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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
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 2017-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4442 2020-03-04 19:21:13Z suehring $
27	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
28	! (was accidantly changed).
29	!
30	! 4441 2020-03-04 19:20:35Z suehring
31	! Correct misplaced preprocessor directive
32	!
33	! 4438 2020-03-03 20:49:28Z suehring
34	! Performance optimizations in velocity-seed calculation:
35	! - random number array is only defined and computed locally (except for
36	! normalization to zero mean and unit variance)
37	! - parallel random number generator is applied independent on the 2D random
38	! numbers in other routines
39	! - option to decide wheter velocity seeds are computed locally without any
40	! further communication or are computed by all processes along the
41	! communicator
42	!
43	! 4346 2019-12-18 11:55:56Z motisi
44	! Introduction of wall_flags_total_0, which currently sets bits based on static
45	! topography information used in wall_flags_static_0
46	!
47	! 4335 2019-12-12 16:39:05Z suehring
48	! Commentation of last commit
49	!
50	! 4332 2019-12-10 19:44:12Z suehring
51	! Limit initial velocity seeds in restart runs, if not the seed calculation
52	! may become unstable. Further, minor bugfix in initial velocity seed
53	! calculation.
54	!
55	! 4329 2019-12-10 15:46:36Z motisi
56	! Renamed wall_flags_0 to wall_flags_static_0
57	!
58	! 4309 2019-11-26 18:49:59Z suehring
59	! Computation of velocity seeds optimized. This implies that random numbers
60	! are computed now using the parallel random number generator. Random numbers
61	! are now only computed and normalized locally, while distributed over all
62	! mpi ranks afterwards, instead of computing random numbers on a global array.
63	! Further, the number of calls for the time-consuming velocity-seed generation
64	! is reduced - now the left and right, as well as the north and south boundary
65	! share the same velocity-seed matrices.
66	!
67	! 4182 2019-08-22 15:20:23Z scharf
68	! Corrected "Former revisions" section
69	!
70	! 4148 2019-08-08 11:26:00Z suehring
71	! Remove unused variable
72	!
73	! 4144 2019-08-06 09:11:47Z raasch
74	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
75	!
76	! 4071 2019-07-03 20:02:00Z suehring
77	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
78	! information is not read from file.
79	!
80	! 4022 2019-06-12 11:52:39Z suehring
81	! Several bugfixes and improvements
82	! - revise bias correction of the imposed perturbations (correction via volume
83	! flow can create instabilities in case the mean volume flow is close to zero)
84	! - introduce lower limits in calculation of coefficient matrix, else the
85	! calculation may become numerically unstable
86	! - impose perturbations every timestep, even though no new set of perturbations
87	! is generated in case dt_stg_call /= dt_3d
88	! - Implement a gradual decrease of Reynolds stress and length scales above
89	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
90	! discontinuous decrease
91	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
92	!
93	! 3987 2019-05-22 09:52:13Z kanani
94	! Introduce alternative switch for debug output during timestepping
95	!
96	! 3938 2019-04-29 16:06:25Z suehring
97	! Remove unused variables
98	!
99	! 3937 2019-04-29 15:09:07Z suehring
100	! Minor bugfix in case of a very early restart where mc_factor is sill not
101	! present.
102	! Some modification and fixing of potential bugs in the calculation of scaling
103	! parameters used for synthetic turbulence parametrization.
104	!
105	! 3909 2019-04-17 09:13:25Z suehring
106	! Minor bugfix for last commit
107	!
108	! 3900 2019-04-16 15:17:43Z suehring
109	! Missing re-calculation of perturbation seeds in case of restarts
110	!
111	! 3891 2019-04-12 17:52:01Z suehring
112	! Bugfix in initialization in case of restart runs.
113	!
114	! 3885 2019-04-11 11:29:34Z kanani
115	! Changes related to global restructuring of location messages and introduction
116	! of additional debug messages
117	!
118	!
119	! removed unused variables
120	!
121	! 3719 2019-02-06 13:10:18Z kanani
122	! Removed log_point measurement from stg_init, since this part is counted to
123	! log_point(2) 'initialisation' already. Moved other log_points to calls of
124	! the subroutines in time_integration for better overview.
125	!
126	! 2259 2017-06-08 09:09:11Z gronemeier
127	! Initial revision
128	!
129	! Authors:
130	! --------
131	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
132	!
133	!
134	! Description:
135	! ------------
136	!> The module generates turbulence at the inflow boundary based on a method by
137	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
138	!> correction by Kim et al. (2013).
139	!> The turbulence is correlated based on length scales in y- and z-direction and
140	!> a time scale for each velocity component. The profiles of length and time
141	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
142	!> tensor can be either read from file STG_PROFILES, or will be parametrized
143	!> within the boundary layer.
144	!>
145	!> @todo test restart
146	!> enable cyclic_fill
147	!> implement turbulence generation for e and pt
148	!> @todo Input of height-constant length scales via namelist
149	!> @note <Enter notes on the module>
150	!> @bug Height information from input file is not used. Profiles from input
151	!> must match with current PALM grid.
152	!> In case of restart, velocity seeds differ from precursor run if a11,
153	!> a22, or a33 are zero.
154	!------------------------------------------------------------------------------!
155	MODULE synthetic_turbulence_generator_mod
156
157
158	USE arrays_3d, &
159	ONLY: dzw, &
160	ddzw, &
161	drho_air, &
162	mean_inflow_profiles, &
163	q, &
164	q_init, &
165	pt, &
166	pt_init, &
167	u, &
168	u_init, &
169	v, &
170	v_init, &
171	w, &
172	zu, &
173	zw
174
175	USE basic_constants_and_equations_mod, &
176	ONLY: g, &
177	kappa, &
178	pi
179
180	USE control_parameters, &
181	ONLY: bc_lr, &
182	bc_ns, &
183	child_domain, &
184	coupling_char, &
185	debug_output_timestep, &
186	dt_3d, &
187	e_init, &
188	humidity, &
189	initializing_actions, &
190	intermediate_timestep_count, &
191	intermediate_timestep_count_max, &
192	length, &
193	message_string, &
194	nesting_offline, &
195	neutral, &
196	num_mean_inflow_profiles, &
197	random_generator, &
198	rans_mode, &
199	restart_string, &
200	syn_turb_gen, &
201	time_since_reference_point, &
202	turbulent_inflow
203
204	USE cpulog, &
205	ONLY: cpu_log, &
206	log_point_s
207
208	USE grid_variables, &
209	ONLY: ddx, &
210	ddy, &
211	dx, &
212	dy
213
214	USE indices, &
215	ONLY: nbgp, &
216	nz, &
217	nzb, &
218	nzt, &
219	nx, &
220	nxl, &
221	nxlu, &
222	nxr, &
223	ny, &
224	nys, &
225	nysv, &
226	nyn, &
227	wall_flags_total_0
228
229	USE kinds
230
231	#if defined( __parallel ) && !defined( __mpifh )
232	USE MPI
233	#endif
234
235	USE nesting_offl_mod, &
236	ONLY: nesting_offl_calc_zi, &
237	zi_ribulk
238
239	USE pegrid, &
240	ONLY: comm1dx, &
241	comm1dy, &
242	comm2d, &
243	ierr, &
244	myidx, &
245	myidy, &
246	pdims
247
248	USE pmc_interface, &
249	ONLY : rans_mode_parent
250
251	USE random_generator_parallel, &
252	ONLY: init_parallel_random_generator, &
253	random_dummy, &
254	random_number_parallel, &
255	random_seed_parallel
256
257	USE transpose_indices, &
258	ONLY: nzb_x, &
259	nzt_x
260
261	USE surface_mod, &
262	ONLY: surf_def_h, &
263	surf_lsm_h, &
264	surf_usm_h
265
266	IMPLICIT NONE
267
268	#if defined( __parallel ) && defined( __mpifh )
269	INCLUDE "mpif.h"
270	#endif
271
272
273	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
274	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
275	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
276	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
277	!< is distributed over several processes
278
279	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
280	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
281	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
282	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
283	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
284	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
285	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
286	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
287	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
288	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
289	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
290	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
291	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
292
293	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
294	!< required for bias correction of imposed perturbations
295	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
296	!< required for bias correction of imposed perturbations
297
298	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
299	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
300	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
301	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
302	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
303	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
308	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
311
312	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
313	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
314	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
315	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
316
317	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
318	!< scales above the boundary layer
319	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
320	!< one length scale above ABL top
321	REAL(wp) :: d_l !< blend_coeff/length_scale
322	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
323	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
324	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
325	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
326	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
327	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
328	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
329	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
330
331	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
332
333
334	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
335	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
336	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
337	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
338	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
339	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
340
341	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
342	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
343	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
344	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
345	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
346	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
347	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
348	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
349	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
350
351	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
352	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
353	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
354	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
355	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
356	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
357	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
372
373	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
374	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
375
376	!
377	!-- PALM interfaces:
378	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
379	INTERFACE stg_adjust
380	MODULE PROCEDURE stg_adjust
381	END INTERFACE stg_adjust
382	!
383	!-- Input parameter checks to be done in check_parameters
384	INTERFACE stg_check_parameters
385	MODULE PROCEDURE stg_check_parameters
386	END INTERFACE stg_check_parameters
387
388	!
389	!-- Calculate filter functions
390	INTERFACE stg_filter_func
391	MODULE PROCEDURE stg_filter_func
392	END INTERFACE stg_filter_func
393
394	!
395	!-- Generate velocity seeds at south and north domain boundary
396	INTERFACE stg_generate_seed_xz
397	MODULE PROCEDURE stg_generate_seed_xz
398	END INTERFACE stg_generate_seed_xz
399	!
400	!-- Generate velocity seeds at left and/or right domain boundary
401	INTERFACE stg_generate_seed_yz
402	MODULE PROCEDURE stg_generate_seed_yz
403	END INTERFACE stg_generate_seed_yz
404
405	!
406	!-- Output of information to the header file
407	INTERFACE stg_header
408	MODULE PROCEDURE stg_header
409	END INTERFACE stg_header
410
411	!
412	!-- Initialization actions
413	INTERFACE stg_init
414	MODULE PROCEDURE stg_init
415	END INTERFACE stg_init
416
417	!
418	!-- Main procedure of synth. turb. gen.
419	INTERFACE stg_main
420	MODULE PROCEDURE stg_main
421	END INTERFACE stg_main
422
423	!
424	!-- Reading of NAMELIST parameters
425	INTERFACE stg_parin
426	MODULE PROCEDURE stg_parin
427	END INTERFACE stg_parin
428
429	!
430	!-- Reading of parameters for restart runs
431	INTERFACE stg_rrd_global
432	MODULE PROCEDURE stg_rrd_global
433	END INTERFACE stg_rrd_global
434
435	!
436	!-- Writing of binary output for restart runs
437	INTERFACE stg_wrd_global
438	MODULE PROCEDURE stg_wrd_global
439	END INTERFACE stg_wrd_global
440
441	SAVE
442
443	PRIVATE
444
445	!
446	!-- Public interfaces
447	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
448	stg_parin, stg_rrd_global, stg_wrd_global
449
450	!
451	!-- Public variables
452	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
453	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
454	time_stg_adjust, time_stg_call, use_syn_turb_gen
455
456
457	CONTAINS
458
459
460	!------------------------------------------------------------------------------!
461	! Description:
462	! ------------
463	!> Check parameters routine for synthetic turbulence generator
464	!------------------------------------------------------------------------------!
465	SUBROUTINE stg_check_parameters
466
467	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
468	nesting_offline ) THEN
469	message_string = 'Synthetic turbulence generator is required ' // &
470	'if offline nesting is applied and PALM operates ' // &
471	'in LES mode.'
472	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
473	ENDIF
474
475	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
476	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
477	message_string = 'Synthetic turbulence generator is required ' // &
478	'when nesting is applied and parent operates in ' // &
479	'RANS-mode but current child in LES mode.'
480	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
481	ENDIF
482
483	IF ( use_syn_turb_gen ) THEN
484
485	IF ( child_domain .AND. .NOT. rans_mode .AND. &
486	.NOT. rans_mode_parent ) THEN
487	message_string = 'Using synthetic turbulence generator ' // &
488	'is not allowed in LES-LES nesting.'
489	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
490
491	ENDIF
492
493	IF ( child_domain .AND. rans_mode .AND. &
494	rans_mode_parent ) THEN
495	message_string = 'Using synthetic turbulence generator ' // &
496	'is not allowed in RANS-RANS nesting.'
497	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
498
499	ENDIF
500
501	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
502
503	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
504	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
505	message_string = 'Using synthetic turbulence generator ' // &
506	'requires %initializing_actions = ' // &
507	'"set_constant_profiles" or "read_restart_data"' //&
508	', if not offline nesting is applied.'
509	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
510	ENDIF
511
512	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
513	message_string = 'Using synthetic turbulence generator ' // &
514	'requires &bc_lr = "dirichlet/radiation", ' // &
515	'if not offline nesting is applied.'
516	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
517	ENDIF
518	IF ( bc_ns /= 'cyclic' ) THEN
519	message_string = 'Using synthetic turbulence generator ' // &
520	'requires &bc_ns = "cyclic", ' // &
521	'if not offline nesting is applied.'
522	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
523	ENDIF
524
525	ENDIF
526
527	IF ( turbulent_inflow ) THEN
528	message_string = 'Using synthetic turbulence generator ' // &
529	'in combination &with turbulent_inflow = .T. '// &
530	'is not allowed'
531	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
532	ENDIF
533	!
534	!-- Synthetic turbulence generator requires the parallel random generator
535	IF ( random_generator /= 'random-parallel' ) THEN
536	message_string = 'Using synthetic turbulence generator ' // &
537	'requires random_generator = random-parallel.'
538	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
539	ENDIF
540
541	ENDIF
542
543	END SUBROUTINE stg_check_parameters
544
545
546	!------------------------------------------------------------------------------!
547	! Description:
548	! ------------
549	!> Header output for synthetic turbulence generator
550	!------------------------------------------------------------------------------!
551	SUBROUTINE stg_header ( io )
552
553	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
554
555	!
556	!-- Write synthetic turbulence generator Header
557	WRITE( io, 1 )
558	IF ( use_syn_turb_gen ) THEN
559	WRITE( io, 2 )
560	ELSE
561	WRITE( io, 3 )
562	ENDIF
563
564	IF ( parametrize_inflow_turbulence ) THEN
565	WRITE( io, 4 ) dt_stg_adjust
566	ELSE
567	WRITE( io, 5 )
568	ENDIF
569
570	1 FORMAT (//' Synthetic turbulence generator information:'/ &
571	' ------------------------------------------'/)
572	2 FORMAT (' synthetic turbulence generator is switched on')
573	3 FORMAT (' synthetic turbulence generator is switched off')
574	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
575	5 FORMAT (' imposed turbulence is read from file' )
576
577	END SUBROUTINE stg_header
578
579
580	!------------------------------------------------------------------------------!
581	! Description:
582	! ------------
583	!> Initialization of the synthetic turbulence generator
584	!------------------------------------------------------------------------------!
585	SUBROUTINE stg_init
586
587	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
588
589	#if defined( __parallel )
590	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
591	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
592	#endif
593
594	INTEGER(iwp) :: i !> grid index in x-direction
595	INTEGER(iwp) :: j !> loop index
596	INTEGER(iwp) :: k !< index
597	INTEGER(iwp) :: newtype !< dummy MPI type
598	INTEGER(iwp) :: realsize !< size of REAL variables
599
600	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
601	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
602	!
603	!-- Dummy variables used for reading profiles
604	REAL(wp) :: d1 !< u profile
605	REAL(wp) :: d2 !< v profile
606	REAL(wp) :: d3 !< w profile
607	REAL(wp) :: d5 !< e profile
608	REAL(wp) :: luy !< length scale for u in y direction
609	REAL(wp) :: luz !< length scale for u in z direction
610	REAL(wp) :: lvy !< length scale for v in y direction
611	REAL(wp) :: lvz !< length scale for v in z direction
612	REAL(wp) :: lwy !< length scale for w in y direction
613	REAL(wp) :: lwz !< length scale for w in z direction
614	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
615	REAL(wp) :: zz !< height
616
617
618	#if defined( __parallel )
619	CALL MPI_BARRIER( comm2d, ierr )
620	#endif
621	!
622	!-- Create mpi-datatypes for exchange in case of non-local but distributed
623	!-- computation of the velocity seeds. This option is useful in
624	!-- case large turbulent length scales are presentm, where the computational
625	!-- effort becomes large and need to be parallelized. For parametrized
626	!-- turbulence the length scales are small and computing the velocity seeds
627	!-- locally is faster (no overhead by communication).
628	IF ( .NOT. compute_velocity_seeds_local ) THEN
629	#if defined( __parallel )
630	!
631	!-- Determine processor decomposition of z-axis along x- and y-direction
632	nnz = nz / pdims(1)
633	nzb_x_stg = 1 + myidx * INT( nnz )
634	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
635
636	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
637	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
638
639	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
640	.AND. .NOT. rans_mode ) ) THEN
641	nnz = nz / pdims(2)
642	nzb_y_stg = 1 + myidy * INT( nnz )
643	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
644
645	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
646	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
647	ENDIF
648
649	!
650	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
651	!-- velocity seeds
652	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
653	extent = 1 * realsize
654	!
655	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
656	!-- layer
657	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
658	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
659	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
660	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
661	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
662	CALL MPI_TYPE_FREE( newtype, ierr )
663
664	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
665	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
666	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
667	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
668	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
669	CALL MPI_TYPE_FREE( newtype, ierr )
670
671	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
672	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
673
674	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
675	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
676
677	DO j = 1, pdims(1)
678	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
679	ENDDO
680	!
681	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
682	!-- layer
683	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
684	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
685	.AND. .NOT. rans_mode ) ) THEN
686	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
687	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
688	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
689	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
690	CALL MPI_TYPE_FREE( newtype, ierr )
691
692	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
693	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
694	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
695	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
696	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
697	CALL MPI_TYPE_FREE( newtype, ierr )
698
699	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
700	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
701
702	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
703	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
704
705	DO j = 1, pdims(2)
706	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
707	ENDDO
708
709	ENDIF
710	#endif
711	ENDIF
712	!
713	!-- Allocate required arrays.
714	!-- In case no offline nesting or self nesting is used, the arrary
715	!-- mean_inflow profiles is required. Check if it is already allocated, else
716	!-- allocate and initialize it appropriately. Note, in case turbulence and
717	!-- inflow information is read from file, mean_inflow_profiles is already
718	!-- allocated and initialized appropriately.
719	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
720	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
721	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
722	mean_inflow_profiles = 0.0_wp
723	mean_inflow_profiles(:,1) = u_init
724	mean_inflow_profiles(:,2) = v_init
725	!
726	!-- Even though potential temperature and humidity are not perturbed,
727	!-- they need to be initialized appropriately.
728	IF ( .NOT. neutral ) &
729	mean_inflow_profiles(:,4) = pt_init
730	IF ( humidity ) &
731	mean_inflow_profiles(:,6) = q_init
732	ENDIF
733	ENDIF
734
735	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
736	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
737	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
738	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
739	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
740	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
741	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
742	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
743
744	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
745	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
746	dist_xz = 0.0_wp
747	dist_yz = 0.0_wp
748	!
749	!-- Read inflow profile
750	!-- Height levels of profiles in input profile is as follows:
751	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
752	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
753	!-- WARNING: zz is not used at the moment
754	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
755	EXIST = file_stg_exist )
756
757	IF ( file_stg_exist ) THEN
758
759	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
760	FORM='FORMATTED')
761	!
762	!-- Skip header
763	READ( 90, * )
764
765	DO k = nzb+1, nzt+1
766	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
767	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
768	d1, d2, d3, d5
769
770	!
771	!-- Convert length scales from meter to number of grid points.
772	nuy(k) = INT( luy * ddy )
773	nuz(k) = INT( luz * ddzw(k) )
774	nvy(k) = INT( lvy * ddy )
775	nvz(k) = INT( lvz * ddzw(k) )
776	nwy(k) = INT( lwy * ddy )
777	nwz(k) = INT( lwz * ddzw(k) )
778	!
779	!-- Workaround, assume isotropic turbulence
780	nwx(k) = nwy(k)
781	nvx(k) = nvy(k)
782	nux(k) = nuy(k)
783	!
784	!-- Save Mean inflow profiles
785	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
786	mean_inflow_profiles(k,1) = d1
787	mean_inflow_profiles(k,2) = d2
788	! mean_inflow_profiles(k,4) = d4
789	mean_inflow_profiles(k,5) = d5
790	ENDIF
791	ENDDO
792	!
793	!-- Set lenght scales at surface grid point
794	nuy(nzb) = nuy(nzb+1)
795	nuz(nzb) = nuz(nzb+1)
796	nvy(nzb) = nvy(nzb+1)
797	nvz(nzb) = nvz(nzb+1)
798	nwy(nzb) = nwy(nzb+1)
799	nwz(nzb) = nwz(nzb+1)
800
801	CLOSE( 90 )
802	!
803	!-- Calculate coefficient matrix from Reynolds stress tensor
804	!-- (Lund rotation)
805	CALL calc_coeff_matrix
806	!
807	!-- No information about turbulence and its length scales are available.
808	!-- Instead, parametrize turbulence which is imposed at the boundaries.
809	!-- Set flag which indicates that turbulence is parametrized, which is done
810	!-- later when energy-balance models are already initialized. This is
811	!-- because the STG needs information about surface properties such as
812	!-- roughness to build 'realistic' turbulence profiles.
813	ELSE
814	!
815	!-- Define length scale for the imposed turbulence, which is defined as
816	!-- 8 times the minimum grid spacing
817	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
818	!
819	!-- Define constant to gradually decrease length scales and Reynolds stress
820	!-- above ABL top. Assure that no zero length scales are used.
821	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
822	!
823	!-- Set flag indicating that turbulence is parametrized
824	parametrize_inflow_turbulence = .TRUE.
825	!
826	!-- In case of dirichlet inflow boundary conditions only at one lateral
827	!-- boundary, i.e. in the case no offline or self nesting is applied but
828	!-- synthetic turbulence shall be parametrized nevertheless, the
829	!-- boundary-layer depth need to determined first.
830	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
831	CALL nesting_offl_calc_zi
832	!
833	!-- Determine boundary-layer depth, which is used to initialize lenght
834	!-- scales
835	CALL calc_scaling_variables
836	!
837	!-- Initialize lenght and time scales, which in turn are used
838	!-- to initialize the filter functions.
839	CALL calc_length_and_time_scale
840	!
841	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
842	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
843	!-- Rotach et al. (1996) and is based on boundary-layer depth,
844	!-- friction velocity and velocity scale.
845	CALL parametrize_reynolds_stress
846	!
847	!-- Calculate coefficient matrix from Reynolds stress tensor
848	!-- (Lund rotation)
849	CALL calc_coeff_matrix
850
851	ENDIF
852
853	!
854	!-- Assign initial profiles. Note, this is only required if turbulent
855	!-- inflow from the left is desired, not in case of any of the
856	!-- nesting (offline or self nesting) approaches.
857	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
858	u_init = mean_inflow_profiles(:,1)
859	v_init = mean_inflow_profiles(:,2)
860	!pt_init = mean_inflow_profiles(:,4)
861	e_init = MAXVAL( mean_inflow_profiles(:,5) )
862	ENDIF
863
864	!
865	!-- Define the size of the filter functions and allocate them.
866	mergp = 0
867
868	! arrays must be large enough to cover the largest length scale
869	DO k = nzb, nzt+1
870	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
871	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
872	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
873	IF ( j > mergp ) mergp = j
874	ENDDO
875
876	! mergp = 2 * mergp
877	! mergp = mergp
878
879	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
880	buy(-mergp:mergp,nzb:nzt+1), &
881	buz(-mergp:mergp,nzb:nzt+1), &
882	bvx(-mergp:mergp,nzb:nzt+1), &
883	bvy(-mergp:mergp,nzb:nzt+1), &
884	bvz(-mergp:mergp,nzb:nzt+1), &
885	bwx(-mergp:mergp,nzb:nzt+1), &
886	bwy(-mergp:mergp,nzb:nzt+1), &
887	bwz(-mergp:mergp,nzb:nzt+1) )
888
889	!
890	!-- Allocate velocity seeds for turbulence at xz-layer
891	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
892	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
893	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
894
895	!
896	!-- Allocate velocity seeds for turbulence at yz-layer
897	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
898	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
899	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
900
901	fu_xz = 0.0_wp
902	fuo_xz = 0.0_wp
903	fv_xz = 0.0_wp
904	fvo_xz = 0.0_wp
905	fw_xz = 0.0_wp
906	fwo_xz = 0.0_wp
907
908	fu_yz = 0.0_wp
909	fuo_yz = 0.0_wp
910	fv_yz = 0.0_wp
911	fvo_yz = 0.0_wp
912	fw_yz = 0.0_wp
913	fwo_yz = 0.0_wp
914
915	!
916	!-- Create filter functions
917	CALL stg_filter_func( nux, bux ) !filter ux
918	CALL stg_filter_func( nuy, buy ) !filter uy
919	CALL stg_filter_func( nuz, buz ) !filter uz
920	CALL stg_filter_func( nvx, bvx ) !filter vx
921	CALL stg_filter_func( nvy, bvy ) !filter vy
922	CALL stg_filter_func( nvz, bvz ) !filter vz
923	CALL stg_filter_func( nwx, bwx ) !filter wx
924	CALL stg_filter_func( nwy, bwy ) !filter wy
925	CALL stg_filter_func( nwz, bwz ) !filter wz
926
927	#if defined( __parallel )
928	CALL MPI_BARRIER( comm2d, ierr )
929	#endif
930
931	!
932	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
933	! time step.
934	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
935	! are 0 compared to the prerun. This is mostly for k=nzt+1.
936	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
937	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
938
939	IF ( myidx == id_stg_left ) i = -1
940	IF ( myidx == id_stg_right ) i = nxr+1
941
942	DO j = nys, nyn
943	DO k = nzb, nzt+1
944	IF ( a11(k) > 10E-8_wp ) THEN
945	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
946	ELSE
947	fu_yz(k,j) = 10E-8_wp
948	ENDIF
949
950	IF ( a22(k) > 10E-8_wp ) THEN
951	fv_yz(k,j) = ( v(k,j,i) - &
952	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
953	ELSE
954	fv_yz(k,j) = 10E-8_wp
955	ENDIF
956
957	IF ( a33(k) > 10E-8_wp ) THEN
958	fw_yz(k,j) = ( w(k,j,i) - &
959	a31(k) * fu_yz(k,j) - a32(k) * &
960	fv_yz(k,j) ) / a33(k)
961	ELSE
962	fw_yz(k,j) = 10E-8_wp
963	ENDIF
964	ENDDO
965	ENDDO
966	ENDIF
967
968	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
969
970	IF ( myidy == id_stg_south ) j = -1
971	IF ( myidy == id_stg_north ) j = nyn+1
972
973	DO i = nxl, nxr
974	DO k = nzb, nzt+1
975	!
976	!-- In case the correlation coefficients are very small, the
977	!-- velocity seeds may become very large finally creating
978	!-- numerical instabilities in the synthetic turbulence generator.
979	!-- Empirically, a value of 10E-8 seems to be sufficient.
980	IF ( a11(k) > 10E-8_wp ) THEN
981	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
982	ELSE
983	fu_xz(k,i) = 10E-8_wp
984	ENDIF
985
986	IF ( a22(k) > 10E-8_wp ) THEN
987	fv_xz(k,i) = ( v(k,j,i) - &
988	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
989	ELSE
990	fv_xz(k,i) = 10E-8_wp
991	ENDIF
992
993	IF ( a33(k) > 10E-8_wp ) THEN
994	fw_xz(k,i) = ( w(k,j,i) - &
995	a31(k) * fu_xz(k,i) - &
996	a32(k) * fv_xz(k,i) ) / a33(k)
997	ELSE
998	fw_xz(k,i) = 10E-8_wp
999	ENDIF
1000
1001	ENDDO
1002	ENDDO
1003	ENDIF
1004	ENDIF
1005	!
1006	!-- Count the number of non-topography grid points at the boundaries where
1007	!-- perturbations are imposed. This number is later used for bias corrections
1008	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1009	!-- due to the asymetry of u and v along x and y direction, respectively,
1010	!-- different cases must be distinguished.
1011	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1012	!
1013	!-- Number of grid points where perturbations are imposed on u
1014	IF ( myidx == id_stg_left ) i = nxl
1015	IF ( myidx == id_stg_right ) i = nxr+1
1016
1017	nr_non_topo_yz_l(1) = SUM( &
1018	MERGE( 1, 0, &
1019	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1020	!
1021	!-- Number of grid points where perturbations are imposed on v and w
1022	IF ( myidx == id_stg_left ) i = nxl-1
1023	IF ( myidx == id_stg_right ) i = nxr+1
1024
1025	nr_non_topo_yz_l(2) = SUM( &
1026	MERGE( 1, 0, &
1027	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1028	nr_non_topo_yz_l(3) = SUM( &
1029	MERGE( 1, 0, &
1030	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1031
1032	#if defined( __parallel )
1033	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1034	MPI_SUM, comm1dy, ierr )
1035	#else
1036	nr_non_topo_yz = nr_non_topo_yz_l
1037	#endif
1038	ENDIF
1039
1040	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1041	!
1042	!-- Number of grid points where perturbations are imposed on v
1043	IF ( myidy == id_stg_south ) j = nys
1044	IF ( myidy == id_stg_north ) j = nyn+1
1045
1046	nr_non_topo_xz_l(2) = SUM( &
1047	MERGE( 1, 0, &
1048	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1049	!
1050	!-- Number of grid points where perturbations are imposed on u and w
1051	IF ( myidy == id_stg_south ) j = nys-1
1052	IF ( myidy == id_stg_north ) j = nyn+1
1053
1054	nr_non_topo_xz_l(1) = SUM( &
1055	MERGE( 1, 0, &
1056	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1057	nr_non_topo_xz_l(3) = SUM( &
1058	MERGE( 1, 0, &
1059	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1060
1061	#if defined( __parallel )
1062	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1063	MPI_SUM, comm1dx, ierr )
1064	#else
1065	nr_non_topo_xz = nr_non_topo_xz_l
1066	#endif
1067	ENDIF
1068	!
1069	!-- Initialize random number generator at xz- and yz-layers. Random numbers
1070	!-- are initialized at each core. In case there is only inflow from the left,
1071	!-- it is sufficient to generate only random numbers for the yz-layer, else
1072	!-- random numbers for the xz-layer are also required.
1073	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1074	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1075	id_rand_yz = 0
1076	seq_rand_yz = 0
1077
1078	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
1079	id_rand_yz, seq_rand_yz )
1080
1081	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1082	.AND. .NOT. rans_mode ) ) THEN
1083	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1084	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1085	id_rand_xz = 0
1086	seq_rand_xz = 0
1087
1088	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
1089	id_rand_xz, seq_rand_xz )
1090	ENDIF
1091
1092
1093
1094	END SUBROUTINE stg_init
1095
1096
1097	!------------------------------------------------------------------------------!
1098	! Description:
1099	! ------------
1100	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1101	!> (Xie and Castro, 2008)
1102	!------------------------------------------------------------------------------!
1103	SUBROUTINE stg_filter_func( nxx, bxx )
1104
1105	INTEGER(iwp) :: k !< loop index
1106	INTEGER(iwp) :: n_k !< length scale nXX in height k
1107	INTEGER(iwp) :: nf !< index for length scales
1108
1109	REAL(wp) :: bdenom !< denominator for filter functions bXX
1110	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1111
1112	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1113
1114	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1115
1116
1117	bxx = 0.0_wp
1118
1119	DO k = nzb, nzt+1
1120	bdenom = 0.0_wp
1121	n_k = nxx(k)
1122	IF ( n_k /= 0 ) THEN
1123
1124	!
1125	!-- ( Eq.10 )^2
1126	DO nf = -n_k, n_k
1127	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1128	ENDDO
1129
1130	!
1131	!-- ( Eq.9 )
1132	bdenom = SQRT( bdenom )
1133	DO nf = -n_k, n_k
1134	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1135	ENDDO
1136	ENDIF
1137	ENDDO
1138
1139	END SUBROUTINE stg_filter_func
1140
1141
1142	!------------------------------------------------------------------------------!
1143	! Description:
1144	! ------------
1145	!> Parin for &stg_par for synthetic turbulence generator
1146	!------------------------------------------------------------------------------!
1147	SUBROUTINE stg_parin
1148
1149	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1150
1151
1152	NAMELIST /stg_par/ dt_stg_adjust, &
1153	dt_stg_call, &
1154	use_syn_turb_gen, &
1155	compute_velocity_seeds_local
1156
1157	line = ' '
1158	!
1159	!-- Try to find stg package
1160	REWIND ( 11 )
1161	line = ' '
1162	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1163	READ ( 11, '(A)', END=20 ) line
1164	ENDDO
1165	BACKSPACE ( 11 )
1166
1167	!
1168	!-- Read namelist
1169	READ ( 11, stg_par, ERR = 10, END = 20 )
1170
1171	!
1172	!-- Set flag that indicates that the synthetic turbulence generator is switched
1173	!-- on
1174	syn_turb_gen = .TRUE.
1175	GOTO 20
1176
1177	10 BACKSPACE( 11 )
1178	READ( 11 , '(A)') line
1179	CALL parin_fail_message( 'stg_par', line )
1180
1181	20 CONTINUE
1182
1183	END SUBROUTINE stg_parin
1184
1185
1186	!------------------------------------------------------------------------------!
1187	! Description:
1188	! ------------
1189	!> This routine reads the respective restart data.
1190	!------------------------------------------------------------------------------!
1191	SUBROUTINE stg_rrd_global( found )
1192
1193	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1194
1195	found = .TRUE.
1196
1197
1198	SELECT CASE ( restart_string(1:length) )
1199
1200	CASE ( 'time_stg_adjust' )
1201	READ ( 13 ) time_stg_adjust
1202
1203	CASE ( 'time_stg_call' )
1204	READ ( 13 ) time_stg_call
1205
1206	CASE ( 'use_syn_turb_gen' )
1207	READ ( 13 ) use_syn_turb_gen
1208
1209	CASE DEFAULT
1210
1211	found = .FALSE.
1212
1213	END SELECT
1214
1215
1216	END SUBROUTINE stg_rrd_global
1217
1218
1219	!------------------------------------------------------------------------------!
1220	! Description:
1221	! ------------
1222	!> This routine writes the respective restart data.
1223	!------------------------------------------------------------------------------!
1224	SUBROUTINE stg_wrd_global
1225
1226	CALL wrd_write_string( 'time_stg_adjust' )
1227	WRITE ( 14 ) time_stg_adjust
1228
1229	CALL wrd_write_string( 'time_stg_call' )
1230	WRITE ( 14 ) time_stg_call
1231
1232	CALL wrd_write_string( 'use_syn_turb_gen' )
1233	WRITE ( 14 ) use_syn_turb_gen
1234
1235
1236	END SUBROUTINE stg_wrd_global
1237
1238
1239	!------------------------------------------------------------------------------!
1240	! Description:
1241	! ------------
1242	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1243	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1244	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1245	!> (Lund, 1998).
1246	!------------------------------------------------------------------------------!
1247	SUBROUTINE stg_main
1248
1249	INTEGER(iwp) :: i !< grid index in x-direction
1250	INTEGER(iwp) :: j !< loop index in y-direction
1251	INTEGER(iwp) :: k !< loop index in z-direction
1252
1253	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1254
1255	REAL(wp) :: dt_stg !< wheighted subtimestep
1256
1257	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1258
1259	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1260	!
1261	!-- Calculate time step which is needed for filter functions
1262	dt_stg = MAX( dt_3d, dt_stg_call )
1263	!
1264	!-- Check if synthetic turbulence generator needs to be called and new
1265	!-- perturbations need to be created or if old disturbances can be imposed
1266	!-- again.
1267	IF ( time_stg_call >= dt_stg_call .AND. &
1268	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1269	stg_call = .TRUE.
1270	ELSE
1271	stg_call = .FALSE.
1272	ENDIF
1273	!
1274	!-- Initial value of fu, fv, fw
1275	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1276	!
1277	!-- Generate turbulence at the left and right boundary. Random numbers
1278	!-- for the yz-planes at the left/right boundary are generated by the
1279	!-- left-sided mpi ranks only. After random numbers are calculated, they
1280	!-- are distributed to all other mpi ranks in the model, so that the
1281	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1282	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1283	!-- that the left- and the right-sided lateral boundary have the same initial
1284	!-- seeds.
1285	!-- Note, in case of inflow from the right only, only turbulence at the left
1286	!-- boundary is required.
1287	IF ( .NOT. ( nesting_offline .OR. &
1288	( child_domain .AND. rans_mode_parent &
1289	.AND. .NOT. rans_mode ) ) ) THEN
1290	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1291	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1292	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1293	ELSE
1294	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1295	id_stg_left, id_stg_right )
1296	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1297	id_stg_left, id_stg_right )
1298	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1299	id_stg_left, id_stg_right )
1300	!
1301	!-- Generate turbulence at the south and north boundary. Random numbers
1302	!-- for the xz-planes at the south/north boundary are generated by the
1303	!-- south-sided mpi ranks only. Please see also comment above.
1304	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1305	id_stg_south, id_stg_north )
1306	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1307	id_stg_south, id_stg_north )
1308	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1309	id_stg_south, id_stg_north )
1310	ENDIF
1311	velocity_seed_initialized = .TRUE.
1312	ENDIF
1313	!
1314	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1315	!-- seeds are only required at the left boundary, while in case of offline
1316	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1317	!-- right, south and north boundaries.
1318	IF ( stg_call ) THEN
1319	IF ( .NOT. ( nesting_offline .OR. &
1320	( child_domain .AND. rans_mode_parent &
1321	.AND. .NOT. rans_mode ) ) ) THEN
1322	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1323	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1324	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1325
1326	ELSE
1327	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1328	id_stg_left, id_stg_right )
1329	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1330	id_stg_left, id_stg_right )
1331	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1332	id_stg_left, id_stg_right )
1333
1334	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1335	id_stg_south, id_stg_north )
1336	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1337	id_stg_south, id_stg_north )
1338	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1339	id_stg_south, id_stg_north )
1340	ENDIF
1341	ENDIF
1342
1343	!
1344	!-- Turbulence generation at left and/or right boundary
1345	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1346	!
1347	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1348	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1349	!-- imposed
1350	IF ( stg_call ) THEN
1351
1352	DO j = nys, nyn
1353	DO k = nzb, nzt + 1
1354	!
1355	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1356	IF ( tu(k) == 0.0_wp ) THEN
1357	fu_yz(k,j) = fuo_yz(k,j)
1358	ELSE
1359	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1360	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1361	ENDIF
1362
1363	IF ( tv(k) == 0.0_wp ) THEN
1364	fv_yz(k,j) = fvo_yz(k,j)
1365	ELSE
1366	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1367	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1368	ENDIF
1369
1370	IF ( tw(k) == 0.0_wp ) THEN
1371	fw_yz(k,j) = fwo_yz(k,j)
1372	ELSE
1373	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1374	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1375	ENDIF
1376	ENDDO
1377	ENDDO
1378
1379	dist_yz(nzb,:,1) = 0.0_wp
1380	dist_yz(nzb,:,2) = 0.0_wp
1381	dist_yz(nzb,:,3) = 0.0_wp
1382
1383	IF ( myidx == id_stg_left ) i = nxl
1384	IF ( myidx == id_stg_right ) i = nxr+1
1385	DO j = nys, nyn
1386	DO k = nzb+1, nzt + 1
1387	!
1388	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1389	!-- Additional factors are added to improve the variance of v and w
1390	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1391	MERGE( 1.0_wp, 0.0_wp, &
1392	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1393	ENDDO
1394	ENDDO
1395
1396	IF ( myidx == id_stg_left ) i = nxl-1
1397	IF ( myidx == id_stg_right ) i = nxr+1
1398	DO j = nys, nyn
1399	DO k = nzb+1, nzt + 1
1400	!
1401	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1402	!-- Additional factors are added to improve the variance of v and w
1403	!-- experimental test of 1.2
1404	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1405	* 1.2_wp ) &
1406	* ( a21(k) * fu_yz(k,j) &
1407	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1408	MERGE( 1.0_wp, 0.0_wp, &
1409	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1410	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1411	* 1.3_wp ) &
1412	* ( a31(k) * fu_yz(k,j) &
1413	+ a32(k) * fv_yz(k,j) &
1414	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1415	MERGE( 1.0_wp, 0.0_wp, &
1416	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1417	ENDDO
1418	ENDDO
1419	ENDIF
1420	!
1421	!-- Mass flux correction following Kim et al. (2013)
1422	!-- This correction factor insures that the mass flux is preserved at the
1423	!-- inflow boundary. First, calculate mean value of the imposed
1424	!-- perturbations at yz boundary.
1425	!-- Note, this needs to be done only after the last RK3-substep, else
1426	!-- the boundary values won't be accessed.
1427	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1428	mc_factor_l = 0.0_wp
1429	mc_factor = 0.0_wp
1430	!
1431	!-- Sum up the original volume flows (with and without perturbations).
1432	!-- Note, for non-normal components (here v and w) it is actually no
1433	!-- volume flow.
1434	IF ( myidx == id_stg_left ) i = nxl
1435	IF ( myidx == id_stg_right ) i = nxr+1
1436
1437	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1438	* MERGE( 1.0_wp, 0.0_wp, &
1439	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1440
1441	IF ( myidx == id_stg_left ) i = nxl-1
1442	IF ( myidx == id_stg_right ) i = nxr+1
1443
1444	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1445	* MERGE( 1.0_wp, 0.0_wp, &
1446	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1447	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1448	* MERGE( 1.0_wp, 0.0_wp, &
1449	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1450
1451	#if defined( __parallel )
1452	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1453	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1454	#else
1455	mc_factor = mc_factor_l
1456	#endif
1457	!
1458	!-- Calculate correction factor and force zero mean perturbations.
1459	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1460
1461	IF ( myidx == id_stg_left ) i = nxl
1462	IF ( myidx == id_stg_right ) i = nxr+1
1463
1464	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
1465	* MERGE( 1.0_wp, 0.0_wp, &
1466	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1467
1468
1469	IF ( myidx == id_stg_left ) i = nxl-1
1470	IF ( myidx == id_stg_right ) i = nxr+1
1471
1472	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
1473	* MERGE( 1.0_wp, 0.0_wp, &
1474	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1475
1476	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
1477	* MERGE( 1.0_wp, 0.0_wp, &
1478	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1479	!
1480	!-- Add disturbances
1481	IF ( myidx == id_stg_left ) THEN
1482	!
1483	!-- For the left boundary distinguish between mesoscale offline / self
1484	!-- nesting and turbulent inflow at the left boundary only. In the latter
1485	!-- case turbulence is imposed on the mean inflow profiles.
1486	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1487	!
1488	!-- Add disturbance at the inflow
1489	DO j = nys, nyn
1490	DO k = nzb, nzt+1
1491	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1492	dist_yz(k,j,1) ) &
1493	* MERGE( 1.0_wp, 0.0_wp, &
1494	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1495	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1496	dist_yz(k,j,2) ) &
1497	* MERGE( 1.0_wp, 0.0_wp, &
1498	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1499	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1500	* MERGE( 1.0_wp, 0.0_wp, &
1501	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1502	ENDDO
1503	ENDDO
1504	ELSE
1505
1506	DO j = nys, nyn
1507	DO k = nzb+1, nzt
1508	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1509	* MERGE( 1.0_wp, 0.0_wp, &
1510	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1511	u(k,j,-1) = u(k,j,0)
1512	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1513	* MERGE( 1.0_wp, 0.0_wp, &
1514	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1515	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1516	* MERGE( 1.0_wp, 0.0_wp, &
1517	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1518	ENDDO
1519	ENDDO
1520	ENDIF
1521	ENDIF
1522	IF ( myidx == id_stg_right ) THEN
1523	DO j = nys, nyn
1524	DO k = nzb+1, nzt
1525	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1526	* MERGE( 1.0_wp, 0.0_wp, &
1527	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1528	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1529	* MERGE( 1.0_wp, 0.0_wp, &
1530	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1531	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1532	* MERGE( 1.0_wp, 0.0_wp, &
1533	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1534	ENDDO
1535	ENDDO
1536	ENDIF
1537	ENDIF
1538	ENDIF
1539	!
1540	!-- Turbulence generation at north and south boundary
1541	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1542	!
1543	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1544	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1545	!-- 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 ) 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 ) 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 ) 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) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1588	* 1.2_wp ) &
1589	* ( a21(k) * fu_xz(k,i) &
1590	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1591	MERGE( 1.0_wp, 0.0_wp, &
1592	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1593	ENDDO
1594	ENDDO
1595
1596	IF ( myidy == id_stg_south ) j = nys-1
1597	IF ( myidy == id_stg_north ) j = nyn+1
1598	DO i = nxl, nxr
1599	DO k = nzb+1, nzt + 1
1600	!
1601	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1602	!-- Additional factors are added to improve the variance of v and w
1603	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1604	MERGE( 1.0_wp, 0.0_wp, &
1605	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1606
1607	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1608	* 1.3_wp ) &
1609	* ( a31(k) * fu_xz(k,i) &
1610	+ a32(k) * fv_xz(k,i) &
1611	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1612	MERGE( 1.0_wp, 0.0_wp, &
1613	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1614	ENDDO
1615	ENDDO
1616	ENDIF
1617
1618	!
1619	!-- Mass flux correction following Kim et al. (2013)
1620	!-- This correction factor insures that the mass flux is preserved at the
1621	!-- inflow boundary. First, calculate mean value of the imposed
1622	!-- perturbations at yz boundary.
1623	!-- Note, this needs to be done only after the last RK3-substep, else
1624	!-- the boundary values won't be accessed.
1625	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1626	mc_factor_l = 0.0_wp
1627	mc_factor = 0.0_wp
1628
1629	IF ( myidy == id_stg_south ) j = nys
1630	IF ( myidy == id_stg_north ) j = nyn+1
1631
1632	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1633	* MERGE( 1.0_wp, 0.0_wp, &
1634	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1635
1636	IF ( myidy == id_stg_south ) j = nys-1
1637	IF ( myidy == id_stg_north ) j = nyn+1
1638
1639	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1640	* MERGE( 1.0_wp, 0.0_wp, &
1641	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1642	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1643	* MERGE( 1.0_wp, 0.0_wp, &
1644	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1645
1646	#if defined( __parallel )
1647	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1648	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1649	#else
1650	mc_factor = mc_factor_l
1651	#endif
1652
1653	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1654
1655	IF ( myidy == id_stg_south ) j = nys
1656	IF ( myidy == id_stg_north ) j = nyn+1
1657
1658	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
1659	* MERGE( 1.0_wp, 0.0_wp, &
1660	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1661
1662
1663	IF ( myidy == id_stg_south ) j = nys-1
1664	IF ( myidy == id_stg_north ) j = nyn+1
1665
1666	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
1667	* MERGE( 1.0_wp, 0.0_wp, &
1668	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1669
1670	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
1671	* MERGE( 1.0_wp, 0.0_wp, &
1672	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1673	!
1674	!-- Add disturbances
1675	IF ( myidy == id_stg_south ) THEN
1676	DO i = nxl, nxr
1677	DO k = nzb+1, nzt
1678	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1679	* MERGE( 1.0_wp, 0.0_wp, &
1680	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1681	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1682	* MERGE( 1.0_wp, 0.0_wp, &
1683	BTEST( wall_flags_total_0(k,0,i), 2 ) )
1684	v(k,-1,i) = v(k,0,i)
1685	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1686	* MERGE( 1.0_wp, 0.0_wp, &
1687	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1688	ENDDO
1689	ENDDO
1690	ENDIF
1691	IF ( myidy == id_stg_north ) THEN
1692
1693	DO i = nxl, nxr
1694	DO k = nzb+1, nzt
1695	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1696	* MERGE( 1.0_wp, 0.0_wp, &
1697	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1698	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1699	* MERGE( 1.0_wp, 0.0_wp, &
1700	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1701	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1702	* MERGE( 1.0_wp, 0.0_wp, &
1703	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1704	ENDDO
1705	ENDDO
1706	ENDIF
1707	ENDIF
1708	ENDIF
1709	!
1710	!-- Exchange ghost points.
1711	CALL exchange_horiz( u, nbgp )
1712	CALL exchange_horiz( v, nbgp )
1713	CALL exchange_horiz( w, nbgp )
1714	!
1715	!-- Finally, set time counter for calling STG to zero
1716	IF ( stg_call ) time_stg_call = 0.0_wp
1717
1718	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1719
1720	END SUBROUTINE stg_main
1721
1722	!------------------------------------------------------------------------------!
1723	! Description:
1724	! ------------
1725	!> Generate a set of random number rand_it wich is equal on each PE
1726	!> and calculate the velocity seed f_n.
1727	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1728	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1729	!> parts are collected to form the full array.
1730	!------------------------------------------------------------------------------!
1731	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1732
1733	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1734	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1735	INTEGER(iwp) :: j !< loop index in y-direction
1736	INTEGER(iwp) :: jj !< loop index in y-direction
1737	INTEGER(iwp) :: k !< loop index in z-direction
1738	INTEGER(iwp) :: kk !< loop index in z-direction
1739	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1740
1741	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1742	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1743
1744	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1745	REAL(wp) :: rand_av !< average of random number
1746	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1747
1748	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1749	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1750
1751	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1752	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1753
1754	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1755	!
1756	!-- Generate random numbers using the parallel random generator.
1757	!-- The set of random numbers are modified to have an average of 0 and
1758	!-- unit variance. Note, at the end the random number array must be defined
1759	!-- globally in order to compute the correlation matrices. However,
1760	!-- the calculation and normalization of random numbers is done locally,
1761	!-- while the result is later distributed to all processes. Further,
1762	!-- please note, a set of random numbers is only calculated for the
1763	!-- left boundary, while the right boundary uses the same random numbers
1764	!-- and thus also computes the same correlation matrix.
1765	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1766	rand_it = 0.0_wp
1767
1768	rand_av = 0.0_wp
1769	rand_sigma_inv = 0.0_wp
1770	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1771	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
1772	KIND=wp )
1773	!
1774	!-- Compute and normalize random numbers.
1775	DO j = nys - mergp, nyn + mergp
1776	!
1777	!-- Put the random seeds at grid point j
1778	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1779	DO k = nzb - mergp, nzt + 1 + mergp
1780	CALL random_number_parallel( random_dummy )
1781	rand_it(k,j) = random_dummy
1782	ENDDO
1783	!
1784	!-- Get the new random seeds from last call at grid point j
1785	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1786	ENDDO
1787	!
1788	!-- For normalization to zero mean, sum-up the global random numers.
1789	!-- To normalize the global set of random numbers,
1790	!-- the inner ghost layers mergp must not be summed-up, else
1791	!-- the random numbers on the ghost layers will be stronger weighted as they
1792	!-- also occur on the inner subdomains.
1793	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1794	MERGE( nyn, nyn + mergp, nyn /= ny )
1795	DO k = nzb - mergp, nzt + 1 + mergp
1796	rand_av = rand_av + rand_it(k,j)
1797	ENDDO
1798	ENDDO
1799
1800	#if defined( __parallel )
1801	!
1802	!-- Sum-up the local averages of the random numbers
1803	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1804	MPI_SUM, comm1dy, ierr )
1805	#endif
1806	rand_av = rand_av * nyz_inv
1807	!
1808	!-- Obtain zero mean
1809	rand_it= rand_it - rand_av
1810	!
1811	!-- Now, compute the variance
1812	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1813	MERGE( nyn, nyn + mergp, nyn /= ny )
1814	DO k = nzb - mergp, nzt + 1 + mergp
1815	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1816	ENDDO
1817	ENDDO
1818
1819	#if defined( __parallel )
1820	!
1821	!-- Sum-up the local quadratic averages of the random numbers
1822	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1823	MPI_SUM, comm1dy, ierr )
1824	#endif
1825	!
1826	!-- Compute standard deviation
1827	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1828	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1829	ELSE
1830	rand_sigma_inv = 1.0_wp
1831	ENDIF
1832	!
1833	!-- Normalize with standard deviation to obtain unit variance
1834	rand_it = rand_it * rand_sigma_inv
1835
1836	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1837	!
1838	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
1839	!-- are two options. In the first one, the computation of the seeds is
1840	!-- distributed to all processes along the communicator comm1dy and
1841	!-- gathered on the leftmost and, if necessary, on the rightmost process.
1842	!-- For huge length scales the computational effort can become quite huge
1843	!-- (it scales with the turbulent length scales), so that gain by parallelization
1844	!-- exceeds the costs by the subsequent communication.
1845	!-- In the second option, which performs better when the turbulent length scales
1846	!-- are parametrized and thus the loops are smaller, the seeds are computed
1847	!-- locally and no communication is necessary.
1848	IF ( compute_velocity_seeds_local ) THEN
1849
1850	f_n = 0.0_wp
1851	DO j = nys, nyn
1852	DO k = nzb, nzt+1
1853	DO jj = -n_y(k), n_y(k)
1854	DO kk = -n_z(k), n_z(k)
1855	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1856	ENDDO
1857	ENDDO
1858	ENDDO
1859	ENDDO
1860
1861	ELSE
1862
1863	f_n_l = 0.0_wp
1864	DO j = nys, nyn
1865	DO k = nzb_x_stg, nzt_x_stg+1
1866	DO jj = -n_y(k), n_y(k)
1867	DO kk = -n_z(k), n_z(k)
1868	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1869	ENDDO
1870	ENDDO
1871	ENDDO
1872	ENDDO
1873	!
1874	!-- Gather velocity seeds of full subdomain
1875	send_count = nzt_x_stg - nzb_x_stg + 1
1876	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1877
1878	#if defined( __parallel )
1879	!
1880	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1881	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1882	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1883	id_left, comm1dx, ierr )
1884	!
1885	!-- If required, gather the same velocity seed matrix on right boundary
1886	!-- mpi ranks (in offline nesting for example).
1887	IF ( PRESENT( id_right ) ) THEN
1888	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1889	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1890	id_right, comm1dx, ierr )
1891	ENDIF
1892	#else
1893	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1894	#endif
1895
1896	ENDIF
1897
1898	DEALLOCATE( rand_it )
1899
1900	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1901
1902	END SUBROUTINE stg_generate_seed_yz
1903
1904
1905	!------------------------------------------------------------------------------!
1906	! Description:
1907	! ------------
1908	!> Generate a set of random number rand_it wich is equal on each PE
1909	!> and calculate the velocity seed f_n.
1910	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1911	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1912	!> parts are collected to form the full array.
1913	!------------------------------------------------------------------------------!
1914	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1915
1916	INTEGER(iwp) :: i !< loop index in x-direction
1917	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1918	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1919	INTEGER(iwp) :: ii !< loop index in x-direction
1920	INTEGER(iwp) :: k !< loop index in z-direction
1921	INTEGER(iwp) :: kk !< loop index in z-direction
1922	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1923
1924	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1925	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1926
1927	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1928	REAL(wp) :: rand_av !< average of random number
1929	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1930
1931	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1932	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1933
1934	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1935	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1936
1937	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1938
1939	!
1940	!-- Generate random numbers using the parallel random generator.
1941	!-- The set of random numbers are modified to have an average of 0 and
1942	!-- unit variance. Note, at the end the random number array must be defined
1943	!-- globally in order to compute the correlation matrices. However,
1944	!-- the calculation and normalization of random numbers is done locally,
1945	!-- while the result is later distributed to all processes. Further,
1946	!-- please note, a set of random numbers is only calculated for the
1947	!-- left boundary, while the right boundary uses the same random numbers
1948	!-- and thus also computes the same correlation matrix.
1949	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
1950	rand_it = 0.0_wp
1951
1952	rand_av = 0.0_wp
1953	rand_sigma_inv = 0.0_wp
1954	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1955	* ( nx + mergp - ( 0 - mergp ) +1 ), &
1956	KIND=wp )
1957	!
1958	!-- Compute and normalize random numbers.
1959	DO i = nxl - mergp, nxr + mergp
1960	!
1961	!-- Put the random seeds at grid point ii
1962	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1963	DO k = nzb - mergp, nzt + 1 + mergp
1964	CALL random_number_parallel( random_dummy )
1965	rand_it(k,i) = random_dummy
1966	ENDDO
1967	!
1968	!-- Get the new random seeds from last call at grid point ii
1969	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1970	ENDDO
1971	!
1972	!-- For normalization to zero mean, sum-up the global random numers.
1973	!-- To normalize the global set of random numbers,
1974	!-- the inner ghost layers mergp must not be summed-up, else
1975	!-- the random numbers on the ghost layers will be stronger weighted as they
1976	!-- also occur on the inner subdomains.
1977	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1978	MERGE( nxr, nxr + mergp, nxr /= nx )
1979	DO k = nzb - mergp, nzt + 1 + mergp
1980	rand_av = rand_av + rand_it(k,i)
1981	ENDDO
1982	ENDDO
1983
1984	#if defined( __parallel )
1985	!
1986	!-- Sum-up the local averages of the random numbers
1987	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1988	MPI_SUM, comm1dx, ierr )
1989	#endif
1990	rand_av = rand_av * nxz_inv
1991	!
1992	!-- Obtain zero mean
1993	rand_it= rand_it - rand_av
1994	!
1995	!-- Now, compute the variance
1996	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1997	MERGE( nxr, nxr + mergp, nxr /= nx )
1998	DO k = nzb - mergp, nzt + 1 + mergp
1999	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2000	ENDDO
2001	ENDDO
2002
2003	#if defined( __parallel )
2004	!
2005	!-- Sum-up the local quadratic averages of the random numbers
2006	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
2007	MPI_SUM, comm1dx, ierr )
2008	#endif
2009	!
2010	!-- Compute standard deviation
2011	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2012	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2013	ELSE
2014	rand_sigma_inv = 1.0_wp
2015	ENDIF
2016	!
2017	!-- Normalize with standard deviation to obtain unit variance
2018	rand_it = rand_it * rand_sigma_inv
2019
2020	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2021	!
2022	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
2023	!-- are two options. In the first one, the computation of the seeds is
2024	!-- distributed to all processes along the communicator comm1dx and
2025	!-- gathered on the southmost and, if necessary, on the northmost process.
2026	!-- For huge length scales the computational effort can become quite huge
2027	!-- (it scales with the turbulent length scales), so that gain by parallelization
2028	!-- exceeds the costs by the subsequent communication.
2029	!-- In the second option, which performs better when the turbulent length scales
2030	!-- are parametrized and thus the loops are smaller, the seeds are computed
2031	!-- locally and no communication is necessary.
2032	IF ( compute_velocity_seeds_local ) THEN
2033
2034	f_n = 0.0_wp
2035	DO i = nxl, nxr
2036	DO k = nzb, nzt+1
2037	DO ii = -n_x(k), n_x(k)
2038	DO kk = -n_z(k), n_z(k)
2039	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2040	ENDDO
2041	ENDDO
2042	ENDDO
2043	ENDDO
2044
2045	ELSE
2046
2047	f_n_l = 0.0_wp
2048	DO i = nxl, nxr
2049	DO k = nzb_y_stg, nzt_y_stg+1
2050	DO ii = -n_x(k), n_x(k)
2051	DO kk = -n_z(k), n_z(k)
2052	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2053	ENDDO
2054	ENDDO
2055	ENDDO
2056	ENDDO
2057	!
2058	!-- Gather velocity seeds of full subdomain
2059	send_count = nzt_y_stg - nzb_y_stg + 1
2060	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2061
2062	#if defined( __parallel )
2063	!
2064	!-- Gather the processed velocity seed on south boundary mpi ranks.
2065	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2066	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2067	id_south, comm1dy, ierr )
2068	!
2069	!-- Gather the processed velocity seed on north boundary mpi ranks.
2070	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2071	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2072	id_north, comm1dy, ierr )
2073	#else
2074	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2075	#endif
2076
2077	ENDIF
2078
2079	DEALLOCATE( rand_it )
2080
2081	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2082
2083	END SUBROUTINE stg_generate_seed_xz
2084
2085	!------------------------------------------------------------------------------!
2086	! Description:
2087	! ------------
2088	!> Parametrization of the Reynolds stress tensor, following the parametrization
2089	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2090	!> dispserion modelling. Please note, the parametrization does not distinguish
2091	!> between along-wind and cross-wind turbulence.
2092	!------------------------------------------------------------------------------!
2093	SUBROUTINE parametrize_reynolds_stress
2094
2095	INTEGER(iwp) :: k !< loop index in z-direction
2096
2097	REAL(wp) :: zzi !< ratio of z/zi
2098
2099	DO k = nzb+1, nzt+1
2100	!
2101	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2102	!-- The function decreases to 1/10 after one length scale above the
2103	!-- ABL top.
2104	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2105	!
2106	!-- Determine normalized height coordinate
2107	zzi = zu(k) / zi_ribulk
2108	!
2109	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2110	!-- to the denominator, else the mergpe-function can crash if scale_l is
2111	!-- zero.
2112	r11(k) = scale_us*2 ( &
2113	MERGE( 0.35_wp * ABS( &
2114	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2115	)**( 2.0_wp / 3.0_wp ), &
2116	0.0_wp, &
2117	scale_l < 0.0_wp ) &
2118	+ 5.0_wp - 4.0_wp * zzi &
2119	) * blend
2120
2121	r22(k) = r11(k)
2122	!
2123	!-- w'w'
2124	r33(k) = scale_wm*2 ( &
2125	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2126	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2127	) * blend
2128	!
2129	!-- u'w' and v'w'. Assume isotropy.
2130	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2131	r32(k) = r31(k)
2132	!
2133	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2134	!-- a similar profile as for u'w'.
2135	r21(k) = r31(k)
2136	ENDDO
2137
2138	!
2139	!-- Set bottom boundary condition
2140	r11(nzb) = r11(nzb+1)
2141	r22(nzb) = r22(nzb+1)
2142	r33(nzb) = r33(nzb+1)
2143
2144	r21(nzb) = r11(nzb+1)
2145	r31(nzb) = r31(nzb+1)
2146	r32(nzb) = r32(nzb+1)
2147
2148
2149	END SUBROUTINE parametrize_reynolds_stress
2150
2151	!------------------------------------------------------------------------------!
2152	! Description:
2153	! ------------
2154	!> Calculate the coefficient matrix from the Lund rotation.
2155	!------------------------------------------------------------------------------!
2156	SUBROUTINE calc_coeff_matrix
2157
2158	INTEGER(iwp) :: k !< loop index in z-direction
2159
2160	!
2161	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2162	DO k = nzb+1, nzt+1
2163	IF ( r11(k) > 10E-6_wp ) THEN
2164	a11(k) = SQRT( r11(k) )
2165	a21(k) = r21(k) / a11(k)
2166	a31(k) = r31(k) / a11(k)
2167	ELSE
2168	a11(k) = 10E-8_wp
2169	a21(k) = 10E-8_wp
2170	a31(k) = 10E-8_wp
2171	ENDIF
2172	ENDDO
2173	DO k = nzb+1, nzt+1
2174	a22(k) = r22(k) - a21(k)**2
2175	IF ( a22(k) > 10E-6_wp ) THEN
2176	a22(k) = SQRT( a22(k) )
2177	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2178	ELSE
2179	a22(k) = 10E-8_wp
2180	a32(k) = 10E-8_wp
2181	ENDIF
2182	ENDDO
2183	DO k = nzb+1, nzt+1
2184	a33(k) = r33(k) - a31(k)2 - a32(k)2
2185	IF ( a33(k) > 10E-6_wp ) THEN
2186	a33(k) = SQRT( a33(k) )
2187	ELSE
2188	a33(k) = 10E-8_wp
2189	ENDIF
2190	ENDDO
2191	!
2192	!-- Set bottom boundary condition
2193	a11(nzb) = a11(nzb+1)
2194	a22(nzb) = a22(nzb+1)
2195	a21(nzb) = a21(nzb+1)
2196	a33(nzb) = a33(nzb+1)
2197	a31(nzb) = a31(nzb+1)
2198	a32(nzb) = a32(nzb+1)
2199
2200	END SUBROUTINE calc_coeff_matrix
2201
2202	!------------------------------------------------------------------------------!
2203	! Description:
2204	! ------------
2205	!> This routine controls the re-adjustment of the turbulence statistics used
2206	!> for generating turbulence at the lateral boundaries.
2207	!------------------------------------------------------------------------------!
2208	SUBROUTINE stg_adjust
2209
2210	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2211	!
2212	!-- In case of dirichlet inflow boundary conditions only at one lateral
2213	!-- boundary, i.e. in the case no offline or self nesting is applied but
2214	!-- synthetic turbulence shall be parametrized nevertheless, the
2215	!-- boundary-layer depth need to determined first.
2216	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2217	CALL nesting_offl_calc_zi
2218	!
2219	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2220	!-- are calculated.
2221	CALL calc_scaling_variables
2222	!
2223	!-- Set length and time scales depending on boundary-layer height
2224	CALL calc_length_and_time_scale
2225	!
2226	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2227	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2228	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2229	!-- friction velocity and velocity scale.
2230	CALL parametrize_reynolds_stress
2231	!
2232	!-- Calculate coefficient matrix from Reynolds stress tensor
2233	!-- (Lund rotation)
2234	CALL calc_coeff_matrix
2235	!
2236	!-- Determine filter functions on basis of updated length scales
2237	CALL stg_filter_func( nux, bux ) !filter ux
2238	CALL stg_filter_func( nuy, buy ) !filter uy
2239	CALL stg_filter_func( nuz, buz ) !filter uz
2240	CALL stg_filter_func( nvx, bvx ) !filter vx
2241	CALL stg_filter_func( nvy, bvy ) !filter vy
2242	CALL stg_filter_func( nvz, bvz ) !filter vz
2243	CALL stg_filter_func( nwx, bwx ) !filter wx
2244	CALL stg_filter_func( nwy, bwy ) !filter wy
2245	CALL stg_filter_func( nwz, bwz ) !filter wz
2246	!
2247	!-- Reset time counter for controlling next adjustment to zero
2248	time_stg_adjust = 0.0_wp
2249
2250	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2251
2252	END SUBROUTINE stg_adjust
2253
2254
2255	!------------------------------------------------------------------------------!
2256	! Description:
2257	! ------------
2258	!> Calculates turbuluent length and time scales if these are not available
2259	!> from measurements.
2260	!------------------------------------------------------------------------------!
2261	SUBROUTINE calc_length_and_time_scale
2262
2263	INTEGER(iwp) :: k !< loop index in z-direction
2264
2265	REAL(wp) :: length_scale_dum !< effectively used length scale
2266
2267	!
2268	!-- In initial call the boundary-layer depth can be zero. This case, set
2269	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2270	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2271	!
2272	!-- Set-up default turbulent length scales. From the numerical point of
2273	!-- view the imposed perturbations should not be immediately dissipated
2274	!-- by the numerics. The numerical dissipation, however, acts on scales
2275	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2276	!-- length scale to 8 time the grid spacing. Further, above the boundary
2277	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2278	!-- imposing any perturbations) in order to save computational costs.
2279	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2280	!-- using the length scales and the mean profiles of u- and v-component.
2281	DO k = nzb+1, nzt+1
2282	!
2283	!-- Determine blending parameter. Within the boundary layer length scales
2284	!-- are constant, while above lengths scales approach gradully zero,
2285	!-- i.e. imposed turbulence is not correlated in space and time,
2286	!-- just white noise, which saves computations power as the loops for the
2287	!-- computation of the filter functions depend on the length scales.
2288	!-- The value decreases to 1/10 after one length scale above the
2289	!-- ABL top.
2290	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2291	!
2292	!-- Assume isotropic turbulence length scales
2293	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2294	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2295	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2296	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2297	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2298	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2299	!
2300	!-- Along the vertical direction limit the length scale further by the
2301	!-- boundary-layer depth to assure that no length scales larger than
2302	!-- the boundary-layer depth are used
2303	length_scale_dum = MIN( length_scale, zi_ribulk )
2304
2305	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2306	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2307	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2308	!
2309	!-- Limit time scales, else they become very larger for low wind speed,
2310	!-- imposing long-living inflow perturbations which in turn propagate
2311	!-- further into the model domain. Use u_init and v_init to calculate
2312	!-- the time scales, which will be equal to the inflow profiles, both,
2313	!-- in offline nesting mode or in dirichlet/radiation mode.
2314	tu(k) = MIN( dt_stg_adjust, length_scale / &
2315	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2316	tv(k) = MIN( dt_stg_adjust, length_scale / &
2317	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2318	!
2319	!-- Time scale of w-component is a mixture from u- and v-component.
2320	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2321
2322	ENDDO
2323	!
2324	!-- Set bottom boundary condition for the length and time scales
2325	nux(nzb) = nux(nzb+1)
2326	nuy(nzb) = nuy(nzb+1)
2327	nuz(nzb) = nuz(nzb+1)
2328	nvx(nzb) = nvx(nzb+1)
2329	nvy(nzb) = nvy(nzb+1)
2330	nvz(nzb) = nvz(nzb+1)
2331	nwx(nzb) = nwx(nzb+1)
2332	nwy(nzb) = nwy(nzb+1)
2333	nwz(nzb) = nwz(nzb+1)
2334
2335	tu(nzb) = tu(nzb+1)
2336	tv(nzb) = tv(nzb+1)
2337	tw(nzb) = tw(nzb+1)
2338
2339
2340	END SUBROUTINE calc_length_and_time_scale
2341
2342	!------------------------------------------------------------------------------!
2343	! Description:
2344	! ------------
2345	!> Calculate scaling variables which are used for turbulence parametrization
2346	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2347	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2348	!------------------------------------------------------------------------------!
2349	SUBROUTINE calc_scaling_variables
2350
2351	INTEGER(iwp) :: i !< loop index in x-direction
2352	INTEGER(iwp) :: j !< loop index in y-direction
2353	INTEGER(iwp) :: k !< loop index in z-direction
2354	INTEGER(iwp) :: m !< surface element index
2355
2356	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2357	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2358	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2359	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2360	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2361	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2362	REAL(wp) :: w_convective !< convective velocity scale
2363
2364	!
2365	!-- Calculate mean friction velocity, velocity scale, heat flux and
2366	!-- near-surface temperature in the model domain.
2367	pt_surf_mean_l = 0.0_wp
2368	shf_mean_l = 0.0_wp
2369	scale_l_l = 0.0_wp
2370	friction_vel_l = 0.0_wp
2371	DO m = 1, surf_def_h(0)%ns
2372	i = surf_def_h(0)%i(m)
2373	j = surf_def_h(0)%j(m)
2374	k = surf_def_h(0)%k(m)
2375	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2376	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2377	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2378	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2379	ENDDO
2380	DO m = 1, surf_lsm_h%ns
2381	i = surf_lsm_h%i(m)
2382	j = surf_lsm_h%j(m)
2383	k = surf_lsm_h%k(m)
2384	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2385	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2386	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2387	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2388	ENDDO
2389	DO m = 1, surf_usm_h%ns
2390	i = surf_usm_h%i(m)
2391	j = surf_usm_h%j(m)
2392	k = surf_usm_h%k(m)
2393	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2394	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2395	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2396	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2397	ENDDO
2398
2399	#if defined( __parallel )
2400	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2401	comm2d, ierr )
2402	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2403	comm2d, ierr )
2404	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2405	comm2d, ierr )
2406	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2407	comm2d, ierr )
2408	#else
2409	scale_us = friction_vel_l
2410	shf_mean = shf_mean_l
2411	scale_l = scale_l_l
2412	pt_surf_mean = pt_surf_mean_l
2413	#endif
2414
2415	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2416	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2417	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2418	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2419	!
2420	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2421	!-- is negative, set convective velocity scale to zero.
2422	IF ( shf_mean > 0.0_wp ) THEN
2423	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2424	ELSE
2425	w_convective = 0.0_wp
2426	ENDIF
2427	!
2428	!-- Finally, in order to consider also neutral or stable stratification,
2429	!-- compute momentum velocity scale from u* and convective velocity scale,
2430	!-- according to Rotach et al. (1996).
2431	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2432
2433	END SUBROUTINE calc_scaling_variables
2434
2435	END MODULE synthetic_turbulence_generator_mod

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