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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4329

Last change on this file since 4329 was 4329, checked in by motisi, 4 years ago
Renamed wall_flags_0 to wall_flags_static_0
Property svn:keywords set to `Id`
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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 4329 2019-12-10 15:46:36Z motisi $
27	! Renamed wall_flags_0 to wall_flags_static_0
28	!
29	! 4309 2019-11-26 18:49:59Z suehring
30	! Computation of velocity seeds optimized. This implies that random numbers
31	! are computed now using the parallel random number generator. Random numbers
32	! are now only computed and normalized locally, while distributed over all
33	! mpi ranks afterwards, instead of computing random numbers on a global array.
34	! Further, the number of calls for the time-consuming velocity-seed generation
35	! is reduced - now the left and right, as well as the north and south boundary
36	! share the same velocity-seed matrices.
37	!
38	! 4182 2019-08-22 15:20:23Z scharf
39	! Corrected "Former revisions" section
40	!
41	! 4148 2019-08-08 11:26:00Z suehring
42	! Remove unused variable
43	!
44	! 4144 2019-08-06 09:11:47Z raasch
45	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
46	!
47	! 4071 2019-07-03 20:02:00Z suehring
48	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
49	! information is not read from file.
50	!
51	! 4022 2019-06-12 11:52:39Z suehring
52	! Several bugfixes and improvements
53	! - revise bias correction of the imposed perturbations (correction via volume
54	! flow can create instabilities in case the mean volume flow is close to zero)
55	! - introduce lower limits in calculation of coefficient matrix, else the
56	! calculation may become numerically unstable
57	! - impose perturbations every timestep, even though no new set of perturbations
58	! is generated in case dt_stg_call /= dt_3d
59	! - Implement a gradual decrease of Reynolds stress and length scales above
60	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
61	! discontinuous decrease
62	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
63	!
64	! 3987 2019-05-22 09:52:13Z kanani
65	! Introduce alternative switch for debug output during timestepping
66	!
67	! 3938 2019-04-29 16:06:25Z suehring
68	! Remove unused variables
69	!
70	! 3937 2019-04-29 15:09:07Z suehring
71	! Minor bugfix in case of a very early restart where mc_factor is sill not
72	! present.
73	! Some modification and fixing of potential bugs in the calculation of scaling
74	! parameters used for synthetic turbulence parametrization.
75	!
76	! 3909 2019-04-17 09:13:25Z suehring
77	! Minor bugfix for last commit
78	!
79	! 3900 2019-04-16 15:17:43Z suehring
80	! Missing re-calculation of perturbation seeds in case of restarts
81	!
82	! 3891 2019-04-12 17:52:01Z suehring
83	! Bugfix in initialization in case of restart runs.
84	!
85	! 3885 2019-04-11 11:29:34Z kanani
86	! Changes related to global restructuring of location messages and introduction
87	! of additional debug messages
88	!
89	!
90	! removed unused variables
91	!
92	! 3719 2019-02-06 13:10:18Z kanani
93	! Removed log_point measurement from stg_init, since this part is counted to
94	! log_point(2) 'initialisation' already. Moved other log_points to calls of
95	! the subroutines in time_integration for better overview.
96	!
97	! 2259 2017-06-08 09:09:11Z gronemeier
98	! Initial revision
99	!
100	! Authors:
101	! --------
102	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
103	!
104	!
105	! Description:
106	! ------------
107	!> The module generates turbulence at the inflow boundary based on a method by
108	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
109	!> correction by Kim et al. (2013).
110	!> The turbulence is correlated based on length scales in y- and z-direction and
111	!> a time scale for each velocity component. The profiles of length and time
112	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
113	!> tensor can be either read from file STG_PROFILES, or will be parametrized
114	!> within the boundary layer.
115	!>
116	!> @todo test restart
117	!> enable cyclic_fill
118	!> implement turbulence generation for e and pt
119	!> @todo Input of height-constant length scales via namelist
120	!> @note <Enter notes on the module>
121	!> @bug Height information from input file is not used. Profiles from input
122	!> must match with current PALM grid.
123	!> In case of restart, velocity seeds differ from precursor run if a11,
124	!> a22, or a33 are zero.
125	!------------------------------------------------------------------------------!
126	MODULE synthetic_turbulence_generator_mod
127
128
129	USE arrays_3d, &
130	ONLY: dzw, &
131	ddzw, &
132	drho_air, &
133	mean_inflow_profiles, &
134	q, &
135	q_init, &
136	pt, &
137	pt_init, &
138	u, &
139	u_init, &
140	v, &
141	v_init, &
142	w, &
143	zu, &
144	zw
145
146	USE basic_constants_and_equations_mod, &
147	ONLY: g, &
148	kappa, &
149	pi
150
151	USE control_parameters, &
152	ONLY: bc_lr, &
153	bc_ns, &
154	child_domain, &
155	coupling_char, &
156	debug_output_timestep, &
157	dt_3d, &
158	e_init, &
159	humidity, &
160	initializing_actions, &
161	intermediate_timestep_count, &
162	intermediate_timestep_count_max, &
163	length, &
164	message_string, &
165	nesting_offline, &
166	neutral, &
167	num_mean_inflow_profiles, &
168	random_generator, &
169	rans_mode, &
170	restart_string, &
171	syn_turb_gen, &
172	time_since_reference_point, &
173	turbulent_inflow
174
175	USE grid_variables, &
176	ONLY: ddx, &
177	ddy, &
178	dx, &
179	dy
180
181	USE indices, &
182	ONLY: nbgp, &
183	nz, &
184	nzb, &
185	nzt, &
186	nx, &
187	nxl, &
188	nxlu, &
189	nxlg, &
190	nxr, &
191	nxrg, &
192	ny, &
193	nys, &
194	nysv, &
195	nyn, &
196	nyng, &
197	nysg, &
198	wall_flags_static_0
199
200	USE kinds
201
202	#if defined( __parallel ) && !defined( __mpifh )
203	USE MPI
204	#endif
205
206	USE nesting_offl_mod, &
207	ONLY: nesting_offl_calc_zi, &
208	zi_ribulk
209
210	USE pegrid, &
211	ONLY: comm1dx, &
212	comm1dy, &
213	comm2d, &
214	ierr, &
215	myidx, &
216	myidy, &
217	pdims
218
219	USE pmc_interface, &
220	ONLY : rans_mode_parent
221
222	USE random_generator_parallel, &
223	ONLY: random_dummy, &
224	random_number_parallel, &
225	random_seed_parallel, &
226	seq_random_array
227
228	USE transpose_indices, &
229	ONLY: nzb_x, &
230	nzt_x
231
232
233	IMPLICIT NONE
234
235	#if defined( __parallel ) && defined( __mpifh )
236	INCLUDE "mpif.h"
237	#endif
238
239
240	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
241	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
242	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
243
244	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
245	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
246	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
247	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
248	INTEGER(iwp) :: merg !< maximum length scale (in gp)
249	INTEGER(iwp) :: mergp !< merg + nbgp
250	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
251	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
252	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
253	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
254	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
255	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
256	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
257	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
258
259	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
260	!< required for bias correction of imposed perturbations
261	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
262	!< required for bias correction of imposed perturbations
263
264	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
265	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
266	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
267	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
268	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
269	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
270	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
271	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
272	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
273	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
274	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
275	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
276	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
277
278	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
279	!< scales above the boundary layer
280	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
281	!< one length scale above ABL top
282	REAL(wp) :: d_l !< blend_coeff/length_scale
283	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
284	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
285	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
286	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
287	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
288	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
289	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
290	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
291
292	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
293
294
295	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
296	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
297	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
298	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
299	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
300	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
301
302	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
303	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
304	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
305	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
306	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
307	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
308	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
309	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
310	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
311
312	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
313	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
314	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
315	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
316	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
317	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
318	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
319	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
320	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
321	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
322	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
323	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
324	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
325	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
326	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
327	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
328	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
329	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
330	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
331	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
332	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
333
334	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
335	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
336
337	!
338	!-- PALM interfaces:
339	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
340	INTERFACE stg_adjust
341	MODULE PROCEDURE stg_adjust
342	END INTERFACE stg_adjust
343	!
344	!-- Input parameter checks to be done in check_parameters
345	INTERFACE stg_check_parameters
346	MODULE PROCEDURE stg_check_parameters
347	END INTERFACE stg_check_parameters
348
349	!
350	!-- Calculate filter functions
351	INTERFACE stg_filter_func
352	MODULE PROCEDURE stg_filter_func
353	END INTERFACE stg_filter_func
354
355	!
356	!-- Generate velocity seeds at south and north domain boundary
357	INTERFACE stg_generate_seed_xz
358	MODULE PROCEDURE stg_generate_seed_xz
359	END INTERFACE stg_generate_seed_xz
360	!
361	!-- Generate velocity seeds at left and/or right domain boundary
362	INTERFACE stg_generate_seed_yz
363	MODULE PROCEDURE stg_generate_seed_yz
364	END INTERFACE stg_generate_seed_yz
365
366	!
367	!-- Output of information to the header file
368	INTERFACE stg_header
369	MODULE PROCEDURE stg_header
370	END INTERFACE stg_header
371
372	!
373	!-- Initialization actions
374	INTERFACE stg_init
375	MODULE PROCEDURE stg_init
376	END INTERFACE stg_init
377
378	!
379	!-- Main procedure of synth. turb. gen.
380	INTERFACE stg_main
381	MODULE PROCEDURE stg_main
382	END INTERFACE stg_main
383
384	!
385	!-- Reading of NAMELIST parameters
386	INTERFACE stg_parin
387	MODULE PROCEDURE stg_parin
388	END INTERFACE stg_parin
389
390	!
391	!-- Reading of parameters for restart runs
392	INTERFACE stg_rrd_global
393	MODULE PROCEDURE stg_rrd_global
394	END INTERFACE stg_rrd_global
395
396	!
397	!-- Writing of binary output for restart runs
398	INTERFACE stg_wrd_global
399	MODULE PROCEDURE stg_wrd_global
400	END INTERFACE stg_wrd_global
401
402	SAVE
403
404	PRIVATE
405
406	!
407	!-- Public interfaces
408	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
409	stg_parin, stg_rrd_global, stg_wrd_global
410
411	!
412	!-- Public variables
413	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
414	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
415	time_stg_adjust, time_stg_call, use_syn_turb_gen
416
417
418	CONTAINS
419
420
421	!------------------------------------------------------------------------------!
422	! Description:
423	! ------------
424	!> Check parameters routine for synthetic turbulence generator
425	!------------------------------------------------------------------------------!
426	SUBROUTINE stg_check_parameters
427
428	IMPLICIT NONE
429
430	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
431	nesting_offline ) THEN
432	message_string = 'Synthetic turbulence generator is required ' // &
433	'if offline nesting is applied and PALM operates ' // &
434	'in LES mode.'
435	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
436	ENDIF
437
438	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
439	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
440	message_string = 'Synthetic turbulence generator is required ' // &
441	'when nesting is applied and parent operates in ' // &
442	'RANS-mode but current child in LES mode.'
443	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
444	ENDIF
445
446	IF ( use_syn_turb_gen ) THEN
447
448	IF ( child_domain .AND. .NOT. rans_mode .AND. &
449	.NOT. rans_mode_parent ) THEN
450	message_string = 'Using synthetic turbulence generator ' // &
451	'is not allowed in LES-LES nesting.'
452	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
453
454	ENDIF
455
456	IF ( child_domain .AND. rans_mode .AND. &
457	rans_mode_parent ) THEN
458	message_string = 'Using synthetic turbulence generator ' // &
459	'is not allowed in RANS-RANS nesting.'
460	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
461
462	ENDIF
463
464	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
465
466	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
467	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
468	message_string = 'Using synthetic turbulence generator ' // &
469	'requires %initializing_actions = ' // &
470	'"set_constant_profiles" or "read_restart_data"' //&
471	', if not offline nesting is applied.'
472	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
473	ENDIF
474
475	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
476	message_string = 'Using synthetic turbulence generator ' // &
477	'requires &bc_lr = "dirichlet/radiation", ' // &
478	'if not offline nesting is applied.'
479	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
480	ENDIF
481	IF ( bc_ns /= 'cyclic' ) THEN
482	message_string = 'Using synthetic turbulence generator ' // &
483	'requires &bc_ns = "cyclic", ' // &
484	'if not offline nesting is applied.'
485	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
486	ENDIF
487
488	ENDIF
489
490	IF ( turbulent_inflow ) THEN
491	message_string = 'Using synthetic turbulence generator ' // &
492	'in combination &with turbulent_inflow = .T. '// &
493	'is not allowed'
494	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
495	ENDIF
496	!
497	!-- Synthetic turbulence generator requires the parallel random generator
498	IF ( random_generator /= 'random-parallel' ) THEN
499	message_string = 'Using synthetic turbulence generator ' // &
500	'requires random_generator = random-parallel.'
501	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
502	ENDIF
503
504	ENDIF
505
506	END SUBROUTINE stg_check_parameters
507
508
509	!------------------------------------------------------------------------------!
510	! Description:
511	! ------------
512	!> Header output for synthetic turbulence generator
513	!------------------------------------------------------------------------------!
514	SUBROUTINE stg_header ( io )
515
516
517	IMPLICIT NONE
518
519	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
520
521	!
522	!-- Write synthetic turbulence generator Header
523	WRITE( io, 1 )
524	IF ( use_syn_turb_gen ) THEN
525	WRITE( io, 2 )
526	ELSE
527	WRITE( io, 3 )
528	ENDIF
529
530	IF ( parametrize_inflow_turbulence ) THEN
531	WRITE( io, 4 ) dt_stg_adjust
532	ELSE
533	WRITE( io, 5 )
534	ENDIF
535
536	1 FORMAT (//' Synthetic turbulence generator information:'/ &
537	' ------------------------------------------'/)
538	2 FORMAT (' synthetic turbulence generator is switched on')
539	3 FORMAT (' synthetic turbulence generator is switched off')
540	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
541	5 FORMAT (' imposed turbulence is read from file' )
542
543	END SUBROUTINE stg_header
544
545
546	!------------------------------------------------------------------------------!
547	! Description:
548	! ------------
549	!> Initialization of the synthetic turbulence generator
550	!------------------------------------------------------------------------------!
551	SUBROUTINE stg_init
552
553	IMPLICIT NONE
554
555	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
556
557	#if defined( __parallel )
558	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
559	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
560	#endif
561
562	INTEGER(iwp) :: i !> grid index in x-direction
563	INTEGER(iwp) :: j !> loop index
564	INTEGER(iwp) :: k !< index
565	INTEGER(iwp) :: newtype !< dummy MPI type
566	INTEGER(iwp) :: realsize !< size of REAL variables
567
568	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
569	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
570	!
571	!-- Dummy variables used for reading profiles
572	REAL(wp) :: d1 !< u profile
573	REAL(wp) :: d2 !< v profile
574	REAL(wp) :: d3 !< w profile
575	REAL(wp) :: d5 !< e profile
576	REAL(wp) :: luy !< length scale for u in y direction
577	REAL(wp) :: luz !< length scale for u in z direction
578	REAL(wp) :: lvy !< length scale for v in y direction
579	REAL(wp) :: lvz !< length scale for v in z direction
580	REAL(wp) :: lwy !< length scale for w in y direction
581	REAL(wp) :: lwz !< length scale for w in z direction
582	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
583	REAL(wp) :: zz !< height
584
585
586	#if defined( __parallel )
587	CALL MPI_BARRIER( comm2d, ierr )
588	#endif
589
590	#if defined( __parallel )
591	!
592	!-- Determine processor decomposition of z-axis along x- and y-direction
593	nnz = nz / pdims(1)
594	nzb_x_stg = 1 + myidx * INT( nnz )
595	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
596
597	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
598	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
599
600	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
601	.AND. .NOT. rans_mode ) ) THEN
602	nnz = nz / pdims(2)
603	nzb_y_stg = 1 + myidy * INT( nnz )
604	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
605
606	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
607	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
608	ENDIF
609
610	!
611	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
612	!-- velocity seeds
613	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
614	extent = 1 * realsize
615	!
616	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
617	!-- layer
618	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
619	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
620	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
621	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
622	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
623	CALL MPI_TYPE_FREE( newtype, ierr )
624
625	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
626	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
627	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
628	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
629	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
630	CALL MPI_TYPE_FREE( newtype, ierr )
631
632	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
633	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
634
635	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
636	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
637
638	DO j = 1, pdims(1)
639	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
640	ENDDO
641	!
642	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
643	!-- layer
644	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
645	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
646	.AND. .NOT. rans_mode ) ) THEN
647	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
648	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
649	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
650	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
651	CALL MPI_TYPE_FREE( newtype, ierr )
652
653	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
654	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
655	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
656	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
657	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
658	CALL MPI_TYPE_FREE( newtype, ierr )
659
660	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
661	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
662
663	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
664	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
665
666	DO j = 1, pdims(2)
667	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
668	ENDDO
669
670	ENDIF
671
672	#endif
673	!
674	!-- Allocate required arrays.
675	!-- In case no offline nesting or self nesting is used, the arrary
676	!-- mean_inflow profiles is required. Check if it is already allocated, else
677	!-- allocate and initialize it appropriately. Note, in case turbulence and
678	!-- inflow information is read from file, mean_inflow_profiles is already
679	!-- allocated and initialized appropriately.
680	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
681	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
682	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
683	mean_inflow_profiles = 0.0_wp
684	mean_inflow_profiles(:,1) = u_init
685	mean_inflow_profiles(:,2) = v_init
686	!
687	!-- Even though potential temperature and humidity are not perturbed,
688	!-- they need to be initialized appropriately.
689	IF ( .NOT. neutral ) &
690	mean_inflow_profiles(:,4) = pt_init
691	IF ( humidity ) &
692	mean_inflow_profiles(:,6) = q_init
693	ENDIF
694	ENDIF
695
696	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
697	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
698	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
699	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
700	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
701	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
702	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
703	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
704
705	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
706	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
707	dist_xz = 0.0_wp
708	dist_yz = 0.0_wp
709	!
710	!-- Read inflow profile
711	!-- Height levels of profiles in input profile is as follows:
712	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
713	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
714	!-- WARNING: zz is not used at the moment
715	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
716	EXIST = file_stg_exist )
717
718	IF ( file_stg_exist ) THEN
719
720	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
721	FORM='FORMATTED')
722	!
723	!-- Skip header
724	READ( 90, * )
725
726	DO k = nzb+1, nzt+1
727	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
728	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
729	d1, d2, d3, d5
730
731	!
732	!-- Convert length scales from meter to number of grid points.
733	nuy(k) = INT( luy * ddy )
734	nuz(k) = INT( luz * ddzw(k) )
735	nvy(k) = INT( lvy * ddy )
736	nvz(k) = INT( lvz * ddzw(k) )
737	nwy(k) = INT( lwy * ddy )
738	nwz(k) = INT( lwz * ddzw(k) )
739	!
740	!-- Workaround, assume isotropic turbulence
741	nwx(k) = nwy(k)
742	nvx(k) = nvy(k)
743	nux(k) = nuy(k)
744	!
745	!-- Save Mean inflow profiles
746	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
747	mean_inflow_profiles(k,1) = d1
748	mean_inflow_profiles(k,2) = d2
749	! mean_inflow_profiles(k,4) = d4
750	mean_inflow_profiles(k,5) = d5
751	ENDIF
752	ENDDO
753	!
754	!-- Set lenght scales at surface grid point
755	nuy(nzb) = nuy(nzb+1)
756	nuz(nzb) = nuz(nzb+1)
757	nvy(nzb) = nvy(nzb+1)
758	nvz(nzb) = nvz(nzb+1)
759	nwy(nzb) = nwy(nzb+1)
760	nwz(nzb) = nwz(nzb+1)
761
762	CLOSE( 90 )
763	!
764	!-- Calculate coefficient matrix from Reynolds stress tensor
765	!-- (Lund rotation)
766	CALL calc_coeff_matrix
767	!
768	!-- No information about turbulence and its length scales are available.
769	!-- Instead, parametrize turbulence which is imposed at the boundaries.
770	!-- Set flag which indicates that turbulence is parametrized, which is done
771	!-- later when energy-balance models are already initialized. This is
772	!-- because the STG needs information about surface properties such as
773	!-- roughness to build 'realistic' turbulence profiles.
774	ELSE
775	!
776	!-- Define length scale for the imposed turbulence, which is defined as
777	!-- 8 times the minimum grid spacing
778	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
779	!
780	!-- Define constant to gradually decrease length scales and Reynolds stress
781	!-- above ABL top. Assure that no zero length scales are used.
782	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
783	!
784	!-- Set flag indicating that turbulence is parametrized
785	parametrize_inflow_turbulence = .TRUE.
786	!
787	!-- In case of dirichlet inflow boundary conditions only at one lateral
788	!-- boundary, i.e. in the case no offline or self nesting is applied but
789	!-- synthetic turbulence shall be parametrized nevertheless, the
790	!-- boundary-layer depth need to determined first.
791	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
792	CALL nesting_offl_calc_zi
793	!
794	!-- Determine boundary-layer depth, which is used to initialize lenght
795	!-- scales
796	CALL calc_scaling_variables
797	!
798	!-- Initialize lenght and time scales, which in turn are used
799	!-- to initialize the filter functions.
800	CALL calc_length_and_time_scale
801	!
802	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
803	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
804	!-- Rotach et al. (1996) and is based on boundary-layer depth,
805	!-- friction velocity and velocity scale.
806	CALL parametrize_reynolds_stress
807	!
808	!-- Calculate coefficient matrix from Reynolds stress tensor
809	!-- (Lund rotation)
810	CALL calc_coeff_matrix
811
812	ENDIF
813
814	!
815	!-- Assign initial profiles. Note, this is only required if turbulent
816	!-- inflow from the left is desired, not in case of any of the
817	!-- nesting (offline or self nesting) approaches.
818	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
819	u_init = mean_inflow_profiles(:,1)
820	v_init = mean_inflow_profiles(:,2)
821	!pt_init = mean_inflow_profiles(:,4)
822	e_init = MAXVAL( mean_inflow_profiles(:,5) )
823	ENDIF
824
825	!
826	!-- Define the size of the filter functions and allocate them.
827	merg = 0
828
829	! arrays must be large enough to cover the largest length scale
830	DO k = nzb, nzt+1
831	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
832	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
833	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
834	IF ( j > merg ) merg = j
835	ENDDO
836
837	merg = 2 * merg
838	mergp = merg + nbgp
839
840	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
841	buy(-merg:merg,nzb:nzt+1), &
842	buz(-merg:merg,nzb:nzt+1), &
843	bvx(-merg:merg,nzb:nzt+1), &
844	bvy(-merg:merg,nzb:nzt+1), &
845	bvz(-merg:merg,nzb:nzt+1), &
846	bwx(-merg:merg,nzb:nzt+1), &
847	bwy(-merg:merg,nzb:nzt+1), &
848	bwz(-merg:merg,nzb:nzt+1) )
849
850	!
851	!-- Allocate velocity seeds for turbulence at xz-layer
852	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
853	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
854	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
855
856	!
857	!-- Allocate velocity seeds for turbulence at yz-layer
858	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
859	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
860	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
861
862	fu_xz = 0.0_wp
863	fuo_xz = 0.0_wp
864	fv_xz = 0.0_wp
865	fvo_xz = 0.0_wp
866	fw_xz = 0.0_wp
867	fwo_xz = 0.0_wp
868
869	fu_yz = 0.0_wp
870	fuo_yz = 0.0_wp
871	fv_yz = 0.0_wp
872	fvo_yz = 0.0_wp
873	fw_yz = 0.0_wp
874	fwo_yz = 0.0_wp
875
876	!
877	!-- Create filter functions
878	CALL stg_filter_func( nux, bux ) !filter ux
879	CALL stg_filter_func( nuy, buy ) !filter uy
880	CALL stg_filter_func( nuz, buz ) !filter uz
881	CALL stg_filter_func( nvx, bvx ) !filter vx
882	CALL stg_filter_func( nvy, bvy ) !filter vy
883	CALL stg_filter_func( nvz, bvz ) !filter vz
884	CALL stg_filter_func( nwx, bwx ) !filter wx
885	CALL stg_filter_func( nwy, bwy ) !filter wy
886	CALL stg_filter_func( nwz, bwz ) !filter wz
887
888	#if defined( __parallel )
889	CALL MPI_BARRIER( comm2d, ierr )
890	#endif
891
892	!
893	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
894	! time step.
895	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
896	! are 0 compared to the prerun. This is mostly for k=nzt+1.
897	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
898	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
899
900	IF ( myidx == id_stg_left ) i = -1
901	IF ( myidx == id_stg_right ) i = nxr+1
902
903	DO j = nysg, nyng
904	DO k = nzb, nzt+1
905	IF ( a11(k) /= 0.0_wp ) THEN
906	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
907	ELSE
908	fu_yz(k,j) = 0.0_wp
909	ENDIF
910
911	IF ( a22(k) /= 0.0_wp ) THEN
912	fv_yz(k,j) = ( v(k,j,i) - &
913	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
914	ELSE
915	fv_yz(k,j) = 0.0_wp
916	ENDIF
917
918	IF ( a33(k) /= 0.0_wp ) THEN
919	fw_yz(k,j) = ( w(k,j,i) - &
920	a31(k) * fu_yz(k,j) - a32(k) * &
921	fv_yz(k,j) ) / a33(k)
922	ELSE
923	fw_yz = 0._wp
924	ENDIF
925
926	ENDDO
927	ENDDO
928	ENDIF
929
930	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
931
932	IF ( myidy == id_stg_south ) j = -1
933	IF ( myidy == id_stg_north ) j = nyn+1
934
935	DO i = nxlg, nxrg
936	DO k = nzb, nzt+1
937
938	IF ( a11(k) /= 0.0_wp ) THEN
939	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
940	ELSE
941	fu_xz(k,i) = 0.0_wp
942	ENDIF
943
944	IF ( a22(k) /= 0.0_wp ) THEN
945	fv_xz(k,i) = ( v(k,j,i) - &
946	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
947	ELSE
948	fv_xz(k,i) = 0.0_wp
949	ENDIF
950
951	IF ( a33(k) /= 0.0_wp ) THEN
952	fw_xz(k,i) = ( w(k,j,i) - &
953	a31(k) * fu_xz(k,i) - &
954	a32(k) * fv_xz(k,i) ) / a33(k)
955	ELSE
956	fw_xz = 0._wp
957	ENDIF
958
959	ENDDO
960	ENDDO
961	ENDIF
962	ENDIF
963	!
964	!-- Count the number of non-topography grid points at the boundaries where
965	!-- perturbations are imposed. This number is later used for bias corrections
966	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
967	!-- due to the asymetry of u and v along x and y direction, respectively,
968	!-- different cases must be distinguished.
969	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
970	!
971	!-- Number of grid points where perturbations are imposed on u
972	IF ( myidx == id_stg_left ) i = nxl
973	IF ( myidx == id_stg_right ) i = nxr+1
974
975	nr_non_topo_yz_l(1) = SUM( &
976	MERGE( 1, 0, &
977	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
978	!
979	!-- Number of grid points where perturbations are imposed on v and w
980	IF ( myidx == id_stg_left ) i = nxl-1
981	IF ( myidx == id_stg_right ) i = nxr+1
982
983	nr_non_topo_yz_l(2) = SUM( &
984	MERGE( 1, 0, &
985	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
986	nr_non_topo_yz_l(3) = SUM( &
987	MERGE( 1, 0, &
988	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
989
990	#if defined( __parallel )
991	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
992	MPI_SUM, comm1dy, ierr )
993	#else
994	nr_non_topo_yz = nr_non_topo_yz_l
995	#endif
996	ENDIF
997
998	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
999	!
1000	!-- Number of grid points where perturbations are imposed on v
1001	IF ( myidy == id_stg_south ) j = nys
1002	IF ( myidy == id_stg_north ) j = nyn+1
1003
1004	nr_non_topo_xz_l(2) = SUM( &
1005	MERGE( 1, 0, &
1006	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1007	!
1008	!-- Number of grid points where perturbations are imposed on u and w
1009	IF ( myidy == id_stg_south ) j = nys-1
1010	IF ( myidy == id_stg_north ) j = nyn+1
1011
1012	nr_non_topo_xz_l(1) = SUM( &
1013	MERGE( 1, 0, &
1014	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1015	nr_non_topo_xz_l(3) = SUM( &
1016	MERGE( 1, 0, &
1017	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1018
1019	#if defined( __parallel )
1020	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1021	MPI_SUM, comm1dx, ierr )
1022	#else
1023	nr_non_topo_xz = nr_non_topo_xz_l
1024	#endif
1025	ENDIF
1026
1027
1028	END SUBROUTINE stg_init
1029
1030
1031	!------------------------------------------------------------------------------!
1032	! Description:
1033	! ------------
1034	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1035	!> (Xie and Castro, 2008)
1036	!------------------------------------------------------------------------------!
1037	SUBROUTINE stg_filter_func( nxx, bxx )
1038
1039
1040	IMPLICIT NONE
1041
1042	INTEGER(iwp) :: k !< loop index
1043	INTEGER(iwp) :: n_k !< length scale nXX in height k
1044	INTEGER(iwp) :: n_k2 !< n_k * 2
1045	INTEGER(iwp) :: nf !< index for length scales
1046
1047	REAL(wp) :: bdenom !< denominator for filter functions bXX
1048	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1049
1050	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
1051
1052	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
1053
1054
1055	bxx = 0.0_wp
1056
1057	DO k = nzb, nzt+1
1058	bdenom = 0.0_wp
1059	n_k = nxx(k)
1060	IF ( n_k /= 0 ) THEN
1061	n_k2 = n_k * 2
1062
1063	!
1064	!-- ( Eq.10 )^2
1065	DO nf = -n_k2, n_k2
1066	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1067	ENDDO
1068
1069	!
1070	!-- ( Eq.9 )
1071	bdenom = SQRT( bdenom )
1072	DO nf = -n_k2, n_k2
1073	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1074	ENDDO
1075	ENDIF
1076	ENDDO
1077
1078	END SUBROUTINE stg_filter_func
1079
1080
1081	!------------------------------------------------------------------------------!
1082	! Description:
1083	! ------------
1084	!> Parin for &stg_par for synthetic turbulence generator
1085	!------------------------------------------------------------------------------!
1086	SUBROUTINE stg_parin
1087
1088
1089	IMPLICIT NONE
1090
1091	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1092
1093
1094	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
1095
1096	line = ' '
1097
1098	!
1099	!-- Try to find stg package
1100	REWIND ( 11 )
1101	line = ' '
1102	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1103	READ ( 11, '(A)', END=20 ) line
1104	ENDDO
1105	BACKSPACE ( 11 )
1106
1107	!
1108	!-- Read namelist
1109	READ ( 11, stg_par, ERR = 10, END = 20 )
1110
1111	!
1112	!-- Set flag that indicates that the synthetic turbulence generator is switched
1113	!-- on
1114	syn_turb_gen = .TRUE.
1115	GOTO 20
1116
1117	10 BACKSPACE( 11 )
1118	READ( 11 , '(A)') line
1119	CALL parin_fail_message( 'stg_par', line )
1120
1121	20 CONTINUE
1122
1123	END SUBROUTINE stg_parin
1124
1125
1126	!------------------------------------------------------------------------------!
1127	! Description:
1128	! ------------
1129	!> This routine reads the respective restart data.
1130	!------------------------------------------------------------------------------!
1131	SUBROUTINE stg_rrd_global( found )
1132
1133
1134	IMPLICIT NONE
1135
1136	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1137
1138
1139	found = .TRUE.
1140
1141
1142	SELECT CASE ( restart_string(1:length) )
1143
1144	CASE ( 'time_stg_adjust' )
1145	READ ( 13 ) time_stg_adjust
1146
1147	CASE ( 'time_stg_call' )
1148	READ ( 13 ) time_stg_call
1149
1150	CASE ( 'use_syn_turb_gen' )
1151	READ ( 13 ) use_syn_turb_gen
1152
1153	CASE DEFAULT
1154
1155	found = .FALSE.
1156
1157	END SELECT
1158
1159
1160	END SUBROUTINE stg_rrd_global
1161
1162
1163	!------------------------------------------------------------------------------!
1164	! Description:
1165	! ------------
1166	!> This routine writes the respective restart data.
1167	!------------------------------------------------------------------------------!
1168	SUBROUTINE stg_wrd_global
1169
1170
1171	IMPLICIT NONE
1172
1173	CALL wrd_write_string( 'time_stg_adjust' )
1174	WRITE ( 14 ) time_stg_adjust
1175
1176	CALL wrd_write_string( 'time_stg_call' )
1177	WRITE ( 14 ) time_stg_call
1178
1179	CALL wrd_write_string( 'use_syn_turb_gen' )
1180	WRITE ( 14 ) use_syn_turb_gen
1181
1182
1183	END SUBROUTINE stg_wrd_global
1184
1185
1186	!------------------------------------------------------------------------------!
1187	! Description:
1188	! ------------
1189	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1190	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1191	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1192	!> (Lund, 1998).
1193	!------------------------------------------------------------------------------!
1194	SUBROUTINE stg_main
1195
1196	IMPLICIT NONE
1197
1198	INTEGER(iwp) :: i !< grid index in x-direction
1199	INTEGER(iwp) :: j !< loop index in y-direction
1200	INTEGER(iwp) :: k !< loop index in z-direction
1201
1202	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1203
1204	REAL(wp) :: dt_stg !< wheighted subtimestep
1205
1206	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1207
1208	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1209	!
1210	!-- Calculate time step which is needed for filter functions
1211	dt_stg = MAX( dt_3d, dt_stg_call )
1212	!
1213	!-- Check if synthetic turbulence generator needs to be called and new
1214	!-- perturbations need to be created or if old disturbances can be imposed
1215	!-- again.
1216	IF ( time_stg_call >= dt_stg_call .AND. &
1217	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1218	stg_call = .TRUE.
1219	ELSE
1220	stg_call = .FALSE.
1221	ENDIF
1222	!
1223	!-- Initial value of fu, fv, fw
1224	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1225	!
1226	!-- Generate turbulence at the left and right boundary. Random numbers
1227	!-- for the yz-planes at the left/right boundary are generated by the
1228	!-- left-sided mpi ranks only. After random numbers are calculated, they
1229	!-- are distributed to all other mpi ranks in the model, so that the
1230	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1231	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1232	!-- that the left- and the right-sided lateral boundary have the same initial
1233	!-- seeds.
1234	!-- Note, in case of inflow from the right only, only turbulence at the left
1235	!-- boundary is required.
1236	IF ( .NOT. ( nesting_offline .OR. &
1237	( child_domain .AND. rans_mode_parent &
1238	.AND. .NOT. rans_mode ) ) ) THEN
1239
1240	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1241	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1242	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1243	ELSE
1244	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1245	id_stg_left, id_stg_right )
1246	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1247	id_stg_left, id_stg_right )
1248	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1249	id_stg_left, id_stg_right )
1250	!
1251	!-- Generate turbulence at the south and north boundary. Random numbers
1252	!-- for the xz-planes at the south/north boundary are generated by the
1253	!-- south-sided mpi ranks only. Please see also comment above.
1254	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1255	id_stg_south, id_stg_north )
1256	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1257	id_stg_south, id_stg_north )
1258	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1259	id_stg_south, id_stg_north )
1260	ENDIF
1261	velocity_seed_initialized = .TRUE.
1262	ENDIF
1263	!
1264	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1265	!-- seeds are only required at the left boundary, while in case of offline
1266	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1267	!-- right, south and north boundaries.
1268	IF ( stg_call ) THEN
1269	IF ( .NOT. ( nesting_offline .OR. &
1270	( child_domain .AND. rans_mode_parent &
1271	.AND. .NOT. rans_mode ) ) ) THEN
1272	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1273	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1274	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1275
1276	ELSE
1277	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1278	id_stg_left, id_stg_right )
1279	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1280	id_stg_left, id_stg_right )
1281	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1282	id_stg_left, id_stg_right )
1283
1284	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1285	id_stg_south, id_stg_north )
1286	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1287	id_stg_south, id_stg_north )
1288	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1289	id_stg_south, id_stg_north )
1290	ENDIF
1291	ENDIF
1292
1293	!
1294	!-- Turbulence generation at left and/or right boundary
1295	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1296	!
1297	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1298	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1299	!-- imposed
1300	IF ( stg_call ) THEN
1301
1302	DO j = nysg, nyng
1303	DO k = nzb, nzt + 1
1304	!
1305	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1306	IF ( tu(k) == 0.0_wp ) THEN
1307	fu_yz(k,j) = fuo_yz(k,j)
1308	ELSE
1309	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1310	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1311	ENDIF
1312
1313	IF ( tv(k) == 0.0_wp ) THEN
1314	fv_yz(k,j) = fvo_yz(k,j)
1315	ELSE
1316	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1317	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1318	ENDIF
1319
1320	IF ( tw(k) == 0.0_wp ) THEN
1321	fw_yz(k,j) = fwo_yz(k,j)
1322	ELSE
1323	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1324	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1325	ENDIF
1326	ENDDO
1327	ENDDO
1328
1329	dist_yz(nzb,:,1) = 0.0_wp
1330	dist_yz(nzb,:,2) = 0.0_wp
1331	dist_yz(nzb,:,3) = 0.0_wp
1332
1333	IF ( myidx == id_stg_left ) i = nxl
1334	IF ( myidx == id_stg_right ) i = nxr+1
1335	DO j = nysg, nyng
1336	DO k = nzb+1, nzt + 1
1337	!
1338	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1339	!-- Additional factors are added to improve the variance of v and w
1340	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1341	MERGE( 1.0_wp, 0.0_wp, &
1342	BTEST( wall_flags_static_0(k,j,i), 1 ) )
1343	ENDDO
1344	ENDDO
1345
1346	IF ( myidx == id_stg_left ) i = nxl-1
1347	IF ( myidx == id_stg_right ) i = nxr+1
1348	DO j = nysg, nyng
1349	DO k = nzb+1, nzt + 1
1350	!
1351	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1352	!-- Additional factors are added to improve the variance of v and w
1353	!-- experimental test of 1.2
1354	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1355	* 1.2_wp ) &
1356	* ( a21(k) * fu_yz(k,j) &
1357	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1358	MERGE( 1.0_wp, 0.0_wp, &
1359	BTEST( wall_flags_static_0(k,j,i), 2 ) )
1360	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1361	* 1.3_wp ) &
1362	* ( a31(k) * fu_yz(k,j) &
1363	+ a32(k) * fv_yz(k,j) &
1364	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1365	MERGE( 1.0_wp, 0.0_wp, &
1366	BTEST( wall_flags_static_0(k,j,i), 3 ) )
1367	ENDDO
1368	ENDDO
1369	ENDIF
1370	!
1371	!-- Mass flux correction following Kim et al. (2013)
1372	!-- This correction factor insures that the mass flux is preserved at the
1373	!-- inflow boundary. First, calculate mean value of the imposed
1374	!-- perturbations at yz boundary.
1375	!-- Note, this needs to be done only after the last RK3-substep, else
1376	!-- the boundary values won't be accessed.
1377	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1378	mc_factor_l = 0.0_wp
1379	mc_factor = 0.0_wp
1380	!
1381	!-- Sum up the original volume flows (with and without perturbations).
1382	!-- Note, for non-normal components (here v and w) it is actually no
1383	!-- volume flow.
1384	IF ( myidx == id_stg_left ) i = nxl
1385	IF ( myidx == id_stg_right ) i = nxr+1
1386
1387	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1388	* MERGE( 1.0_wp, 0.0_wp, &
1389	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1390
1391	IF ( myidx == id_stg_left ) i = nxl-1
1392	IF ( myidx == id_stg_right ) i = nxr+1
1393
1394	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1395	* MERGE( 1.0_wp, 0.0_wp, &
1396	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1397	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1398	* MERGE( 1.0_wp, 0.0_wp, &
1399	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1400
1401	#if defined( __parallel )
1402	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1403	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1404	#else
1405	mc_factor = mc_factor_l
1406	#endif
1407	!
1408	!-- Calculate correction factor and force zero mean perturbations.
1409	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1410
1411	IF ( myidx == id_stg_left ) i = nxl
1412	IF ( myidx == id_stg_right ) i = nxr+1
1413
1414	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
1415	* MERGE( 1.0_wp, 0.0_wp, &
1416	BTEST( wall_flags_static_0(:,:,i), 1 ) )
1417
1418
1419	IF ( myidx == id_stg_left ) i = nxl-1
1420	IF ( myidx == id_stg_right ) i = nxr+1
1421
1422	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
1423	* MERGE( 1.0_wp, 0.0_wp, &
1424	BTEST( wall_flags_static_0(:,:,i), 2 ) )
1425
1426	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
1427	* MERGE( 1.0_wp, 0.0_wp, &
1428	BTEST( wall_flags_static_0(:,:,i), 3 ) )
1429	!
1430	!-- Add disturbances
1431	IF ( myidx == id_stg_left ) THEN
1432	!
1433	!-- For the left boundary distinguish between mesoscale offline / self
1434	!-- nesting and turbulent inflow at the left boundary only. In the latter
1435	!-- case turbulence is imposed on the mean inflow profiles.
1436	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1437	!
1438	!-- Add disturbance at the inflow
1439	DO j = nysg, nyng
1440	DO k = nzb, nzt+1
1441	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1442	dist_yz(k,j,1) ) &
1443	* MERGE( 1.0_wp, 0.0_wp, &
1444	BTEST( wall_flags_static_0(k,j,0), 1 ) )
1445	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1446	dist_yz(k,j,2) ) &
1447	* MERGE( 1.0_wp, 0.0_wp, &
1448	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
1449	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1450	* MERGE( 1.0_wp, 0.0_wp, &
1451	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
1452	ENDDO
1453	ENDDO
1454	ELSE
1455
1456	DO j = nys, nyn
1457	DO k = nzb+1, nzt
1458	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1459	* MERGE( 1.0_wp, 0.0_wp, &
1460	BTEST( wall_flags_static_0(k,j,0), 1 ) )
1461	u(k,j,-1) = u(k,j,0)
1462	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1463	* MERGE( 1.0_wp, 0.0_wp, &
1464	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
1465	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1466	* MERGE( 1.0_wp, 0.0_wp, &
1467	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
1468	ENDDO
1469	ENDDO
1470	ENDIF
1471	ENDIF
1472	IF ( myidx == id_stg_right ) THEN
1473	DO j = nys, nyn
1474	DO k = nzb+1, nzt
1475	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1476	* MERGE( 1.0_wp, 0.0_wp, &
1477	BTEST( wall_flags_static_0(k,j,nxr+1), 1 ) )
1478	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1479	* MERGE( 1.0_wp, 0.0_wp, &
1480	BTEST( wall_flags_static_0(k,j,nxr+1), 2 ) )
1481	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1482	* MERGE( 1.0_wp, 0.0_wp, &
1483	BTEST( wall_flags_static_0(k,j,nxr+1), 3 ) )
1484	ENDDO
1485	ENDDO
1486	ENDIF
1487	ENDIF
1488	ENDIF
1489	!
1490	!-- Turbulence generation at north and south boundary
1491	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1492	!
1493	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1494	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1495	!-- imposed
1496	IF ( stg_call ) THEN
1497	DO i = nxlg, nxrg
1498	DO k = nzb, nzt + 1
1499	!
1500	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1501	IF ( tu(k) == 0.0_wp ) THEN
1502	fu_xz(k,i) = fuo_xz(k,i)
1503	ELSE
1504	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1505	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1506	ENDIF
1507
1508	IF ( tv(k) == 0.0_wp ) THEN
1509	fv_xz(k,i) = fvo_xz(k,i)
1510	ELSE
1511	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1512	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1513	ENDIF
1514
1515	IF ( tw(k) == 0.0_wp ) THEN
1516	fw_xz(k,i) = fwo_xz(k,i)
1517	ELSE
1518	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1519	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1520	ENDIF
1521	ENDDO
1522	ENDDO
1523
1524
1525	dist_xz(nzb,:,1) = 0.0_wp
1526	dist_xz(nzb,:,2) = 0.0_wp
1527	dist_xz(nzb,:,3) = 0.0_wp
1528
1529	IF ( myidy == id_stg_south ) j = nys
1530	IF ( myidy == id_stg_north ) j = nyn+1
1531	DO i = nxlg, nxrg
1532	DO k = nzb+1, nzt + 1
1533	!
1534	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1535	!-- Additional factors are added to improve the variance of v and w
1536	!experimental test of 1.2
1537	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1538	* 1.2_wp ) &
1539	* ( a21(k) * fu_xz(k,i) &
1540	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1541	MERGE( 1.0_wp, 0.0_wp, &
1542	BTEST( wall_flags_static_0(k,j,i), 2 ) )
1543	ENDDO
1544	ENDDO
1545
1546	IF ( myidy == id_stg_south ) j = nys-1
1547	IF ( myidy == id_stg_north ) j = nyn+1
1548	DO i = nxlg, nxrg
1549	DO k = nzb+1, nzt + 1
1550	!
1551	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1552	!-- Additional factors are added to improve the variance of v and w
1553	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1554	MERGE( 1.0_wp, 0.0_wp, &
1555	BTEST( wall_flags_static_0(k,j,i), 1 ) )
1556
1557	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1558	* 1.3_wp ) &
1559	* ( a31(k) * fu_xz(k,i) &
1560	+ a32(k) * fv_xz(k,i) &
1561	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1562	MERGE( 1.0_wp, 0.0_wp, &
1563	BTEST( wall_flags_static_0(k,j,i), 3 ) )
1564	ENDDO
1565	ENDDO
1566	ENDIF
1567
1568	!
1569	!-- Mass flux correction following Kim et al. (2013)
1570	!-- This correction factor insures that the mass flux is preserved at the
1571	!-- inflow boundary. First, calculate mean value of the imposed
1572	!-- perturbations at yz boundary.
1573	!-- Note, this needs to be done only after the last RK3-substep, else
1574	!-- the boundary values won't be accessed.
1575	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1576	mc_factor_l = 0.0_wp
1577	mc_factor = 0.0_wp
1578
1579	IF ( myidy == id_stg_south ) j = nys
1580	IF ( myidy == id_stg_north ) j = nyn+1
1581
1582	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1583	* MERGE( 1.0_wp, 0.0_wp, &
1584	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1585
1586	IF ( myidy == id_stg_south ) j = nys-1
1587	IF ( myidy == id_stg_north ) j = nyn+1
1588
1589	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1590	* MERGE( 1.0_wp, 0.0_wp, &
1591	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1592	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1593	* MERGE( 1.0_wp, 0.0_wp, &
1594	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1595
1596	#if defined( __parallel )
1597	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1598	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1599	#else
1600	mc_factor = mc_factor_l
1601	#endif
1602
1603	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1604
1605	IF ( myidy == id_stg_south ) j = nys
1606	IF ( myidy == id_stg_north ) j = nyn+1
1607
1608	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
1609	* MERGE( 1.0_wp, 0.0_wp, &
1610	BTEST( wall_flags_static_0(:,j,:), 2 ) )
1611
1612
1613	IF ( myidy == id_stg_south ) j = nys-1
1614	IF ( myidy == id_stg_north ) j = nyn+1
1615
1616	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
1617	* MERGE( 1.0_wp, 0.0_wp, &
1618	BTEST( wall_flags_static_0(:,j,:), 1 ) )
1619
1620	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
1621	* MERGE( 1.0_wp, 0.0_wp, &
1622	BTEST( wall_flags_static_0(:,j,:), 3 ) )
1623	!
1624	!-- Add disturbances
1625	IF ( myidy == id_stg_south ) THEN
1626	DO i = nxl, nxr
1627	DO k = nzb+1, nzt
1628	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1629	* MERGE( 1.0_wp, 0.0_wp, &
1630	BTEST( wall_flags_static_0(k,-1,i), 1 ) )
1631	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1632	* MERGE( 1.0_wp, 0.0_wp, &
1633	BTEST( wall_flags_static_0(k,0,i), 2 ) )
1634	v(k,-1,i) = v(k,0,i)
1635	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1636	* MERGE( 1.0_wp, 0.0_wp, &
1637	BTEST( wall_flags_static_0(k,-1,i), 3 ) )
1638	ENDDO
1639	ENDDO
1640	ENDIF
1641	IF ( myidy == id_stg_north ) THEN
1642
1643	DO i = nxl, nxr
1644	DO k = nzb+1, nzt
1645	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1646	* MERGE( 1.0_wp, 0.0_wp, &
1647	BTEST( wall_flags_static_0(k,nyn+1,i), 1 ) )
1648	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1649	* MERGE( 1.0_wp, 0.0_wp, &
1650	BTEST( wall_flags_static_0(k,nyn+1,i), 2 ) )
1651	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1652	* MERGE( 1.0_wp, 0.0_wp, &
1653	BTEST( wall_flags_static_0(k,nyn+1,i), 3 ) )
1654	ENDDO
1655	ENDDO
1656	ENDIF
1657	ENDIF
1658	ENDIF
1659	!
1660	!-- Finally, set time counter for calling STG to zero
1661	IF ( stg_call ) time_stg_call = 0.0_wp
1662
1663	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1664
1665	END SUBROUTINE stg_main
1666
1667	!------------------------------------------------------------------------------!
1668	! Description:
1669	! ------------
1670	!> Generate a set of random number rand_it wich is equal on each PE
1671	!> and calculate the velocity seed f_n.
1672	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1673	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1674	!> parts are collected to form the full array.
1675	!------------------------------------------------------------------------------!
1676	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1677
1678	USE pegrid
1679
1680	IMPLICIT NONE
1681
1682	INTEGER(iwp) :: i !< grid index x-direction
1683	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1684	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1685	INTEGER(iwp) :: j !< loop index in y-direction
1686	INTEGER(iwp) :: jj !< loop index in y-direction
1687	INTEGER(iwp) :: k !< loop index in z-direction
1688	INTEGER(iwp) :: kk !< loop index in z-direction
1689	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1690
1691	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1692	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1693	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
1694	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1695
1696	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1697	REAL(wp) :: rand_av !< average of random number
1698	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1699
1700	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
1701	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1702
1703	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
1704	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
1705
1706	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1707	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
1708
1709	!
1710	!-- Generate random numbers using the parallel random generator.
1711	!-- The set of random numbers are modified to have an average of 0 and
1712	!-- unit variance. Note, at the end the random number array must be defined
1713	!-- globally in order to compute the correlation matrices. However,
1714	!-- the calculation and normalization of random numbers is done locally,
1715	!-- while the result is later distributed to all processes. Further,
1716	!-- please note, a set of random numbers is only calculated for the
1717	!-- left boundary, while the right boundary uses the same random numbers
1718	!-- and thus also computes the same correlation matrix.
1719	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
1720	rand_it = 0.0_wp
1721
1722	rand_av = 0.0_wp
1723	rand_sigma_inv = 0.0_wp
1724	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
1725	!
1726	!-- Compute and normalize random numbers only on left-boundary ranks.
1727	IF ( myidx == id_stg_left ) THEN
1728	!
1729	!-- Allocate array for local set of random numbers
1730	ALLOCATE( rand_it_l(nzb:nzt+1,nys:nyn) )
1731	rand_it_l = 0.0_wp
1732
1733	i = nxl
1734	DO j = nys, nyn
1735	!
1736	!-- Put the random seeds at grid point j,i
1737	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
1738	DO k = nzb, nzt+1
1739	CALL random_number_parallel( random_dummy )
1740	rand_it_l(k,j) = random_dummy
1741	rand_av = rand_av + rand_it_l(k,j)
1742	ENDDO
1743	!
1744	!-- Get the new random seeds from last call at grid point j,i
1745	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
1746	ENDDO
1747	#if defined( __parallel )
1748	!
1749	!-- Sum-up the local averages of the random numbers
1750	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1751	MPI_SUM, comm1dy, ierr )
1752	#endif
1753	rand_av = rand_av * nyz_inv
1754	!
1755	!-- Obtain zero mean
1756	rand_it_l = rand_it_l - rand_av
1757	!
1758	!-- Now, compute the variance
1759	DO j = nys, nyn
1760	DO k = nzb, nzt+1
1761	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,j)**2
1762	ENDDO
1763	ENDDO
1764
1765	#if defined( __parallel )
1766	!
1767	!-- Sum-up the local quadratic averages of the random numbers
1768	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1769	MPI_SUM, comm1dy, ierr )
1770	#endif
1771	!
1772	!-- Compute standard deviation
1773	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1774	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1775	ELSE
1776	rand_sigma_inv = 1.0_wp
1777	ENDIF
1778	!
1779	!-- Normalize with standard deviation to obtain unit variance
1780	rand_it_l = rand_it_l * rand_sigma_inv
1781	!
1782	!-- Copy local random numbers on the global array
1783	rand_it(nzb:nzt+1,nys:nyn) = rand_it_l(nzb:nzt+1,nys:nyn)
1784	!
1785	!-- Deallocate local array
1786	DEALLOCATE( rand_it_l )
1787	!
1788	!-- Now, distribute the final set of random numbers to all mpi ranks located
1789	!-- on the left boundary. Here, an allreduce with sum reduction is sufficient,
1790	!-- or, in the non-parallel case, nothing need to be done at all.
1791	#if defined( __parallel )
1792	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1793	MPI_SUM, comm1dy, ierr )
1794	#endif
1795	ENDIF
1796	!
1797	!-- Finally, distribute the set of random numbers (defined on the leftmost-
1798	!-- located mpi ranks) to all other mpi ranks. Here, a allreduce with sum
1799	!-- option is sufficient, because rand_it is zero on all other mpi_ranks.
1800	!-- Note, the reduce operation is only performed with communicator comm1dx,
1801	!-- where only 1 rank within the communicator has non-zero random numbers.
1802	#if defined( __parallel )
1803	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1804	MPI_SUM, comm1dx, ierr )
1805	#endif
1806	!
1807	!-- Periodic fill of random numbers in space
1808	DO j = 0, ny
1809	DO k = 1, mergp
1810	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
1811	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
1812	ENDDO
1813	ENDDO
1814	DO j = 1, mergp
1815	DO k = nzb-mergp, nzt+1+mergp
1816	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
1817	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
1818	ENDDO
1819	ENDDO
1820
1821	!
1822	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1823	n_y2 = n_y * 2
1824	n_z2 = n_z * 2
1825	f_n_l = 0.0_wp
1826
1827	DO j = nysg, nyng
1828	DO k = nzb_x_stg, nzt_x_stg+1
1829	DO jj = -n_y2(k), n_y2(k)
1830	DO kk = -n_z2(k), n_z2(k)
1831	f_n_l(k,j) = f_n_l(k,j) &
1832	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1833	ENDDO
1834	ENDDO
1835	ENDDO
1836	ENDDO
1837
1838	DEALLOCATE( rand_it )
1839	!
1840	!-- Gather velocity seeds of full subdomain
1841	send_count = nzt_x_stg - nzb_x_stg + 1
1842	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1843
1844	#if defined( __parallel )
1845	!
1846	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1847	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1848	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
1849	id_left, comm1dx, ierr )
1850	!
1851	!-- If required, gather the same velocity seed matrix on right boundary
1852	!-- mpi ranks (in offline nesting for example).
1853	IF ( PRESENT( id_right ) ) THEN
1854	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1855	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz,&
1856	id_right, comm1dx, ierr )
1857	ENDIF
1858	#else
1859	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
1860	#endif
1861
1862
1863	END SUBROUTINE stg_generate_seed_yz
1864
1865
1866	!------------------------------------------------------------------------------!
1867	! Description:
1868	! ------------
1869	!> Generate a set of random number rand_it wich is equal on each PE
1870	!> and calculate the velocity seed f_n.
1871	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1872	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1873	!> parts are collected to form the full array.
1874	!------------------------------------------------------------------------------!
1875	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1876
1877	IMPLICIT NONE
1878
1879	INTEGER(iwp) :: i !< loop index in x-direction
1880	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1881	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1882	INTEGER(iwp) :: ii !< loop index in x-direction
1883	INTEGER(iwp) :: j !< grid index y-direction
1884	INTEGER(iwp) :: k !< loop index in z-direction
1885	INTEGER(iwp) :: kk !< loop index in z-direction
1886	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1887
1888	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1889	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1890	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
1891	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1892
1893	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1894	REAL(wp) :: rand_av !< average of random number
1895	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1896
1897	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
1898	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1899
1900	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
1901	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
1902
1903	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1904	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
1905
1906	!
1907	!-- Generate random numbers using the parallel random generator.
1908	!-- The set of random numbers are modified to have an average of 0 and
1909	!-- unit variance. Note, at the end the random number array must be defined
1910	!-- globally in order to compute the correlation matrices. However,
1911	!-- the calculation and normalization of random numbers is done locally,
1912	!-- while the result is later distributed to all processes. Further,
1913	!-- please note, a set of random numbers is only calculated for the
1914	!-- left boundary, while the right boundary uses the same random numbers
1915	!-- and thus also computes the same correlation matrix.
1916	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
1917	rand_it = 0.0_wp
1918
1919	rand_av = 0.0_wp
1920	rand_sigma_inv = 0.0_wp
1921	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
1922	!
1923	!-- Compute and normalize random numbers only on south-boundary ranks.
1924	IF ( myidy == id_stg_south ) THEN
1925	!
1926	!-- Allocate array for local set of random numbers
1927	ALLOCATE( rand_it_l(nzb:nzt+1,nxl:nxr) )
1928	rand_it_l = 0.0_wp
1929
1930	j = nys
1931	DO i = nxl, nxr
1932	!
1933	!-- Put the random seeds at grid point j,i
1934	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
1935	DO k = nzb, nzt+1
1936	CALL random_number_parallel( random_dummy )
1937	rand_it_l(k,i) = random_dummy
1938	rand_av = rand_av + rand_it_l(k,i)
1939	ENDDO
1940	!
1941	!-- Get the new random seeds from last call at grid point j,i
1942	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
1943	ENDDO
1944	#if defined( __parallel )
1945	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1946	MPI_SUM, comm1dx, ierr )
1947	#endif
1948	rand_av = rand_av * nxz_inv
1949	!
1950	!-- Obtain zero mean
1951	rand_it_l = rand_it_l - rand_av
1952	!
1953	!-- Now, compute the variance
1954	DO i = nxl, nxr
1955	DO k = nzb, nzt+1
1956	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,i)**2
1957	ENDDO
1958	ENDDO
1959
1960	#if defined( __parallel )
1961	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1962	MPI_SUM, comm1dx, ierr )
1963	#endif
1964	!
1965	!-- Compute standard deviation
1966	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1967	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1968	ELSE
1969	rand_sigma_inv = 1.0_wp
1970	ENDIF
1971	!
1972	!-- Normalize with standard deviation to obtain unit variance
1973	rand_it_l = rand_it_l * rand_sigma_inv
1974	!
1975	!-- Copy local random numbers on the global array
1976	rand_it(nzb:nzt+1,nxl:nxr) = rand_it_l(nzb:nzt+1,nxl:nxr)
1977	!
1978	!-- Deallocate local array
1979	DEALLOCATE( rand_it_l )
1980	!
1981	!-- Now, distribute the final set of random numbers to all mpi ranks located
1982	!-- on the south boundary. Here, an allreduce with sum reduction is sufficient.
1983	#if defined( __parallel )
1984	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1985	MPI_SUM, comm1dx, ierr )
1986	#endif
1987	ENDIF
1988	!
1989	!-- Finally, distribute the set of random numbers (defined on the
1990	!-- southmost-located mpi ranks) to all other mpi ranks. Here, a allreduce
1991	!-- with sum option is sufficient, because rand_it is zero on all other
1992	!-- mpi_ranks. Note, the reduce operation is only performed with communicator
1993	!-- comm1dy, where only 1 rank within the communicator has non zero random numbers.
1994	#if defined( __parallel )
1995	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1996	MPI_SUM, comm1dy, ierr )
1997	#endif
1998	!
1999	!-- Periodic fill of random number in space
2000	DO i = 0, nx
2001	DO k = 1, mergp
2002	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
2003	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
2004	ENDDO
2005	ENDDO
2006	DO i = 1, mergp
2007	DO k = nzb-mergp, nzt+1+mergp
2008	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
2009	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
2010	ENDDO
2011	ENDDO
2012	!
2013	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
2014	n_x2 = n_x * 2
2015	n_z2 = n_z * 2
2016	f_n_l = 0.0_wp
2017
2018	DO i = nxlg, nxrg
2019	DO k = nzb_y_stg, nzt_y_stg+1
2020	DO ii = -n_x2(k), n_x2(k)
2021	DO kk = -n_z2(k), n_z2(k)
2022	f_n_l(k,i) = f_n_l(k,i) &
2023	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2024	ENDDO
2025	ENDDO
2026	ENDDO
2027	ENDDO
2028
2029	DEALLOCATE( rand_it )
2030
2031	!
2032	!-- Gather velocity seeds of full subdomain
2033	send_count = nzt_y_stg - nzb_y_stg + 1
2034	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2035
2036	#if defined( __parallel )
2037	!
2038	!-- Gather the processed velocity seed on south boundary mpi ranks.
2039	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
2040	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
2041	id_south, comm1dy, ierr )
2042	!
2043	!-- Gather the processed velocity seed on north boundary mpi ranks.
2044	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
2045	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
2046	id_north, comm1dy, ierr )
2047	#else
2048	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
2049	#endif
2050
2051	END SUBROUTINE stg_generate_seed_xz
2052
2053	!------------------------------------------------------------------------------!
2054	! Description:
2055	! ------------
2056	!> Parametrization of the Reynolds stress tensor, following the parametrization
2057	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2058	!> dispserion modelling. Please note, the parametrization does not distinguish
2059	!> between along-wind and cross-wind turbulence.
2060	!------------------------------------------------------------------------------!
2061	SUBROUTINE parametrize_reynolds_stress
2062
2063	IMPLICIT NONE
2064
2065	INTEGER(iwp) :: k !< loop index in z-direction
2066
2067	REAL(wp) :: zzi !< ratio of z/zi
2068
2069	DO k = nzb+1, nzt+1
2070	!
2071	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2072	!-- The function decreases to 1/10 after one length scale above the
2073	!-- ABL top.
2074	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2075	!
2076	!-- Determine normalized height coordinate
2077	zzi = zu(k) / zi_ribulk
2078	!
2079	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2080	!-- to the denominator, else the merge-function can crash if scale_l is
2081	!-- zero.
2082	r11(k) = scale_us*2 ( &
2083	MERGE( 0.35_wp * ABS( &
2084	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2085	)**( 2.0_wp / 3.0_wp ), &
2086	0.0_wp, &
2087	scale_l < 0.0_wp ) &
2088	+ 5.0_wp - 4.0_wp * zzi &
2089	) * blend
2090
2091	r22(k) = r11(k)
2092	!
2093	!-- w'w'
2094	r33(k) = scale_wm*2 ( &
2095	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2096	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2097	) * blend
2098	!
2099	!-- u'w' and v'w'. Assume isotropy.
2100	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2101	r32(k) = r31(k)
2102	!
2103	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2104	!-- a similar profile as for u'w'.
2105	r21(k) = r31(k)
2106	ENDDO
2107
2108	!
2109	!-- Set bottom boundary condition
2110	r11(nzb) = r11(nzb+1)
2111	r22(nzb) = r22(nzb+1)
2112	r33(nzb) = r33(nzb+1)
2113
2114	r21(nzb) = r11(nzb+1)
2115	r31(nzb) = r31(nzb+1)
2116	r32(nzb) = r32(nzb+1)
2117
2118
2119	END SUBROUTINE parametrize_reynolds_stress
2120
2121	!------------------------------------------------------------------------------!
2122	! Description:
2123	! ------------
2124	!> Calculate the coefficient matrix from the Lund rotation.
2125	!------------------------------------------------------------------------------!
2126	SUBROUTINE calc_coeff_matrix
2127
2128	IMPLICIT NONE
2129
2130	INTEGER(iwp) :: k !< loop index in z-direction
2131
2132	!
2133	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2134	DO k = nzb+1, nzt+1
2135	IF ( r11(k) > 10E-6_wp ) THEN
2136	a11(k) = SQRT( r11(k) )
2137	a21(k) = r21(k) / a11(k)
2138	a31(k) = r31(k) / a11(k)
2139	ELSE
2140	a11(k) = 10E-8_wp
2141	a21(k) = 10E-8_wp
2142	a31(k) = 10E-8_wp
2143	ENDIF
2144	ENDDO
2145	DO k = nzb+1, nzt+1
2146	a22(k) = r22(k) - a21(k)**2
2147	IF ( a22(k) > 10E-6_wp ) THEN
2148	a22(k) = SQRT( a22(k) )
2149	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2150	ELSE
2151	a22(k) = 10E-8_wp
2152	a32(k) = 10E-8_wp
2153	ENDIF
2154	ENDDO
2155	DO k = nzb+1, nzt+1
2156	a33(k) = r33(k) - a31(k)2 - a32(k)2
2157	IF ( a33(k) > 10E-6_wp ) THEN
2158	a33(k) = SQRT( a33(k) )
2159	ELSE
2160	a33(k) = 10E-8_wp
2161	ENDIF
2162	ENDDO
2163	!
2164	!-- Set bottom boundary condition
2165	a11(nzb) = a11(nzb+1)
2166	a22(nzb) = a22(nzb+1)
2167	a21(nzb) = a21(nzb+1)
2168	a33(nzb) = a33(nzb+1)
2169	a31(nzb) = a31(nzb+1)
2170	a32(nzb) = a32(nzb+1)
2171
2172	END SUBROUTINE calc_coeff_matrix
2173
2174	!------------------------------------------------------------------------------!
2175	! Description:
2176	! ------------
2177	!> This routine controls the re-adjustment of the turbulence statistics used
2178	!> for generating turbulence at the lateral boundaries.
2179	!------------------------------------------------------------------------------!
2180	SUBROUTINE stg_adjust
2181
2182	IMPLICIT NONE
2183
2184
2185	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2186	!
2187	!-- In case of dirichlet inflow boundary conditions only at one lateral
2188	!-- boundary, i.e. in the case no offline or self nesting is applied but
2189	!-- synthetic turbulence shall be parametrized nevertheless, the
2190	!-- boundary-layer depth need to determined first.
2191	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2192	CALL nesting_offl_calc_zi
2193	!
2194	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2195	!-- are calculated.
2196	CALL calc_scaling_variables
2197	!
2198	!-- Set length and time scales depending on boundary-layer height
2199	CALL calc_length_and_time_scale
2200	!
2201	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2202	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2203	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2204	!-- friction velocity and velocity scale.
2205	CALL parametrize_reynolds_stress
2206	!
2207	!-- Calculate coefficient matrix from Reynolds stress tensor
2208	!-- (Lund rotation)
2209	CALL calc_coeff_matrix
2210	!
2211	!-- Determine filter functions on basis of updated length scales
2212	CALL stg_filter_func( nux, bux ) !filter ux
2213	CALL stg_filter_func( nuy, buy ) !filter uy
2214	CALL stg_filter_func( nuz, buz ) !filter uz
2215	CALL stg_filter_func( nvx, bvx ) !filter vx
2216	CALL stg_filter_func( nvy, bvy ) !filter vy
2217	CALL stg_filter_func( nvz, bvz ) !filter vz
2218	CALL stg_filter_func( nwx, bwx ) !filter wx
2219	CALL stg_filter_func( nwy, bwy ) !filter wy
2220	CALL stg_filter_func( nwz, bwz ) !filter wz
2221	!
2222	!-- Reset time counter for controlling next adjustment to zero
2223	time_stg_adjust = 0.0_wp
2224
2225	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2226
2227	END SUBROUTINE stg_adjust
2228
2229
2230	!------------------------------------------------------------------------------!
2231	! Description:
2232	! ------------
2233	!> Calculates turbuluent length and time scales if these are not available
2234	!> from measurements.
2235	!------------------------------------------------------------------------------!
2236	SUBROUTINE calc_length_and_time_scale
2237
2238	IMPLICIT NONE
2239
2240
2241	INTEGER(iwp) :: k !< loop index in z-direction
2242
2243	REAL(wp) :: length_scale_dum !< effectively used length scale
2244
2245	!
2246	!-- In initial call the boundary-layer depth can be zero. This case, set
2247	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2248	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2249	!
2250	!-- Set-up default turbulent length scales. From the numerical point of
2251	!-- view the imposed perturbations should not be immediately dissipated
2252	!-- by the numerics. The numerical dissipation, however, acts on scales
2253	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2254	!-- length scale to 8 time the grid spacing. Further, above the boundary
2255	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2256	!-- imposing any perturbations) in order to save computational costs.
2257	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2258	!-- using the length scales and the mean profiles of u- and v-component.
2259	DO k = nzb+1, nzt+1
2260	!
2261	!-- Determine blending parameter. Within the boundary layer length scales
2262	!-- are constant, while above lengths scales approach gradully zero,
2263	!-- i.e. imposed turbulence is not correlated in space and time,
2264	!-- just white noise, which saves computations power as the loops for the
2265	!-- computation of the filter functions depend on the length scales.
2266	!-- The value decreases to 1/10 after one length scale above the
2267	!-- ABL top.
2268	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2269	!
2270	!-- Assume isotropic turbulence length scales
2271	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2272	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2273	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2274	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2275	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2276	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2277	!
2278	!-- Along the vertical direction limit the length scale further by the
2279	!-- boundary-layer depth to assure that no length scales larger than
2280	!-- the boundary-layer depth are used
2281	length_scale_dum = MIN( length_scale, zi_ribulk )
2282
2283	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2284	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2285	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2286	!
2287	!-- Limit time scales, else they become very larger for low wind speed,
2288	!-- imposing long-living inflow perturbations which in turn propagate
2289	!-- further into the model domain. Use u_init and v_init to calculate
2290	!-- the time scales, which will be equal to the inflow profiles, both,
2291	!-- in offline nesting mode or in dirichlet/radiation mode.
2292	tu(k) = MIN( dt_stg_adjust, length_scale / &
2293	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2294	tv(k) = MIN( dt_stg_adjust, length_scale / &
2295	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2296	!
2297	!-- Time scale of w-component is a mixture from u- and v-component.
2298	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2299
2300	ENDDO
2301	!
2302	!-- Set bottom boundary condition for the length and time scales
2303	nux(nzb) = nux(nzb+1)
2304	nuy(nzb) = nuy(nzb+1)
2305	nuz(nzb) = nuz(nzb+1)
2306	nvx(nzb) = nvx(nzb+1)
2307	nvy(nzb) = nvy(nzb+1)
2308	nvz(nzb) = nvz(nzb+1)
2309	nwx(nzb) = nwx(nzb+1)
2310	nwy(nzb) = nwy(nzb+1)
2311	nwz(nzb) = nwz(nzb+1)
2312
2313	tu(nzb) = tu(nzb+1)
2314	tv(nzb) = tv(nzb+1)
2315	tw(nzb) = tw(nzb+1)
2316
2317
2318	END SUBROUTINE calc_length_and_time_scale
2319
2320	!------------------------------------------------------------------------------!
2321	! Description:
2322	! ------------
2323	!> Calculate scaling variables which are used for turbulence parametrization
2324	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2325	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2326	!------------------------------------------------------------------------------!
2327	SUBROUTINE calc_scaling_variables
2328
2329	USE surface_mod, &
2330	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
2331
2332	IMPLICIT NONE
2333
2334	INTEGER(iwp) :: i !< loop index in x-direction
2335	INTEGER(iwp) :: j !< loop index in y-direction
2336	INTEGER(iwp) :: k !< loop index in z-direction
2337	INTEGER(iwp) :: m !< surface element index
2338
2339	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2340	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2341	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2342	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2343	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2344	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2345	REAL(wp) :: w_convective !< convective velocity scale
2346
2347	!
2348	!-- Calculate mean friction velocity, velocity scale, heat flux and
2349	!-- near-surface temperature in the model domain.
2350	pt_surf_mean_l = 0.0_wp
2351	shf_mean_l = 0.0_wp
2352	scale_l_l = 0.0_wp
2353	friction_vel_l = 0.0_wp
2354	DO m = 1, surf_def_h(0)%ns
2355	i = surf_def_h(0)%i(m)
2356	j = surf_def_h(0)%j(m)
2357	k = surf_def_h(0)%k(m)
2358	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2359	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2360	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2361	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2362	ENDDO
2363	DO m = 1, surf_lsm_h%ns
2364	i = surf_lsm_h%i(m)
2365	j = surf_lsm_h%j(m)
2366	k = surf_lsm_h%k(m)
2367	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2368	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2369	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2370	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2371	ENDDO
2372	DO m = 1, surf_usm_h%ns
2373	i = surf_usm_h%i(m)
2374	j = surf_usm_h%j(m)
2375	k = surf_usm_h%k(m)
2376	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2377	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2378	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2379	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2380	ENDDO
2381
2382	#if defined( __parallel )
2383	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2384	comm2d, ierr )
2385	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2386	comm2d, ierr )
2387	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2388	comm2d, ierr )
2389	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2390	comm2d, ierr )
2391	#else
2392	scale_us = friction_vel_l
2393	shf_mean = shf_mean_l
2394	scale_l = scale_l_l
2395	pt_surf_mean = pt_surf_mean_l
2396	#endif
2397
2398	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2399	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2400	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2401	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2402	!
2403	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2404	!-- is negative, set convective velocity scale to zero.
2405	IF ( shf_mean > 0.0_wp ) THEN
2406	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2407	ELSE
2408	w_convective = 0.0_wp
2409	ENDIF
2410	!
2411	!-- Finally, in order to consider also neutral or stable stratification,
2412	!-- compute momentum velocity scale from u* and convective velocity scale,
2413	!-- according to Rotach et al. (1996).
2414	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2415
2416	END SUBROUTINE calc_scaling_variables
2417
2418	END MODULE synthetic_turbulence_generator_mod

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