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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4148

Last change on this file since 4148 was 4148, checked in by suehring, 5 years ago
indoor_model_mod: Revision of indoor model; urban_surface_mod: parameters for waste heat from cooling and heating are introduced to building data base; initialization of building data base moved to an earlier point of time before indoor model will be initialized; radiation_model_mod: minor improvement in some comments; synthetic_turbulence_generator: unused variable removed
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File size: 100.4 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 4148 2019-08-08 11:26:00Z suehring $
27	! Remove unused variable
28	!
29	! 4144 2019-08-06 09:11:47Z raasch
30	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
31	!
32	! 4071 2019-07-03 20:02:00Z suehring
33	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
34	! information is not read from file.
35	!
36	! 4022 2019-06-12 11:52:39Z suehring
37	! Several bugfixes and improvements
38	! - revise bias correction of the imposed perturbations (correction via volume
39	! flow can create instabilities in case the mean volume flow is close to zero)
40	! - introduce lower limits in calculation of coefficient matrix, else the
41	! calculation may become numerically unstable
42	! - impose perturbations every timestep, even though no new set of perturbations
43	! is generated in case dt_stg_call /= dt_3d
44	! - Implement a gradual decrease of Reynolds stress and length scales above
45	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
46	! discontinuous decrease
47	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
48	!
49	! 3987 2019-05-22 09:52:13Z kanani
50	! Introduce alternative switch for debug output during timestepping
51	!
52	! 3938 2019-04-29 16:06:25Z suehring
53	! Remove unused variables
54	!
55	! 3937 2019-04-29 15:09:07Z suehring
56	! Minor bugfix in case of a very early restart where mc_factor is sill not
57	! present.
58	! Some modification and fixing of potential bugs in the calculation of scaling
59	! parameters used for synthetic turbulence parametrization.
60	!
61	! 3909 2019-04-17 09:13:25Z suehring
62	! Minor bugfix for last commit
63	!
64	! 3900 2019-04-16 15:17:43Z suehring
65	! Missing re-calculation of perturbation seeds in case of restarts
66	!
67	! 3891 2019-04-12 17:52:01Z suehring
68	! Bugfix in initialization in case of restart runs.
69	!
70	! 3885 2019-04-11 11:29:34Z kanani
71	! Changes related to global restructuring of location messages and introduction
72	! of additional debug messages
73	!
74	!
75	! removed unused variables
76	!
77	! 3719 2019-02-06 13:10:18Z kanani
78	! Removed log_point measurement from stg_init, since this part is counted to
79	! log_point(2) 'initialisation' already. Moved other log_points to calls of
80	! the subroutines in time_integration for better overview.
81	!
82	! 3646 2018-12-28 17:58:49Z kanani
83	! Bugfix: use time_since_reference_point instead of simulated_time (relevant
84	! when using wall/soil spinup)
85	!
86	! 3579 2018-11-29 15:32:39Z suehring
87	! - Bugfix in calculation of turbulence scaling parameters for turbulence
88	! generator in case of topography
89	! - Additional checks implemented - no STG in RANS-RANS nesting or LES-LES
90	! nesting
91	!
92	! 3376 2018-10-19 10:15:32Z suehring
93	! Error messages and numbers reivsed.
94	!
95	! 3349 2018-10-15 16:39:41Z suehring
96	! Fix for format descriptor
97	!
98	! 3348 2018-10-15 14:30:51Z suehring
99	! - Revise structure of init routine
100	! - introduce new parameters to skip STG for some timesteps
101	! - introduce time-dependent parametrization of Reynolds-stress tensor
102	! - Bugfix in allocation of mean_inflow_profiles
103	!
104	! 3341 2018-10-15 10:31:27Z suehring
105	! Introduce module parameter for number of inflow profiles
106	!
107	! 3288 2018-09-28 10:23:08Z suehring
108	! Modularization of all bulk cloud physics code components
109	!
110	! 3248 2018-09-14 09:42:06Z sward
111	! Minor formating changes
112	!
113	! 3246 2018-09-13 15:14:50Z sward
114	! Added error handling for input namelist via parin_fail_message
115	!
116	! 3241 2018-09-12 15:02:00Z raasch
117	! unused variables removed
118	!
119	! 3186 2018-07-30 17:07:14Z suehring
120	! Mask topography while imposing inflow perturbations at the boundaries; do not
121	! impose perturbations at top boundary as well as ghost points
122	!
123	! 3183 2018-07-27 14:25:55Z suehring
124	! Rename variables and extend error message
125	! Enable geneartor also for stretched grids
126	!
127	! 3182 2018-07-27 13:36:03Z suehring
128	! Error message related to vertical stretching has been added, dz was replaced
129	! by dz(1)
130	!
131	! 3051 2018-05-30 17:43:55Z suehring
132	! Bugfix in calculation of initial Reynolds-stress tensor.
133	!
134	! 3045 2018-05-28 07:55:41Z Giersch
135	! Error messages revised
136	!
137	! 3044 2018-05-25 10:59:41Z gronemeier
138	! Add missing variable descriptions
139	!
140	! 3038 2018-05-24 10:54:00Z gronemeier
141	! updated variable descriptions
142	!
143	! 2967 2018-04-13 11:22:08Z raasch
144	! bugfix: missing parallel cpp-directives added
145	!
146	! 2946 2018-04-04 17:01:23Z suehring
147	! Remove unused module load
148	!
149	! 2945 2018-04-04 16:27:14Z suehring
150	! - Bugfix in parallelization of synthetic turbulence generator in case the
151	! z-dimension is not an integral divisor of the number of processors along
152	! the x- and y-dimension
153	! - Revision in control mimic in case of RAN-LES nesting
154	!
155	! 2938 2018-03-27 15:52:42Z suehring
156	! Apply turbulence generator at all non-cyclic lateral boundaries in case of
157	! realistic Inifor large-scale forcing or RANS-LES nesting
158	!
159	! 2936 2018-03-27 14:49:27Z suehring
160	! variable named found has been introduced for checking if restart data was found,
161	! reading of restart strings has been moved completely to read_restart_data_mod,
162	! redundant skipping function has been removed, stg_read/write_restart_data
163	! have been renamed to stg_r/wrd_global, stg_rrd_global is called in
164	! read_restart_data_mod now, flag syn_turb_gen_prerun and marker *** end stg
165	! *** have been removed (Giersch), strings and their respective lengths are
166	! written out and read now in case of restart runs to get rid of prescribed
167	! character lengths (Giersch), CASE DEFAULT was added if restart data is read
168	!
169	! 2841 2018-02-27 15:02:57Z suehring
170	! Bugfix: wrong placement of include 'mpif.h' corrected
171	!
172	! 2836 2018-02-26 13:40:05Z Giersch
173	! The variables synthetic_turbulence_generator and
174	! use_synthetic_turbulence_generator have been abbreviated + syn_turb_gen_prerun
175	! flag is used to define if module related parameters were outputted as restart
176	! data
177	!
178	! 2716 2017-12-29 16:35:59Z kanani
179	! Corrected "Former revisions" section
180	!
181	! 2696 2017-12-14 17:12:51Z kanani
182	! Change in file header (GPL part)
183	!
184	! 2669 2017-12-06 16:03:27Z raasch
185	! unit number for file containing turbulence generator data changed to 90
186	! bugfix: preprocessor directives added for MPI specific code
187	!
188	! 2576 2017-10-24 13:49:46Z Giersch
189	! Definition of a new function called stg_skip_global to skip module
190	! parameters during reading restart data
191	!
192	! 2563 2017-10-19 15:36:10Z Giersch
193	! stg_read_restart_data is called in stg_parin in the case of a restart run
194	!
195	! 2259 2017-06-08 09:09:11Z gronemeier
196	! Initial revision
197	!
198	!
199	!
200	! Authors:
201	! --------
202	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
203	!
204	!
205	!
206	! Description:
207	! ------------
208	!> The module generates turbulence at the inflow boundary based on a method by
209	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
210	!> correction by Kim et al. (2013).
211	!> The turbulence is correlated based on length scales in y- and z-direction and
212	!> a time scale for each velocity component. The profiles of length and time
213	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
214	!> tensor can be either read from file STG_PROFILES, or will be parametrized
215	!> within the boundary layer.
216	!>
217	!> @todo test restart
218	!> enable cyclic_fill
219	!> implement turbulence generation for e and pt
220	!> @todo Input of height-constant length scales via namelist
221	!> @note <Enter notes on the module>
222	!> @bug Height information from input file is not used. Profiles from input
223	!> must match with current PALM grid.
224	!> In case of restart, velocity seeds differ from precursor run if a11,
225	!> a22, or a33 are zero.
226	!------------------------------------------------------------------------------!
227	MODULE synthetic_turbulence_generator_mod
228
229
230	USE arrays_3d, &
231	ONLY: dzw, &
232	ddzw, &
233	drho_air, &
234	mean_inflow_profiles, &
235	q, &
236	q_init, &
237	pt, &
238	pt_init, &
239	u, &
240	u_init, &
241	v, &
242	v_init, &
243	w, &
244	zu, &
245	zw
246
247	USE basic_constants_and_equations_mod, &
248	ONLY: g, &
249	kappa, &
250	pi
251
252	USE control_parameters, &
253	ONLY: bc_lr, &
254	bc_ns, &
255	child_domain, &
256	coupling_char, &
257	debug_output_timestep, &
258	dt_3d, &
259	e_init, &
260	humidity, &
261	initializing_actions, &
262	intermediate_timestep_count, &
263	intermediate_timestep_count_max, &
264	length, &
265	message_string, &
266	nesting_offline, &
267	neutral, &
268	num_mean_inflow_profiles, &
269	rans_mode, &
270	restart_string, &
271	syn_turb_gen, &
272	time_since_reference_point, &
273	turbulent_inflow
274
275	USE grid_variables, &
276	ONLY: ddx, &
277	ddy, &
278	dx, &
279	dy
280
281	USE indices, &
282	ONLY: nbgp, &
283	nz, &
284	nzb, &
285	nzt, &
286	nx, &
287	nxl, &
288	nxlu, &
289	nxlg, &
290	nxr, &
291	nxrg, &
292	ny, &
293	nys, &
294	nysv, &
295	nyn, &
296	nyng, &
297	nysg, &
298	wall_flags_0
299
300	USE kinds
301
302	#if defined( __parallel ) && !defined( __mpifh )
303	USE MPI
304	#endif
305
306	USE nesting_offl_mod, &
307	ONLY: nesting_offl_calc_zi, &
308	zi_ribulk
309
310	USE pegrid, &
311	ONLY: comm1dx, &
312	comm1dy, &
313	comm2d, &
314	ierr, &
315	myidx, &
316	myidy, &
317	pdims
318
319	USE pmc_interface, &
320	ONLY : rans_mode_parent
321
322	USE transpose_indices, &
323	ONLY: nzb_x, &
324	nzt_x
325
326
327	IMPLICIT NONE
328
329	#if defined( __parallel ) && defined( __mpifh )
330	INCLUDE "mpif.h"
331	#endif
332
333
334	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
335	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
336	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
337
338	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
339	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
340	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
341	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
342	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
343	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
344	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
345	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
346	INTEGER(iwp) :: merg !< maximum length scale (in gp)
347	INTEGER(iwp) :: mergp !< merg + nbgp
348	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
349	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
350	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
351	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
352
353	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
354	!< required for bias correction of imposed perturbations
355	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
356	!< required for bias correction of imposed perturbations
357
358	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
359	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
360	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
361	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
362	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
363	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
364	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
365	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
366	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
367	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
368	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
369	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
370	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
371	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed !< seed of random number for rn-generator
372
373	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
374	!< scales above the boundary layer
375	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
376	!< one length scale above ABL top
377	REAL(wp) :: d_l !< blend_coeff/length_scale
378	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
379	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
380	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
381	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
382	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
383	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
384	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
385	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
386
387	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
388
389
390	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
391	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
392	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
393	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
394	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
395	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
396
397	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
398	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
399	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
400	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
401	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
402	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
403	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
404	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
405	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
406
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
418	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
419	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
420	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
421	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
422	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
423	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
424	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
425	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
426	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
427	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
428
429	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
430	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
431
432	!
433	!-- PALM interfaces:
434	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
435	INTERFACE stg_adjust
436	MODULE PROCEDURE stg_adjust
437	END INTERFACE stg_adjust
438	!
439	!-- Input parameter checks to be done in check_parameters
440	INTERFACE stg_check_parameters
441	MODULE PROCEDURE stg_check_parameters
442	END INTERFACE stg_check_parameters
443
444	!
445	!-- Calculate filter functions
446	INTERFACE stg_filter_func
447	MODULE PROCEDURE stg_filter_func
448	END INTERFACE stg_filter_func
449
450	!
451	!-- Generate velocity seeds at south and north domain boundary
452	INTERFACE stg_generate_seed_xz
453	MODULE PROCEDURE stg_generate_seed_xz
454	END INTERFACE stg_generate_seed_xz
455	!
456	!-- Generate velocity seeds at left and/or right domain boundary
457	INTERFACE stg_generate_seed_yz
458	MODULE PROCEDURE stg_generate_seed_yz
459	END INTERFACE stg_generate_seed_yz
460
461	!
462	!-- Output of information to the header file
463	INTERFACE stg_header
464	MODULE PROCEDURE stg_header
465	END INTERFACE stg_header
466
467	!
468	!-- Initialization actions
469	INTERFACE stg_init
470	MODULE PROCEDURE stg_init
471	END INTERFACE stg_init
472
473	!
474	!-- Main procedure of synth. turb. gen.
475	INTERFACE stg_main
476	MODULE PROCEDURE stg_main
477	END INTERFACE stg_main
478
479	!
480	!-- Reading of NAMELIST parameters
481	INTERFACE stg_parin
482	MODULE PROCEDURE stg_parin
483	END INTERFACE stg_parin
484
485	!
486	!-- Reading of parameters for restart runs
487	INTERFACE stg_rrd_global
488	MODULE PROCEDURE stg_rrd_global
489	END INTERFACE stg_rrd_global
490
491	!
492	!-- Writing of binary output for restart runs
493	INTERFACE stg_wrd_global
494	MODULE PROCEDURE stg_wrd_global
495	END INTERFACE stg_wrd_global
496
497	SAVE
498
499	PRIVATE
500
501	!
502	!-- Public interfaces
503	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
504	stg_parin, stg_rrd_global, stg_wrd_global
505
506	!
507	!-- Public variables
508	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
509	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
510	time_stg_adjust, time_stg_call, use_syn_turb_gen
511
512
513	CONTAINS
514
515
516	!------------------------------------------------------------------------------!
517	! Description:
518	! ------------
519	!> Check parameters routine for synthetic turbulence generator
520	!------------------------------------------------------------------------------!
521	SUBROUTINE stg_check_parameters
522
523	IMPLICIT NONE
524
525	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
526	nesting_offline ) THEN
527	message_string = 'Synthetic turbulence generator is required ' // &
528	'if offline nesting is applied and PALM operates ' // &
529	'in LES mode.'
530	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
531	ENDIF
532
533	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
534	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
535	message_string = 'Synthetic turbulence generator is required ' // &
536	'when nesting is applied and parent operates in ' // &
537	'RANS-mode but current child in LES mode.'
538	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
539	ENDIF
540
541	IF ( use_syn_turb_gen ) THEN
542
543	IF ( child_domain .AND. .NOT. rans_mode .AND. &
544	.NOT. rans_mode_parent ) THEN
545	message_string = 'Using synthetic turbulence generator ' // &
546	'is not allowed in LES-LES nesting.'
547	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
548
549	ENDIF
550
551	IF ( child_domain .AND. rans_mode .AND. &
552	rans_mode_parent ) THEN
553	message_string = 'Using synthetic turbulence generator ' // &
554	'is not allowed in RANS-RANS nesting.'
555	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
556
557	ENDIF
558
559	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
560
561	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
562	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
563	message_string = 'Using synthetic turbulence generator ' // &
564	'requires %initializing_actions = ' // &
565	'"set_constant_profiles" or "read_restart_data"' //&
566	', if not offline nesting is applied.'
567	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
568	ENDIF
569
570	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
571	message_string = 'Using synthetic turbulence generator ' // &
572	'requires &bc_lr = "dirichlet/radiation", ' // &
573	'if not offline nesting is applied.'
574	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
575	ENDIF
576	IF ( bc_ns /= 'cyclic' ) THEN
577	message_string = 'Using synthetic turbulence generator ' // &
578	'requires &bc_ns = "cyclic", ' // &
579	'if not offline nesting is applied.'
580	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
581	ENDIF
582
583	ENDIF
584
585	IF ( turbulent_inflow ) THEN
586	message_string = 'Using synthetic turbulence generator ' // &
587	'in combination &with turbulent_inflow = .T. '// &
588	'is not allowed'
589	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
590	ENDIF
591
592	ENDIF
593
594	END SUBROUTINE stg_check_parameters
595
596
597	!------------------------------------------------------------------------------!
598	! Description:
599	! ------------
600	!> Header output for synthetic turbulence generator
601	!------------------------------------------------------------------------------!
602	SUBROUTINE stg_header ( io )
603
604
605	IMPLICIT NONE
606
607	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
608
609	!
610	!-- Write synthetic turbulence generator Header
611	WRITE( io, 1 )
612	IF ( use_syn_turb_gen ) THEN
613	WRITE( io, 2 )
614	ELSE
615	WRITE( io, 3 )
616	ENDIF
617
618	IF ( parametrize_inflow_turbulence ) THEN
619	WRITE( io, 4 ) dt_stg_adjust
620	ELSE
621	WRITE( io, 5 )
622	ENDIF
623
624	1 FORMAT (//' Synthetic turbulence generator information:'/ &
625	' ------------------------------------------'/)
626	2 FORMAT (' synthetic turbulence generator is switched on')
627	3 FORMAT (' synthetic turbulence generator is switched off')
628	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
629	5 FORMAT (' imposed turbulence is read from file' )
630
631	END SUBROUTINE stg_header
632
633
634	!------------------------------------------------------------------------------!
635	! Description:
636	! ------------
637	!> Initialization of the synthetic turbulence generator
638	!------------------------------------------------------------------------------!
639	SUBROUTINE stg_init
640
641	IMPLICIT NONE
642
643	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
644
645	#if defined( __parallel )
646	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
647	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
648	#endif
649
650	INTEGER(iwp) :: i !> grid index in x-direction
651	INTEGER(iwp) :: j !> loop index
652	INTEGER(iwp) :: k !< index
653	INTEGER(iwp) :: newtype !< dummy MPI type
654	INTEGER(iwp) :: realsize !< size of REAL variables
655	INTEGER(iwp) :: nseed !< dimension of random number seed
656	INTEGER(iwp) :: startseed = 1234567890 !< start seed for random number generator
657
658	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
659	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
660	!
661	!-- Dummy variables used for reading profiles
662	REAL(wp) :: d1 !< u profile
663	REAL(wp) :: d2 !< v profile
664	REAL(wp) :: d3 !< w profile
665	REAL(wp) :: d5 !< e profile
666	REAL(wp) :: luy !< length scale for u in y direction
667	REAL(wp) :: luz !< length scale for u in z direction
668	REAL(wp) :: lvy !< length scale for v in y direction
669	REAL(wp) :: lvz !< length scale for v in z direction
670	REAL(wp) :: lwy !< length scale for w in y direction
671	REAL(wp) :: lwz !< length scale for w in z direction
672	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
673	REAL(wp) :: zz !< height
674
675
676	#if defined( __parallel )
677	CALL MPI_BARRIER( comm2d, ierr )
678	#endif
679
680	#if defined( __parallel )
681	!
682	!-- Determine processor decomposition of z-axis along x- and y-direction
683	nnz = nz / pdims(1)
684	nzb_x_stg = 1 + myidx * INT( nnz )
685	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
686
687	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
688	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
689
690	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
691	.AND. .NOT. rans_mode ) ) THEN
692	nnz = nz / pdims(2)
693	nzb_y_stg = 1 + myidy * INT( nnz )
694	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
695
696	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
697	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
698	ENDIF
699
700	!
701	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
702	!-- velocity seeds
703	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
704	extent = 1 * realsize
705	!
706	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
707	!-- layer
708	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
709	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
710	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
711	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
712	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
713	CALL MPI_TYPE_FREE( newtype, ierr )
714
715	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
716	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
717	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
718	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
719	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
720	CALL MPI_TYPE_FREE( newtype, ierr )
721
722	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
723	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
724
725	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
726	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
727
728	DO j = 1, pdims(1)
729	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
730	ENDDO
731	!
732	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
733	!-- layer
734	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
735	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
736	.AND. .NOT. rans_mode ) ) THEN
737	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
738	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
739	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
740	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
741	CALL MPI_TYPE_FREE( newtype, ierr )
742
743	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
744	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
745	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
746	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
747	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
748	CALL MPI_TYPE_FREE( newtype, ierr )
749
750	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
751	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
752
753	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
754	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
755
756	DO j = 1, pdims(2)
757	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
758	ENDDO
759
760	ENDIF
761
762	#endif
763	!
764	!-- Define seed of random number
765	CALL RANDOM_SEED()
766	CALL RANDOM_SEED( size=nseed )
767	ALLOCATE( seed(1:nseed) )
768	DO j = 1, nseed
769	seed(j) = startseed + j
770	ENDDO
771	CALL RANDOM_SEED(put=seed)
772	!
773	!-- Allocate required arrays.
774	!-- In case no offline nesting or self nesting is used, the arrary
775	!-- mean_inflow profiles is required. Check if it is already allocated, else
776	!-- allocate and initialize it appropriately. Note, in case turbulence and
777	!-- inflow information is read from file, mean_inflow_profiles is already
778	!-- allocated and initialized appropriately.
779	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
780	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
781	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
782	mean_inflow_profiles = 0.0_wp
783	mean_inflow_profiles(:,1) = u_init
784	mean_inflow_profiles(:,2) = v_init
785	!
786	!-- Even though potential temperature and humidity are not perturbed,
787	!-- they need to be initialized appropriately.
788	IF ( .NOT. neutral ) &
789	mean_inflow_profiles(:,4) = pt_init
790	IF ( humidity ) &
791	mean_inflow_profiles(:,6) = q_init
792	ENDIF
793	ENDIF
794
795	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
796	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
797	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
798	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
799	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
800	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
801	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
802	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
803
804	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
805	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
806	dist_xz = 0.0_wp
807	dist_yz = 0.0_wp
808	!
809	!-- Read inflow profile
810	!-- Height levels of profiles in input profile is as follows:
811	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
812	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
813	!-- WARNING: zz is not used at the moment
814	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
815	EXIST = file_stg_exist )
816
817	IF ( file_stg_exist ) THEN
818
819	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
820	FORM='FORMATTED')
821	!
822	!-- Skip header
823	READ( 90, * )
824
825	DO k = nzb+1, nzt+1
826	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
827	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
828	d1, d2, d3, d5
829
830	!
831	!-- Convert length scales from meter to number of grid points.
832	nuy(k) = INT( luy * ddy )
833	nuz(k) = INT( luz * ddzw(k) )
834	nvy(k) = INT( lvy * ddy )
835	nvz(k) = INT( lvz * ddzw(k) )
836	nwy(k) = INT( lwy * ddy )
837	nwz(k) = INT( lwz * ddzw(k) )
838	!
839	!-- Workaround, assume isotropic turbulence
840	nwx(k) = nwy(k)
841	nvx(k) = nvy(k)
842	nux(k) = nuy(k)
843	!
844	!-- Save Mean inflow profiles
845	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
846	mean_inflow_profiles(k,1) = d1
847	mean_inflow_profiles(k,2) = d2
848	! mean_inflow_profiles(k,4) = d4
849	mean_inflow_profiles(k,5) = d5
850	ENDIF
851	ENDDO
852	!
853	!-- Set lenght scales at surface grid point
854	nuy(nzb) = nuy(nzb+1)
855	nuz(nzb) = nuz(nzb+1)
856	nvy(nzb) = nvy(nzb+1)
857	nvz(nzb) = nvz(nzb+1)
858	nwy(nzb) = nwy(nzb+1)
859	nwz(nzb) = nwz(nzb+1)
860
861	CLOSE( 90 )
862	!
863	!-- Calculate coefficient matrix from Reynolds stress tensor
864	!-- (Lund rotation)
865	CALL calc_coeff_matrix
866	!
867	!-- No information about turbulence and its length scales are available.
868	!-- Instead, parametrize turbulence which is imposed at the boundaries.
869	!-- Set flag which indicates that turbulence is parametrized, which is done
870	!-- later when energy-balance models are already initialized. This is
871	!-- because the STG needs information about surface properties such as
872	!-- roughness to build 'realistic' turbulence profiles.
873	ELSE
874	!
875	!-- Define length scale for the imposed turbulence, which is defined as
876	!-- 8 times the minimum grid spacing
877	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
878	!
879	!-- Define constant to gradually decrease length scales and Reynolds stress
880	!-- above ABL top. Assure that no zero length scales are used.
881	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
882	!
883	!-- Set flag indicating that turbulence is parametrized
884	parametrize_inflow_turbulence = .TRUE.
885	!
886	!-- In case of dirichlet inflow boundary conditions only at one lateral
887	!-- boundary, i.e. in the case no offline or self nesting is applied but
888	!-- synthetic turbulence shall be parametrized nevertheless, the
889	!-- boundary-layer depth need to determined first.
890	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
891	CALL nesting_offl_calc_zi
892	!
893	!-- Determine boundary-layer depth, which is used to initialize lenght
894	!-- scales
895	CALL calc_scaling_variables
896	!
897	!-- Initialize lenght and time scales, which in turn are used
898	!-- to initialize the filter functions.
899	CALL calc_length_and_time_scale
900	!
901	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
902	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
903	!-- Rotach et al. (1996) and is based on boundary-layer depth,
904	!-- friction velocity and velocity scale.
905	CALL parametrize_reynolds_stress
906	!
907	!-- Calculate coefficient matrix from Reynolds stress tensor
908	!-- (Lund rotation)
909	CALL calc_coeff_matrix
910
911	ENDIF
912
913	!
914	!-- Assign initial profiles. Note, this is only required if turbulent
915	!-- inflow from the left is desired, not in case of any of the
916	!-- nesting (offline or self nesting) approaches.
917	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
918	u_init = mean_inflow_profiles(:,1)
919	v_init = mean_inflow_profiles(:,2)
920	!pt_init = mean_inflow_profiles(:,4)
921	e_init = MAXVAL( mean_inflow_profiles(:,5) )
922	ENDIF
923
924	!
925	!-- Define the size of the filter functions and allocate them.
926	merg = 0
927
928	! arrays must be large enough to cover the largest length scale
929	DO k = nzb, nzt+1
930	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
931	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
932	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
933	IF ( j > merg ) merg = j
934	ENDDO
935
936	merg = 2 * merg
937	mergp = merg + nbgp
938
939	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
940	buy(-merg:merg,nzb:nzt+1), &
941	buz(-merg:merg,nzb:nzt+1), &
942	bvx(-merg:merg,nzb:nzt+1), &
943	bvy(-merg:merg,nzb:nzt+1), &
944	bvz(-merg:merg,nzb:nzt+1), &
945	bwx(-merg:merg,nzb:nzt+1), &
946	bwy(-merg:merg,nzb:nzt+1), &
947	bwz(-merg:merg,nzb:nzt+1) )
948
949	!
950	!-- Allocate velocity seeds for turbulence at xz-layer
951	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
952	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
953	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
954
955	!
956	!-- Allocate velocity seeds for turbulence at yz-layer
957	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
958	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
959	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
960
961	fu_xz = 0.0_wp
962	fuo_xz = 0.0_wp
963	fv_xz = 0.0_wp
964	fvo_xz = 0.0_wp
965	fw_xz = 0.0_wp
966	fwo_xz = 0.0_wp
967
968	fu_yz = 0.0_wp
969	fuo_yz = 0.0_wp
970	fv_yz = 0.0_wp
971	fvo_yz = 0.0_wp
972	fw_yz = 0.0_wp
973	fwo_yz = 0.0_wp
974
975	!
976	!-- Create filter functions
977	CALL stg_filter_func( nux, bux ) !filter ux
978	CALL stg_filter_func( nuy, buy ) !filter uy
979	CALL stg_filter_func( nuz, buz ) !filter uz
980	CALL stg_filter_func( nvx, bvx ) !filter vx
981	CALL stg_filter_func( nvy, bvy ) !filter vy
982	CALL stg_filter_func( nvz, bvz ) !filter vz
983	CALL stg_filter_func( nwx, bwx ) !filter wx
984	CALL stg_filter_func( nwy, bwy ) !filter wy
985	CALL stg_filter_func( nwz, bwz ) !filter wz
986
987	#if defined( __parallel )
988	CALL MPI_BARRIER( comm2d, ierr )
989	#endif
990
991	!
992	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
993	! time step.
994	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
995	! are 0 compared to the prerun. This is mostly for k=nzt+1.
996	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
997	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
998
999	IF ( myidx == id_stg_left ) i = -1
1000	IF ( myidx == id_stg_right ) i = nxr+1
1001
1002	DO j = nysg, nyng
1003	DO k = nzb, nzt+1
1004	IF ( a11(k) /= 0.0_wp ) THEN
1005	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
1006	ELSE
1007	fu_yz(k,j) = 0.0_wp
1008	ENDIF
1009
1010	IF ( a22(k) /= 0.0_wp ) THEN
1011	fv_yz(k,j) = ( v(k,j,i) - &
1012	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
1013	ELSE
1014	fv_yz(k,j) = 0.0_wp
1015	ENDIF
1016
1017	IF ( a33(k) /= 0.0_wp ) THEN
1018	fw_yz(k,j) = ( w(k,j,i) - &
1019	a31(k) * fu_yz(k,j) - a32(k) * &
1020	fv_yz(k,j) ) / a33(k)
1021	ELSE
1022	fw_yz = 0._wp
1023	ENDIF
1024
1025	ENDDO
1026	ENDDO
1027	ENDIF
1028
1029	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1030
1031	IF ( myidy == id_stg_south ) j = -1
1032	IF ( myidy == id_stg_north ) j = nyn+1
1033
1034	DO i = nxlg, nxrg
1035	DO k = nzb, nzt+1
1036
1037	IF ( a11(k) /= 0.0_wp ) THEN
1038	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1039	ELSE
1040	fu_xz(k,i) = 0.0_wp
1041	ENDIF
1042
1043	IF ( a22(k) /= 0.0_wp ) THEN
1044	fv_xz(k,i) = ( v(k,j,i) - &
1045	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1046	ELSE
1047	fv_xz(k,i) = 0.0_wp
1048	ENDIF
1049
1050	IF ( a33(k) /= 0.0_wp ) THEN
1051	fw_xz(k,i) = ( w(k,j,i) - &
1052	a31(k) * fu_xz(k,i) - &
1053	a32(k) * fv_xz(k,i) ) / a33(k)
1054	ELSE
1055	fw_xz = 0._wp
1056	ENDIF
1057
1058	ENDDO
1059	ENDDO
1060	ENDIF
1061	ENDIF
1062	!
1063	!-- Count the number of non-topography grid points at the boundaries where
1064	!-- perturbations are imposed. This number is later used for bias corrections
1065	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1066	!-- due to the asymetry of u and v along x and y direction, respectively,
1067	!-- different cases must be distinguished.
1068	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1069	!
1070	!-- Number of grid points where perturbations are imposed on u
1071	IF ( myidx == id_stg_left ) i = nxl
1072	IF ( myidx == id_stg_right ) i = nxr+1
1073
1074	nr_non_topo_yz_l(1) = SUM( &
1075	MERGE( 1, 0, &
1076	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1077	!
1078	!-- Number of grid points where perturbations are imposed on v and w
1079	IF ( myidx == id_stg_left ) i = nxl-1
1080	IF ( myidx == id_stg_right ) i = nxr+1
1081
1082	nr_non_topo_yz_l(2) = SUM( &
1083	MERGE( 1, 0, &
1084	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1085	nr_non_topo_yz_l(3) = SUM( &
1086	MERGE( 1, 0, &
1087	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1088
1089	#if defined( __parallel )
1090	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1091	MPI_SUM, comm1dy, ierr )
1092	#else
1093	nr_non_topo_yz = nr_non_topo_yz_l
1094	#endif
1095	ENDIF
1096
1097	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1098	!
1099	!-- Number of grid points where perturbations are imposed on v
1100	IF ( myidy == id_stg_south ) j = nys
1101	IF ( myidy == id_stg_north ) j = nyn+1
1102
1103	nr_non_topo_xz_l(2) = SUM( &
1104	MERGE( 1, 0, &
1105	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1106	!
1107	!-- Number of grid points where perturbations are imposed on u and w
1108	IF ( myidy == id_stg_south ) j = nys-1
1109	IF ( myidy == id_stg_north ) j = nyn+1
1110
1111	nr_non_topo_xz_l(1) = SUM( &
1112	MERGE( 1, 0, &
1113	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1114	nr_non_topo_xz_l(3) = SUM( &
1115	MERGE( 1, 0, &
1116	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1117
1118	#if defined( __parallel )
1119	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1120	MPI_SUM, comm1dx, ierr )
1121	#else
1122	nr_non_topo_xz = nr_non_topo_xz_l
1123	#endif
1124	ENDIF
1125
1126
1127	END SUBROUTINE stg_init
1128
1129
1130	!------------------------------------------------------------------------------!
1131	! Description:
1132	! ------------
1133	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1134	!> (Xie and Castro, 2008)
1135	!------------------------------------------------------------------------------!
1136	SUBROUTINE stg_filter_func( nxx, bxx )
1137
1138
1139	IMPLICIT NONE
1140
1141	INTEGER(iwp) :: k !< loop index
1142	INTEGER(iwp) :: n_k !< length scale nXX in height k
1143	INTEGER(iwp) :: n_k2 !< n_k * 2
1144	INTEGER(iwp) :: nf !< index for length scales
1145
1146	REAL(wp) :: bdenom !< denominator for filter functions bXX
1147	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1148
1149	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
1150
1151	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
1152
1153
1154	bxx = 0.0_wp
1155
1156	DO k = nzb, nzt+1
1157	bdenom = 0.0_wp
1158	n_k = nxx(k)
1159	IF ( n_k /= 0 ) THEN
1160	n_k2 = n_k * 2
1161
1162	!
1163	!-- ( Eq.10 )^2
1164	DO nf = -n_k2, n_k2
1165	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1166	ENDDO
1167
1168	!
1169	!-- ( Eq.9 )
1170	bdenom = SQRT( bdenom )
1171	DO nf = -n_k2, n_k2
1172	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1173	ENDDO
1174	ENDIF
1175	ENDDO
1176
1177	END SUBROUTINE stg_filter_func
1178
1179
1180	!------------------------------------------------------------------------------!
1181	! Description:
1182	! ------------
1183	!> Parin for &stg_par for synthetic turbulence generator
1184	!------------------------------------------------------------------------------!
1185	SUBROUTINE stg_parin
1186
1187
1188	IMPLICIT NONE
1189
1190	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1191
1192
1193	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
1194
1195	line = ' '
1196
1197	!
1198	!-- Try to find stg package
1199	REWIND ( 11 )
1200	line = ' '
1201	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1202	READ ( 11, '(A)', END=20 ) line
1203	ENDDO
1204	BACKSPACE ( 11 )
1205
1206	!
1207	!-- Read namelist
1208	READ ( 11, stg_par, ERR = 10, END = 20 )
1209
1210	!
1211	!-- Set flag that indicates that the synthetic turbulence generator is switched
1212	!-- on
1213	syn_turb_gen = .TRUE.
1214	GOTO 20
1215
1216	10 BACKSPACE( 11 )
1217	READ( 11 , '(A)') line
1218	CALL parin_fail_message( 'stg_par', line )
1219
1220	20 CONTINUE
1221
1222	END SUBROUTINE stg_parin
1223
1224
1225	!------------------------------------------------------------------------------!
1226	! Description:
1227	! ------------
1228	!> This routine reads the respective restart data.
1229	!------------------------------------------------------------------------------!
1230	SUBROUTINE stg_rrd_global( found )
1231
1232
1233	IMPLICIT NONE
1234
1235	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1236
1237
1238	found = .TRUE.
1239
1240
1241	SELECT CASE ( restart_string(1:length) )
1242
1243	CASE ( 'time_stg_adjust' )
1244	READ ( 13 ) time_stg_adjust
1245
1246	CASE ( 'time_stg_call' )
1247	READ ( 13 ) time_stg_call
1248
1249	CASE ( 'use_syn_turb_gen' )
1250	READ ( 13 ) use_syn_turb_gen
1251
1252	CASE DEFAULT
1253
1254	found = .FALSE.
1255
1256	END SELECT
1257
1258
1259	END SUBROUTINE stg_rrd_global
1260
1261
1262	!------------------------------------------------------------------------------!
1263	! Description:
1264	! ------------
1265	!> This routine writes the respective restart data.
1266	!------------------------------------------------------------------------------!
1267	SUBROUTINE stg_wrd_global
1268
1269
1270	IMPLICIT NONE
1271
1272	CALL wrd_write_string( 'time_stg_adjust' )
1273	WRITE ( 14 ) time_stg_adjust
1274
1275	CALL wrd_write_string( 'time_stg_call' )
1276	WRITE ( 14 ) time_stg_call
1277
1278	CALL wrd_write_string( 'use_syn_turb_gen' )
1279	WRITE ( 14 ) use_syn_turb_gen
1280
1281
1282	END SUBROUTINE stg_wrd_global
1283
1284
1285	!------------------------------------------------------------------------------!
1286	! Description:
1287	! ------------
1288	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1289	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1290	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1291	!> (Lund, 1998).
1292	!------------------------------------------------------------------------------!
1293	SUBROUTINE stg_main
1294
1295	IMPLICIT NONE
1296
1297	INTEGER(iwp) :: i !< grid index in x-direction
1298	INTEGER(iwp) :: j !< loop index in y-direction
1299	INTEGER(iwp) :: k !< loop index in z-direction
1300
1301	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1302
1303	REAL(wp) :: dt_stg !< wheighted subtimestep
1304
1305	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1306
1307	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1308	!
1309	!-- Calculate time step which is needed for filter functions
1310	dt_stg = MAX( dt_3d, dt_stg_call )
1311	!
1312	!-- Check if synthetic turbulence generator needs to be called and new
1313	!-- perturbations need to be created or if old disturbances can be imposed
1314	!-- again.
1315	IF ( time_stg_call >= dt_stg_call .AND. &
1316	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1317	stg_call = .TRUE.
1318	ELSE
1319	stg_call = .FALSE.
1320	ENDIF
1321	!
1322	!-- Initial value of fu, fv, fw
1323	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1324	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1325	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1326	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1327
1328	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1329	.AND. .NOT. rans_mode ) ) THEN
1330	!
1331	!-- Generate turbulence at right boundary
1332	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_right )
1333	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_right )
1334	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_right )
1335	!
1336	!-- Generate turbulence at north boundary
1337	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_north )
1338	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_north )
1339	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_north )
1340	!
1341	!-- Generate turbulence at south boundary
1342	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south )
1343	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south )
1344	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south )
1345	ENDIF
1346	velocity_seed_initialized = .TRUE.
1347	ENDIF
1348
1349	!
1350	!-- New set of fu, fv, fw
1351	IF ( stg_call ) THEN
1352	!
1353	!-- Generate turbulence at left boundary (required in all applications,
1354	!-- i.e. offline nesting and turbulent inflow from the left)
1355	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1356	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1357	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1358
1359	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1360	.AND. .NOT. rans_mode ) ) THEN
1361	!
1362	!-- Generate turbulence at right boundary
1363	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_right )
1364	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_right )
1365	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_right )
1366	!
1367	!-- Generate turbulence at north boundary
1368	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_north )
1369	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_north )
1370	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_north )
1371	!
1372	!-- Generate turbulence at south boundary
1373	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south )
1374	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south )
1375	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south )
1376	ENDIF
1377	ENDIF
1378
1379	!
1380	!-- Turbulence generation at left and or right boundary
1381	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1382	!
1383	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1384	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1385	!-- imposed
1386	IF ( stg_call ) THEN
1387
1388	DO j = nysg, nyng
1389	DO k = nzb, nzt + 1
1390	!
1391	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1392	IF ( tu(k) == 0.0_wp ) THEN
1393	fu_yz(k,j) = fuo_yz(k,j)
1394	ELSE
1395	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1396	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1397	ENDIF
1398
1399	IF ( tv(k) == 0.0_wp ) THEN
1400	fv_yz(k,j) = fvo_yz(k,j)
1401	ELSE
1402	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1403	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1404	ENDIF
1405
1406	IF ( tw(k) == 0.0_wp ) THEN
1407	fw_yz(k,j) = fwo_yz(k,j)
1408	ELSE
1409	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1410	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1411	ENDIF
1412	ENDDO
1413	ENDDO
1414
1415	dist_yz(nzb,:,1) = 0.0_wp
1416	dist_yz(nzb,:,2) = 0.0_wp
1417	dist_yz(nzb,:,3) = 0.0_wp
1418
1419	IF ( myidx == id_stg_left ) i = nxl
1420	IF ( myidx == id_stg_right ) i = nxr+1
1421	DO j = nysg, nyng
1422	DO k = nzb+1, nzt + 1
1423	!
1424	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1425	!-- Additional factors are added to improve the variance of v and w
1426	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1427	MERGE( 1.0_wp, 0.0_wp, &
1428	BTEST( wall_flags_0(k,j,i), 1 ) )
1429	ENDDO
1430	ENDDO
1431
1432	IF ( myidx == id_stg_left ) i = nxl-1
1433	IF ( myidx == id_stg_right ) i = nxr+1
1434	DO j = nysg, nyng
1435	DO k = nzb+1, nzt + 1
1436	!
1437	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1438	!-- Additional factors are added to improve the variance of v and w
1439	!-- experimental test of 1.2
1440	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1441	* 1.2_wp ) &
1442	* ( a21(k) * fu_yz(k,j) &
1443	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1444	MERGE( 1.0_wp, 0.0_wp, &
1445	BTEST( wall_flags_0(k,j,i), 2 ) )
1446	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1447	* 1.3_wp ) &
1448	* ( a31(k) * fu_yz(k,j) &
1449	+ a32(k) * fv_yz(k,j) &
1450	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1451	MERGE( 1.0_wp, 0.0_wp, &
1452	BTEST( wall_flags_0(k,j,i), 3 ) )
1453	ENDDO
1454	ENDDO
1455	ENDIF
1456
1457	!
1458	!-- Mass flux correction following Kim et al. (2013)
1459	!-- This correction factor insures that the mass flux is preserved at the
1460	!-- inflow boundary. First, calculate mean value of the imposed
1461	!-- perturbations at yz boundary.
1462	!-- Note, this needs to be done only after the last RK3-substep, else
1463	!-- the boundary values won't be accessed.
1464	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1465	mc_factor_l = 0.0_wp
1466	mc_factor = 0.0_wp
1467	!
1468	!-- Sum up the original volume flows (with and without perturbations).
1469	!-- Note, for non-normal components (here v and w) it is actually no
1470	!-- volume flow.
1471	IF ( myidx == id_stg_left ) i = nxl
1472	IF ( myidx == id_stg_right ) i = nxr+1
1473
1474	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1475	* MERGE( 1.0_wp, 0.0_wp, &
1476	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1477
1478	IF ( myidx == id_stg_left ) i = nxl-1
1479	IF ( myidx == id_stg_right ) i = nxr+1
1480
1481	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1482	* MERGE( 1.0_wp, 0.0_wp, &
1483	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1484	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1485	* MERGE( 1.0_wp, 0.0_wp, &
1486	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1487
1488	#if defined( __parallel )
1489	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1490	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1491	#else
1492	mc_factor = mc_factor_l
1493	#endif
1494	!
1495	!-- Calculate correction factor and force zero mean perturbations.
1496	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1497
1498	IF ( myidx == id_stg_left ) i = nxl
1499	IF ( myidx == id_stg_right ) i = nxr+1
1500
1501	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
1502	* MERGE( 1.0_wp, 0.0_wp, &
1503	BTEST( wall_flags_0(:,:,i), 1 ) )
1504
1505
1506	IF ( myidx == id_stg_left ) i = nxl-1
1507	IF ( myidx == id_stg_right ) i = nxr+1
1508
1509	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
1510	* MERGE( 1.0_wp, 0.0_wp, &
1511	BTEST( wall_flags_0(:,:,i), 2 ) )
1512
1513	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
1514	* MERGE( 1.0_wp, 0.0_wp, &
1515	BTEST( wall_flags_0(:,:,i), 3 ) )
1516	!
1517	!-- Add disturbances
1518	IF ( myidx == id_stg_left ) THEN
1519	!
1520	!-- For the left boundary distinguish between mesoscale offline / self
1521	!-- nesting and turbulent inflow at the left boundary only. In the latter
1522	!-- case turbulence is imposed on the mean inflow profiles.
1523	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1524	!
1525	!-- Add disturbance at the inflow
1526	DO j = nysg, nyng
1527	DO k = nzb, nzt+1
1528	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1529	dist_yz(k,j,1) ) &
1530	* MERGE( 1.0_wp, 0.0_wp, &
1531	BTEST( wall_flags_0(k,j,0), 1 ) )
1532	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1533	dist_yz(k,j,2) ) &
1534	* MERGE( 1.0_wp, 0.0_wp, &
1535	BTEST( wall_flags_0(k,j,-1), 2 ) )
1536	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1537	* MERGE( 1.0_wp, 0.0_wp, &
1538	BTEST( wall_flags_0(k,j,-1), 3 ) )
1539	ENDDO
1540	ENDDO
1541	ELSE
1542
1543	DO j = nys, nyn
1544	DO k = nzb+1, nzt
1545	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1546	* MERGE( 1.0_wp, 0.0_wp, &
1547	BTEST( wall_flags_0(k,j,0), 1 ) )
1548	u(k,j,-1) = u(k,j,0)
1549	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1550	* MERGE( 1.0_wp, 0.0_wp, &
1551	BTEST( wall_flags_0(k,j,-1), 2 ) )
1552	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1553	* MERGE( 1.0_wp, 0.0_wp, &
1554	BTEST( wall_flags_0(k,j,-1), 3 ) )
1555	ENDDO
1556	ENDDO
1557	ENDIF
1558	ENDIF
1559	IF ( myidx == id_stg_right ) THEN
1560	DO j = nys, nyn
1561	DO k = nzb+1, nzt
1562	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1563	* MERGE( 1.0_wp, 0.0_wp, &
1564	BTEST( wall_flags_0(k,j,nxr+1), 1 ) )
1565	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1566	* MERGE( 1.0_wp, 0.0_wp, &
1567	BTEST( wall_flags_0(k,j,nxr+1), 2 ) )
1568	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1569	* MERGE( 1.0_wp, 0.0_wp, &
1570	BTEST( wall_flags_0(k,j,nxr+1), 3 ) )
1571	ENDDO
1572	ENDDO
1573	ENDIF
1574	ENDIF
1575	ENDIF
1576	!
1577	!-- Turbulence generation at north and south boundary
1578	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1579	!
1580	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1581	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1582	!-- imposed
1583	IF ( stg_call ) THEN
1584	DO i = nxlg, nxrg
1585	DO k = nzb, nzt + 1
1586	!
1587	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1588	IF ( tu(k) == 0.0_wp ) THEN
1589	fu_xz(k,i) = fuo_xz(k,i)
1590	ELSE
1591	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1592	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1593	ENDIF
1594
1595	IF ( tv(k) == 0.0_wp ) THEN
1596	fv_xz(k,i) = fvo_xz(k,i)
1597	ELSE
1598	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1599	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1600	ENDIF
1601
1602	IF ( tw(k) == 0.0_wp ) THEN
1603	fw_xz(k,i) = fwo_xz(k,i)
1604	ELSE
1605	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1606	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1607	ENDIF
1608	ENDDO
1609	ENDDO
1610
1611
1612	dist_xz(nzb,:,1) = 0.0_wp
1613	dist_xz(nzb,:,2) = 0.0_wp
1614	dist_xz(nzb,:,3) = 0.0_wp
1615
1616	IF ( myidy == id_stg_south ) j = nys
1617	IF ( myidy == id_stg_north ) j = nyn+1
1618	DO i = nxlg, nxrg
1619	DO k = nzb+1, nzt + 1
1620	!
1621	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1622	!-- Additional factors are added to improve the variance of v and w
1623	!experimental test of 1.2
1624	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1625	* 1.2_wp ) &
1626	* ( a21(k) * fu_xz(k,i) &
1627	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1628	MERGE( 1.0_wp, 0.0_wp, &
1629	BTEST( wall_flags_0(k,j,i), 2 ) )
1630	ENDDO
1631	ENDDO
1632
1633	IF ( myidy == id_stg_south ) j = nys-1
1634	IF ( myidy == id_stg_north ) j = nyn+1
1635	DO i = nxlg, nxrg
1636	DO k = nzb+1, nzt + 1
1637	!
1638	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1639	!-- Additional factors are added to improve the variance of v and w
1640	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1641	MERGE( 1.0_wp, 0.0_wp, &
1642	BTEST( wall_flags_0(k,j,i), 1 ) )
1643
1644	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1645	* 1.3_wp ) &
1646	* ( a31(k) * fu_xz(k,i) &
1647	+ a32(k) * fv_xz(k,i) &
1648	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1649	MERGE( 1.0_wp, 0.0_wp, &
1650	BTEST( wall_flags_0(k,j,i), 3 ) )
1651	ENDDO
1652	ENDDO
1653	ENDIF
1654
1655	!
1656	!-- Mass flux correction following Kim et al. (2013)
1657	!-- This correction factor insures that the mass flux is preserved at the
1658	!-- inflow boundary. First, calculate mean value of the imposed
1659	!-- perturbations at yz boundary.
1660	!-- Note, this needs to be done only after the last RK3-substep, else
1661	!-- the boundary values won't be accessed.
1662	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1663	mc_factor_l = 0.0_wp
1664	mc_factor = 0.0_wp
1665
1666	IF ( myidy == id_stg_south ) j = nys
1667	IF ( myidy == id_stg_north ) j = nyn+1
1668
1669	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1670	* MERGE( 1.0_wp, 0.0_wp, &
1671	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1672
1673	IF ( myidy == id_stg_south ) j = nys-1
1674	IF ( myidy == id_stg_north ) j = nyn+1
1675
1676	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1677	* MERGE( 1.0_wp, 0.0_wp, &
1678	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1679	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1680	* MERGE( 1.0_wp, 0.0_wp, &
1681	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1682
1683	#if defined( __parallel )
1684	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1685	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1686	#else
1687	mc_factor = mc_factor_l
1688	#endif
1689
1690	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1691
1692	IF ( myidy == id_stg_south ) j = nys
1693	IF ( myidy == id_stg_north ) j = nyn+1
1694
1695	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
1696	* MERGE( 1.0_wp, 0.0_wp, &
1697	BTEST( wall_flags_0(:,j,:), 2 ) )
1698
1699
1700	IF ( myidy == id_stg_south ) j = nys-1
1701	IF ( myidy == id_stg_north ) j = nyn+1
1702
1703	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
1704	* MERGE( 1.0_wp, 0.0_wp, &
1705	BTEST( wall_flags_0(:,j,:), 1 ) )
1706
1707	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
1708	* MERGE( 1.0_wp, 0.0_wp, &
1709	BTEST( wall_flags_0(:,j,:), 3 ) )
1710	!
1711	!-- Add disturbances
1712	IF ( myidy == id_stg_south ) THEN
1713	DO i = nxl, nxr
1714	DO k = nzb+1, nzt
1715	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1716	* MERGE( 1.0_wp, 0.0_wp, &
1717	BTEST( wall_flags_0(k,-1,i), 1 ) )
1718	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1719	* MERGE( 1.0_wp, 0.0_wp, &
1720	BTEST( wall_flags_0(k,0,i), 2 ) )
1721	v(k,-1,i) = v(k,0,i)
1722	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1723	* MERGE( 1.0_wp, 0.0_wp, &
1724	BTEST( wall_flags_0(k,-1,i), 3 ) )
1725	ENDDO
1726	ENDDO
1727	ENDIF
1728	IF ( myidy == id_stg_north ) THEN
1729
1730	DO i = nxl, nxr
1731	DO k = nzb+1, nzt
1732	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1733	* MERGE( 1.0_wp, 0.0_wp, &
1734	BTEST( wall_flags_0(k,nyn+1,i), 1 ) )
1735	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1736	* MERGE( 1.0_wp, 0.0_wp, &
1737	BTEST( wall_flags_0(k,nyn+1,i), 2 ) )
1738	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1739	* MERGE( 1.0_wp, 0.0_wp, &
1740	BTEST( wall_flags_0(k,nyn+1,i), 3 ) )
1741	ENDDO
1742	ENDDO
1743	ENDIF
1744	ENDIF
1745	ENDIF
1746	!
1747	!-- Finally, set time counter for calling STG to zero
1748	IF ( stg_call ) time_stg_call = 0.0_wp
1749
1750	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1751
1752	END SUBROUTINE stg_main
1753
1754	!------------------------------------------------------------------------------!
1755	! Description:
1756	! ------------
1757	!> Generate a set of random number rand_it wich is equal on each PE
1758	!> and calculate the velocity seed f_n.
1759	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1760	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1761	!> parts are collected to form the full array.
1762	!------------------------------------------------------------------------------!
1763	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id )
1764
1765	IMPLICIT NONE
1766
1767	INTEGER(iwp) :: id !< core ids at respective boundaries
1768	INTEGER(iwp) :: j !< loop index in y-direction
1769	INTEGER(iwp) :: jj !< loop index in y-direction
1770	INTEGER(iwp) :: k !< loop index in z-direction
1771	INTEGER(iwp) :: kk !< loop index in z-direction
1772	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1773
1774	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1775	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1776	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
1777	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1778
1779	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1780	REAL(wp) :: rand_av !< average of random number
1781	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1782
1783	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
1784	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1785	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
1786	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
1787	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1788
1789
1790	!
1791	!-- Generate random numbers using a seed generated in stg_init.
1792	!-- The set of random numbers are modified to have an average of 0 and
1793	!-- unit variance.
1794	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
1795
1796	rand_av = 0.0_wp
1797	rand_sigma_inv = 0.0_wp
1798	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
1799
1800	DO j = 0, ny
1801	DO k = nzb, nzt+1
1802	CALL RANDOM_NUMBER( rand_it(k,j) )
1803	rand_av = rand_av + rand_it(k,j)
1804	ENDDO
1805	ENDDO
1806
1807	rand_av = rand_av * nyz_inv
1808
1809	DO j = 0, ny
1810	DO k = nzb, nzt+1
1811	rand_it(k,j) = rand_it(k,j) - rand_av
1812	rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
1813	ENDDO
1814	ENDDO
1815
1816	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)
1817
1818	DO j = 0, ny
1819	DO k = nzb, nzt+1
1820	rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
1821	ENDDO
1822	ENDDO
1823
1824	!
1825	!-- Periodic fill of random number in space
1826	DO j = 0, ny
1827	DO k = 1, mergp
1828	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
1829	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
1830	ENDDO
1831	ENDDO
1832	DO j = 1, mergp
1833	DO k = nzb-mergp, nzt+1+mergp
1834	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
1835	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
1836	ENDDO
1837	ENDDO
1838
1839	!
1840	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1841	n_y2 = n_y * 2
1842	n_z2 = n_z * 2
1843	f_n_l = 0.0_wp
1844
1845	DO j = nysg, nyng
1846	DO k = nzb_x_stg, nzt_x_stg+1
1847	DO jj = -n_y2(k), n_y2(k)
1848	DO kk = -n_z2(k), n_z2(k)
1849	f_n_l(k,j) = f_n_l(k,j) &
1850	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1851	ENDDO
1852	ENDDO
1853	ENDDO
1854	ENDDO
1855
1856	DEALLOCATE( rand_it )
1857	!
1858	!-- Gather velocity seeds of full subdomain
1859	send_count = nzt_x_stg - nzb_x_stg + 1
1860	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1861
1862	#if defined( __parallel )
1863	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1864	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
1865	id, comm1dx, ierr )
1866	#else
1867	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
1868	#endif
1869
1870
1871	END SUBROUTINE stg_generate_seed_yz
1872
1873
1874
1875
1876	!------------------------------------------------------------------------------!
1877	! Description:
1878	! ------------
1879	!> Generate a set of random number rand_it wich is equal on each PE
1880	!> and calculate the velocity seed f_n.
1881	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1882	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1883	!> parts are collected to form the full array.
1884	!------------------------------------------------------------------------------!
1885	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id )
1886
1887	IMPLICIT NONE
1888
1889	INTEGER(iwp) :: id !< core ids at respective boundaries
1890	INTEGER(iwp) :: i !< loop index in x-direction
1891	INTEGER(iwp) :: ii !< loop index in x-direction
1892	INTEGER(iwp) :: k !< loop index in z-direction
1893	INTEGER(iwp) :: kk !< loop index in z-direction
1894	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1895
1896	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1897	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1898	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
1899	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1900
1901	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1902	REAL(wp) :: rand_av !< average of random number
1903	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1904
1905	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
1906	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1907	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
1908	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
1909	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1910
1911
1912	!
1913	!-- Generate random numbers using a seed generated in stg_init.
1914	!-- The set of random numbers are modified to have an average of 0 and
1915	!-- unit variance.
1916	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
1917
1918	rand_av = 0.0_wp
1919	rand_sigma_inv = 0.0_wp
1920	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
1921
1922	DO i = 0, nx
1923	DO k = nzb, nzt+1
1924	CALL RANDOM_NUMBER( rand_it(k,i) )
1925	rand_av = rand_av + rand_it(k,i)
1926	ENDDO
1927	ENDDO
1928
1929	rand_av = rand_av * nxz_inv
1930
1931	DO i = 0, nx
1932	DO k = nzb, nzt+1
1933	rand_it(k,i) = rand_it(k,i) - rand_av
1934	rand_sigma_inv = rand_sigma_inv + rand_it(k,i) ** 2
1935	ENDDO
1936	ENDDO
1937
1938	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nxz_inv)
1939
1940	DO i = 0, nx
1941	DO k = nzb, nzt+1
1942	rand_it(k,i) = rand_it(k,i) * rand_sigma_inv
1943	ENDDO
1944	ENDDO
1945
1946	!
1947	!-- Periodic fill of random number in space
1948	DO i = 0, nx
1949	DO k = 1, mergp
1950	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
1951	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
1952	ENDDO
1953	ENDDO
1954	DO i = 1, mergp
1955	DO k = nzb-mergp, nzt+1+mergp
1956	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
1957	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
1958	ENDDO
1959	ENDDO
1960
1961	!
1962	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1963	n_x2 = n_x * 2
1964	n_z2 = n_z * 2
1965	f_n_l = 0.0_wp
1966
1967	DO i = nxlg, nxrg
1968	DO k = nzb_y_stg, nzt_y_stg+1
1969	DO ii = -n_x2(k), n_x2(k)
1970	DO kk = -n_z2(k), n_z2(k)
1971	f_n_l(k,i) = f_n_l(k,i) &
1972	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1973	ENDDO
1974	ENDDO
1975	ENDDO
1976	ENDDO
1977
1978	DEALLOCATE( rand_it )
1979
1980	!
1981	!-- Gather velocity seeds of full subdomain
1982	send_count = nzt_y_stg - nzb_y_stg + 1
1983	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
1984
1985
1986	#if defined( __parallel )
1987	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
1988	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
1989	id, comm1dy, ierr )
1990	#else
1991	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
1992	#endif
1993
1994
1995	END SUBROUTINE stg_generate_seed_xz
1996
1997	!------------------------------------------------------------------------------!
1998	! Description:
1999	! ------------
2000	!> Parametrization of the Reynolds stress tensor, following the parametrization
2001	!> described in Rotach et al. (1996), which is applied in state-of-the-art
2002	!> dispserion modelling. Please note, the parametrization does not distinguish
2003	!> between along-wind and cross-wind turbulence.
2004	!------------------------------------------------------------------------------!
2005	SUBROUTINE parametrize_reynolds_stress
2006
2007	IMPLICIT NONE
2008
2009	INTEGER(iwp) :: k !< loop index in z-direction
2010
2011	REAL(wp) :: zzi !< ratio of z/zi
2012
2013	DO k = nzb+1, nzt+1
2014	!
2015	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2016	!-- The function decreases to 1/10 after one length scale above the
2017	!-- ABL top.
2018	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2019	!
2020	!-- Determine normalized height coordinate
2021	zzi = zu(k) / zi_ribulk
2022	!
2023	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2024	!-- to the denominator, else the merge-function can crash if scale_l is
2025	!-- zero.
2026	r11(k) = scale_us*2 ( &
2027	MERGE( 0.35_wp * ABS( &
2028	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2029	)**( 2.0_wp / 3.0_wp ), &
2030	0.0_wp, &
2031	scale_l < 0.0_wp ) &
2032	+ 5.0_wp - 4.0_wp * zzi &
2033	) * blend
2034
2035	r22(k) = r11(k)
2036	!
2037	!-- w'w'
2038	r33(k) = scale_wm*2 ( &
2039	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2040	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2041	) * blend
2042	!
2043	!-- u'w' and v'w'. Assume isotropy.
2044	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2045	r32(k) = r31(k)
2046	!
2047	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2048	!-- a similar profile as for u'w'.
2049	r21(k) = r31(k)
2050	ENDDO
2051
2052	!
2053	!-- Set bottom boundary condition
2054	r11(nzb) = r11(nzb+1)
2055	r22(nzb) = r22(nzb+1)
2056	r33(nzb) = r33(nzb+1)
2057
2058	r21(nzb) = r11(nzb+1)
2059	r31(nzb) = r31(nzb+1)
2060	r32(nzb) = r32(nzb+1)
2061
2062
2063	END SUBROUTINE parametrize_reynolds_stress
2064
2065	!------------------------------------------------------------------------------!
2066	! Description:
2067	! ------------
2068	!> Calculate the coefficient matrix from the Lund rotation.
2069	!------------------------------------------------------------------------------!
2070	SUBROUTINE calc_coeff_matrix
2071
2072	IMPLICIT NONE
2073
2074	INTEGER(iwp) :: k !< loop index in z-direction
2075
2076	!
2077	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2078	DO k = nzb+1, nzt+1
2079	IF ( r11(k) > 10E-6_wp ) THEN
2080	a11(k) = SQRT( r11(k) )
2081	a21(k) = r21(k) / a11(k)
2082	a31(k) = r31(k) / a11(k)
2083	ELSE
2084	a11(k) = 10E-8_wp
2085	a21(k) = 10E-8_wp
2086	a31(k) = 10E-8_wp
2087	ENDIF
2088	ENDDO
2089	DO k = nzb+1, nzt+1
2090	a22(k) = r22(k) - a21(k)**2
2091	IF ( a22(k) > 10E-6_wp ) THEN
2092	a22(k) = SQRT( a22(k) )
2093	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2094	ELSE
2095	a22(k) = 10E-8_wp
2096	a32(k) = 10E-8_wp
2097	ENDIF
2098	ENDDO
2099	DO k = nzb+1, nzt+1
2100	a33(k) = r33(k) - a31(k)2 - a32(k)2
2101	IF ( a33(k) > 10E-6_wp ) THEN
2102	a33(k) = SQRT( a33(k) )
2103	ELSE
2104	a33(k) = 10E-8_wp
2105	ENDIF
2106	ENDDO
2107	!
2108	!-- Set bottom boundary condition
2109	a11(nzb) = a11(nzb+1)
2110	a22(nzb) = a22(nzb+1)
2111	a21(nzb) = a21(nzb+1)
2112	a33(nzb) = a33(nzb+1)
2113	a31(nzb) = a31(nzb+1)
2114	a32(nzb) = a32(nzb+1)
2115
2116	END SUBROUTINE calc_coeff_matrix
2117
2118	!------------------------------------------------------------------------------!
2119	! Description:
2120	! ------------
2121	!> This routine controls the re-adjustment of the turbulence statistics used
2122	!> for generating turbulence at the lateral boundaries.
2123	!------------------------------------------------------------------------------!
2124	SUBROUTINE stg_adjust
2125
2126	IMPLICIT NONE
2127
2128
2129	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2130	!
2131	!-- In case of dirichlet inflow boundary conditions only at one lateral
2132	!-- boundary, i.e. in the case no offline or self nesting is applied but
2133	!-- synthetic turbulence shall be parametrized nevertheless, the
2134	!-- boundary-layer depth need to determined first.
2135	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2136	CALL nesting_offl_calc_zi
2137	!
2138	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2139	!-- are calculated.
2140	CALL calc_scaling_variables
2141	!
2142	!-- Set length and time scales depending on boundary-layer height
2143	CALL calc_length_and_time_scale
2144	!
2145	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2146	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2147	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2148	!-- friction velocity and velocity scale.
2149	CALL parametrize_reynolds_stress
2150	!
2151	!-- Calculate coefficient matrix from Reynolds stress tensor
2152	!-- (Lund rotation)
2153	CALL calc_coeff_matrix
2154	!
2155	!-- Determine filter functions on basis of updated length scales
2156	CALL stg_filter_func( nux, bux ) !filter ux
2157	CALL stg_filter_func( nuy, buy ) !filter uy
2158	CALL stg_filter_func( nuz, buz ) !filter uz
2159	CALL stg_filter_func( nvx, bvx ) !filter vx
2160	CALL stg_filter_func( nvy, bvy ) !filter vy
2161	CALL stg_filter_func( nvz, bvz ) !filter vz
2162	CALL stg_filter_func( nwx, bwx ) !filter wx
2163	CALL stg_filter_func( nwy, bwy ) !filter wy
2164	CALL stg_filter_func( nwz, bwz ) !filter wz
2165	!
2166	!-- Reset time counter for controlling next adjustment to zero
2167	time_stg_adjust = 0.0_wp
2168
2169	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2170
2171	END SUBROUTINE stg_adjust
2172
2173
2174	!------------------------------------------------------------------------------!
2175	! Description:
2176	! ------------
2177	!> Calculates turbuluent length and time scales if these are not available
2178	!> from measurements.
2179	!------------------------------------------------------------------------------!
2180	SUBROUTINE calc_length_and_time_scale
2181
2182	IMPLICIT NONE
2183
2184
2185	INTEGER(iwp) :: k !< loop index in z-direction
2186
2187	REAL(wp) :: length_scale_dum !< effectively used length scale
2188
2189	!
2190	!-- In initial call the boundary-layer depth can be zero. This case, set
2191	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2192	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2193	!
2194	!-- Set-up default turbulent length scales. From the numerical point of
2195	!-- view the imposed perturbations should not be immediately dissipated
2196	!-- by the numerics. The numerical dissipation, however, acts on scales
2197	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2198	!-- length scale to 8 time the grid spacing. Further, above the boundary
2199	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2200	!-- imposing any perturbations) in order to save computational costs.
2201	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2202	!-- using the length scales and the mean profiles of u- and v-component.
2203	DO k = nzb+1, nzt+1
2204	!
2205	!-- Determine blending parameter. Within the boundary layer length scales
2206	!-- are constant, while above lengths scales approach gradully zero,
2207	!-- i.e. imposed turbulence is not correlated in space and time,
2208	!-- just white noise, which saves computations power as the loops for the
2209	!-- computation of the filter functions depend on the length scales.
2210	!-- The value decreases to 1/10 after one length scale above the
2211	!-- ABL top.
2212	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2213	!
2214	!-- Assume isotropic turbulence length scales
2215	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2216	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2217	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2218	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2219	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2220	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2221	!
2222	!-- Along the vertical direction limit the length scale further by the
2223	!-- boundary-layer depth to assure that no length scales larger than
2224	!-- the boundary-layer depth are used
2225	length_scale_dum = MIN( length_scale, zi_ribulk )
2226
2227	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2228	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2229	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2230	!
2231	!-- Limit time scales, else they become very larger for low wind speed,
2232	!-- imposing long-living inflow perturbations which in turn propagate
2233	!-- further into the model domain. Use u_init and v_init to calculate
2234	!-- the time scales, which will be equal to the inflow profiles, both,
2235	!-- in offline nesting mode or in dirichlet/radiation mode.
2236	tu(k) = MIN( dt_stg_adjust, length_scale / &
2237	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2238	tv(k) = MIN( dt_stg_adjust, length_scale / &
2239	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2240	!
2241	!-- Time scale of w-component is a mixture from u- and v-component.
2242	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2243
2244	ENDDO
2245	!
2246	!-- Set bottom boundary condition for the length and time scales
2247	nux(nzb) = nux(nzb+1)
2248	nuy(nzb) = nuy(nzb+1)
2249	nuz(nzb) = nuz(nzb+1)
2250	nvx(nzb) = nvx(nzb+1)
2251	nvy(nzb) = nvy(nzb+1)
2252	nvz(nzb) = nvz(nzb+1)
2253	nwx(nzb) = nwx(nzb+1)
2254	nwy(nzb) = nwy(nzb+1)
2255	nwz(nzb) = nwz(nzb+1)
2256
2257	tu(nzb) = tu(nzb+1)
2258	tv(nzb) = tv(nzb+1)
2259	tw(nzb) = tw(nzb+1)
2260
2261
2262	END SUBROUTINE calc_length_and_time_scale
2263
2264	!------------------------------------------------------------------------------!
2265	! Description:
2266	! ------------
2267	!> Calculate scaling variables which are used for turbulence parametrization
2268	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2269	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2270	!------------------------------------------------------------------------------!
2271	SUBROUTINE calc_scaling_variables
2272
2273	USE surface_mod, &
2274	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
2275
2276	IMPLICIT NONE
2277
2278	INTEGER(iwp) :: i !< loop index in x-direction
2279	INTEGER(iwp) :: j !< loop index in y-direction
2280	INTEGER(iwp) :: k !< loop index in z-direction
2281	INTEGER(iwp) :: m !< surface element index
2282
2283	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2284	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2285	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2286	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2287	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2288	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2289	REAL(wp) :: w_convective !< convective velocity scale
2290
2291	!
2292	!-- Calculate mean friction velocity, velocity scale, heat flux and
2293	!-- near-surface temperature in the model domain.
2294	pt_surf_mean_l = 0.0_wp
2295	shf_mean_l = 0.0_wp
2296	scale_l_l = 0.0_wp
2297	friction_vel_l = 0.0_wp
2298	DO m = 1, surf_def_h(0)%ns
2299	i = surf_def_h(0)%i(m)
2300	j = surf_def_h(0)%j(m)
2301	k = surf_def_h(0)%k(m)
2302	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2303	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2304	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2305	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2306	ENDDO
2307	DO m = 1, surf_lsm_h%ns
2308	i = surf_lsm_h%i(m)
2309	j = surf_lsm_h%j(m)
2310	k = surf_lsm_h%k(m)
2311	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2312	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2313	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2314	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2315	ENDDO
2316	DO m = 1, surf_usm_h%ns
2317	i = surf_usm_h%i(m)
2318	j = surf_usm_h%j(m)
2319	k = surf_usm_h%k(m)
2320	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2321	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2322	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2323	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2324	ENDDO
2325
2326	#if defined( __parallel )
2327	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2328	comm2d, ierr )
2329	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2330	comm2d, ierr )
2331	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2332	comm2d, ierr )
2333	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2334	comm2d, ierr )
2335	#else
2336	scale_us = friction_vel_l
2337	shf_mean = shf_mean_l
2338	scale_l = scale_l_l
2339	pt_surf_mean = pt_surf_mean_l
2340	#endif
2341
2342	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2343	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2344	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2345	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2346	!
2347	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2348	!-- is negative, set convective velocity scale to zero.
2349	IF ( shf_mean > 0.0_wp ) THEN
2350	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2351	ELSE
2352	w_convective = 0.0_wp
2353	ENDIF
2354	!
2355	!-- Finally, in order to consider also neutral or stable stratification,
2356	!-- compute momentum velocity scale from u* and convective velocity scale,
2357	!-- according to Rotach et al. (1996).
2358	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2359
2360	END SUBROUTINE calc_scaling_variables
2361
2362	END MODULE synthetic_turbulence_generator_mod

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