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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4835

Last change on this file since 4835 was 4828, checked in by Giersch, 4 years ago
Copyright updated to year 2021, interface pmc_sort removed to accelarate the nesting code
Property svn:keywords set to `Id`
File size: 112.6 KB

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1	!> @synthetic_turbulence_generator_mod.f90
2	!--------------------------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2021 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4828 2021-01-05 11:21:41Z raasch $
27	! Implementation of downward facing USM and LSM surfaces
28	!
29	! 4647 2020-08-24 16:36:18Z suehring
30	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
31	! By default, the random-seed computation is now distributed among several cores. Especially for
32	! large length scales this is significantly faster.
33	!
34	! 4640 2020-08-11 16:28:32Z suehring
35	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
36	! Obukhov length (term is not valid for near neutral conditions)
37	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
38	! the vertical transport of horizontal momentum
39	!
40	! 4629 2020-07-29 09:37:56Z raasch
41	! support for MPI Fortran77 interface (mpif.h) removed
42	!
43	! 4603 2020-07-14 16:08:30Z suehring
44	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
45	! initialized properly
46	!
47	! 4566 2020-06-16 10:11:51Z suehring
48	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
49	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
50	! - change default value of time interval to adjust turbulence parametrization
51	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
52	!
53	! 4562 2020-06-12 08:38:47Z raasch
54	! Parts of r4559 re-formatted
55	!
56	! 4559 2020-06-11 08:51:48Z raasch
57	! File re-formatted to follow the PALM coding standard
58	!
59	! 4535 2020-05-15 12:07:23Z raasch
60	! Bugfix for restart data format query
61	!
62	! 4495 2020-04-13 20:11:20Z raasch
63	! Restart data handling with MPI-IO added
64	!
65	! 4481 2020-03-31 18:55:54Z maronga
66	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
67	!
68	! 4442 2020-03-04 19:21:13Z suehring
69	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
70	! (was accidantly changed).
71	!
72	! 4441 2020-03-04 19:20:35Z suehring
73	! Correct misplaced preprocessor directive
74	!
75	! 4438 2020-03-03 20:49:28Z suehring
76	! Performance optimizations in velocity-seed calculation:
77	! - Random number array is only defined and computed locally (except for normalization to zero mean
78	! and unit variance)
79	! - Parallel random number generator is applied independent on the 2D random numbers in other
80	! routines
81	! - Option to decide wheter velocity seeds are computed locally without any further communication
82	! or are computed by all processes along the communicator
83	!
84	! 4346 2019-12-18 11:55:56Z motisi
85	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
86	! information used in wall_flags_static_0
87	!
88	! 4335 2019-12-12 16:39:05Z suehring
89	! Commentation of last commit
90	!
91	! 4332 2019-12-10 19:44:12Z suehring
92	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
93	! Further, minor bugfix in initial velocity seed calculation.
94	!
95	! 4329 2019-12-10 15:46:36Z motisi
96	! Renamed wall_flags_0 to wall_flags_static_0
97	!
98	! 4309 2019-11-26 18:49:59Z suehring
99	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
100	! the parallel random number generator. Random numbers are now only computed and normalized locally,
101	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
102	! array.
103	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
104	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
105	!
106	! 4182 2019-08-22 15:20:23Z scharf
107	! Corrected "Former revisions" section
108	!
109	! 4148 2019-08-08 11:26:00Z suehring
110	! Remove unused variable
111	!
112	! 4144 2019-08-06 09:11:47Z raasch
113	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
114	!
115	! 4071 2019-07-03 20:02:00Z suehring
116	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
117	! file.
118	!
119	! 4022 2019-06-12 11:52:39Z suehring
120	! Several bugfixes and improvements
121	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
122	! instabilities in case the mean volume flow is close to zero)
123	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
124	! numerically unstable
125	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
126	! case dt_stg_call /= dt_3d
127	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
128	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
129	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
130	!
131	! 3987 2019-05-22 09:52:13Z kanani
132	! Introduce alternative switch for debug output during timestepping
133	!
134	! 3938 2019-04-29 16:06:25Z suehring
135	! Remove unused variables
136	!
137	! 3937 2019-04-29 15:09:07Z suehring
138	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
139	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
140	! synthetic turbulence parametrization.
141	!
142	! 3909 2019-04-17 09:13:25Z suehring
143	! Minor bugfix for last commit
144	!
145	! 3900 2019-04-16 15:17:43Z suehring
146	! Missing re-calculation of perturbation seeds in case of restarts
147	!
148	! 3891 2019-04-12 17:52:01Z suehring
149	! Bugfix in initialization in case of restart runs.
150	!
151	! 3885 2019-04-11 11:29:34Z kanani
152	! Changes related to global restructuring of location messages and introduction of additional debug
153	! messages
154	!
155	!
156	! Removed unused variables
157	!
158	! 3719 2019-02-06 13:10:18Z kanani
159	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
160	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
161	! for better overview.
162	!
163	! 2259 2017-06-08 09:09:11Z gronemeier
164	! Initial revision
165	!
166	! Authors:
167	! --------
168	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
169	!
170	!
171	! Description:
172	! ------------
173	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
174	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
175	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
176	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
177	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
178	!> parametrized within the boundary layer.
179	!>
180	!> @todo Enable cyclic_fill
181	!> Implement turbulence generation for e and pt
182	!> @note <Enter notes on the module>
183	!> @bug Height information from input file is not used. Profiles from input must match with current
184	!> PALM grid.
185	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
186	!--------------------------------------------------------------------------------------------------!
187	MODULE synthetic_turbulence_generator_mod
188
189
190	USE arrays_3d, &
191	ONLY: dzw, &
192	ddzw, &
193	drho_air, &
194	mean_inflow_profiles, &
195	pt, &
196	pt_init, &
197	q, &
198	q_init, &
199	u, &
200	u_init, &
201	v, &
202	v_init, &
203	w, &
204	zu, &
205	zw
206
207	USE basic_constants_and_equations_mod, &
208	ONLY: g, &
209	kappa, &
210	pi
211
212	USE control_parameters, &
213	ONLY: bc_lr, &
214	bc_ns, &
215	child_domain, &
216	coupling_char, &
217	debug_output_timestep, &
218	dt_3d, &
219	e_init, &
220	humidity, &
221	initializing_actions, &
222	intermediate_timestep_count, &
223	intermediate_timestep_count_max, &
224	length, &
225	message_string, &
226	nesting_offline, &
227	neutral, &
228	num_mean_inflow_profiles, &
229	random_generator, &
230	rans_mode, &
231	restart_data_format_output, &
232	restart_string, &
233	syn_turb_gen, &
234	time_since_reference_point, &
235	turbulent_inflow
236
237	USE cpulog, &
238	ONLY: cpu_log, &
239	log_point_s
240
241	USE grid_variables, &
242	ONLY: ddx, &
243	ddy, &
244	dx, &
245	dy
246
247	USE indices, &
248	ONLY: nbgp, &
249	nz, &
250	nzb, &
251	nzt, &
252	nx, &
253	nxl, &
254	nxlu, &
255	nxr, &
256	ny, &
257	nys, &
258	nysv, &
259	nyn, &
260	wall_flags_total_0
261
262	USE kinds
263
264	#if defined( __parallel )
265	USE MPI
266	#endif
267
268	USE nesting_offl_mod, &
269	ONLY: nesting_offl_calc_zi, &
270	zi_ribulk
271
272	USE pegrid, &
273	ONLY: comm1dx, &
274	comm1dy, &
275	comm2d, &
276	ierr, &
277	myidx, &
278	myidy, &
279	pdims
280
281	USE pmc_interface, &
282	ONLY : rans_mode_parent
283
284	USE random_generator_parallel, &
285	ONLY: init_parallel_random_generator, &
286	random_dummy, &
287	random_number_parallel, &
288	random_seed_parallel
289
290	USE restart_data_mpi_io_mod, &
291	ONLY: rrd_mpi_io, &
292	wrd_mpi_io
293
294	USE transpose_indices, &
295	ONLY: nzb_x, &
296	nzt_x
297
298	USE surface_mod, &
299	ONLY: surf_def_h, &
300	surf_lsm_h, &
301	surf_usm_h
302
303	IMPLICIT NONE
304
305	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
306	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
307	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
308	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
309	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
310	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
311	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
312	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
313	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
314	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
315	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
316	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
317	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
318	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
319	#if defined( __parallel )
320	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
321	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
322	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
323	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
324	#endif
325
326	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
327	!< required for bias correction of imposed perturbations
328	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
329	!< required for bias correction of imposed perturbations
330
331	#if defined( __parallel )
332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
333	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
334	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
335	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
336	#endif
337	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
338	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
339	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
340	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
341	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
342	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
343	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
344	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
345	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
346
347	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
348	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
349	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
350	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
351
352
353	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
354	!< no time correlation to the timestep before should be considered
355	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
356	!< or if computation is distributed over several processes
357	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
358	!< (.FALSE.) or if it parametrized
359	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
360	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
361
362
363	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
364	!< scales above the boundary layer
365	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
366	!< one length scale above ABL top
367	REAL(wp) :: d_l !< blend_coeff/length_scale
368	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
369	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
370	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
371	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
372	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
373	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
374	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
375	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
376
377	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
378
379
380	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
381	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
382	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
383	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
384	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
385	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
386
387	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
388	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
389	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
390	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
391	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
392	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
393	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
394	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
395	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
396
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
418
419	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
420	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
421
422	!
423	!-- PALM interfaces:
424	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
425	INTERFACE stg_adjust
426	MODULE PROCEDURE stg_adjust
427	END INTERFACE stg_adjust
428	!
429	!-- Input parameter checks to be done in check_parameters
430	INTERFACE stg_check_parameters
431	MODULE PROCEDURE stg_check_parameters
432	END INTERFACE stg_check_parameters
433
434	!
435	!-- Calculate filter functions
436	INTERFACE stg_filter_func
437	MODULE PROCEDURE stg_filter_func
438	END INTERFACE stg_filter_func
439
440	!
441	!-- Generate velocity seeds at south and north domain boundary
442	INTERFACE stg_generate_seed_xz
443	MODULE PROCEDURE stg_generate_seed_xz
444	END INTERFACE stg_generate_seed_xz
445	!
446	!-- Generate velocity seeds at left and/or right domain boundary
447	INTERFACE stg_generate_seed_yz
448	MODULE PROCEDURE stg_generate_seed_yz
449	END INTERFACE stg_generate_seed_yz
450
451	!
452	!-- Output of information to the header file
453	INTERFACE stg_header
454	MODULE PROCEDURE stg_header
455	END INTERFACE stg_header
456
457	!
458	!-- Initialization actions
459	INTERFACE stg_init
460	MODULE PROCEDURE stg_init
461	END INTERFACE stg_init
462
463	!
464	!-- Main procedure of synth. turb. gen.
465	INTERFACE stg_main
466	MODULE PROCEDURE stg_main
467	END INTERFACE stg_main
468
469	!
470	!-- Reading of NAMELIST parameters
471	INTERFACE stg_parin
472	MODULE PROCEDURE stg_parin
473	END INTERFACE stg_parin
474
475	!
476	!-- Reading of parameters for restart runs
477	INTERFACE stg_rrd_global
478	MODULE PROCEDURE stg_rrd_global_ftn
479	MODULE PROCEDURE stg_rrd_global_mpi
480	END INTERFACE stg_rrd_global
481
482	!
483	!-- Writing of binary output for restart runs
484	INTERFACE stg_wrd_global
485	MODULE PROCEDURE stg_wrd_global
486	END INTERFACE stg_wrd_global
487
488	SAVE
489
490	PRIVATE
491
492	!
493	!-- Public interfaces
494	PUBLIC stg_adjust, &
495	stg_check_parameters, &
496	stg_header, &
497	stg_init, &
498	stg_main, &
499	stg_parin, &
500	stg_rrd_global, &
501	stg_wrd_global
502
503	!
504	!-- Public variables
505	PUBLIC dt_stg_call, &
506	dt_stg_adjust, &
507	id_stg_left, &
508	id_stg_north, &
509	id_stg_right, &
510	id_stg_south, &
511	parametrize_inflow_turbulence, &
512	time_stg_adjust, &
513	time_stg_call, &
514	use_syn_turb_gen
515
516
517	CONTAINS
518
519
520	!--------------------------------------------------------------------------------------------------!
521	! Description:
522	! ------------
523	!> Check parameters routine for synthetic turbulence generator
524	!--------------------------------------------------------------------------------------------------!
525	SUBROUTINE stg_check_parameters
526
527	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
528	nesting_offline ) THEN
529	message_string = 'Synthetic turbulence generator is required ' // &
530	'if offline nesting is applied and PALM operates in LES mode.'
531	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
532	ENDIF
533
534	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
535	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
536	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
537	'and parent operates in RANS-mode but current child in LES mode.'
538	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
539	ENDIF
540
541	IF ( use_syn_turb_gen ) THEN
542
543	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
544	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
545	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
546
547	ENDIF
548
549	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
550	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
551	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
552
553	ENDIF
554
555	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
556
557	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
558	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
559	message_string = 'Using synthetic turbulence generator requires ' // &
560	'%initializing_actions = "set_constant_profiles" or ' // &
561	' "read_restart_data", if not offline nesting is applied.'
562	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
563	ENDIF
564
565	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
566	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
567	' "dirichlet/radiation", if not offline nesting is applied.'
568	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
569	ENDIF
570	IF ( bc_ns /= 'cyclic' ) THEN
571	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
572	' "cyclic", if not offline nesting is applied.'
573	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
574	ENDIF
575
576	ENDIF
577
578	IF ( turbulent_inflow ) THEN
579	message_string = 'Using synthetic turbulence generator in combination ' // &
580	'&with turbulent_inflow = .T. is not allowed'
581	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
582	ENDIF
583	!
584	!-- Synthetic turbulence generator requires the parallel random generator
585	IF ( random_generator /= 'random-parallel' ) THEN
586	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
587	'random-parallel.'
588	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
589	ENDIF
590
591	ENDIF
592
593	END SUBROUTINE stg_check_parameters
594
595
596	!--------------------------------------------------------------------------------------------------!
597	! Description:
598	! ------------
599	!> Header output for synthetic turbulence generator
600	!--------------------------------------------------------------------------------------------------!
601	SUBROUTINE stg_header ( io )
602
603	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
604
605	!
606	!-- Write synthetic turbulence generator Header
607	WRITE( io, 1 )
608	IF ( use_syn_turb_gen ) THEN
609	WRITE( io, 2 )
610	ELSE
611	WRITE( io, 3 )
612	ENDIF
613
614	IF ( parametrize_inflow_turbulence ) THEN
615	WRITE( io, 4 ) dt_stg_adjust
616	ELSE
617	WRITE( io, 5 )
618	ENDIF
619
620	1 FORMAT (//' Synthetic turbulence generator information:'/ &
621	' ------------------------------------------'/)
622	2 FORMAT (' synthetic turbulence generator is switched on')
623	3 FORMAT (' synthetic turbulence generator is switched off')
624	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
625	5 FORMAT (' imposed turbulence is read from file' )
626
627	END SUBROUTINE stg_header
628
629
630	!--------------------------------------------------------------------------------------------------!
631	! Description:
632	! ------------
633	!> Initialization of the synthetic turbulence generator
634	!--------------------------------------------------------------------------------------------------!
635	SUBROUTINE stg_init
636
637	#if defined( __parallel )
638	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
639	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
640	#endif
641
642	INTEGER(iwp) :: i !> grid index in x-direction
643	INTEGER(iwp) :: j !> loop index
644	INTEGER(iwp) :: k !< index
645	#if defined( __parallel )
646	INTEGER(iwp) :: newtype !< dummy MPI type
647	INTEGER(iwp) :: realsize !< size of REAL variables
648	#endif
649
650	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
651	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
652
653
654	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
655
656	!
657	!-- Dummy variables used for reading profiles
658	REAL(wp) :: d1 !< u profile
659	REAL(wp) :: d2 !< v profile
660	REAL(wp) :: d3 !< w profile
661	REAL(wp) :: d5 !< e profile
662	REAL(wp) :: luy !< length scale for u in y direction
663	REAL(wp) :: luz !< length scale for u in z direction
664	REAL(wp) :: lvy !< length scale for v in y direction
665	REAL(wp) :: lvz !< length scale for v in z direction
666	REAL(wp) :: lwy !< length scale for w in y direction
667	REAL(wp) :: lwz !< length scale for w in z direction
668	#if defined( __parallel )
669	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
670	#endif
671	REAL(wp) :: zz !< height
672
673
674	#if defined( __parallel )
675	CALL MPI_BARRIER( comm2d, ierr )
676	#endif
677	!
678	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
679	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
680	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
681	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
682	!-- communication).
683	IF ( .NOT. compute_velocity_seeds_local ) THEN
684	#if defined( __parallel )
685	!
686	!-- Determine processor decomposition of z-axis along x- and y-direction
687	nnz = nz / pdims(1)
688	nzb_x_stg = 1 + myidx * INT( nnz )
689	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
690
691	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
692	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
693
694	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
695	.AND. .NOT. rans_mode ) ) THEN
696	nnz = nz / pdims(2)
697	nzb_y_stg = 1 + myidy * INT( nnz )
698	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
699
700	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
701	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
702	ENDIF
703
704	!
705	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
706	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
707	extent = 1 * realsize
708	!
709	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
710	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
711	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
712	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
713	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
714	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
715	CALL MPI_TYPE_FREE( newtype, ierr )
716
717	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
718	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
719	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
720	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
721	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
722	CALL MPI_TYPE_FREE( newtype, ierr )
723
724	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
725	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
726
727	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
728	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
729
730	DO j = 1, pdims(1)
731	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
732	ENDDO
733	!
734	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
735	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
736	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
737	.AND. .NOT. rans_mode ) ) THEN
738	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
739	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
740	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
741	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
742	CALL MPI_TYPE_FREE( newtype, ierr )
743
744	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
745	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
746	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
747	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
748	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
749	CALL MPI_TYPE_FREE( newtype, ierr )
750
751	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
752	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
753
754	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
755	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
756
757	DO j = 1, pdims(2)
758	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
759	ENDDO
760
761	ENDIF
762	#endif
763	ENDIF
764	!
765	!-- Allocate required arrays.
766	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
767	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
768	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
769	!-- and initialized appropriately.
770	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
771	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
772	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
773	mean_inflow_profiles = 0.0_wp
774	mean_inflow_profiles(:,1) = u_init
775	mean_inflow_profiles(:,2) = v_init
776	!
777	!-- Even though potential temperature and humidity are not perturbed, they need to be
778	!-- initialized appropriately.
779	IF ( .NOT. neutral ) &
780	mean_inflow_profiles(:,4) = pt_init
781	IF ( humidity ) &
782	mean_inflow_profiles(:,6) = q_init
783	ENDIF
784	ENDIF
785	!
786	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
787	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
788	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
789	u_init = mean_inflow_profiles(:,1)
790	v_init = mean_inflow_profiles(:,2)
791	e_init = MAXVAL( mean_inflow_profiles(:,5) )
792	ENDIF
793
794	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
795	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
796	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
797	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
798	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
799	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
800	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
801	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
802
803	r11 = 0.0_wp
804	r21 = 0.0_wp
805	r22 = 0.0_wp
806	r31 = 0.0_wp
807	r32 = 0.0_wp
808	r33 = 0.0_wp
809	tu = 0.0_wp
810	tv = 0.0_wp
811	tw = 0.0_wp
812
813	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
814	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
815	dist_xz = 0.0_wp
816	dist_yz = 0.0_wp
817	!
818	!-- Read inflow profile
819	!-- Height levels of profiles in input profile is as follows:
820	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
821	!-- WARNING: zz is not used at the moment
822	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
823
824	IF ( file_stg_exist ) THEN
825
826	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
827	!
828	!-- Skip header
829	READ( 90, * )
830
831	DO k = nzb, nzt
832	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
833	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
834
835	!
836	!-- Convert length scales from meter to number of grid points.
837	IF ( k /= nzb ) THEN
838	nuz(k) = INT( luz * ddzw(k) )
839	nvz(k) = INT( lvz * ddzw(k) )
840	nwz(k) = INT( lwz * ddzw(k) )
841	ELSE
842	nuz(k) = INT( luz * ddzw(k+1) )
843	nvz(k) = INT( lvz * ddzw(k+1) )
844	nwz(k) = INT( lwz * ddzw(k+1) )
845	ENDIF
846
847	nuy(k) = INT( luy * ddy )
848	nvy(k) = INT( lvy * ddy )
849	nwy(k) = INT( lwy * ddy )
850	!
851	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
852	!-- y-direction.
853	nwx(k) = nwy(k)
854	nvx(k) = nvy(k)
855	nux(k) = nuy(k)
856	!
857	!-- Save Mean inflow profiles
858	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
859	mean_inflow_profiles(k,1) = d1
860	mean_inflow_profiles(k,2) = d2
861	! mean_inflow_profiles(k,4) = d4
862	mean_inflow_profiles(k,5) = d5
863	ENDIF
864	ENDDO
865	!
866	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
867	!-- simply overwritten.
868	nwx(nzb) = nwy(nzb+1)
869	nvx(nzb) = nvy(nzb+1)
870	nux(nzb) = nuy(nzb+1)
871	nuy(nzb) = nuy(nzb+1)
872	nuz(nzb) = nuz(nzb+1)
873	nvy(nzb) = nvy(nzb+1)
874	nvz(nzb) = nvz(nzb+1)
875	nwy(nzb) = nwy(nzb+1)
876	nwz(nzb) = nwz(nzb+1)
877
878	nwx(nzt+1) = nwy(nzt)
879	nvx(nzt+1) = nvy(nzt)
880	nux(nzt+1) = nuy(nzt)
881	nuy(nzt+1) = nuy(nzt)
882	nuz(nzt+1) = nuz(nzt)
883	nvy(nzt+1) = nvy(nzt)
884	nvz(nzt+1) = nvz(nzt)
885	nwy(nzt+1) = nwy(nzt)
886	nwz(nzt+1) = nwz(nzt)
887
888	CLOSE( 90 )
889	!
890	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
891	CALL calc_coeff_matrix
892	!
893	!-- No information about turbulence and its length scales are available. Instead, parametrize
894	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
895	!-- parametrized, which is done later when energy-balance models are already initialized. This is
896	!-- because the STG needs information about surface properties such as roughness to build
897	!-- 'realistic' turbulence profiles.
898	ELSE
899	!
900	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
901	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
902	!
903	!-- Set flag indicating that turbulence is parametrized
904	parametrize_inflow_turbulence = .TRUE.
905	!
906	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
907	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
908	!-- nevertheless, the boundary-layer depth needs to be determined first.
909	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
910	CALL nesting_offl_calc_zi
911	!
912	!-- Determine boundary-layer depth, which is used to initialize lenght scales
913	CALL calc_scaling_variables
914	!
915	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
916	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
917	!-- friction velocity and velocity scale.
918	CALL parametrize_turbulence
919	!
920	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
921	CALL calc_coeff_matrix
922
923	ENDIF
924	!
925	!-- Initial filter functions
926	CALL stg_setup_filter_function
927	!
928	!-- Allocate velocity seeds for turbulence at xz-layer
929	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
930	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
931	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
932
933	!
934	!-- Allocate velocity seeds for turbulence at yz-layer
935	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
936	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
937	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
938
939	fu_xz = 0.0_wp
940	fuo_xz = 0.0_wp
941	fv_xz = 0.0_wp
942	fvo_xz = 0.0_wp
943	fw_xz = 0.0_wp
944	fwo_xz = 0.0_wp
945
946	fu_yz = 0.0_wp
947	fuo_yz = 0.0_wp
948	fv_yz = 0.0_wp
949	fvo_yz = 0.0_wp
950	fw_yz = 0.0_wp
951	fwo_yz = 0.0_wp
952
953	#if defined( __parallel )
954	CALL MPI_BARRIER( comm2d, ierr )
955	#endif
956
957	!
958	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
959	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
960	!-- This is mostly for k=nzt+1.
961	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
962	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
963
964	IF ( myidx == id_stg_left ) i = -1
965	IF ( myidx == id_stg_right ) i = nxr+1
966
967	DO j = nys, nyn
968	DO k = nzb, nzt+1
969	IF ( a11(k) > 10E-8_wp ) THEN
970	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
971	ELSE
972	fu_yz(k,j) = 10E-8_wp
973	ENDIF
974
975	IF ( a22(k) > 10E-8_wp ) THEN
976	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
977	ELSE
978	fv_yz(k,j) = 10E-8_wp
979	ENDIF
980
981	IF ( a33(k) > 10E-8_wp ) THEN
982	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
983	ELSE
984	fw_yz(k,j) = 10E-8_wp
985	ENDIF
986	ENDDO
987	ENDDO
988	ENDIF
989
990	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
991
992	IF ( myidy == id_stg_south ) j = -1
993	IF ( myidy == id_stg_north ) j = nyn+1
994
995	DO i = nxl, nxr
996	DO k = nzb, nzt+1
997	!
998	!-- In case the correlation coefficients are very small, the velocity seeds may become
999	!-- very large finally creating numerical instabilities in the synthetic turbulence
1000	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
1001	IF ( a11(k) > 10E-8_wp ) THEN
1002	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1003	ELSE
1004	fu_xz(k,i) = 10E-8_wp
1005	ENDIF
1006
1007	IF ( a22(k) > 10E-8_wp ) THEN
1008	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1009	ELSE
1010	fv_xz(k,i) = 10E-8_wp
1011	ENDIF
1012
1013	IF ( a33(k) > 10E-8_wp ) THEN
1014	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1015	ELSE
1016	fw_xz(k,i) = 10E-8_wp
1017	ENDIF
1018
1019	ENDDO
1020	ENDDO
1021	ENDIF
1022	ENDIF
1023	!
1024	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1025	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1026	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1027	!-- different cases must be distinguished.
1028	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1029	!
1030	!-- Number of grid points where perturbations are imposed on u
1031	IF ( myidx == id_stg_left ) i = nxl
1032	IF ( myidx == id_stg_right ) i = nxr+1
1033
1034	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1035	!
1036	!-- Number of grid points where perturbations are imposed on v and w
1037	IF ( myidx == id_stg_left ) i = nxl-1
1038	IF ( myidx == id_stg_right ) i = nxr+1
1039
1040	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1041	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1042
1043	#if defined( __parallel )
1044	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1045	#else
1046	nr_non_topo_yz = nr_non_topo_yz_l
1047	#endif
1048	ENDIF
1049
1050	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1051	!
1052	!-- Number of grid points where perturbations are imposed on v
1053	IF ( myidy == id_stg_south ) j = nys
1054	IF ( myidy == id_stg_north ) j = nyn+1
1055
1056	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1057	!
1058	!-- Number of grid points where perturbations are imposed on u and w
1059	IF ( myidy == id_stg_south ) j = nys-1
1060	IF ( myidy == id_stg_north ) j = nyn+1
1061
1062	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1063	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1064
1065	#if defined( __parallel )
1066	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1067	#else
1068	nr_non_topo_xz = nr_non_topo_xz_l
1069	#endif
1070	ENDIF
1071	!
1072	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1073	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1074	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1075	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1076	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1077	id_rand_yz = 0
1078	seq_rand_yz = 0
1079
1080	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1081
1082	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1083	.AND. .NOT. rans_mode ) ) THEN
1084	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1085	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1086	id_rand_xz = 0
1087	seq_rand_xz = 0
1088
1089	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1090	ENDIF
1091
1092	END SUBROUTINE stg_init
1093
1094
1095	!--------------------------------------------------------------------------------------------------!
1096	! Description:
1097	! ------------
1098	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1099	!--------------------------------------------------------------------------------------------------!
1100	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1101
1102	INTEGER(iwp) :: k !< loop index
1103	INTEGER(iwp) :: mergp !< passed length scale in grid points
1104	INTEGER(iwp) :: n_k !< length scale nXX in height k
1105	INTEGER(iwp) :: nf !< index for length scales
1106
1107	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1108
1109	REAL(wp) :: bdenom !< denominator for filter functions bXX
1110	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1111
1112	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1113
1114
1115	bxx = 0.0_wp
1116
1117	DO k = nzb, nzt+1
1118	bdenom = 0.0_wp
1119	n_k = nxx(k)
1120	IF ( n_k /= 0 ) THEN
1121
1122	!
1123	!-- ( Eq.10 )^2
1124	DO nf = -n_k, n_k
1125	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1126	ENDDO
1127
1128	!
1129	!-- ( Eq.9 )
1130	bdenom = SQRT( bdenom )
1131	DO nf = -n_k, n_k
1132	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1133	ENDDO
1134	ENDIF
1135	ENDDO
1136
1137	END SUBROUTINE stg_filter_func
1138
1139
1140	!------------------------------------------------------------------------------!
1141	! Description:
1142	! ------------
1143	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1144	!> (Xie and Castro, 2008)
1145	!------------------------------------------------------------------------------!
1146	SUBROUTINE stg_setup_filter_function
1147
1148	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1149	INTEGER(iwp) :: k !< loop index along vertical direction
1150	!
1151	!-- Define the size of the filter functions and allocate them.
1152	mergp_x = 0
1153	mergp_y = 0
1154	mergp_z = 0
1155
1156	DO k = nzb, nzt+1
1157	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1158	IF ( j > mergp_x ) mergp_x = j
1159	ENDDO
1160	DO k = nzb, nzt+1
1161	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1162	IF ( j > mergp_y ) mergp_y = j
1163	ENDDO
1164	DO k = nzb, nzt+1
1165	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1166	IF ( j > mergp_z ) mergp_z = j
1167	ENDDO
1168
1169	mergp_xy = MAX( mergp_x, mergp_y )
1170
1171	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1172	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1173	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1174	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1175	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1176	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1177	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1178	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1179	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1180
1181	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1182	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1183	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1184	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1185	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1186	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1187	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1188	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1189	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1190	!
1191	!-- Create filter functions
1192	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1193	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1194	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1195	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1196	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1197	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1198	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1199	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1200	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1201
1202	END SUBROUTINE stg_setup_filter_function
1203
1204	!--------------------------------------------------------------------------------------------------!
1205	! Description:
1206	! ------------
1207	!> Parin for &stg_par for synthetic turbulence generator
1208	!--------------------------------------------------------------------------------------------------!
1209	SUBROUTINE stg_parin
1210
1211	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1212
1213
1214	NAMELIST /stg_par/ dt_stg_adjust, &
1215	dt_stg_call, &
1216	use_syn_turb_gen, &
1217	compute_velocity_seeds_local
1218
1219	line = ' '
1220	!
1221	!-- Try to find stg package
1222	REWIND ( 11 )
1223	line = ' '
1224	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1225	READ ( 11, '(A)', END = 20 ) line
1226	ENDDO
1227	BACKSPACE ( 11 )
1228
1229	!
1230	!-- Read namelist
1231	READ ( 11, stg_par, ERR = 10, END = 20 )
1232
1233	!
1234	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1235	syn_turb_gen = .TRUE.
1236	GOTO 20
1237
1238	10 BACKSPACE( 11 )
1239	READ( 11 , '(A)') line
1240	CALL parin_fail_message( 'stg_par', line )
1241
1242	20 CONTINUE
1243
1244	END SUBROUTINE stg_parin
1245
1246
1247	!--------------------------------------------------------------------------------------------------!
1248	! Description:
1249	! ------------
1250	!> Read module-specific global restart data (Fortran binary format).
1251	!--------------------------------------------------------------------------------------------------!
1252	SUBROUTINE stg_rrd_global_ftn( found )
1253
1254	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1255
1256	found = .TRUE.
1257
1258
1259	SELECT CASE ( restart_string(1:length) )
1260
1261	CASE ( 'time_stg_adjust' )
1262	READ ( 13 ) time_stg_adjust
1263
1264	CASE ( 'time_stg_call' )
1265	READ ( 13 ) time_stg_call
1266
1267	CASE ( 'use_syn_turb_gen' )
1268	READ ( 13 ) use_syn_turb_gen
1269
1270	CASE DEFAULT
1271
1272	found = .FALSE.
1273
1274	END SELECT
1275
1276
1277	END SUBROUTINE stg_rrd_global_ftn
1278
1279
1280	!--------------------------------------------------------------------------------------------------!
1281	! Description:
1282	! ------------
1283	!> Read module-specific global restart data (MPI-IO).
1284	!--------------------------------------------------------------------------------------------------!
1285	SUBROUTINE stg_rrd_global_mpi
1286
1287	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1288	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1289	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1290
1291	END SUBROUTINE stg_rrd_global_mpi
1292
1293
1294	!--------------------------------------------------------------------------------------------------!
1295	! Description:
1296	! ------------
1297	!> This routine writes the respective restart data.
1298	!--------------------------------------------------------------------------------------------------!
1299	SUBROUTINE stg_wrd_global
1300
1301	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1302
1303	CALL wrd_write_string( 'time_stg_adjust' )
1304	WRITE ( 14 ) time_stg_adjust
1305
1306	CALL wrd_write_string( 'time_stg_call' )
1307	WRITE ( 14 ) time_stg_call
1308
1309	CALL wrd_write_string( 'use_syn_turb_gen' )
1310	WRITE ( 14 ) use_syn_turb_gen
1311
1312	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1313
1314	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1315	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1316	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1317
1318	ENDIF
1319
1320	END SUBROUTINE stg_wrd_global
1321
1322
1323	!--------------------------------------------------------------------------------------------------!
1324	! Description:
1325	! ------------
1326	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1327	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1328	!> (2013), and using a Lund rotation (Lund, 1998).
1329	!--------------------------------------------------------------------------------------------------!
1330	SUBROUTINE stg_main
1331
1332	USE exchange_horiz_mod, &
1333	ONLY: exchange_horiz
1334
1335	INTEGER(iwp) :: i !< grid index in x-direction
1336	INTEGER(iwp) :: j !< loop index in y-direction
1337	INTEGER(iwp) :: k !< loop index in z-direction
1338
1339	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1340
1341	REAL(wp) :: dt_stg !< time interval the STG is called
1342
1343	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1344
1345	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1346	!
1347	!-- Calculate time step which is needed for filter functions
1348	dt_stg = MAX( dt_3d, dt_stg_call )
1349	!
1350	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1351	!-- created or if old disturbances can be imposed again.
1352	IF ( time_stg_call >= dt_stg_call .AND. &
1353	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1354	stg_call = .TRUE.
1355	ELSE
1356	stg_call = .FALSE.
1357	ENDIF
1358	!
1359	!-- Initial value of fu, fv, fw
1360	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1361	!
1362	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1363	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1364	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1365	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1366	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1367	!-- have the same initial seeds.
1368	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1369	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1370	.AND. .NOT. rans_mode ) ) ) THEN
1371	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1372	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1373	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1374	ELSE
1375	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1376	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1377	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1378	!
1379	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1380	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1381	!-- comment above.
1382	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1383	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1384	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1385	ENDIF
1386	velocity_seed_initialized = .TRUE.
1387	ENDIF
1388	!
1389	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1390	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1391	!-- seeds are required also at the right, south and north boundaries.
1392	IF ( stg_call ) THEN
1393	IF ( .NOT. ( nesting_offline .OR. &
1394	( child_domain .AND. rans_mode_parent &
1395	.AND. .NOT. rans_mode ) ) ) THEN
1396	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1397	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1398	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1399
1400	ELSE
1401	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1402	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1403	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1404
1405	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1406	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1407	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1408	ENDIF
1409	ENDIF
1410
1411	!
1412	!-- Turbulence generation at left and/or right boundary
1413	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1414	!
1415	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1416	!-- exceeded. Else the old set of perturbations is imposed
1417	IF ( stg_call ) THEN
1418
1419	DO j = nys, nyn
1420	DO k = nzb, nzt + 1
1421	!
1422	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1423	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1424	fu_yz(k,j) = fuo_yz(k,j)
1425	ELSE
1426	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1427	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1428	ENDIF
1429
1430	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1431	fv_yz(k,j) = fvo_yz(k,j)
1432	ELSE
1433	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1434	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1435	ENDIF
1436
1437	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1438	fw_yz(k,j) = fwo_yz(k,j)
1439	ELSE
1440	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1441	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1442	ENDIF
1443	ENDDO
1444	ENDDO
1445
1446	dist_yz(nzb,:,1) = 0.0_wp
1447	dist_yz(nzb,:,2) = 0.0_wp
1448	dist_yz(nzb,:,3) = 0.0_wp
1449
1450	IF ( myidx == id_stg_left ) i = nxl
1451	IF ( myidx == id_stg_right ) i = nxr+1
1452	DO j = nys, nyn
1453	DO k = nzb+1, nzt + 1
1454	!
1455	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1456	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1457	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1458
1459	ENDDO
1460	ENDDO
1461
1462	IF ( myidx == id_stg_left ) i = nxl-1
1463	IF ( myidx == id_stg_right ) i = nxr+1
1464	DO j = nys, nyn
1465	DO k = nzb+1, nzt + 1
1466	!
1467	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1468	!-- Additional factors are added to improve the variance of v and w experimental test
1469	!-- of 1.2
1470	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1471	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1472	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1473	a33(k) * fw_yz(k,j) ) * &
1474	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1475
1476	ENDDO
1477	ENDDO
1478	ENDIF
1479	!
1480	!-- Mass flux correction following Kim et al. (2013)
1481	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1482	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1483	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1484	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1485	mc_factor_l = 0.0_wp
1486	mc_factor = 0.0_wp
1487	!
1488	!-- Sum up the original volume flows (with and without perturbations).
1489	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1490	IF ( myidx == id_stg_left ) i = nxl
1491	IF ( myidx == id_stg_right ) i = nxr+1
1492
1493	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1494	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1495
1496	IF ( myidx == id_stg_left ) i = nxl-1
1497	IF ( myidx == id_stg_right ) i = nxr+1
1498
1499	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1500	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1501	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1502	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1503
1504	#if defined( __parallel )
1505	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1506	#else
1507	mc_factor = mc_factor_l
1508	#endif
1509	!
1510	!-- Calculate correction factor and force zero mean perturbations.
1511	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1512
1513	IF ( myidx == id_stg_left ) i = nxl
1514	IF ( myidx == id_stg_right ) i = nxr+1
1515
1516	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1517	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1518
1519
1520	IF ( myidx == id_stg_left ) i = nxl-1
1521	IF ( myidx == id_stg_right ) i = nxr+1
1522
1523	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1524	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1525
1526	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1527	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1528	!
1529	!-- Add disturbances
1530	IF ( myidx == id_stg_left ) THEN
1531	!
1532	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1533	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1534	!-- the mean inflow profiles.
1535	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1536	!
1537	!-- Add disturbance at the inflow
1538	DO j = nys, nyn
1539	DO k = nzb, nzt+1
1540	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1541	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1542	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1543	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1544	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1545	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1546	ENDDO
1547	ENDDO
1548	ELSE
1549
1550	DO j = nys, nyn
1551	DO k = nzb+1, nzt
1552	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1553	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1554	u(k,j,-1) = u(k,j,0)
1555	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1556	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1557	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1558	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1559	ENDDO
1560	ENDDO
1561	ENDIF
1562	ENDIF
1563	IF ( myidx == id_stg_right ) THEN
1564	DO j = nys, nyn
1565	DO k = nzb+1, nzt
1566	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1567	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1568	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1569	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1570	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1571	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1572	ENDDO
1573	ENDDO
1574	ENDIF
1575	ENDIF
1576	ENDIF
1577	!
1578	!-- Turbulence generation at north and south boundary
1579	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1580	!
1581	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1582	!-- exceeded. Else the old set of perturbations is imposed
1583	IF ( stg_call ) THEN
1584	DO i = nxl, nxr
1585	DO k = nzb, nzt + 1
1586	!
1587	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1588	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1589	fu_xz(k,i) = fuo_xz(k,i)
1590	ELSE
1591	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1592	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1593	ENDIF
1594
1595	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1596	fv_xz(k,i) = fvo_xz(k,i)
1597	ELSE
1598	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1599	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1600	ENDIF
1601
1602	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1603	fw_xz(k,i) = fwo_xz(k,i)
1604	ELSE
1605	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1606	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1607	ENDIF
1608	ENDDO
1609	ENDDO
1610
1611
1612	dist_xz(nzb,:,1) = 0.0_wp
1613	dist_xz(nzb,:,2) = 0.0_wp
1614	dist_xz(nzb,:,3) = 0.0_wp
1615
1616	IF ( myidy == id_stg_south ) j = nys
1617	IF ( myidy == id_stg_north ) j = nyn+1
1618	DO i = nxl, nxr
1619	DO k = nzb+1, nzt + 1
1620	!
1621	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1622	!-- Additional factors are added to improve the variance of v and w
1623	!experimental test of 1.2
1624	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1625	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1626	ENDDO
1627	ENDDO
1628
1629	IF ( myidy == id_stg_south ) j = nys-1
1630	IF ( myidy == id_stg_north ) j = nyn+1
1631	DO i = nxl, nxr
1632	DO k = nzb+1, nzt + 1
1633	!
1634	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1635	!-- Additional factors are added to improve the variance of v and w
1636	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1637	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1638
1639	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1640	a33(k) * fw_xz(k,i) ) * &
1641	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1642	ENDDO
1643	ENDDO
1644	ENDIF
1645
1646	!
1647	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1648	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1649	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1650	!-- else the boundary values won't be accessed.
1651	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1652	mc_factor_l = 0.0_wp
1653	mc_factor = 0.0_wp
1654
1655	IF ( myidy == id_stg_south ) j = nys
1656	IF ( myidy == id_stg_north ) j = nyn+1
1657
1658	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1659	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1660
1661	IF ( myidy == id_stg_south ) j = nys-1
1662	IF ( myidy == id_stg_north ) j = nyn+1
1663
1664	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1665	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1666	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1667	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1668
1669	#if defined( __parallel )
1670	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1671	#else
1672	mc_factor = mc_factor_l
1673	#endif
1674
1675	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1676
1677	IF ( myidy == id_stg_south ) j = nys
1678	IF ( myidy == id_stg_north ) j = nyn+1
1679
1680	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1681	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1682
1683
1684	IF ( myidy == id_stg_south ) j = nys-1
1685	IF ( myidy == id_stg_north ) j = nyn+1
1686
1687	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1688	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1689
1690	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1691	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1692	!
1693	!-- Add disturbances
1694	IF ( myidy == id_stg_south ) THEN
1695	DO i = nxl, nxr
1696	DO k = nzb+1, nzt
1697	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1698	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1699	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1700	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1701	v(k,-1,i) = v(k,0,i)
1702	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1703	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1704	ENDDO
1705	ENDDO
1706	ENDIF
1707	IF ( myidy == id_stg_north ) THEN
1708
1709	DO i = nxl, nxr
1710	DO k = nzb+1, nzt
1711	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1712	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1713	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1714	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1715	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1716	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1717	ENDDO
1718	ENDDO
1719	ENDIF
1720	ENDIF
1721	ENDIF
1722	!
1723	!-- Exchange ghost points.
1724	CALL exchange_horiz( u, nbgp )
1725	CALL exchange_horiz( v, nbgp )
1726	CALL exchange_horiz( w, nbgp )
1727	!
1728	!-- Finally, set time counter for calling STG to zero
1729	IF ( stg_call ) time_stg_call = 0.0_wp
1730	!
1731	!-- Set adjustment step to False to indicate that time correlation can be
1732	!-- switched-on again.
1733	adjustment_step = .FALSE.
1734
1735	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1736
1737	END SUBROUTINE stg_main
1738
1739	!--------------------------------------------------------------------------------------------------!
1740	! Description:
1741	! ------------
1742	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1743	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1744	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1745	!> array.
1746	!--------------------------------------------------------------------------------------------------!
1747	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1748
1749	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1750	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1751	INTEGER(iwp) :: j !< loop index in y-direction
1752	INTEGER(iwp) :: jj !< loop index in y-direction
1753	INTEGER(iwp) :: k !< loop index in z-direction
1754	INTEGER(iwp) :: kk !< loop index in z-direction
1755	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1756
1757	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1758	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1759
1760	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1761	REAL(wp) :: rand_av !< average of random number
1762	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1763
1764	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1765	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1766
1767	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1768	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1769
1770	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1771	!
1772	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1773	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1774	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1775	!-- and normalization of random numbers is done locally, while the result is later distributed to
1776	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1777	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1778	!-- correlation matrix.
1779	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1780	rand_it = 0.0_wp
1781
1782	rand_av = 0.0_wp
1783	rand_sigma_inv = 0.0_wp
1784	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1785	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1786	!
1787	!-- Compute and normalize random numbers.
1788	DO j = nys - mergp_y, nyn + mergp_y
1789	!
1790	!-- Put the random seeds at grid point j
1791	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1792	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1793	CALL random_number_parallel( random_dummy )
1794	rand_it(k,j) = random_dummy
1795	ENDDO
1796	!
1797	!-- Get the new random seeds from last call at grid point j
1798	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1799	ENDDO
1800	!
1801	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1802	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1803	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1804	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1805	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1806	rand_av = rand_av + rand_it(k,j)
1807	ENDDO
1808	ENDDO
1809
1810	#if defined( __parallel )
1811	!
1812	!-- Sum-up the local averages of the random numbers
1813	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1814	#endif
1815	rand_av = rand_av * nyz_inv
1816	!
1817	!-- Obtain zero mean
1818	rand_it= rand_it - rand_av
1819	!
1820	!-- Now, compute the variance
1821	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1822	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1823	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1824	ENDDO
1825	ENDDO
1826
1827	#if defined( __parallel )
1828	!
1829	!-- Sum-up the local quadratic averages of the random numbers
1830	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1831	#endif
1832	!
1833	!-- Compute standard deviation
1834	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1835	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1836	ELSE
1837	rand_sigma_inv = 1.0_wp
1838	ENDIF
1839	!
1840	!-- Normalize with standard deviation to obtain unit variance
1841	rand_it = rand_it * rand_sigma_inv
1842
1843	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1844	!
1845	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1846	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1847	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1848	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1849	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1850	!-- communication. In the second option, which performs better when the turbulent length scales
1851	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1852	!-- communication is necessary.
1853	IF ( compute_velocity_seeds_local ) THEN
1854
1855	f_n = 0.0_wp
1856	DO j = nys, nyn
1857	DO k = nzb, nzt+1
1858	DO jj = -n_y(k), n_y(k)
1859	DO kk = -n_z(k), n_z(k)
1860	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1861	ENDDO
1862	ENDDO
1863	ENDDO
1864	ENDDO
1865
1866	ELSE
1867
1868	f_n_l = 0.0_wp
1869	DO j = nys, nyn
1870	DO k = nzb_x_stg, nzt_x_stg+1
1871	DO jj = -n_y(k), n_y(k)
1872	DO kk = -n_z(k), n_z(k)
1873	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1874	ENDDO
1875	ENDDO
1876	ENDDO
1877	ENDDO
1878	!
1879	!-- Gather velocity seeds of full subdomain
1880	send_count = nzt_x_stg - nzb_x_stg + 1
1881	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1882
1883	#if defined( __parallel )
1884	!
1885	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1886	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1887	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1888	!
1889	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1890	!-- nesting for example).
1891	IF ( PRESENT( id_right ) ) THEN
1892	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1893	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1894	ENDIF
1895	#else
1896	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1897	!
1898	!-- Next line required to avoid compile errors because of unused dummy arguments
1899	IF ( id_left == 0 ) id_right = 0
1900	#endif
1901
1902	ENDIF
1903
1904	DEALLOCATE( rand_it )
1905
1906	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1907
1908	END SUBROUTINE stg_generate_seed_yz
1909
1910
1911	!--------------------------------------------------------------------------------------------------!
1912	! Description:
1913	! ------------
1914	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1915	!> f_n.
1916	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1917	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1918	!> full array.
1919	!--------------------------------------------------------------------------------------------------!
1920	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1921
1922	INTEGER(iwp) :: i !< loop index in x-direction
1923	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1924	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1925	INTEGER(iwp) :: ii !< loop index in x-direction
1926	INTEGER(iwp) :: k !< loop index in z-direction
1927	INTEGER(iwp) :: kk !< loop index in z-direction
1928	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1929
1930	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1931	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1932
1933	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1934	REAL(wp) :: rand_av !< average of random number
1935	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1936
1937	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1938	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1939
1940	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1941	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1942
1943	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1944
1945	!
1946	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1947	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1948	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1949	!-- and normalization of random numbers is done locally, while the result is later distributed to
1950	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1951	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1952	!-- correlation matrix.
1953	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1954	rand_it = 0.0_wp
1955
1956	rand_av = 0.0_wp
1957	rand_sigma_inv = 0.0_wp
1958	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1959	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1960	!
1961	!-- Compute and normalize random numbers.
1962	DO i = nxl - mergp_x, nxr + mergp_x
1963	!
1964	!-- Put the random seeds at grid point ii
1965	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1966	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1967	CALL random_number_parallel( random_dummy )
1968	rand_it(k,i) = random_dummy
1969	ENDDO
1970	!
1971	!-- Get the new random seeds from last call at grid point ii
1972	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1973	ENDDO
1974	!
1975	!-- For normalization to zero mean, sum-up the global random numers.
1976	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1977	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1978	!-- also occur on the inner subdomains.
1979	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1980	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1981	rand_av = rand_av + rand_it(k,i)
1982	ENDDO
1983	ENDDO
1984
1985	#if defined( __parallel )
1986	!
1987	!-- Sum-up the local averages of the random numbers
1988	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1989	#endif
1990	rand_av = rand_av * nxz_inv
1991	!
1992	!-- Obtain zero mean
1993	rand_it= rand_it - rand_av
1994	!
1995	!-- Now, compute the variance
1996	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1997	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1998	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1999	ENDDO
2000	ENDDO
2001
2002	#if defined( __parallel )
2003	!
2004	!-- Sum-up the local quadratic averages of the random numbers
2005	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2006	#endif
2007	!
2008	!-- Compute standard deviation
2009	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2010	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2011	ELSE
2012	rand_sigma_inv = 1.0_wp
2013	ENDIF
2014	!
2015	!-- Normalize with standard deviation to obtain unit variance
2016	rand_it = rand_it * rand_sigma_inv
2017
2018	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2019	!
2020	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2021	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2022	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2023	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2024	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2025	!-- In the second option, which performs better when the turbulent length scales are parametrized
2026	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2027	IF ( compute_velocity_seeds_local ) THEN
2028
2029	f_n = 0.0_wp
2030	DO i = nxl, nxr
2031	DO k = nzb, nzt+1
2032	DO ii = -n_x(k), n_x(k)
2033	DO kk = -n_z(k), n_z(k)
2034	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2035	ENDDO
2036	ENDDO
2037	ENDDO
2038	ENDDO
2039
2040	ELSE
2041
2042	f_n_l = 0.0_wp
2043	DO i = nxl, nxr
2044	DO k = nzb_y_stg, nzt_y_stg+1
2045	DO ii = -n_x(k), n_x(k)
2046	DO kk = -n_z(k), n_z(k)
2047	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2048	ENDDO
2049	ENDDO
2050	ENDDO
2051	ENDDO
2052	!
2053	!-- Gather velocity seeds of full subdomain
2054	send_count = nzt_y_stg - nzb_y_stg + 1
2055	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2056
2057	#if defined( __parallel )
2058	!
2059	!-- Gather the processed velocity seed on south boundary mpi ranks.
2060	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2061	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2062	!
2063	!-- Gather the processed velocity seed on north boundary mpi ranks.
2064	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2065	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2066	#else
2067	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2068	!
2069	!-- Next line required to avoid compile errors because of unused dummy arguments
2070	IF ( id_north == 0 ) id_south = 0
2071	#endif
2072
2073	ENDIF
2074
2075	DEALLOCATE( rand_it )
2076
2077	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2078
2079	END SUBROUTINE stg_generate_seed_xz
2080
2081	!--------------------------------------------------------------------------------------------------!
2082	! Description:
2083	! ------------
2084	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2085	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2086	!> which is applied in state-of-the-art dispserion modelling.
2087	!--------------------------------------------------------------------------------------------------!
2088	SUBROUTINE parametrize_turbulence
2089
2090	INTEGER(iwp) :: k !< loop index in z-direction
2091
2092	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2093	REAL(wp) :: d_zi !< inverse boundary-layer depth
2094	REAL(wp) :: length_scale_lon !< length scale in flow direction
2095	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2096	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2097	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2098	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2099	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2100	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2101	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2102	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2103	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2104	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2105	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2106	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2107	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2108	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2109	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2110	REAL(wp) :: zzi !< ratio of z/zi
2111
2112	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2113	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2114	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2115
2116	!
2117	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2118	!-- criterion according to Heinze et al. (2017).
2119	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2120	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2121	k_zi = MIN( k_zi, nzt )
2122	!
2123	!-- Calculate angle between flow direction and x-axis.
2124	DO k = nzb+1, nzt + 1
2125	IF ( u_init(k) /= 0.0_wp ) THEN
2126	phi(k) = ATAN( v_init(k) / u_init(k) )
2127	ELSE
2128	phi(k) = 0.5 * pi
2129	ENDIF
2130	!
2131	!-- Pre-calculate sine and cosine.
2132	cos_phi(k) = COS( phi(k) )
2133	sin_phi(k) = SIN( phi(k) )
2134	ENDDO
2135	!
2136	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2137	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2138	!-- coincide with the grid axis. Hence, components are rotated after computation.
2139	d_zi = 1.0_wp / zi_ribulk
2140	DO k = nzb+1, k_zi
2141
2142	corr_term_uh = MERGE( 0.35_wp * ABS( &
2143	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2144	)**( 2.0_wp / 3.0_wp ), &
2145	0.0_wp, &
2146	scale_l < -5.0_wp )
2147	!
2148	!-- Determine normalized height coordinate
2149	zzi = zu(k) * d_zi
2150	!
2151	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2152	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2153	!-- variances cannot become negative, take the absolute values.
2154	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2155	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2156
2157	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2158	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2159	!
2160	!-- w'w'
2161	r33(k) = scale_wm*2 ( &
2162	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2163	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2164	)
2165	!
2166	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2167	!-- these are projected along the x- and y-direction. Note, it is assumed that
2168	!-- the flux within the boundary points opposite to the vertical gradient.
2169	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2170	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2171
2172	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2173	- ( u_init(k+1) - u_init(k-1) ) )
2174	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2175	- ( v_init(k+1) - v_init(k-1) ) )
2176	!
2177	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2178	!-- for the vertical transport.
2179	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2180	!
2181	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2182	!-- limited to the adjustment time scales.
2183	tu(k) = MIN( dt_stg_adjust, &
2184	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2185
2186	tv(k) = tu(k)
2187	tw(k) = tu(k)
2188
2189	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2190	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2191	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2192	!
2193	!-- Assume isotropic turbulence length scales
2194	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2195	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2196	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2197	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2198	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2199	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2200	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2201	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2202	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2203
2204	ENDDO
2205	!
2206	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2207	!-- reduced to zero by a blending function.
2208	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2209	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2210	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2211
2212	time_scale_zi = tu(k_zi)
2213	r11_zi = r11(k_zi)
2214	r22_zi = r22(k_zi)
2215	r33_zi = r33(k_zi)
2216	r31_zi = r31(k_zi)
2217	r32_zi = r32(k_zi)
2218
2219	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2220
2221	DO k = k_zi+1, nzt+1
2222	!
2223	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2224	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2225	!
2226	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2227	!-- the mergpe-function can crash if scale_l is zero.
2228	r11(k) = r11_zi * blend
2229	r22(k) = r22_zi * blend
2230	r33(k) = r33_zi * blend
2231	r31(k) = r31_zi * blend
2232	r32(k) = r32_zi * blend
2233	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2234
2235	!
2236	!-- Compute turbulent time scales according to Brost et al. (1982).
2237	!-- Note, time scales are limited to the adjustment time scales.
2238	tu(k) = time_scale_zi * blend
2239	tv(k) = time_scale_zi * blend
2240	tw(k) = time_scale_zi * blend
2241
2242	length_scale_lon = length_scale_lon_zi * blend
2243	length_scale_lat = length_scale_lat_zi * blend
2244	length_scale_vert = length_scale_vert_zi * blend
2245	!
2246	!-- Assume isotropic turbulence length scales
2247	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2248	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2249	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2250	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2251	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2252	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2253	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2254	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2255	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2256	ENDDO
2257	!
2258	!-- Set bottom boundary condition for reynolds stresses
2259	r11(nzb) = r11(nzb+1)
2260	r22(nzb) = r22(nzb+1)
2261	r33(nzb) = r33(nzb+1)
2262
2263	r21(nzb) = r11(nzb+1)
2264	r31(nzb) = r31(nzb+1)
2265	r32(nzb) = r32(nzb+1)
2266
2267	!
2268	!-- Set bottom boundary condition for the length and time scales
2269	nux(nzb) = nux(nzb+1)
2270	nuy(nzb) = nuy(nzb+1)
2271	nuz(nzb) = nuz(nzb+1)
2272	nvx(nzb) = nvx(nzb+1)
2273	nvy(nzb) = nvy(nzb+1)
2274	nvz(nzb) = nvz(nzb+1)
2275	nwx(nzb) = nwx(nzb+1)
2276	nwy(nzb) = nwy(nzb+1)
2277	nwz(nzb) = nwz(nzb+1)
2278
2279	tu(nzb) = tu(nzb+1)
2280	tv(nzb) = tv(nzb+1)
2281	tw(nzb) = tw(nzb+1)
2282
2283	adjustment_step = .TRUE.
2284
2285	END SUBROUTINE parametrize_turbulence
2286
2287	!--------------------------------------------------------------------------------------------------!
2288	! Description:
2289	! ------------
2290	!> Calculate the coefficient matrix from the Lund rotation.
2291	!--------------------------------------------------------------------------------------------------!
2292	SUBROUTINE calc_coeff_matrix
2293
2294	INTEGER(iwp) :: k !< loop index in z-direction
2295
2296	!
2297	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2298	DO k = nzb+1, nzt+1
2299	IF ( r11(k) > 10E-6_wp ) THEN
2300	a11(k) = SQRT( r11(k) )
2301	a21(k) = r21(k) / a11(k)
2302	a31(k) = r31(k) / a11(k)
2303	ELSE
2304	a11(k) = 10E-8_wp
2305	a21(k) = 10E-8_wp
2306	a31(k) = 10E-8_wp
2307	ENDIF
2308	ENDDO
2309	DO k = nzb+1, nzt+1
2310	a22(k) = r22(k) - a21(k)**2
2311	IF ( a22(k) > 10E-6_wp ) THEN
2312	a22(k) = SQRT( a22(k) )
2313	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2314	ELSE
2315	a22(k) = 10E-8_wp
2316	a32(k) = 10E-8_wp
2317	ENDIF
2318	ENDDO
2319	DO k = nzb+1, nzt+1
2320	a33(k) = r33(k) - a31(k)2 - a32(k)2
2321	IF ( a33(k) > 10E-6_wp ) THEN
2322	a33(k) = SQRT( a33(k) )
2323	ELSE
2324	a33(k) = 10E-8_wp
2325	ENDIF
2326	ENDDO
2327	!
2328	!-- Set bottom boundary condition
2329	a11(nzb) = a11(nzb+1)
2330	a22(nzb) = a22(nzb+1)
2331	a21(nzb) = a21(nzb+1)
2332	a33(nzb) = a33(nzb+1)
2333	a31(nzb) = a31(nzb+1)
2334	a32(nzb) = a32(nzb+1)
2335
2336	END SUBROUTINE calc_coeff_matrix
2337
2338	!--------------------------------------------------------------------------------------------------!
2339	! Description:
2340	! ------------
2341	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2342	!> turbulence at the lateral boundaries.
2343	!--------------------------------------------------------------------------------------------------!
2344	SUBROUTINE stg_adjust
2345
2346	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2347	!
2348	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2349	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2350	!-- nevertheless, the boundary-layer depth need to determined first.
2351	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2352	CALL nesting_offl_calc_zi
2353	!
2354	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2355	CALL calc_scaling_variables
2356	!
2357	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2358	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2359	!-- velocity and velocity scale.
2360	CALL parametrize_turbulence
2361	!
2362	!-- Calculate coefficient matrix from Reynolds stress tensor
2363	!-- (Lund rotation)
2364	CALL calc_coeff_matrix
2365	!
2366	!-- Setup filter functions according to updated length scales.
2367	CALL stg_setup_filter_function
2368	!
2369	!-- Reset time counter for controlling next adjustment to zero
2370	time_stg_adjust = 0.0_wp
2371
2372	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2373
2374	END SUBROUTINE stg_adjust
2375
2376
2377	!--------------------------------------------------------------------------------------------------!
2378	! Description:
2379	! ------------
2380	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2381	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2382	!> scale, and Obukhov length.
2383	!--------------------------------------------------------------------------------------------------!
2384	SUBROUTINE calc_scaling_variables
2385
2386	INTEGER(iwp) :: i !< loop index in x-direction
2387	INTEGER(iwp) :: j !< loop index in y-direction
2388	INTEGER(iwp) :: k !< loop index in z-direction
2389	INTEGER(iwp) :: m !< surface element index
2390
2391	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2392	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2393	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2394	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2395	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2396	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2397	REAL(wp) :: w_convective !< convective velocity scale
2398
2399	!
2400	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2401	!-- model domain.
2402	pt_surf_mean_l = 0.0_wp
2403	shf_mean_l = 0.0_wp
2404	scale_l_l = 0.0_wp
2405	friction_vel_l = 0.0_wp
2406	DO m = 1, surf_def_h(0)%ns
2407	i = surf_def_h(0)%i(m)
2408	j = surf_def_h(0)%j(m)
2409	k = surf_def_h(0)%k(m)
2410	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2411	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2412	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2413	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2414	ENDDO
2415	DO m = 1, surf_lsm_h(0)%ns
2416	i = surf_lsm_h(0)%i(m)
2417	j = surf_lsm_h(0)%j(m)
2418	k = surf_lsm_h(0)%k(m)
2419	friction_vel_l = friction_vel_l + surf_lsm_h(0)%us(m)
2420	shf_mean_l = shf_mean_l + surf_lsm_h(0)%shf(m) * drho_air(k)
2421	scale_l_l = scale_l_l + surf_lsm_h(0)%ol(m)
2422	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2423	ENDDO
2424	DO m = 1, surf_usm_h(0)%ns
2425	i = surf_usm_h(0)%i(m)
2426	j = surf_usm_h(0)%j(m)
2427	k = surf_usm_h(0)%k(m)
2428	friction_vel_l = friction_vel_l + surf_usm_h(0)%us(m)
2429	shf_mean_l = shf_mean_l + surf_usm_h(0)%shf(m) * drho_air(k)
2430	scale_l_l = scale_l_l + surf_usm_h(0)%ol(m)
2431	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2432	ENDDO
2433
2434	#if defined( __parallel )
2435	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2436	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2437	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2438	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2439	#else
2440	scale_us = friction_vel_l
2441	shf_mean = shf_mean_l
2442	scale_l = scale_l_l
2443	pt_surf_mean = pt_surf_mean_l
2444	#endif
2445
2446	scale_us = scale_us * d_nxy
2447	shf_mean = shf_mean * d_nxy
2448	scale_l = scale_l * d_nxy
2449	pt_surf_mean = pt_surf_mean * d_nxy
2450	!
2451	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2452	!-- convective velocity scale to zero.
2453	IF ( shf_mean > 0.0_wp ) THEN
2454	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2455	ELSE
2456	w_convective = 0.0_wp
2457	ENDIF
2458	!
2459	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2460	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2461	!-- value of friction velocity for the reynolds-stress parametrization.
2462	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2463	!
2464	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2465	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2466	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2467
2468	END SUBROUTINE calc_scaling_variables
2469
2470	END MODULE synthetic_turbulence_generator_mod

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