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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4479

Last change on this file since 4479 was 4457, checked in by raasch, 5 years ago
ghost point exchange modularized, bugfix for wrong 2d-exchange
Property svn:keywords set to `Id`
File size: 109.3 KB

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1	!> @synthetic_turbulence_generator_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
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 4457 2020-03-11 14:20:43Z monakurppa $
27	! bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
28	!
29	! 4442 2020-03-04 19:21:13Z suehring
30	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
31	! (was accidantly changed).
32	!
33	! 4441 2020-03-04 19:20:35Z suehring
34	! Correct misplaced preprocessor directive
35	!
36	! 4438 2020-03-03 20:49:28Z suehring
37	! Performance optimizations in velocity-seed calculation:
38	! - random number array is only defined and computed locally (except for
39	! normalization to zero mean and unit variance)
40	! - parallel random number generator is applied independent on the 2D random
41	! numbers in other routines
42	! - option to decide wheter velocity seeds are computed locally without any
43	! further communication or are computed by all processes along the
44	! communicator
45	!
46	! 4346 2019-12-18 11:55:56Z motisi
47	! Introduction of wall_flags_total_0, which currently sets bits based on static
48	! topography information used in wall_flags_static_0
49	!
50	! 4335 2019-12-12 16:39:05Z suehring
51	! Commentation of last commit
52	!
53	! 4332 2019-12-10 19:44:12Z suehring
54	! Limit initial velocity seeds in restart runs, if not the seed calculation
55	! may become unstable. Further, minor bugfix in initial velocity seed
56	! calculation.
57	!
58	! 4329 2019-12-10 15:46:36Z motisi
59	! Renamed wall_flags_0 to wall_flags_static_0
60	!
61	! 4309 2019-11-26 18:49:59Z suehring
62	! Computation of velocity seeds optimized. This implies that random numbers
63	! are computed now using the parallel random number generator. Random numbers
64	! are now only computed and normalized locally, while distributed over all
65	! mpi ranks afterwards, instead of computing random numbers on a global array.
66	! Further, the number of calls for the time-consuming velocity-seed generation
67	! is reduced - now the left and right, as well as the north and south boundary
68	! share the same velocity-seed matrices.
69	!
70	! 4182 2019-08-22 15:20:23Z scharf
71	! Corrected "Former revisions" section
72	!
73	! 4148 2019-08-08 11:26:00Z suehring
74	! Remove unused variable
75	!
76	! 4144 2019-08-06 09:11:47Z raasch
77	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
78	!
79	! 4071 2019-07-03 20:02:00Z suehring
80	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
81	! information is not read from file.
82	!
83	! 4022 2019-06-12 11:52:39Z suehring
84	! Several bugfixes and improvements
85	! - revise bias correction of the imposed perturbations (correction via volume
86	! flow can create instabilities in case the mean volume flow is close to zero)
87	! - introduce lower limits in calculation of coefficient matrix, else the
88	! calculation may become numerically unstable
89	! - impose perturbations every timestep, even though no new set of perturbations
90	! is generated in case dt_stg_call /= dt_3d
91	! - Implement a gradual decrease of Reynolds stress and length scales above
92	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
93	! discontinuous decrease
94	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
95	!
96	! 3987 2019-05-22 09:52:13Z kanani
97	! Introduce alternative switch for debug output during timestepping
98	!
99	! 3938 2019-04-29 16:06:25Z suehring
100	! Remove unused variables
101	!
102	! 3937 2019-04-29 15:09:07Z suehring
103	! Minor bugfix in case of a very early restart where mc_factor is sill not
104	! present.
105	! Some modification and fixing of potential bugs in the calculation of scaling
106	! parameters used for synthetic turbulence parametrization.
107	!
108	! 3909 2019-04-17 09:13:25Z suehring
109	! Minor bugfix for last commit
110	!
111	! 3900 2019-04-16 15:17:43Z suehring
112	! Missing re-calculation of perturbation seeds in case of restarts
113	!
114	! 3891 2019-04-12 17:52:01Z suehring
115	! Bugfix in initialization in case of restart runs.
116	!
117	! 3885 2019-04-11 11:29:34Z kanani
118	! Changes related to global restructuring of location messages and introduction
119	! of additional debug messages
120	!
121	!
122	! removed unused variables
123	!
124	! 3719 2019-02-06 13:10:18Z kanani
125	! Removed log_point measurement from stg_init, since this part is counted to
126	! log_point(2) 'initialisation' already. Moved other log_points to calls of
127	! the subroutines in time_integration for better overview.
128	!
129	! 2259 2017-06-08 09:09:11Z gronemeier
130	! Initial revision
131	!
132	! Authors:
133	! --------
134	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
135	!
136	!
137	! Description:
138	! ------------
139	!> The module generates turbulence at the inflow boundary based on a method by
140	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
141	!> correction by Kim et al. (2013).
142	!> The turbulence is correlated based on length scales in y- and z-direction and
143	!> a time scale for each velocity component. The profiles of length and time
144	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
145	!> tensor can be either read from file STG_PROFILES, or will be parametrized
146	!> within the boundary layer.
147	!>
148	!> @todo test restart
149	!> enable cyclic_fill
150	!> implement turbulence generation for e and pt
151	!> @todo Input of height-constant length scales via namelist
152	!> @note <Enter notes on the module>
153	!> @bug Height information from input file is not used. Profiles from input
154	!> must match with current PALM grid.
155	!> In case of restart, velocity seeds differ from precursor run if a11,
156	!> a22, or a33 are zero.
157	!------------------------------------------------------------------------------!
158	MODULE synthetic_turbulence_generator_mod
159
160
161	USE arrays_3d, &
162	ONLY: dzw, &
163	ddzw, &
164	drho_air, &
165	mean_inflow_profiles, &
166	q, &
167	q_init, &
168	pt, &
169	pt_init, &
170	u, &
171	u_init, &
172	v, &
173	v_init, &
174	w, &
175	zu, &
176	zw
177
178	USE basic_constants_and_equations_mod, &
179	ONLY: g, &
180	kappa, &
181	pi
182
183	USE control_parameters, &
184	ONLY: bc_lr, &
185	bc_ns, &
186	child_domain, &
187	coupling_char, &
188	debug_output_timestep, &
189	dt_3d, &
190	e_init, &
191	humidity, &
192	initializing_actions, &
193	intermediate_timestep_count, &
194	intermediate_timestep_count_max, &
195	length, &
196	message_string, &
197	nesting_offline, &
198	neutral, &
199	num_mean_inflow_profiles, &
200	random_generator, &
201	rans_mode, &
202	restart_string, &
203	syn_turb_gen, &
204	time_since_reference_point, &
205	turbulent_inflow
206
207	USE cpulog, &
208	ONLY: cpu_log, &
209	log_point_s
210
211	USE grid_variables, &
212	ONLY: ddx, &
213	ddy, &
214	dx, &
215	dy
216
217	USE indices, &
218	ONLY: nbgp, &
219	nz, &
220	nzb, &
221	nzt, &
222	nx, &
223	nxl, &
224	nxlu, &
225	nxr, &
226	ny, &
227	nys, &
228	nysv, &
229	nyn, &
230	wall_flags_total_0
231
232	USE kinds
233
234	#if defined( __parallel ) && !defined( __mpifh )
235	USE MPI
236	#endif
237
238	USE nesting_offl_mod, &
239	ONLY: nesting_offl_calc_zi, &
240	zi_ribulk
241
242	USE pegrid, &
243	ONLY: comm1dx, &
244	comm1dy, &
245	comm2d, &
246	ierr, &
247	myidx, &
248	myidy, &
249	pdims
250
251	USE pmc_interface, &
252	ONLY : rans_mode_parent
253
254	USE random_generator_parallel, &
255	ONLY: init_parallel_random_generator, &
256	random_dummy, &
257	random_number_parallel, &
258	random_seed_parallel
259
260	USE transpose_indices, &
261	ONLY: nzb_x, &
262	nzt_x
263
264	USE surface_mod, &
265	ONLY: surf_def_h, &
266	surf_lsm_h, &
267	surf_usm_h
268
269	IMPLICIT NONE
270
271	#if defined( __parallel ) && defined( __mpifh )
272	INCLUDE "mpif.h"
273	#endif
274
275
276	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
277	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
278	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
279	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
280	!< is distributed over several processes
281
282	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
283	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
284	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
285	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
286	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
287	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
288	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
289	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
290	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
291	#if defined( __parallel )
292	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
293	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
294	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
295	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
296	#endif
297
298	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
299	!< required for bias correction of imposed perturbations
300	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
301	!< required for bias correction of imposed perturbations
302
303	#if defined( __parallel )
304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
308	#endif
309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
311	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
312	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
313	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
314	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
318
319	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
320	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
321	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
322	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
323
324	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
325	!< scales above the boundary layer
326	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
327	!< one length scale above ABL top
328	REAL(wp) :: d_l !< blend_coeff/length_scale
329	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
330	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
331	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
332	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
333	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
334	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
335	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
336	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
337
338	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
339
340
341	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
342	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
343	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
344	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
345	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
346	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
347
348	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
349	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
350	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
351	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
352	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
353	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
354	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
355	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
356	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
357
358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
379
380	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
381	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
382
383	!
384	!-- PALM interfaces:
385	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
386	INTERFACE stg_adjust
387	MODULE PROCEDURE stg_adjust
388	END INTERFACE stg_adjust
389	!
390	!-- Input parameter checks to be done in check_parameters
391	INTERFACE stg_check_parameters
392	MODULE PROCEDURE stg_check_parameters
393	END INTERFACE stg_check_parameters
394
395	!
396	!-- Calculate filter functions
397	INTERFACE stg_filter_func
398	MODULE PROCEDURE stg_filter_func
399	END INTERFACE stg_filter_func
400
401	!
402	!-- Generate velocity seeds at south and north domain boundary
403	INTERFACE stg_generate_seed_xz
404	MODULE PROCEDURE stg_generate_seed_xz
405	END INTERFACE stg_generate_seed_xz
406	!
407	!-- Generate velocity seeds at left and/or right domain boundary
408	INTERFACE stg_generate_seed_yz
409	MODULE PROCEDURE stg_generate_seed_yz
410	END INTERFACE stg_generate_seed_yz
411
412	!
413	!-- Output of information to the header file
414	INTERFACE stg_header
415	MODULE PROCEDURE stg_header
416	END INTERFACE stg_header
417
418	!
419	!-- Initialization actions
420	INTERFACE stg_init
421	MODULE PROCEDURE stg_init
422	END INTERFACE stg_init
423
424	!
425	!-- Main procedure of synth. turb. gen.
426	INTERFACE stg_main
427	MODULE PROCEDURE stg_main
428	END INTERFACE stg_main
429
430	!
431	!-- Reading of NAMELIST parameters
432	INTERFACE stg_parin
433	MODULE PROCEDURE stg_parin
434	END INTERFACE stg_parin
435
436	!
437	!-- Reading of parameters for restart runs
438	INTERFACE stg_rrd_global
439	MODULE PROCEDURE stg_rrd_global
440	END INTERFACE stg_rrd_global
441
442	!
443	!-- Writing of binary output for restart runs
444	INTERFACE stg_wrd_global
445	MODULE PROCEDURE stg_wrd_global
446	END INTERFACE stg_wrd_global
447
448	SAVE
449
450	PRIVATE
451
452	!
453	!-- Public interfaces
454	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
455	stg_parin, stg_rrd_global, stg_wrd_global
456
457	!
458	!-- Public variables
459	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
460	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
461	time_stg_adjust, time_stg_call, use_syn_turb_gen
462
463
464	CONTAINS
465
466
467	!------------------------------------------------------------------------------!
468	! Description:
469	! ------------
470	!> Check parameters routine for synthetic turbulence generator
471	!------------------------------------------------------------------------------!
472	SUBROUTINE stg_check_parameters
473
474	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
475	nesting_offline ) THEN
476	message_string = 'Synthetic turbulence generator is required ' // &
477	'if offline nesting is applied and PALM operates ' // &
478	'in LES mode.'
479	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
480	ENDIF
481
482	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
483	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
484	message_string = 'Synthetic turbulence generator is required ' // &
485	'when nesting is applied and parent operates in ' // &
486	'RANS-mode but current child in LES mode.'
487	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
488	ENDIF
489
490	IF ( use_syn_turb_gen ) THEN
491
492	IF ( child_domain .AND. .NOT. rans_mode .AND. &
493	.NOT. rans_mode_parent ) THEN
494	message_string = 'Using synthetic turbulence generator ' // &
495	'is not allowed in LES-LES nesting.'
496	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
497
498	ENDIF
499
500	IF ( child_domain .AND. rans_mode .AND. &
501	rans_mode_parent ) THEN
502	message_string = 'Using synthetic turbulence generator ' // &
503	'is not allowed in RANS-RANS nesting.'
504	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
505
506	ENDIF
507
508	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
509
510	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
511	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
512	message_string = 'Using synthetic turbulence generator ' // &
513	'requires %initializing_actions = ' // &
514	'"set_constant_profiles" or "read_restart_data"' //&
515	', if not offline nesting is applied.'
516	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
517	ENDIF
518
519	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
520	message_string = 'Using synthetic turbulence generator ' // &
521	'requires &bc_lr = "dirichlet/radiation", ' // &
522	'if not offline nesting is applied.'
523	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
524	ENDIF
525	IF ( bc_ns /= 'cyclic' ) THEN
526	message_string = 'Using synthetic turbulence generator ' // &
527	'requires &bc_ns = "cyclic", ' // &
528	'if not offline nesting is applied.'
529	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
530	ENDIF
531
532	ENDIF
533
534	IF ( turbulent_inflow ) THEN
535	message_string = 'Using synthetic turbulence generator ' // &
536	'in combination &with turbulent_inflow = .T. '// &
537	'is not allowed'
538	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
539	ENDIF
540	!
541	!-- Synthetic turbulence generator requires the parallel random generator
542	IF ( random_generator /= 'random-parallel' ) THEN
543	message_string = 'Using synthetic turbulence generator ' // &
544	'requires random_generator = random-parallel.'
545	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
546	ENDIF
547
548	ENDIF
549
550	END SUBROUTINE stg_check_parameters
551
552
553	!------------------------------------------------------------------------------!
554	! Description:
555	! ------------
556	!> Header output for synthetic turbulence generator
557	!------------------------------------------------------------------------------!
558	SUBROUTINE stg_header ( io )
559
560	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
561
562	!
563	!-- Write synthetic turbulence generator Header
564	WRITE( io, 1 )
565	IF ( use_syn_turb_gen ) THEN
566	WRITE( io, 2 )
567	ELSE
568	WRITE( io, 3 )
569	ENDIF
570
571	IF ( parametrize_inflow_turbulence ) THEN
572	WRITE( io, 4 ) dt_stg_adjust
573	ELSE
574	WRITE( io, 5 )
575	ENDIF
576
577	1 FORMAT (//' Synthetic turbulence generator information:'/ &
578	' ------------------------------------------'/)
579	2 FORMAT (' synthetic turbulence generator is switched on')
580	3 FORMAT (' synthetic turbulence generator is switched off')
581	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
582	5 FORMAT (' imposed turbulence is read from file' )
583
584	END SUBROUTINE stg_header
585
586
587	!------------------------------------------------------------------------------!
588	! Description:
589	! ------------
590	!> Initialization of the synthetic turbulence generator
591	!------------------------------------------------------------------------------!
592	SUBROUTINE stg_init
593
594	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
595
596	#if defined( __parallel )
597	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
598	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
599	#endif
600
601	INTEGER(iwp) :: i !> grid index in x-direction
602	INTEGER(iwp) :: j !> loop index
603	INTEGER(iwp) :: k !< index
604	#if defined( __parallel )
605	INTEGER(iwp) :: newtype !< dummy MPI type
606	INTEGER(iwp) :: realsize !< size of REAL variables
607	#endif
608
609	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
610	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
611	!
612	!-- Dummy variables used for reading profiles
613	REAL(wp) :: d1 !< u profile
614	REAL(wp) :: d2 !< v profile
615	REAL(wp) :: d3 !< w profile
616	REAL(wp) :: d5 !< e profile
617	REAL(wp) :: luy !< length scale for u in y direction
618	REAL(wp) :: luz !< length scale for u in z direction
619	REAL(wp) :: lvy !< length scale for v in y direction
620	REAL(wp) :: lvz !< length scale for v in z direction
621	REAL(wp) :: lwy !< length scale for w in y direction
622	REAL(wp) :: lwz !< length scale for w in z direction
623	#if defined( __parallel )
624	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
625	#endif
626	REAL(wp) :: zz !< height
627
628
629	#if defined( __parallel )
630	CALL MPI_BARRIER( comm2d, ierr )
631	#endif
632	!
633	!-- Create mpi-datatypes for exchange in case of non-local but distributed
634	!-- computation of the velocity seeds. This option is useful in
635	!-- case large turbulent length scales are present, where the computational
636	!-- effort becomes large and need to be parallelized. For parameterized
637	!-- turbulence the length scales are small and computing the velocity seeds
638	!-- locally is faster (no overhead by communication).
639	IF ( .NOT. compute_velocity_seeds_local ) THEN
640	#if defined( __parallel )
641	!
642	!-- Determine processor decomposition of z-axis along x- and y-direction
643	nnz = nz / pdims(1)
644	nzb_x_stg = 1 + myidx * INT( nnz )
645	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
646
647	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
648	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
649
650	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
651	.AND. .NOT. rans_mode ) ) THEN
652	nnz = nz / pdims(2)
653	nzb_y_stg = 1 + myidy * INT( nnz )
654	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
655
656	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
657	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
658	ENDIF
659
660	!
661	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
662	!-- velocity seeds
663	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
664	extent = 1 * realsize
665	!
666	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
667	!-- layer
668	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
669	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
670	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
671	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
672	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
673	CALL MPI_TYPE_FREE( newtype, ierr )
674
675	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
676	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
677	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
678	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
679	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
680	CALL MPI_TYPE_FREE( newtype, ierr )
681
682	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
683	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
684
685	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
686	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
687
688	DO j = 1, pdims(1)
689	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
690	ENDDO
691	!
692	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
693	!-- layer
694	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
695	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
696	.AND. .NOT. rans_mode ) ) THEN
697	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
698	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
699	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
700	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
701	CALL MPI_TYPE_FREE( newtype, ierr )
702
703	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
704	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
705	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
706	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
707	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
708	CALL MPI_TYPE_FREE( newtype, ierr )
709
710	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
711	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
712
713	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
714	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
715
716	DO j = 1, pdims(2)
717	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
718	ENDDO
719
720	ENDIF
721	#endif
722	ENDIF
723	!
724	!-- Allocate required arrays.
725	!-- In case no offline nesting or self nesting is used, the arrary
726	!-- mean_inflow profiles is required. Check if it is already allocated, else
727	!-- allocate and initialize it appropriately. Note, in case turbulence and
728	!-- inflow information is read from file, mean_inflow_profiles is already
729	!-- allocated and initialized appropriately.
730	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
731	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
732	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
733	mean_inflow_profiles = 0.0_wp
734	mean_inflow_profiles(:,1) = u_init
735	mean_inflow_profiles(:,2) = v_init
736	!
737	!-- Even though potential temperature and humidity are not perturbed,
738	!-- they need to be initialized appropriately.
739	IF ( .NOT. neutral ) &
740	mean_inflow_profiles(:,4) = pt_init
741	IF ( humidity ) &
742	mean_inflow_profiles(:,6) = q_init
743	ENDIF
744	ENDIF
745
746	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
747	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
748	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
749	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
750	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
751	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
752	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
753	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
754
755	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
756	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
757	dist_xz = 0.0_wp
758	dist_yz = 0.0_wp
759	!
760	!-- Read inflow profile
761	!-- Height levels of profiles in input profile is as follows:
762	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
763	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
764	!-- WARNING: zz is not used at the moment
765	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
766	EXIST = file_stg_exist )
767
768	IF ( file_stg_exist ) THEN
769
770	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
771	FORM='FORMATTED')
772	!
773	!-- Skip header
774	READ( 90, * )
775
776	DO k = nzb+1, nzt+1
777	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
778	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
779	d1, d2, d3, d5
780
781	!
782	!-- Convert length scales from meter to number of grid points.
783	nuy(k) = INT( luy * ddy )
784	nuz(k) = INT( luz * ddzw(k) )
785	nvy(k) = INT( lvy * ddy )
786	nvz(k) = INT( lvz * ddzw(k) )
787	nwy(k) = INT( lwy * ddy )
788	nwz(k) = INT( lwz * ddzw(k) )
789	!
790	!-- Workaround, assume isotropic turbulence
791	nwx(k) = nwy(k)
792	nvx(k) = nvy(k)
793	nux(k) = nuy(k)
794	!
795	!-- Save Mean inflow profiles
796	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
797	mean_inflow_profiles(k,1) = d1
798	mean_inflow_profiles(k,2) = d2
799	! mean_inflow_profiles(k,4) = d4
800	mean_inflow_profiles(k,5) = d5
801	ENDIF
802	ENDDO
803	!
804	!-- Set lenght scales at surface grid point
805	nuy(nzb) = nuy(nzb+1)
806	nuz(nzb) = nuz(nzb+1)
807	nvy(nzb) = nvy(nzb+1)
808	nvz(nzb) = nvz(nzb+1)
809	nwy(nzb) = nwy(nzb+1)
810	nwz(nzb) = nwz(nzb+1)
811
812	CLOSE( 90 )
813	!
814	!-- Calculate coefficient matrix from Reynolds stress tensor
815	!-- (Lund rotation)
816	CALL calc_coeff_matrix
817	!
818	!-- No information about turbulence and its length scales are available.
819	!-- Instead, parametrize turbulence which is imposed at the boundaries.
820	!-- Set flag which indicates that turbulence is parametrized, which is done
821	!-- later when energy-balance models are already initialized. This is
822	!-- because the STG needs information about surface properties such as
823	!-- roughness to build 'realistic' turbulence profiles.
824	ELSE
825	!
826	!-- Define length scale for the imposed turbulence, which is defined as
827	!-- 8 times the minimum grid spacing
828	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
829	!
830	!-- Define constant to gradually decrease length scales and Reynolds stress
831	!-- above ABL top. Assure that no zero length scales are used.
832	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
833	!
834	!-- Set flag indicating that turbulence is parametrized
835	parametrize_inflow_turbulence = .TRUE.
836	!
837	!-- In case of dirichlet inflow boundary conditions only at one lateral
838	!-- boundary, i.e. in the case no offline or self nesting is applied but
839	!-- synthetic turbulence shall be parametrized nevertheless, the
840	!-- boundary-layer depth need to determined first.
841	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
842	CALL nesting_offl_calc_zi
843	!
844	!-- Determine boundary-layer depth, which is used to initialize lenght
845	!-- scales
846	CALL calc_scaling_variables
847	!
848	!-- Initialize lenght and time scales, which in turn are used
849	!-- to initialize the filter functions.
850	CALL calc_length_and_time_scale
851	!
852	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
853	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
854	!-- Rotach et al. (1996) and is based on boundary-layer depth,
855	!-- friction velocity and velocity scale.
856	CALL parametrize_reynolds_stress
857	!
858	!-- Calculate coefficient matrix from Reynolds stress tensor
859	!-- (Lund rotation)
860	CALL calc_coeff_matrix
861
862	ENDIF
863
864	!
865	!-- Assign initial profiles. Note, this is only required if turbulent
866	!-- inflow from the left is desired, not in case of any of the
867	!-- nesting (offline or self nesting) approaches.
868	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
869	u_init = mean_inflow_profiles(:,1)
870	v_init = mean_inflow_profiles(:,2)
871	!pt_init = mean_inflow_profiles(:,4)
872	e_init = MAXVAL( mean_inflow_profiles(:,5) )
873	ENDIF
874
875	!
876	!-- Define the size of the filter functions and allocate them.
877	mergp = 0
878
879	! arrays must be large enough to cover the largest length scale
880	DO k = nzb, nzt+1
881	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
882	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
883	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
884	IF ( j > mergp ) mergp = j
885	ENDDO
886
887	! mergp = 2 * mergp
888	! mergp = mergp
889
890	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
891	buy(-mergp:mergp,nzb:nzt+1), &
892	buz(-mergp:mergp,nzb:nzt+1), &
893	bvx(-mergp:mergp,nzb:nzt+1), &
894	bvy(-mergp:mergp,nzb:nzt+1), &
895	bvz(-mergp:mergp,nzb:nzt+1), &
896	bwx(-mergp:mergp,nzb:nzt+1), &
897	bwy(-mergp:mergp,nzb:nzt+1), &
898	bwz(-mergp:mergp,nzb:nzt+1) )
899
900	!
901	!-- Allocate velocity seeds for turbulence at xz-layer
902	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
903	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
904	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
905
906	!
907	!-- Allocate velocity seeds for turbulence at yz-layer
908	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
909	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
910	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
911
912	fu_xz = 0.0_wp
913	fuo_xz = 0.0_wp
914	fv_xz = 0.0_wp
915	fvo_xz = 0.0_wp
916	fw_xz = 0.0_wp
917	fwo_xz = 0.0_wp
918
919	fu_yz = 0.0_wp
920	fuo_yz = 0.0_wp
921	fv_yz = 0.0_wp
922	fvo_yz = 0.0_wp
923	fw_yz = 0.0_wp
924	fwo_yz = 0.0_wp
925
926	!
927	!-- Create filter functions
928	CALL stg_filter_func( nux, bux ) !filter ux
929	CALL stg_filter_func( nuy, buy ) !filter uy
930	CALL stg_filter_func( nuz, buz ) !filter uz
931	CALL stg_filter_func( nvx, bvx ) !filter vx
932	CALL stg_filter_func( nvy, bvy ) !filter vy
933	CALL stg_filter_func( nvz, bvz ) !filter vz
934	CALL stg_filter_func( nwx, bwx ) !filter wx
935	CALL stg_filter_func( nwy, bwy ) !filter wy
936	CALL stg_filter_func( nwz, bwz ) !filter wz
937
938	#if defined( __parallel )
939	CALL MPI_BARRIER( comm2d, ierr )
940	#endif
941
942	!
943	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
944	! time step.
945	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
946	! are 0 compared to the prerun. This is mostly for k=nzt+1.
947	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
948	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
949
950	IF ( myidx == id_stg_left ) i = -1
951	IF ( myidx == id_stg_right ) i = nxr+1
952
953	DO j = nys, nyn
954	DO k = nzb, nzt+1
955	IF ( a11(k) > 10E-8_wp ) THEN
956	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
957	ELSE
958	fu_yz(k,j) = 10E-8_wp
959	ENDIF
960
961	IF ( a22(k) > 10E-8_wp ) THEN
962	fv_yz(k,j) = ( v(k,j,i) - &
963	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
964	ELSE
965	fv_yz(k,j) = 10E-8_wp
966	ENDIF
967
968	IF ( a33(k) > 10E-8_wp ) THEN
969	fw_yz(k,j) = ( w(k,j,i) - &
970	a31(k) * fu_yz(k,j) - a32(k) * &
971	fv_yz(k,j) ) / a33(k)
972	ELSE
973	fw_yz(k,j) = 10E-8_wp
974	ENDIF
975	ENDDO
976	ENDDO
977	ENDIF
978
979	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
980
981	IF ( myidy == id_stg_south ) j = -1
982	IF ( myidy == id_stg_north ) j = nyn+1
983
984	DO i = nxl, nxr
985	DO k = nzb, nzt+1
986	!
987	!-- In case the correlation coefficients are very small, the
988	!-- velocity seeds may become very large finally creating
989	!-- numerical instabilities in the synthetic turbulence generator.
990	!-- Empirically, a value of 10E-8 seems to be sufficient.
991	IF ( a11(k) > 10E-8_wp ) THEN
992	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
993	ELSE
994	fu_xz(k,i) = 10E-8_wp
995	ENDIF
996
997	IF ( a22(k) > 10E-8_wp ) THEN
998	fv_xz(k,i) = ( v(k,j,i) - &
999	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1000	ELSE
1001	fv_xz(k,i) = 10E-8_wp
1002	ENDIF
1003
1004	IF ( a33(k) > 10E-8_wp ) THEN
1005	fw_xz(k,i) = ( w(k,j,i) - &
1006	a31(k) * fu_xz(k,i) - &
1007	a32(k) * fv_xz(k,i) ) / a33(k)
1008	ELSE
1009	fw_xz(k,i) = 10E-8_wp
1010	ENDIF
1011
1012	ENDDO
1013	ENDDO
1014	ENDIF
1015	ENDIF
1016	!
1017	!-- Count the number of non-topography grid points at the boundaries where
1018	!-- perturbations are imposed. This number is later used for bias corrections
1019	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1020	!-- due to the asymetry of u and v along x and y direction, respectively,
1021	!-- different cases must be distinguished.
1022	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1023	!
1024	!-- Number of grid points where perturbations are imposed on u
1025	IF ( myidx == id_stg_left ) i = nxl
1026	IF ( myidx == id_stg_right ) i = nxr+1
1027
1028	nr_non_topo_yz_l(1) = SUM( &
1029	MERGE( 1, 0, &
1030	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1031	!
1032	!-- Number of grid points where perturbations are imposed on v and w
1033	IF ( myidx == id_stg_left ) i = nxl-1
1034	IF ( myidx == id_stg_right ) i = nxr+1
1035
1036	nr_non_topo_yz_l(2) = SUM( &
1037	MERGE( 1, 0, &
1038	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1039	nr_non_topo_yz_l(3) = SUM( &
1040	MERGE( 1, 0, &
1041	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1042
1043	#if defined( __parallel )
1044	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1045	MPI_SUM, comm1dy, ierr )
1046	#else
1047	nr_non_topo_yz = nr_non_topo_yz_l
1048	#endif
1049	ENDIF
1050
1051	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1052	!
1053	!-- Number of grid points where perturbations are imposed on v
1054	IF ( myidy == id_stg_south ) j = nys
1055	IF ( myidy == id_stg_north ) j = nyn+1
1056
1057	nr_non_topo_xz_l(2) = SUM( &
1058	MERGE( 1, 0, &
1059	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1060	!
1061	!-- Number of grid points where perturbations are imposed on u and w
1062	IF ( myidy == id_stg_south ) j = nys-1
1063	IF ( myidy == id_stg_north ) j = nyn+1
1064
1065	nr_non_topo_xz_l(1) = SUM( &
1066	MERGE( 1, 0, &
1067	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1068	nr_non_topo_xz_l(3) = SUM( &
1069	MERGE( 1, 0, &
1070	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1071
1072	#if defined( __parallel )
1073	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1074	MPI_SUM, comm1dx, ierr )
1075	#else
1076	nr_non_topo_xz = nr_non_topo_xz_l
1077	#endif
1078	ENDIF
1079	!
1080	!-- Initialize random number generator at xz- and yz-layers. Random numbers
1081	!-- are initialized at each core. In case there is only inflow from the left,
1082	!-- it is sufficient to generate only random numbers for the yz-layer, else
1083	!-- random numbers for the xz-layer are also required.
1084	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
1085	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
1086	id_rand_yz = 0
1087	seq_rand_yz = 0
1088
1089	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
1090	id_rand_yz, seq_rand_yz )
1091
1092	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1093	.AND. .NOT. rans_mode ) ) THEN
1094	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
1095	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
1096	id_rand_xz = 0
1097	seq_rand_xz = 0
1098
1099	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
1100	id_rand_xz, seq_rand_xz )
1101	ENDIF
1102
1103
1104
1105	END SUBROUTINE stg_init
1106
1107
1108	!------------------------------------------------------------------------------!
1109	! Description:
1110	! ------------
1111	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1112	!> (Xie and Castro, 2008)
1113	!------------------------------------------------------------------------------!
1114	SUBROUTINE stg_filter_func( nxx, bxx )
1115
1116	INTEGER(iwp) :: k !< loop index
1117	INTEGER(iwp) :: n_k !< length scale nXX in height k
1118	INTEGER(iwp) :: nf !< index for length scales
1119
1120	REAL(wp) :: bdenom !< denominator for filter functions bXX
1121	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1122
1123	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
1124
1125	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
1126
1127
1128	bxx = 0.0_wp
1129
1130	DO k = nzb, nzt+1
1131	bdenom = 0.0_wp
1132	n_k = nxx(k)
1133	IF ( n_k /= 0 ) THEN
1134
1135	!
1136	!-- ( Eq.10 )^2
1137	DO nf = -n_k, n_k
1138	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1139	ENDDO
1140
1141	!
1142	!-- ( Eq.9 )
1143	bdenom = SQRT( bdenom )
1144	DO nf = -n_k, n_k
1145	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1146	ENDDO
1147	ENDIF
1148	ENDDO
1149
1150	END SUBROUTINE stg_filter_func
1151
1152
1153	!------------------------------------------------------------------------------!
1154	! Description:
1155	! ------------
1156	!> Parin for &stg_par for synthetic turbulence generator
1157	!------------------------------------------------------------------------------!
1158	SUBROUTINE stg_parin
1159
1160	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1161
1162
1163	NAMELIST /stg_par/ dt_stg_adjust, &
1164	dt_stg_call, &
1165	use_syn_turb_gen, &
1166	compute_velocity_seeds_local
1167
1168	line = ' '
1169	!
1170	!-- Try to find stg package
1171	REWIND ( 11 )
1172	line = ' '
1173	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1174	READ ( 11, '(A)', END=20 ) line
1175	ENDDO
1176	BACKSPACE ( 11 )
1177
1178	!
1179	!-- Read namelist
1180	READ ( 11, stg_par, ERR = 10, END = 20 )
1181
1182	!
1183	!-- Set flag that indicates that the synthetic turbulence generator is switched
1184	!-- on
1185	syn_turb_gen = .TRUE.
1186	GOTO 20
1187
1188	10 BACKSPACE( 11 )
1189	READ( 11 , '(A)') line
1190	CALL parin_fail_message( 'stg_par', line )
1191
1192	20 CONTINUE
1193
1194	END SUBROUTINE stg_parin
1195
1196
1197	!------------------------------------------------------------------------------!
1198	! Description:
1199	! ------------
1200	!> This routine reads the respective restart data.
1201	!------------------------------------------------------------------------------!
1202	SUBROUTINE stg_rrd_global( found )
1203
1204	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1205
1206	found = .TRUE.
1207
1208
1209	SELECT CASE ( restart_string(1:length) )
1210
1211	CASE ( 'time_stg_adjust' )
1212	READ ( 13 ) time_stg_adjust
1213
1214	CASE ( 'time_stg_call' )
1215	READ ( 13 ) time_stg_call
1216
1217	CASE ( 'use_syn_turb_gen' )
1218	READ ( 13 ) use_syn_turb_gen
1219
1220	CASE DEFAULT
1221
1222	found = .FALSE.
1223
1224	END SELECT
1225
1226
1227	END SUBROUTINE stg_rrd_global
1228
1229
1230	!------------------------------------------------------------------------------!
1231	! Description:
1232	! ------------
1233	!> This routine writes the respective restart data.
1234	!------------------------------------------------------------------------------!
1235	SUBROUTINE stg_wrd_global
1236
1237	CALL wrd_write_string( 'time_stg_adjust' )
1238	WRITE ( 14 ) time_stg_adjust
1239
1240	CALL wrd_write_string( 'time_stg_call' )
1241	WRITE ( 14 ) time_stg_call
1242
1243	CALL wrd_write_string( 'use_syn_turb_gen' )
1244	WRITE ( 14 ) use_syn_turb_gen
1245
1246
1247	END SUBROUTINE stg_wrd_global
1248
1249
1250	!------------------------------------------------------------------------------!
1251	! Description:
1252	! ------------
1253	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1254	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1255	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1256	!> (Lund, 1998).
1257	!------------------------------------------------------------------------------!
1258	SUBROUTINE stg_main
1259
1260	USE exchange_horiz_mod, &
1261	ONLY: exchange_horiz
1262
1263	INTEGER(iwp) :: i !< grid index in x-direction
1264	INTEGER(iwp) :: j !< loop index in y-direction
1265	INTEGER(iwp) :: k !< loop index in z-direction
1266
1267	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1268
1269	REAL(wp) :: dt_stg !< wheighted subtimestep
1270
1271	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1272
1273	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1274	!
1275	!-- Calculate time step which is needed for filter functions
1276	dt_stg = MAX( dt_3d, dt_stg_call )
1277	!
1278	!-- Check if synthetic turbulence generator needs to be called and new
1279	!-- perturbations need to be created or if old disturbances can be imposed
1280	!-- again.
1281	IF ( time_stg_call >= dt_stg_call .AND. &
1282	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1283	stg_call = .TRUE.
1284	ELSE
1285	stg_call = .FALSE.
1286	ENDIF
1287	!
1288	!-- Initial value of fu, fv, fw
1289	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1290	!
1291	!-- Generate turbulence at the left and right boundary. Random numbers
1292	!-- for the yz-planes at the left/right boundary are generated by the
1293	!-- left-sided mpi ranks only. After random numbers are calculated, they
1294	!-- are distributed to all other mpi ranks in the model, so that the
1295	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1296	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1297	!-- that the left- and the right-sided lateral boundary have the same initial
1298	!-- seeds.
1299	!-- Note, in case of inflow from the right only, only turbulence at the left
1300	!-- boundary is required.
1301	IF ( .NOT. ( nesting_offline .OR. &
1302	( child_domain .AND. rans_mode_parent &
1303	.AND. .NOT. rans_mode ) ) ) THEN
1304	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1305	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1306	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1307	ELSE
1308	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1309	id_stg_left, id_stg_right )
1310	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1311	id_stg_left, id_stg_right )
1312	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1313	id_stg_left, id_stg_right )
1314	!
1315	!-- Generate turbulence at the south and north boundary. Random numbers
1316	!-- for the xz-planes at the south/north boundary are generated by the
1317	!-- south-sided mpi ranks only. Please see also comment above.
1318	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1319	id_stg_south, id_stg_north )
1320	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1321	id_stg_south, id_stg_north )
1322	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1323	id_stg_south, id_stg_north )
1324	ENDIF
1325	velocity_seed_initialized = .TRUE.
1326	ENDIF
1327	!
1328	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1329	!-- seeds are only required at the left boundary, while in case of offline
1330	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1331	!-- right, south and north boundaries.
1332	IF ( stg_call ) THEN
1333	IF ( .NOT. ( nesting_offline .OR. &
1334	( child_domain .AND. rans_mode_parent &
1335	.AND. .NOT. rans_mode ) ) ) THEN
1336	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1337	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1338	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1339
1340	ELSE
1341	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1342	id_stg_left, id_stg_right )
1343	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1344	id_stg_left, id_stg_right )
1345	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1346	id_stg_left, id_stg_right )
1347
1348	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1349	id_stg_south, id_stg_north )
1350	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1351	id_stg_south, id_stg_north )
1352	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1353	id_stg_south, id_stg_north )
1354	ENDIF
1355	ENDIF
1356
1357	!
1358	!-- Turbulence generation at left and/or right boundary
1359	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1360	!
1361	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1362	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1363	!-- imposed
1364	IF ( stg_call ) THEN
1365
1366	DO j = nys, nyn
1367	DO k = nzb, nzt + 1
1368	!
1369	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1370	IF ( tu(k) == 0.0_wp ) THEN
1371	fu_yz(k,j) = fuo_yz(k,j)
1372	ELSE
1373	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1374	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1375	ENDIF
1376
1377	IF ( tv(k) == 0.0_wp ) THEN
1378	fv_yz(k,j) = fvo_yz(k,j)
1379	ELSE
1380	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1381	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1382	ENDIF
1383
1384	IF ( tw(k) == 0.0_wp ) THEN
1385	fw_yz(k,j) = fwo_yz(k,j)
1386	ELSE
1387	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1388	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1389	ENDIF
1390	ENDDO
1391	ENDDO
1392
1393	dist_yz(nzb,:,1) = 0.0_wp
1394	dist_yz(nzb,:,2) = 0.0_wp
1395	dist_yz(nzb,:,3) = 0.0_wp
1396
1397	IF ( myidx == id_stg_left ) i = nxl
1398	IF ( myidx == id_stg_right ) i = nxr+1
1399	DO j = nys, nyn
1400	DO k = nzb+1, nzt + 1
1401	!
1402	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1403	!-- Additional factors are added to improve the variance of v and w
1404	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1405	MERGE( 1.0_wp, 0.0_wp, &
1406	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1407	ENDDO
1408	ENDDO
1409
1410	IF ( myidx == id_stg_left ) i = nxl-1
1411	IF ( myidx == id_stg_right ) i = nxr+1
1412	DO j = nys, nyn
1413	DO k = nzb+1, nzt + 1
1414	!
1415	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1416	!-- Additional factors are added to improve the variance of v and w
1417	!-- experimental test of 1.2
1418	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1419	* 1.2_wp ) &
1420	* ( a21(k) * fu_yz(k,j) &
1421	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1422	MERGE( 1.0_wp, 0.0_wp, &
1423	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1424	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1425	* 1.3_wp ) &
1426	* ( a31(k) * fu_yz(k,j) &
1427	+ a32(k) * fv_yz(k,j) &
1428	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1429	MERGE( 1.0_wp, 0.0_wp, &
1430	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1431	ENDDO
1432	ENDDO
1433	ENDIF
1434	!
1435	!-- Mass flux correction following Kim et al. (2013)
1436	!-- This correction factor insures that the mass flux is preserved at the
1437	!-- inflow boundary. First, calculate mean value of the imposed
1438	!-- perturbations at yz boundary.
1439	!-- Note, this needs to be done only after the last RK3-substep, else
1440	!-- the boundary values won't be accessed.
1441	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1442	mc_factor_l = 0.0_wp
1443	mc_factor = 0.0_wp
1444	!
1445	!-- Sum up the original volume flows (with and without perturbations).
1446	!-- Note, for non-normal components (here v and w) it is actually no
1447	!-- volume flow.
1448	IF ( myidx == id_stg_left ) i = nxl
1449	IF ( myidx == id_stg_right ) i = nxr+1
1450
1451	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1452	* MERGE( 1.0_wp, 0.0_wp, &
1453	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1454
1455	IF ( myidx == id_stg_left ) i = nxl-1
1456	IF ( myidx == id_stg_right ) i = nxr+1
1457
1458	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1459	* MERGE( 1.0_wp, 0.0_wp, &
1460	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1461	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1462	* MERGE( 1.0_wp, 0.0_wp, &
1463	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1464
1465	#if defined( __parallel )
1466	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1467	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1468	#else
1469	mc_factor = mc_factor_l
1470	#endif
1471	!
1472	!-- Calculate correction factor and force zero mean perturbations.
1473	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1474
1475	IF ( myidx == id_stg_left ) i = nxl
1476	IF ( myidx == id_stg_right ) i = nxr+1
1477
1478	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
1479	* MERGE( 1.0_wp, 0.0_wp, &
1480	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
1481
1482
1483	IF ( myidx == id_stg_left ) i = nxl-1
1484	IF ( myidx == id_stg_right ) i = nxr+1
1485
1486	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
1487	* MERGE( 1.0_wp, 0.0_wp, &
1488	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
1489
1490	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
1491	* MERGE( 1.0_wp, 0.0_wp, &
1492	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
1493	!
1494	!-- Add disturbances
1495	IF ( myidx == id_stg_left ) THEN
1496	!
1497	!-- For the left boundary distinguish between mesoscale offline / self
1498	!-- nesting and turbulent inflow at the left boundary only. In the latter
1499	!-- case turbulence is imposed on the mean inflow profiles.
1500	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1501	!
1502	!-- Add disturbance at the inflow
1503	DO j = nys, nyn
1504	DO k = nzb, nzt+1
1505	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1506	dist_yz(k,j,1) ) &
1507	* MERGE( 1.0_wp, 0.0_wp, &
1508	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1509	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1510	dist_yz(k,j,2) ) &
1511	* MERGE( 1.0_wp, 0.0_wp, &
1512	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1513	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1514	* MERGE( 1.0_wp, 0.0_wp, &
1515	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1516	ENDDO
1517	ENDDO
1518	ELSE
1519
1520	DO j = nys, nyn
1521	DO k = nzb+1, nzt
1522	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1523	* MERGE( 1.0_wp, 0.0_wp, &
1524	BTEST( wall_flags_total_0(k,j,0), 1 ) )
1525	u(k,j,-1) = u(k,j,0)
1526	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1527	* MERGE( 1.0_wp, 0.0_wp, &
1528	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
1529	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1530	* MERGE( 1.0_wp, 0.0_wp, &
1531	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
1532	ENDDO
1533	ENDDO
1534	ENDIF
1535	ENDIF
1536	IF ( myidx == id_stg_right ) THEN
1537	DO j = nys, nyn
1538	DO k = nzb+1, nzt
1539	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1540	* MERGE( 1.0_wp, 0.0_wp, &
1541	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
1542	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1543	* MERGE( 1.0_wp, 0.0_wp, &
1544	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
1545	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1546	* MERGE( 1.0_wp, 0.0_wp, &
1547	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
1548	ENDDO
1549	ENDDO
1550	ENDIF
1551	ENDIF
1552	ENDIF
1553	!
1554	!-- Turbulence generation at north and south boundary
1555	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1556	!
1557	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1558	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1559	!-- imposed
1560	IF ( stg_call ) THEN
1561	DO i = nxl, nxr
1562	DO k = nzb, nzt + 1
1563	!
1564	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1565	IF ( tu(k) == 0.0_wp ) THEN
1566	fu_xz(k,i) = fuo_xz(k,i)
1567	ELSE
1568	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1569	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1570	ENDIF
1571
1572	IF ( tv(k) == 0.0_wp ) THEN
1573	fv_xz(k,i) = fvo_xz(k,i)
1574	ELSE
1575	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1576	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1577	ENDIF
1578
1579	IF ( tw(k) == 0.0_wp ) THEN
1580	fw_xz(k,i) = fwo_xz(k,i)
1581	ELSE
1582	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1583	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1584	ENDIF
1585	ENDDO
1586	ENDDO
1587
1588
1589	dist_xz(nzb,:,1) = 0.0_wp
1590	dist_xz(nzb,:,2) = 0.0_wp
1591	dist_xz(nzb,:,3) = 0.0_wp
1592
1593	IF ( myidy == id_stg_south ) j = nys
1594	IF ( myidy == id_stg_north ) j = nyn+1
1595	DO i = nxl, nxr
1596	DO k = nzb+1, nzt + 1
1597	!
1598	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1599	!-- Additional factors are added to improve the variance of v and w
1600	!experimental test of 1.2
1601	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1602	* 1.2_wp ) &
1603	* ( a21(k) * fu_xz(k,i) &
1604	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1605	MERGE( 1.0_wp, 0.0_wp, &
1606	BTEST( wall_flags_total_0(k,j,i), 2 ) )
1607	ENDDO
1608	ENDDO
1609
1610	IF ( myidy == id_stg_south ) j = nys-1
1611	IF ( myidy == id_stg_north ) j = nyn+1
1612	DO i = nxl, nxr
1613	DO k = nzb+1, nzt + 1
1614	!
1615	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1616	!-- Additional factors are added to improve the variance of v and w
1617	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1618	MERGE( 1.0_wp, 0.0_wp, &
1619	BTEST( wall_flags_total_0(k,j,i), 1 ) )
1620
1621	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1622	* 1.3_wp ) &
1623	* ( a31(k) * fu_xz(k,i) &
1624	+ a32(k) * fv_xz(k,i) &
1625	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1626	MERGE( 1.0_wp, 0.0_wp, &
1627	BTEST( wall_flags_total_0(k,j,i), 3 ) )
1628	ENDDO
1629	ENDDO
1630	ENDIF
1631
1632	!
1633	!-- Mass flux correction following Kim et al. (2013)
1634	!-- This correction factor insures that the mass flux is preserved at the
1635	!-- inflow boundary. First, calculate mean value of the imposed
1636	!-- perturbations at yz boundary.
1637	!-- Note, this needs to be done only after the last RK3-substep, else
1638	!-- the boundary values won't be accessed.
1639	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1640	mc_factor_l = 0.0_wp
1641	mc_factor = 0.0_wp
1642
1643	IF ( myidy == id_stg_south ) j = nys
1644	IF ( myidy == id_stg_north ) j = nyn+1
1645
1646	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1647	* MERGE( 1.0_wp, 0.0_wp, &
1648	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1649
1650	IF ( myidy == id_stg_south ) j = nys-1
1651	IF ( myidy == id_stg_north ) j = nyn+1
1652
1653	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1654	* MERGE( 1.0_wp, 0.0_wp, &
1655	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1656	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1657	* MERGE( 1.0_wp, 0.0_wp, &
1658	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1659
1660	#if defined( __parallel )
1661	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1662	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1663	#else
1664	mc_factor = mc_factor_l
1665	#endif
1666
1667	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1668
1669	IF ( myidy == id_stg_south ) j = nys
1670	IF ( myidy == id_stg_north ) j = nyn+1
1671
1672	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
1673	* MERGE( 1.0_wp, 0.0_wp, &
1674	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
1675
1676
1677	IF ( myidy == id_stg_south ) j = nys-1
1678	IF ( myidy == id_stg_north ) j = nyn+1
1679
1680	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
1681	* MERGE( 1.0_wp, 0.0_wp, &
1682	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
1683
1684	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
1685	* MERGE( 1.0_wp, 0.0_wp, &
1686	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
1687	!
1688	!-- Add disturbances
1689	IF ( myidy == id_stg_south ) THEN
1690	DO i = nxl, nxr
1691	DO k = nzb+1, nzt
1692	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1693	* MERGE( 1.0_wp, 0.0_wp, &
1694	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
1695	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1696	* MERGE( 1.0_wp, 0.0_wp, &
1697	BTEST( wall_flags_total_0(k,0,i), 2 ) )
1698	v(k,-1,i) = v(k,0,i)
1699	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1700	* MERGE( 1.0_wp, 0.0_wp, &
1701	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
1702	ENDDO
1703	ENDDO
1704	ENDIF
1705	IF ( myidy == id_stg_north ) THEN
1706
1707	DO i = nxl, nxr
1708	DO k = nzb+1, nzt
1709	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1710	* MERGE( 1.0_wp, 0.0_wp, &
1711	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
1712	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1713	* MERGE( 1.0_wp, 0.0_wp, &
1714	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
1715	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1716	* MERGE( 1.0_wp, 0.0_wp, &
1717	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
1718	ENDDO
1719	ENDDO
1720	ENDIF
1721	ENDIF
1722	ENDIF
1723	!
1724	!-- Exchange ghost points.
1725	CALL exchange_horiz( u, nbgp )
1726	CALL exchange_horiz( v, nbgp )
1727	CALL exchange_horiz( w, nbgp )
1728	!
1729	!-- Finally, set time counter for calling STG to zero
1730	IF ( stg_call ) time_stg_call = 0.0_wp
1731
1732	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1733
1734	END SUBROUTINE stg_main
1735
1736	!------------------------------------------------------------------------------!
1737	! Description:
1738	! ------------
1739	!> Generate a set of random number rand_it wich is equal on each PE
1740	!> and calculate the velocity seed f_n.
1741	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1742	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1743	!> parts are collected to form the full array.
1744	!------------------------------------------------------------------------------!
1745	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1746
1747	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1748	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1749	INTEGER(iwp) :: j !< loop index in y-direction
1750	INTEGER(iwp) :: jj !< loop index in y-direction
1751	INTEGER(iwp) :: k !< loop index in z-direction
1752	INTEGER(iwp) :: kk !< loop index in z-direction
1753	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1754
1755	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1756	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1757
1758	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1759	REAL(wp) :: rand_av !< average of random number
1760	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1761
1762	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
1763	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1764
1765	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
1766	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
1767
1768	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1769	!
1770	!-- Generate random numbers using the parallel random generator.
1771	!-- The set of random numbers are modified to have an average of 0 and
1772	!-- unit variance. Note, at the end the random number array must be defined
1773	!-- globally in order to compute the correlation matrices. However,
1774	!-- the calculation and normalization of random numbers is done locally,
1775	!-- while the result is later distributed to all processes. Further,
1776	!-- please note, a set of random numbers is only calculated for the
1777	!-- left boundary, while the right boundary uses the same random numbers
1778	!-- and thus also computes the same correlation matrix.
1779	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
1780	rand_it = 0.0_wp
1781
1782	rand_av = 0.0_wp
1783	rand_sigma_inv = 0.0_wp
1784	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1785	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
1786	KIND=wp )
1787	!
1788	!-- Compute and normalize random numbers.
1789	DO j = nys - mergp, nyn + mergp
1790	!
1791	!-- Put the random seeds at grid point j
1792	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
1793	DO k = nzb - mergp, nzt + 1 + mergp
1794	CALL random_number_parallel( random_dummy )
1795	rand_it(k,j) = random_dummy
1796	ENDDO
1797	!
1798	!-- Get the new random seeds from last call at grid point j
1799	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
1800	ENDDO
1801	!
1802	!-- For normalization to zero mean, sum-up the global random numers.
1803	!-- To normalize the global set of random numbers,
1804	!-- the inner ghost layers mergp must not be summed-up, else
1805	!-- the random numbers on the ghost layers will be stronger weighted as they
1806	!-- also occur on the inner subdomains.
1807	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1808	MERGE( nyn, nyn + mergp, nyn /= ny )
1809	DO k = nzb - mergp, nzt + 1 + mergp
1810	rand_av = rand_av + rand_it(k,j)
1811	ENDDO
1812	ENDDO
1813
1814	#if defined( __parallel )
1815	!
1816	!-- Sum-up the local averages of the random numbers
1817	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1818	MPI_SUM, comm1dy, ierr )
1819	#endif
1820	rand_av = rand_av * nyz_inv
1821	!
1822	!-- Obtain zero mean
1823	rand_it= rand_it - rand_av
1824	!
1825	!-- Now, compute the variance
1826	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
1827	MERGE( nyn, nyn + mergp, nyn /= ny )
1828	DO k = nzb - mergp, nzt + 1 + mergp
1829	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
1830	ENDDO
1831	ENDDO
1832
1833	#if defined( __parallel )
1834	!
1835	!-- Sum-up the local quadratic averages of the random numbers
1836	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1837	MPI_SUM, comm1dy, ierr )
1838	#endif
1839	!
1840	!-- Compute standard deviation
1841	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1842	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1843	ELSE
1844	rand_sigma_inv = 1.0_wp
1845	ENDIF
1846	!
1847	!-- Normalize with standard deviation to obtain unit variance
1848	rand_it = rand_it * rand_sigma_inv
1849
1850	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
1851	!
1852	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
1853	!-- are two options. In the first one, the computation of the seeds is
1854	!-- distributed to all processes along the communicator comm1dy and
1855	!-- gathered on the leftmost and, if necessary, on the rightmost process.
1856	!-- For huge length scales the computational effort can become quite huge
1857	!-- (it scales with the turbulent length scales), so that gain by parallelization
1858	!-- exceeds the costs by the subsequent communication.
1859	!-- In the second option, which performs better when the turbulent length scales
1860	!-- are parametrized and thus the loops are smaller, the seeds are computed
1861	!-- locally and no communication is necessary.
1862	IF ( compute_velocity_seeds_local ) THEN
1863
1864	f_n = 0.0_wp
1865	DO j = nys, nyn
1866	DO k = nzb, nzt+1
1867	DO jj = -n_y(k), n_y(k)
1868	DO kk = -n_z(k), n_z(k)
1869	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1870	ENDDO
1871	ENDDO
1872	ENDDO
1873	ENDDO
1874
1875	ELSE
1876
1877	f_n_l = 0.0_wp
1878	DO j = nys, nyn
1879	DO k = nzb_x_stg, nzt_x_stg+1
1880	DO jj = -n_y(k), n_y(k)
1881	DO kk = -n_z(k), n_z(k)
1882	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1883	ENDDO
1884	ENDDO
1885	ENDDO
1886	ENDDO
1887	!
1888	!-- Gather velocity seeds of full subdomain
1889	send_count = nzt_x_stg - nzb_x_stg + 1
1890	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1891
1892	#if defined( __parallel )
1893	!
1894	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1895	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1896	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1897	id_left, comm1dx, ierr )
1898	!
1899	!-- If required, gather the same velocity seed matrix on right boundary
1900	!-- mpi ranks (in offline nesting for example).
1901	IF ( PRESENT( id_right ) ) THEN
1902	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
1903	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
1904	id_right, comm1dx, ierr )
1905	ENDIF
1906	#else
1907	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
1908	!
1909	!-- Next line required to avoid compile errors because of unused dummy arguments
1910	IF ( id_left == 0 ) id_right = 0
1911	#endif
1912
1913	ENDIF
1914
1915	DEALLOCATE( rand_it )
1916
1917	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
1918
1919	END SUBROUTINE stg_generate_seed_yz
1920
1921
1922	!------------------------------------------------------------------------------!
1923	! Description:
1924	! ------------
1925	!> Generate a set of random number rand_it wich is equal on each PE
1926	!> and calculate the velocity seed f_n.
1927	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1928	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1929	!> parts are collected to form the full array.
1930	!------------------------------------------------------------------------------!
1931	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1932
1933	INTEGER(iwp) :: i !< loop index in x-direction
1934	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1935	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1936	INTEGER(iwp) :: ii !< loop index in x-direction
1937	INTEGER(iwp) :: k !< loop index in z-direction
1938	INTEGER(iwp) :: kk !< loop index in z-direction
1939	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1940
1941	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1942	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1943
1944	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1945	REAL(wp) :: rand_av !< average of random number
1946	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1947
1948	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
1949	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
1950
1951	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
1952	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
1953
1954	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1955
1956	!
1957	!-- Generate random numbers using the parallel random generator.
1958	!-- The set of random numbers are modified to have an average of 0 and
1959	!-- unit variance. Note, at the end the random number array must be defined
1960	!-- globally in order to compute the correlation matrices. However,
1961	!-- the calculation and normalization of random numbers is done locally,
1962	!-- while the result is later distributed to all processes. Further,
1963	!-- please note, a set of random numbers is only calculated for the
1964	!-- left boundary, while the right boundary uses the same random numbers
1965	!-- and thus also computes the same correlation matrix.
1966	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
1967	rand_it = 0.0_wp
1968
1969	rand_av = 0.0_wp
1970	rand_sigma_inv = 0.0_wp
1971	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
1972	* ( nx + mergp - ( 0 - mergp ) +1 ), &
1973	KIND=wp )
1974	!
1975	!-- Compute and normalize random numbers.
1976	DO i = nxl - mergp, nxr + mergp
1977	!
1978	!-- Put the random seeds at grid point ii
1979	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
1980	DO k = nzb - mergp, nzt + 1 + mergp
1981	CALL random_number_parallel( random_dummy )
1982	rand_it(k,i) = random_dummy
1983	ENDDO
1984	!
1985	!-- Get the new random seeds from last call at grid point ii
1986	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
1987	ENDDO
1988	!
1989	!-- For normalization to zero mean, sum-up the global random numers.
1990	!-- To normalize the global set of random numbers,
1991	!-- the inner ghost layers mergp must not be summed-up, else
1992	!-- the random numbers on the ghost layers will be stronger weighted as they
1993	!-- also occur on the inner subdomains.
1994	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
1995	MERGE( nxr, nxr + mergp, nxr /= nx )
1996	DO k = nzb - mergp, nzt + 1 + mergp
1997	rand_av = rand_av + rand_it(k,i)
1998	ENDDO
1999	ENDDO
2000
2001	#if defined( __parallel )
2002	!
2003	!-- Sum-up the local averages of the random numbers
2004	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
2005	MPI_SUM, comm1dx, ierr )
2006	#endif
2007	rand_av = rand_av * nxz_inv
2008	!
2009	!-- Obtain zero mean
2010	rand_it= rand_it - rand_av
2011	!
2012	!-- Now, compute the variance
2013	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
2014	MERGE( nxr, nxr + mergp, nxr /= nx )
2015	DO k = nzb - mergp, nzt + 1 + mergp
2016	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
2017	ENDDO
2018	ENDDO
2019
2020	#if defined( __parallel )
2021	!
2022	!-- Sum-up the local quadratic averages of the random numbers
2023	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
2024	MPI_SUM, comm1dx, ierr )
2025	#endif
2026	!
2027	!-- Compute standard deviation
2028	IF ( rand_sigma_inv /= 0.0_wp ) THEN
2029	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
2030	ELSE
2031	rand_sigma_inv = 1.0_wp
2032	ENDIF
2033	!
2034	!-- Normalize with standard deviation to obtain unit variance
2035	rand_it = rand_it * rand_sigma_inv
2036
2037	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
2038	!
2039	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
2040	!-- are two options. In the first one, the computation of the seeds is
2041	!-- distributed to all processes along the communicator comm1dx and
2042	!-- gathered on the southmost and, if necessary, on the northmost process.
2043	!-- For huge length scales the computational effort can become quite huge
2044	!-- (it scales with the turbulent length scales), so that gain by parallelization
2045	!-- exceeds the costs by the subsequent communication.
2046	!-- In the second option, which performs better when the turbulent length scales
2047	!-- are parametrized and thus the loops are smaller, the seeds are computed
2048	!-- locally and no communication is necessary.
2049	IF ( compute_velocity_seeds_local ) THEN
2050
2051	f_n = 0.0_wp
2052	DO i = nxl, nxr
2053	DO k = nzb, nzt+1
2054	DO ii = -n_x(k), n_x(k)
2055	DO kk = -n_z(k), n_z(k)
2056	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2057	ENDDO
2058	ENDDO
2059	ENDDO
2060	ENDDO
2061
2062	ELSE
2063
2064	f_n_l = 0.0_wp
2065	DO i = nxl, nxr
2066	DO k = nzb_y_stg, nzt_y_stg+1
2067	DO ii = -n_x(k), n_x(k)
2068	DO kk = -n_z(k), n_z(k)
2069	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2070	ENDDO
2071	ENDDO
2072	ENDDO
2073	ENDDO
2074	!
2075	!-- Gather velocity seeds of full subdomain
2076	send_count = nzt_y_stg - nzb_y_stg + 1
2077	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2078
2079	#if defined( __parallel )
2080	!
2081	!-- Gather the processed velocity seed on south boundary mpi ranks.
2082	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2083	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2084	id_south, comm1dy, ierr )
2085	!
2086	!-- Gather the processed velocity seed on north boundary mpi ranks.
2087	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
2088	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
2089	id_north, comm1dy, ierr )
2090	#else
2091	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
2092	!
2093	!-- Next line required to avoid compile errors because of unused dummy arguments
2094	IF ( id_north == 0 ) id_south = 0
2095	#endif
2096
2097	ENDIF
2098
2099	DEALLOCATE( rand_it )
2100
2101	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
2102
2103	END SUBROUTINE stg_generate_seed_xz
2104
2105	!------------------------------------------------------------------------------!
2106	! Description:
2107	! ------------
2108	!> Parametrization of the Reynolds stress tensor, following the parametrization
2109	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2110	!> dispserion modelling. Please note, the parametrization does not distinguish
2111	!> between along-wind and cross-wind turbulence.
2112	!------------------------------------------------------------------------------!
2113	SUBROUTINE parametrize_reynolds_stress
2114
2115	INTEGER(iwp) :: k !< loop index in z-direction
2116
2117	REAL(wp) :: zzi !< ratio of z/zi
2118
2119	DO k = nzb+1, nzt+1
2120	!
2121	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2122	!-- The function decreases to 1/10 after one length scale above the
2123	!-- ABL top.
2124	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2125	!
2126	!-- Determine normalized height coordinate
2127	zzi = zu(k) / zi_ribulk
2128	!
2129	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2130	!-- to the denominator, else the mergpe-function can crash if scale_l is
2131	!-- zero.
2132	r11(k) = scale_us*2 ( &
2133	MERGE( 0.35_wp * ABS( &
2134	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2135	)**( 2.0_wp / 3.0_wp ), &
2136	0.0_wp, &
2137	scale_l < 0.0_wp ) &
2138	+ 5.0_wp - 4.0_wp * zzi &
2139	) * blend
2140
2141	r22(k) = r11(k)
2142	!
2143	!-- w'w'
2144	r33(k) = scale_wm*2 ( &
2145	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2146	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2147	) * blend
2148	!
2149	!-- u'w' and v'w'. Assume isotropy.
2150	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2151	r32(k) = r31(k)
2152	!
2153	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2154	!-- a similar profile as for u'w'.
2155	r21(k) = r31(k)
2156	ENDDO
2157
2158	!
2159	!-- Set bottom boundary condition
2160	r11(nzb) = r11(nzb+1)
2161	r22(nzb) = r22(nzb+1)
2162	r33(nzb) = r33(nzb+1)
2163
2164	r21(nzb) = r11(nzb+1)
2165	r31(nzb) = r31(nzb+1)
2166	r32(nzb) = r32(nzb+1)
2167
2168
2169	END SUBROUTINE parametrize_reynolds_stress
2170
2171	!------------------------------------------------------------------------------!
2172	! Description:
2173	! ------------
2174	!> Calculate the coefficient matrix from the Lund rotation.
2175	!------------------------------------------------------------------------------!
2176	SUBROUTINE calc_coeff_matrix
2177
2178	INTEGER(iwp) :: k !< loop index in z-direction
2179
2180	!
2181	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2182	DO k = nzb+1, nzt+1
2183	IF ( r11(k) > 10E-6_wp ) THEN
2184	a11(k) = SQRT( r11(k) )
2185	a21(k) = r21(k) / a11(k)
2186	a31(k) = r31(k) / a11(k)
2187	ELSE
2188	a11(k) = 10E-8_wp
2189	a21(k) = 10E-8_wp
2190	a31(k) = 10E-8_wp
2191	ENDIF
2192	ENDDO
2193	DO k = nzb+1, nzt+1
2194	a22(k) = r22(k) - a21(k)**2
2195	IF ( a22(k) > 10E-6_wp ) THEN
2196	a22(k) = SQRT( a22(k) )
2197	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2198	ELSE
2199	a22(k) = 10E-8_wp
2200	a32(k) = 10E-8_wp
2201	ENDIF
2202	ENDDO
2203	DO k = nzb+1, nzt+1
2204	a33(k) = r33(k) - a31(k)2 - a32(k)2
2205	IF ( a33(k) > 10E-6_wp ) THEN
2206	a33(k) = SQRT( a33(k) )
2207	ELSE
2208	a33(k) = 10E-8_wp
2209	ENDIF
2210	ENDDO
2211	!
2212	!-- Set bottom boundary condition
2213	a11(nzb) = a11(nzb+1)
2214	a22(nzb) = a22(nzb+1)
2215	a21(nzb) = a21(nzb+1)
2216	a33(nzb) = a33(nzb+1)
2217	a31(nzb) = a31(nzb+1)
2218	a32(nzb) = a32(nzb+1)
2219
2220	END SUBROUTINE calc_coeff_matrix
2221
2222	!------------------------------------------------------------------------------!
2223	! Description:
2224	! ------------
2225	!> This routine controls the re-adjustment of the turbulence statistics used
2226	!> for generating turbulence at the lateral boundaries.
2227	!------------------------------------------------------------------------------!
2228	SUBROUTINE stg_adjust
2229
2230	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2231	!
2232	!-- In case of dirichlet inflow boundary conditions only at one lateral
2233	!-- boundary, i.e. in the case no offline or self nesting is applied but
2234	!-- synthetic turbulence shall be parametrized nevertheless, the
2235	!-- boundary-layer depth need to determined first.
2236	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2237	CALL nesting_offl_calc_zi
2238	!
2239	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2240	!-- are calculated.
2241	CALL calc_scaling_variables
2242	!
2243	!-- Set length and time scales depending on boundary-layer height
2244	CALL calc_length_and_time_scale
2245	!
2246	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2247	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2248	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2249	!-- friction velocity and velocity scale.
2250	CALL parametrize_reynolds_stress
2251	!
2252	!-- Calculate coefficient matrix from Reynolds stress tensor
2253	!-- (Lund rotation)
2254	CALL calc_coeff_matrix
2255	!
2256	!-- Determine filter functions on basis of updated length scales
2257	CALL stg_filter_func( nux, bux ) !filter ux
2258	CALL stg_filter_func( nuy, buy ) !filter uy
2259	CALL stg_filter_func( nuz, buz ) !filter uz
2260	CALL stg_filter_func( nvx, bvx ) !filter vx
2261	CALL stg_filter_func( nvy, bvy ) !filter vy
2262	CALL stg_filter_func( nvz, bvz ) !filter vz
2263	CALL stg_filter_func( nwx, bwx ) !filter wx
2264	CALL stg_filter_func( nwy, bwy ) !filter wy
2265	CALL stg_filter_func( nwz, bwz ) !filter wz
2266	!
2267	!-- Reset time counter for controlling next adjustment to zero
2268	time_stg_adjust = 0.0_wp
2269
2270	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2271
2272	END SUBROUTINE stg_adjust
2273
2274
2275	!------------------------------------------------------------------------------!
2276	! Description:
2277	! ------------
2278	!> Calculates turbuluent length and time scales if these are not available
2279	!> from measurements.
2280	!------------------------------------------------------------------------------!
2281	SUBROUTINE calc_length_and_time_scale
2282
2283	INTEGER(iwp) :: k !< loop index in z-direction
2284
2285	REAL(wp) :: length_scale_dum !< effectively used length scale
2286
2287	!
2288	!-- In initial call the boundary-layer depth can be zero. This case, set
2289	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2290	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2291	!
2292	!-- Set-up default turbulent length scales. From the numerical point of
2293	!-- view the imposed perturbations should not be immediately dissipated
2294	!-- by the numerics. The numerical dissipation, however, acts on scales
2295	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2296	!-- length scale to 8 time the grid spacing. Further, above the boundary
2297	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2298	!-- imposing any perturbations) in order to save computational costs.
2299	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2300	!-- using the length scales and the mean profiles of u- and v-component.
2301	DO k = nzb+1, nzt+1
2302	!
2303	!-- Determine blending parameter. Within the boundary layer length scales
2304	!-- are constant, while above lengths scales approach gradully zero,
2305	!-- i.e. imposed turbulence is not correlated in space and time,
2306	!-- just white noise, which saves computations power as the loops for the
2307	!-- computation of the filter functions depend on the length scales.
2308	!-- The value decreases to 1/10 after one length scale above the
2309	!-- ABL top.
2310	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2311	!
2312	!-- Assume isotropic turbulence length scales
2313	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2314	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2315	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2316	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2317	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2318	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2319	!
2320	!-- Along the vertical direction limit the length scale further by the
2321	!-- boundary-layer depth to assure that no length scales larger than
2322	!-- the boundary-layer depth are used
2323	length_scale_dum = MIN( length_scale, zi_ribulk )
2324
2325	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2326	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2327	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2328	!
2329	!-- Limit time scales, else they become very larger for low wind speed,
2330	!-- imposing long-living inflow perturbations which in turn propagate
2331	!-- further into the model domain. Use u_init and v_init to calculate
2332	!-- the time scales, which will be equal to the inflow profiles, both,
2333	!-- in offline nesting mode or in dirichlet/radiation mode.
2334	tu(k) = MIN( dt_stg_adjust, length_scale / &
2335	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2336	tv(k) = MIN( dt_stg_adjust, length_scale / &
2337	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2338	!
2339	!-- Time scale of w-component is a mixture from u- and v-component.
2340	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2341
2342	ENDDO
2343	!
2344	!-- Set bottom boundary condition for the length and time scales
2345	nux(nzb) = nux(nzb+1)
2346	nuy(nzb) = nuy(nzb+1)
2347	nuz(nzb) = nuz(nzb+1)
2348	nvx(nzb) = nvx(nzb+1)
2349	nvy(nzb) = nvy(nzb+1)
2350	nvz(nzb) = nvz(nzb+1)
2351	nwx(nzb) = nwx(nzb+1)
2352	nwy(nzb) = nwy(nzb+1)
2353	nwz(nzb) = nwz(nzb+1)
2354
2355	tu(nzb) = tu(nzb+1)
2356	tv(nzb) = tv(nzb+1)
2357	tw(nzb) = tw(nzb+1)
2358
2359
2360	END SUBROUTINE calc_length_and_time_scale
2361
2362	!------------------------------------------------------------------------------!
2363	! Description:
2364	! ------------
2365	!> Calculate scaling variables which are used for turbulence parametrization
2366	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2367	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2368	!------------------------------------------------------------------------------!
2369	SUBROUTINE calc_scaling_variables
2370
2371	INTEGER(iwp) :: i !< loop index in x-direction
2372	INTEGER(iwp) :: j !< loop index in y-direction
2373	INTEGER(iwp) :: k !< loop index in z-direction
2374	INTEGER(iwp) :: m !< surface element index
2375
2376	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2377	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2378	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2379	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2380	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2381	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2382	REAL(wp) :: w_convective !< convective velocity scale
2383
2384	!
2385	!-- Calculate mean friction velocity, velocity scale, heat flux and
2386	!-- near-surface temperature in the model domain.
2387	pt_surf_mean_l = 0.0_wp
2388	shf_mean_l = 0.0_wp
2389	scale_l_l = 0.0_wp
2390	friction_vel_l = 0.0_wp
2391	DO m = 1, surf_def_h(0)%ns
2392	i = surf_def_h(0)%i(m)
2393	j = surf_def_h(0)%j(m)
2394	k = surf_def_h(0)%k(m)
2395	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2396	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2397	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2398	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2399	ENDDO
2400	DO m = 1, surf_lsm_h%ns
2401	i = surf_lsm_h%i(m)
2402	j = surf_lsm_h%j(m)
2403	k = surf_lsm_h%k(m)
2404	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2405	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2406	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2407	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2408	ENDDO
2409	DO m = 1, surf_usm_h%ns
2410	i = surf_usm_h%i(m)
2411	j = surf_usm_h%j(m)
2412	k = surf_usm_h%k(m)
2413	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2414	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2415	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2416	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2417	ENDDO
2418
2419	#if defined( __parallel )
2420	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2421	comm2d, ierr )
2422	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2423	comm2d, ierr )
2424	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2425	comm2d, ierr )
2426	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2427	comm2d, ierr )
2428	#else
2429	scale_us = friction_vel_l
2430	shf_mean = shf_mean_l
2431	scale_l = scale_l_l
2432	pt_surf_mean = pt_surf_mean_l
2433	#endif
2434
2435	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2436	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2437	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2438	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2439	!
2440	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2441	!-- is negative, set convective velocity scale to zero.
2442	IF ( shf_mean > 0.0_wp ) THEN
2443	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2444	ELSE
2445	w_convective = 0.0_wp
2446	ENDIF
2447	!
2448	!-- Finally, in order to consider also neutral or stable stratification,
2449	!-- compute momentum velocity scale from u* and convective velocity scale,
2450	!-- according to Rotach et al. (1996).
2451	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2452
2453	END SUBROUTINE calc_scaling_variables
2454
2455	END MODULE synthetic_turbulence_generator_mod

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