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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4635

Last change on this file since 4635 was 4629, checked in by raasch, 4 years ago
support for MPI Fortran77 interface (mpif.h) removed
Property svn:keywords set to `Id`
File size: 111.8 KB

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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 4629 2020-07-29 09:37:56Z suehring $
27	! support for MPI Fortran77 interface (mpif.h) removed
28	!
29	! 4603 2020-07-14 16:08:30Z suehring
30	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
31	! initialized properly
32	!
33	! 4566 2020-06-16 10:11:51Z suehring
34	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
35	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
36	! - change default value of time interval to adjust turbulence parametrization
37	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
38	!
39	! 4562 2020-06-12 08:38:47Z raasch
40	! Parts of r4559 re-formatted
41	!
42	! 4559 2020-06-11 08:51:48Z raasch
43	! File re-formatted to follow the PALM coding standard
44	!
45	! 4535 2020-05-15 12:07:23Z raasch
46	! Bugfix for restart data format query
47	!
48	! 4495 2020-04-13 20:11:20Z raasch
49	! Restart data handling with MPI-IO added
50	!
51	! 4481 2020-03-31 18:55:54Z maronga
52	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
53	!
54	! 4442 2020-03-04 19:21:13Z suehring
55	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
56	! (was accidantly changed).
57	!
58	! 4441 2020-03-04 19:20:35Z suehring
59	! Correct misplaced preprocessor directive
60	!
61	! 4438 2020-03-03 20:49:28Z suehring
62	! Performance optimizations in velocity-seed calculation:
63	! - Random number array is only defined and computed locally (except for normalization to zero mean
64	! and unit variance)
65	! - Parallel random number generator is applied independent on the 2D random numbers in other
66	! routines
67	! - Option to decide wheter velocity seeds are computed locally without any further communication
68	! or are computed by all processes along the communicator
69	!
70	! 4346 2019-12-18 11:55:56Z motisi
71	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
72	! information used in wall_flags_static_0
73	!
74	! 4335 2019-12-12 16:39:05Z suehring
75	! Commentation of last commit
76	!
77	! 4332 2019-12-10 19:44:12Z suehring
78	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
79	! Further, minor bugfix in initial velocity seed calculation.
80	!
81	! 4329 2019-12-10 15:46:36Z motisi
82	! Renamed wall_flags_0 to wall_flags_static_0
83	!
84	! 4309 2019-11-26 18:49:59Z suehring
85	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
86	! the parallel random number generator. Random numbers are now only computed and normalized locally,
87	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
88	! array.
89	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
90	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
91	!
92	! 4182 2019-08-22 15:20:23Z scharf
93	! Corrected "Former revisions" section
94	!
95	! 4148 2019-08-08 11:26:00Z suehring
96	! Remove unused variable
97	!
98	! 4144 2019-08-06 09:11:47Z raasch
99	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
100	!
101	! 4071 2019-07-03 20:02:00Z suehring
102	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
103	! file.
104	!
105	! 4022 2019-06-12 11:52:39Z suehring
106	! Several bugfixes and improvements
107	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
108	! instabilities in case the mean volume flow is close to zero)
109	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
110	! numerically unstable
111	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
112	! case dt_stg_call /= dt_3d
113	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
114	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
115	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
116	!
117	! 3987 2019-05-22 09:52:13Z kanani
118	! Introduce alternative switch for debug output during timestepping
119	!
120	! 3938 2019-04-29 16:06:25Z suehring
121	! Remove unused variables
122	!
123	! 3937 2019-04-29 15:09:07Z suehring
124	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
125	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
126	! synthetic turbulence parametrization.
127	!
128	! 3909 2019-04-17 09:13:25Z suehring
129	! Minor bugfix for last commit
130	!
131	! 3900 2019-04-16 15:17:43Z suehring
132	! Missing re-calculation of perturbation seeds in case of restarts
133	!
134	! 3891 2019-04-12 17:52:01Z suehring
135	! Bugfix in initialization in case of restart runs.
136	!
137	! 3885 2019-04-11 11:29:34Z kanani
138	! Changes related to global restructuring of location messages and introduction of additional debug
139	! messages
140	!
141	!
142	! Removed unused variables
143	!
144	! 3719 2019-02-06 13:10:18Z kanani
145	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
146	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
147	! for better overview.
148	!
149	! 2259 2017-06-08 09:09:11Z gronemeier
150	! Initial revision
151	!
152	! Authors:
153	! --------
154	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
155	!
156	!
157	! Description:
158	! ------------
159	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
160	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
161	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
162	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
163	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
164	!> parametrized within the boundary layer.
165	!>
166	!> @todo Enable cyclic_fill
167	!> Implement turbulence generation for e and pt
168	!> @note <Enter notes on the module>
169	!> @bug Height information from input file is not used. Profiles from input must match with current
170	!> PALM grid.
171	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
172	!--------------------------------------------------------------------------------------------------!
173	MODULE synthetic_turbulence_generator_mod
174
175
176	USE arrays_3d, &
177	ONLY: dzw, &
178	ddzw, &
179	drho_air, &
180	mean_inflow_profiles, &
181	pt, &
182	pt_init, &
183	q, &
184	q_init, &
185	u, &
186	u_init, &
187	v, &
188	v_init, &
189	w, &
190	zu, &
191	zw
192
193	USE basic_constants_and_equations_mod, &
194	ONLY: g, &
195	kappa, &
196	pi
197
198	USE control_parameters, &
199	ONLY: bc_lr, &
200	bc_ns, &
201	child_domain, &
202	coupling_char, &
203	debug_output_timestep, &
204	dt_3d, &
205	e_init, &
206	humidity, &
207	initializing_actions, &
208	intermediate_timestep_count, &
209	intermediate_timestep_count_max, &
210	length, &
211	message_string, &
212	nesting_offline, &
213	neutral, &
214	num_mean_inflow_profiles, &
215	random_generator, &
216	rans_mode, &
217	restart_data_format_output, &
218	restart_string, &
219	syn_turb_gen, &
220	time_since_reference_point, &
221	turbulent_inflow
222
223	USE cpulog, &
224	ONLY: cpu_log, &
225	log_point_s
226
227	USE grid_variables, &
228	ONLY: ddx, &
229	ddy, &
230	dx, &
231	dy
232
233	USE indices, &
234	ONLY: nbgp, &
235	nz, &
236	nzb, &
237	nzt, &
238	nx, &
239	nxl, &
240	nxlu, &
241	nxr, &
242	ny, &
243	nys, &
244	nysv, &
245	nyn, &
246	wall_flags_total_0
247
248	USE kinds
249
250	#if defined( __parallel )
251	USE MPI
252	#endif
253
254	USE nesting_offl_mod, &
255	ONLY: nesting_offl_calc_zi, &
256	zi_ribulk
257
258	USE pegrid, &
259	ONLY: comm1dx, &
260	comm1dy, &
261	comm2d, &
262	ierr, &
263	myidx, &
264	myidy, &
265	pdims
266
267	USE pmc_interface, &
268	ONLY : rans_mode_parent
269
270	USE random_generator_parallel, &
271	ONLY: init_parallel_random_generator, &
272	random_dummy, &
273	random_number_parallel, &
274	random_seed_parallel
275
276	USE restart_data_mpi_io_mod, &
277	ONLY: rrd_mpi_io, &
278	wrd_mpi_io
279
280	USE transpose_indices, &
281	ONLY: nzb_x, &
282	nzt_x
283
284	USE surface_mod, &
285	ONLY: surf_def_h, &
286	surf_lsm_h, &
287	surf_usm_h
288
289	IMPLICIT NONE
290
291	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
292	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
293	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
294	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
295	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
296	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
297	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
298	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
299	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
300	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
301	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
302	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
303	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
304	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
305	#if defined( __parallel )
306	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
307	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
308	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
309	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
310	#endif
311
312	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
313	!< required for bias correction of imposed perturbations
314	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
315	!< required for bias correction of imposed perturbations
316
317	#if defined( __parallel )
318	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
319	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
320	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
322	#endif
323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
330	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
331	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
332
333	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
334	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
335	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
336	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
337
338
339	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
340	!< no time correlation to the timestep before should be considered
341	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
342	!< or if computation is distributed over several processes
343	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
344	!< (.FALSE.) or if it parametrized
345	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
346	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
347
348
349	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
350	!< scales above the boundary layer
351	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
352	!< one length scale above ABL top
353	REAL(wp) :: d_l !< blend_coeff/length_scale
354	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
355	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
356	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
357	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
358	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
359	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
360	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
361	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
362
363	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
364
365
366	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
367	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
368	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
369	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
370	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
371	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
372
373	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
374	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
375	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
376	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
377	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
378	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
379	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
380	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
381	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
382
383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
404
405	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
406	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
407
408	!
409	!-- PALM interfaces:
410	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
411	INTERFACE stg_adjust
412	MODULE PROCEDURE stg_adjust
413	END INTERFACE stg_adjust
414	!
415	!-- Input parameter checks to be done in check_parameters
416	INTERFACE stg_check_parameters
417	MODULE PROCEDURE stg_check_parameters
418	END INTERFACE stg_check_parameters
419
420	!
421	!-- Calculate filter functions
422	INTERFACE stg_filter_func
423	MODULE PROCEDURE stg_filter_func
424	END INTERFACE stg_filter_func
425
426	!
427	!-- Generate velocity seeds at south and north domain boundary
428	INTERFACE stg_generate_seed_xz
429	MODULE PROCEDURE stg_generate_seed_xz
430	END INTERFACE stg_generate_seed_xz
431	!
432	!-- Generate velocity seeds at left and/or right domain boundary
433	INTERFACE stg_generate_seed_yz
434	MODULE PROCEDURE stg_generate_seed_yz
435	END INTERFACE stg_generate_seed_yz
436
437	!
438	!-- Output of information to the header file
439	INTERFACE stg_header
440	MODULE PROCEDURE stg_header
441	END INTERFACE stg_header
442
443	!
444	!-- Initialization actions
445	INTERFACE stg_init
446	MODULE PROCEDURE stg_init
447	END INTERFACE stg_init
448
449	!
450	!-- Main procedure of synth. turb. gen.
451	INTERFACE stg_main
452	MODULE PROCEDURE stg_main
453	END INTERFACE stg_main
454
455	!
456	!-- Reading of NAMELIST parameters
457	INTERFACE stg_parin
458	MODULE PROCEDURE stg_parin
459	END INTERFACE stg_parin
460
461	!
462	!-- Reading of parameters for restart runs
463	INTERFACE stg_rrd_global
464	MODULE PROCEDURE stg_rrd_global_ftn
465	MODULE PROCEDURE stg_rrd_global_mpi
466	END INTERFACE stg_rrd_global
467
468	!
469	!-- Writing of binary output for restart runs
470	INTERFACE stg_wrd_global
471	MODULE PROCEDURE stg_wrd_global
472	END INTERFACE stg_wrd_global
473
474	SAVE
475
476	PRIVATE
477
478	!
479	!-- Public interfaces
480	PUBLIC stg_adjust, &
481	stg_check_parameters, &
482	stg_header, &
483	stg_init, &
484	stg_main, &
485	stg_parin, &
486	stg_rrd_global, &
487	stg_wrd_global
488
489	!
490	!-- Public variables
491	PUBLIC dt_stg_call, &
492	dt_stg_adjust, &
493	id_stg_left, &
494	id_stg_north, &
495	id_stg_right, &
496	id_stg_south, &
497	parametrize_inflow_turbulence, &
498	time_stg_adjust, &
499	time_stg_call, &
500	use_syn_turb_gen
501
502
503	CONTAINS
504
505
506	!--------------------------------------------------------------------------------------------------!
507	! Description:
508	! ------------
509	!> Check parameters routine for synthetic turbulence generator
510	!--------------------------------------------------------------------------------------------------!
511	SUBROUTINE stg_check_parameters
512
513	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
514	nesting_offline ) THEN
515	message_string = 'Synthetic turbulence generator is required ' // &
516	'if offline nesting is applied and PALM operates in LES mode.'
517	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
518	ENDIF
519
520	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
521	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
522	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
523	'and parent operates in RANS-mode but current child in LES mode.'
524	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
525	ENDIF
526
527	IF ( use_syn_turb_gen ) THEN
528
529	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
530	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
531	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
532
533	ENDIF
534
535	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
536	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
537	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
538
539	ENDIF
540
541	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
542
543	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
544	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
545	message_string = 'Using synthetic turbulence generator requires ' // &
546	'%initializing_actions = "set_constant_profiles" or ' // &
547	' "read_restart_data", if not offline nesting is applied.'
548	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
549	ENDIF
550
551	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
552	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
553	' "dirichlet/radiation", if not offline nesting is applied.'
554	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
555	ENDIF
556	IF ( bc_ns /= 'cyclic' ) THEN
557	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
558	' "cyclic", if not offline nesting is applied.'
559	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
560	ENDIF
561
562	ENDIF
563
564	IF ( turbulent_inflow ) THEN
565	message_string = 'Using synthetic turbulence generator in combination ' // &
566	'&with turbulent_inflow = .T. is not allowed'
567	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
568	ENDIF
569	!
570	!-- Synthetic turbulence generator requires the parallel random generator
571	IF ( random_generator /= 'random-parallel' ) THEN
572	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
573	'random-parallel.'
574	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
575	ENDIF
576
577	ENDIF
578
579	END SUBROUTINE stg_check_parameters
580
581
582	!--------------------------------------------------------------------------------------------------!
583	! Description:
584	! ------------
585	!> Header output for synthetic turbulence generator
586	!--------------------------------------------------------------------------------------------------!
587	SUBROUTINE stg_header ( io )
588
589	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
590
591	!
592	!-- Write synthetic turbulence generator Header
593	WRITE( io, 1 )
594	IF ( use_syn_turb_gen ) THEN
595	WRITE( io, 2 )
596	ELSE
597	WRITE( io, 3 )
598	ENDIF
599
600	IF ( parametrize_inflow_turbulence ) THEN
601	WRITE( io, 4 ) dt_stg_adjust
602	ELSE
603	WRITE( io, 5 )
604	ENDIF
605
606	1 FORMAT (//' Synthetic turbulence generator information:'/ &
607	' ------------------------------------------'/)
608	2 FORMAT (' synthetic turbulence generator is switched on')
609	3 FORMAT (' synthetic turbulence generator is switched off')
610	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
611	5 FORMAT (' imposed turbulence is read from file' )
612
613	END SUBROUTINE stg_header
614
615
616	!--------------------------------------------------------------------------------------------------!
617	! Description:
618	! ------------
619	!> Initialization of the synthetic turbulence generator
620	!--------------------------------------------------------------------------------------------------!
621	SUBROUTINE stg_init
622
623	#if defined( __parallel )
624	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
625	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
626	#endif
627
628	INTEGER(iwp) :: i !> grid index in x-direction
629	INTEGER(iwp) :: j !> loop index
630	INTEGER(iwp) :: k !< index
631	#if defined( __parallel )
632	INTEGER(iwp) :: newtype !< dummy MPI type
633	INTEGER(iwp) :: realsize !< size of REAL variables
634	#endif
635
636	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
637	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
638
639
640	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
641
642	!
643	!-- Dummy variables used for reading profiles
644	REAL(wp) :: d1 !< u profile
645	REAL(wp) :: d2 !< v profile
646	REAL(wp) :: d3 !< w profile
647	REAL(wp) :: d5 !< e profile
648	REAL(wp) :: luy !< length scale for u in y direction
649	REAL(wp) :: luz !< length scale for u in z direction
650	REAL(wp) :: lvy !< length scale for v in y direction
651	REAL(wp) :: lvz !< length scale for v in z direction
652	REAL(wp) :: lwy !< length scale for w in y direction
653	REAL(wp) :: lwz !< length scale for w in z direction
654	#if defined( __parallel )
655	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
656	#endif
657	REAL(wp) :: zz !< height
658
659
660	#if defined( __parallel )
661	CALL MPI_BARRIER( comm2d, ierr )
662	#endif
663	!
664	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
665	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
666	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
667	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
668	!-- communication).
669	IF ( .NOT. compute_velocity_seeds_local ) THEN
670	#if defined( __parallel )
671	!
672	!-- Determine processor decomposition of z-axis along x- and y-direction
673	nnz = nz / pdims(1)
674	nzb_x_stg = 1 + myidx * INT( nnz )
675	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
676
677	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
678	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
679
680	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
681	.AND. .NOT. rans_mode ) ) THEN
682	nnz = nz / pdims(2)
683	nzb_y_stg = 1 + myidy * INT( nnz )
684	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
685
686	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
687	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
688	ENDIF
689
690	!
691	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
692	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
693	extent = 1 * realsize
694	!
695	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
696	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
697	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
698	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
699	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
700	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
701	CALL MPI_TYPE_FREE( newtype, ierr )
702
703	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
704	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
705	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
706	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
707	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
708	CALL MPI_TYPE_FREE( newtype, ierr )
709
710	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
711	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
712
713	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
714	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
715
716	DO j = 1, pdims(1)
717	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
718	ENDDO
719	!
720	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
721	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
722	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
723	.AND. .NOT. rans_mode ) ) THEN
724	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
725	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
726	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
727	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
728	CALL MPI_TYPE_FREE( newtype, ierr )
729
730	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
731	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
732	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
733	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
734	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
735	CALL MPI_TYPE_FREE( newtype, ierr )
736
737	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
738	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
739
740	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
741	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
742
743	DO j = 1, pdims(2)
744	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
745	ENDDO
746
747	ENDIF
748	#endif
749	ENDIF
750	!
751	!-- Allocate required arrays.
752	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
753	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
754	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
755	!-- and initialized appropriately.
756	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
757	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
758	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
759	mean_inflow_profiles = 0.0_wp
760	mean_inflow_profiles(:,1) = u_init
761	mean_inflow_profiles(:,2) = v_init
762	!
763	!-- Even though potential temperature and humidity are not perturbed, they need to be
764	!-- initialized appropriately.
765	IF ( .NOT. neutral ) &
766	mean_inflow_profiles(:,4) = pt_init
767	IF ( humidity ) &
768	mean_inflow_profiles(:,6) = q_init
769	ENDIF
770	ENDIF
771	!
772	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
773	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
774	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
775	u_init = mean_inflow_profiles(:,1)
776	v_init = mean_inflow_profiles(:,2)
777	e_init = MAXVAL( mean_inflow_profiles(:,5) )
778	ENDIF
779
780	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
781	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
782	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
783	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
784	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
785	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
786	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
787	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
788
789	r11 = 0.0_wp
790	r21 = 0.0_wp
791	r22 = 0.0_wp
792	r31 = 0.0_wp
793	r32 = 0.0_wp
794	r33 = 0.0_wp
795	tu = 0.0_wp
796	tv = 0.0_wp
797	tw = 0.0_wp
798
799	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
800	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
801	dist_xz = 0.0_wp
802	dist_yz = 0.0_wp
803	!
804	!-- Read inflow profile
805	!-- Height levels of profiles in input profile is as follows:
806	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
807	!-- WARNING: zz is not used at the moment
808	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
809
810	IF ( file_stg_exist ) THEN
811
812	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
813	!
814	!-- Skip header
815	READ( 90, * )
816
817	DO k = nzb, nzt
818	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
819	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
820
821	!
822	!-- Convert length scales from meter to number of grid points.
823	IF ( k /= nzb ) THEN
824	nuz(k) = INT( luz * ddzw(k) )
825	nvz(k) = INT( lvz * ddzw(k) )
826	nwz(k) = INT( lwz * ddzw(k) )
827	ELSE
828	nuz(k) = INT( luz * ddzw(k+1) )
829	nvz(k) = INT( lvz * ddzw(k+1) )
830	nwz(k) = INT( lwz * ddzw(k+1) )
831	ENDIF
832
833	nuy(k) = INT( luy * ddy )
834	nvy(k) = INT( lvy * ddy )
835	nwy(k) = INT( lwy * ddy )
836	!
837	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
838	!-- y-direction.
839	nwx(k) = nwy(k)
840	nvx(k) = nvy(k)
841	nux(k) = nuy(k)
842	!
843	!-- Save Mean inflow profiles
844	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
845	mean_inflow_profiles(k,1) = d1
846	mean_inflow_profiles(k,2) = d2
847	! mean_inflow_profiles(k,4) = d4
848	mean_inflow_profiles(k,5) = d5
849	ENDIF
850	ENDDO
851	!
852	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
853	!-- simply overwritten.
854	nwx(nzb) = nwy(nzb+1)
855	nvx(nzb) = nvy(nzb+1)
856	nux(nzb) = nuy(nzb+1)
857	nuy(nzb) = nuy(nzb+1)
858	nuz(nzb) = nuz(nzb+1)
859	nvy(nzb) = nvy(nzb+1)
860	nvz(nzb) = nvz(nzb+1)
861	nwy(nzb) = nwy(nzb+1)
862	nwz(nzb) = nwz(nzb+1)
863
864	nwx(nzt+1) = nwy(nzt)
865	nvx(nzt+1) = nvy(nzt)
866	nux(nzt+1) = nuy(nzt)
867	nuy(nzt+1) = nuy(nzt)
868	nuz(nzt+1) = nuz(nzt)
869	nvy(nzt+1) = nvy(nzt)
870	nvz(nzt+1) = nvz(nzt)
871	nwy(nzt+1) = nwy(nzt)
872	nwz(nzt+1) = nwz(nzt)
873
874	CLOSE( 90 )
875	!
876	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
877	CALL calc_coeff_matrix
878	!
879	!-- No information about turbulence and its length scales are available. Instead, parametrize
880	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
881	!-- parametrized, which is done later when energy-balance models are already initialized. This is
882	!-- because the STG needs information about surface properties such as roughness to build
883	!-- 'realistic' turbulence profiles.
884	ELSE
885	!
886	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
887	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
888	!
889	!-- Set flag indicating that turbulence is parametrized
890	parametrize_inflow_turbulence = .TRUE.
891	!
892	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
893	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
894	!-- nevertheless, the boundary-layer depth needs to be determined first.
895	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
896	CALL nesting_offl_calc_zi
897	!
898	!-- Determine boundary-layer depth, which is used to initialize lenght scales
899	CALL calc_scaling_variables
900	!
901	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
902	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
903	!-- friction velocity and velocity scale.
904	CALL parametrize_turbulence
905	!
906	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
907	CALL calc_coeff_matrix
908
909	ENDIF
910	!
911	!-- Initial filter functions
912	CALL stg_setup_filter_function
913	!
914	!-- Allocate velocity seeds for turbulence at xz-layer
915	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
916	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
917	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
918
919	!
920	!-- Allocate velocity seeds for turbulence at yz-layer
921	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
922	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
923	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
924
925	fu_xz = 0.0_wp
926	fuo_xz = 0.0_wp
927	fv_xz = 0.0_wp
928	fvo_xz = 0.0_wp
929	fw_xz = 0.0_wp
930	fwo_xz = 0.0_wp
931
932	fu_yz = 0.0_wp
933	fuo_yz = 0.0_wp
934	fv_yz = 0.0_wp
935	fvo_yz = 0.0_wp
936	fw_yz = 0.0_wp
937	fwo_yz = 0.0_wp
938
939	#if defined( __parallel )
940	CALL MPI_BARRIER( comm2d, ierr )
941	#endif
942
943	!
944	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
945	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
946	!-- This is mostly for k=nzt+1.
947	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
948	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
949
950	IF ( myidx == id_stg_left ) i = -1
951	IF ( myidx == id_stg_right ) i = nxr+1
952
953	DO j = nys, nyn
954	DO k = nzb, nzt+1
955	IF ( a11(k) > 10E-8_wp ) THEN
956	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
957	ELSE
958	fu_yz(k,j) = 10E-8_wp
959	ENDIF
960
961	IF ( a22(k) > 10E-8_wp ) THEN
962	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
963	ELSE
964	fv_yz(k,j) = 10E-8_wp
965	ENDIF
966
967	IF ( a33(k) > 10E-8_wp ) THEN
968	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
969	ELSE
970	fw_yz(k,j) = 10E-8_wp
971	ENDIF
972	ENDDO
973	ENDDO
974	ENDIF
975
976	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
977
978	IF ( myidy == id_stg_south ) j = -1
979	IF ( myidy == id_stg_north ) j = nyn+1
980
981	DO i = nxl, nxr
982	DO k = nzb, nzt+1
983	!
984	!-- In case the correlation coefficients are very small, the velocity seeds may become
985	!-- very large finally creating numerical instabilities in the synthetic turbulence
986	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
987	IF ( a11(k) > 10E-8_wp ) THEN
988	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
989	ELSE
990	fu_xz(k,i) = 10E-8_wp
991	ENDIF
992
993	IF ( a22(k) > 10E-8_wp ) THEN
994	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
995	ELSE
996	fv_xz(k,i) = 10E-8_wp
997	ENDIF
998
999	IF ( a33(k) > 10E-8_wp ) THEN
1000	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1001	ELSE
1002	fw_xz(k,i) = 10E-8_wp
1003	ENDIF
1004
1005	ENDDO
1006	ENDDO
1007	ENDIF
1008	ENDIF
1009	!
1010	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1011	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1012	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1013	!-- different cases must be distinguished.
1014	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1015	!
1016	!-- Number of grid points where perturbations are imposed on u
1017	IF ( myidx == id_stg_left ) i = nxl
1018	IF ( myidx == id_stg_right ) i = nxr+1
1019
1020	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1021	!
1022	!-- Number of grid points where perturbations are imposed on v and w
1023	IF ( myidx == id_stg_left ) i = nxl-1
1024	IF ( myidx == id_stg_right ) i = nxr+1
1025
1026	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1027	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1028
1029	#if defined( __parallel )
1030	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1031	#else
1032	nr_non_topo_yz = nr_non_topo_yz_l
1033	#endif
1034	ENDIF
1035
1036	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1037	!
1038	!-- Number of grid points where perturbations are imposed on v
1039	IF ( myidy == id_stg_south ) j = nys
1040	IF ( myidy == id_stg_north ) j = nyn+1
1041
1042	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1043	!
1044	!-- Number of grid points where perturbations are imposed on u and w
1045	IF ( myidy == id_stg_south ) j = nys-1
1046	IF ( myidy == id_stg_north ) j = nyn+1
1047
1048	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1049	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1050
1051	#if defined( __parallel )
1052	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1053	#else
1054	nr_non_topo_xz = nr_non_topo_xz_l
1055	#endif
1056	ENDIF
1057	!
1058	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1059	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1060	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1061	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1062	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1063	id_rand_yz = 0
1064	seq_rand_yz = 0
1065
1066	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1067
1068	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1069	.AND. .NOT. rans_mode ) ) THEN
1070	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1071	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1072	id_rand_xz = 0
1073	seq_rand_xz = 0
1074
1075	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1076	ENDIF
1077
1078	END SUBROUTINE stg_init
1079
1080
1081	!--------------------------------------------------------------------------------------------------!
1082	! Description:
1083	! ------------
1084	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1085	!--------------------------------------------------------------------------------------------------!
1086	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1087
1088	INTEGER(iwp) :: k !< loop index
1089	INTEGER(iwp) :: mergp !< passed length scale in grid points
1090	INTEGER(iwp) :: n_k !< length scale nXX in height k
1091	INTEGER(iwp) :: nf !< index for length scales
1092
1093	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1094
1095	REAL(wp) :: bdenom !< denominator for filter functions bXX
1096	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1097
1098	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1099
1100
1101	bxx = 0.0_wp
1102
1103	DO k = nzb, nzt+1
1104	bdenom = 0.0_wp
1105	n_k = nxx(k)
1106	IF ( n_k /= 0 ) THEN
1107
1108	!
1109	!-- ( Eq.10 )^2
1110	DO nf = -n_k, n_k
1111	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1112	ENDDO
1113
1114	!
1115	!-- ( Eq.9 )
1116	bdenom = SQRT( bdenom )
1117	DO nf = -n_k, n_k
1118	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1119	ENDDO
1120	ENDIF
1121	ENDDO
1122
1123	END SUBROUTINE stg_filter_func
1124
1125
1126	!------------------------------------------------------------------------------!
1127	! Description:
1128	! ------------
1129	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1130	!> (Xie and Castro, 2008)
1131	!------------------------------------------------------------------------------!
1132	SUBROUTINE stg_setup_filter_function
1133
1134	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1135	INTEGER(iwp) :: k !< loop index along vertical direction
1136	!
1137	!-- Define the size of the filter functions and allocate them.
1138	mergp_x = 0
1139	mergp_y = 0
1140	mergp_z = 0
1141
1142	DO k = nzb, nzt+1
1143	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1144	IF ( j > mergp_x ) mergp_x = j
1145	ENDDO
1146	DO k = nzb, nzt+1
1147	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1148	IF ( j > mergp_y ) mergp_y = j
1149	ENDDO
1150	DO k = nzb, nzt+1
1151	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1152	IF ( j > mergp_z ) mergp_z = j
1153	ENDDO
1154
1155	mergp_xy = MAX( mergp_x, mergp_y )
1156
1157	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1158	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1159	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1160	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1161	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1162	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1163	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1164	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1165	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1166
1167	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1168	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1169	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1170	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1171	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1172	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1173	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1174	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1175	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1176	!
1177	!-- Create filter functions
1178	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1179	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1180	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1181	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1182	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1183	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1184	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1185	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1186	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1187
1188	END SUBROUTINE stg_setup_filter_function
1189
1190	!--------------------------------------------------------------------------------------------------!
1191	! Description:
1192	! ------------
1193	!> Parin for &stg_par for synthetic turbulence generator
1194	!--------------------------------------------------------------------------------------------------!
1195	SUBROUTINE stg_parin
1196
1197	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1198
1199
1200	NAMELIST /stg_par/ dt_stg_adjust, &
1201	dt_stg_call, &
1202	use_syn_turb_gen, &
1203	compute_velocity_seeds_local
1204
1205	line = ' '
1206	!
1207	!-- Try to find stg package
1208	REWIND ( 11 )
1209	line = ' '
1210	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1211	READ ( 11, '(A)', END = 20 ) line
1212	ENDDO
1213	BACKSPACE ( 11 )
1214
1215	!
1216	!-- Read namelist
1217	READ ( 11, stg_par, ERR = 10, END = 20 )
1218
1219	!
1220	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1221	syn_turb_gen = .TRUE.
1222	GOTO 20
1223
1224	10 BACKSPACE( 11 )
1225	READ( 11 , '(A)') line
1226	CALL parin_fail_message( 'stg_par', line )
1227
1228	20 CONTINUE
1229
1230	END SUBROUTINE stg_parin
1231
1232
1233	!--------------------------------------------------------------------------------------------------!
1234	! Description:
1235	! ------------
1236	!> Read module-specific global restart data (Fortran binary format).
1237	!--------------------------------------------------------------------------------------------------!
1238	SUBROUTINE stg_rrd_global_ftn( found )
1239
1240	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1241
1242	found = .TRUE.
1243
1244
1245	SELECT CASE ( restart_string(1:length) )
1246
1247	CASE ( 'time_stg_adjust' )
1248	READ ( 13 ) time_stg_adjust
1249
1250	CASE ( 'time_stg_call' )
1251	READ ( 13 ) time_stg_call
1252
1253	CASE ( 'use_syn_turb_gen' )
1254	READ ( 13 ) use_syn_turb_gen
1255
1256	CASE DEFAULT
1257
1258	found = .FALSE.
1259
1260	END SELECT
1261
1262
1263	END SUBROUTINE stg_rrd_global_ftn
1264
1265
1266	!--------------------------------------------------------------------------------------------------!
1267	! Description:
1268	! ------------
1269	!> Read module-specific global restart data (MPI-IO).
1270	!--------------------------------------------------------------------------------------------------!
1271	SUBROUTINE stg_rrd_global_mpi
1272
1273	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1274	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1275	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1276
1277	END SUBROUTINE stg_rrd_global_mpi
1278
1279
1280	!--------------------------------------------------------------------------------------------------!
1281	! Description:
1282	! ------------
1283	!> This routine writes the respective restart data.
1284	!--------------------------------------------------------------------------------------------------!
1285	SUBROUTINE stg_wrd_global
1286
1287	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1288
1289	CALL wrd_write_string( 'time_stg_adjust' )
1290	WRITE ( 14 ) time_stg_adjust
1291
1292	CALL wrd_write_string( 'time_stg_call' )
1293	WRITE ( 14 ) time_stg_call
1294
1295	CALL wrd_write_string( 'use_syn_turb_gen' )
1296	WRITE ( 14 ) use_syn_turb_gen
1297
1298	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1299
1300	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1301	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1302	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1303
1304	ENDIF
1305
1306	END SUBROUTINE stg_wrd_global
1307
1308
1309	!--------------------------------------------------------------------------------------------------!
1310	! Description:
1311	! ------------
1312	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1313	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1314	!> (2013), and using a Lund rotation (Lund, 1998).
1315	!--------------------------------------------------------------------------------------------------!
1316	SUBROUTINE stg_main
1317
1318	USE exchange_horiz_mod, &
1319	ONLY: exchange_horiz
1320
1321	INTEGER(iwp) :: i !< grid index in x-direction
1322	INTEGER(iwp) :: j !< loop index in y-direction
1323	INTEGER(iwp) :: k !< loop index in z-direction
1324
1325	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1326
1327	REAL(wp) :: dt_stg !< time interval the STG is called
1328
1329	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1330
1331	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1332	!
1333	!-- Calculate time step which is needed for filter functions
1334	dt_stg = MAX( dt_3d, dt_stg_call )
1335	!
1336	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1337	!-- created or if old disturbances can be imposed again.
1338	IF ( time_stg_call >= dt_stg_call .AND. &
1339	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1340	stg_call = .TRUE.
1341	ELSE
1342	stg_call = .FALSE.
1343	ENDIF
1344	!
1345	!-- Initial value of fu, fv, fw
1346	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1347	!
1348	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1349	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1350	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1351	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1352	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1353	!-- have the same initial seeds.
1354	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1355	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1356	.AND. .NOT. rans_mode ) ) ) THEN
1357	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1358	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1359	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1360	ELSE
1361	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1362	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1363	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1364	!
1365	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1366	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1367	!-- comment above.
1368	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1369	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1370	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1371	ENDIF
1372	velocity_seed_initialized = .TRUE.
1373	ENDIF
1374	!
1375	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1376	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1377	!-- seeds are required also at the right, south and north boundaries.
1378	IF ( stg_call ) THEN
1379	IF ( .NOT. ( nesting_offline .OR. &
1380	( child_domain .AND. rans_mode_parent &
1381	.AND. .NOT. rans_mode ) ) ) THEN
1382	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1383	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1384	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1385
1386	ELSE
1387	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1388	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1389	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1390
1391	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1392	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1393	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1394	ENDIF
1395	ENDIF
1396
1397	!
1398	!-- Turbulence generation at left and/or right boundary
1399	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1400	!
1401	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1402	!-- exceeded. Else the old set of perturbations is imposed
1403	IF ( stg_call ) THEN
1404
1405	DO j = nys, nyn
1406	DO k = nzb, nzt + 1
1407	!
1408	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1409	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1410	fu_yz(k,j) = fuo_yz(k,j)
1411	ELSE
1412	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1413	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1414	ENDIF
1415
1416	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1417	fv_yz(k,j) = fvo_yz(k,j)
1418	ELSE
1419	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1420	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1421	ENDIF
1422
1423	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1424	fw_yz(k,j) = fwo_yz(k,j)
1425	ELSE
1426	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1427	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1428	ENDIF
1429	ENDDO
1430	ENDDO
1431
1432	dist_yz(nzb,:,1) = 0.0_wp
1433	dist_yz(nzb,:,2) = 0.0_wp
1434	dist_yz(nzb,:,3) = 0.0_wp
1435
1436	IF ( myidx == id_stg_left ) i = nxl
1437	IF ( myidx == id_stg_right ) i = nxr+1
1438	DO j = nys, nyn
1439	DO k = nzb+1, nzt + 1
1440	!
1441	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1442	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1443	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1444
1445	ENDDO
1446	ENDDO
1447
1448	IF ( myidx == id_stg_left ) i = nxl-1
1449	IF ( myidx == id_stg_right ) i = nxr+1
1450	DO j = nys, nyn
1451	DO k = nzb+1, nzt + 1
1452	!
1453	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1454	!-- Additional factors are added to improve the variance of v and w experimental test
1455	!-- of 1.2
1456	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1457	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1458	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1459	a33(k) * fw_yz(k,j) ) * &
1460	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1461
1462	ENDDO
1463	ENDDO
1464	ENDIF
1465	!
1466	!-- Mass flux correction following Kim et al. (2013)
1467	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1468	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1469	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1470	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1471	mc_factor_l = 0.0_wp
1472	mc_factor = 0.0_wp
1473	!
1474	!-- Sum up the original volume flows (with and without perturbations).
1475	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1476	IF ( myidx == id_stg_left ) i = nxl
1477	IF ( myidx == id_stg_right ) i = nxr+1
1478
1479	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1480	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1481
1482	IF ( myidx == id_stg_left ) i = nxl-1
1483	IF ( myidx == id_stg_right ) i = nxr+1
1484
1485	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1486	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1487	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1488	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1489
1490	#if defined( __parallel )
1491	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1492	#else
1493	mc_factor = mc_factor_l
1494	#endif
1495	!
1496	!-- Calculate correction factor and force zero mean perturbations.
1497	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1498
1499	IF ( myidx == id_stg_left ) i = nxl
1500	IF ( myidx == id_stg_right ) i = nxr+1
1501
1502	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1503	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1504
1505
1506	IF ( myidx == id_stg_left ) i = nxl-1
1507	IF ( myidx == id_stg_right ) i = nxr+1
1508
1509	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1510	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1511
1512	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1513	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1514	!
1515	!-- Add disturbances
1516	IF ( myidx == id_stg_left ) THEN
1517	!
1518	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1519	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1520	!-- the mean inflow profiles.
1521	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1522	!
1523	!-- Add disturbance at the inflow
1524	DO j = nys, nyn
1525	DO k = nzb, nzt+1
1526	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1527	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1528	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1529	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1530	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1531	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1532	ENDDO
1533	ENDDO
1534	ELSE
1535
1536	DO j = nys, nyn
1537	DO k = nzb+1, nzt
1538	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1539	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1540	u(k,j,-1) = u(k,j,0)
1541	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1542	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1543	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1544	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1545	ENDDO
1546	ENDDO
1547	ENDIF
1548	ENDIF
1549	IF ( myidx == id_stg_right ) THEN
1550	DO j = nys, nyn
1551	DO k = nzb+1, nzt
1552	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1553	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1554	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1556	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1557	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1558	ENDDO
1559	ENDDO
1560	ENDIF
1561	ENDIF
1562	ENDIF
1563	!
1564	!-- Turbulence generation at north and south boundary
1565	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1566	!
1567	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1568	!-- exceeded. Else the old set of perturbations is imposed
1569	IF ( stg_call ) THEN
1570	DO i = nxl, nxr
1571	DO k = nzb, nzt + 1
1572	!
1573	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1574	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1575	fu_xz(k,i) = fuo_xz(k,i)
1576	ELSE
1577	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1578	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1579	ENDIF
1580
1581	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1582	fv_xz(k,i) = fvo_xz(k,i)
1583	ELSE
1584	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1585	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1586	ENDIF
1587
1588	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1589	fw_xz(k,i) = fwo_xz(k,i)
1590	ELSE
1591	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1592	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1593	ENDIF
1594	ENDDO
1595	ENDDO
1596
1597
1598	dist_xz(nzb,:,1) = 0.0_wp
1599	dist_xz(nzb,:,2) = 0.0_wp
1600	dist_xz(nzb,:,3) = 0.0_wp
1601
1602	IF ( myidy == id_stg_south ) j = nys
1603	IF ( myidy == id_stg_north ) j = nyn+1
1604	DO i = nxl, nxr
1605	DO k = nzb+1, nzt + 1
1606	!
1607	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1608	!-- Additional factors are added to improve the variance of v and w
1609	!experimental test of 1.2
1610	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1611	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1612	ENDDO
1613	ENDDO
1614
1615	IF ( myidy == id_stg_south ) j = nys-1
1616	IF ( myidy == id_stg_north ) j = nyn+1
1617	DO i = nxl, nxr
1618	DO k = nzb+1, nzt + 1
1619	!
1620	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1621	!-- Additional factors are added to improve the variance of v and w
1622	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1623	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1624
1625	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1626	a33(k) * fw_xz(k,i) ) * &
1627	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1628	ENDDO
1629	ENDDO
1630	ENDIF
1631
1632	!
1633	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1634	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1635	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1636	!-- else the boundary values won't be accessed.
1637	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1638	mc_factor_l = 0.0_wp
1639	mc_factor = 0.0_wp
1640
1641	IF ( myidy == id_stg_south ) j = nys
1642	IF ( myidy == id_stg_north ) j = nyn+1
1643
1644	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1645	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1646
1647	IF ( myidy == id_stg_south ) j = nys-1
1648	IF ( myidy == id_stg_north ) j = nyn+1
1649
1650	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1651	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1652	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1653	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1654
1655	#if defined( __parallel )
1656	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1657	#else
1658	mc_factor = mc_factor_l
1659	#endif
1660
1661	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1662
1663	IF ( myidy == id_stg_south ) j = nys
1664	IF ( myidy == id_stg_north ) j = nyn+1
1665
1666	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1667	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1668
1669
1670	IF ( myidy == id_stg_south ) j = nys-1
1671	IF ( myidy == id_stg_north ) j = nyn+1
1672
1673	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1674	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1675
1676	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1677	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1678	!
1679	!-- Add disturbances
1680	IF ( myidy == id_stg_south ) THEN
1681	DO i = nxl, nxr
1682	DO k = nzb+1, nzt
1683	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1684	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1685	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1686	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1687	v(k,-1,i) = v(k,0,i)
1688	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1689	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1690	ENDDO
1691	ENDDO
1692	ENDIF
1693	IF ( myidy == id_stg_north ) THEN
1694
1695	DO i = nxl, nxr
1696	DO k = nzb+1, nzt
1697	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1698	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1699	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1700	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1701	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1702	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1703	ENDDO
1704	ENDDO
1705	ENDIF
1706	ENDIF
1707	ENDIF
1708	!
1709	!-- Exchange ghost points.
1710	CALL exchange_horiz( u, nbgp )
1711	CALL exchange_horiz( v, nbgp )
1712	CALL exchange_horiz( w, nbgp )
1713	!
1714	!-- Finally, set time counter for calling STG to zero
1715	IF ( stg_call ) time_stg_call = 0.0_wp
1716	!
1717	!-- Set adjustment step to False to indicate that time correlation can be
1718	!-- switched-on again.
1719	adjustment_step = .FALSE.
1720
1721	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1722
1723	END SUBROUTINE stg_main
1724
1725	!--------------------------------------------------------------------------------------------------!
1726	! Description:
1727	! ------------
1728	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1729	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1730	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1731	!> array.
1732	!--------------------------------------------------------------------------------------------------!
1733	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1734
1735	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1736	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1737	INTEGER(iwp) :: j !< loop index in y-direction
1738	INTEGER(iwp) :: jj !< loop index in y-direction
1739	INTEGER(iwp) :: k !< loop index in z-direction
1740	INTEGER(iwp) :: kk !< loop index in z-direction
1741	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1742
1743	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1744	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1745
1746	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1747	REAL(wp) :: rand_av !< average of random number
1748	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1749
1750	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1751	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1752
1753	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1754	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1755
1756	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1757	!
1758	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1759	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1760	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1761	!-- and normalization of random numbers is done locally, while the result is later distributed to
1762	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1763	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1764	!-- correlation matrix.
1765	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1766	rand_it = 0.0_wp
1767
1768	rand_av = 0.0_wp
1769	rand_sigma_inv = 0.0_wp
1770	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1771	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1772	!
1773	!-- Compute and normalize random numbers.
1774	DO j = nys - mergp_y, nyn + mergp_y
1775	!
1776	!-- Put the random seeds at grid point j
1777	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1778	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1779	CALL random_number_parallel( random_dummy )
1780	rand_it(k,j) = random_dummy
1781	ENDDO
1782	!
1783	!-- Get the new random seeds from last call at grid point j
1784	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1785	ENDDO
1786	!
1787	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1788	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1789	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1790	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1791	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1792	rand_av = rand_av + rand_it(k,j)
1793	ENDDO
1794	ENDDO
1795
1796	#if defined( __parallel )
1797	!
1798	!-- Sum-up the local averages of the random numbers
1799	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1800	#endif
1801	rand_av = rand_av * nyz_inv
1802	!
1803	!-- Obtain zero mean
1804	rand_it= rand_it - rand_av
1805	!
1806	!-- Now, compute the variance
1807	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1808	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1809	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1810	ENDDO
1811	ENDDO
1812
1813	#if defined( __parallel )
1814	!
1815	!-- Sum-up the local quadratic averages of the random numbers
1816	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1817	#endif
1818	!
1819	!-- Compute standard deviation
1820	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1821	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1822	ELSE
1823	rand_sigma_inv = 1.0_wp
1824	ENDIF
1825	!
1826	!-- Normalize with standard deviation to obtain unit variance
1827	rand_it = rand_it * rand_sigma_inv
1828
1829	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1830	!
1831	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1832	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1833	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1834	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1835	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1836	!-- communication. In the second option, which performs better when the turbulent length scales
1837	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1838	!-- communication is necessary.
1839	IF ( compute_velocity_seeds_local ) THEN
1840
1841	f_n = 0.0_wp
1842	DO j = nys, nyn
1843	DO k = nzb, nzt+1
1844	DO jj = -n_y(k), n_y(k)
1845	DO kk = -n_z(k), n_z(k)
1846	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1847	ENDDO
1848	ENDDO
1849	ENDDO
1850	ENDDO
1851
1852	ELSE
1853
1854	f_n_l = 0.0_wp
1855	DO j = nys, nyn
1856	DO k = nzb_x_stg, nzt_x_stg+1
1857	DO jj = -n_y(k), n_y(k)
1858	DO kk = -n_z(k), n_z(k)
1859	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1860	ENDDO
1861	ENDDO
1862	ENDDO
1863	ENDDO
1864	!
1865	!-- Gather velocity seeds of full subdomain
1866	send_count = nzt_x_stg - nzb_x_stg + 1
1867	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1868
1869	#if defined( __parallel )
1870	!
1871	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1872	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1873	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1874	!
1875	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1876	!-- nesting for example).
1877	IF ( PRESENT( id_right ) ) THEN
1878	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1879	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1880	ENDIF
1881	#else
1882	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1883	!
1884	!-- Next line required to avoid compile errors because of unused dummy arguments
1885	IF ( id_left == 0 ) id_right = 0
1886	#endif
1887
1888	ENDIF
1889
1890	DEALLOCATE( rand_it )
1891
1892	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1893
1894	END SUBROUTINE stg_generate_seed_yz
1895
1896
1897	!--------------------------------------------------------------------------------------------------!
1898	! Description:
1899	! ------------
1900	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1901	!> f_n.
1902	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1903	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1904	!> full array.
1905	!--------------------------------------------------------------------------------------------------!
1906	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1907
1908	INTEGER(iwp) :: i !< loop index in x-direction
1909	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1910	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1911	INTEGER(iwp) :: ii !< loop index in x-direction
1912	INTEGER(iwp) :: k !< loop index in z-direction
1913	INTEGER(iwp) :: kk !< loop index in z-direction
1914	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1915
1916	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1917	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1918
1919	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1920	REAL(wp) :: rand_av !< average of random number
1921	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1922
1923	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1924	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1925
1926	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1927	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1928
1929	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1930
1931	!
1932	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1933	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1934	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1935	!-- and normalization of random numbers is done locally, while the result is later distributed to
1936	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1937	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1938	!-- correlation matrix.
1939	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1940	rand_it = 0.0_wp
1941
1942	rand_av = 0.0_wp
1943	rand_sigma_inv = 0.0_wp
1944	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1945	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1946	!
1947	!-- Compute and normalize random numbers.
1948	DO i = nxl - mergp_x, nxr + mergp_x
1949	!
1950	!-- Put the random seeds at grid point ii
1951	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1952	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1953	CALL random_number_parallel( random_dummy )
1954	rand_it(k,i) = random_dummy
1955	ENDDO
1956	!
1957	!-- Get the new random seeds from last call at grid point ii
1958	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1959	ENDDO
1960	!
1961	!-- For normalization to zero mean, sum-up the global random numers.
1962	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1963	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1964	!-- also occur on the inner subdomains.
1965	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1966	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1967	rand_av = rand_av + rand_it(k,i)
1968	ENDDO
1969	ENDDO
1970
1971	#if defined( __parallel )
1972	!
1973	!-- Sum-up the local averages of the random numbers
1974	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1975	#endif
1976	rand_av = rand_av * nxz_inv
1977	!
1978	!-- Obtain zero mean
1979	rand_it= rand_it - rand_av
1980	!
1981	!-- Now, compute the variance
1982	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1983	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1984	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1985	ENDDO
1986	ENDDO
1987
1988	#if defined( __parallel )
1989	!
1990	!-- Sum-up the local quadratic averages of the random numbers
1991	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1992	#endif
1993	!
1994	!-- Compute standard deviation
1995	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1996	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1997	ELSE
1998	rand_sigma_inv = 1.0_wp
1999	ENDIF
2000	!
2001	!-- Normalize with standard deviation to obtain unit variance
2002	rand_it = rand_it * rand_sigma_inv
2003
2004	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2005	!
2006	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2007	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2008	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2009	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2010	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2011	!-- In the second option, which performs better when the turbulent length scales are parametrized
2012	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2013	IF ( compute_velocity_seeds_local ) THEN
2014
2015	f_n = 0.0_wp
2016	DO i = nxl, nxr
2017	DO k = nzb, nzt+1
2018	DO ii = -n_x(k), n_x(k)
2019	DO kk = -n_z(k), n_z(k)
2020	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2021	ENDDO
2022	ENDDO
2023	ENDDO
2024	ENDDO
2025
2026	ELSE
2027
2028	f_n_l = 0.0_wp
2029	DO i = nxl, nxr
2030	DO k = nzb_y_stg, nzt_y_stg+1
2031	DO ii = -n_x(k), n_x(k)
2032	DO kk = -n_z(k), n_z(k)
2033	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2034	ENDDO
2035	ENDDO
2036	ENDDO
2037	ENDDO
2038	!
2039	!-- Gather velocity seeds of full subdomain
2040	send_count = nzt_y_stg - nzb_y_stg + 1
2041	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2042
2043	#if defined( __parallel )
2044	!
2045	!-- Gather the processed velocity seed on south boundary mpi ranks.
2046	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2047	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2048	!
2049	!-- Gather the processed velocity seed on north boundary mpi ranks.
2050	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2051	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2052	#else
2053	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2054	!
2055	!-- Next line required to avoid compile errors because of unused dummy arguments
2056	IF ( id_north == 0 ) id_south = 0
2057	#endif
2058
2059	ENDIF
2060
2061	DEALLOCATE( rand_it )
2062
2063	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2064
2065	END SUBROUTINE stg_generate_seed_xz
2066
2067	!--------------------------------------------------------------------------------------------------!
2068	! Description:
2069	! ------------
2070	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2071	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2072	!> which is applied in state-of-the-art dispserion modelling.
2073	!--------------------------------------------------------------------------------------------------!
2074	SUBROUTINE parametrize_turbulence
2075
2076	INTEGER(iwp) :: k !< loop index in z-direction
2077
2078	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2079	REAL(wp) :: d_zi !< inverse boundary-layer depth
2080	REAL(wp) :: length_scale_lon !< length scale in flow direction
2081	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2082	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2083	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2084	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2085	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2086	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2087	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2088	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2089	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2090	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2091	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2092	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2093	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2094	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2095	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2096	REAL(wp) :: zzi !< ratio of z/zi
2097
2098	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2099	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2100	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2101
2102	!
2103	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2104	!-- criterion according to Heinze et al. (2017).
2105	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2106	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2107	k_zi = MIN( k_zi, nzt )
2108	!
2109	!-- Calculate angle between flow direction and x-axis.
2110	DO k = nzb+1, nzt + 1
2111	IF ( u_init(k) /= 0.0_wp ) THEN
2112	phi(k) = ATAN( v_init(k) / u_init(k) )
2113	ELSE
2114	phi(k) = 0.5 * pi
2115	ENDIF
2116	!
2117	!-- Pre-calculate sine and cosine.
2118	cos_phi(k) = COS( phi(k) )
2119	sin_phi(k) = SIN( phi(k) )
2120	ENDDO
2121	!
2122	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2123	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2124	!-- coincide with the grid axis. Hence, components are rotated after computation.
2125	d_zi = 1.0_wp / zi_ribulk
2126	DO k = nzb+1, k_zi
2127
2128	corr_term_uh = MERGE( 0.35_wp * ABS( &
2129	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2130	)**( 2.0_wp / 3.0_wp ), &
2131	0.0_wp, &
2132	scale_l < 0.0_wp )
2133	!
2134	!-- Determine normalized height coordinate
2135	zzi = zu(k) * d_zi
2136	!
2137	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2138	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2139	!-- variances cannot become negative, take the absolute values.
2140	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2141	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2142
2143	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2144	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2145	!
2146	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as
2147	!-- for u'w'.
2148	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
2149	!
2150	!-- w'w'
2151	r33(k) = scale_wm*2 ( &
2152	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2153	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2154	)
2155	!
2156	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2157	!-- these are projected along the x- and y-direction. Note, it is assumed that
2158	!-- the flux within the boundary points opposite to the vertical gradient.
2159	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2160	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2161
2162	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2163	- ( u_init(k+1) - u_init(k-1) ) )
2164	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2165	- ( v_init(k+1) - v_init(k-1) ) )
2166	!
2167	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2168	!-- limited to the adjustment time scales.
2169	tu(k) = MIN( dt_stg_adjust, &
2170	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2171
2172	tv(k) = tu(k)
2173	tw(k) = tu(k)
2174
2175	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2176	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2177	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2178	!
2179	!-- Assume isotropic turbulence length scales
2180	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2181	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2182	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2183	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2184	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2185	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2186	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2187	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2188	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2189
2190	ENDDO
2191	!
2192	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2193	!-- reduced to zero by a blending function.
2194	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2195	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2196	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2197
2198	time_scale_zi = tu(k_zi)
2199	r11_zi = r11(k_zi)
2200	r22_zi = r22(k_zi)
2201	r33_zi = r33(k_zi)
2202	r31_zi = r31(k_zi)
2203	r32_zi = r32(k_zi)
2204
2205	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2206
2207	DO k = k_zi+1, nzt+1
2208	!
2209	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2210	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2211	!
2212	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2213	!-- the mergpe-function can crash if scale_l is zero.
2214	r11(k) = r11_zi * blend
2215	r22(k) = r22_zi * blend
2216	r33(k) = r33_zi * blend
2217	r31(k) = r31_zi * blend
2218	r32(k) = r32_zi * blend
2219	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
2220
2221	!
2222	!-- Compute turbulent time scales according to Brost et al. (1982).
2223	!-- Note, time scales are limited to the adjustment time scales.
2224	tu(k) = time_scale_zi * blend
2225	tv(k) = time_scale_zi * blend
2226	tw(k) = time_scale_zi * blend
2227
2228	length_scale_lon = length_scale_lon_zi * blend
2229	length_scale_lat = length_scale_lat_zi * blend
2230	length_scale_vert = length_scale_vert_zi * blend
2231	!
2232	!-- Assume isotropic turbulence length scales
2233	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2234	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2235	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2236	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2237	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2238	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2239	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2240	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2241	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2242	ENDDO
2243	!
2244	!-- Set bottom boundary condition for reynolds stresses
2245	r11(nzb) = r11(nzb+1)
2246	r22(nzb) = r22(nzb+1)
2247	r33(nzb) = r33(nzb+1)
2248
2249	r21(nzb) = r11(nzb+1)
2250	r31(nzb) = r31(nzb+1)
2251	r32(nzb) = r32(nzb+1)
2252
2253	!
2254	!-- Set bottom boundary condition for the length and time scales
2255	nux(nzb) = nux(nzb+1)
2256	nuy(nzb) = nuy(nzb+1)
2257	nuz(nzb) = nuz(nzb+1)
2258	nvx(nzb) = nvx(nzb+1)
2259	nvy(nzb) = nvy(nzb+1)
2260	nvz(nzb) = nvz(nzb+1)
2261	nwx(nzb) = nwx(nzb+1)
2262	nwy(nzb) = nwy(nzb+1)
2263	nwz(nzb) = nwz(nzb+1)
2264
2265	tu(nzb) = tu(nzb+1)
2266	tv(nzb) = tv(nzb+1)
2267	tw(nzb) = tw(nzb+1)
2268
2269	adjustment_step = .TRUE.
2270
2271	END SUBROUTINE parametrize_turbulence
2272
2273	!--------------------------------------------------------------------------------------------------!
2274	! Description:
2275	! ------------
2276	!> Calculate the coefficient matrix from the Lund rotation.
2277	!--------------------------------------------------------------------------------------------------!
2278	SUBROUTINE calc_coeff_matrix
2279
2280	INTEGER(iwp) :: k !< loop index in z-direction
2281
2282	!
2283	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2284	DO k = nzb+1, nzt+1
2285	IF ( r11(k) > 10E-6_wp ) THEN
2286	a11(k) = SQRT( r11(k) )
2287	a21(k) = r21(k) / a11(k)
2288	a31(k) = r31(k) / a11(k)
2289	ELSE
2290	a11(k) = 10E-8_wp
2291	a21(k) = 10E-8_wp
2292	a31(k) = 10E-8_wp
2293	ENDIF
2294	ENDDO
2295	DO k = nzb+1, nzt+1
2296	a22(k) = r22(k) - a21(k)**2
2297	IF ( a22(k) > 10E-6_wp ) THEN
2298	a22(k) = SQRT( a22(k) )
2299	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2300	ELSE
2301	a22(k) = 10E-8_wp
2302	a32(k) = 10E-8_wp
2303	ENDIF
2304	ENDDO
2305	DO k = nzb+1, nzt+1
2306	a33(k) = r33(k) - a31(k)2 - a32(k)2
2307	IF ( a33(k) > 10E-6_wp ) THEN
2308	a33(k) = SQRT( a33(k) )
2309	ELSE
2310	a33(k) = 10E-8_wp
2311	ENDIF
2312	ENDDO
2313	!
2314	!-- Set bottom boundary condition
2315	a11(nzb) = a11(nzb+1)
2316	a22(nzb) = a22(nzb+1)
2317	a21(nzb) = a21(nzb+1)
2318	a33(nzb) = a33(nzb+1)
2319	a31(nzb) = a31(nzb+1)
2320	a32(nzb) = a32(nzb+1)
2321
2322	END SUBROUTINE calc_coeff_matrix
2323
2324	!--------------------------------------------------------------------------------------------------!
2325	! Description:
2326	! ------------
2327	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2328	!> turbulence at the lateral boundaries.
2329	!--------------------------------------------------------------------------------------------------!
2330	SUBROUTINE stg_adjust
2331
2332	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2333	!
2334	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2335	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2336	!-- nevertheless, the boundary-layer depth need to determined first.
2337	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2338	CALL nesting_offl_calc_zi
2339	!
2340	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2341	CALL calc_scaling_variables
2342	!
2343	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2344	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2345	!-- velocity and velocity scale.
2346	CALL parametrize_turbulence
2347	!
2348	!-- Calculate coefficient matrix from Reynolds stress tensor
2349	!-- (Lund rotation)
2350	CALL calc_coeff_matrix
2351	!
2352	!-- Setup filter functions according to updated length scales.
2353	CALL stg_setup_filter_function
2354	!
2355	!-- Reset time counter for controlling next adjustment to zero
2356	time_stg_adjust = 0.0_wp
2357
2358	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2359
2360	END SUBROUTINE stg_adjust
2361
2362
2363	!--------------------------------------------------------------------------------------------------!
2364	! Description:
2365	! ------------
2366	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2367	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2368	!> scale, and Obukhov length.
2369	!--------------------------------------------------------------------------------------------------!
2370	SUBROUTINE calc_scaling_variables
2371
2372	INTEGER(iwp) :: i !< loop index in x-direction
2373	INTEGER(iwp) :: j !< loop index in y-direction
2374	INTEGER(iwp) :: k !< loop index in z-direction
2375	INTEGER(iwp) :: m !< surface element index
2376
2377	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2378	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2379	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2380	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2381	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2382	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2383	REAL(wp) :: w_convective !< convective velocity scale
2384
2385	!
2386	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2387	!-- model domain.
2388	pt_surf_mean_l = 0.0_wp
2389	shf_mean_l = 0.0_wp
2390	scale_l_l = 0.0_wp
2391	friction_vel_l = 0.0_wp
2392	DO m = 1, surf_def_h(0)%ns
2393	i = surf_def_h(0)%i(m)
2394	j = surf_def_h(0)%j(m)
2395	k = surf_def_h(0)%k(m)
2396	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2397	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2398	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2399	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2400	ENDDO
2401	DO m = 1, surf_lsm_h%ns
2402	i = surf_lsm_h%i(m)
2403	j = surf_lsm_h%j(m)
2404	k = surf_lsm_h%k(m)
2405	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2406	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2407	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2408	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2409	ENDDO
2410	DO m = 1, surf_usm_h%ns
2411	i = surf_usm_h%i(m)
2412	j = surf_usm_h%j(m)
2413	k = surf_usm_h%k(m)
2414	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2415	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2416	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2417	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2418	ENDDO
2419
2420	#if defined( __parallel )
2421	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2422	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2423	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2424	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2425	#else
2426	scale_us = friction_vel_l
2427	shf_mean = shf_mean_l
2428	scale_l = scale_l_l
2429	pt_surf_mean = pt_surf_mean_l
2430	#endif
2431
2432	scale_us = scale_us * d_nxy
2433	shf_mean = shf_mean * d_nxy
2434	scale_l = scale_l * d_nxy
2435	pt_surf_mean = pt_surf_mean * d_nxy
2436	!
2437	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2438	!-- convective velocity scale to zero.
2439	IF ( shf_mean > 0.0_wp ) THEN
2440	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2441	ELSE
2442	w_convective = 0.0_wp
2443	ENDIF
2444	!
2445	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2446	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2447	!-- value of friction velocity for the reynolds-stress parametrization.
2448	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2449	!
2450	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2451	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2452	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2453
2454	END SUBROUTINE calc_scaling_variables
2455
2456	END MODULE synthetic_turbulence_generator_mod

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