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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4112

Last change on this file since 4112 was 4071, checked in by suehring, 5 years ago
Bugfix in synthetic turbulence generator in non-nested cases (offline or self nesting) when no cyclic fill is used: in order to get correct initial inflow profiles at the left boundary the array mean_inflow_profiles need to be initialized accordingly.
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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 4071 2019-07-03 20:02:00Z suehring $
27	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
28	! information is not read from file.
29	!
30	! 4022 2019-06-12 11:52:39Z suehring
31	! Several bugfixes and improvements
32	! - revise bias correction of the imposed perturbations (correction via volume
33	! flow can create instabilities in case the mean volume flow is close to zero)
34	! - introduce lower limits in calculation of coefficient matrix, else the
35	! calculation may become numerically unstable
36	! - impose perturbations every timestep, even though no new set of perturbations
37	! is generated in case dt_stg_call /= dt_3d
38	! - Implement a gradual decrease of Reynolds stress and length scales above
39	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
40	! discontinuous decrease
41	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
42	!
43	! 3987 2019-05-22 09:52:13Z kanani
44	! Introduce alternative switch for debug output during timestepping
45	!
46	! 3938 2019-04-29 16:06:25Z suehring
47	! Remove unused variables
48	!
49	! 3937 2019-04-29 15:09:07Z suehring
50	! Minor bugfix in case of a very early restart where mc_factor is sill not
51	! present.
52	! Some modification and fixing of potential bugs in the calculation of scaling
53	! parameters used for synthetic turbulence parametrization.
54	!
55	! 3909 2019-04-17 09:13:25Z suehring
56	! Minor bugfix for last commit
57	!
58	! 3900 2019-04-16 15:17:43Z suehring
59	! Missing re-calculation of perturbation seeds in case of restarts
60	!
61	! 3891 2019-04-12 17:52:01Z suehring
62	! Bugfix in initialization in case of restart runs.
63	!
64	! 3885 2019-04-11 11:29:34Z kanani
65	! Changes related to global restructuring of location messages and introduction
66	! of additional debug messages
67	!
68	!
69	! removed unused variables
70	!
71	! 3719 2019-02-06 13:10:18Z kanani
72	! Removed log_point measurement from stg_init, since this part is counted to
73	! log_point(2) 'initialisation' already. Moved other log_points to calls of
74	! the subroutines in time_integration for better overview.
75	!
76	! 3646 2018-12-28 17:58:49Z kanani
77	! Bugfix: use time_since_reference_point instead of simulated_time (relevant
78	! when using wall/soil spinup)
79	!
80	! 3579 2018-11-29 15:32:39Z suehring
81	! - Bugfix in calculation of turbulence scaling parameters for turbulence
82	! generator in case of topography
83	! - Additional checks implemented - no STG in RANS-RANS nesting or LES-LES
84	! nesting
85	!
86	! 3376 2018-10-19 10:15:32Z suehring
87	! Error messages and numbers reivsed.
88	!
89	! 3349 2018-10-15 16:39:41Z suehring
90	! Fix for format descriptor
91	!
92	! 3348 2018-10-15 14:30:51Z suehring
93	! - Revise structure of init routine
94	! - introduce new parameters to skip STG for some timesteps
95	! - introduce time-dependent parametrization of Reynolds-stress tensor
96	! - Bugfix in allocation of mean_inflow_profiles
97	!
98	! 3341 2018-10-15 10:31:27Z suehring
99	! Introduce module parameter for number of inflow profiles
100	!
101	! 3288 2018-09-28 10:23:08Z suehring
102	! Modularization of all bulk cloud physics code components
103	!
104	! 3248 2018-09-14 09:42:06Z sward
105	! Minor formating changes
106	!
107	! 3246 2018-09-13 15:14:50Z sward
108	! Added error handling for input namelist via parin_fail_message
109	!
110	! 3241 2018-09-12 15:02:00Z raasch
111	! unused variables removed
112	!
113	! 3186 2018-07-30 17:07:14Z suehring
114	! Mask topography while imposing inflow perturbations at the boundaries; do not
115	! impose perturbations at top boundary as well as ghost points
116	!
117	! 3183 2018-07-27 14:25:55Z suehring
118	! Rename variables and extend error message
119	! Enable geneartor also for stretched grids
120	!
121	! 3182 2018-07-27 13:36:03Z suehring
122	! Error message related to vertical stretching has been added, dz was replaced
123	! by dz(1)
124	!
125	! 3051 2018-05-30 17:43:55Z suehring
126	! Bugfix in calculation of initial Reynolds-stress tensor.
127	!
128	! 3045 2018-05-28 07:55:41Z Giersch
129	! Error messages revised
130	!
131	! 3044 2018-05-25 10:59:41Z gronemeier
132	! Add missing variable descriptions
133	!
134	! 3038 2018-05-24 10:54:00Z gronemeier
135	! updated variable descriptions
136	!
137	! 2967 2018-04-13 11:22:08Z raasch
138	! bugfix: missing parallel cpp-directives added
139	!
140	! 2946 2018-04-04 17:01:23Z suehring
141	! Remove unused module load
142	!
143	! 2945 2018-04-04 16:27:14Z suehring
144	! - Bugfix in parallelization of synthetic turbulence generator in case the
145	! z-dimension is not an integral divisor of the number of processors along
146	! the x- and y-dimension
147	! - Revision in control mimic in case of RAN-LES nesting
148	!
149	! 2938 2018-03-27 15:52:42Z suehring
150	! Apply turbulence generator at all non-cyclic lateral boundaries in case of
151	! realistic Inifor large-scale forcing or RANS-LES nesting
152	!
153	! 2936 2018-03-27 14:49:27Z suehring
154	! variable named found has been introduced for checking if restart data was found,
155	! reading of restart strings has been moved completely to read_restart_data_mod,
156	! redundant skipping function has been removed, stg_read/write_restart_data
157	! have been renamed to stg_r/wrd_global, stg_rrd_global is called in
158	! read_restart_data_mod now, flag syn_turb_gen_prerun and marker *** end stg
159	! *** have been removed (Giersch), strings and their respective lengths are
160	! written out and read now in case of restart runs to get rid of prescribed
161	! character lengths (Giersch), CASE DEFAULT was added if restart data is read
162	!
163	! 2841 2018-02-27 15:02:57Z suehring
164	! Bugfix: wrong placement of include 'mpif.h' corrected
165	!
166	! 2836 2018-02-26 13:40:05Z Giersch
167	! The variables synthetic_turbulence_generator and
168	! use_synthetic_turbulence_generator have been abbreviated + syn_turb_gen_prerun
169	! flag is used to define if module related parameters were outputted as restart
170	! data
171	!
172	! 2716 2017-12-29 16:35:59Z kanani
173	! Corrected "Former revisions" section
174	!
175	! 2696 2017-12-14 17:12:51Z kanani
176	! Change in file header (GPL part)
177	!
178	! 2669 2017-12-06 16:03:27Z raasch
179	! unit number for file containing turbulence generator data changed to 90
180	! bugfix: preprocessor directives added for MPI specific code
181	!
182	! 2576 2017-10-24 13:49:46Z Giersch
183	! Definition of a new function called stg_skip_global to skip module
184	! parameters during reading restart data
185	!
186	! 2563 2017-10-19 15:36:10Z Giersch
187	! stg_read_restart_data is called in stg_parin in the case of a restart run
188	!
189	! 2259 2017-06-08 09:09:11Z gronemeier
190	! Initial revision
191	!
192	!
193	!
194	! Authors:
195	! --------
196	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
197	!
198	!
199	!
200	! Description:
201	! ------------
202	!> The module generates turbulence at the inflow boundary based on a method by
203	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
204	!> correction by Kim et al. (2013).
205	!> The turbulence is correlated based on length scales in y- and z-direction and
206	!> a time scale for each velocity component. The profiles of length and time
207	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
208	!> tensor can be either read from file STG_PROFILES, or will be parametrized
209	!> within the boundary layer.
210	!>
211	!> @todo test restart
212	!> enable cyclic_fill
213	!> implement turbulence generation for e and pt
214	!> @todo Input of height-constant length scales via namelist
215	!> @note <Enter notes on the module>
216	!> @bug Height information from input file is not used. Profiles from input
217	!> must match with current PALM grid.
218	!> In case of restart, velocity seeds differ from precursor run if a11,
219	!> a22, or a33 are zero.
220	!------------------------------------------------------------------------------!
221	MODULE synthetic_turbulence_generator_mod
222
223
224	USE arrays_3d, &
225	ONLY: dzw, &
226	ddzw, &
227	drho_air, &
228	mean_inflow_profiles, &
229	q, &
230	q_init, &
231	pt, &
232	pt_init, &
233	u, &
234	u_init, &
235	v, &
236	v_init, &
237	w, &
238	zu, &
239	zw
240
241	USE basic_constants_and_equations_mod, &
242	ONLY: g, &
243	kappa, &
244	pi
245
246	USE control_parameters, &
247	ONLY: bc_lr, &
248	bc_ns, &
249	child_domain, &
250	coupling_char, &
251	debug_output_timestep, &
252	dt_3d, &
253	e_init, &
254	humidity, &
255	initializing_actions, &
256	intermediate_timestep_count, &
257	intermediate_timestep_count_max, &
258	length, &
259	message_string, &
260	nesting_offline, &
261	neutral, &
262	num_mean_inflow_profiles, &
263	rans_mode, &
264	restart_string, &
265	syn_turb_gen, &
266	time_since_reference_point, &
267	turbulent_inflow
268
269	USE grid_variables, &
270	ONLY: ddx, &
271	ddy, &
272	dx, &
273	dy
274
275	USE indices, &
276	ONLY: nbgp, &
277	nz, &
278	nzb, &
279	nzt, &
280	nx, &
281	nxl, &
282	nxlu, &
283	nxlg, &
284	nxr, &
285	nxrg, &
286	ny, &
287	nys, &
288	nysv, &
289	nyn, &
290	nyng, &
291	nysg, &
292	wall_flags_0
293
294	USE kinds
295
296	#if defined( __parallel ) && !defined( __mpifh )
297	USE MPI
298	#endif
299
300	USE nesting_offl_mod, &
301	ONLY: nesting_offl_calc_zi, &
302	zi_ribulk
303
304	USE pegrid, &
305	ONLY: comm1dx, &
306	comm1dy, &
307	comm2d, &
308	ierr, &
309	myidx, &
310	myidy, &
311	pdims
312
313	USE pmc_interface, &
314	ONLY : rans_mode_parent
315
316	USE transpose_indices, &
317	ONLY: nzb_x, &
318	nzt_x
319
320
321	IMPLICIT NONE
322
323	#if defined( __parallel ) && defined( __mpifh )
324	INCLUDE "mpif.h"
325	#endif
326
327
328	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
329	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
330	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
331
332	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
333	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
334	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
335	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
336	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
337	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
338	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
339	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
340	INTEGER(iwp) :: merg !< maximum length scale (in gp)
341	INTEGER(iwp) :: mergp !< merg + nbgp
342	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
343	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
344	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
345	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
346
347	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
348	!< required for bias correction of imposed perturbations
349	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
350	!< required for bias correction of imposed perturbations
351
352	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
353	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
354	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
355	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
356	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
357	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
358	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
359	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
360	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
361	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
362	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
363	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
364	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
365	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed !< seed of random number for rn-generator
366
367	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
368	!< scales above the boundary layer
369	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
370	!< one length scale above ABL top
371	REAL(wp) :: d_l !< blend_coeff/length_scale
372	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
373	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
374	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
375	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
376	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
377	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
378	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
379	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
380
381	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
382
383
384	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
385	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
386	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
387	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
388	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
389	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
390
391	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
392	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
393	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
394	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
395	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
396	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
397	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
398	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
399	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
400
401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
418	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
419	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
420	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
421	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
422
423	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
424	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
425
426	!
427	!-- PALM interfaces:
428	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
429	INTERFACE stg_adjust
430	MODULE PROCEDURE stg_adjust
431	END INTERFACE stg_adjust
432	!
433	!-- Input parameter checks to be done in check_parameters
434	INTERFACE stg_check_parameters
435	MODULE PROCEDURE stg_check_parameters
436	END INTERFACE stg_check_parameters
437
438	!
439	!-- Calculate filter functions
440	INTERFACE stg_filter_func
441	MODULE PROCEDURE stg_filter_func
442	END INTERFACE stg_filter_func
443
444	!
445	!-- Generate velocity seeds at south and north domain boundary
446	INTERFACE stg_generate_seed_xz
447	MODULE PROCEDURE stg_generate_seed_xz
448	END INTERFACE stg_generate_seed_xz
449	!
450	!-- Generate velocity seeds at left and/or right domain boundary
451	INTERFACE stg_generate_seed_yz
452	MODULE PROCEDURE stg_generate_seed_yz
453	END INTERFACE stg_generate_seed_yz
454
455	!
456	!-- Output of information to the header file
457	INTERFACE stg_header
458	MODULE PROCEDURE stg_header
459	END INTERFACE stg_header
460
461	!
462	!-- Initialization actions
463	INTERFACE stg_init
464	MODULE PROCEDURE stg_init
465	END INTERFACE stg_init
466
467	!
468	!-- Main procedure of synth. turb. gen.
469	INTERFACE stg_main
470	MODULE PROCEDURE stg_main
471	END INTERFACE stg_main
472
473	!
474	!-- Reading of NAMELIST parameters
475	INTERFACE stg_parin
476	MODULE PROCEDURE stg_parin
477	END INTERFACE stg_parin
478
479	!
480	!-- Reading of parameters for restart runs
481	INTERFACE stg_rrd_global
482	MODULE PROCEDURE stg_rrd_global
483	END INTERFACE stg_rrd_global
484
485	!
486	!-- Writing of binary output for restart runs
487	INTERFACE stg_wrd_global
488	MODULE PROCEDURE stg_wrd_global
489	END INTERFACE stg_wrd_global
490
491	SAVE
492
493	PRIVATE
494
495	!
496	!-- Public interfaces
497	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
498	stg_parin, stg_rrd_global, stg_wrd_global
499
500	!
501	!-- Public variables
502	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
503	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
504	time_stg_adjust, time_stg_call, use_syn_turb_gen
505
506
507	CONTAINS
508
509
510	!------------------------------------------------------------------------------!
511	! Description:
512	! ------------
513	!> Check parameters routine for synthetic turbulence generator
514	!------------------------------------------------------------------------------!
515	SUBROUTINE stg_check_parameters
516
517	IMPLICIT NONE
518
519	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
520	nesting_offline ) THEN
521	message_string = 'Synthetic turbulence generator is required ' // &
522	'if offline nesting is applied and PALM operates ' // &
523	'in LES mode.'
524	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
525	ENDIF
526
527	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
528	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
529	message_string = 'Synthetic turbulence generator is required ' // &
530	'when nesting is applied and parent operates in ' // &
531	'RANS-mode but current child in LES mode.'
532	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
533	ENDIF
534
535	IF ( use_syn_turb_gen ) THEN
536
537	IF ( child_domain .AND. .NOT. rans_mode .AND. &
538	.NOT. rans_mode_parent ) THEN
539	message_string = 'Using synthetic turbulence generator ' // &
540	'is not allowed in LES-LES nesting.'
541	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
542
543	ENDIF
544
545	IF ( child_domain .AND. rans_mode .AND. &
546	rans_mode_parent ) THEN
547	message_string = 'Using synthetic turbulence generator ' // &
548	'is not allowed in RANS-RANS nesting.'
549	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
550
551	ENDIF
552
553	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
554
555	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
556	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
557	message_string = 'Using synthetic turbulence generator ' // &
558	'requires %initializing_actions = ' // &
559	'"set_constant_profiles" or "read_restart_data"' //&
560	', if not offline nesting is applied.'
561	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
562	ENDIF
563
564	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
565	message_string = 'Using synthetic turbulence generator ' // &
566	'requires &bc_lr = "dirichlet/radiation", ' // &
567	'if not offline nesting is applied.'
568	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
569	ENDIF
570	IF ( bc_ns /= 'cyclic' ) THEN
571	message_string = 'Using synthetic turbulence generator ' // &
572	'requires &bc_ns = "cyclic", ' // &
573	'if not offline nesting is applied.'
574	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
575	ENDIF
576
577	ENDIF
578
579	IF ( turbulent_inflow ) THEN
580	message_string = 'Using synthetic turbulence generator ' // &
581	'in combination &with turbulent_inflow = .T. '// &
582	'is not allowed'
583	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
584	ENDIF
585
586	ENDIF
587
588	END SUBROUTINE stg_check_parameters
589
590
591	!------------------------------------------------------------------------------!
592	! Description:
593	! ------------
594	!> Header output for synthetic turbulence generator
595	!------------------------------------------------------------------------------!
596	SUBROUTINE stg_header ( io )
597
598
599	IMPLICIT NONE
600
601	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
602
603	!
604	!-- Write synthetic turbulence generator Header
605	WRITE( io, 1 )
606	IF ( use_syn_turb_gen ) THEN
607	WRITE( io, 2 )
608	ELSE
609	WRITE( io, 3 )
610	ENDIF
611
612	IF ( parametrize_inflow_turbulence ) THEN
613	WRITE( io, 4 ) dt_stg_adjust
614	ELSE
615	WRITE( io, 5 )
616	ENDIF
617
618	1 FORMAT (//' Synthetic turbulence generator information:'/ &
619	' ------------------------------------------'/)
620	2 FORMAT (' synthetic turbulence generator is switched on')
621	3 FORMAT (' synthetic turbulence generator is switched off')
622	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
623	5 FORMAT (' imposed turbulence is read from file' )
624
625	END SUBROUTINE stg_header
626
627
628	!------------------------------------------------------------------------------!
629	! Description:
630	! ------------
631	!> Initialization of the synthetic turbulence generator
632	!------------------------------------------------------------------------------!
633	SUBROUTINE stg_init
634
635	IMPLICIT NONE
636
637	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
638
639	#if defined( __parallel )
640	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
641	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
642	#endif
643
644	INTEGER(iwp) :: i !> grid index in x-direction
645	INTEGER(iwp) :: j !> loop index
646	INTEGER(iwp) :: k !< index
647	INTEGER(iwp) :: newtype !< dummy MPI type
648	INTEGER(iwp) :: realsize !< size of REAL variables
649	INTEGER(iwp) :: nseed !< dimension of random number seed
650	INTEGER(iwp) :: startseed = 1234567890 !< start seed for random number generator
651
652	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
653	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
654	!
655	!-- Dummy variables used for reading profiles
656	REAL(wp) :: d1 !< u profile
657	REAL(wp) :: d2 !< v profile
658	REAL(wp) :: d3 !< w profile
659	REAL(wp) :: d5 !< e profile
660	REAL(wp) :: luy !< length scale for u in y direction
661	REAL(wp) :: luz !< length scale for u in z direction
662	REAL(wp) :: lvy !< length scale for v in y direction
663	REAL(wp) :: lvz !< length scale for v in z direction
664	REAL(wp) :: lwy !< length scale for w in y direction
665	REAL(wp) :: lwz !< length scale for w in z direction
666	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
667	REAL(wp) :: zz !< height
668
669
670	#if defined( __parallel )
671	CALL MPI_BARRIER( comm2d, ierr )
672	#endif
673
674	#if defined( __parallel )
675	!
676	!-- Determine processor decomposition of z-axis along x- and y-direction
677	nnz = nz / pdims(1)
678	nzb_x_stg = 1 + myidx * INT( nnz )
679	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
680
681	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
682	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
683
684	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
685	.AND. .NOT. rans_mode ) ) THEN
686	nnz = nz / pdims(2)
687	nzb_y_stg = 1 + myidy * INT( nnz )
688	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
689
690	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
691	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
692	ENDIF
693
694	!
695	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
696	!-- velocity seeds
697	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
698	extent = 1 * realsize
699	!
700	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
701	!-- layer
702	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
703	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
704	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
705	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
706	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
707	CALL MPI_TYPE_FREE( newtype, ierr )
708
709	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
710	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
711	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
712	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
713	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
714	CALL MPI_TYPE_FREE( newtype, ierr )
715
716	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
717	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
718
719	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
720	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
721
722	DO j = 1, pdims(1)
723	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
724	ENDDO
725	!
726	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
727	!-- layer
728	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
729	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
730	.AND. .NOT. rans_mode ) ) THEN
731	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
732	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
733	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
734	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
735	CALL MPI_TYPE_FREE( newtype, ierr )
736
737	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
738	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
739	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
740	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
741	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
742	CALL MPI_TYPE_FREE( newtype, ierr )
743
744	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
745	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
746
747	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
748	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
749
750	DO j = 1, pdims(2)
751	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
752	ENDDO
753
754	ENDIF
755
756	#endif
757	!
758	!-- Define seed of random number
759	CALL RANDOM_SEED()
760	CALL RANDOM_SEED( size=nseed )
761	ALLOCATE( seed(1:nseed) )
762	DO j = 1, nseed
763	seed(j) = startseed + j
764	ENDDO
765	CALL RANDOM_SEED(put=seed)
766	!
767	!-- Allocate required arrays.
768	!-- In case no offline nesting or self nesting is used, the arrary
769	!-- mean_inflow profiles is required. Check if it is already allocated, else
770	!-- allocate and initialize it appropriately. Note, in case turbulence and
771	!-- inflow information is read from file, mean_inflow_profiles is already
772	!-- allocated and initialized appropriately.
773	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
774	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
775	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
776	mean_inflow_profiles = 0.0_wp
777	mean_inflow_profiles(:,1) = u_init
778	mean_inflow_profiles(:,2) = v_init
779	!
780	!-- Even though potential temperature and humidity are not perturbed,
781	!-- they need to be initialized appropriately.
782	IF ( .NOT. neutral ) &
783	mean_inflow_profiles(:,4) = pt_init
784	IF ( humidity ) &
785	mean_inflow_profiles(:,6) = q_init
786	ENDIF
787	ENDIF
788
789	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
790	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
791	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
792	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
793	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
794	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
795	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
796	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
797
798	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
799	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
800	dist_xz = 0.0_wp
801	dist_yz = 0.0_wp
802	!
803	!-- Read inflow profile
804	!-- Height levels of profiles in input profile is as follows:
805	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
806	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
807	!-- WARNING: zz is not used at the moment
808	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
809	EXIST = file_stg_exist )
810
811	IF ( file_stg_exist ) THEN
812
813	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
814	FORM='FORMATTED')
815	!
816	!-- Skip header
817	READ( 90, * )
818
819	DO k = nzb+1, nzt+1
820	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
821	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
822	d1, d2, d3, d5
823
824	!
825	!-- Convert length scales from meter to number of grid points.
826	nuy(k) = INT( luy * ddy )
827	nuz(k) = INT( luz * ddzw(k) )
828	nvy(k) = INT( lvy * ddy )
829	nvz(k) = INT( lvz * ddzw(k) )
830	nwy(k) = INT( lwy * ddy )
831	nwz(k) = INT( lwz * ddzw(k) )
832	!
833	!-- Workaround, assume isotropic turbulence
834	nwx(k) = nwy(k)
835	nvx(k) = nvy(k)
836	nux(k) = nuy(k)
837	!
838	!-- Save Mean inflow profiles
839	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
840	mean_inflow_profiles(k,1) = d1
841	mean_inflow_profiles(k,2) = d2
842	! mean_inflow_profiles(k,4) = d4
843	mean_inflow_profiles(k,5) = d5
844	ENDIF
845	ENDDO
846	!
847	!-- Set lenght scales at surface grid point
848	nuy(nzb) = nuy(nzb+1)
849	nuz(nzb) = nuz(nzb+1)
850	nvy(nzb) = nvy(nzb+1)
851	nvz(nzb) = nvz(nzb+1)
852	nwy(nzb) = nwy(nzb+1)
853	nwz(nzb) = nwz(nzb+1)
854
855	CLOSE( 90 )
856	!
857	!-- Calculate coefficient matrix from Reynolds stress tensor
858	!-- (Lund rotation)
859	CALL calc_coeff_matrix
860	!
861	!-- No information about turbulence and its length scales are available.
862	!-- Instead, parametrize turbulence which is imposed at the boundaries.
863	!-- Set flag which indicates that turbulence is parametrized, which is done
864	!-- later when energy-balance models are already initialized. This is
865	!-- because the STG needs information about surface properties such as
866	!-- roughness to build 'realistic' turbulence profiles.
867	ELSE
868	!
869	!-- Define length scale for the imposed turbulence, which is defined as
870	!-- 8 times the minimum grid spacing
871	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
872	!
873	!-- Define constant to gradually decrease length scales and Reynolds stress
874	!-- above ABL top. Assure that no zero length scales are used.
875	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
876	!
877	!-- Set flag indicating that turbulence is parametrized
878	parametrize_inflow_turbulence = .TRUE.
879	!
880	!-- In case of dirichlet inflow boundary conditions only at one lateral
881	!-- boundary, i.e. in the case no offline or self nesting is applied but
882	!-- synthetic turbulence shall be parametrized nevertheless, the
883	!-- boundary-layer depth need to determined first.
884	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
885	CALL nesting_offl_calc_zi
886	!
887	!-- Determine boundary-layer depth, which is used to initialize lenght
888	!-- scales
889	CALL calc_scaling_variables
890	!
891	!-- Initialize lenght and time scales, which in turn are used
892	!-- to initialize the filter functions.
893	CALL calc_length_and_time_scale
894	!
895	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
896	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
897	!-- Rotach et al. (1996) and is based on boundary-layer depth,
898	!-- friction velocity and velocity scale.
899	CALL parametrize_reynolds_stress
900	!
901	!-- Calculate coefficient matrix from Reynolds stress tensor
902	!-- (Lund rotation)
903	CALL calc_coeff_matrix
904
905	ENDIF
906
907	!
908	!-- Assign initial profiles. Note, this is only required if turbulent
909	!-- inflow from the left is desired, not in case of any of the
910	!-- nesting (offline or self nesting) approaches.
911	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
912	u_init = mean_inflow_profiles(:,1)
913	v_init = mean_inflow_profiles(:,2)
914	!pt_init = mean_inflow_profiles(:,4)
915	e_init = MAXVAL( mean_inflow_profiles(:,5) )
916	ENDIF
917
918	!
919	!-- Define the size of the filter functions and allocate them.
920	merg = 0
921
922	! arrays must be large enough to cover the largest length scale
923	DO k = nzb, nzt+1
924	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
925	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
926	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
927	IF ( j > merg ) merg = j
928	ENDDO
929
930	merg = 2 * merg
931	mergp = merg + nbgp
932
933	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
934	buy(-merg:merg,nzb:nzt+1), &
935	buz(-merg:merg,nzb:nzt+1), &
936	bvx(-merg:merg,nzb:nzt+1), &
937	bvy(-merg:merg,nzb:nzt+1), &
938	bvz(-merg:merg,nzb:nzt+1), &
939	bwx(-merg:merg,nzb:nzt+1), &
940	bwy(-merg:merg,nzb:nzt+1), &
941	bwz(-merg:merg,nzb:nzt+1) )
942
943	!
944	!-- Allocate velocity seeds for turbulence at xz-layer
945	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
946	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
947	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
948
949	!
950	!-- Allocate velocity seeds for turbulence at yz-layer
951	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
952	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
953	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
954
955	fu_xz = 0.0_wp
956	fuo_xz = 0.0_wp
957	fv_xz = 0.0_wp
958	fvo_xz = 0.0_wp
959	fw_xz = 0.0_wp
960	fwo_xz = 0.0_wp
961
962	fu_yz = 0.0_wp
963	fuo_yz = 0.0_wp
964	fv_yz = 0.0_wp
965	fvo_yz = 0.0_wp
966	fw_yz = 0.0_wp
967	fwo_yz = 0.0_wp
968
969	!
970	!-- Create filter functions
971	CALL stg_filter_func( nux, bux ) !filter ux
972	CALL stg_filter_func( nuy, buy ) !filter uy
973	CALL stg_filter_func( nuz, buz ) !filter uz
974	CALL stg_filter_func( nvx, bvx ) !filter vx
975	CALL stg_filter_func( nvy, bvy ) !filter vy
976	CALL stg_filter_func( nvz, bvz ) !filter vz
977	CALL stg_filter_func( nwx, bwx ) !filter wx
978	CALL stg_filter_func( nwy, bwy ) !filter wy
979	CALL stg_filter_func( nwz, bwz ) !filter wz
980
981	#if defined( __parallel )
982	CALL MPI_BARRIER( comm2d, ierr )
983	#endif
984
985	!
986	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
987	! time step.
988	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
989	! are 0 compared to the prerun. This is mostly for k=nzt+1.
990	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
991	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
992
993	IF ( myidx == id_stg_left ) i = -1
994	IF ( myidx == id_stg_right ) i = nxr+1
995
996	DO j = nysg, nyng
997	DO k = nzb, nzt+1
998	IF ( a11(k) .NE. 0._wp ) THEN
999	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
1000	ELSE
1001	fu_yz(k,j) = 0._wp
1002	ENDIF
1003
1004	IF ( a22(k) .NE. 0._wp ) THEN
1005	fv_yz(k,j) = ( v(k,j,i) - &
1006	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
1007	ELSE
1008	fv_yz(k,j) = 0._wp
1009	ENDIF
1010
1011	IF ( a33(k) .NE. 0._wp ) THEN
1012	fw_yz(k,j) = ( w(k,j,i) - &
1013	a31(k) * fu_yz(k,j) - a32(k) * &
1014	fv_yz(k,j) ) / a33(k)
1015	ELSE
1016	fw_yz = 0._wp
1017	ENDIF
1018
1019	ENDDO
1020	ENDDO
1021	ENDIF
1022
1023	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1024
1025	IF ( myidy == id_stg_south ) j = -1
1026	IF ( myidy == id_stg_north ) j = nyn+1
1027
1028	DO i = nxlg, nxrg
1029	DO k = nzb, nzt+1
1030
1031	IF ( a11(k) .NE. 0._wp ) THEN
1032	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
1033	ELSE
1034	fu_xz(k,i) = 0._wp
1035	ENDIF
1036
1037	IF ( a22(k) .NE. 0._wp ) THEN
1038	fv_xz(k,i) = ( v(k,j,i) - &
1039	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
1040	ELSE
1041	fv_xz(k,i) = 0._wp
1042	ENDIF
1043
1044	IF ( a33(k) .NE. 0._wp ) THEN
1045	fw_xz(k,i) = ( w(k,j,i) - &
1046	a31(k) * fu_xz(k,i) - &
1047	a32(k) * fv_xz(k,i) ) / a33(k)
1048	ELSE
1049	fw_xz = 0._wp
1050	ENDIF
1051
1052	ENDDO
1053	ENDDO
1054	ENDIF
1055	ENDIF
1056	!
1057	!-- Count the number of non-topography grid points at the boundaries where
1058	!-- perturbations are imposed. This number is later used for bias corrections
1059	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
1060	!-- due to the asymetry of u and v along x and y direction, respectively,
1061	!-- different cases must be distinguished.
1062	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1063	!
1064	!-- Number of grid points where perturbations are imposed on u
1065	IF ( myidx == id_stg_left ) i = nxl
1066	IF ( myidx == id_stg_right ) i = nxr+1
1067
1068	nr_non_topo_yz_l(1) = SUM( &
1069	MERGE( 1, 0, &
1070	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1071	!
1072	!-- Number of grid points where perturbations are imposed on v and w
1073	IF ( myidx == id_stg_left ) i = nxl-1
1074	IF ( myidx == id_stg_right ) i = nxr+1
1075
1076	nr_non_topo_yz_l(2) = SUM( &
1077	MERGE( 1, 0, &
1078	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1079	nr_non_topo_yz_l(3) = SUM( &
1080	MERGE( 1, 0, &
1081	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1082
1083	#if defined( __parallel )
1084	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
1085	MPI_SUM, comm1dy, ierr )
1086	#else
1087	nr_non_topo_yz = nr_non_topo_yz_l
1088	#endif
1089	ENDIF
1090
1091	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
1092	!
1093	!-- Number of grid points where perturbations are imposed on v
1094	IF ( myidy == id_stg_south ) j = nys
1095	IF ( myidy == id_stg_north ) j = nyn+1
1096
1097	nr_non_topo_xz_l(2) = SUM( &
1098	MERGE( 1, 0, &
1099	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1100	!
1101	!-- Number of grid points where perturbations are imposed on u and w
1102	IF ( myidy == id_stg_south ) j = nys-1
1103	IF ( myidy == id_stg_north ) j = nyn+1
1104
1105	nr_non_topo_xz_l(1) = SUM( &
1106	MERGE( 1, 0, &
1107	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1108	nr_non_topo_xz_l(3) = SUM( &
1109	MERGE( 1, 0, &
1110	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1111
1112	#if defined( __parallel )
1113	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
1114	MPI_SUM, comm1dx, ierr )
1115	#else
1116	nr_non_topo_xz = nr_non_topo_xz_l
1117	#endif
1118	ENDIF
1119
1120
1121	END SUBROUTINE stg_init
1122
1123
1124	!------------------------------------------------------------------------------!
1125	! Description:
1126	! ------------
1127	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
1128	!> (Xie and Castro, 2008)
1129	!------------------------------------------------------------------------------!
1130	SUBROUTINE stg_filter_func( nxx, bxx )
1131
1132
1133	IMPLICIT NONE
1134
1135	INTEGER(iwp) :: k !< loop index
1136	INTEGER(iwp) :: n_k !< length scale nXX in height k
1137	INTEGER(iwp) :: n_k2 !< n_k * 2
1138	INTEGER(iwp) :: nf !< index for length scales
1139
1140	REAL(wp) :: bdenom !< denominator for filter functions bXX
1141	REAL(wp) :: qsi = 1.0_wp !< minimization factor
1142
1143	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
1144
1145	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
1146
1147
1148	bxx = 0.0_wp
1149
1150	DO k = nzb, nzt+1
1151	bdenom = 0.0_wp
1152	n_k = nxx(k)
1153	IF ( n_k /= 0 ) THEN
1154	n_k2 = n_k * 2
1155
1156	!
1157	!-- ( Eq.10 )^2
1158	DO nf = -n_k2, n_k2
1159	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
1160	ENDDO
1161
1162	!
1163	!-- ( Eq.9 )
1164	bdenom = SQRT( bdenom )
1165	DO nf = -n_k2, n_k2
1166	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
1167	ENDDO
1168	ENDIF
1169	ENDDO
1170
1171	END SUBROUTINE stg_filter_func
1172
1173
1174	!------------------------------------------------------------------------------!
1175	! Description:
1176	! ------------
1177	!> Parin for &stg_par for synthetic turbulence generator
1178	!------------------------------------------------------------------------------!
1179	SUBROUTINE stg_parin
1180
1181
1182	IMPLICIT NONE
1183
1184	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1185
1186
1187	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
1188
1189	line = ' '
1190
1191	!
1192	!-- Try to find stg package
1193	REWIND ( 11 )
1194	line = ' '
1195	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
1196	READ ( 11, '(A)', END=20 ) line
1197	ENDDO
1198	BACKSPACE ( 11 )
1199
1200	!
1201	!-- Read namelist
1202	READ ( 11, stg_par, ERR = 10, END = 20 )
1203
1204	!
1205	!-- Set flag that indicates that the synthetic turbulence generator is switched
1206	!-- on
1207	syn_turb_gen = .TRUE.
1208	GOTO 20
1209
1210	10 BACKSPACE( 11 )
1211	READ( 11 , '(A)') line
1212	CALL parin_fail_message( 'stg_par', line )
1213
1214	20 CONTINUE
1215
1216	END SUBROUTINE stg_parin
1217
1218
1219	!------------------------------------------------------------------------------!
1220	! Description:
1221	! ------------
1222	!> This routine reads the respective restart data.
1223	!------------------------------------------------------------------------------!
1224	SUBROUTINE stg_rrd_global( found )
1225
1226
1227	IMPLICIT NONE
1228
1229	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
1230
1231
1232	found = .TRUE.
1233
1234
1235	SELECT CASE ( restart_string(1:length) )
1236
1237	CASE ( 'time_stg_adjust' )
1238	READ ( 13 ) time_stg_adjust
1239
1240	CASE ( 'time_stg_call' )
1241	READ ( 13 ) time_stg_call
1242
1243	CASE ( 'use_syn_turb_gen' )
1244	READ ( 13 ) use_syn_turb_gen
1245
1246	CASE DEFAULT
1247
1248	found = .FALSE.
1249
1250	END SELECT
1251
1252
1253	END SUBROUTINE stg_rrd_global
1254
1255
1256	!------------------------------------------------------------------------------!
1257	! Description:
1258	! ------------
1259	!> This routine writes the respective restart data.
1260	!------------------------------------------------------------------------------!
1261	SUBROUTINE stg_wrd_global
1262
1263
1264	IMPLICIT NONE
1265
1266	CALL wrd_write_string( 'time_stg_adjust' )
1267	WRITE ( 14 ) time_stg_adjust
1268
1269	CALL wrd_write_string( 'time_stg_call' )
1270	WRITE ( 14 ) time_stg_call
1271
1272	CALL wrd_write_string( 'use_syn_turb_gen' )
1273	WRITE ( 14 ) use_syn_turb_gen
1274
1275
1276	END SUBROUTINE stg_wrd_global
1277
1278
1279	!------------------------------------------------------------------------------!
1280	! Description:
1281	! ------------
1282	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
1283	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
1284	!> following suggestions of Kim et al. (2013), and using a Lund rotation
1285	!> (Lund, 1998).
1286	!------------------------------------------------------------------------------!
1287	SUBROUTINE stg_main
1288
1289	IMPLICIT NONE
1290
1291	INTEGER(iwp) :: i !< grid index in x-direction
1292	INTEGER(iwp) :: j !< loop index in y-direction
1293	INTEGER(iwp) :: k !< loop index in z-direction
1294
1295	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
1296
1297	REAL(wp) :: dt_stg !< wheighted subtimestep
1298
1299	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
1300
1301	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
1302	!
1303	!-- Calculate time step which is needed for filter functions
1304	dt_stg = MAX( dt_3d, dt_stg_call )
1305	!
1306	!-- Check if synthetic turbulence generator needs to be called and new
1307	!-- perturbations need to be created or if old disturbances can be imposed
1308	!-- again.
1309	IF ( time_stg_call >= dt_stg_call .AND. &
1310	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1311	stg_call = .TRUE.
1312	ELSE
1313	stg_call = .FALSE.
1314	ENDIF
1315	!
1316	!-- Initial value of fu, fv, fw
1317	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
1318	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
1319	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
1320	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
1321
1322	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1323	.AND. .NOT. rans_mode ) ) THEN
1324	!
1325	!-- Generate turbulence at right boundary
1326	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_right )
1327	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_right )
1328	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_right )
1329	!
1330	!-- Generate turbulence at north boundary
1331	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_north )
1332	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_north )
1333	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_north )
1334	!
1335	!-- Generate turbulence at south boundary
1336	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south )
1337	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south )
1338	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south )
1339	ENDIF
1340	velocity_seed_initialized = .TRUE.
1341	ENDIF
1342
1343	!
1344	!-- New set of fu, fv, fw
1345	IF ( stg_call ) THEN
1346	!
1347	!-- Generate turbulence at left boundary (required in all applications,
1348	!-- i.e. offline nesting and turbulent inflow from the left)
1349	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
1350	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
1351	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
1352
1353	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
1354	.AND. .NOT. rans_mode ) ) THEN
1355	!
1356	!-- Generate turbulence at right boundary
1357	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_right )
1358	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_right )
1359	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_right )
1360	!
1361	!-- Generate turbulence at north boundary
1362	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_north )
1363	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_north )
1364	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_north )
1365	!
1366	!-- Generate turbulence at south boundary
1367	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south )
1368	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south )
1369	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south )
1370	ENDIF
1371	ENDIF
1372
1373	!
1374	!-- Turbulence generation at left and or right boundary
1375	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
1376	!
1377	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1378	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1379	!-- imposed
1380	IF ( stg_call ) THEN
1381
1382	DO j = nysg, nyng
1383	DO k = nzb, nzt + 1
1384	!
1385	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1386	IF ( tu(k) == 0.0_wp ) THEN
1387	fu_yz(k,j) = fuo_yz(k,j)
1388	ELSE
1389	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1390	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1391	ENDIF
1392
1393	IF ( tv(k) == 0.0_wp ) THEN
1394	fv_yz(k,j) = fvo_yz(k,j)
1395	ELSE
1396	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1397	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1398	ENDIF
1399
1400	IF ( tw(k) == 0.0_wp ) THEN
1401	fw_yz(k,j) = fwo_yz(k,j)
1402	ELSE
1403	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1404	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1405	ENDIF
1406	ENDDO
1407	ENDDO
1408
1409	dist_yz(nzb,:,1) = 0.0_wp
1410	dist_yz(nzb,:,2) = 0.0_wp
1411	dist_yz(nzb,:,3) = 0.0_wp
1412
1413	IF ( myidx == id_stg_left ) i = nxl
1414	IF ( myidx == id_stg_right ) i = nxr+1
1415	DO j = nysg, nyng
1416	DO k = nzb+1, nzt + 1
1417	!
1418	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1419	!-- Additional factors are added to improve the variance of v and w
1420	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
1421	MERGE( 1.0_wp, 0.0_wp, &
1422	BTEST( wall_flags_0(k,j,i), 1 ) )
1423	ENDDO
1424	ENDDO
1425
1426	IF ( myidx == id_stg_left ) i = nxl-1
1427	IF ( myidx == id_stg_right ) i = nxr+1
1428	DO j = nysg, nyng
1429	DO k = nzb+1, nzt + 1
1430	!
1431	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1432	!-- Additional factors are added to improve the variance of v and w
1433	!-- experimental test of 1.2
1434	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1435	* 1.2_wp ) &
1436	* ( a21(k) * fu_yz(k,j) &
1437	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
1438	MERGE( 1.0_wp, 0.0_wp, &
1439	BTEST( wall_flags_0(k,j,i), 2 ) )
1440	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1441	* 1.3_wp ) &
1442	* ( a31(k) * fu_yz(k,j) &
1443	+ a32(k) * fv_yz(k,j) &
1444	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
1445	MERGE( 1.0_wp, 0.0_wp, &
1446	BTEST( wall_flags_0(k,j,i), 3 ) )
1447	ENDDO
1448	ENDDO
1449	ENDIF
1450
1451	!
1452	!-- Mass flux correction following Kim et al. (2013)
1453	!-- This correction factor insures that the mass flux is preserved at the
1454	!-- inflow boundary. First, calculate mean value of the imposed
1455	!-- perturbations at yz boundary.
1456	!-- Note, this needs to be done only after the last RK3-substep, else
1457	!-- the boundary values won't be accessed.
1458	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1459	mc_factor_l = 0.0_wp
1460	mc_factor = 0.0_wp
1461	!
1462	!-- Sum up the original volume flows (with and without perturbations).
1463	!-- Note, for non-normal components (here v and w) it is actually no
1464	!-- volume flow.
1465	IF ( myidx == id_stg_left ) i = nxl
1466	IF ( myidx == id_stg_right ) i = nxr+1
1467
1468	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
1469	* MERGE( 1.0_wp, 0.0_wp, &
1470	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
1471
1472	IF ( myidx == id_stg_left ) i = nxl-1
1473	IF ( myidx == id_stg_right ) i = nxr+1
1474
1475	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
1476	* MERGE( 1.0_wp, 0.0_wp, &
1477	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
1478	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
1479	* MERGE( 1.0_wp, 0.0_wp, &
1480	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
1481
1482	#if defined( __parallel )
1483	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1484	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
1485	#else
1486	mc_factor = mc_factor_l
1487	#endif
1488	!
1489	!-- Calculate correction factor and force zero mean perturbations.
1490	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
1491
1492	IF ( myidx == id_stg_left ) i = nxl
1493	IF ( myidx == id_stg_right ) i = nxr+1
1494
1495	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
1496	* MERGE( 1.0_wp, 0.0_wp, &
1497	BTEST( wall_flags_0(:,:,i), 1 ) )
1498
1499
1500	IF ( myidx == id_stg_left ) i = nxl-1
1501	IF ( myidx == id_stg_right ) i = nxr+1
1502
1503	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
1504	* MERGE( 1.0_wp, 0.0_wp, &
1505	BTEST( wall_flags_0(:,:,i), 2 ) )
1506
1507	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
1508	* MERGE( 1.0_wp, 0.0_wp, &
1509	BTEST( wall_flags_0(:,:,i), 3 ) )
1510	!
1511	!-- Add disturbances
1512	IF ( myidx == id_stg_left ) THEN
1513	!
1514	!-- For the left boundary distinguish between mesoscale offline / self
1515	!-- nesting and turbulent inflow at the left boundary only. In the latter
1516	!-- case turbulence is imposed on the mean inflow profiles.
1517	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
1518	!
1519	!-- Add disturbance at the inflow
1520	DO j = nysg, nyng
1521	DO k = nzb, nzt+1
1522	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
1523	dist_yz(k,j,1) ) &
1524	* MERGE( 1.0_wp, 0.0_wp, &
1525	BTEST( wall_flags_0(k,j,0), 1 ) )
1526	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
1527	dist_yz(k,j,2) ) &
1528	* MERGE( 1.0_wp, 0.0_wp, &
1529	BTEST( wall_flags_0(k,j,-1), 2 ) )
1530	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
1531	* MERGE( 1.0_wp, 0.0_wp, &
1532	BTEST( wall_flags_0(k,j,-1), 3 ) )
1533	ENDDO
1534	ENDDO
1535	ELSE
1536
1537	DO j = nys, nyn
1538	DO k = nzb+1, nzt
1539	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
1540	* MERGE( 1.0_wp, 0.0_wp, &
1541	BTEST( wall_flags_0(k,j,0), 1 ) )
1542	u(k,j,-1) = u(k,j,0)
1543	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
1544	* MERGE( 1.0_wp, 0.0_wp, &
1545	BTEST( wall_flags_0(k,j,-1), 2 ) )
1546	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
1547	* MERGE( 1.0_wp, 0.0_wp, &
1548	BTEST( wall_flags_0(k,j,-1), 3 ) )
1549	ENDDO
1550	ENDDO
1551	ENDIF
1552	ENDIF
1553	IF ( myidx == id_stg_right ) THEN
1554	DO j = nys, nyn
1555	DO k = nzb+1, nzt
1556	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
1557	* MERGE( 1.0_wp, 0.0_wp, &
1558	BTEST( wall_flags_0(k,j,nxr+1), 1 ) )
1559	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
1560	* MERGE( 1.0_wp, 0.0_wp, &
1561	BTEST( wall_flags_0(k,j,nxr+1), 2 ) )
1562	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
1563	* MERGE( 1.0_wp, 0.0_wp, &
1564	BTEST( wall_flags_0(k,j,nxr+1), 3 ) )
1565	ENDDO
1566	ENDDO
1567	ENDIF
1568	ENDIF
1569	ENDIF
1570	!
1571	!-- Turbulence generation at north and south boundary
1572	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
1573	!
1574	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
1575	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
1576	!-- imposed
1577	IF ( stg_call ) THEN
1578	DO i = nxlg, nxrg
1579	DO k = nzb, nzt + 1
1580	!
1581	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
1582	IF ( tu(k) == 0.0_wp ) THEN
1583	fu_xz(k,i) = fuo_xz(k,i)
1584	ELSE
1585	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
1586	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
1587	ENDIF
1588
1589	IF ( tv(k) == 0.0_wp ) THEN
1590	fv_xz(k,i) = fvo_xz(k,i)
1591	ELSE
1592	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
1593	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
1594	ENDIF
1595
1596	IF ( tw(k) == 0.0_wp ) THEN
1597	fw_xz(k,i) = fwo_xz(k,i)
1598	ELSE
1599	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
1600	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
1601	ENDIF
1602	ENDDO
1603	ENDDO
1604
1605
1606	dist_xz(nzb,:,1) = 0.0_wp
1607	dist_xz(nzb,:,2) = 0.0_wp
1608	dist_xz(nzb,:,3) = 0.0_wp
1609
1610	IF ( myidy == id_stg_south ) j = nys
1611	IF ( myidy == id_stg_north ) j = nyn+1
1612	DO i = nxlg, nxrg
1613	DO k = nzb+1, nzt + 1
1614	!
1615	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1616	!-- Additional factors are added to improve the variance of v and w
1617	!experimental test of 1.2
1618	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
1619	* 1.2_wp ) &
1620	* ( a21(k) * fu_xz(k,i) &
1621	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
1622	MERGE( 1.0_wp, 0.0_wp, &
1623	BTEST( wall_flags_0(k,j,i), 2 ) )
1624	ENDDO
1625	ENDDO
1626
1627	IF ( myidy == id_stg_south ) j = nys-1
1628	IF ( myidy == id_stg_north ) j = nyn+1
1629	DO i = nxlg, nxrg
1630	DO k = nzb+1, nzt + 1
1631	!
1632	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
1633	!-- Additional factors are added to improve the variance of v and w
1634	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
1635	MERGE( 1.0_wp, 0.0_wp, &
1636	BTEST( wall_flags_0(k,j,i), 1 ) )
1637
1638	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
1639	* 1.3_wp ) &
1640	* ( a31(k) * fu_xz(k,i) &
1641	+ a32(k) * fv_xz(k,i) &
1642	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
1643	MERGE( 1.0_wp, 0.0_wp, &
1644	BTEST( wall_flags_0(k,j,i), 3 ) )
1645	ENDDO
1646	ENDDO
1647	ENDIF
1648
1649	!
1650	!-- Mass flux correction following Kim et al. (2013)
1651	!-- This correction factor insures that the mass flux is preserved at the
1652	!-- inflow boundary. First, calculate mean value of the imposed
1653	!-- perturbations at yz boundary.
1654	!-- Note, this needs to be done only after the last RK3-substep, else
1655	!-- the boundary values won't be accessed.
1656	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
1657	mc_factor_l = 0.0_wp
1658	mc_factor = 0.0_wp
1659
1660	IF ( myidy == id_stg_south ) j = nys
1661	IF ( myidy == id_stg_north ) j = nyn+1
1662
1663	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
1664	* MERGE( 1.0_wp, 0.0_wp, &
1665	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
1666
1667	IF ( myidy == id_stg_south ) j = nys-1
1668	IF ( myidy == id_stg_north ) j = nyn+1
1669
1670	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
1671	* MERGE( 1.0_wp, 0.0_wp, &
1672	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
1673	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
1674	* MERGE( 1.0_wp, 0.0_wp, &
1675	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
1676
1677	#if defined( __parallel )
1678	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
1679	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
1680	#else
1681	mc_factor = mc_factor_l
1682	#endif
1683
1684	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
1685
1686	IF ( myidy == id_stg_south ) j = nys
1687	IF ( myidy == id_stg_north ) j = nyn+1
1688
1689	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
1690	* MERGE( 1.0_wp, 0.0_wp, &
1691	BTEST( wall_flags_0(:,j,:), 2 ) )
1692
1693
1694	IF ( myidy == id_stg_south ) j = nys-1
1695	IF ( myidy == id_stg_north ) j = nyn+1
1696
1697	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
1698	* MERGE( 1.0_wp, 0.0_wp, &
1699	BTEST( wall_flags_0(:,j,:), 1 ) )
1700
1701	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
1702	* MERGE( 1.0_wp, 0.0_wp, &
1703	BTEST( wall_flags_0(:,j,:), 3 ) )
1704	!
1705	!-- Add disturbances
1706	IF ( myidy == id_stg_south ) THEN
1707	DO i = nxl, nxr
1708	DO k = nzb+1, nzt
1709	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
1710	* MERGE( 1.0_wp, 0.0_wp, &
1711	BTEST( wall_flags_0(k,-1,i), 1 ) )
1712	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
1713	* MERGE( 1.0_wp, 0.0_wp, &
1714	BTEST( wall_flags_0(k,0,i), 2 ) )
1715	v(k,-1,i) = v(k,0,i)
1716	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
1717	* MERGE( 1.0_wp, 0.0_wp, &
1718	BTEST( wall_flags_0(k,-1,i), 3 ) )
1719	ENDDO
1720	ENDDO
1721	ENDIF
1722	IF ( myidy == id_stg_north ) THEN
1723
1724	DO i = nxl, nxr
1725	DO k = nzb+1, nzt
1726	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
1727	* MERGE( 1.0_wp, 0.0_wp, &
1728	BTEST( wall_flags_0(k,nyn+1,i), 1 ) )
1729	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
1730	* MERGE( 1.0_wp, 0.0_wp, &
1731	BTEST( wall_flags_0(k,nyn+1,i), 2 ) )
1732	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
1733	* MERGE( 1.0_wp, 0.0_wp, &
1734	BTEST( wall_flags_0(k,nyn+1,i), 3 ) )
1735	ENDDO
1736	ENDDO
1737	ENDIF
1738	ENDIF
1739	ENDIF
1740	!
1741	!-- Finally, set time counter for calling STG to zero
1742	IF ( stg_call ) time_stg_call = 0.0_wp
1743
1744	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
1745
1746	END SUBROUTINE stg_main
1747
1748	!------------------------------------------------------------------------------!
1749	! Description:
1750	! ------------
1751	!> Generate a set of random number rand_it wich is equal on each PE
1752	!> and calculate the velocity seed f_n.
1753	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
1754	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1755	!> parts are collected to form the full array.
1756	!------------------------------------------------------------------------------!
1757	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id )
1758
1759	IMPLICIT NONE
1760
1761	INTEGER(iwp) :: id !< core ids at respective boundaries
1762	INTEGER(iwp) :: j !< loop index in y-direction
1763	INTEGER(iwp) :: jj !< loop index in y-direction
1764	INTEGER(iwp) :: k !< loop index in z-direction
1765	INTEGER(iwp) :: kk !< loop index in z-direction
1766	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1767
1768	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
1769	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1770	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
1771	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1772
1773	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
1774	REAL(wp) :: rand_av !< average of random number
1775	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1776
1777	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
1778	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1779	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
1780	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
1781	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1782
1783
1784	!
1785	!-- Generate random numbers using a seed generated in stg_init.
1786	!-- The set of random numbers are modified to have an average of 0 and
1787	!-- unit variance.
1788	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
1789
1790	rand_av = 0.0_wp
1791	rand_sigma_inv = 0.0_wp
1792	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
1793
1794	DO j = 0, ny
1795	DO k = nzb, nzt+1
1796	CALL RANDOM_NUMBER( rand_it(k,j) )
1797	rand_av = rand_av + rand_it(k,j)
1798	ENDDO
1799	ENDDO
1800
1801	rand_av = rand_av * nyz_inv
1802
1803	DO j = 0, ny
1804	DO k = nzb, nzt+1
1805	rand_it(k,j) = rand_it(k,j) - rand_av
1806	rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
1807	ENDDO
1808	ENDDO
1809
1810	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)
1811
1812	DO j = 0, ny
1813	DO k = nzb, nzt+1
1814	rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
1815	ENDDO
1816	ENDDO
1817
1818	!
1819	!-- Periodic fill of random number in space
1820	DO j = 0, ny
1821	DO k = 1, mergp
1822	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
1823	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
1824	ENDDO
1825	ENDDO
1826	DO j = 1, mergp
1827	DO k = nzb-mergp, nzt+1+mergp
1828	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
1829	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
1830	ENDDO
1831	ENDDO
1832
1833	!
1834	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1835	n_y2 = n_y * 2
1836	n_z2 = n_z * 2
1837	f_n_l = 0.0_wp
1838
1839	DO j = nysg, nyng
1840	DO k = nzb_x_stg, nzt_x_stg+1
1841	DO jj = -n_y2(k), n_y2(k)
1842	DO kk = -n_z2(k), n_z2(k)
1843	f_n_l(k,j) = f_n_l(k,j) &
1844	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
1845	ENDDO
1846	ENDDO
1847	ENDDO
1848	ENDDO
1849
1850	DEALLOCATE( rand_it )
1851	!
1852	!-- Gather velocity seeds of full subdomain
1853	send_count = nzt_x_stg - nzb_x_stg + 1
1854	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
1855
1856	#if defined( __parallel )
1857	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
1858	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
1859	id, comm1dx, ierr )
1860	#else
1861	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
1862	#endif
1863
1864
1865	END SUBROUTINE stg_generate_seed_yz
1866
1867
1868
1869
1870	!------------------------------------------------------------------------------!
1871	! Description:
1872	! ------------
1873	!> Generate a set of random number rand_it wich is equal on each PE
1874	!> and calculate the velocity seed f_n.
1875	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
1876	!> and each PE calculates a vertical subsection of f_n. At the the end, all
1877	!> parts are collected to form the full array.
1878	!------------------------------------------------------------------------------!
1879	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id )
1880
1881	IMPLICIT NONE
1882
1883	INTEGER(iwp) :: id !< core ids at respective boundaries
1884	INTEGER(iwp) :: i !< loop index in x-direction
1885	INTEGER(iwp) :: ii !< loop index in x-direction
1886	INTEGER(iwp) :: k !< loop index in z-direction
1887	INTEGER(iwp) :: kk !< loop index in z-direction
1888	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
1889
1890	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
1891	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
1892	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
1893	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
1894
1895	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
1896	REAL(wp) :: rand_av !< average of random number
1897	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
1898
1899	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
1900	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
1901	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
1902	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
1903	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
1904
1905
1906	!
1907	!-- Generate random numbers using a seed generated in stg_init.
1908	!-- The set of random numbers are modified to have an average of 0 and
1909	!-- unit variance.
1910	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
1911
1912	rand_av = 0.0_wp
1913	rand_sigma_inv = 0.0_wp
1914	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
1915
1916	DO i = 0, nx
1917	DO k = nzb, nzt+1
1918	CALL RANDOM_NUMBER( rand_it(k,i) )
1919	rand_av = rand_av + rand_it(k,i)
1920	ENDDO
1921	ENDDO
1922
1923	rand_av = rand_av * nxz_inv
1924
1925	DO i = 0, nx
1926	DO k = nzb, nzt+1
1927	rand_it(k,i) = rand_it(k,i) - rand_av
1928	rand_sigma_inv = rand_sigma_inv + rand_it(k,i) ** 2
1929	ENDDO
1930	ENDDO
1931
1932	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nxz_inv)
1933
1934	DO i = 0, nx
1935	DO k = nzb, nzt+1
1936	rand_it(k,i) = rand_it(k,i) * rand_sigma_inv
1937	ENDDO
1938	ENDDO
1939
1940	!
1941	!-- Periodic fill of random number in space
1942	DO i = 0, nx
1943	DO k = 1, mergp
1944	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
1945	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
1946	ENDDO
1947	ENDDO
1948	DO i = 1, mergp
1949	DO k = nzb-mergp, nzt+1+mergp
1950	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
1951	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
1952	ENDDO
1953	ENDDO
1954
1955	!
1956	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
1957	n_x2 = n_x * 2
1958	n_z2 = n_z * 2
1959	f_n_l = 0.0_wp
1960
1961	DO i = nxlg, nxrg
1962	DO k = nzb_y_stg, nzt_y_stg+1
1963	DO ii = -n_x2(k), n_x2(k)
1964	DO kk = -n_z2(k), n_z2(k)
1965	f_n_l(k,i) = f_n_l(k,i) &
1966	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
1967	ENDDO
1968	ENDDO
1969	ENDDO
1970	ENDDO
1971
1972	DEALLOCATE( rand_it )
1973
1974	!
1975	!-- Gather velocity seeds of full subdomain
1976	send_count = nzt_y_stg - nzb_y_stg + 1
1977	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
1978
1979
1980	#if defined( __parallel )
1981	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
1982	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
1983	id, comm1dy, ierr )
1984	#else
1985	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
1986	#endif
1987
1988
1989	END SUBROUTINE stg_generate_seed_xz
1990
1991	!------------------------------------------------------------------------------!
1992	! Description:
1993	! ------------
1994	!> Parametrization of the Reynolds stress tensor, following the parametrization
1995	!> described in Rotach et al. (1996), which is applied in state-of-the-art
1996	!> dispserion modelling. Please note, the parametrization does not distinguish
1997	!> between along-wind and cross-wind turbulence.
1998	!------------------------------------------------------------------------------!
1999	SUBROUTINE parametrize_reynolds_stress
2000
2001	IMPLICIT NONE
2002
2003	INTEGER(iwp) :: k !< loop index in z-direction
2004
2005	REAL(wp) :: zzi !< ratio of z/zi
2006
2007	DO k = nzb+1, nzt+1
2008	!
2009	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
2010	!-- The function decreases to 1/10 after one length scale above the
2011	!-- ABL top.
2012	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2013	!
2014	!-- Determine normalized height coordinate
2015	zzi = zu(k) / zi_ribulk
2016	!
2017	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
2018	!-- to the denominator, else the merge-function can crash if scale_l is
2019	!-- zero.
2020	r11(k) = scale_us*2 ( &
2021	MERGE( 0.35_wp * ABS( &
2022	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
2023	)**( 2.0_wp / 3.0_wp ), &
2024	0.0_wp, &
2025	scale_l < 0.0_wp ) &
2026	+ 5.0_wp - 4.0_wp * zzi &
2027	) * blend
2028
2029	r22(k) = r11(k)
2030	!
2031	!-- w'w'
2032	r33(k) = scale_wm*2 ( &
2033	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
2034	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
2035	) * blend
2036	!
2037	!-- u'w' and v'w'. Assume isotropy.
2038	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
2039	r32(k) = r31(k)
2040	!
2041	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
2042	!-- a similar profile as for u'w'.
2043	r21(k) = r31(k)
2044	ENDDO
2045
2046	!
2047	!-- Set bottom boundary condition
2048	r11(nzb) = r11(nzb+1)
2049	r22(nzb) = r22(nzb+1)
2050	r33(nzb) = r33(nzb+1)
2051
2052	r21(nzb) = r11(nzb+1)
2053	r31(nzb) = r31(nzb+1)
2054	r32(nzb) = r32(nzb+1)
2055
2056
2057	END SUBROUTINE parametrize_reynolds_stress
2058
2059	!------------------------------------------------------------------------------!
2060	! Description:
2061	! ------------
2062	!> Calculate the coefficient matrix from the Lund rotation.
2063	!------------------------------------------------------------------------------!
2064	SUBROUTINE calc_coeff_matrix
2065
2066	IMPLICIT NONE
2067
2068	INTEGER(iwp) :: k !< loop index in z-direction
2069
2070	!
2071	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
2072	DO k = nzb+1, nzt+1
2073	IF ( r11(k) > 10E-6_wp ) THEN
2074	a11(k) = SQRT( r11(k) )
2075	a21(k) = r21(k) / a11(k)
2076	a31(k) = r31(k) / a11(k)
2077	ELSE
2078	a11(k) = 10E-8_wp
2079	a21(k) = 10E-8_wp
2080	a31(k) = 10E-8_wp
2081	ENDIF
2082	ENDDO
2083	DO k = nzb+1, nzt+1
2084	a22(k) = r22(k) - a21(k)**2
2085	IF ( a22(k) > 10E-6_wp ) THEN
2086	a22(k) = SQRT( a22(k) )
2087	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
2088	ELSE
2089	a22(k) = 10E-8_wp
2090	a32(k) = 10E-8_wp
2091	ENDIF
2092	ENDDO
2093	DO k = nzb+1, nzt+1
2094	a33(k) = r33(k) - a31(k)2 - a32(k)2
2095	IF ( a33(k) > 10E-6_wp ) THEN
2096	a33(k) = SQRT( a33(k) )
2097	ELSE
2098	a33(k) = 10E-8_wp
2099	ENDIF
2100	ENDDO
2101	!
2102	!-- Set bottom boundary condition
2103	a11(nzb) = a11(nzb+1)
2104	a22(nzb) = a22(nzb+1)
2105	a21(nzb) = a21(nzb+1)
2106	a33(nzb) = a33(nzb+1)
2107	a31(nzb) = a31(nzb+1)
2108	a32(nzb) = a32(nzb+1)
2109
2110	END SUBROUTINE calc_coeff_matrix
2111
2112	!------------------------------------------------------------------------------!
2113	! Description:
2114	! ------------
2115	!> This routine controls the re-adjustment of the turbulence statistics used
2116	!> for generating turbulence at the lateral boundaries.
2117	!------------------------------------------------------------------------------!
2118	SUBROUTINE stg_adjust
2119
2120	IMPLICIT NONE
2121
2122
2123	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
2124	!
2125	!-- In case of dirichlet inflow boundary conditions only at one lateral
2126	!-- boundary, i.e. in the case no offline or self nesting is applied but
2127	!-- synthetic turbulence shall be parametrized nevertheless, the
2128	!-- boundary-layer depth need to determined first.
2129	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
2130	CALL nesting_offl_calc_zi
2131	!
2132	!-- Compute scaling parameters (domain-averaged), such as friction velocity
2133	!-- are calculated.
2134	CALL calc_scaling_variables
2135	!
2136	!-- Set length and time scales depending on boundary-layer height
2137	CALL calc_length_and_time_scale
2138	!
2139	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
2140	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
2141	!-- Rotach et al. (1996) and is based on boundary-layer depth,
2142	!-- friction velocity and velocity scale.
2143	CALL parametrize_reynolds_stress
2144	!
2145	!-- Calculate coefficient matrix from Reynolds stress tensor
2146	!-- (Lund rotation)
2147	CALL calc_coeff_matrix
2148	!
2149	!-- Determine filter functions on basis of updated length scales
2150	CALL stg_filter_func( nux, bux ) !filter ux
2151	CALL stg_filter_func( nuy, buy ) !filter uy
2152	CALL stg_filter_func( nuz, buz ) !filter uz
2153	CALL stg_filter_func( nvx, bvx ) !filter vx
2154	CALL stg_filter_func( nvy, bvy ) !filter vy
2155	CALL stg_filter_func( nvz, bvz ) !filter vz
2156	CALL stg_filter_func( nwx, bwx ) !filter wx
2157	CALL stg_filter_func( nwy, bwy ) !filter wy
2158	CALL stg_filter_func( nwz, bwz ) !filter wz
2159	!
2160	!-- Reset time counter for controlling next adjustment to zero
2161	time_stg_adjust = 0.0_wp
2162
2163	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
2164
2165	END SUBROUTINE stg_adjust
2166
2167
2168	!------------------------------------------------------------------------------!
2169	! Description:
2170	! ------------
2171	!> Calculates turbuluent length and time scales if these are not available
2172	!> from measurements.
2173	!------------------------------------------------------------------------------!
2174	SUBROUTINE calc_length_and_time_scale
2175
2176	IMPLICIT NONE
2177
2178
2179	INTEGER(iwp) :: k !< loop index in z-direction
2180
2181	REAL(wp) :: length_scale_dum !< effectively used length scale
2182
2183	!
2184	!-- In initial call the boundary-layer depth can be zero. This case, set
2185	!-- minimum value for boundary-layer depth, to setup length scales correctly.
2186	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
2187	!
2188	!-- Set-up default turbulent length scales. From the numerical point of
2189	!-- view the imposed perturbations should not be immediately dissipated
2190	!-- by the numerics. The numerical dissipation, however, acts on scales
2191	!-- up to 8 x the grid spacing. For this reason, set the turbulence
2192	!-- length scale to 8 time the grid spacing. Further, above the boundary
2193	!-- layer height, set turbulence lenght scales to zero (equivalent to not
2194	!-- imposing any perturbations) in order to save computational costs.
2195	!-- Typical time scales are derived by assuming Taylors's hypothesis,
2196	!-- using the length scales and the mean profiles of u- and v-component.
2197	DO k = nzb+1, nzt+1
2198	!
2199	!-- Determine blending parameter. Within the boundary layer length scales
2200	!-- are constant, while above lengths scales approach gradully zero,
2201	!-- i.e. imposed turbulence is not correlated in space and time,
2202	!-- just white noise, which saves computations power as the loops for the
2203	!-- computation of the filter functions depend on the length scales.
2204	!-- The value decreases to 1/10 after one length scale above the
2205	!-- ABL top.
2206	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
2207	!
2208	!-- Assume isotropic turbulence length scales
2209	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2210	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2211	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2212	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2213	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
2214	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
2215	!
2216	!-- Along the vertical direction limit the length scale further by the
2217	!-- boundary-layer depth to assure that no length scales larger than
2218	!-- the boundary-layer depth are used
2219	length_scale_dum = MIN( length_scale, zi_ribulk )
2220
2221	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2222	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2223	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
2224	!
2225	!-- Limit time scales, else they become very larger for low wind speed,
2226	!-- imposing long-living inflow perturbations which in turn propagate
2227	!-- further into the model domain. Use u_init and v_init to calculate
2228	!-- the time scales, which will be equal to the inflow profiles, both,
2229	!-- in offline nesting mode or in dirichlet/radiation mode.
2230	tu(k) = MIN( dt_stg_adjust, length_scale / &
2231	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
2232	tv(k) = MIN( dt_stg_adjust, length_scale / &
2233	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
2234	!
2235	!-- Time scale of w-component is a mixture from u- and v-component.
2236	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
2237
2238	ENDDO
2239	!
2240	!-- Set bottom boundary condition for the length and time scales
2241	nux(nzb) = nux(nzb+1)
2242	nuy(nzb) = nuy(nzb+1)
2243	nuz(nzb) = nuz(nzb+1)
2244	nvx(nzb) = nvx(nzb+1)
2245	nvy(nzb) = nvy(nzb+1)
2246	nvz(nzb) = nvz(nzb+1)
2247	nwx(nzb) = nwx(nzb+1)
2248	nwy(nzb) = nwy(nzb+1)
2249	nwz(nzb) = nwz(nzb+1)
2250
2251	tu(nzb) = tu(nzb+1)
2252	tv(nzb) = tv(nzb+1)
2253	tw(nzb) = tw(nzb+1)
2254
2255
2256	END SUBROUTINE calc_length_and_time_scale
2257
2258	!------------------------------------------------------------------------------!
2259	! Description:
2260	! ------------
2261	!> Calculate scaling variables which are used for turbulence parametrization
2262	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
2263	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
2264	!------------------------------------------------------------------------------!
2265	SUBROUTINE calc_scaling_variables
2266
2267	USE surface_mod, &
2268	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
2269
2270	IMPLICIT NONE
2271
2272	INTEGER(iwp) :: i !< loop index in x-direction
2273	INTEGER(iwp) :: j !< loop index in y-direction
2274	INTEGER(iwp) :: k !< loop index in z-direction
2275	INTEGER(iwp) :: m !< surface element index
2276
2277	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
2278	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
2279	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
2280	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
2281	REAL(wp) :: shf_mean !< mean surface sensible heat flux
2282	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
2283	REAL(wp) :: w_convective !< convective velocity scale
2284
2285	!
2286	!-- Calculate mean friction velocity, velocity scale, heat flux and
2287	!-- near-surface temperature in the model domain.
2288	pt_surf_mean_l = 0.0_wp
2289	shf_mean_l = 0.0_wp
2290	scale_l_l = 0.0_wp
2291	friction_vel_l = 0.0_wp
2292	DO m = 1, surf_def_h(0)%ns
2293	i = surf_def_h(0)%i(m)
2294	j = surf_def_h(0)%j(m)
2295	k = surf_def_h(0)%k(m)
2296	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
2297	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
2298	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
2299	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2300	ENDDO
2301	DO m = 1, surf_lsm_h%ns
2302	i = surf_lsm_h%i(m)
2303	j = surf_lsm_h%j(m)
2304	k = surf_lsm_h%k(m)
2305	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
2306	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
2307	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
2308	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2309	ENDDO
2310	DO m = 1, surf_usm_h%ns
2311	i = surf_usm_h%i(m)
2312	j = surf_usm_h%j(m)
2313	k = surf_usm_h%k(m)
2314	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
2315	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
2316	scale_l_l = scale_l_l + surf_usm_h%ol(m)
2317	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
2318	ENDDO
2319
2320	#if defined( __parallel )
2321	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
2322	comm2d, ierr )
2323	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
2324	comm2d, ierr )
2325	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
2326	comm2d, ierr )
2327	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
2328	comm2d, ierr )
2329	#else
2330	scale_us = friction_vel_l
2331	shf_mean = shf_mean_l
2332	scale_l = scale_l_l
2333	pt_surf_mean = pt_surf_mean_l
2334	#endif
2335
2336	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2337	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2338	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2339	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
2340	!
2341	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
2342	!-- is negative, set convective velocity scale to zero.
2343	IF ( shf_mean > 0.0_wp ) THEN
2344	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
2345	ELSE
2346	w_convective = 0.0_wp
2347	ENDIF
2348	!
2349	!-- Finally, in order to consider also neutral or stable stratification,
2350	!-- compute momentum velocity scale from u* and convective velocity scale,
2351	!-- according to Rotach et al. (1996).
2352	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
2353
2354	END SUBROUTINE calc_scaling_variables
2355
2356	END MODULE synthetic_turbulence_generator_mod

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