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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4561

Last change on this file since 4561 was 4559, checked in by raasch, 4 years ago
files re-formatted to follow the PALM coding standard
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1	!> @synthetic_turbulence_generator_mod.f90
2	!--------------------------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2020 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4559 2020-06-11 08:51:48Z suehring $
27	! File re-formatted to follow the PALM coding standard
28	!
29	! 4535 2020-05-15 12:07:23Z raasch
30	! Bugfix for restart data format query
31	!
32	! 4495 2020-04-13 20:11:20Z raasch
33	! Restart data handling with MPI-IO added
34	!
35	! 4481 2020-03-31 18:55:54Z maronga
36	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
37	!
38	! 4442 2020-03-04 19:21:13Z suehring
39	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
40	! (was accidantly changed).
41	!
42	! 4441 2020-03-04 19:20:35Z suehring
43	! Correct misplaced preprocessor directive
44	!
45	! 4438 2020-03-03 20:49:28Z suehring
46	! Performance optimizations in velocity-seed calculation:
47	! - Random number array is only defined and computed locally (except for normalization to zero mean
48	! and unit variance)
49	! - Parallel random number generator is applied independent on the 2D random numbers in other
50	! routines
51	! - Option to decide wheter velocity seeds are computed locally without any further communication
52	! or are computed by all processes along the communicator
53	!
54	! 4346 2019-12-18 11:55:56Z motisi
55	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
56	! information used in wall_flags_static_0
57	!
58	! 4335 2019-12-12 16:39:05Z suehring
59	! Commentation of last commit
60	!
61	! 4332 2019-12-10 19:44:12Z suehring
62	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
63	! Further, minor bugfix in initial velocity seed calculation.
64	!
65	! 4329 2019-12-10 15:46:36Z motisi
66	! Renamed wall_flags_0 to wall_flags_static_0
67	!
68	! 4309 2019-11-26 18:49:59Z suehring
69	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
70	! the parallel random number generator. Random numbers are now only computed and normalized locally,
71	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
72	! array.
73	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
74	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
75	!
76	! 4182 2019-08-22 15:20:23Z scharf
77	! Corrected "Former revisions" section
78	!
79	! 4148 2019-08-08 11:26:00Z suehring
80	! Remove unused variable
81	!
82	! 4144 2019-08-06 09:11:47Z raasch
83	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
84	!
85	! 4071 2019-07-03 20:02:00Z suehring
86	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
87	! file.
88	!
89	! 4022 2019-06-12 11:52:39Z suehring
90	! Several bugfixes and improvements
91	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
92	! instabilities in case the mean volume flow is close to zero)
93	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
94	! numerically unstable
95	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
96	! case dt_stg_call /= dt_3d
97	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
98	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
99	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
100	!
101	! 3987 2019-05-22 09:52:13Z kanani
102	! Introduce alternative switch for debug output during timestepping
103	!
104	! 3938 2019-04-29 16:06:25Z suehring
105	! Remove unused variables
106	!
107	! 3937 2019-04-29 15:09:07Z suehring
108	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
109	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
110	! synthetic turbulence parametrization.
111	!
112	! 3909 2019-04-17 09:13:25Z suehring
113	! Minor bugfix for last commit
114	!
115	! 3900 2019-04-16 15:17:43Z suehring
116	! Missing re-calculation of perturbation seeds in case of restarts
117	!
118	! 3891 2019-04-12 17:52:01Z suehring
119	! Bugfix in initialization in case of restart runs.
120	!
121	! 3885 2019-04-11 11:29:34Z kanani
122	! Changes related to global restructuring of location messages and introduction of additional debug
123	! messages
124	!
125	!
126	! Removed unused variables
127	!
128	! 3719 2019-02-06 13:10:18Z kanani
129	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
130	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
131	! for better overview.
132	!
133	! 2259 2017-06-08 09:09:11Z gronemeier
134	! Initial revision
135	!
136	! Authors:
137	! --------
138	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
139	!
140	!
141	! Description:
142	! ------------
143	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
144	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
145	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
146	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
147	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
148	!> parametrized within the boundary layer.
149	!>
150	!> @todo test restart
151	!> Enable cyclic_fill
152	!> Implement turbulence generation for e and pt
153	!> @todo Input of height-constant length scales via namelist
154	!> @note <Enter notes on the module>
155	!> @bug Height information from input file is not used. Profiles from input must match with current
156	!> PALM grid.
157	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
158	!--------------------------------------------------------------------------------------------------!
159	MODULE synthetic_turbulence_generator_mod
160
161
162	USE arrays_3d, &
163	ONLY: dzw, &
164	ddzw, &
165	drho_air, &
166	mean_inflow_profiles, &
167	pt, &
168	pt_init, &
169	q, &
170	q_init, &
171	u, &
172	u_init, &
173	v, &
174	v_init, &
175	w, &
176	zu, &
177	zw
178
179	USE basic_constants_and_equations_mod, &
180	ONLY: g, &
181	kappa, &
182	pi
183
184	USE control_parameters, &
185	ONLY: bc_lr, &
186	bc_ns, &
187	child_domain, &
188	coupling_char, &
189	debug_output_timestep, &
190	dt_3d, &
191	e_init, &
192	humidity, &
193	initializing_actions, &
194	intermediate_timestep_count, &
195	intermediate_timestep_count_max, &
196	length, &
197	message_string, &
198	nesting_offline, &
199	neutral, &
200	num_mean_inflow_profiles, &
201	random_generator, &
202	rans_mode, &
203	restart_data_format_output, &
204	restart_string, &
205	syn_turb_gen, &
206	time_since_reference_point, &
207	turbulent_inflow
208
209	USE cpulog, &
210	ONLY: cpu_log, &
211	log_point_s
212
213	USE grid_variables, &
214	ONLY: ddx, &
215	ddy, &
216	dx, &
217	dy
218
219	USE indices, &
220	ONLY: nbgp, &
221	nz, &
222	nzb, &
223	nzt, &
224	nx, &
225	nxl, &
226	nxlu, &
227	nxr, &
228	ny, &
229	nys, &
230	nysv, &
231	nyn, &
232	wall_flags_total_0
233
234	USE kinds
235
236	#if defined( __parallel ) && !defined( __mpifh )
237	USE MPI
238	#endif
239
240	USE nesting_offl_mod, &
241	ONLY: nesting_offl_calc_zi, &
242	zi_ribulk
243
244	USE pegrid, &
245	ONLY: comm1dx, &
246	comm1dy, &
247	comm2d, &
248	ierr, &
249	myidx, &
250	myidy, &
251	pdims
252
253	USE pmc_interface, &
254	ONLY : rans_mode_parent
255
256	USE random_generator_parallel, &
257	ONLY: init_parallel_random_generator, &
258	random_dummy, &
259	random_number_parallel, &
260	random_seed_parallel
261
262	USE restart_data_mpi_io_mod, &
263	ONLY: rrd_mpi_io, &
264	wrd_mpi_io
265
266	USE transpose_indices, &
267	ONLY: nzb_x, &
268	nzt_x
269
270	USE surface_mod, &
271	ONLY: surf_def_h, &
272	surf_lsm_h, &
273	surf_usm_h
274
275	IMPLICIT NONE
276
277	#if defined( __parallel ) && defined( __mpifh )
278	INCLUDE "mpif.h"
279	#endif
280
281
282	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
283	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
284	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
285	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
286	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
287	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
288	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
289	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
290	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
291	#if defined( __parallel )
292	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
293	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
294	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
295	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
296	#endif
297
298	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
299	!< required for bias correction of imposed perturbations
300	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
301	!< required for bias correction of imposed perturbations
302
303	#if defined( __parallel )
304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
308	#endif
309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
311	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
312	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
313	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
314	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
318
319	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
320	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
321	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
322	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
323
324
325	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
326	!< or if computation is distributed over several processes
327	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
328	!< (.FALSE.) or if it parametrized
329	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
330	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
331
332
333	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
334	!< scales above the boundary layer
335	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
336	!< one length scale above ABL top
337	REAL(wp) :: d_l !< blend_coeff/length_scale
338	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
339	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
340	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
341	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
342	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
343	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
344	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
345	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
346
347	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
348
349
350	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
351	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
352	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
353	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
354	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
355	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
356
357	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
358	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
359	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
360	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
361	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
362	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
363	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
364	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
365	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
366
367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
379	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
380	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
388
389	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
390	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
391
392	!
393	!-- PALM interfaces:
394	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
395	INTERFACE stg_adjust
396	MODULE PROCEDURE stg_adjust
397	END INTERFACE stg_adjust
398	!
399	!-- Input parameter checks to be done in check_parameters
400	INTERFACE stg_check_parameters
401	MODULE PROCEDURE stg_check_parameters
402	END INTERFACE stg_check_parameters
403
404	!
405	!-- Calculate filter functions
406	INTERFACE stg_filter_func
407	MODULE PROCEDURE stg_filter_func
408	END INTERFACE stg_filter_func
409
410	!
411	!-- Generate velocity seeds at south and north domain boundary
412	INTERFACE stg_generate_seed_xz
413	MODULE PROCEDURE stg_generate_seed_xz
414	END INTERFACE stg_generate_seed_xz
415	!
416	!-- Generate velocity seeds at left and/or right domain boundary
417	INTERFACE stg_generate_seed_yz
418	MODULE PROCEDURE stg_generate_seed_yz
419	END INTERFACE stg_generate_seed_yz
420
421	!
422	!-- Output of information to the header file
423	INTERFACE stg_header
424	MODULE PROCEDURE stg_header
425	END INTERFACE stg_header
426
427	!
428	!-- Initialization actions
429	INTERFACE stg_init
430	MODULE PROCEDURE stg_init
431	END INTERFACE stg_init
432
433	!
434	!-- Main procedure of synth. turb. gen.
435	INTERFACE stg_main
436	MODULE PROCEDURE stg_main
437	END INTERFACE stg_main
438
439	!
440	!-- Reading of NAMELIST parameters
441	INTERFACE stg_parin
442	MODULE PROCEDURE stg_parin
443	END INTERFACE stg_parin
444
445	!
446	!-- Reading of parameters for restart runs
447	INTERFACE stg_rrd_global
448	MODULE PROCEDURE stg_rrd_global_ftn
449	MODULE PROCEDURE stg_rrd_global_mpi
450	END INTERFACE stg_rrd_global
451
452	!
453	!-- Writing of binary output for restart runs
454	INTERFACE stg_wrd_global
455	MODULE PROCEDURE stg_wrd_global
456	END INTERFACE stg_wrd_global
457
458	SAVE
459
460	PRIVATE
461
462	!
463	!-- Public interfaces
464	PUBLIC stg_adjust, &
465	stg_check_parameters, &
466	stg_header, &
467	stg_init, &
468	stg_main, &
469	stg_parin, &
470	stg_rrd_global, &
471	stg_wrd_global
472
473	!
474	!-- Public variables
475	PUBLIC dt_stg_call, &
476	dt_stg_adjust, &
477	id_stg_left, &
478	id_stg_north, &
479	id_stg_right, &
480	id_stg_south, &
481	parametrize_inflow_turbulence, &
482	time_stg_adjust, &
483	time_stg_call, &
484	use_syn_turb_gen
485
486
487	CONTAINS
488
489
490	!--------------------------------------------------------------------------------------------------!
491	! Description:
492	! ------------
493	!> Check parameters routine for synthetic turbulence generator
494	!--------------------------------------------------------------------------------------------------!
495	SUBROUTINE stg_check_parameters
496
497	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
498	nesting_offline ) THEN
499	message_string = 'Synthetic turbulence generator is required ' // &
500	'if offline nesting is applied and PALM operates in LES mode.'
501	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
502	ENDIF
503
504	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
505	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
506	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
507	'and parent operates in RANS-mode but current child in LES mode.'
508	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
509	ENDIF
510
511	IF ( use_syn_turb_gen ) THEN
512
513	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
514	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
515	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
516
517	ENDIF
518
519	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
520	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
521	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
522
523	ENDIF
524
525	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
526
527	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
528	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
529	message_string = 'Using synthetic turbulence generator requires ' // &
530	'%initializing_actions = "set_constant_profiles" or ' // &
531	' "read_restart_data", if not offline nesting is applied.'
532	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
533	ENDIF
534
535	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
536	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
537	' "dirichlet/radiation", if not offline nesting is applied.'
538	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
539	ENDIF
540	IF ( bc_ns /= 'cyclic' ) THEN
541	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
542	' "cyclic", if not offline nesting is applied.'
543	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
544	ENDIF
545
546	ENDIF
547
548	IF ( turbulent_inflow ) THEN
549	message_string = 'Using synthetic turbulence generator in combination ' // &
550	'&with turbulent_inflow = .T. is not allowed'
551	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
552	ENDIF
553	!
554	!-- Synthetic turbulence generator requires the parallel random generator
555	IF ( random_generator /= 'random-parallel' ) THEN
556	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
557	'random-parallel.'
558	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
559	ENDIF
560
561	ENDIF
562
563	END SUBROUTINE stg_check_parameters
564
565
566	!--------------------------------------------------------------------------------------------------!
567	! Description:
568	! ------------
569	!> Header output for synthetic turbulence generator
570	!--------------------------------------------------------------------------------------------------!
571	SUBROUTINE stg_header ( io )
572
573	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
574
575	!
576	!-- Write synthetic turbulence generator Header
577	WRITE( io, 1 )
578	IF ( use_syn_turb_gen ) THEN
579	WRITE( io, 2 )
580	ELSE
581	WRITE( io, 3 )
582	ENDIF
583
584	IF ( parametrize_inflow_turbulence ) THEN
585	WRITE( io, 4 ) dt_stg_adjust
586	ELSE
587	WRITE( io, 5 )
588	ENDIF
589
590	1 FORMAT (//' Synthetic turbulence generator information:'/ &
591	' ------------------------------------------'/)
592	2 FORMAT (' synthetic turbulence generator is switched on')
593	3 FORMAT (' synthetic turbulence generator is switched off')
594	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
595	5 FORMAT (' imposed turbulence is read from file' )
596
597	END SUBROUTINE stg_header
598
599
600	!--------------------------------------------------------------------------------------------------!
601	! Description:
602	! ------------
603	!> Initialization of the synthetic turbulence generator
604	!--------------------------------------------------------------------------------------------------!
605	SUBROUTINE stg_init
606
607	#if defined( __parallel )
608	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
609	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
610	#endif
611
612	INTEGER(iwp) :: i !> grid index in x-direction
613	INTEGER(iwp) :: j !> loop index
614	INTEGER(iwp) :: k !< index
615	#if defined( __parallel )
616	INTEGER(iwp) :: newtype !< dummy MPI type
617	INTEGER(iwp) :: realsize !< size of REAL variables
618	#endif
619
620	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
621	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
622
623
624	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
625
626	!
627	!-- Dummy variables used for reading profiles
628	REAL(wp) :: d1 !< u profile
629	REAL(wp) :: d2 !< v profile
630	REAL(wp) :: d3 !< w profile
631	REAL(wp) :: d5 !< e profile
632	REAL(wp) :: luy !< length scale for u in y direction
633	REAL(wp) :: luz !< length scale for u in z direction
634	REAL(wp) :: lvy !< length scale for v in y direction
635	REAL(wp) :: lvz !< length scale for v in z direction
636	REAL(wp) :: lwy !< length scale for w in y direction
637	REAL(wp) :: lwz !< length scale for w in z direction
638	#if defined( __parallel )
639	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
640	#endif
641	REAL(wp) :: zz !< height
642
643
644	#if defined( __parallel )
645	CALL MPI_BARRIER( comm2d, ierr )
646	#endif
647	!
648	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
649	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
650	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
651	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
652	!-- communication).
653	IF ( .NOT. compute_velocity_seeds_local ) THEN
654	#if defined( __parallel )
655	!
656	!-- Determine processor decomposition of z-axis along x- and y-direction
657	nnz = nz / pdims(1)
658	nzb_x_stg = 1 + myidx * INT( nnz )
659	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
660
661	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
662	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
663
664	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
665	.AND. .NOT. rans_mode ) ) THEN
666	nnz = nz / pdims(2)
667	nzb_y_stg = 1 + myidy * INT( nnz )
668	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
669
670	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
671	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
672	ENDIF
673
674	!
675	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
676	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
677	extent = 1 * realsize
678	!
679	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
680	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
681	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
682	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
683	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
684	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
685	CALL MPI_TYPE_FREE( newtype, ierr )
686
687	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
688	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
689	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
690	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
691	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
692	CALL MPI_TYPE_FREE( newtype, ierr )
693
694	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
695	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
696
697	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
698	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
699
700	DO j = 1, pdims(1)
701	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
702	ENDDO
703	!
704	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
705	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
706	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
707	.AND. .NOT. rans_mode ) ) THEN
708	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
709	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
710	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
711	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
712	CALL MPI_TYPE_FREE( newtype, ierr )
713
714	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
715	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
716	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
717	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
718	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
719	CALL MPI_TYPE_FREE( newtype, ierr )
720
721	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
722	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
723
724	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
725	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
726
727	DO j = 1, pdims(2)
728	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
729	ENDDO
730
731	ENDIF
732	#endif
733	ENDIF
734	!
735	!-- Allocate required arrays.
736	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
737	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
738	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
739	!-- and initialized appropriately.
740	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
741	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
742	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
743	mean_inflow_profiles = 0.0_wp
744	mean_inflow_profiles(:,1) = u_init
745	mean_inflow_profiles(:,2) = v_init
746	!
747	!-- Even though potential temperature and humidity are not perturbed, they need to be
748	!-- initialized appropriately.
749	IF ( .NOT. neutral ) &
750	mean_inflow_profiles(:,4) = pt_init
751	IF ( humidity ) &
752	mean_inflow_profiles(:,6) = q_init
753	ENDIF
754	ENDIF
755
756	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
757	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
758	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
759	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
760	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
761	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
762	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
763	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
764
765	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
766	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
767	dist_xz = 0.0_wp
768	dist_yz = 0.0_wp
769	!
770	!-- Read inflow profile
771	!-- Height levels of profiles in input profile is as follows:
772	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
773	!-- WARNING: zz is not used at the moment
774	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
775
776	IF ( file_stg_exist ) THEN
777
778	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
779	!
780	!-- Skip header
781	READ( 90, * )
782
783	DO k = nzb+1, nzt+1
784	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
785	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
786
787	!
788	!-- Convert length scales from meter to number of grid points.
789	nuy(k) = INT( luy * ddy )
790	nuz(k) = INT( luz * ddzw(k) )
791	nvy(k) = INT( lvy * ddy )
792	nvz(k) = INT( lvz * ddzw(k) )
793	nwy(k) = INT( lwy * ddy )
794	nwz(k) = INT( lwz * ddzw(k) )
795	!
796	!-- Workaround, assume isotropic turbulence
797	nwx(k) = nwy(k)
798	nvx(k) = nvy(k)
799	nux(k) = nuy(k)
800	!
801	!-- Save Mean inflow profiles
802	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
803	mean_inflow_profiles(k,1) = d1
804	mean_inflow_profiles(k,2) = d2
805	! mean_inflow_profiles(k,4) = d4
806	mean_inflow_profiles(k,5) = d5
807	ENDIF
808	ENDDO
809	!
810	!-- Set lenght scales at surface grid point
811	nuy(nzb) = nuy(nzb+1)
812	nuz(nzb) = nuz(nzb+1)
813	nvy(nzb) = nvy(nzb+1)
814	nvz(nzb) = nvz(nzb+1)
815	nwy(nzb) = nwy(nzb+1)
816	nwz(nzb) = nwz(nzb+1)
817
818	CLOSE( 90 )
819	!
820	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
821	CALL calc_coeff_matrix
822	!
823	!-- No information about turbulence and its length scales are available. Instead, parametrize
824	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
825	!-- parametrized, which is done later when energy-balance models are already initialized. This is
826	!-- because the STG needs information about surface properties such as roughness to build
827	!-- 'realistic' turbulence profiles.
828	ELSE
829	!
830	!-- Define length scale for the imposed turbulence, which is defined as 8 times the minimum grid
831	!-- spacing
832	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
833	!
834	!-- Define constant to gradually decreasing length scales and Reynolds stress above ABL top.
835	!-- Assure that no zero length scales are used.
836	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
837	!
838	!-- Set flag indicating that turbulence is parametrized
839	parametrize_inflow_turbulence = .TRUE.
840	!
841	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
842	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
843	!-- nevertheless, the boundary-layer depth needs to be determined first.
844	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
845	CALL nesting_offl_calc_zi
846	!
847	!-- Determine boundary-layer depth, which is used to initialize lenght scales
848	CALL calc_scaling_variables
849	!
850	!-- Initialize lenght and time scales, which in turn are used to initialize the filter functions.
851	CALL calc_length_and_time_scale
852	!
853	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
854	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
855	!-- friction velocity and velocity scale.
856	CALL parametrize_reynolds_stress
857	!
858	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
859	CALL calc_coeff_matrix
860
861	ENDIF
862
863	!
864	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
865	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
866	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
867	u_init = mean_inflow_profiles(:,1)
868	v_init = mean_inflow_profiles(:,2)
869	!pt_init = mean_inflow_profiles(:,4)
870	e_init = MAXVAL( mean_inflow_profiles(:,5) )
871	ENDIF
872
873	!
874	!-- Define the size of the filter functions and allocate them.
875	mergp = 0
876
877	! arrays must be large enough to cover the largest length scale
878	DO k = nzb, nzt+1
879	j = MAX( ABS( nux(k) ), ABS( nuy(k) ), ABS( nuz(k) ), &
880	ABS( nvx(k) ), ABS( nvy(k) ), ABS( nvz(k) ), &
881	ABS( nwx(k) ), ABS( nwy(k) ), ABS( nwz(k) ) )
882	IF ( j > mergp ) mergp = j
883	ENDDO
884
885	! mergp = 2 * mergp
886	! mergp = mergp
887
888	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
889	buy(-mergp:mergp,nzb:nzt+1), &
890	buz(-mergp:mergp,nzb:nzt+1), &
891	bvx(-mergp:mergp,nzb:nzt+1), &
892	bvy(-mergp:mergp,nzb:nzt+1), &
893	bvz(-mergp:mergp,nzb:nzt+1), &
894	bwx(-mergp:mergp,nzb:nzt+1), &
895	bwy(-mergp:mergp,nzb:nzt+1), &
896	bwz(-mergp:mergp,nzb:nzt+1) )
897
898	!
899	!-- Allocate velocity seeds for turbulence at xz-layer
900	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
901	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
902	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
903
904	!
905	!-- Allocate velocity seeds for turbulence at yz-layer
906	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
907	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
908	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
909
910	fu_xz = 0.0_wp
911	fuo_xz = 0.0_wp
912	fv_xz = 0.0_wp
913	fvo_xz = 0.0_wp
914	fw_xz = 0.0_wp
915	fwo_xz = 0.0_wp
916
917	fu_yz = 0.0_wp
918	fuo_yz = 0.0_wp
919	fv_yz = 0.0_wp
920	fvo_yz = 0.0_wp
921	fw_yz = 0.0_wp
922	fwo_yz = 0.0_wp
923
924	!
925	!-- Create filter functions
926	CALL stg_filter_func( nux, bux ) !filter ux
927	CALL stg_filter_func( nuy, buy ) !filter uy
928	CALL stg_filter_func( nuz, buz ) !filter uz
929	CALL stg_filter_func( nvx, bvx ) !filter vx
930	CALL stg_filter_func( nvy, bvy ) !filter vy
931	CALL stg_filter_func( nvz, bvz ) !filter vz
932	CALL stg_filter_func( nwx, bwx ) !filter wx
933	CALL stg_filter_func( nwy, bwy ) !filter wy
934	CALL stg_filter_func( nwz, bwz ) !filter wz
935
936	#if defined( __parallel )
937	CALL MPI_BARRIER( comm2d, ierr )
938	#endif
939
940	!
941	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
942	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
943	!-- This is mostly for k=nzt+1.
944	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
945	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
946
947	IF ( myidx == id_stg_left ) i = -1
948	IF ( myidx == id_stg_right ) i = nxr+1
949
950	DO j = nys, nyn
951	DO k = nzb, nzt+1
952	IF ( a11(k) > 10E-8_wp ) THEN
953	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
954	ELSE
955	fu_yz(k,j) = 10E-8_wp
956	ENDIF
957
958	IF ( a22(k) > 10E-8_wp ) THEN
959	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
960	ELSE
961	fv_yz(k,j) = 10E-8_wp
962	ENDIF
963
964	IF ( a33(k) > 10E-8_wp ) THEN
965	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
966	ELSE
967	fw_yz(k,j) = 10E-8_wp
968	ENDIF
969	ENDDO
970	ENDDO
971	ENDIF
972
973	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
974
975	IF ( myidy == id_stg_south ) j = -1
976	IF ( myidy == id_stg_north ) j = nyn+1
977
978	DO i = nxl, nxr
979	DO k = nzb, nzt+1
980	!
981	!-- In case the correlation coefficients are very small, the velocity seeds may become
982	!-- very large finally creating numerical instabilities in the synthetic turbulence
983	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
984	IF ( a11(k) > 10E-8_wp ) THEN
985	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
986	ELSE
987	fu_xz(k,i) = 10E-8_wp
988	ENDIF
989
990	IF ( a22(k) > 10E-8_wp ) THEN
991	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
992	ELSE
993	fv_xz(k,i) = 10E-8_wp
994	ENDIF
995
996	IF ( a33(k) > 10E-8_wp ) THEN
997	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
998	ELSE
999	fw_xz(k,i) = 10E-8_wp
1000	ENDIF
1001
1002	ENDDO
1003	ENDDO
1004	ENDIF
1005	ENDIF
1006	!
1007	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1008	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1009	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1010	!-- different cases must be distinguished.
1011	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1012	!
1013	!-- Number of grid points where perturbations are imposed on u
1014	IF ( myidx == id_stg_left ) i = nxl
1015	IF ( myidx == id_stg_right ) i = nxr+1
1016
1017	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1018	!
1019	!-- Number of grid points where perturbations are imposed on v and w
1020	IF ( myidx == id_stg_left ) i = nxl-1
1021	IF ( myidx == id_stg_right ) i = nxr+1
1022
1023	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1024	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1025
1026	#if defined( __parallel )
1027	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1028	#else
1029	nr_non_topo_yz = nr_non_topo_yz_l
1030	#endif
1031	ENDIF
1032
1033	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1034	!
1035	!-- Number of grid points where perturbations are imposed on v
1036	IF ( myidy == id_stg_south ) j = nys
1037	IF ( myidy == id_stg_north ) j = nyn+1
1038
1039	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1040	!
1041	!-- Number of grid points where perturbations are imposed on u and w
1042	IF ( myidy == id_stg_south ) j = nys-1
1043	IF ( myidy == id_stg_north ) j = nyn+1
1044
1045	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1046	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1047
1048	#if defined( __parallel )
1049	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1050	#else
1051	nr_non_topo_xz = nr_non_topo_xz_l
1052	#endif
1053	ENDIF
1054	!
1055	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1056	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1057	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1058	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1059	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1060	id_rand_yz = 0
1061	seq_rand_yz = 0
1062
1063	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, id_rand_yz, seq_rand_yz )
1064
1065	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1066	.AND. .NOT. rans_mode ) ) THEN
1067	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1068	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1069	id_rand_xz = 0
1070	seq_rand_xz = 0
1071
1072	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, id_rand_xz, seq_rand_xz )
1073	ENDIF
1074
1075
1076
1077	END SUBROUTINE stg_init
1078
1079
1080	!--------------------------------------------------------------------------------------------------!
1081	! Description:
1082	! ------------
1083	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1084	!--------------------------------------------------------------------------------------------------!
1085	SUBROUTINE stg_filter_func( nxx, bxx )
1086
1087	INTEGER(iwp) :: k !< loop index
1088	INTEGER(iwp) :: n_k !< length scale nXX in height k
1089	INTEGER(iwp) :: nf !< index for length scales
1090
1091	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1092
1093	REAL(wp) :: bdenom !< denominator for filter functions bXX
1094	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1095
1096	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1097
1098
1099	bxx = 0.0_wp
1100
1101	DO k = nzb, nzt+1
1102	bdenom = 0.0_wp
1103	n_k = nxx(k)
1104	IF ( n_k /= 0 ) THEN
1105
1106	!
1107	!-- ( Eq.10 )^2
1108	DO nf = -n_k, n_k
1109	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1110	ENDDO
1111
1112	!
1113	!-- ( Eq.9 )
1114	bdenom = SQRT( bdenom )
1115	DO nf = -n_k, n_k
1116	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1117	ENDDO
1118	ENDIF
1119	ENDDO
1120
1121	END SUBROUTINE stg_filter_func
1122
1123
1124	!--------------------------------------------------------------------------------------------------!
1125	! Description:
1126	! ------------
1127	!> Parin for &stg_par for synthetic turbulence generator
1128	!--------------------------------------------------------------------------------------------------!
1129	SUBROUTINE stg_parin
1130
1131	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1132
1133
1134	NAMELIST /stg_par/ dt_stg_adjust, &
1135	dt_stg_call, &
1136	use_syn_turb_gen, &
1137	compute_velocity_seeds_local
1138
1139	line = ' '
1140	!
1141	!-- Try to find stg package
1142	REWIND ( 11 )
1143	line = ' '
1144	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1145	READ ( 11, '(A)', END = 20 ) line
1146	ENDDO
1147	BACKSPACE ( 11 )
1148
1149	!
1150	!-- Read namelist
1151	READ ( 11, stg_par, ERR = 10, END = 20 )
1152
1153	!
1154	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1155	syn_turb_gen = .TRUE.
1156	GOTO 20
1157
1158	10 BACKSPACE( 11 )
1159	READ( 11 , '(A)') line
1160	CALL parin_fail_message( 'stg_par', line )
1161
1162	20 CONTINUE
1163
1164	END SUBROUTINE stg_parin
1165
1166
1167	!--------------------------------------------------------------------------------------------------!
1168	! Description:
1169	! ------------
1170	!> Read module-specific global restart data (Fortran binary format).
1171	!--------------------------------------------------------------------------------------------------!
1172	SUBROUTINE stg_rrd_global_ftn( found )
1173
1174	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1175
1176	found = .TRUE.
1177
1178
1179	SELECT CASE ( restart_string(1:length) )
1180
1181	CASE ( 'time_stg_adjust' )
1182	READ ( 13 ) time_stg_adjust
1183
1184	CASE ( 'time_stg_call' )
1185	READ ( 13 ) time_stg_call
1186
1187	CASE ( 'use_syn_turb_gen' )
1188	READ ( 13 ) use_syn_turb_gen
1189
1190	CASE DEFAULT
1191
1192	found = .FALSE.
1193
1194	END SELECT
1195
1196
1197	END SUBROUTINE stg_rrd_global_ftn
1198
1199
1200	!--------------------------------------------------------------------------------------------------!
1201	! Description:
1202	! ------------
1203	!> Read module-specific global restart data (MPI-IO).
1204	!--------------------------------------------------------------------------------------------------!
1205	SUBROUTINE stg_rrd_global_mpi
1206
1207	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1208	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1209	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1210
1211	END SUBROUTINE stg_rrd_global_mpi
1212
1213
1214	!--------------------------------------------------------------------------------------------------!
1215	! Description:
1216	! ------------
1217	!> This routine writes the respective restart data.
1218	!--------------------------------------------------------------------------------------------------!
1219	SUBROUTINE stg_wrd_global
1220
1221	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1222
1223	CALL wrd_write_string( 'time_stg_adjust' )
1224	WRITE ( 14 ) time_stg_adjust
1225
1226	CALL wrd_write_string( 'time_stg_call' )
1227	WRITE ( 14 ) time_stg_call
1228
1229	CALL wrd_write_string( 'use_syn_turb_gen' )
1230	WRITE ( 14 ) use_syn_turb_gen
1231
1232	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1233
1234	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1235	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1236	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1237
1238	ENDIF
1239
1240	END SUBROUTINE stg_wrd_global
1241
1242
1243	!--------------------------------------------------------------------------------------------------!
1244	! Description:
1245	! ------------
1246	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1247	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1248	!> (2013), and using a Lund rotation (Lund, 1998).
1249	!--------------------------------------------------------------------------------------------------!
1250	SUBROUTINE stg_main
1251
1252	USE exchange_horiz_mod, &
1253	ONLY: exchange_horiz
1254
1255	INTEGER(iwp) :: i !< grid index in x-direction
1256	INTEGER(iwp) :: j !< loop index in y-direction
1257	INTEGER(iwp) :: k !< loop index in z-direction
1258
1259	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1260
1261	REAL(wp) :: dt_stg !< wheighted subtimestep
1262
1263	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1264
1265	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1266	!
1267	!-- Calculate time step which is needed for filter functions
1268	dt_stg = MAX( dt_3d, dt_stg_call )
1269	!
1270	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1271	!-- created or if old disturbances can be imposed again.
1272	IF ( time_stg_call >= dt_stg_call .AND. &
1273	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1274	stg_call = .TRUE.
1275	ELSE
1276	stg_call = .FALSE.
1277	ENDIF
1278	!
1279	!-- Initial value of fu, fv, fw
1280	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1281	!
1282	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1283	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1284	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1285	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1286	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1287	!-- have the same initial seeds.
1288	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1289	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1290	.AND. .NOT. rans_mode ) ) ) THEN
1291	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1292	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1293	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1294	ELSE
1295	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1296	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1297	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1298	!
1299	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1300	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1301	!-- comment above.
1302	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1303	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1304	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1305	ENDIF
1306	velocity_seed_initialized = .TRUE.
1307	ENDIF
1308	!
1309	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1310	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1311	!-- seeds are required also at the right, south and north boundaries.
1312	IF ( stg_call ) THEN
1313	IF ( .NOT. ( nesting_offline .OR. &
1314	( child_domain .AND. rans_mode_parent &
1315	.AND. .NOT. rans_mode ) ) ) THEN
1316	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1317	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1318	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1319
1320	ELSE
1321	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1322	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1323	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1324
1325	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1326	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1327	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1328	ENDIF
1329	ENDIF
1330
1331	!
1332	!-- Turbulence generation at left and/or right boundary
1333	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1334	!
1335	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1336	!-- exceeded. Else the old set of perturbations is imposed
1337	IF ( stg_call ) THEN
1338
1339	DO j = nys, nyn
1340	DO k = nzb, nzt + 1
1341	!
1342	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1343	IF ( tu(k) == 0.0_wp ) THEN
1344	fu_yz(k,j) = fuo_yz(k,j)
1345	ELSE
1346	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1347	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1348	ENDIF
1349
1350	IF ( tv(k) == 0.0_wp ) THEN
1351	fv_yz(k,j) = fvo_yz(k,j)
1352	ELSE
1353	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1354	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1355	ENDIF
1356
1357	IF ( tw(k) == 0.0_wp ) THEN
1358	fw_yz(k,j) = fwo_yz(k,j)
1359	ELSE
1360	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1361	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1362	ENDIF
1363	ENDDO
1364	ENDDO
1365
1366	dist_yz(nzb,:,1) = 0.0_wp
1367	dist_yz(nzb,:,2) = 0.0_wp
1368	dist_yz(nzb,:,3) = 0.0_wp
1369
1370	IF ( myidx == id_stg_left ) i = nxl
1371	IF ( myidx == id_stg_right ) i = nxr+1
1372	DO j = nys, nyn
1373	DO k = nzb+1, nzt + 1
1374	!
1375	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1376	!-- Additional factors are added to improve the variance of v and w
1377	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * MERGE( 1.0_wp, 0.0_wp, &
1378	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1379	ENDDO
1380	ENDDO
1381
1382	IF ( myidx == id_stg_left ) i = nxl-1
1383	IF ( myidx == id_stg_right ) i = nxr+1
1384	DO j = nys, nyn
1385	DO k = nzb+1, nzt + 1
1386	!
1387	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1388	!-- Additional factors are added to improve the variance of v and w experimental test
1389	!-- of 1.2
1390	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL( a22 ) ) * 1.2_wp ) &
1391	* ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1392	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1393	dist_yz(k,j,3) = MIN( ( SQRT( a33(k) / MAXVAL( a33 ) ) * 1.3_wp ) * &
1394	( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + a33(k) &
1395	* fw_yz(k,j) ), 3.0_wp ) * MERGE( 1.0_wp, 0.0_wp, &
1396	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1397	ENDDO
1398	ENDDO
1399	ENDIF
1400	!
1401	!-- Mass flux correction following Kim et al. (2013)
1402	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1403	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1404	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1405	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1406	mc_factor_l = 0.0_wp
1407	mc_factor = 0.0_wp
1408	!
1409	!-- Sum up the original volume flows (with and without perturbations).
1410	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1411	IF ( myidx == id_stg_left ) i = nxl
1412	IF ( myidx == id_stg_right ) i = nxr+1
1413
1414	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * MERGE( 1.0_wp, 0.0_wp, &
1415	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1416
1417	IF ( myidx == id_stg_left ) i = nxl-1
1418	IF ( myidx == id_stg_right ) i = nxr+1
1419
1420	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * MERGE( 1.0_wp, 0.0_wp, &
1421	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1422	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * MERGE( 1.0_wp, 0.0_wp, &
1423	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1424
1425	#if defined( __parallel )
1426	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1427	#else
1428	mc_factor = mc_factor_l
1429	#endif
1430	!
1431	!-- Calculate correction factor and force zero mean perturbations.
1432	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1433
1434	IF ( myidx == id_stg_left ) i = nxl
1435	IF ( myidx == id_stg_right ) i = nxr+1
1436
1437	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * MERGE( 1.0_wp, 0.0_wp, &
1438	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1439
1440
1441	IF ( myidx == id_stg_left ) i = nxl-1
1442	IF ( myidx == id_stg_right ) i = nxr+1
1443
1444	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * MERGE( 1.0_wp, 0.0_wp, &
1445	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1446
1447	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * MERGE( 1.0_wp, 0.0_wp, &
1448	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1449	!
1450	!-- Add disturbances
1451	IF ( myidx == id_stg_left ) THEN
1452	!
1453	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1454	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1455	!-- the mean inflow profiles.
1456	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1457	!
1458	!-- Add disturbance at the inflow
1459	DO j = nys, nyn
1460	DO k = nzb, nzt+1
1461	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) &
1462	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1463	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) &
1464	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1465	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * MERGE( 1.0_wp, 0.0_wp, &
1466	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1467	ENDDO
1468	ENDDO
1469	ELSE
1470
1471	DO j = nys, nyn
1472	DO k = nzb+1, nzt
1473	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * MERGE( 1.0_wp, 0.0_wp, &
1474	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1475	u(k,j,-1) = u(k,j,0)
1476	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * MERGE( 1.0_wp, 0.0_wp, &
1477	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1478	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * MERGE( 1.0_wp, 0.0_wp, &
1479	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1480	ENDDO
1481	ENDDO
1482	ENDIF
1483	ENDIF
1484	IF ( myidx == id_stg_right ) THEN
1485	DO j = nys, nyn
1486	DO k = nzb+1, nzt
1487	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * MERGE( 1.0_wp, 0.0_wp, &
1488	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1489	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * MERGE( 1.0_wp, 0.0_wp, &
1490	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1491	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * MERGE( 1.0_wp, 0.0_wp, &
1492	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1493	ENDDO
1494	ENDDO
1495	ENDIF
1496	ENDIF
1497	ENDIF
1498	!
1499	!-- Turbulence generation at north and south boundary
1500	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1501	!
1502	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1503	!-- exceeded. Else the old set of perturbations is imposed
1504	IF ( stg_call ) THEN
1505	DO i = nxl, nxr
1506	DO k = nzb, nzt + 1
1507	!
1508	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1509	IF ( tu(k) == 0.0_wp ) THEN
1510	fu_xz(k,i) = fuo_xz(k,i)
1511	ELSE
1512	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1513	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1514	ENDIF
1515
1516	IF ( tv(k) == 0.0_wp ) THEN
1517	fv_xz(k,i) = fvo_xz(k,i)
1518	ELSE
1519	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1520	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1521	ENDIF
1522
1523	IF ( tw(k) == 0.0_wp ) THEN
1524	fw_xz(k,i) = fwo_xz(k,i)
1525	ELSE
1526	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1527	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1528	ENDIF
1529	ENDDO
1530	ENDDO
1531
1532
1533	dist_xz(nzb,:,1) = 0.0_wp
1534	dist_xz(nzb,:,2) = 0.0_wp
1535	dist_xz(nzb,:,3) = 0.0_wp
1536
1537	IF ( myidy == id_stg_south ) j = nys
1538	IF ( myidy == id_stg_north ) j = nyn+1
1539	DO i = nxl, nxr
1540	DO k = nzb+1, nzt + 1
1541	!
1542	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1543	!-- Additional factors are added to improve the variance of v and w
1544	!experimental test of 1.2
1545	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL( a22 ) ) * 1.2_wp ) &
1546	* ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1547	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1548	ENDDO
1549	ENDDO
1550
1551	IF ( myidy == id_stg_south ) j = nys-1
1552	IF ( myidy == id_stg_north ) j = nyn+1
1553	DO i = nxl, nxr
1554	DO k = nzb+1, nzt + 1
1555	!
1556	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1557	!-- Additional factors are added to improve the variance of v and w
1558	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * MERGE( 1.0_wp, 0.0_wp, &
1559	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1560
1561	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL( a33 ) ) * 1.3_wp ) &
1562	* ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + a33(k) &
1563	* fw_xz(k,i) ), 3.0_wp ) * MERGE( 1.0_wp, 0.0_wp, &
1564	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1565	ENDDO
1566	ENDDO
1567	ENDIF
1568
1569	!
1570	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1571	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1572	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1573	!-- else the boundary values won't be accessed.
1574	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1575	mc_factor_l = 0.0_wp
1576	mc_factor = 0.0_wp
1577
1578	IF ( myidy == id_stg_south ) j = nys
1579	IF ( myidy == id_stg_north ) j = nyn+1
1580
1581	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * MERGE( 1.0_wp, 0.0_wp, &
1582	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1583
1584	IF ( myidy == id_stg_south ) j = nys-1
1585	IF ( myidy == id_stg_north ) j = nyn+1
1586
1587	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * MERGE( 1.0_wp, 0.0_wp, &
1588	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1589	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * MERGE( 1.0_wp, 0.0_wp, &
1590	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1591
1592	#if defined( __parallel )
1593	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1594	#else
1595	mc_factor = mc_factor_l
1596	#endif
1597
1598	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1599
1600	IF ( myidy == id_stg_south ) j = nys
1601	IF ( myidy == id_stg_north ) j = nyn+1
1602
1603	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * MERGE( 1.0_wp, 0.0_wp, &
1604	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1605
1606
1607	IF ( myidy == id_stg_south ) j = nys-1
1608	IF ( myidy == id_stg_north ) j = nyn+1
1609
1610	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * MERGE( 1.0_wp, 0.0_wp, &
1611	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1612
1613	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * MERGE( 1.0_wp, 0.0_wp, &
1614	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1615	!
1616	!-- Add disturbances
1617	IF ( myidy == id_stg_south ) THEN
1618	DO i = nxl, nxr
1619	DO k = nzb+1, nzt
1620	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1621	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1622	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1623	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1624	v(k,-1,i) = v(k,0,i)
1625	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1626	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1627	ENDDO
1628	ENDDO
1629	ENDIF
1630	IF ( myidy == id_stg_north ) THEN
1631
1632	DO i = nxl, nxr
1633	DO k = nzb+1, nzt
1634	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * MERGE( 1.0_wp, 0.0_wp, &
1635	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1636	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * MERGE( 1.0_wp, 0.0_wp, &
1637	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1638	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * MERGE( 1.0_wp, 0.0_wp, &
1639	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1640	ENDDO
1641	ENDDO
1642	ENDIF
1643	ENDIF
1644	ENDIF
1645	!
1646	!-- Exchange ghost points.
1647	CALL exchange_horiz( u, nbgp )
1648	CALL exchange_horiz( v, nbgp )
1649	CALL exchange_horiz( w, nbgp )
1650	!
1651	!-- Finally, set time counter for calling STG to zero
1652	IF ( stg_call ) time_stg_call = 0.0_wp
1653
1654	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1655
1656	END SUBROUTINE stg_main
1657
1658	!--------------------------------------------------------------------------------------------------!
1659	! Description:
1660	! ------------
1661	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1662	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1663	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1664	!> array.
1665	!--------------------------------------------------------------------------------------------------!
1666	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1667
1668	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1669	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1670	INTEGER(iwp) :: j !< loop index in y-direction
1671	INTEGER(iwp) :: jj !< loop index in y-direction
1672	INTEGER(iwp) :: k !< loop index in z-direction
1673	INTEGER(iwp) :: kk !< loop index in z-direction
1674	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1675
1676	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1677	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1678
1679	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1680	REAL(wp) :: rand_av !< average of random number
1681	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1682
1683	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1684	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1685
1686	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1687	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1688
1689	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1690	!
1691	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1692	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1693	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1694	!-- and normalization of random numbers is done locally, while the result is later distributed to
1695	!-- all processes. Further, please note, a set of random numbers is only calculated for the left
1696	!-- boundary, while the right boundary uses the same random numbers and thus also computes the same
1697	!-- correlation matrix.
1698	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1699	rand_it = 0.0_wp
1700
1701	rand_av = 0.0_wp
1702	rand_sigma_inv = 0.0_wp
1703	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1704	* ( ny + mergp - ( 0 - mergp ) + 1 ), KIND = wp )
1705	!
1706	!-- Compute and normalize random numbers.
1707	DO j = nys - mergp, nyn + mergp
1708	!
1709	!-- Put the random seeds at grid point j
1710	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1711	DO k = nzb - mergp, nzt + 1 + mergp
1712	CALL random_number_parallel( random_dummy )
1713	rand_it(k,j) = random_dummy
1714	ENDDO
1715	!
1716	!-- Get the new random seeds from last call at grid point j
1717	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1718	ENDDO
1719	!
1720	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1721	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1722	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1723	DO j = MERGE( nys, nys - mergp, nys /= 0 ), MERGE( nyn, nyn + mergp, nyn /= ny )
1724	DO k = nzb - mergp, nzt + 1 + mergp
1725	rand_av = rand_av + rand_it(k,j)
1726	ENDDO
1727	ENDDO
1728
1729	#if defined( __parallel )
1730	!
1731	!-- Sum-up the local averages of the random numbers
1732	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1733	#endif
1734	rand_av = rand_av * nyz_inv
1735	!
1736	!-- Obtain zero mean
1737	rand_it= rand_it - rand_av
1738	!
1739	!-- Now, compute the variance
1740	DO j = MERGE( nys, nys - mergp, nys /= 0 ), MERGE( nyn, nyn + mergp, nyn /= ny )
1741	DO k = nzb - mergp, nzt + 1 + mergp
1742	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1743	ENDDO
1744	ENDDO
1745
1746	#if defined( __parallel )
1747	!
1748	!-- Sum-up the local quadratic averages of the random numbers
1749	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1750	#endif
1751	!
1752	!-- Compute standard deviation
1753	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1754	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1755	ELSE
1756	rand_sigma_inv = 1.0_wp
1757	ENDIF
1758	!
1759	!-- Normalize with standard deviation to obtain unit variance
1760	rand_it = rand_it * rand_sigma_inv
1761
1762	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1763	!
1764	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1765	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1766	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1767	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1768	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1769	!-- communication. In the second option, which performs better when the turbulent length scales
1770	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1771	!-- communication is necessary.
1772	IF ( compute_velocity_seeds_local ) THEN
1773
1774	f_n = 0.0_wp
1775	DO j = nys, nyn
1776	DO k = nzb, nzt+1
1777	DO jj = -n_y(k), n_y(k)
1778	DO kk = -n_z(k), n_z(k)
1779	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1780	ENDDO
1781	ENDDO
1782	ENDDO
1783	ENDDO
1784
1785	ELSE
1786
1787	f_n_l = 0.0_wp
1788	DO j = nys, nyn
1789	DO k = nzb_x_stg, nzt_x_stg+1
1790	DO jj = -n_y(k), n_y(k)
1791	DO kk = -n_z(k), n_z(k)
1792	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1793	ENDDO
1794	ENDDO
1795	ENDDO
1796	ENDDO
1797	!
1798	!-- Gather velocity seeds of full subdomain
1799	send_count = nzt_x_stg - nzb_x_stg + 1
1800	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1801
1802	#if defined( __parallel )
1803	!
1804	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1805	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1806	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1807	!
1808	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1809	!-- nesting for example).
1810	IF ( PRESENT( id_right ) ) THEN
1811	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1812	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1813	ENDIF
1814	#else
1815	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1816	!
1817	!-- Next line required to avoid compile errors because of unused dummy arguments
1818	IF ( id_left == 0 ) id_right = 0
1819	#endif
1820
1821	ENDIF
1822
1823	DEALLOCATE( rand_it )
1824
1825	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1826
1827	END SUBROUTINE stg_generate_seed_yz
1828
1829
1830	!--------------------------------------------------------------------------------------------------!
1831	! Description:
1832	! ------------
1833	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1834	!> f_n.
1835	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1836	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1837	!> full array.
1838	!--------------------------------------------------------------------------------------------------!
1839	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1840
1841	INTEGER(iwp) :: i !< loop index in x-direction
1842	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1843	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1844	INTEGER(iwp) :: ii !< loop index in x-direction
1845	INTEGER(iwp) :: k !< loop index in z-direction
1846	INTEGER(iwp) :: kk !< loop index in z-direction
1847	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1848
1849	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1850	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1851
1852	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1853	REAL(wp) :: rand_av !< average of random number
1854	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1855
1856	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1857	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1858
1859	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1860	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1861
1862	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1863
1864	!
1865	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1866	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1867	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1868	!-- and normalization of random numbers is done locally, while the result is later distributed to
1869	!-- all processes. Further, please note, a set of random numbers is only calculated for the left
1870	!-- boundary, while the right boundary uses the same random numbers and thus also computes the same
1871	!-- correlation matrix.
1872	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
1873	rand_it = 0.0_wp
1874
1875	rand_av = 0.0_wp
1876	rand_sigma_inv = 0.0_wp
1877	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1878	* ( nx + mergp - ( 0 - mergp ) +1 ), KIND = wp )
1879	!
1880	!-- Compute and normalize random numbers.
1881	DO i = nxl - mergp, nxr + mergp
1882	!
1883	!-- Put the random seeds at grid point ii
1884	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1885	DO k = nzb - mergp, nzt + 1 + mergp
1886	CALL random_number_parallel( random_dummy )
1887	rand_it(k,i) = random_dummy
1888	ENDDO
1889	!
1890	!-- Get the new random seeds from last call at grid point ii
1891	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1892	ENDDO
1893	!
1894	!-- For normalization to zero mean, sum-up the global random numers.
1895	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1896	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1897	!-- also occur on the inner subdomains.
1898	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), MERGE( nxr, nxr + mergp, nxr /= nx )
1899	DO k = nzb - mergp, nzt + 1 + mergp
1900	rand_av = rand_av + rand_it(k,i)
1901	ENDDO
1902	ENDDO
1903
1904	#if defined( __parallel )
1905	!
1906	!-- Sum-up the local averages of the random numbers
1907	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1908	#endif
1909	rand_av = rand_av * nxz_inv
1910	!
1911	!-- Obtain zero mean
1912	rand_it= rand_it - rand_av
1913	!
1914	!-- Now, compute the variance
1915	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), MERGE( nxr, nxr + mergp, nxr /= nx )
1916	DO k = nzb - mergp, nzt + 1 + mergp
1917	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1918	ENDDO
1919	ENDDO
1920
1921	#if defined( __parallel )
1922	!
1923	!-- Sum-up the local quadratic averages of the random numbers
1924	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1925	#endif
1926	!
1927	!-- Compute standard deviation
1928	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1929	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1930	ELSE
1931	rand_sigma_inv = 1.0_wp
1932	ENDIF
1933	!
1934	!-- Normalize with standard deviation to obtain unit variance
1935	rand_it = rand_it * rand_sigma_inv
1936
1937	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1938	!
1939	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1940	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1941	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
1942	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1943	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
1944	!-- In the second option, which performs better when the turbulent length scales are parametrized
1945	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
1946	IF ( compute_velocity_seeds_local ) THEN
1947
1948	f_n = 0.0_wp
1949	DO i = nxl, nxr
1950	DO k = nzb, nzt+1
1951	DO ii = -n_x(k), n_x(k)
1952	DO kk = -n_z(k), n_z(k)
1953	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1954	ENDDO
1955	ENDDO
1956	ENDDO
1957	ENDDO
1958
1959	ELSE
1960
1961	f_n_l = 0.0_wp
1962	DO i = nxl, nxr
1963	DO k = nzb_y_stg, nzt_y_stg+1
1964	DO ii = -n_x(k), n_x(k)
1965	DO kk = -n_z(k), n_z(k)
1966	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1967	ENDDO
1968	ENDDO
1969	ENDDO
1970	ENDDO
1971	!
1972	!-- Gather velocity seeds of full subdomain
1973	send_count = nzt_y_stg - nzb_y_stg + 1
1974	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
1975
1976	#if defined( __parallel )
1977	!
1978	!-- Gather the processed velocity seed on south boundary mpi ranks.
1979	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
1980	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
1981	!
1982	!-- Gather the processed velocity seed on north boundary mpi ranks.
1983	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
1984	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
1985	#else
1986	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
1987	!
1988	!-- Next line required to avoid compile errors because of unused dummy arguments
1989	IF ( id_north == 0 ) id_south = 0
1990	#endif
1991
1992	ENDIF
1993
1994	DEALLOCATE( rand_it )
1995
1996	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1997
1998	END SUBROUTINE stg_generate_seed_xz
1999
2000	!--------------------------------------------------------------------------------------------------!
2001	! Description:
2002	! ------------
2003	!> Parametrization of the Reynolds stress tensor, following the parametrization described in Rotach
2004	!> et al. (1996), which is applied in state-of-the-art dispserion modelling. Please note, the
2005	!> parametrization does not distinguish between along-wind and cross-wind turbulence.
2006	!--------------------------------------------------------------------------------------------------!
2007	SUBROUTINE parametrize_reynolds_stress
2008
2009	INTEGER(iwp) :: k !< loop index in z-direction
2010
2011	REAL(wp) :: zzi !< ratio of z/zi
2012
2013	DO k = nzb+1, nzt+1
2014	!
2015	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2016	!-- The function decreases to 1/10 after one length scale above the ABL top.
2017	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2018	!
2019	!-- Determine normalized height coordinate
2020	zzi = zu(k) / zi_ribulk
2021	!
2022	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2023	!-- the mergpe-function can crash if scale_l is zero.
2024	r11(k) = scale_us*2 ( MERGE( 0.35_wp &
2025	* ABS( - zi_ribulk / ( kappa * scale_l - 10E-4_wp ) )**( 2.0_wp / 3.0_wp ), &
2026	0.0_wp, scale_l < 0.0_wp ) + 5.0_wp - 4.0_wp * zzi ) * blend
2027
2028	r22(k) = r11(k)
2029	!
2030	!-- w'w'
2031	r33(k) = scale_wm*2 ( 1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2032	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )*2 ) blend
2033	!
2034	!-- u'w' and v'w'. Assume isotropy.
2035	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2036	r32(k) = r31(k)
2037	!
2038	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as for
2039	!-- u'w'.
2040	r21(k) = r31(k)
2041	ENDDO
2042
2043	!
2044	!-- Set bottom boundary condition
2045	r11(nzb) = r11(nzb+1)
2046	r22(nzb) = r22(nzb+1)
2047	r33(nzb) = r33(nzb+1)
2048
2049	r21(nzb) = r11(nzb+1)
2050	r31(nzb) = r31(nzb+1)
2051	r32(nzb) = r32(nzb+1)
2052
2053
2054	END SUBROUTINE parametrize_reynolds_stress
2055
2056	!--------------------------------------------------------------------------------------------------!
2057	! Description:
2058	! ------------
2059	!> Calculate the coefficient matrix from the Lund rotation.
2060	!--------------------------------------------------------------------------------------------------!
2061	SUBROUTINE calc_coeff_matrix
2062
2063	INTEGER(iwp) :: k !< loop index in z-direction
2064
2065	!
2066	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2067	DO k = nzb+1, nzt+1
2068	IF ( r11(k) > 10E-6_wp ) THEN
2069	a11(k) = SQRT( r11(k) )
2070	a21(k) = r21(k) / a11(k)
2071	a31(k) = r31(k) / a11(k)
2072	ELSE
2073	a11(k) = 10E-8_wp
2074	a21(k) = 10E-8_wp
2075	a31(k) = 10E-8_wp
2076	ENDIF
2077	ENDDO
2078	DO k = nzb+1, nzt+1
2079	a22(k) = r22(k) - a21(k)**2
2080	IF ( a22(k) > 10E-6_wp ) THEN
2081	a22(k) = SQRT( a22(k) )
2082	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2083	ELSE
2084	a22(k) = 10E-8_wp
2085	a32(k) = 10E-8_wp
2086	ENDIF
2087	ENDDO
2088	DO k = nzb+1, nzt+1
2089	a33(k) = r33(k) - a31(k)2 - a32(k)2
2090	IF ( a33(k) > 10E-6_wp ) THEN
2091	a33(k) = SQRT( a33(k) )
2092	ELSE
2093	a33(k) = 10E-8_wp
2094	ENDIF
2095	ENDDO
2096	!
2097	!-- Set bottom boundary condition
2098	a11(nzb) = a11(nzb+1)
2099	a22(nzb) = a22(nzb+1)
2100	a21(nzb) = a21(nzb+1)
2101	a33(nzb) = a33(nzb+1)
2102	a31(nzb) = a31(nzb+1)
2103	a32(nzb) = a32(nzb+1)
2104
2105	END SUBROUTINE calc_coeff_matrix
2106
2107	!--------------------------------------------------------------------------------------------------!
2108	! Description:
2109	! ------------
2110	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2111	!> turbulence at the lateral boundaries.
2112	!--------------------------------------------------------------------------------------------------!
2113	SUBROUTINE stg_adjust
2114
2115	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2116	!
2117	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2118	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2119	!-- nevertheless, the boundary-layer depth need to determined first.
2120	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2121	CALL nesting_offl_calc_zi
2122	!
2123	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2124	CALL calc_scaling_variables
2125	!
2126	!-- Set length and time scales depending on boundary-layer height
2127	CALL calc_length_and_time_scale
2128	!
2129	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
2130	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
2131	!-- friction velocity and velocity scale.
2132	CALL parametrize_reynolds_stress
2133	!
2134	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
2135	CALL calc_coeff_matrix
2136	!
2137	!-- Determine filter functions on basis of updated length scales
2138	CALL stg_filter_func( nux, bux ) !filter ux
2139	CALL stg_filter_func( nuy, buy ) !filter uy
2140	CALL stg_filter_func( nuz, buz ) !filter uz
2141	CALL stg_filter_func( nvx, bvx ) !filter vx
2142	CALL stg_filter_func( nvy, bvy ) !filter vy
2143	CALL stg_filter_func( nvz, bvz ) !filter vz
2144	CALL stg_filter_func( nwx, bwx ) !filter wx
2145	CALL stg_filter_func( nwy, bwy ) !filter wy
2146	CALL stg_filter_func( nwz, bwz ) !filter wz
2147	!
2148	!-- Reset time counter for controlling next adjustment to zero
2149	time_stg_adjust = 0.0_wp
2150
2151	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2152
2153	END SUBROUTINE stg_adjust
2154
2155
2156	!--------------------------------------------------------------------------------------------------!
2157	! Description:
2158	! ------------
2159	!> Calculates turbuluent length and time scales if these are not available from measurements.
2160	!--------------------------------------------------------------------------------------------------!
2161	SUBROUTINE calc_length_and_time_scale
2162
2163	INTEGER(iwp) :: k !< loop index in z-direction
2164
2165	REAL(wp) :: length_scale_dum !< effectively used length scale
2166
2167	!
2168	!-- In initial call the boundary-layer depth can be zero. This case, set minimum value for
2169	!-- boundary-layer depth, to setup length scales correctly.
2170	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2171	!
2172	!-- Set-up default turbulent length scales. From the numerical point of view the imposed
2173	!-- perturbations should not be immediately dissipated by the numerics. The numerical dissipation,
2174	!-- however, acts on scales up to 8 x the grid spacing. For this reason, set the turbulence length
2175	!-- scale to 8 time the grid spacing. Further, above the boundary layer height, set turbulence
2176	!-- lenght scales to zero (equivalent to not imposing any perturbations) in order to save
2177	!-- computational costs. Typical time scales are derived by assuming Taylors's hypothesis, using
2178	!-- the length scales and the mean profiles of u- and v-component.
2179	DO k = nzb+1, nzt+1
2180	!
2181	!-- Determine blending parameter. Within the boundary layer length scales are constant, while
2182	!-- above lengths scales approach gradully zero, i.e. imposed turbulence is not correlated in
2183	!-- space and time, just white noise, which saves computations power as the loops for the
2184	!-- computation of the filter functions depend on the length scales. The value decreases to
2185	!-- 1/10 after one length scale above the ABL top.
2186	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2187	!
2188	!-- Assume isotropic turbulence length scales
2189	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2190	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2191	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2192	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2193	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2194	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2195	!
2196	!-- Along the vertical direction limit the length scale further by the boundary-layer depth to
2197	!-- assure that no length scales larger than the boundary-layer depth are used
2198	length_scale_dum = MIN( length_scale, zi_ribulk )
2199
2200	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2201	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2202	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2203	!
2204	!-- Limit time scales, else they become very larger for low wind speed, imposing long-living
2205	!-- inflow perturbations which in turn propagate further into the model domain. Use u_init and
2206	!-- v_init to calculate the time scales, which will be equal to the inflow profiles, both, in
2207	!-- offline nesting mode or in dirichlet/radiation mode.
2208	tu(k) = MIN( dt_stg_adjust, length_scale / ( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2209	tv(k) = MIN( dt_stg_adjust, length_scale / ( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2210	!
2211	!-- Time scale of w-component is a mixture from u- and v-component.
2212	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2213
2214	ENDDO
2215	!
2216	!-- Set bottom boundary condition for the length and time scales
2217	nux(nzb) = nux(nzb+1)
2218	nuy(nzb) = nuy(nzb+1)
2219	nuz(nzb) = nuz(nzb+1)
2220	nvx(nzb) = nvx(nzb+1)
2221	nvy(nzb) = nvy(nzb+1)
2222	nvz(nzb) = nvz(nzb+1)
2223	nwx(nzb) = nwx(nzb+1)
2224	nwy(nzb) = nwy(nzb+1)
2225	nwz(nzb) = nwz(nzb+1)
2226
2227	tu(nzb) = tu(nzb+1)
2228	tv(nzb) = tv(nzb+1)
2229	tw(nzb) = tw(nzb+1)
2230
2231
2232	END SUBROUTINE calc_length_and_time_scale
2233
2234	!--------------------------------------------------------------------------------------------------!
2235	! Description:
2236	! ------------
2237	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2238	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2239	!> scale, and Obukhov length.
2240	!--------------------------------------------------------------------------------------------------!
2241	SUBROUTINE calc_scaling_variables
2242
2243	INTEGER(iwp) :: i !< loop index in x-direction
2244	INTEGER(iwp) :: j !< loop index in y-direction
2245	INTEGER(iwp) :: k !< loop index in z-direction
2246	INTEGER(iwp) :: m !< surface element index
2247
2248	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2249	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2250	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2251	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2252	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2253	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2254	REAL(wp) :: w_convective !< convective velocity scale
2255
2256	!
2257	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2258	!-- model domain.
2259	pt_surf_mean_l = 0.0_wp
2260	shf_mean_l = 0.0_wp
2261	scale_l_l = 0.0_wp
2262	friction_vel_l = 0.0_wp
2263	DO m = 1, surf_def_h(0)%ns
2264	i = surf_def_h(0)%i(m)
2265	j = surf_def_h(0)%j(m)
2266	k = surf_def_h(0)%k(m)
2267	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2268	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2269	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2270	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2271	ENDDO
2272	DO m = 1, surf_lsm_h%ns
2273	i = surf_lsm_h%i(m)
2274	j = surf_lsm_h%j(m)
2275	k = surf_lsm_h%k(m)
2276	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2277	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2278	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2279	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2280	ENDDO
2281	DO m = 1, surf_usm_h%ns
2282	i = surf_usm_h%i(m)
2283	j = surf_usm_h%j(m)
2284	k = surf_usm_h%k(m)
2285	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2286	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2287	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2288	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2289	ENDDO
2290
2291	#if defined( __parallel )
2292	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2293	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2294	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2295	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2296	#else
2297	scale_us = friction_vel_l
2298	shf_mean = shf_mean_l
2299	scale_l = scale_l_l
2300	pt_surf_mean = pt_surf_mean_l
2301	#endif
2302
2303	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2304	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2305	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2306	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2307	!
2308	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2309	!-- convective velocity scale to zero.
2310	IF ( shf_mean > 0.0_wp ) THEN
2311	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2312	ELSE
2313	w_convective = 0.0_wp
2314	ENDIF
2315	!
2316	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2317	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2318	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2319
2320	END SUBROUTINE calc_scaling_variables
2321
2322	END MODULE synthetic_turbulence_generator_mod

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