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synthetic_turbulence_generator_mod.f90

Last change on this file was 4851, checked in by gronemeier, 3 years ago
bugfix: deactivated header output (dynamics_mod); change: formatting clean-up (synthetic_turbulence_generator_mod)
Property svn:keywords set to `Id`
File size: 113.0 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 4851 2021-01-22 09:25:05Z banzhafs $
27	! formatting clean-up
28	!
29	! 4848 2021-01-21 15:51:51Z gronemeier
30	! replaced use_syn_turb_gen by syn_turb_gen
31	!
32	! 4843 2021-01-15 15:22:11Z raasch
33	! local namelist parameter added to switch off the module although the respective module namelist
34	! appears in the namelist file
35	!
36	! 4842 2021-01-14 10:42:28Z raasch
37	! reading of namelist file and actions in case of namelist errors revised so that statement labels
38	! and goto statements are not required any more
39	!
40	! 4828 2021-01-05 11:21:41Z Giersch
41	! Implementation of downward facing USM and LSM surfaces
42	!
43	! 4647 2020-08-24 16:36:18Z suehring
44	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
45	! By default, the random-seed computation is now distributed among several cores. Especially for
46	! large length scales this is significantly faster.
47	!
48	! 4640 2020-08-11 16:28:32Z suehring
49	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
50	! Obukhov length (term is not valid for near neutral conditions)
51	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
52	! the vertical transport of horizontal momentum
53	!
54	! 4629 2020-07-29 09:37:56Z raasch
55	! support for MPI Fortran77 interface (mpif.h) removed
56	!
57	! 4603 2020-07-14 16:08:30Z suehring
58	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
59	! initialized properly
60	!
61	! 4566 2020-06-16 10:11:51Z suehring
62	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
63	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
64	! - change default value of time interval to adjust turbulence parametrization
65	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
66	!
67	! 4562 2020-06-12 08:38:47Z raasch
68	! Parts of r4559 re-formatted
69	!
70	! 4559 2020-06-11 08:51:48Z raasch
71	! File re-formatted to follow the PALM coding standard
72	!
73	! 4535 2020-05-15 12:07:23Z raasch
74	! Bugfix for restart data format query
75	!
76	! 4495 2020-04-13 20:11:20Z raasch
77	! Restart data handling with MPI-IO added
78	!
79	! 4481 2020-03-31 18:55:54Z maronga
80	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
81	!
82	! 4442 2020-03-04 19:21:13Z suehring
83	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
84	! (was accidantly changed).
85	!
86	! 4441 2020-03-04 19:20:35Z suehring
87	! Correct misplaced preprocessor directive
88	!
89	! 4438 2020-03-03 20:49:28Z suehring
90	! Performance optimizations in velocity-seed calculation:
91	! - Random number array is only defined and computed locally (except for normalization to zero mean
92	! and unit variance)
93	! - Parallel random number generator is applied independent on the 2D random numbers in other
94	! routines
95	! - Option to decide wheter velocity seeds are computed locally without any further communication
96	! or are computed by all processes along the communicator
97	!
98	! 4346 2019-12-18 11:55:56Z motisi
99	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
100	! information used in wall_flags_static_0
101	!
102	! 4335 2019-12-12 16:39:05Z suehring
103	! Commentation of last commit
104	!
105	! 4332 2019-12-10 19:44:12Z suehring
106	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
107	! Further, minor bugfix in initial velocity seed calculation.
108	!
109	! 4329 2019-12-10 15:46:36Z motisi
110	! Renamed wall_flags_0 to wall_flags_static_0
111	!
112	! 4309 2019-11-26 18:49:59Z suehring
113	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
114	! the parallel random number generator. Random numbers are now only computed and normalized locally,
115	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
116	! array.
117	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
118	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
119	!
120	! 4182 2019-08-22 15:20:23Z scharf
121	! Corrected "Former revisions" section
122	!
123	! 4148 2019-08-08 11:26:00Z suehring
124	! Remove unused variable
125	!
126	! 4144 2019-08-06 09:11:47Z raasch
127	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
128	!
129	! 4071 2019-07-03 20:02:00Z suehring
130	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
131	! file.
132	!
133	! 4022 2019-06-12 11:52:39Z suehring
134	! Several bugfixes and improvements
135	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
136	! instabilities in case the mean volume flow is close to zero)
137	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
138	! numerically unstable
139	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
140	! case dt_stg_call /= dt_3d
141	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
142	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
143	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
144	!
145	! 3987 2019-05-22 09:52:13Z kanani
146	! Introduce alternative switch for debug output during timestepping
147	!
148	! 3938 2019-04-29 16:06:25Z suehring
149	! Remove unused variables
150	!
151	! 3937 2019-04-29 15:09:07Z suehring
152	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
153	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
154	! synthetic turbulence parametrization.
155	!
156	! 3909 2019-04-17 09:13:25Z suehring
157	! Minor bugfix for last commit
158	!
159	! 3900 2019-04-16 15:17:43Z suehring
160	! Missing re-calculation of perturbation seeds in case of restarts
161	!
162	! 3891 2019-04-12 17:52:01Z suehring
163	! Bugfix in initialization in case of restart runs.
164	!
165	! 3885 2019-04-11 11:29:34Z kanani
166	! Changes related to global restructuring of location messages and introduction of additional debug
167	! messages
168	!
169	!
170	! Removed unused variables
171	!
172	! 3719 2019-02-06 13:10:18Z kanani
173	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
174	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
175	! for better overview.
176	!
177	! 2259 2017-06-08 09:09:11Z gronemeier
178	! Initial revision
179	!
180	! Authors:
181	! --------
182	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
183	!
184	!
185	! Description:
186	! ------------
187	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
188	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
189	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
190	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
191	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
192	!> parametrized within the boundary layer.
193	!>
194	!> @todo Enable cyclic_fill
195	!> Implement turbulence generation for e and pt
196	!> @note <Enter notes on the module>
197	!> @bug Height information from input file is not used. Profiles from input must match with current
198	!> PALM grid.
199	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
200	!--------------------------------------------------------------------------------------------------!
201	MODULE synthetic_turbulence_generator_mod
202
203
204	USE arrays_3d, &
205	ONLY: dzw, &
206	ddzw, &
207	drho_air, &
208	mean_inflow_profiles, &
209	pt, &
210	pt_init, &
211	q, &
212	q_init, &
213	u, &
214	u_init, &
215	v, &
216	v_init, &
217	w, &
218	zu, &
219	zw
220
221	USE basic_constants_and_equations_mod, &
222	ONLY: g, &
223	kappa, &
224	pi
225
226	USE control_parameters, &
227	ONLY: bc_lr, &
228	bc_ns, &
229	child_domain, &
230	coupling_char, &
231	debug_output_timestep, &
232	dt_3d, &
233	e_init, &
234	humidity, &
235	initializing_actions, &
236	intermediate_timestep_count, &
237	intermediate_timestep_count_max, &
238	length, &
239	message_string, &
240	nesting_offline, &
241	neutral, &
242	num_mean_inflow_profiles, &
243	random_generator, &
244	rans_mode, &
245	restart_data_format_output, &
246	restart_string, &
247	syn_turb_gen, &
248	time_since_reference_point, &
249	turbulent_inflow
250
251	USE cpulog, &
252	ONLY: cpu_log, &
253	log_point_s
254
255	USE grid_variables, &
256	ONLY: ddx, &
257	ddy, &
258	dx, &
259	dy
260
261	USE indices, &
262	ONLY: nbgp, &
263	nz, &
264	nzb, &
265	nzt, &
266	nx, &
267	nxl, &
268	nxlu, &
269	nxr, &
270	ny, &
271	nys, &
272	nysv, &
273	nyn, &
274	wall_flags_total_0
275
276	USE kinds
277
278	#if defined( __parallel )
279	USE MPI
280	#endif
281
282	USE nesting_offl_mod, &
283	ONLY: nesting_offl_calc_zi, &
284	zi_ribulk
285
286	USE pegrid, &
287	ONLY: comm1dx, &
288	comm1dy, &
289	comm2d, &
290	ierr, &
291	myidx, &
292	myidy, &
293	pdims
294
295	USE pmc_interface, &
296	ONLY : rans_mode_parent
297
298	USE random_generator_parallel, &
299	ONLY: init_parallel_random_generator, &
300	random_dummy, &
301	random_number_parallel, &
302	random_seed_parallel
303
304	USE restart_data_mpi_io_mod, &
305	ONLY: rrd_mpi_io, &
306	wrd_mpi_io
307
308	USE transpose_indices, &
309	ONLY: nzb_x, &
310	nzt_x
311
312	USE surface_mod, &
313	ONLY: surf_def_h, &
314	surf_lsm_h, &
315	surf_usm_h
316
317	IMPLICIT NONE
318
319	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
320	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
321	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
322	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
323	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
324	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
325	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
326	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
327	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
328	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
329	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
330	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
331	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
332	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
333	#if defined( __parallel )
334	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
335	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
336	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
337	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
338	#endif
339
340	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
341	!< required for bias correction of imposed perturbations
342	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
343	!< required for bias correction of imposed perturbations
344
345	#if defined( __parallel )
346	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
347	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
348	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
349	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
350	#endif
351	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
352	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
353	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
354	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
355	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
356	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
357	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
358	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
359	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
360
361	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
362	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
363	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
364	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
365
366
367	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
368	!< no time correlation to the timestep before should be considered
369	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
370	!< or if computation is distributed over several processes
371	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
372	!< (.FALSE.) or if it parametrized
373	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
374
375
376	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
377	!< scales above the boundary layer
378	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
379	!< one length scale above ABL top
380	REAL(wp) :: d_l !< blend_coeff/length_scale
381	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
382	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
383	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
384	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
385	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
386	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
387	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
388	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
389
390	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
391
392
393	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
394	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
395	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
396	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
397	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
398	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
399
400	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
401	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
402	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
403	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
404	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
405	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
406	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
407	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
408	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
409
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
418	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
419	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
420	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
421	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
422	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
423	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
424	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
425	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
426	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
427	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
428	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
429	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
430	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
431
432	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
433	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
434
435	!
436	!-- PALM interfaces:
437	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
438	INTERFACE stg_adjust
439	MODULE PROCEDURE stg_adjust
440	END INTERFACE stg_adjust
441	!
442	!-- Input parameter checks to be done in check_parameters
443	INTERFACE stg_check_parameters
444	MODULE PROCEDURE stg_check_parameters
445	END INTERFACE stg_check_parameters
446
447	!
448	!-- Calculate filter functions
449	INTERFACE stg_filter_func
450	MODULE PROCEDURE stg_filter_func
451	END INTERFACE stg_filter_func
452
453	!
454	!-- Generate velocity seeds at south and north domain boundary
455	INTERFACE stg_generate_seed_xz
456	MODULE PROCEDURE stg_generate_seed_xz
457	END INTERFACE stg_generate_seed_xz
458	!
459	!-- Generate velocity seeds at left and/or right domain boundary
460	INTERFACE stg_generate_seed_yz
461	MODULE PROCEDURE stg_generate_seed_yz
462	END INTERFACE stg_generate_seed_yz
463
464	!
465	!-- Output of information to the header file
466	INTERFACE stg_header
467	MODULE PROCEDURE stg_header
468	END INTERFACE stg_header
469
470	!
471	!-- Initialization actions
472	INTERFACE stg_init
473	MODULE PROCEDURE stg_init
474	END INTERFACE stg_init
475
476	!
477	!-- Main procedure of synth. turb. gen.
478	INTERFACE stg_main
479	MODULE PROCEDURE stg_main
480	END INTERFACE stg_main
481
482	!
483	!-- Reading of NAMELIST parameters
484	INTERFACE stg_parin
485	MODULE PROCEDURE stg_parin
486	END INTERFACE stg_parin
487
488	!
489	!-- Reading of parameters for restart runs
490	INTERFACE stg_rrd_global
491	MODULE PROCEDURE stg_rrd_global_ftn
492	MODULE PROCEDURE stg_rrd_global_mpi
493	END INTERFACE stg_rrd_global
494
495	!
496	!-- Writing of binary output for restart runs
497	INTERFACE stg_wrd_global
498	MODULE PROCEDURE stg_wrd_global
499	END INTERFACE stg_wrd_global
500
501	SAVE
502
503	PRIVATE
504
505	!
506	!-- Public interfaces
507	PUBLIC stg_adjust, &
508	stg_check_parameters, &
509	stg_header, &
510	stg_init, &
511	stg_main, &
512	stg_parin, &
513	stg_rrd_global, &
514	stg_wrd_global
515
516	!
517	!-- Public variables
518	PUBLIC dt_stg_call, &
519	dt_stg_adjust, &
520	id_stg_left, &
521	id_stg_north, &
522	id_stg_right, &
523	id_stg_south, &
524	parametrize_inflow_turbulence, &
525	time_stg_adjust, &
526	time_stg_call
527
528
529	CONTAINS
530
531
532	!--------------------------------------------------------------------------------------------------!
533	! Description:
534	! ------------
535	!> Check parameters routine for synthetic turbulence generator
536	!--------------------------------------------------------------------------------------------------!
537	SUBROUTINE stg_check_parameters
538
539	IF ( .NOT. syn_turb_gen .AND. .NOT. rans_mode .AND. &
540	nesting_offline ) THEN
541	message_string = 'Synthetic turbulence generator is required ' // &
542	'if offline nesting is applied and PALM operates in LES mode.'
543	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
544	ENDIF
545
546	IF ( .NOT. syn_turb_gen .AND. child_domain &
547	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
548	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
549	'and parent operates in RANS-mode but current child in LES mode.'
550	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
551	ENDIF
552
553	IF ( syn_turb_gen ) THEN
554
555	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
556	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
557	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
558
559	ENDIF
560
561	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
562	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
563	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
564
565	ENDIF
566
567	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
568
569	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
570	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
571	message_string = 'Using synthetic turbulence generator requires ' // &
572	'%initializing_actions = "set_constant_profiles" or ' // &
573	' "read_restart_data", if not offline nesting is applied.'
574	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
575	ENDIF
576
577	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
578	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
579	' "dirichlet/radiation", if not offline nesting is applied.'
580	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
581	ENDIF
582	IF ( bc_ns /= 'cyclic' ) THEN
583	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
584	' "cyclic", if not offline nesting is applied.'
585	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
586	ENDIF
587
588	ENDIF
589
590	IF ( turbulent_inflow ) THEN
591	message_string = 'Using synthetic turbulence generator in combination ' // &
592	'&with turbulent_inflow = .T. is not allowed'
593	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
594	ENDIF
595	!
596	!-- Synthetic turbulence generator requires the parallel random generator
597	IF ( random_generator /= 'random-parallel' ) THEN
598	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
599	'random-parallel.'
600	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
601	ENDIF
602
603	ENDIF
604
605	END SUBROUTINE stg_check_parameters
606
607
608	!--------------------------------------------------------------------------------------------------!
609	! Description:
610	! ------------
611	!> Header output for synthetic turbulence generator
612	!--------------------------------------------------------------------------------------------------!
613	SUBROUTINE stg_header ( io )
614
615	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
616
617	!
618	!-- Write synthetic turbulence generator Header
619	IF ( syn_turb_gen ) THEN
620	WRITE( io, 1 )
621	IF ( parametrize_inflow_turbulence ) THEN
622	WRITE( io, 4 ) dt_stg_adjust
623	ELSE
624	WRITE( io, 5 )
625	ENDIF
626	ENDIF
627
628	1 FORMAT (//' Synthetic turbulence generator information:'/ &
629	' ------------------------------------------'/)
630	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
631	5 FORMAT (' imposed turbulence is read from file' )
632
633	END SUBROUTINE stg_header
634
635
636	!--------------------------------------------------------------------------------------------------!
637	! Description:
638	! ------------
639	!> Initialization of the synthetic turbulence generator
640	!--------------------------------------------------------------------------------------------------!
641	SUBROUTINE stg_init
642
643	#if defined( __parallel )
644	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
645	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
646	#endif
647
648	INTEGER(iwp) :: i !> grid index in x-direction
649	INTEGER(iwp) :: j !> loop index
650	INTEGER(iwp) :: k !< index
651	#if defined( __parallel )
652	INTEGER(iwp) :: newtype !< dummy MPI type
653	INTEGER(iwp) :: realsize !< size of REAL variables
654	#endif
655
656	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
657	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
658
659
660	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
661
662	!
663	!-- Dummy variables used for reading profiles
664	REAL(wp) :: d1 !< u profile
665	REAL(wp) :: d2 !< v profile
666	REAL(wp) :: d3 !< w profile
667	REAL(wp) :: d5 !< e profile
668	REAL(wp) :: luy !< length scale for u in y direction
669	REAL(wp) :: luz !< length scale for u in z direction
670	REAL(wp) :: lvy !< length scale for v in y direction
671	REAL(wp) :: lvz !< length scale for v in z direction
672	REAL(wp) :: lwy !< length scale for w in y direction
673	REAL(wp) :: lwz !< length scale for w in z direction
674	#if defined( __parallel )
675	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
676	#endif
677	REAL(wp) :: zz !< height
678
679
680	#if defined( __parallel )
681	CALL MPI_BARRIER( comm2d, ierr )
682	#endif
683	!
684	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
685	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
686	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
687	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
688	!-- communication).
689	IF ( .NOT. compute_velocity_seeds_local ) THEN
690	#if defined( __parallel )
691	!
692	!-- Determine processor decomposition of z-axis along x- and y-direction
693	nnz = nz / pdims(1)
694	nzb_x_stg = 1 + myidx * INT( nnz )
695	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
696
697	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
698	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
699
700	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
701	.AND. .NOT. rans_mode ) ) THEN
702	nnz = nz / pdims(2)
703	nzb_y_stg = 1 + myidy * INT( nnz )
704	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
705
706	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
707	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
708	ENDIF
709
710	!
711	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
712	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
713	extent = 1 * realsize
714	!
715	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
716	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
717	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
718	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
719	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
720	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
721	CALL MPI_TYPE_FREE( newtype, ierr )
722
723	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
724	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
725	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
726	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
727	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
728	CALL MPI_TYPE_FREE( newtype, ierr )
729
730	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
731	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
732
733	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
734	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
735
736	DO j = 1, pdims(1)
737	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
738	ENDDO
739	!
740	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
741	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
742	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
743	.AND. .NOT. rans_mode ) ) THEN
744	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
745	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
746	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
747	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
748	CALL MPI_TYPE_FREE( newtype, ierr )
749
750	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
751	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
752	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
753	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
754	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
755	CALL MPI_TYPE_FREE( newtype, ierr )
756
757	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
758	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
759
760	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
761	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
762
763	DO j = 1, pdims(2)
764	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
765	ENDDO
766
767	ENDIF
768	#endif
769	ENDIF
770	!
771	!-- Allocate required arrays.
772	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
773	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
774	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
775	!-- and initialized appropriately.
776	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
777	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
778	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
779	mean_inflow_profiles = 0.0_wp
780	mean_inflow_profiles(:,1) = u_init
781	mean_inflow_profiles(:,2) = v_init
782	!
783	!-- Even though potential temperature and humidity are not perturbed, they need to be
784	!-- initialized appropriately.
785	IF ( .NOT. neutral ) &
786	mean_inflow_profiles(:,4) = pt_init
787	IF ( humidity ) &
788	mean_inflow_profiles(:,6) = q_init
789	ENDIF
790	ENDIF
791	!
792	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
793	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
794	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
795	u_init = mean_inflow_profiles(:,1)
796	v_init = mean_inflow_profiles(:,2)
797	e_init = MAXVAL( mean_inflow_profiles(:,5) )
798	ENDIF
799
800	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
801	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
802	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
803	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
804	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
805	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
806	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
807	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
808
809	r11 = 0.0_wp
810	r21 = 0.0_wp
811	r22 = 0.0_wp
812	r31 = 0.0_wp
813	r32 = 0.0_wp
814	r33 = 0.0_wp
815	tu = 0.0_wp
816	tv = 0.0_wp
817	tw = 0.0_wp
818
819	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
820	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
821	dist_xz = 0.0_wp
822	dist_yz = 0.0_wp
823	!
824	!-- Read inflow profile
825	!-- Height levels of profiles in input profile is as follows:
826	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
827	!-- WARNING: zz is not used at the moment
828	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
829
830	IF ( file_stg_exist ) THEN
831
832	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
833	!
834	!-- Skip header
835	READ( 90, * )
836
837	DO k = nzb, nzt
838	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
839	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
840
841	!
842	!-- Convert length scales from meter to number of grid points.
843	IF ( k /= nzb ) THEN
844	nuz(k) = INT( luz * ddzw(k) )
845	nvz(k) = INT( lvz * ddzw(k) )
846	nwz(k) = INT( lwz * ddzw(k) )
847	ELSE
848	nuz(k) = INT( luz * ddzw(k+1) )
849	nvz(k) = INT( lvz * ddzw(k+1) )
850	nwz(k) = INT( lwz * ddzw(k+1) )
851	ENDIF
852
853	nuy(k) = INT( luy * ddy )
854	nvy(k) = INT( lvy * ddy )
855	nwy(k) = INT( lwy * ddy )
856	!
857	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
858	!-- y-direction.
859	nwx(k) = nwy(k)
860	nvx(k) = nvy(k)
861	nux(k) = nuy(k)
862	!
863	!-- Save Mean inflow profiles
864	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
865	mean_inflow_profiles(k,1) = d1
866	mean_inflow_profiles(k,2) = d2
867	! mean_inflow_profiles(k,4) = d4
868	mean_inflow_profiles(k,5) = d5
869	ENDIF
870	ENDDO
871	!
872	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
873	!-- simply overwritten.
874	nwx(nzb) = nwy(nzb+1)
875	nvx(nzb) = nvy(nzb+1)
876	nux(nzb) = nuy(nzb+1)
877	nuy(nzb) = nuy(nzb+1)
878	nuz(nzb) = nuz(nzb+1)
879	nvy(nzb) = nvy(nzb+1)
880	nvz(nzb) = nvz(nzb+1)
881	nwy(nzb) = nwy(nzb+1)
882	nwz(nzb) = nwz(nzb+1)
883
884	nwx(nzt+1) = nwy(nzt)
885	nvx(nzt+1) = nvy(nzt)
886	nux(nzt+1) = nuy(nzt)
887	nuy(nzt+1) = nuy(nzt)
888	nuz(nzt+1) = nuz(nzt)
889	nvy(nzt+1) = nvy(nzt)
890	nvz(nzt+1) = nvz(nzt)
891	nwy(nzt+1) = nwy(nzt)
892	nwz(nzt+1) = nwz(nzt)
893
894	CLOSE( 90 )
895	!
896	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
897	CALL calc_coeff_matrix
898	!
899	!-- No information about turbulence and its length scales are available. Instead, parametrize
900	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
901	!-- parametrized, which is done later when energy-balance models are already initialized. This is
902	!-- because the STG needs information about surface properties such as roughness to build
903	!-- 'realistic' turbulence profiles.
904	ELSE
905	!
906	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
907	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
908	!
909	!-- Set flag indicating that turbulence is parametrized
910	parametrize_inflow_turbulence = .TRUE.
911	!
912	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
913	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
914	!-- nevertheless, the boundary-layer depth needs to be determined first.
915	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
916	CALL nesting_offl_calc_zi
917	!
918	!-- Determine boundary-layer depth, which is used to initialize lenght scales
919	CALL calc_scaling_variables
920	!
921	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
922	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
923	!-- friction velocity and velocity scale.
924	CALL parametrize_turbulence
925	!
926	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
927	CALL calc_coeff_matrix
928
929	ENDIF
930	!
931	!-- Initial filter functions
932	CALL stg_setup_filter_function
933	!
934	!-- Allocate velocity seeds for turbulence at xz-layer
935	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
936	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
937	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
938
939	!
940	!-- Allocate velocity seeds for turbulence at yz-layer
941	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
942	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
943	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
944
945	fu_xz = 0.0_wp
946	fuo_xz = 0.0_wp
947	fv_xz = 0.0_wp
948	fvo_xz = 0.0_wp
949	fw_xz = 0.0_wp
950	fwo_xz = 0.0_wp
951
952	fu_yz = 0.0_wp
953	fuo_yz = 0.0_wp
954	fv_yz = 0.0_wp
955	fvo_yz = 0.0_wp
956	fw_yz = 0.0_wp
957	fwo_yz = 0.0_wp
958
959	#if defined( __parallel )
960	CALL MPI_BARRIER( comm2d, ierr )
961	#endif
962
963	!
964	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
965	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
966	!-- This is mostly for k=nzt+1.
967	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
968	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
969
970	IF ( myidx == id_stg_left ) i = -1
971	IF ( myidx == id_stg_right ) i = nxr+1
972
973	DO j = nys, nyn
974	DO k = nzb, nzt+1
975	IF ( a11(k) > 10E-8_wp ) THEN
976	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
977	ELSE
978	fu_yz(k,j) = 10E-8_wp
979	ENDIF
980
981	IF ( a22(k) > 10E-8_wp ) THEN
982	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
983	ELSE
984	fv_yz(k,j) = 10E-8_wp
985	ENDIF
986
987	IF ( a33(k) > 10E-8_wp ) THEN
988	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
989	ELSE
990	fw_yz(k,j) = 10E-8_wp
991	ENDIF
992	ENDDO
993	ENDDO
994	ENDIF
995
996	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
997
998	IF ( myidy == id_stg_south ) j = -1
999	IF ( myidy == id_stg_north ) j = nyn+1
1000
1001	DO i = nxl, nxr
1002	DO k = nzb, nzt+1
1003	!
1004	!-- In case the correlation coefficients are very small, the velocity seeds may become
1005	!-- very large finally creating numerical instabilities in the synthetic turbulence
1006	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
1007	IF ( a11(k) > 10E-8_wp ) THEN
1008	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1009	ELSE
1010	fu_xz(k,i) = 10E-8_wp
1011	ENDIF
1012
1013	IF ( a22(k) > 10E-8_wp ) THEN
1014	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1015	ELSE
1016	fv_xz(k,i) = 10E-8_wp
1017	ENDIF
1018
1019	IF ( a33(k) > 10E-8_wp ) THEN
1020	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
1021	ELSE
1022	fw_xz(k,i) = 10E-8_wp
1023	ENDIF
1024
1025	ENDDO
1026	ENDDO
1027	ENDIF
1028	ENDIF
1029	!
1030	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
1031	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
1032	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
1033	!-- different cases must be distinguished.
1034	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1035	!
1036	!-- Number of grid points where perturbations are imposed on u
1037	IF ( myidx == id_stg_left ) i = nxl
1038	IF ( myidx == id_stg_right ) i = nxr+1
1039
1040	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1041	!
1042	!-- Number of grid points where perturbations are imposed on v and w
1043	IF ( myidx == id_stg_left ) i = nxl-1
1044	IF ( myidx == id_stg_right ) i = nxr+1
1045
1046	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1047	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1048
1049	#if defined( __parallel )
1050	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1051	#else
1052	nr_non_topo_yz = nr_non_topo_yz_l
1053	#endif
1054	ENDIF
1055
1056	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1057	!
1058	!-- Number of grid points where perturbations are imposed on v
1059	IF ( myidy == id_stg_south ) j = nys
1060	IF ( myidy == id_stg_north ) j = nyn+1
1061
1062	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1063	!
1064	!-- Number of grid points where perturbations are imposed on u and w
1065	IF ( myidy == id_stg_south ) j = nys-1
1066	IF ( myidy == id_stg_north ) j = nyn+1
1067
1068	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1069	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1070
1071	#if defined( __parallel )
1072	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1073	#else
1074	nr_non_topo_xz = nr_non_topo_xz_l
1075	#endif
1076	ENDIF
1077	!
1078	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1079	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1080	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1081	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1082	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1083	id_rand_yz = 0
1084	seq_rand_yz = 0
1085
1086	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1087
1088	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1089	.AND. .NOT. rans_mode ) ) THEN
1090	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1091	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1092	id_rand_xz = 0
1093	seq_rand_xz = 0
1094
1095	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1096	ENDIF
1097
1098	END SUBROUTINE stg_init
1099
1100
1101	!--------------------------------------------------------------------------------------------------!
1102	! Description:
1103	! ------------
1104	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1105	!--------------------------------------------------------------------------------------------------!
1106	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1107
1108	INTEGER(iwp) :: k !< loop index
1109	INTEGER(iwp) :: mergp !< passed length scale in grid points
1110	INTEGER(iwp) :: n_k !< length scale nXX in height k
1111	INTEGER(iwp) :: nf !< index for length scales
1112
1113	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1114
1115	REAL(wp) :: bdenom !< denominator for filter functions bXX
1116	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1117
1118	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1119
1120
1121	bxx = 0.0_wp
1122
1123	DO k = nzb, nzt+1
1124	bdenom = 0.0_wp
1125	n_k = nxx(k)
1126	IF ( n_k /= 0 ) THEN
1127
1128	!
1129	!-- ( Eq.10 )^2
1130	DO nf = -n_k, n_k
1131	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1132	ENDDO
1133
1134	!
1135	!-- ( Eq.9 )
1136	bdenom = SQRT( bdenom )
1137	DO nf = -n_k, n_k
1138	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1139	ENDDO
1140	ENDIF
1141	ENDDO
1142
1143	END SUBROUTINE stg_filter_func
1144
1145
1146	!------------------------------------------------------------------------------!
1147	! Description:
1148	! ------------
1149	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1150	!> (Xie and Castro, 2008)
1151	!------------------------------------------------------------------------------!
1152	SUBROUTINE stg_setup_filter_function
1153
1154	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1155	INTEGER(iwp) :: k !< loop index along vertical direction
1156	!
1157	!-- Define the size of the filter functions and allocate them.
1158	mergp_x = 0
1159	mergp_y = 0
1160	mergp_z = 0
1161
1162	DO k = nzb, nzt+1
1163	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1164	IF ( j > mergp_x ) mergp_x = j
1165	ENDDO
1166	DO k = nzb, nzt+1
1167	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1168	IF ( j > mergp_y ) mergp_y = j
1169	ENDDO
1170	DO k = nzb, nzt+1
1171	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1172	IF ( j > mergp_z ) mergp_z = j
1173	ENDDO
1174
1175	mergp_xy = MAX( mergp_x, mergp_y )
1176
1177	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1178	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1179	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1180	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1181	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1182	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1183	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1184	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1185	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1186
1187	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1188	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1189	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1190	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1191	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1192	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1193	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1194	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1195	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1196	!
1197	!-- Create filter functions
1198	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1199	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1200	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1201	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1202	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1203	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1204	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1205	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1206	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1207
1208	END SUBROUTINE stg_setup_filter_function
1209
1210	!--------------------------------------------------------------------------------------------------!
1211	! Description:
1212	! ------------
1213	!> Parin for &stg_par for synthetic turbulence generator
1214	!--------------------------------------------------------------------------------------------------!
1215	SUBROUTINE stg_parin
1216
1217	CHARACTER(LEN=100) :: line !< dummy string that contains the current line of the parameter file
1218
1219	INTEGER(iwp) :: io_status !< status after reading the namelist file
1220
1221	LOGICAL :: switch_off_module = .FALSE. !< local namelist parameter to switch off the module
1222	!< although the respective module namelist appears in
1223	!< the namelist file
1224
1225	NAMELIST /stg_par/ compute_velocity_seeds_local, &
1226	dt_stg_adjust, &
1227	dt_stg_call, &
1228	switch_off_module
1229
1230
1231	!
1232	!-- Move to the beginning of the namelist file and try to find and read the namelist.
1233	REWIND( 11 )
1234	READ( 11, stg_par, IOSTAT=io_status )
1235
1236	!
1237	!-- Action depending on the READ status
1238	IF ( io_status == 0 ) THEN
1239	!
1240	!-- stg_par namelist was found and read correctly. Set flag that indicates that the synthetic
1241	!-- turbulence generator is switched on.
1242	IF ( .NOT. switch_off_module ) syn_turb_gen = .TRUE.
1243
1244	ELSEIF ( io_status > 0 ) THEN
1245	!
1246	!-- stg_par namelist was found but contained errors. Print an error message including the line
1247	!-- that caused the problem.
1248	BACKSPACE( 11 )
1249	READ( 11 , '(A)') line
1250	CALL parin_fail_message( 'stg_par', line )
1251
1252	ENDIF
1253
1254	END SUBROUTINE stg_parin
1255
1256
1257	!--------------------------------------------------------------------------------------------------!
1258	! Description:
1259	! ------------
1260	!> Read module-specific global restart data (Fortran binary format).
1261	!--------------------------------------------------------------------------------------------------!
1262	SUBROUTINE stg_rrd_global_ftn( found )
1263
1264	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1265
1266	found = .TRUE.
1267
1268
1269	SELECT CASE ( restart_string(1:length) )
1270
1271	CASE ( 'time_stg_adjust' )
1272	READ ( 13 ) time_stg_adjust
1273
1274	CASE ( 'time_stg_call' )
1275	READ ( 13 ) time_stg_call
1276
1277	CASE DEFAULT
1278
1279	found = .FALSE.
1280
1281	END SELECT
1282
1283
1284	END SUBROUTINE stg_rrd_global_ftn
1285
1286
1287	!--------------------------------------------------------------------------------------------------!
1288	! Description:
1289	! ------------
1290	!> Read module-specific global restart data (MPI-IO).
1291	!--------------------------------------------------------------------------------------------------!
1292	SUBROUTINE stg_rrd_global_mpi
1293
1294	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1295	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1296
1297	END SUBROUTINE stg_rrd_global_mpi
1298
1299
1300	!--------------------------------------------------------------------------------------------------!
1301	! Description:
1302	! ------------
1303	!> This routine writes the respective restart data.
1304	!--------------------------------------------------------------------------------------------------!
1305	SUBROUTINE stg_wrd_global
1306
1307	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1308
1309	CALL wrd_write_string( 'time_stg_adjust' )
1310	WRITE ( 14 ) time_stg_adjust
1311
1312	CALL wrd_write_string( 'time_stg_call' )
1313	WRITE ( 14 ) time_stg_call
1314
1315	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1316
1317	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1318	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1319
1320	ENDIF
1321
1322	END SUBROUTINE stg_wrd_global
1323
1324
1325	!--------------------------------------------------------------------------------------------------!
1326	! Description:
1327	! ------------
1328	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1329	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1330	!> (2013), and using a Lund rotation (Lund, 1998).
1331	!--------------------------------------------------------------------------------------------------!
1332	SUBROUTINE stg_main
1333
1334	USE exchange_horiz_mod, &
1335	ONLY: exchange_horiz
1336
1337	INTEGER(iwp) :: i !< grid index in x-direction
1338	INTEGER(iwp) :: j !< loop index in y-direction
1339	INTEGER(iwp) :: k !< loop index in z-direction
1340
1341	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1342
1343	REAL(wp) :: dt_stg !< time interval the STG is called
1344
1345	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1346
1347	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1348	!
1349	!-- Calculate time step which is needed for filter functions
1350	dt_stg = MAX( dt_3d, dt_stg_call )
1351	!
1352	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1353	!-- created or if old disturbances can be imposed again.
1354	IF ( time_stg_call >= dt_stg_call .AND. &
1355	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1356	stg_call = .TRUE.
1357	ELSE
1358	stg_call = .FALSE.
1359	ENDIF
1360	!
1361	!-- Initial value of fu, fv, fw
1362	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1363	!
1364	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1365	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1366	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1367	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1368	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1369	!-- have the same initial seeds.
1370	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1371	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1372	.AND. .NOT. rans_mode ) ) ) THEN
1373	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1374	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1375	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1376	ELSE
1377	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1378	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1379	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1380	!
1381	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1382	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1383	!-- comment above.
1384	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1385	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1386	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1387	ENDIF
1388	velocity_seed_initialized = .TRUE.
1389	ENDIF
1390	!
1391	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1392	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1393	!-- seeds are required also at the right, south and north boundaries.
1394	IF ( stg_call ) THEN
1395	IF ( .NOT. ( nesting_offline .OR. &
1396	( child_domain .AND. rans_mode_parent &
1397	.AND. .NOT. rans_mode ) ) ) THEN
1398	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1399	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1400	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1401
1402	ELSE
1403	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1404	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1405	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1406
1407	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1408	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1409	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1410	ENDIF
1411	ENDIF
1412
1413	!
1414	!-- Turbulence generation at left and/or right boundary
1415	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1416	!
1417	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1418	!-- exceeded. Else the old set of perturbations is imposed
1419	IF ( stg_call ) THEN
1420
1421	DO j = nys, nyn
1422	DO k = nzb, nzt + 1
1423	!
1424	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1425	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1426	fu_yz(k,j) = fuo_yz(k,j)
1427	ELSE
1428	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1429	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1430	ENDIF
1431
1432	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1433	fv_yz(k,j) = fvo_yz(k,j)
1434	ELSE
1435	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1436	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1437	ENDIF
1438
1439	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1440	fw_yz(k,j) = fwo_yz(k,j)
1441	ELSE
1442	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1443	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1444	ENDIF
1445	ENDDO
1446	ENDDO
1447
1448	dist_yz(nzb,:,1) = 0.0_wp
1449	dist_yz(nzb,:,2) = 0.0_wp
1450	dist_yz(nzb,:,3) = 0.0_wp
1451
1452	IF ( myidx == id_stg_left ) i = nxl
1453	IF ( myidx == id_stg_right ) i = nxr+1
1454	DO j = nys, nyn
1455	DO k = nzb+1, nzt + 1
1456	!
1457	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1458	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1459	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1460
1461	ENDDO
1462	ENDDO
1463
1464	IF ( myidx == id_stg_left ) i = nxl-1
1465	IF ( myidx == id_stg_right ) i = nxr+1
1466	DO j = nys, nyn
1467	DO k = nzb+1, nzt + 1
1468	!
1469	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1470	!-- Additional factors are added to improve the variance of v and w experimental test
1471	!-- of 1.2
1472	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1473	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1474	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1475	a33(k) * fw_yz(k,j) ) * &
1476	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1477
1478	ENDDO
1479	ENDDO
1480	ENDIF
1481	!
1482	!-- Mass flux correction following Kim et al. (2013)
1483	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1484	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1485	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1486	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1487	mc_factor_l = 0.0_wp
1488	mc_factor = 0.0_wp
1489	!
1490	!-- Sum up the original volume flows (with and without perturbations).
1491	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1492	IF ( myidx == id_stg_left ) i = nxl
1493	IF ( myidx == id_stg_right ) i = nxr+1
1494
1495	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1496	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1497
1498	IF ( myidx == id_stg_left ) i = nxl-1
1499	IF ( myidx == id_stg_right ) i = nxr+1
1500
1501	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1502	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1503	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1504	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1505
1506	#if defined( __parallel )
1507	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1508	#else
1509	mc_factor = mc_factor_l
1510	#endif
1511	!
1512	!-- Calculate correction factor and force zero mean perturbations.
1513	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1514
1515	IF ( myidx == id_stg_left ) i = nxl
1516	IF ( myidx == id_stg_right ) i = nxr+1
1517
1518	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1519	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1520
1521
1522	IF ( myidx == id_stg_left ) i = nxl-1
1523	IF ( myidx == id_stg_right ) i = nxr+1
1524
1525	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1526	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1527
1528	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1529	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1530	!
1531	!-- Add disturbances
1532	IF ( myidx == id_stg_left ) THEN
1533	!
1534	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1535	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1536	!-- the mean inflow profiles.
1537	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1538	!
1539	!-- Add disturbance at the inflow
1540	DO j = nys, nyn
1541	DO k = nzb, nzt+1
1542	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1543	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1544	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1545	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1546	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1547	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1548	ENDDO
1549	ENDDO
1550	ELSE
1551
1552	DO j = nys, nyn
1553	DO k = nzb+1, nzt
1554	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1556	u(k,j,-1) = u(k,j,0)
1557	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1558	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1559	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1560	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1561	ENDDO
1562	ENDDO
1563	ENDIF
1564	ENDIF
1565	IF ( myidx == id_stg_right ) THEN
1566	DO j = nys, nyn
1567	DO k = nzb+1, nzt
1568	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1569	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1570	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1571	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1572	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1573	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1574	ENDDO
1575	ENDDO
1576	ENDIF
1577	ENDIF
1578	ENDIF
1579	!
1580	!-- Turbulence generation at north and south boundary
1581	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1582	!
1583	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1584	!-- exceeded. Else the old set of perturbations is imposed
1585	IF ( stg_call ) THEN
1586	DO i = nxl, nxr
1587	DO k = nzb, nzt + 1
1588	!
1589	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1590	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1591	fu_xz(k,i) = fuo_xz(k,i)
1592	ELSE
1593	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1594	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1595	ENDIF
1596
1597	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1598	fv_xz(k,i) = fvo_xz(k,i)
1599	ELSE
1600	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1601	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1602	ENDIF
1603
1604	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1605	fw_xz(k,i) = fwo_xz(k,i)
1606	ELSE
1607	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1608	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1609	ENDIF
1610	ENDDO
1611	ENDDO
1612
1613
1614	dist_xz(nzb,:,1) = 0.0_wp
1615	dist_xz(nzb,:,2) = 0.0_wp
1616	dist_xz(nzb,:,3) = 0.0_wp
1617
1618	IF ( myidy == id_stg_south ) j = nys
1619	IF ( myidy == id_stg_north ) j = nyn+1
1620	DO i = nxl, nxr
1621	DO k = nzb+1, nzt + 1
1622	!
1623	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1624	!-- Additional factors are added to improve the variance of v and w
1625	!experimental test of 1.2
1626	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1627	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1628	ENDDO
1629	ENDDO
1630
1631	IF ( myidy == id_stg_south ) j = nys-1
1632	IF ( myidy == id_stg_north ) j = nyn+1
1633	DO i = nxl, nxr
1634	DO k = nzb+1, nzt + 1
1635	!
1636	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1637	!-- Additional factors are added to improve the variance of v and w
1638	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1639	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1640
1641	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1642	a33(k) * fw_xz(k,i) ) * &
1643	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1644	ENDDO
1645	ENDDO
1646	ENDIF
1647
1648	!
1649	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1650	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1651	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1652	!-- else the boundary values won't be accessed.
1653	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1654	mc_factor_l = 0.0_wp
1655	mc_factor = 0.0_wp
1656
1657	IF ( myidy == id_stg_south ) j = nys
1658	IF ( myidy == id_stg_north ) j = nyn+1
1659
1660	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1661	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1662
1663	IF ( myidy == id_stg_south ) j = nys-1
1664	IF ( myidy == id_stg_north ) j = nyn+1
1665
1666	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1667	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1668	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1669	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1670
1671	#if defined( __parallel )
1672	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1673	#else
1674	mc_factor = mc_factor_l
1675	#endif
1676
1677	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1678
1679	IF ( myidy == id_stg_south ) j = nys
1680	IF ( myidy == id_stg_north ) j = nyn+1
1681
1682	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1683	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1684
1685
1686	IF ( myidy == id_stg_south ) j = nys-1
1687	IF ( myidy == id_stg_north ) j = nyn+1
1688
1689	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1690	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1691
1692	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1693	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1694	!
1695	!-- Add disturbances
1696	IF ( myidy == id_stg_south ) THEN
1697	DO i = nxl, nxr
1698	DO k = nzb+1, nzt
1699	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1700	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1701	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1702	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1703	v(k,-1,i) = v(k,0,i)
1704	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1705	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1706	ENDDO
1707	ENDDO
1708	ENDIF
1709	IF ( myidy == id_stg_north ) THEN
1710
1711	DO i = nxl, nxr
1712	DO k = nzb+1, nzt
1713	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1714	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1715	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1716	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1717	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1718	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1719	ENDDO
1720	ENDDO
1721	ENDIF
1722	ENDIF
1723	ENDIF
1724	!
1725	!-- Exchange ghost points.
1726	CALL exchange_horiz( u, nbgp )
1727	CALL exchange_horiz( v, nbgp )
1728	CALL exchange_horiz( w, nbgp )
1729	!
1730	!-- Finally, set time counter for calling STG to zero
1731	IF ( stg_call ) time_stg_call = 0.0_wp
1732	!
1733	!-- Set adjustment step to False to indicate that time correlation can be
1734	!-- switched-on again.
1735	adjustment_step = .FALSE.
1736
1737	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1738
1739	END SUBROUTINE stg_main
1740
1741	!--------------------------------------------------------------------------------------------------!
1742	! Description:
1743	! ------------
1744	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1745	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1746	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1747	!> array.
1748	!--------------------------------------------------------------------------------------------------!
1749	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1750
1751	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1752	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1753	INTEGER(iwp) :: j !< loop index in y-direction
1754	INTEGER(iwp) :: jj !< loop index in y-direction
1755	INTEGER(iwp) :: k !< loop index in z-direction
1756	INTEGER(iwp) :: kk !< loop index in z-direction
1757	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1758
1759	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1760	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1761
1762	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1763	REAL(wp) :: rand_av !< average of random number
1764	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1765
1766	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1767	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1768
1769	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1770	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1771
1772	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1773	!
1774	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1775	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1776	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1777	!-- and normalization of random numbers is done locally, while the result is later distributed to
1778	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1779	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1780	!-- correlation matrix.
1781	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1782	rand_it = 0.0_wp
1783
1784	rand_av = 0.0_wp
1785	rand_sigma_inv = 0.0_wp
1786	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1787	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1788	!
1789	!-- Compute and normalize random numbers.
1790	DO j = nys - mergp_y, nyn + mergp_y
1791	!
1792	!-- Put the random seeds at grid point j
1793	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1794	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1795	CALL random_number_parallel( random_dummy )
1796	rand_it(k,j) = random_dummy
1797	ENDDO
1798	!
1799	!-- Get the new random seeds from last call at grid point j
1800	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1801	ENDDO
1802	!
1803	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1804	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1805	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1806	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1807	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1808	rand_av = rand_av + rand_it(k,j)
1809	ENDDO
1810	ENDDO
1811
1812	#if defined( __parallel )
1813	!
1814	!-- Sum-up the local averages of the random numbers
1815	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1816	#endif
1817	rand_av = rand_av * nyz_inv
1818	!
1819	!-- Obtain zero mean
1820	rand_it= rand_it - rand_av
1821	!
1822	!-- Now, compute the variance
1823	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1824	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1825	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1826	ENDDO
1827	ENDDO
1828
1829	#if defined( __parallel )
1830	!
1831	!-- Sum-up the local quadratic averages of the random numbers
1832	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1833	#endif
1834	!
1835	!-- Compute standard deviation
1836	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1837	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1838	ELSE
1839	rand_sigma_inv = 1.0_wp
1840	ENDIF
1841	!
1842	!-- Normalize with standard deviation to obtain unit variance
1843	rand_it = rand_it * rand_sigma_inv
1844
1845	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1846	!
1847	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1848	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1849	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1850	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1851	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1852	!-- communication. In the second option, which performs better when the turbulent length scales
1853	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1854	!-- communication is necessary.
1855	IF ( compute_velocity_seeds_local ) THEN
1856
1857	f_n = 0.0_wp
1858	DO j = nys, nyn
1859	DO k = nzb, nzt+1
1860	DO jj = -n_y(k), n_y(k)
1861	DO kk = -n_z(k), n_z(k)
1862	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1863	ENDDO
1864	ENDDO
1865	ENDDO
1866	ENDDO
1867
1868	ELSE
1869
1870	f_n_l = 0.0_wp
1871	DO j = nys, nyn
1872	DO k = nzb_x_stg, nzt_x_stg+1
1873	DO jj = -n_y(k), n_y(k)
1874	DO kk = -n_z(k), n_z(k)
1875	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1876	ENDDO
1877	ENDDO
1878	ENDDO
1879	ENDDO
1880	!
1881	!-- Gather velocity seeds of full subdomain
1882	send_count = nzt_x_stg - nzb_x_stg + 1
1883	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1884
1885	#if defined( __parallel )
1886	!
1887	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1888	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1889	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1890	!
1891	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1892	!-- nesting for example).
1893	IF ( PRESENT( id_right ) ) THEN
1894	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1895	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1896	ENDIF
1897	#else
1898	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1899	!
1900	!-- Next line required to avoid compile errors because of unused dummy arguments
1901	IF ( id_left == 0 ) id_right = 0
1902	#endif
1903
1904	ENDIF
1905
1906	DEALLOCATE( rand_it )
1907
1908	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1909
1910	END SUBROUTINE stg_generate_seed_yz
1911
1912
1913	!--------------------------------------------------------------------------------------------------!
1914	! Description:
1915	! ------------
1916	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1917	!> f_n.
1918	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1919	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1920	!> full array.
1921	!--------------------------------------------------------------------------------------------------!
1922	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1923
1924	INTEGER(iwp) :: i !< loop index in x-direction
1925	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1926	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1927	INTEGER(iwp) :: ii !< loop index in x-direction
1928	INTEGER(iwp) :: k !< loop index in z-direction
1929	INTEGER(iwp) :: kk !< loop index in z-direction
1930	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1931
1932	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1933	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1934
1935	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1936	REAL(wp) :: rand_av !< average of random number
1937	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1938
1939	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1940	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1941
1942	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1943	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1944
1945	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1946
1947	!
1948	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1949	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1950	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1951	!-- and normalization of random numbers is done locally, while the result is later distributed to
1952	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1953	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1954	!-- correlation matrix.
1955	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1956	rand_it = 0.0_wp
1957
1958	rand_av = 0.0_wp
1959	rand_sigma_inv = 0.0_wp
1960	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1961	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1962	!
1963	!-- Compute and normalize random numbers.
1964	DO i = nxl - mergp_x, nxr + mergp_x
1965	!
1966	!-- Put the random seeds at grid point ii
1967	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1968	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1969	CALL random_number_parallel( random_dummy )
1970	rand_it(k,i) = random_dummy
1971	ENDDO
1972	!
1973	!-- Get the new random seeds from last call at grid point ii
1974	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1975	ENDDO
1976	!
1977	!-- For normalization to zero mean, sum-up the global random numers.
1978	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1979	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1980	!-- also occur on the inner subdomains.
1981	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1982	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1983	rand_av = rand_av + rand_it(k,i)
1984	ENDDO
1985	ENDDO
1986
1987	#if defined( __parallel )
1988	!
1989	!-- Sum-up the local averages of the random numbers
1990	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1991	#endif
1992	rand_av = rand_av * nxz_inv
1993	!
1994	!-- Obtain zero mean
1995	rand_it= rand_it - rand_av
1996	!
1997	!-- Now, compute the variance
1998	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1999	DO k = nzb - mergp_z, nzt + 1 + mergp_z
2000	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2001	ENDDO
2002	ENDDO
2003
2004	#if defined( __parallel )
2005	!
2006	!-- Sum-up the local quadratic averages of the random numbers
2007	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
2008	#endif
2009	!
2010	!-- Compute standard deviation
2011	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2012	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2013	ELSE
2014	rand_sigma_inv = 1.0_wp
2015	ENDIF
2016	!
2017	!-- Normalize with standard deviation to obtain unit variance
2018	rand_it = rand_it * rand_sigma_inv
2019
2020	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2021	!
2022	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
2023	!-- first one, the computation of the seeds is distributed to all processes along the communicator
2024	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
2025	!-- length scales the computational effort can become quite huge (it scales with the turbulent
2026	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
2027	!-- In the second option, which performs better when the turbulent length scales are parametrized
2028	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
2029	IF ( compute_velocity_seeds_local ) THEN
2030
2031	f_n = 0.0_wp
2032	DO i = nxl, nxr
2033	DO k = nzb, nzt+1
2034	DO ii = -n_x(k), n_x(k)
2035	DO kk = -n_z(k), n_z(k)
2036	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2037	ENDDO
2038	ENDDO
2039	ENDDO
2040	ENDDO
2041
2042	ELSE
2043
2044	f_n_l = 0.0_wp
2045	DO i = nxl, nxr
2046	DO k = nzb_y_stg, nzt_y_stg+1
2047	DO ii = -n_x(k), n_x(k)
2048	DO kk = -n_z(k), n_z(k)
2049	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2050	ENDDO
2051	ENDDO
2052	ENDDO
2053	ENDDO
2054	!
2055	!-- Gather velocity seeds of full subdomain
2056	send_count = nzt_y_stg - nzb_y_stg + 1
2057	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2058
2059	#if defined( __parallel )
2060	!
2061	!-- Gather the processed velocity seed on south boundary mpi ranks.
2062	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2063	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2064	!
2065	!-- Gather the processed velocity seed on north boundary mpi ranks.
2066	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2067	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2068	#else
2069	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2070	!
2071	!-- Next line required to avoid compile errors because of unused dummy arguments
2072	IF ( id_north == 0 ) id_south = 0
2073	#endif
2074
2075	ENDIF
2076
2077	DEALLOCATE( rand_it )
2078
2079	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2080
2081	END SUBROUTINE stg_generate_seed_xz
2082
2083	!--------------------------------------------------------------------------------------------------!
2084	! Description:
2085	! ------------
2086	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2087	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2088	!> which is applied in state-of-the-art dispserion modelling.
2089	!--------------------------------------------------------------------------------------------------!
2090	SUBROUTINE parametrize_turbulence
2091
2092	INTEGER(iwp) :: k !< loop index in z-direction
2093
2094	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2095	REAL(wp) :: d_zi !< inverse boundary-layer depth
2096	REAL(wp) :: length_scale_lon !< length scale in flow direction
2097	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2098	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2099	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2100	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2101	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2102	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2103	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2104	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2105	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2106	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2107	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2108	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2109	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2110	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2111	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2112	REAL(wp) :: zzi !< ratio of z/zi
2113
2114	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2115	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2116	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2117
2118	!
2119	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2120	!-- criterion according to Heinze et al. (2017).
2121	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2122	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2123	k_zi = MIN( k_zi, nzt )
2124	!
2125	!-- Calculate angle between flow direction and x-axis.
2126	DO k = nzb+1, nzt + 1
2127	IF ( u_init(k) /= 0.0_wp ) THEN
2128	phi(k) = ATAN( v_init(k) / u_init(k) )
2129	ELSE
2130	phi(k) = 0.5 * pi
2131	ENDIF
2132	!
2133	!-- Pre-calculate sine and cosine.
2134	cos_phi(k) = COS( phi(k) )
2135	sin_phi(k) = SIN( phi(k) )
2136	ENDDO
2137	!
2138	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2139	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2140	!-- coincide with the grid axis. Hence, components are rotated after computation.
2141	d_zi = 1.0_wp / zi_ribulk
2142	DO k = nzb+1, k_zi
2143
2144	corr_term_uh = MERGE( 0.35_wp * ABS( &
2145	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2146	)**( 2.0_wp / 3.0_wp ), &
2147	0.0_wp, &
2148	scale_l < -5.0_wp )
2149	!
2150	!-- Determine normalized height coordinate
2151	zzi = zu(k) * d_zi
2152	!
2153	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2154	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2155	!-- variances cannot become negative, take the absolute values.
2156	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2157	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2158
2159	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2160	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2161	!
2162	!-- w'w'
2163	r33(k) = scale_wm*2 ( &
2164	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2165	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2166	)
2167	!
2168	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2169	!-- these are projected along the x- and y-direction. Note, it is assumed that
2170	!-- the flux within the boundary points opposite to the vertical gradient.
2171	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2172	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2173
2174	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2175	- ( u_init(k+1) - u_init(k-1) ) )
2176	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2177	- ( v_init(k+1) - v_init(k-1) ) )
2178	!
2179	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
2180	!-- for the vertical transport.
2181	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2182	!
2183	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2184	!-- limited to the adjustment time scales.
2185	tu(k) = MIN( dt_stg_adjust, &
2186	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2187
2188	tv(k) = tu(k)
2189	tw(k) = tu(k)
2190
2191	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2192	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2193	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2194	!
2195	!-- Assume isotropic turbulence length scales
2196	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2197	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2198	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2199	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2200	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2201	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2202	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2203	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2204	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2205
2206	ENDDO
2207	!
2208	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2209	!-- reduced to zero by a blending function.
2210	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2211	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2212	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2213
2214	time_scale_zi = tu(k_zi)
2215	r11_zi = r11(k_zi)
2216	r22_zi = r22(k_zi)
2217	r33_zi = r33(k_zi)
2218	r31_zi = r31(k_zi)
2219	r32_zi = r32(k_zi)
2220
2221	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2222
2223	DO k = k_zi+1, nzt+1
2224	!
2225	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2226	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2227	!
2228	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2229	!-- the mergpe-function can crash if scale_l is zero.
2230	r11(k) = r11_zi * blend
2231	r22(k) = r22_zi * blend
2232	r33(k) = r33_zi * blend
2233	r31(k) = r31_zi * blend
2234	r32(k) = r32_zi * blend
2235	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
2236
2237	!
2238	!-- Compute turbulent time scales according to Brost et al. (1982).
2239	!-- Note, time scales are limited to the adjustment time scales.
2240	tu(k) = time_scale_zi * blend
2241	tv(k) = time_scale_zi * blend
2242	tw(k) = time_scale_zi * blend
2243
2244	length_scale_lon = length_scale_lon_zi * blend
2245	length_scale_lat = length_scale_lat_zi * blend
2246	length_scale_vert = length_scale_vert_zi * blend
2247	!
2248	!-- Assume isotropic turbulence length scales
2249	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2250	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2251	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2252	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2253	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2254	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2255	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2256	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2257	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2258	ENDDO
2259	!
2260	!-- Set bottom boundary condition for reynolds stresses
2261	r11(nzb) = r11(nzb+1)
2262	r22(nzb) = r22(nzb+1)
2263	r33(nzb) = r33(nzb+1)
2264
2265	r21(nzb) = r11(nzb+1)
2266	r31(nzb) = r31(nzb+1)
2267	r32(nzb) = r32(nzb+1)
2268
2269	!
2270	!-- Set bottom boundary condition for the length and time scales
2271	nux(nzb) = nux(nzb+1)
2272	nuy(nzb) = nuy(nzb+1)
2273	nuz(nzb) = nuz(nzb+1)
2274	nvx(nzb) = nvx(nzb+1)
2275	nvy(nzb) = nvy(nzb+1)
2276	nvz(nzb) = nvz(nzb+1)
2277	nwx(nzb) = nwx(nzb+1)
2278	nwy(nzb) = nwy(nzb+1)
2279	nwz(nzb) = nwz(nzb+1)
2280
2281	tu(nzb) = tu(nzb+1)
2282	tv(nzb) = tv(nzb+1)
2283	tw(nzb) = tw(nzb+1)
2284
2285	adjustment_step = .TRUE.
2286
2287	END SUBROUTINE parametrize_turbulence
2288
2289	!--------------------------------------------------------------------------------------------------!
2290	! Description:
2291	! ------------
2292	!> Calculate the coefficient matrix from the Lund rotation.
2293	!--------------------------------------------------------------------------------------------------!
2294	SUBROUTINE calc_coeff_matrix
2295
2296	INTEGER(iwp) :: k !< loop index in z-direction
2297
2298	!
2299	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2300	DO k = nzb+1, nzt+1
2301	IF ( r11(k) > 10E-6_wp ) THEN
2302	a11(k) = SQRT( r11(k) )
2303	a21(k) = r21(k) / a11(k)
2304	a31(k) = r31(k) / a11(k)
2305	ELSE
2306	a11(k) = 10E-8_wp
2307	a21(k) = 10E-8_wp
2308	a31(k) = 10E-8_wp
2309	ENDIF
2310	ENDDO
2311	DO k = nzb+1, nzt+1
2312	a22(k) = r22(k) - a21(k)**2
2313	IF ( a22(k) > 10E-6_wp ) THEN
2314	a22(k) = SQRT( a22(k) )
2315	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2316	ELSE
2317	a22(k) = 10E-8_wp
2318	a32(k) = 10E-8_wp
2319	ENDIF
2320	ENDDO
2321	DO k = nzb+1, nzt+1
2322	a33(k) = r33(k) - a31(k)2 - a32(k)2
2323	IF ( a33(k) > 10E-6_wp ) THEN
2324	a33(k) = SQRT( a33(k) )
2325	ELSE
2326	a33(k) = 10E-8_wp
2327	ENDIF
2328	ENDDO
2329	!
2330	!-- Set bottom boundary condition
2331	a11(nzb) = a11(nzb+1)
2332	a22(nzb) = a22(nzb+1)
2333	a21(nzb) = a21(nzb+1)
2334	a33(nzb) = a33(nzb+1)
2335	a31(nzb) = a31(nzb+1)
2336	a32(nzb) = a32(nzb+1)
2337
2338	END SUBROUTINE calc_coeff_matrix
2339
2340	!--------------------------------------------------------------------------------------------------!
2341	! Description:
2342	! ------------
2343	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2344	!> turbulence at the lateral boundaries.
2345	!--------------------------------------------------------------------------------------------------!
2346	SUBROUTINE stg_adjust
2347
2348	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2349	!
2350	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2351	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2352	!-- nevertheless, the boundary-layer depth need to determined first.
2353	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2354	CALL nesting_offl_calc_zi
2355	!
2356	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2357	CALL calc_scaling_variables
2358	!
2359	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2360	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2361	!-- velocity and velocity scale.
2362	CALL parametrize_turbulence
2363	!
2364	!-- Calculate coefficient matrix from Reynolds stress tensor
2365	!-- (Lund rotation)
2366	CALL calc_coeff_matrix
2367	!
2368	!-- Setup filter functions according to updated length scales.
2369	CALL stg_setup_filter_function
2370	!
2371	!-- Reset time counter for controlling next adjustment to zero
2372	time_stg_adjust = 0.0_wp
2373
2374	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2375
2376	END SUBROUTINE stg_adjust
2377
2378
2379	!--------------------------------------------------------------------------------------------------!
2380	! Description:
2381	! ------------
2382	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2383	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2384	!> scale, and Obukhov length.
2385	!--------------------------------------------------------------------------------------------------!
2386	SUBROUTINE calc_scaling_variables
2387
2388	INTEGER(iwp) :: i !< loop index in x-direction
2389	INTEGER(iwp) :: j !< loop index in y-direction
2390	INTEGER(iwp) :: k !< loop index in z-direction
2391	INTEGER(iwp) :: m !< surface element index
2392
2393	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2394	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2395	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2396	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2397	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2398	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2399	REAL(wp) :: w_convective !< convective velocity scale
2400
2401	!
2402	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2403	!-- model domain.
2404	pt_surf_mean_l = 0.0_wp
2405	shf_mean_l = 0.0_wp
2406	scale_l_l = 0.0_wp
2407	friction_vel_l = 0.0_wp
2408	DO m = 1, surf_def_h(0)%ns
2409	i = surf_def_h(0)%i(m)
2410	j = surf_def_h(0)%j(m)
2411	k = surf_def_h(0)%k(m)
2412	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2413	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2414	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2415	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2416	ENDDO
2417	DO m = 1, surf_lsm_h(0)%ns
2418	i = surf_lsm_h(0)%i(m)
2419	j = surf_lsm_h(0)%j(m)
2420	k = surf_lsm_h(0)%k(m)
2421	friction_vel_l = friction_vel_l + surf_lsm_h(0)%us(m)
2422	shf_mean_l = shf_mean_l + surf_lsm_h(0)%shf(m) * drho_air(k)
2423	scale_l_l = scale_l_l + surf_lsm_h(0)%ol(m)
2424	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2425	ENDDO
2426	DO m = 1, surf_usm_h(0)%ns
2427	i = surf_usm_h(0)%i(m)
2428	j = surf_usm_h(0)%j(m)
2429	k = surf_usm_h(0)%k(m)
2430	friction_vel_l = friction_vel_l + surf_usm_h(0)%us(m)
2431	shf_mean_l = shf_mean_l + surf_usm_h(0)%shf(m) * drho_air(k)
2432	scale_l_l = scale_l_l + surf_usm_h(0)%ol(m)
2433	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2434	ENDDO
2435
2436	#if defined( __parallel )
2437	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2438	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2439	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2440	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2441	#else
2442	scale_us = friction_vel_l
2443	shf_mean = shf_mean_l
2444	scale_l = scale_l_l
2445	pt_surf_mean = pt_surf_mean_l
2446	#endif
2447
2448	scale_us = scale_us * d_nxy
2449	shf_mean = shf_mean * d_nxy
2450	scale_l = scale_l * d_nxy
2451	pt_surf_mean = pt_surf_mean * d_nxy
2452	!
2453	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2454	!-- convective velocity scale to zero.
2455	IF ( shf_mean > 0.0_wp ) THEN
2456	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2457	ELSE
2458	w_convective = 0.0_wp
2459	ENDIF
2460	!
2461	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2462	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2463	!-- value of friction velocity for the reynolds-stress parametrization.
2464	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2465	!
2466	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2467	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2468	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2469
2470	END SUBROUTINE calc_scaling_variables
2471
2472	END MODULE synthetic_turbulence_generator_mod

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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90

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