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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4440

Last change on this file since 4440 was 4440, checked in by suehring, 4 years ago
Correct misplaced preprocessor directive
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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 4440 2020-03-04 09:46:52Z suehring $
27	! Correct misplaced preprocessor directive
28	!
29	! 4438 2020-03-03 20:49:28Z suehring
30	! Performance optimizations in velocity-seed calculation:
31	! - random number array is only defined and computed locally (except for
32	! normalization to zero mean and unit variance)
33	! - parallel random number generator is applied independent on the 2D random
34	! numbers in other routines
35	! - option to decide wheter velocity seeds are computed locally without any
36	! further communication or are computed by all processes along the
37	! communicator
38	!
39	! 4346 2019-12-18 11:55:56Z motisi
40	! Introduction of wall_flags_total_0, which currently sets bits based on static
41	! topography information used in wall_flags_static_0
42	!
43	! 4335 2019-12-12 16:39:05Z suehring
44	! Commentation of last commit
45	!
46	! 4332 2019-12-10 19:44:12Z suehring
47	! Limit initial velocity seeds in restart runs, if not the seed calculation
48	! may become unstable. Further, minor bugfix in initial velocity seed
49	! calculation.
50	!
51	! 4329 2019-12-10 15:46:36Z motisi
52	! Renamed wall_flags_0 to wall_flags_static_0
53	!
54	! 4309 2019-11-26 18:49:59Z suehring
55	! Computation of velocity seeds optimized. This implies that random numbers
56	! are computed now using the parallel random number generator. Random numbers
57	! are now only computed and normalized locally, while distributed over all
58	! mpi ranks afterwards, instead of computing random numbers on a global array.
59	! Further, the number of calls for the time-consuming velocity-seed generation
60	! is reduced - now the left and right, as well as the north and south boundary
61	! share the same velocity-seed matrices.
62	!
63	! 4182 2019-08-22 15:20:23Z scharf
64	! Corrected "Former revisions" section
65	!
66	! 4148 2019-08-08 11:26:00Z suehring
67	! Remove unused variable
68	!
69	! 4144 2019-08-06 09:11:47Z raasch
70	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
71	!
72	! 4071 2019-07-03 20:02:00Z suehring
73	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
74	! information is not read from file.
75	!
76	! 4022 2019-06-12 11:52:39Z suehring
77	! Several bugfixes and improvements
78	! - revise bias correction of the imposed perturbations (correction via volume
79	! flow can create instabilities in case the mean volume flow is close to zero)
80	! - introduce lower limits in calculation of coefficient matrix, else the
81	! calculation may become numerically unstable
82	! - impose perturbations every timestep, even though no new set of perturbations
83	! is generated in case dt_stg_call /= dt_3d
84	! - Implement a gradual decrease of Reynolds stress and length scales above
85	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
86	! discontinuous decrease
87	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
88	!
89	! 3987 2019-05-22 09:52:13Z kanani
90	! Introduce alternative switch for debug output during timestepping
91	!
92	! 3938 2019-04-29 16:06:25Z suehring
93	! Remove unused variables
94	!
95	! 3937 2019-04-29 15:09:07Z suehring
96	! Minor bugfix in case of a very early restart where mc_factor is sill not
97	! present.
98	! Some modification and fixing of potential bugs in the calculation of scaling
99	! parameters used for synthetic turbulence parametrization.
100	!
101	! 3909 2019-04-17 09:13:25Z suehring
102	! Minor bugfix for last commit
103	!
104	! 3900 2019-04-16 15:17:43Z suehring
105	! Missing re-calculation of perturbation seeds in case of restarts
106	!
107	! 3891 2019-04-12 17:52:01Z suehring
108	! Bugfix in initialization in case of restart runs.
109	!
110	! 3885 2019-04-11 11:29:34Z kanani
111	! Changes related to global restructuring of location messages and introduction
112	! of additional debug messages
113	!
114	!
115	! removed unused variables
116	!
117	! 3719 2019-02-06 13:10:18Z kanani
118	! Removed log_point measurement from stg_init, since this part is counted to
119	! log_point(2) 'initialisation' already. Moved other log_points to calls of
120	! the subroutines in time_integration for better overview.
121	!
122	! 2259 2017-06-08 09:09:11Z gronemeier
123	! Initial revision
124	!
125	! Authors:
126	! --------
127	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
128	!
129	!
130	! Description:
131	! ------------
132	!> The module generates turbulence at the inflow boundary based on a method by
133	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
134	!> correction by Kim et al. (2013).
135	!> The turbulence is correlated based on length scales in y- and z-direction and
136	!> a time scale for each velocity component. The profiles of length and time
137	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
138	!> tensor can be either read from file STG_PROFILES, or will be parametrized
139	!> within the boundary layer.
140	!>
141	!> @todo test restart
142	!> enable cyclic_fill
143	!> implement turbulence generation for e and pt
144	!> @todo Input of height-constant length scales via namelist
145	!> @note <Enter notes on the module>
146	!> @bug Height information from input file is not used. Profiles from input
147	!> must match with current PALM grid.
148	!> In case of restart, velocity seeds differ from precursor run if a11,
149	!> a22, or a33 are zero.
150	!------------------------------------------------------------------------------!
151	MODULE synthetic_turbulence_generator_mod
152
153
154	USE arrays_3d, &
155	ONLY: dzw, &
156	ddzw, &
157	drho_air, &
158	mean_inflow_profiles, &
159	q, &
160	q_init, &
161	pt, &
162	pt_init, &
163	u, &
164	u_init, &
165	v, &
166	v_init, &
167	w, &
168	zu, &
169	zw
170
171	USE basic_constants_and_equations_mod, &
172	ONLY: g, &
173	kappa, &
174	pi
175
176	USE control_parameters, &
177	ONLY: bc_lr, &
178	bc_ns, &
179	child_domain, &
180	coupling_char, &
181	debug_output_timestep, &
182	dt_3d, &
183	e_init, &
184	humidity, &
185	initializing_actions, &
186	intermediate_timestep_count, &
187	intermediate_timestep_count_max, &
188	length, &
189	message_string, &
190	nesting_offline, &
191	neutral, &
192	num_mean_inflow_profiles, &
193	random_generator, &
194	rans_mode, &
195	restart_string, &
196	syn_turb_gen, &
197	time_since_reference_point, &
198	turbulent_inflow
199
200	USE cpulog, &
201	ONLY: cpu_log, &
202	log_point_s
203
204	USE grid_variables, &
205	ONLY: ddx, &
206	ddy, &
207	dx, &
208	dy
209
210	USE indices, &
211	ONLY: nbgp, &
212	nz, &
213	nzb, &
214	nzt, &
215	nx, &
216	nxl, &
217	nxlu, &
218	nxr, &
219	ny, &
220	nys, &
221	nysv, &
222	nyn, &
223	wall_flags_total_0
224
225	USE kinds
226
227	#if defined( __parallel ) && !defined( __mpifh )
228	USE MPI
229	#endif
230
231	USE nesting_offl_mod, &
232	ONLY: nesting_offl_calc_zi, &
233	zi_ribulk
234
235	USE pegrid, &
236	ONLY: comm1dx, &
237	comm1dy, &
238	comm2d, &
239	ierr, &
240	myidx, &
241	myidy, &
242	pdims
243
244	USE pmc_interface, &
245	ONLY : rans_mode_parent
246
247	USE random_generator_parallel, &
248	ONLY: init_parallel_random_generator, &
249	random_dummy, &
250	random_number_parallel, &
251	random_seed_parallel
252
253	USE transpose_indices, &
254	ONLY: nzb_x, &
255	nzt_x
256
257	USE surface_mod, &
258	ONLY: surf_def_h, &
259	surf_lsm_h, &
260	surf_usm_h
261
262	IMPLICIT NONE
263
264	#if defined( __parallel ) && defined( __mpifh )
265	INCLUDE "mpif.h"
266	#endif
267
268
269	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
270	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
271	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
272	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
273	!< is distributed over several processes
274
275	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
276	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
277	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
278	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
279	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
280	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
281	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
282	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
283	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
284	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
285	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
286	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
287	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
288
289	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
290	!< required for bias correction of imposed perturbations
291	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
292	!< required for bias correction of imposed perturbations
293
294	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
295	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
296	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
297	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
298	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
299	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
300	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
301	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
302	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
303	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
307
308	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
309	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
310	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
311	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
312
313	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
314	!< scales above the boundary layer
315	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
316	!< one length scale above ABL top
317	REAL(wp) :: d_l !< blend_coeff/length_scale
318	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
319	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
320	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
321	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
322	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
323	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
324	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
325	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
326
327	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
328
329
330	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
331	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
332	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
333	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
334	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
335	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
336
337	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
338	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
339	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
340	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
341	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
342	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
343	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
344	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
345	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
346
347	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
348	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
349	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
350	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
351	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
352	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
353	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
354	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
355	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
356	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
357	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
368
369	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
370	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
371
372	!
373	!-- PALM interfaces:
374	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
375	INTERFACE stg_adjust
376	MODULE PROCEDURE stg_adjust
377	END INTERFACE stg_adjust
378	!
379	!-- Input parameter checks to be done in check_parameters
380	INTERFACE stg_check_parameters
381	MODULE PROCEDURE stg_check_parameters
382	END INTERFACE stg_check_parameters
383
384	!
385	!-- Calculate filter functions
386	INTERFACE stg_filter_func
387	MODULE PROCEDURE stg_filter_func
388	END INTERFACE stg_filter_func
389
390	!
391	!-- Generate velocity seeds at south and north domain boundary
392	INTERFACE stg_generate_seed_xz
393	MODULE PROCEDURE stg_generate_seed_xz
394	END INTERFACE stg_generate_seed_xz
395	!
396	!-- Generate velocity seeds at left and/or right domain boundary
397	INTERFACE stg_generate_seed_yz
398	MODULE PROCEDURE stg_generate_seed_yz
399	END INTERFACE stg_generate_seed_yz
400
401	!
402	!-- Output of information to the header file
403	INTERFACE stg_header
404	MODULE PROCEDURE stg_header
405	END INTERFACE stg_header
406
407	!
408	!-- Initialization actions
409	INTERFACE stg_init
410	MODULE PROCEDURE stg_init
411	END INTERFACE stg_init
412
413	!
414	!-- Main procedure of synth. turb. gen.
415	INTERFACE stg_main
416	MODULE PROCEDURE stg_main
417	END INTERFACE stg_main
418
419	!
420	!-- Reading of NAMELIST parameters
421	INTERFACE stg_parin
422	MODULE PROCEDURE stg_parin
423	END INTERFACE stg_parin
424
425	!
426	!-- Reading of parameters for restart runs
427	INTERFACE stg_rrd_global
428	MODULE PROCEDURE stg_rrd_global
429	END INTERFACE stg_rrd_global
430
431	!
432	!-- Writing of binary output for restart runs
433	INTERFACE stg_wrd_global
434	MODULE PROCEDURE stg_wrd_global
435	END INTERFACE stg_wrd_global
436
437	SAVE
438
439	PRIVATE
440
441	!
442	!-- Public interfaces
443	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
444	stg_parin, stg_rrd_global, stg_wrd_global
445
446	!
447	!-- Public variables
448	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
449	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
450	time_stg_adjust, time_stg_call, use_syn_turb_gen
451
452
453	CONTAINS
454
455
456	!------------------------------------------------------------------------------!
457	! Description:
458	! ------------
459	!> Check parameters routine for synthetic turbulence generator
460	!------------------------------------------------------------------------------!
461	SUBROUTINE stg_check_parameters
462
463	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
464	nesting_offline ) THEN
465	message_string = 'Synthetic turbulence generator is required ' // &
466	'if offline nesting is applied and PALM operates ' // &
467	'in LES mode.'
468	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
469	ENDIF
470
471	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
472	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
473	message_string = 'Synthetic turbulence generator is required ' // &
474	'when nesting is applied and parent operates in ' // &
475	'RANS-mode but current child in LES mode.'
476	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
477	ENDIF
478
479	IF ( use_syn_turb_gen ) THEN
480
481	IF ( child_domain .AND. .NOT. rans_mode .AND. &
482	.NOT. rans_mode_parent ) THEN
483	message_string = 'Using synthetic turbulence generator ' // &
484	'is not allowed in LES-LES nesting.'
485	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
486
487	ENDIF
488
489	IF ( child_domain .AND. rans_mode .AND. &
490	rans_mode_parent ) THEN
491	message_string = 'Using synthetic turbulence generator ' // &
492	'is not allowed in RANS-RANS nesting.'
493	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
494
495	ENDIF
496
497	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
498
499	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
500	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
501	message_string = 'Using synthetic turbulence generator ' // &
502	'requires %initializing_actions = ' // &
503	'"set_constant_profiles" or "read_restart_data"' //&
504	', if not offline nesting is applied.'
505	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
506	ENDIF
507
508	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
509	message_string = 'Using synthetic turbulence generator ' // &
510	'requires &bc_lr = "dirichlet/radiation", ' // &
511	'if not offline nesting is applied.'
512	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
513	ENDIF
514	IF ( bc_ns /= 'cyclic' ) THEN
515	message_string = 'Using synthetic turbulence generator ' // &
516	'requires &bc_ns = "cyclic", ' // &
517	'if not offline nesting is applied.'
518	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
519	ENDIF
520
521	ENDIF
522
523	IF ( turbulent_inflow ) THEN
524	message_string = 'Using synthetic turbulence generator ' // &
525	'in combination &with turbulent_inflow = .T. '// &
526	'is not allowed'
527	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
528	ENDIF
529	!
530	!-- Synthetic turbulence generator requires the parallel random generator
531	IF ( random_generator /= 'random-parallel' ) THEN
532	message_string = 'Using synthetic turbulence generator ' // &
533	'requires random_generator = random-parallel.'
534	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
535	ENDIF
536
537	ENDIF
538
539	END SUBROUTINE stg_check_parameters
540
541
542	!------------------------------------------------------------------------------!
543	! Description:
544	! ------------
545	!> Header output for synthetic turbulence generator
546	!------------------------------------------------------------------------------!
547	SUBROUTINE stg_header ( io )
548
549	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
550
551	!
552	!-- Write synthetic turbulence generator Header
553	WRITE( io, 1 )
554	IF ( use_syn_turb_gen ) THEN
555	WRITE( io, 2 )
556	ELSE
557	WRITE( io, 3 )
558	ENDIF
559
560	IF ( parametrize_inflow_turbulence ) THEN
561	WRITE( io, 4 ) dt_stg_adjust
562	ELSE
563	WRITE( io, 5 )
564	ENDIF
565
566	1 FORMAT (//' Synthetic turbulence generator information:'/ &
567	' ------------------------------------------'/)
568	2 FORMAT (' synthetic turbulence generator is switched on')
569	3 FORMAT (' synthetic turbulence generator is switched off')
570	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
571	5 FORMAT (' imposed turbulence is read from file' )
572
573	END SUBROUTINE stg_header
574
575
576	!------------------------------------------------------------------------------!
577	! Description:
578	! ------------
579	!> Initialization of the synthetic turbulence generator
580	!------------------------------------------------------------------------------!
581	SUBROUTINE stg_init
582
583	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
584
585	#if defined( __parallel )
586	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
587	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
588	#endif
589
590	INTEGER(iwp) :: i !> grid index in x-direction
591	INTEGER(iwp) :: j !> loop index
592	INTEGER(iwp) :: k !< index
593	INTEGER(iwp) :: newtype !< dummy MPI type
594	INTEGER(iwp) :: realsize !< size of REAL variables
595
596	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
597	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
598	!
599	!-- Dummy variables used for reading profiles
600	REAL(wp) :: d1 !< u profile
601	REAL(wp) :: d2 !< v profile
602	REAL(wp) :: d3 !< w profile
603	REAL(wp) :: d5 !< e profile
604	REAL(wp) :: luy !< length scale for u in y direction
605	REAL(wp) :: luz !< length scale for u in z direction
606	REAL(wp) :: lvy !< length scale for v in y direction
607	REAL(wp) :: lvz !< length scale for v in z direction
608	REAL(wp) :: lwy !< length scale for w in y direction
609	REAL(wp) :: lwz !< length scale for w in z direction
610	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
611	REAL(wp) :: zz !< height
612
613
614	#if defined( __parallel )
615	CALL MPI_BARRIER( comm2d, ierr )
616	#endif
617	!
618	!-- Create mpi-datatypes for exchange in case of non-local but distributed
619	!-- computation of the velocity seeds. This option is useful in
620	!-- case large turbulent length scales are presentm, where the computational
621	!-- effort becomes large and need to be parallelized. For parametrized
622	!-- turbulence the length scales are small and computing the velocity seeds
623	!-- locally is faster (no overhead by communication).
624	IF ( .NOT. compute_velocity_seeds_local ) THEN
625	#if defined( __parallel )
626	!
627	!-- Determine processor decomposition of z-axis along x- and y-direction
628	nnz = nz / pdims(1)
629	nzb_x_stg = 1 + myidx * INT( nnz )
630	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
631
632	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
633	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
634
635	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
636	.AND. .NOT. rans_mode ) ) THEN
637	nnz = nz / pdims(2)
638	nzb_y_stg = 1 + myidy * INT( nnz )
639	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
640
641	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
642	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
643	ENDIF
644
645	!
646	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
647	!-- velocity seeds
648	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
649	extent = 1 * realsize
650	!
651	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
652	!-- layer
653	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
654	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
655	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
656	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
657	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
658	CALL MPI_TYPE_FREE( newtype, ierr )
659
660	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
661	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
662	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
663	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
664	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
665	CALL MPI_TYPE_FREE( newtype, ierr )
666
667	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
668	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
669
670	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
671	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
672
673	DO j = 1, pdims(1)
674	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
675	ENDDO
676	!
677	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
678	!-- layer
679	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
680	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
681	.AND. .NOT. rans_mode ) ) THEN
682	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
683	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
684	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
685	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
686	CALL MPI_TYPE_FREE( newtype, ierr )
687
688	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
689	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
690	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
691	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
692	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
693	CALL MPI_TYPE_FREE( newtype, ierr )
694
695	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
696	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
697
698	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
699	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
700
701	DO j = 1, pdims(2)
702	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
703	ENDDO
704
705	ENDIF
706	#endif
707	ENDIF
708	!
709	!-- Allocate required arrays.
710	!-- In case no offline nesting or self nesting is used, the arrary
711	!-- mean_inflow profiles is required. Check if it is already allocated, else
712	!-- allocate and initialize it appropriately. Note, in case turbulence and
713	!-- inflow information is read from file, mean_inflow_profiles is already
714	!-- allocated and initialized appropriately.
715	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
716	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
717	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
718	mean_inflow_profiles = 0.0_wp
719	mean_inflow_profiles(:,1) = u_init
720	mean_inflow_profiles(:,2) = v_init
721	!
722	!-- Even though potential temperature and humidity are not perturbed,
723	!-- they need to be initialized appropriately.
724	IF ( .NOT. neutral ) &
725	mean_inflow_profiles(:,4) = pt_init
726	IF ( humidity ) &
727	mean_inflow_profiles(:,6) = q_init
728	ENDIF
729	ENDIF
730
731	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
732	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
733	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
734	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
735	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
736	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
737	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
738	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
739
740	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
741	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
742	dist_xz = 0.0_wp
743	dist_yz = 0.0_wp
744	!
745	!-- Read inflow profile
746	!-- Height levels of profiles in input profile is as follows:
747	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
748	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
749	!-- WARNING: zz is not used at the moment
750	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
751	EXIST = file_stg_exist )
752
753	IF ( file_stg_exist ) THEN
754
755	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
756	FORM='FORMATTED')
757	!
758	!-- Skip header
759	READ( 90, * )
760
761	DO k = nzb+1, nzt+1
762	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
763	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
764	d1, d2, d3, d5
765
766	!
767	!-- Convert length scales from meter to number of grid points.
768	nuy(k) = INT( luy * ddy )
769	nuz(k) = INT( luz * ddzw(k) )
770	nvy(k) = INT( lvy * ddy )
771	nvz(k) = INT( lvz * ddzw(k) )
772	nwy(k) = INT( lwy * ddy )
773	nwz(k) = INT( lwz * ddzw(k) )
774	!
775	!-- Workaround, assume isotropic turbulence
776	nwx(k) = nwy(k)
777	nvx(k) = nvy(k)
778	nux(k) = nuy(k)
779	!
780	!-- Save Mean inflow profiles
781	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
782	mean_inflow_profiles(k,1) = d1
783	mean_inflow_profiles(k,2) = d2
784	! mean_inflow_profiles(k,4) = d4
785	mean_inflow_profiles(k,5) = d5
786	ENDIF
787	ENDDO
788	!
789	!-- Set lenght scales at surface grid point
790	nuy(nzb) = nuy(nzb+1)
791	nuz(nzb) = nuz(nzb+1)
792	nvy(nzb) = nvy(nzb+1)
793	nvz(nzb) = nvz(nzb+1)
794	nwy(nzb) = nwy(nzb+1)
795	nwz(nzb) = nwz(nzb+1)
796
797	CLOSE( 90 )
798	!
799	!-- Calculate coefficient matrix from Reynolds stress tensor
800	!-- (Lund rotation)
801	CALL calc_coeff_matrix
802	!
803	!-- No information about turbulence and its length scales are available.
804	!-- Instead, parametrize turbulence which is imposed at the boundaries.
805	!-- Set flag which indicates that turbulence is parametrized, which is done
806	!-- later when energy-balance models are already initialized. This is
807	!-- because the STG needs information about surface properties such as
808	!-- roughness to build 'realistic' turbulence profiles.
809	ELSE
810	!
811	!-- Define length scale for the imposed turbulence, which is defined as
812	!-- 8 times the minimum grid spacing
813	length_scale = 30.0_wp * MIN( dx, dy, MINVAL( dzw ) ) !8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
814	!
815	!-- Define constant to gradually decrease length scales and Reynolds stress
816	!-- above ABL top. Assure that no zero length scales are used.
817	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
818	!
819	!-- Set flag indicating that turbulence is parametrized
820	parametrize_inflow_turbulence = .TRUE.
821	!
822	!-- In case of dirichlet inflow boundary conditions only at one lateral
823	!-- boundary, i.e. in the case no offline or self nesting is applied but
824	!-- synthetic turbulence shall be parametrized nevertheless, the
825	!-- boundary-layer depth need to determined first.
826	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
827	CALL nesting_offl_calc_zi
828	!
829	!-- Determine boundary-layer depth, which is used to initialize lenght
830	!-- scales
831	CALL calc_scaling_variables
832	!
833	!-- Initialize lenght and time scales, which in turn are used
834	!-- to initialize the filter functions.
835	CALL calc_length_and_time_scale
836	!
837	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
838	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
839	!-- Rotach et al. (1996) and is based on boundary-layer depth,
840	!-- friction velocity and velocity scale.
841	CALL parametrize_reynolds_stress
842	!
843	!-- Calculate coefficient matrix from Reynolds stress tensor
844	!-- (Lund rotation)
845	CALL calc_coeff_matrix
846
847	ENDIF
848
849	!
850	!-- Assign initial profiles. Note, this is only required if turbulent
851	!-- inflow from the left is desired, not in case of any of the
852	!-- nesting (offline or self nesting) approaches.
853	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
854	u_init = mean_inflow_profiles(:,1)
855	v_init = mean_inflow_profiles(:,2)
856	!pt_init = mean_inflow_profiles(:,4)
857	e_init = MAXVAL( mean_inflow_profiles(:,5) )
858	ENDIF
859
860	!
861	!-- Define the size of the filter functions and allocate them.
862	mergp = 0
863
864	! arrays must be large enough to cover the largest length scale
865	DO k = nzb, nzt+1
866	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
867	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
868	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
869	IF ( j > mergp ) mergp = j
870	ENDDO
871
872	! mergp = 2 * mergp
873	! mergp = mergp
874
875	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
876	buy(-mergp:mergp,nzb:nzt+1), &
877	buz(-mergp:mergp,nzb:nzt+1), &
878	bvx(-mergp:mergp,nzb:nzt+1), &
879	bvy(-mergp:mergp,nzb:nzt+1), &
880	bvz(-mergp:mergp,nzb:nzt+1), &
881	bwx(-mergp:mergp,nzb:nzt+1), &
882	bwy(-mergp:mergp,nzb:nzt+1), &
883	bwz(-mergp:mergp,nzb:nzt+1) )
884
885	!
886	!-- Allocate velocity seeds for turbulence at xz-layer
887	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
888	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
889	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
890
891	!
892	!-- Allocate velocity seeds for turbulence at yz-layer
893	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
894	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
895	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
896
897	fu_xz = 0.0_wp
898	fuo_xz = 0.0_wp
899	fv_xz = 0.0_wp
900	fvo_xz = 0.0_wp
901	fw_xz = 0.0_wp
902	fwo_xz = 0.0_wp
903
904	fu_yz = 0.0_wp
905	fuo_yz = 0.0_wp
906	fv_yz = 0.0_wp
907	fvo_yz = 0.0_wp
908	fw_yz = 0.0_wp
909	fwo_yz = 0.0_wp
910
911	!
912	!-- Create filter functions
913	CALL stg_filter_func( nux, bux ) !filter ux
914	CALL stg_filter_func( nuy, buy ) !filter uy
915	CALL stg_filter_func( nuz, buz ) !filter uz
916	CALL stg_filter_func( nvx, bvx ) !filter vx
917	CALL stg_filter_func( nvy, bvy ) !filter vy
918	CALL stg_filter_func( nvz, bvz ) !filter vz
919	CALL stg_filter_func( nwx, bwx ) !filter wx
920	CALL stg_filter_func( nwy, bwy ) !filter wy
921	CALL stg_filter_func( nwz, bwz ) !filter wz
922
923	#if defined( __parallel )
924	CALL MPI_BARRIER( comm2d, ierr )
925	#endif
926
927	!
928	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
929	! time step.
930	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
931	! are 0 compared to the prerun. This is mostly for k=nzt+1.
932	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
933	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
934
935	IF ( myidx == id_stg_left ) i = -1
936	IF ( myidx == id_stg_right ) i = nxr+1
937
938	DO j = nys, nyn
939	DO k = nzb, nzt+1
940	IF ( a11(k) > 10E-8_wp ) THEN
941	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
942	ELSE
943	fu_yz(k,j) = 10E-8_wp
944	ENDIF
945
946	IF ( a22(k) > 10E-8_wp ) THEN
947	fv_yz(k,j) = ( v(k,j,i) - &
948	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
949	ELSE
950	fv_yz(k,j) = 10E-8_wp
951	ENDIF
952
953	IF ( a33(k) > 10E-8_wp ) THEN
954	fw_yz(k,j) = ( w(k,j,i) - &
955	a31(k) * fu_yz(k,j) - a32(k) * &
956	fv_yz(k,j) ) / a33(k)
957	ELSE
958	fw_yz(k,j) = 10E-8_wp
959	ENDIF
960	ENDDO
961	ENDDO
962	ENDIF
963
964	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
965
966	IF ( myidy == id_stg_south ) j = -1
967	IF ( myidy == id_stg_north ) j = nyn+1
968
969	DO i = nxl, nxr
970	DO k = nzb, nzt+1
971	!
972	!-- In case the correlation coefficients are very small, the
973	!-- velocity seeds may become very large finally creating
974	!-- numerical instabilities in the synthetic turbulence generator.
975	!-- Empirically, a value of 10E-8 seems to be sufficient.
976	IF ( a11(k) > 10E-8_wp ) THEN
977	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
978	ELSE
979	fu_xz(k,i) = 10E-8_wp
980	ENDIF
981
982	IF ( a22(k) > 10E-8_wp ) THEN
983	fv_xz(k,i) = ( v(k,j,i) - &
984	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
985	ELSE
986	fv_xz(k,i) = 10E-8_wp
987	ENDIF
988
989	IF ( a33(k) > 10E-8_wp ) THEN
990	fw_xz(k,i) = ( w(k,j,i) - &
991	a31(k) * fu_xz(k,i) - &
992	a32(k) * fv_xz(k,i) ) / a33(k)
993	ELSE
994	fw_xz(k,i) = 10E-8_wp
995	ENDIF
996
997	ENDDO
998	ENDDO
999	ENDIF
1000	ENDIF
1001	!
1002	!-- Count the number of non-topography grid points at the boundaries where
1003	!-- perturbations are imposed. This number is later used for bias corrections
1004	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1005	!-- due to the asymetry of u and v along x and y direction, respectively,
1006	!-- different cases must be distinguished.
1007	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1008	!
1009	!-- Number of grid points where perturbations are imposed on u
1010	IF ( myidx == id_stg_left ) i = nxl
1011	IF ( myidx == id_stg_right ) i = nxr+1
1012
1013	nr_non_topo_yz_l(1) = SUM( &
1014	MERGE( 1, 0, &
1015	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1016	!
1017	!-- Number of grid points where perturbations are imposed on v and w
1018	IF ( myidx == id_stg_left ) i = nxl-1
1019	IF ( myidx == id_stg_right ) i = nxr+1
1020
1021	nr_non_topo_yz_l(2) = SUM( &
1022	MERGE( 1, 0, &
1023	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1024	nr_non_topo_yz_l(3) = SUM( &
1025	MERGE( 1, 0, &
1026	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1027
1028	#if defined( __parallel )
1029	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1030	MPI_SUM, comm1dy, ierr )
1031	#else
1032	nr_non_topo_yz = nr_non_topo_yz_l
1033	#endif
1034	ENDIF
1035
1036	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1037	!
1038	!-- Number of grid points where perturbations are imposed on v
1039	IF ( myidy == id_stg_south ) j = nys
1040	IF ( myidy == id_stg_north ) j = nyn+1
1041
1042	nr_non_topo_xz_l(2) = SUM( &
1043	MERGE( 1, 0, &
1044	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1045	!
1046	!-- Number of grid points where perturbations are imposed on u and w
1047	IF ( myidy == id_stg_south ) j = nys-1
1048	IF ( myidy == id_stg_north ) j = nyn+1
1049
1050	nr_non_topo_xz_l(1) = SUM( &
1051	MERGE( 1, 0, &
1052	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1053	nr_non_topo_xz_l(3) = SUM( &
1054	MERGE( 1, 0, &
1055	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1056
1057	#if defined( __parallel )
1058	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1059	MPI_SUM, comm1dx, ierr )
1060	#else
1061	nr_non_topo_xz = nr_non_topo_xz_l
1062	#endif
1063	ENDIF
1064	!
1065	!-- Initialize random number generator at xz- and yz-layers. Random numbers
1066	!-- are initialized at each core. In case there is only inflow from the left,
1067	!-- it is sufficient to generate only random numbers for the yz-layer, else
1068	!-- random numbers for the xz-layer are also required.
1069	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1070	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1071	id_rand_yz = 0
1072	seq_rand_yz = 0
1073
1074	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
1075	id_rand_yz, seq_rand_yz )
1076
1077	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1078	.AND. .NOT. rans_mode ) ) THEN
1079	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1080	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1081	id_rand_xz = 0
1082	seq_rand_xz = 0
1083
1084	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
1085	id_rand_xz, seq_rand_xz )
1086	ENDIF
1087
1088
1089
1090	END SUBROUTINE stg_init
1091
1092
1093	!------------------------------------------------------------------------------!
1094	! Description:
1095	! ------------
1096	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1097	!> (Xie and Castro, 2008)
1098	!------------------------------------------------------------------------------!
1099	SUBROUTINE stg_filter_func( nxx, bxx )
1100
1101	INTEGER(iwp) :: k !< loop index
1102	INTEGER(iwp) :: n_k !< length scale nXX in height k
1103	INTEGER(iwp) :: nf !< index for length scales
1104
1105	REAL(wp) :: bdenom !< denominator for filter functions bXX
1106	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1107
1108	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1109
1110	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1111
1112
1113	bxx = 0.0_wp
1114
1115	DO k = nzb, nzt+1
1116	bdenom = 0.0_wp
1117	n_k = nxx(k)
1118	IF ( n_k /= 0 ) THEN
1119
1120	!
1121	!-- ( Eq.10 )^2
1122	DO nf = -n_k, n_k
1123	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1124	ENDDO
1125
1126	!
1127	!-- ( Eq.9 )
1128	bdenom = SQRT( bdenom )
1129	DO nf = -n_k, n_k
1130	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1131	ENDDO
1132	ENDIF
1133	ENDDO
1134
1135	END SUBROUTINE stg_filter_func
1136
1137
1138	!------------------------------------------------------------------------------!
1139	! Description:
1140	! ------------
1141	!> Parin for &stg_par for synthetic turbulence generator
1142	!------------------------------------------------------------------------------!
1143	SUBROUTINE stg_parin
1144
1145	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1146
1147
1148	NAMELIST /stg_par/ dt_stg_adjust, &
1149	dt_stg_call, &
1150	use_syn_turb_gen, &
1151	compute_velocity_seeds_local
1152
1153	line = ' '
1154	!
1155	!-- Try to find stg package
1156	REWIND ( 11 )
1157	line = ' '
1158	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1159	READ ( 11, '(A)', END=20 ) line
1160	ENDDO
1161	BACKSPACE ( 11 )
1162
1163	!
1164	!-- Read namelist
1165	READ ( 11, stg_par, ERR = 10, END = 20 )
1166
1167	!
1168	!-- Set flag that indicates that the synthetic turbulence generator is switched
1169	!-- on
1170	syn_turb_gen = .TRUE.
1171	GOTO 20
1172
1173	10 BACKSPACE( 11 )
1174	READ( 11 , '(A)') line
1175	CALL parin_fail_message( 'stg_par', line )
1176
1177	20 CONTINUE
1178
1179	END SUBROUTINE stg_parin
1180
1181
1182	!------------------------------------------------------------------------------!
1183	! Description:
1184	! ------------
1185	!> This routine reads the respective restart data.
1186	!------------------------------------------------------------------------------!
1187	SUBROUTINE stg_rrd_global( found )
1188
1189	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1190
1191	found = .TRUE.
1192
1193
1194	SELECT CASE ( restart_string(1:length) )
1195
1196	CASE ( 'time_stg_adjust' )
1197	READ ( 13 ) time_stg_adjust
1198
1199	CASE ( 'time_stg_call' )
1200	READ ( 13 ) time_stg_call
1201
1202	CASE ( 'use_syn_turb_gen' )
1203	READ ( 13 ) use_syn_turb_gen
1204
1205	CASE DEFAULT
1206
1207	found = .FALSE.
1208
1209	END SELECT
1210
1211
1212	END SUBROUTINE stg_rrd_global
1213
1214
1215	!------------------------------------------------------------------------------!
1216	! Description:
1217	! ------------
1218	!> This routine writes the respective restart data.
1219	!------------------------------------------------------------------------------!
1220	SUBROUTINE stg_wrd_global
1221
1222	CALL wrd_write_string( 'time_stg_adjust' )
1223	WRITE ( 14 ) time_stg_adjust
1224
1225	CALL wrd_write_string( 'time_stg_call' )
1226	WRITE ( 14 ) time_stg_call
1227
1228	CALL wrd_write_string( 'use_syn_turb_gen' )
1229	WRITE ( 14 ) use_syn_turb_gen
1230
1231
1232	END SUBROUTINE stg_wrd_global
1233
1234
1235	!------------------------------------------------------------------------------!
1236	! Description:
1237	! ------------
1238	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1239	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1240	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1241	!> (Lund, 1998).
1242	!------------------------------------------------------------------------------!
1243	SUBROUTINE stg_main
1244
1245	INTEGER(iwp) :: i !< grid index in x-direction
1246	INTEGER(iwp) :: j !< loop index in y-direction
1247	INTEGER(iwp) :: k !< loop index in z-direction
1248
1249	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1250
1251	REAL(wp) :: dt_stg !< wheighted subtimestep
1252
1253	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1254
1255	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1256	!
1257	!-- Calculate time step which is needed for filter functions
1258	dt_stg = MAX( dt_3d, dt_stg_call )
1259	!
1260	!-- Check if synthetic turbulence generator needs to be called and new
1261	!-- perturbations need to be created or if old disturbances can be imposed
1262	!-- again.
1263	IF ( time_stg_call >= dt_stg_call .AND. &
1264	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1265	stg_call = .TRUE.
1266	ELSE
1267	stg_call = .FALSE.
1268	ENDIF
1269	!
1270	!-- Initial value of fu, fv, fw
1271	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1272	!
1273	!-- Generate turbulence at the left and right boundary. Random numbers
1274	!-- for the yz-planes at the left/right boundary are generated by the
1275	!-- left-sided mpi ranks only. After random numbers are calculated, they
1276	!-- are distributed to all other mpi ranks in the model, so that the
1277	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1278	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1279	!-- that the left- and the right-sided lateral boundary have the same initial
1280	!-- seeds.
1281	!-- Note, in case of inflow from the right only, only turbulence at the left
1282	!-- boundary is required.
1283	IF ( .NOT. ( nesting_offline .OR. &
1284	( child_domain .AND. rans_mode_parent &
1285	.AND. .NOT. rans_mode ) ) ) THEN
1286	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1287	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1288	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1289	ELSE
1290	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1291	id_stg_left, id_stg_right )
1292	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1293	id_stg_left, id_stg_right )
1294	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1295	id_stg_left, id_stg_right )
1296	!
1297	!-- Generate turbulence at the south and north boundary. Random numbers
1298	!-- for the xz-planes at the south/north boundary are generated by the
1299	!-- south-sided mpi ranks only. Please see also comment above.
1300	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1301	id_stg_south, id_stg_north )
1302	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1303	id_stg_south, id_stg_north )
1304	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1305	id_stg_south, id_stg_north )
1306	ENDIF
1307	velocity_seed_initialized = .TRUE.
1308	ENDIF
1309	!
1310	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1311	!-- seeds are only required at the left boundary, while in case of offline
1312	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1313	!-- right, south and north boundaries.
1314	IF ( stg_call ) THEN
1315	IF ( .NOT. ( nesting_offline .OR. &
1316	( child_domain .AND. rans_mode_parent &
1317	.AND. .NOT. rans_mode ) ) ) THEN
1318	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1319	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1320	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1321
1322	ELSE
1323	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1324	id_stg_left, id_stg_right )
1325	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1326	id_stg_left, id_stg_right )
1327	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1328	id_stg_left, id_stg_right )
1329
1330	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1331	id_stg_south, id_stg_north )
1332	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1333	id_stg_south, id_stg_north )
1334	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1335	id_stg_south, id_stg_north )
1336	ENDIF
1337	ENDIF
1338
1339	!
1340	!-- Turbulence generation at left and/or right boundary
1341	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1342	!
1343	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1344	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1345	!-- imposed
1346	IF ( stg_call ) THEN
1347
1348	DO j = nys, nyn
1349	DO k = nzb, nzt + 1
1350	!
1351	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1352	IF ( tu(k) == 0.0_wp ) THEN
1353	fu_yz(k,j) = fuo_yz(k,j)
1354	ELSE
1355	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1356	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1357	ENDIF
1358
1359	IF ( tv(k) == 0.0_wp ) THEN
1360	fv_yz(k,j) = fvo_yz(k,j)
1361	ELSE
1362	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1363	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1364	ENDIF
1365
1366	IF ( tw(k) == 0.0_wp ) THEN
1367	fw_yz(k,j) = fwo_yz(k,j)
1368	ELSE
1369	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1370	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1371	ENDIF
1372	ENDDO
1373	ENDDO
1374
1375	dist_yz(nzb,:,1) = 0.0_wp
1376	dist_yz(nzb,:,2) = 0.0_wp
1377	dist_yz(nzb,:,3) = 0.0_wp
1378
1379	IF ( myidx == id_stg_left ) i = nxl
1380	IF ( myidx == id_stg_right ) i = nxr+1
1381	DO j = nys, nyn
1382	DO k = nzb+1, nzt + 1
1383	!
1384	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1385	!-- Additional factors are added to improve the variance of v and w
1386	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1387	MERGE( 1.0_wp, 0.0_wp, &
1388	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1389	ENDDO
1390	ENDDO
1391
1392	IF ( myidx == id_stg_left ) i = nxl-1
1393	IF ( myidx == id_stg_right ) i = nxr+1
1394	DO j = nys, nyn
1395	DO k = nzb+1, nzt + 1
1396	!
1397	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1398	!-- Additional factors are added to improve the variance of v and w
1399	!-- experimental test of 1.2
1400	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1401	* 1.2_wp ) &
1402	* ( a21(k) * fu_yz(k,j) &
1403	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1404	MERGE( 1.0_wp, 0.0_wp, &
1405	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1406	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1407	* 1.3_wp ) &
1408	* ( a31(k) * fu_yz(k,j) &
1409	+ a32(k) * fv_yz(k,j) &
1410	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1411	MERGE( 1.0_wp, 0.0_wp, &
1412	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1413	ENDDO
1414	ENDDO
1415	ENDIF
1416	!
1417	!-- Mass flux correction following Kim et al. (2013)
1418	!-- This correction factor insures that the mass flux is preserved at the
1419	!-- inflow boundary. First, calculate mean value of the imposed
1420	!-- perturbations at yz boundary.
1421	!-- Note, this needs to be done only after the last RK3-substep, else
1422	!-- the boundary values won't be accessed.
1423	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1424	mc_factor_l = 0.0_wp
1425	mc_factor = 0.0_wp
1426	!
1427	!-- Sum up the original volume flows (with and without perturbations).
1428	!-- Note, for non-normal components (here v and w) it is actually no
1429	!-- volume flow.
1430	IF ( myidx == id_stg_left ) i = nxl
1431	IF ( myidx == id_stg_right ) i = nxr+1
1432
1433	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1434	* MERGE( 1.0_wp, 0.0_wp, &
1435	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1436
1437	IF ( myidx == id_stg_left ) i = nxl-1
1438	IF ( myidx == id_stg_right ) i = nxr+1
1439
1440	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1441	* MERGE( 1.0_wp, 0.0_wp, &
1442	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1443	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1444	* MERGE( 1.0_wp, 0.0_wp, &
1445	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1446
1447	#if defined( __parallel )
1448	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1449	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1450	#else
1451	mc_factor = mc_factor_l
1452	#endif
1453	!
1454	!-- Calculate correction factor and force zero mean perturbations.
1455	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1456
1457	IF ( myidx == id_stg_left ) i = nxl
1458	IF ( myidx == id_stg_right ) i = nxr+1
1459
1460	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
1461	* MERGE( 1.0_wp, 0.0_wp, &
1462	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1463
1464
1465	IF ( myidx == id_stg_left ) i = nxl-1
1466	IF ( myidx == id_stg_right ) i = nxr+1
1467
1468	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
1469	* MERGE( 1.0_wp, 0.0_wp, &
1470	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1471
1472	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
1473	* MERGE( 1.0_wp, 0.0_wp, &
1474	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1475	!
1476	!-- Add disturbances
1477	IF ( myidx == id_stg_left ) THEN
1478	!
1479	!-- For the left boundary distinguish between mesoscale offline / self
1480	!-- nesting and turbulent inflow at the left boundary only. In the latter
1481	!-- case turbulence is imposed on the mean inflow profiles.
1482	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1483	!
1484	!-- Add disturbance at the inflow
1485	DO j = nys, nyn
1486	DO k = nzb, nzt+1
1487	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1488	dist_yz(k,j,1) ) &
1489	* MERGE( 1.0_wp, 0.0_wp, &
1490	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1491	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1492	dist_yz(k,j,2) ) &
1493	* MERGE( 1.0_wp, 0.0_wp, &
1494	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1495	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1496	* MERGE( 1.0_wp, 0.0_wp, &
1497	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1498	ENDDO
1499	ENDDO
1500	ELSE
1501
1502	DO j = nys, nyn
1503	DO k = nzb+1, nzt
1504	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1505	* MERGE( 1.0_wp, 0.0_wp, &
1506	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1507	u(k,j,-1) = u(k,j,0)
1508	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1509	* MERGE( 1.0_wp, 0.0_wp, &
1510	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1511	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1512	* MERGE( 1.0_wp, 0.0_wp, &
1513	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1514	ENDDO
1515	ENDDO
1516	ENDIF
1517	ENDIF
1518	IF ( myidx == id_stg_right ) THEN
1519	DO j = nys, nyn
1520	DO k = nzb+1, nzt
1521	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1522	* MERGE( 1.0_wp, 0.0_wp, &
1523	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1524	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1525	* MERGE( 1.0_wp, 0.0_wp, &
1526	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1527	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1528	* MERGE( 1.0_wp, 0.0_wp, &
1529	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1530	ENDDO
1531	ENDDO
1532	ENDIF
1533	ENDIF
1534	ENDIF
1535	!
1536	!-- Turbulence generation at north and south boundary
1537	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1538	!
1539	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1540	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1541	!-- imposed
1542	IF ( stg_call ) THEN
1543	DO i = nxl, nxr
1544	DO k = nzb, nzt + 1
1545	!
1546	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1547	IF ( tu(k) == 0.0_wp ) THEN
1548	fu_xz(k,i) = fuo_xz(k,i)
1549	ELSE
1550	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1551	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1552	ENDIF
1553
1554	IF ( tv(k) == 0.0_wp ) THEN
1555	fv_xz(k,i) = fvo_xz(k,i)
1556	ELSE
1557	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1558	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1559	ENDIF
1560
1561	IF ( tw(k) == 0.0_wp ) THEN
1562	fw_xz(k,i) = fwo_xz(k,i)
1563	ELSE
1564	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1565	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1566	ENDIF
1567	ENDDO
1568	ENDDO
1569
1570
1571	dist_xz(nzb,:,1) = 0.0_wp
1572	dist_xz(nzb,:,2) = 0.0_wp
1573	dist_xz(nzb,:,3) = 0.0_wp
1574
1575	IF ( myidy == id_stg_south ) j = nys
1576	IF ( myidy == id_stg_north ) j = nyn+1
1577	DO i = nxl, nxr
1578	DO k = nzb+1, nzt + 1
1579	!
1580	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1581	!-- Additional factors are added to improve the variance of v and w
1582	!experimental test of 1.2
1583	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1584	* 1.2_wp ) &
1585	* ( a21(k) * fu_xz(k,i) &
1586	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1587	MERGE( 1.0_wp, 0.0_wp, &
1588	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1589	ENDDO
1590	ENDDO
1591
1592	IF ( myidy == id_stg_south ) j = nys-1
1593	IF ( myidy == id_stg_north ) j = nyn+1
1594	DO i = nxl, nxr
1595	DO k = nzb+1, nzt + 1
1596	!
1597	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1598	!-- Additional factors are added to improve the variance of v and w
1599	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1600	MERGE( 1.0_wp, 0.0_wp, &
1601	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1602
1603	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1604	* 1.3_wp ) &
1605	* ( a31(k) * fu_xz(k,i) &
1606	+ a32(k) * fv_xz(k,i) &
1607	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1608	MERGE( 1.0_wp, 0.0_wp, &
1609	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1610	ENDDO
1611	ENDDO
1612	ENDIF
1613
1614	!
1615	!-- Mass flux correction following Kim et al. (2013)
1616	!-- This correction factor insures that the mass flux is preserved at the
1617	!-- inflow boundary. First, calculate mean value of the imposed
1618	!-- perturbations at yz boundary.
1619	!-- Note, this needs to be done only after the last RK3-substep, else
1620	!-- the boundary values won't be accessed.
1621	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1622	mc_factor_l = 0.0_wp
1623	mc_factor = 0.0_wp
1624
1625	IF ( myidy == id_stg_south ) j = nys
1626	IF ( myidy == id_stg_north ) j = nyn+1
1627
1628	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1629	* MERGE( 1.0_wp, 0.0_wp, &
1630	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1631
1632	IF ( myidy == id_stg_south ) j = nys-1
1633	IF ( myidy == id_stg_north ) j = nyn+1
1634
1635	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1636	* MERGE( 1.0_wp, 0.0_wp, &
1637	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1638	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1639	* MERGE( 1.0_wp, 0.0_wp, &
1640	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1641
1642	#if defined( __parallel )
1643	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1644	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1645	#else
1646	mc_factor = mc_factor_l
1647	#endif
1648
1649	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1650
1651	IF ( myidy == id_stg_south ) j = nys
1652	IF ( myidy == id_stg_north ) j = nyn+1
1653
1654	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
1655	* MERGE( 1.0_wp, 0.0_wp, &
1656	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1657
1658
1659	IF ( myidy == id_stg_south ) j = nys-1
1660	IF ( myidy == id_stg_north ) j = nyn+1
1661
1662	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
1663	* MERGE( 1.0_wp, 0.0_wp, &
1664	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1665
1666	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
1667	* MERGE( 1.0_wp, 0.0_wp, &
1668	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1669	!
1670	!-- Add disturbances
1671	IF ( myidy == id_stg_south ) THEN
1672	DO i = nxl, nxr
1673	DO k = nzb+1, nzt
1674	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1675	* MERGE( 1.0_wp, 0.0_wp, &
1676	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1677	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1678	* MERGE( 1.0_wp, 0.0_wp, &
1679	BTEST( wall_flags_total_0(k,0,i), 2 ) )
1680	v(k,-1,i) = v(k,0,i)
1681	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1682	* MERGE( 1.0_wp, 0.0_wp, &
1683	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1684	ENDDO
1685	ENDDO
1686	ENDIF
1687	IF ( myidy == id_stg_north ) THEN
1688
1689	DO i = nxl, nxr
1690	DO k = nzb+1, nzt
1691	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1692	* MERGE( 1.0_wp, 0.0_wp, &
1693	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1694	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1695	* MERGE( 1.0_wp, 0.0_wp, &
1696	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1697	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1698	* MERGE( 1.0_wp, 0.0_wp, &
1699	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1700	ENDDO
1701	ENDDO
1702	ENDIF
1703	ENDIF
1704	ENDIF
1705	!
1706	!-- Exchange ghost points.
1707	CALL exchange_horiz( u, nbgp )
1708	CALL exchange_horiz( v, nbgp )
1709	CALL exchange_horiz( w, nbgp )
1710	!
1711	!-- Finally, set time counter for calling STG to zero
1712	IF ( stg_call ) time_stg_call = 0.0_wp
1713
1714	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1715
1716	END SUBROUTINE stg_main
1717
1718	!------------------------------------------------------------------------------!
1719	! Description:
1720	! ------------
1721	!> Generate a set of random number rand_it wich is equal on each PE
1722	!> and calculate the velocity seed f_n.
1723	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1724	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1725	!> parts are collected to form the full array.
1726	!------------------------------------------------------------------------------!
1727	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1728
1729	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1730	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1731	INTEGER(iwp) :: j !< loop index in y-direction
1732	INTEGER(iwp) :: jj !< loop index in y-direction
1733	INTEGER(iwp) :: k !< loop index in z-direction
1734	INTEGER(iwp) :: kk !< loop index in z-direction
1735	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1736
1737	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1738	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1739
1740	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1741	REAL(wp) :: rand_av !< average of random number
1742	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1743
1744	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1745	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1746
1747	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1748	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1749
1750	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1751	!
1752	!-- Generate random numbers using the parallel random generator.
1753	!-- The set of random numbers are modified to have an average of 0 and
1754	!-- unit variance. Note, at the end the random number array must be defined
1755	!-- globally in order to compute the correlation matrices. However,
1756	!-- the calculation and normalization of random numbers is done locally,
1757	!-- while the result is later distributed to all processes. Further,
1758	!-- please note, a set of random numbers is only calculated for the
1759	!-- left boundary, while the right boundary uses the same random numbers
1760	!-- and thus also computes the same correlation matrix.
1761	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1762	rand_it = 0.0_wp
1763
1764	rand_av = 0.0_wp
1765	rand_sigma_inv = 0.0_wp
1766	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1767	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
1768	KIND=wp )
1769	!
1770	!-- Compute and normalize random numbers.
1771	DO j = nys - mergp, nyn + mergp
1772	!
1773	!-- Put the random seeds at grid point j
1774	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1775	DO k = nzb - mergp, nzt + 1 + mergp
1776	CALL random_number_parallel( random_dummy )
1777	rand_it(k,j) = random_dummy
1778	ENDDO
1779	!
1780	!-- Get the new random seeds from last call at grid point j
1781	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1782	ENDDO
1783	!
1784	!-- For normalization to zero mean, sum-up the global random numers.
1785	!-- To normalize the global set of random numbers,
1786	!-- the inner ghost layers mergp must not be summed-up, else
1787	!-- the random numbers on the ghost layers will be stronger weighted as they
1788	!-- also occur on the inner subdomains.
1789	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1790	MERGE( nyn, nyn + mergp, nyn /= ny )
1791	DO k = nzb - mergp, nzt + 1 + mergp
1792	rand_av = rand_av + rand_it(k,j)
1793	ENDDO
1794	ENDDO
1795
1796	#if defined( __parallel )
1797	!
1798	!-- Sum-up the local averages of the random numbers
1799	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1800	MPI_SUM, comm1dy, ierr )
1801	#endif
1802	rand_av = rand_av * nyz_inv
1803	!
1804	!-- Obtain zero mean
1805	rand_it= rand_it - rand_av
1806	!
1807	!-- Now, compute the variance
1808	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1809	MERGE( nyn, nyn + mergp, nyn /= ny )
1810	DO k = nzb - mergp, nzt + 1 + mergp
1811	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1812	ENDDO
1813	ENDDO
1814
1815	#if defined( __parallel )
1816	!
1817	!-- Sum-up the local quadratic averages of the random numbers
1818	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1819	MPI_SUM, comm1dy, ierr )
1820	#endif
1821	!
1822	!-- Compute standard deviation
1823	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1824	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1825	ELSE
1826	rand_sigma_inv = 1.0_wp
1827	ENDIF
1828	!
1829	!-- Normalize with standard deviation to obtain unit variance
1830	rand_it = rand_it * rand_sigma_inv
1831
1832	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1833	!
1834	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
1835	!-- are two options. In the first one, the computation of the seeds is
1836	!-- distributed to all processes along the communicator comm1dy and
1837	!-- gathered on the leftmost and, if necessary, on the rightmost process.
1838	!-- For huge length scales the computational effort can become quite huge
1839	!-- (it scales with the turbulent length scales), so that gain by parallelization
1840	!-- exceeds the costs by the subsequent communication.
1841	!-- In the second option, which performs better when the turbulent length scales
1842	!-- are parametrized and thus the loops are smaller, the seeds are computed
1843	!-- locally and no communication is necessary.
1844	IF ( compute_velocity_seeds_local ) THEN
1845
1846	f_n = 0.0_wp
1847	DO j = nys, nyn
1848	DO k = nzb, nzt+1
1849	DO jj = -n_y(k), n_y(k)
1850	DO kk = -n_z(k), n_z(k)
1851	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1852	ENDDO
1853	ENDDO
1854	ENDDO
1855	ENDDO
1856
1857	ELSE
1858
1859	f_n_l = 0.0_wp
1860	DO j = nys, nyn
1861	DO k = nzb_x_stg, nzt_x_stg+1
1862	DO jj = -n_y(k), n_y(k)
1863	DO kk = -n_z(k), n_z(k)
1864	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1865	ENDDO
1866	ENDDO
1867	ENDDO
1868	ENDDO
1869	!
1870	!-- Gather velocity seeds of full subdomain
1871	send_count = nzt_x_stg - nzb_x_stg + 1
1872	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1873
1874	#if defined( __parallel )
1875	!
1876	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1877	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1878	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1879	id_left, comm1dx, ierr )
1880	!
1881	!-- If required, gather the same velocity seed matrix on right boundary
1882	!-- mpi ranks (in offline nesting for example).
1883	IF ( PRESENT( id_right ) ) THEN
1884	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1885	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1886	id_right, comm1dx, ierr )
1887	ENDIF
1888	#else
1889	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1890	#endif
1891
1892	ENDIF
1893
1894	DEALLOCATE( rand_it )
1895
1896	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1897
1898	END SUBROUTINE stg_generate_seed_yz
1899
1900
1901	!------------------------------------------------------------------------------!
1902	! Description:
1903	! ------------
1904	!> Generate a set of random number rand_it wich is equal on each PE
1905	!> and calculate the velocity seed f_n.
1906	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1907	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1908	!> parts are collected to form the full array.
1909	!------------------------------------------------------------------------------!
1910	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1911
1912	INTEGER(iwp) :: i !< loop index in x-direction
1913	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1914	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1915	INTEGER(iwp) :: ii !< loop index in x-direction
1916	INTEGER(iwp) :: k !< loop index in z-direction
1917	INTEGER(iwp) :: kk !< loop index in z-direction
1918	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1919
1920	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1921	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1922
1923	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1924	REAL(wp) :: rand_av !< average of random number
1925	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1926
1927	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1928	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1929
1930	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1931	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1932
1933	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1934
1935	!
1936	!-- Generate random numbers using the parallel random generator.
1937	!-- The set of random numbers are modified to have an average of 0 and
1938	!-- unit variance. Note, at the end the random number array must be defined
1939	!-- globally in order to compute the correlation matrices. However,
1940	!-- the calculation and normalization of random numbers is done locally,
1941	!-- while the result is later distributed to all processes. Further,
1942	!-- please note, a set of random numbers is only calculated for the
1943	!-- left boundary, while the right boundary uses the same random numbers
1944	!-- and thus also computes the same correlation matrix.
1945	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
1946	rand_it = 0.0_wp
1947
1948	rand_av = 0.0_wp
1949	rand_sigma_inv = 0.0_wp
1950	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1951	* ( nx + mergp - ( 0 - mergp ) +1 ), &
1952	KIND=wp )
1953	!
1954	!-- Compute and normalize random numbers.
1955	DO i = nxl - mergp, nxr + mergp
1956	!
1957	!-- Put the random seeds at grid point ii
1958	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1959	DO k = nzb - mergp, nzt + 1 + mergp
1960	CALL random_number_parallel( random_dummy )
1961	rand_it(k,i) = random_dummy
1962	ENDDO
1963	!
1964	!-- Get the new random seeds from last call at grid point ii
1965	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1966	ENDDO
1967	!
1968	!-- For normalization to zero mean, sum-up the global random numers.
1969	!-- To normalize the global set of random numbers,
1970	!-- the inner ghost layers mergp must not be summed-up, else
1971	!-- the random numbers on the ghost layers will be stronger weighted as they
1972	!-- also occur on the inner subdomains.
1973	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1974	MERGE( nxr, nxr + mergp, nxr /= nx )
1975	DO k = nzb - mergp, nzt + 1 + mergp
1976	rand_av = rand_av + rand_it(k,i)
1977	ENDDO
1978	ENDDO
1979
1980	#if defined( __parallel )
1981	!
1982	!-- Sum-up the local averages of the random numbers
1983	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1984	MPI_SUM, comm1dx, ierr )
1985	#endif
1986	rand_av = rand_av * nxz_inv
1987	!
1988	!-- Obtain zero mean
1989	rand_it= rand_it - rand_av
1990	!
1991	!-- Now, compute the variance
1992	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1993	MERGE( nxr, nxr + mergp, nxr /= nx )
1994	DO k = nzb - mergp, nzt + 1 + mergp
1995	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
1996	ENDDO
1997	ENDDO
1998
1999	#if defined( __parallel )
2000	!
2001	!-- Sum-up the local quadratic averages of the random numbers
2002	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
2003	MPI_SUM, comm1dx, ierr )
2004	#endif
2005	!
2006	!-- Compute standard deviation
2007	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2008	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2009	ELSE
2010	rand_sigma_inv = 1.0_wp
2011	ENDIF
2012	!
2013	!-- Normalize with standard deviation to obtain unit variance
2014	rand_it = rand_it * rand_sigma_inv
2015
2016	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2017	!
2018	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
2019	!-- are two options. In the first one, the computation of the seeds is
2020	!-- distributed to all processes along the communicator comm1dx and
2021	!-- gathered on the southmost and, if necessary, on the northmost process.
2022	!-- For huge length scales the computational effort can become quite huge
2023	!-- (it scales with the turbulent length scales), so that gain by parallelization
2024	!-- exceeds the costs by the subsequent communication.
2025	!-- In the second option, which performs better when the turbulent length scales
2026	!-- are parametrized and thus the loops are smaller, the seeds are computed
2027	!-- locally and no communication is necessary.
2028	IF ( compute_velocity_seeds_local ) THEN
2029
2030	f_n = 0.0_wp
2031	DO i = nxl, nxr
2032	DO k = nzb, nzt+1
2033	DO ii = -n_x(k), n_x(k)
2034	DO kk = -n_z(k), n_z(k)
2035	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2036	ENDDO
2037	ENDDO
2038	ENDDO
2039	ENDDO
2040
2041	ELSE
2042
2043	f_n_l = 0.0_wp
2044	DO i = nxl, nxr
2045	DO k = nzb_y_stg, nzt_y_stg+1
2046	DO ii = -n_x(k), n_x(k)
2047	DO kk = -n_z(k), n_z(k)
2048	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2049	ENDDO
2050	ENDDO
2051	ENDDO
2052	ENDDO
2053	!
2054	!-- Gather velocity seeds of full subdomain
2055	send_count = nzt_y_stg - nzb_y_stg + 1
2056	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2057
2058	#if defined( __parallel )
2059	!
2060	!-- Gather the processed velocity seed on south boundary mpi ranks.
2061	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2062	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2063	id_south, comm1dy, ierr )
2064	!
2065	!-- Gather the processed velocity seed on north boundary mpi ranks.
2066	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2067	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2068	id_north, comm1dy, ierr )
2069	#else
2070	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2071	#endif
2072
2073	ENDIF
2074
2075	DEALLOCATE( rand_it )
2076
2077	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2078
2079	END SUBROUTINE stg_generate_seed_xz
2080
2081	!------------------------------------------------------------------------------!
2082	! Description:
2083	! ------------
2084	!> Parametrization of the Reynolds stress tensor, following the parametrization
2085	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2086	!> dispserion modelling. Please note, the parametrization does not distinguish
2087	!> between along-wind and cross-wind turbulence.
2088	!------------------------------------------------------------------------------!
2089	SUBROUTINE parametrize_reynolds_stress
2090
2091	INTEGER(iwp) :: k !< loop index in z-direction
2092
2093	REAL(wp) :: zzi !< ratio of z/zi
2094
2095	DO k = nzb+1, nzt+1
2096	!
2097	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2098	!-- The function decreases to 1/10 after one length scale above the
2099	!-- ABL top.
2100	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2101	!
2102	!-- Determine normalized height coordinate
2103	zzi = zu(k) / zi_ribulk
2104	!
2105	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2106	!-- to the denominator, else the mergpe-function can crash if scale_l is
2107	!-- zero.
2108	r11(k) = scale_us*2 ( &
2109	MERGE( 0.35_wp * ABS( &
2110	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2111	)**( 2.0_wp / 3.0_wp ), &
2112	0.0_wp, &
2113	scale_l < 0.0_wp ) &
2114	+ 5.0_wp - 4.0_wp * zzi &
2115	) * blend
2116
2117	r22(k) = r11(k)
2118	!
2119	!-- w'w'
2120	r33(k) = scale_wm*2 ( &
2121	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2122	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2123	) * blend
2124	!
2125	!-- u'w' and v'w'. Assume isotropy.
2126	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2127	r32(k) = r31(k)
2128	!
2129	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2130	!-- a similar profile as for u'w'.
2131	r21(k) = r31(k)
2132	ENDDO
2133
2134	!
2135	!-- Set bottom boundary condition
2136	r11(nzb) = r11(nzb+1)
2137	r22(nzb) = r22(nzb+1)
2138	r33(nzb) = r33(nzb+1)
2139
2140	r21(nzb) = r11(nzb+1)
2141	r31(nzb) = r31(nzb+1)
2142	r32(nzb) = r32(nzb+1)
2143
2144
2145	END SUBROUTINE parametrize_reynolds_stress
2146
2147	!------------------------------------------------------------------------------!
2148	! Description:
2149	! ------------
2150	!> Calculate the coefficient matrix from the Lund rotation.
2151	!------------------------------------------------------------------------------!
2152	SUBROUTINE calc_coeff_matrix
2153
2154	INTEGER(iwp) :: k !< loop index in z-direction
2155
2156	!
2157	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2158	DO k = nzb+1, nzt+1
2159	IF ( r11(k) > 10E-6_wp ) THEN
2160	a11(k) = SQRT( r11(k) )
2161	a21(k) = r21(k) / a11(k)
2162	a31(k) = r31(k) / a11(k)
2163	ELSE
2164	a11(k) = 10E-8_wp
2165	a21(k) = 10E-8_wp
2166	a31(k) = 10E-8_wp
2167	ENDIF
2168	ENDDO
2169	DO k = nzb+1, nzt+1
2170	a22(k) = r22(k) - a21(k)**2
2171	IF ( a22(k) > 10E-6_wp ) THEN
2172	a22(k) = SQRT( a22(k) )
2173	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2174	ELSE
2175	a22(k) = 10E-8_wp
2176	a32(k) = 10E-8_wp
2177	ENDIF
2178	ENDDO
2179	DO k = nzb+1, nzt+1
2180	a33(k) = r33(k) - a31(k)2 - a32(k)2
2181	IF ( a33(k) > 10E-6_wp ) THEN
2182	a33(k) = SQRT( a33(k) )
2183	ELSE
2184	a33(k) = 10E-8_wp
2185	ENDIF
2186	ENDDO
2187	!
2188	!-- Set bottom boundary condition
2189	a11(nzb) = a11(nzb+1)
2190	a22(nzb) = a22(nzb+1)
2191	a21(nzb) = a21(nzb+1)
2192	a33(nzb) = a33(nzb+1)
2193	a31(nzb) = a31(nzb+1)
2194	a32(nzb) = a32(nzb+1)
2195
2196	END SUBROUTINE calc_coeff_matrix
2197
2198	!------------------------------------------------------------------------------!
2199	! Description:
2200	! ------------
2201	!> This routine controls the re-adjustment of the turbulence statistics used
2202	!> for generating turbulence at the lateral boundaries.
2203	!------------------------------------------------------------------------------!
2204	SUBROUTINE stg_adjust
2205
2206	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2207	!
2208	!-- In case of dirichlet inflow boundary conditions only at one lateral
2209	!-- boundary, i.e. in the case no offline or self nesting is applied but
2210	!-- synthetic turbulence shall be parametrized nevertheless, the
2211	!-- boundary-layer depth need to determined first.
2212	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2213	CALL nesting_offl_calc_zi
2214	!
2215	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2216	!-- are calculated.
2217	CALL calc_scaling_variables
2218	!
2219	!-- Set length and time scales depending on boundary-layer height
2220	CALL calc_length_and_time_scale
2221	!
2222	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2223	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2224	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2225	!-- friction velocity and velocity scale.
2226	CALL parametrize_reynolds_stress
2227	!
2228	!-- Calculate coefficient matrix from Reynolds stress tensor
2229	!-- (Lund rotation)
2230	CALL calc_coeff_matrix
2231	!
2232	!-- Determine filter functions on basis of updated length scales
2233	CALL stg_filter_func( nux, bux ) !filter ux
2234	CALL stg_filter_func( nuy, buy ) !filter uy
2235	CALL stg_filter_func( nuz, buz ) !filter uz
2236	CALL stg_filter_func( nvx, bvx ) !filter vx
2237	CALL stg_filter_func( nvy, bvy ) !filter vy
2238	CALL stg_filter_func( nvz, bvz ) !filter vz
2239	CALL stg_filter_func( nwx, bwx ) !filter wx
2240	CALL stg_filter_func( nwy, bwy ) !filter wy
2241	CALL stg_filter_func( nwz, bwz ) !filter wz
2242	!
2243	!-- Reset time counter for controlling next adjustment to zero
2244	time_stg_adjust = 0.0_wp
2245
2246	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2247
2248	END SUBROUTINE stg_adjust
2249
2250
2251	!------------------------------------------------------------------------------!
2252	! Description:
2253	! ------------
2254	!> Calculates turbuluent length and time scales if these are not available
2255	!> from measurements.
2256	!------------------------------------------------------------------------------!
2257	SUBROUTINE calc_length_and_time_scale
2258
2259	INTEGER(iwp) :: k !< loop index in z-direction
2260
2261	REAL(wp) :: length_scale_dum !< effectively used length scale
2262
2263	!
2264	!-- In initial call the boundary-layer depth can be zero. This case, set
2265	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2266	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2267	!
2268	!-- Set-up default turbulent length scales. From the numerical point of
2269	!-- view the imposed perturbations should not be immediately dissipated
2270	!-- by the numerics. The numerical dissipation, however, acts on scales
2271	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2272	!-- length scale to 8 time the grid spacing. Further, above the boundary
2273	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2274	!-- imposing any perturbations) in order to save computational costs.
2275	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2276	!-- using the length scales and the mean profiles of u- and v-component.
2277	DO k = nzb+1, nzt+1
2278	!
2279	!-- Determine blending parameter. Within the boundary layer length scales
2280	!-- are constant, while above lengths scales approach gradully zero,
2281	!-- i.e. imposed turbulence is not correlated in space and time,
2282	!-- just white noise, which saves computations power as the loops for the
2283	!-- computation of the filter functions depend on the length scales.
2284	!-- The value decreases to 1/10 after one length scale above the
2285	!-- ABL top.
2286	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2287	!
2288	!-- Assume isotropic turbulence length scales
2289	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2290	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2291	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2292	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2293	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2294	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2295	!
2296	!-- Along the vertical direction limit the length scale further by the
2297	!-- boundary-layer depth to assure that no length scales larger than
2298	!-- the boundary-layer depth are used
2299	length_scale_dum = MIN( length_scale, zi_ribulk )
2300
2301	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2302	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2303	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2304	!
2305	!-- Limit time scales, else they become very larger for low wind speed,
2306	!-- imposing long-living inflow perturbations which in turn propagate
2307	!-- further into the model domain. Use u_init and v_init to calculate
2308	!-- the time scales, which will be equal to the inflow profiles, both,
2309	!-- in offline nesting mode or in dirichlet/radiation mode.
2310	tu(k) = MIN( dt_stg_adjust, length_scale / &
2311	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2312	tv(k) = MIN( dt_stg_adjust, length_scale / &
2313	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2314	!
2315	!-- Time scale of w-component is a mixture from u- and v-component.
2316	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2317
2318	ENDDO
2319	!
2320	!-- Set bottom boundary condition for the length and time scales
2321	nux(nzb) = nux(nzb+1)
2322	nuy(nzb) = nuy(nzb+1)
2323	nuz(nzb) = nuz(nzb+1)
2324	nvx(nzb) = nvx(nzb+1)
2325	nvy(nzb) = nvy(nzb+1)
2326	nvz(nzb) = nvz(nzb+1)
2327	nwx(nzb) = nwx(nzb+1)
2328	nwy(nzb) = nwy(nzb+1)
2329	nwz(nzb) = nwz(nzb+1)
2330
2331	tu(nzb) = tu(nzb+1)
2332	tv(nzb) = tv(nzb+1)
2333	tw(nzb) = tw(nzb+1)
2334
2335
2336	END SUBROUTINE calc_length_and_time_scale
2337
2338	!------------------------------------------------------------------------------!
2339	! Description:
2340	! ------------
2341	!> Calculate scaling variables which are used for turbulence parametrization
2342	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2343	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2344	!------------------------------------------------------------------------------!
2345	SUBROUTINE calc_scaling_variables
2346
2347	INTEGER(iwp) :: i !< loop index in x-direction
2348	INTEGER(iwp) :: j !< loop index in y-direction
2349	INTEGER(iwp) :: k !< loop index in z-direction
2350	INTEGER(iwp) :: m !< surface element index
2351
2352	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2353	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2354	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2355	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2356	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2357	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2358	REAL(wp) :: w_convective !< convective velocity scale
2359
2360	!
2361	!-- Calculate mean friction velocity, velocity scale, heat flux and
2362	!-- near-surface temperature in the model domain.
2363	pt_surf_mean_l = 0.0_wp
2364	shf_mean_l = 0.0_wp
2365	scale_l_l = 0.0_wp
2366	friction_vel_l = 0.0_wp
2367	DO m = 1, surf_def_h(0)%ns
2368	i = surf_def_h(0)%i(m)
2369	j = surf_def_h(0)%j(m)
2370	k = surf_def_h(0)%k(m)
2371	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2372	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2373	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2374	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2375	ENDDO
2376	DO m = 1, surf_lsm_h%ns
2377	i = surf_lsm_h%i(m)
2378	j = surf_lsm_h%j(m)
2379	k = surf_lsm_h%k(m)
2380	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2381	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2382	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2383	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2384	ENDDO
2385	DO m = 1, surf_usm_h%ns
2386	i = surf_usm_h%i(m)
2387	j = surf_usm_h%j(m)
2388	k = surf_usm_h%k(m)
2389	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2390	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2391	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2392	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2393	ENDDO
2394
2395	#if defined( __parallel )
2396	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2397	comm2d, ierr )
2398	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2399	comm2d, ierr )
2400	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2401	comm2d, ierr )
2402	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2403	comm2d, ierr )
2404	#else
2405	scale_us = friction_vel_l
2406	shf_mean = shf_mean_l
2407	scale_l = scale_l_l
2408	pt_surf_mean = pt_surf_mean_l
2409	#endif
2410
2411	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2412	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2413	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2414	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2415	!
2416	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2417	!-- is negative, set convective velocity scale to zero.
2418	IF ( shf_mean > 0.0_wp ) THEN
2419	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2420	ELSE
2421	w_convective = 0.0_wp
2422	ENDIF
2423	!
2424	!-- Finally, in order to consider also neutral or stable stratification,
2425	!-- compute momentum velocity scale from u* and convective velocity scale,
2426	!-- according to Rotach et al. (1996).
2427	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2428
2429	END SUBROUTINE calc_scaling_variables
2430
2431	END MODULE synthetic_turbulence_generator_mod

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