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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4663

Last change on this file since 4663 was 4647, checked in by suehring, 4 years ago
Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local. By default, the random-seed computation is now distributed among several cores. Especially for large length scales this is significantly faster.
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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 4647 2020-08-24 16:36:18Z gronemeier $
27	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
28	! By default, the random-seed computation is now distributed among several cores. Especially for
29	! large length scales this is significantly faster.
30	!
31	! 4640 2020-08-11 16:28:32Z suehring
32	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
33	! Obukhov length (term is not valid for near neutral conditions)
34	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
35	! the vertical transport of horizontal momentum
36	!
37	! 4629 2020-07-29 09:37:56Z raasch
38	! support for MPI Fortran77 interface (mpif.h) removed
39	!
40	! 4603 2020-07-14 16:08:30Z suehring
41	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
42	! initialized properly
43	!
44	! 4566 2020-06-16 10:11:51Z suehring
45	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
46	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
47	! - change default value of time interval to adjust turbulence parametrization
48	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
49	!
50	! 4562 2020-06-12 08:38:47Z raasch
51	! Parts of r4559 re-formatted
52	!
53	! 4559 2020-06-11 08:51:48Z raasch
54	! File re-formatted to follow the PALM coding standard
55	!
56	! 4535 2020-05-15 12:07:23Z raasch
57	! Bugfix for restart data format query
58	!
59	! 4495 2020-04-13 20:11:20Z raasch
60	! Restart data handling with MPI-IO added
61	!
62	! 4481 2020-03-31 18:55:54Z maronga
63	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
64	!
65	! 4442 2020-03-04 19:21:13Z suehring
66	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
67	! (was accidantly changed).
68	!
69	! 4441 2020-03-04 19:20:35Z suehring
70	! Correct misplaced preprocessor directive
71	!
72	! 4438 2020-03-03 20:49:28Z suehring
73	! Performance optimizations in velocity-seed calculation:
74	! - Random number array is only defined and computed locally (except for normalization to zero mean
75	! and unit variance)
76	! - Parallel random number generator is applied independent on the 2D random numbers in other
77	! routines
78	! - Option to decide wheter velocity seeds are computed locally without any further communication
79	! or are computed by all processes along the communicator
80	!
81	! 4346 2019-12-18 11:55:56Z motisi
82	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
83	! information used in wall_flags_static_0
84	!
85	! 4335 2019-12-12 16:39:05Z suehring
86	! Commentation of last commit
87	!
88	! 4332 2019-12-10 19:44:12Z suehring
89	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
90	! Further, minor bugfix in initial velocity seed calculation.
91	!
92	! 4329 2019-12-10 15:46:36Z motisi
93	! Renamed wall_flags_0 to wall_flags_static_0
94	!
95	! 4309 2019-11-26 18:49:59Z suehring
96	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
97	! the parallel random number generator. Random numbers are now only computed and normalized locally,
98	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
99	! array.
100	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
101	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
102	!
103	! 4182 2019-08-22 15:20:23Z scharf
104	! Corrected "Former revisions" section
105	!
106	! 4148 2019-08-08 11:26:00Z suehring
107	! Remove unused variable
108	!
109	! 4144 2019-08-06 09:11:47Z raasch
110	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
111	!
112	! 4071 2019-07-03 20:02:00Z suehring
113	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
114	! file.
115	!
116	! 4022 2019-06-12 11:52:39Z suehring
117	! Several bugfixes and improvements
118	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
119	! instabilities in case the mean volume flow is close to zero)
120	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
121	! numerically unstable
122	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
123	! case dt_stg_call /= dt_3d
124	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
125	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
126	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
127	!
128	! 3987 2019-05-22 09:52:13Z kanani
129	! Introduce alternative switch for debug output during timestepping
130	!
131	! 3938 2019-04-29 16:06:25Z suehring
132	! Remove unused variables
133	!
134	! 3937 2019-04-29 15:09:07Z suehring
135	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
136	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
137	! synthetic turbulence parametrization.
138	!
139	! 3909 2019-04-17 09:13:25Z suehring
140	! Minor bugfix for last commit
141	!
142	! 3900 2019-04-16 15:17:43Z suehring
143	! Missing re-calculation of perturbation seeds in case of restarts
144	!
145	! 3891 2019-04-12 17:52:01Z suehring
146	! Bugfix in initialization in case of restart runs.
147	!
148	! 3885 2019-04-11 11:29:34Z kanani
149	! Changes related to global restructuring of location messages and introduction of additional debug
150	! messages
151	!
152	!
153	! Removed unused variables
154	!
155	! 3719 2019-02-06 13:10:18Z kanani
156	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
157	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
158	! for better overview.
159	!
160	! 2259 2017-06-08 09:09:11Z gronemeier
161	! Initial revision
162	!
163	! Authors:
164	! --------
165	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
166	!
167	!
168	! Description:
169	! ------------
170	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
171	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
172	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
173	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
174	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
175	!> parametrized within the boundary layer.
176	!>
177	!> @todo Enable cyclic_fill
178	!> Implement turbulence generation for e and pt
179	!> @note <Enter notes on the module>
180	!> @bug Height information from input file is not used. Profiles from input must match with current
181	!> PALM grid.
182	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
183	!--------------------------------------------------------------------------------------------------!
184	MODULE synthetic_turbulence_generator_mod
185
186
187	USE arrays_3d, &
188	ONLY: dzw, &
189	ddzw, &
190	drho_air, &
191	mean_inflow_profiles, &
192	pt, &
193	pt_init, &
194	q, &
195	q_init, &
196	u, &
197	u_init, &
198	v, &
199	v_init, &
200	w, &
201	zu, &
202	zw
203
204	USE basic_constants_and_equations_mod, &
205	ONLY: g, &
206	kappa, &
207	pi
208
209	USE control_parameters, &
210	ONLY: bc_lr, &
211	bc_ns, &
212	child_domain, &
213	coupling_char, &
214	debug_output_timestep, &
215	dt_3d, &
216	e_init, &
217	humidity, &
218	initializing_actions, &
219	intermediate_timestep_count, &
220	intermediate_timestep_count_max, &
221	length, &
222	message_string, &
223	nesting_offline, &
224	neutral, &
225	num_mean_inflow_profiles, &
226	random_generator, &
227	rans_mode, &
228	restart_data_format_output, &
229	restart_string, &
230	syn_turb_gen, &
231	time_since_reference_point, &
232	turbulent_inflow
233
234	USE cpulog, &
235	ONLY: cpu_log, &
236	log_point_s
237
238	USE grid_variables, &
239	ONLY: ddx, &
240	ddy, &
241	dx, &
242	dy
243
244	USE indices, &
245	ONLY: nbgp, &
246	nz, &
247	nzb, &
248	nzt, &
249	nx, &
250	nxl, &
251	nxlu, &
252	nxr, &
253	ny, &
254	nys, &
255	nysv, &
256	nyn, &
257	wall_flags_total_0
258
259	USE kinds
260
261	#if defined( __parallel )
262	USE MPI
263	#endif
264
265	USE nesting_offl_mod, &
266	ONLY: nesting_offl_calc_zi, &
267	zi_ribulk
268
269	USE pegrid, &
270	ONLY: comm1dx, &
271	comm1dy, &
272	comm2d, &
273	ierr, &
274	myidx, &
275	myidy, &
276	pdims
277
278	USE pmc_interface, &
279	ONLY : rans_mode_parent
280
281	USE random_generator_parallel, &
282	ONLY: init_parallel_random_generator, &
283	random_dummy, &
284	random_number_parallel, &
285	random_seed_parallel
286
287	USE restart_data_mpi_io_mod, &
288	ONLY: rrd_mpi_io, &
289	wrd_mpi_io
290
291	USE transpose_indices, &
292	ONLY: nzb_x, &
293	nzt_x
294
295	USE surface_mod, &
296	ONLY: surf_def_h, &
297	surf_lsm_h, &
298	surf_usm_h
299
300	IMPLICIT NONE
301
302	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
303	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
304	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
305	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
306	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
307	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
308	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
309	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
310	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
311	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
312	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
313	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
314	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
315	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
316	#if defined( __parallel )
317	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
318	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
319	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
320	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
321	#endif
322
323	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
324	!< required for bias correction of imposed perturbations
325	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
326	!< required for bias correction of imposed perturbations
327
328	#if defined( __parallel )
329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
330	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
331	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
333	#endif
334	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
335	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
336	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
337	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
338	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
339	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
340	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
341	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
342	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
343
344	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
345	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
346	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
347	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
348
349
350	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
351	!< no time correlation to the timestep before should be considered
352	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
353	!< or if computation is distributed over several processes
354	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
355	!< (.FALSE.) or if it parametrized
356	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
357	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
358
359
360	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
361	!< scales above the boundary layer
362	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
363	!< one length scale above ABL top
364	REAL(wp) :: d_l !< blend_coeff/length_scale
365	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
366	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
367	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
368	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
369	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
370	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
371	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
372	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
373
374	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
375
376
377	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
378	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
379	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
380	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
381	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
382	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
383
384	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
385	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
386	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
387	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
388	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
389	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
390	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
391	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
392	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
393
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
415
416	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
417	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
418
419	!
420	!-- PALM interfaces:
421	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
422	INTERFACE stg_adjust
423	MODULE PROCEDURE stg_adjust
424	END INTERFACE stg_adjust
425	!
426	!-- Input parameter checks to be done in check_parameters
427	INTERFACE stg_check_parameters
428	MODULE PROCEDURE stg_check_parameters
429	END INTERFACE stg_check_parameters
430
431	!
432	!-- Calculate filter functions
433	INTERFACE stg_filter_func
434	MODULE PROCEDURE stg_filter_func
435	END INTERFACE stg_filter_func
436
437	!
438	!-- Generate velocity seeds at south and north domain boundary
439	INTERFACE stg_generate_seed_xz
440	MODULE PROCEDURE stg_generate_seed_xz
441	END INTERFACE stg_generate_seed_xz
442	!
443	!-- Generate velocity seeds at left and/or right domain boundary
444	INTERFACE stg_generate_seed_yz
445	MODULE PROCEDURE stg_generate_seed_yz
446	END INTERFACE stg_generate_seed_yz
447
448	!
449	!-- Output of information to the header file
450	INTERFACE stg_header
451	MODULE PROCEDURE stg_header
452	END INTERFACE stg_header
453
454	!
455	!-- Initialization actions
456	INTERFACE stg_init
457	MODULE PROCEDURE stg_init
458	END INTERFACE stg_init
459
460	!
461	!-- Main procedure of synth. turb. gen.
462	INTERFACE stg_main
463	MODULE PROCEDURE stg_main
464	END INTERFACE stg_main
465
466	!
467	!-- Reading of NAMELIST parameters
468	INTERFACE stg_parin
469	MODULE PROCEDURE stg_parin
470	END INTERFACE stg_parin
471
472	!
473	!-- Reading of parameters for restart runs
474	INTERFACE stg_rrd_global
475	MODULE PROCEDURE stg_rrd_global_ftn
476	MODULE PROCEDURE stg_rrd_global_mpi
477	END INTERFACE stg_rrd_global
478
479	!
480	!-- Writing of binary output for restart runs
481	INTERFACE stg_wrd_global
482	MODULE PROCEDURE stg_wrd_global
483	END INTERFACE stg_wrd_global
484
485	SAVE
486
487	PRIVATE
488
489	!
490	!-- Public interfaces
491	PUBLIC stg_adjust, &
492	stg_check_parameters, &
493	stg_header, &
494	stg_init, &
495	stg_main, &
496	stg_parin, &
497	stg_rrd_global, &
498	stg_wrd_global
499
500	!
501	!-- Public variables
502	PUBLIC dt_stg_call, &
503	dt_stg_adjust, &
504	id_stg_left, &
505	id_stg_north, &
506	id_stg_right, &
507	id_stg_south, &
508	parametrize_inflow_turbulence, &
509	time_stg_adjust, &
510	time_stg_call, &
511	use_syn_turb_gen
512
513
514	CONTAINS
515
516
517	!--------------------------------------------------------------------------------------------------!
518	! Description:
519	! ------------
520	!> Check parameters routine for synthetic turbulence generator
521	!--------------------------------------------------------------------------------------------------!
522	SUBROUTINE stg_check_parameters
523
524	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
525	nesting_offline ) THEN
526	message_string = 'Synthetic turbulence generator is required ' // &
527	'if offline nesting is applied and PALM operates in LES mode.'
528	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
529	ENDIF
530
531	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
532	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
533	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
534	'and parent operates in RANS-mode but current child in LES mode.'
535	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
536	ENDIF
537
538	IF ( use_syn_turb_gen ) THEN
539
540	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
541	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
542	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
543
544	ENDIF
545
546	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
547	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
548	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
549
550	ENDIF
551
552	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
553
554	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
555	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
556	message_string = 'Using synthetic turbulence generator requires ' // &
557	'%initializing_actions = "set_constant_profiles" or ' // &
558	' "read_restart_data", if not offline nesting is applied.'
559	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
560	ENDIF
561
562	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
563	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
564	' "dirichlet/radiation", if not offline nesting is applied.'
565	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
566	ENDIF
567	IF ( bc_ns /= 'cyclic' ) THEN
568	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
569	' "cyclic", if not offline nesting is applied.'
570	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
571	ENDIF
572
573	ENDIF
574
575	IF ( turbulent_inflow ) THEN
576	message_string = 'Using synthetic turbulence generator in combination ' // &
577	'&with turbulent_inflow = .T. is not allowed'
578	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
579	ENDIF
580	!
581	!-- Synthetic turbulence generator requires the parallel random generator
582	IF ( random_generator /= 'random-parallel' ) THEN
583	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
584	'random-parallel.'
585	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
586	ENDIF
587
588	ENDIF
589
590	END SUBROUTINE stg_check_parameters
591
592
593	!--------------------------------------------------------------------------------------------------!
594	! Description:
595	! ------------
596	!> Header output for synthetic turbulence generator
597	!--------------------------------------------------------------------------------------------------!
598	SUBROUTINE stg_header ( io )
599
600	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
601
602	!
603	!-- Write synthetic turbulence generator Header
604	WRITE( io, 1 )
605	IF ( use_syn_turb_gen ) THEN
606	WRITE( io, 2 )
607	ELSE
608	WRITE( io, 3 )
609	ENDIF
610
611	IF ( parametrize_inflow_turbulence ) THEN
612	WRITE( io, 4 ) dt_stg_adjust
613	ELSE
614	WRITE( io, 5 )
615	ENDIF
616
617	1 FORMAT (//' Synthetic turbulence generator information:'/ &
618	' ------------------------------------------'/)
619	2 FORMAT (' synthetic turbulence generator is switched on')
620	3 FORMAT (' synthetic turbulence generator is switched off')
621	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
622	5 FORMAT (' imposed turbulence is read from file' )
623
624	END SUBROUTINE stg_header
625
626
627	!--------------------------------------------------------------------------------------------------!
628	! Description:
629	! ------------
630	!> Initialization of the synthetic turbulence generator
631	!--------------------------------------------------------------------------------------------------!
632	SUBROUTINE stg_init
633
634	#if defined( __parallel )
635	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
636	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
637	#endif
638
639	INTEGER(iwp) :: i !> grid index in x-direction
640	INTEGER(iwp) :: j !> loop index
641	INTEGER(iwp) :: k !< index
642	#if defined( __parallel )
643	INTEGER(iwp) :: newtype !< dummy MPI type
644	INTEGER(iwp) :: realsize !< size of REAL variables
645	#endif
646
647	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
648	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
649
650
651	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
652
653	!
654	!-- Dummy variables used for reading profiles
655	REAL(wp) :: d1 !< u profile
656	REAL(wp) :: d2 !< v profile
657	REAL(wp) :: d3 !< w profile
658	REAL(wp) :: d5 !< e profile
659	REAL(wp) :: luy !< length scale for u in y direction
660	REAL(wp) :: luz !< length scale for u in z direction
661	REAL(wp) :: lvy !< length scale for v in y direction
662	REAL(wp) :: lvz !< length scale for v in z direction
663	REAL(wp) :: lwy !< length scale for w in y direction
664	REAL(wp) :: lwz !< length scale for w in z direction
665	#if defined( __parallel )
666	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
667	#endif
668	REAL(wp) :: zz !< height
669
670
671	#if defined( __parallel )
672	CALL MPI_BARRIER( comm2d, ierr )
673	#endif
674	!
675	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
676	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
677	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
678	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
679	!-- communication).
680	IF ( .NOT. compute_velocity_seeds_local ) THEN
681	#if defined( __parallel )
682	!
683	!-- Determine processor decomposition of z-axis along x- and y-direction
684	nnz = nz / pdims(1)
685	nzb_x_stg = 1 + myidx * INT( nnz )
686	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
687
688	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
689	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
690
691	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
692	.AND. .NOT. rans_mode ) ) THEN
693	nnz = nz / pdims(2)
694	nzb_y_stg = 1 + myidy * INT( nnz )
695	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
696
697	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
698	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
699	ENDIF
700
701	!
702	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
703	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
704	extent = 1 * realsize
705	!
706	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
707	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
708	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
709	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
710	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
711	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
712	CALL MPI_TYPE_FREE( newtype, ierr )
713
714	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
715	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
716	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
717	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
718	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
719	CALL MPI_TYPE_FREE( newtype, ierr )
720
721	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
722	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
723
724	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
725	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
726
727	DO j = 1, pdims(1)
728	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
729	ENDDO
730	!
731	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
732	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
733	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
734	.AND. .NOT. rans_mode ) ) THEN
735	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
736	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
737	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
738	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
739	CALL MPI_TYPE_FREE( newtype, ierr )
740
741	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
742	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
743	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
744	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
745	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
746	CALL MPI_TYPE_FREE( newtype, ierr )
747
748	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
749	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
750
751	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
752	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
753
754	DO j = 1, pdims(2)
755	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
756	ENDDO
757
758	ENDIF
759	#endif
760	ENDIF
761	!
762	!-- Allocate required arrays.
763	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
764	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
765	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
766	!-- and initialized appropriately.
767	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
768	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
769	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
770	mean_inflow_profiles = 0.0_wp
771	mean_inflow_profiles(:,1) = u_init
772	mean_inflow_profiles(:,2) = v_init
773	!
774	!-- Even though potential temperature and humidity are not perturbed, they need to be
775	!-- initialized appropriately.
776	IF ( .NOT. neutral ) &
777	mean_inflow_profiles(:,4) = pt_init
778	IF ( humidity ) &
779	mean_inflow_profiles(:,6) = q_init
780	ENDIF
781	ENDIF
782	!
783	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
784	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
785	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
786	u_init = mean_inflow_profiles(:,1)
787	v_init = mean_inflow_profiles(:,2)
788	e_init = MAXVAL( mean_inflow_profiles(:,5) )
789	ENDIF
790
791	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
792	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
793	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
794	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
795	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
796	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
797	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
798	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
799
800	r11 = 0.0_wp
801	r21 = 0.0_wp
802	r22 = 0.0_wp
803	r31 = 0.0_wp
804	r32 = 0.0_wp
805	r33 = 0.0_wp
806	tu = 0.0_wp
807	tv = 0.0_wp
808	tw = 0.0_wp
809
810	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
811	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
812	dist_xz = 0.0_wp
813	dist_yz = 0.0_wp
814	!
815	!-- Read inflow profile
816	!-- Height levels of profiles in input profile is as follows:
817	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
818	!-- WARNING: zz is not used at the moment
819	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
820
821	IF ( file_stg_exist ) THEN
822
823	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
824	!
825	!-- Skip header
826	READ( 90, * )
827
828	DO k = nzb, nzt
829	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
830	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
831
832	!
833	!-- Convert length scales from meter to number of grid points.
834	IF ( k /= nzb ) THEN
835	nuz(k) = INT( luz * ddzw(k) )
836	nvz(k) = INT( lvz * ddzw(k) )
837	nwz(k) = INT( lwz * ddzw(k) )
838	ELSE
839	nuz(k) = INT( luz * ddzw(k+1) )
840	nvz(k) = INT( lvz * ddzw(k+1) )
841	nwz(k) = INT( lwz * ddzw(k+1) )
842	ENDIF
843
844	nuy(k) = INT( luy * ddy )
845	nvy(k) = INT( lvy * ddy )
846	nwy(k) = INT( lwy * ddy )
847	!
848	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
849	!-- y-direction.
850	nwx(k) = nwy(k)
851	nvx(k) = nvy(k)
852	nux(k) = nuy(k)
853	!
854	!-- Save Mean inflow profiles
855	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
856	mean_inflow_profiles(k,1) = d1
857	mean_inflow_profiles(k,2) = d2
858	! mean_inflow_profiles(k,4) = d4
859	mean_inflow_profiles(k,5) = d5
860	ENDIF
861	ENDDO
862	!
863	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
864	!-- simply overwritten.
865	nwx(nzb) = nwy(nzb+1)
866	nvx(nzb) = nvy(nzb+1)
867	nux(nzb) = nuy(nzb+1)
868	nuy(nzb) = nuy(nzb+1)
869	nuz(nzb) = nuz(nzb+1)
870	nvy(nzb) = nvy(nzb+1)
871	nvz(nzb) = nvz(nzb+1)
872	nwy(nzb) = nwy(nzb+1)
873	nwz(nzb) = nwz(nzb+1)
874
875	nwx(nzt+1) = nwy(nzt)
876	nvx(nzt+1) = nvy(nzt)
877	nux(nzt+1) = nuy(nzt)
878	nuy(nzt+1) = nuy(nzt)
879	nuz(nzt+1) = nuz(nzt)
880	nvy(nzt+1) = nvy(nzt)
881	nvz(nzt+1) = nvz(nzt)
882	nwy(nzt+1) = nwy(nzt)
883	nwz(nzt+1) = nwz(nzt)
884
885	CLOSE( 90 )
886	!
887	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
888	CALL calc_coeff_matrix
889	!
890	!-- No information about turbulence and its length scales are available. Instead, parametrize
891	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
892	!-- parametrized, which is done later when energy-balance models are already initialized. This is
893	!-- because the STG needs information about surface properties such as roughness to build
894	!-- 'realistic' turbulence profiles.
895	ELSE
896	!
897	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
898	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
899	!
900	!-- Set flag indicating that turbulence is parametrized
901	parametrize_inflow_turbulence = .TRUE.
902	!
903	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
904	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
905	!-- nevertheless, the boundary-layer depth needs to be determined first.
906	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
907	CALL nesting_offl_calc_zi
908	!
909	!-- Determine boundary-layer depth, which is used to initialize lenght scales
910	CALL calc_scaling_variables
911	!
912	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
913	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
914	!-- friction velocity and velocity scale.
915	CALL parametrize_turbulence
916	!
917	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
918	CALL calc_coeff_matrix
919
920	ENDIF
921	!
922	!-- Initial filter functions
923	CALL stg_setup_filter_function
924	!
925	!-- Allocate velocity seeds for turbulence at xz-layer
926	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
927	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
928	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
929
930	!
931	!-- Allocate velocity seeds for turbulence at yz-layer
932	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
933	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
934	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
935
936	fu_xz = 0.0_wp
937	fuo_xz = 0.0_wp
938	fv_xz = 0.0_wp
939	fvo_xz = 0.0_wp
940	fw_xz = 0.0_wp
941	fwo_xz = 0.0_wp
942
943	fu_yz = 0.0_wp
944	fuo_yz = 0.0_wp
945	fv_yz = 0.0_wp
946	fvo_yz = 0.0_wp
947	fw_yz = 0.0_wp
948	fwo_yz = 0.0_wp
949
950	#if defined( __parallel )
951	CALL MPI_BARRIER( comm2d, ierr )
952	#endif
953
954	!
955	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
956	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
957	!-- This is mostly for k=nzt+1.
958	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
959	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
960
961	IF ( myidx == id_stg_left ) i = -1
962	IF ( myidx == id_stg_right ) i = nxr+1
963
964	DO j = nys, nyn
965	DO k = nzb, nzt+1
966	IF ( a11(k) > 10E-8_wp ) THEN
967	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
968	ELSE
969	fu_yz(k,j) = 10E-8_wp
970	ENDIF
971
972	IF ( a22(k) > 10E-8_wp ) THEN
973	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
974	ELSE
975	fv_yz(k,j) = 10E-8_wp
976	ENDIF
977
978	IF ( a33(k) > 10E-8_wp ) THEN
979	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
980	ELSE
981	fw_yz(k,j) = 10E-8_wp
982	ENDIF
983	ENDDO
984	ENDDO
985	ENDIF
986
987	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
988
989	IF ( myidy == id_stg_south ) j = -1
990	IF ( myidy == id_stg_north ) j = nyn+1
991
992	DO i = nxl, nxr
993	DO k = nzb, nzt+1
994	!
995	!-- In case the correlation coefficients are very small, the velocity seeds may become
996	!-- very large finally creating numerical instabilities in the synthetic turbulence
997	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
998	IF ( a11(k) > 10E-8_wp ) THEN
999	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1000	ELSE
1001	fu_xz(k,i) = 10E-8_wp
1002	ENDIF
1003
1004	IF ( a22(k) > 10E-8_wp ) THEN
1005	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1006	ELSE
1007	fv_xz(k,i) = 10E-8_wp
1008	ENDIF
1009
1010	IF ( a33(k) > 10E-8_wp ) THEN
1011	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1012	ELSE
1013	fw_xz(k,i) = 10E-8_wp
1014	ENDIF
1015
1016	ENDDO
1017	ENDDO
1018	ENDIF
1019	ENDIF
1020	!
1021	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1022	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1023	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1024	!-- different cases must be distinguished.
1025	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1026	!
1027	!-- Number of grid points where perturbations are imposed on u
1028	IF ( myidx == id_stg_left ) i = nxl
1029	IF ( myidx == id_stg_right ) i = nxr+1
1030
1031	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1032	!
1033	!-- Number of grid points where perturbations are imposed on v and w
1034	IF ( myidx == id_stg_left ) i = nxl-1
1035	IF ( myidx == id_stg_right ) i = nxr+1
1036
1037	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1038	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1039
1040	#if defined( __parallel )
1041	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1042	#else
1043	nr_non_topo_yz = nr_non_topo_yz_l
1044	#endif
1045	ENDIF
1046
1047	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1048	!
1049	!-- Number of grid points where perturbations are imposed on v
1050	IF ( myidy == id_stg_south ) j = nys
1051	IF ( myidy == id_stg_north ) j = nyn+1
1052
1053	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1054	!
1055	!-- Number of grid points where perturbations are imposed on u and w
1056	IF ( myidy == id_stg_south ) j = nys-1
1057	IF ( myidy == id_stg_north ) j = nyn+1
1058
1059	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1060	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1061
1062	#if defined( __parallel )
1063	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1064	#else
1065	nr_non_topo_xz = nr_non_topo_xz_l
1066	#endif
1067	ENDIF
1068	!
1069	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1070	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1071	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1072	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1073	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1074	id_rand_yz = 0
1075	seq_rand_yz = 0
1076
1077	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1078
1079	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1080	.AND. .NOT. rans_mode ) ) THEN
1081	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1082	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1083	id_rand_xz = 0
1084	seq_rand_xz = 0
1085
1086	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1087	ENDIF
1088
1089	END SUBROUTINE stg_init
1090
1091
1092	!--------------------------------------------------------------------------------------------------!
1093	! Description:
1094	! ------------
1095	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1096	!--------------------------------------------------------------------------------------------------!
1097	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1098
1099	INTEGER(iwp) :: k !< loop index
1100	INTEGER(iwp) :: mergp !< passed length scale in grid points
1101	INTEGER(iwp) :: n_k !< length scale nXX in height k
1102	INTEGER(iwp) :: nf !< index for length scales
1103
1104	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1105
1106	REAL(wp) :: bdenom !< denominator for filter functions bXX
1107	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1108
1109	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1110
1111
1112	bxx = 0.0_wp
1113
1114	DO k = nzb, nzt+1
1115	bdenom = 0.0_wp
1116	n_k = nxx(k)
1117	IF ( n_k /= 0 ) THEN
1118
1119	!
1120	!-- ( Eq.10 )^2
1121	DO nf = -n_k, n_k
1122	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1123	ENDDO
1124
1125	!
1126	!-- ( Eq.9 )
1127	bdenom = SQRT( bdenom )
1128	DO nf = -n_k, n_k
1129	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1130	ENDDO
1131	ENDIF
1132	ENDDO
1133
1134	END SUBROUTINE stg_filter_func
1135
1136
1137	!------------------------------------------------------------------------------!
1138	! Description:
1139	! ------------
1140	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1141	!> (Xie and Castro, 2008)
1142	!------------------------------------------------------------------------------!
1143	SUBROUTINE stg_setup_filter_function
1144
1145	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1146	INTEGER(iwp) :: k !< loop index along vertical direction
1147	!
1148	!-- Define the size of the filter functions and allocate them.
1149	mergp_x = 0
1150	mergp_y = 0
1151	mergp_z = 0
1152
1153	DO k = nzb, nzt+1
1154	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1155	IF ( j > mergp_x ) mergp_x = j
1156	ENDDO
1157	DO k = nzb, nzt+1
1158	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1159	IF ( j > mergp_y ) mergp_y = j
1160	ENDDO
1161	DO k = nzb, nzt+1
1162	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1163	IF ( j > mergp_z ) mergp_z = j
1164	ENDDO
1165
1166	mergp_xy = MAX( mergp_x, mergp_y )
1167
1168	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1169	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1170	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1171	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1172	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1173	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1174	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1175	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1176	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1177
1178	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1179	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1180	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1181	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1182	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1183	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1184	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1185	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1186	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1187	!
1188	!-- Create filter functions
1189	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1190	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1191	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1192	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1193	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1194	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1195	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1196	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1197	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1198
1199	END SUBROUTINE stg_setup_filter_function
1200
1201	!--------------------------------------------------------------------------------------------------!
1202	! Description:
1203	! ------------
1204	!> Parin for &stg_par for synthetic turbulence generator
1205	!--------------------------------------------------------------------------------------------------!
1206	SUBROUTINE stg_parin
1207
1208	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1209
1210
1211	NAMELIST /stg_par/ dt_stg_adjust, &
1212	dt_stg_call, &
1213	use_syn_turb_gen, &
1214	compute_velocity_seeds_local
1215
1216	line = ' '
1217	!
1218	!-- Try to find stg package
1219	REWIND ( 11 )
1220	line = ' '
1221	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1222	READ ( 11, '(A)', END = 20 ) line
1223	ENDDO
1224	BACKSPACE ( 11 )
1225
1226	!
1227	!-- Read namelist
1228	READ ( 11, stg_par, ERR = 10, END = 20 )
1229
1230	!
1231	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1232	syn_turb_gen = .TRUE.
1233	GOTO 20
1234
1235	10 BACKSPACE( 11 )
1236	READ( 11 , '(A)') line
1237	CALL parin_fail_message( 'stg_par', line )
1238
1239	20 CONTINUE
1240
1241	END SUBROUTINE stg_parin
1242
1243
1244	!--------------------------------------------------------------------------------------------------!
1245	! Description:
1246	! ------------
1247	!> Read module-specific global restart data (Fortran binary format).
1248	!--------------------------------------------------------------------------------------------------!
1249	SUBROUTINE stg_rrd_global_ftn( found )
1250
1251	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1252
1253	found = .TRUE.
1254
1255
1256	SELECT CASE ( restart_string(1:length) )
1257
1258	CASE ( 'time_stg_adjust' )
1259	READ ( 13 ) time_stg_adjust
1260
1261	CASE ( 'time_stg_call' )
1262	READ ( 13 ) time_stg_call
1263
1264	CASE ( 'use_syn_turb_gen' )
1265	READ ( 13 ) use_syn_turb_gen
1266
1267	CASE DEFAULT
1268
1269	found = .FALSE.
1270
1271	END SELECT
1272
1273
1274	END SUBROUTINE stg_rrd_global_ftn
1275
1276
1277	!--------------------------------------------------------------------------------------------------!
1278	! Description:
1279	! ------------
1280	!> Read module-specific global restart data (MPI-IO).
1281	!--------------------------------------------------------------------------------------------------!
1282	SUBROUTINE stg_rrd_global_mpi
1283
1284	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1285	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1286	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1287
1288	END SUBROUTINE stg_rrd_global_mpi
1289
1290
1291	!--------------------------------------------------------------------------------------------------!
1292	! Description:
1293	! ------------
1294	!> This routine writes the respective restart data.
1295	!--------------------------------------------------------------------------------------------------!
1296	SUBROUTINE stg_wrd_global
1297
1298	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1299
1300	CALL wrd_write_string( 'time_stg_adjust' )
1301	WRITE ( 14 ) time_stg_adjust
1302
1303	CALL wrd_write_string( 'time_stg_call' )
1304	WRITE ( 14 ) time_stg_call
1305
1306	CALL wrd_write_string( 'use_syn_turb_gen' )
1307	WRITE ( 14 ) use_syn_turb_gen
1308
1309	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1310
1311	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1312	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1313	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1314
1315	ENDIF
1316
1317	END SUBROUTINE stg_wrd_global
1318
1319
1320	!--------------------------------------------------------------------------------------------------!
1321	! Description:
1322	! ------------
1323	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1324	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1325	!> (2013), and using a Lund rotation (Lund, 1998).
1326	!--------------------------------------------------------------------------------------------------!
1327	SUBROUTINE stg_main
1328
1329	USE exchange_horiz_mod, &
1330	ONLY: exchange_horiz
1331
1332	INTEGER(iwp) :: i !< grid index in x-direction
1333	INTEGER(iwp) :: j !< loop index in y-direction
1334	INTEGER(iwp) :: k !< loop index in z-direction
1335
1336	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1337
1338	REAL(wp) :: dt_stg !< time interval the STG is called
1339
1340	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1341
1342	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1343	!
1344	!-- Calculate time step which is needed for filter functions
1345	dt_stg = MAX( dt_3d, dt_stg_call )
1346	!
1347	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1348	!-- created or if old disturbances can be imposed again.
1349	IF ( time_stg_call >= dt_stg_call .AND. &
1350	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1351	stg_call = .TRUE.
1352	ELSE
1353	stg_call = .FALSE.
1354	ENDIF
1355	!
1356	!-- Initial value of fu, fv, fw
1357	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1358	!
1359	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1360	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1361	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1362	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1363	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1364	!-- have the same initial seeds.
1365	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1366	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1367	.AND. .NOT. rans_mode ) ) ) THEN
1368	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1369	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1370	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1371	ELSE
1372	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1373	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1374	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1375	!
1376	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1377	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1378	!-- comment above.
1379	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1380	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1381	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1382	ENDIF
1383	velocity_seed_initialized = .TRUE.
1384	ENDIF
1385	!
1386	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1387	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1388	!-- seeds are required also at the right, south and north boundaries.
1389	IF ( stg_call ) THEN
1390	IF ( .NOT. ( nesting_offline .OR. &
1391	( child_domain .AND. rans_mode_parent &
1392	.AND. .NOT. rans_mode ) ) ) THEN
1393	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1394	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1395	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1396
1397	ELSE
1398	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1399	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1400	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1401
1402	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1403	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1404	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1405	ENDIF
1406	ENDIF
1407
1408	!
1409	!-- Turbulence generation at left and/or right boundary
1410	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1411	!
1412	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1413	!-- exceeded. Else the old set of perturbations is imposed
1414	IF ( stg_call ) THEN
1415
1416	DO j = nys, nyn
1417	DO k = nzb, nzt + 1
1418	!
1419	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1420	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1421	fu_yz(k,j) = fuo_yz(k,j)
1422	ELSE
1423	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1424	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1425	ENDIF
1426
1427	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1428	fv_yz(k,j) = fvo_yz(k,j)
1429	ELSE
1430	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1431	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1432	ENDIF
1433
1434	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1435	fw_yz(k,j) = fwo_yz(k,j)
1436	ELSE
1437	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1438	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1439	ENDIF
1440	ENDDO
1441	ENDDO
1442
1443	dist_yz(nzb,:,1) = 0.0_wp
1444	dist_yz(nzb,:,2) = 0.0_wp
1445	dist_yz(nzb,:,3) = 0.0_wp
1446
1447	IF ( myidx == id_stg_left ) i = nxl
1448	IF ( myidx == id_stg_right ) i = nxr+1
1449	DO j = nys, nyn
1450	DO k = nzb+1, nzt + 1
1451	!
1452	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1453	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1454	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1455
1456	ENDDO
1457	ENDDO
1458
1459	IF ( myidx == id_stg_left ) i = nxl-1
1460	IF ( myidx == id_stg_right ) i = nxr+1
1461	DO j = nys, nyn
1462	DO k = nzb+1, nzt + 1
1463	!
1464	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1465	!-- Additional factors are added to improve the variance of v and w experimental test
1466	!-- of 1.2
1467	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1468	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1469	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1470	a33(k) * fw_yz(k,j) ) * &
1471	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1472
1473	ENDDO
1474	ENDDO
1475	ENDIF
1476	!
1477	!-- Mass flux correction following Kim et al. (2013)
1478	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1479	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1480	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1481	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1482	mc_factor_l = 0.0_wp
1483	mc_factor = 0.0_wp
1484	!
1485	!-- Sum up the original volume flows (with and without perturbations).
1486	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1487	IF ( myidx == id_stg_left ) i = nxl
1488	IF ( myidx == id_stg_right ) i = nxr+1
1489
1490	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1491	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1492
1493	IF ( myidx == id_stg_left ) i = nxl-1
1494	IF ( myidx == id_stg_right ) i = nxr+1
1495
1496	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1497	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1498	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1499	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1500
1501	#if defined( __parallel )
1502	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1503	#else
1504	mc_factor = mc_factor_l
1505	#endif
1506	!
1507	!-- Calculate correction factor and force zero mean perturbations.
1508	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1509
1510	IF ( myidx == id_stg_left ) i = nxl
1511	IF ( myidx == id_stg_right ) i = nxr+1
1512
1513	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1514	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1515
1516
1517	IF ( myidx == id_stg_left ) i = nxl-1
1518	IF ( myidx == id_stg_right ) i = nxr+1
1519
1520	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1521	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1522
1523	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1524	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1525	!
1526	!-- Add disturbances
1527	IF ( myidx == id_stg_left ) THEN
1528	!
1529	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1530	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1531	!-- the mean inflow profiles.
1532	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1533	!
1534	!-- Add disturbance at the inflow
1535	DO j = nys, nyn
1536	DO k = nzb, nzt+1
1537	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1538	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1539	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1540	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1541	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1542	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1543	ENDDO
1544	ENDDO
1545	ELSE
1546
1547	DO j = nys, nyn
1548	DO k = nzb+1, nzt
1549	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1550	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1551	u(k,j,-1) = u(k,j,0)
1552	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1553	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1554	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1556	ENDDO
1557	ENDDO
1558	ENDIF
1559	ENDIF
1560	IF ( myidx == id_stg_right ) THEN
1561	DO j = nys, nyn
1562	DO k = nzb+1, nzt
1563	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1564	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1565	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1566	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1567	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1568	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1569	ENDDO
1570	ENDDO
1571	ENDIF
1572	ENDIF
1573	ENDIF
1574	!
1575	!-- Turbulence generation at north and south boundary
1576	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1577	!
1578	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1579	!-- exceeded. Else the old set of perturbations is imposed
1580	IF ( stg_call ) THEN
1581	DO i = nxl, nxr
1582	DO k = nzb, nzt + 1
1583	!
1584	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1585	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1586	fu_xz(k,i) = fuo_xz(k,i)
1587	ELSE
1588	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1589	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1590	ENDIF
1591
1592	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1593	fv_xz(k,i) = fvo_xz(k,i)
1594	ELSE
1595	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1596	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1597	ENDIF
1598
1599	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1600	fw_xz(k,i) = fwo_xz(k,i)
1601	ELSE
1602	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1603	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1604	ENDIF
1605	ENDDO
1606	ENDDO
1607
1608
1609	dist_xz(nzb,:,1) = 0.0_wp
1610	dist_xz(nzb,:,2) = 0.0_wp
1611	dist_xz(nzb,:,3) = 0.0_wp
1612
1613	IF ( myidy == id_stg_south ) j = nys
1614	IF ( myidy == id_stg_north ) j = nyn+1
1615	DO i = nxl, nxr
1616	DO k = nzb+1, nzt + 1
1617	!
1618	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1619	!-- Additional factors are added to improve the variance of v and w
1620	!experimental test of 1.2
1621	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1622	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1623	ENDDO
1624	ENDDO
1625
1626	IF ( myidy == id_stg_south ) j = nys-1
1627	IF ( myidy == id_stg_north ) j = nyn+1
1628	DO i = nxl, nxr
1629	DO k = nzb+1, nzt + 1
1630	!
1631	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1632	!-- Additional factors are added to improve the variance of v and w
1633	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1634	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1635
1636	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1637	a33(k) * fw_xz(k,i) ) * &
1638	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1639	ENDDO
1640	ENDDO
1641	ENDIF
1642
1643	!
1644	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1645	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1646	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1647	!-- else the boundary values won't be accessed.
1648	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1649	mc_factor_l = 0.0_wp
1650	mc_factor = 0.0_wp
1651
1652	IF ( myidy == id_stg_south ) j = nys
1653	IF ( myidy == id_stg_north ) j = nyn+1
1654
1655	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1656	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1657
1658	IF ( myidy == id_stg_south ) j = nys-1
1659	IF ( myidy == id_stg_north ) j = nyn+1
1660
1661	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1662	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1663	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1664	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1665
1666	#if defined( __parallel )
1667	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1668	#else
1669	mc_factor = mc_factor_l
1670	#endif
1671
1672	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1673
1674	IF ( myidy == id_stg_south ) j = nys
1675	IF ( myidy == id_stg_north ) j = nyn+1
1676
1677	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1678	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1679
1680
1681	IF ( myidy == id_stg_south ) j = nys-1
1682	IF ( myidy == id_stg_north ) j = nyn+1
1683
1684	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1685	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1686
1687	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1688	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1689	!
1690	!-- Add disturbances
1691	IF ( myidy == id_stg_south ) THEN
1692	DO i = nxl, nxr
1693	DO k = nzb+1, nzt
1694	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1695	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1696	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1697	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1698	v(k,-1,i) = v(k,0,i)
1699	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1700	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1701	ENDDO
1702	ENDDO
1703	ENDIF
1704	IF ( myidy == id_stg_north ) THEN
1705
1706	DO i = nxl, nxr
1707	DO k = nzb+1, nzt
1708	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1709	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1710	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1711	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1712	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1713	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1714	ENDDO
1715	ENDDO
1716	ENDIF
1717	ENDIF
1718	ENDIF
1719	!
1720	!-- Exchange ghost points.
1721	CALL exchange_horiz( u, nbgp )
1722	CALL exchange_horiz( v, nbgp )
1723	CALL exchange_horiz( w, nbgp )
1724	!
1725	!-- Finally, set time counter for calling STG to zero
1726	IF ( stg_call ) time_stg_call = 0.0_wp
1727	!
1728	!-- Set adjustment step to False to indicate that time correlation can be
1729	!-- switched-on again.
1730	adjustment_step = .FALSE.
1731
1732	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1733
1734	END SUBROUTINE stg_main
1735
1736	!--------------------------------------------------------------------------------------------------!
1737	! Description:
1738	! ------------
1739	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1740	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1741	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1742	!> array.
1743	!--------------------------------------------------------------------------------------------------!
1744	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1745
1746	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1747	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1748	INTEGER(iwp) :: j !< loop index in y-direction
1749	INTEGER(iwp) :: jj !< loop index in y-direction
1750	INTEGER(iwp) :: k !< loop index in z-direction
1751	INTEGER(iwp) :: kk !< loop index in z-direction
1752	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1753
1754	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1755	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1756
1757	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1758	REAL(wp) :: rand_av !< average of random number
1759	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1760
1761	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1762	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1763
1764	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1765	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1766
1767	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1768	!
1769	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1770	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1771	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1772	!-- and normalization of random numbers is done locally, while the result is later distributed to
1773	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1774	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1775	!-- correlation matrix.
1776	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1777	rand_it = 0.0_wp
1778
1779	rand_av = 0.0_wp
1780	rand_sigma_inv = 0.0_wp
1781	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1782	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1783	!
1784	!-- Compute and normalize random numbers.
1785	DO j = nys - mergp_y, nyn + mergp_y
1786	!
1787	!-- Put the random seeds at grid point j
1788	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1789	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1790	CALL random_number_parallel( random_dummy )
1791	rand_it(k,j) = random_dummy
1792	ENDDO
1793	!
1794	!-- Get the new random seeds from last call at grid point j
1795	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1796	ENDDO
1797	!
1798	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1799	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1800	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1801	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1802	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1803	rand_av = rand_av + rand_it(k,j)
1804	ENDDO
1805	ENDDO
1806
1807	#if defined( __parallel )
1808	!
1809	!-- Sum-up the local averages of the random numbers
1810	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1811	#endif
1812	rand_av = rand_av * nyz_inv
1813	!
1814	!-- Obtain zero mean
1815	rand_it= rand_it - rand_av
1816	!
1817	!-- Now, compute the variance
1818	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1819	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1820	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1821	ENDDO
1822	ENDDO
1823
1824	#if defined( __parallel )
1825	!
1826	!-- Sum-up the local quadratic averages of the random numbers
1827	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1828	#endif
1829	!
1830	!-- Compute standard deviation
1831	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1832	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1833	ELSE
1834	rand_sigma_inv = 1.0_wp
1835	ENDIF
1836	!
1837	!-- Normalize with standard deviation to obtain unit variance
1838	rand_it = rand_it * rand_sigma_inv
1839
1840	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1841	!
1842	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1843	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1844	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1845	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1846	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1847	!-- communication. In the second option, which performs better when the turbulent length scales
1848	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1849	!-- communication is necessary.
1850	IF ( compute_velocity_seeds_local ) THEN
1851
1852	f_n = 0.0_wp
1853	DO j = nys, nyn
1854	DO k = nzb, nzt+1
1855	DO jj = -n_y(k), n_y(k)
1856	DO kk = -n_z(k), n_z(k)
1857	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1858	ENDDO
1859	ENDDO
1860	ENDDO
1861	ENDDO
1862
1863	ELSE
1864
1865	f_n_l = 0.0_wp
1866	DO j = nys, nyn
1867	DO k = nzb_x_stg, nzt_x_stg+1
1868	DO jj = -n_y(k), n_y(k)
1869	DO kk = -n_z(k), n_z(k)
1870	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1871	ENDDO
1872	ENDDO
1873	ENDDO
1874	ENDDO
1875	!
1876	!-- Gather velocity seeds of full subdomain
1877	send_count = nzt_x_stg - nzb_x_stg + 1
1878	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1879
1880	#if defined( __parallel )
1881	!
1882	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1883	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1884	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1885	!
1886	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1887	!-- nesting for example).
1888	IF ( PRESENT( id_right ) ) THEN
1889	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1890	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1891	ENDIF
1892	#else
1893	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1894	!
1895	!-- Next line required to avoid compile errors because of unused dummy arguments
1896	IF ( id_left == 0 ) id_right = 0
1897	#endif
1898
1899	ENDIF
1900
1901	DEALLOCATE( rand_it )
1902
1903	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1904
1905	END SUBROUTINE stg_generate_seed_yz
1906
1907
1908	!--------------------------------------------------------------------------------------------------!
1909	! Description:
1910	! ------------
1911	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1912	!> f_n.
1913	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1914	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1915	!> full array.
1916	!--------------------------------------------------------------------------------------------------!
1917	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1918
1919	INTEGER(iwp) :: i !< loop index in x-direction
1920	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1921	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1922	INTEGER(iwp) :: ii !< loop index in x-direction
1923	INTEGER(iwp) :: k !< loop index in z-direction
1924	INTEGER(iwp) :: kk !< loop index in z-direction
1925	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1926
1927	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1928	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1929
1930	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1931	REAL(wp) :: rand_av !< average of random number
1932	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1933
1934	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1935	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1936
1937	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1938	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1939
1940	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1941
1942	!
1943	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1944	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1945	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1946	!-- and normalization of random numbers is done locally, while the result is later distributed to
1947	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1948	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1949	!-- correlation matrix.
1950	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1951	rand_it = 0.0_wp
1952
1953	rand_av = 0.0_wp
1954	rand_sigma_inv = 0.0_wp
1955	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1956	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1957	!
1958	!-- Compute and normalize random numbers.
1959	DO i = nxl - mergp_x, nxr + mergp_x
1960	!
1961	!-- Put the random seeds at grid point ii
1962	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1963	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1964	CALL random_number_parallel( random_dummy )
1965	rand_it(k,i) = random_dummy
1966	ENDDO
1967	!
1968	!-- Get the new random seeds from last call at grid point ii
1969	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1970	ENDDO
1971	!
1972	!-- For normalization to zero mean, sum-up the global random numers.
1973	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1974	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1975	!-- also occur on the inner subdomains.
1976	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1977	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1978	rand_av = rand_av + rand_it(k,i)
1979	ENDDO
1980	ENDDO
1981
1982	#if defined( __parallel )
1983	!
1984	!-- Sum-up the local averages of the random numbers
1985	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1986	#endif
1987	rand_av = rand_av * nxz_inv
1988	!
1989	!-- Obtain zero mean
1990	rand_it= rand_it - rand_av
1991	!
1992	!-- Now, compute the variance
1993	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1994	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1995	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1996	ENDDO
1997	ENDDO
1998
1999	#if defined( __parallel )
2000	!
2001	!-- Sum-up the local quadratic averages of the random numbers
2002	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2003	#endif
2004	!
2005	!-- Compute standard deviation
2006	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2007	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2008	ELSE
2009	rand_sigma_inv = 1.0_wp
2010	ENDIF
2011	!
2012	!-- Normalize with standard deviation to obtain unit variance
2013	rand_it = rand_it * rand_sigma_inv
2014
2015	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2016	!
2017	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2018	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2019	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2020	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2021	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2022	!-- In the second option, which performs better when the turbulent length scales are parametrized
2023	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2024	IF ( compute_velocity_seeds_local ) THEN
2025
2026	f_n = 0.0_wp
2027	DO i = nxl, nxr
2028	DO k = nzb, nzt+1
2029	DO ii = -n_x(k), n_x(k)
2030	DO kk = -n_z(k), n_z(k)
2031	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2032	ENDDO
2033	ENDDO
2034	ENDDO
2035	ENDDO
2036
2037	ELSE
2038
2039	f_n_l = 0.0_wp
2040	DO i = nxl, nxr
2041	DO k = nzb_y_stg, nzt_y_stg+1
2042	DO ii = -n_x(k), n_x(k)
2043	DO kk = -n_z(k), n_z(k)
2044	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2045	ENDDO
2046	ENDDO
2047	ENDDO
2048	ENDDO
2049	!
2050	!-- Gather velocity seeds of full subdomain
2051	send_count = nzt_y_stg - nzb_y_stg + 1
2052	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2053
2054	#if defined( __parallel )
2055	!
2056	!-- Gather the processed velocity seed on south boundary mpi ranks.
2057	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2058	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2059	!
2060	!-- Gather the processed velocity seed on north boundary mpi ranks.
2061	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2062	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2063	#else
2064	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2065	!
2066	!-- Next line required to avoid compile errors because of unused dummy arguments
2067	IF ( id_north == 0 ) id_south = 0
2068	#endif
2069
2070	ENDIF
2071
2072	DEALLOCATE( rand_it )
2073
2074	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2075
2076	END SUBROUTINE stg_generate_seed_xz
2077
2078	!--------------------------------------------------------------------------------------------------!
2079	! Description:
2080	! ------------
2081	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2082	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2083	!> which is applied in state-of-the-art dispserion modelling.
2084	!--------------------------------------------------------------------------------------------------!
2085	SUBROUTINE parametrize_turbulence
2086
2087	INTEGER(iwp) :: k !< loop index in z-direction
2088
2089	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2090	REAL(wp) :: d_zi !< inverse boundary-layer depth
2091	REAL(wp) :: length_scale_lon !< length scale in flow direction
2092	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2093	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2094	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2095	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2096	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2097	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2098	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2099	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2100	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2101	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2102	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2103	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2104	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2105	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2106	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2107	REAL(wp) :: zzi !< ratio of z/zi
2108
2109	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2110	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2111	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2112
2113	!
2114	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2115	!-- criterion according to Heinze et al. (2017).
2116	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2117	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2118	k_zi = MIN( k_zi, nzt )
2119	!
2120	!-- Calculate angle between flow direction and x-axis.
2121	DO k = nzb+1, nzt + 1
2122	IF ( u_init(k) /= 0.0_wp ) THEN
2123	phi(k) = ATAN( v_init(k) / u_init(k) )
2124	ELSE
2125	phi(k) = 0.5 * pi
2126	ENDIF
2127	!
2128	!-- Pre-calculate sine and cosine.
2129	cos_phi(k) = COS( phi(k) )
2130	sin_phi(k) = SIN( phi(k) )
2131	ENDDO
2132	!
2133	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2134	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2135	!-- coincide with the grid axis. Hence, components are rotated after computation.
2136	d_zi = 1.0_wp / zi_ribulk
2137	DO k = nzb+1, k_zi
2138
2139	corr_term_uh = MERGE( 0.35_wp * ABS( &
2140	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2141	)**( 2.0_wp / 3.0_wp ), &
2142	0.0_wp, &
2143	scale_l < -5.0_wp )
2144	!
2145	!-- Determine normalized height coordinate
2146	zzi = zu(k) * d_zi
2147	!
2148	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2149	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2150	!-- variances cannot become negative, take the absolute values.
2151	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2152	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2153
2154	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2155	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2156	!
2157	!-- w'w'
2158	r33(k) = scale_wm*2 ( &
2159	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2160	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2161	)
2162	!
2163	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2164	!-- these are projected along the x- and y-direction. Note, it is assumed that
2165	!-- the flux within the boundary points opposite to the vertical gradient.
2166	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2167	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2168
2169	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2170	- ( u_init(k+1) - u_init(k-1) ) )
2171	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2172	- ( v_init(k+1) - v_init(k-1) ) )
2173	!
2174	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2175	!-- for the vertical transport.
2176	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2177	!
2178	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2179	!-- limited to the adjustment time scales.
2180	tu(k) = MIN( dt_stg_adjust, &
2181	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2182
2183	tv(k) = tu(k)
2184	tw(k) = tu(k)
2185
2186	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2187	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2188	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2189	!
2190	!-- Assume isotropic turbulence length scales
2191	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2192	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2193	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2194	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2195	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2196	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2197	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2198	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2199	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2200
2201	ENDDO
2202	!
2203	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2204	!-- reduced to zero by a blending function.
2205	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2206	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2207	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2208
2209	time_scale_zi = tu(k_zi)
2210	r11_zi = r11(k_zi)
2211	r22_zi = r22(k_zi)
2212	r33_zi = r33(k_zi)
2213	r31_zi = r31(k_zi)
2214	r32_zi = r32(k_zi)
2215
2216	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2217
2218	DO k = k_zi+1, nzt+1
2219	!
2220	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2221	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2222	!
2223	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2224	!-- the mergpe-function can crash if scale_l is zero.
2225	r11(k) = r11_zi * blend
2226	r22(k) = r22_zi * blend
2227	r33(k) = r33_zi * blend
2228	r31(k) = r31_zi * blend
2229	r32(k) = r32_zi * blend
2230	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2231
2232	!
2233	!-- Compute turbulent time scales according to Brost et al. (1982).
2234	!-- Note, time scales are limited to the adjustment time scales.
2235	tu(k) = time_scale_zi * blend
2236	tv(k) = time_scale_zi * blend
2237	tw(k) = time_scale_zi * blend
2238
2239	length_scale_lon = length_scale_lon_zi * blend
2240	length_scale_lat = length_scale_lat_zi * blend
2241	length_scale_vert = length_scale_vert_zi * blend
2242	!
2243	!-- Assume isotropic turbulence length scales
2244	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2245	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2246	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2247	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2248	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2249	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2250	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2251	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2252	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2253	ENDDO
2254	!
2255	!-- Set bottom boundary condition for reynolds stresses
2256	r11(nzb) = r11(nzb+1)
2257	r22(nzb) = r22(nzb+1)
2258	r33(nzb) = r33(nzb+1)
2259
2260	r21(nzb) = r11(nzb+1)
2261	r31(nzb) = r31(nzb+1)
2262	r32(nzb) = r32(nzb+1)
2263
2264	!
2265	!-- Set bottom boundary condition for the length and time scales
2266	nux(nzb) = nux(nzb+1)
2267	nuy(nzb) = nuy(nzb+1)
2268	nuz(nzb) = nuz(nzb+1)
2269	nvx(nzb) = nvx(nzb+1)
2270	nvy(nzb) = nvy(nzb+1)
2271	nvz(nzb) = nvz(nzb+1)
2272	nwx(nzb) = nwx(nzb+1)
2273	nwy(nzb) = nwy(nzb+1)
2274	nwz(nzb) = nwz(nzb+1)
2275
2276	tu(nzb) = tu(nzb+1)
2277	tv(nzb) = tv(nzb+1)
2278	tw(nzb) = tw(nzb+1)
2279
2280	adjustment_step = .TRUE.
2281
2282	END SUBROUTINE parametrize_turbulence
2283
2284	!--------------------------------------------------------------------------------------------------!
2285	! Description:
2286	! ------------
2287	!> Calculate the coefficient matrix from the Lund rotation.
2288	!--------------------------------------------------------------------------------------------------!
2289	SUBROUTINE calc_coeff_matrix
2290
2291	INTEGER(iwp) :: k !< loop index in z-direction
2292
2293	!
2294	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2295	DO k = nzb+1, nzt+1
2296	IF ( r11(k) > 10E-6_wp ) THEN
2297	a11(k) = SQRT( r11(k) )
2298	a21(k) = r21(k) / a11(k)
2299	a31(k) = r31(k) / a11(k)
2300	ELSE
2301	a11(k) = 10E-8_wp
2302	a21(k) = 10E-8_wp
2303	a31(k) = 10E-8_wp
2304	ENDIF
2305	ENDDO
2306	DO k = nzb+1, nzt+1
2307	a22(k) = r22(k) - a21(k)**2
2308	IF ( a22(k) > 10E-6_wp ) THEN
2309	a22(k) = SQRT( a22(k) )
2310	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2311	ELSE
2312	a22(k) = 10E-8_wp
2313	a32(k) = 10E-8_wp
2314	ENDIF
2315	ENDDO
2316	DO k = nzb+1, nzt+1
2317	a33(k) = r33(k) - a31(k)2 - a32(k)2
2318	IF ( a33(k) > 10E-6_wp ) THEN
2319	a33(k) = SQRT( a33(k) )
2320	ELSE
2321	a33(k) = 10E-8_wp
2322	ENDIF
2323	ENDDO
2324	!
2325	!-- Set bottom boundary condition
2326	a11(nzb) = a11(nzb+1)
2327	a22(nzb) = a22(nzb+1)
2328	a21(nzb) = a21(nzb+1)
2329	a33(nzb) = a33(nzb+1)
2330	a31(nzb) = a31(nzb+1)
2331	a32(nzb) = a32(nzb+1)
2332
2333	END SUBROUTINE calc_coeff_matrix
2334
2335	!--------------------------------------------------------------------------------------------------!
2336	! Description:
2337	! ------------
2338	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2339	!> turbulence at the lateral boundaries.
2340	!--------------------------------------------------------------------------------------------------!
2341	SUBROUTINE stg_adjust
2342
2343	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2344	!
2345	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2346	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2347	!-- nevertheless, the boundary-layer depth need to determined first.
2348	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2349	CALL nesting_offl_calc_zi
2350	!
2351	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2352	CALL calc_scaling_variables
2353	!
2354	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2355	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2356	!-- velocity and velocity scale.
2357	CALL parametrize_turbulence
2358	!
2359	!-- Calculate coefficient matrix from Reynolds stress tensor
2360	!-- (Lund rotation)
2361	CALL calc_coeff_matrix
2362	!
2363	!-- Setup filter functions according to updated length scales.
2364	CALL stg_setup_filter_function
2365	!
2366	!-- Reset time counter for controlling next adjustment to zero
2367	time_stg_adjust = 0.0_wp
2368
2369	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2370
2371	END SUBROUTINE stg_adjust
2372
2373
2374	!--------------------------------------------------------------------------------------------------!
2375	! Description:
2376	! ------------
2377	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2378	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2379	!> scale, and Obukhov length.
2380	!--------------------------------------------------------------------------------------------------!
2381	SUBROUTINE calc_scaling_variables
2382
2383	INTEGER(iwp) :: i !< loop index in x-direction
2384	INTEGER(iwp) :: j !< loop index in y-direction
2385	INTEGER(iwp) :: k !< loop index in z-direction
2386	INTEGER(iwp) :: m !< surface element index
2387
2388	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2389	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2390	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2391	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2392	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2393	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2394	REAL(wp) :: w_convective !< convective velocity scale
2395
2396	!
2397	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2398	!-- model domain.
2399	pt_surf_mean_l = 0.0_wp
2400	shf_mean_l = 0.0_wp
2401	scale_l_l = 0.0_wp
2402	friction_vel_l = 0.0_wp
2403	DO m = 1, surf_def_h(0)%ns
2404	i = surf_def_h(0)%i(m)
2405	j = surf_def_h(0)%j(m)
2406	k = surf_def_h(0)%k(m)
2407	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2408	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2409	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2410	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2411	ENDDO
2412	DO m = 1, surf_lsm_h%ns
2413	i = surf_lsm_h%i(m)
2414	j = surf_lsm_h%j(m)
2415	k = surf_lsm_h%k(m)
2416	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2417	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2418	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2419	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2420	ENDDO
2421	DO m = 1, surf_usm_h%ns
2422	i = surf_usm_h%i(m)
2423	j = surf_usm_h%j(m)
2424	k = surf_usm_h%k(m)
2425	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2426	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2427	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2428	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2429	ENDDO
2430
2431	#if defined( __parallel )
2432	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2433	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2434	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2435	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2436	#else
2437	scale_us = friction_vel_l
2438	shf_mean = shf_mean_l
2439	scale_l = scale_l_l
2440	pt_surf_mean = pt_surf_mean_l
2441	#endif
2442
2443	scale_us = scale_us * d_nxy
2444	shf_mean = shf_mean * d_nxy
2445	scale_l = scale_l * d_nxy
2446	pt_surf_mean = pt_surf_mean * d_nxy
2447	!
2448	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2449	!-- convective velocity scale to zero.
2450	IF ( shf_mean > 0.0_wp ) THEN
2451	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2452	ELSE
2453	w_convective = 0.0_wp
2454	ENDIF
2455	!
2456	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2457	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2458	!-- value of friction velocity for the reynolds-stress parametrization.
2459	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2460	!
2461	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2462	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2463	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2464
2465	END SUBROUTINE calc_scaling_variables
2466
2467	END MODULE synthetic_turbulence_generator_mod

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