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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4447

Last change on this file since 4447 was 4444, checked in by raasch, 5 years ago
bugfix: cpp-directives for serial mode added
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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 4444 2020-03-05 15:59:50Z oliver.maas $
27	! bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
28	!
29	! 4442 2020-03-04 19:21:13Z suehring
30	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
31	! (was accidantly changed).
32	!
33	! 4441 2020-03-04 19:20:35Z suehring
34	! Correct misplaced preprocessor directive
35	!
36	! 4438 2020-03-03 20:49:28Z suehring
37	! Performance optimizations in velocity-seed calculation:
38	! - random number array is only defined and computed locally (except for
39	! normalization to zero mean and unit variance)
40	! - parallel random number generator is applied independent on the 2D random
41	! numbers in other routines
42	! - option to decide wheter velocity seeds are computed locally without any
43	! further communication or are computed by all processes along the
44	! communicator
45	!
46	! 4346 2019-12-18 11:55:56Z motisi
47	! Introduction of wall_flags_total_0, which currently sets bits based on static
48	! topography information used in wall_flags_static_0
49	!
50	! 4335 2019-12-12 16:39:05Z suehring
51	! Commentation of last commit
52	!
53	! 4332 2019-12-10 19:44:12Z suehring
54	! Limit initial velocity seeds in restart runs, if not the seed calculation
55	! may become unstable. Further, minor bugfix in initial velocity seed
56	! calculation.
57	!
58	! 4329 2019-12-10 15:46:36Z motisi
59	! Renamed wall_flags_0 to wall_flags_static_0
60	!
61	! 4309 2019-11-26 18:49:59Z suehring
62	! Computation of velocity seeds optimized. This implies that random numbers
63	! are computed now using the parallel random number generator. Random numbers
64	! are now only computed and normalized locally, while distributed over all
65	! mpi ranks afterwards, instead of computing random numbers on a global array.
66	! Further, the number of calls for the time-consuming velocity-seed generation
67	! is reduced - now the left and right, as well as the north and south boundary
68	! share the same velocity-seed matrices.
69	!
70	! 4182 2019-08-22 15:20:23Z scharf
71	! Corrected "Former revisions" section
72	!
73	! 4148 2019-08-08 11:26:00Z suehring
74	! Remove unused variable
75	!
76	! 4144 2019-08-06 09:11:47Z raasch
77	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
78	!
79	! 4071 2019-07-03 20:02:00Z suehring
80	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
81	! information is not read from file.
82	!
83	! 4022 2019-06-12 11:52:39Z suehring
84	! Several bugfixes and improvements
85	! - revise bias correction of the imposed perturbations (correction via volume
86	! flow can create instabilities in case the mean volume flow is close to zero)
87	! - introduce lower limits in calculation of coefficient matrix, else the
88	! calculation may become numerically unstable
89	! - impose perturbations every timestep, even though no new set of perturbations
90	! is generated in case dt_stg_call /= dt_3d
91	! - Implement a gradual decrease of Reynolds stress and length scales above
92	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
93	! discontinuous decrease
94	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
95	!
96	! 3987 2019-05-22 09:52:13Z kanani
97	! Introduce alternative switch for debug output during timestepping
98	!
99	! 3938 2019-04-29 16:06:25Z suehring
100	! Remove unused variables
101	!
102	! 3937 2019-04-29 15:09:07Z suehring
103	! Minor bugfix in case of a very early restart where mc_factor is sill not
104	! present.
105	! Some modification and fixing of potential bugs in the calculation of scaling
106	! parameters used for synthetic turbulence parametrization.
107	!
108	! 3909 2019-04-17 09:13:25Z suehring
109	! Minor bugfix for last commit
110	!
111	! 3900 2019-04-16 15:17:43Z suehring
112	! Missing re-calculation of perturbation seeds in case of restarts
113	!
114	! 3891 2019-04-12 17:52:01Z suehring
115	! Bugfix in initialization in case of restart runs.
116	!
117	! 3885 2019-04-11 11:29:34Z kanani
118	! Changes related to global restructuring of location messages and introduction
119	! of additional debug messages
120	!
121	!
122	! removed unused variables
123	!
124	! 3719 2019-02-06 13:10:18Z kanani
125	! Removed log_point measurement from stg_init, since this part is counted to
126	! log_point(2) 'initialisation' already. Moved other log_points to calls of
127	! the subroutines in time_integration for better overview.
128	!
129	! 2259 2017-06-08 09:09:11Z gronemeier
130	! Initial revision
131	!
132	! Authors:
133	! --------
134	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
135	!
136	!
137	! Description:
138	! ------------
139	!> The module generates turbulence at the inflow boundary based on a method by
140	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
141	!> correction by Kim et al. (2013).
142	!> The turbulence is correlated based on length scales in y- and z-direction and
143	!> a time scale for each velocity component. The profiles of length and time
144	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
145	!> tensor can be either read from file STG_PROFILES, or will be parametrized
146	!> within the boundary layer.
147	!>
148	!> @todo test restart
149	!> enable cyclic_fill
150	!> implement turbulence generation for e and pt
151	!> @todo Input of height-constant length scales via namelist
152	!> @note <Enter notes on the module>
153	!> @bug Height information from input file is not used. Profiles from input
154	!> must match with current PALM grid.
155	!> In case of restart, velocity seeds differ from precursor run if a11,
156	!> a22, or a33 are zero.
157	!------------------------------------------------------------------------------!
158	MODULE synthetic_turbulence_generator_mod
159
160
161	USE arrays_3d, &
162	ONLY: dzw, &
163	ddzw, &
164	drho_air, &
165	mean_inflow_profiles, &
166	q, &
167	q_init, &
168	pt, &
169	pt_init, &
170	u, &
171	u_init, &
172	v, &
173	v_init, &
174	w, &
175	zu, &
176	zw
177
178	USE basic_constants_and_equations_mod, &
179	ONLY: g, &
180	kappa, &
181	pi
182
183	USE control_parameters, &
184	ONLY: bc_lr, &
185	bc_ns, &
186	child_domain, &
187	coupling_char, &
188	debug_output_timestep, &
189	dt_3d, &
190	e_init, &
191	humidity, &
192	initializing_actions, &
193	intermediate_timestep_count, &
194	intermediate_timestep_count_max, &
195	length, &
196	message_string, &
197	nesting_offline, &
198	neutral, &
199	num_mean_inflow_profiles, &
200	random_generator, &
201	rans_mode, &
202	restart_string, &
203	syn_turb_gen, &
204	time_since_reference_point, &
205	turbulent_inflow
206
207	USE cpulog, &
208	ONLY: cpu_log, &
209	log_point_s
210
211	USE grid_variables, &
212	ONLY: ddx, &
213	ddy, &
214	dx, &
215	dy
216
217	USE indices, &
218	ONLY: nbgp, &
219	nz, &
220	nzb, &
221	nzt, &
222	nx, &
223	nxl, &
224	nxlu, &
225	nxr, &
226	ny, &
227	nys, &
228	nysv, &
229	nyn, &
230	wall_flags_total_0
231
232	USE kinds
233
234	#if defined( __parallel ) && !defined( __mpifh )
235	USE MPI
236	#endif
237
238	USE nesting_offl_mod, &
239	ONLY: nesting_offl_calc_zi, &
240	zi_ribulk
241
242	USE pegrid, &
243	ONLY: comm1dx, &
244	comm1dy, &
245	comm2d, &
246	ierr, &
247	myidx, &
248	myidy, &
249	pdims
250
251	USE pmc_interface, &
252	ONLY : rans_mode_parent
253
254	USE random_generator_parallel, &
255	ONLY: init_parallel_random_generator, &
256	random_dummy, &
257	random_number_parallel, &
258	random_seed_parallel
259
260	USE transpose_indices, &
261	ONLY: nzb_x, &
262	nzt_x
263
264	USE surface_mod, &
265	ONLY: surf_def_h, &
266	surf_lsm_h, &
267	surf_usm_h
268
269	IMPLICIT NONE
270
271	#if defined( __parallel ) && defined( __mpifh )
272	INCLUDE "mpif.h"
273	#endif
274
275
276	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
277	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
278	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
279	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
280	!< is distributed over several processes
281
282	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
283	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
284	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
285	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
286	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
287	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
288	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
289	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
290	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
291	#if defined( __parallel )
292	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
293	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
294	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
295	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
296	#endif
297
298	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
299	!< required for bias correction of imposed perturbations
300	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
301	!< required for bias correction of imposed perturbations
302
303	#if defined( __parallel )
304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
308	#endif
309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
311	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
312	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
313	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
314	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
318
319	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
320	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
321	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
322	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
323
324	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
325	!< scales above the boundary layer
326	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
327	!< one length scale above ABL top
328	REAL(wp) :: d_l !< blend_coeff/length_scale
329	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
330	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
331	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
332	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
333	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
334	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
335	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
336	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
337
338	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
339
340
341	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
342	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
343	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
344	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
345	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
346	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
347
348	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
349	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
350	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
351	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
352	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
353	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
354	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
355	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
356	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
357
358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
379
380	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
381	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
382
383	!
384	!-- PALM interfaces:
385	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
386	INTERFACE stg_adjust
387	MODULE PROCEDURE stg_adjust
388	END INTERFACE stg_adjust
389	!
390	!-- Input parameter checks to be done in check_parameters
391	INTERFACE stg_check_parameters
392	MODULE PROCEDURE stg_check_parameters
393	END INTERFACE stg_check_parameters
394
395	!
396	!-- Calculate filter functions
397	INTERFACE stg_filter_func
398	MODULE PROCEDURE stg_filter_func
399	END INTERFACE stg_filter_func
400
401	!
402	!-- Generate velocity seeds at south and north domain boundary
403	INTERFACE stg_generate_seed_xz
404	MODULE PROCEDURE stg_generate_seed_xz
405	END INTERFACE stg_generate_seed_xz
406	!
407	!-- Generate velocity seeds at left and/or right domain boundary
408	INTERFACE stg_generate_seed_yz
409	MODULE PROCEDURE stg_generate_seed_yz
410	END INTERFACE stg_generate_seed_yz
411
412	!
413	!-- Output of information to the header file
414	INTERFACE stg_header
415	MODULE PROCEDURE stg_header
416	END INTERFACE stg_header
417
418	!
419	!-- Initialization actions
420	INTERFACE stg_init
421	MODULE PROCEDURE stg_init
422	END INTERFACE stg_init
423
424	!
425	!-- Main procedure of synth. turb. gen.
426	INTERFACE stg_main
427	MODULE PROCEDURE stg_main
428	END INTERFACE stg_main
429
430	!
431	!-- Reading of NAMELIST parameters
432	INTERFACE stg_parin
433	MODULE PROCEDURE stg_parin
434	END INTERFACE stg_parin
435
436	!
437	!-- Reading of parameters for restart runs
438	INTERFACE stg_rrd_global
439	MODULE PROCEDURE stg_rrd_global
440	END INTERFACE stg_rrd_global
441
442	!
443	!-- Writing of binary output for restart runs
444	INTERFACE stg_wrd_global
445	MODULE PROCEDURE stg_wrd_global
446	END INTERFACE stg_wrd_global
447
448	SAVE
449
450	PRIVATE
451
452	!
453	!-- Public interfaces
454	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
455	stg_parin, stg_rrd_global, stg_wrd_global
456
457	!
458	!-- Public variables
459	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
460	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
461	time_stg_adjust, time_stg_call, use_syn_turb_gen
462
463
464	CONTAINS
465
466
467	!------------------------------------------------------------------------------!
468	! Description:
469	! ------------
470	!> Check parameters routine for synthetic turbulence generator
471	!------------------------------------------------------------------------------!
472	SUBROUTINE stg_check_parameters
473
474	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
475	nesting_offline ) THEN
476	message_string = 'Synthetic turbulence generator is required ' // &
477	'if offline nesting is applied and PALM operates ' // &
478	'in LES mode.'
479	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
480	ENDIF
481
482	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
483	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
484	message_string = 'Synthetic turbulence generator is required ' // &
485	'when nesting is applied and parent operates in ' // &
486	'RANS-mode but current child in LES mode.'
487	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
488	ENDIF
489
490	IF ( use_syn_turb_gen ) THEN
491
492	IF ( child_domain .AND. .NOT. rans_mode .AND. &
493	.NOT. rans_mode_parent ) THEN
494	message_string = 'Using synthetic turbulence generator ' // &
495	'is not allowed in LES-LES nesting.'
496	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
497
498	ENDIF
499
500	IF ( child_domain .AND. rans_mode .AND. &
501	rans_mode_parent ) THEN
502	message_string = 'Using synthetic turbulence generator ' // &
503	'is not allowed in RANS-RANS nesting.'
504	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
505
506	ENDIF
507
508	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
509
510	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
511	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
512	message_string = 'Using synthetic turbulence generator ' // &
513	'requires %initializing_actions = ' // &
514	'"set_constant_profiles" or "read_restart_data"' //&
515	', if not offline nesting is applied.'
516	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
517	ENDIF
518
519	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
520	message_string = 'Using synthetic turbulence generator ' // &
521	'requires &bc_lr = "dirichlet/radiation", ' // &
522	'if not offline nesting is applied.'
523	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
524	ENDIF
525	IF ( bc_ns /= 'cyclic' ) THEN
526	message_string = 'Using synthetic turbulence generator ' // &
527	'requires &bc_ns = "cyclic", ' // &
528	'if not offline nesting is applied.'
529	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
530	ENDIF
531
532	ENDIF
533
534	IF ( turbulent_inflow ) THEN
535	message_string = 'Using synthetic turbulence generator ' // &
536	'in combination &with turbulent_inflow = .T. '// &
537	'is not allowed'
538	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
539	ENDIF
540	!
541	!-- Synthetic turbulence generator requires the parallel random generator
542	IF ( random_generator /= 'random-parallel' ) THEN
543	message_string = 'Using synthetic turbulence generator ' // &
544	'requires random_generator = random-parallel.'
545	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
546	ENDIF
547
548	ENDIF
549
550	END SUBROUTINE stg_check_parameters
551
552
553	!------------------------------------------------------------------------------!
554	! Description:
555	! ------------
556	!> Header output for synthetic turbulence generator
557	!------------------------------------------------------------------------------!
558	SUBROUTINE stg_header ( io )
559
560	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
561
562	!
563	!-- Write synthetic turbulence generator Header
564	WRITE( io, 1 )
565	IF ( use_syn_turb_gen ) THEN
566	WRITE( io, 2 )
567	ELSE
568	WRITE( io, 3 )
569	ENDIF
570
571	IF ( parametrize_inflow_turbulence ) THEN
572	WRITE( io, 4 ) dt_stg_adjust
573	ELSE
574	WRITE( io, 5 )
575	ENDIF
576
577	1 FORMAT (//' Synthetic turbulence generator information:'/ &
578	' ------------------------------------------'/)
579	2 FORMAT (' synthetic turbulence generator is switched on')
580	3 FORMAT (' synthetic turbulence generator is switched off')
581	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
582	5 FORMAT (' imposed turbulence is read from file' )
583
584	END SUBROUTINE stg_header
585
586
587	!------------------------------------------------------------------------------!
588	! Description:
589	! ------------
590	!> Initialization of the synthetic turbulence generator
591	!------------------------------------------------------------------------------!
592	SUBROUTINE stg_init
593
594	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
595
596	#if defined( __parallel )
597	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
598	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
599	#endif
600
601	INTEGER(iwp) :: i !> grid index in x-direction
602	INTEGER(iwp) :: j !> loop index
603	INTEGER(iwp) :: k !< index
604	#if defined( __parallel )
605	INTEGER(iwp) :: newtype !< dummy MPI type
606	INTEGER(iwp) :: realsize !< size of REAL variables
607	#endif
608
609	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
610	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
611	!
612	!-- Dummy variables used for reading profiles
613	REAL(wp) :: d1 !< u profile
614	REAL(wp) :: d2 !< v profile
615	REAL(wp) :: d3 !< w profile
616	REAL(wp) :: d5 !< e profile
617	REAL(wp) :: luy !< length scale for u in y direction
618	REAL(wp) :: luz !< length scale for u in z direction
619	REAL(wp) :: lvy !< length scale for v in y direction
620	REAL(wp) :: lvz !< length scale for v in z direction
621	REAL(wp) :: lwy !< length scale for w in y direction
622	REAL(wp) :: lwz !< length scale for w in z direction
623	#if defined( __parallel )
624	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
625	#endif
626	REAL(wp) :: zz !< height
627
628
629	#if defined( __parallel )
630	CALL MPI_BARRIER( comm2d, ierr )
631	#endif
632	!
633	!-- Create mpi-datatypes for exchange in case of non-local but distributed
634	!-- computation of the velocity seeds. This option is useful in
635	!-- case large turbulent length scales are present, where the computational
636	!-- effort becomes large and need to be parallelized. For parameterized
637	!-- turbulence the length scales are small and computing the velocity seeds
638	!-- locally is faster (no overhead by communication).
639	IF ( .NOT. compute_velocity_seeds_local ) THEN
640	#if defined( __parallel )
641	!
642	!-- Determine processor decomposition of z-axis along x- and y-direction
643	nnz = nz / pdims(1)
644	nzb_x_stg = 1 + myidx * INT( nnz )
645	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
646
647	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
648	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
649
650	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
651	.AND. .NOT. rans_mode ) ) THEN
652	nnz = nz / pdims(2)
653	nzb_y_stg = 1 + myidy * INT( nnz )
654	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
655
656	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
657	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
658	ENDIF
659
660	!
661	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
662	!-- velocity seeds
663	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
664	extent = 1 * realsize
665	!
666	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
667	!-- layer
668	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
669	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
670	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
671	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
672	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
673	CALL MPI_TYPE_FREE( newtype, ierr )
674
675	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
676	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
677	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
678	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
679	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
680	CALL MPI_TYPE_FREE( newtype, ierr )
681
682	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
683	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
684
685	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
686	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
687
688	DO j = 1, pdims(1)
689	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
690	ENDDO
691	!
692	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
693	!-- layer
694	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
695	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
696	.AND. .NOT. rans_mode ) ) THEN
697	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
698	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
699	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
700	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
701	CALL MPI_TYPE_FREE( newtype, ierr )
702
703	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
704	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
705	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
706	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
707	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
708	CALL MPI_TYPE_FREE( newtype, ierr )
709
710	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
711	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
712
713	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
714	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
715
716	DO j = 1, pdims(2)
717	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
718	ENDDO
719
720	ENDIF
721	#endif
722	ENDIF
723	!
724	!-- Allocate required arrays.
725	!-- In case no offline nesting or self nesting is used, the arrary
726	!-- mean_inflow profiles is required. Check if it is already allocated, else
727	!-- allocate and initialize it appropriately. Note, in case turbulence and
728	!-- inflow information is read from file, mean_inflow_profiles is already
729	!-- allocated and initialized appropriately.
730	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
731	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
732	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
733	mean_inflow_profiles = 0.0_wp
734	mean_inflow_profiles(:,1) = u_init
735	mean_inflow_profiles(:,2) = v_init
736	!
737	!-- Even though potential temperature and humidity are not perturbed,
738	!-- they need to be initialized appropriately.
739	IF ( .NOT. neutral ) &
740	mean_inflow_profiles(:,4) = pt_init
741	IF ( humidity ) &
742	mean_inflow_profiles(:,6) = q_init
743	ENDIF
744	ENDIF
745
746	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
747	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
748	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
749	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
750	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
751	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
752	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
753	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
754
755	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
756	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
757	dist_xz = 0.0_wp
758	dist_yz = 0.0_wp
759	!
760	!-- Read inflow profile
761	!-- Height levels of profiles in input profile is as follows:
762	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
763	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
764	!-- WARNING: zz is not used at the moment
765	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
766	EXIST = file_stg_exist )
767
768	IF ( file_stg_exist ) THEN
769
770	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
771	FORM='FORMATTED')
772	!
773	!-- Skip header
774	READ( 90, * )
775
776	DO k = nzb+1, nzt+1
777	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
778	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
779	d1, d2, d3, d5
780
781	!
782	!-- Convert length scales from meter to number of grid points.
783	nuy(k) = INT( luy * ddy )
784	nuz(k) = INT( luz * ddzw(k) )
785	nvy(k) = INT( lvy * ddy )
786	nvz(k) = INT( lvz * ddzw(k) )
787	nwy(k) = INT( lwy * ddy )
788	nwz(k) = INT( lwz * ddzw(k) )
789	!
790	!-- Workaround, assume isotropic turbulence
791	nwx(k) = nwy(k)
792	nvx(k) = nvy(k)
793	nux(k) = nuy(k)
794	!
795	!-- Save Mean inflow profiles
796	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
797	mean_inflow_profiles(k,1) = d1
798	mean_inflow_profiles(k,2) = d2
799	! mean_inflow_profiles(k,4) = d4
800	mean_inflow_profiles(k,5) = d5
801	ENDIF
802	ENDDO
803	!
804	!-- Set lenght scales at surface grid point
805	nuy(nzb) = nuy(nzb+1)
806	nuz(nzb) = nuz(nzb+1)
807	nvy(nzb) = nvy(nzb+1)
808	nvz(nzb) = nvz(nzb+1)
809	nwy(nzb) = nwy(nzb+1)
810	nwz(nzb) = nwz(nzb+1)
811
812	CLOSE( 90 )
813	!
814	!-- Calculate coefficient matrix from Reynolds stress tensor
815	!-- (Lund rotation)
816	CALL calc_coeff_matrix
817	!
818	!-- No information about turbulence and its length scales are available.
819	!-- Instead, parametrize turbulence which is imposed at the boundaries.
820	!-- Set flag which indicates that turbulence is parametrized, which is done
821	!-- later when energy-balance models are already initialized. This is
822	!-- because the STG needs information about surface properties such as
823	!-- roughness to build 'realistic' turbulence profiles.
824	ELSE
825	!
826	!-- Define length scale for the imposed turbulence, which is defined as
827	!-- 8 times the minimum grid spacing
828	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
829	!
830	!-- Define constant to gradually decrease length scales and Reynolds stress
831	!-- above ABL top. Assure that no zero length scales are used.
832	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
833	!
834	!-- Set flag indicating that turbulence is parametrized
835	parametrize_inflow_turbulence = .TRUE.
836	!
837	!-- In case of dirichlet inflow boundary conditions only at one lateral
838	!-- boundary, i.e. in the case no offline or self nesting is applied but
839	!-- synthetic turbulence shall be parametrized nevertheless, the
840	!-- boundary-layer depth need to determined first.
841	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
842	CALL nesting_offl_calc_zi
843	!
844	!-- Determine boundary-layer depth, which is used to initialize lenght
845	!-- scales
846	CALL calc_scaling_variables
847	!
848	!-- Initialize lenght and time scales, which in turn are used
849	!-- to initialize the filter functions.
850	CALL calc_length_and_time_scale
851	!
852	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
853	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
854	!-- Rotach et al. (1996) and is based on boundary-layer depth,
855	!-- friction velocity and velocity scale.
856	CALL parametrize_reynolds_stress
857	!
858	!-- Calculate coefficient matrix from Reynolds stress tensor
859	!-- (Lund rotation)
860	CALL calc_coeff_matrix
861
862	ENDIF
863
864	!
865	!-- Assign initial profiles. Note, this is only required if turbulent
866	!-- inflow from the left is desired, not in case of any of the
867	!-- nesting (offline or self nesting) approaches.
868	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
869	u_init = mean_inflow_profiles(:,1)
870	v_init = mean_inflow_profiles(:,2)
871	!pt_init = mean_inflow_profiles(:,4)
872	e_init = MAXVAL( mean_inflow_profiles(:,5) )
873	ENDIF
874
875	!
876	!-- Define the size of the filter functions and allocate them.
877	mergp = 0
878
879	! arrays must be large enough to cover the largest length scale
880	DO k = nzb, nzt+1
881	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
882	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
883	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
884	IF ( j > mergp ) mergp = j
885	ENDDO
886
887	! mergp = 2 * mergp
888	! mergp = mergp
889
890	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
891	buy(-mergp:mergp,nzb:nzt+1), &
892	buz(-mergp:mergp,nzb:nzt+1), &
893	bvx(-mergp:mergp,nzb:nzt+1), &
894	bvy(-mergp:mergp,nzb:nzt+1), &
895	bvz(-mergp:mergp,nzb:nzt+1), &
896	bwx(-mergp:mergp,nzb:nzt+1), &
897	bwy(-mergp:mergp,nzb:nzt+1), &
898	bwz(-mergp:mergp,nzb:nzt+1) )
899
900	!
901	!-- Allocate velocity seeds for turbulence at xz-layer
902	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
903	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
904	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
905
906	!
907	!-- Allocate velocity seeds for turbulence at yz-layer
908	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
909	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
910	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
911
912	fu_xz = 0.0_wp
913	fuo_xz = 0.0_wp
914	fv_xz = 0.0_wp
915	fvo_xz = 0.0_wp
916	fw_xz = 0.0_wp
917	fwo_xz = 0.0_wp
918
919	fu_yz = 0.0_wp
920	fuo_yz = 0.0_wp
921	fv_yz = 0.0_wp
922	fvo_yz = 0.0_wp
923	fw_yz = 0.0_wp
924	fwo_yz = 0.0_wp
925
926	!
927	!-- Create filter functions
928	CALL stg_filter_func( nux, bux ) !filter ux
929	CALL stg_filter_func( nuy, buy ) !filter uy
930	CALL stg_filter_func( nuz, buz ) !filter uz
931	CALL stg_filter_func( nvx, bvx ) !filter vx
932	CALL stg_filter_func( nvy, bvy ) !filter vy
933	CALL stg_filter_func( nvz, bvz ) !filter vz
934	CALL stg_filter_func( nwx, bwx ) !filter wx
935	CALL stg_filter_func( nwy, bwy ) !filter wy
936	CALL stg_filter_func( nwz, bwz ) !filter wz
937
938	#if defined( __parallel )
939	CALL MPI_BARRIER( comm2d, ierr )
940	#endif
941
942	!
943	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
944	! time step.
945	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
946	! are 0 compared to the prerun. This is mostly for k=nzt+1.
947	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
948	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
949
950	IF ( myidx == id_stg_left ) i = -1
951	IF ( myidx == id_stg_right ) i = nxr+1
952
953	DO j = nys, nyn
954	DO k = nzb, nzt+1
955	IF ( a11(k) > 10E-8_wp ) THEN
956	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
957	ELSE
958	fu_yz(k,j) = 10E-8_wp
959	ENDIF
960
961	IF ( a22(k) > 10E-8_wp ) THEN
962	fv_yz(k,j) = ( v(k,j,i) - &
963	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
964	ELSE
965	fv_yz(k,j) = 10E-8_wp
966	ENDIF
967
968	IF ( a33(k) > 10E-8_wp ) THEN
969	fw_yz(k,j) = ( w(k,j,i) - &
970	a31(k) * fu_yz(k,j) - a32(k) * &
971	fv_yz(k,j) ) / a33(k)
972	ELSE
973	fw_yz(k,j) = 10E-8_wp
974	ENDIF
975	ENDDO
976	ENDDO
977	ENDIF
978
979	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
980
981	IF ( myidy == id_stg_south ) j = -1
982	IF ( myidy == id_stg_north ) j = nyn+1
983
984	DO i = nxl, nxr
985	DO k = nzb, nzt+1
986	!
987	!-- In case the correlation coefficients are very small, the
988	!-- velocity seeds may become very large finally creating
989	!-- numerical instabilities in the synthetic turbulence generator.
990	!-- Empirically, a value of 10E-8 seems to be sufficient.
991	IF ( a11(k) > 10E-8_wp ) THEN
992	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
993	ELSE
994	fu_xz(k,i) = 10E-8_wp
995	ENDIF
996
997	IF ( a22(k) > 10E-8_wp ) THEN
998	fv_xz(k,i) = ( v(k,j,i) - &
999	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1000	ELSE
1001	fv_xz(k,i) = 10E-8_wp
1002	ENDIF
1003
1004	IF ( a33(k) > 10E-8_wp ) THEN
1005	fw_xz(k,i) = ( w(k,j,i) - &
1006	a31(k) * fu_xz(k,i) - &
1007	a32(k) * fv_xz(k,i) ) / a33(k)
1008	ELSE
1009	fw_xz(k,i) = 10E-8_wp
1010	ENDIF
1011
1012	ENDDO
1013	ENDDO
1014	ENDIF
1015	ENDIF
1016	!
1017	!-- Count the number of non-topography grid points at the boundaries where
1018	!-- perturbations are imposed. This number is later used for bias corrections
1019	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1020	!-- due to the asymetry of u and v along x and y direction, respectively,
1021	!-- different cases must be distinguished.
1022	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1023	!
1024	!-- Number of grid points where perturbations are imposed on u
1025	IF ( myidx == id_stg_left ) i = nxl
1026	IF ( myidx == id_stg_right ) i = nxr+1
1027
1028	nr_non_topo_yz_l(1) = SUM( &
1029	MERGE( 1, 0, &
1030	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1031	!
1032	!-- Number of grid points where perturbations are imposed on v and w
1033	IF ( myidx == id_stg_left ) i = nxl-1
1034	IF ( myidx == id_stg_right ) i = nxr+1
1035
1036	nr_non_topo_yz_l(2) = SUM( &
1037	MERGE( 1, 0, &
1038	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1039	nr_non_topo_yz_l(3) = SUM( &
1040	MERGE( 1, 0, &
1041	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1042
1043	#if defined( __parallel )
1044	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1045	MPI_SUM, comm1dy, ierr )
1046	#else
1047	nr_non_topo_yz = nr_non_topo_yz_l
1048	#endif
1049	ENDIF
1050
1051	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1052	!
1053	!-- Number of grid points where perturbations are imposed on v
1054	IF ( myidy == id_stg_south ) j = nys
1055	IF ( myidy == id_stg_north ) j = nyn+1
1056
1057	nr_non_topo_xz_l(2) = SUM( &
1058	MERGE( 1, 0, &
1059	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1060	!
1061	!-- Number of grid points where perturbations are imposed on u and w
1062	IF ( myidy == id_stg_south ) j = nys-1
1063	IF ( myidy == id_stg_north ) j = nyn+1
1064
1065	nr_non_topo_xz_l(1) = SUM( &
1066	MERGE( 1, 0, &
1067	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1068	nr_non_topo_xz_l(3) = SUM( &
1069	MERGE( 1, 0, &
1070	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1071
1072	#if defined( __parallel )
1073	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1074	MPI_SUM, comm1dx, ierr )
1075	#else
1076	nr_non_topo_xz = nr_non_topo_xz_l
1077	#endif
1078	ENDIF
1079	!
1080	!-- Initialize random number generator at xz- and yz-layers. Random numbers
1081	!-- are initialized at each core. In case there is only inflow from the left,
1082	!-- it is sufficient to generate only random numbers for the yz-layer, else
1083	!-- random numbers for the xz-layer are also required.
1084	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1085	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1086	id_rand_yz = 0
1087	seq_rand_yz = 0
1088
1089	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
1090	id_rand_yz, seq_rand_yz )
1091
1092	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1093	.AND. .NOT. rans_mode ) ) THEN
1094	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1095	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1096	id_rand_xz = 0
1097	seq_rand_xz = 0
1098
1099	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
1100	id_rand_xz, seq_rand_xz )
1101	ENDIF
1102
1103
1104
1105	END SUBROUTINE stg_init
1106
1107
1108	!------------------------------------------------------------------------------!
1109	! Description:
1110	! ------------
1111	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1112	!> (Xie and Castro, 2008)
1113	!------------------------------------------------------------------------------!
1114	SUBROUTINE stg_filter_func( nxx, bxx )
1115
1116	INTEGER(iwp) :: k !< loop index
1117	INTEGER(iwp) :: n_k !< length scale nXX in height k
1118	INTEGER(iwp) :: nf !< index for length scales
1119
1120	REAL(wp) :: bdenom !< denominator for filter functions bXX
1121	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1122
1123	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1124
1125	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1126
1127
1128	bxx = 0.0_wp
1129
1130	DO k = nzb, nzt+1
1131	bdenom = 0.0_wp
1132	n_k = nxx(k)
1133	IF ( n_k /= 0 ) THEN
1134
1135	!
1136	!-- ( Eq.10 )^2
1137	DO nf = -n_k, n_k
1138	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1139	ENDDO
1140
1141	!
1142	!-- ( Eq.9 )
1143	bdenom = SQRT( bdenom )
1144	DO nf = -n_k, n_k
1145	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1146	ENDDO
1147	ENDIF
1148	ENDDO
1149
1150	END SUBROUTINE stg_filter_func
1151
1152
1153	!------------------------------------------------------------------------------!
1154	! Description:
1155	! ------------
1156	!> Parin for &stg_par for synthetic turbulence generator
1157	!------------------------------------------------------------------------------!
1158	SUBROUTINE stg_parin
1159
1160	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1161
1162
1163	NAMELIST /stg_par/ dt_stg_adjust, &
1164	dt_stg_call, &
1165	use_syn_turb_gen, &
1166	compute_velocity_seeds_local
1167
1168	line = ' '
1169	!
1170	!-- Try to find stg package
1171	REWIND ( 11 )
1172	line = ' '
1173	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1174	READ ( 11, '(A)', END=20 ) line
1175	ENDDO
1176	BACKSPACE ( 11 )
1177
1178	!
1179	!-- Read namelist
1180	READ ( 11, stg_par, ERR = 10, END = 20 )
1181
1182	!
1183	!-- Set flag that indicates that the synthetic turbulence generator is switched
1184	!-- on
1185	syn_turb_gen = .TRUE.
1186	GOTO 20
1187
1188	10 BACKSPACE( 11 )
1189	READ( 11 , '(A)') line
1190	CALL parin_fail_message( 'stg_par', line )
1191
1192	20 CONTINUE
1193
1194	END SUBROUTINE stg_parin
1195
1196
1197	!------------------------------------------------------------------------------!
1198	! Description:
1199	! ------------
1200	!> This routine reads the respective restart data.
1201	!------------------------------------------------------------------------------!
1202	SUBROUTINE stg_rrd_global( found )
1203
1204	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1205
1206	found = .TRUE.
1207
1208
1209	SELECT CASE ( restart_string(1:length) )
1210
1211	CASE ( 'time_stg_adjust' )
1212	READ ( 13 ) time_stg_adjust
1213
1214	CASE ( 'time_stg_call' )
1215	READ ( 13 ) time_stg_call
1216
1217	CASE ( 'use_syn_turb_gen' )
1218	READ ( 13 ) use_syn_turb_gen
1219
1220	CASE DEFAULT
1221
1222	found = .FALSE.
1223
1224	END SELECT
1225
1226
1227	END SUBROUTINE stg_rrd_global
1228
1229
1230	!------------------------------------------------------------------------------!
1231	! Description:
1232	! ------------
1233	!> This routine writes the respective restart data.
1234	!------------------------------------------------------------------------------!
1235	SUBROUTINE stg_wrd_global
1236
1237	CALL wrd_write_string( 'time_stg_adjust' )
1238	WRITE ( 14 ) time_stg_adjust
1239
1240	CALL wrd_write_string( 'time_stg_call' )
1241	WRITE ( 14 ) time_stg_call
1242
1243	CALL wrd_write_string( 'use_syn_turb_gen' )
1244	WRITE ( 14 ) use_syn_turb_gen
1245
1246
1247	END SUBROUTINE stg_wrd_global
1248
1249
1250	!------------------------------------------------------------------------------!
1251	! Description:
1252	! ------------
1253	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1254	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1255	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1256	!> (Lund, 1998).
1257	!------------------------------------------------------------------------------!
1258	SUBROUTINE stg_main
1259
1260	INTEGER(iwp) :: i !< grid index in x-direction
1261	INTEGER(iwp) :: j !< loop index in y-direction
1262	INTEGER(iwp) :: k !< loop index in z-direction
1263
1264	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1265
1266	REAL(wp) :: dt_stg !< wheighted subtimestep
1267
1268	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1269
1270	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1271	!
1272	!-- Calculate time step which is needed for filter functions
1273	dt_stg = MAX( dt_3d, dt_stg_call )
1274	!
1275	!-- Check if synthetic turbulence generator needs to be called and new
1276	!-- perturbations need to be created or if old disturbances can be imposed
1277	!-- again.
1278	IF ( time_stg_call >= dt_stg_call .AND. &
1279	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1280	stg_call = .TRUE.
1281	ELSE
1282	stg_call = .FALSE.
1283	ENDIF
1284	!
1285	!-- Initial value of fu, fv, fw
1286	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1287	!
1288	!-- Generate turbulence at the left and right boundary. Random numbers
1289	!-- for the yz-planes at the left/right boundary are generated by the
1290	!-- left-sided mpi ranks only. After random numbers are calculated, they
1291	!-- are distributed to all other mpi ranks in the model, so that the
1292	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1293	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1294	!-- that the left- and the right-sided lateral boundary have the same initial
1295	!-- seeds.
1296	!-- Note, in case of inflow from the right only, only turbulence at the left
1297	!-- boundary is required.
1298	IF ( .NOT. ( nesting_offline .OR. &
1299	( child_domain .AND. rans_mode_parent &
1300	.AND. .NOT. rans_mode ) ) ) THEN
1301	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1302	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1303	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1304	ELSE
1305	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1306	id_stg_left, id_stg_right )
1307	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1308	id_stg_left, id_stg_right )
1309	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1310	id_stg_left, id_stg_right )
1311	!
1312	!-- Generate turbulence at the south and north boundary. Random numbers
1313	!-- for the xz-planes at the south/north boundary are generated by the
1314	!-- south-sided mpi ranks only. Please see also comment above.
1315	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1316	id_stg_south, id_stg_north )
1317	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1318	id_stg_south, id_stg_north )
1319	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1320	id_stg_south, id_stg_north )
1321	ENDIF
1322	velocity_seed_initialized = .TRUE.
1323	ENDIF
1324	!
1325	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1326	!-- seeds are only required at the left boundary, while in case of offline
1327	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1328	!-- right, south and north boundaries.
1329	IF ( stg_call ) THEN
1330	IF ( .NOT. ( nesting_offline .OR. &
1331	( child_domain .AND. rans_mode_parent &
1332	.AND. .NOT. rans_mode ) ) ) THEN
1333	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1334	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1335	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1336
1337	ELSE
1338	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1339	id_stg_left, id_stg_right )
1340	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1341	id_stg_left, id_stg_right )
1342	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1343	id_stg_left, id_stg_right )
1344
1345	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1346	id_stg_south, id_stg_north )
1347	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1348	id_stg_south, id_stg_north )
1349	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1350	id_stg_south, id_stg_north )
1351	ENDIF
1352	ENDIF
1353
1354	!
1355	!-- Turbulence generation at left and/or right boundary
1356	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1357	!
1358	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1359	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1360	!-- imposed
1361	IF ( stg_call ) THEN
1362
1363	DO j = nys, nyn
1364	DO k = nzb, nzt + 1
1365	!
1366	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1367	IF ( tu(k) == 0.0_wp ) THEN
1368	fu_yz(k,j) = fuo_yz(k,j)
1369	ELSE
1370	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1371	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1372	ENDIF
1373
1374	IF ( tv(k) == 0.0_wp ) THEN
1375	fv_yz(k,j) = fvo_yz(k,j)
1376	ELSE
1377	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1378	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1379	ENDIF
1380
1381	IF ( tw(k) == 0.0_wp ) THEN
1382	fw_yz(k,j) = fwo_yz(k,j)
1383	ELSE
1384	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1385	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1386	ENDIF
1387	ENDDO
1388	ENDDO
1389
1390	dist_yz(nzb,:,1) = 0.0_wp
1391	dist_yz(nzb,:,2) = 0.0_wp
1392	dist_yz(nzb,:,3) = 0.0_wp
1393
1394	IF ( myidx == id_stg_left ) i = nxl
1395	IF ( myidx == id_stg_right ) i = nxr+1
1396	DO j = nys, nyn
1397	DO k = nzb+1, nzt + 1
1398	!
1399	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1400	!-- Additional factors are added to improve the variance of v and w
1401	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1402	MERGE( 1.0_wp, 0.0_wp, &
1403	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1404	ENDDO
1405	ENDDO
1406
1407	IF ( myidx == id_stg_left ) i = nxl-1
1408	IF ( myidx == id_stg_right ) i = nxr+1
1409	DO j = nys, nyn
1410	DO k = nzb+1, nzt + 1
1411	!
1412	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1413	!-- Additional factors are added to improve the variance of v and w
1414	!-- experimental test of 1.2
1415	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1416	* 1.2_wp ) &
1417	* ( a21(k) * fu_yz(k,j) &
1418	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1419	MERGE( 1.0_wp, 0.0_wp, &
1420	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1421	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1422	* 1.3_wp ) &
1423	* ( a31(k) * fu_yz(k,j) &
1424	+ a32(k) * fv_yz(k,j) &
1425	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1426	MERGE( 1.0_wp, 0.0_wp, &
1427	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1428	ENDDO
1429	ENDDO
1430	ENDIF
1431	!
1432	!-- Mass flux correction following Kim et al. (2013)
1433	!-- This correction factor insures that the mass flux is preserved at the
1434	!-- inflow boundary. First, calculate mean value of the imposed
1435	!-- perturbations at yz boundary.
1436	!-- Note, this needs to be done only after the last RK3-substep, else
1437	!-- the boundary values won't be accessed.
1438	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1439	mc_factor_l = 0.0_wp
1440	mc_factor = 0.0_wp
1441	!
1442	!-- Sum up the original volume flows (with and without perturbations).
1443	!-- Note, for non-normal components (here v and w) it is actually no
1444	!-- volume flow.
1445	IF ( myidx == id_stg_left ) i = nxl
1446	IF ( myidx == id_stg_right ) i = nxr+1
1447
1448	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1449	* MERGE( 1.0_wp, 0.0_wp, &
1450	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1451
1452	IF ( myidx == id_stg_left ) i = nxl-1
1453	IF ( myidx == id_stg_right ) i = nxr+1
1454
1455	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1456	* MERGE( 1.0_wp, 0.0_wp, &
1457	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1458	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1459	* MERGE( 1.0_wp, 0.0_wp, &
1460	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1461
1462	#if defined( __parallel )
1463	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1464	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1465	#else
1466	mc_factor = mc_factor_l
1467	#endif
1468	!
1469	!-- Calculate correction factor and force zero mean perturbations.
1470	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1471
1472	IF ( myidx == id_stg_left ) i = nxl
1473	IF ( myidx == id_stg_right ) i = nxr+1
1474
1475	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
1476	* MERGE( 1.0_wp, 0.0_wp, &
1477	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1478
1479
1480	IF ( myidx == id_stg_left ) i = nxl-1
1481	IF ( myidx == id_stg_right ) i = nxr+1
1482
1483	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
1484	* MERGE( 1.0_wp, 0.0_wp, &
1485	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1486
1487	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
1488	* MERGE( 1.0_wp, 0.0_wp, &
1489	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1490	!
1491	!-- Add disturbances
1492	IF ( myidx == id_stg_left ) THEN
1493	!
1494	!-- For the left boundary distinguish between mesoscale offline / self
1495	!-- nesting and turbulent inflow at the left boundary only. In the latter
1496	!-- case turbulence is imposed on the mean inflow profiles.
1497	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1498	!
1499	!-- Add disturbance at the inflow
1500	DO j = nys, nyn
1501	DO k = nzb, nzt+1
1502	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1503	dist_yz(k,j,1) ) &
1504	* MERGE( 1.0_wp, 0.0_wp, &
1505	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1506	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1507	dist_yz(k,j,2) ) &
1508	* MERGE( 1.0_wp, 0.0_wp, &
1509	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1510	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1511	* MERGE( 1.0_wp, 0.0_wp, &
1512	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1513	ENDDO
1514	ENDDO
1515	ELSE
1516
1517	DO j = nys, nyn
1518	DO k = nzb+1, nzt
1519	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1520	* MERGE( 1.0_wp, 0.0_wp, &
1521	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1522	u(k,j,-1) = u(k,j,0)
1523	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1524	* MERGE( 1.0_wp, 0.0_wp, &
1525	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1526	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1527	* MERGE( 1.0_wp, 0.0_wp, &
1528	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1529	ENDDO
1530	ENDDO
1531	ENDIF
1532	ENDIF
1533	IF ( myidx == id_stg_right ) THEN
1534	DO j = nys, nyn
1535	DO k = nzb+1, nzt
1536	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1537	* MERGE( 1.0_wp, 0.0_wp, &
1538	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1539	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1540	* MERGE( 1.0_wp, 0.0_wp, &
1541	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1542	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1543	* MERGE( 1.0_wp, 0.0_wp, &
1544	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1545	ENDDO
1546	ENDDO
1547	ENDIF
1548	ENDIF
1549	ENDIF
1550	!
1551	!-- Turbulence generation at north and south boundary
1552	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1553	!
1554	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1555	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1556	!-- imposed
1557	IF ( stg_call ) THEN
1558	DO i = nxl, nxr
1559	DO k = nzb, nzt + 1
1560	!
1561	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1562	IF ( tu(k) == 0.0_wp ) THEN
1563	fu_xz(k,i) = fuo_xz(k,i)
1564	ELSE
1565	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1566	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1567	ENDIF
1568
1569	IF ( tv(k) == 0.0_wp ) THEN
1570	fv_xz(k,i) = fvo_xz(k,i)
1571	ELSE
1572	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1573	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1574	ENDIF
1575
1576	IF ( tw(k) == 0.0_wp ) THEN
1577	fw_xz(k,i) = fwo_xz(k,i)
1578	ELSE
1579	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1580	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1581	ENDIF
1582	ENDDO
1583	ENDDO
1584
1585
1586	dist_xz(nzb,:,1) = 0.0_wp
1587	dist_xz(nzb,:,2) = 0.0_wp
1588	dist_xz(nzb,:,3) = 0.0_wp
1589
1590	IF ( myidy == id_stg_south ) j = nys
1591	IF ( myidy == id_stg_north ) j = nyn+1
1592	DO i = nxl, nxr
1593	DO k = nzb+1, nzt + 1
1594	!
1595	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1596	!-- Additional factors are added to improve the variance of v and w
1597	!experimental test of 1.2
1598	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1599	* 1.2_wp ) &
1600	* ( a21(k) * fu_xz(k,i) &
1601	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1602	MERGE( 1.0_wp, 0.0_wp, &
1603	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1604	ENDDO
1605	ENDDO
1606
1607	IF ( myidy == id_stg_south ) j = nys-1
1608	IF ( myidy == id_stg_north ) j = nyn+1
1609	DO i = nxl, nxr
1610	DO k = nzb+1, nzt + 1
1611	!
1612	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1613	!-- Additional factors are added to improve the variance of v and w
1614	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1615	MERGE( 1.0_wp, 0.0_wp, &
1616	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1617
1618	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1619	* 1.3_wp ) &
1620	* ( a31(k) * fu_xz(k,i) &
1621	+ a32(k) * fv_xz(k,i) &
1622	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1623	MERGE( 1.0_wp, 0.0_wp, &
1624	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1625	ENDDO
1626	ENDDO
1627	ENDIF
1628
1629	!
1630	!-- Mass flux correction following Kim et al. (2013)
1631	!-- This correction factor insures that the mass flux is preserved at the
1632	!-- inflow boundary. First, calculate mean value of the imposed
1633	!-- perturbations at yz boundary.
1634	!-- Note, this needs to be done only after the last RK3-substep, else
1635	!-- the boundary values won't be accessed.
1636	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1637	mc_factor_l = 0.0_wp
1638	mc_factor = 0.0_wp
1639
1640	IF ( myidy == id_stg_south ) j = nys
1641	IF ( myidy == id_stg_north ) j = nyn+1
1642
1643	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1644	* MERGE( 1.0_wp, 0.0_wp, &
1645	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1646
1647	IF ( myidy == id_stg_south ) j = nys-1
1648	IF ( myidy == id_stg_north ) j = nyn+1
1649
1650	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1651	* MERGE( 1.0_wp, 0.0_wp, &
1652	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1653	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1654	* MERGE( 1.0_wp, 0.0_wp, &
1655	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1656
1657	#if defined( __parallel )
1658	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1659	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1660	#else
1661	mc_factor = mc_factor_l
1662	#endif
1663
1664	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1665
1666	IF ( myidy == id_stg_south ) j = nys
1667	IF ( myidy == id_stg_north ) j = nyn+1
1668
1669	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
1670	* MERGE( 1.0_wp, 0.0_wp, &
1671	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1672
1673
1674	IF ( myidy == id_stg_south ) j = nys-1
1675	IF ( myidy == id_stg_north ) j = nyn+1
1676
1677	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
1678	* MERGE( 1.0_wp, 0.0_wp, &
1679	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1680
1681	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
1682	* MERGE( 1.0_wp, 0.0_wp, &
1683	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1684	!
1685	!-- Add disturbances
1686	IF ( myidy == id_stg_south ) THEN
1687	DO i = nxl, nxr
1688	DO k = nzb+1, nzt
1689	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1690	* MERGE( 1.0_wp, 0.0_wp, &
1691	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1692	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1693	* MERGE( 1.0_wp, 0.0_wp, &
1694	BTEST( wall_flags_total_0(k,0,i), 2 ) )
1695	v(k,-1,i) = v(k,0,i)
1696	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1697	* MERGE( 1.0_wp, 0.0_wp, &
1698	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1699	ENDDO
1700	ENDDO
1701	ENDIF
1702	IF ( myidy == id_stg_north ) THEN
1703
1704	DO i = nxl, nxr
1705	DO k = nzb+1, nzt
1706	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1707	* MERGE( 1.0_wp, 0.0_wp, &
1708	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1709	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1710	* MERGE( 1.0_wp, 0.0_wp, &
1711	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1712	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1713	* MERGE( 1.0_wp, 0.0_wp, &
1714	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1715	ENDDO
1716	ENDDO
1717	ENDIF
1718	ENDIF
1719	ENDIF
1720	!
1721	!-- Exchange ghost points.
1722	CALL exchange_horiz( u, nbgp )
1723	CALL exchange_horiz( v, nbgp )
1724	CALL exchange_horiz( w, nbgp )
1725	!
1726	!-- Finally, set time counter for calling STG to zero
1727	IF ( stg_call ) time_stg_call = 0.0_wp
1728
1729	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1730
1731	END SUBROUTINE stg_main
1732
1733	!------------------------------------------------------------------------------!
1734	! Description:
1735	! ------------
1736	!> Generate a set of random number rand_it wich is equal on each PE
1737	!> and calculate the velocity seed f_n.
1738	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1739	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1740	!> parts are collected to form the full array.
1741	!------------------------------------------------------------------------------!
1742	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1743
1744	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1745	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1746	INTEGER(iwp) :: j !< loop index in y-direction
1747	INTEGER(iwp) :: jj !< loop index in y-direction
1748	INTEGER(iwp) :: k !< loop index in z-direction
1749	INTEGER(iwp) :: kk !< loop index in z-direction
1750	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1751
1752	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1753	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1754
1755	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1756	REAL(wp) :: rand_av !< average of random number
1757	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1758
1759	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1760	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1761
1762	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1763	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1764
1765	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1766	!
1767	!-- Generate random numbers using the parallel random generator.
1768	!-- The set of random numbers are modified to have an average of 0 and
1769	!-- unit variance. Note, at the end the random number array must be defined
1770	!-- globally in order to compute the correlation matrices. However,
1771	!-- the calculation and normalization of random numbers is done locally,
1772	!-- while the result is later distributed to all processes. Further,
1773	!-- please note, a set of random numbers is only calculated for the
1774	!-- left boundary, while the right boundary uses the same random numbers
1775	!-- and thus also computes the same correlation matrix.
1776	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1777	rand_it = 0.0_wp
1778
1779	rand_av = 0.0_wp
1780	rand_sigma_inv = 0.0_wp
1781	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1782	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
1783	KIND=wp )
1784	!
1785	!-- Compute and normalize random numbers.
1786	DO j = nys - mergp, nyn + mergp
1787	!
1788	!-- Put the random seeds at grid point j
1789	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1790	DO k = nzb - mergp, nzt + 1 + mergp
1791	CALL random_number_parallel( random_dummy )
1792	rand_it(k,j) = random_dummy
1793	ENDDO
1794	!
1795	!-- Get the new random seeds from last call at grid point j
1796	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1797	ENDDO
1798	!
1799	!-- For normalization to zero mean, sum-up the global random numers.
1800	!-- To normalize the global set of random numbers,
1801	!-- the inner ghost layers mergp must not be summed-up, else
1802	!-- the random numbers on the ghost layers will be stronger weighted as they
1803	!-- also occur on the inner subdomains.
1804	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1805	MERGE( nyn, nyn + mergp, nyn /= ny )
1806	DO k = nzb - mergp, nzt + 1 + mergp
1807	rand_av = rand_av + rand_it(k,j)
1808	ENDDO
1809	ENDDO
1810
1811	#if defined( __parallel )
1812	!
1813	!-- Sum-up the local averages of the random numbers
1814	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1815	MPI_SUM, comm1dy, ierr )
1816	#endif
1817	rand_av = rand_av * nyz_inv
1818	!
1819	!-- Obtain zero mean
1820	rand_it= rand_it - rand_av
1821	!
1822	!-- Now, compute the variance
1823	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1824	MERGE( nyn, nyn + mergp, nyn /= ny )
1825	DO k = nzb - mergp, nzt + 1 + mergp
1826	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1827	ENDDO
1828	ENDDO
1829
1830	#if defined( __parallel )
1831	!
1832	!-- Sum-up the local quadratic averages of the random numbers
1833	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1834	MPI_SUM, comm1dy, ierr )
1835	#endif
1836	!
1837	!-- Compute standard deviation
1838	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1839	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1840	ELSE
1841	rand_sigma_inv = 1.0_wp
1842	ENDIF
1843	!
1844	!-- Normalize with standard deviation to obtain unit variance
1845	rand_it = rand_it * rand_sigma_inv
1846
1847	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1848	!
1849	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
1850	!-- are two options. In the first one, the computation of the seeds is
1851	!-- distributed to all processes along the communicator comm1dy and
1852	!-- gathered on the leftmost and, if necessary, on the rightmost process.
1853	!-- For huge length scales the computational effort can become quite huge
1854	!-- (it scales with the turbulent length scales), so that gain by parallelization
1855	!-- exceeds the costs by the subsequent communication.
1856	!-- In the second option, which performs better when the turbulent length scales
1857	!-- are parametrized and thus the loops are smaller, the seeds are computed
1858	!-- locally and no communication is necessary.
1859	IF ( compute_velocity_seeds_local ) THEN
1860
1861	f_n = 0.0_wp
1862	DO j = nys, nyn
1863	DO k = nzb, nzt+1
1864	DO jj = -n_y(k), n_y(k)
1865	DO kk = -n_z(k), n_z(k)
1866	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1867	ENDDO
1868	ENDDO
1869	ENDDO
1870	ENDDO
1871
1872	ELSE
1873
1874	f_n_l = 0.0_wp
1875	DO j = nys, nyn
1876	DO k = nzb_x_stg, nzt_x_stg+1
1877	DO jj = -n_y(k), n_y(k)
1878	DO kk = -n_z(k), n_z(k)
1879	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1880	ENDDO
1881	ENDDO
1882	ENDDO
1883	ENDDO
1884	!
1885	!-- Gather velocity seeds of full subdomain
1886	send_count = nzt_x_stg - nzb_x_stg + 1
1887	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1888
1889	#if defined( __parallel )
1890	!
1891	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1892	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1893	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1894	id_left, comm1dx, ierr )
1895	!
1896	!-- If required, gather the same velocity seed matrix on right boundary
1897	!-- mpi ranks (in offline nesting for example).
1898	IF ( PRESENT( id_right ) ) THEN
1899	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1900	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1901	id_right, comm1dx, ierr )
1902	ENDIF
1903	#else
1904	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1905	!
1906	!-- Next line required to avoid compile errors because of unused dummy arguments
1907	IF ( id_left == 0 ) id_right = 0
1908	#endif
1909
1910	ENDIF
1911
1912	DEALLOCATE( rand_it )
1913
1914	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1915
1916	END SUBROUTINE stg_generate_seed_yz
1917
1918
1919	!------------------------------------------------------------------------------!
1920	! Description:
1921	! ------------
1922	!> Generate a set of random number rand_it wich is equal on each PE
1923	!> and calculate the velocity seed f_n.
1924	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1925	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1926	!> parts are collected to form the full array.
1927	!------------------------------------------------------------------------------!
1928	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1929
1930	INTEGER(iwp) :: i !< loop index in x-direction
1931	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1932	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1933	INTEGER(iwp) :: ii !< loop index in x-direction
1934	INTEGER(iwp) :: k !< loop index in z-direction
1935	INTEGER(iwp) :: kk !< loop index in z-direction
1936	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1937
1938	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1939	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1940
1941	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1942	REAL(wp) :: rand_av !< average of random number
1943	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1944
1945	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1946	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1947
1948	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1949	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1950
1951	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1952
1953	!
1954	!-- Generate random numbers using the parallel random generator.
1955	!-- The set of random numbers are modified to have an average of 0 and
1956	!-- unit variance. Note, at the end the random number array must be defined
1957	!-- globally in order to compute the correlation matrices. However,
1958	!-- the calculation and normalization of random numbers is done locally,
1959	!-- while the result is later distributed to all processes. Further,
1960	!-- please note, a set of random numbers is only calculated for the
1961	!-- left boundary, while the right boundary uses the same random numbers
1962	!-- and thus also computes the same correlation matrix.
1963	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
1964	rand_it = 0.0_wp
1965
1966	rand_av = 0.0_wp
1967	rand_sigma_inv = 0.0_wp
1968	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1969	* ( nx + mergp - ( 0 - mergp ) +1 ), &
1970	KIND=wp )
1971	!
1972	!-- Compute and normalize random numbers.
1973	DO i = nxl - mergp, nxr + mergp
1974	!
1975	!-- Put the random seeds at grid point ii
1976	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1977	DO k = nzb - mergp, nzt + 1 + mergp
1978	CALL random_number_parallel( random_dummy )
1979	rand_it(k,i) = random_dummy
1980	ENDDO
1981	!
1982	!-- Get the new random seeds from last call at grid point ii
1983	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1984	ENDDO
1985	!
1986	!-- For normalization to zero mean, sum-up the global random numers.
1987	!-- To normalize the global set of random numbers,
1988	!-- the inner ghost layers mergp must not be summed-up, else
1989	!-- the random numbers on the ghost layers will be stronger weighted as they
1990	!-- also occur on the inner subdomains.
1991	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1992	MERGE( nxr, nxr + mergp, nxr /= nx )
1993	DO k = nzb - mergp, nzt + 1 + mergp
1994	rand_av = rand_av + rand_it(k,i)
1995	ENDDO
1996	ENDDO
1997
1998	#if defined( __parallel )
1999	!
2000	!-- Sum-up the local averages of the random numbers
2001	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
2002	MPI_SUM, comm1dx, ierr )
2003	#endif
2004	rand_av = rand_av * nxz_inv
2005	!
2006	!-- Obtain zero mean
2007	rand_it= rand_it - rand_av
2008	!
2009	!-- Now, compute the variance
2010	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
2011	MERGE( nxr, nxr + mergp, nxr /= nx )
2012	DO k = nzb - mergp, nzt + 1 + mergp
2013	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2014	ENDDO
2015	ENDDO
2016
2017	#if defined( __parallel )
2018	!
2019	!-- Sum-up the local quadratic averages of the random numbers
2020	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
2021	MPI_SUM, comm1dx, ierr )
2022	#endif
2023	!
2024	!-- Compute standard deviation
2025	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2026	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2027	ELSE
2028	rand_sigma_inv = 1.0_wp
2029	ENDIF
2030	!
2031	!-- Normalize with standard deviation to obtain unit variance
2032	rand_it = rand_it * rand_sigma_inv
2033
2034	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2035	!
2036	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
2037	!-- are two options. In the first one, the computation of the seeds is
2038	!-- distributed to all processes along the communicator comm1dx and
2039	!-- gathered on the southmost and, if necessary, on the northmost process.
2040	!-- For huge length scales the computational effort can become quite huge
2041	!-- (it scales with the turbulent length scales), so that gain by parallelization
2042	!-- exceeds the costs by the subsequent communication.
2043	!-- In the second option, which performs better when the turbulent length scales
2044	!-- are parametrized and thus the loops are smaller, the seeds are computed
2045	!-- locally and no communication is necessary.
2046	IF ( compute_velocity_seeds_local ) THEN
2047
2048	f_n = 0.0_wp
2049	DO i = nxl, nxr
2050	DO k = nzb, nzt+1
2051	DO ii = -n_x(k), n_x(k)
2052	DO kk = -n_z(k), n_z(k)
2053	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2054	ENDDO
2055	ENDDO
2056	ENDDO
2057	ENDDO
2058
2059	ELSE
2060
2061	f_n_l = 0.0_wp
2062	DO i = nxl, nxr
2063	DO k = nzb_y_stg, nzt_y_stg+1
2064	DO ii = -n_x(k), n_x(k)
2065	DO kk = -n_z(k), n_z(k)
2066	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2067	ENDDO
2068	ENDDO
2069	ENDDO
2070	ENDDO
2071	!
2072	!-- Gather velocity seeds of full subdomain
2073	send_count = nzt_y_stg - nzb_y_stg + 1
2074	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2075
2076	#if defined( __parallel )
2077	!
2078	!-- Gather the processed velocity seed on south boundary mpi ranks.
2079	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2080	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2081	id_south, comm1dy, ierr )
2082	!
2083	!-- Gather the processed velocity seed on north boundary mpi ranks.
2084	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2085	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2086	id_north, comm1dy, ierr )
2087	#else
2088	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2089	!
2090	!-- Next line required to avoid compile errors because of unused dummy arguments
2091	IF ( id_north == 0 ) id_south = 0
2092	#endif
2093
2094	ENDIF
2095
2096	DEALLOCATE( rand_it )
2097
2098	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2099
2100	END SUBROUTINE stg_generate_seed_xz
2101
2102	!------------------------------------------------------------------------------!
2103	! Description:
2104	! ------------
2105	!> Parametrization of the Reynolds stress tensor, following the parametrization
2106	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2107	!> dispserion modelling. Please note, the parametrization does not distinguish
2108	!> between along-wind and cross-wind turbulence.
2109	!------------------------------------------------------------------------------!
2110	SUBROUTINE parametrize_reynolds_stress
2111
2112	INTEGER(iwp) :: k !< loop index in z-direction
2113
2114	REAL(wp) :: zzi !< ratio of z/zi
2115
2116	DO k = nzb+1, nzt+1
2117	!
2118	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2119	!-- The function decreases to 1/10 after one length scale above the
2120	!-- ABL top.
2121	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2122	!
2123	!-- Determine normalized height coordinate
2124	zzi = zu(k) / zi_ribulk
2125	!
2126	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2127	!-- to the denominator, else the mergpe-function can crash if scale_l is
2128	!-- zero.
2129	r11(k) = scale_us*2 ( &
2130	MERGE( 0.35_wp * ABS( &
2131	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2132	)**( 2.0_wp / 3.0_wp ), &
2133	0.0_wp, &
2134	scale_l < 0.0_wp ) &
2135	+ 5.0_wp - 4.0_wp * zzi &
2136	) * blend
2137
2138	r22(k) = r11(k)
2139	!
2140	!-- w'w'
2141	r33(k) = scale_wm*2 ( &
2142	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2143	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2144	) * blend
2145	!
2146	!-- u'w' and v'w'. Assume isotropy.
2147	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2148	r32(k) = r31(k)
2149	!
2150	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2151	!-- a similar profile as for u'w'.
2152	r21(k) = r31(k)
2153	ENDDO
2154
2155	!
2156	!-- Set bottom boundary condition
2157	r11(nzb) = r11(nzb+1)
2158	r22(nzb) = r22(nzb+1)
2159	r33(nzb) = r33(nzb+1)
2160
2161	r21(nzb) = r11(nzb+1)
2162	r31(nzb) = r31(nzb+1)
2163	r32(nzb) = r32(nzb+1)
2164
2165
2166	END SUBROUTINE parametrize_reynolds_stress
2167
2168	!------------------------------------------------------------------------------!
2169	! Description:
2170	! ------------
2171	!> Calculate the coefficient matrix from the Lund rotation.
2172	!------------------------------------------------------------------------------!
2173	SUBROUTINE calc_coeff_matrix
2174
2175	INTEGER(iwp) :: k !< loop index in z-direction
2176
2177	!
2178	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2179	DO k = nzb+1, nzt+1
2180	IF ( r11(k) > 10E-6_wp ) THEN
2181	a11(k) = SQRT( r11(k) )
2182	a21(k) = r21(k) / a11(k)
2183	a31(k) = r31(k) / a11(k)
2184	ELSE
2185	a11(k) = 10E-8_wp
2186	a21(k) = 10E-8_wp
2187	a31(k) = 10E-8_wp
2188	ENDIF
2189	ENDDO
2190	DO k = nzb+1, nzt+1
2191	a22(k) = r22(k) - a21(k)**2
2192	IF ( a22(k) > 10E-6_wp ) THEN
2193	a22(k) = SQRT( a22(k) )
2194	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2195	ELSE
2196	a22(k) = 10E-8_wp
2197	a32(k) = 10E-8_wp
2198	ENDIF
2199	ENDDO
2200	DO k = nzb+1, nzt+1
2201	a33(k) = r33(k) - a31(k)2 - a32(k)2
2202	IF ( a33(k) > 10E-6_wp ) THEN
2203	a33(k) = SQRT( a33(k) )
2204	ELSE
2205	a33(k) = 10E-8_wp
2206	ENDIF
2207	ENDDO
2208	!
2209	!-- Set bottom boundary condition
2210	a11(nzb) = a11(nzb+1)
2211	a22(nzb) = a22(nzb+1)
2212	a21(nzb) = a21(nzb+1)
2213	a33(nzb) = a33(nzb+1)
2214	a31(nzb) = a31(nzb+1)
2215	a32(nzb) = a32(nzb+1)
2216
2217	END SUBROUTINE calc_coeff_matrix
2218
2219	!------------------------------------------------------------------------------!
2220	! Description:
2221	! ------------
2222	!> This routine controls the re-adjustment of the turbulence statistics used
2223	!> for generating turbulence at the lateral boundaries.
2224	!------------------------------------------------------------------------------!
2225	SUBROUTINE stg_adjust
2226
2227	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2228	!
2229	!-- In case of dirichlet inflow boundary conditions only at one lateral
2230	!-- boundary, i.e. in the case no offline or self nesting is applied but
2231	!-- synthetic turbulence shall be parametrized nevertheless, the
2232	!-- boundary-layer depth need to determined first.
2233	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2234	CALL nesting_offl_calc_zi
2235	!
2236	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2237	!-- are calculated.
2238	CALL calc_scaling_variables
2239	!
2240	!-- Set length and time scales depending on boundary-layer height
2241	CALL calc_length_and_time_scale
2242	!
2243	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2244	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2245	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2246	!-- friction velocity and velocity scale.
2247	CALL parametrize_reynolds_stress
2248	!
2249	!-- Calculate coefficient matrix from Reynolds stress tensor
2250	!-- (Lund rotation)
2251	CALL calc_coeff_matrix
2252	!
2253	!-- Determine filter functions on basis of updated length scales
2254	CALL stg_filter_func( nux, bux ) !filter ux
2255	CALL stg_filter_func( nuy, buy ) !filter uy
2256	CALL stg_filter_func( nuz, buz ) !filter uz
2257	CALL stg_filter_func( nvx, bvx ) !filter vx
2258	CALL stg_filter_func( nvy, bvy ) !filter vy
2259	CALL stg_filter_func( nvz, bvz ) !filter vz
2260	CALL stg_filter_func( nwx, bwx ) !filter wx
2261	CALL stg_filter_func( nwy, bwy ) !filter wy
2262	CALL stg_filter_func( nwz, bwz ) !filter wz
2263	!
2264	!-- Reset time counter for controlling next adjustment to zero
2265	time_stg_adjust = 0.0_wp
2266
2267	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2268
2269	END SUBROUTINE stg_adjust
2270
2271
2272	!------------------------------------------------------------------------------!
2273	! Description:
2274	! ------------
2275	!> Calculates turbuluent length and time scales if these are not available
2276	!> from measurements.
2277	!------------------------------------------------------------------------------!
2278	SUBROUTINE calc_length_and_time_scale
2279
2280	INTEGER(iwp) :: k !< loop index in z-direction
2281
2282	REAL(wp) :: length_scale_dum !< effectively used length scale
2283
2284	!
2285	!-- In initial call the boundary-layer depth can be zero. This case, set
2286	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2287	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2288	!
2289	!-- Set-up default turbulent length scales. From the numerical point of
2290	!-- view the imposed perturbations should not be immediately dissipated
2291	!-- by the numerics. The numerical dissipation, however, acts on scales
2292	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2293	!-- length scale to 8 time the grid spacing. Further, above the boundary
2294	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2295	!-- imposing any perturbations) in order to save computational costs.
2296	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2297	!-- using the length scales and the mean profiles of u- and v-component.
2298	DO k = nzb+1, nzt+1
2299	!
2300	!-- Determine blending parameter. Within the boundary layer length scales
2301	!-- are constant, while above lengths scales approach gradully zero,
2302	!-- i.e. imposed turbulence is not correlated in space and time,
2303	!-- just white noise, which saves computations power as the loops for the
2304	!-- computation of the filter functions depend on the length scales.
2305	!-- The value decreases to 1/10 after one length scale above the
2306	!-- ABL top.
2307	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2308	!
2309	!-- Assume isotropic turbulence length scales
2310	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2311	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2312	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2313	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2314	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2315	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2316	!
2317	!-- Along the vertical direction limit the length scale further by the
2318	!-- boundary-layer depth to assure that no length scales larger than
2319	!-- the boundary-layer depth are used
2320	length_scale_dum = MIN( length_scale, zi_ribulk )
2321
2322	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2323	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2324	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2325	!
2326	!-- Limit time scales, else they become very larger for low wind speed,
2327	!-- imposing long-living inflow perturbations which in turn propagate
2328	!-- further into the model domain. Use u_init and v_init to calculate
2329	!-- the time scales, which will be equal to the inflow profiles, both,
2330	!-- in offline nesting mode or in dirichlet/radiation mode.
2331	tu(k) = MIN( dt_stg_adjust, length_scale / &
2332	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2333	tv(k) = MIN( dt_stg_adjust, length_scale / &
2334	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2335	!
2336	!-- Time scale of w-component is a mixture from u- and v-component.
2337	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2338
2339	ENDDO
2340	!
2341	!-- Set bottom boundary condition for the length and time scales
2342	nux(nzb) = nux(nzb+1)
2343	nuy(nzb) = nuy(nzb+1)
2344	nuz(nzb) = nuz(nzb+1)
2345	nvx(nzb) = nvx(nzb+1)
2346	nvy(nzb) = nvy(nzb+1)
2347	nvz(nzb) = nvz(nzb+1)
2348	nwx(nzb) = nwx(nzb+1)
2349	nwy(nzb) = nwy(nzb+1)
2350	nwz(nzb) = nwz(nzb+1)
2351
2352	tu(nzb) = tu(nzb+1)
2353	tv(nzb) = tv(nzb+1)
2354	tw(nzb) = tw(nzb+1)
2355
2356
2357	END SUBROUTINE calc_length_and_time_scale
2358
2359	!------------------------------------------------------------------------------!
2360	! Description:
2361	! ------------
2362	!> Calculate scaling variables which are used for turbulence parametrization
2363	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2364	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2365	!------------------------------------------------------------------------------!
2366	SUBROUTINE calc_scaling_variables
2367
2368	INTEGER(iwp) :: i !< loop index in x-direction
2369	INTEGER(iwp) :: j !< loop index in y-direction
2370	INTEGER(iwp) :: k !< loop index in z-direction
2371	INTEGER(iwp) :: m !< surface element index
2372
2373	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2374	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2375	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2376	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2377	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2378	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2379	REAL(wp) :: w_convective !< convective velocity scale
2380
2381	!
2382	!-- Calculate mean friction velocity, velocity scale, heat flux and
2383	!-- near-surface temperature in the model domain.
2384	pt_surf_mean_l = 0.0_wp
2385	shf_mean_l = 0.0_wp
2386	scale_l_l = 0.0_wp
2387	friction_vel_l = 0.0_wp
2388	DO m = 1, surf_def_h(0)%ns
2389	i = surf_def_h(0)%i(m)
2390	j = surf_def_h(0)%j(m)
2391	k = surf_def_h(0)%k(m)
2392	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2393	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2394	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2395	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2396	ENDDO
2397	DO m = 1, surf_lsm_h%ns
2398	i = surf_lsm_h%i(m)
2399	j = surf_lsm_h%j(m)
2400	k = surf_lsm_h%k(m)
2401	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2402	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2403	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2404	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2405	ENDDO
2406	DO m = 1, surf_usm_h%ns
2407	i = surf_usm_h%i(m)
2408	j = surf_usm_h%j(m)
2409	k = surf_usm_h%k(m)
2410	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2411	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2412	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2413	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2414	ENDDO
2415
2416	#if defined( __parallel )
2417	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2418	comm2d, ierr )
2419	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2420	comm2d, ierr )
2421	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2422	comm2d, ierr )
2423	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2424	comm2d, ierr )
2425	#else
2426	scale_us = friction_vel_l
2427	shf_mean = shf_mean_l
2428	scale_l = scale_l_l
2429	pt_surf_mean = pt_surf_mean_l
2430	#endif
2431
2432	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2433	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2434	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2435	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2436	!
2437	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2438	!-- is negative, set convective velocity scale to zero.
2439	IF ( shf_mean > 0.0_wp ) THEN
2440	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2441	ELSE
2442	w_convective = 0.0_wp
2443	ENDIF
2444	!
2445	!-- Finally, in order to consider also neutral or stable stratification,
2446	!-- compute momentum velocity scale from u* and convective velocity scale,
2447	!-- according to Rotach et al. (1996).
2448	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2449
2450	END SUBROUTINE calc_scaling_variables
2451
2452	END MODULE synthetic_turbulence_generator_mod

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