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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4586

Last change on this file since 4586 was 4566, checked in by suehring, 4 years ago
synthetic turbulence generator: revise parametrization for reynolds-stress components, turbulent length- and time scales; revise computation of velocity disturbances to be consistent to Xie and Castro (2008); change default value of time interval to adjust turbulence parametrization; bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
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[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	!
[4559]	16	! Copyright 1997-2020 Leibniz Universitaet Hannover
	17	!--------------------------------------------------------------------------------------------------!
[2259]	18	!
[4559]	19	!
[2259]	20	! Current revisions:
	21	! -----------------
	22	!
[4442]	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4566 2020-06-16 10:11:51Z gronemeier $
[4566]	27	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
	28	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
	29	! - change default value of time interval to adjust turbulence parametrization
	30	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
	31	!
	32	! 4562 2020-06-12 08:38:47Z raasch
[4562]	33	! Parts of r4559 re-formatted
	34	!
	35	! 4559 2020-06-11 08:51:48Z raasch
[4559]	36	! File re-formatted to follow the PALM coding standard
	37	!
	38	! 4535 2020-05-15 12:07:23Z raasch
	39	! Bugfix for restart data format query
	40	!
[4535]	41	! 4495 2020-04-13 20:11:20Z raasch
[4559]	42	! Restart data handling with MPI-IO added
	43	!
[4495]	44	! 4481 2020-03-31 18:55:54Z maronga
[4559]	45	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
	46	!
[4444]	47	! 4442 2020-03-04 19:21:13Z suehring
[4442]	48	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	49	! (was accidantly changed).
[4559]	50	!
[4442]	51	! 4441 2020-03-04 19:20:35Z suehring
[4440]	52	! Correct misplaced preprocessor directive
[4559]	53	!
[4440]	54	! 4438 2020-03-03 20:49:28Z suehring
[4438]	55	! Performance optimizations in velocity-seed calculation:
[4559]	56	! - Random number array is only defined and computed locally (except for normalization to zero mean
	57	! and unit variance)
	58	! - Parallel random number generator is applied independent on the 2D random numbers in other
	59	! routines
	60	! - Option to decide wheter velocity seeds are computed locally without any further communication
	61	! or are computed by all processes along the communicator
	62	!
[4438]	63	! 4346 2019-12-18 11:55:56Z motisi
[4559]	64	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
	65	! information used in wall_flags_static_0
	66	!
[4346]	67	! 4335 2019-12-12 16:39:05Z suehring
[4335]	68	! Commentation of last commit
[4559]	69	!
[4335]	70	! 4332 2019-12-10 19:44:12Z suehring
[4559]	71	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
	72	! Further, minor bugfix in initial velocity seed calculation.
	73	!
[4332]	74	! 4329 2019-12-10 15:46:36Z motisi
[4329]	75	! Renamed wall_flags_0 to wall_flags_static_0
[4559]	76	!
[4329]	77	! 4309 2019-11-26 18:49:59Z suehring
[4559]	78	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
	79	! the parallel random number generator. Random numbers are now only computed and normalized locally,
	80	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
	81	! array.
	82	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
	83	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
	84	!
[4309]	85	! 4182 2019-08-22 15:20:23Z scharf
[4182]	86	! Corrected "Former revisions" section
[4559]	87	!
[4182]	88	! 4148 2019-08-08 11:26:00Z suehring
[4148]	89	! Remove unused variable
[4559]	90	!
[4148]	91	! 4144 2019-08-06 09:11:47Z raasch
[4559]	92	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	93	!
[4144]	94	! 4071 2019-07-03 20:02:00Z suehring
[4559]	95	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
	96	! file.
	97	!
[4071]	98	! 4022 2019-06-12 11:52:39Z suehring
[4022]	99	! Several bugfixes and improvements
[4559]	100	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
	101	! instabilities in case the mean volume flow is close to zero)
	102	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
	103	! numerically unstable
	104	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
	105	! case dt_stg_call /= dt_3d
	106	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
	107	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
[4022]	108	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
[4559]	109	!
[4022]	110	! 3987 2019-05-22 09:52:13Z kanani
[3987]	111	! Introduce alternative switch for debug output during timestepping
[4559]	112	!
[3987]	113	! 3938 2019-04-29 16:06:25Z suehring
[3938]	114	! Remove unused variables
[4559]	115	!
[3938]	116	! 3937 2019-04-29 15:09:07Z suehring
[4559]	117	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
	118	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
	119	! synthetic turbulence parametrization.
	120	!
[3937]	121	! 3909 2019-04-17 09:13:25Z suehring
[3909]	122	! Minor bugfix for last commit
[4559]	123	!
[3909]	124	! 3900 2019-04-16 15:17:43Z suehring
[3900]	125	! Missing re-calculation of perturbation seeds in case of restarts
[4559]	126	!
[3900]	127	! 3891 2019-04-12 17:52:01Z suehring
[4559]	128	! Bugfix in initialization in case of restart runs.
	129	!
[3891]	130	! 3885 2019-04-11 11:29:34Z kanani
[4559]	131	! Changes related to global restructuring of location messages and introduction of additional debug
	132	! messages
	133	!
	134	!
	135	! Removed unused variables
	136	!
[3775]	137	! 3719 2019-02-06 13:10:18Z kanani
[4559]	138	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
	139	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
	140	! for better overview.
	141	!
[4182]	142	! 2259 2017-06-08 09:09:11Z gronemeier
	143	! Initial revision
[3044]	144	!
[4182]	145	! Authors:
	146	! --------
	147	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	148	!
	149	!
[2259]	150	! Description:
	151	! ------------
[4559]	152	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
	153	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
	154	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
	155	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
	156	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
	157	!> parametrized within the boundary layer.
[2259]	158	!>
[4566]	159	!> @todo Enable cyclic_fill
[4559]	160	!> Implement turbulence generation for e and pt
[2259]	161	!> @note <Enter notes on the module>
[4559]	162	!> @bug Height information from input file is not used. Profiles from input must match with current
	163	!> PALM grid.
	164	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
	165	!--------------------------------------------------------------------------------------------------!
[2259]	166	MODULE synthetic_turbulence_generator_mod
	167
	168
[4559]	169	USE arrays_3d, &
	170	ONLY: dzw, &
	171	ddzw, &
	172	drho_air, &
	173	mean_inflow_profiles, &
	174	pt, &
	175	pt_init, &
	176	q, &
	177	q_init, &
	178	u, &
	179	u_init, &
	180	v, &
	181	v_init, &
	182	w, &
	183	zu, &
[4022]	184	zw
[2259]	185
[4559]	186	USE basic_constants_and_equations_mod, &
	187	ONLY: g, &
	188	kappa, &
[4022]	189	pi
[2259]	190
[4559]	191	USE control_parameters, &
	192	ONLY: bc_lr, &
	193	bc_ns, &
	194	child_domain, &
	195	coupling_char, &
	196	debug_output_timestep, &
	197	dt_3d, &
	198	e_init, &
	199	humidity, &
	200	initializing_actions, &
	201	intermediate_timestep_count, &
	202	intermediate_timestep_count_max, &
	203	length, &
	204	message_string, &
	205	nesting_offline, &
	206	neutral, &
	207	num_mean_inflow_profiles, &
	208	random_generator, &
	209	rans_mode, &
	210	restart_data_format_output, &
	211	restart_string, &
	212	syn_turb_gen, &
	213	time_since_reference_point, &
[4022]	214	turbulent_inflow
[4438]	215
[4559]	216	USE cpulog, &
	217	ONLY: cpu_log, &
[4438]	218	log_point_s
	219
[4559]	220	USE grid_variables, &
	221	ONLY: ddx, &
	222	ddy, &
	223	dx, &
[4022]	224	dy
[2259]	225
[4559]	226	USE indices, &
	227	ONLY: nbgp, &
	228	nz, &
	229	nzb, &
	230	nzt, &
	231	nx, &
	232	nxl, &
	233	nxlu, &
	234	nxr, &
	235	ny, &
	236	nys, &
	237	nysv, &
	238	nyn, &
[4346]	239	wall_flags_total_0
[2259]	240
	241	USE kinds
	242
[2967]	243	#if defined( __parallel ) && !defined( __mpifh )
[2259]	244	USE MPI
[2841]	245	#endif
[2259]	246
[4559]	247	USE nesting_offl_mod, &
	248	ONLY: nesting_offl_calc_zi, &
[4022]	249	zi_ribulk
[3347]	250
[4559]	251	USE pegrid, &
	252	ONLY: comm1dx, &
	253	comm1dy, &
	254	comm2d, &
	255	ierr, &
	256	myidx, &
	257	myidy, &
[4022]	258	pdims
[4438]	259
[4559]	260	USE pmc_interface, &
[4022]	261	ONLY : rans_mode_parent
[4438]	262
[4559]	263	USE random_generator_parallel, &
	264	ONLY: init_parallel_random_generator, &
	265	random_dummy, &
	266	random_number_parallel, &
[4438]	267	random_seed_parallel
[2259]	268
[4495]	269	USE restart_data_mpi_io_mod, &
	270	ONLY: rrd_mpi_io, &
	271	wrd_mpi_io
	272
[4559]	273	USE transpose_indices, &
	274	ONLY: nzb_x, &
	275	nzt_x
[2259]	276
[4559]	277	USE surface_mod, &
	278	ONLY: surf_def_h, &
	279	surf_lsm_h, &
[4438]	280	surf_usm_h
[2259]	281
	282	IMPLICIT NONE
	283
[2967]	284	#if defined( __parallel ) && defined( __mpifh )
[2841]	285	INCLUDE "mpif.h"
	286	#endif
	287
[3182]	288
[3038]	289	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	290	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	291	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	292	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4566]	293	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
	294	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
	295	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
	296	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
	297	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
	298	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
[3038]	299	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	300	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	301	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	302	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4444]	303	#if defined( __parallel )
[4309]	304	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	305	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	306	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	307	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[4444]	308	#endif
[2259]	309
[4559]	310	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	311	!< required for bias correction of imposed perturbations
	312	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	313	!< required for bias correction of imposed perturbations
	314
[4444]	315	#if defined( __parallel )
[3347]	316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	318	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	319	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
[4444]	320	#endif
[3347]	321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	330
[4559]	331	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	332	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	333	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	334	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
[4438]	335
[2259]	336
[4566]	337	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
	338	!< no time correlation to the timestep before should be considered
[4559]	339	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
	340	!< or if computation is distributed over several processes
	341	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
	342	!< (.FALSE.) or if it parametrized
	343	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
	344	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
[2259]	345
[4559]	346
	347	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	348	!< scales above the boundary layer
[4566]	349	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
[4559]	350	!< one length scale above ABL top
	351	REAL(wp) :: d_l !< blend_coeff/length_scale
[4566]	352	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
	353	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
[4559]	354	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
	355	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	356	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	357	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	358	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	359	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	360
	361	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
	362
	363
	364	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	365	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	366	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	367	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	368	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	369	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	370
	371	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	372	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	373	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	374	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	375	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	376	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	377	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	378	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	379	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
	380
	381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	402
[4566]	403	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
	404	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
[4559]	405
[2259]	406	!
	407	!-- PALM interfaces:
[3347]	408	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	409	INTERFACE stg_adjust
	410	MODULE PROCEDURE stg_adjust
	411	END INTERFACE stg_adjust
	412	!
[2259]	413	!-- Input parameter checks to be done in check_parameters
	414	INTERFACE stg_check_parameters
	415	MODULE PROCEDURE stg_check_parameters
	416	END INTERFACE stg_check_parameters
	417
	418	!
	419	!-- Calculate filter functions
	420	INTERFACE stg_filter_func
	421	MODULE PROCEDURE stg_filter_func
	422	END INTERFACE stg_filter_func
	423
	424	!
[2938]	425	!-- Generate velocity seeds at south and north domain boundary
	426	INTERFACE stg_generate_seed_xz
	427	MODULE PROCEDURE stg_generate_seed_xz
	428	END INTERFACE stg_generate_seed_xz
	429	!
	430	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	431	INTERFACE stg_generate_seed_yz
	432	MODULE PROCEDURE stg_generate_seed_yz
	433	END INTERFACE stg_generate_seed_yz
	434
	435	!
	436	!-- Output of information to the header file
	437	INTERFACE stg_header
	438	MODULE PROCEDURE stg_header
	439	END INTERFACE stg_header
	440
	441	!
	442	!-- Initialization actions
	443	INTERFACE stg_init
	444	MODULE PROCEDURE stg_init
	445	END INTERFACE stg_init
	446
	447	!
	448	!-- Main procedure of synth. turb. gen.
	449	INTERFACE stg_main
	450	MODULE PROCEDURE stg_main
	451	END INTERFACE stg_main
	452
	453	!
	454	!-- Reading of NAMELIST parameters
	455	INTERFACE stg_parin
	456	MODULE PROCEDURE stg_parin
	457	END INTERFACE stg_parin
	458
	459	!
	460	!-- Reading of parameters for restart runs
[2894]	461	INTERFACE stg_rrd_global
[4495]	462	MODULE PROCEDURE stg_rrd_global_ftn
	463	MODULE PROCEDURE stg_rrd_global_mpi
[2894]	464	END INTERFACE stg_rrd_global
[2259]	465
	466	!
	467	!-- Writing of binary output for restart runs
[2894]	468	INTERFACE stg_wrd_global
	469	MODULE PROCEDURE stg_wrd_global
	470	END INTERFACE stg_wrd_global
[2259]	471
	472	SAVE
	473
	474	PRIVATE
	475
	476	!
	477	!-- Public interfaces
[4559]	478	PUBLIC stg_adjust, &
	479	stg_check_parameters, &
	480	stg_header, &
	481	stg_init, &
	482	stg_main, &
	483	stg_parin, &
	484	stg_rrd_global, &
	485	stg_wrd_global
[2259]	486
	487	!
	488	!-- Public variables
[4559]	489	PUBLIC dt_stg_call, &
	490	dt_stg_adjust, &
	491	id_stg_left, &
	492	id_stg_north, &
	493	id_stg_right, &
	494	id_stg_south, &
	495	parametrize_inflow_turbulence, &
	496	time_stg_adjust, &
	497	time_stg_call, &
	498	use_syn_turb_gen
[2259]	499
	500
	501	CONTAINS
	502
	503
[4559]	504	!--------------------------------------------------------------------------------------------------!
[2259]	505	! Description:
	506	! ------------
	507	!> Check parameters routine for synthetic turbulence generator
[4559]	508	!--------------------------------------------------------------------------------------------------!
[2259]	509	SUBROUTINE stg_check_parameters
	510
[4559]	511	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
[3182]	512	nesting_offline ) THEN
[4559]	513	message_string = 'Synthetic turbulence generator is required ' // &
	514	'if offline nesting is applied and PALM operates in LES mode.'
[3376]	515	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	516	ENDIF
	517
[4559]	518	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	519	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[4559]	520	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
	521	'and parent operates in RANS-mode but current child in LES mode.'
[3376]	522	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	523	ENDIF
	524
[2776]	525	IF ( use_syn_turb_gen ) THEN
[2259]	526
[4559]	527	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
	528	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
[3579]	529	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
[4559]	530
[3579]	531	ENDIF
[4559]	532
	533	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
	534	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
[3579]	535	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
[4559]	536
[3579]	537	ENDIF
[4559]	538
	539	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	540
	541	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	542	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	543	message_string = 'Using synthetic turbulence generator requires ' // &
	544	'%initializing_actions = "set_constant_profiles" or ' // &
	545	' "read_restart_data", if not offline nesting is applied.'
[2938]	546	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	547	ENDIF
	548
	549	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
[4559]	550	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
	551	' "dirichlet/radiation", if not offline nesting is applied.'
[2938]	552	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	553	ENDIF
	554	IF ( bc_ns /= 'cyclic' ) THEN
[4559]	555	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
	556	' "cyclic", if not offline nesting is applied.'
[2938]	557	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	558	ENDIF
	559
[2259]	560	ENDIF
	561
	562	IF ( turbulent_inflow ) THEN
[4559]	563	message_string = 'Using synthetic turbulence generator in combination ' // &
	564	'&with turbulent_inflow = .T. is not allowed'
[2259]	565	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	566	ENDIF
[4309]	567	!
	568	!-- Synthetic turbulence generator requires the parallel random generator
	569	IF ( random_generator /= 'random-parallel' ) THEN
[4559]	570	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
	571	'random-parallel.'
[4309]	572	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	573	ENDIF
[2259]	574
	575	ENDIF
	576
	577	END SUBROUTINE stg_check_parameters
	578
	579
[4559]	580	!--------------------------------------------------------------------------------------------------!
[2259]	581	! Description:
	582	! ------------
	583	!> Header output for synthetic turbulence generator
[4559]	584	!--------------------------------------------------------------------------------------------------!
[2259]	585	SUBROUTINE stg_header ( io )
	586
[4559]	587	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
[2259]	588
	589	!
	590	!-- Write synthetic turbulence generator Header
	591	WRITE( io, 1 )
[2776]	592	IF ( use_syn_turb_gen ) THEN
[2259]	593	WRITE( io, 2 )
	594	ELSE
	595	WRITE( io, 3 )
	596	ENDIF
[4559]	597
[3347]	598	IF ( parametrize_inflow_turbulence ) THEN
	599	WRITE( io, 4 ) dt_stg_adjust
	600	ELSE
	601	WRITE( io, 5 )
	602	ENDIF
[2259]	603
[4559]	604	1 FORMAT (//' Synthetic turbulence generator information:'/ &
[2259]	605	' ------------------------------------------'/)
[3347]	606	2 FORMAT (' synthetic turbulence generator is switched on')
	607	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	608	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	609	5 FORMAT (' imposed turbulence is read from file' )
[2259]	610
	611	END SUBROUTINE stg_header
	612
	613
[4559]	614	!--------------------------------------------------------------------------------------------------!
[2259]	615	! Description:
	616	! ------------
	617	!> Initialization of the synthetic turbulence generator
[4559]	618	!--------------------------------------------------------------------------------------------------!
[2259]	619	SUBROUTINE stg_init
	620
[2669]	621	#if defined( __parallel )
[4559]	622	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	623	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
[2669]	624	#endif
[2259]	625
[4559]	626	INTEGER(iwp) :: i !> grid index in x-direction
	627	INTEGER(iwp) :: j !> loop index
	628	INTEGER(iwp) :: k !< index
[4444]	629	#if defined( __parallel )
[4559]	630	INTEGER(iwp) :: newtype !< dummy MPI type
	631	INTEGER(iwp) :: realsize !< size of REAL variables
[4444]	632	#endif
[4309]	633
[4022]	634	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	635	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[4559]	636
	637
	638	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
	639
[2259]	640	!
	641	!-- Dummy variables used for reading profiles
[4559]	642	REAL(wp) :: d1 !< u profile
	643	REAL(wp) :: d2 !< v profile
	644	REAL(wp) :: d3 !< w profile
	645	REAL(wp) :: d5 !< e profile
	646	REAL(wp) :: luy !< length scale for u in y direction
	647	REAL(wp) :: luz !< length scale for u in z direction
	648	REAL(wp) :: lvy !< length scale for v in y direction
	649	REAL(wp) :: lvz !< length scale for v in z direction
	650	REAL(wp) :: lwy !< length scale for w in y direction
	651	REAL(wp) :: lwz !< length scale for w in z direction
[4444]	652	#if defined( __parallel )
[4559]	653	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[4444]	654	#endif
[4559]	655	REAL(wp) :: zz !< height
[2259]	656
[2938]	657
[2259]	658	#if defined( __parallel )
	659	CALL MPI_BARRIER( comm2d, ierr )
	660	#endif
[4438]	661	!
[4559]	662	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
	663	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
	664	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
	665	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
	666	!-- communication).
[4438]	667	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	668	#if defined( __parallel )
[4559]	669	!
[4438]	670	!-- Determine processor decomposition of z-axis along x- and y-direction
	671	nnz = nz / pdims(1)
	672	nzb_x_stg = 1 + myidx * INT( nnz )
	673	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[4559]	674
	675	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[4438]	676	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[4559]	677
	678	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
[4438]	679	.AND. .NOT. rans_mode ) ) THEN
	680	nnz = nz / pdims(2)
	681	nzb_y_stg = 1 + myidy * INT( nnz )
	682	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[4559]	683
	684	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[4438]	685	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	686	ENDIF
[4559]	687
	688	!
	689	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
[4438]	690	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	691	extent = 1 * realsize
[4559]	692	!
	693	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
[4438]	694	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[4559]	695	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
[4438]	696	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	697	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	698	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	699	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	700
[4438]	701	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[4559]	702	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
[4438]	703	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	704	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	705	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	706	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	707
	708	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	709	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[4559]	710
[4438]	711	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	712	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[4559]	713
[4438]	714	DO j = 1, pdims(1)
	715	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	716	ENDDO
[4559]	717	!
	718	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
[4438]	719	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	720	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	721	.AND. .NOT. rans_mode ) ) THEN
	722	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	723	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	724	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	725	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	726	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	727
[4438]	728	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	729	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	730	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	731	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	732	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	733	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	734
	735	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	736	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
[4559]	737
[4438]	738	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	739	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
[4559]	740
[4438]	741	DO j = 1, pdims(2)
	742	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	743	ENDDO
[4559]	744
[4438]	745	ENDIF
[4440]	746	#endif
[2938]	747	ENDIF
[2259]	748	!
[4071]	749	!-- Allocate required arrays.
[4559]	750	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
	751	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
	752	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
	753	!-- and initialized appropriately.
	754	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	755	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	756	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	757	mean_inflow_profiles = 0.0_wp
	758	mean_inflow_profiles(:,1) = u_init
	759	mean_inflow_profiles(:,2) = v_init
	760	!
[4559]	761	!-- Even though potential temperature and humidity are not perturbed, they need to be
	762	!-- initialized appropriately.
	763	IF ( .NOT. neutral ) &
[4071]	764	mean_inflow_profiles(:,4) = pt_init
[4559]	765	IF ( humidity ) &
	766	mean_inflow_profiles(:,6) = q_init
	767	ENDIF
[3347]	768	ENDIF
[4566]	769	!
	770	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
	771	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
	772	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	773	u_init = mean_inflow_profiles(:,1)
	774	v_init = mean_inflow_profiles(:,2)
	775	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	776	ENDIF
[2259]	777
[4559]	778	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	779	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	780	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	781	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	782	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	783	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	784	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	785	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	786
[4566]	787	r11 = 0.0_wp
	788	r21 = 0.0_wp
	789	r22 = 0.0_wp
	790	r31 = 0.0_wp
	791	r32 = 0.0_wp
	792	r33 = 0.0_wp
	793	tu = 0.0_wp
	794	tv = 0.0_wp
	795	tw = 0.0_wp
	796
[4438]	797	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	798	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	799	dist_xz = 0.0_wp
	800	dist_yz = 0.0_wp
	801	!
[2259]	802	!-- Read inflow profile
	803	!-- Height levels of profiles in input profile is as follows:
[4559]	804	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
[2259]	805	!-- WARNING: zz is not used at the moment
[4559]	806	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
[2259]	807
[2938]	808	IF ( file_stg_exist ) THEN
[2259]	809
[4559]	810	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
[2938]	811	!
	812	!-- Skip header
	813	READ( 90, * )
[2259]	814
[3182]	815	DO k = nzb+1, nzt+1
[4559]	816	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
	817	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
[2938]	818
[2259]	819	!
[4559]	820	!-- Convert length scales from meter to number of grid points.
[2938]	821	nuy(k) = INT( luy * ddy )
[3182]	822	nuz(k) = INT( luz * ddzw(k) )
[2938]	823	nvy(k) = INT( lvy * ddy )
[3182]	824	nvz(k) = INT( lvz * ddzw(k) )
[2938]	825	nwy(k) = INT( lwy * ddy )
[3182]	826	nwz(k) = INT( lwz * ddzw(k) )
[2938]	827	!
	828	!-- Workaround, assume isotropic turbulence
	829	nwx(k) = nwy(k)
	830	nvx(k) = nvy(k)
	831	nux(k) = nuy(k)
	832	!
	833	!-- Save Mean inflow profiles
	834	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	835	mean_inflow_profiles(k,1) = d1
	836	mean_inflow_profiles(k,2) = d2
	837	! mean_inflow_profiles(k,4) = d4
	838	mean_inflow_profiles(k,5) = d5
	839	ENDIF
	840	ENDDO
[3182]	841	!
	842	!-- Set lenght scales at surface grid point
[4559]	843	nuy(nzb) = nuy(nzb+1)
[3182]	844	nuz(nzb) = nuz(nzb+1)
	845	nvy(nzb) = nvy(nzb+1)
	846	nvz(nzb) = nvz(nzb+1)
	847	nwy(nzb) = nwy(nzb+1)
	848	nwz(nzb) = nwz(nzb+1)
[4559]	849
[2938]	850	CLOSE( 90 )
[3347]	851	!
[4559]	852	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3347]	853	CALL calc_coeff_matrix
	854	!
[4559]	855	!-- No information about turbulence and its length scales are available. Instead, parametrize
	856	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
	857	!-- parametrized, which is done later when energy-balance models are already initialized. This is
	858	!-- because the STG needs information about surface properties such as roughness to build
	859	!-- 'realistic' turbulence profiles.
[2938]	860	ELSE
[2259]	861	!
[4566]	862	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
	863	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[4022]	864	!
[3347]	865	!-- Set flag indicating that turbulence is parametrized
	866	parametrize_inflow_turbulence = .TRUE.
	867	!
[4559]	868	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
	869	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
	870	!-- nevertheless, the boundary-layer depth needs to be determined first.
	871	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
[4022]	872	CALL nesting_offl_calc_zi
	873	!
[4559]	874	!-- Determine boundary-layer depth, which is used to initialize lenght scales
[3347]	875	CALL calc_scaling_variables
	876	!
[4559]	877	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
	878	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
	879	!-- friction velocity and velocity scale.
[4566]	880	CALL parametrize_turbulence
[4559]	881	!
	882	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3891]	883	CALL calc_coeff_matrix
[4559]	884
[2938]	885	ENDIF
[2259]	886	!
[4566]	887	!-- Initial filter functions
	888	CALL stg_setup_filter_function
[4559]	889
[2938]	890	!
	891	!-- Allocate velocity seeds for turbulence at xz-layer
[4559]	892	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	893	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	894	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	895
[2938]	896	!
	897	!-- Allocate velocity seeds for turbulence at yz-layer
[4559]	898	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	899	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	900	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	901
[2938]	902	fu_xz = 0.0_wp
	903	fuo_xz = 0.0_wp
	904	fv_xz = 0.0_wp
	905	fvo_xz = 0.0_wp
	906	fw_xz = 0.0_wp
	907	fwo_xz = 0.0_wp
	908
	909	fu_yz = 0.0_wp
	910	fuo_yz = 0.0_wp
	911	fv_yz = 0.0_wp
	912	fvo_yz = 0.0_wp
	913	fw_yz = 0.0_wp
	914	fwo_yz = 0.0_wp
	915
[2259]	916	#if defined( __parallel )
	917	CALL MPI_BARRIER( comm2d, ierr )
	918	#endif
	919
	920	!
[4559]	921	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
	922	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
	923	!-- This is mostly for k=nzt+1.
[2259]	924	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	925	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	926
	927	IF ( myidx == id_stg_left ) i = -1
	928	IF ( myidx == id_stg_right ) i = nxr+1
	929
[4438]	930	DO j = nys, nyn
[2259]	931	DO k = nzb, nzt+1
[4332]	932	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	933	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	934	ELSE
[4332]	935	fu_yz(k,j) = 10E-8_wp
[2259]	936	ENDIF
	937
[4332]	938	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	939	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	940	ELSE
[4332]	941	fv_yz(k,j) = 10E-8_wp
[2259]	942	ENDIF
	943
[4332]	944	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	945	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
[2259]	946	ELSE
[4332]	947	fw_yz(k,j) = 10E-8_wp
[2259]	948	ENDIF
	949	ENDDO
	950	ENDDO
	951	ENDIF
[4559]	952
[3900]	953	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	954
	955	IF ( myidy == id_stg_south ) j = -1
	956	IF ( myidy == id_stg_north ) j = nyn+1
	957
[4438]	958	DO i = nxl, nxr
[3900]	959	DO k = nzb, nzt+1
[4335]	960	!
[4559]	961	!-- In case the correlation coefficients are very small, the velocity seeds may become
	962	!-- very large finally creating numerical instabilities in the synthetic turbulence
	963	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
[4332]	964	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	965	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	966	ELSE
[4332]	967	fu_xz(k,i) = 10E-8_wp
[3900]	968	ENDIF
	969
[4332]	970	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	971	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	972	ELSE
[4332]	973	fv_xz(k,i) = 10E-8_wp
[3900]	974	ENDIF
	975
[4332]	976	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	977	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	978	ELSE
[4332]	979	fw_xz(k,i) = 10E-8_wp
[3900]	980	ENDIF
	981
	982	ENDDO
	983	ENDDO
	984	ENDIF
[2259]	985	ENDIF
[4022]	986	!
[4559]	987	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
	988	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
	989	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
	990	!-- different cases must be distinguished.
[4022]	991	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	992	!
	993	!-- Number of grid points where perturbations are imposed on u
	994	IF ( myidx == id_stg_left ) i = nxl
	995	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	996
	997	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	998	!
[4559]	999	!-- Number of grid points where perturbations are imposed on v and w
[4022]	1000	IF ( myidx == id_stg_left ) i = nxl-1
	1001	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1002
	1003	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1004	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	1005
[4022]	1006	#if defined( __parallel )
[4559]	1007	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
[4022]	1008	#else
	1009	nr_non_topo_yz = nr_non_topo_yz_l
[4559]	1010	#endif
[4022]	1011	ENDIF
[4559]	1012
[4022]	1013	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1014	!
	1015	!-- Number of grid points where perturbations are imposed on v
	1016	IF ( myidy == id_stg_south ) j = nys
	1017	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1018
	1019	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1020	!
[4559]	1021	!-- Number of grid points where perturbations are imposed on u and w
[4022]	1022	IF ( myidy == id_stg_south ) j = nys-1
	1023	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1024
	1025	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1026	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1027
[4022]	1028	#if defined( __parallel )
[4559]	1029	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
[4022]	1030	#else
	1031	nr_non_topo_xz = nr_non_topo_xz_l
[4559]	1032	#endif
[4022]	1033	ENDIF
[4438]	1034	!
[4559]	1035	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
	1036	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
	1037	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
[4566]	1038	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
	1039	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
[4438]	1040	id_rand_yz = 0
	1041	seq_rand_yz = 0
[2259]	1042
[4566]	1043	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
[4022]	1044
[4559]	1045	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1046	.AND. .NOT. rans_mode ) ) THEN
[4566]	1047	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
	1048	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
[4438]	1049	id_rand_xz = 0
	1050	seq_rand_xz = 0
	1051
[4566]	1052	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
[4438]	1053	ENDIF
	1054
[2259]	1055	END SUBROUTINE stg_init
	1056
	1057
[4559]	1058	!--------------------------------------------------------------------------------------------------!
[2259]	1059	! Description:
	1060	! ------------
[4559]	1061	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
	1062	!--------------------------------------------------------------------------------------------------!
[4566]	1063	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
[2259]	1064
[4566]	1065	INTEGER(iwp) :: k !< loop index
	1066	INTEGER(iwp) :: mergp !< passed length scale in grid points
	1067	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1068	INTEGER(iwp) :: nf !< index for length scales
[2259]	1069
[4559]	1070	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
	1071
[2259]	1072	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1073	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1074
[4438]	1075	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1076
	1077
	1078	bxx = 0.0_wp
	1079
	1080	DO k = nzb, nzt+1
	1081	bdenom = 0.0_wp
	1082	n_k = nxx(k)
	1083	IF ( n_k /= 0 ) THEN
	1084
	1085	!
	1086	!-- ( Eq.10 )^2
[4438]	1087	DO nf = -n_k, n_k
[4559]	1088	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
[2259]	1089	ENDDO
	1090
	1091	!
	1092	!-- ( Eq.9 )
	1093	bdenom = SQRT( bdenom )
[4438]	1094	DO nf = -n_k, n_k
[4559]	1095	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
[2259]	1096	ENDDO
	1097	ENDIF
	1098	ENDDO
	1099
[3347]	1100	END SUBROUTINE stg_filter_func
[2259]	1101
	1102
[4566]	1103	!------------------------------------------------------------------------------!
	1104	! Description:
	1105	! ------------
	1106	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1107	!> (Xie and Castro, 2008)
	1108	!------------------------------------------------------------------------------!
	1109	SUBROUTINE stg_setup_filter_function
	1110
	1111	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
	1112	INTEGER(iwp) :: k !< loop index along vertical direction
	1113	!
	1114	!-- Define the size of the filter functions and allocate them.
	1115	mergp_x = 0
	1116	mergp_y = 0
	1117	mergp_z = 0
	1118
	1119	DO k = nzb, nzt+1
	1120	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
	1121	IF ( j > mergp_x ) mergp_x = j
	1122	ENDDO
	1123	DO k = nzb, nzt+1
	1124	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
	1125	IF ( j > mergp_y ) mergp_y = j
	1126	ENDDO
	1127	DO k = nzb, nzt+1
	1128	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
	1129	IF ( j > mergp_z ) mergp_z = j
	1130	ENDDO
	1131
	1132	mergp_xy = MAX( mergp_x, mergp_y )
	1133
	1134	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
	1135	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
	1136	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
	1137	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
	1138	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
	1139	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
	1140	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
	1141	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
	1142	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
	1143
	1144	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
	1145	buy(-mergp_y:mergp_y,nzb:nzt+1), &
	1146	buz(-mergp_z:mergp_z,nzb:nzt+1), &
	1147	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
	1148	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
	1149	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
	1150	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
	1151	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
	1152	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
	1153	!
	1154	!-- Create filter functions
	1155	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
	1156	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
	1157	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
	1158	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
	1159	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
	1160	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
	1161	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
	1162	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
	1163	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
	1164
	1165	END SUBROUTINE stg_setup_filter_function
	1166
[4559]	1167	!--------------------------------------------------------------------------------------------------!
[2259]	1168	! Description:
	1169	! ------------
	1170	!> Parin for &stg_par for synthetic turbulence generator
[4559]	1171	!--------------------------------------------------------------------------------------------------!
[2259]	1172	SUBROUTINE stg_parin
	1173
[4559]	1174	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
[2259]	1175
	1176
[4559]	1177	NAMELIST /stg_par/ dt_stg_adjust, &
	1178	dt_stg_call, &
	1179	use_syn_turb_gen, &
[4438]	1180	compute_velocity_seeds_local
[2259]	1181
	1182	line = ' '
	1183	!
	1184	!-- Try to find stg package
	1185	REWIND ( 11 )
	1186	line = ' '
	1187	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[4559]	1188	READ ( 11, '(A)', END = 20 ) line
[2259]	1189	ENDDO
	1190	BACKSPACE ( 11 )
	1191
	1192	!
	1193	!-- Read namelist
[3246]	1194	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1195
	1196	!
[4559]	1197	!-- Set flag that indicates that the synthetic turbulence generator is switched on
[2776]	1198	syn_turb_gen = .TRUE.
[3246]	1199	GOTO 20
[2259]	1200
[3246]	1201	10 BACKSPACE( 11 )
[3248]	1202	READ( 11 , '(A)') line
	1203	CALL parin_fail_message( 'stg_par', line )
[2563]	1204
[3246]	1205	20 CONTINUE
[2259]	1206
	1207	END SUBROUTINE stg_parin
	1208
	1209
[4559]	1210	!--------------------------------------------------------------------------------------------------!
[2259]	1211	! Description:
	1212	! ------------
[4495]	1213	!> Read module-specific global restart data (Fortran binary format).
[4559]	1214	!--------------------------------------------------------------------------------------------------!
[4495]	1215	SUBROUTINE stg_rrd_global_ftn( found )
[2576]	1216
[4559]	1217	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1218
[2894]	1219	found = .TRUE.
[2259]	1220
[3038]	1221
[2894]	1222	SELECT CASE ( restart_string(1:length) )
[4559]	1223
[4022]	1224	CASE ( 'time_stg_adjust' )
	1225	READ ( 13 ) time_stg_adjust
[4559]	1226
[4022]	1227	CASE ( 'time_stg_call' )
	1228	READ ( 13 ) time_stg_call
[4559]	1229
[2894]	1230	CASE ( 'use_syn_turb_gen' )
	1231	READ ( 13 ) use_syn_turb_gen
[2259]	1232
[2894]	1233	CASE DEFAULT
[2259]	1234
[3038]	1235	found = .FALSE.
[2259]	1236
[2894]	1237	END SELECT
[2259]	1238
	1239
[4495]	1240	END SUBROUTINE stg_rrd_global_ftn
[2259]	1241
	1242
[4559]	1243	!--------------------------------------------------------------------------------------------------!
[2259]	1244	! Description:
	1245	! ------------
[4495]	1246	!> Read module-specific global restart data (MPI-IO).
[4559]	1247	!--------------------------------------------------------------------------------------------------!
[4495]	1248	SUBROUTINE stg_rrd_global_mpi
	1249
	1250	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1251	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
	1252	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1253
	1254	END SUBROUTINE stg_rrd_global_mpi
	1255
	1256
[4559]	1257	!--------------------------------------------------------------------------------------------------!
[4495]	1258	! Description:
	1259	! ------------
[2259]	1260	!> This routine writes the respective restart data.
[4559]	1261	!--------------------------------------------------------------------------------------------------!
[2894]	1262	SUBROUTINE stg_wrd_global
[2259]	1263
[4495]	1264	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
	1265
	1266	CALL wrd_write_string( 'time_stg_adjust' )
	1267	WRITE ( 14 ) time_stg_adjust
[4559]	1268
[4495]	1269	CALL wrd_write_string( 'time_stg_call' )
	1270	WRITE ( 14 ) time_stg_call
[2259]	1271
[4495]	1272	CALL wrd_write_string( 'use_syn_turb_gen' )
	1273	WRITE ( 14 ) use_syn_turb_gen
[2259]	1274
[4535]	1275	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
[2259]	1276
[4495]	1277	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1278	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
	1279	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1280
	1281	ENDIF
	1282
[2894]	1283	END SUBROUTINE stg_wrd_global
[2259]	1284
[2894]	1285
[4559]	1286	!--------------------------------------------------------------------------------------------------!
[2259]	1287	! Description:
	1288	! ------------
[4559]	1289	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
	1290	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
	1291	!> (2013), and using a Lund rotation (Lund, 1998).
	1292	!--------------------------------------------------------------------------------------------------!
[2259]	1293	SUBROUTINE stg_main
	1294
[4559]	1295	USE exchange_horiz_mod, &
[4457]	1296	ONLY: exchange_horiz
	1297
[4559]	1298	INTEGER(iwp) :: i !< grid index in x-direction
	1299	INTEGER(iwp) :: j !< loop index in y-direction
	1300	INTEGER(iwp) :: k !< loop index in z-direction
[2259]	1301
[4559]	1302	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1303
[4566]	1304	REAL(wp) :: dt_stg !< time interval the STG is called
[4559]	1305
	1306	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
	1307
[3987]	1308	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1309	!
	1310	!-- Calculate time step which is needed for filter functions
[3775]	1311	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1312	!
[4559]	1313	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
	1314	!-- created or if old disturbances can be imposed again.
	1315	IF ( time_stg_call >= dt_stg_call .AND. &
[4022]	1316	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1317	stg_call = .TRUE.
	1318	ELSE
	1319	stg_call = .FALSE.
	1320	ENDIF
	1321	!
[2259]	1322	!-- Initial value of fu, fv, fw
[3646]	1323	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1324	!
[4559]	1325	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
	1326	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
	1327	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
	1328	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
	1329	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
	1330	!-- have the same initial seeds.
	1331	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
	1332	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1333	.AND. .NOT. rans_mode ) ) ) THEN
[4309]	1334	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1335	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1336	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1337	ELSE
[4559]	1338	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
	1339	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
	1340	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
[2938]	1341	!
[4559]	1342	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
	1343	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
	1344	!-- comment above.
	1345	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
	1346	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
	1347	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
[2938]	1348	ENDIF
[2259]	1349	velocity_seed_initialized = .TRUE.
	1350	ENDIF
	1351	!
[4559]	1352	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
	1353	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
	1354	!-- seeds are required also at the right, south and north boundaries.
[4022]	1355	IF ( stg_call ) THEN
[4559]	1356	IF ( .NOT. ( nesting_offline .OR. &
	1357	( child_domain .AND. rans_mode_parent &
[4309]	1358	.AND. .NOT. rans_mode ) ) ) THEN
	1359	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1360	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1361	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1362
	1363	ELSE
[4559]	1364	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
	1365	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
	1366	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
[4309]	1367
[4559]	1368	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
	1369	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
	1370	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
[4022]	1371	ENDIF
[2938]	1372	ENDIF
[4559]	1373
[2938]	1374	!
[4309]	1375	!-- Turbulence generation at left and/or right boundary
[2938]	1376	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1377	!
[4559]	1378	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1379	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1380	IF ( stg_call ) THEN
[4559]	1381
[4438]	1382	DO j = nys, nyn
[4022]	1383	DO k = nzb, nzt + 1
[4559]	1384	!
[4022]	1385	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1386	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1387	fu_yz(k,j) = fuo_yz(k,j)
	1388	ELSE
[4559]	1389	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1390	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
[4022]	1391	ENDIF
[4559]	1392
[4566]	1393	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1394	fv_yz(k,j) = fvo_yz(k,j)
	1395	ELSE
[4559]	1396	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1397	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
[4022]	1398	ENDIF
[4559]	1399
[4566]	1400	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1401	fw_yz(k,j) = fwo_yz(k,j)
	1402	ELSE
[4559]	1403	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1404	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
[4022]	1405	ENDIF
	1406	ENDDO
	1407	ENDDO
[4559]	1408
[4022]	1409	dist_yz(nzb,:,1) = 0.0_wp
	1410	dist_yz(nzb,:,2) = 0.0_wp
	1411	dist_yz(nzb,:,3) = 0.0_wp
[4559]	1412
[4022]	1413	IF ( myidx == id_stg_left ) i = nxl
[4559]	1414	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1415	DO j = nys, nyn
[4022]	1416	DO k = nzb+1, nzt + 1
[4559]	1417	!
[4022]	1418	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4566]	1419	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
[4562]	1420	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4566]	1421
[4022]	1422	ENDDO
	1423	ENDDO
[4309]	1424
[4022]	1425	IF ( myidx == id_stg_left ) i = nxl-1
	1426	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1427	DO j = nys, nyn
[4022]	1428	DO k = nzb+1, nzt + 1
[4559]	1429	!
[4022]	1430	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1431	!-- Additional factors are added to improve the variance of v and w experimental test
	1432	!-- of 1.2
[4566]	1433	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
[4559]	1434	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4566]	1435	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
	1436	a33(k) * fw_yz(k,j) ) * &
	1437	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
	1438
[4022]	1439	ENDDO
[2259]	1440	ENDDO
[4022]	1441	ENDIF
[2259]	1442	!
	1443	!-- Mass flux correction following Kim et al. (2013)
[4559]	1444	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
	1445	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
	1446	!-- only after the last RK3-substep, else the boundary values won't be accessed.
[4022]	1447	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1448	mc_factor_l = 0.0_wp
	1449	mc_factor = 0.0_wp
	1450	!
	1451	!-- Sum up the original volume flows (with and without perturbations).
	1452	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
[2938]	1453	IF ( myidx == id_stg_left ) i = nxl
	1454	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1455
[4562]	1456	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
	1457	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4559]	1458
[4022]	1459	IF ( myidx == id_stg_left ) i = nxl-1
	1460	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1461
[4562]	1462	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
	1463	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1464	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
	1465	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4559]	1466
[2938]	1467	#if defined( __parallel )
[4559]	1468	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1469	#else
	1470	mc_factor = mc_factor_l
[2938]	1471	#endif
[4559]	1472	!
	1473	!-- Calculate correction factor and force zero mean perturbations.
	1474	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1475
	1476	IF ( myidx == id_stg_left ) i = nxl
	1477	IF ( myidx == id_stg_right ) i = nxr+1
	1478
[4562]	1479	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
	1480	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4559]	1481
	1482
	1483	IF ( myidx == id_stg_left ) i = nxl-1
	1484	IF ( myidx == id_stg_right ) i = nxr+1
	1485
[4562]	1486	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
	1487	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4559]	1488
[4562]	1489	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
	1490	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4559]	1491	!
[2938]	1492	!-- Add disturbances
	1493	IF ( myidx == id_stg_left ) THEN
[4559]	1494	!
	1495	!-- For the left boundary distinguish between mesoscale offline / self nesting and
	1496	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
	1497	!-- the mean inflow profiles.
	1498	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1499	!
[4022]	1500	!-- Add disturbance at the inflow
[4438]	1501	DO j = nys, nyn
[4022]	1502	DO k = nzb, nzt+1
[4562]	1503	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
	1504	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
	1505	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
	1506	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1507	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
	1508	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1509	ENDDO
[2938]	1510	ENDDO
[4022]	1511	ELSE
[4559]	1512
[4022]	1513	DO j = nys, nyn
	1514	DO k = nzb+1, nzt
[4562]	1515	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
	1516	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1517	u(k,j,-1) = u(k,j,0)
[4562]	1518	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
	1519	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1520	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
	1521	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1522	ENDDO
	1523	ENDDO
	1524	ENDIF
[2938]	1525	ENDIF
	1526	IF ( myidx == id_stg_right ) THEN
[3186]	1527	DO j = nys, nyn
[3347]	1528	DO k = nzb+1, nzt
[4562]	1529	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
	1530	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
	1531	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
	1532	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
	1533	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
	1534	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1535	ENDDO
	1536	ENDDO
	1537	ENDIF
	1538	ENDIF
	1539	ENDIF
	1540	!
	1541	!-- Turbulence generation at north and south boundary
	1542	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1543	!
[4559]	1544	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1545	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1546	IF ( stg_call ) THEN
[4438]	1547	DO i = nxl, nxr
[4022]	1548	DO k = nzb, nzt + 1
[4559]	1549	!
[4022]	1550	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1551	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1552	fu_xz(k,i) = fuo_xz(k,i)
	1553	ELSE
[4559]	1554	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1555	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
[4022]	1556	ENDIF
[4559]	1557
[4566]	1558	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1559	fv_xz(k,i) = fvo_xz(k,i)
	1560	ELSE
[4559]	1561	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1562	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
[4022]	1563	ENDIF
[4559]	1564
[4566]	1565	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1566	fw_xz(k,i) = fwo_xz(k,i)
	1567	ELSE
[4559]	1568	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1569	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
[4022]	1570	ENDIF
	1571	ENDDO
	1572	ENDDO
[4559]	1573
	1574
[4022]	1575	dist_xz(nzb,:,1) = 0.0_wp
	1576	dist_xz(nzb,:,2) = 0.0_wp
	1577	dist_xz(nzb,:,3) = 0.0_wp
[4559]	1578
[4022]	1579	IF ( myidy == id_stg_south ) j = nys
	1580	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1581	DO i = nxl, nxr
[4022]	1582	DO k = nzb+1, nzt + 1
[4559]	1583	!
[4022]	1584	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1585	!-- Additional factors are added to improve the variance of v and w
	1586	!experimental test of 1.2
[4566]	1587	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
[4559]	1588	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1589	ENDDO
	1590	ENDDO
[4559]	1591
[4022]	1592	IF ( myidy == id_stg_south ) j = nys-1
	1593	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1594	DO i = nxl, nxr
[4022]	1595	DO k = nzb+1, nzt + 1
[4559]	1596	!
[4022]	1597	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1598	!-- Additional factors are added to improve the variance of v and w
[4566]	1599	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
[4562]	1600	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4559]	1601
[4566]	1602	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
	1603	a33(k) * fw_xz(k,i) ) * &
[4562]	1604	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1605	ENDDO
[2938]	1606	ENDDO
[4022]	1607	ENDIF
[3347]	1608
[2938]	1609	!
[4559]	1610	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
	1611	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
	1612	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
	1613	!-- else the boundary values won't be accessed.
[4022]	1614	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1615	mc_factor_l = 0.0_wp
	1616	mc_factor = 0.0_wp
	1617
[4022]	1618	IF ( myidy == id_stg_south ) j = nys
	1619	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1620
[4562]	1621	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
	1622	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4559]	1623
	1624	IF ( myidy == id_stg_south ) j = nys-1
	1625	IF ( myidy == id_stg_north ) j = nyn+1
	1626
[4562]	1627	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
	1628	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1629	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
	1630	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4559]	1631
[2938]	1632	#if defined( __parallel )
[4559]	1633	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1634	#else
[4022]	1635	mc_factor = mc_factor_l
[2938]	1636	#endif
[4559]	1637
[4022]	1638	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
[4559]	1639
	1640	IF ( myidy == id_stg_south ) j = nys
	1641	IF ( myidy == id_stg_north ) j = nyn+1
	1642
[4562]	1643	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
	1644	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4559]	1645
	1646
	1647	IF ( myidy == id_stg_south ) j = nys-1
	1648	IF ( myidy == id_stg_north ) j = nyn+1
	1649
[4562]	1650	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
	1651	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4559]	1652
[4562]	1653	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
	1654	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4559]	1655	!
[4022]	1656	!-- Add disturbances
[4559]	1657	IF ( myidy == id_stg_south ) THEN
[4022]	1658	DO i = nxl, nxr
	1659	DO k = nzb+1, nzt
[4559]	1660	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1661	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
	1662	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1663	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1664	v(k,-1,i) = v(k,0,i)
[4559]	1665	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1666	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1667	ENDDO
[2938]	1668	ENDDO
[4022]	1669	ENDIF
	1670	IF ( myidy == id_stg_north ) THEN
[4559]	1671
[4022]	1672	DO i = nxl, nxr
	1673	DO k = nzb+1, nzt
[4562]	1674	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
	1675	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
	1676	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
	1677	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
	1678	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
	1679	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1680	ENDDO
[2938]	1681	ENDDO
[4022]	1682	ENDIF
[2938]	1683	ENDIF
[2259]	1684	ENDIF
[3347]	1685	!
[4438]	1686	!-- Exchange ghost points.
	1687	CALL exchange_horiz( u, nbgp )
	1688	CALL exchange_horiz( v, nbgp )
	1689	CALL exchange_horiz( w, nbgp )
	1690	!
[3347]	1691	!-- Finally, set time counter for calling STG to zero
[4022]	1692	IF ( stg_call ) time_stg_call = 0.0_wp
[4566]	1693	!
	1694	!-- Set adjustment step to False to indicate that time correlation can be
	1695	!-- switched-on again.
	1696	adjustment_step = .FALSE.
[2259]	1697
[3987]	1698	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1699
[2259]	1700	END SUBROUTINE stg_main
	1701
[4559]	1702	!--------------------------------------------------------------------------------------------------!
[2259]	1703	! Description:
	1704	! ------------
[4559]	1705	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1706	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
	1707	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
	1708	!> array.
	1709	!--------------------------------------------------------------------------------------------------!
[4309]	1710	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1711
[4559]	1712	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1713	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1714	INTEGER(iwp) :: j !< loop index in y-direction
	1715	INTEGER(iwp) :: jj !< loop index in y-direction
	1716	INTEGER(iwp) :: k !< loop index in z-direction
	1717	INTEGER(iwp) :: kk !< loop index in z-direction
	1718	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1719
[4559]	1720	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1721	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2259]	1722
[4559]	1723	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1724	REAL(wp) :: rand_av !< average of random number
	1725	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2259]	1726
[4566]	1727	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
	1728	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
[4559]	1729
	1730	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1731	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
	1732
	1733	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1734	!
[4559]	1735	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1736	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1737	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1738	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1739	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
	1740	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
[4559]	1741	!-- correlation matrix.
[4566]	1742	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
[4438]	1743	rand_it = 0.0_wp
[2259]	1744
	1745	rand_av = 0.0_wp
	1746	rand_sigma_inv = 0.0_wp
[4566]	1747	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1748	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
[4309]	1749	!
[4438]	1750	!-- Compute and normalize random numbers.
[4566]	1751	DO j = nys - mergp_y, nyn + mergp_y
[4309]	1752	!
[4438]	1753	!-- Put the random seeds at grid point j
	1754	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
[4566]	1755	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1756	CALL random_number_parallel( random_dummy )
	1757	rand_it(k,j) = random_dummy
	1758	ENDDO
[4309]	1759	!
[4438]	1760	!-- Get the new random seeds from last call at grid point j
	1761	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1762	ENDDO
[4309]	1763	!
[4559]	1764	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
	1765	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
	1766	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
[4566]	1767	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1768	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1769	rand_av = rand_av + rand_it(k,j)
[2259]	1770	ENDDO
[4438]	1771	ENDDO
[4566]	1772
[4309]	1773	#if defined( __parallel )
	1774	!
[4438]	1775	!-- Sum-up the local averages of the random numbers
[4559]	1776	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1777	#endif
[4438]	1778	rand_av = rand_av * nyz_inv
[4309]	1779	!
[4438]	1780	!-- Obtain zero mean
	1781	rand_it= rand_it - rand_av
[4309]	1782	!
[4438]	1783	!-- Now, compute the variance
[4566]	1784	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1785	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1786	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1787	ENDDO
[4438]	1788	ENDDO
[2259]	1789
[4309]	1790	#if defined( __parallel )
[2259]	1791	!
[4438]	1792	!-- Sum-up the local quadratic averages of the random numbers
[4559]	1793	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1794	#endif
	1795	!
[4438]	1796	!-- Compute standard deviation
	1797	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1798	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1799	ELSE
	1800	rand_sigma_inv = 1.0_wp
[4309]	1801	ENDIF
	1802	!
[4438]	1803	!-- Normalize with standard deviation to obtain unit variance
	1804	rand_it = rand_it * rand_sigma_inv
	1805
	1806	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1807	!
[4559]	1808	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	1809	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	1810	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
	1811	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	1812	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
	1813	!-- communication. In the second option, which performs better when the turbulent length scales
	1814	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
	1815	!-- communication is necessary.
[4438]	1816	IF ( compute_velocity_seeds_local ) THEN
	1817
	1818	f_n = 0.0_wp
	1819	DO j = nys, nyn
	1820	DO k = nzb, nzt+1
	1821	DO jj = -n_y(k), n_y(k)
	1822	DO kk = -n_z(k), n_z(k)
	1823	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1824	ENDDO
	1825	ENDDO
	1826	ENDDO
[2259]	1827	ENDDO
	1828
[4438]	1829	ELSE
[2259]	1830
[4438]	1831	f_n_l = 0.0_wp
	1832	DO j = nys, nyn
	1833	DO k = nzb_x_stg, nzt_x_stg+1
	1834	DO jj = -n_y(k), n_y(k)
	1835	DO kk = -n_z(k), n_z(k)
	1836	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1837	ENDDO
[2259]	1838	ENDDO
	1839	ENDDO
	1840	ENDDO
	1841	!
[4438]	1842	!-- Gather velocity seeds of full subdomain
	1843	send_count = nzt_x_stg - nzb_x_stg + 1
	1844	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1845
	1846	#if defined( __parallel )
[4309]	1847	!
[4438]	1848	!-- Gather the velocity seed matrix on left boundary mpi ranks.
[4559]	1849	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1850	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
[4309]	1851	!
[4559]	1852	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
	1853	!-- nesting for example).
[4438]	1854	IF ( PRESENT( id_right ) ) THEN
[4559]	1855	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1856	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
[4438]	1857	ENDIF
[2259]	1858	#else
[4438]	1859	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[4444]	1860	!
	1861	!-- Next line required to avoid compile errors because of unused dummy arguments
	1862	IF ( id_left == 0 ) id_right = 0
[2259]	1863	#endif
	1864
[4438]	1865	ENDIF
[2259]	1866
[4438]	1867	DEALLOCATE( rand_it )
	1868
	1869	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1870
[2259]	1871	END SUBROUTINE stg_generate_seed_yz
	1872
[2938]	1873
[4559]	1874	!--------------------------------------------------------------------------------------------------!
[2938]	1875	! Description:
	1876	! ------------
[4559]	1877	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1878	!> f_n.
	1879	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
	1880	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
	1881	!> full array.
	1882	!--------------------------------------------------------------------------------------------------!
[4309]	1883	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1884
[4566]	1885	INTEGER(iwp) :: i !< loop index in x-direction
	1886	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1887	INTEGER(iwp) :: id_south !< core ids at respective boundaries
	1888	INTEGER(iwp) :: ii !< loop index in x-direction
	1889	INTEGER(iwp) :: k !< loop index in z-direction
	1890	INTEGER(iwp) :: kk !< loop index in z-direction
	1891	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2938]	1892
[4566]	1893	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1894	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2938]	1895
[4566]	1896	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1897	REAL(wp) :: rand_av !< average of random number
	1898	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2938]	1899
[4566]	1900	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
	1901	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
	1902
	1903	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1904	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1905
[4566]	1906	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1907
	1908	!
[4559]	1909	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1910	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1911	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1912	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1913	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
	1914	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
[4559]	1915	!-- correlation matrix.
[4566]	1916	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
[4438]	1917	rand_it = 0.0_wp
[2938]	1918
	1919	rand_av = 0.0_wp
	1920	rand_sigma_inv = 0.0_wp
[4566]	1921	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1922	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
[4309]	1923	!
[4438]	1924	!-- Compute and normalize random numbers.
[4566]	1925	DO i = nxl - mergp_x, nxr + mergp_x
[4309]	1926	!
[4438]	1927	!-- Put the random seeds at grid point ii
	1928	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
[4566]	1929	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1930	CALL random_number_parallel( random_dummy )
	1931	rand_it(k,i) = random_dummy
	1932	ENDDO
[4309]	1933	!
[4438]	1934	!-- Get the new random seeds from last call at grid point ii
	1935	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1936	ENDDO
[4309]	1937	!
[4438]	1938	!-- For normalization to zero mean, sum-up the global random numers.
[4559]	1939	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
	1940	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
[4438]	1941	!-- also occur on the inner subdomains.
[4566]	1942	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1943	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1944	rand_av = rand_av + rand_it(k,i)
[2938]	1945	ENDDO
[4438]	1946	ENDDO
[4566]	1947
[4309]	1948	#if defined( __parallel )
[4438]	1949	!
	1950	!-- Sum-up the local averages of the random numbers
[4559]	1951	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	1952	#endif
[4438]	1953	rand_av = rand_av * nxz_inv
[4309]	1954	!
[4438]	1955	!-- Obtain zero mean
	1956	rand_it= rand_it - rand_av
[4309]	1957	!
[4438]	1958	!-- Now, compute the variance
[4566]	1959	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1960	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1961	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	1962	ENDDO
[4438]	1963	ENDDO
[2938]	1964
[4309]	1965	#if defined( __parallel )
[4438]	1966	!
	1967	!-- Sum-up the local quadratic averages of the random numbers
[4559]	1968	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	1969	#endif
[2938]	1970	!
[4438]	1971	!-- Compute standard deviation
	1972	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1973	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	1974	ELSE
	1975	rand_sigma_inv = 1.0_wp
[4309]	1976	ENDIF
	1977	!
[4438]	1978	!-- Normalize with standard deviation to obtain unit variance
	1979	rand_it = rand_it * rand_sigma_inv
	1980
	1981	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1982	!
[4559]	1983	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	1984	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	1985	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
	1986	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	1987	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
	1988	!-- In the second option, which performs better when the turbulent length scales are parametrized
	1989	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
[4438]	1990	IF ( compute_velocity_seeds_local ) THEN
[2938]	1991
[4438]	1992	f_n = 0.0_wp
	1993	DO i = nxl, nxr
	1994	DO k = nzb, nzt+1
	1995	DO ii = -n_x(k), n_x(k)
	1996	DO kk = -n_z(k), n_z(k)
	1997	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	1998	ENDDO
[2938]	1999	ENDDO
	2000	ENDDO
	2001	ENDDO
	2002
[4438]	2003	ELSE
[2938]	2004
[4438]	2005	f_n_l = 0.0_wp
	2006	DO i = nxl, nxr
	2007	DO k = nzb_y_stg, nzt_y_stg+1
	2008	DO ii = -n_x(k), n_x(k)
	2009	DO kk = -n_z(k), n_z(k)
	2010	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2011	ENDDO
	2012	ENDDO
	2013	ENDDO
	2014	ENDDO
[2938]	2015	!
[4438]	2016	!-- Gather velocity seeds of full subdomain
	2017	send_count = nzt_y_stg - nzb_y_stg + 1
	2018	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2019
	2020	#if defined( __parallel )
[4309]	2021	!
[4438]	2022	!-- Gather the processed velocity seed on south boundary mpi ranks.
[4559]	2023	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2024	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
[4309]	2025	!
[4438]	2026	!-- Gather the processed velocity seed on north boundary mpi ranks.
[4559]	2027	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2028	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
[2938]	2029	#else
[4438]	2030	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[4444]	2031	!
	2032	!-- Next line required to avoid compile errors because of unused dummy arguments
	2033	IF ( id_north == 0 ) id_south = 0
[2938]	2034	#endif
	2035
[4438]	2036	ENDIF
	2037
	2038	DEALLOCATE( rand_it )
	2039
	2040	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2041
[2938]	2042	END SUBROUTINE stg_generate_seed_xz
	2043
[4559]	2044	!--------------------------------------------------------------------------------------------------!
[3347]	2045	! Description:
	2046	! ------------
[4566]	2047	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
	2048	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
	2049	!> which is applied in state-of-the-art dispserion modelling.
[4559]	2050	!--------------------------------------------------------------------------------------------------!
[4566]	2051	SUBROUTINE parametrize_turbulence
[3347]	2052
[4566]	2053	INTEGER(iwp) :: k !< loop index in z-direction
[4559]	2054
[4566]	2055	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
	2056	REAL(wp) :: d_zi !< inverse boundary-layer depth
	2057	REAL(wp) :: length_scale_lon !< length scale in flow direction
	2058	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
	2059	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
	2060	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
	2061	REAL(wp) :: length_scale_vert !< length scale in vertical direction
	2062	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
	2063	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
	2064	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
	2065	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
	2066	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
	2067	REAL(wp) :: r31_zi !< r31 at boundary-layer top
	2068	REAL(wp) :: r32_zi !< r32 at boundary-layer top
	2069	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
	2070	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
	2071	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
	2072	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
	2073	REAL(wp) :: zzi !< ratio of z/zi
[4559]	2074
[4566]	2075	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
	2076	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
	2077	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
	2078
[3347]	2079	!
[4566]	2080	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
	2081	!-- criterion according to Heinze et al. (2017).
	2082	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
	2083	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
	2084	k_zi = MIN( k_zi, nzt )
[3347]	2085	!
[4566]	2086	!-- Calculate angle between flow direction and x-axis.
	2087	DO k = nzb+1, nzt + 1
	2088	IF ( u_init(k) /= 0.0_wp ) THEN
	2089	phi(k) = ATAN( v_init(k) / u_init(k) )
	2090	ELSE
	2091	phi(k) = 0.5 * pi
	2092	ENDIF
	2093	!
	2094	!-- Pre-calculate sine and cosine.
	2095	cos_phi(k) = COS( phi(k) )
	2096	sin_phi(k) = SIN( phi(k) )
	2097	ENDDO
	2098	!
	2099	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
	2100	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
	2101	!-- coincide with the grid axis. Hence, components are rotated after computation.
	2102	d_zi = 1.0_wp / zi_ribulk
	2103	DO k = nzb+1, k_zi
	2104
	2105	corr_term_uh = MERGE( 0.35_wp * ABS( &
	2106	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2107	)**( 2.0_wp / 3.0_wp ), &
	2108	0.0_wp, &
	2109	scale_l < 0.0_wp )
	2110	!
[4022]	2111	!-- Determine normalized height coordinate
[4566]	2112	zzi = zu(k) * d_zi
[3347]	2113	!
[4566]	2114	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
	2115	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
	2116	!-- variances cannot become negative, take the absolute values.
	2117	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
	2118	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
[4559]	2119
[4566]	2120	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
	2121	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
[4559]	2122	!
[4566]	2123	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as
	2124	!-- for u'w'.
	2125	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
	2126	!
[4559]	2127	!-- w'w'
[4566]	2128	r33(k) = scale_wm*2 ( &
	2129	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2130	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2131	)
[4559]	2132	!
[4566]	2133	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
	2134	!-- these are projected along the x- and y-direction. Note, it is assumed that
	2135	!-- the flux within the boundary points opposite to the vertical gradient.
	2136	rlon2 = scale_us*2 ( zzi - 1.0_wp )
	2137	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
	2138
	2139	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
	2140	- ( u_init(k+1) - u_init(k-1) ) )
	2141	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
	2142	- ( v_init(k+1) - v_init(k-1) ) )
[3347]	2143	!
[4566]	2144	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
	2145	!-- limited to the adjustment time scales.
	2146	tu(k) = MIN( dt_stg_adjust, &
	2147	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
	2148
	2149	tv(k) = tu(k)
	2150	tw(k) = tu(k)
	2151
	2152	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
	2153	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
	2154	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
	2155	!
	2156	!-- Assume isotropic turbulence length scales
	2157	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2158	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2159	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2160	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2161	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2162	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2163	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2164	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2165	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2166
[3347]	2167	ENDDO
[4566]	2168	!
	2169	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
	2170	!-- reduced to zero by a blending function.
	2171	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
	2172	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
	2173	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
[3347]	2174
[4566]	2175	time_scale_zi = tu(k_zi)
	2176	r11_zi = r11(k_zi)
	2177	r22_zi = r22(k_zi)
	2178	r33_zi = r33(k_zi)
	2179	r31_zi = r31(k_zi)
	2180	r32_zi = r32(k_zi)
	2181
	2182	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
	2183
	2184	DO k = k_zi+1, nzt+1
[3347]	2185	!
[4566]	2186	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2187	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
	2188	!
	2189	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
	2190	!-- the mergpe-function can crash if scale_l is zero.
	2191	r11(k) = r11_zi * blend
	2192	r22(k) = r22_zi * blend
	2193	r33(k) = r33_zi * blend
	2194	r31(k) = r31_zi * blend
	2195	r32(k) = r32_zi * blend
	2196	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
	2197
	2198	!
	2199	!-- Compute turbulent time scales according to Brost et al. (1982).
	2200	!-- Note, time scales are limited to the adjustment time scales.
	2201	tu(k) = time_scale_zi * blend
	2202	tv(k) = time_scale_zi * blend
	2203	tw(k) = time_scale_zi * blend
	2204
	2205	length_scale_lon = length_scale_lon_zi * blend
	2206	length_scale_lat = length_scale_lat_zi * blend
	2207	length_scale_vert = length_scale_vert_zi * blend
	2208	!
	2209	!-- Assume isotropic turbulence length scales
	2210	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2211	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2212	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2213	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2214	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2215	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2216	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2217	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2218	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2219	ENDDO
	2220	!
	2221	!-- Set bottom boundary condition for reynolds stresses
[3347]	2222	r11(nzb) = r11(nzb+1)
	2223	r22(nzb) = r22(nzb+1)
	2224	r33(nzb) = r33(nzb+1)
	2225
	2226	r21(nzb) = r11(nzb+1)
	2227	r31(nzb) = r31(nzb+1)
	2228	r32(nzb) = r32(nzb+1)
	2229
[4566]	2230	!
	2231	!-- Set bottom boundary condition for the length and time scales
	2232	nux(nzb) = nux(nzb+1)
	2233	nuy(nzb) = nuy(nzb+1)
	2234	nuz(nzb) = nuz(nzb+1)
	2235	nvx(nzb) = nvx(nzb+1)
	2236	nvy(nzb) = nvy(nzb+1)
	2237	nvz(nzb) = nvz(nzb+1)
	2238	nwx(nzb) = nwx(nzb+1)
	2239	nwy(nzb) = nwy(nzb+1)
	2240	nwz(nzb) = nwz(nzb+1)
[4559]	2241
[4566]	2242	tu(nzb) = tu(nzb+1)
	2243	tv(nzb) = tv(nzb+1)
	2244	tw(nzb) = tw(nzb+1)
[4559]	2245
[4566]	2246	adjustment_step = .TRUE.
	2247
	2248	END SUBROUTINE parametrize_turbulence
	2249
[4559]	2250	!--------------------------------------------------------------------------------------------------!
[3347]	2251	! Description:
	2252	! ------------
[4559]	2253	!> Calculate the coefficient matrix from the Lund rotation.
	2254	!--------------------------------------------------------------------------------------------------!
[3347]	2255	SUBROUTINE calc_coeff_matrix
	2256
[4559]	2257	INTEGER(iwp) :: k !< loop index in z-direction
	2258
[3347]	2259	!
	2260	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2261	DO k = nzb+1, nzt+1
[4022]	2262	IF ( r11(k) > 10E-6_wp ) THEN
[4566]	2263	a11(k) = SQRT( r11(k) )
[3347]	2264	a21(k) = r21(k) / a11(k)
	2265	a31(k) = r31(k) / a11(k)
	2266	ELSE
	2267	a11(k) = 10E-8_wp
	2268	a21(k) = 10E-8_wp
	2269	a31(k) = 10E-8_wp
	2270	ENDIF
	2271	ENDDO
	2272	DO k = nzb+1, nzt+1
[4566]	2273	a22(k) = r22(k) - a21(k)**2
[4022]	2274	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2275	a22(k) = SQRT( a22(k) )
[4566]	2276	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
	2277	ELSE
[3347]	2278	a22(k) = 10E-8_wp
	2279	a32(k) = 10E-8_wp
	2280	ENDIF
	2281	ENDDO
	2282	DO k = nzb+1, nzt+1
	2283	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2284	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2285	a33(k) = SQRT( a33(k) )
	2286	ELSE
	2287	a33(k) = 10E-8_wp
	2288	ENDIF
[4559]	2289	ENDDO
[3347]	2290	!
	2291	!-- Set bottom boundary condition
	2292	a11(nzb) = a11(nzb+1)
	2293	a22(nzb) = a22(nzb+1)
	2294	a21(nzb) = a21(nzb+1)
[4559]	2295	a33(nzb) = a33(nzb+1)
[3347]	2296	a31(nzb) = a31(nzb+1)
[4559]	2297	a32(nzb) = a32(nzb+1)
[3347]	2298
	2299	END SUBROUTINE calc_coeff_matrix
[4559]	2300
	2301	!--------------------------------------------------------------------------------------------------!
[3347]	2302	! Description:
	2303	! ------------
[4559]	2304	!> This routine controls the re-adjustment of the turbulence statistics used for generating
	2305	!> turbulence at the lateral boundaries.
	2306	!--------------------------------------------------------------------------------------------------!
[3347]	2307	SUBROUTINE stg_adjust
	2308
[3987]	2309	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2310	!
[4559]	2311	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
	2312	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
	2313	!-- nevertheless, the boundary-layer depth need to determined first.
	2314	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2315	CALL nesting_offl_calc_zi
[4022]	2316	!
[4559]	2317	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
[3347]	2318	CALL calc_scaling_variables
	2319	!
[4566]	2320	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
	2321	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
	2322	!-- velocity and velocity scale.
	2323	CALL parametrize_turbulence
[3347]	2324	!
[4566]	2325	!-- Calculate coefficient matrix from Reynolds stress tensor
	2326	!-- (Lund rotation)
[3347]	2327	CALL calc_coeff_matrix
	2328	!
[4566]	2329	!-- Setup filter functions according to updated length scales.
	2330	CALL stg_setup_filter_function
[3347]	2331	!
	2332	!-- Reset time counter for controlling next adjustment to zero
	2333	time_stg_adjust = 0.0_wp
[3987]	2334
	2335	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[4559]	2336
	2337	END SUBROUTINE stg_adjust
	2338
	2339
	2340	!--------------------------------------------------------------------------------------------------!
[3347]	2341	! Description:
	2342	! ------------
[4559]	2343	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
	2344	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
	2345	!> scale, and Obukhov length.
	2346	!--------------------------------------------------------------------------------------------------!
[3347]	2347	SUBROUTINE calc_scaling_variables
	2348
[4559]	2349	INTEGER(iwp) :: i !< loop index in x-direction
	2350	INTEGER(iwp) :: j !< loop index in y-direction
	2351	INTEGER(iwp) :: k !< loop index in z-direction
	2352	INTEGER(iwp) :: m !< surface element index
[3347]	2353
[4559]	2354	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
	2355	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2356	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2357	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
	2358	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2359	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2360	REAL(wp) :: w_convective !< convective velocity scale
	2361
[3347]	2362	!
[4559]	2363	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
	2364	!-- model domain.
[3937]	2365	pt_surf_mean_l = 0.0_wp
	2366	shf_mean_l = 0.0_wp
	2367	scale_l_l = 0.0_wp
	2368	friction_vel_l = 0.0_wp
[3347]	2369	DO m = 1, surf_def_h(0)%ns
[3937]	2370	i = surf_def_h(0)%i(m)
	2371	j = surf_def_h(0)%j(m)
	2372	k = surf_def_h(0)%k(m)
	2373	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2374	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2375	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2376	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[4559]	2377	ENDDO
[3347]	2378	DO m = 1, surf_lsm_h%ns
[3937]	2379	i = surf_lsm_h%i(m)
	2380	j = surf_lsm_h%j(m)
	2381	k = surf_lsm_h%k(m)
	2382	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2383	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2384	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2385	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2386	ENDDO
	2387	DO m = 1, surf_usm_h%ns
[3937]	2388	i = surf_usm_h%i(m)
	2389	j = surf_usm_h%j(m)
	2390	k = surf_usm_h%k(m)
	2391	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2392	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2393	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2394	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2395	ENDDO
[4559]	2396
[3347]	2397	#if defined( __parallel )
[4559]	2398	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2399	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2400	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2401	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
[3347]	2402	#else
[3937]	2403	scale_us = friction_vel_l
	2404	shf_mean = shf_mean_l
	2405	scale_l = scale_l_l
	2406	pt_surf_mean = pt_surf_mean_l
[3347]	2407	#endif
	2408
[4566]	2409	scale_us = scale_us * d_nxy
	2410	shf_mean = shf_mean * d_nxy
	2411	scale_l = scale_l * d_nxy
	2412	pt_surf_mean = pt_surf_mean * d_nxy
[3347]	2413	!
[4559]	2414	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
	2415	!-- convective velocity scale to zero.
[3347]	2416	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2417	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2418	ELSE
	2419	w_convective = 0.0_wp
	2420	ENDIF
	2421	!
[4566]	2422	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
	2423	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
	2424	!-- value of friction velocity for the reynolds-stress parametrization.
	2425	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
	2426	!
[4559]	2427	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
	2428	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
[3347]	2429	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
[4559]	2430
[3347]	2431	END SUBROUTINE calc_scaling_variables
	2432
[2259]	2433	END MODULE synthetic_turbulence_generator_mod

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