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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4830

Last change on this file since 4830 was 4828, checked in by Giersch, 4 years ago
Copyright updated to year 2021, interface pmc_sort removed to accelarate the nesting code
Property svn:keywords set to `Id`
File size: 112.6 KB

Rev	Line
[2259]	1	!> @synthetic_turbulence_generator_mod.f90
[4559]	2	!--------------------------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[2259]	4	!
[4559]	5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
	6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
	7	! (at your option) any later version.
[2259]	8	!
[4559]	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
	10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
	11	! Public License for more details.
[2259]	12	!
[4559]	13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
	14	! <http://www.gnu.org/licenses/>.
[2259]	15	!
[4828]	16	! Copyright 1997-2021 Leibniz Universitaet Hannover
[4559]	17	!--------------------------------------------------------------------------------------------------!
[2259]	18	!
[4559]	19	!
[2259]	20	! Current revisions:
	21	! -----------------
[4603]	22	!
	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4828 2021-01-05 11:21:41Z Giersch $
[4671]	27	! Implementation of downward facing USM and LSM surfaces
	28	!
	29	! 4647 2020-08-24 16:36:18Z suehring
[4647]	30	! Change default value of synthetic turbulence adjustment as well as compute_velocity_seeds_local
	31	! By default, the random-seed computation is now distributed among several cores. Especially for
	32	! large length scales this is significantly faster.
	33	!
	34	! 4640 2020-08-11 16:28:32Z suehring
[4640]	35	! - to avoid that the correction term in r11/r22 computation becomes unrealistically high, limit
	36	! Obukhov length (term is not valid for near neutral conditions)
	37	! - to avoid unrealistically large perturbations, change computation of r21 so that this resembles
	38	! the vertical transport of horizontal momentum
	39	!
	40	! 4629 2020-07-29 09:37:56Z raasch
[4629]	41	! support for MPI Fortran77 interface (mpif.h) removed
	42	!
	43	! 4603 2020-07-14 16:08:30Z suehring
[4603]	44	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
	45	! initialized properly
	46	!
	47	! 4566 2020-06-16 10:11:51Z suehring
[4566]	48	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
	49	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
	50	! - change default value of time interval to adjust turbulence parametrization
	51	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
	52	!
	53	! 4562 2020-06-12 08:38:47Z raasch
[4562]	54	! Parts of r4559 re-formatted
	55	!
	56	! 4559 2020-06-11 08:51:48Z raasch
[4559]	57	! File re-formatted to follow the PALM coding standard
	58	!
	59	! 4535 2020-05-15 12:07:23Z raasch
	60	! Bugfix for restart data format query
	61	!
[4535]	62	! 4495 2020-04-13 20:11:20Z raasch
[4559]	63	! Restart data handling with MPI-IO added
	64	!
[4495]	65	! 4481 2020-03-31 18:55:54Z maronga
[4559]	66	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
	67	!
[4444]	68	! 4442 2020-03-04 19:21:13Z suehring
[4442]	69	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	70	! (was accidantly changed).
[4559]	71	!
[4442]	72	! 4441 2020-03-04 19:20:35Z suehring
[4440]	73	! Correct misplaced preprocessor directive
[4559]	74	!
[4440]	75	! 4438 2020-03-03 20:49:28Z suehring
[4438]	76	! Performance optimizations in velocity-seed calculation:
[4559]	77	! - Random number array is only defined and computed locally (except for normalization to zero mean
	78	! and unit variance)
	79	! - Parallel random number generator is applied independent on the 2D random numbers in other
	80	! routines
	81	! - Option to decide wheter velocity seeds are computed locally without any further communication
	82	! or are computed by all processes along the communicator
	83	!
[4438]	84	! 4346 2019-12-18 11:55:56Z motisi
[4559]	85	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
	86	! information used in wall_flags_static_0
	87	!
[4346]	88	! 4335 2019-12-12 16:39:05Z suehring
[4335]	89	! Commentation of last commit
[4559]	90	!
[4335]	91	! 4332 2019-12-10 19:44:12Z suehring
[4559]	92	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
	93	! Further, minor bugfix in initial velocity seed calculation.
	94	!
[4332]	95	! 4329 2019-12-10 15:46:36Z motisi
[4329]	96	! Renamed wall_flags_0 to wall_flags_static_0
[4559]	97	!
[4329]	98	! 4309 2019-11-26 18:49:59Z suehring
[4559]	99	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
	100	! the parallel random number generator. Random numbers are now only computed and normalized locally,
	101	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
	102	! array.
	103	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
	104	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
	105	!
[4309]	106	! 4182 2019-08-22 15:20:23Z scharf
[4182]	107	! Corrected "Former revisions" section
[4559]	108	!
[4182]	109	! 4148 2019-08-08 11:26:00Z suehring
[4148]	110	! Remove unused variable
[4559]	111	!
[4148]	112	! 4144 2019-08-06 09:11:47Z raasch
[4559]	113	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	114	!
[4144]	115	! 4071 2019-07-03 20:02:00Z suehring
[4559]	116	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
	117	! file.
	118	!
[4071]	119	! 4022 2019-06-12 11:52:39Z suehring
[4022]	120	! Several bugfixes and improvements
[4559]	121	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
	122	! instabilities in case the mean volume flow is close to zero)
	123	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
	124	! numerically unstable
	125	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
	126	! case dt_stg_call /= dt_3d
	127	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
	128	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
[4022]	129	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
[4559]	130	!
[4022]	131	! 3987 2019-05-22 09:52:13Z kanani
[3987]	132	! Introduce alternative switch for debug output during timestepping
[4559]	133	!
[3987]	134	! 3938 2019-04-29 16:06:25Z suehring
[3938]	135	! Remove unused variables
[4559]	136	!
[3938]	137	! 3937 2019-04-29 15:09:07Z suehring
[4559]	138	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
	139	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
	140	! synthetic turbulence parametrization.
	141	!
[3937]	142	! 3909 2019-04-17 09:13:25Z suehring
[3909]	143	! Minor bugfix for last commit
[4559]	144	!
[3909]	145	! 3900 2019-04-16 15:17:43Z suehring
[3900]	146	! Missing re-calculation of perturbation seeds in case of restarts
[4559]	147	!
[3900]	148	! 3891 2019-04-12 17:52:01Z suehring
[4559]	149	! Bugfix in initialization in case of restart runs.
	150	!
[3891]	151	! 3885 2019-04-11 11:29:34Z kanani
[4559]	152	! Changes related to global restructuring of location messages and introduction of additional debug
	153	! messages
	154	!
	155	!
	156	! Removed unused variables
	157	!
[3775]	158	! 3719 2019-02-06 13:10:18Z kanani
[4559]	159	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
	160	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
	161	! for better overview.
	162	!
[4182]	163	! 2259 2017-06-08 09:09:11Z gronemeier
	164	! Initial revision
[3044]	165	!
[4182]	166	! Authors:
	167	! --------
	168	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	169	!
	170	!
[2259]	171	! Description:
	172	! ------------
[4559]	173	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
	174	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
	175	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
	176	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
	177	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
	178	!> parametrized within the boundary layer.
[2259]	179	!>
[4566]	180	!> @todo Enable cyclic_fill
[4559]	181	!> Implement turbulence generation for e and pt
[2259]	182	!> @note <Enter notes on the module>
[4559]	183	!> @bug Height information from input file is not used. Profiles from input must match with current
	184	!> PALM grid.
	185	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
	186	!--------------------------------------------------------------------------------------------------!
[2259]	187	MODULE synthetic_turbulence_generator_mod
	188
	189
[4559]	190	USE arrays_3d, &
	191	ONLY: dzw, &
	192	ddzw, &
	193	drho_air, &
	194	mean_inflow_profiles, &
	195	pt, &
	196	pt_init, &
	197	q, &
	198	q_init, &
	199	u, &
	200	u_init, &
	201	v, &
	202	v_init, &
	203	w, &
	204	zu, &
[4022]	205	zw
[2259]	206
[4559]	207	USE basic_constants_and_equations_mod, &
	208	ONLY: g, &
	209	kappa, &
[4022]	210	pi
[2259]	211
[4559]	212	USE control_parameters, &
	213	ONLY: bc_lr, &
	214	bc_ns, &
	215	child_domain, &
	216	coupling_char, &
	217	debug_output_timestep, &
	218	dt_3d, &
	219	e_init, &
	220	humidity, &
	221	initializing_actions, &
	222	intermediate_timestep_count, &
	223	intermediate_timestep_count_max, &
	224	length, &
	225	message_string, &
	226	nesting_offline, &
	227	neutral, &
	228	num_mean_inflow_profiles, &
	229	random_generator, &
	230	rans_mode, &
	231	restart_data_format_output, &
	232	restart_string, &
	233	syn_turb_gen, &
	234	time_since_reference_point, &
[4022]	235	turbulent_inflow
[4438]	236
[4559]	237	USE cpulog, &
	238	ONLY: cpu_log, &
[4438]	239	log_point_s
	240
[4559]	241	USE grid_variables, &
	242	ONLY: ddx, &
	243	ddy, &
	244	dx, &
[4022]	245	dy
[2259]	246
[4559]	247	USE indices, &
	248	ONLY: nbgp, &
	249	nz, &
	250	nzb, &
	251	nzt, &
	252	nx, &
	253	nxl, &
	254	nxlu, &
	255	nxr, &
	256	ny, &
	257	nys, &
	258	nysv, &
	259	nyn, &
[4346]	260	wall_flags_total_0
[2259]	261
	262	USE kinds
	263
[4629]	264	#if defined( __parallel )
[2259]	265	USE MPI
[2841]	266	#endif
[2259]	267
[4559]	268	USE nesting_offl_mod, &
	269	ONLY: nesting_offl_calc_zi, &
[4022]	270	zi_ribulk
[3347]	271
[4559]	272	USE pegrid, &
	273	ONLY: comm1dx, &
	274	comm1dy, &
	275	comm2d, &
	276	ierr, &
	277	myidx, &
	278	myidy, &
[4022]	279	pdims
[4438]	280
[4559]	281	USE pmc_interface, &
[4022]	282	ONLY : rans_mode_parent
[4438]	283
[4559]	284	USE random_generator_parallel, &
	285	ONLY: init_parallel_random_generator, &
	286	random_dummy, &
	287	random_number_parallel, &
[4438]	288	random_seed_parallel
[2259]	289
[4495]	290	USE restart_data_mpi_io_mod, &
	291	ONLY: rrd_mpi_io, &
	292	wrd_mpi_io
	293
[4559]	294	USE transpose_indices, &
	295	ONLY: nzb_x, &
	296	nzt_x
[2259]	297
[4559]	298	USE surface_mod, &
	299	ONLY: surf_def_h, &
	300	surf_lsm_h, &
[4438]	301	surf_usm_h
[2259]	302
	303	IMPLICIT NONE
	304
[3038]	305	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	306	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	307	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	308	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4566]	309	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
	310	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
	311	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
	312	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
	313	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
	314	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
[3038]	315	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	316	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	317	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	318	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4444]	319	#if defined( __parallel )
[4309]	320	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	321	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	322	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	323	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[4444]	324	#endif
[2259]	325
[4559]	326	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	327	!< required for bias correction of imposed perturbations
	328	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	329	!< required for bias correction of imposed perturbations
	330
[4444]	331	#if defined( __parallel )
[3347]	332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	333	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	334	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	335	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
[4444]	336	#endif
[3347]	337	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	338	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	339	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	340	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	341	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	342	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	343	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	344	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	345	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	346
[4559]	347	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	348	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	349	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	350	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
[4438]	351
[2259]	352
[4566]	353	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
	354	!< no time correlation to the timestep before should be considered
[4647]	355	LOGICAL :: compute_velocity_seeds_local = .FALSE. !< switch to decide whether velocity seeds are computed locally
[4559]	356	!< or if computation is distributed over several processes
	357	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
	358	!< (.FALSE.) or if it parametrized
	359	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
	360	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
[2259]	361
[4559]	362
	363	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	364	!< scales above the boundary layer
[4566]	365	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
[4559]	366	!< one length scale above ABL top
	367	REAL(wp) :: d_l !< blend_coeff/length_scale
[4566]	368	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
	369	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
[4559]	370	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
	371	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	372	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	373	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	374	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	375	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	376
	377	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
	378
	379
	380	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	381	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	382	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	383	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	384	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	385	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	386
	387	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	388	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	389	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	390	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	391	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	392	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	393	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	394	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	395	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
	396
	397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	406	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	407	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	408	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	409	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	411	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	415	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	416	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	417	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	418
[4566]	419	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
	420	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
[4559]	421
[2259]	422	!
	423	!-- PALM interfaces:
[3347]	424	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	425	INTERFACE stg_adjust
	426	MODULE PROCEDURE stg_adjust
	427	END INTERFACE stg_adjust
	428	!
[2259]	429	!-- Input parameter checks to be done in check_parameters
	430	INTERFACE stg_check_parameters
	431	MODULE PROCEDURE stg_check_parameters
	432	END INTERFACE stg_check_parameters
	433
	434	!
	435	!-- Calculate filter functions
	436	INTERFACE stg_filter_func
	437	MODULE PROCEDURE stg_filter_func
	438	END INTERFACE stg_filter_func
	439
	440	!
[2938]	441	!-- Generate velocity seeds at south and north domain boundary
	442	INTERFACE stg_generate_seed_xz
	443	MODULE PROCEDURE stg_generate_seed_xz
	444	END INTERFACE stg_generate_seed_xz
	445	!
	446	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	447	INTERFACE stg_generate_seed_yz
	448	MODULE PROCEDURE stg_generate_seed_yz
	449	END INTERFACE stg_generate_seed_yz
	450
	451	!
	452	!-- Output of information to the header file
	453	INTERFACE stg_header
	454	MODULE PROCEDURE stg_header
	455	END INTERFACE stg_header
	456
	457	!
	458	!-- Initialization actions
	459	INTERFACE stg_init
	460	MODULE PROCEDURE stg_init
	461	END INTERFACE stg_init
	462
	463	!
	464	!-- Main procedure of synth. turb. gen.
	465	INTERFACE stg_main
	466	MODULE PROCEDURE stg_main
	467	END INTERFACE stg_main
	468
	469	!
	470	!-- Reading of NAMELIST parameters
	471	INTERFACE stg_parin
	472	MODULE PROCEDURE stg_parin
	473	END INTERFACE stg_parin
	474
	475	!
	476	!-- Reading of parameters for restart runs
[2894]	477	INTERFACE stg_rrd_global
[4495]	478	MODULE PROCEDURE stg_rrd_global_ftn
	479	MODULE PROCEDURE stg_rrd_global_mpi
[2894]	480	END INTERFACE stg_rrd_global
[2259]	481
	482	!
	483	!-- Writing of binary output for restart runs
[2894]	484	INTERFACE stg_wrd_global
	485	MODULE PROCEDURE stg_wrd_global
	486	END INTERFACE stg_wrd_global
[2259]	487
	488	SAVE
	489
	490	PRIVATE
	491
	492	!
	493	!-- Public interfaces
[4559]	494	PUBLIC stg_adjust, &
	495	stg_check_parameters, &
	496	stg_header, &
	497	stg_init, &
	498	stg_main, &
	499	stg_parin, &
	500	stg_rrd_global, &
	501	stg_wrd_global
[2259]	502
	503	!
	504	!-- Public variables
[4559]	505	PUBLIC dt_stg_call, &
	506	dt_stg_adjust, &
	507	id_stg_left, &
	508	id_stg_north, &
	509	id_stg_right, &
	510	id_stg_south, &
	511	parametrize_inflow_turbulence, &
	512	time_stg_adjust, &
	513	time_stg_call, &
	514	use_syn_turb_gen
[2259]	515
	516
	517	CONTAINS
	518
	519
[4559]	520	!--------------------------------------------------------------------------------------------------!
[2259]	521	! Description:
	522	! ------------
	523	!> Check parameters routine for synthetic turbulence generator
[4559]	524	!--------------------------------------------------------------------------------------------------!
[2259]	525	SUBROUTINE stg_check_parameters
	526
[4559]	527	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
[3182]	528	nesting_offline ) THEN
[4559]	529	message_string = 'Synthetic turbulence generator is required ' // &
	530	'if offline nesting is applied and PALM operates in LES mode.'
[3376]	531	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	532	ENDIF
	533
[4559]	534	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	535	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[4559]	536	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
	537	'and parent operates in RANS-mode but current child in LES mode.'
[3376]	538	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	539	ENDIF
	540
[2776]	541	IF ( use_syn_turb_gen ) THEN
[2259]	542
[4559]	543	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
	544	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
[3579]	545	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
[4559]	546
[3579]	547	ENDIF
[4559]	548
	549	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
	550	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
[3579]	551	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
[4559]	552
[3579]	553	ENDIF
[4559]	554
	555	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	556
	557	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	558	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	559	message_string = 'Using synthetic turbulence generator requires ' // &
	560	'%initializing_actions = "set_constant_profiles" or ' // &
	561	' "read_restart_data", if not offline nesting is applied.'
[2938]	562	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	563	ENDIF
	564
	565	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
[4559]	566	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
	567	' "dirichlet/radiation", if not offline nesting is applied.'
[2938]	568	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	569	ENDIF
	570	IF ( bc_ns /= 'cyclic' ) THEN
[4559]	571	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
	572	' "cyclic", if not offline nesting is applied.'
[2938]	573	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	574	ENDIF
	575
[2259]	576	ENDIF
	577
	578	IF ( turbulent_inflow ) THEN
[4559]	579	message_string = 'Using synthetic turbulence generator in combination ' // &
	580	'&with turbulent_inflow = .T. is not allowed'
[2259]	581	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	582	ENDIF
[4309]	583	!
	584	!-- Synthetic turbulence generator requires the parallel random generator
	585	IF ( random_generator /= 'random-parallel' ) THEN
[4559]	586	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
	587	'random-parallel.'
[4309]	588	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	589	ENDIF
[2259]	590
	591	ENDIF
	592
	593	END SUBROUTINE stg_check_parameters
	594
	595
[4559]	596	!--------------------------------------------------------------------------------------------------!
[2259]	597	! Description:
	598	! ------------
	599	!> Header output for synthetic turbulence generator
[4559]	600	!--------------------------------------------------------------------------------------------------!
[2259]	601	SUBROUTINE stg_header ( io )
	602
[4559]	603	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
[2259]	604
	605	!
	606	!-- Write synthetic turbulence generator Header
	607	WRITE( io, 1 )
[2776]	608	IF ( use_syn_turb_gen ) THEN
[2259]	609	WRITE( io, 2 )
	610	ELSE
	611	WRITE( io, 3 )
	612	ENDIF
[4559]	613
[3347]	614	IF ( parametrize_inflow_turbulence ) THEN
	615	WRITE( io, 4 ) dt_stg_adjust
	616	ELSE
	617	WRITE( io, 5 )
	618	ENDIF
[2259]	619
[4559]	620	1 FORMAT (//' Synthetic turbulence generator information:'/ &
[2259]	621	' ------------------------------------------'/)
[3347]	622	2 FORMAT (' synthetic turbulence generator is switched on')
	623	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	624	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	625	5 FORMAT (' imposed turbulence is read from file' )
[2259]	626
	627	END SUBROUTINE stg_header
	628
	629
[4559]	630	!--------------------------------------------------------------------------------------------------!
[2259]	631	! Description:
	632	! ------------
	633	!> Initialization of the synthetic turbulence generator
[4559]	634	!--------------------------------------------------------------------------------------------------!
[2259]	635	SUBROUTINE stg_init
	636
[2669]	637	#if defined( __parallel )
[4559]	638	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	639	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
[2669]	640	#endif
[2259]	641
[4559]	642	INTEGER(iwp) :: i !> grid index in x-direction
	643	INTEGER(iwp) :: j !> loop index
	644	INTEGER(iwp) :: k !< index
[4444]	645	#if defined( __parallel )
[4559]	646	INTEGER(iwp) :: newtype !< dummy MPI type
	647	INTEGER(iwp) :: realsize !< size of REAL variables
[4444]	648	#endif
[4309]	649
[4022]	650	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	651	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[4559]	652
	653
	654	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
	655
[2259]	656	!
	657	!-- Dummy variables used for reading profiles
[4559]	658	REAL(wp) :: d1 !< u profile
	659	REAL(wp) :: d2 !< v profile
	660	REAL(wp) :: d3 !< w profile
	661	REAL(wp) :: d5 !< e profile
	662	REAL(wp) :: luy !< length scale for u in y direction
	663	REAL(wp) :: luz !< length scale for u in z direction
	664	REAL(wp) :: lvy !< length scale for v in y direction
	665	REAL(wp) :: lvz !< length scale for v in z direction
	666	REAL(wp) :: lwy !< length scale for w in y direction
	667	REAL(wp) :: lwz !< length scale for w in z direction
[4444]	668	#if defined( __parallel )
[4559]	669	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[4444]	670	#endif
[4559]	671	REAL(wp) :: zz !< height
[2259]	672
[2938]	673
[2259]	674	#if defined( __parallel )
	675	CALL MPI_BARRIER( comm2d, ierr )
	676	#endif
[4438]	677	!
[4559]	678	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
	679	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
	680	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
	681	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
	682	!-- communication).
[4438]	683	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	684	#if defined( __parallel )
[4559]	685	!
[4438]	686	!-- Determine processor decomposition of z-axis along x- and y-direction
	687	nnz = nz / pdims(1)
	688	nzb_x_stg = 1 + myidx * INT( nnz )
	689	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[4559]	690
	691	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[4438]	692	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[4559]	693
	694	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
[4438]	695	.AND. .NOT. rans_mode ) ) THEN
	696	nnz = nz / pdims(2)
	697	nzb_y_stg = 1 + myidy * INT( nnz )
	698	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[4559]	699
	700	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[4438]	701	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	702	ENDIF
[4559]	703
	704	!
	705	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
[4438]	706	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	707	extent = 1 * realsize
[4559]	708	!
	709	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
[4438]	710	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[4559]	711	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
[4438]	712	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	713	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	714	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	715	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	716
[4438]	717	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[4559]	718	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
[4438]	719	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	720	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	721	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	722	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	723
	724	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	725	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[4559]	726
[4438]	727	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	728	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[4559]	729
[4438]	730	DO j = 1, pdims(1)
	731	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	732	ENDDO
[4559]	733	!
	734	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
[4438]	735	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	736	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	737	.AND. .NOT. rans_mode ) ) THEN
	738	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	739	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	740	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	741	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	742	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	743
[4438]	744	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	745	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	746	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	747	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	748	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	749	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	750
	751	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	752	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
[4559]	753
[4438]	754	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	755	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
[4559]	756
[4438]	757	DO j = 1, pdims(2)
	758	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	759	ENDDO
[4559]	760
[4438]	761	ENDIF
[4440]	762	#endif
[2938]	763	ENDIF
[2259]	764	!
[4071]	765	!-- Allocate required arrays.
[4559]	766	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
	767	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
	768	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
	769	!-- and initialized appropriately.
	770	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	771	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	772	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	773	mean_inflow_profiles = 0.0_wp
	774	mean_inflow_profiles(:,1) = u_init
	775	mean_inflow_profiles(:,2) = v_init
	776	!
[4559]	777	!-- Even though potential temperature and humidity are not perturbed, they need to be
	778	!-- initialized appropriately.
	779	IF ( .NOT. neutral ) &
[4071]	780	mean_inflow_profiles(:,4) = pt_init
[4559]	781	IF ( humidity ) &
	782	mean_inflow_profiles(:,6) = q_init
	783	ENDIF
[3347]	784	ENDIF
[4566]	785	!
	786	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
	787	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
	788	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	789	u_init = mean_inflow_profiles(:,1)
	790	v_init = mean_inflow_profiles(:,2)
	791	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	792	ENDIF
[2259]	793
[4559]	794	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	795	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	796	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	797	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	798	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	799	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	800	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	801	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	802
[4566]	803	r11 = 0.0_wp
	804	r21 = 0.0_wp
	805	r22 = 0.0_wp
	806	r31 = 0.0_wp
	807	r32 = 0.0_wp
	808	r33 = 0.0_wp
	809	tu = 0.0_wp
	810	tv = 0.0_wp
	811	tw = 0.0_wp
	812
[4438]	813	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	814	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	815	dist_xz = 0.0_wp
	816	dist_yz = 0.0_wp
	817	!
[2259]	818	!-- Read inflow profile
	819	!-- Height levels of profiles in input profile is as follows:
[4559]	820	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
[2259]	821	!-- WARNING: zz is not used at the moment
[4559]	822	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
[2259]	823
[2938]	824	IF ( file_stg_exist ) THEN
[2259]	825
[4559]	826	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
[2938]	827	!
	828	!-- Skip header
	829	READ( 90, * )
[2259]	830
[4603]	831	DO k = nzb, nzt
[4559]	832	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
	833	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
[2938]	834
[2259]	835	!
[4559]	836	!-- Convert length scales from meter to number of grid points.
[4603]	837	IF ( k /= nzb ) THEN
	838	nuz(k) = INT( luz * ddzw(k) )
	839	nvz(k) = INT( lvz * ddzw(k) )
	840	nwz(k) = INT( lwz * ddzw(k) )
	841	ELSE
	842	nuz(k) = INT( luz * ddzw(k+1) )
	843	nvz(k) = INT( lvz * ddzw(k+1) )
	844	nwz(k) = INT( lwz * ddzw(k+1) )
	845	ENDIF
	846
[2938]	847	nuy(k) = INT( luy * ddy )
	848	nvy(k) = INT( lvy * ddy )
	849	nwy(k) = INT( lwy * ddy )
	850	!
[4603]	851	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
	852	!-- y-direction.
[2938]	853	nwx(k) = nwy(k)
	854	nvx(k) = nvy(k)
	855	nux(k) = nuy(k)
	856	!
	857	!-- Save Mean inflow profiles
	858	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	859	mean_inflow_profiles(k,1) = d1
	860	mean_inflow_profiles(k,2) = d2
	861	! mean_inflow_profiles(k,4) = d4
	862	mean_inflow_profiles(k,5) = d5
	863	ENDIF
	864	ENDDO
[3182]	865	!
[4603]	866	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
	867	!-- simply overwritten.
	868	nwx(nzb) = nwy(nzb+1)
	869	nvx(nzb) = nvy(nzb+1)
	870	nux(nzb) = nuy(nzb+1)
[4559]	871	nuy(nzb) = nuy(nzb+1)
[3182]	872	nuz(nzb) = nuz(nzb+1)
	873	nvy(nzb) = nvy(nzb+1)
	874	nvz(nzb) = nvz(nzb+1)
	875	nwy(nzb) = nwy(nzb+1)
	876	nwz(nzb) = nwz(nzb+1)
[4559]	877
[4603]	878	nwx(nzt+1) = nwy(nzt)
	879	nvx(nzt+1) = nvy(nzt)
	880	nux(nzt+1) = nuy(nzt)
	881	nuy(nzt+1) = nuy(nzt)
	882	nuz(nzt+1) = nuz(nzt)
	883	nvy(nzt+1) = nvy(nzt)
	884	nvz(nzt+1) = nvz(nzt)
	885	nwy(nzt+1) = nwy(nzt)
	886	nwz(nzt+1) = nwz(nzt)
	887
[2938]	888	CLOSE( 90 )
[3347]	889	!
[4559]	890	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3347]	891	CALL calc_coeff_matrix
	892	!
[4559]	893	!-- No information about turbulence and its length scales are available. Instead, parametrize
	894	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
	895	!-- parametrized, which is done later when energy-balance models are already initialized. This is
	896	!-- because the STG needs information about surface properties such as roughness to build
	897	!-- 'realistic' turbulence profiles.
[2938]	898	ELSE
[2259]	899	!
[4566]	900	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
	901	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[4022]	902	!
[3347]	903	!-- Set flag indicating that turbulence is parametrized
	904	parametrize_inflow_turbulence = .TRUE.
	905	!
[4559]	906	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
	907	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
	908	!-- nevertheless, the boundary-layer depth needs to be determined first.
	909	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
[4022]	910	CALL nesting_offl_calc_zi
	911	!
[4559]	912	!-- Determine boundary-layer depth, which is used to initialize lenght scales
[3347]	913	CALL calc_scaling_variables
	914	!
[4559]	915	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
	916	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
	917	!-- friction velocity and velocity scale.
[4566]	918	CALL parametrize_turbulence
[4559]	919	!
	920	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3891]	921	CALL calc_coeff_matrix
[4559]	922
[2938]	923	ENDIF
[2259]	924	!
[4566]	925	!-- Initial filter functions
	926	CALL stg_setup_filter_function
[2938]	927	!
	928	!-- Allocate velocity seeds for turbulence at xz-layer
[4559]	929	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	930	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	931	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	932
[2938]	933	!
	934	!-- Allocate velocity seeds for turbulence at yz-layer
[4559]	935	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	936	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	937	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	938
[2938]	939	fu_xz = 0.0_wp
	940	fuo_xz = 0.0_wp
	941	fv_xz = 0.0_wp
	942	fvo_xz = 0.0_wp
	943	fw_xz = 0.0_wp
	944	fwo_xz = 0.0_wp
	945
	946	fu_yz = 0.0_wp
	947	fuo_yz = 0.0_wp
	948	fv_yz = 0.0_wp
	949	fvo_yz = 0.0_wp
	950	fw_yz = 0.0_wp
	951	fwo_yz = 0.0_wp
	952
[2259]	953	#if defined( __parallel )
	954	CALL MPI_BARRIER( comm2d, ierr )
	955	#endif
	956
	957	!
[4559]	958	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
	959	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
	960	!-- This is mostly for k=nzt+1.
[2259]	961	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	962	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	963
	964	IF ( myidx == id_stg_left ) i = -1
	965	IF ( myidx == id_stg_right ) i = nxr+1
	966
[4438]	967	DO j = nys, nyn
[2259]	968	DO k = nzb, nzt+1
[4332]	969	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	970	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	971	ELSE
[4332]	972	fu_yz(k,j) = 10E-8_wp
[2259]	973	ENDIF
	974
[4332]	975	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	976	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	977	ELSE
[4332]	978	fv_yz(k,j) = 10E-8_wp
[2259]	979	ENDIF
	980
[4332]	981	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	982	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
[2259]	983	ELSE
[4332]	984	fw_yz(k,j) = 10E-8_wp
[2259]	985	ENDIF
	986	ENDDO
	987	ENDDO
	988	ENDIF
[4559]	989
[3900]	990	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	991
	992	IF ( myidy == id_stg_south ) j = -1
	993	IF ( myidy == id_stg_north ) j = nyn+1
	994
[4438]	995	DO i = nxl, nxr
[3900]	996	DO k = nzb, nzt+1
[4335]	997	!
[4559]	998	!-- In case the correlation coefficients are very small, the velocity seeds may become
	999	!-- very large finally creating numerical instabilities in the synthetic turbulence
	1000	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
[4332]	1001	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	1002	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	1003	ELSE
[4332]	1004	fu_xz(k,i) = 10E-8_wp
[3900]	1005	ENDIF
	1006
[4332]	1007	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	1008	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	1009	ELSE
[4332]	1010	fv_xz(k,i) = 10E-8_wp
[3900]	1011	ENDIF
	1012
[4332]	1013	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	1014	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	1015	ELSE
[4332]	1016	fw_xz(k,i) = 10E-8_wp
[3900]	1017	ENDIF
	1018
	1019	ENDDO
	1020	ENDDO
	1021	ENDIF
[2259]	1022	ENDIF
[4022]	1023	!
[4559]	1024	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
	1025	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
	1026	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
	1027	!-- different cases must be distinguished.
[4022]	1028	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1029	!
	1030	!-- Number of grid points where perturbations are imposed on u
	1031	IF ( myidx == id_stg_left ) i = nxl
	1032	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1033
	1034	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1035	!
[4559]	1036	!-- Number of grid points where perturbations are imposed on v and w
[4022]	1037	IF ( myidx == id_stg_left ) i = nxl-1
	1038	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1039
	1040	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1041	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	1042
[4022]	1043	#if defined( __parallel )
[4559]	1044	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
[4022]	1045	#else
	1046	nr_non_topo_yz = nr_non_topo_yz_l
[4559]	1047	#endif
[4022]	1048	ENDIF
[4559]	1049
[4022]	1050	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1051	!
	1052	!-- Number of grid points where perturbations are imposed on v
	1053	IF ( myidy == id_stg_south ) j = nys
	1054	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1055
	1056	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1057	!
[4559]	1058	!-- Number of grid points where perturbations are imposed on u and w
[4022]	1059	IF ( myidy == id_stg_south ) j = nys-1
	1060	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1061
	1062	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1063	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1064
[4022]	1065	#if defined( __parallel )
[4559]	1066	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
[4022]	1067	#else
	1068	nr_non_topo_xz = nr_non_topo_xz_l
[4559]	1069	#endif
[4022]	1070	ENDIF
[4438]	1071	!
[4559]	1072	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
	1073	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
	1074	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
[4566]	1075	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
	1076	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
[4438]	1077	id_rand_yz = 0
	1078	seq_rand_yz = 0
[2259]	1079
[4566]	1080	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
[4022]	1081
[4559]	1082	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1083	.AND. .NOT. rans_mode ) ) THEN
[4566]	1084	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
	1085	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
[4438]	1086	id_rand_xz = 0
	1087	seq_rand_xz = 0
	1088
[4566]	1089	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
[4438]	1090	ENDIF
	1091
[2259]	1092	END SUBROUTINE stg_init
	1093
	1094
[4559]	1095	!--------------------------------------------------------------------------------------------------!
[2259]	1096	! Description:
	1097	! ------------
[4559]	1098	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
	1099	!--------------------------------------------------------------------------------------------------!
[4566]	1100	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
[2259]	1101
[4566]	1102	INTEGER(iwp) :: k !< loop index
	1103	INTEGER(iwp) :: mergp !< passed length scale in grid points
	1104	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1105	INTEGER(iwp) :: nf !< index for length scales
[2259]	1106
[4559]	1107	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
	1108
[2259]	1109	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1110	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1111
[4438]	1112	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1113
	1114
	1115	bxx = 0.0_wp
	1116
	1117	DO k = nzb, nzt+1
	1118	bdenom = 0.0_wp
	1119	n_k = nxx(k)
	1120	IF ( n_k /= 0 ) THEN
	1121
	1122	!
	1123	!-- ( Eq.10 )^2
[4438]	1124	DO nf = -n_k, n_k
[4559]	1125	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
[2259]	1126	ENDDO
	1127
	1128	!
	1129	!-- ( Eq.9 )
	1130	bdenom = SQRT( bdenom )
[4438]	1131	DO nf = -n_k, n_k
[4559]	1132	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
[2259]	1133	ENDDO
	1134	ENDIF
	1135	ENDDO
	1136
[3347]	1137	END SUBROUTINE stg_filter_func
[2259]	1138
	1139
[4566]	1140	!------------------------------------------------------------------------------!
	1141	! Description:
	1142	! ------------
	1143	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1144	!> (Xie and Castro, 2008)
	1145	!------------------------------------------------------------------------------!
	1146	SUBROUTINE stg_setup_filter_function
	1147
	1148	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
	1149	INTEGER(iwp) :: k !< loop index along vertical direction
	1150	!
	1151	!-- Define the size of the filter functions and allocate them.
	1152	mergp_x = 0
	1153	mergp_y = 0
	1154	mergp_z = 0
	1155
	1156	DO k = nzb, nzt+1
	1157	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
	1158	IF ( j > mergp_x ) mergp_x = j
	1159	ENDDO
	1160	DO k = nzb, nzt+1
	1161	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
	1162	IF ( j > mergp_y ) mergp_y = j
	1163	ENDDO
	1164	DO k = nzb, nzt+1
	1165	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
	1166	IF ( j > mergp_z ) mergp_z = j
	1167	ENDDO
	1168
	1169	mergp_xy = MAX( mergp_x, mergp_y )
	1170
	1171	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
	1172	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
	1173	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
	1174	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
	1175	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
	1176	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
	1177	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
	1178	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
	1179	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
	1180
	1181	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
	1182	buy(-mergp_y:mergp_y,nzb:nzt+1), &
	1183	buz(-mergp_z:mergp_z,nzb:nzt+1), &
	1184	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
	1185	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
	1186	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
	1187	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
	1188	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
	1189	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
	1190	!
	1191	!-- Create filter functions
	1192	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
	1193	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
	1194	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
	1195	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
	1196	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
	1197	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
	1198	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
	1199	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
	1200	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
	1201
	1202	END SUBROUTINE stg_setup_filter_function
	1203
[4559]	1204	!--------------------------------------------------------------------------------------------------!
[2259]	1205	! Description:
	1206	! ------------
	1207	!> Parin for &stg_par for synthetic turbulence generator
[4559]	1208	!--------------------------------------------------------------------------------------------------!
[2259]	1209	SUBROUTINE stg_parin
	1210
[4559]	1211	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
[2259]	1212
	1213
[4559]	1214	NAMELIST /stg_par/ dt_stg_adjust, &
	1215	dt_stg_call, &
	1216	use_syn_turb_gen, &
[4438]	1217	compute_velocity_seeds_local
[2259]	1218
	1219	line = ' '
	1220	!
	1221	!-- Try to find stg package
	1222	REWIND ( 11 )
	1223	line = ' '
	1224	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[4559]	1225	READ ( 11, '(A)', END = 20 ) line
[2259]	1226	ENDDO
	1227	BACKSPACE ( 11 )
	1228
	1229	!
	1230	!-- Read namelist
[3246]	1231	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1232
	1233	!
[4559]	1234	!-- Set flag that indicates that the synthetic turbulence generator is switched on
[2776]	1235	syn_turb_gen = .TRUE.
[3246]	1236	GOTO 20
[2259]	1237
[3246]	1238	10 BACKSPACE( 11 )
[3248]	1239	READ( 11 , '(A)') line
	1240	CALL parin_fail_message( 'stg_par', line )
[2563]	1241
[3246]	1242	20 CONTINUE
[2259]	1243
	1244	END SUBROUTINE stg_parin
	1245
	1246
[4559]	1247	!--------------------------------------------------------------------------------------------------!
[2259]	1248	! Description:
	1249	! ------------
[4495]	1250	!> Read module-specific global restart data (Fortran binary format).
[4559]	1251	!--------------------------------------------------------------------------------------------------!
[4495]	1252	SUBROUTINE stg_rrd_global_ftn( found )
[2576]	1253
[4559]	1254	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1255
[2894]	1256	found = .TRUE.
[2259]	1257
[3038]	1258
[2894]	1259	SELECT CASE ( restart_string(1:length) )
[4559]	1260
[4022]	1261	CASE ( 'time_stg_adjust' )
	1262	READ ( 13 ) time_stg_adjust
[4559]	1263
[4022]	1264	CASE ( 'time_stg_call' )
	1265	READ ( 13 ) time_stg_call
[4559]	1266
[2894]	1267	CASE ( 'use_syn_turb_gen' )
	1268	READ ( 13 ) use_syn_turb_gen
[2259]	1269
[2894]	1270	CASE DEFAULT
[2259]	1271
[3038]	1272	found = .FALSE.
[2259]	1273
[2894]	1274	END SELECT
[2259]	1275
	1276
[4495]	1277	END SUBROUTINE stg_rrd_global_ftn
[2259]	1278
	1279
[4559]	1280	!--------------------------------------------------------------------------------------------------!
[2259]	1281	! Description:
	1282	! ------------
[4495]	1283	!> Read module-specific global restart data (MPI-IO).
[4559]	1284	!--------------------------------------------------------------------------------------------------!
[4495]	1285	SUBROUTINE stg_rrd_global_mpi
	1286
	1287	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1288	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
	1289	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1290
	1291	END SUBROUTINE stg_rrd_global_mpi
	1292
	1293
[4559]	1294	!--------------------------------------------------------------------------------------------------!
[4495]	1295	! Description:
	1296	! ------------
[2259]	1297	!> This routine writes the respective restart data.
[4559]	1298	!--------------------------------------------------------------------------------------------------!
[2894]	1299	SUBROUTINE stg_wrd_global
[2259]	1300
[4495]	1301	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
	1302
	1303	CALL wrd_write_string( 'time_stg_adjust' )
	1304	WRITE ( 14 ) time_stg_adjust
[4559]	1305
[4495]	1306	CALL wrd_write_string( 'time_stg_call' )
	1307	WRITE ( 14 ) time_stg_call
[2259]	1308
[4495]	1309	CALL wrd_write_string( 'use_syn_turb_gen' )
	1310	WRITE ( 14 ) use_syn_turb_gen
[2259]	1311
[4535]	1312	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
[2259]	1313
[4495]	1314	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1315	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
	1316	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1317
	1318	ENDIF
	1319
[2894]	1320	END SUBROUTINE stg_wrd_global
[2259]	1321
[2894]	1322
[4559]	1323	!--------------------------------------------------------------------------------------------------!
[2259]	1324	! Description:
	1325	! ------------
[4559]	1326	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
	1327	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
	1328	!> (2013), and using a Lund rotation (Lund, 1998).
	1329	!--------------------------------------------------------------------------------------------------!
[2259]	1330	SUBROUTINE stg_main
	1331
[4559]	1332	USE exchange_horiz_mod, &
[4457]	1333	ONLY: exchange_horiz
	1334
[4559]	1335	INTEGER(iwp) :: i !< grid index in x-direction
	1336	INTEGER(iwp) :: j !< loop index in y-direction
	1337	INTEGER(iwp) :: k !< loop index in z-direction
[2259]	1338
[4559]	1339	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1340
[4566]	1341	REAL(wp) :: dt_stg !< time interval the STG is called
[4559]	1342
	1343	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
	1344
[3987]	1345	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1346	!
	1347	!-- Calculate time step which is needed for filter functions
[3775]	1348	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1349	!
[4559]	1350	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
	1351	!-- created or if old disturbances can be imposed again.
	1352	IF ( time_stg_call >= dt_stg_call .AND. &
[4022]	1353	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1354	stg_call = .TRUE.
	1355	ELSE
	1356	stg_call = .FALSE.
	1357	ENDIF
	1358	!
[2259]	1359	!-- Initial value of fu, fv, fw
[3646]	1360	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1361	!
[4559]	1362	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
	1363	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
	1364	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
	1365	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
	1366	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
	1367	!-- have the same initial seeds.
	1368	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
	1369	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1370	.AND. .NOT. rans_mode ) ) ) THEN
[4309]	1371	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1372	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1373	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1374	ELSE
[4559]	1375	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
	1376	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
	1377	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
[2938]	1378	!
[4559]	1379	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
	1380	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
	1381	!-- comment above.
	1382	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
	1383	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
	1384	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
[2938]	1385	ENDIF
[2259]	1386	velocity_seed_initialized = .TRUE.
	1387	ENDIF
	1388	!
[4559]	1389	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
	1390	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
	1391	!-- seeds are required also at the right, south and north boundaries.
[4022]	1392	IF ( stg_call ) THEN
[4559]	1393	IF ( .NOT. ( nesting_offline .OR. &
	1394	( child_domain .AND. rans_mode_parent &
[4309]	1395	.AND. .NOT. rans_mode ) ) ) THEN
	1396	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1397	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1398	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1399
	1400	ELSE
[4559]	1401	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
	1402	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
	1403	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
[4309]	1404
[4559]	1405	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
	1406	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
	1407	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
[4022]	1408	ENDIF
[2938]	1409	ENDIF
[4559]	1410
[2938]	1411	!
[4309]	1412	!-- Turbulence generation at left and/or right boundary
[2938]	1413	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1414	!
[4559]	1415	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1416	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1417	IF ( stg_call ) THEN
[4559]	1418
[4438]	1419	DO j = nys, nyn
[4022]	1420	DO k = nzb, nzt + 1
[4559]	1421	!
[4022]	1422	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1423	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1424	fu_yz(k,j) = fuo_yz(k,j)
	1425	ELSE
[4559]	1426	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1427	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
[4022]	1428	ENDIF
[4559]	1429
[4566]	1430	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1431	fv_yz(k,j) = fvo_yz(k,j)
	1432	ELSE
[4559]	1433	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1434	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
[4022]	1435	ENDIF
[4559]	1436
[4566]	1437	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1438	fw_yz(k,j) = fwo_yz(k,j)
	1439	ELSE
[4559]	1440	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1441	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
[4022]	1442	ENDIF
	1443	ENDDO
	1444	ENDDO
[4559]	1445
[4022]	1446	dist_yz(nzb,:,1) = 0.0_wp
	1447	dist_yz(nzb,:,2) = 0.0_wp
	1448	dist_yz(nzb,:,3) = 0.0_wp
[4559]	1449
[4022]	1450	IF ( myidx == id_stg_left ) i = nxl
[4559]	1451	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1452	DO j = nys, nyn
[4022]	1453	DO k = nzb+1, nzt + 1
[4559]	1454	!
[4022]	1455	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4566]	1456	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
[4562]	1457	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4566]	1458
[4022]	1459	ENDDO
	1460	ENDDO
[4309]	1461
[4022]	1462	IF ( myidx == id_stg_left ) i = nxl-1
	1463	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1464	DO j = nys, nyn
[4022]	1465	DO k = nzb+1, nzt + 1
[4559]	1466	!
[4022]	1467	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1468	!-- Additional factors are added to improve the variance of v and w experimental test
	1469	!-- of 1.2
[4566]	1470	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
[4559]	1471	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4566]	1472	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
	1473	a33(k) * fw_yz(k,j) ) * &
	1474	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
	1475
[4022]	1476	ENDDO
[2259]	1477	ENDDO
[4022]	1478	ENDIF
[2259]	1479	!
	1480	!-- Mass flux correction following Kim et al. (2013)
[4559]	1481	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
	1482	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
	1483	!-- only after the last RK3-substep, else the boundary values won't be accessed.
[4022]	1484	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1485	mc_factor_l = 0.0_wp
	1486	mc_factor = 0.0_wp
	1487	!
	1488	!-- Sum up the original volume flows (with and without perturbations).
	1489	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
[2938]	1490	IF ( myidx == id_stg_left ) i = nxl
	1491	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1492
[4562]	1493	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
	1494	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4559]	1495
[4022]	1496	IF ( myidx == id_stg_left ) i = nxl-1
	1497	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1498
[4562]	1499	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
	1500	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1501	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
	1502	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4559]	1503
[2938]	1504	#if defined( __parallel )
[4559]	1505	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1506	#else
	1507	mc_factor = mc_factor_l
[2938]	1508	#endif
[4559]	1509	!
	1510	!-- Calculate correction factor and force zero mean perturbations.
	1511	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1512
	1513	IF ( myidx == id_stg_left ) i = nxl
	1514	IF ( myidx == id_stg_right ) i = nxr+1
	1515
[4562]	1516	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
	1517	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4559]	1518
	1519
	1520	IF ( myidx == id_stg_left ) i = nxl-1
	1521	IF ( myidx == id_stg_right ) i = nxr+1
	1522
[4562]	1523	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
	1524	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4559]	1525
[4562]	1526	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
	1527	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4559]	1528	!
[2938]	1529	!-- Add disturbances
	1530	IF ( myidx == id_stg_left ) THEN
[4559]	1531	!
	1532	!-- For the left boundary distinguish between mesoscale offline / self nesting and
	1533	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
	1534	!-- the mean inflow profiles.
	1535	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1536	!
[4022]	1537	!-- Add disturbance at the inflow
[4438]	1538	DO j = nys, nyn
[4022]	1539	DO k = nzb, nzt+1
[4562]	1540	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
	1541	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
	1542	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
	1543	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1544	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
	1545	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1546	ENDDO
[2938]	1547	ENDDO
[4022]	1548	ELSE
[4559]	1549
[4022]	1550	DO j = nys, nyn
	1551	DO k = nzb+1, nzt
[4562]	1552	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
	1553	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1554	u(k,j,-1) = u(k,j,0)
[4562]	1555	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
	1556	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1557	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
	1558	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1559	ENDDO
	1560	ENDDO
	1561	ENDIF
[2938]	1562	ENDIF
	1563	IF ( myidx == id_stg_right ) THEN
[3186]	1564	DO j = nys, nyn
[3347]	1565	DO k = nzb+1, nzt
[4562]	1566	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
	1567	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
	1568	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
	1569	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
	1570	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
	1571	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1572	ENDDO
	1573	ENDDO
	1574	ENDIF
	1575	ENDIF
	1576	ENDIF
	1577	!
	1578	!-- Turbulence generation at north and south boundary
	1579	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1580	!
[4559]	1581	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1582	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1583	IF ( stg_call ) THEN
[4438]	1584	DO i = nxl, nxr
[4022]	1585	DO k = nzb, nzt + 1
[4559]	1586	!
[4022]	1587	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1588	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1589	fu_xz(k,i) = fuo_xz(k,i)
	1590	ELSE
[4559]	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) ) )
[4022]	1593	ENDIF
[4559]	1594
[4566]	1595	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1596	fv_xz(k,i) = fvo_xz(k,i)
	1597	ELSE
[4559]	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) ) )
[4022]	1600	ENDIF
[4559]	1601
[4566]	1602	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1603	fw_xz(k,i) = fwo_xz(k,i)
	1604	ELSE
[4559]	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) ) )
[4022]	1607	ENDIF
	1608	ENDDO
	1609	ENDDO
[4559]	1610
	1611
[4022]	1612	dist_xz(nzb,:,1) = 0.0_wp
	1613	dist_xz(nzb,:,2) = 0.0_wp
	1614	dist_xz(nzb,:,3) = 0.0_wp
[4559]	1615
[4022]	1616	IF ( myidy == id_stg_south ) j = nys
	1617	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1618	DO i = nxl, nxr
[4022]	1619	DO k = nzb+1, nzt + 1
[4559]	1620	!
[4022]	1621	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1622	!-- Additional factors are added to improve the variance of v and w
	1623	!experimental test of 1.2
[4566]	1624	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
[4559]	1625	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1626	ENDDO
	1627	ENDDO
[4559]	1628
[4022]	1629	IF ( myidy == id_stg_south ) j = nys-1
	1630	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1631	DO i = nxl, nxr
[4022]	1632	DO k = nzb+1, nzt + 1
[4559]	1633	!
[4022]	1634	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1635	!-- Additional factors are added to improve the variance of v and w
[4566]	1636	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
[4562]	1637	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4559]	1638
[4566]	1639	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
	1640	a33(k) * fw_xz(k,i) ) * &
[4562]	1641	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1642	ENDDO
[2938]	1643	ENDDO
[4022]	1644	ENDIF
[3347]	1645
[2938]	1646	!
[4559]	1647	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
	1648	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
	1649	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
	1650	!-- else the boundary values won't be accessed.
[4022]	1651	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1652	mc_factor_l = 0.0_wp
	1653	mc_factor = 0.0_wp
	1654
[4022]	1655	IF ( myidy == id_stg_south ) j = nys
	1656	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1657
[4562]	1658	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
	1659	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4559]	1660
	1661	IF ( myidy == id_stg_south ) j = nys-1
	1662	IF ( myidy == id_stg_north ) j = nyn+1
	1663
[4562]	1664	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
	1665	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1666	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
	1667	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4559]	1668
[2938]	1669	#if defined( __parallel )
[4559]	1670	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1671	#else
[4022]	1672	mc_factor = mc_factor_l
[2938]	1673	#endif
[4559]	1674
[4022]	1675	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
[4559]	1676
	1677	IF ( myidy == id_stg_south ) j = nys
	1678	IF ( myidy == id_stg_north ) j = nyn+1
	1679
[4562]	1680	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
	1681	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4559]	1682
	1683
	1684	IF ( myidy == id_stg_south ) j = nys-1
	1685	IF ( myidy == id_stg_north ) j = nyn+1
	1686
[4562]	1687	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
	1688	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4559]	1689
[4562]	1690	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
	1691	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4559]	1692	!
[4022]	1693	!-- Add disturbances
[4559]	1694	IF ( myidy == id_stg_south ) THEN
[4022]	1695	DO i = nxl, nxr
	1696	DO k = nzb+1, nzt
[4559]	1697	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1698	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
	1699	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1700	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1701	v(k,-1,i) = v(k,0,i)
[4559]	1702	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1703	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1704	ENDDO
[2938]	1705	ENDDO
[4022]	1706	ENDIF
	1707	IF ( myidy == id_stg_north ) THEN
[4559]	1708
[4022]	1709	DO i = nxl, nxr
	1710	DO k = nzb+1, nzt
[4562]	1711	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
	1712	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
	1713	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
	1714	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
	1715	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
	1716	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1717	ENDDO
[2938]	1718	ENDDO
[4022]	1719	ENDIF
[2938]	1720	ENDIF
[2259]	1721	ENDIF
[3347]	1722	!
[4438]	1723	!-- Exchange ghost points.
	1724	CALL exchange_horiz( u, nbgp )
	1725	CALL exchange_horiz( v, nbgp )
	1726	CALL exchange_horiz( w, nbgp )
	1727	!
[3347]	1728	!-- Finally, set time counter for calling STG to zero
[4022]	1729	IF ( stg_call ) time_stg_call = 0.0_wp
[4566]	1730	!
	1731	!-- Set adjustment step to False to indicate that time correlation can be
	1732	!-- switched-on again.
	1733	adjustment_step = .FALSE.
[2259]	1734
[3987]	1735	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1736
[2259]	1737	END SUBROUTINE stg_main
	1738
[4559]	1739	!--------------------------------------------------------------------------------------------------!
[2259]	1740	! Description:
	1741	! ------------
[4559]	1742	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1743	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
	1744	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
	1745	!> array.
	1746	!--------------------------------------------------------------------------------------------------!
[4309]	1747	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1748
[4559]	1749	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1750	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1751	INTEGER(iwp) :: j !< loop index in y-direction
	1752	INTEGER(iwp) :: jj !< loop index in y-direction
	1753	INTEGER(iwp) :: k !< loop index in z-direction
	1754	INTEGER(iwp) :: kk !< loop index in z-direction
	1755	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1756
[4559]	1757	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1758	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2259]	1759
[4559]	1760	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1761	REAL(wp) :: rand_av !< average of random number
	1762	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2259]	1763
[4566]	1764	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
	1765	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
[4559]	1766
	1767	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1768	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
	1769
	1770	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1771	!
[4559]	1772	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1773	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1774	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1775	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1776	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
	1777	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
[4559]	1778	!-- correlation matrix.
[4566]	1779	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
[4438]	1780	rand_it = 0.0_wp
[2259]	1781
	1782	rand_av = 0.0_wp
	1783	rand_sigma_inv = 0.0_wp
[4566]	1784	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1785	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
[4309]	1786	!
[4438]	1787	!-- Compute and normalize random numbers.
[4566]	1788	DO j = nys - mergp_y, nyn + mergp_y
[4309]	1789	!
[4438]	1790	!-- Put the random seeds at grid point j
	1791	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
[4566]	1792	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1793	CALL random_number_parallel( random_dummy )
	1794	rand_it(k,j) = random_dummy
	1795	ENDDO
[4309]	1796	!
[4438]	1797	!-- Get the new random seeds from last call at grid point j
	1798	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1799	ENDDO
[4309]	1800	!
[4559]	1801	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
	1802	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
	1803	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
[4566]	1804	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1805	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1806	rand_av = rand_av + rand_it(k,j)
[2259]	1807	ENDDO
[4438]	1808	ENDDO
[4566]	1809
[4309]	1810	#if defined( __parallel )
	1811	!
[4438]	1812	!-- Sum-up the local averages of the random numbers
[4559]	1813	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1814	#endif
[4438]	1815	rand_av = rand_av * nyz_inv
[4309]	1816	!
[4438]	1817	!-- Obtain zero mean
	1818	rand_it= rand_it - rand_av
[4309]	1819	!
[4438]	1820	!-- Now, compute the variance
[4566]	1821	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1822	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1823	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1824	ENDDO
[4438]	1825	ENDDO
[2259]	1826
[4309]	1827	#if defined( __parallel )
[2259]	1828	!
[4438]	1829	!-- Sum-up the local quadratic averages of the random numbers
[4559]	1830	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1831	#endif
	1832	!
[4438]	1833	!-- Compute standard deviation
	1834	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1835	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1836	ELSE
	1837	rand_sigma_inv = 1.0_wp
[4309]	1838	ENDIF
	1839	!
[4438]	1840	!-- Normalize with standard deviation to obtain unit variance
	1841	rand_it = rand_it * rand_sigma_inv
	1842
	1843	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1844	!
[4559]	1845	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	1846	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	1847	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
	1848	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	1849	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
	1850	!-- communication. In the second option, which performs better when the turbulent length scales
	1851	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
	1852	!-- communication is necessary.
[4438]	1853	IF ( compute_velocity_seeds_local ) THEN
	1854
	1855	f_n = 0.0_wp
	1856	DO j = nys, nyn
	1857	DO k = nzb, nzt+1
	1858	DO jj = -n_y(k), n_y(k)
	1859	DO kk = -n_z(k), n_z(k)
	1860	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1861	ENDDO
	1862	ENDDO
	1863	ENDDO
[2259]	1864	ENDDO
	1865
[4438]	1866	ELSE
[2259]	1867
[4438]	1868	f_n_l = 0.0_wp
	1869	DO j = nys, nyn
	1870	DO k = nzb_x_stg, nzt_x_stg+1
	1871	DO jj = -n_y(k), n_y(k)
	1872	DO kk = -n_z(k), n_z(k)
	1873	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1874	ENDDO
[2259]	1875	ENDDO
	1876	ENDDO
	1877	ENDDO
	1878	!
[4438]	1879	!-- Gather velocity seeds of full subdomain
	1880	send_count = nzt_x_stg - nzb_x_stg + 1
	1881	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1882
	1883	#if defined( __parallel )
[4309]	1884	!
[4438]	1885	!-- Gather the velocity seed matrix on left boundary mpi ranks.
[4559]	1886	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1887	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
[4309]	1888	!
[4559]	1889	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
	1890	!-- nesting for example).
[4438]	1891	IF ( PRESENT( id_right ) ) THEN
[4559]	1892	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1893	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
[4438]	1894	ENDIF
[2259]	1895	#else
[4438]	1896	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[4444]	1897	!
	1898	!-- Next line required to avoid compile errors because of unused dummy arguments
	1899	IF ( id_left == 0 ) id_right = 0
[2259]	1900	#endif
	1901
[4438]	1902	ENDIF
[2259]	1903
[4438]	1904	DEALLOCATE( rand_it )
	1905
	1906	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1907
[2259]	1908	END SUBROUTINE stg_generate_seed_yz
	1909
[2938]	1910
[4559]	1911	!--------------------------------------------------------------------------------------------------!
[2938]	1912	! Description:
	1913	! ------------
[4559]	1914	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1915	!> f_n.
	1916	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
	1917	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
	1918	!> full array.
	1919	!--------------------------------------------------------------------------------------------------!
[4309]	1920	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1921
[4566]	1922	INTEGER(iwp) :: i !< loop index in x-direction
	1923	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1924	INTEGER(iwp) :: id_south !< core ids at respective boundaries
	1925	INTEGER(iwp) :: ii !< loop index in x-direction
	1926	INTEGER(iwp) :: k !< loop index in z-direction
	1927	INTEGER(iwp) :: kk !< loop index in z-direction
	1928	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2938]	1929
[4566]	1930	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1931	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2938]	1932
[4566]	1933	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1934	REAL(wp) :: rand_av !< average of random number
	1935	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2938]	1936
[4566]	1937	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
	1938	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
	1939
	1940	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1941	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1942
[4566]	1943	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1944
	1945	!
[4559]	1946	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1947	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1948	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1949	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1950	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
	1951	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
[4559]	1952	!-- correlation matrix.
[4566]	1953	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
[4438]	1954	rand_it = 0.0_wp
[2938]	1955
	1956	rand_av = 0.0_wp
	1957	rand_sigma_inv = 0.0_wp
[4566]	1958	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1959	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
[4309]	1960	!
[4438]	1961	!-- Compute and normalize random numbers.
[4566]	1962	DO i = nxl - mergp_x, nxr + mergp_x
[4309]	1963	!
[4438]	1964	!-- Put the random seeds at grid point ii
	1965	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
[4566]	1966	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1967	CALL random_number_parallel( random_dummy )
	1968	rand_it(k,i) = random_dummy
	1969	ENDDO
[4309]	1970	!
[4438]	1971	!-- Get the new random seeds from last call at grid point ii
	1972	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1973	ENDDO
[4309]	1974	!
[4438]	1975	!-- For normalization to zero mean, sum-up the global random numers.
[4559]	1976	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
	1977	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
[4438]	1978	!-- also occur on the inner subdomains.
[4566]	1979	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1980	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1981	rand_av = rand_av + rand_it(k,i)
[2938]	1982	ENDDO
[4438]	1983	ENDDO
[4566]	1984
[4309]	1985	#if defined( __parallel )
[4438]	1986	!
	1987	!-- Sum-up the local averages of the random numbers
[4559]	1988	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	1989	#endif
[4438]	1990	rand_av = rand_av * nxz_inv
[4309]	1991	!
[4438]	1992	!-- Obtain zero mean
	1993	rand_it= rand_it - rand_av
[4309]	1994	!
[4438]	1995	!-- Now, compute the variance
[4566]	1996	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1997	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1998	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	1999	ENDDO
[4438]	2000	ENDDO
[2938]	2001
[4309]	2002	#if defined( __parallel )
[4438]	2003	!
	2004	!-- Sum-up the local quadratic averages of the random numbers
[4559]	2005	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	2006	#endif
[2938]	2007	!
[4438]	2008	!-- Compute standard deviation
	2009	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	2010	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	2011	ELSE
	2012	rand_sigma_inv = 1.0_wp
[4309]	2013	ENDIF
	2014	!
[4438]	2015	!-- Normalize with standard deviation to obtain unit variance
	2016	rand_it = rand_it * rand_sigma_inv
	2017
	2018	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2019	!
[4559]	2020	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	2021	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	2022	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
	2023	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	2024	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
	2025	!-- In the second option, which performs better when the turbulent length scales are parametrized
	2026	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
[4438]	2027	IF ( compute_velocity_seeds_local ) THEN
[2938]	2028
[4438]	2029	f_n = 0.0_wp
	2030	DO i = nxl, nxr
	2031	DO k = nzb, nzt+1
	2032	DO ii = -n_x(k), n_x(k)
	2033	DO kk = -n_z(k), n_z(k)
	2034	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2035	ENDDO
[2938]	2036	ENDDO
	2037	ENDDO
	2038	ENDDO
	2039
[4438]	2040	ELSE
[2938]	2041
[4438]	2042	f_n_l = 0.0_wp
	2043	DO i = nxl, nxr
	2044	DO k = nzb_y_stg, nzt_y_stg+1
	2045	DO ii = -n_x(k), n_x(k)
	2046	DO kk = -n_z(k), n_z(k)
	2047	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2048	ENDDO
	2049	ENDDO
	2050	ENDDO
	2051	ENDDO
[2938]	2052	!
[4438]	2053	!-- Gather velocity seeds of full subdomain
	2054	send_count = nzt_y_stg - nzb_y_stg + 1
	2055	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2056
	2057	#if defined( __parallel )
[4309]	2058	!
[4438]	2059	!-- Gather the processed velocity seed on south boundary mpi ranks.
[4559]	2060	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2061	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
[4309]	2062	!
[4438]	2063	!-- Gather the processed velocity seed on north boundary mpi ranks.
[4559]	2064	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2065	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
[2938]	2066	#else
[4438]	2067	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[4444]	2068	!
	2069	!-- Next line required to avoid compile errors because of unused dummy arguments
	2070	IF ( id_north == 0 ) id_south = 0
[2938]	2071	#endif
	2072
[4438]	2073	ENDIF
	2074
	2075	DEALLOCATE( rand_it )
	2076
	2077	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2078
[2938]	2079	END SUBROUTINE stg_generate_seed_xz
	2080
[4559]	2081	!--------------------------------------------------------------------------------------------------!
[3347]	2082	! Description:
	2083	! ------------
[4566]	2084	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
	2085	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
	2086	!> which is applied in state-of-the-art dispserion modelling.
[4559]	2087	!--------------------------------------------------------------------------------------------------!
[4566]	2088	SUBROUTINE parametrize_turbulence
[3347]	2089
[4566]	2090	INTEGER(iwp) :: k !< loop index in z-direction
[4559]	2091
[4566]	2092	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
	2093	REAL(wp) :: d_zi !< inverse boundary-layer depth
	2094	REAL(wp) :: length_scale_lon !< length scale in flow direction
	2095	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
	2096	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
	2097	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
	2098	REAL(wp) :: length_scale_vert !< length scale in vertical direction
	2099	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
	2100	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
	2101	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
	2102	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
	2103	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
	2104	REAL(wp) :: r31_zi !< r31 at boundary-layer top
	2105	REAL(wp) :: r32_zi !< r32 at boundary-layer top
	2106	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
	2107	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
	2108	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
	2109	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
	2110	REAL(wp) :: zzi !< ratio of z/zi
[4559]	2111
[4566]	2112	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
	2113	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
	2114	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
	2115
[3347]	2116	!
[4566]	2117	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
	2118	!-- criterion according to Heinze et al. (2017).
	2119	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
	2120	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
	2121	k_zi = MIN( k_zi, nzt )
[3347]	2122	!
[4566]	2123	!-- Calculate angle between flow direction and x-axis.
	2124	DO k = nzb+1, nzt + 1
	2125	IF ( u_init(k) /= 0.0_wp ) THEN
	2126	phi(k) = ATAN( v_init(k) / u_init(k) )
	2127	ELSE
	2128	phi(k) = 0.5 * pi
	2129	ENDIF
	2130	!
	2131	!-- Pre-calculate sine and cosine.
	2132	cos_phi(k) = COS( phi(k) )
	2133	sin_phi(k) = SIN( phi(k) )
	2134	ENDDO
	2135	!
	2136	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
	2137	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
	2138	!-- coincide with the grid axis. Hence, components are rotated after computation.
	2139	d_zi = 1.0_wp / zi_ribulk
	2140	DO k = nzb+1, k_zi
	2141
	2142	corr_term_uh = MERGE( 0.35_wp * ABS( &
	2143	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2144	)**( 2.0_wp / 3.0_wp ), &
	2145	0.0_wp, &
[4640]	2146	scale_l < -5.0_wp )
[4566]	2147	!
[4022]	2148	!-- Determine normalized height coordinate
[4566]	2149	zzi = zu(k) * d_zi
[3347]	2150	!
[4566]	2151	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
	2152	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
	2153	!-- variances cannot become negative, take the absolute values.
	2154	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
	2155	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
[4559]	2156
[4566]	2157	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
	2158	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
[4559]	2159	!
	2160	!-- w'w'
[4566]	2161	r33(k) = scale_wm*2 ( &
	2162	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2163	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2164	)
[4559]	2165	!
[4566]	2166	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
	2167	!-- these are projected along the x- and y-direction. Note, it is assumed that
	2168	!-- the flux within the boundary points opposite to the vertical gradient.
	2169	rlon2 = scale_us*2 ( zzi - 1.0_wp )
	2170	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
	2171
	2172	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
	2173	- ( u_init(k+1) - u_init(k-1) ) )
	2174	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
	2175	- ( v_init(k+1) - v_init(k-1) ) )
[3347]	2176	!
[4640]	2177	!-- For u'v' no parametrization exist so far. For simplicity assume a similar profile as
	2178	!-- for the vertical transport.
	2179	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
	2180	!
[4566]	2181	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
	2182	!-- limited to the adjustment time scales.
	2183	tu(k) = MIN( dt_stg_adjust, &
	2184	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
	2185
	2186	tv(k) = tu(k)
	2187	tw(k) = tu(k)
	2188
	2189	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
	2190	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
	2191	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
	2192	!
	2193	!-- Assume isotropic turbulence length scales
	2194	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2195	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2196	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2197	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2198	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2199	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2200	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2201	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2202	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2203
[3347]	2204	ENDDO
[4566]	2205	!
	2206	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
	2207	!-- reduced to zero by a blending function.
	2208	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
	2209	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
	2210	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
[3347]	2211
[4566]	2212	time_scale_zi = tu(k_zi)
	2213	r11_zi = r11(k_zi)
	2214	r22_zi = r22(k_zi)
	2215	r33_zi = r33(k_zi)
	2216	r31_zi = r31(k_zi)
	2217	r32_zi = r32(k_zi)
	2218
	2219	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
	2220
	2221	DO k = k_zi+1, nzt+1
[3347]	2222	!
[4566]	2223	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2224	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
	2225	!
	2226	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
	2227	!-- the mergpe-function can crash if scale_l is zero.
	2228	r11(k) = r11_zi * blend
	2229	r22(k) = r22_zi * blend
	2230	r33(k) = r33_zi * blend
	2231	r31(k) = r31_zi * blend
	2232	r32(k) = r32_zi * blend
[4640]	2233	r21(k) = 0.5_wp * ( r31(k) + r32(k) )
[4566]	2234
	2235	!
	2236	!-- Compute turbulent time scales according to Brost et al. (1982).
	2237	!-- Note, time scales are limited to the adjustment time scales.
	2238	tu(k) = time_scale_zi * blend
	2239	tv(k) = time_scale_zi * blend
	2240	tw(k) = time_scale_zi * blend
	2241
	2242	length_scale_lon = length_scale_lon_zi * blend
	2243	length_scale_lat = length_scale_lat_zi * blend
	2244	length_scale_vert = length_scale_vert_zi * blend
	2245	!
	2246	!-- Assume isotropic turbulence length scales
	2247	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2248	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2249	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2250	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2251	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2252	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2253	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2254	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2255	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2256	ENDDO
	2257	!
	2258	!-- Set bottom boundary condition for reynolds stresses
[3347]	2259	r11(nzb) = r11(nzb+1)
	2260	r22(nzb) = r22(nzb+1)
	2261	r33(nzb) = r33(nzb+1)
	2262
	2263	r21(nzb) = r11(nzb+1)
	2264	r31(nzb) = r31(nzb+1)
	2265	r32(nzb) = r32(nzb+1)
	2266
[4566]	2267	!
	2268	!-- Set bottom boundary condition for the length and time scales
	2269	nux(nzb) = nux(nzb+1)
	2270	nuy(nzb) = nuy(nzb+1)
	2271	nuz(nzb) = nuz(nzb+1)
	2272	nvx(nzb) = nvx(nzb+1)
	2273	nvy(nzb) = nvy(nzb+1)
	2274	nvz(nzb) = nvz(nzb+1)
	2275	nwx(nzb) = nwx(nzb+1)
	2276	nwy(nzb) = nwy(nzb+1)
	2277	nwz(nzb) = nwz(nzb+1)
[4559]	2278
[4566]	2279	tu(nzb) = tu(nzb+1)
	2280	tv(nzb) = tv(nzb+1)
	2281	tw(nzb) = tw(nzb+1)
[4559]	2282
[4566]	2283	adjustment_step = .TRUE.
	2284
	2285	END SUBROUTINE parametrize_turbulence
	2286
[4559]	2287	!--------------------------------------------------------------------------------------------------!
[3347]	2288	! Description:
	2289	! ------------
[4559]	2290	!> Calculate the coefficient matrix from the Lund rotation.
	2291	!--------------------------------------------------------------------------------------------------!
[3347]	2292	SUBROUTINE calc_coeff_matrix
	2293
[4559]	2294	INTEGER(iwp) :: k !< loop index in z-direction
	2295
[3347]	2296	!
	2297	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2298	DO k = nzb+1, nzt+1
[4022]	2299	IF ( r11(k) > 10E-6_wp ) THEN
[4566]	2300	a11(k) = SQRT( r11(k) )
[3347]	2301	a21(k) = r21(k) / a11(k)
	2302	a31(k) = r31(k) / a11(k)
	2303	ELSE
	2304	a11(k) = 10E-8_wp
	2305	a21(k) = 10E-8_wp
	2306	a31(k) = 10E-8_wp
	2307	ENDIF
	2308	ENDDO
	2309	DO k = nzb+1, nzt+1
[4566]	2310	a22(k) = r22(k) - a21(k)**2
[4022]	2311	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2312	a22(k) = SQRT( a22(k) )
[4566]	2313	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
	2314	ELSE
[3347]	2315	a22(k) = 10E-8_wp
	2316	a32(k) = 10E-8_wp
	2317	ENDIF
	2318	ENDDO
	2319	DO k = nzb+1, nzt+1
	2320	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2321	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2322	a33(k) = SQRT( a33(k) )
	2323	ELSE
	2324	a33(k) = 10E-8_wp
	2325	ENDIF
[4559]	2326	ENDDO
[3347]	2327	!
	2328	!-- Set bottom boundary condition
	2329	a11(nzb) = a11(nzb+1)
	2330	a22(nzb) = a22(nzb+1)
	2331	a21(nzb) = a21(nzb+1)
[4559]	2332	a33(nzb) = a33(nzb+1)
[3347]	2333	a31(nzb) = a31(nzb+1)
[4559]	2334	a32(nzb) = a32(nzb+1)
[3347]	2335
	2336	END SUBROUTINE calc_coeff_matrix
[4559]	2337
	2338	!--------------------------------------------------------------------------------------------------!
[3347]	2339	! Description:
	2340	! ------------
[4559]	2341	!> This routine controls the re-adjustment of the turbulence statistics used for generating
	2342	!> turbulence at the lateral boundaries.
	2343	!--------------------------------------------------------------------------------------------------!
[3347]	2344	SUBROUTINE stg_adjust
	2345
[3987]	2346	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2347	!
[4559]	2348	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
	2349	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
	2350	!-- nevertheless, the boundary-layer depth need to determined first.
	2351	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2352	CALL nesting_offl_calc_zi
[4022]	2353	!
[4559]	2354	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
[3347]	2355	CALL calc_scaling_variables
	2356	!
[4566]	2357	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
	2358	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
	2359	!-- velocity and velocity scale.
	2360	CALL parametrize_turbulence
[3347]	2361	!
[4566]	2362	!-- Calculate coefficient matrix from Reynolds stress tensor
	2363	!-- (Lund rotation)
[3347]	2364	CALL calc_coeff_matrix
	2365	!
[4566]	2366	!-- Setup filter functions according to updated length scales.
	2367	CALL stg_setup_filter_function
[3347]	2368	!
	2369	!-- Reset time counter for controlling next adjustment to zero
	2370	time_stg_adjust = 0.0_wp
[3987]	2371
	2372	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[4559]	2373
	2374	END SUBROUTINE stg_adjust
	2375
	2376
	2377	!--------------------------------------------------------------------------------------------------!
[3347]	2378	! Description:
	2379	! ------------
[4559]	2380	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
	2381	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
	2382	!> scale, and Obukhov length.
	2383	!--------------------------------------------------------------------------------------------------!
[3347]	2384	SUBROUTINE calc_scaling_variables
	2385
[4559]	2386	INTEGER(iwp) :: i !< loop index in x-direction
	2387	INTEGER(iwp) :: j !< loop index in y-direction
	2388	INTEGER(iwp) :: k !< loop index in z-direction
	2389	INTEGER(iwp) :: m !< surface element index
[3347]	2390
[4559]	2391	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
	2392	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2393	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2394	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
	2395	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2396	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2397	REAL(wp) :: w_convective !< convective velocity scale
	2398
[3347]	2399	!
[4559]	2400	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
	2401	!-- model domain.
[3937]	2402	pt_surf_mean_l = 0.0_wp
	2403	shf_mean_l = 0.0_wp
	2404	scale_l_l = 0.0_wp
	2405	friction_vel_l = 0.0_wp
[3347]	2406	DO m = 1, surf_def_h(0)%ns
[3937]	2407	i = surf_def_h(0)%i(m)
	2408	j = surf_def_h(0)%j(m)
	2409	k = surf_def_h(0)%k(m)
	2410	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2411	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2412	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2413	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[4559]	2414	ENDDO
[4671]	2415	DO m = 1, surf_lsm_h(0)%ns
	2416	i = surf_lsm_h(0)%i(m)
	2417	j = surf_lsm_h(0)%j(m)
	2418	k = surf_lsm_h(0)%k(m)
	2419	friction_vel_l = friction_vel_l + surf_lsm_h(0)%us(m)
	2420	shf_mean_l = shf_mean_l + surf_lsm_h(0)%shf(m) * drho_air(k)
	2421	scale_l_l = scale_l_l + surf_lsm_h(0)%ol(m)
[3937]	2422	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2423	ENDDO
[4671]	2424	DO m = 1, surf_usm_h(0)%ns
	2425	i = surf_usm_h(0)%i(m)
	2426	j = surf_usm_h(0)%j(m)
	2427	k = surf_usm_h(0)%k(m)
	2428	friction_vel_l = friction_vel_l + surf_usm_h(0)%us(m)
	2429	shf_mean_l = shf_mean_l + surf_usm_h(0)%shf(m) * drho_air(k)
	2430	scale_l_l = scale_l_l + surf_usm_h(0)%ol(m)
[3937]	2431	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2432	ENDDO
[4559]	2433
[3347]	2434	#if defined( __parallel )
[4559]	2435	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2436	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2437	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2438	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
[3347]	2439	#else
[3937]	2440	scale_us = friction_vel_l
	2441	shf_mean = shf_mean_l
	2442	scale_l = scale_l_l
	2443	pt_surf_mean = pt_surf_mean_l
[3347]	2444	#endif
	2445
[4566]	2446	scale_us = scale_us * d_nxy
	2447	shf_mean = shf_mean * d_nxy
	2448	scale_l = scale_l * d_nxy
	2449	pt_surf_mean = pt_surf_mean * d_nxy
[3347]	2450	!
[4559]	2451	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
	2452	!-- convective velocity scale to zero.
[3347]	2453	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2454	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2455	ELSE
	2456	w_convective = 0.0_wp
	2457	ENDIF
	2458	!
[4566]	2459	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
	2460	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
	2461	!-- value of friction velocity for the reynolds-stress parametrization.
	2462	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
	2463	!
[4559]	2464	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
	2465	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
[3347]	2466	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
[4559]	2467
[3347]	2468	END SUBROUTINE calc_scaling_variables
	2469
[2259]	2470	END MODULE synthetic_turbulence_generator_mod

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