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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4051

Last change on this file since 4051 was 4022, checked in by suehring, 5 years ago
Synthetic turbulence generator: Revise bias correction of imposed perturbations (correction via volume flow can create instabilities in case the mean volume flow is close to zero); Introduce lower limits in calculation of coefficient matrix, else the calculation may become numerically unstable; Impose perturbations every timestep, even though no new set of perturbations is generated in case dt_stg_call /= dt_3d; Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1 length scale above ABL depth to 1/10) rather than an abrupt decline; Bugfix in non-nested case: use ABL height for parametrized turbulence; Offline nesting: Rename subroutine for ABL height calculation and make it public; Change top boundary condition for pressure back to Neumann
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File size: 99.0 KB

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1	!> @synthetic_turbulence_generator_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 2017-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: synthetic_turbulence_generator_mod.f90 4022 2019-06-12 11:52:39Z suehring $
27	! Several bugfixes and improvements
28	! - revise bias correction of the imposed perturbations (correction via volume
29	! flow can create instabilities in case the mean volume flow is close to zero)
30	! - introduce lower limits in calculation of coefficient matrix, else the
31	! calculation may become numerically unstable
32	! - impose perturbations every timestep, even though no new set of perturbations
33	! is generated in case dt_stg_call /= dt_3d
34	! - Implement a gradual decrease of Reynolds stress and length scales above
35	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
36	! discontinuous decrease
37	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
38	!
39	! 3987 2019-05-22 09:52:13Z kanani
40	! Introduce alternative switch for debug output during timestepping
41	!
42	! 3938 2019-04-29 16:06:25Z suehring
43	! Remove unused variables
44	!
45	! 3937 2019-04-29 15:09:07Z suehring
46	! Minor bugfix in case of a very early restart where mc_factor is sill not
47	! present.
48	! Some modification and fixing of potential bugs in the calculation of scaling
49	! parameters used for synthetic turbulence parametrization.
50	!
51	! 3909 2019-04-17 09:13:25Z suehring
52	! Minor bugfix for last commit
53	!
54	! 3900 2019-04-16 15:17:43Z suehring
55	! Missing re-calculation of perturbation seeds in case of restarts
56	!
57	! 3891 2019-04-12 17:52:01Z suehring
58	! Bugfix in initialization in case of restart runs.
59	!
60	! 3885 2019-04-11 11:29:34Z kanani
61	! Changes related to global restructuring of location messages and introduction
62	! of additional debug messages
63	!
64	!
65	! removed unused variables
66	!
67	! 3719 2019-02-06 13:10:18Z kanani
68	! Removed log_point measurement from stg_init, since this part is counted to
69	! log_point(2) 'initialisation' already. Moved other log_points to calls of
70	! the subroutines in time_integration for better overview.
71	!
72	! 3646 2018-12-28 17:58:49Z kanani
73	! Bugfix: use time_since_reference_point instead of simulated_time (relevant
74	! when using wall/soil spinup)
75	!
76	! 3579 2018-11-29 15:32:39Z suehring
77	! - Bugfix in calculation of turbulence scaling parameters for turbulence
78	! generator in case of topography
79	! - Additional checks implemented - no STG in RANS-RANS nesting or LES-LES
80	! nesting
81	!
82	! 3376 2018-10-19 10:15:32Z suehring
83	! Error messages and numbers reivsed.
84	!
85	! 3349 2018-10-15 16:39:41Z suehring
86	! Fix for format descriptor
87	!
88	! 3348 2018-10-15 14:30:51Z suehring
89	! - Revise structure of init routine
90	! - introduce new parameters to skip STG for some timesteps
91	! - introduce time-dependent parametrization of Reynolds-stress tensor
92	! - Bugfix in allocation of mean_inflow_profiles
93	!
94	! 3341 2018-10-15 10:31:27Z suehring
95	! Introduce module parameter for number of inflow profiles
96	!
97	! 3288 2018-09-28 10:23:08Z suehring
98	! Modularization of all bulk cloud physics code components
99	!
100	! 3248 2018-09-14 09:42:06Z sward
101	! Minor formating changes
102	!
103	! 3246 2018-09-13 15:14:50Z sward
104	! Added error handling for input namelist via parin_fail_message
105	!
106	! 3241 2018-09-12 15:02:00Z raasch
107	! unused variables removed
108	!
109	! 3186 2018-07-30 17:07:14Z suehring
110	! Mask topography while imposing inflow perturbations at the boundaries; do not
111	! impose perturbations at top boundary as well as ghost points
112	!
113	! 3183 2018-07-27 14:25:55Z suehring
114	! Rename variables and extend error message
115	! Enable geneartor also for stretched grids
116	!
117	! 3182 2018-07-27 13:36:03Z suehring
118	! Error message related to vertical stretching has been added, dz was replaced
119	! by dz(1)
120	!
121	! 3051 2018-05-30 17:43:55Z suehring
122	! Bugfix in calculation of initial Reynolds-stress tensor.
123	!
124	! 3045 2018-05-28 07:55:41Z Giersch
125	! Error messages revised
126	!
127	! 3044 2018-05-25 10:59:41Z gronemeier
128	! Add missing variable descriptions
129	!
130	! 3038 2018-05-24 10:54:00Z gronemeier
131	! updated variable descriptions
132	!
133	! 2967 2018-04-13 11:22:08Z raasch
134	! bugfix: missing parallel cpp-directives added
135	!
136	! 2946 2018-04-04 17:01:23Z suehring
137	! Remove unused module load
138	!
139	! 2945 2018-04-04 16:27:14Z suehring
140	! - Bugfix in parallelization of synthetic turbulence generator in case the
141	! z-dimension is not an integral divisor of the number of processors along
142	! the x- and y-dimension
143	! - Revision in control mimic in case of RAN-LES nesting
144	!
145	! 2938 2018-03-27 15:52:42Z suehring
146	! Apply turbulence generator at all non-cyclic lateral boundaries in case of
147	! realistic Inifor large-scale forcing or RANS-LES nesting
148	!
149	! 2936 2018-03-27 14:49:27Z suehring
150	! variable named found has been introduced for checking if restart data was found,
151	! reading of restart strings has been moved completely to read_restart_data_mod,
152	! redundant skipping function has been removed, stg_read/write_restart_data
153	! have been renamed to stg_r/wrd_global, stg_rrd_global is called in
154	! read_restart_data_mod now, flag syn_turb_gen_prerun and marker *** end stg
155	! *** have been removed (Giersch), strings and their respective lengths are
156	! written out and read now in case of restart runs to get rid of prescribed
157	! character lengths (Giersch), CASE DEFAULT was added if restart data is read
158	!
159	! 2841 2018-02-27 15:02:57Z suehring
160	! Bugfix: wrong placement of include 'mpif.h' corrected
161	!
162	! 2836 2018-02-26 13:40:05Z Giersch
163	! The variables synthetic_turbulence_generator and
164	! use_synthetic_turbulence_generator have been abbreviated + syn_turb_gen_prerun
165	! flag is used to define if module related parameters were outputted as restart
166	! data
167	!
168	! 2716 2017-12-29 16:35:59Z kanani
169	! Corrected "Former revisions" section
170	!
171	! 2696 2017-12-14 17:12:51Z kanani
172	! Change in file header (GPL part)
173	!
174	! 2669 2017-12-06 16:03:27Z raasch
175	! unit number for file containing turbulence generator data changed to 90
176	! bugfix: preprocessor directives added for MPI specific code
177	!
178	! 2576 2017-10-24 13:49:46Z Giersch
179	! Definition of a new function called stg_skip_global to skip module
180	! parameters during reading restart data
181	!
182	! 2563 2017-10-19 15:36:10Z Giersch
183	! stg_read_restart_data is called in stg_parin in the case of a restart run
184	!
185	! 2259 2017-06-08 09:09:11Z gronemeier
186	! Initial revision
187	!
188	!
189	!
190	! Authors:
191	! --------
192	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
193	!
194	!
195	!
196	! Description:
197	! ------------
198	!> The module generates turbulence at the inflow boundary based on a method by
199	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
200	!> correction by Kim et al. (2013).
201	!> The turbulence is correlated based on length scales in y- and z-direction and
202	!> a time scale for each velocity component. The profiles of length and time
203	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
204	!> tensor can be either read from file STG_PROFILES, or will be parametrized
205	!> within the boundary layer.
206	!>
207	!> @todo test restart
208	!> enable cyclic_fill
209	!> implement turbulence generation for e and pt
210	!> @todo Input of height-constant length scales via namelist
211	!> @note <Enter notes on the module>
212	!> @bug Height information from input file is not used. Profiles from input
213	!> must match with current PALM grid.
214	!> In case of restart, velocity seeds differ from precursor run if a11,
215	!> a22, or a33 are zero.
216	!------------------------------------------------------------------------------!
217	MODULE synthetic_turbulence_generator_mod
218
219
220	USE arrays_3d, &
221	ONLY: dzw, &
222	ddzw, &
223	drho_air, &
224	mean_inflow_profiles, &
225	q, &
226	pt, &
227	u, &
228	u_init, &
229	v, &
230	v_init, &
231	w, &
232	zu, &
233	zw
234
235	USE basic_constants_and_equations_mod, &
236	ONLY: g, &
237	kappa, &
238	pi
239
240	USE control_parameters, &
241	ONLY: bc_lr, &
242	bc_ns, &
243	child_domain, &
244	coupling_char, &
245	debug_output_timestep, &
246	dt_3d, &
247	e_init, &
248	initializing_actions, &
249	intermediate_timestep_count, &
250	intermediate_timestep_count_max, &
251	length, &
252	message_string, &
253	nesting_offline, &
254	num_mean_inflow_profiles, &
255	rans_mode, &
256	restart_string, &
257	syn_turb_gen, &
258	time_since_reference_point, &
259	turbulent_inflow
260
261	USE grid_variables, &
262	ONLY: ddx, &
263	ddy, &
264	dx, &
265	dy
266
267	USE indices, &
268	ONLY: nbgp, &
269	nz, &
270	nzb, &
271	nzt, &
272	nx, &
273	nxl, &
274	nxlu, &
275	nxlg, &
276	nxr, &
277	nxrg, &
278	ny, &
279	nys, &
280	nysv, &
281	nyn, &
282	nyng, &
283	nysg, &
284	wall_flags_0
285
286	USE kinds
287
288	#if defined( __parallel ) && !defined( __mpifh )
289	USE MPI
290	#endif
291
292	USE nesting_offl_mod, &
293	ONLY: nesting_offl_calc_zi, &
294	zi_ribulk
295
296	USE pegrid, &
297	ONLY: comm1dx, &
298	comm1dy, &
299	comm2d, &
300	ierr, &
301	myidx, &
302	myidy, &
303	pdims
304
305	USE pmc_interface, &
306	ONLY : rans_mode_parent
307
308	USE transpose_indices, &
309	ONLY: nzb_x, &
310	nzt_x
311
312
313	IMPLICIT NONE
314
315	#if defined( __parallel ) && defined( __mpifh )
316	INCLUDE "mpif.h"
317	#endif
318
319
320	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
321	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
322	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
323
324	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
325	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
326	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
327	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
328	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
329	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
330	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
331	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
332	INTEGER(iwp) :: merg !< maximum length scale (in gp)
333	INTEGER(iwp) :: mergp !< merg + nbgp
334	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
335	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
336	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
337	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
338
339	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
340	!< required for bias correction of imposed perturbations
341	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
342	!< required for bias correction of imposed perturbations
343
344	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
345	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
346	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
347	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
348	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
349	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
350	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
351	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
352	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
353	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
354	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
355	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
356	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
357	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed !< seed of random number for rn-generator
358
359	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
360	!< scales above the boundary layer
361	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
362	!< one length scale above ABL top
363	REAL(wp) :: d_l !< blend_coeff/length_scale
364	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
365	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
366	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
367	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
368	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
369	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
370	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
371	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
372
373	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
374
375
376	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
377	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
378	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
379	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
380	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
381	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
382
383	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
384	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
385	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
386	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
387	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
388	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
389	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
390	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
391	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
392
393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
414
415	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
416	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
417
418	!
419	!-- PALM interfaces:
420	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
421	INTERFACE stg_adjust
422	MODULE PROCEDURE stg_adjust
423	END INTERFACE stg_adjust
424	!
425	!-- Input parameter checks to be done in check_parameters
426	INTERFACE stg_check_parameters
427	MODULE PROCEDURE stg_check_parameters
428	END INTERFACE stg_check_parameters
429
430	!
431	!-- Calculate filter functions
432	INTERFACE stg_filter_func
433	MODULE PROCEDURE stg_filter_func
434	END INTERFACE stg_filter_func
435
436	!
437	!-- Generate velocity seeds at south and north domain boundary
438	INTERFACE stg_generate_seed_xz
439	MODULE PROCEDURE stg_generate_seed_xz
440	END INTERFACE stg_generate_seed_xz
441	!
442	!-- Generate velocity seeds at left and/or right domain boundary
443	INTERFACE stg_generate_seed_yz
444	MODULE PROCEDURE stg_generate_seed_yz
445	END INTERFACE stg_generate_seed_yz
446
447	!
448	!-- Output of information to the header file
449	INTERFACE stg_header
450	MODULE PROCEDURE stg_header
451	END INTERFACE stg_header
452
453	!
454	!-- Initialization actions
455	INTERFACE stg_init
456	MODULE PROCEDURE stg_init
457	END INTERFACE stg_init
458
459	!
460	!-- Main procedure of synth. turb. gen.
461	INTERFACE stg_main
462	MODULE PROCEDURE stg_main
463	END INTERFACE stg_main
464
465	!
466	!-- Reading of NAMELIST parameters
467	INTERFACE stg_parin
468	MODULE PROCEDURE stg_parin
469	END INTERFACE stg_parin
470
471	!
472	!-- Reading of parameters for restart runs
473	INTERFACE stg_rrd_global
474	MODULE PROCEDURE stg_rrd_global
475	END INTERFACE stg_rrd_global
476
477	!
478	!-- Writing of binary output for restart runs
479	INTERFACE stg_wrd_global
480	MODULE PROCEDURE stg_wrd_global
481	END INTERFACE stg_wrd_global
482
483	SAVE
484
485	PRIVATE
486
487	!
488	!-- Public interfaces
489	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
490	stg_parin, stg_rrd_global, stg_wrd_global
491
492	!
493	!-- Public variables
494	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
495	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
496	time_stg_adjust, time_stg_call, use_syn_turb_gen
497
498
499	CONTAINS
500
501
502	!------------------------------------------------------------------------------!
503	! Description:
504	! ------------
505	!> Check parameters routine for synthetic turbulence generator
506	!------------------------------------------------------------------------------!
507	SUBROUTINE stg_check_parameters
508
509	IMPLICIT NONE
510
511	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
512	nesting_offline ) THEN
513	message_string = 'Synthetic turbulence generator is required ' // &
514	'if offline nesting is applied and PALM operates ' // &
515	'in LES mode.'
516	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
517	ENDIF
518
519	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
520	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
521	message_string = 'Synthetic turbulence generator is required ' // &
522	'when nesting is applied and parent operates in ' // &
523	'RANS-mode but current child in LES mode.'
524	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
525	ENDIF
526
527	IF ( use_syn_turb_gen ) THEN
528
529	IF ( child_domain .AND. .NOT. rans_mode .AND. &
530	.NOT. rans_mode_parent ) THEN
531	message_string = 'Using synthetic turbulence generator ' // &
532	'is not allowed in LES-LES nesting.'
533	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
534
535	ENDIF
536
537	IF ( child_domain .AND. rans_mode .AND. &
538	rans_mode_parent ) THEN
539	message_string = 'Using synthetic turbulence generator ' // &
540	'is not allowed in RANS-RANS nesting.'
541	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
542
543	ENDIF
544
545	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
546
547	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
548	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
549	message_string = 'Using synthetic turbulence generator ' // &
550	'requires %initializing_actions = ' // &
551	'"set_constant_profiles" or "read_restart_data"' //&
552	', if not offline nesting is applied.'
553	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
554	ENDIF
555
556	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
557	message_string = 'Using synthetic turbulence generator ' // &
558	'requires &bc_lr = "dirichlet/radiation", ' // &
559	'if not offline nesting is applied.'
560	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
561	ENDIF
562	IF ( bc_ns /= 'cyclic' ) THEN
563	message_string = 'Using synthetic turbulence generator ' // &
564	'requires &bc_ns = "cyclic", ' // &
565	'if not offline nesting is applied.'
566	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
567	ENDIF
568
569	ENDIF
570
571	IF ( turbulent_inflow ) THEN
572	message_string = 'Using synthetic turbulence generator ' // &
573	'in combination &with turbulent_inflow = .T. '// &
574	'is not allowed'
575	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
576	ENDIF
577
578	ENDIF
579
580	END SUBROUTINE stg_check_parameters
581
582
583	!------------------------------------------------------------------------------!
584	! Description:
585	! ------------
586	!> Header output for synthetic turbulence generator
587	!------------------------------------------------------------------------------!
588	SUBROUTINE stg_header ( io )
589
590
591	IMPLICIT NONE
592
593	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
594
595	!
596	!-- Write synthetic turbulence generator Header
597	WRITE( io, 1 )
598	IF ( use_syn_turb_gen ) THEN
599	WRITE( io, 2 )
600	ELSE
601	WRITE( io, 3 )
602	ENDIF
603
604	IF ( parametrize_inflow_turbulence ) THEN
605	WRITE( io, 4 ) dt_stg_adjust
606	ELSE
607	WRITE( io, 5 )
608	ENDIF
609
610	1 FORMAT (//' Synthetic turbulence generator information:'/ &
611	' ------------------------------------------'/)
612	2 FORMAT (' synthetic turbulence generator is switched on')
613	3 FORMAT (' synthetic turbulence generator is switched off')
614	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
615	5 FORMAT (' imposed turbulence is read from file' )
616
617	END SUBROUTINE stg_header
618
619
620	!------------------------------------------------------------------------------!
621	! Description:
622	! ------------
623	!> Initialization of the synthetic turbulence generator
624	!------------------------------------------------------------------------------!
625	SUBROUTINE stg_init
626
627	IMPLICIT NONE
628
629	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
630
631	#if defined( __parallel )
632	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
633	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
634	#endif
635
636	INTEGER(iwp) :: i !> grid index in x-direction
637	INTEGER(iwp) :: j !> loop index
638	INTEGER(iwp) :: k !< index
639	INTEGER(iwp) :: newtype !< dummy MPI type
640	INTEGER(iwp) :: realsize !< size of REAL variables
641	INTEGER(iwp) :: nseed !< dimension of random number seed
642	INTEGER(iwp) :: startseed = 1234567890 !< start seed for random number generator
643
644	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
645	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
646	!
647	!-- Dummy variables used for reading profiles
648	REAL(wp) :: d1 !< u profile
649	REAL(wp) :: d2 !< v profile
650	REAL(wp) :: d3 !< w profile
651	REAL(wp) :: d5 !< e profile
652	REAL(wp) :: luy !< length scale for u in y direction
653	REAL(wp) :: luz !< length scale for u in z direction
654	REAL(wp) :: lvy !< length scale for v in y direction
655	REAL(wp) :: lvz !< length scale for v in z direction
656	REAL(wp) :: lwy !< length scale for w in y direction
657	REAL(wp) :: lwz !< length scale for w in z direction
658	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
659	REAL(wp) :: zz !< height
660
661
662	#if defined( __parallel )
663	CALL MPI_BARRIER( comm2d, ierr )
664	#endif
665
666	#if defined( __parallel )
667	!
668	!-- Determine processor decomposition of z-axis along x- and y-direction
669	nnz = nz / pdims(1)
670	nzb_x_stg = 1 + myidx * INT( nnz )
671	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
672
673	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
674	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
675
676	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
677	.AND. .NOT. rans_mode ) ) THEN
678	nnz = nz / pdims(2)
679	nzb_y_stg = 1 + myidy * INT( nnz )
680	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
681
682	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
683	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
684	ENDIF
685
686	!
687	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
688	!-- velocity seeds
689	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
690	extent = 1 * realsize
691	!
692	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
693	!-- layer
694	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
695	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
696	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
697	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
698	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
699	CALL MPI_TYPE_FREE( newtype, ierr )
700
701	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
702	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
703	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
704	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
705	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
706	CALL MPI_TYPE_FREE( newtype, ierr )
707
708	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
709	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
710
711	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
712	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
713
714	DO j = 1, pdims(1)
715	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
716	ENDDO
717	!
718	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
719	!-- layer
720	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
721	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
722	.AND. .NOT. rans_mode ) ) THEN
723	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
724	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
725	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
726	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
727	CALL MPI_TYPE_FREE( newtype, ierr )
728
729	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
730	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
731	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
732	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
733	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
734	CALL MPI_TYPE_FREE( newtype, ierr )
735
736	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
737	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
738
739	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
740	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
741
742	DO j = 1, pdims(2)
743	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
744	ENDDO
745
746	ENDIF
747
748	#endif
749	!
750	!-- Define seed of random number
751	CALL RANDOM_SEED()
752	CALL RANDOM_SEED( size=nseed )
753	ALLOCATE( seed(1:nseed) )
754	DO j = 1, nseed
755	seed(j) = startseed + j
756	ENDDO
757	CALL RANDOM_SEED(put=seed)
758	!
759	!-- Allocate required arrays
760	!-- mean_inflow profiles must not be allocated in offline nesting
761	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
762	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) &
763	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
764	ENDIF
765
766	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
767	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
768	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
769	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
770	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
771	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
772	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
773	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
774
775	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
776	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
777	dist_xz = 0.0_wp
778	dist_yz = 0.0_wp
779	!
780	!-- Read inflow profile
781	!-- Height levels of profiles in input profile is as follows:
782	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
783	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
784	!-- WARNING: zz is not used at the moment
785	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
786	EXIST = file_stg_exist )
787
788	IF ( file_stg_exist ) THEN
789
790	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
791	FORM='FORMATTED')
792	!
793	!-- Skip header
794	READ( 90, * )
795
796	DO k = nzb+1, nzt+1
797	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
798	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
799	d1, d2, d3, d5
800
801	!
802	!-- Convert length scales from meter to number of grid points.
803	nuy(k) = INT( luy * ddy )
804	nuz(k) = INT( luz * ddzw(k) )
805	nvy(k) = INT( lvy * ddy )
806	nvz(k) = INT( lvz * ddzw(k) )
807	nwy(k) = INT( lwy * ddy )
808	nwz(k) = INT( lwz * ddzw(k) )
809	!
810	!-- Workaround, assume isotropic turbulence
811	nwx(k) = nwy(k)
812	nvx(k) = nvy(k)
813	nux(k) = nuy(k)
814	!
815	!-- Save Mean inflow profiles
816	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
817	mean_inflow_profiles(k,1) = d1
818	mean_inflow_profiles(k,2) = d2
819	! mean_inflow_profiles(k,4) = d4
820	mean_inflow_profiles(k,5) = d5
821	ENDIF
822	ENDDO
823	!
824	!-- Set lenght scales at surface grid point
825	nuy(nzb) = nuy(nzb+1)
826	nuz(nzb) = nuz(nzb+1)
827	nvy(nzb) = nvy(nzb+1)
828	nvz(nzb) = nvz(nzb+1)
829	nwy(nzb) = nwy(nzb+1)
830	nwz(nzb) = nwz(nzb+1)
831
832	CLOSE( 90 )
833	!
834	!-- Calculate coefficient matrix from Reynolds stress tensor
835	!-- (Lund rotation)
836	CALL calc_coeff_matrix
837	!
838	!-- No information about turbulence and its length scales are available.
839	!-- Instead, parametrize turbulence which is imposed at the boundaries.
840	!-- Set flag which indicates that turbulence is parametrized, which is done
841	!-- later when energy-balance models are already initialized. This is
842	!-- because the STG needs information about surface properties such as
843	!-- roughness to build 'realistic' turbulence profiles.
844	ELSE
845	!
846	!-- Define length scale for the imposed turbulence, which is defined as
847	!-- 8 times the minimum grid spacing
848	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
849	!
850	!-- Define constant to gradually decrease length scales and Reynolds stress
851	!-- above ABL top. Assure that no zero length scales are used.
852	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
853	!
854	!-- Set flag indicating that turbulence is parametrized
855	parametrize_inflow_turbulence = .TRUE.
856	!
857	!-- In case of dirichlet inflow boundary conditions only at one lateral
858	!-- boundary, i.e. in the case no offline or self nesting is applied but
859	!-- synthetic turbulence shall be parametrized nevertheless, the
860	!-- boundary-layer depth need to determined first.
861	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
862	CALL nesting_offl_calc_zi
863	!
864	!-- Determine boundary-layer depth, which is used to initialize lenght
865	!-- scales
866	CALL calc_scaling_variables
867	!
868	!-- Initialize lenght and time scales, which in turn are used
869	!-- to initialize the filter functions.
870	CALL calc_length_and_time_scale
871	!
872	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
873	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
874	!-- Rotach et al. (1996) and is based on boundary-layer depth,
875	!-- friction velocity and velocity scale.
876	CALL parametrize_reynolds_stress
877	!
878	!-- Calculate coefficient matrix from Reynolds stress tensor
879	!-- (Lund rotation)
880	CALL calc_coeff_matrix
881
882	ENDIF
883
884	!
885	!-- Assign initial profiles. Note, this is only required if turbulent
886	!-- inflow from the left is desired, not in case of any of the
887	!-- nesting (offline or self nesting) approaches.
888	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
889	u_init = mean_inflow_profiles(:,1)
890	v_init = mean_inflow_profiles(:,2)
891	!pt_init = mean_inflow_profiles(:,4)
892	e_init = MAXVAL( mean_inflow_profiles(:,5) )
893	ENDIF
894
895	!
896	!-- Define the size of the filter functions and allocate them.
897	merg = 0
898
899	! arrays must be large enough to cover the largest length scale
900	DO k = nzb, nzt+1
901	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
902	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
903	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
904	IF ( j > merg ) merg = j
905	ENDDO
906
907	merg = 2 * merg
908	mergp = merg + nbgp
909
910	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
911	buy(-merg:merg,nzb:nzt+1), &
912	buz(-merg:merg,nzb:nzt+1), &
913	bvx(-merg:merg,nzb:nzt+1), &
914	bvy(-merg:merg,nzb:nzt+1), &
915	bvz(-merg:merg,nzb:nzt+1), &
916	bwx(-merg:merg,nzb:nzt+1), &
917	bwy(-merg:merg,nzb:nzt+1), &
918	bwz(-merg:merg,nzb:nzt+1) )
919
920	!
921	!-- Allocate velocity seeds for turbulence at xz-layer
922	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
923	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
924	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
925
926	!
927	!-- Allocate velocity seeds for turbulence at yz-layer
928	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
929	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
930	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
931
932	fu_xz = 0.0_wp
933	fuo_xz = 0.0_wp
934	fv_xz = 0.0_wp
935	fvo_xz = 0.0_wp
936	fw_xz = 0.0_wp
937	fwo_xz = 0.0_wp
938
939	fu_yz = 0.0_wp
940	fuo_yz = 0.0_wp
941	fv_yz = 0.0_wp
942	fvo_yz = 0.0_wp
943	fw_yz = 0.0_wp
944	fwo_yz = 0.0_wp
945
946	!
947	!-- Create filter functions
948	CALL stg_filter_func( nux, bux ) !filter ux
949	CALL stg_filter_func( nuy, buy ) !filter uy
950	CALL stg_filter_func( nuz, buz ) !filter uz
951	CALL stg_filter_func( nvx, bvx ) !filter vx
952	CALL stg_filter_func( nvy, bvy ) !filter vy
953	CALL stg_filter_func( nvz, bvz ) !filter vz
954	CALL stg_filter_func( nwx, bwx ) !filter wx
955	CALL stg_filter_func( nwy, bwy ) !filter wy
956	CALL stg_filter_func( nwz, bwz ) !filter wz
957
958	#if defined( __parallel )
959	CALL MPI_BARRIER( comm2d, ierr )
960	#endif
961
962	!
963	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
964	! time step.
965	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
966	! are 0 compared to the prerun. This is mostly for k=nzt+1.
967	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
968	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
969
970	IF ( myidx == id_stg_left ) i = -1
971	IF ( myidx == id_stg_right ) i = nxr+1
972
973	DO j = nysg, nyng
974	DO k = nzb, nzt+1
975	IF ( a11(k) .NE. 0._wp ) THEN
976	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
977	ELSE
978	fu_yz(k,j) = 0._wp
979	ENDIF
980
981	IF ( a22(k) .NE. 0._wp ) THEN
982	fv_yz(k,j) = ( v(k,j,i) - &
983	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
984	ELSE
985	fv_yz(k,j) = 0._wp
986	ENDIF
987
988	IF ( a33(k) .NE. 0._wp ) THEN
989	fw_yz(k,j) = ( w(k,j,i) - &
990	a31(k) * fu_yz(k,j) - a32(k) * &
991	fv_yz(k,j) ) / a33(k)
992	ELSE
993	fw_yz = 0._wp
994	ENDIF
995
996	ENDDO
997	ENDDO
998	ENDIF
999
1000	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1001
1002	IF ( myidy == id_stg_south ) j = -1
1003	IF ( myidy == id_stg_north ) j = nyn+1
1004
1005	DO i = nxlg, nxrg
1006	DO k = nzb, nzt+1
1007
1008	IF ( a11(k) .NE. 0._wp ) THEN
1009	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1010	ELSE
1011	fu_xz(k,i) = 0._wp
1012	ENDIF
1013
1014	IF ( a22(k) .NE. 0._wp ) THEN
1015	fv_xz(k,i) = ( v(k,j,i) - &
1016	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1017	ELSE
1018	fv_xz(k,i) = 0._wp
1019	ENDIF
1020
1021	IF ( a33(k) .NE. 0._wp ) THEN
1022	fw_xz(k,i) = ( w(k,j,i) - &
1023	a31(k) * fu_xz(k,i) - &
1024	a32(k) * fv_xz(k,i) ) / a33(k)
1025	ELSE
1026	fw_xz = 0._wp
1027	ENDIF
1028
1029	ENDDO
1030	ENDDO
1031	ENDIF
1032	ENDIF
1033	!
1034	!-- Count the number of non-topography grid points at the boundaries where
1035	!-- perturbations are imposed. This number is later used for bias corrections
1036	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1037	!-- due to the asymetry of u and v along x and y direction, respectively,
1038	!-- different cases must be distinguished.
1039	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1040	!
1041	!-- Number of grid points where perturbations are imposed on u
1042	IF ( myidx == id_stg_left ) i = nxl
1043	IF ( myidx == id_stg_right ) i = nxr+1
1044
1045	nr_non_topo_yz_l(1) = SUM( &
1046	MERGE( 1, 0, &
1047	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1048	!
1049	!-- Number of grid points where perturbations are imposed on v and w
1050	IF ( myidx == id_stg_left ) i = nxl-1
1051	IF ( myidx == id_stg_right ) i = nxr+1
1052
1053	nr_non_topo_yz_l(2) = SUM( &
1054	MERGE( 1, 0, &
1055	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1056	nr_non_topo_yz_l(3) = SUM( &
1057	MERGE( 1, 0, &
1058	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1059
1060	#if defined( __parallel )
1061	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1062	MPI_SUM, comm1dy, ierr )
1063	#else
1064	nr_non_topo_yz = nr_non_topo_yz_l
1065	#endif
1066	ENDIF
1067
1068	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1069	!
1070	!-- Number of grid points where perturbations are imposed on v
1071	IF ( myidy == id_stg_south ) j = nys
1072	IF ( myidy == id_stg_north ) j = nyn+1
1073
1074	nr_non_topo_xz_l(2) = SUM( &
1075	MERGE( 1, 0, &
1076	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1077	!
1078	!-- Number of grid points where perturbations are imposed on u and w
1079	IF ( myidy == id_stg_south ) j = nys-1
1080	IF ( myidy == id_stg_north ) j = nyn+1
1081
1082	nr_non_topo_xz_l(1) = SUM( &
1083	MERGE( 1, 0, &
1084	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1085	nr_non_topo_xz_l(3) = SUM( &
1086	MERGE( 1, 0, &
1087	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1088
1089	#if defined( __parallel )
1090	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1091	MPI_SUM, comm1dx, ierr )
1092	#else
1093	nr_non_topo_xz = nr_non_topo_xz_l
1094	#endif
1095	ENDIF
1096
1097
1098	END SUBROUTINE stg_init
1099
1100
1101	!------------------------------------------------------------------------------!
1102	! Description:
1103	! ------------
1104	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1105	!> (Xie and Castro, 2008)
1106	!------------------------------------------------------------------------------!
1107	SUBROUTINE stg_filter_func( nxx, bxx )
1108
1109
1110	IMPLICIT NONE
1111
1112	INTEGER(iwp) :: k !< loop index
1113	INTEGER(iwp) :: n_k !< length scale nXX in height k
1114	INTEGER(iwp) :: n_k2 !< n_k * 2
1115	INTEGER(iwp) :: nf !< index for length scales
1116
1117	REAL(wp) :: bdenom !< denominator for filter functions bXX
1118	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1119
1120	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
1121
1122	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
1123
1124
1125	bxx = 0.0_wp
1126
1127	DO k = nzb, nzt+1
1128	bdenom = 0.0_wp
1129	n_k = nxx(k)
1130	IF ( n_k /= 0 ) THEN
1131	n_k2 = n_k * 2
1132
1133	!
1134	!-- ( Eq.10 )^2
1135	DO nf = -n_k2, n_k2
1136	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1137	ENDDO
1138
1139	!
1140	!-- ( Eq.9 )
1141	bdenom = SQRT( bdenom )
1142	DO nf = -n_k2, n_k2
1143	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1144	ENDDO
1145	ENDIF
1146	ENDDO
1147
1148	END SUBROUTINE stg_filter_func
1149
1150
1151	!------------------------------------------------------------------------------!
1152	! Description:
1153	! ------------
1154	!> Parin for &stg_par for synthetic turbulence generator
1155	!------------------------------------------------------------------------------!
1156	SUBROUTINE stg_parin
1157
1158
1159	IMPLICIT NONE
1160
1161	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1162
1163
1164	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
1165
1166	line = ' '
1167
1168	!
1169	!-- Try to find stg package
1170	REWIND ( 11 )
1171	line = ' '
1172	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1173	READ ( 11, '(A)', END=20 ) line
1174	ENDDO
1175	BACKSPACE ( 11 )
1176
1177	!
1178	!-- Read namelist
1179	READ ( 11, stg_par, ERR = 10, END = 20 )
1180
1181	!
1182	!-- Set flag that indicates that the synthetic turbulence generator is switched
1183	!-- on
1184	syn_turb_gen = .TRUE.
1185	GOTO 20
1186
1187	10 BACKSPACE( 11 )
1188	READ( 11 , '(A)') line
1189	CALL parin_fail_message( 'stg_par', line )
1190
1191	20 CONTINUE
1192
1193	END SUBROUTINE stg_parin
1194
1195
1196	!------------------------------------------------------------------------------!
1197	! Description:
1198	! ------------
1199	!> This routine reads the respective restart data.
1200	!------------------------------------------------------------------------------!
1201	SUBROUTINE stg_rrd_global( found )
1202
1203
1204	IMPLICIT NONE
1205
1206	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1207
1208
1209	found = .TRUE.
1210
1211
1212	SELECT CASE ( restart_string(1:length) )
1213
1214	CASE ( 'time_stg_adjust' )
1215	READ ( 13 ) time_stg_adjust
1216
1217	CASE ( 'time_stg_call' )
1218	READ ( 13 ) time_stg_call
1219
1220	CASE ( 'use_syn_turb_gen' )
1221	READ ( 13 ) use_syn_turb_gen
1222
1223	CASE DEFAULT
1224
1225	found = .FALSE.
1226
1227	END SELECT
1228
1229
1230	END SUBROUTINE stg_rrd_global
1231
1232
1233	!------------------------------------------------------------------------------!
1234	! Description:
1235	! ------------
1236	!> This routine writes the respective restart data.
1237	!------------------------------------------------------------------------------!
1238	SUBROUTINE stg_wrd_global
1239
1240
1241	IMPLICIT NONE
1242
1243	CALL wrd_write_string( 'time_stg_adjust' )
1244	WRITE ( 14 ) time_stg_adjust
1245
1246	CALL wrd_write_string( 'time_stg_call' )
1247	WRITE ( 14 ) time_stg_call
1248
1249	CALL wrd_write_string( 'use_syn_turb_gen' )
1250	WRITE ( 14 ) use_syn_turb_gen
1251
1252
1253	END SUBROUTINE stg_wrd_global
1254
1255
1256	!------------------------------------------------------------------------------!
1257	! Description:
1258	! ------------
1259	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1260	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1261	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1262	!> (Lund, 1998).
1263	!------------------------------------------------------------------------------!
1264	SUBROUTINE stg_main
1265
1266	IMPLICIT NONE
1267
1268	INTEGER(iwp) :: i !< grid index in x-direction
1269	INTEGER(iwp) :: j !< loop index in y-direction
1270	INTEGER(iwp) :: k !< loop index in z-direction
1271
1272	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1273
1274	REAL(wp) :: dt_stg !< wheighted subtimestep
1275
1276	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1277
1278	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1279	!
1280	!-- Calculate time step which is needed for filter functions
1281	dt_stg = MAX( dt_3d, dt_stg_call )
1282	!
1283	!-- Check if synthetic turbulence generator needs to be called and new
1284	!-- perturbations need to be created or if old disturbances can be imposed
1285	!-- again.
1286	IF ( time_stg_call >= dt_stg_call .AND. &
1287	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1288	stg_call = .TRUE.
1289	ELSE
1290	stg_call = .FALSE.
1291	ENDIF
1292	!
1293	!-- Initial value of fu, fv, fw
1294	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1295	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1296	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1297	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1298
1299	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1300	.AND. .NOT. rans_mode ) ) THEN
1301	!
1302	!-- Generate turbulence at right boundary
1303	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_right )
1304	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_right )
1305	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_right )
1306	!
1307	!-- Generate turbulence at north boundary
1308	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_north )
1309	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_north )
1310	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_north )
1311	!
1312	!-- Generate turbulence at south boundary
1313	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south )
1314	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south )
1315	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south )
1316	ENDIF
1317	velocity_seed_initialized = .TRUE.
1318	ENDIF
1319
1320	!
1321	!-- New set of fu, fv, fw
1322	IF ( stg_call ) THEN
1323	!
1324	!-- Generate turbulence at left boundary (required in all applications,
1325	!-- i.e. offline nesting and turbulent inflow from the left)
1326	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1327	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1328	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1329
1330	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1331	.AND. .NOT. rans_mode ) ) THEN
1332	!
1333	!-- Generate turbulence at right boundary
1334	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_right )
1335	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_right )
1336	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_right )
1337	!
1338	!-- Generate turbulence at north boundary
1339	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_north )
1340	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_north )
1341	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_north )
1342	!
1343	!-- Generate turbulence at south boundary
1344	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south )
1345	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south )
1346	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south )
1347	ENDIF
1348	ENDIF
1349
1350	!
1351	!-- Turbulence generation at left and or right boundary
1352	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1353	!
1354	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1355	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1356	!-- imposed
1357	IF ( stg_call ) THEN
1358
1359	DO j = nysg, nyng
1360	DO k = nzb, nzt + 1
1361	!
1362	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1363	IF ( tu(k) == 0.0_wp ) THEN
1364	fu_yz(k,j) = fuo_yz(k,j)
1365	ELSE
1366	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1367	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1368	ENDIF
1369
1370	IF ( tv(k) == 0.0_wp ) THEN
1371	fv_yz(k,j) = fvo_yz(k,j)
1372	ELSE
1373	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1374	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1375	ENDIF
1376
1377	IF ( tw(k) == 0.0_wp ) THEN
1378	fw_yz(k,j) = fwo_yz(k,j)
1379	ELSE
1380	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1381	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1382	ENDIF
1383	ENDDO
1384	ENDDO
1385
1386	dist_yz(nzb,:,1) = 0.0_wp
1387	dist_yz(nzb,:,2) = 0.0_wp
1388	dist_yz(nzb,:,3) = 0.0_wp
1389
1390	IF ( myidx == id_stg_left ) i = nxl
1391	IF ( myidx == id_stg_right ) i = nxr+1
1392	DO j = nysg, nyng
1393	DO k = nzb+1, nzt + 1
1394	!
1395	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1396	!-- Additional factors are added to improve the variance of v and w
1397	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1398	MERGE( 1.0_wp, 0.0_wp, &
1399	BTEST( wall_flags_0(k,j,i), 1 ) )
1400	ENDDO
1401	ENDDO
1402
1403	IF ( myidx == id_stg_left ) i = nxl-1
1404	IF ( myidx == id_stg_right ) i = nxr+1
1405	DO j = nysg, nyng
1406	DO k = nzb+1, nzt + 1
1407	!
1408	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1409	!-- Additional factors are added to improve the variance of v and w
1410	!-- experimental test of 1.2
1411	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1412	* 1.2_wp ) &
1413	* ( a21(k) * fu_yz(k,j) &
1414	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1415	MERGE( 1.0_wp, 0.0_wp, &
1416	BTEST( wall_flags_0(k,j,i), 2 ) )
1417	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1418	* 1.3_wp ) &
1419	* ( a31(k) * fu_yz(k,j) &
1420	+ a32(k) * fv_yz(k,j) &
1421	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1422	MERGE( 1.0_wp, 0.0_wp, &
1423	BTEST( wall_flags_0(k,j,i), 3 ) )
1424	ENDDO
1425	ENDDO
1426	ENDIF
1427
1428	!
1429	!-- Mass flux correction following Kim et al. (2013)
1430	!-- This correction factor insures that the mass flux is preserved at the
1431	!-- inflow boundary. First, calculate mean value of the imposed
1432	!-- perturbations at yz boundary.
1433	!-- Note, this needs to be done only after the last RK3-substep, else
1434	!-- the boundary values won't be accessed.
1435	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1436	mc_factor_l = 0.0_wp
1437	mc_factor = 0.0_wp
1438	!
1439	!-- Sum up the original volume flows (with and without perturbations).
1440	!-- Note, for non-normal components (here v and w) it is actually no
1441	!-- volume flow.
1442	IF ( myidx == id_stg_left ) i = nxl
1443	IF ( myidx == id_stg_right ) i = nxr+1
1444
1445	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1446	* MERGE( 1.0_wp, 0.0_wp, &
1447	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1448
1449	IF ( myidx == id_stg_left ) i = nxl-1
1450	IF ( myidx == id_stg_right ) i = nxr+1
1451
1452	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1453	* MERGE( 1.0_wp, 0.0_wp, &
1454	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1455	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1456	* MERGE( 1.0_wp, 0.0_wp, &
1457	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1458
1459	#if defined( __parallel )
1460	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1461	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1462	#else
1463	mc_factor = mc_factor_l
1464	#endif
1465	!
1466	!-- Calculate correction factor and force zero mean perturbations.
1467	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1468
1469	IF ( myidx == id_stg_left ) i = nxl
1470	IF ( myidx == id_stg_right ) i = nxr+1
1471
1472	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
1473	* MERGE( 1.0_wp, 0.0_wp, &
1474	BTEST( wall_flags_0(:,:,i), 1 ) )
1475
1476
1477	IF ( myidx == id_stg_left ) i = nxl-1
1478	IF ( myidx == id_stg_right ) i = nxr+1
1479
1480	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
1481	* MERGE( 1.0_wp, 0.0_wp, &
1482	BTEST( wall_flags_0(:,:,i), 2 ) )
1483
1484	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
1485	* MERGE( 1.0_wp, 0.0_wp, &
1486	BTEST( wall_flags_0(:,:,i), 3 ) )
1487	!
1488	!-- Add disturbances
1489	IF ( myidx == id_stg_left ) THEN
1490	!
1491	!-- For the left boundary distinguish between mesoscale offline / self
1492	!-- nesting and turbulent inflow at the left boundary only. In the latter
1493	!-- case turbulence is imposed on the mean inflow profiles.
1494	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1495	!
1496	!-- Add disturbance at the inflow
1497	DO j = nysg, nyng
1498	DO k = nzb, nzt+1
1499	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1500	dist_yz(k,j,1) ) &
1501	* MERGE( 1.0_wp, 0.0_wp, &
1502	BTEST( wall_flags_0(k,j,0), 1 ) )
1503	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1504	dist_yz(k,j,2) ) &
1505	* MERGE( 1.0_wp, 0.0_wp, &
1506	BTEST( wall_flags_0(k,j,-1), 2 ) )
1507	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1508	* MERGE( 1.0_wp, 0.0_wp, &
1509	BTEST( wall_flags_0(k,j,-1), 3 ) )
1510	ENDDO
1511	ENDDO
1512	ELSE
1513
1514	DO j = nys, nyn
1515	DO k = nzb+1, nzt
1516	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1517	* MERGE( 1.0_wp, 0.0_wp, &
1518	BTEST( wall_flags_0(k,j,0), 1 ) )
1519	u(k,j,-1) = u(k,j,0)
1520	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1521	* MERGE( 1.0_wp, 0.0_wp, &
1522	BTEST( wall_flags_0(k,j,-1), 2 ) )
1523	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1524	* MERGE( 1.0_wp, 0.0_wp, &
1525	BTEST( wall_flags_0(k,j,-1), 3 ) )
1526	ENDDO
1527	ENDDO
1528	ENDIF
1529	ENDIF
1530	IF ( myidx == id_stg_right ) THEN
1531	DO j = nys, nyn
1532	DO k = nzb+1, nzt
1533	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1534	* MERGE( 1.0_wp, 0.0_wp, &
1535	BTEST( wall_flags_0(k,j,nxr+1), 1 ) )
1536	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1537	* MERGE( 1.0_wp, 0.0_wp, &
1538	BTEST( wall_flags_0(k,j,nxr+1), 2 ) )
1539	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1540	* MERGE( 1.0_wp, 0.0_wp, &
1541	BTEST( wall_flags_0(k,j,nxr+1), 3 ) )
1542	ENDDO
1543	ENDDO
1544	ENDIF
1545	ENDIF
1546	ENDIF
1547	!
1548	!-- Turbulence generation at north and south boundary
1549	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1550	!
1551	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1552	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1553	!-- imposed
1554	IF ( stg_call ) THEN
1555	DO i = nxlg, nxrg
1556	DO k = nzb, nzt + 1
1557	!
1558	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1559	IF ( tu(k) == 0.0_wp ) THEN
1560	fu_xz(k,i) = fuo_xz(k,i)
1561	ELSE
1562	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1563	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1564	ENDIF
1565
1566	IF ( tv(k) == 0.0_wp ) THEN
1567	fv_xz(k,i) = fvo_xz(k,i)
1568	ELSE
1569	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1570	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1571	ENDIF
1572
1573	IF ( tw(k) == 0.0_wp ) THEN
1574	fw_xz(k,i) = fwo_xz(k,i)
1575	ELSE
1576	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1577	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1578	ENDIF
1579	ENDDO
1580	ENDDO
1581
1582
1583	dist_xz(nzb,:,1) = 0.0_wp
1584	dist_xz(nzb,:,2) = 0.0_wp
1585	dist_xz(nzb,:,3) = 0.0_wp
1586
1587	IF ( myidy == id_stg_south ) j = nys
1588	IF ( myidy == id_stg_north ) j = nyn+1
1589	DO i = nxlg, nxrg
1590	DO k = nzb+1, nzt + 1
1591	!
1592	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1593	!-- Additional factors are added to improve the variance of v and w
1594	!experimental test of 1.2
1595	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1596	* 1.2_wp ) &
1597	* ( a21(k) * fu_xz(k,i) &
1598	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1599	MERGE( 1.0_wp, 0.0_wp, &
1600	BTEST( wall_flags_0(k,j,i), 2 ) )
1601	ENDDO
1602	ENDDO
1603
1604	IF ( myidy == id_stg_south ) j = nys-1
1605	IF ( myidy == id_stg_north ) j = nyn+1
1606	DO i = nxlg, nxrg
1607	DO k = nzb+1, nzt + 1
1608	!
1609	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1610	!-- Additional factors are added to improve the variance of v and w
1611	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1612	MERGE( 1.0_wp, 0.0_wp, &
1613	BTEST( wall_flags_0(k,j,i), 1 ) )
1614
1615	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1616	* 1.3_wp ) &
1617	* ( a31(k) * fu_xz(k,i) &
1618	+ a32(k) * fv_xz(k,i) &
1619	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1620	MERGE( 1.0_wp, 0.0_wp, &
1621	BTEST( wall_flags_0(k,j,i), 3 ) )
1622	ENDDO
1623	ENDDO
1624	ENDIF
1625
1626	!
1627	!-- Mass flux correction following Kim et al. (2013)
1628	!-- This correction factor insures that the mass flux is preserved at the
1629	!-- inflow boundary. First, calculate mean value of the imposed
1630	!-- perturbations at yz boundary.
1631	!-- Note, this needs to be done only after the last RK3-substep, else
1632	!-- the boundary values won't be accessed.
1633	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1634	mc_factor_l = 0.0_wp
1635	mc_factor = 0.0_wp
1636
1637	IF ( myidy == id_stg_south ) j = nys
1638	IF ( myidy == id_stg_north ) j = nyn+1
1639
1640	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1641	* MERGE( 1.0_wp, 0.0_wp, &
1642	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1643
1644	IF ( myidy == id_stg_south ) j = nys-1
1645	IF ( myidy == id_stg_north ) j = nyn+1
1646
1647	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1648	* MERGE( 1.0_wp, 0.0_wp, &
1649	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1650	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1651	* MERGE( 1.0_wp, 0.0_wp, &
1652	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1653
1654	#if defined( __parallel )
1655	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1656	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1657	#else
1658	mc_factor = mc_factor_l
1659	#endif
1660
1661	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1662
1663	IF ( myidy == id_stg_south ) j = nys
1664	IF ( myidy == id_stg_north ) j = nyn+1
1665
1666	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
1667	* MERGE( 1.0_wp, 0.0_wp, &
1668	BTEST( wall_flags_0(:,j,:), 2 ) )
1669
1670
1671	IF ( myidy == id_stg_south ) j = nys-1
1672	IF ( myidy == id_stg_north ) j = nyn+1
1673
1674	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
1675	* MERGE( 1.0_wp, 0.0_wp, &
1676	BTEST( wall_flags_0(:,j,:), 1 ) )
1677
1678	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
1679	* MERGE( 1.0_wp, 0.0_wp, &
1680	BTEST( wall_flags_0(:,j,:), 3 ) )
1681	!
1682	!-- Add disturbances
1683	IF ( myidy == id_stg_south ) THEN
1684	DO i = nxl, nxr
1685	DO k = nzb+1, nzt
1686	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1687	* MERGE( 1.0_wp, 0.0_wp, &
1688	BTEST( wall_flags_0(k,-1,i), 1 ) )
1689	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1690	* MERGE( 1.0_wp, 0.0_wp, &
1691	BTEST( wall_flags_0(k,0,i), 2 ) )
1692	v(k,-1,i) = v(k,0,i)
1693	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1694	* MERGE( 1.0_wp, 0.0_wp, &
1695	BTEST( wall_flags_0(k,-1,i), 3 ) )
1696	ENDDO
1697	ENDDO
1698	ENDIF
1699	IF ( myidy == id_stg_north ) THEN
1700
1701	DO i = nxl, nxr
1702	DO k = nzb+1, nzt
1703	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1704	* MERGE( 1.0_wp, 0.0_wp, &
1705	BTEST( wall_flags_0(k,nyn+1,i), 1 ) )
1706	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1707	* MERGE( 1.0_wp, 0.0_wp, &
1708	BTEST( wall_flags_0(k,nyn+1,i), 2 ) )
1709	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1710	* MERGE( 1.0_wp, 0.0_wp, &
1711	BTEST( wall_flags_0(k,nyn+1,i), 3 ) )
1712	ENDDO
1713	ENDDO
1714	ENDIF
1715	ENDIF
1716	ENDIF
1717	!
1718	!-- Finally, set time counter for calling STG to zero
1719	IF ( stg_call ) time_stg_call = 0.0_wp
1720
1721	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1722
1723	END SUBROUTINE stg_main
1724
1725	!------------------------------------------------------------------------------!
1726	! Description:
1727	! ------------
1728	!> Generate a set of random number rand_it wich is equal on each PE
1729	!> and calculate the velocity seed f_n.
1730	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1731	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1732	!> parts are collected to form the full array.
1733	!------------------------------------------------------------------------------!
1734	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id )
1735
1736	IMPLICIT NONE
1737
1738	INTEGER(iwp) :: id !< core ids at respective boundaries
1739	INTEGER(iwp) :: j !< loop index in y-direction
1740	INTEGER(iwp) :: jj !< loop index in y-direction
1741	INTEGER(iwp) :: k !< loop index in z-direction
1742	INTEGER(iwp) :: kk !< loop index in z-direction
1743	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1744
1745	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1746	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1747	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
1748	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1749
1750	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1751	REAL(wp) :: rand_av !< average of random number
1752	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1753
1754	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
1755	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1756	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
1757	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
1758	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1759
1760
1761	!
1762	!-- Generate random numbers using a seed generated in stg_init.
1763	!-- The set of random numbers are modified to have an average of 0 and
1764	!-- unit variance.
1765	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
1766
1767	rand_av = 0.0_wp
1768	rand_sigma_inv = 0.0_wp
1769	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
1770
1771	DO j = 0, ny
1772	DO k = nzb, nzt+1
1773	CALL RANDOM_NUMBER( rand_it(k,j) )
1774	rand_av = rand_av + rand_it(k,j)
1775	ENDDO
1776	ENDDO
1777
1778	rand_av = rand_av * nyz_inv
1779
1780	DO j = 0, ny
1781	DO k = nzb, nzt+1
1782	rand_it(k,j) = rand_it(k,j) - rand_av
1783	rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
1784	ENDDO
1785	ENDDO
1786
1787	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)
1788
1789	DO j = 0, ny
1790	DO k = nzb, nzt+1
1791	rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
1792	ENDDO
1793	ENDDO
1794
1795	!
1796	!-- Periodic fill of random number in space
1797	DO j = 0, ny
1798	DO k = 1, mergp
1799	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
1800	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
1801	ENDDO
1802	ENDDO
1803	DO j = 1, mergp
1804	DO k = nzb-mergp, nzt+1+mergp
1805	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
1806	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
1807	ENDDO
1808	ENDDO
1809
1810	!
1811	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1812	n_y2 = n_y * 2
1813	n_z2 = n_z * 2
1814	f_n_l = 0.0_wp
1815
1816	DO j = nysg, nyng
1817	DO k = nzb_x_stg, nzt_x_stg+1
1818	DO jj = -n_y2(k), n_y2(k)
1819	DO kk = -n_z2(k), n_z2(k)
1820	f_n_l(k,j) = f_n_l(k,j) &
1821	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1822	ENDDO
1823	ENDDO
1824	ENDDO
1825	ENDDO
1826
1827	DEALLOCATE( rand_it )
1828	!
1829	!-- Gather velocity seeds of full subdomain
1830	send_count = nzt_x_stg - nzb_x_stg + 1
1831	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1832
1833	#if defined( __parallel )
1834	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1835	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
1836	id, comm1dx, ierr )
1837	#else
1838	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
1839	#endif
1840
1841
1842	END SUBROUTINE stg_generate_seed_yz
1843
1844
1845
1846
1847	!------------------------------------------------------------------------------!
1848	! Description:
1849	! ------------
1850	!> Generate a set of random number rand_it wich is equal on each PE
1851	!> and calculate the velocity seed f_n.
1852	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1853	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1854	!> parts are collected to form the full array.
1855	!------------------------------------------------------------------------------!
1856	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id )
1857
1858	IMPLICIT NONE
1859
1860	INTEGER(iwp) :: id !< core ids at respective boundaries
1861	INTEGER(iwp) :: i !< loop index in x-direction
1862	INTEGER(iwp) :: ii !< loop index in x-direction
1863	INTEGER(iwp) :: k !< loop index in z-direction
1864	INTEGER(iwp) :: kk !< loop index in z-direction
1865	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1866
1867	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1868	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1869	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
1870	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1871
1872	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1873	REAL(wp) :: rand_av !< average of random number
1874	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1875
1876	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
1877	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1878	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
1879	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
1880	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1881
1882
1883	!
1884	!-- Generate random numbers using a seed generated in stg_init.
1885	!-- The set of random numbers are modified to have an average of 0 and
1886	!-- unit variance.
1887	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
1888
1889	rand_av = 0.0_wp
1890	rand_sigma_inv = 0.0_wp
1891	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
1892
1893	DO i = 0, nx
1894	DO k = nzb, nzt+1
1895	CALL RANDOM_NUMBER( rand_it(k,i) )
1896	rand_av = rand_av + rand_it(k,i)
1897	ENDDO
1898	ENDDO
1899
1900	rand_av = rand_av * nxz_inv
1901
1902	DO i = 0, nx
1903	DO k = nzb, nzt+1
1904	rand_it(k,i) = rand_it(k,i) - rand_av
1905	rand_sigma_inv = rand_sigma_inv + rand_it(k,i) ** 2
1906	ENDDO
1907	ENDDO
1908
1909	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nxz_inv)
1910
1911	DO i = 0, nx
1912	DO k = nzb, nzt+1
1913	rand_it(k,i) = rand_it(k,i) * rand_sigma_inv
1914	ENDDO
1915	ENDDO
1916
1917	!
1918	!-- Periodic fill of random number in space
1919	DO i = 0, nx
1920	DO k = 1, mergp
1921	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
1922	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
1923	ENDDO
1924	ENDDO
1925	DO i = 1, mergp
1926	DO k = nzb-mergp, nzt+1+mergp
1927	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
1928	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
1929	ENDDO
1930	ENDDO
1931
1932	!
1933	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1934	n_x2 = n_x * 2
1935	n_z2 = n_z * 2
1936	f_n_l = 0.0_wp
1937
1938	DO i = nxlg, nxrg
1939	DO k = nzb_y_stg, nzt_y_stg+1
1940	DO ii = -n_x2(k), n_x2(k)
1941	DO kk = -n_z2(k), n_z2(k)
1942	f_n_l(k,i) = f_n_l(k,i) &
1943	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1944	ENDDO
1945	ENDDO
1946	ENDDO
1947	ENDDO
1948
1949	DEALLOCATE( rand_it )
1950
1951	!
1952	!-- Gather velocity seeds of full subdomain
1953	send_count = nzt_y_stg - nzb_y_stg + 1
1954	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
1955
1956
1957	#if defined( __parallel )
1958	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
1959	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
1960	id, comm1dy, ierr )
1961	#else
1962	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
1963	#endif
1964
1965
1966	END SUBROUTINE stg_generate_seed_xz
1967
1968	!------------------------------------------------------------------------------!
1969	! Description:
1970	! ------------
1971	!> Parametrization of the Reynolds stress tensor, following the parametrization
1972	!> described in Rotach et al. (1996), which is applied in state-of-the-art
1973	!> dispserion modelling. Please note, the parametrization does not distinguish
1974	!> between along-wind and cross-wind turbulence.
1975	!------------------------------------------------------------------------------!
1976	SUBROUTINE parametrize_reynolds_stress
1977
1978	IMPLICIT NONE
1979
1980	INTEGER(iwp) :: k !< loop index in z-direction
1981
1982	REAL(wp) :: zzi !< ratio of z/zi
1983
1984	DO k = nzb+1, nzt+1
1985	!
1986	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
1987	!-- The function decreases to 1/10 after one length scale above the
1988	!-- ABL top.
1989	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
1990	!
1991	!-- Determine normalized height coordinate
1992	zzi = zu(k) / zi_ribulk
1993	!
1994	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
1995	!-- to the denominator, else the merge-function can crash if scale_l is
1996	!-- zero.
1997	r11(k) = scale_us*2 ( &
1998	MERGE( 0.35_wp * ABS( &
1999	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2000	)**( 2.0_wp / 3.0_wp ), &
2001	0.0_wp, &
2002	scale_l < 0.0_wp ) &
2003	+ 5.0_wp - 4.0_wp * zzi &
2004	) * blend
2005
2006	r22(k) = r11(k)
2007	!
2008	!-- w'w'
2009	r33(k) = scale_wm*2 ( &
2010	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2011	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2012	) * blend
2013	!
2014	!-- u'w' and v'w'. Assume isotropy.
2015	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2016	r32(k) = r31(k)
2017	!
2018	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2019	!-- a similar profile as for u'w'.
2020	r21(k) = r31(k)
2021	ENDDO
2022
2023	!
2024	!-- Set bottom boundary condition
2025	r11(nzb) = r11(nzb+1)
2026	r22(nzb) = r22(nzb+1)
2027	r33(nzb) = r33(nzb+1)
2028
2029	r21(nzb) = r11(nzb+1)
2030	r31(nzb) = r31(nzb+1)
2031	r32(nzb) = r32(nzb+1)
2032
2033
2034	END SUBROUTINE parametrize_reynolds_stress
2035
2036	!------------------------------------------------------------------------------!
2037	! Description:
2038	! ------------
2039	!> Calculate the coefficient matrix from the Lund rotation.
2040	!------------------------------------------------------------------------------!
2041	SUBROUTINE calc_coeff_matrix
2042
2043	IMPLICIT NONE
2044
2045	INTEGER(iwp) :: k !< loop index in z-direction
2046
2047	!
2048	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2049	DO k = nzb+1, nzt+1
2050	IF ( r11(k) > 10E-6_wp ) THEN
2051	a11(k) = SQRT( r11(k) )
2052	a21(k) = r21(k) / a11(k)
2053	a31(k) = r31(k) / a11(k)
2054	ELSE
2055	a11(k) = 10E-8_wp
2056	a21(k) = 10E-8_wp
2057	a31(k) = 10E-8_wp
2058	ENDIF
2059	ENDDO
2060	DO k = nzb+1, nzt+1
2061	a22(k) = r22(k) - a21(k)**2
2062	IF ( a22(k) > 10E-6_wp ) THEN
2063	a22(k) = SQRT( a22(k) )
2064	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2065	ELSE
2066	a22(k) = 10E-8_wp
2067	a32(k) = 10E-8_wp
2068	ENDIF
2069	ENDDO
2070	DO k = nzb+1, nzt+1
2071	a33(k) = r33(k) - a31(k)2 - a32(k)2
2072	IF ( a33(k) > 10E-6_wp ) THEN
2073	a33(k) = SQRT( a33(k) )
2074	ELSE
2075	a33(k) = 10E-8_wp
2076	ENDIF
2077	ENDDO
2078	!
2079	!-- Set bottom boundary condition
2080	a11(nzb) = a11(nzb+1)
2081	a22(nzb) = a22(nzb+1)
2082	a21(nzb) = a21(nzb+1)
2083	a33(nzb) = a33(nzb+1)
2084	a31(nzb) = a31(nzb+1)
2085	a32(nzb) = a32(nzb+1)
2086
2087	END SUBROUTINE calc_coeff_matrix
2088
2089	!------------------------------------------------------------------------------!
2090	! Description:
2091	! ------------
2092	!> This routine controls the re-adjustment of the turbulence statistics used
2093	!> for generating turbulence at the lateral boundaries.
2094	!------------------------------------------------------------------------------!
2095	SUBROUTINE stg_adjust
2096
2097	IMPLICIT NONE
2098
2099
2100	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2101	!
2102	!-- In case of dirichlet inflow boundary conditions only at one lateral
2103	!-- boundary, i.e. in the case no offline or self nesting is applied but
2104	!-- synthetic turbulence shall be parametrized nevertheless, the
2105	!-- boundary-layer depth need to determined first.
2106	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2107	CALL nesting_offl_calc_zi
2108	!
2109	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2110	!-- are calculated.
2111	CALL calc_scaling_variables
2112	!
2113	!-- Set length and time scales depending on boundary-layer height
2114	CALL calc_length_and_time_scale
2115	!
2116	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2117	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2118	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2119	!-- friction velocity and velocity scale.
2120	CALL parametrize_reynolds_stress
2121	!
2122	!-- Calculate coefficient matrix from Reynolds stress tensor
2123	!-- (Lund rotation)
2124	CALL calc_coeff_matrix
2125	!
2126	!-- Determine filter functions on basis of updated length scales
2127	CALL stg_filter_func( nux, bux ) !filter ux
2128	CALL stg_filter_func( nuy, buy ) !filter uy
2129	CALL stg_filter_func( nuz, buz ) !filter uz
2130	CALL stg_filter_func( nvx, bvx ) !filter vx
2131	CALL stg_filter_func( nvy, bvy ) !filter vy
2132	CALL stg_filter_func( nvz, bvz ) !filter vz
2133	CALL stg_filter_func( nwx, bwx ) !filter wx
2134	CALL stg_filter_func( nwy, bwy ) !filter wy
2135	CALL stg_filter_func( nwz, bwz ) !filter wz
2136	!
2137	!-- Reset time counter for controlling next adjustment to zero
2138	time_stg_adjust = 0.0_wp
2139
2140	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2141
2142	END SUBROUTINE stg_adjust
2143
2144
2145	!------------------------------------------------------------------------------!
2146	! Description:
2147	! ------------
2148	!> Calculates turbuluent length and time scales if these are not available
2149	!> from measurements.
2150	!------------------------------------------------------------------------------!
2151	SUBROUTINE calc_length_and_time_scale
2152
2153	IMPLICIT NONE
2154
2155
2156	INTEGER(iwp) :: k !< loop index in z-direction
2157
2158	REAL(wp) :: length_scale_dum !< effectively used length scale
2159
2160	!
2161	!-- In initial call the boundary-layer depth can be zero. This case, set
2162	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2163	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2164	!
2165	!-- Set-up default turbulent length scales. From the numerical point of
2166	!-- view the imposed perturbations should not be immediately dissipated
2167	!-- by the numerics. The numerical dissipation, however, acts on scales
2168	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2169	!-- length scale to 8 time the grid spacing. Further, above the boundary
2170	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2171	!-- imposing any perturbations) in order to save computational costs.
2172	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2173	!-- using the length scales and the mean profiles of u- and v-component.
2174	DO k = nzb+1, nzt+1
2175	!
2176	!-- Determine blending parameter. Within the boundary layer length scales
2177	!-- are constant, while above lengths scales approach gradully zero,
2178	!-- i.e. imposed turbulence is not correlated in space and time,
2179	!-- just white noise, which saves computations power as the loops for the
2180	!-- computation of the filter functions depend on the length scales.
2181	!-- The value decreases to 1/10 after one length scale above the
2182	!-- ABL top.
2183	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2184	!
2185	!-- Assume isotropic turbulence length scales
2186	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2187	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2188	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2189	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2190	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2191	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2192	!
2193	!-- Along the vertical direction limit the length scale further by the
2194	!-- boundary-layer depth to assure that no length scales larger than
2195	!-- the boundary-layer depth are used
2196	length_scale_dum = MIN( length_scale, zi_ribulk )
2197
2198	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2199	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2200	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2201	!
2202	!-- Limit time scales, else they become very larger for low wind speed,
2203	!-- imposing long-living inflow perturbations which in turn propagate
2204	!-- further into the model domain. Use u_init and v_init to calculate
2205	!-- the time scales, which will be equal to the inflow profiles, both,
2206	!-- in offline nesting mode or in dirichlet/radiation mode.
2207	tu(k) = MIN( dt_stg_adjust, length_scale / &
2208	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2209	tv(k) = MIN( dt_stg_adjust, length_scale / &
2210	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2211	!
2212	!-- Time scale of w-component is a mixture from u- and v-component.
2213	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2214
2215	ENDDO
2216	!
2217	!-- Set bottom boundary condition for the length and time scales
2218	nux(nzb) = nux(nzb+1)
2219	nuy(nzb) = nuy(nzb+1)
2220	nuz(nzb) = nuz(nzb+1)
2221	nvx(nzb) = nvx(nzb+1)
2222	nvy(nzb) = nvy(nzb+1)
2223	nvz(nzb) = nvz(nzb+1)
2224	nwx(nzb) = nwx(nzb+1)
2225	nwy(nzb) = nwy(nzb+1)
2226	nwz(nzb) = nwz(nzb+1)
2227
2228	tu(nzb) = tu(nzb+1)
2229	tv(nzb) = tv(nzb+1)
2230	tw(nzb) = tw(nzb+1)
2231
2232
2233	END SUBROUTINE calc_length_and_time_scale
2234
2235	!------------------------------------------------------------------------------!
2236	! Description:
2237	! ------------
2238	!> Calculate scaling variables which are used for turbulence parametrization
2239	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2240	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2241	!------------------------------------------------------------------------------!
2242	SUBROUTINE calc_scaling_variables
2243
2244	USE surface_mod, &
2245	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
2246
2247	IMPLICIT NONE
2248
2249	INTEGER(iwp) :: i !< loop index in x-direction
2250	INTEGER(iwp) :: j !< loop index in y-direction
2251	INTEGER(iwp) :: k !< loop index in z-direction
2252	INTEGER(iwp) :: m !< surface element index
2253
2254	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2255	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2256	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2257	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2258	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2259	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2260	REAL(wp) :: w_convective !< convective velocity scale
2261
2262	!
2263	!-- Calculate mean friction velocity, velocity scale, heat flux and
2264	!-- near-surface temperature in the model domain.
2265	pt_surf_mean_l = 0.0_wp
2266	shf_mean_l = 0.0_wp
2267	scale_l_l = 0.0_wp
2268	friction_vel_l = 0.0_wp
2269	DO m = 1, surf_def_h(0)%ns
2270	i = surf_def_h(0)%i(m)
2271	j = surf_def_h(0)%j(m)
2272	k = surf_def_h(0)%k(m)
2273	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2274	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2275	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2276	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2277	ENDDO
2278	DO m = 1, surf_lsm_h%ns
2279	i = surf_lsm_h%i(m)
2280	j = surf_lsm_h%j(m)
2281	k = surf_lsm_h%k(m)
2282	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2283	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2284	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2285	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2286	ENDDO
2287	DO m = 1, surf_usm_h%ns
2288	i = surf_usm_h%i(m)
2289	j = surf_usm_h%j(m)
2290	k = surf_usm_h%k(m)
2291	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2292	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2293	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2294	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2295	ENDDO
2296
2297	#if defined( __parallel )
2298	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2299	comm2d, ierr )
2300	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2301	comm2d, ierr )
2302	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2303	comm2d, ierr )
2304	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2305	comm2d, ierr )
2306	#else
2307	scale_us = friction_vel_l
2308	shf_mean = shf_mean_l
2309	scale_l = scale_l_l
2310	pt_surf_mean = pt_surf_mean_l
2311	#endif
2312
2313	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2314	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2315	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2316	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2317	!
2318	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2319	!-- is negative, set convective velocity scale to zero.
2320	IF ( shf_mean > 0.0_wp ) THEN
2321	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2322	ELSE
2323	w_convective = 0.0_wp
2324	ENDIF
2325	!
2326	!-- Finally, in order to consider also neutral or stable stratification,
2327	!-- compute momentum velocity scale from u* and convective velocity scale,
2328	!-- according to Rotach et al. (1996).
2329	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2330
2331	END SUBROUTINE calc_scaling_variables
2332
2333	END MODULE synthetic_turbulence_generator_mod

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