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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4332

Last change on this file since 4332 was 4332, checked in by suehring, 5 years ago
Synthetic turbulence: Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
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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 4332 2019-12-10 19:44:12Z suehring $
27	! Limit initial velocity seeds in restart runs, if not the seed calculation
28	! may become unstable. Further, minor bugfix in initial velocity seed
29	! calculation.
30	!
31	! 4329 2019-12-10 15:46:36Z motisi
32	! Renamed wall_flags_0 to wall_flags_static_0
33	!
34	! 4309 2019-11-26 18:49:59Z suehring
35	! Computation of velocity seeds optimized. This implies that random numbers
36	! are computed now using the parallel random number generator. Random numbers
37	! are now only computed and normalized locally, while distributed over all
38	! mpi ranks afterwards, instead of computing random numbers on a global array.
39	! Further, the number of calls for the time-consuming velocity-seed generation
40	! is reduced - now the left and right, as well as the north and south boundary
41	! share the same velocity-seed matrices.
42	!
43	! 4182 2019-08-22 15:20:23Z scharf
44	! Corrected "Former revisions" section
45	!
46	! 4148 2019-08-08 11:26:00Z suehring
47	! Remove unused variable
48	!
49	! 4144 2019-08-06 09:11:47Z raasch
50	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
51	!
52	! 4071 2019-07-03 20:02:00Z suehring
53	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
54	! information is not read from file.
55	!
56	! 4022 2019-06-12 11:52:39Z suehring
57	! Several bugfixes and improvements
58	! - revise bias correction of the imposed perturbations (correction via volume
59	! flow can create instabilities in case the mean volume flow is close to zero)
60	! - introduce lower limits in calculation of coefficient matrix, else the
61	! calculation may become numerically unstable
62	! - impose perturbations every timestep, even though no new set of perturbations
63	! is generated in case dt_stg_call /= dt_3d
64	! - Implement a gradual decrease of Reynolds stress and length scales above
65	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
66	! discontinuous decrease
67	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
68	!
69	! 3987 2019-05-22 09:52:13Z kanani
70	! Introduce alternative switch for debug output during timestepping
71	!
72	! 3938 2019-04-29 16:06:25Z suehring
73	! Remove unused variables
74	!
75	! 3937 2019-04-29 15:09:07Z suehring
76	! Minor bugfix in case of a very early restart where mc_factor is sill not
77	! present.
78	! Some modification and fixing of potential bugs in the calculation of scaling
79	! parameters used for synthetic turbulence parametrization.
80	!
81	! 3909 2019-04-17 09:13:25Z suehring
82	! Minor bugfix for last commit
83	!
84	! 3900 2019-04-16 15:17:43Z suehring
85	! Missing re-calculation of perturbation seeds in case of restarts
86	!
87	! 3891 2019-04-12 17:52:01Z suehring
88	! Bugfix in initialization in case of restart runs.
89	!
90	! 3885 2019-04-11 11:29:34Z kanani
91	! Changes related to global restructuring of location messages and introduction
92	! of additional debug messages
93	!
94	!
95	! removed unused variables
96	!
97	! 3719 2019-02-06 13:10:18Z kanani
98	! Removed log_point measurement from stg_init, since this part is counted to
99	! log_point(2) 'initialisation' already. Moved other log_points to calls of
100	! the subroutines in time_integration for better overview.
101	!
102	! 2259 2017-06-08 09:09:11Z gronemeier
103	! Initial revision
104	!
105	! Authors:
106	! --------
107	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
108	!
109	!
110	! Description:
111	! ------------
112	!> The module generates turbulence at the inflow boundary based on a method by
113	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
114	!> correction by Kim et al. (2013).
115	!> The turbulence is correlated based on length scales in y- and z-direction and
116	!> a time scale for each velocity component. The profiles of length and time
117	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
118	!> tensor can be either read from file STG_PROFILES, or will be parametrized
119	!> within the boundary layer.
120	!>
121	!> @todo test restart
122	!> enable cyclic_fill
123	!> implement turbulence generation for e and pt
124	!> @todo Input of height-constant length scales via namelist
125	!> @note <Enter notes on the module>
126	!> @bug Height information from input file is not used. Profiles from input
127	!> must match with current PALM grid.
128	!> In case of restart, velocity seeds differ from precursor run if a11,
129	!> a22, or a33 are zero.
130	!------------------------------------------------------------------------------!
131	MODULE synthetic_turbulence_generator_mod
132
133
134	USE arrays_3d, &
135	ONLY: dzw, &
136	ddzw, &
137	drho_air, &
138	mean_inflow_profiles, &
139	q, &
140	q_init, &
141	pt, &
142	pt_init, &
143	u, &
144	u_init, &
145	v, &
146	v_init, &
147	w, &
148	zu, &
149	zw
150
151	USE basic_constants_and_equations_mod, &
152	ONLY: g, &
153	kappa, &
154	pi
155
156	USE control_parameters, &
157	ONLY: bc_lr, &
158	bc_ns, &
159	child_domain, &
160	coupling_char, &
161	debug_output_timestep, &
162	dt_3d, &
163	e_init, &
164	humidity, &
165	initializing_actions, &
166	intermediate_timestep_count, &
167	intermediate_timestep_count_max, &
168	length, &
169	message_string, &
170	nesting_offline, &
171	neutral, &
172	num_mean_inflow_profiles, &
173	random_generator, &
174	rans_mode, &
175	restart_string, &
176	syn_turb_gen, &
177	time_since_reference_point, &
178	turbulent_inflow
179
180	USE grid_variables, &
181	ONLY: ddx, &
182	ddy, &
183	dx, &
184	dy
185
186	USE indices, &
187	ONLY: nbgp, &
188	nz, &
189	nzb, &
190	nzt, &
191	nx, &
192	nxl, &
193	nxlu, &
194	nxlg, &
195	nxr, &
196	nxrg, &
197	ny, &
198	nys, &
199	nysv, &
200	nyn, &
201	nyng, &
202	nysg, &
203	wall_flags_static_0
204
205	USE kinds
206
207	#if defined( __parallel ) && !defined( __mpifh )
208	USE MPI
209	#endif
210
211	USE nesting_offl_mod, &
212	ONLY: nesting_offl_calc_zi, &
213	zi_ribulk
214
215	USE pegrid, &
216	ONLY: comm1dx, &
217	comm1dy, &
218	comm2d, &
219	ierr, &
220	myidx, &
221	myidy, &
222	pdims
223
224	USE pmc_interface, &
225	ONLY : rans_mode_parent
226
227	USE random_generator_parallel, &
228	ONLY: random_dummy, &
229	random_number_parallel, &
230	random_seed_parallel, &
231	seq_random_array
232
233	USE transpose_indices, &
234	ONLY: nzb_x, &
235	nzt_x
236
237
238	IMPLICIT NONE
239
240	#if defined( __parallel ) && defined( __mpifh )
241	INCLUDE "mpif.h"
242	#endif
243
244
245	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
246	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
247	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
248
249	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
250	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
251	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
252	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
253	INTEGER(iwp) :: merg !< maximum length scale (in gp)
254	INTEGER(iwp) :: mergp !< merg + nbgp
255	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
256	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
257	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
258	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
259	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
260	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
261	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
262	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
263
264	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
265	!< required for bias correction of imposed perturbations
266	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
267	!< required for bias correction of imposed perturbations
268
269	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
270	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
271	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
272	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
273	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
274	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
275	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
276	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
277	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
278	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
279	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
280	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
281	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
282
283	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
284	!< scales above the boundary layer
285	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
286	!< one length scale above ABL top
287	REAL(wp) :: d_l !< blend_coeff/length_scale
288	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
289	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
290	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
291	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
292	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
293	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
294	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
295	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
296
297	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
298
299
300	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
301	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
302	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
303	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
304	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
305	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
306
307	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
308	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
309	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
310	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
311	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
312	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
313	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
314	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
315	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
316
317	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
318	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
319	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
320	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
321	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
322	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
323	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
324	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
325	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
326	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
327	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
328	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
329	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
330	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
331	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
332	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
333	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
334	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
335	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
336	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
337	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
338
339	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
340	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
341
342	!
343	!-- PALM interfaces:
344	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
345	INTERFACE stg_adjust
346	MODULE PROCEDURE stg_adjust
347	END INTERFACE stg_adjust
348	!
349	!-- Input parameter checks to be done in check_parameters
350	INTERFACE stg_check_parameters
351	MODULE PROCEDURE stg_check_parameters
352	END INTERFACE stg_check_parameters
353
354	!
355	!-- Calculate filter functions
356	INTERFACE stg_filter_func
357	MODULE PROCEDURE stg_filter_func
358	END INTERFACE stg_filter_func
359
360	!
361	!-- Generate velocity seeds at south and north domain boundary
362	INTERFACE stg_generate_seed_xz
363	MODULE PROCEDURE stg_generate_seed_xz
364	END INTERFACE stg_generate_seed_xz
365	!
366	!-- Generate velocity seeds at left and/or right domain boundary
367	INTERFACE stg_generate_seed_yz
368	MODULE PROCEDURE stg_generate_seed_yz
369	END INTERFACE stg_generate_seed_yz
370
371	!
372	!-- Output of information to the header file
373	INTERFACE stg_header
374	MODULE PROCEDURE stg_header
375	END INTERFACE stg_header
376
377	!
378	!-- Initialization actions
379	INTERFACE stg_init
380	MODULE PROCEDURE stg_init
381	END INTERFACE stg_init
382
383	!
384	!-- Main procedure of synth. turb. gen.
385	INTERFACE stg_main
386	MODULE PROCEDURE stg_main
387	END INTERFACE stg_main
388
389	!
390	!-- Reading of NAMELIST parameters
391	INTERFACE stg_parin
392	MODULE PROCEDURE stg_parin
393	END INTERFACE stg_parin
394
395	!
396	!-- Reading of parameters for restart runs
397	INTERFACE stg_rrd_global
398	MODULE PROCEDURE stg_rrd_global
399	END INTERFACE stg_rrd_global
400
401	!
402	!-- Writing of binary output for restart runs
403	INTERFACE stg_wrd_global
404	MODULE PROCEDURE stg_wrd_global
405	END INTERFACE stg_wrd_global
406
407	SAVE
408
409	PRIVATE
410
411	!
412	!-- Public interfaces
413	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
414	stg_parin, stg_rrd_global, stg_wrd_global
415
416	!
417	!-- Public variables
418	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
419	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
420	time_stg_adjust, time_stg_call, use_syn_turb_gen
421
422
423	CONTAINS
424
425
426	!------------------------------------------------------------------------------!
427	! Description:
428	! ------------
429	!> Check parameters routine for synthetic turbulence generator
430	!------------------------------------------------------------------------------!
431	SUBROUTINE stg_check_parameters
432
433	IMPLICIT NONE
434
435	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
436	nesting_offline ) THEN
437	message_string = 'Synthetic turbulence generator is required ' // &
438	'if offline nesting is applied and PALM operates ' // &
439	'in LES mode.'
440	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
441	ENDIF
442
443	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
444	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
445	message_string = 'Synthetic turbulence generator is required ' // &
446	'when nesting is applied and parent operates in ' // &
447	'RANS-mode but current child in LES mode.'
448	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
449	ENDIF
450
451	IF ( use_syn_turb_gen ) THEN
452
453	IF ( child_domain .AND. .NOT. rans_mode .AND. &
454	.NOT. rans_mode_parent ) THEN
455	message_string = 'Using synthetic turbulence generator ' // &
456	'is not allowed in LES-LES nesting.'
457	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
458
459	ENDIF
460
461	IF ( child_domain .AND. rans_mode .AND. &
462	rans_mode_parent ) THEN
463	message_string = 'Using synthetic turbulence generator ' // &
464	'is not allowed in RANS-RANS nesting.'
465	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
466
467	ENDIF
468
469	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
470
471	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
472	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
473	message_string = 'Using synthetic turbulence generator ' // &
474	'requires %initializing_actions = ' // &
475	'"set_constant_profiles" or "read_restart_data"' //&
476	', if not offline nesting is applied.'
477	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
478	ENDIF
479
480	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
481	message_string = 'Using synthetic turbulence generator ' // &
482	'requires &bc_lr = "dirichlet/radiation", ' // &
483	'if not offline nesting is applied.'
484	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
485	ENDIF
486	IF ( bc_ns /= 'cyclic' ) THEN
487	message_string = 'Using synthetic turbulence generator ' // &
488	'requires &bc_ns = "cyclic", ' // &
489	'if not offline nesting is applied.'
490	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
491	ENDIF
492
493	ENDIF
494
495	IF ( turbulent_inflow ) THEN
496	message_string = 'Using synthetic turbulence generator ' // &
497	'in combination &with turbulent_inflow = .T. '// &
498	'is not allowed'
499	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
500	ENDIF
501	!
502	!-- Synthetic turbulence generator requires the parallel random generator
503	IF ( random_generator /= 'random-parallel' ) THEN
504	message_string = 'Using synthetic turbulence generator ' // &
505	'requires random_generator = random-parallel.'
506	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
507	ENDIF
508
509	ENDIF
510
511	END SUBROUTINE stg_check_parameters
512
513
514	!------------------------------------------------------------------------------!
515	! Description:
516	! ------------
517	!> Header output for synthetic turbulence generator
518	!------------------------------------------------------------------------------!
519	SUBROUTINE stg_header ( io )
520
521
522	IMPLICIT NONE
523
524	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
525
526	!
527	!-- Write synthetic turbulence generator Header
528	WRITE( io, 1 )
529	IF ( use_syn_turb_gen ) THEN
530	WRITE( io, 2 )
531	ELSE
532	WRITE( io, 3 )
533	ENDIF
534
535	IF ( parametrize_inflow_turbulence ) THEN
536	WRITE( io, 4 ) dt_stg_adjust
537	ELSE
538	WRITE( io, 5 )
539	ENDIF
540
541	1 FORMAT (//' Synthetic turbulence generator information:'/ &
542	' ------------------------------------------'/)
543	2 FORMAT (' synthetic turbulence generator is switched on')
544	3 FORMAT (' synthetic turbulence generator is switched off')
545	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
546	5 FORMAT (' imposed turbulence is read from file' )
547
548	END SUBROUTINE stg_header
549
550
551	!------------------------------------------------------------------------------!
552	! Description:
553	! ------------
554	!> Initialization of the synthetic turbulence generator
555	!------------------------------------------------------------------------------!
556	SUBROUTINE stg_init
557
558	IMPLICIT NONE
559
560	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
561
562	#if defined( __parallel )
563	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
564	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
565	#endif
566
567	INTEGER(iwp) :: i !> grid index in x-direction
568	INTEGER(iwp) :: j !> loop index
569	INTEGER(iwp) :: k !< index
570	INTEGER(iwp) :: newtype !< dummy MPI type
571	INTEGER(iwp) :: realsize !< size of REAL variables
572
573	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
574	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
575	!
576	!-- Dummy variables used for reading profiles
577	REAL(wp) :: d1 !< u profile
578	REAL(wp) :: d2 !< v profile
579	REAL(wp) :: d3 !< w profile
580	REAL(wp) :: d5 !< e profile
581	REAL(wp) :: luy !< length scale for u in y direction
582	REAL(wp) :: luz !< length scale for u in z direction
583	REAL(wp) :: lvy !< length scale for v in y direction
584	REAL(wp) :: lvz !< length scale for v in z direction
585	REAL(wp) :: lwy !< length scale for w in y direction
586	REAL(wp) :: lwz !< length scale for w in z direction
587	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
588	REAL(wp) :: zz !< height
589
590
591	#if defined( __parallel )
592	CALL MPI_BARRIER( comm2d, ierr )
593	#endif
594
595	#if defined( __parallel )
596	!
597	!-- Determine processor decomposition of z-axis along x- and y-direction
598	nnz = nz / pdims(1)
599	nzb_x_stg = 1 + myidx * INT( nnz )
600	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
601
602	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
603	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
604
605	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
606	.AND. .NOT. rans_mode ) ) THEN
607	nnz = nz / pdims(2)
608	nzb_y_stg = 1 + myidy * INT( nnz )
609	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
610
611	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
612	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
613	ENDIF
614
615	!
616	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
617	!-- velocity seeds
618	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
619	extent = 1 * realsize
620	!
621	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
622	!-- layer
623	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
624	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
625	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
626	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
627	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
628	CALL MPI_TYPE_FREE( newtype, ierr )
629
630	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
631	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
632	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
633	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
634	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
635	CALL MPI_TYPE_FREE( newtype, ierr )
636
637	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
638	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
639
640	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
641	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
642
643	DO j = 1, pdims(1)
644	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
645	ENDDO
646	!
647	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
648	!-- layer
649	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
650	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
651	.AND. .NOT. rans_mode ) ) THEN
652	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
653	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
654	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
655	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
656	CALL MPI_TYPE_FREE( newtype, ierr )
657
658	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
659	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
660	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
661	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
662	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
663	CALL MPI_TYPE_FREE( newtype, ierr )
664
665	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
666	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
667
668	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
669	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
670
671	DO j = 1, pdims(2)
672	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
673	ENDDO
674
675	ENDIF
676
677	#endif
678	!
679	!-- Allocate required arrays.
680	!-- In case no offline nesting or self nesting is used, the arrary
681	!-- mean_inflow profiles is required. Check if it is already allocated, else
682	!-- allocate and initialize it appropriately. Note, in case turbulence and
683	!-- inflow information is read from file, mean_inflow_profiles is already
684	!-- allocated and initialized appropriately.
685	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
686	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
687	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
688	mean_inflow_profiles = 0.0_wp
689	mean_inflow_profiles(:,1) = u_init
690	mean_inflow_profiles(:,2) = v_init
691	!
692	!-- Even though potential temperature and humidity are not perturbed,
693	!-- they need to be initialized appropriately.
694	IF ( .NOT. neutral ) &
695	mean_inflow_profiles(:,4) = pt_init
696	IF ( humidity ) &
697	mean_inflow_profiles(:,6) = q_init
698	ENDIF
699	ENDIF
700
701	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
702	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
703	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
704	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
705	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
706	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
707	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
708	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
709
710	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
711	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
712	dist_xz = 0.0_wp
713	dist_yz = 0.0_wp
714	!
715	!-- Read inflow profile
716	!-- Height levels of profiles in input profile is as follows:
717	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
718	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
719	!-- WARNING: zz is not used at the moment
720	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
721	EXIST = file_stg_exist )
722
723	IF ( file_stg_exist ) THEN
724
725	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
726	FORM='FORMATTED')
727	!
728	!-- Skip header
729	READ( 90, * )
730
731	DO k = nzb+1, nzt+1
732	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
733	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
734	d1, d2, d3, d5
735
736	!
737	!-- Convert length scales from meter to number of grid points.
738	nuy(k) = INT( luy * ddy )
739	nuz(k) = INT( luz * ddzw(k) )
740	nvy(k) = INT( lvy * ddy )
741	nvz(k) = INT( lvz * ddzw(k) )
742	nwy(k) = INT( lwy * ddy )
743	nwz(k) = INT( lwz * ddzw(k) )
744	!
745	!-- Workaround, assume isotropic turbulence
746	nwx(k) = nwy(k)
747	nvx(k) = nvy(k)
748	nux(k) = nuy(k)
749	!
750	!-- Save Mean inflow profiles
751	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
752	mean_inflow_profiles(k,1) = d1
753	mean_inflow_profiles(k,2) = d2
754	! mean_inflow_profiles(k,4) = d4
755	mean_inflow_profiles(k,5) = d5
756	ENDIF
757	ENDDO
758	!
759	!-- Set lenght scales at surface grid point
760	nuy(nzb) = nuy(nzb+1)
761	nuz(nzb) = nuz(nzb+1)
762	nvy(nzb) = nvy(nzb+1)
763	nvz(nzb) = nvz(nzb+1)
764	nwy(nzb) = nwy(nzb+1)
765	nwz(nzb) = nwz(nzb+1)
766
767	CLOSE( 90 )
768	!
769	!-- Calculate coefficient matrix from Reynolds stress tensor
770	!-- (Lund rotation)
771	CALL calc_coeff_matrix
772	!
773	!-- No information about turbulence and its length scales are available.
774	!-- Instead, parametrize turbulence which is imposed at the boundaries.
775	!-- Set flag which indicates that turbulence is parametrized, which is done
776	!-- later when energy-balance models are already initialized. This is
777	!-- because the STG needs information about surface properties such as
778	!-- roughness to build 'realistic' turbulence profiles.
779	ELSE
780	!
781	!-- Define length scale for the imposed turbulence, which is defined as
782	!-- 8 times the minimum grid spacing
783	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
784	!
785	!-- Define constant to gradually decrease length scales and Reynolds stress
786	!-- above ABL top. Assure that no zero length scales are used.
787	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
788	!
789	!-- Set flag indicating that turbulence is parametrized
790	parametrize_inflow_turbulence = .TRUE.
791	!
792	!-- In case of dirichlet inflow boundary conditions only at one lateral
793	!-- boundary, i.e. in the case no offline or self nesting is applied but
794	!-- synthetic turbulence shall be parametrized nevertheless, the
795	!-- boundary-layer depth need to determined first.
796	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
797	CALL nesting_offl_calc_zi
798	!
799	!-- Determine boundary-layer depth, which is used to initialize lenght
800	!-- scales
801	CALL calc_scaling_variables
802	!
803	!-- Initialize lenght and time scales, which in turn are used
804	!-- to initialize the filter functions.
805	CALL calc_length_and_time_scale
806	!
807	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
808	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
809	!-- Rotach et al. (1996) and is based on boundary-layer depth,
810	!-- friction velocity and velocity scale.
811	CALL parametrize_reynolds_stress
812	!
813	!-- Calculate coefficient matrix from Reynolds stress tensor
814	!-- (Lund rotation)
815	CALL calc_coeff_matrix
816
817	ENDIF
818
819	!
820	!-- Assign initial profiles. Note, this is only required if turbulent
821	!-- inflow from the left is desired, not in case of any of the
822	!-- nesting (offline or self nesting) approaches.
823	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
824	u_init = mean_inflow_profiles(:,1)
825	v_init = mean_inflow_profiles(:,2)
826	!pt_init = mean_inflow_profiles(:,4)
827	e_init = MAXVAL( mean_inflow_profiles(:,5) )
828	ENDIF
829
830	!
831	!-- Define the size of the filter functions and allocate them.
832	merg = 0
833
834	! arrays must be large enough to cover the largest length scale
835	DO k = nzb, nzt+1
836	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
837	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
838	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
839	IF ( j > merg ) merg = j
840	ENDDO
841
842	merg = 2 * merg
843	mergp = merg + nbgp
844
845	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
846	buy(-merg:merg,nzb:nzt+1), &
847	buz(-merg:merg,nzb:nzt+1), &
848	bvx(-merg:merg,nzb:nzt+1), &
849	bvy(-merg:merg,nzb:nzt+1), &
850	bvz(-merg:merg,nzb:nzt+1), &
851	bwx(-merg:merg,nzb:nzt+1), &
852	bwy(-merg:merg,nzb:nzt+1), &
853	bwz(-merg:merg,nzb:nzt+1) )
854
855	!
856	!-- Allocate velocity seeds for turbulence at xz-layer
857	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
858	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
859	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
860
861	!
862	!-- Allocate velocity seeds for turbulence at yz-layer
863	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
864	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
865	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
866
867	fu_xz = 0.0_wp
868	fuo_xz = 0.0_wp
869	fv_xz = 0.0_wp
870	fvo_xz = 0.0_wp
871	fw_xz = 0.0_wp
872	fwo_xz = 0.0_wp
873
874	fu_yz = 0.0_wp
875	fuo_yz = 0.0_wp
876	fv_yz = 0.0_wp
877	fvo_yz = 0.0_wp
878	fw_yz = 0.0_wp
879	fwo_yz = 0.0_wp
880
881	!
882	!-- Create filter functions
883	CALL stg_filter_func( nux, bux ) !filter ux
884	CALL stg_filter_func( nuy, buy ) !filter uy
885	CALL stg_filter_func( nuz, buz ) !filter uz
886	CALL stg_filter_func( nvx, bvx ) !filter vx
887	CALL stg_filter_func( nvy, bvy ) !filter vy
888	CALL stg_filter_func( nvz, bvz ) !filter vz
889	CALL stg_filter_func( nwx, bwx ) !filter wx
890	CALL stg_filter_func( nwy, bwy ) !filter wy
891	CALL stg_filter_func( nwz, bwz ) !filter wz
892
893	#if defined( __parallel )
894	CALL MPI_BARRIER( comm2d, ierr )
895	#endif
896
897	!
898	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
899	! time step.
900	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
901	! are 0 compared to the prerun. This is mostly for k=nzt+1.
902	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
903	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
904
905	IF ( myidx == id_stg_left ) i = -1
906	IF ( myidx == id_stg_right ) i = nxr+1
907
908	DO j = nysg, nyng
909	DO k = nzb, nzt+1
910	IF ( a11(k) > 10E-8_wp ) THEN
911	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
912	ELSE
913	fu_yz(k,j) = 10E-8_wp
914	ENDIF
915
916	IF ( a22(k) > 10E-8_wp ) THEN
917	fv_yz(k,j) = ( v(k,j,i) - &
918	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
919	ELSE
920	fv_yz(k,j) = 10E-8_wp
921	ENDIF
922
923	IF ( a33(k) > 10E-8_wp ) THEN
924	fw_yz(k,j) = ( w(k,j,i) - &
925	a31(k) * fu_yz(k,j) - a32(k) * &
926	fv_yz(k,j) ) / a33(k)
927	ELSE
928	fw_yz(k,j) = 10E-8_wp
929	ENDIF
930	ENDDO
931	ENDDO
932	ENDIF
933
934	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
935
936	IF ( myidy == id_stg_south ) j = -1
937	IF ( myidy == id_stg_north ) j = nyn+1
938
939	DO i = nxlg, nxrg
940	DO k = nzb, nzt+1
941
942	IF ( a11(k) > 10E-8_wp ) THEN
943	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
944	ELSE
945	fu_xz(k,i) = 10E-8_wp
946	ENDIF
947
948	IF ( a22(k) > 10E-8_wp ) THEN
949	fv_xz(k,i) = ( v(k,j,i) - &
950	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
951	ELSE
952	fv_xz(k,i) = 10E-8_wp
953	ENDIF
954
955	IF ( a33(k) > 10E-8_wp ) THEN
956	fw_xz(k,i) = ( w(k,j,i) - &
957	a31(k) * fu_xz(k,i) - &
958	a32(k) * fv_xz(k,i) ) / a33(k)
959	ELSE
960	fw_xz(k,i) = 10E-8_wp
961	ENDIF
962
963	ENDDO
964	ENDDO
965	ENDIF
966	ENDIF
967	!
968	!-- Count the number of non-topography grid points at the boundaries where
969	!-- perturbations are imposed. This number is later used for bias corrections
970	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
971	!-- due to the asymetry of u and v along x and y direction, respectively,
972	!-- different cases must be distinguished.
973	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
974	!
975	!-- Number of grid points where perturbations are imposed on u
976	IF ( myidx == id_stg_left ) i = nxl
977	IF ( myidx == id_stg_right ) i = nxr+1
978
979	nr_non_topo_yz_l(1) = SUM( &
980	MERGE( 1, 0, &
981	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
982	!
983	!-- Number of grid points where perturbations are imposed on v and w
984	IF ( myidx == id_stg_left ) i = nxl-1
985	IF ( myidx == id_stg_right ) i = nxr+1
986
987	nr_non_topo_yz_l(2) = SUM( &
988	MERGE( 1, 0, &
989	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
990	nr_non_topo_yz_l(3) = SUM( &
991	MERGE( 1, 0, &
992	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
993
994	#if defined( __parallel )
995	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
996	MPI_SUM, comm1dy, ierr )
997	#else
998	nr_non_topo_yz = nr_non_topo_yz_l
999	#endif
1000	ENDIF
1001
1002	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1003	!
1004	!-- Number of grid points where perturbations are imposed on v
1005	IF ( myidy == id_stg_south ) j = nys
1006	IF ( myidy == id_stg_north ) j = nyn+1
1007
1008	nr_non_topo_xz_l(2) = SUM( &
1009	MERGE( 1, 0, &
1010	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1011	!
1012	!-- Number of grid points where perturbations are imposed on u and w
1013	IF ( myidy == id_stg_south ) j = nys-1
1014	IF ( myidy == id_stg_north ) j = nyn+1
1015
1016	nr_non_topo_xz_l(1) = SUM( &
1017	MERGE( 1, 0, &
1018	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1019	nr_non_topo_xz_l(3) = SUM( &
1020	MERGE( 1, 0, &
1021	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1022
1023	#if defined( __parallel )
1024	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1025	MPI_SUM, comm1dx, ierr )
1026	#else
1027	nr_non_topo_xz = nr_non_topo_xz_l
1028	#endif
1029	ENDIF
1030
1031
1032	END SUBROUTINE stg_init
1033
1034
1035	!------------------------------------------------------------------------------!
1036	! Description:
1037	! ------------
1038	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1039	!> (Xie and Castro, 2008)
1040	!------------------------------------------------------------------------------!
1041	SUBROUTINE stg_filter_func( nxx, bxx )
1042
1043
1044	IMPLICIT NONE
1045
1046	INTEGER(iwp) :: k !< loop index
1047	INTEGER(iwp) :: n_k !< length scale nXX in height k
1048	INTEGER(iwp) :: n_k2 !< n_k * 2
1049	INTEGER(iwp) :: nf !< index for length scales
1050
1051	REAL(wp) :: bdenom !< denominator for filter functions bXX
1052	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1053
1054	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
1055
1056	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
1057
1058
1059	bxx = 0.0_wp
1060
1061	DO k = nzb, nzt+1
1062	bdenom = 0.0_wp
1063	n_k = nxx(k)
1064	IF ( n_k /= 0 ) THEN
1065	n_k2 = n_k * 2
1066
1067	!
1068	!-- ( Eq.10 )^2
1069	DO nf = -n_k2, n_k2
1070	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1071	ENDDO
1072
1073	!
1074	!-- ( Eq.9 )
1075	bdenom = SQRT( bdenom )
1076	DO nf = -n_k2, n_k2
1077	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1078	ENDDO
1079	ENDIF
1080	ENDDO
1081
1082	END SUBROUTINE stg_filter_func
1083
1084
1085	!------------------------------------------------------------------------------!
1086	! Description:
1087	! ------------
1088	!> Parin for &stg_par for synthetic turbulence generator
1089	!------------------------------------------------------------------------------!
1090	SUBROUTINE stg_parin
1091
1092
1093	IMPLICIT NONE
1094
1095	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1096
1097
1098	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
1099
1100	line = ' '
1101
1102	!
1103	!-- Try to find stg package
1104	REWIND ( 11 )
1105	line = ' '
1106	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1107	READ ( 11, '(A)', END=20 ) line
1108	ENDDO
1109	BACKSPACE ( 11 )
1110
1111	!
1112	!-- Read namelist
1113	READ ( 11, stg_par, ERR = 10, END = 20 )
1114
1115	!
1116	!-- Set flag that indicates that the synthetic turbulence generator is switched
1117	!-- on
1118	syn_turb_gen = .TRUE.
1119	GOTO 20
1120
1121	10 BACKSPACE( 11 )
1122	READ( 11 , '(A)') line
1123	CALL parin_fail_message( 'stg_par', line )
1124
1125	20 CONTINUE
1126
1127	END SUBROUTINE stg_parin
1128
1129
1130	!------------------------------------------------------------------------------!
1131	! Description:
1132	! ------------
1133	!> This routine reads the respective restart data.
1134	!------------------------------------------------------------------------------!
1135	SUBROUTINE stg_rrd_global( found )
1136
1137
1138	IMPLICIT NONE
1139
1140	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1141
1142
1143	found = .TRUE.
1144
1145
1146	SELECT CASE ( restart_string(1:length) )
1147
1148	CASE ( 'time_stg_adjust' )
1149	READ ( 13 ) time_stg_adjust
1150
1151	CASE ( 'time_stg_call' )
1152	READ ( 13 ) time_stg_call
1153
1154	CASE ( 'use_syn_turb_gen' )
1155	READ ( 13 ) use_syn_turb_gen
1156
1157	CASE DEFAULT
1158
1159	found = .FALSE.
1160
1161	END SELECT
1162
1163
1164	END SUBROUTINE stg_rrd_global
1165
1166
1167	!------------------------------------------------------------------------------!
1168	! Description:
1169	! ------------
1170	!> This routine writes the respective restart data.
1171	!------------------------------------------------------------------------------!
1172	SUBROUTINE stg_wrd_global
1173
1174
1175	IMPLICIT NONE
1176
1177	CALL wrd_write_string( 'time_stg_adjust' )
1178	WRITE ( 14 ) time_stg_adjust
1179
1180	CALL wrd_write_string( 'time_stg_call' )
1181	WRITE ( 14 ) time_stg_call
1182
1183	CALL wrd_write_string( 'use_syn_turb_gen' )
1184	WRITE ( 14 ) use_syn_turb_gen
1185
1186
1187	END SUBROUTINE stg_wrd_global
1188
1189
1190	!------------------------------------------------------------------------------!
1191	! Description:
1192	! ------------
1193	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1194	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1195	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1196	!> (Lund, 1998).
1197	!------------------------------------------------------------------------------!
1198	SUBROUTINE stg_main
1199
1200	IMPLICIT NONE
1201
1202	INTEGER(iwp) :: i !< grid index in x-direction
1203	INTEGER(iwp) :: j !< loop index in y-direction
1204	INTEGER(iwp) :: k !< loop index in z-direction
1205
1206	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1207
1208	REAL(wp) :: dt_stg !< wheighted subtimestep
1209
1210	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1211
1212	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1213	!
1214	!-- Calculate time step which is needed for filter functions
1215	dt_stg = MAX( dt_3d, dt_stg_call )
1216	!
1217	!-- Check if synthetic turbulence generator needs to be called and new
1218	!-- perturbations need to be created or if old disturbances can be imposed
1219	!-- again.
1220	IF ( time_stg_call >= dt_stg_call .AND. &
1221	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1222	stg_call = .TRUE.
1223	ELSE
1224	stg_call = .FALSE.
1225	ENDIF
1226	!
1227	!-- Initial value of fu, fv, fw
1228	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1229	!
1230	!-- Generate turbulence at the left and right boundary. Random numbers
1231	!-- for the yz-planes at the left/right boundary are generated by the
1232	!-- left-sided mpi ranks only. After random numbers are calculated, they
1233	!-- are distributed to all other mpi ranks in the model, so that the
1234	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
1235	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
1236	!-- that the left- and the right-sided lateral boundary have the same initial
1237	!-- seeds.
1238	!-- Note, in case of inflow from the right only, only turbulence at the left
1239	!-- boundary is required.
1240	IF ( .NOT. ( nesting_offline .OR. &
1241	( child_domain .AND. rans_mode_parent &
1242	.AND. .NOT. rans_mode ) ) ) THEN
1243
1244	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1245	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1246	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1247	ELSE
1248	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
1249	id_stg_left, id_stg_right )
1250	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
1251	id_stg_left, id_stg_right )
1252	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
1253	id_stg_left, id_stg_right )
1254	!
1255	!-- Generate turbulence at the south and north boundary. Random numbers
1256	!-- for the xz-planes at the south/north boundary are generated by the
1257	!-- south-sided mpi ranks only. Please see also comment above.
1258	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
1259	id_stg_south, id_stg_north )
1260	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
1261	id_stg_south, id_stg_north )
1262	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
1263	id_stg_south, id_stg_north )
1264	ENDIF
1265	velocity_seed_initialized = .TRUE.
1266	ENDIF
1267	!
1268	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
1269	!-- seeds are only required at the left boundary, while in case of offline
1270	!-- nesting or RANS-LES nesting velocity seeds are required also at the
1271	!-- right, south and north boundaries.
1272	IF ( stg_call ) THEN
1273	IF ( .NOT. ( nesting_offline .OR. &
1274	( child_domain .AND. rans_mode_parent &
1275	.AND. .NOT. rans_mode ) ) ) THEN
1276	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1277	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1278	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1279
1280	ELSE
1281	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
1282	id_stg_left, id_stg_right )
1283	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
1284	id_stg_left, id_stg_right )
1285	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
1286	id_stg_left, id_stg_right )
1287
1288	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
1289	id_stg_south, id_stg_north )
1290	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
1291	id_stg_south, id_stg_north )
1292	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
1293	id_stg_south, id_stg_north )
1294	ENDIF
1295	ENDIF
1296
1297	!
1298	!-- Turbulence generation at left and/or right boundary
1299	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1300	!
1301	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1302	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1303	!-- imposed
1304	IF ( stg_call ) THEN
1305
1306	DO j = nysg, nyng
1307	DO k = nzb, nzt + 1
1308	!
1309	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1310	IF ( tu(k) == 0.0_wp ) THEN
1311	fu_yz(k,j) = fuo_yz(k,j)
1312	ELSE
1313	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1314	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1315	ENDIF
1316
1317	IF ( tv(k) == 0.0_wp ) THEN
1318	fv_yz(k,j) = fvo_yz(k,j)
1319	ELSE
1320	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1321	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1322	ENDIF
1323
1324	IF ( tw(k) == 0.0_wp ) THEN
1325	fw_yz(k,j) = fwo_yz(k,j)
1326	ELSE
1327	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1328	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1329	ENDIF
1330	ENDDO
1331	ENDDO
1332
1333	dist_yz(nzb,:,1) = 0.0_wp
1334	dist_yz(nzb,:,2) = 0.0_wp
1335	dist_yz(nzb,:,3) = 0.0_wp
1336
1337	IF ( myidx == id_stg_left ) i = nxl
1338	IF ( myidx == id_stg_right ) i = nxr+1
1339	DO j = nysg, nyng
1340	DO k = nzb+1, nzt + 1
1341	!
1342	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1343	!-- Additional factors are added to improve the variance of v and w
1344	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1345	MERGE( 1.0_wp, 0.0_wp, &
1346	BTEST( wall_flags_static_0(k,j,i), 1 ) )
1347	ENDDO
1348	ENDDO
1349
1350	IF ( myidx == id_stg_left ) i = nxl-1
1351	IF ( myidx == id_stg_right ) i = nxr+1
1352	DO j = nysg, nyng
1353	DO k = nzb+1, nzt + 1
1354	!
1355	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1356	!-- Additional factors are added to improve the variance of v and w
1357	!-- experimental test of 1.2
1358	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1359	* 1.2_wp ) &
1360	* ( a21(k) * fu_yz(k,j) &
1361	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1362	MERGE( 1.0_wp, 0.0_wp, &
1363	BTEST( wall_flags_static_0(k,j,i), 2 ) )
1364	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1365	* 1.3_wp ) &
1366	* ( a31(k) * fu_yz(k,j) &
1367	+ a32(k) * fv_yz(k,j) &
1368	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1369	MERGE( 1.0_wp, 0.0_wp, &
1370	BTEST( wall_flags_static_0(k,j,i), 3 ) )
1371	ENDDO
1372	ENDDO
1373	ENDIF
1374	!
1375	!-- Mass flux correction following Kim et al. (2013)
1376	!-- This correction factor insures that the mass flux is preserved at the
1377	!-- inflow boundary. First, calculate mean value of the imposed
1378	!-- perturbations at yz boundary.
1379	!-- Note, this needs to be done only after the last RK3-substep, else
1380	!-- the boundary values won't be accessed.
1381	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1382	mc_factor_l = 0.0_wp
1383	mc_factor = 0.0_wp
1384	!
1385	!-- Sum up the original volume flows (with and without perturbations).
1386	!-- Note, for non-normal components (here v and w) it is actually no
1387	!-- volume flow.
1388	IF ( myidx == id_stg_left ) i = nxl
1389	IF ( myidx == id_stg_right ) i = nxr+1
1390
1391	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1392	* MERGE( 1.0_wp, 0.0_wp, &
1393	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1394
1395	IF ( myidx == id_stg_left ) i = nxl-1
1396	IF ( myidx == id_stg_right ) i = nxr+1
1397
1398	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1399	* MERGE( 1.0_wp, 0.0_wp, &
1400	BTEST( wall_flags_static_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1401	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1402	* MERGE( 1.0_wp, 0.0_wp, &
1403	BTEST( wall_flags_static_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1404
1405	#if defined( __parallel )
1406	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1407	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1408	#else
1409	mc_factor = mc_factor_l
1410	#endif
1411	!
1412	!-- Calculate correction factor and force zero mean perturbations.
1413	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1414
1415	IF ( myidx == id_stg_left ) i = nxl
1416	IF ( myidx == id_stg_right ) i = nxr+1
1417
1418	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
1419	* MERGE( 1.0_wp, 0.0_wp, &
1420	BTEST( wall_flags_static_0(:,:,i), 1 ) )
1421
1422
1423	IF ( myidx == id_stg_left ) i = nxl-1
1424	IF ( myidx == id_stg_right ) i = nxr+1
1425
1426	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
1427	* MERGE( 1.0_wp, 0.0_wp, &
1428	BTEST( wall_flags_static_0(:,:,i), 2 ) )
1429
1430	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
1431	* MERGE( 1.0_wp, 0.0_wp, &
1432	BTEST( wall_flags_static_0(:,:,i), 3 ) )
1433	!
1434	!-- Add disturbances
1435	IF ( myidx == id_stg_left ) THEN
1436	!
1437	!-- For the left boundary distinguish between mesoscale offline / self
1438	!-- nesting and turbulent inflow at the left boundary only. In the latter
1439	!-- case turbulence is imposed on the mean inflow profiles.
1440	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1441	!
1442	!-- Add disturbance at the inflow
1443	DO j = nysg, nyng
1444	DO k = nzb, nzt+1
1445	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1446	dist_yz(k,j,1) ) &
1447	* MERGE( 1.0_wp, 0.0_wp, &
1448	BTEST( wall_flags_static_0(k,j,0), 1 ) )
1449	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1450	dist_yz(k,j,2) ) &
1451	* MERGE( 1.0_wp, 0.0_wp, &
1452	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
1453	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1454	* MERGE( 1.0_wp, 0.0_wp, &
1455	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
1456	ENDDO
1457	ENDDO
1458	ELSE
1459
1460	DO j = nys, nyn
1461	DO k = nzb+1, nzt
1462	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1463	* MERGE( 1.0_wp, 0.0_wp, &
1464	BTEST( wall_flags_static_0(k,j,0), 1 ) )
1465	u(k,j,-1) = u(k,j,0)
1466	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1467	* MERGE( 1.0_wp, 0.0_wp, &
1468	BTEST( wall_flags_static_0(k,j,-1), 2 ) )
1469	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1470	* MERGE( 1.0_wp, 0.0_wp, &
1471	BTEST( wall_flags_static_0(k,j,-1), 3 ) )
1472	ENDDO
1473	ENDDO
1474	ENDIF
1475	ENDIF
1476	IF ( myidx == id_stg_right ) THEN
1477	DO j = nys, nyn
1478	DO k = nzb+1, nzt
1479	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1480	* MERGE( 1.0_wp, 0.0_wp, &
1481	BTEST( wall_flags_static_0(k,j,nxr+1), 1 ) )
1482	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1483	* MERGE( 1.0_wp, 0.0_wp, &
1484	BTEST( wall_flags_static_0(k,j,nxr+1), 2 ) )
1485	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1486	* MERGE( 1.0_wp, 0.0_wp, &
1487	BTEST( wall_flags_static_0(k,j,nxr+1), 3 ) )
1488	ENDDO
1489	ENDDO
1490	ENDIF
1491	ENDIF
1492	ENDIF
1493	!
1494	!-- Turbulence generation at north and south boundary
1495	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1496	!
1497	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1498	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1499	!-- imposed
1500	IF ( stg_call ) THEN
1501	DO i = nxlg, nxrg
1502	DO k = nzb, nzt + 1
1503	!
1504	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1505	IF ( tu(k) == 0.0_wp ) THEN
1506	fu_xz(k,i) = fuo_xz(k,i)
1507	ELSE
1508	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1509	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1510	ENDIF
1511
1512	IF ( tv(k) == 0.0_wp ) THEN
1513	fv_xz(k,i) = fvo_xz(k,i)
1514	ELSE
1515	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1516	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1517	ENDIF
1518
1519	IF ( tw(k) == 0.0_wp ) THEN
1520	fw_xz(k,i) = fwo_xz(k,i)
1521	ELSE
1522	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1523	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1524	ENDIF
1525	ENDDO
1526	ENDDO
1527
1528
1529	dist_xz(nzb,:,1) = 0.0_wp
1530	dist_xz(nzb,:,2) = 0.0_wp
1531	dist_xz(nzb,:,3) = 0.0_wp
1532
1533	IF ( myidy == id_stg_south ) j = nys
1534	IF ( myidy == id_stg_north ) j = nyn+1
1535	DO i = nxlg, nxrg
1536	DO k = nzb+1, nzt + 1
1537	!
1538	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1539	!-- Additional factors are added to improve the variance of v and w
1540	!experimental test of 1.2
1541	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1542	* 1.2_wp ) &
1543	* ( a21(k) * fu_xz(k,i) &
1544	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1545	MERGE( 1.0_wp, 0.0_wp, &
1546	BTEST( wall_flags_static_0(k,j,i), 2 ) )
1547	ENDDO
1548	ENDDO
1549
1550	IF ( myidy == id_stg_south ) j = nys-1
1551	IF ( myidy == id_stg_north ) j = nyn+1
1552	DO i = nxlg, nxrg
1553	DO k = nzb+1, nzt + 1
1554	!
1555	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1556	!-- Additional factors are added to improve the variance of v and w
1557	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1558	MERGE( 1.0_wp, 0.0_wp, &
1559	BTEST( wall_flags_static_0(k,j,i), 1 ) )
1560
1561	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1562	* 1.3_wp ) &
1563	* ( a31(k) * fu_xz(k,i) &
1564	+ a32(k) * fv_xz(k,i) &
1565	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1566	MERGE( 1.0_wp, 0.0_wp, &
1567	BTEST( wall_flags_static_0(k,j,i), 3 ) )
1568	ENDDO
1569	ENDDO
1570	ENDIF
1571
1572	!
1573	!-- Mass flux correction following Kim et al. (2013)
1574	!-- This correction factor insures that the mass flux is preserved at the
1575	!-- inflow boundary. First, calculate mean value of the imposed
1576	!-- perturbations at yz boundary.
1577	!-- Note, this needs to be done only after the last RK3-substep, else
1578	!-- the boundary values won't be accessed.
1579	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1580	mc_factor_l = 0.0_wp
1581	mc_factor = 0.0_wp
1582
1583	IF ( myidy == id_stg_south ) j = nys
1584	IF ( myidy == id_stg_north ) j = nyn+1
1585
1586	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1587	* MERGE( 1.0_wp, 0.0_wp, &
1588	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1589
1590	IF ( myidy == id_stg_south ) j = nys-1
1591	IF ( myidy == id_stg_north ) j = nyn+1
1592
1593	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1594	* MERGE( 1.0_wp, 0.0_wp, &
1595	BTEST( wall_flags_static_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1596	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1597	* MERGE( 1.0_wp, 0.0_wp, &
1598	BTEST( wall_flags_static_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1599
1600	#if defined( __parallel )
1601	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1602	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1603	#else
1604	mc_factor = mc_factor_l
1605	#endif
1606
1607	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1608
1609	IF ( myidy == id_stg_south ) j = nys
1610	IF ( myidy == id_stg_north ) j = nyn+1
1611
1612	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
1613	* MERGE( 1.0_wp, 0.0_wp, &
1614	BTEST( wall_flags_static_0(:,j,:), 2 ) )
1615
1616
1617	IF ( myidy == id_stg_south ) j = nys-1
1618	IF ( myidy == id_stg_north ) j = nyn+1
1619
1620	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
1621	* MERGE( 1.0_wp, 0.0_wp, &
1622	BTEST( wall_flags_static_0(:,j,:), 1 ) )
1623
1624	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
1625	* MERGE( 1.0_wp, 0.0_wp, &
1626	BTEST( wall_flags_static_0(:,j,:), 3 ) )
1627	!
1628	!-- Add disturbances
1629	IF ( myidy == id_stg_south ) THEN
1630	DO i = nxl, nxr
1631	DO k = nzb+1, nzt
1632	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1633	* MERGE( 1.0_wp, 0.0_wp, &
1634	BTEST( wall_flags_static_0(k,-1,i), 1 ) )
1635	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1636	* MERGE( 1.0_wp, 0.0_wp, &
1637	BTEST( wall_flags_static_0(k,0,i), 2 ) )
1638	v(k,-1,i) = v(k,0,i)
1639	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1640	* MERGE( 1.0_wp, 0.0_wp, &
1641	BTEST( wall_flags_static_0(k,-1,i), 3 ) )
1642	ENDDO
1643	ENDDO
1644	ENDIF
1645	IF ( myidy == id_stg_north ) THEN
1646
1647	DO i = nxl, nxr
1648	DO k = nzb+1, nzt
1649	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1650	* MERGE( 1.0_wp, 0.0_wp, &
1651	BTEST( wall_flags_static_0(k,nyn+1,i), 1 ) )
1652	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1653	* MERGE( 1.0_wp, 0.0_wp, &
1654	BTEST( wall_flags_static_0(k,nyn+1,i), 2 ) )
1655	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1656	* MERGE( 1.0_wp, 0.0_wp, &
1657	BTEST( wall_flags_static_0(k,nyn+1,i), 3 ) )
1658	ENDDO
1659	ENDDO
1660	ENDIF
1661	ENDIF
1662	ENDIF
1663	!
1664	!-- Finally, set time counter for calling STG to zero
1665	IF ( stg_call ) time_stg_call = 0.0_wp
1666
1667	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1668
1669	END SUBROUTINE stg_main
1670
1671	!------------------------------------------------------------------------------!
1672	! Description:
1673	! ------------
1674	!> Generate a set of random number rand_it wich is equal on each PE
1675	!> and calculate the velocity seed f_n.
1676	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1677	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1678	!> parts are collected to form the full array.
1679	!------------------------------------------------------------------------------!
1680	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
1681
1682	USE pegrid
1683
1684	IMPLICIT NONE
1685
1686	INTEGER(iwp) :: i !< grid index x-direction
1687	INTEGER(iwp) :: id_left !< core ids at respective boundaries
1688	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
1689	INTEGER(iwp) :: j !< loop index in y-direction
1690	INTEGER(iwp) :: jj !< loop index in y-direction
1691	INTEGER(iwp) :: k !< loop index in z-direction
1692	INTEGER(iwp) :: kk !< loop index in z-direction
1693	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1694
1695	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1696	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1697	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
1698	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1699
1700	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1701	REAL(wp) :: rand_av !< average of random number
1702	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1703
1704	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
1705	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1706
1707	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
1708	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
1709
1710	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1711	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
1712
1713	!
1714	!-- Generate random numbers using the parallel random generator.
1715	!-- The set of random numbers are modified to have an average of 0 and
1716	!-- unit variance. Note, at the end the random number array must be defined
1717	!-- globally in order to compute the correlation matrices. However,
1718	!-- the calculation and normalization of random numbers is done locally,
1719	!-- while the result is later distributed to all processes. Further,
1720	!-- please note, a set of random numbers is only calculated for the
1721	!-- left boundary, while the right boundary uses the same random numbers
1722	!-- and thus also computes the same correlation matrix.
1723	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
1724	rand_it = 0.0_wp
1725
1726	rand_av = 0.0_wp
1727	rand_sigma_inv = 0.0_wp
1728	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
1729	!
1730	!-- Compute and normalize random numbers only on left-boundary ranks.
1731	IF ( myidx == id_stg_left ) THEN
1732	!
1733	!-- Allocate array for local set of random numbers
1734	ALLOCATE( rand_it_l(nzb:nzt+1,nys:nyn) )
1735	rand_it_l = 0.0_wp
1736
1737	i = nxl
1738	DO j = nys, nyn
1739	!
1740	!-- Put the random seeds at grid point j,i
1741	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
1742	DO k = nzb, nzt+1
1743	CALL random_number_parallel( random_dummy )
1744	rand_it_l(k,j) = random_dummy
1745	rand_av = rand_av + rand_it_l(k,j)
1746	ENDDO
1747	!
1748	!-- Get the new random seeds from last call at grid point j,i
1749	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
1750	ENDDO
1751	#if defined( __parallel )
1752	!
1753	!-- Sum-up the local averages of the random numbers
1754	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1755	MPI_SUM, comm1dy, ierr )
1756	#endif
1757	rand_av = rand_av * nyz_inv
1758	!
1759	!-- Obtain zero mean
1760	rand_it_l = rand_it_l - rand_av
1761	!
1762	!-- Now, compute the variance
1763	DO j = nys, nyn
1764	DO k = nzb, nzt+1
1765	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,j)**2
1766	ENDDO
1767	ENDDO
1768
1769	#if defined( __parallel )
1770	!
1771	!-- Sum-up the local quadratic averages of the random numbers
1772	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1773	MPI_SUM, comm1dy, ierr )
1774	#endif
1775	!
1776	!-- Compute standard deviation
1777	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1778	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
1779	ELSE
1780	rand_sigma_inv = 1.0_wp
1781	ENDIF
1782	!
1783	!-- Normalize with standard deviation to obtain unit variance
1784	rand_it_l = rand_it_l * rand_sigma_inv
1785	!
1786	!-- Copy local random numbers on the global array
1787	rand_it(nzb:nzt+1,nys:nyn) = rand_it_l(nzb:nzt+1,nys:nyn)
1788	!
1789	!-- Deallocate local array
1790	DEALLOCATE( rand_it_l )
1791	!
1792	!-- Now, distribute the final set of random numbers to all mpi ranks located
1793	!-- on the left boundary. Here, an allreduce with sum reduction is sufficient,
1794	!-- or, in the non-parallel case, nothing need to be done at all.
1795	#if defined( __parallel )
1796	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1797	MPI_SUM, comm1dy, ierr )
1798	#endif
1799	ENDIF
1800	!
1801	!-- Finally, distribute the set of random numbers (defined on the leftmost-
1802	!-- located mpi ranks) to all other mpi ranks. Here, a allreduce with sum
1803	!-- option is sufficient, because rand_it is zero on all other mpi_ranks.
1804	!-- Note, the reduce operation is only performed with communicator comm1dx,
1805	!-- where only 1 rank within the communicator has non-zero random numbers.
1806	#if defined( __parallel )
1807	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1808	MPI_SUM, comm1dx, ierr )
1809	#endif
1810	!
1811	!-- Periodic fill of random numbers in space
1812	DO j = 0, ny
1813	DO k = 1, mergp
1814	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
1815	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
1816	ENDDO
1817	ENDDO
1818	DO j = 1, mergp
1819	DO k = nzb-mergp, nzt+1+mergp
1820	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
1821	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
1822	ENDDO
1823	ENDDO
1824
1825	!
1826	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1827	n_y2 = n_y * 2
1828	n_z2 = n_z * 2
1829	f_n_l = 0.0_wp
1830
1831	DO j = nysg, nyng
1832	DO k = nzb_x_stg, nzt_x_stg+1
1833	DO jj = -n_y2(k), n_y2(k)
1834	DO kk = -n_z2(k), n_z2(k)
1835	f_n_l(k,j) = f_n_l(k,j) &
1836	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1837	ENDDO
1838	ENDDO
1839	ENDDO
1840	ENDDO
1841
1842	DEALLOCATE( rand_it )
1843	!
1844	!-- Gather velocity seeds of full subdomain
1845	send_count = nzt_x_stg - nzb_x_stg + 1
1846	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1847
1848	#if defined( __parallel )
1849	!
1850	!-- Gather the velocity seed matrix on left boundary mpi ranks.
1851	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1852	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
1853	id_left, comm1dx, ierr )
1854	!
1855	!-- If required, gather the same velocity seed matrix on right boundary
1856	!-- mpi ranks (in offline nesting for example).
1857	IF ( PRESENT( id_right ) ) THEN
1858	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1859	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz,&
1860	id_right, comm1dx, ierr )
1861	ENDIF
1862	#else
1863	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
1864	#endif
1865
1866
1867	END SUBROUTINE stg_generate_seed_yz
1868
1869
1870	!------------------------------------------------------------------------------!
1871	! Description:
1872	! ------------
1873	!> Generate a set of random number rand_it wich is equal on each PE
1874	!> and calculate the velocity seed f_n.
1875	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1876	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1877	!> parts are collected to form the full array.
1878	!------------------------------------------------------------------------------!
1879	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
1880
1881	IMPLICIT NONE
1882
1883	INTEGER(iwp) :: i !< loop index in x-direction
1884	INTEGER(iwp) :: id_north !< core ids at respective boundaries
1885	INTEGER(iwp) :: id_south !< core ids at respective boundaries
1886	INTEGER(iwp) :: ii !< loop index in x-direction
1887	INTEGER(iwp) :: j !< grid index y-direction
1888	INTEGER(iwp) :: k !< loop index in z-direction
1889	INTEGER(iwp) :: kk !< loop index in z-direction
1890	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1891
1892	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1893	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1894	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
1895	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1896
1897	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1898	REAL(wp) :: rand_av !< average of random number
1899	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1900
1901	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
1902	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1903
1904	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
1905	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
1906
1907	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
1908	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it_l !< local array of random numbers
1909
1910	!
1911	!-- Generate random numbers using the parallel random generator.
1912	!-- The set of random numbers are modified to have an average of 0 and
1913	!-- unit variance. Note, at the end the random number array must be defined
1914	!-- globally in order to compute the correlation matrices. However,
1915	!-- the calculation and normalization of random numbers is done locally,
1916	!-- while the result is later distributed to all processes. Further,
1917	!-- please note, a set of random numbers is only calculated for the
1918	!-- left boundary, while the right boundary uses the same random numbers
1919	!-- and thus also computes the same correlation matrix.
1920	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
1921	rand_it = 0.0_wp
1922
1923	rand_av = 0.0_wp
1924	rand_sigma_inv = 0.0_wp
1925	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
1926	!
1927	!-- Compute and normalize random numbers only on south-boundary ranks.
1928	IF ( myidy == id_stg_south ) THEN
1929	!
1930	!-- Allocate array for local set of random numbers
1931	ALLOCATE( rand_it_l(nzb:nzt+1,nxl:nxr) )
1932	rand_it_l = 0.0_wp
1933
1934	j = nys
1935	DO i = nxl, nxr
1936	!
1937	!-- Put the random seeds at grid point j,i
1938	CALL random_seed_parallel( put=seq_random_array(:, j, i) )
1939	DO k = nzb, nzt+1
1940	CALL random_number_parallel( random_dummy )
1941	rand_it_l(k,i) = random_dummy
1942	rand_av = rand_av + rand_it_l(k,i)
1943	ENDDO
1944	!
1945	!-- Get the new random seeds from last call at grid point j,i
1946	CALL random_seed_parallel( get=seq_random_array(:, j, i) )
1947	ENDDO
1948	#if defined( __parallel )
1949	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
1950	MPI_SUM, comm1dx, ierr )
1951	#endif
1952	rand_av = rand_av * nxz_inv
1953	!
1954	!-- Obtain zero mean
1955	rand_it_l = rand_it_l - rand_av
1956	!
1957	!-- Now, compute the variance
1958	DO i = nxl, nxr
1959	DO k = nzb, nzt+1
1960	rand_sigma_inv = rand_sigma_inv + rand_it_l(k,i)**2
1961	ENDDO
1962	ENDDO
1963
1964	#if defined( __parallel )
1965	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
1966	MPI_SUM, comm1dx, ierr )
1967	#endif
1968	!
1969	!-- Compute standard deviation
1970	IF ( rand_sigma_inv /= 0.0_wp ) THEN
1971	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
1972	ELSE
1973	rand_sigma_inv = 1.0_wp
1974	ENDIF
1975	!
1976	!-- Normalize with standard deviation to obtain unit variance
1977	rand_it_l = rand_it_l * rand_sigma_inv
1978	!
1979	!-- Copy local random numbers on the global array
1980	rand_it(nzb:nzt+1,nxl:nxr) = rand_it_l(nzb:nzt+1,nxl:nxr)
1981	!
1982	!-- Deallocate local array
1983	DEALLOCATE( rand_it_l )
1984	!
1985	!-- Now, distribute the final set of random numbers to all mpi ranks located
1986	!-- on the south boundary. Here, an allreduce with sum reduction is sufficient.
1987	#if defined( __parallel )
1988	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
1989	MPI_SUM, comm1dx, ierr )
1990	#endif
1991	ENDIF
1992	!
1993	!-- Finally, distribute the set of random numbers (defined on the
1994	!-- southmost-located mpi ranks) to all other mpi ranks. Here, a allreduce
1995	!-- with sum option is sufficient, because rand_it is zero on all other
1996	!-- mpi_ranks. Note, the reduce operation is only performed with communicator
1997	!-- comm1dy, where only 1 rank within the communicator has non zero random numbers.
1998	#if defined( __parallel )
1999	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_it, SIZE( rand_it ), MPI_REAL, &
2000	MPI_SUM, comm1dy, ierr )
2001	#endif
2002	!
2003	!-- Periodic fill of random number in space
2004	DO i = 0, nx
2005	DO k = 1, mergp
2006	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
2007	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
2008	ENDDO
2009	ENDDO
2010	DO i = 1, mergp
2011	DO k = nzb-mergp, nzt+1+mergp
2012	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
2013	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
2014	ENDDO
2015	ENDDO
2016	!
2017	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
2018	n_x2 = n_x * 2
2019	n_z2 = n_z * 2
2020	f_n_l = 0.0_wp
2021
2022	DO i = nxlg, nxrg
2023	DO k = nzb_y_stg, nzt_y_stg+1
2024	DO ii = -n_x2(k), n_x2(k)
2025	DO kk = -n_z2(k), n_z2(k)
2026	f_n_l(k,i) = f_n_l(k,i) &
2027	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
2028	ENDDO
2029	ENDDO
2030	ENDDO
2031	ENDDO
2032
2033	DEALLOCATE( rand_it )
2034
2035	!
2036	!-- Gather velocity seeds of full subdomain
2037	send_count = nzt_y_stg - nzb_y_stg + 1
2038	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
2039
2040	#if defined( __parallel )
2041	!
2042	!-- Gather the processed velocity seed on south boundary mpi ranks.
2043	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
2044	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
2045	id_south, comm1dy, ierr )
2046	!
2047	!-- Gather the processed velocity seed on north boundary mpi ranks.
2048	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
2049	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
2050	id_north, comm1dy, ierr )
2051	#else
2052	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
2053	#endif
2054
2055	END SUBROUTINE stg_generate_seed_xz
2056
2057	!------------------------------------------------------------------------------!
2058	! Description:
2059	! ------------
2060	!> Parametrization of the Reynolds stress tensor, following the parametrization
2061	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2062	!> dispserion modelling. Please note, the parametrization does not distinguish
2063	!> between along-wind and cross-wind turbulence.
2064	!------------------------------------------------------------------------------!
2065	SUBROUTINE parametrize_reynolds_stress
2066
2067	IMPLICIT NONE
2068
2069	INTEGER(iwp) :: k !< loop index in z-direction
2070
2071	REAL(wp) :: zzi !< ratio of z/zi
2072
2073	DO k = nzb+1, nzt+1
2074	!
2075	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2076	!-- The function decreases to 1/10 after one length scale above the
2077	!-- ABL top.
2078	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2079	!
2080	!-- Determine normalized height coordinate
2081	zzi = zu(k) / zi_ribulk
2082	!
2083	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2084	!-- to the denominator, else the merge-function can crash if scale_l is
2085	!-- zero.
2086	r11(k) = scale_us*2 ( &
2087	MERGE( 0.35_wp * ABS( &
2088	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2089	)**( 2.0_wp / 3.0_wp ), &
2090	0.0_wp, &
2091	scale_l < 0.0_wp ) &
2092	+ 5.0_wp - 4.0_wp * zzi &
2093	) * blend
2094
2095	r22(k) = r11(k)
2096	!
2097	!-- w'w'
2098	r33(k) = scale_wm*2 ( &
2099	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2100	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2101	) * blend
2102	!
2103	!-- u'w' and v'w'. Assume isotropy.
2104	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2105	r32(k) = r31(k)
2106	!
2107	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2108	!-- a similar profile as for u'w'.
2109	r21(k) = r31(k)
2110	ENDDO
2111
2112	!
2113	!-- Set bottom boundary condition
2114	r11(nzb) = r11(nzb+1)
2115	r22(nzb) = r22(nzb+1)
2116	r33(nzb) = r33(nzb+1)
2117
2118	r21(nzb) = r11(nzb+1)
2119	r31(nzb) = r31(nzb+1)
2120	r32(nzb) = r32(nzb+1)
2121
2122
2123	END SUBROUTINE parametrize_reynolds_stress
2124
2125	!------------------------------------------------------------------------------!
2126	! Description:
2127	! ------------
2128	!> Calculate the coefficient matrix from the Lund rotation.
2129	!------------------------------------------------------------------------------!
2130	SUBROUTINE calc_coeff_matrix
2131
2132	IMPLICIT NONE
2133
2134	INTEGER(iwp) :: k !< loop index in z-direction
2135
2136	!
2137	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2138	DO k = nzb+1, nzt+1
2139	IF ( r11(k) > 10E-6_wp ) THEN
2140	a11(k) = SQRT( r11(k) )
2141	a21(k) = r21(k) / a11(k)
2142	a31(k) = r31(k) / a11(k)
2143	ELSE
2144	a11(k) = 10E-8_wp
2145	a21(k) = 10E-8_wp
2146	a31(k) = 10E-8_wp
2147	ENDIF
2148	ENDDO
2149	DO k = nzb+1, nzt+1
2150	a22(k) = r22(k) - a21(k)**2
2151	IF ( a22(k) > 10E-6_wp ) THEN
2152	a22(k) = SQRT( a22(k) )
2153	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2154	ELSE
2155	a22(k) = 10E-8_wp
2156	a32(k) = 10E-8_wp
2157	ENDIF
2158	ENDDO
2159	DO k = nzb+1, nzt+1
2160	a33(k) = r33(k) - a31(k)2 - a32(k)2
2161	IF ( a33(k) > 10E-6_wp ) THEN
2162	a33(k) = SQRT( a33(k) )
2163	ELSE
2164	a33(k) = 10E-8_wp
2165	ENDIF
2166	ENDDO
2167	!
2168	!-- Set bottom boundary condition
2169	a11(nzb) = a11(nzb+1)
2170	a22(nzb) = a22(nzb+1)
2171	a21(nzb) = a21(nzb+1)
2172	a33(nzb) = a33(nzb+1)
2173	a31(nzb) = a31(nzb+1)
2174	a32(nzb) = a32(nzb+1)
2175
2176	END SUBROUTINE calc_coeff_matrix
2177
2178	!------------------------------------------------------------------------------!
2179	! Description:
2180	! ------------
2181	!> This routine controls the re-adjustment of the turbulence statistics used
2182	!> for generating turbulence at the lateral boundaries.
2183	!------------------------------------------------------------------------------!
2184	SUBROUTINE stg_adjust
2185
2186	IMPLICIT NONE
2187
2188
2189	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2190	!
2191	!-- In case of dirichlet inflow boundary conditions only at one lateral
2192	!-- boundary, i.e. in the case no offline or self nesting is applied but
2193	!-- synthetic turbulence shall be parametrized nevertheless, the
2194	!-- boundary-layer depth need to determined first.
2195	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2196	CALL nesting_offl_calc_zi
2197	!
2198	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2199	!-- are calculated.
2200	CALL calc_scaling_variables
2201	!
2202	!-- Set length and time scales depending on boundary-layer height
2203	CALL calc_length_and_time_scale
2204	!
2205	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2206	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2207	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2208	!-- friction velocity and velocity scale.
2209	CALL parametrize_reynolds_stress
2210	!
2211	!-- Calculate coefficient matrix from Reynolds stress tensor
2212	!-- (Lund rotation)
2213	CALL calc_coeff_matrix
2214	!
2215	!-- Determine filter functions on basis of updated length scales
2216	CALL stg_filter_func( nux, bux ) !filter ux
2217	CALL stg_filter_func( nuy, buy ) !filter uy
2218	CALL stg_filter_func( nuz, buz ) !filter uz
2219	CALL stg_filter_func( nvx, bvx ) !filter vx
2220	CALL stg_filter_func( nvy, bvy ) !filter vy
2221	CALL stg_filter_func( nvz, bvz ) !filter vz
2222	CALL stg_filter_func( nwx, bwx ) !filter wx
2223	CALL stg_filter_func( nwy, bwy ) !filter wy
2224	CALL stg_filter_func( nwz, bwz ) !filter wz
2225	!
2226	!-- Reset time counter for controlling next adjustment to zero
2227	time_stg_adjust = 0.0_wp
2228
2229	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2230
2231	END SUBROUTINE stg_adjust
2232
2233
2234	!------------------------------------------------------------------------------!
2235	! Description:
2236	! ------------
2237	!> Calculates turbuluent length and time scales if these are not available
2238	!> from measurements.
2239	!------------------------------------------------------------------------------!
2240	SUBROUTINE calc_length_and_time_scale
2241
2242	IMPLICIT NONE
2243
2244
2245	INTEGER(iwp) :: k !< loop index in z-direction
2246
2247	REAL(wp) :: length_scale_dum !< effectively used length scale
2248
2249	!
2250	!-- In initial call the boundary-layer depth can be zero. This case, set
2251	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2252	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2253	!
2254	!-- Set-up default turbulent length scales. From the numerical point of
2255	!-- view the imposed perturbations should not be immediately dissipated
2256	!-- by the numerics. The numerical dissipation, however, acts on scales
2257	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2258	!-- length scale to 8 time the grid spacing. Further, above the boundary
2259	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2260	!-- imposing any perturbations) in order to save computational costs.
2261	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2262	!-- using the length scales and the mean profiles of u- and v-component.
2263	DO k = nzb+1, nzt+1
2264	!
2265	!-- Determine blending parameter. Within the boundary layer length scales
2266	!-- are constant, while above lengths scales approach gradully zero,
2267	!-- i.e. imposed turbulence is not correlated in space and time,
2268	!-- just white noise, which saves computations power as the loops for the
2269	!-- computation of the filter functions depend on the length scales.
2270	!-- The value decreases to 1/10 after one length scale above the
2271	!-- ABL top.
2272	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2273	!
2274	!-- Assume isotropic turbulence length scales
2275	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2276	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2277	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2278	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2279	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2280	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2281	!
2282	!-- Along the vertical direction limit the length scale further by the
2283	!-- boundary-layer depth to assure that no length scales larger than
2284	!-- the boundary-layer depth are used
2285	length_scale_dum = MIN( length_scale, zi_ribulk )
2286
2287	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2288	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2289	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2290	!
2291	!-- Limit time scales, else they become very larger for low wind speed,
2292	!-- imposing long-living inflow perturbations which in turn propagate
2293	!-- further into the model domain. Use u_init and v_init to calculate
2294	!-- the time scales, which will be equal to the inflow profiles, both,
2295	!-- in offline nesting mode or in dirichlet/radiation mode.
2296	tu(k) = MIN( dt_stg_adjust, length_scale / &
2297	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2298	tv(k) = MIN( dt_stg_adjust, length_scale / &
2299	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2300	!
2301	!-- Time scale of w-component is a mixture from u- and v-component.
2302	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2303
2304	ENDDO
2305	!
2306	!-- Set bottom boundary condition for the length and time scales
2307	nux(nzb) = nux(nzb+1)
2308	nuy(nzb) = nuy(nzb+1)
2309	nuz(nzb) = nuz(nzb+1)
2310	nvx(nzb) = nvx(nzb+1)
2311	nvy(nzb) = nvy(nzb+1)
2312	nvz(nzb) = nvz(nzb+1)
2313	nwx(nzb) = nwx(nzb+1)
2314	nwy(nzb) = nwy(nzb+1)
2315	nwz(nzb) = nwz(nzb+1)
2316
2317	tu(nzb) = tu(nzb+1)
2318	tv(nzb) = tv(nzb+1)
2319	tw(nzb) = tw(nzb+1)
2320
2321
2322	END SUBROUTINE calc_length_and_time_scale
2323
2324	!------------------------------------------------------------------------------!
2325	! Description:
2326	! ------------
2327	!> Calculate scaling variables which are used for turbulence parametrization
2328	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2329	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2330	!------------------------------------------------------------------------------!
2331	SUBROUTINE calc_scaling_variables
2332
2333	USE surface_mod, &
2334	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
2335
2336	IMPLICIT NONE
2337
2338	INTEGER(iwp) :: i !< loop index in x-direction
2339	INTEGER(iwp) :: j !< loop index in y-direction
2340	INTEGER(iwp) :: k !< loop index in z-direction
2341	INTEGER(iwp) :: m !< surface element index
2342
2343	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2344	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2345	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2346	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2347	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2348	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2349	REAL(wp) :: w_convective !< convective velocity scale
2350
2351	!
2352	!-- Calculate mean friction velocity, velocity scale, heat flux and
2353	!-- near-surface temperature in the model domain.
2354	pt_surf_mean_l = 0.0_wp
2355	shf_mean_l = 0.0_wp
2356	scale_l_l = 0.0_wp
2357	friction_vel_l = 0.0_wp
2358	DO m = 1, surf_def_h(0)%ns
2359	i = surf_def_h(0)%i(m)
2360	j = surf_def_h(0)%j(m)
2361	k = surf_def_h(0)%k(m)
2362	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2363	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2364	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2365	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2366	ENDDO
2367	DO m = 1, surf_lsm_h%ns
2368	i = surf_lsm_h%i(m)
2369	j = surf_lsm_h%j(m)
2370	k = surf_lsm_h%k(m)
2371	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2372	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2373	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2374	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2375	ENDDO
2376	DO m = 1, surf_usm_h%ns
2377	i = surf_usm_h%i(m)
2378	j = surf_usm_h%j(m)
2379	k = surf_usm_h%k(m)
2380	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2381	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2382	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2383	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2384	ENDDO
2385
2386	#if defined( __parallel )
2387	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2388	comm2d, ierr )
2389	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2390	comm2d, ierr )
2391	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2392	comm2d, ierr )
2393	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2394	comm2d, ierr )
2395	#else
2396	scale_us = friction_vel_l
2397	shf_mean = shf_mean_l
2398	scale_l = scale_l_l
2399	pt_surf_mean = pt_surf_mean_l
2400	#endif
2401
2402	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2403	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2404	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2405	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2406	!
2407	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2408	!-- is negative, set convective velocity scale to zero.
2409	IF ( shf_mean > 0.0_wp ) THEN
2410	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2411	ELSE
2412	w_convective = 0.0_wp
2413	ENDIF
2414	!
2415	!-- Finally, in order to consider also neutral or stable stratification,
2416	!-- compute momentum velocity scale from u* and convective velocity scale,
2417	!-- according to Rotach et al. (1996).
2418	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2419
2420	END SUBROUTINE calc_scaling_variables
2421
2422	END MODULE synthetic_turbulence_generator_mod

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