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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4850

Last change on this file since 4850 was 4848, checked in by gronemeier, 3 years ago
bugfix: removed syn_turb_gen from restart files, replaced use_syn_turb_gen by syn_turb_gen
Property svn:keywords set to `Id`
File size: 112.9 KB

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1	!> @synthetic_turbulence_generator_mod.f90
2	!--------------------------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2021 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4848 2021-01-21 15:51:51Z suehring $
27	! replaced use_syn_turb_gen by syn_turb_gen
28	!
29	! 4843 2021-01-15 15:22:11Z raasch
30	! local namelist parameter added to switch off the module although the respective module namelist
31	! appears in the namelist file
32	!
33	! 4842 2021-01-14 10:42:28Z raasch
34	! reading of namelist file and actions in case of namelist errors revised so that statement labels
35	! and goto statements are not required any more
36	!
37	! 4828 2021-01-05 11:21:41Z Giersch
38	! Implementation of downward facing USM and LSM surfaces
39	!
40	! 4647 2020-08-24 16:36:18Z suehring
41	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
42	! By default, the random-seed computation is now distributed among several cores. Especially for
43	! large length scales this is significantly faster.
44	!
45	! 4640 2020-08-11 16:28:32Z suehring
46	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
47	! Obukhov length (term is not valid for near neutral conditions)
48	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
49	! the vertical transport of horizontal momentum
50	!
51	! 4629 2020-07-29 09:37:56Z raasch
52	! support for MPI Fortran77 interface (mpif.h) removed
53	!
54	! 4603 2020-07-14 16:08:30Z suehring
55	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
56	! initialized properly
57	!
58	! 4566 2020-06-16 10:11:51Z suehring
59	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
60	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
61	! - change default value of time interval to adjust turbulence parametrization
62	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
63	!
64	! 4562 2020-06-12 08:38:47Z raasch
65	! Parts of r4559 re-formatted
66	!
67	! 4559 2020-06-11 08:51:48Z raasch
68	! File re-formatted to follow the PALM coding standard
69	!
70	! 4535 2020-05-15 12:07:23Z raasch
71	! Bugfix for restart data format query
72	!
73	! 4495 2020-04-13 20:11:20Z raasch
74	! Restart data handling with MPI-IO added
75	!
76	! 4481 2020-03-31 18:55:54Z maronga
77	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
78	!
79	! 4442 2020-03-04 19:21:13Z suehring
80	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
81	! (was accidantly changed).
82	!
83	! 4441 2020-03-04 19:20:35Z suehring
84	! Correct misplaced preprocessor directive
85	!
86	! 4438 2020-03-03 20:49:28Z suehring
87	! Performance optimizations in velocity-seed calculation:
88	! - Random number array is only defined and computed locally (except for normalization to zero mean
89	! and unit variance)
90	! - Parallel random number generator is applied independent on the 2D random numbers in other
91	! routines
92	! - Option to decide wheter velocity seeds are computed locally without any further communication
93	! or are computed by all processes along the communicator
94	!
95	! 4346 2019-12-18 11:55:56Z motisi
96	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
97	! information used in wall_flags_static_0
98	!
99	! 4335 2019-12-12 16:39:05Z suehring
100	! Commentation of last commit
101	!
102	! 4332 2019-12-10 19:44:12Z suehring
103	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
104	! Further, minor bugfix in initial velocity seed calculation.
105	!
106	! 4329 2019-12-10 15:46:36Z motisi
107	! Renamed wall_flags_0 to wall_flags_static_0
108	!
109	! 4309 2019-11-26 18:49:59Z suehring
110	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
111	! the parallel random number generator. Random numbers are now only computed and normalized locally,
112	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
113	! array.
114	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
115	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
116	!
117	! 4182 2019-08-22 15:20:23Z scharf
118	! Corrected "Former revisions" section
119	!
120	! 4148 2019-08-08 11:26:00Z suehring
121	! Remove unused variable
122	!
123	! 4144 2019-08-06 09:11:47Z raasch
124	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
125	!
126	! 4071 2019-07-03 20:02:00Z suehring
127	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
128	! file.
129	!
130	! 4022 2019-06-12 11:52:39Z suehring
131	! Several bugfixes and improvements
132	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
133	! instabilities in case the mean volume flow is close to zero)
134	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
135	! numerically unstable
136	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
137	! case dt_stg_call /= dt_3d
138	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
139	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
140	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
141	!
142	! 3987 2019-05-22 09:52:13Z kanani
143	! Introduce alternative switch for debug output during timestepping
144	!
145	! 3938 2019-04-29 16:06:25Z suehring
146	! Remove unused variables
147	!
148	! 3937 2019-04-29 15:09:07Z suehring
149	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
150	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
151	! synthetic turbulence parametrization.
152	!
153	! 3909 2019-04-17 09:13:25Z suehring
154	! Minor bugfix for last commit
155	!
156	! 3900 2019-04-16 15:17:43Z suehring
157	! Missing re-calculation of perturbation seeds in case of restarts
158	!
159	! 3891 2019-04-12 17:52:01Z suehring
160	! Bugfix in initialization in case of restart runs.
161	!
162	! 3885 2019-04-11 11:29:34Z kanani
163	! Changes related to global restructuring of location messages and introduction of additional debug
164	! messages
165	!
166	!
167	! Removed unused variables
168	!
169	! 3719 2019-02-06 13:10:18Z kanani
170	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
171	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
172	! for better overview.
173	!
174	! 2259 2017-06-08 09:09:11Z gronemeier
175	! Initial revision
176	!
177	! Authors:
178	! --------
179	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
180	!
181	!
182	! Description:
183	! ------------
184	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
185	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
186	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
187	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
188	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
189	!> parametrized within the boundary layer.
190	!>
191	!> @todo Enable cyclic_fill
192	!> Implement turbulence generation for e and pt
193	!> @note <Enter notes on the module>
194	!> @bug Height information from input file is not used. Profiles from input must match with current
195	!> PALM grid.
196	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
197	!--------------------------------------------------------------------------------------------------!
198	MODULE synthetic_turbulence_generator_mod
199
200
201	USE arrays_3d, &
202	ONLY: dzw, &
203	ddzw, &
204	drho_air, &
205	mean_inflow_profiles, &
206	pt, &
207	pt_init, &
208	q, &
209	q_init, &
210	u, &
211	u_init, &
212	v, &
213	v_init, &
214	w, &
215	zu, &
216	zw
217
218	USE basic_constants_and_equations_mod, &
219	ONLY: g, &
220	kappa, &
221	pi
222
223	USE control_parameters, &
224	ONLY: bc_lr, &
225	bc_ns, &
226	child_domain, &
227	coupling_char, &
228	debug_output_timestep, &
229	dt_3d, &
230	e_init, &
231	humidity, &
232	initializing_actions, &
233	intermediate_timestep_count, &
234	intermediate_timestep_count_max, &
235	length, &
236	message_string, &
237	nesting_offline, &
238	neutral, &
239	num_mean_inflow_profiles, &
240	random_generator, &
241	rans_mode, &
242	restart_data_format_output, &
243	restart_string, &
244	syn_turb_gen, &
245	time_since_reference_point, &
246	turbulent_inflow
247
248	USE cpulog, &
249	ONLY: cpu_log, &
250	log_point_s
251
252	USE grid_variables, &
253	ONLY: ddx, &
254	ddy, &
255	dx, &
256	dy
257
258	USE indices, &
259	ONLY: nbgp, &
260	nz, &
261	nzb, &
262	nzt, &
263	nx, &
264	nxl, &
265	nxlu, &
266	nxr, &
267	ny, &
268	nys, &
269	nysv, &
270	nyn, &
271	wall_flags_total_0
272
273	USE kinds
274
275	#if defined( __parallel )
276	USE MPI
277	#endif
278
279	USE nesting_offl_mod, &
280	ONLY: nesting_offl_calc_zi, &
281	zi_ribulk
282
283	USE pegrid, &
284	ONLY: comm1dx, &
285	comm1dy, &
286	comm2d, &
287	ierr, &
288	myidx, &
289	myidy, &
290	pdims
291
292	USE pmc_interface, &
293	ONLY : rans_mode_parent
294
295	USE random_generator_parallel, &
296	ONLY: init_parallel_random_generator, &
297	random_dummy, &
298	random_number_parallel, &
299	random_seed_parallel
300
301	USE restart_data_mpi_io_mod, &
302	ONLY: rrd_mpi_io, &
303	wrd_mpi_io
304
305	USE transpose_indices, &
306	ONLY: nzb_x, &
307	nzt_x
308
309	USE surface_mod, &
310	ONLY: surf_def_h, &
311	surf_lsm_h, &
312	surf_usm_h
313
314	IMPLICIT NONE
315
316	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
317	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
318	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
319	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
320	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
321	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
322	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
323	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
324	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
325	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
326	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
327	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
328	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
329	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
330	#if defined( __parallel )
331	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
332	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
333	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
334	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
335	#endif
336
337	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
338	!< required for bias correction of imposed perturbations
339	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
340	!< required for bias correction of imposed perturbations
341
342	#if defined( __parallel )
343	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
344	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
345	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
346	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
347	#endif
348	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
349	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
350	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
351	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
352	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
353	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
354	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
355	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
356	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
357
358	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
359	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
360	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
361	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
362
363
364	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
365	!< no time correlation to the timestep before should be considered
366	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
367	!< or if computation is distributed over several processes
368	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
369	!< (.FALSE.) or if it parametrized
370	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
371
372
373	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
374	!< scales above the boundary layer
375	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
376	!< one length scale above ABL top
377	REAL(wp) :: d_l !< blend_coeff/length_scale
378	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
379	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
380	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
381	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
382	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
383	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
384	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
385	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
386
387	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
388
389
390	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
391	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
392	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
393	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
394	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
395	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
396
397	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
398	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
399	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
400	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
401	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
402	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
403	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
404	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
405	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
406
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
418	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
419	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
420	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
421	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
422	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
423	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
424	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
425	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
426	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
427	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
428
429	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
430	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
431
432	!
433	!-- PALM interfaces:
434	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
435	INTERFACE stg_adjust
436	MODULE PROCEDURE stg_adjust
437	END INTERFACE stg_adjust
438	!
439	!-- Input parameter checks to be done in check_parameters
440	INTERFACE stg_check_parameters
441	MODULE PROCEDURE stg_check_parameters
442	END INTERFACE stg_check_parameters
443
444	!
445	!-- Calculate filter functions
446	INTERFACE stg_filter_func
447	MODULE PROCEDURE stg_filter_func
448	END INTERFACE stg_filter_func
449
450	!
451	!-- Generate velocity seeds at south and north domain boundary
452	INTERFACE stg_generate_seed_xz
453	MODULE PROCEDURE stg_generate_seed_xz
454	END INTERFACE stg_generate_seed_xz
455	!
456	!-- Generate velocity seeds at left and/or right domain boundary
457	INTERFACE stg_generate_seed_yz
458	MODULE PROCEDURE stg_generate_seed_yz
459	END INTERFACE stg_generate_seed_yz
460
461	!
462	!-- Output of information to the header file
463	INTERFACE stg_header
464	MODULE PROCEDURE stg_header
465	END INTERFACE stg_header
466
467	!
468	!-- Initialization actions
469	INTERFACE stg_init
470	MODULE PROCEDURE stg_init
471	END INTERFACE stg_init
472
473	!
474	!-- Main procedure of synth. turb. gen.
475	INTERFACE stg_main
476	MODULE PROCEDURE stg_main
477	END INTERFACE stg_main
478
479	!
480	!-- Reading of NAMELIST parameters
481	INTERFACE stg_parin
482	MODULE PROCEDURE stg_parin
483	END INTERFACE stg_parin
484
485	!
486	!-- Reading of parameters for restart runs
487	INTERFACE stg_rrd_global
488	MODULE PROCEDURE stg_rrd_global_ftn
489	MODULE PROCEDURE stg_rrd_global_mpi
490	END INTERFACE stg_rrd_global
491
492	!
493	!-- Writing of binary output for restart runs
494	INTERFACE stg_wrd_global
495	MODULE PROCEDURE stg_wrd_global
496	END INTERFACE stg_wrd_global
497
498	SAVE
499
500	PRIVATE
501
502	!
503	!-- Public interfaces
504	PUBLIC stg_adjust, &
505	stg_check_parameters, &
506	stg_header, &
507	stg_init, &
508	stg_main, &
509	stg_parin, &
510	stg_rrd_global, &
511	stg_wrd_global
512
513	!
514	!-- Public variables
515	PUBLIC dt_stg_call, &
516	dt_stg_adjust, &
517	id_stg_left, &
518	id_stg_north, &
519	id_stg_right, &
520	id_stg_south, &
521	parametrize_inflow_turbulence, &
522	time_stg_adjust, &
523	time_stg_call
524
525
526	CONTAINS
527
528
529	!--------------------------------------------------------------------------------------------------!
530	! Description:
531	! ------------
532	!> Check parameters routine for synthetic turbulence generator
533	!--------------------------------------------------------------------------------------------------!
534	SUBROUTINE stg_check_parameters
535
536	IF ( .NOT. syn_turb_gen .AND. .NOT. rans_mode .AND. &
537	nesting_offline ) THEN
538	message_string = 'Synthetic turbulence generator is required ' // &
539	'if offline nesting is applied and PALM operates in LES mode.'
540	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
541	ENDIF
542
543	IF ( .NOT. syn_turb_gen .AND. child_domain &
544	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
545	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
546	'and parent operates in RANS-mode but current child in LES mode.'
547	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
548	ENDIF
549
550	IF ( syn_turb_gen ) THEN
551
552	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
553	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
554	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
555
556	ENDIF
557
558	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
559	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
560	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
561
562	ENDIF
563
564	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
565
566	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
567	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
568	message_string = 'Using synthetic turbulence generator requires ' // &
569	'%initializing_actions = "set_constant_profiles" or ' // &
570	' "read_restart_data", if not offline nesting is applied.'
571	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
572	ENDIF
573
574	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
575	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
576	' "dirichlet/radiation", if not offline nesting is applied.'
577	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
578	ENDIF
579	IF ( bc_ns /= 'cyclic' ) THEN
580	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
581	' "cyclic", if not offline nesting is applied.'
582	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
583	ENDIF
584
585	ENDIF
586
587	IF ( turbulent_inflow ) THEN
588	message_string = 'Using synthetic turbulence generator in combination ' // &
589	'&with turbulent_inflow = .T. is not allowed'
590	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
591	ENDIF
592	!
593	!-- Synthetic turbulence generator requires the parallel random generator
594	IF ( random_generator /= 'random-parallel' ) THEN
595	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
596	'random-parallel.'
597	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
598	ENDIF
599
600	ENDIF
601
602	END SUBROUTINE stg_check_parameters
603
604
605	!--------------------------------------------------------------------------------------------------!
606	! Description:
607	! ------------
608	!> Header output for synthetic turbulence generator
609	!--------------------------------------------------------------------------------------------------!
610	SUBROUTINE stg_header ( io )
611
612	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
613
614	!
615	!-- Write synthetic turbulence generator Header
616	IF ( syn_turb_gen ) THEN
617	WRITE( io, 1 )
618	IF ( parametrize_inflow_turbulence ) THEN
619	WRITE( io, 4 ) dt_stg_adjust
620	ELSE
621	WRITE( io, 5 )
622	ENDIF
623	ENDIF
624
625	1 FORMAT (//' Synthetic turbulence generator information:'/ &
626	' ------------------------------------------'/)
627	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
628	5 FORMAT (' imposed turbulence is read from file' )
629
630	END SUBROUTINE stg_header
631
632
633	!--------------------------------------------------------------------------------------------------!
634	! Description:
635	! ------------
636	!> Initialization of the synthetic turbulence generator
637	!--------------------------------------------------------------------------------------------------!
638	SUBROUTINE stg_init
639
640	#if defined( __parallel )
641	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
642	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
643	#endif
644
645	INTEGER(iwp) :: i !> grid index in x-direction
646	INTEGER(iwp) :: j !> loop index
647	INTEGER(iwp) :: k !< index
648	#if defined( __parallel )
649	INTEGER(iwp) :: newtype !< dummy MPI type
650	INTEGER(iwp) :: realsize !< size of REAL variables
651	#endif
652
653	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
654	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
655
656
657	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
658
659	!
660	!-- Dummy variables used for reading profiles
661	REAL(wp) :: d1 !< u profile
662	REAL(wp) :: d2 !< v profile
663	REAL(wp) :: d3 !< w profile
664	REAL(wp) :: d5 !< e profile
665	REAL(wp) :: luy !< length scale for u in y direction
666	REAL(wp) :: luz !< length scale for u in z direction
667	REAL(wp) :: lvy !< length scale for v in y direction
668	REAL(wp) :: lvz !< length scale for v in z direction
669	REAL(wp) :: lwy !< length scale for w in y direction
670	REAL(wp) :: lwz !< length scale for w in z direction
671	#if defined( __parallel )
672	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
673	#endif
674	REAL(wp) :: zz !< height
675
676
677	#if defined( __parallel )
678	CALL MPI_BARRIER( comm2d, ierr )
679	#endif
680	!
681	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
682	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
683	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
684	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
685	!-- communication).
686	IF ( .NOT. compute_velocity_seeds_local ) THEN
687	#if defined( __parallel )
688	!
689	!-- Determine processor decomposition of z-axis along x- and y-direction
690	nnz = nz / pdims(1)
691	nzb_x_stg = 1 + myidx * INT( nnz )
692	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
693
694	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
695	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
696
697	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
698	.AND. .NOT. rans_mode ) ) THEN
699	nnz = nz / pdims(2)
700	nzb_y_stg = 1 + myidy * INT( nnz )
701	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
702
703	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
704	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
705	ENDIF
706
707	!
708	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
709	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
710	extent = 1 * realsize
711	!
712	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
713	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
714	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
715	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
716	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
717	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
718	CALL MPI_TYPE_FREE( newtype, ierr )
719
720	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
721	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
722	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
723	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
724	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
725	CALL MPI_TYPE_FREE( newtype, ierr )
726
727	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
728	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
729
730	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
731	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
732
733	DO j = 1, pdims(1)
734	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
735	ENDDO
736	!
737	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
738	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
739	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
740	.AND. .NOT. rans_mode ) ) THEN
741	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
742	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
743	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
744	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
745	CALL MPI_TYPE_FREE( newtype, ierr )
746
747	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
748	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
749	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
750	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
751	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
752	CALL MPI_TYPE_FREE( newtype, ierr )
753
754	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
755	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
756
757	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
758	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
759
760	DO j = 1, pdims(2)
761	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
762	ENDDO
763
764	ENDIF
765	#endif
766	ENDIF
767	!
768	!-- Allocate required arrays.
769	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
770	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
771	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
772	!-- and initialized appropriately.
773	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
774	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
775	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
776	mean_inflow_profiles = 0.0_wp
777	mean_inflow_profiles(:,1) = u_init
778	mean_inflow_profiles(:,2) = v_init
779	!
780	!-- Even though potential temperature and humidity are not perturbed, they need to be
781	!-- initialized appropriately.
782	IF ( .NOT. neutral ) &
783	mean_inflow_profiles(:,4) = pt_init
784	IF ( humidity ) &
785	mean_inflow_profiles(:,6) = q_init
786	ENDIF
787	ENDIF
788	!
789	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
790	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
791	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
792	u_init = mean_inflow_profiles(:,1)
793	v_init = mean_inflow_profiles(:,2)
794	e_init = MAXVAL( mean_inflow_profiles(:,5) )
795	ENDIF
796
797	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
798	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
799	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
800	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
801	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
802	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
803	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
804	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
805
806	r11 = 0.0_wp
807	r21 = 0.0_wp
808	r22 = 0.0_wp
809	r31 = 0.0_wp
810	r32 = 0.0_wp
811	r33 = 0.0_wp
812	tu = 0.0_wp
813	tv = 0.0_wp
814	tw = 0.0_wp
815
816	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
817	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
818	dist_xz = 0.0_wp
819	dist_yz = 0.0_wp
820	!
821	!-- Read inflow profile
822	!-- Height levels of profiles in input profile is as follows:
823	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
824	!-- WARNING: zz is not used at the moment
825	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
826
827	IF ( file_stg_exist ) THEN
828
829	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
830	!
831	!-- Skip header
832	READ( 90, * )
833
834	DO k = nzb, nzt
835	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
836	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
837
838	!
839	!-- Convert length scales from meter to number of grid points.
840	IF ( k /= nzb ) THEN
841	nuz(k) = INT( luz * ddzw(k) )
842	nvz(k) = INT( lvz * ddzw(k) )
843	nwz(k) = INT( lwz * ddzw(k) )
844	ELSE
845	nuz(k) = INT( luz * ddzw(k+1) )
846	nvz(k) = INT( lvz * ddzw(k+1) )
847	nwz(k) = INT( lwz * ddzw(k+1) )
848	ENDIF
849
850	nuy(k) = INT( luy * ddy )
851	nvy(k) = INT( lvy * ddy )
852	nwy(k) = INT( lwy * ddy )
853	!
854	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
855	!-- y-direction.
856	nwx(k) = nwy(k)
857	nvx(k) = nvy(k)
858	nux(k) = nuy(k)
859	!
860	!-- Save Mean inflow profiles
861	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
862	mean_inflow_profiles(k,1) = d1
863	mean_inflow_profiles(k,2) = d2
864	! mean_inflow_profiles(k,4) = d4
865	mean_inflow_profiles(k,5) = d5
866	ENDIF
867	ENDDO
868	!
869	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
870	!-- simply overwritten.
871	nwx(nzb) = nwy(nzb+1)
872	nvx(nzb) = nvy(nzb+1)
873	nux(nzb) = nuy(nzb+1)
874	nuy(nzb) = nuy(nzb+1)
875	nuz(nzb) = nuz(nzb+1)
876	nvy(nzb) = nvy(nzb+1)
877	nvz(nzb) = nvz(nzb+1)
878	nwy(nzb) = nwy(nzb+1)
879	nwz(nzb) = nwz(nzb+1)
880
881	nwx(nzt+1) = nwy(nzt)
882	nvx(nzt+1) = nvy(nzt)
883	nux(nzt+1) = nuy(nzt)
884	nuy(nzt+1) = nuy(nzt)
885	nuz(nzt+1) = nuz(nzt)
886	nvy(nzt+1) = nvy(nzt)
887	nvz(nzt+1) = nvz(nzt)
888	nwy(nzt+1) = nwy(nzt)
889	nwz(nzt+1) = nwz(nzt)
890
891	CLOSE( 90 )
892	!
893	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
894	CALL calc_coeff_matrix
895	!
896	!-- No information about turbulence and its length scales are available. Instead, parametrize
897	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
898	!-- parametrized, which is done later when energy-balance models are already initialized. This is
899	!-- because the STG needs information about surface properties such as roughness to build
900	!-- 'realistic' turbulence profiles.
901	ELSE
902	!
903	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
904	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
905	!
906	!-- Set flag indicating that turbulence is parametrized
907	parametrize_inflow_turbulence = .TRUE.
908	!
909	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
910	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
911	!-- nevertheless, the boundary-layer depth needs to be determined first.
912	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
913	CALL nesting_offl_calc_zi
914	!
915	!-- Determine boundary-layer depth, which is used to initialize lenght scales
916	CALL calc_scaling_variables
917	!
918	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
919	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
920	!-- friction velocity and velocity scale.
921	CALL parametrize_turbulence
922	!
923	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
924	CALL calc_coeff_matrix
925
926	ENDIF
927	!
928	!-- Initial filter functions
929	CALL stg_setup_filter_function
930	!
931	!-- Allocate velocity seeds for turbulence at xz-layer
932	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
933	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
934	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
935
936	!
937	!-- Allocate velocity seeds for turbulence at yz-layer
938	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
939	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
940	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
941
942	fu_xz = 0.0_wp
943	fuo_xz = 0.0_wp
944	fv_xz = 0.0_wp
945	fvo_xz = 0.0_wp
946	fw_xz = 0.0_wp
947	fwo_xz = 0.0_wp
948
949	fu_yz = 0.0_wp
950	fuo_yz = 0.0_wp
951	fv_yz = 0.0_wp
952	fvo_yz = 0.0_wp
953	fw_yz = 0.0_wp
954	fwo_yz = 0.0_wp
955
956	#if defined( __parallel )
957	CALL MPI_BARRIER( comm2d, ierr )
958	#endif
959
960	!
961	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
962	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
963	!-- This is mostly for k=nzt+1.
964	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
965	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
966
967	IF ( myidx == id_stg_left ) i = -1
968	IF ( myidx == id_stg_right ) i = nxr+1
969
970	DO j = nys, nyn
971	DO k = nzb, nzt+1
972	IF ( a11(k) > 10E-8_wp ) THEN
973	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
974	ELSE
975	fu_yz(k,j) = 10E-8_wp
976	ENDIF
977
978	IF ( a22(k) > 10E-8_wp ) THEN
979	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
980	ELSE
981	fv_yz(k,j) = 10E-8_wp
982	ENDIF
983
984	IF ( a33(k) > 10E-8_wp ) THEN
985	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
986	ELSE
987	fw_yz(k,j) = 10E-8_wp
988	ENDIF
989	ENDDO
990	ENDDO
991	ENDIF
992
993	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
994
995	IF ( myidy == id_stg_south ) j = -1
996	IF ( myidy == id_stg_north ) j = nyn+1
997
998	DO i = nxl, nxr
999	DO k = nzb, nzt+1
1000	!
1001	!-- In case the correlation coefficients are very small, the velocity seeds may become
1002	!-- very large finally creating numerical instabilities in the synthetic turbulence
1003	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
1004	IF ( a11(k) > 10E-8_wp ) THEN
1005	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1006	ELSE
1007	fu_xz(k,i) = 10E-8_wp
1008	ENDIF
1009
1010	IF ( a22(k) > 10E-8_wp ) THEN
1011	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1012	ELSE
1013	fv_xz(k,i) = 10E-8_wp
1014	ENDIF
1015
1016	IF ( a33(k) > 10E-8_wp ) THEN
1017	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1018	ELSE
1019	fw_xz(k,i) = 10E-8_wp
1020	ENDIF
1021
1022	ENDDO
1023	ENDDO
1024	ENDIF
1025	ENDIF
1026	!
1027	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1028	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1029	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1030	!-- different cases must be distinguished.
1031	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1032	!
1033	!-- Number of grid points where perturbations are imposed on u
1034	IF ( myidx == id_stg_left ) i = nxl
1035	IF ( myidx == id_stg_right ) i = nxr+1
1036
1037	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1038	!
1039	!-- Number of grid points where perturbations are imposed on v and w
1040	IF ( myidx == id_stg_left ) i = nxl-1
1041	IF ( myidx == id_stg_right ) i = nxr+1
1042
1043	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1044	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1045
1046	#if defined( __parallel )
1047	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1048	#else
1049	nr_non_topo_yz = nr_non_topo_yz_l
1050	#endif
1051	ENDIF
1052
1053	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1054	!
1055	!-- Number of grid points where perturbations are imposed on v
1056	IF ( myidy == id_stg_south ) j = nys
1057	IF ( myidy == id_stg_north ) j = nyn+1
1058
1059	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1060	!
1061	!-- Number of grid points where perturbations are imposed on u and w
1062	IF ( myidy == id_stg_south ) j = nys-1
1063	IF ( myidy == id_stg_north ) j = nyn+1
1064
1065	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1066	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1067
1068	#if defined( __parallel )
1069	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1070	#else
1071	nr_non_topo_xz = nr_non_topo_xz_l
1072	#endif
1073	ENDIF
1074	!
1075	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1076	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1077	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1078	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1079	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1080	id_rand_yz = 0
1081	seq_rand_yz = 0
1082
1083	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1084
1085	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1086	.AND. .NOT. rans_mode ) ) THEN
1087	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1088	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1089	id_rand_xz = 0
1090	seq_rand_xz = 0
1091
1092	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1093	ENDIF
1094
1095	END SUBROUTINE stg_init
1096
1097
1098	!--------------------------------------------------------------------------------------------------!
1099	! Description:
1100	! ------------
1101	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1102	!--------------------------------------------------------------------------------------------------!
1103	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1104
1105	INTEGER(iwp) :: k !< loop index
1106	INTEGER(iwp) :: mergp !< passed length scale in grid points
1107	INTEGER(iwp) :: n_k !< length scale nXX in height k
1108	INTEGER(iwp) :: nf !< index for length scales
1109
1110	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1111
1112	REAL(wp) :: bdenom !< denominator for filter functions bXX
1113	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1114
1115	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1116
1117
1118	bxx = 0.0_wp
1119
1120	DO k = nzb, nzt+1
1121	bdenom = 0.0_wp
1122	n_k = nxx(k)
1123	IF ( n_k /= 0 ) THEN
1124
1125	!
1126	!-- ( Eq.10 )^2
1127	DO nf = -n_k, n_k
1128	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1129	ENDDO
1130
1131	!
1132	!-- ( Eq.9 )
1133	bdenom = SQRT( bdenom )
1134	DO nf = -n_k, n_k
1135	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1136	ENDDO
1137	ENDIF
1138	ENDDO
1139
1140	END SUBROUTINE stg_filter_func
1141
1142
1143	!------------------------------------------------------------------------------!
1144	! Description:
1145	! ------------
1146	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1147	!> (Xie and Castro, 2008)
1148	!------------------------------------------------------------------------------!
1149	SUBROUTINE stg_setup_filter_function
1150
1151	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1152	INTEGER(iwp) :: k !< loop index along vertical direction
1153	!
1154	!-- Define the size of the filter functions and allocate them.
1155	mergp_x = 0
1156	mergp_y = 0
1157	mergp_z = 0
1158
1159	DO k = nzb, nzt+1
1160	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1161	IF ( j > mergp_x ) mergp_x = j
1162	ENDDO
1163	DO k = nzb, nzt+1
1164	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1165	IF ( j > mergp_y ) mergp_y = j
1166	ENDDO
1167	DO k = nzb, nzt+1
1168	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1169	IF ( j > mergp_z ) mergp_z = j
1170	ENDDO
1171
1172	mergp_xy = MAX( mergp_x, mergp_y )
1173
1174	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1175	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1176	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1177	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1178	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1179	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1180	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1181	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1182	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1183
1184	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1185	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1186	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1187	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1188	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1189	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1190	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1191	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1192	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1193	!
1194	!-- Create filter functions
1195	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1196	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1197	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1198	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1199	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1200	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1201	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1202	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1203	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1204
1205	END SUBROUTINE stg_setup_filter_function
1206
1207	!--------------------------------------------------------------------------------------------------!
1208	! Description:
1209	! ------------
1210	!> Parin for &stg_par for synthetic turbulence generator
1211	!--------------------------------------------------------------------------------------------------!
1212	SUBROUTINE stg_parin
1213
1214	CHARACTER(LEN=100) :: line !< dummy string that contains the current line of the parameter file
1215
1216	INTEGER(iwp) :: io_status !< status after reading the namelist file
1217
1218	LOGICAL :: switch_off_module = .FALSE. !< local namelist parameter to switch off the module
1219	!< although the respective module namelist appears in
1220	!< the namelist file
1221
1222	NAMELIST /stg_par/ compute_velocity_seeds_local, &
1223	dt_stg_adjust, &
1224	dt_stg_call, &
1225	switch_off_module
1226
1227
1228	!
1229	!-- Move to the beginning of the namelist file and try to find and read the namelist.
1230	REWIND( 11 )
1231	READ( 11, stg_par, IOSTAT=io_status )
1232
1233	!
1234	!-- Action depending on the READ status
1235	IF ( io_status == 0 ) THEN
1236	!
1237	!-- stg_par namelist was found and read correctly. Set flag that indicates that the synthetic
1238	!-- turbulence generator is switched on.
1239	IF ( .NOT. switch_off_module ) syn_turb_gen = .TRUE.
1240
1241	ELSEIF ( io_status > 0 ) THEN
1242	!
1243	!-- stg_par namelist was found but contained errors. Print an error message including the line
1244	!-- that caused the problem.
1245	BACKSPACE( 11 )
1246	READ( 11 , '(A)') line
1247	CALL parin_fail_message( 'stg_par', line )
1248
1249	ENDIF
1250
1251	END SUBROUTINE stg_parin
1252
1253
1254	!--------------------------------------------------------------------------------------------------!
1255	! Description:
1256	! ------------
1257	!> Read module-specific global restart data (Fortran binary format).
1258	!--------------------------------------------------------------------------------------------------!
1259	SUBROUTINE stg_rrd_global_ftn( found )
1260
1261	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1262
1263	found = .TRUE.
1264
1265
1266	SELECT CASE ( restart_string(1:length) )
1267
1268	CASE ( 'time_stg_adjust' )
1269	READ ( 13 ) time_stg_adjust
1270
1271	CASE ( 'time_stg_call' )
1272	READ ( 13 ) time_stg_call
1273
1274	CASE DEFAULT
1275
1276	found = .FALSE.
1277
1278	END SELECT
1279
1280
1281	END SUBROUTINE stg_rrd_global_ftn
1282
1283
1284	!--------------------------------------------------------------------------------------------------!
1285	! Description:
1286	! ------------
1287	!> Read module-specific global restart data (MPI-IO).
1288	!--------------------------------------------------------------------------------------------------!
1289	SUBROUTINE stg_rrd_global_mpi
1290
1291	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1292	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1293
1294	END SUBROUTINE stg_rrd_global_mpi
1295
1296
1297	!--------------------------------------------------------------------------------------------------!
1298	! Description:
1299	! ------------
1300	!> This routine writes the respective restart data.
1301	!--------------------------------------------------------------------------------------------------!
1302	SUBROUTINE stg_wrd_global
1303
1304	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1305
1306	CALL wrd_write_string( 'time_stg_adjust' )
1307	WRITE ( 14 ) time_stg_adjust
1308
1309	CALL wrd_write_string( 'time_stg_call' )
1310	WRITE ( 14 ) time_stg_call
1311
1312	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1313
1314	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1315	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1316
1317	ENDIF
1318
1319	END SUBROUTINE stg_wrd_global
1320
1321
1322	!--------------------------------------------------------------------------------------------------!
1323	! Description:
1324	! ------------
1325	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1326	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1327	!> (2013), and using a Lund rotation (Lund, 1998).
1328	!--------------------------------------------------------------------------------------------------!
1329	SUBROUTINE stg_main
1330
1331	USE exchange_horiz_mod, &
1332	ONLY: exchange_horiz
1333
1334	INTEGER(iwp) :: i !< grid index in x-direction
1335	INTEGER(iwp) :: j !< loop index in y-direction
1336	INTEGER(iwp) :: k !< loop index in z-direction
1337
1338	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1339
1340	REAL(wp) :: dt_stg !< time interval the STG is called
1341
1342	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1343
1344	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1345	!
1346	!-- Calculate time step which is needed for filter functions
1347	dt_stg = MAX( dt_3d, dt_stg_call )
1348	!
1349	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1350	!-- created or if old disturbances can be imposed again.
1351	IF ( time_stg_call >= dt_stg_call .AND. &
1352	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1353	stg_call = .TRUE.
1354	ELSE
1355	stg_call = .FALSE.
1356	ENDIF
1357	!
1358	!-- Initial value of fu, fv, fw
1359	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1360	!
1361	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1362	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1363	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1364	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1365	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1366	!-- have the same initial seeds.
1367	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1368	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1369	.AND. .NOT. rans_mode ) ) ) THEN
1370	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1371	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1372	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1373	ELSE
1374	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1375	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1376	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1377	!
1378	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1379	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1380	!-- comment above.
1381	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1382	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1383	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1384	ENDIF
1385	velocity_seed_initialized = .TRUE.
1386	ENDIF
1387	!
1388	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1389	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1390	!-- seeds are required also at the right, south and north boundaries.
1391	IF ( stg_call ) THEN
1392	IF ( .NOT. ( nesting_offline .OR. &
1393	( child_domain .AND. rans_mode_parent &
1394	.AND. .NOT. rans_mode ) ) ) THEN
1395	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1396	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1397	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1398
1399	ELSE
1400	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1401	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1402	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1403
1404	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1405	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1406	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1407	ENDIF
1408	ENDIF
1409
1410	!
1411	!-- Turbulence generation at left and/or right boundary
1412	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1413	!
1414	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1415	!-- exceeded. Else the old set of perturbations is imposed
1416	IF ( stg_call ) THEN
1417
1418	DO j = nys, nyn
1419	DO k = nzb, nzt + 1
1420	!
1421	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1422	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1423	fu_yz(k,j) = fuo_yz(k,j)
1424	ELSE
1425	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1426	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1427	ENDIF
1428
1429	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1430	fv_yz(k,j) = fvo_yz(k,j)
1431	ELSE
1432	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1433	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1434	ENDIF
1435
1436	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1437	fw_yz(k,j) = fwo_yz(k,j)
1438	ELSE
1439	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1440	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1441	ENDIF
1442	ENDDO
1443	ENDDO
1444
1445	dist_yz(nzb,:,1) = 0.0_wp
1446	dist_yz(nzb,:,2) = 0.0_wp
1447	dist_yz(nzb,:,3) = 0.0_wp
1448
1449	IF ( myidx == id_stg_left ) i = nxl
1450	IF ( myidx == id_stg_right ) i = nxr+1
1451	DO j = nys, nyn
1452	DO k = nzb+1, nzt + 1
1453	!
1454	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1455	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1456	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1457
1458	ENDDO
1459	ENDDO
1460
1461	IF ( myidx == id_stg_left ) i = nxl-1
1462	IF ( myidx == id_stg_right ) i = nxr+1
1463	DO j = nys, nyn
1464	DO k = nzb+1, nzt + 1
1465	!
1466	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1467	!-- Additional factors are added to improve the variance of v and w experimental test
1468	!-- of 1.2
1469	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1470	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1471	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1472	a33(k) * fw_yz(k,j) ) * &
1473	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1474
1475	ENDDO
1476	ENDDO
1477	ENDIF
1478	!
1479	!-- Mass flux correction following Kim et al. (2013)
1480	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1481	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1482	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1483	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1484	mc_factor_l = 0.0_wp
1485	mc_factor = 0.0_wp
1486	!
1487	!-- Sum up the original volume flows (with and without perturbations).
1488	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1489	IF ( myidx == id_stg_left ) i = nxl
1490	IF ( myidx == id_stg_right ) i = nxr+1
1491
1492	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1493	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1494
1495	IF ( myidx == id_stg_left ) i = nxl-1
1496	IF ( myidx == id_stg_right ) i = nxr+1
1497
1498	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1499	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1500	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1501	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1502
1503	#if defined( __parallel )
1504	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1505	#else
1506	mc_factor = mc_factor_l
1507	#endif
1508	!
1509	!-- Calculate correction factor and force zero mean perturbations.
1510	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1511
1512	IF ( myidx == id_stg_left ) i = nxl
1513	IF ( myidx == id_stg_right ) i = nxr+1
1514
1515	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1516	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1517
1518
1519	IF ( myidx == id_stg_left ) i = nxl-1
1520	IF ( myidx == id_stg_right ) i = nxr+1
1521
1522	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1523	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1524
1525	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1526	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1527	!
1528	!-- Add disturbances
1529	IF ( myidx == id_stg_left ) THEN
1530	!
1531	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1532	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1533	!-- the mean inflow profiles.
1534	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1535	!
1536	!-- Add disturbance at the inflow
1537	DO j = nys, nyn
1538	DO k = nzb, nzt+1
1539	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1540	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1541	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1542	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1543	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1544	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1545	ENDDO
1546	ENDDO
1547	ELSE
1548
1549	DO j = nys, nyn
1550	DO k = nzb+1, nzt
1551	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1552	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1553	u(k,j,-1) = u(k,j,0)
1554	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1556	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1557	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1558	ENDDO
1559	ENDDO
1560	ENDIF
1561	ENDIF
1562	IF ( myidx == id_stg_right ) THEN
1563	DO j = nys, nyn
1564	DO k = nzb+1, nzt
1565	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1566	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1567	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1568	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1569	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1570	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1571	ENDDO
1572	ENDDO
1573	ENDIF
1574	ENDIF
1575	ENDIF
1576	!
1577	!-- Turbulence generation at north and south boundary
1578	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1579	!
1580	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1581	!-- exceeded. Else the old set of perturbations is imposed
1582	IF ( stg_call ) THEN
1583	DO i = nxl, nxr
1584	DO k = nzb, nzt + 1
1585	!
1586	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1587	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1588	fu_xz(k,i) = fuo_xz(k,i)
1589	ELSE
1590	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1591	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1592	ENDIF
1593
1594	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1595	fv_xz(k,i) = fvo_xz(k,i)
1596	ELSE
1597	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1598	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1599	ENDIF
1600
1601	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1602	fw_xz(k,i) = fwo_xz(k,i)
1603	ELSE
1604	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1605	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1606	ENDIF
1607	ENDDO
1608	ENDDO
1609
1610
1611	dist_xz(nzb,:,1) = 0.0_wp
1612	dist_xz(nzb,:,2) = 0.0_wp
1613	dist_xz(nzb,:,3) = 0.0_wp
1614
1615	IF ( myidy == id_stg_south ) j = nys
1616	IF ( myidy == id_stg_north ) j = nyn+1
1617	DO i = nxl, nxr
1618	DO k = nzb+1, nzt + 1
1619	!
1620	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1621	!-- Additional factors are added to improve the variance of v and w
1622	!experimental test of 1.2
1623	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1624	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1625	ENDDO
1626	ENDDO
1627
1628	IF ( myidy == id_stg_south ) j = nys-1
1629	IF ( myidy == id_stg_north ) j = nyn+1
1630	DO i = nxl, nxr
1631	DO k = nzb+1, nzt + 1
1632	!
1633	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1634	!-- Additional factors are added to improve the variance of v and w
1635	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1636	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1637
1638	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1639	a33(k) * fw_xz(k,i) ) * &
1640	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1641	ENDDO
1642	ENDDO
1643	ENDIF
1644
1645	!
1646	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1647	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1648	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1649	!-- else the boundary values won't be accessed.
1650	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1651	mc_factor_l = 0.0_wp
1652	mc_factor = 0.0_wp
1653
1654	IF ( myidy == id_stg_south ) j = nys
1655	IF ( myidy == id_stg_north ) j = nyn+1
1656
1657	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1658	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1659
1660	IF ( myidy == id_stg_south ) j = nys-1
1661	IF ( myidy == id_stg_north ) j = nyn+1
1662
1663	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1664	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1665	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1666	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1667
1668	#if defined( __parallel )
1669	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1670	#else
1671	mc_factor = mc_factor_l
1672	#endif
1673
1674	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1675
1676	IF ( myidy == id_stg_south ) j = nys
1677	IF ( myidy == id_stg_north ) j = nyn+1
1678
1679	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1680	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1681
1682
1683	IF ( myidy == id_stg_south ) j = nys-1
1684	IF ( myidy == id_stg_north ) j = nyn+1
1685
1686	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1687	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1688
1689	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1690	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1691	!
1692	!-- Add disturbances
1693	IF ( myidy == id_stg_south ) THEN
1694	DO i = nxl, nxr
1695	DO k = nzb+1, nzt
1696	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1697	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1698	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1699	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1700	v(k,-1,i) = v(k,0,i)
1701	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1702	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1703	ENDDO
1704	ENDDO
1705	ENDIF
1706	IF ( myidy == id_stg_north ) THEN
1707
1708	DO i = nxl, nxr
1709	DO k = nzb+1, nzt
1710	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1711	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1712	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1713	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1714	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1715	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1716	ENDDO
1717	ENDDO
1718	ENDIF
1719	ENDIF
1720	ENDIF
1721	!
1722	!-- Exchange ghost points.
1723	CALL exchange_horiz( u, nbgp )
1724	CALL exchange_horiz( v, nbgp )
1725	CALL exchange_horiz( w, nbgp )
1726	!
1727	!-- Finally, set time counter for calling STG to zero
1728	IF ( stg_call ) time_stg_call = 0.0_wp
1729	!
1730	!-- Set adjustment step to False to indicate that time correlation can be
1731	!-- switched-on again.
1732	adjustment_step = .FALSE.
1733
1734	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1735
1736	END SUBROUTINE stg_main
1737
1738	!--------------------------------------------------------------------------------------------------!
1739	! Description:
1740	! ------------
1741	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1742	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1743	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1744	!> array.
1745	!--------------------------------------------------------------------------------------------------!
1746	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1747
1748	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1749	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1750	INTEGER(iwp) :: j !< loop index in y-direction
1751	INTEGER(iwp) :: jj !< loop index in y-direction
1752	INTEGER(iwp) :: k !< loop index in z-direction
1753	INTEGER(iwp) :: kk !< loop index in z-direction
1754	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1755
1756	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1757	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1758
1759	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1760	REAL(wp) :: rand_av !< average of random number
1761	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1762
1763	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1764	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1765
1766	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1767	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1768
1769	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1770	!
1771	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1772	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1773	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1774	!-- and normalization of random numbers is done locally, while the result is later distributed to
1775	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1776	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1777	!-- correlation matrix.
1778	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1779	rand_it = 0.0_wp
1780
1781	rand_av = 0.0_wp
1782	rand_sigma_inv = 0.0_wp
1783	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1784	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1785	!
1786	!-- Compute and normalize random numbers.
1787	DO j = nys - mergp_y, nyn + mergp_y
1788	!
1789	!-- Put the random seeds at grid point j
1790	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1791	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1792	CALL random_number_parallel( random_dummy )
1793	rand_it(k,j) = random_dummy
1794	ENDDO
1795	!
1796	!-- Get the new random seeds from last call at grid point j
1797	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1798	ENDDO
1799	!
1800	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1801	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1802	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1803	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1804	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1805	rand_av = rand_av + rand_it(k,j)
1806	ENDDO
1807	ENDDO
1808
1809	#if defined( __parallel )
1810	!
1811	!-- Sum-up the local averages of the random numbers
1812	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1813	#endif
1814	rand_av = rand_av * nyz_inv
1815	!
1816	!-- Obtain zero mean
1817	rand_it= rand_it - rand_av
1818	!
1819	!-- Now, compute the variance
1820	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1821	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1822	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1823	ENDDO
1824	ENDDO
1825
1826	#if defined( __parallel )
1827	!
1828	!-- Sum-up the local quadratic averages of the random numbers
1829	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1830	#endif
1831	!
1832	!-- Compute standard deviation
1833	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1834	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1835	ELSE
1836	rand_sigma_inv = 1.0_wp
1837	ENDIF
1838	!
1839	!-- Normalize with standard deviation to obtain unit variance
1840	rand_it = rand_it * rand_sigma_inv
1841
1842	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1843	!
1844	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1845	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1846	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1847	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1848	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1849	!-- communication. In the second option, which performs better when the turbulent length scales
1850	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1851	!-- communication is necessary.
1852	IF ( compute_velocity_seeds_local ) THEN
1853
1854	f_n = 0.0_wp
1855	DO j = nys, nyn
1856	DO k = nzb, nzt+1
1857	DO jj = -n_y(k), n_y(k)
1858	DO kk = -n_z(k), n_z(k)
1859	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1860	ENDDO
1861	ENDDO
1862	ENDDO
1863	ENDDO
1864
1865	ELSE
1866
1867	f_n_l = 0.0_wp
1868	DO j = nys, nyn
1869	DO k = nzb_x_stg, nzt_x_stg+1
1870	DO jj = -n_y(k), n_y(k)
1871	DO kk = -n_z(k), n_z(k)
1872	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1873	ENDDO
1874	ENDDO
1875	ENDDO
1876	ENDDO
1877	!
1878	!-- Gather velocity seeds of full subdomain
1879	send_count = nzt_x_stg - nzb_x_stg + 1
1880	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1881
1882	#if defined( __parallel )
1883	!
1884	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1885	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1886	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1887	!
1888	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1889	!-- nesting for example).
1890	IF ( PRESENT( id_right ) ) THEN
1891	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1892	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1893	ENDIF
1894	#else
1895	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1896	!
1897	!-- Next line required to avoid compile errors because of unused dummy arguments
1898	IF ( id_left == 0 ) id_right = 0
1899	#endif
1900
1901	ENDIF
1902
1903	DEALLOCATE( rand_it )
1904
1905	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1906
1907	END SUBROUTINE stg_generate_seed_yz
1908
1909
1910	!--------------------------------------------------------------------------------------------------!
1911	! Description:
1912	! ------------
1913	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1914	!> f_n.
1915	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1916	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1917	!> full array.
1918	!--------------------------------------------------------------------------------------------------!
1919	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1920
1921	INTEGER(iwp) :: i !< loop index in x-direction
1922	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1923	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1924	INTEGER(iwp) :: ii !< loop index in x-direction
1925	INTEGER(iwp) :: k !< loop index in z-direction
1926	INTEGER(iwp) :: kk !< loop index in z-direction
1927	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1928
1929	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1930	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1931
1932	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1933	REAL(wp) :: rand_av !< average of random number
1934	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1935
1936	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1937	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1938
1939	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1940	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1941
1942	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1943
1944	!
1945	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1946	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1947	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1948	!-- and normalization of random numbers is done locally, while the result is later distributed to
1949	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1950	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1951	!-- correlation matrix.
1952	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1953	rand_it = 0.0_wp
1954
1955	rand_av = 0.0_wp
1956	rand_sigma_inv = 0.0_wp
1957	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1958	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1959	!
1960	!-- Compute and normalize random numbers.
1961	DO i = nxl - mergp_x, nxr + mergp_x
1962	!
1963	!-- Put the random seeds at grid point ii
1964	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1965	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1966	CALL random_number_parallel( random_dummy )
1967	rand_it(k,i) = random_dummy
1968	ENDDO
1969	!
1970	!-- Get the new random seeds from last call at grid point ii
1971	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1972	ENDDO
1973	!
1974	!-- For normalization to zero mean, sum-up the global random numers.
1975	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1976	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1977	!-- also occur on the inner subdomains.
1978	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1979	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1980	rand_av = rand_av + rand_it(k,i)
1981	ENDDO
1982	ENDDO
1983
1984	#if defined( __parallel )
1985	!
1986	!-- Sum-up the local averages of the random numbers
1987	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1988	#endif
1989	rand_av = rand_av * nxz_inv
1990	!
1991	!-- Obtain zero mean
1992	rand_it= rand_it - rand_av
1993	!
1994	!-- Now, compute the variance
1995	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1996	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1997	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1998	ENDDO
1999	ENDDO
2000
2001	#if defined( __parallel )
2002	!
2003	!-- Sum-up the local quadratic averages of the random numbers
2004	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2005	#endif
2006	!
2007	!-- Compute standard deviation
2008	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2009	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2010	ELSE
2011	rand_sigma_inv = 1.0_wp
2012	ENDIF
2013	!
2014	!-- Normalize with standard deviation to obtain unit variance
2015	rand_it = rand_it * rand_sigma_inv
2016
2017	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2018	!
2019	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2020	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2021	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2022	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2023	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2024	!-- In the second option, which performs better when the turbulent length scales are parametrized
2025	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2026	IF ( compute_velocity_seeds_local ) THEN
2027
2028	f_n = 0.0_wp
2029	DO i = nxl, nxr
2030	DO k = nzb, nzt+1
2031	DO ii = -n_x(k), n_x(k)
2032	DO kk = -n_z(k), n_z(k)
2033	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2034	ENDDO
2035	ENDDO
2036	ENDDO
2037	ENDDO
2038
2039	ELSE
2040
2041	f_n_l = 0.0_wp
2042	DO i = nxl, nxr
2043	DO k = nzb_y_stg, nzt_y_stg+1
2044	DO ii = -n_x(k), n_x(k)
2045	DO kk = -n_z(k), n_z(k)
2046	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2047	ENDDO
2048	ENDDO
2049	ENDDO
2050	ENDDO
2051	!
2052	!-- Gather velocity seeds of full subdomain
2053	send_count = nzt_y_stg - nzb_y_stg + 1
2054	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2055
2056	#if defined( __parallel )
2057	!
2058	!-- Gather the processed velocity seed on south boundary mpi ranks.
2059	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2060	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2061	!
2062	!-- Gather the processed velocity seed on north boundary mpi ranks.
2063	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2064	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2065	#else
2066	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2067	!
2068	!-- Next line required to avoid compile errors because of unused dummy arguments
2069	IF ( id_north == 0 ) id_south = 0
2070	#endif
2071
2072	ENDIF
2073
2074	DEALLOCATE( rand_it )
2075
2076	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2077
2078	END SUBROUTINE stg_generate_seed_xz
2079
2080	!--------------------------------------------------------------------------------------------------!
2081	! Description:
2082	! ------------
2083	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2084	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2085	!> which is applied in state-of-the-art dispserion modelling.
2086	!--------------------------------------------------------------------------------------------------!
2087	SUBROUTINE parametrize_turbulence
2088
2089	INTEGER(iwp) :: k !< loop index in z-direction
2090
2091	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2092	REAL(wp) :: d_zi !< inverse boundary-layer depth
2093	REAL(wp) :: length_scale_lon !< length scale in flow direction
2094	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2095	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2096	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2097	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2098	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2099	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2100	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2101	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2102	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2103	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2104	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2105	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2106	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2107	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2108	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2109	REAL(wp) :: zzi !< ratio of z/zi
2110
2111	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2112	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2113	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2114
2115	!
2116	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2117	!-- criterion according to Heinze et al. (2017).
2118	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2119	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2120	k_zi = MIN( k_zi, nzt )
2121	!
2122	!-- Calculate angle between flow direction and x-axis.
2123	DO k = nzb+1, nzt + 1
2124	IF ( u_init(k) /= 0.0_wp ) THEN
2125	phi(k) = ATAN( v_init(k) / u_init(k) )
2126	ELSE
2127	phi(k) = 0.5 * pi
2128	ENDIF
2129	!
2130	!-- Pre-calculate sine and cosine.
2131	cos_phi(k) = COS( phi(k) )
2132	sin_phi(k) = SIN( phi(k) )
2133	ENDDO
2134	!
2135	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2136	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2137	!-- coincide with the grid axis. Hence, components are rotated after computation.
2138	d_zi = 1.0_wp / zi_ribulk
2139	DO k = nzb+1, k_zi
2140
2141	corr_term_uh = MERGE( 0.35_wp * ABS( &
2142	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2143	)**( 2.0_wp / 3.0_wp ), &
2144	0.0_wp, &
2145	scale_l < -5.0_wp )
2146	!
2147	!-- Determine normalized height coordinate
2148	zzi = zu(k) * d_zi
2149	!
2150	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2151	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2152	!-- variances cannot become negative, take the absolute values.
2153	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2154	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2155
2156	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2157	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2158	!
2159	!-- w'w'
2160	r33(k) = scale_wm*2 ( &
2161	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2162	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2163	)
2164	!
2165	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2166	!-- these are projected along the x- and y-direction. Note, it is assumed that
2167	!-- the flux within the boundary points opposite to the vertical gradient.
2168	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2169	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2170
2171	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2172	- ( u_init(k+1) - u_init(k-1) ) )
2173	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2174	- ( v_init(k+1) - v_init(k-1) ) )
2175	!
2176	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2177	!-- for the vertical transport.
2178	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2179	!
2180	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2181	!-- limited to the adjustment time scales.
2182	tu(k) = MIN( dt_stg_adjust, &
2183	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2184
2185	tv(k) = tu(k)
2186	tw(k) = tu(k)
2187
2188	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2189	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2190	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2191	!
2192	!-- Assume isotropic turbulence length scales
2193	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2194	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2195	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2196	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2197	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2198	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2199	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2200	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2201	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2202
2203	ENDDO
2204	!
2205	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2206	!-- reduced to zero by a blending function.
2207	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2208	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2209	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2210
2211	time_scale_zi = tu(k_zi)
2212	r11_zi = r11(k_zi)
2213	r22_zi = r22(k_zi)
2214	r33_zi = r33(k_zi)
2215	r31_zi = r31(k_zi)
2216	r32_zi = r32(k_zi)
2217
2218	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2219
2220	DO k = k_zi+1, nzt+1
2221	!
2222	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2223	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2224	!
2225	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2226	!-- the mergpe-function can crash if scale_l is zero.
2227	r11(k) = r11_zi * blend
2228	r22(k) = r22_zi * blend
2229	r33(k) = r33_zi * blend
2230	r31(k) = r31_zi * blend
2231	r32(k) = r32_zi * blend
2232	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2233
2234	!
2235	!-- Compute turbulent time scales according to Brost et al. (1982).
2236	!-- Note, time scales are limited to the adjustment time scales.
2237	tu(k) = time_scale_zi * blend
2238	tv(k) = time_scale_zi * blend
2239	tw(k) = time_scale_zi * blend
2240
2241	length_scale_lon = length_scale_lon_zi * blend
2242	length_scale_lat = length_scale_lat_zi * blend
2243	length_scale_vert = length_scale_vert_zi * blend
2244	!
2245	!-- Assume isotropic turbulence length scales
2246	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2247	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2248	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2249	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2250	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2251	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2252	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2253	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2254	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2255	ENDDO
2256	!
2257	!-- Set bottom boundary condition for reynolds stresses
2258	r11(nzb) = r11(nzb+1)
2259	r22(nzb) = r22(nzb+1)
2260	r33(nzb) = r33(nzb+1)
2261
2262	r21(nzb) = r11(nzb+1)
2263	r31(nzb) = r31(nzb+1)
2264	r32(nzb) = r32(nzb+1)
2265
2266	!
2267	!-- Set bottom boundary condition for the length and time scales
2268	nux(nzb) = nux(nzb+1)
2269	nuy(nzb) = nuy(nzb+1)
2270	nuz(nzb) = nuz(nzb+1)
2271	nvx(nzb) = nvx(nzb+1)
2272	nvy(nzb) = nvy(nzb+1)
2273	nvz(nzb) = nvz(nzb+1)
2274	nwx(nzb) = nwx(nzb+1)
2275	nwy(nzb) = nwy(nzb+1)
2276	nwz(nzb) = nwz(nzb+1)
2277
2278	tu(nzb) = tu(nzb+1)
2279	tv(nzb) = tv(nzb+1)
2280	tw(nzb) = tw(nzb+1)
2281
2282	adjustment_step = .TRUE.
2283
2284	END SUBROUTINE parametrize_turbulence
2285
2286	!--------------------------------------------------------------------------------------------------!
2287	! Description:
2288	! ------------
2289	!> Calculate the coefficient matrix from the Lund rotation.
2290	!--------------------------------------------------------------------------------------------------!
2291	SUBROUTINE calc_coeff_matrix
2292
2293	INTEGER(iwp) :: k !< loop index in z-direction
2294
2295	!
2296	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2297	DO k = nzb+1, nzt+1
2298	IF ( r11(k) > 10E-6_wp ) THEN
2299	a11(k) = SQRT( r11(k) )
2300	a21(k) = r21(k) / a11(k)
2301	a31(k) = r31(k) / a11(k)
2302	ELSE
2303	a11(k) = 10E-8_wp
2304	a21(k) = 10E-8_wp
2305	a31(k) = 10E-8_wp
2306	ENDIF
2307	ENDDO
2308	DO k = nzb+1, nzt+1
2309	a22(k) = r22(k) - a21(k)**2
2310	IF ( a22(k) > 10E-6_wp ) THEN
2311	a22(k) = SQRT( a22(k) )
2312	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2313	ELSE
2314	a22(k) = 10E-8_wp
2315	a32(k) = 10E-8_wp
2316	ENDIF
2317	ENDDO
2318	DO k = nzb+1, nzt+1
2319	a33(k) = r33(k) - a31(k)2 - a32(k)2
2320	IF ( a33(k) > 10E-6_wp ) THEN
2321	a33(k) = SQRT( a33(k) )
2322	ELSE
2323	a33(k) = 10E-8_wp
2324	ENDIF
2325	ENDDO
2326	!
2327	!-- Set bottom boundary condition
2328	a11(nzb) = a11(nzb+1)
2329	a22(nzb) = a22(nzb+1)
2330	a21(nzb) = a21(nzb+1)
2331	a33(nzb) = a33(nzb+1)
2332	a31(nzb) = a31(nzb+1)
2333	a32(nzb) = a32(nzb+1)
2334
2335	END SUBROUTINE calc_coeff_matrix
2336
2337	!--------------------------------------------------------------------------------------------------!
2338	! Description:
2339	! ------------
2340	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2341	!> turbulence at the lateral boundaries.
2342	!--------------------------------------------------------------------------------------------------!
2343	SUBROUTINE stg_adjust
2344
2345	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2346	!
2347	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2348	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2349	!-- nevertheless, the boundary-layer depth need to determined first.
2350	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2351	CALL nesting_offl_calc_zi
2352	!
2353	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2354	CALL calc_scaling_variables
2355	!
2356	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2357	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2358	!-- velocity and velocity scale.
2359	CALL parametrize_turbulence
2360	!
2361	!-- Calculate coefficient matrix from Reynolds stress tensor
2362	!-- (Lund rotation)
2363	CALL calc_coeff_matrix
2364	!
2365	!-- Setup filter functions according to updated length scales.
2366	CALL stg_setup_filter_function
2367	!
2368	!-- Reset time counter for controlling next adjustment to zero
2369	time_stg_adjust = 0.0_wp
2370
2371	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2372
2373	END SUBROUTINE stg_adjust
2374
2375
2376	!--------------------------------------------------------------------------------------------------!
2377	! Description:
2378	! ------------
2379	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2380	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2381	!> scale, and Obukhov length.
2382	!--------------------------------------------------------------------------------------------------!
2383	SUBROUTINE calc_scaling_variables
2384
2385	INTEGER(iwp) :: i !< loop index in x-direction
2386	INTEGER(iwp) :: j !< loop index in y-direction
2387	INTEGER(iwp) :: k !< loop index in z-direction
2388	INTEGER(iwp) :: m !< surface element index
2389
2390	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2391	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2392	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2393	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2394	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2395	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2396	REAL(wp) :: w_convective !< convective velocity scale
2397
2398	!
2399	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2400	!-- model domain.
2401	pt_surf_mean_l = 0.0_wp
2402	shf_mean_l = 0.0_wp
2403	scale_l_l = 0.0_wp
2404	friction_vel_l = 0.0_wp
2405	DO m = 1, surf_def_h(0)%ns
2406	i = surf_def_h(0)%i(m)
2407	j = surf_def_h(0)%j(m)
2408	k = surf_def_h(0)%k(m)
2409	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2410	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2411	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2412	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2413	ENDDO
2414	DO m = 1, surf_lsm_h(0)%ns
2415	i = surf_lsm_h(0)%i(m)
2416	j = surf_lsm_h(0)%j(m)
2417	k = surf_lsm_h(0)%k(m)
2418	friction_vel_l = friction_vel_l + surf_lsm_h(0)%us(m)
2419	shf_mean_l = shf_mean_l + surf_lsm_h(0)%shf(m) * drho_air(k)
2420	scale_l_l = scale_l_l + surf_lsm_h(0)%ol(m)
2421	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2422	ENDDO
2423	DO m = 1, surf_usm_h(0)%ns
2424	i = surf_usm_h(0)%i(m)
2425	j = surf_usm_h(0)%j(m)
2426	k = surf_usm_h(0)%k(m)
2427	friction_vel_l = friction_vel_l + surf_usm_h(0)%us(m)
2428	shf_mean_l = shf_mean_l + surf_usm_h(0)%shf(m) * drho_air(k)
2429	scale_l_l = scale_l_l + surf_usm_h(0)%ol(m)
2430	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2431	ENDDO
2432
2433	#if defined( __parallel )
2434	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2435	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2436	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2437	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2438	#else
2439	scale_us = friction_vel_l
2440	shf_mean = shf_mean_l
2441	scale_l = scale_l_l
2442	pt_surf_mean = pt_surf_mean_l
2443	#endif
2444
2445	scale_us = scale_us * d_nxy
2446	shf_mean = shf_mean * d_nxy
2447	scale_l = scale_l * d_nxy
2448	pt_surf_mean = pt_surf_mean * d_nxy
2449	!
2450	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2451	!-- convective velocity scale to zero.
2452	IF ( shf_mean > 0.0_wp ) THEN
2453	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2454	ELSE
2455	w_convective = 0.0_wp
2456	ENDIF
2457	!
2458	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2459	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2460	!-- value of friction velocity for the reynolds-stress parametrization.
2461	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2462	!
2463	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2464	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2465	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2466
2467	END SUBROUTINE calc_scaling_variables
2468
2469	END MODULE synthetic_turbulence_generator_mod

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