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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4843

Last change on this file since 4843 was 4843, checked in by raasch, 3 years ago
local namelist parameter added to switch off the module although the respective module namelist appears in the namelist file, further copyright updates
Property svn:keywords set to `Id`
File size: 113.6 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 4843 2021-01-15 15:22:11Z raasch $
27	! local namelist parameter added to switch off the module although the respective module namelist
28	! appears in the namelist file
29	!
30	! 4842 2021-01-14 10:42:28Z raasch
31	! reading of namelist file and actions in case of namelist errors revised so that statement labels
32	! and goto statements are not required any more
33	!
34	! 4828 2021-01-05 11:21:41Z Giersch
35	! Implementation of downward facing USM and LSM surfaces
36	!
37	! 4647 2020-08-24 16:36:18Z suehring
38	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
39	! By default, the random-seed computation is now distributed among several cores. Especially for
40	! large length scales this is significantly faster.
41	!
42	! 4640 2020-08-11 16:28:32Z suehring
43	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
44	! Obukhov length (term is not valid for near neutral conditions)
45	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
46	! the vertical transport of horizontal momentum
47	!
48	! 4629 2020-07-29 09:37:56Z raasch
49	! support for MPI Fortran77 interface (mpif.h) removed
50	!
51	! 4603 2020-07-14 16:08:30Z suehring
52	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
53	! initialized properly
54	!
55	! 4566 2020-06-16 10:11:51Z suehring
56	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
57	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
58	! - change default value of time interval to adjust turbulence parametrization
59	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
60	!
61	! 4562 2020-06-12 08:38:47Z raasch
62	! Parts of r4559 re-formatted
63	!
64	! 4559 2020-06-11 08:51:48Z raasch
65	! File re-formatted to follow the PALM coding standard
66	!
67	! 4535 2020-05-15 12:07:23Z raasch
68	! Bugfix for restart data format query
69	!
70	! 4495 2020-04-13 20:11:20Z raasch
71	! Restart data handling with MPI-IO added
72	!
73	! 4481 2020-03-31 18:55:54Z maronga
74	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
75	!
76	! 4442 2020-03-04 19:21:13Z suehring
77	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
78	! (was accidantly changed).
79	!
80	! 4441 2020-03-04 19:20:35Z suehring
81	! Correct misplaced preprocessor directive
82	!
83	! 4438 2020-03-03 20:49:28Z suehring
84	! Performance optimizations in velocity-seed calculation:
85	! - Random number array is only defined and computed locally (except for normalization to zero mean
86	! and unit variance)
87	! - Parallel random number generator is applied independent on the 2D random numbers in other
88	! routines
89	! - Option to decide wheter velocity seeds are computed locally without any further communication
90	! or are computed by all processes along the communicator
91	!
92	! 4346 2019-12-18 11:55:56Z motisi
93	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
94	! information used in wall_flags_static_0
95	!
96	! 4335 2019-12-12 16:39:05Z suehring
97	! Commentation of last commit
98	!
99	! 4332 2019-12-10 19:44:12Z suehring
100	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
101	! Further, minor bugfix in initial velocity seed calculation.
102	!
103	! 4329 2019-12-10 15:46:36Z motisi
104	! Renamed wall_flags_0 to wall_flags_static_0
105	!
106	! 4309 2019-11-26 18:49:59Z suehring
107	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
108	! the parallel random number generator. Random numbers are now only computed and normalized locally,
109	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
110	! array.
111	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
112	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
113	!
114	! 4182 2019-08-22 15:20:23Z scharf
115	! Corrected "Former revisions" section
116	!
117	! 4148 2019-08-08 11:26:00Z suehring
118	! Remove unused variable
119	!
120	! 4144 2019-08-06 09:11:47Z raasch
121	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
122	!
123	! 4071 2019-07-03 20:02:00Z suehring
124	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
125	! file.
126	!
127	! 4022 2019-06-12 11:52:39Z suehring
128	! Several bugfixes and improvements
129	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
130	! instabilities in case the mean volume flow is close to zero)
131	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
132	! numerically unstable
133	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
134	! case dt_stg_call /= dt_3d
135	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
136	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
137	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
138	!
139	! 3987 2019-05-22 09:52:13Z kanani
140	! Introduce alternative switch for debug output during timestepping
141	!
142	! 3938 2019-04-29 16:06:25Z suehring
143	! Remove unused variables
144	!
145	! 3937 2019-04-29 15:09:07Z suehring
146	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
147	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
148	! synthetic turbulence parametrization.
149	!
150	! 3909 2019-04-17 09:13:25Z suehring
151	! Minor bugfix for last commit
152	!
153	! 3900 2019-04-16 15:17:43Z suehring
154	! Missing re-calculation of perturbation seeds in case of restarts
155	!
156	! 3891 2019-04-12 17:52:01Z suehring
157	! Bugfix in initialization in case of restart runs.
158	!
159	! 3885 2019-04-11 11:29:34Z kanani
160	! Changes related to global restructuring of location messages and introduction of additional debug
161	! messages
162	!
163	!
164	! Removed unused variables
165	!
166	! 3719 2019-02-06 13:10:18Z kanani
167	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
168	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
169	! for better overview.
170	!
171	! 2259 2017-06-08 09:09:11Z gronemeier
172	! Initial revision
173	!
174	! Authors:
175	! --------
176	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
177	!
178	!
179	! Description:
180	! ------------
181	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
182	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
183	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
184	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
185	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
186	!> parametrized within the boundary layer.
187	!>
188	!> @todo Enable cyclic_fill
189	!> Implement turbulence generation for e and pt
190	!> @note <Enter notes on the module>
191	!> @bug Height information from input file is not used. Profiles from input must match with current
192	!> PALM grid.
193	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
194	!--------------------------------------------------------------------------------------------------!
195	MODULE synthetic_turbulence_generator_mod
196
197
198	USE arrays_3d, &
199	ONLY: dzw, &
200	ddzw, &
201	drho_air, &
202	mean_inflow_profiles, &
203	pt, &
204	pt_init, &
205	q, &
206	q_init, &
207	u, &
208	u_init, &
209	v, &
210	v_init, &
211	w, &
212	zu, &
213	zw
214
215	USE basic_constants_and_equations_mod, &
216	ONLY: g, &
217	kappa, &
218	pi
219
220	USE control_parameters, &
221	ONLY: bc_lr, &
222	bc_ns, &
223	child_domain, &
224	coupling_char, &
225	debug_output_timestep, &
226	dt_3d, &
227	e_init, &
228	humidity, &
229	initializing_actions, &
230	intermediate_timestep_count, &
231	intermediate_timestep_count_max, &
232	length, &
233	message_string, &
234	nesting_offline, &
235	neutral, &
236	num_mean_inflow_profiles, &
237	random_generator, &
238	rans_mode, &
239	restart_data_format_output, &
240	restart_string, &
241	syn_turb_gen, &
242	time_since_reference_point, &
243	turbulent_inflow
244
245	USE cpulog, &
246	ONLY: cpu_log, &
247	log_point_s
248
249	USE grid_variables, &
250	ONLY: ddx, &
251	ddy, &
252	dx, &
253	dy
254
255	USE indices, &
256	ONLY: nbgp, &
257	nz, &
258	nzb, &
259	nzt, &
260	nx, &
261	nxl, &
262	nxlu, &
263	nxr, &
264	ny, &
265	nys, &
266	nysv, &
267	nyn, &
268	wall_flags_total_0
269
270	USE kinds
271
272	#if defined( __parallel )
273	USE MPI
274	#endif
275
276	USE nesting_offl_mod, &
277	ONLY: nesting_offl_calc_zi, &
278	zi_ribulk
279
280	USE pegrid, &
281	ONLY: comm1dx, &
282	comm1dy, &
283	comm2d, &
284	ierr, &
285	myidx, &
286	myidy, &
287	pdims
288
289	USE pmc_interface, &
290	ONLY : rans_mode_parent
291
292	USE random_generator_parallel, &
293	ONLY: init_parallel_random_generator, &
294	random_dummy, &
295	random_number_parallel, &
296	random_seed_parallel
297
298	USE restart_data_mpi_io_mod, &
299	ONLY: rrd_mpi_io, &
300	wrd_mpi_io
301
302	USE transpose_indices, &
303	ONLY: nzb_x, &
304	nzt_x
305
306	USE surface_mod, &
307	ONLY: surf_def_h, &
308	surf_lsm_h, &
309	surf_usm_h
310
311	IMPLICIT NONE
312
313	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
314	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
315	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
316	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
317	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
318	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
319	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
320	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
321	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
322	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
323	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
324	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
325	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
326	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
327	#if defined( __parallel )
328	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
329	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
330	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
331	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
332	#endif
333
334	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
335	!< required for bias correction of imposed perturbations
336	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
337	!< required for bias correction of imposed perturbations
338
339	#if defined( __parallel )
340	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
341	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
342	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
343	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
344	#endif
345	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
346	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
347	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
348	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
349	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
350	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
351	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
352	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
353	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
354
355	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
356	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
357	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
358	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
359
360
361	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
362	!< no time correlation to the timestep before should be considered
363	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
364	!< or if computation is distributed over several processes
365	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
366	!< (.FALSE.) or if it parametrized
367	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
368	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
369
370
371	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
372	!< scales above the boundary layer
373	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
374	!< one length scale above ABL top
375	REAL(wp) :: d_l !< blend_coeff/length_scale
376	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
377	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
378	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
379	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
380	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
381	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
382	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
383	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
384
385	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
386
387
388	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
389	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
390	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
391	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
392	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
393	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
394
395	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
396	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
397	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
398	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
399	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
400	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
401	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
402	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
403	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
404
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
418	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
419	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
420	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
421	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
422	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
423	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
424	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
425	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
426
427	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
428	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
429
430	!
431	!-- PALM interfaces:
432	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
433	INTERFACE stg_adjust
434	MODULE PROCEDURE stg_adjust
435	END INTERFACE stg_adjust
436	!
437	!-- Input parameter checks to be done in check_parameters
438	INTERFACE stg_check_parameters
439	MODULE PROCEDURE stg_check_parameters
440	END INTERFACE stg_check_parameters
441
442	!
443	!-- Calculate filter functions
444	INTERFACE stg_filter_func
445	MODULE PROCEDURE stg_filter_func
446	END INTERFACE stg_filter_func
447
448	!
449	!-- Generate velocity seeds at south and north domain boundary
450	INTERFACE stg_generate_seed_xz
451	MODULE PROCEDURE stg_generate_seed_xz
452	END INTERFACE stg_generate_seed_xz
453	!
454	!-- Generate velocity seeds at left and/or right domain boundary
455	INTERFACE stg_generate_seed_yz
456	MODULE PROCEDURE stg_generate_seed_yz
457	END INTERFACE stg_generate_seed_yz
458
459	!
460	!-- Output of information to the header file
461	INTERFACE stg_header
462	MODULE PROCEDURE stg_header
463	END INTERFACE stg_header
464
465	!
466	!-- Initialization actions
467	INTERFACE stg_init
468	MODULE PROCEDURE stg_init
469	END INTERFACE stg_init
470
471	!
472	!-- Main procedure of synth. turb. gen.
473	INTERFACE stg_main
474	MODULE PROCEDURE stg_main
475	END INTERFACE stg_main
476
477	!
478	!-- Reading of NAMELIST parameters
479	INTERFACE stg_parin
480	MODULE PROCEDURE stg_parin
481	END INTERFACE stg_parin
482
483	!
484	!-- Reading of parameters for restart runs
485	INTERFACE stg_rrd_global
486	MODULE PROCEDURE stg_rrd_global_ftn
487	MODULE PROCEDURE stg_rrd_global_mpi
488	END INTERFACE stg_rrd_global
489
490	!
491	!-- Writing of binary output for restart runs
492	INTERFACE stg_wrd_global
493	MODULE PROCEDURE stg_wrd_global
494	END INTERFACE stg_wrd_global
495
496	SAVE
497
498	PRIVATE
499
500	!
501	!-- Public interfaces
502	PUBLIC stg_adjust, &
503	stg_check_parameters, &
504	stg_header, &
505	stg_init, &
506	stg_main, &
507	stg_parin, &
508	stg_rrd_global, &
509	stg_wrd_global
510
511	!
512	!-- Public variables
513	PUBLIC dt_stg_call, &
514	dt_stg_adjust, &
515	id_stg_left, &
516	id_stg_north, &
517	id_stg_right, &
518	id_stg_south, &
519	parametrize_inflow_turbulence, &
520	time_stg_adjust, &
521	time_stg_call, &
522	use_syn_turb_gen
523
524
525	CONTAINS
526
527
528	!--------------------------------------------------------------------------------------------------!
529	! Description:
530	! ------------
531	!> Check parameters routine for synthetic turbulence generator
532	!--------------------------------------------------------------------------------------------------!
533	SUBROUTINE stg_check_parameters
534
535	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
536	nesting_offline ) THEN
537	message_string = 'Synthetic turbulence generator is required ' // &
538	'if offline nesting is applied and PALM operates in LES mode.'
539	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
540	ENDIF
541
542	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
543	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
544	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
545	'and parent operates in RANS-mode but current child in LES mode.'
546	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
547	ENDIF
548
549	IF ( use_syn_turb_gen ) THEN
550
551	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
552	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
553	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
554
555	ENDIF
556
557	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
558	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
559	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
560
561	ENDIF
562
563	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
564
565	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
566	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
567	message_string = 'Using synthetic turbulence generator requires ' // &
568	'%initializing_actions = "set_constant_profiles" or ' // &
569	' "read_restart_data", if not offline nesting is applied.'
570	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
571	ENDIF
572
573	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
574	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
575	' "dirichlet/radiation", if not offline nesting is applied.'
576	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
577	ENDIF
578	IF ( bc_ns /= 'cyclic' ) THEN
579	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
580	' "cyclic", if not offline nesting is applied.'
581	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
582	ENDIF
583
584	ENDIF
585
586	IF ( turbulent_inflow ) THEN
587	message_string = 'Using synthetic turbulence generator in combination ' // &
588	'&with turbulent_inflow = .T. is not allowed'
589	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
590	ENDIF
591	!
592	!-- Synthetic turbulence generator requires the parallel random generator
593	IF ( random_generator /= 'random-parallel' ) THEN
594	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
595	'random-parallel.'
596	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
597	ENDIF
598
599	ENDIF
600
601	END SUBROUTINE stg_check_parameters
602
603
604	!--------------------------------------------------------------------------------------------------!
605	! Description:
606	! ------------
607	!> Header output for synthetic turbulence generator
608	!--------------------------------------------------------------------------------------------------!
609	SUBROUTINE stg_header ( io )
610
611	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
612
613	!
614	!-- Write synthetic turbulence generator Header
615	WRITE( io, 1 )
616	IF ( use_syn_turb_gen ) THEN
617	WRITE( io, 2 )
618	ELSE
619	WRITE( io, 3 )
620	ENDIF
621
622	IF ( parametrize_inflow_turbulence ) THEN
623	WRITE( io, 4 ) dt_stg_adjust
624	ELSE
625	WRITE( io, 5 )
626	ENDIF
627
628	1 FORMAT (//' Synthetic turbulence generator information:'/ &
629	' ------------------------------------------'/)
630	2 FORMAT (' synthetic turbulence generator is switched on')
631	3 FORMAT (' synthetic turbulence generator is switched off')
632	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
633	5 FORMAT (' imposed turbulence is read from file' )
634
635	END SUBROUTINE stg_header
636
637
638	!--------------------------------------------------------------------------------------------------!
639	! Description:
640	! ------------
641	!> Initialization of the synthetic turbulence generator
642	!--------------------------------------------------------------------------------------------------!
643	SUBROUTINE stg_init
644
645	#if defined( __parallel )
646	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
647	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
648	#endif
649
650	INTEGER(iwp) :: i !> grid index in x-direction
651	INTEGER(iwp) :: j !> loop index
652	INTEGER(iwp) :: k !< index
653	#if defined( __parallel )
654	INTEGER(iwp) :: newtype !< dummy MPI type
655	INTEGER(iwp) :: realsize !< size of REAL variables
656	#endif
657
658	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
659	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
660
661
662	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
663
664	!
665	!-- Dummy variables used for reading profiles
666	REAL(wp) :: d1 !< u profile
667	REAL(wp) :: d2 !< v profile
668	REAL(wp) :: d3 !< w profile
669	REAL(wp) :: d5 !< e profile
670	REAL(wp) :: luy !< length scale for u in y direction
671	REAL(wp) :: luz !< length scale for u in z direction
672	REAL(wp) :: lvy !< length scale for v in y direction
673	REAL(wp) :: lvz !< length scale for v in z direction
674	REAL(wp) :: lwy !< length scale for w in y direction
675	REAL(wp) :: lwz !< length scale for w in z direction
676	#if defined( __parallel )
677	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
678	#endif
679	REAL(wp) :: zz !< height
680
681
682	#if defined( __parallel )
683	CALL MPI_BARRIER( comm2d, ierr )
684	#endif
685	!
686	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
687	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
688	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
689	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
690	!-- communication).
691	IF ( .NOT. compute_velocity_seeds_local ) THEN
692	#if defined( __parallel )
693	!
694	!-- Determine processor decomposition of z-axis along x- and y-direction
695	nnz = nz / pdims(1)
696	nzb_x_stg = 1 + myidx * INT( nnz )
697	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
698
699	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
700	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
701
702	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
703	.AND. .NOT. rans_mode ) ) THEN
704	nnz = nz / pdims(2)
705	nzb_y_stg = 1 + myidy * INT( nnz )
706	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
707
708	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
709	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
710	ENDIF
711
712	!
713	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
714	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
715	extent = 1 * realsize
716	!
717	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
718	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
719	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
720	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
721	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
722	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
723	CALL MPI_TYPE_FREE( newtype, ierr )
724
725	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
726	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
727	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
728	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
729	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
730	CALL MPI_TYPE_FREE( newtype, ierr )
731
732	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
733	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
734
735	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
736	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
737
738	DO j = 1, pdims(1)
739	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
740	ENDDO
741	!
742	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
743	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
744	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
745	.AND. .NOT. rans_mode ) ) THEN
746	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
747	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
748	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
749	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
750	CALL MPI_TYPE_FREE( newtype, ierr )
751
752	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
753	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
754	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
755	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
756	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
757	CALL MPI_TYPE_FREE( newtype, ierr )
758
759	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
760	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
761
762	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
763	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
764
765	DO j = 1, pdims(2)
766	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
767	ENDDO
768
769	ENDIF
770	#endif
771	ENDIF
772	!
773	!-- Allocate required arrays.
774	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
775	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
776	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
777	!-- and initialized appropriately.
778	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
779	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
780	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
781	mean_inflow_profiles = 0.0_wp
782	mean_inflow_profiles(:,1) = u_init
783	mean_inflow_profiles(:,2) = v_init
784	!
785	!-- Even though potential temperature and humidity are not perturbed, they need to be
786	!-- initialized appropriately.
787	IF ( .NOT. neutral ) &
788	mean_inflow_profiles(:,4) = pt_init
789	IF ( humidity ) &
790	mean_inflow_profiles(:,6) = q_init
791	ENDIF
792	ENDIF
793	!
794	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
795	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
796	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
797	u_init = mean_inflow_profiles(:,1)
798	v_init = mean_inflow_profiles(:,2)
799	e_init = MAXVAL( mean_inflow_profiles(:,5) )
800	ENDIF
801
802	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
803	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
804	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
805	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
806	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
807	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
808	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
809	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
810
811	r11 = 0.0_wp
812	r21 = 0.0_wp
813	r22 = 0.0_wp
814	r31 = 0.0_wp
815	r32 = 0.0_wp
816	r33 = 0.0_wp
817	tu = 0.0_wp
818	tv = 0.0_wp
819	tw = 0.0_wp
820
821	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
822	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
823	dist_xz = 0.0_wp
824	dist_yz = 0.0_wp
825	!
826	!-- Read inflow profile
827	!-- Height levels of profiles in input profile is as follows:
828	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
829	!-- WARNING: zz is not used at the moment
830	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
831
832	IF ( file_stg_exist ) THEN
833
834	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
835	!
836	!-- Skip header
837	READ( 90, * )
838
839	DO k = nzb, nzt
840	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
841	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
842
843	!
844	!-- Convert length scales from meter to number of grid points.
845	IF ( k /= nzb ) THEN
846	nuz(k) = INT( luz * ddzw(k) )
847	nvz(k) = INT( lvz * ddzw(k) )
848	nwz(k) = INT( lwz * ddzw(k) )
849	ELSE
850	nuz(k) = INT( luz * ddzw(k+1) )
851	nvz(k) = INT( lvz * ddzw(k+1) )
852	nwz(k) = INT( lwz * ddzw(k+1) )
853	ENDIF
854
855	nuy(k) = INT( luy * ddy )
856	nvy(k) = INT( lvy * ddy )
857	nwy(k) = INT( lwy * ddy )
858	!
859	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
860	!-- y-direction.
861	nwx(k) = nwy(k)
862	nvx(k) = nvy(k)
863	nux(k) = nuy(k)
864	!
865	!-- Save Mean inflow profiles
866	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
867	mean_inflow_profiles(k,1) = d1
868	mean_inflow_profiles(k,2) = d2
869	! mean_inflow_profiles(k,4) = d4
870	mean_inflow_profiles(k,5) = d5
871	ENDIF
872	ENDDO
873	!
874	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
875	!-- simply overwritten.
876	nwx(nzb) = nwy(nzb+1)
877	nvx(nzb) = nvy(nzb+1)
878	nux(nzb) = nuy(nzb+1)
879	nuy(nzb) = nuy(nzb+1)
880	nuz(nzb) = nuz(nzb+1)
881	nvy(nzb) = nvy(nzb+1)
882	nvz(nzb) = nvz(nzb+1)
883	nwy(nzb) = nwy(nzb+1)
884	nwz(nzb) = nwz(nzb+1)
885
886	nwx(nzt+1) = nwy(nzt)
887	nvx(nzt+1) = nvy(nzt)
888	nux(nzt+1) = nuy(nzt)
889	nuy(nzt+1) = nuy(nzt)
890	nuz(nzt+1) = nuz(nzt)
891	nvy(nzt+1) = nvy(nzt)
892	nvz(nzt+1) = nvz(nzt)
893	nwy(nzt+1) = nwy(nzt)
894	nwz(nzt+1) = nwz(nzt)
895
896	CLOSE( 90 )
897	!
898	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
899	CALL calc_coeff_matrix
900	!
901	!-- No information about turbulence and its length scales are available. Instead, parametrize
902	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
903	!-- parametrized, which is done later when energy-balance models are already initialized. This is
904	!-- because the STG needs information about surface properties such as roughness to build
905	!-- 'realistic' turbulence profiles.
906	ELSE
907	!
908	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
909	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
910	!
911	!-- Set flag indicating that turbulence is parametrized
912	parametrize_inflow_turbulence = .TRUE.
913	!
914	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
915	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
916	!-- nevertheless, the boundary-layer depth needs to be determined first.
917	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
918	CALL nesting_offl_calc_zi
919	!
920	!-- Determine boundary-layer depth, which is used to initialize lenght scales
921	CALL calc_scaling_variables
922	!
923	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
924	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
925	!-- friction velocity and velocity scale.
926	CALL parametrize_turbulence
927	!
928	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
929	CALL calc_coeff_matrix
930
931	ENDIF
932	!
933	!-- Initial filter functions
934	CALL stg_setup_filter_function
935	!
936	!-- Allocate velocity seeds for turbulence at xz-layer
937	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
938	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
939	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
940
941	!
942	!-- Allocate velocity seeds for turbulence at yz-layer
943	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
944	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
945	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
946
947	fu_xz = 0.0_wp
948	fuo_xz = 0.0_wp
949	fv_xz = 0.0_wp
950	fvo_xz = 0.0_wp
951	fw_xz = 0.0_wp
952	fwo_xz = 0.0_wp
953
954	fu_yz = 0.0_wp
955	fuo_yz = 0.0_wp
956	fv_yz = 0.0_wp
957	fvo_yz = 0.0_wp
958	fw_yz = 0.0_wp
959	fwo_yz = 0.0_wp
960
961	#if defined( __parallel )
962	CALL MPI_BARRIER( comm2d, ierr )
963	#endif
964
965	!
966	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
967	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
968	!-- This is mostly for k=nzt+1.
969	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
970	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
971
972	IF ( myidx == id_stg_left ) i = -1
973	IF ( myidx == id_stg_right ) i = nxr+1
974
975	DO j = nys, nyn
976	DO k = nzb, nzt+1
977	IF ( a11(k) > 10E-8_wp ) THEN
978	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
979	ELSE
980	fu_yz(k,j) = 10E-8_wp
981	ENDIF
982
983	IF ( a22(k) > 10E-8_wp ) THEN
984	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
985	ELSE
986	fv_yz(k,j) = 10E-8_wp
987	ENDIF
988
989	IF ( a33(k) > 10E-8_wp ) THEN
990	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
991	ELSE
992	fw_yz(k,j) = 10E-8_wp
993	ENDIF
994	ENDDO
995	ENDDO
996	ENDIF
997
998	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
999
1000	IF ( myidy == id_stg_south ) j = -1
1001	IF ( myidy == id_stg_north ) j = nyn+1
1002
1003	DO i = nxl, nxr
1004	DO k = nzb, nzt+1
1005	!
1006	!-- In case the correlation coefficients are very small, the velocity seeds may become
1007	!-- very large finally creating numerical instabilities in the synthetic turbulence
1008	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
1009	IF ( a11(k) > 10E-8_wp ) THEN
1010	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1011	ELSE
1012	fu_xz(k,i) = 10E-8_wp
1013	ENDIF
1014
1015	IF ( a22(k) > 10E-8_wp ) THEN
1016	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1017	ELSE
1018	fv_xz(k,i) = 10E-8_wp
1019	ENDIF
1020
1021	IF ( a33(k) > 10E-8_wp ) THEN
1022	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1023	ELSE
1024	fw_xz(k,i) = 10E-8_wp
1025	ENDIF
1026
1027	ENDDO
1028	ENDDO
1029	ENDIF
1030	ENDIF
1031	!
1032	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1033	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1034	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1035	!-- different cases must be distinguished.
1036	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1037	!
1038	!-- Number of grid points where perturbations are imposed on u
1039	IF ( myidx == id_stg_left ) i = nxl
1040	IF ( myidx == id_stg_right ) i = nxr+1
1041
1042	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1043	!
1044	!-- Number of grid points where perturbations are imposed on v and w
1045	IF ( myidx == id_stg_left ) i = nxl-1
1046	IF ( myidx == id_stg_right ) i = nxr+1
1047
1048	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1049	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1050
1051	#if defined( __parallel )
1052	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1053	#else
1054	nr_non_topo_yz = nr_non_topo_yz_l
1055	#endif
1056	ENDIF
1057
1058	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1059	!
1060	!-- Number of grid points where perturbations are imposed on v
1061	IF ( myidy == id_stg_south ) j = nys
1062	IF ( myidy == id_stg_north ) j = nyn+1
1063
1064	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1065	!
1066	!-- Number of grid points where perturbations are imposed on u and w
1067	IF ( myidy == id_stg_south ) j = nys-1
1068	IF ( myidy == id_stg_north ) j = nyn+1
1069
1070	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1071	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1072
1073	#if defined( __parallel )
1074	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1075	#else
1076	nr_non_topo_xz = nr_non_topo_xz_l
1077	#endif
1078	ENDIF
1079	!
1080	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1081	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1082	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1083	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1084	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1085	id_rand_yz = 0
1086	seq_rand_yz = 0
1087
1088	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1089
1090	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1091	.AND. .NOT. rans_mode ) ) THEN
1092	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1093	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1094	id_rand_xz = 0
1095	seq_rand_xz = 0
1096
1097	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1098	ENDIF
1099
1100	END SUBROUTINE stg_init
1101
1102
1103	!--------------------------------------------------------------------------------------------------!
1104	! Description:
1105	! ------------
1106	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1107	!--------------------------------------------------------------------------------------------------!
1108	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1109
1110	INTEGER(iwp) :: k !< loop index
1111	INTEGER(iwp) :: mergp !< passed length scale in grid points
1112	INTEGER(iwp) :: n_k !< length scale nXX in height k
1113	INTEGER(iwp) :: nf !< index for length scales
1114
1115	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1116
1117	REAL(wp) :: bdenom !< denominator for filter functions bXX
1118	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1119
1120	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1121
1122
1123	bxx = 0.0_wp
1124
1125	DO k = nzb, nzt+1
1126	bdenom = 0.0_wp
1127	n_k = nxx(k)
1128	IF ( n_k /= 0 ) THEN
1129
1130	!
1131	!-- ( Eq.10 )^2
1132	DO nf = -n_k, n_k
1133	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1134	ENDDO
1135
1136	!
1137	!-- ( Eq.9 )
1138	bdenom = SQRT( bdenom )
1139	DO nf = -n_k, n_k
1140	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1141	ENDDO
1142	ENDIF
1143	ENDDO
1144
1145	END SUBROUTINE stg_filter_func
1146
1147
1148	!------------------------------------------------------------------------------!
1149	! Description:
1150	! ------------
1151	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1152	!> (Xie and Castro, 2008)
1153	!------------------------------------------------------------------------------!
1154	SUBROUTINE stg_setup_filter_function
1155
1156	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1157	INTEGER(iwp) :: k !< loop index along vertical direction
1158	!
1159	!-- Define the size of the filter functions and allocate them.
1160	mergp_x = 0
1161	mergp_y = 0
1162	mergp_z = 0
1163
1164	DO k = nzb, nzt+1
1165	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1166	IF ( j > mergp_x ) mergp_x = j
1167	ENDDO
1168	DO k = nzb, nzt+1
1169	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1170	IF ( j > mergp_y ) mergp_y = j
1171	ENDDO
1172	DO k = nzb, nzt+1
1173	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1174	IF ( j > mergp_z ) mergp_z = j
1175	ENDDO
1176
1177	mergp_xy = MAX( mergp_x, mergp_y )
1178
1179	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1180	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1181	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1182	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1183	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1184	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1185	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1186	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1187	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1188
1189	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1190	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1191	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1192	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1193	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1194	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1195	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1196	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1197	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1198	!
1199	!-- Create filter functions
1200	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1201	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1202	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1203	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1204	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1205	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1206	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1207	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1208	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1209
1210	END SUBROUTINE stg_setup_filter_function
1211
1212	!--------------------------------------------------------------------------------------------------!
1213	! Description:
1214	! ------------
1215	!> Parin for &stg_par for synthetic turbulence generator
1216	!--------------------------------------------------------------------------------------------------!
1217	SUBROUTINE stg_parin
1218
1219	CHARACTER(LEN=100) :: line !< dummy string that contains the current line of the parameter file
1220
1221	INTEGER(iwp) :: io_status !< status after reading the namelist file
1222
1223	LOGICAL :: switch_off_module = .FALSE. !< local namelist parameter to switch off the module
1224	!< although the respective module namelist appears in
1225	!< the namelist file
1226
1227	NAMELIST /stg_par/ compute_velocity_seeds_local, &
1228	dt_stg_adjust, &
1229	dt_stg_call, &
1230	switch_off_module, &
1231	use_syn_turb_gen
1232
1233
1234	!
1235	!-- Move to the beginning of the namelist file and try to find and read the namelist.
1236	REWIND( 11 )
1237	READ( 11, stg_par, IOSTAT=io_status )
1238
1239	!
1240	!-- Action depending on the READ status
1241	IF ( io_status == 0 ) THEN
1242	!
1243	!-- stg_par namelist was found and read correctly. Set flag that indicates that the synthetic
1244	!-- turbulence generator is switched on.
1245	IF ( .NOT. switch_off_module ) syn_turb_gen = .TRUE.
1246
1247	ELSEIF ( io_status > 0 ) THEN
1248	!
1249	!-- stg_par namelist was found but contained errors. Print an error message including the line
1250	!-- that caused the problem.
1251	BACKSPACE( 11 )
1252	READ( 11 , '(A)') line
1253	CALL parin_fail_message( 'stg_par', line )
1254
1255	ENDIF
1256
1257	END SUBROUTINE stg_parin
1258
1259
1260	!--------------------------------------------------------------------------------------------------!
1261	! Description:
1262	! ------------
1263	!> Read module-specific global restart data (Fortran binary format).
1264	!--------------------------------------------------------------------------------------------------!
1265	SUBROUTINE stg_rrd_global_ftn( found )
1266
1267	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1268
1269	found = .TRUE.
1270
1271
1272	SELECT CASE ( restart_string(1:length) )
1273
1274	CASE ( 'time_stg_adjust' )
1275	READ ( 13 ) time_stg_adjust
1276
1277	CASE ( 'time_stg_call' )
1278	READ ( 13 ) time_stg_call
1279
1280	CASE ( 'use_syn_turb_gen' )
1281	READ ( 13 ) use_syn_turb_gen
1282
1283	CASE DEFAULT
1284
1285	found = .FALSE.
1286
1287	END SELECT
1288
1289
1290	END SUBROUTINE stg_rrd_global_ftn
1291
1292
1293	!--------------------------------------------------------------------------------------------------!
1294	! Description:
1295	! ------------
1296	!> Read module-specific global restart data (MPI-IO).
1297	!--------------------------------------------------------------------------------------------------!
1298	SUBROUTINE stg_rrd_global_mpi
1299
1300	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1301	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1302	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1303
1304	END SUBROUTINE stg_rrd_global_mpi
1305
1306
1307	!--------------------------------------------------------------------------------------------------!
1308	! Description:
1309	! ------------
1310	!> This routine writes the respective restart data.
1311	!--------------------------------------------------------------------------------------------------!
1312	SUBROUTINE stg_wrd_global
1313
1314	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1315
1316	CALL wrd_write_string( 'time_stg_adjust' )
1317	WRITE ( 14 ) time_stg_adjust
1318
1319	CALL wrd_write_string( 'time_stg_call' )
1320	WRITE ( 14 ) time_stg_call
1321
1322	CALL wrd_write_string( 'use_syn_turb_gen' )
1323	WRITE ( 14 ) use_syn_turb_gen
1324
1325	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1326
1327	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1328	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1329	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1330
1331	ENDIF
1332
1333	END SUBROUTINE stg_wrd_global
1334
1335
1336	!--------------------------------------------------------------------------------------------------!
1337	! Description:
1338	! ------------
1339	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1340	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1341	!> (2013), and using a Lund rotation (Lund, 1998).
1342	!--------------------------------------------------------------------------------------------------!
1343	SUBROUTINE stg_main
1344
1345	USE exchange_horiz_mod, &
1346	ONLY: exchange_horiz
1347
1348	INTEGER(iwp) :: i !< grid index in x-direction
1349	INTEGER(iwp) :: j !< loop index in y-direction
1350	INTEGER(iwp) :: k !< loop index in z-direction
1351
1352	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1353
1354	REAL(wp) :: dt_stg !< time interval the STG is called
1355
1356	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1357
1358	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1359	!
1360	!-- Calculate time step which is needed for filter functions
1361	dt_stg = MAX( dt_3d, dt_stg_call )
1362	!
1363	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1364	!-- created or if old disturbances can be imposed again.
1365	IF ( time_stg_call >= dt_stg_call .AND. &
1366	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1367	stg_call = .TRUE.
1368	ELSE
1369	stg_call = .FALSE.
1370	ENDIF
1371	!
1372	!-- Initial value of fu, fv, fw
1373	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1374	!
1375	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1376	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1377	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1378	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1379	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1380	!-- have the same initial seeds.
1381	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1382	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1383	.AND. .NOT. rans_mode ) ) ) THEN
1384	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1385	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1386	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1387	ELSE
1388	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1389	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1390	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1391	!
1392	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1393	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1394	!-- comment above.
1395	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1396	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1397	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1398	ENDIF
1399	velocity_seed_initialized = .TRUE.
1400	ENDIF
1401	!
1402	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1403	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1404	!-- seeds are required also at the right, south and north boundaries.
1405	IF ( stg_call ) THEN
1406	IF ( .NOT. ( nesting_offline .OR. &
1407	( child_domain .AND. rans_mode_parent &
1408	.AND. .NOT. rans_mode ) ) ) THEN
1409	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1410	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1411	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1412
1413	ELSE
1414	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1415	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1416	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1417
1418	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1419	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1420	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1421	ENDIF
1422	ENDIF
1423
1424	!
1425	!-- Turbulence generation at left and/or right boundary
1426	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1427	!
1428	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1429	!-- exceeded. Else the old set of perturbations is imposed
1430	IF ( stg_call ) THEN
1431
1432	DO j = nys, nyn
1433	DO k = nzb, nzt + 1
1434	!
1435	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1436	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1437	fu_yz(k,j) = fuo_yz(k,j)
1438	ELSE
1439	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1440	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1441	ENDIF
1442
1443	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1444	fv_yz(k,j) = fvo_yz(k,j)
1445	ELSE
1446	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1447	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1448	ENDIF
1449
1450	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1451	fw_yz(k,j) = fwo_yz(k,j)
1452	ELSE
1453	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1454	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1455	ENDIF
1456	ENDDO
1457	ENDDO
1458
1459	dist_yz(nzb,:,1) = 0.0_wp
1460	dist_yz(nzb,:,2) = 0.0_wp
1461	dist_yz(nzb,:,3) = 0.0_wp
1462
1463	IF ( myidx == id_stg_left ) i = nxl
1464	IF ( myidx == id_stg_right ) i = nxr+1
1465	DO j = nys, nyn
1466	DO k = nzb+1, nzt + 1
1467	!
1468	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1469	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1470	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1471
1472	ENDDO
1473	ENDDO
1474
1475	IF ( myidx == id_stg_left ) i = nxl-1
1476	IF ( myidx == id_stg_right ) i = nxr+1
1477	DO j = nys, nyn
1478	DO k = nzb+1, nzt + 1
1479	!
1480	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1481	!-- Additional factors are added to improve the variance of v and w experimental test
1482	!-- of 1.2
1483	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1484	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1485	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1486	a33(k) * fw_yz(k,j) ) * &
1487	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1488
1489	ENDDO
1490	ENDDO
1491	ENDIF
1492	!
1493	!-- Mass flux correction following Kim et al. (2013)
1494	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1495	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1496	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1497	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1498	mc_factor_l = 0.0_wp
1499	mc_factor = 0.0_wp
1500	!
1501	!-- Sum up the original volume flows (with and without perturbations).
1502	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1503	IF ( myidx == id_stg_left ) i = nxl
1504	IF ( myidx == id_stg_right ) i = nxr+1
1505
1506	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1507	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1508
1509	IF ( myidx == id_stg_left ) i = nxl-1
1510	IF ( myidx == id_stg_right ) i = nxr+1
1511
1512	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1513	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1514	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1515	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1516
1517	#if defined( __parallel )
1518	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1519	#else
1520	mc_factor = mc_factor_l
1521	#endif
1522	!
1523	!-- Calculate correction factor and force zero mean perturbations.
1524	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1525
1526	IF ( myidx == id_stg_left ) i = nxl
1527	IF ( myidx == id_stg_right ) i = nxr+1
1528
1529	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1530	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1531
1532
1533	IF ( myidx == id_stg_left ) i = nxl-1
1534	IF ( myidx == id_stg_right ) i = nxr+1
1535
1536	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1537	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1538
1539	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1540	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1541	!
1542	!-- Add disturbances
1543	IF ( myidx == id_stg_left ) THEN
1544	!
1545	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1546	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1547	!-- the mean inflow profiles.
1548	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1549	!
1550	!-- Add disturbance at the inflow
1551	DO j = nys, nyn
1552	DO k = nzb, nzt+1
1553	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1554	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1555	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + 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,-nbgp:-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	ELSE
1562
1563	DO j = nys, nyn
1564	DO k = nzb+1, nzt
1565	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1566	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1567	u(k,j,-1) = u(k,j,0)
1568	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1569	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1570	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1571	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1572	ENDDO
1573	ENDDO
1574	ENDIF
1575	ENDIF
1576	IF ( myidx == id_stg_right ) THEN
1577	DO j = nys, nyn
1578	DO k = nzb+1, nzt
1579	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1580	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1581	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1582	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1583	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1584	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1585	ENDDO
1586	ENDDO
1587	ENDIF
1588	ENDIF
1589	ENDIF
1590	!
1591	!-- Turbulence generation at north and south boundary
1592	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1593	!
1594	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1595	!-- exceeded. Else the old set of perturbations is imposed
1596	IF ( stg_call ) THEN
1597	DO i = nxl, nxr
1598	DO k = nzb, nzt + 1
1599	!
1600	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1601	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1602	fu_xz(k,i) = fuo_xz(k,i)
1603	ELSE
1604	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1605	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1606	ENDIF
1607
1608	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1609	fv_xz(k,i) = fvo_xz(k,i)
1610	ELSE
1611	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1612	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1613	ENDIF
1614
1615	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1616	fw_xz(k,i) = fwo_xz(k,i)
1617	ELSE
1618	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1619	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1620	ENDIF
1621	ENDDO
1622	ENDDO
1623
1624
1625	dist_xz(nzb,:,1) = 0.0_wp
1626	dist_xz(nzb,:,2) = 0.0_wp
1627	dist_xz(nzb,:,3) = 0.0_wp
1628
1629	IF ( myidy == id_stg_south ) j = nys
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	!experimental test of 1.2
1637	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1638	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1639	ENDDO
1640	ENDDO
1641
1642	IF ( myidy == id_stg_south ) j = nys-1
1643	IF ( myidy == id_stg_north ) j = nyn+1
1644	DO i = nxl, nxr
1645	DO k = nzb+1, nzt + 1
1646	!
1647	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1648	!-- Additional factors are added to improve the variance of v and w
1649	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1650	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1651
1652	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1653	a33(k) * fw_xz(k,i) ) * &
1654	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1655	ENDDO
1656	ENDDO
1657	ENDIF
1658
1659	!
1660	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1661	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1662	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1663	!-- else the boundary values won't be accessed.
1664	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1665	mc_factor_l = 0.0_wp
1666	mc_factor = 0.0_wp
1667
1668	IF ( myidy == id_stg_south ) j = nys
1669	IF ( myidy == id_stg_north ) j = nyn+1
1670
1671	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1672	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1673
1674	IF ( myidy == id_stg_south ) j = nys-1
1675	IF ( myidy == id_stg_north ) j = nyn+1
1676
1677	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1678	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1679	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1680	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1681
1682	#if defined( __parallel )
1683	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1684	#else
1685	mc_factor = mc_factor_l
1686	#endif
1687
1688	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1689
1690	IF ( myidy == id_stg_south ) j = nys
1691	IF ( myidy == id_stg_north ) j = nyn+1
1692
1693	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1694	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1695
1696
1697	IF ( myidy == id_stg_south ) j = nys-1
1698	IF ( myidy == id_stg_north ) j = nyn+1
1699
1700	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1701	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1702
1703	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1704	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1705	!
1706	!-- Add disturbances
1707	IF ( myidy == id_stg_south ) THEN
1708	DO i = nxl, nxr
1709	DO k = nzb+1, nzt
1710	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1711	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1712	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1713	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1714	v(k,-1,i) = v(k,0,i)
1715	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1716	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1717	ENDDO
1718	ENDDO
1719	ENDIF
1720	IF ( myidy == id_stg_north ) THEN
1721
1722	DO i = nxl, nxr
1723	DO k = nzb+1, nzt
1724	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1725	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1726	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1727	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1728	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1729	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1730	ENDDO
1731	ENDDO
1732	ENDIF
1733	ENDIF
1734	ENDIF
1735	!
1736	!-- Exchange ghost points.
1737	CALL exchange_horiz( u, nbgp )
1738	CALL exchange_horiz( v, nbgp )
1739	CALL exchange_horiz( w, nbgp )
1740	!
1741	!-- Finally, set time counter for calling STG to zero
1742	IF ( stg_call ) time_stg_call = 0.0_wp
1743	!
1744	!-- Set adjustment step to False to indicate that time correlation can be
1745	!-- switched-on again.
1746	adjustment_step = .FALSE.
1747
1748	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1749
1750	END SUBROUTINE stg_main
1751
1752	!--------------------------------------------------------------------------------------------------!
1753	! Description:
1754	! ------------
1755	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1756	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1757	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1758	!> array.
1759	!--------------------------------------------------------------------------------------------------!
1760	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1761
1762	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1763	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1764	INTEGER(iwp) :: j !< loop index in y-direction
1765	INTEGER(iwp) :: jj !< loop index in y-direction
1766	INTEGER(iwp) :: k !< loop index in z-direction
1767	INTEGER(iwp) :: kk !< loop index in z-direction
1768	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1769
1770	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1771	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1772
1773	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1774	REAL(wp) :: rand_av !< average of random number
1775	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1776
1777	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1778	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1779
1780	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1781	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1782
1783	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1784	!
1785	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1786	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1787	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1788	!-- and normalization of random numbers is done locally, while the result is later distributed to
1789	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1790	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1791	!-- correlation matrix.
1792	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1793	rand_it = 0.0_wp
1794
1795	rand_av = 0.0_wp
1796	rand_sigma_inv = 0.0_wp
1797	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1798	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1799	!
1800	!-- Compute and normalize random numbers.
1801	DO j = nys - mergp_y, nyn + mergp_y
1802	!
1803	!-- Put the random seeds at grid point j
1804	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1805	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1806	CALL random_number_parallel( random_dummy )
1807	rand_it(k,j) = random_dummy
1808	ENDDO
1809	!
1810	!-- Get the new random seeds from last call at grid point j
1811	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1812	ENDDO
1813	!
1814	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1815	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1816	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1817	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1818	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1819	rand_av = rand_av + rand_it(k,j)
1820	ENDDO
1821	ENDDO
1822
1823	#if defined( __parallel )
1824	!
1825	!-- Sum-up the local averages of the random numbers
1826	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1827	#endif
1828	rand_av = rand_av * nyz_inv
1829	!
1830	!-- Obtain zero mean
1831	rand_it= rand_it - rand_av
1832	!
1833	!-- Now, compute the variance
1834	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1835	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1836	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1837	ENDDO
1838	ENDDO
1839
1840	#if defined( __parallel )
1841	!
1842	!-- Sum-up the local quadratic averages of the random numbers
1843	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1844	#endif
1845	!
1846	!-- Compute standard deviation
1847	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1848	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1849	ELSE
1850	rand_sigma_inv = 1.0_wp
1851	ENDIF
1852	!
1853	!-- Normalize with standard deviation to obtain unit variance
1854	rand_it = rand_it * rand_sigma_inv
1855
1856	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1857	!
1858	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1859	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1860	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1861	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1862	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1863	!-- communication. In the second option, which performs better when the turbulent length scales
1864	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1865	!-- communication is necessary.
1866	IF ( compute_velocity_seeds_local ) THEN
1867
1868	f_n = 0.0_wp
1869	DO j = nys, nyn
1870	DO k = nzb, nzt+1
1871	DO jj = -n_y(k), n_y(k)
1872	DO kk = -n_z(k), n_z(k)
1873	f_n(k,j) = f_n(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	ELSE
1880
1881	f_n_l = 0.0_wp
1882	DO j = nys, nyn
1883	DO k = nzb_x_stg, nzt_x_stg+1
1884	DO jj = -n_y(k), n_y(k)
1885	DO kk = -n_z(k), n_z(k)
1886	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1887	ENDDO
1888	ENDDO
1889	ENDDO
1890	ENDDO
1891	!
1892	!-- Gather velocity seeds of full subdomain
1893	send_count = nzt_x_stg - nzb_x_stg + 1
1894	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1895
1896	#if defined( __parallel )
1897	!
1898	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1899	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1900	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1901	!
1902	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1903	!-- nesting for example).
1904	IF ( PRESENT( id_right ) ) THEN
1905	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1906	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1907	ENDIF
1908	#else
1909	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1910	!
1911	!-- Next line required to avoid compile errors because of unused dummy arguments
1912	IF ( id_left == 0 ) id_right = 0
1913	#endif
1914
1915	ENDIF
1916
1917	DEALLOCATE( rand_it )
1918
1919	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1920
1921	END SUBROUTINE stg_generate_seed_yz
1922
1923
1924	!--------------------------------------------------------------------------------------------------!
1925	! Description:
1926	! ------------
1927	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1928	!> f_n.
1929	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1930	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1931	!> full array.
1932	!--------------------------------------------------------------------------------------------------!
1933	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1934
1935	INTEGER(iwp) :: i !< loop index in x-direction
1936	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1937	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1938	INTEGER(iwp) :: ii !< loop index in x-direction
1939	INTEGER(iwp) :: k !< loop index in z-direction
1940	INTEGER(iwp) :: kk !< loop index in z-direction
1941	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1942
1943	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1944	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1945
1946	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1947	REAL(wp) :: rand_av !< average of random number
1948	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1949
1950	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1951	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1952
1953	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1954	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1955
1956	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1957
1958	!
1959	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1960	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1961	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1962	!-- and normalization of random numbers is done locally, while the result is later distributed to
1963	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1964	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1965	!-- correlation matrix.
1966	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1967	rand_it = 0.0_wp
1968
1969	rand_av = 0.0_wp
1970	rand_sigma_inv = 0.0_wp
1971	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1972	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1973	!
1974	!-- Compute and normalize random numbers.
1975	DO i = nxl - mergp_x, nxr + mergp_x
1976	!
1977	!-- Put the random seeds at grid point ii
1978	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1979	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1980	CALL random_number_parallel( random_dummy )
1981	rand_it(k,i) = random_dummy
1982	ENDDO
1983	!
1984	!-- Get the new random seeds from last call at grid point ii
1985	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1986	ENDDO
1987	!
1988	!-- For normalization to zero mean, sum-up the global random numers.
1989	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1990	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1991	!-- also occur on the inner subdomains.
1992	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1993	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1994	rand_av = rand_av + rand_it(k,i)
1995	ENDDO
1996	ENDDO
1997
1998	#if defined( __parallel )
1999	!
2000	!-- Sum-up the local averages of the random numbers
2001	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2002	#endif
2003	rand_av = rand_av * nxz_inv
2004	!
2005	!-- Obtain zero mean
2006	rand_it= rand_it - rand_av
2007	!
2008	!-- Now, compute the variance
2009	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
2010	DO k = nzb - mergp_z, nzt + 1 + mergp_z
2011	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2012	ENDDO
2013	ENDDO
2014
2015	#if defined( __parallel )
2016	!
2017	!-- Sum-up the local quadratic averages of the random numbers
2018	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2019	#endif
2020	!
2021	!-- Compute standard deviation
2022	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2023	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2024	ELSE
2025	rand_sigma_inv = 1.0_wp
2026	ENDIF
2027	!
2028	!-- Normalize with standard deviation to obtain unit variance
2029	rand_it = rand_it * rand_sigma_inv
2030
2031	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2032	!
2033	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2034	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2035	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2036	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2037	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2038	!-- In the second option, which performs better when the turbulent length scales are parametrized
2039	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2040	IF ( compute_velocity_seeds_local ) THEN
2041
2042	f_n = 0.0_wp
2043	DO i = nxl, nxr
2044	DO k = nzb, nzt+1
2045	DO ii = -n_x(k), n_x(k)
2046	DO kk = -n_z(k), n_z(k)
2047	f_n(k,i) = f_n(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	ELSE
2054
2055	f_n_l = 0.0_wp
2056	DO i = nxl, nxr
2057	DO k = nzb_y_stg, nzt_y_stg+1
2058	DO ii = -n_x(k), n_x(k)
2059	DO kk = -n_z(k), n_z(k)
2060	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2061	ENDDO
2062	ENDDO
2063	ENDDO
2064	ENDDO
2065	!
2066	!-- Gather velocity seeds of full subdomain
2067	send_count = nzt_y_stg - nzb_y_stg + 1
2068	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2069
2070	#if defined( __parallel )
2071	!
2072	!-- Gather the processed velocity seed on south boundary mpi ranks.
2073	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2074	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2075	!
2076	!-- Gather the processed velocity seed on north boundary mpi ranks.
2077	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2078	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2079	#else
2080	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2081	!
2082	!-- Next line required to avoid compile errors because of unused dummy arguments
2083	IF ( id_north == 0 ) id_south = 0
2084	#endif
2085
2086	ENDIF
2087
2088	DEALLOCATE( rand_it )
2089
2090	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2091
2092	END SUBROUTINE stg_generate_seed_xz
2093
2094	!--------------------------------------------------------------------------------------------------!
2095	! Description:
2096	! ------------
2097	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2098	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2099	!> which is applied in state-of-the-art dispserion modelling.
2100	!--------------------------------------------------------------------------------------------------!
2101	SUBROUTINE parametrize_turbulence
2102
2103	INTEGER(iwp) :: k !< loop index in z-direction
2104
2105	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2106	REAL(wp) :: d_zi !< inverse boundary-layer depth
2107	REAL(wp) :: length_scale_lon !< length scale in flow direction
2108	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2109	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2110	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2111	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2112	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2113	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2114	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2115	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2116	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2117	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2118	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2119	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2120	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2121	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2122	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2123	REAL(wp) :: zzi !< ratio of z/zi
2124
2125	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2126	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2127	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2128
2129	!
2130	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2131	!-- criterion according to Heinze et al. (2017).
2132	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2133	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2134	k_zi = MIN( k_zi, nzt )
2135	!
2136	!-- Calculate angle between flow direction and x-axis.
2137	DO k = nzb+1, nzt + 1
2138	IF ( u_init(k) /= 0.0_wp ) THEN
2139	phi(k) = ATAN( v_init(k) / u_init(k) )
2140	ELSE
2141	phi(k) = 0.5 * pi
2142	ENDIF
2143	!
2144	!-- Pre-calculate sine and cosine.
2145	cos_phi(k) = COS( phi(k) )
2146	sin_phi(k) = SIN( phi(k) )
2147	ENDDO
2148	!
2149	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2150	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2151	!-- coincide with the grid axis. Hence, components are rotated after computation.
2152	d_zi = 1.0_wp / zi_ribulk
2153	DO k = nzb+1, k_zi
2154
2155	corr_term_uh = MERGE( 0.35_wp * ABS( &
2156	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2157	)**( 2.0_wp / 3.0_wp ), &
2158	0.0_wp, &
2159	scale_l < -5.0_wp )
2160	!
2161	!-- Determine normalized height coordinate
2162	zzi = zu(k) * d_zi
2163	!
2164	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2165	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2166	!-- variances cannot become negative, take the absolute values.
2167	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2168	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2169
2170	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2171	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2172	!
2173	!-- w'w'
2174	r33(k) = scale_wm*2 ( &
2175	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2176	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2177	)
2178	!
2179	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2180	!-- these are projected along the x- and y-direction. Note, it is assumed that
2181	!-- the flux within the boundary points opposite to the vertical gradient.
2182	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2183	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2184
2185	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2186	- ( u_init(k+1) - u_init(k-1) ) )
2187	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2188	- ( v_init(k+1) - v_init(k-1) ) )
2189	!
2190	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2191	!-- for the vertical transport.
2192	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2193	!
2194	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2195	!-- limited to the adjustment time scales.
2196	tu(k) = MIN( dt_stg_adjust, &
2197	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2198
2199	tv(k) = tu(k)
2200	tw(k) = tu(k)
2201
2202	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2203	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2204	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2205	!
2206	!-- Assume isotropic turbulence length scales
2207	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2208	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2209	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2210	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2211	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2212	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2213	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2214	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2215	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2216
2217	ENDDO
2218	!
2219	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2220	!-- reduced to zero by a blending function.
2221	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2222	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2223	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2224
2225	time_scale_zi = tu(k_zi)
2226	r11_zi = r11(k_zi)
2227	r22_zi = r22(k_zi)
2228	r33_zi = r33(k_zi)
2229	r31_zi = r31(k_zi)
2230	r32_zi = r32(k_zi)
2231
2232	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2233
2234	DO k = k_zi+1, nzt+1
2235	!
2236	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2237	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2238	!
2239	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2240	!-- the mergpe-function can crash if scale_l is zero.
2241	r11(k) = r11_zi * blend
2242	r22(k) = r22_zi * blend
2243	r33(k) = r33_zi * blend
2244	r31(k) = r31_zi * blend
2245	r32(k) = r32_zi * blend
2246	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2247
2248	!
2249	!-- Compute turbulent time scales according to Brost et al. (1982).
2250	!-- Note, time scales are limited to the adjustment time scales.
2251	tu(k) = time_scale_zi * blend
2252	tv(k) = time_scale_zi * blend
2253	tw(k) = time_scale_zi * blend
2254
2255	length_scale_lon = length_scale_lon_zi * blend
2256	length_scale_lat = length_scale_lat_zi * blend
2257	length_scale_vert = length_scale_vert_zi * blend
2258	!
2259	!-- Assume isotropic turbulence length scales
2260	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2261	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2262	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2263	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2264	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2265	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2266	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2267	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2268	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2269	ENDDO
2270	!
2271	!-- Set bottom boundary condition for reynolds stresses
2272	r11(nzb) = r11(nzb+1)
2273	r22(nzb) = r22(nzb+1)
2274	r33(nzb) = r33(nzb+1)
2275
2276	r21(nzb) = r11(nzb+1)
2277	r31(nzb) = r31(nzb+1)
2278	r32(nzb) = r32(nzb+1)
2279
2280	!
2281	!-- Set bottom boundary condition for the length and time scales
2282	nux(nzb) = nux(nzb+1)
2283	nuy(nzb) = nuy(nzb+1)
2284	nuz(nzb) = nuz(nzb+1)
2285	nvx(nzb) = nvx(nzb+1)
2286	nvy(nzb) = nvy(nzb+1)
2287	nvz(nzb) = nvz(nzb+1)
2288	nwx(nzb) = nwx(nzb+1)
2289	nwy(nzb) = nwy(nzb+1)
2290	nwz(nzb) = nwz(nzb+1)
2291
2292	tu(nzb) = tu(nzb+1)
2293	tv(nzb) = tv(nzb+1)
2294	tw(nzb) = tw(nzb+1)
2295
2296	adjustment_step = .TRUE.
2297
2298	END SUBROUTINE parametrize_turbulence
2299
2300	!--------------------------------------------------------------------------------------------------!
2301	! Description:
2302	! ------------
2303	!> Calculate the coefficient matrix from the Lund rotation.
2304	!--------------------------------------------------------------------------------------------------!
2305	SUBROUTINE calc_coeff_matrix
2306
2307	INTEGER(iwp) :: k !< loop index in z-direction
2308
2309	!
2310	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2311	DO k = nzb+1, nzt+1
2312	IF ( r11(k) > 10E-6_wp ) THEN
2313	a11(k) = SQRT( r11(k) )
2314	a21(k) = r21(k) / a11(k)
2315	a31(k) = r31(k) / a11(k)
2316	ELSE
2317	a11(k) = 10E-8_wp
2318	a21(k) = 10E-8_wp
2319	a31(k) = 10E-8_wp
2320	ENDIF
2321	ENDDO
2322	DO k = nzb+1, nzt+1
2323	a22(k) = r22(k) - a21(k)**2
2324	IF ( a22(k) > 10E-6_wp ) THEN
2325	a22(k) = SQRT( a22(k) )
2326	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2327	ELSE
2328	a22(k) = 10E-8_wp
2329	a32(k) = 10E-8_wp
2330	ENDIF
2331	ENDDO
2332	DO k = nzb+1, nzt+1
2333	a33(k) = r33(k) - a31(k)2 - a32(k)2
2334	IF ( a33(k) > 10E-6_wp ) THEN
2335	a33(k) = SQRT( a33(k) )
2336	ELSE
2337	a33(k) = 10E-8_wp
2338	ENDIF
2339	ENDDO
2340	!
2341	!-- Set bottom boundary condition
2342	a11(nzb) = a11(nzb+1)
2343	a22(nzb) = a22(nzb+1)
2344	a21(nzb) = a21(nzb+1)
2345	a33(nzb) = a33(nzb+1)
2346	a31(nzb) = a31(nzb+1)
2347	a32(nzb) = a32(nzb+1)
2348
2349	END SUBROUTINE calc_coeff_matrix
2350
2351	!--------------------------------------------------------------------------------------------------!
2352	! Description:
2353	! ------------
2354	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2355	!> turbulence at the lateral boundaries.
2356	!--------------------------------------------------------------------------------------------------!
2357	SUBROUTINE stg_adjust
2358
2359	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2360	!
2361	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2362	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2363	!-- nevertheless, the boundary-layer depth need to determined first.
2364	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2365	CALL nesting_offl_calc_zi
2366	!
2367	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2368	CALL calc_scaling_variables
2369	!
2370	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2371	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2372	!-- velocity and velocity scale.
2373	CALL parametrize_turbulence
2374	!
2375	!-- Calculate coefficient matrix from Reynolds stress tensor
2376	!-- (Lund rotation)
2377	CALL calc_coeff_matrix
2378	!
2379	!-- Setup filter functions according to updated length scales.
2380	CALL stg_setup_filter_function
2381	!
2382	!-- Reset time counter for controlling next adjustment to zero
2383	time_stg_adjust = 0.0_wp
2384
2385	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2386
2387	END SUBROUTINE stg_adjust
2388
2389
2390	!--------------------------------------------------------------------------------------------------!
2391	! Description:
2392	! ------------
2393	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2394	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2395	!> scale, and Obukhov length.
2396	!--------------------------------------------------------------------------------------------------!
2397	SUBROUTINE calc_scaling_variables
2398
2399	INTEGER(iwp) :: i !< loop index in x-direction
2400	INTEGER(iwp) :: j !< loop index in y-direction
2401	INTEGER(iwp) :: k !< loop index in z-direction
2402	INTEGER(iwp) :: m !< surface element index
2403
2404	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2405	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2406	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2407	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2408	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2409	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2410	REAL(wp) :: w_convective !< convective velocity scale
2411
2412	!
2413	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2414	!-- model domain.
2415	pt_surf_mean_l = 0.0_wp
2416	shf_mean_l = 0.0_wp
2417	scale_l_l = 0.0_wp
2418	friction_vel_l = 0.0_wp
2419	DO m = 1, surf_def_h(0)%ns
2420	i = surf_def_h(0)%i(m)
2421	j = surf_def_h(0)%j(m)
2422	k = surf_def_h(0)%k(m)
2423	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2424	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2425	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2426	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2427	ENDDO
2428	DO m = 1, surf_lsm_h(0)%ns
2429	i = surf_lsm_h(0)%i(m)
2430	j = surf_lsm_h(0)%j(m)
2431	k = surf_lsm_h(0)%k(m)
2432	friction_vel_l = friction_vel_l + surf_lsm_h(0)%us(m)
2433	shf_mean_l = shf_mean_l + surf_lsm_h(0)%shf(m) * drho_air(k)
2434	scale_l_l = scale_l_l + surf_lsm_h(0)%ol(m)
2435	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2436	ENDDO
2437	DO m = 1, surf_usm_h(0)%ns
2438	i = surf_usm_h(0)%i(m)
2439	j = surf_usm_h(0)%j(m)
2440	k = surf_usm_h(0)%k(m)
2441	friction_vel_l = friction_vel_l + surf_usm_h(0)%us(m)
2442	shf_mean_l = shf_mean_l + surf_usm_h(0)%shf(m) * drho_air(k)
2443	scale_l_l = scale_l_l + surf_usm_h(0)%ol(m)
2444	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2445	ENDDO
2446
2447	#if defined( __parallel )
2448	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2449	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2450	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2451	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2452	#else
2453	scale_us = friction_vel_l
2454	shf_mean = shf_mean_l
2455	scale_l = scale_l_l
2456	pt_surf_mean = pt_surf_mean_l
2457	#endif
2458
2459	scale_us = scale_us * d_nxy
2460	shf_mean = shf_mean * d_nxy
2461	scale_l = scale_l * d_nxy
2462	pt_surf_mean = pt_surf_mean * d_nxy
2463	!
2464	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2465	!-- convective velocity scale to zero.
2466	IF ( shf_mean > 0.0_wp ) THEN
2467	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2468	ELSE
2469	w_convective = 0.0_wp
2470	ENDIF
2471	!
2472	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2473	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2474	!-- value of friction velocity for the reynolds-stress parametrization.
2475	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2476	!
2477	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2478	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2479	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2480
2481	END SUBROUTINE calc_scaling_variables
2482
2483	END MODULE synthetic_turbulence_generator_mod

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