-direction
1914	INTEGER(iwp) :: k !< loop index in z-direction
1915	INTEGER(iwp) :: kk !< loop index in z-direction
1916	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1917
1918	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1919	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1920
1921	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1922	REAL(wp) :: rand_av !< average of random number
1923	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1924
1925	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1926	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1927
1928	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1929	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1930
1931	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1932
1933	!
1934	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1935	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1936	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1937	!-- and normalization of random numbers is done locally, while the result is later distributed to
1938	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1939	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1940	!-- correlation matrix.
1941	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1942	rand_it = 0.0_wp
1943
1944	rand_av = 0.0_wp
1945	rand_sigma_inv = 0.0_wp
1946	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1947	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1948	!
1949	!-- Compute and normalize random numbers.
1950	DO i = nxl - mergp_x, nxr + mergp_x
1951	!
1952	!-- Put the random seeds at grid point ii
1953	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1954	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1955	CALL random_number_parallel( random_dummy )
1956	rand_it(k,i) = random_dummy
1957	ENDDO
1958	!
1959	!-- Get the new random seeds from last call at grid point ii
1960	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1961	ENDDO
1962	!
1963	!-- For normalization to zero mean, sum-up the global random numers.
1964	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1965	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1966	!-- also occur on the inner subdomains.
1967	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1968	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1969	rand_av = rand_av + rand_it(k,i)
1970	ENDDO
1971	ENDDO
1972
1973	#if defined( __parallel )
1974	!
1975	!-- Sum-up the local averages of the random numbers
1976	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1977	#endif
1978	rand_av = rand_av * nxz_inv
1979	!
1980	!-- Obtain zero mean
1981	rand_it= rand_it - rand_av
1982	!
1983	!-- Now, compute the variance
1984	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1985	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1986	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1987	ENDDO
1988	ENDDO
1989
1990	#if defined( __parallel )
1991	!
1992	!-- Sum-up the local quadratic averages of the random numbers
1993	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1994	#endif
1995	!
1996	!-- Compute standard deviation
1997	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1998	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1999	ELSE
2000	rand_sigma_inv = 1.0_wp
2001	ENDIF
2002	!
2003	!-- Normalize with standard deviation to obtain unit variance
2004	rand_it = rand_it * rand_sigma_inv
2005
2006	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2007	!
2008	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2009	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2010	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2011	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2012	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2013	!-- In the second option, which performs better when the turbulent length scales are parametrized
2014	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2015	IF ( compute_velocity_seeds_local ) THEN
2016
2017	f_n = 0.0_wp
2018	DO i = nxl, nxr
2019	DO k = nzb, nzt+1
2020	DO ii = -n_x(k), n_x(k)
2021	DO kk = -n_z(k), n_z(k)
2022	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2023	ENDDO
2024	ENDDO
2025	ENDDO
2026	ENDDO
2027
2028	ELSE
2029
2030	f_n_l = 0.0_wp
2031	DO i = nxl, nxr
2032	DO k = nzb_y_stg, nzt_y_stg+1
2033	DO ii = -n_x(k), n_x(k)
2034	DO kk = -n_z(k), n_z(k)
2035	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2036	ENDDO
2037	ENDDO
2038	ENDDO
2039	ENDDO
2040	!
2041	!-- Gather velocity seeds of full subdomain
2042	send_count = nzt_y_stg - nzb_y_stg + 1
2043	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2044
2045	#if defined( __parallel )
2046	!
2047	!-- Gather the processed velocity seed on south boundary mpi ranks.
2048	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2049	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2050	!
2051	!-- Gather the processed velocity seed on north 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_north, comm1dy, ierr )
2054	#else
2055	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2056	!
2057	!-- Next line required to avoid compile errors because of unused dummy arguments
2058	IF ( id_north == 0 ) id_south = 0
2059	#endif
2060
2061	ENDIF
2062
2063	DEALLOCATE( rand_it )
2064
2065	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2066
2067	END SUBROUTINE stg_generate_seed_xz
2068
2069	!--------------------------------------------------------------------------------------------------!
2070	! Description:
2071	! ------------
2072	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2073	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2074	!> which is applied in state-of-the-art dispserion modelling.
2075	!--------------------------------------------------------------------------------------------------!
2076	SUBROUTINE parametrize_turbulence
2077
2078	INTEGER(iwp) :: k !< loop index in z-direction
2079
2080	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2081	REAL(wp) :: d_zi !< inverse boundary-layer depth
2082	REAL(wp) :: length_scale_lon !< length scale in flow direction
2083	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2084	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2085	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2086	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2087	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2088	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2089	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2090	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2091	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2092	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2093	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2094	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2095	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2096	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2097	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2098	REAL(wp) :: zzi !< ratio of z/zi
2099
2100	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2101	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2102	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2103
2104	!
2105	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2106	!-- criterion according to Heinze et al. (2017).
2107	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2108	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2109	k_zi = MIN( k_zi, nzt )
2110	!
2111	!-- Calculate angle between flow direction and x-axis.
2112	DO k = nzb+1, nzt + 1
2113	IF ( u_init(k) /= 0.0_wp ) THEN
2114	phi(k) = ATAN( v_init(k) / u_init(k) )
2115	ELSE
2116	phi(k) = 0.5 * pi
2117	ENDIF
2118	!
2119	!-- Pre-calculate sine and cosine.
2120	cos_phi(k) = COS( phi(k) )
2121	sin_phi(k) = SIN( phi(k) )
2122	ENDDO
2123	!
2124	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2125	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2126	!-- coincide with the grid axis. Hence, components are rotated after computation.
2127	d_zi = 1.0_wp / zi_ribulk
2128	DO k = nzb+1, k_zi
2129
2130	corr_term_uh = MERGE( 0.35_wp * ABS( &
2131	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2132	)**( 2.0_wp / 3.0_wp ), &
2133	0.0_wp, &
2134	scale_l < 0.0_wp )
2135	!
2136	!-- Determine normalized height coordinate
2137	zzi = zu(k) * d_zi
2138	!
2139	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2140	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2141	!-- variances cannot become negative, take the absolute values.
2142	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2143	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2144
2145	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2146	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2147	!
2148	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as
2149	!-- for u'w'.
2150	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
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	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2170	!-- limited to the adjustment time scales.
2171	tu(k) = MIN( dt_stg_adjust, &
2172	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2173
2174	tv(k) = tu(k)
2175	tw(k) = tu(k)
2176
2177	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2178	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2179	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2180	!
2181	!-- Assume isotropic turbulence length scales
2182	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2183	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2184	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2185	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2186	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2187	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2188	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2189	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2190	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2191
2192	ENDDO
2193	!
2194	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2195	!-- reduced to zero by a blending function.
2196	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2197	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2198	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2199
2200	time_scale_zi = tu(k_zi)
2201	r11_zi = r11(k_zi)
2202	r22_zi = r22(k_zi)
2203	r33_zi = r33(k_zi)
2204	r31_zi = r31(k_zi)
2205	r32_zi = r32(k_zi)
2206
2207	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2208
2209	DO k = k_zi+1, nzt+1
2210	!
2211	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2212	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2213	!
2214	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2215	!-- the mergpe-function can crash if scale_l is zero.
2216	r11(k) = r11_zi * blend
2217	r22(k) = r22_zi * blend
2218	r33(k) = r33_zi * blend
2219	r31(k) = r31_zi * blend
2220	r32(k) = r32_zi * blend
2221	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
2222
2223	!
2224	!-- Compute turbulent time scales according to Brost et al. (1982).
2225	!-- Note, time scales are limited to the adjustment time scales.
2226	tu(k) = time_scale_zi * blend
2227	tv(k) = time_scale_zi * blend
2228	tw(k) = time_scale_zi * blend
2229
2230	length_scale_lon = length_scale_lon_zi * blend
2231	length_scale_lat = length_scale_lat_zi * blend
2232	length_scale_vert = length_scale_vert_zi * blend
2233	!
2234	!-- Assume isotropic turbulence length scales
2235	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2236	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2237	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2238	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2239	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2240	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2241	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2242	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2243	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2244	ENDDO
2245	!
2246	!-- Set bottom boundary condition for reynolds stresses
2247	r11(nzb) = r11(nzb+1)
2248	r22(nzb) = r22(nzb+1)
2249	r33(nzb) = r33(nzb+1)
2250
2251	r21(nzb) = r11(nzb+1)
2252	r31(nzb) = r31(nzb+1)
2253	r32(nzb) = r32(nzb+1)
2254
2255	!
2256	!-- Set bottom boundary condition for the length and time scales
2257	nux(nzb) = nux(nzb+1)
2258	nuy(nzb) = nuy(nzb+1)
2259	nuz(nzb) = nuz(nzb+1)
2260	nvx(nzb) = nvx(nzb+1)
2261	nvy(nzb) = nvy(nzb+1)
2262	nvz(nzb) = nvz(nzb+1)
2263	nwx(nzb) = nwx(nzb+1)
2264	nwy(nzb) = nwy(nzb+1)
2265	nwz(nzb) = nwz(nzb+1)
2266
2267	tu(nzb) = tu(nzb+1)
2268	tv(nzb) = tv(nzb+1)
2269	tw(nzb) = tw(nzb+1)
2270
2271	adjustment_step = .TRUE.
2272
2273	END SUBROUTINE parametrize_turbulence
2274
2275	!--------------------------------------------------------------------------------------------------!
2276	! Description:
2277	! ------------
2278	!> Calculate the coefficient matrix from the Lund rotation.
2279	!--------------------------------------------------------------------------------------------------!
2280	SUBROUTINE calc_coeff_matrix
2281
2282	INTEGER(iwp) :: k !< loop index in z-direction
2283
2284	!
2285	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2286	DO k = nzb+1, nzt+1
2287	IF ( r11(k) > 10E-6_wp ) THEN
2288	a11(k) = SQRT( r11(k) )
2289	a21(k) = r21(k) / a11(k)
2290	a31(k) = r31(k) / a11(k)
2291	ELSE
2292	a11(k) = 10E-8_wp
2293	a21(k) = 10E-8_wp
2294	a31(k) = 10E-8_wp
2295	ENDIF
2296	ENDDO
2297	DO k = nzb+1, nzt+1
2298	a22(k) = r22(k) - a21(k)**2
2299	IF ( a22(k) > 10E-6_wp ) THEN
2300	a22(k) = SQRT( a22(k) )
2301	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2302	ELSE
2303	a22(k) = 10E-8_wp
2304	a32(k) = 10E-8_wp
2305	ENDIF
2306	ENDDO
2307	DO k = nzb+1, nzt+1
2308	a33(k) = r33(k) - a31(k)2 - a32(k)2
2309	IF ( a33(k) > 10E-6_wp ) THEN
2310	a33(k) = SQRT( a33(k) )
2311	ELSE
2312	a33(k) = 10E-8_wp
2313	ENDIF
2314	ENDDO
2315	!
2316	!-- Set bottom boundary condition
2317	a11(nzb) = a11(nzb+1)
2318	a22(nzb) = a22(nzb+1)
2319	a21(nzb) = a21(nzb+1)
2320	a33(nzb) = a33(nzb+1)
2321	a31(nzb) = a31(nzb+1)
2322	a32(nzb) = a32(nzb+1)
2323
2324	END SUBROUTINE calc_coeff_matrix
2325
2326	!--------------------------------------------------------------------------------------------------!
2327	! Description:
2328	! ------------
2329	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2330	!> turbulence at the lateral boundaries.
2331	!--------------------------------------------------------------------------------------------------!
2332	SUBROUTINE stg_adjust
2333
2334	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2335	!
2336	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2337	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2338	!-- nevertheless, the boundary-layer depth need to determined first.
2339	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2340	CALL nesting_offl_calc_zi
2341	!
2342	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2343	CALL calc_scaling_variables
2344	!
2345	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2346	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2347	!-- velocity and velocity scale.
2348	CALL parametrize_turbulence
2349	!
2350	!-- Calculate coefficient matrix from Reynolds stress tensor
2351	!-- (Lund rotation)
2352	CALL calc_coeff_matrix
2353	!
2354	!-- Setup filter functions according to updated length scales.
2355	CALL stg_setup_filter_function
2356	!
2357	!-- Reset time counter for controlling next adjustment to zero
2358	time_stg_adjust = 0.0_wp
2359
2360	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2361
2362	END SUBROUTINE stg_adjust
2363
2364
2365	!--------------------------------------------------------------------------------------------------!
2366	! Description:
2367	! ------------
2368	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2369	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2370	!> scale, and Obukhov length.
2371	!--------------------------------------------------------------------------------------------------!
2372	SUBROUTINE calc_scaling_variables
2373
2374	INTEGER(iwp) :: i !< loop index in x-direction
2375	INTEGER(iwp) :: j !< loop index in y-direction
2376	INTEGER(iwp) :: k !< loop index in z-direction
2377	INTEGER(iwp) :: m !< surface element index
2378
2379	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2380	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2381	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2382	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2383	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2384	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2385	REAL(wp) :: w_convective !< convective velocity scale
2386
2387	!
2388	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2389	!-- model domain.
2390	pt_surf_mean_l = 0.0_wp
2391	shf_mean_l = 0.0_wp
2392	scale_l_l = 0.0_wp
2393	friction_vel_l = 0.0_wp
2394	DO m = 1, surf_def_h(0)%ns
2395	i = surf_def_h(0)%i(m)
2396	j = surf_def_h(0)%j(m)
2397	k = surf_def_h(0)%k(m)
2398	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2399	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2400	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2401	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2402	ENDDO
2403	DO m = 1, surf_lsm_h%ns
2404	i = surf_lsm_h%i(m)
2405	j = surf_lsm_h%j(m)
2406	k = surf_lsm_h%k(m)
2407	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2408	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2409	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2410	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2411	ENDDO
2412	DO m = 1, surf_usm_h%ns
2413	i = surf_usm_h%i(m)
2414	j = surf_usm_h%j(m)
2415	k = surf_usm_h%k(m)
2416	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2417	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2418	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2419	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2420	ENDDO
2421
2422	#if defined( __parallel )
2423	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2424	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2425	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2426	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2427	#else
2428	scale_us = friction_vel_l
2429	shf_mean = shf_mean_l
2430	scale_l = scale_l_l
2431	pt_surf_mean = pt_surf_mean_l
2432	#endif
2433
2434	scale_us = scale_us * d_nxy
2435	shf_mean = shf_mean * d_nxy
2436	scale_l = scale_l * d_nxy
2437	pt_surf_mean = pt_surf_mean * d_nxy
2438	!
2439	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2440	!-- convective velocity scale to zero.
2441	IF ( shf_mean > 0.0_wp ) THEN
2442	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2443	ELSE
2444	w_convective = 0.0_wp
2445	ENDIF
2446	!
2447	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2448	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2449	!-- value of friction velocity for the reynolds-stress parametrization.
2450	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2451	!
2452	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2453	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2454	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2455
2456	END SUBROUTINE calc_scaling_variables
2457
2458	END MODULE synthetic_turbulence_generator_mod

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