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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4597

Last change on this file since 4597 was 4566, checked in by suehring, 4 years ago
synthetic turbulence generator: revise parametrization for reynolds-stress components, turbulent length- and time scales; revise computation of velocity disturbances to be consistent to Xie and Castro (2008); change default value of time interval to adjust turbulence parametrization; bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
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1	!> @synthetic_turbulence_generator_mod.f90
2	!--------------------------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2020 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4566 2020-06-16 10:11:51Z gronemeier $
27	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
28	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
29	! - change default value of time interval to adjust turbulence parametrization
30	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
31	!
32	! 4562 2020-06-12 08:38:47Z raasch
33	! Parts of r4559 re-formatted
34	!
35	! 4559 2020-06-11 08:51:48Z raasch
36	! File re-formatted to follow the PALM coding standard
37	!
38	! 4535 2020-05-15 12:07:23Z raasch
39	! Bugfix for restart data format query
40	!
41	! 4495 2020-04-13 20:11:20Z raasch
42	! Restart data handling with MPI-IO added
43	!
44	! 4481 2020-03-31 18:55:54Z maronga
45	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
46	!
47	! 4442 2020-03-04 19:21:13Z suehring
48	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
49	! (was accidantly changed).
50	!
51	! 4441 2020-03-04 19:20:35Z suehring
52	! Correct misplaced preprocessor directive
53	!
54	! 4438 2020-03-03 20:49:28Z suehring
55	! Performance optimizations in velocity-seed calculation:
56	! - Random number array is only defined and computed locally (except for normalization to zero mean
57	! and unit variance)
58	! - Parallel random number generator is applied independent on the 2D random numbers in other
59	! routines
60	! - Option to decide wheter velocity seeds are computed locally without any further communication
61	! or are computed by all processes along the communicator
62	!
63	! 4346 2019-12-18 11:55:56Z motisi
64	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
65	! information used in wall_flags_static_0
66	!
67	! 4335 2019-12-12 16:39:05Z suehring
68	! Commentation of last commit
69	!
70	! 4332 2019-12-10 19:44:12Z suehring
71	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
72	! Further, minor bugfix in initial velocity seed calculation.
73	!
74	! 4329 2019-12-10 15:46:36Z motisi
75	! Renamed wall_flags_0 to wall_flags_static_0
76	!
77	! 4309 2019-11-26 18:49:59Z suehring
78	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
79	! the parallel random number generator. Random numbers are now only computed and normalized locally,
80	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
81	! array.
82	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
83	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
84	!
85	! 4182 2019-08-22 15:20:23Z scharf
86	! Corrected "Former revisions" section
87	!
88	! 4148 2019-08-08 11:26:00Z suehring
89	! Remove unused variable
90	!
91	! 4144 2019-08-06 09:11:47Z raasch
92	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
93	!
94	! 4071 2019-07-03 20:02:00Z suehring
95	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
96	! file.
97	!
98	! 4022 2019-06-12 11:52:39Z suehring
99	! Several bugfixes and improvements
100	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
101	! instabilities in case the mean volume flow is close to zero)
102	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
103	! numerically unstable
104	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
105	! case dt_stg_call /= dt_3d
106	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
107	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
108	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
109	!
110	! 3987 2019-05-22 09:52:13Z kanani
111	! Introduce alternative switch for debug output during timestepping
112	!
113	! 3938 2019-04-29 16:06:25Z suehring
114	! Remove unused variables
115	!
116	! 3937 2019-04-29 15:09:07Z suehring
117	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
118	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
119	! synthetic turbulence parametrization.
120	!
121	! 3909 2019-04-17 09:13:25Z suehring
122	! Minor bugfix for last commit
123	!
124	! 3900 2019-04-16 15:17:43Z suehring
125	! Missing re-calculation of perturbation seeds in case of restarts
126	!
127	! 3891 2019-04-12 17:52:01Z suehring
128	! Bugfix in initialization in case of restart runs.
129	!
130	! 3885 2019-04-11 11:29:34Z kanani
131	! Changes related to global restructuring of location messages and introduction of additional debug
132	! messages
133	!
134	!
135	! Removed unused variables
136	!
137	! 3719 2019-02-06 13:10:18Z kanani
138	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
139	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
140	! for better overview.
141	!
142	! 2259 2017-06-08 09:09:11Z gronemeier
143	! Initial revision
144	!
145	! Authors:
146	! --------
147	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
148	!
149	!
150	! Description:
151	! ------------
152	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
153	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
154	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
155	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
156	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
157	!> parametrized within the boundary layer.
158	!>
159	!> @todo Enable cyclic_fill
160	!> Implement turbulence generation for e and pt
161	!> @note <Enter notes on the module>
162	!> @bug Height information from input file is not used. Profiles from input must match with current
163	!> PALM grid.
164	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
165	!--------------------------------------------------------------------------------------------------!
166	MODULE synthetic_turbulence_generator_mod
167
168
169	USE arrays_3d, &
170	ONLY: dzw, &
171	ddzw, &
172	drho_air, &
173	mean_inflow_profiles, &
174	pt, &
175	pt_init, &
176	q, &
177	q_init, &
178	u, &
179	u_init, &
180	v, &
181	v_init, &
182	w, &
183	zu, &
184	zw
185
186	USE basic_constants_and_equations_mod, &
187	ONLY: g, &
188	kappa, &
189	pi
190
191	USE control_parameters, &
192	ONLY: bc_lr, &
193	bc_ns, &
194	child_domain, &
195	coupling_char, &
196	debug_output_timestep, &
197	dt_3d, &
198	e_init, &
199	humidity, &
200	initializing_actions, &
201	intermediate_timestep_count, &
202	intermediate_timestep_count_max, &
203	length, &
204	message_string, &
205	nesting_offline, &
206	neutral, &
207	num_mean_inflow_profiles, &
208	random_generator, &
209	rans_mode, &
210	restart_data_format_output, &
211	restart_string, &
212	syn_turb_gen, &
213	time_since_reference_point, &
214	turbulent_inflow
215
216	USE cpulog, &
217	ONLY: cpu_log, &
218	log_point_s
219
220	USE grid_variables, &
221	ONLY: ddx, &
222	ddy, &
223	dx, &
224	dy
225
226	USE indices, &
227	ONLY: nbgp, &
228	nz, &
229	nzb, &
230	nzt, &
231	nx, &
232	nxl, &
233	nxlu, &
234	nxr, &
235	ny, &
236	nys, &
237	nysv, &
238	nyn, &
239	wall_flags_total_0
240
241	USE kinds
242
243	#if defined( __parallel ) && !defined( __mpifh )
244	USE MPI
245	#endif
246
247	USE nesting_offl_mod, &
248	ONLY: nesting_offl_calc_zi, &
249	zi_ribulk
250
251	USE pegrid, &
252	ONLY: comm1dx, &
253	comm1dy, &
254	comm2d, &
255	ierr, &
256	myidx, &
257	myidy, &
258	pdims
259
260	USE pmc_interface, &
261	ONLY : rans_mode_parent
262
263	USE random_generator_parallel, &
264	ONLY: init_parallel_random_generator, &
265	random_dummy, &
266	random_number_parallel, &
267	random_seed_parallel
268
269	USE restart_data_mpi_io_mod, &
270	ONLY: rrd_mpi_io, &
271	wrd_mpi_io
272
273	USE transpose_indices, &
274	ONLY: nzb_x, &
275	nzt_x
276
277	USE surface_mod, &
278	ONLY: surf_def_h, &
279	surf_lsm_h, &
280	surf_usm_h
281
282	IMPLICIT NONE
283
284	#if defined( __parallel ) && defined( __mpifh )
285	INCLUDE "mpif.h"
286	#endif
287
288
289	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
290	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
291	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
292	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
293	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
294	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
295	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
296	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
297	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
298	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
299	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
300	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
301	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
302	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
303	#if defined( __parallel )
304	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
305	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
306	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
307	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
308	#endif
309
310	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
311	!< required for bias correction of imposed perturbations
312	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
313	!< required for bias correction of imposed perturbations
314
315	#if defined( __parallel )
316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
318	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
319	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
320	#endif
321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
330
331	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
332	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
333	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
334	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
335
336
337	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
338	!< no time correlation to the timestep before should be considered
339	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
340	!< or if computation is distributed over several processes
341	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
342	!< (.FALSE.) or if it parametrized
343	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
344	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
345
346
347	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
348	!< scales above the boundary layer
349	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
350	!< one length scale above ABL top
351	REAL(wp) :: d_l !< blend_coeff/length_scale
352	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
353	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
354	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
355	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
356	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
357	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
358	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
359	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
360
361	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
362
363
364	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
365	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
366	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
367	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
368	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
369	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
370
371	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
372	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
373	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
374	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
375	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
376	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
377	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
378	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
379	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
380
381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
402
403	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
404	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
405
406	!
407	!-- PALM interfaces:
408	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
409	INTERFACE stg_adjust
410	MODULE PROCEDURE stg_adjust
411	END INTERFACE stg_adjust
412	!
413	!-- Input parameter checks to be done in check_parameters
414	INTERFACE stg_check_parameters
415	MODULE PROCEDURE stg_check_parameters
416	END INTERFACE stg_check_parameters
417
418	!
419	!-- Calculate filter functions
420	INTERFACE stg_filter_func
421	MODULE PROCEDURE stg_filter_func
422	END INTERFACE stg_filter_func
423
424	!
425	!-- Generate velocity seeds at south and north domain boundary
426	INTERFACE stg_generate_seed_xz
427	MODULE PROCEDURE stg_generate_seed_xz
428	END INTERFACE stg_generate_seed_xz
429	!
430	!-- Generate velocity seeds at left and/or right domain boundary
431	INTERFACE stg_generate_seed_yz
432	MODULE PROCEDURE stg_generate_seed_yz
433	END INTERFACE stg_generate_seed_yz
434
435	!
436	!-- Output of information to the header file
437	INTERFACE stg_header
438	MODULE PROCEDURE stg_header
439	END INTERFACE stg_header
440
441	!
442	!-- Initialization actions
443	INTERFACE stg_init
444	MODULE PROCEDURE stg_init
445	END INTERFACE stg_init
446
447	!
448	!-- Main procedure of synth. turb. gen.
449	INTERFACE stg_main
450	MODULE PROCEDURE stg_main
451	END INTERFACE stg_main
452
453	!
454	!-- Reading of NAMELIST parameters
455	INTERFACE stg_parin
456	MODULE PROCEDURE stg_parin
457	END INTERFACE stg_parin
458
459	!
460	!-- Reading of parameters for restart runs
461	INTERFACE stg_rrd_global
462	MODULE PROCEDURE stg_rrd_global_ftn
463	MODULE PROCEDURE stg_rrd_global_mpi
464	END INTERFACE stg_rrd_global
465
466	!
467	!-- Writing of binary output for restart runs
468	INTERFACE stg_wrd_global
469	MODULE PROCEDURE stg_wrd_global
470	END INTERFACE stg_wrd_global
471
472	SAVE
473
474	PRIVATE
475
476	!
477	!-- Public interfaces
478	PUBLIC stg_adjust, &
479	stg_check_parameters, &
480	stg_header, &
481	stg_init, &
482	stg_main, &
483	stg_parin, &
484	stg_rrd_global, &
485	stg_wrd_global
486
487	!
488	!-- Public variables
489	PUBLIC dt_stg_call, &
490	dt_stg_adjust, &
491	id_stg_left, &
492	id_stg_north, &
493	id_stg_right, &
494	id_stg_south, &
495	parametrize_inflow_turbulence, &
496	time_stg_adjust, &
497	time_stg_call, &
498	use_syn_turb_gen
499
500
501	CONTAINS
502
503
504	!--------------------------------------------------------------------------------------------------!
505	! Description:
506	! ------------
507	!> Check parameters routine for synthetic turbulence generator
508	!--------------------------------------------------------------------------------------------------!
509	SUBROUTINE stg_check_parameters
510
511	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
512	nesting_offline ) THEN
513	message_string = 'Synthetic turbulence generator is required ' // &
514	'if offline nesting is applied and PALM operates in LES mode.'
515	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
516	ENDIF
517
518	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
519	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
520	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
521	'and parent operates in RANS-mode but current child in LES mode.'
522	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
523	ENDIF
524
525	IF ( use_syn_turb_gen ) THEN
526
527	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
528	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
529	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
530
531	ENDIF
532
533	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
534	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
535	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
536
537	ENDIF
538
539	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
540
541	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
542	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
543	message_string = 'Using synthetic turbulence generator requires ' // &
544	'%initializing_actions = "set_constant_profiles" or ' // &
545	' "read_restart_data", if not offline nesting is applied.'
546	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
547	ENDIF
548
549	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
550	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
551	' "dirichlet/radiation", if not offline nesting is applied.'
552	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
553	ENDIF
554	IF ( bc_ns /= 'cyclic' ) THEN
555	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
556	' "cyclic", if not offline nesting is applied.'
557	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
558	ENDIF
559
560	ENDIF
561
562	IF ( turbulent_inflow ) THEN
563	message_string = 'Using synthetic turbulence generator in combination ' // &
564	'&with turbulent_inflow = .T. is not allowed'
565	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
566	ENDIF
567	!
568	!-- Synthetic turbulence generator requires the parallel random generator
569	IF ( random_generator /= 'random-parallel' ) THEN
570	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
571	'random-parallel.'
572	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
573	ENDIF
574
575	ENDIF
576
577	END SUBROUTINE stg_check_parameters
578
579
580	!--------------------------------------------------------------------------------------------------!
581	! Description:
582	! ------------
583	!> Header output for synthetic turbulence generator
584	!--------------------------------------------------------------------------------------------------!
585	SUBROUTINE stg_header ( io )
586
587	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
588
589	!
590	!-- Write synthetic turbulence generator Header
591	WRITE( io, 1 )
592	IF ( use_syn_turb_gen ) THEN
593	WRITE( io, 2 )
594	ELSE
595	WRITE( io, 3 )
596	ENDIF
597
598	IF ( parametrize_inflow_turbulence ) THEN
599	WRITE( io, 4 ) dt_stg_adjust
600	ELSE
601	WRITE( io, 5 )
602	ENDIF
603
604	1 FORMAT (//' Synthetic turbulence generator information:'/ &
605	' ------------------------------------------'/)
606	2 FORMAT (' synthetic turbulence generator is switched on')
607	3 FORMAT (' synthetic turbulence generator is switched off')
608	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
609	5 FORMAT (' imposed turbulence is read from file' )
610
611	END SUBROUTINE stg_header
612
613
614	!--------------------------------------------------------------------------------------------------!
615	! Description:
616	! ------------
617	!> Initialization of the synthetic turbulence generator
618	!--------------------------------------------------------------------------------------------------!
619	SUBROUTINE stg_init
620
621	#if defined( __parallel )
622	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
623	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
624	#endif
625
626	INTEGER(iwp) :: i !> grid index in x-direction
627	INTEGER(iwp) :: j !> loop index
628	INTEGER(iwp) :: k !< index
629	#if defined( __parallel )
630	INTEGER(iwp) :: newtype !< dummy MPI type
631	INTEGER(iwp) :: realsize !< size of REAL variables
632	#endif
633
634	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
635	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
636
637
638	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
639
640	!
641	!-- Dummy variables used for reading profiles
642	REAL(wp) :: d1 !< u profile
643	REAL(wp) :: d2 !< v profile
644	REAL(wp) :: d3 !< w profile
645	REAL(wp) :: d5 !< e profile
646	REAL(wp) :: luy !< length scale for u in y direction
647	REAL(wp) :: luz !< length scale for u in z direction
648	REAL(wp) :: lvy !< length scale for v in y direction
649	REAL(wp) :: lvz !< length scale for v in z direction
650	REAL(wp) :: lwy !< length scale for w in y direction
651	REAL(wp) :: lwz !< length scale for w in z direction
652	#if defined( __parallel )
653	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
654	#endif
655	REAL(wp) :: zz !< height
656
657
658	#if defined( __parallel )
659	CALL MPI_BARRIER( comm2d, ierr )
660	#endif
661	!
662	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
663	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
664	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
665	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
666	!-- communication).
667	IF ( .NOT. compute_velocity_seeds_local ) THEN
668	#if defined( __parallel )
669	!
670	!-- Determine processor decomposition of z-axis along x- and y-direction
671	nnz = nz / pdims(1)
672	nzb_x_stg = 1 + myidx * INT( nnz )
673	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
674
675	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
676	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
677
678	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
679	.AND. .NOT. rans_mode ) ) THEN
680	nnz = nz / pdims(2)
681	nzb_y_stg = 1 + myidy * INT( nnz )
682	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
683
684	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
685	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
686	ENDIF
687
688	!
689	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
690	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
691	extent = 1 * realsize
692	!
693	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
694	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
695	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
696	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
697	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
698	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
699	CALL MPI_TYPE_FREE( newtype, ierr )
700
701	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
702	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
703	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
704	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
705	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
706	CALL MPI_TYPE_FREE( newtype, ierr )
707
708	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
709	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
710
711	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
712	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
713
714	DO j = 1, pdims(1)
715	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
716	ENDDO
717	!
718	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
719	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
720	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
721	.AND. .NOT. rans_mode ) ) THEN
722	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
723	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
724	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
725	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
726	CALL MPI_TYPE_FREE( newtype, ierr )
727
728	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
729	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
730	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
731	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
732	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
733	CALL MPI_TYPE_FREE( newtype, ierr )
734
735	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
736	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
737
738	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
739	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
740
741	DO j = 1, pdims(2)
742	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
743	ENDDO
744
745	ENDIF
746	#endif
747	ENDIF
748	!
749	!-- Allocate required arrays.
750	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
751	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
752	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
753	!-- and initialized appropriately.
754	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
755	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
756	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
757	mean_inflow_profiles = 0.0_wp
758	mean_inflow_profiles(:,1) = u_init
759	mean_inflow_profiles(:,2) = v_init
760	!
761	!-- Even though potential temperature and humidity are not perturbed, they need to be
762	!-- initialized appropriately.
763	IF ( .NOT. neutral ) &
764	mean_inflow_profiles(:,4) = pt_init
765	IF ( humidity ) &
766	mean_inflow_profiles(:,6) = q_init
767	ENDIF
768	ENDIF
769	!
770	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
771	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
772	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
773	u_init = mean_inflow_profiles(:,1)
774	v_init = mean_inflow_profiles(:,2)
775	e_init = MAXVAL( mean_inflow_profiles(:,5) )
776	ENDIF
777
778	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
779	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
780	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
781	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
782	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
783	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
784	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
785	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
786
787	r11 = 0.0_wp
788	r21 = 0.0_wp
789	r22 = 0.0_wp
790	r31 = 0.0_wp
791	r32 = 0.0_wp
792	r33 = 0.0_wp
793	tu = 0.0_wp
794	tv = 0.0_wp
795	tw = 0.0_wp
796
797	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
798	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
799	dist_xz = 0.0_wp
800	dist_yz = 0.0_wp
801	!
802	!-- Read inflow profile
803	!-- Height levels of profiles in input profile is as follows:
804	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
805	!-- WARNING: zz is not used at the moment
806	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
807
808	IF ( file_stg_exist ) THEN
809
810	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
811	!
812	!-- Skip header
813	READ( 90, * )
814
815	DO k = nzb+1, nzt+1
816	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
817	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
818
819	!
820	!-- Convert length scales from meter to number of grid points.
821	nuy(k) = INT( luy * ddy )
822	nuz(k) = INT( luz * ddzw(k) )
823	nvy(k) = INT( lvy * ddy )
824	nvz(k) = INT( lvz * ddzw(k) )
825	nwy(k) = INT( lwy * ddy )
826	nwz(k) = INT( lwz * ddzw(k) )
827	!
828	!-- Workaround, assume isotropic turbulence
829	nwx(k) = nwy(k)
830	nvx(k) = nvy(k)
831	nux(k) = nuy(k)
832	!
833	!-- Save Mean inflow profiles
834	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
835	mean_inflow_profiles(k,1) = d1
836	mean_inflow_profiles(k,2) = d2
837	! mean_inflow_profiles(k,4) = d4
838	mean_inflow_profiles(k,5) = d5
839	ENDIF
840	ENDDO
841	!
842	!-- Set lenght scales at surface grid point
843	nuy(nzb) = nuy(nzb+1)
844	nuz(nzb) = nuz(nzb+1)
845	nvy(nzb) = nvy(nzb+1)
846	nvz(nzb) = nvz(nzb+1)
847	nwy(nzb) = nwy(nzb+1)
848	nwz(nzb) = nwz(nzb+1)
849
850	CLOSE( 90 )
851	!
852	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
853	CALL calc_coeff_matrix
854	!
855	!-- No information about turbulence and its length scales are available. Instead, parametrize
856	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
857	!-- parametrized, which is done later when energy-balance models are already initialized. This is
858	!-- because the STG needs information about surface properties such as roughness to build
859	!-- 'realistic' turbulence profiles.
860	ELSE
861	!
862	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
863	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
864	!
865	!-- Set flag indicating that turbulence is parametrized
866	parametrize_inflow_turbulence = .TRUE.
867	!
868	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
869	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
870	!-- nevertheless, the boundary-layer depth needs to be determined first.
871	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
872	CALL nesting_offl_calc_zi
873	!
874	!-- Determine boundary-layer depth, which is used to initialize lenght scales
875	CALL calc_scaling_variables
876	!
877	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
878	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
879	!-- friction velocity and velocity scale.
880	CALL parametrize_turbulence
881	!
882	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
883	CALL calc_coeff_matrix
884
885	ENDIF
886	!
887	!-- Initial filter functions
888	CALL stg_setup_filter_function
889
890	!
891	!-- Allocate velocity seeds for turbulence at xz-layer
892	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
893	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
894	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
895
896	!
897	!-- Allocate velocity seeds for turbulence at yz-layer
898	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
899	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
900	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
901
902	fu_xz = 0.0_wp
903	fuo_xz = 0.0_wp
904	fv_xz = 0.0_wp
905	fvo_xz = 0.0_wp
906	fw_xz = 0.0_wp
907	fwo_xz = 0.0_wp
908
909	fu_yz = 0.0_wp
910	fuo_yz = 0.0_wp
911	fv_yz = 0.0_wp
912	fvo_yz = 0.0_wp
913	fw_yz = 0.0_wp
914	fwo_yz = 0.0_wp
915
916	#if defined( __parallel )
917	CALL MPI_BARRIER( comm2d, ierr )
918	#endif
919
920	!
921	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
922	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
923	!-- This is mostly for k=nzt+1.
924	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
925	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
926
927	IF ( myidx == id_stg_left ) i = -1
928	IF ( myidx == id_stg_right ) i = nxr+1
929
930	DO j = nys, nyn
931	DO k = nzb, nzt+1
932	IF ( a11(k) > 10E-8_wp ) THEN
933	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
934	ELSE
935	fu_yz(k,j) = 10E-8_wp
936	ENDIF
937
938	IF ( a22(k) > 10E-8_wp ) THEN
939	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
940	ELSE
941	fv_yz(k,j) = 10E-8_wp
942	ENDIF
943
944	IF ( a33(k) > 10E-8_wp ) THEN
945	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
946	ELSE
947	fw_yz(k,j) = 10E-8_wp
948	ENDIF
949	ENDDO
950	ENDDO
951	ENDIF
952
953	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
954
955	IF ( myidy == id_stg_south ) j = -1
956	IF ( myidy == id_stg_north ) j = nyn+1
957
958	DO i = nxl, nxr
959	DO k = nzb, nzt+1
960	!
961	!-- In case the correlation coefficients are very small, the velocity seeds may become
962	!-- very large finally creating numerical instabilities in the synthetic turbulence
963	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
964	IF ( a11(k) > 10E-8_wp ) THEN
965	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
966	ELSE
967	fu_xz(k,i) = 10E-8_wp
968	ENDIF
969
970	IF ( a22(k) > 10E-8_wp ) THEN
971	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
972	ELSE
973	fv_xz(k,i) = 10E-8_wp
974	ENDIF
975
976	IF ( a33(k) > 10E-8_wp ) THEN
977	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
978	ELSE
979	fw_xz(k,i) = 10E-8_wp
980	ENDIF
981
982	ENDDO
983	ENDDO
984	ENDIF
985	ENDIF
986	!
987	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
988	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
989	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
990	!-- different cases must be distinguished.
991	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
992	!
993	!-- Number of grid points where perturbations are imposed on u
994	IF ( myidx == id_stg_left ) i = nxl
995	IF ( myidx == id_stg_right ) i = nxr+1
996
997	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
998	!
999	!-- Number of grid points where perturbations are imposed on v and w
1000	IF ( myidx == id_stg_left ) i = nxl-1
1001	IF ( myidx == id_stg_right ) i = nxr+1
1002
1003	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1004	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1005
1006	#if defined( __parallel )
1007	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
1008	#else
1009	nr_non_topo_yz = nr_non_topo_yz_l
1010	#endif
1011	ENDIF
1012
1013	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1014	!
1015	!-- Number of grid points where perturbations are imposed on v
1016	IF ( myidy == id_stg_south ) j = nys
1017	IF ( myidy == id_stg_north ) j = nyn+1
1018
1019	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1020	!
1021	!-- Number of grid points where perturbations are imposed on u and w
1022	IF ( myidy == id_stg_south ) j = nys-1
1023	IF ( myidy == id_stg_north ) j = nyn+1
1024
1025	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1026	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1027
1028	#if defined( __parallel )
1029	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
1030	#else
1031	nr_non_topo_xz = nr_non_topo_xz_l
1032	#endif
1033	ENDIF
1034	!
1035	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
1036	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
1037	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
1038	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
1039	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
1040	id_rand_yz = 0
1041	seq_rand_yz = 0
1042
1043	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
1044
1045	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1046	.AND. .NOT. rans_mode ) ) THEN
1047	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
1048	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
1049	id_rand_xz = 0
1050	seq_rand_xz = 0
1051
1052	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
1053	ENDIF
1054
1055	END SUBROUTINE stg_init
1056
1057
1058	!--------------------------------------------------------------------------------------------------!
1059	! Description:
1060	! ------------
1061	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
1062	!--------------------------------------------------------------------------------------------------!
1063	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
1064
1065	INTEGER(iwp) :: k !< loop index
1066	INTEGER(iwp) :: mergp !< passed length scale in grid points
1067	INTEGER(iwp) :: n_k !< length scale nXX in height k
1068	INTEGER(iwp) :: nf !< index for length scales
1069
1070	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1071
1072	REAL(wp) :: bdenom !< denominator for filter functions bXX
1073	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1074
1075	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1076
1077
1078	bxx = 0.0_wp
1079
1080	DO k = nzb, nzt+1
1081	bdenom = 0.0_wp
1082	n_k = nxx(k)
1083	IF ( n_k /= 0 ) THEN
1084
1085	!
1086	!-- ( Eq.10 )^2
1087	DO nf = -n_k, n_k
1088	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
1089	ENDDO
1090
1091	!
1092	!-- ( Eq.9 )
1093	bdenom = SQRT( bdenom )
1094	DO nf = -n_k, n_k
1095	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
1096	ENDDO
1097	ENDIF
1098	ENDDO
1099
1100	END SUBROUTINE stg_filter_func
1101
1102
1103	!------------------------------------------------------------------------------!
1104	! Description:
1105	! ------------
1106	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1107	!> (Xie and Castro, 2008)
1108	!------------------------------------------------------------------------------!
1109	SUBROUTINE stg_setup_filter_function
1110
1111	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
1112	INTEGER(iwp) :: k !< loop index along vertical direction
1113	!
1114	!-- Define the size of the filter functions and allocate them.
1115	mergp_x = 0
1116	mergp_y = 0
1117	mergp_z = 0
1118
1119	DO k = nzb, nzt+1
1120	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
1121	IF ( j > mergp_x ) mergp_x = j
1122	ENDDO
1123	DO k = nzb, nzt+1
1124	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
1125	IF ( j > mergp_y ) mergp_y = j
1126	ENDDO
1127	DO k = nzb, nzt+1
1128	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
1129	IF ( j > mergp_z ) mergp_z = j
1130	ENDDO
1131
1132	mergp_xy = MAX( mergp_x, mergp_y )
1133
1134	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
1135	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
1136	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
1137	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
1138	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
1139	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
1140	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
1141	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
1142	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
1143
1144	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
1145	buy(-mergp_y:mergp_y,nzb:nzt+1), &
1146	buz(-mergp_z:mergp_z,nzb:nzt+1), &
1147	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
1148	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
1149	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
1150	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
1151	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
1152	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
1153	!
1154	!-- Create filter functions
1155	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
1156	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
1157	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
1158	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
1159	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
1160	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
1161	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
1162	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
1163	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
1164
1165	END SUBROUTINE stg_setup_filter_function
1166
1167	!--------------------------------------------------------------------------------------------------!
1168	! Description:
1169	! ------------
1170	!> Parin for &stg_par for synthetic turbulence generator
1171	!--------------------------------------------------------------------------------------------------!
1172	SUBROUTINE stg_parin
1173
1174	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1175
1176
1177	NAMELIST /stg_par/ dt_stg_adjust, &
1178	dt_stg_call, &
1179	use_syn_turb_gen, &
1180	compute_velocity_seeds_local
1181
1182	line = ' '
1183	!
1184	!-- Try to find stg package
1185	REWIND ( 11 )
1186	line = ' '
1187	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1188	READ ( 11, '(A)', END = 20 ) line
1189	ENDDO
1190	BACKSPACE ( 11 )
1191
1192	!
1193	!-- Read namelist
1194	READ ( 11, stg_par, ERR = 10, END = 20 )
1195
1196	!
1197	!-- Set flag that indicates that the synthetic turbulence generator is switched on
1198	syn_turb_gen = .TRUE.
1199	GOTO 20
1200
1201	10 BACKSPACE( 11 )
1202	READ( 11 , '(A)') line
1203	CALL parin_fail_message( 'stg_par', line )
1204
1205	20 CONTINUE
1206
1207	END SUBROUTINE stg_parin
1208
1209
1210	!--------------------------------------------------------------------------------------------------!
1211	! Description:
1212	! ------------
1213	!> Read module-specific global restart data (Fortran binary format).
1214	!--------------------------------------------------------------------------------------------------!
1215	SUBROUTINE stg_rrd_global_ftn( found )
1216
1217	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1218
1219	found = .TRUE.
1220
1221
1222	SELECT CASE ( restart_string(1:length) )
1223
1224	CASE ( 'time_stg_adjust' )
1225	READ ( 13 ) time_stg_adjust
1226
1227	CASE ( 'time_stg_call' )
1228	READ ( 13 ) time_stg_call
1229
1230	CASE ( 'use_syn_turb_gen' )
1231	READ ( 13 ) use_syn_turb_gen
1232
1233	CASE DEFAULT
1234
1235	found = .FALSE.
1236
1237	END SELECT
1238
1239
1240	END SUBROUTINE stg_rrd_global_ftn
1241
1242
1243	!--------------------------------------------------------------------------------------------------!
1244	! Description:
1245	! ------------
1246	!> Read module-specific global restart data (MPI-IO).
1247	!--------------------------------------------------------------------------------------------------!
1248	SUBROUTINE stg_rrd_global_mpi
1249
1250	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1251	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
1252	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1253
1254	END SUBROUTINE stg_rrd_global_mpi
1255
1256
1257	!--------------------------------------------------------------------------------------------------!
1258	! Description:
1259	! ------------
1260	!> This routine writes the respective restart data.
1261	!--------------------------------------------------------------------------------------------------!
1262	SUBROUTINE stg_wrd_global
1263
1264	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
1265
1266	CALL wrd_write_string( 'time_stg_adjust' )
1267	WRITE ( 14 ) time_stg_adjust
1268
1269	CALL wrd_write_string( 'time_stg_call' )
1270	WRITE ( 14 ) time_stg_call
1271
1272	CALL wrd_write_string( 'use_syn_turb_gen' )
1273	WRITE ( 14 ) use_syn_turb_gen
1274
1275	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
1276
1277	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
1278	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
1279	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
1280
1281	ENDIF
1282
1283	END SUBROUTINE stg_wrd_global
1284
1285
1286	!--------------------------------------------------------------------------------------------------!
1287	! Description:
1288	! ------------
1289	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
1290	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
1291	!> (2013), and using a Lund rotation (Lund, 1998).
1292	!--------------------------------------------------------------------------------------------------!
1293	SUBROUTINE stg_main
1294
1295	USE exchange_horiz_mod, &
1296	ONLY: exchange_horiz
1297
1298	INTEGER(iwp) :: i !< grid index in x-direction
1299	INTEGER(iwp) :: j !< loop index in y-direction
1300	INTEGER(iwp) :: k !< loop index in z-direction
1301
1302	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1303
1304	REAL(wp) :: dt_stg !< time interval the STG is called
1305
1306	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1307
1308	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1309	!
1310	!-- Calculate time step which is needed for filter functions
1311	dt_stg = MAX( dt_3d, dt_stg_call )
1312	!
1313	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
1314	!-- created or if old disturbances can be imposed again.
1315	IF ( time_stg_call >= dt_stg_call .AND. &
1316	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1317	stg_call = .TRUE.
1318	ELSE
1319	stg_call = .FALSE.
1320	ENDIF
1321	!
1322	!-- Initial value of fu, fv, fw
1323	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1324	!
1325	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
1326	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
1327	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
1328	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
1329	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
1330	!-- have the same initial seeds.
1331	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
1332	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1333	.AND. .NOT. rans_mode ) ) ) THEN
1334	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1335	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1336	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1337	ELSE
1338	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
1339	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
1340	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
1341	!
1342	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
1343	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
1344	!-- comment above.
1345	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
1346	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
1347	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
1348	ENDIF
1349	velocity_seed_initialized = .TRUE.
1350	ENDIF
1351	!
1352	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
1353	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
1354	!-- seeds are required also at the right, south and north boundaries.
1355	IF ( stg_call ) THEN
1356	IF ( .NOT. ( nesting_offline .OR. &
1357	( child_domain .AND. rans_mode_parent &
1358	.AND. .NOT. rans_mode ) ) ) THEN
1359	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1360	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1361	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1362
1363	ELSE
1364	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
1365	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
1366	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
1367
1368	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
1369	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
1370	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
1371	ENDIF
1372	ENDIF
1373
1374	!
1375	!-- Turbulence generation at left and/or right boundary
1376	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1377	!
1378	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1379	!-- exceeded. Else the old set of perturbations is imposed
1380	IF ( stg_call ) THEN
1381
1382	DO j = nys, nyn
1383	DO k = nzb, nzt + 1
1384	!
1385	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1386	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1387	fu_yz(k,j) = fuo_yz(k,j)
1388	ELSE
1389	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1390	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1391	ENDIF
1392
1393	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1394	fv_yz(k,j) = fvo_yz(k,j)
1395	ELSE
1396	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1397	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1398	ENDIF
1399
1400	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1401	fw_yz(k,j) = fwo_yz(k,j)
1402	ELSE
1403	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1404	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1405	ENDIF
1406	ENDDO
1407	ENDDO
1408
1409	dist_yz(nzb,:,1) = 0.0_wp
1410	dist_yz(nzb,:,2) = 0.0_wp
1411	dist_yz(nzb,:,3) = 0.0_wp
1412
1413	IF ( myidx == id_stg_left ) i = nxl
1414	IF ( myidx == id_stg_right ) i = nxr+1
1415	DO j = nys, nyn
1416	DO k = nzb+1, nzt + 1
1417	!
1418	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1419	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
1420	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1421
1422	ENDDO
1423	ENDDO
1424
1425	IF ( myidx == id_stg_left ) i = nxl-1
1426	IF ( myidx == id_stg_right ) i = nxr+1
1427	DO j = nys, nyn
1428	DO k = nzb+1, nzt + 1
1429	!
1430	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1431	!-- Additional factors are added to improve the variance of v and w experimental test
1432	!-- of 1.2
1433	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
1434	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1435	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
1436	a33(k) * fw_yz(k,j) ) * &
1437	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1438
1439	ENDDO
1440	ENDDO
1441	ENDIF
1442	!
1443	!-- Mass flux correction following Kim et al. (2013)
1444	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
1445	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
1446	!-- only after the last RK3-substep, else the boundary values won't be accessed.
1447	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1448	mc_factor_l = 0.0_wp
1449	mc_factor = 0.0_wp
1450	!
1451	!-- Sum up the original volume flows (with and without perturbations).
1452	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
1453	IF ( myidx == id_stg_left ) i = nxl
1454	IF ( myidx == id_stg_right ) i = nxr+1
1455
1456	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
1457	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1458
1459	IF ( myidx == id_stg_left ) i = nxl-1
1460	IF ( myidx == id_stg_right ) i = nxr+1
1461
1462	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
1463	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1464	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
1465	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1466
1467	#if defined( __parallel )
1468	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1469	#else
1470	mc_factor = mc_factor_l
1471	#endif
1472	!
1473	!-- Calculate correction factor and force zero mean perturbations.
1474	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1475
1476	IF ( myidx == id_stg_left ) i = nxl
1477	IF ( myidx == id_stg_right ) i = nxr+1
1478
1479	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
1480	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1481
1482
1483	IF ( myidx == id_stg_left ) i = nxl-1
1484	IF ( myidx == id_stg_right ) i = nxr+1
1485
1486	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
1487	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1488
1489	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
1490	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1491	!
1492	!-- Add disturbances
1493	IF ( myidx == id_stg_left ) THEN
1494	!
1495	!-- For the left boundary distinguish between mesoscale offline / self nesting and
1496	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
1497	!-- the mean inflow profiles.
1498	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1499	!
1500	!-- Add disturbance at the inflow
1501	DO j = nys, nyn
1502	DO k = nzb, nzt+1
1503	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
1504	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1505	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
1506	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1507	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
1508	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1509	ENDDO
1510	ENDDO
1511	ELSE
1512
1513	DO j = nys, nyn
1514	DO k = nzb+1, nzt
1515	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
1516	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
1517	u(k,j,-1) = u(k,j,0)
1518	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
1519	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1520	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
1521	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1522	ENDDO
1523	ENDDO
1524	ENDIF
1525	ENDIF
1526	IF ( myidx == id_stg_right ) THEN
1527	DO j = nys, nyn
1528	DO k = nzb+1, nzt
1529	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
1530	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1531	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
1532	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1533	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
1534	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1535	ENDDO
1536	ENDDO
1537	ENDIF
1538	ENDIF
1539	ENDIF
1540	!
1541	!-- Turbulence generation at north and south boundary
1542	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1543	!
1544	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
1545	!-- exceeded. Else the old set of perturbations is imposed
1546	IF ( stg_call ) THEN
1547	DO i = nxl, nxr
1548	DO k = nzb, nzt + 1
1549	!
1550	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1551	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
1552	fu_xz(k,i) = fuo_xz(k,i)
1553	ELSE
1554	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1555	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1556	ENDIF
1557
1558	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
1559	fv_xz(k,i) = fvo_xz(k,i)
1560	ELSE
1561	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1562	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1563	ENDIF
1564
1565	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
1566	fw_xz(k,i) = fwo_xz(k,i)
1567	ELSE
1568	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1569	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1570	ENDIF
1571	ENDDO
1572	ENDDO
1573
1574
1575	dist_xz(nzb,:,1) = 0.0_wp
1576	dist_xz(nzb,:,2) = 0.0_wp
1577	dist_xz(nzb,:,3) = 0.0_wp
1578
1579	IF ( myidy == id_stg_south ) j = nys
1580	IF ( myidy == id_stg_north ) j = nyn+1
1581	DO i = nxl, nxr
1582	DO k = nzb+1, nzt + 1
1583	!
1584	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1585	!-- Additional factors are added to improve the variance of v and w
1586	!experimental test of 1.2
1587	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
1588	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
1589	ENDDO
1590	ENDDO
1591
1592	IF ( myidy == id_stg_south ) j = nys-1
1593	IF ( myidy == id_stg_north ) j = nyn+1
1594	DO i = nxl, nxr
1595	DO k = nzb+1, nzt + 1
1596	!
1597	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1598	!-- Additional factors are added to improve the variance of v and w
1599	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
1600	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
1601
1602	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
1603	a33(k) * fw_xz(k,i) ) * &
1604	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
1605	ENDDO
1606	ENDDO
1607	ENDIF
1608
1609	!
1610	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
1611	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
1612	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
1613	!-- else the boundary values won't be accessed.
1614	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1615	mc_factor_l = 0.0_wp
1616	mc_factor = 0.0_wp
1617
1618	IF ( myidy == id_stg_south ) j = nys
1619	IF ( myidy == id_stg_north ) j = nyn+1
1620
1621	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
1622	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1623
1624	IF ( myidy == id_stg_south ) j = nys-1
1625	IF ( myidy == id_stg_north ) j = nyn+1
1626
1627	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
1628	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1629	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
1630	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1631
1632	#if defined( __parallel )
1633	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1634	#else
1635	mc_factor = mc_factor_l
1636	#endif
1637
1638	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1639
1640	IF ( myidy == id_stg_south ) j = nys
1641	IF ( myidy == id_stg_north ) j = nyn+1
1642
1643	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
1644	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1645
1646
1647	IF ( myidy == id_stg_south ) j = nys-1
1648	IF ( myidy == id_stg_north ) j = nyn+1
1649
1650	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
1651	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1652
1653	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
1654	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1655	!
1656	!-- Add disturbances
1657	IF ( myidy == id_stg_south ) THEN
1658	DO i = nxl, nxr
1659	DO k = nzb+1, nzt
1660	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1661	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1662	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1663	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
1664	v(k,-1,i) = v(k,0,i)
1665	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1666	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1667	ENDDO
1668	ENDDO
1669	ENDIF
1670	IF ( myidy == id_stg_north ) THEN
1671
1672	DO i = nxl, nxr
1673	DO k = nzb+1, nzt
1674	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
1675	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1676	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
1677	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1678	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
1679	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1680	ENDDO
1681	ENDDO
1682	ENDIF
1683	ENDIF
1684	ENDIF
1685	!
1686	!-- Exchange ghost points.
1687	CALL exchange_horiz( u, nbgp )
1688	CALL exchange_horiz( v, nbgp )
1689	CALL exchange_horiz( w, nbgp )
1690	!
1691	!-- Finally, set time counter for calling STG to zero
1692	IF ( stg_call ) time_stg_call = 0.0_wp
1693	!
1694	!-- Set adjustment step to False to indicate that time correlation can be
1695	!-- switched-on again.
1696	adjustment_step = .FALSE.
1697
1698	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1699
1700	END SUBROUTINE stg_main
1701
1702	!--------------------------------------------------------------------------------------------------!
1703	! Description:
1704	! ------------
1705	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1706	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
1707	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
1708	!> array.
1709	!--------------------------------------------------------------------------------------------------!
1710	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1711
1712	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1713	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1714	INTEGER(iwp) :: j !< loop index in y-direction
1715	INTEGER(iwp) :: jj !< loop index in y-direction
1716	INTEGER(iwp) :: k !< loop index in z-direction
1717	INTEGER(iwp) :: kk !< loop index in z-direction
1718	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1719
1720	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1721	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1722
1723	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1724	REAL(wp) :: rand_av !< average of random number
1725	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1726
1727	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
1728	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1729
1730	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1731	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1732
1733	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1734	!
1735	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1736	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1737	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1738	!-- and normalization of random numbers is done locally, while the result is later distributed to
1739	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
1740	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
1741	!-- correlation matrix.
1742	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
1743	rand_it = 0.0_wp
1744
1745	rand_av = 0.0_wp
1746	rand_sigma_inv = 0.0_wp
1747	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1748	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
1749	!
1750	!-- Compute and normalize random numbers.
1751	DO j = nys - mergp_y, nyn + mergp_y
1752	!
1753	!-- Put the random seeds at grid point j
1754	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1755	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1756	CALL random_number_parallel( random_dummy )
1757	rand_it(k,j) = random_dummy
1758	ENDDO
1759	!
1760	!-- Get the new random seeds from last call at grid point j
1761	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1762	ENDDO
1763	!
1764	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
1765	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
1766	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
1767	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1768	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1769	rand_av = rand_av + rand_it(k,j)
1770	ENDDO
1771	ENDDO
1772
1773	#if defined( __parallel )
1774	!
1775	!-- Sum-up the local averages of the random numbers
1776	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1777	#endif
1778	rand_av = rand_av * nyz_inv
1779	!
1780	!-- Obtain zero mean
1781	rand_it= rand_it - rand_av
1782	!
1783	!-- Now, compute the variance
1784	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
1785	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1786	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1787	ENDDO
1788	ENDDO
1789
1790	#if defined( __parallel )
1791	!
1792	!-- Sum-up the local quadratic averages of the random numbers
1793	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
1794	#endif
1795	!
1796	!-- Compute standard deviation
1797	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1798	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1799	ELSE
1800	rand_sigma_inv = 1.0_wp
1801	ENDIF
1802	!
1803	!-- Normalize with standard deviation to obtain unit variance
1804	rand_it = rand_it * rand_sigma_inv
1805
1806	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1807	!
1808	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1809	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1810	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
1811	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1812	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
1813	!-- communication. In the second option, which performs better when the turbulent length scales
1814	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
1815	!-- communication is necessary.
1816	IF ( compute_velocity_seeds_local ) THEN
1817
1818	f_n = 0.0_wp
1819	DO j = nys, nyn
1820	DO k = nzb, nzt+1
1821	DO jj = -n_y(k), n_y(k)
1822	DO kk = -n_z(k), n_z(k)
1823	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1824	ENDDO
1825	ENDDO
1826	ENDDO
1827	ENDDO
1828
1829	ELSE
1830
1831	f_n_l = 0.0_wp
1832	DO j = nys, nyn
1833	DO k = nzb_x_stg, nzt_x_stg+1
1834	DO jj = -n_y(k), n_y(k)
1835	DO kk = -n_z(k), n_z(k)
1836	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1837	ENDDO
1838	ENDDO
1839	ENDDO
1840	ENDDO
1841	!
1842	!-- Gather velocity seeds of full subdomain
1843	send_count = nzt_x_stg - nzb_x_stg + 1
1844	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1845
1846	#if defined( __parallel )
1847	!
1848	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1849	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1850	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
1851	!
1852	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
1853	!-- nesting for example).
1854	IF ( PRESENT( id_right ) ) THEN
1855	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
1856	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
1857	ENDIF
1858	#else
1859	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1860	!
1861	!-- Next line required to avoid compile errors because of unused dummy arguments
1862	IF ( id_left == 0 ) id_right = 0
1863	#endif
1864
1865	ENDIF
1866
1867	DEALLOCATE( rand_it )
1868
1869	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1870
1871	END SUBROUTINE stg_generate_seed_yz
1872
1873
1874	!--------------------------------------------------------------------------------------------------!
1875	! Description:
1876	! ------------
1877	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
1878	!> f_n.
1879	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
1880	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
1881	!> full array.
1882	!--------------------------------------------------------------------------------------------------!
1883	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1884
1885	INTEGER(iwp) :: i !< loop index in x-direction
1886	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1887	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1888	INTEGER(iwp) :: ii !< loop index in x-direction
1889	INTEGER(iwp) :: k !< loop index in z-direction
1890	INTEGER(iwp) :: kk !< loop index in z-direction
1891	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1892
1893	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1894	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1895
1896	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1897	REAL(wp) :: rand_av !< average of random number
1898	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1899
1900	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
1901	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
1902
1903	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1904	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1905
1906	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1907
1908	!
1909	!-- Generate random numbers using the parallel random generator. The set of random numbers are
1910	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
1911	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
1912	!-- and normalization of random numbers is done locally, while the result is later distributed to
1913	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
1914	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
1915	!-- correlation matrix.
1916	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
1917	rand_it = 0.0_wp
1918
1919	rand_av = 0.0_wp
1920	rand_sigma_inv = 0.0_wp
1921	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
1922	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
1923	!
1924	!-- Compute and normalize random numbers.
1925	DO i = nxl - mergp_x, nxr + mergp_x
1926	!
1927	!-- Put the random seeds at grid point ii
1928	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1929	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1930	CALL random_number_parallel( random_dummy )
1931	rand_it(k,i) = random_dummy
1932	ENDDO
1933	!
1934	!-- Get the new random seeds from last call at grid point ii
1935	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1936	ENDDO
1937	!
1938	!-- For normalization to zero mean, sum-up the global random numers.
1939	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
1940	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
1941	!-- also occur on the inner subdomains.
1942	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1943	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1944	rand_av = rand_av + rand_it(k,i)
1945	ENDDO
1946	ENDDO
1947
1948	#if defined( __parallel )
1949	!
1950	!-- Sum-up the local averages of the random numbers
1951	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1952	#endif
1953	rand_av = rand_av * nxz_inv
1954	!
1955	!-- Obtain zero mean
1956	rand_it= rand_it - rand_av
1957	!
1958	!-- Now, compute the variance
1959	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
1960	DO k = nzb - mergp_z, nzt + 1 + mergp_z
1961	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1962	ENDDO
1963	ENDDO
1964
1965	#if defined( __parallel )
1966	!
1967	!-- Sum-up the local quadratic averages of the random numbers
1968	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
1969	#endif
1970	!
1971	!-- Compute standard deviation
1972	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1973	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1974	ELSE
1975	rand_sigma_inv = 1.0_wp
1976	ENDIF
1977	!
1978	!-- Normalize with standard deviation to obtain unit variance
1979	rand_it = rand_it * rand_sigma_inv
1980
1981	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1982	!
1983	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
1984	!-- first one, the computation of the seeds is distributed to all processes along the communicator
1985	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
1986	!-- length scales the computational effort can become quite huge (it scales with the turbulent
1987	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
1988	!-- In the second option, which performs better when the turbulent length scales are parametrized
1989	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
1990	IF ( compute_velocity_seeds_local ) THEN
1991
1992	f_n = 0.0_wp
1993	DO i = nxl, nxr
1994	DO k = nzb, nzt+1
1995	DO ii = -n_x(k), n_x(k)
1996	DO kk = -n_z(k), n_z(k)
1997	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1998	ENDDO
1999	ENDDO
2000	ENDDO
2001	ENDDO
2002
2003	ELSE
2004
2005	f_n_l = 0.0_wp
2006	DO i = nxl, nxr
2007	DO k = nzb_y_stg, nzt_y_stg+1
2008	DO ii = -n_x(k), n_x(k)
2009	DO kk = -n_z(k), n_z(k)
2010	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2011	ENDDO
2012	ENDDO
2013	ENDDO
2014	ENDDO
2015	!
2016	!-- Gather velocity seeds of full subdomain
2017	send_count = nzt_y_stg - nzb_y_stg + 1
2018	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2019
2020	#if defined( __parallel )
2021	!
2022	!-- Gather the processed velocity seed on south boundary mpi ranks.
2023	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2024	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
2025	!
2026	!-- Gather the processed velocity seed on north boundary mpi ranks.
2027	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
2028	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
2029	#else
2030	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2031	!
2032	!-- Next line required to avoid compile errors because of unused dummy arguments
2033	IF ( id_north == 0 ) id_south = 0
2034	#endif
2035
2036	ENDIF
2037
2038	DEALLOCATE( rand_it )
2039
2040	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2041
2042	END SUBROUTINE stg_generate_seed_xz
2043
2044	!--------------------------------------------------------------------------------------------------!
2045	! Description:
2046	! ------------
2047	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
2048	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
2049	!> which is applied in state-of-the-art dispserion modelling.
2050	!--------------------------------------------------------------------------------------------------!
2051	SUBROUTINE parametrize_turbulence
2052
2053	INTEGER(iwp) :: k !< loop index in z-direction
2054
2055	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
2056	REAL(wp) :: d_zi !< inverse boundary-layer depth
2057	REAL(wp) :: length_scale_lon !< length scale in flow direction
2058	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
2059	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
2060	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
2061	REAL(wp) :: length_scale_vert !< length scale in vertical direction
2062	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
2063	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
2064	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
2065	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
2066	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
2067	REAL(wp) :: r31_zi !< r31 at boundary-layer top
2068	REAL(wp) :: r32_zi !< r32 at boundary-layer top
2069	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
2070	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
2071	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
2072	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
2073	REAL(wp) :: zzi !< ratio of z/zi
2074
2075	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
2076	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
2077	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
2078
2079	!
2080	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
2081	!-- criterion according to Heinze et al. (2017).
2082	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
2083	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
2084	k_zi = MIN( k_zi, nzt )
2085	!
2086	!-- Calculate angle between flow direction and x-axis.
2087	DO k = nzb+1, nzt + 1
2088	IF ( u_init(k) /= 0.0_wp ) THEN
2089	phi(k) = ATAN( v_init(k) / u_init(k) )
2090	ELSE
2091	phi(k) = 0.5 * pi
2092	ENDIF
2093	!
2094	!-- Pre-calculate sine and cosine.
2095	cos_phi(k) = COS( phi(k) )
2096	sin_phi(k) = SIN( phi(k) )
2097	ENDDO
2098	!
2099	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
2100	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
2101	!-- coincide with the grid axis. Hence, components are rotated after computation.
2102	d_zi = 1.0_wp / zi_ribulk
2103	DO k = nzb+1, k_zi
2104
2105	corr_term_uh = MERGE( 0.35_wp * ABS( &
2106	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2107	)**( 2.0_wp / 3.0_wp ), &
2108	0.0_wp, &
2109	scale_l < 0.0_wp )
2110	!
2111	!-- Determine normalized height coordinate
2112	zzi = zu(k) * d_zi
2113	!
2114	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
2115	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
2116	!-- variances cannot become negative, take the absolute values.
2117	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
2118	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
2119
2120	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
2121	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
2122	!
2123	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as
2124	!-- for u'w'.
2125	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
2126	!
2127	!-- w'w'
2128	r33(k) = scale_wm*2 ( &
2129	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2130	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2131	)
2132	!
2133	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
2134	!-- these are projected along the x- and y-direction. Note, it is assumed that
2135	!-- the flux within the boundary points opposite to the vertical gradient.
2136	rlon2 = scale_us*2 ( zzi - 1.0_wp )
2137	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
2138
2139	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
2140	- ( u_init(k+1) - u_init(k-1) ) )
2141	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
2142	- ( v_init(k+1) - v_init(k-1) ) )
2143	!
2144	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
2145	!-- limited to the adjustment time scales.
2146	tu(k) = MIN( dt_stg_adjust, &
2147	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
2148
2149	tv(k) = tu(k)
2150	tw(k) = tu(k)
2151
2152	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
2153	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
2154	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
2155	!
2156	!-- Assume isotropic turbulence length scales
2157	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2158	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2159	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2160	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2161	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2162	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2163	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2164	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2165	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2166
2167	ENDDO
2168	!
2169	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
2170	!-- reduced to zero by a blending function.
2171	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
2172	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
2173	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
2174
2175	time_scale_zi = tu(k_zi)
2176	r11_zi = r11(k_zi)
2177	r22_zi = r22(k_zi)
2178	r33_zi = r33(k_zi)
2179	r31_zi = r31(k_zi)
2180	r32_zi = r32(k_zi)
2181
2182	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
2183
2184	DO k = k_zi+1, nzt+1
2185	!
2186	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2187	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2188	!
2189	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
2190	!-- the mergpe-function can crash if scale_l is zero.
2191	r11(k) = r11_zi * blend
2192	r22(k) = r22_zi * blend
2193	r33(k) = r33_zi * blend
2194	r31(k) = r31_zi * blend
2195	r32(k) = r32_zi * blend
2196	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
2197
2198	!
2199	!-- Compute turbulent time scales according to Brost et al. (1982).
2200	!-- Note, time scales are limited to the adjustment time scales.
2201	tu(k) = time_scale_zi * blend
2202	tv(k) = time_scale_zi * blend
2203	tw(k) = time_scale_zi * blend
2204
2205	length_scale_lon = length_scale_lon_zi * blend
2206	length_scale_lat = length_scale_lat_zi * blend
2207	length_scale_vert = length_scale_vert_zi * blend
2208	!
2209	!-- Assume isotropic turbulence length scales
2210	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2211	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2212	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2213	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2214	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
2215	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
2216	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2217	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2218	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
2219	ENDDO
2220	!
2221	!-- Set bottom boundary condition for reynolds stresses
2222	r11(nzb) = r11(nzb+1)
2223	r22(nzb) = r22(nzb+1)
2224	r33(nzb) = r33(nzb+1)
2225
2226	r21(nzb) = r11(nzb+1)
2227	r31(nzb) = r31(nzb+1)
2228	r32(nzb) = r32(nzb+1)
2229
2230	!
2231	!-- Set bottom boundary condition for the length and time scales
2232	nux(nzb) = nux(nzb+1)
2233	nuy(nzb) = nuy(nzb+1)
2234	nuz(nzb) = nuz(nzb+1)
2235	nvx(nzb) = nvx(nzb+1)
2236	nvy(nzb) = nvy(nzb+1)
2237	nvz(nzb) = nvz(nzb+1)
2238	nwx(nzb) = nwx(nzb+1)
2239	nwy(nzb) = nwy(nzb+1)
2240	nwz(nzb) = nwz(nzb+1)
2241
2242	tu(nzb) = tu(nzb+1)
2243	tv(nzb) = tv(nzb+1)
2244	tw(nzb) = tw(nzb+1)
2245
2246	adjustment_step = .TRUE.
2247
2248	END SUBROUTINE parametrize_turbulence
2249
2250	!--------------------------------------------------------------------------------------------------!
2251	! Description:
2252	! ------------
2253	!> Calculate the coefficient matrix from the Lund rotation.
2254	!--------------------------------------------------------------------------------------------------!
2255	SUBROUTINE calc_coeff_matrix
2256
2257	INTEGER(iwp) :: k !< loop index in z-direction
2258
2259	!
2260	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2261	DO k = nzb+1, nzt+1
2262	IF ( r11(k) > 10E-6_wp ) THEN
2263	a11(k) = SQRT( r11(k) )
2264	a21(k) = r21(k) / a11(k)
2265	a31(k) = r31(k) / a11(k)
2266	ELSE
2267	a11(k) = 10E-8_wp
2268	a21(k) = 10E-8_wp
2269	a31(k) = 10E-8_wp
2270	ENDIF
2271	ENDDO
2272	DO k = nzb+1, nzt+1
2273	a22(k) = r22(k) - a21(k)**2
2274	IF ( a22(k) > 10E-6_wp ) THEN
2275	a22(k) = SQRT( a22(k) )
2276	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
2277	ELSE
2278	a22(k) = 10E-8_wp
2279	a32(k) = 10E-8_wp
2280	ENDIF
2281	ENDDO
2282	DO k = nzb+1, nzt+1
2283	a33(k) = r33(k) - a31(k)2 - a32(k)2
2284	IF ( a33(k) > 10E-6_wp ) THEN
2285	a33(k) = SQRT( a33(k) )
2286	ELSE
2287	a33(k) = 10E-8_wp
2288	ENDIF
2289	ENDDO
2290	!
2291	!-- Set bottom boundary condition
2292	a11(nzb) = a11(nzb+1)
2293	a22(nzb) = a22(nzb+1)
2294	a21(nzb) = a21(nzb+1)
2295	a33(nzb) = a33(nzb+1)
2296	a31(nzb) = a31(nzb+1)
2297	a32(nzb) = a32(nzb+1)
2298
2299	END SUBROUTINE calc_coeff_matrix
2300
2301	!--------------------------------------------------------------------------------------------------!
2302	! Description:
2303	! ------------
2304	!> This routine controls the re-adjustment of the turbulence statistics used for generating
2305	!> turbulence at the lateral boundaries.
2306	!--------------------------------------------------------------------------------------------------!
2307	SUBROUTINE stg_adjust
2308
2309	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2310	!
2311	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
2312	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
2313	!-- nevertheless, the boundary-layer depth need to determined first.
2314	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2315	CALL nesting_offl_calc_zi
2316	!
2317	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
2318	CALL calc_scaling_variables
2319	!
2320	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
2321	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
2322	!-- velocity and velocity scale.
2323	CALL parametrize_turbulence
2324	!
2325	!-- Calculate coefficient matrix from Reynolds stress tensor
2326	!-- (Lund rotation)
2327	CALL calc_coeff_matrix
2328	!
2329	!-- Setup filter functions according to updated length scales.
2330	CALL stg_setup_filter_function
2331	!
2332	!-- Reset time counter for controlling next adjustment to zero
2333	time_stg_adjust = 0.0_wp
2334
2335	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2336
2337	END SUBROUTINE stg_adjust
2338
2339
2340	!--------------------------------------------------------------------------------------------------!
2341	! Description:
2342	! ------------
2343	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
2344	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
2345	!> scale, and Obukhov length.
2346	!--------------------------------------------------------------------------------------------------!
2347	SUBROUTINE calc_scaling_variables
2348
2349	INTEGER(iwp) :: i !< loop index in x-direction
2350	INTEGER(iwp) :: j !< loop index in y-direction
2351	INTEGER(iwp) :: k !< loop index in z-direction
2352	INTEGER(iwp) :: m !< surface element index
2353
2354	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2355	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2356	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2357	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2358	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2359	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2360	REAL(wp) :: w_convective !< convective velocity scale
2361
2362	!
2363	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
2364	!-- model domain.
2365	pt_surf_mean_l = 0.0_wp
2366	shf_mean_l = 0.0_wp
2367	scale_l_l = 0.0_wp
2368	friction_vel_l = 0.0_wp
2369	DO m = 1, surf_def_h(0)%ns
2370	i = surf_def_h(0)%i(m)
2371	j = surf_def_h(0)%j(m)
2372	k = surf_def_h(0)%k(m)
2373	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2374	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2375	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2376	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2377	ENDDO
2378	DO m = 1, surf_lsm_h%ns
2379	i = surf_lsm_h%i(m)
2380	j = surf_lsm_h%j(m)
2381	k = surf_lsm_h%k(m)
2382	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2383	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2384	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2385	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2386	ENDDO
2387	DO m = 1, surf_usm_h%ns
2388	i = surf_usm_h%i(m)
2389	j = surf_usm_h%j(m)
2390	k = surf_usm_h%k(m)
2391	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2392	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2393	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2394	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2395	ENDDO
2396
2397	#if defined( __parallel )
2398	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2399	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2400	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2401	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
2402	#else
2403	scale_us = friction_vel_l
2404	shf_mean = shf_mean_l
2405	scale_l = scale_l_l
2406	pt_surf_mean = pt_surf_mean_l
2407	#endif
2408
2409	scale_us = scale_us * d_nxy
2410	shf_mean = shf_mean * d_nxy
2411	scale_l = scale_l * d_nxy
2412	pt_surf_mean = pt_surf_mean * d_nxy
2413	!
2414	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
2415	!-- convective velocity scale to zero.
2416	IF ( shf_mean > 0.0_wp ) THEN
2417	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2418	ELSE
2419	w_convective = 0.0_wp
2420	ENDIF
2421	!
2422	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
2423	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
2424	!-- value of friction velocity for the reynolds-stress parametrization.
2425	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
2426	!
2427	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
2428	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
2429	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2430
2431	END SUBROUTINE calc_scaling_variables
2432
2433	END MODULE synthetic_turbulence_generator_mod

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