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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4628

Last change on this file since 4628 was 4603, checked in by suehring, 4 years ago
Synthetic turbulence generator: Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not initialized properly
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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	! -----------------
[4603]	22	!
	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4603 2020-07-14 16:08:30Z raasch $
[4603]	27	! Bugfix in initialization from ASCII file - x-length scales at the bottom boundary were not
	28	! initialized properly
	29	!
	30	! 4566 2020-06-16 10:11:51Z suehring
[4566]	31	! - revise parametrization for reynolds-stress components, turbulent length- and time scales
	32	! - revise computation of velocity disturbances to be consistent to Xie and Castro (2008)
	33	! - change default value of time interval to adjust turbulence parametrization
	34	! - bugfix in computation of amplitude-tensor (vertical flux of horizontal momentum)
	35	!
	36	! 4562 2020-06-12 08:38:47Z raasch
[4562]	37	! Parts of r4559 re-formatted
	38	!
	39	! 4559 2020-06-11 08:51:48Z raasch
[4559]	40	! File re-formatted to follow the PALM coding standard
	41	!
	42	! 4535 2020-05-15 12:07:23Z raasch
	43	! Bugfix for restart data format query
	44	!
[4535]	45	! 4495 2020-04-13 20:11:20Z raasch
[4559]	46	! Restart data handling with MPI-IO added
	47	!
[4495]	48	! 4481 2020-03-31 18:55:54Z maronga
[4559]	49	! Bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
	50	!
[4444]	51	! 4442 2020-03-04 19:21:13Z suehring
[4442]	52	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	53	! (was accidantly changed).
[4559]	54	!
[4442]	55	! 4441 2020-03-04 19:20:35Z suehring
[4440]	56	! Correct misplaced preprocessor directive
[4559]	57	!
[4440]	58	! 4438 2020-03-03 20:49:28Z suehring
[4438]	59	! Performance optimizations in velocity-seed calculation:
[4559]	60	! - Random number array is only defined and computed locally (except for normalization to zero mean
	61	! and unit variance)
	62	! - Parallel random number generator is applied independent on the 2D random numbers in other
	63	! routines
	64	! - Option to decide wheter velocity seeds are computed locally without any further communication
	65	! or are computed by all processes along the communicator
	66	!
[4438]	67	! 4346 2019-12-18 11:55:56Z motisi
[4559]	68	! Introduction of wall_flags_total_0, which currently sets bits based on static topography
	69	! information used in wall_flags_static_0
	70	!
[4346]	71	! 4335 2019-12-12 16:39:05Z suehring
[4335]	72	! Commentation of last commit
[4559]	73	!
[4335]	74	! 4332 2019-12-10 19:44:12Z suehring
[4559]	75	! Limit initial velocity seeds in restart runs, if not the seed calculation may become unstable.
	76	! Further, minor bugfix in initial velocity seed calculation.
	77	!
[4332]	78	! 4329 2019-12-10 15:46:36Z motisi
[4329]	79	! Renamed wall_flags_0 to wall_flags_static_0
[4559]	80	!
[4329]	81	! 4309 2019-11-26 18:49:59Z suehring
[4559]	82	! Computation of velocity seeds optimized. This implies that random numbers are computed now using
	83	! the parallel random number generator. Random numbers are now only computed and normalized locally,
	84	! while distributed over all mpi ranks afterwards, instead of computing random numbers on a global
	85	! array.
	86	! Further, the number of calls for the time-consuming velocity-seed generation is reduced - now the
	87	! left and right, as well as the north and south boundary share the same velocity-seed matrices.
	88	!
[4309]	89	! 4182 2019-08-22 15:20:23Z scharf
[4182]	90	! Corrected "Former revisions" section
[4559]	91	!
[4182]	92	! 4148 2019-08-08 11:26:00Z suehring
[4148]	93	! Remove unused variable
[4559]	94	!
[4148]	95	! 4144 2019-08-06 09:11:47Z raasch
[4559]	96	! Relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	97	!
[4144]	98	! 4071 2019-07-03 20:02:00Z suehring
[4559]	99	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow information is not read from
	100	! file.
	101	!
[4071]	102	! 4022 2019-06-12 11:52:39Z suehring
[4022]	103	! Several bugfixes and improvements
[4559]	104	! - Revise bias correction of the imposed perturbations (correction via volume flow can create
	105	! instabilities in case the mean volume flow is close to zero)
	106	! - Introduce lower limits in calculation of coefficient matrix, else the calculation may become
	107	! numerically unstable
	108	! - Impose perturbations every timestep, even though no new set of perturbations is generated in
	109	! case dt_stg_call /= dt_3d
	110	! - Implement a gradual decrease of Reynolds stress and length scales above ABL height (within 1
	111	! length scale above ABL depth to 1/10) rather than a discontinuous decrease
[4022]	112	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
[4559]	113	!
[4022]	114	! 3987 2019-05-22 09:52:13Z kanani
[3987]	115	! Introduce alternative switch for debug output during timestepping
[4559]	116	!
[3987]	117	! 3938 2019-04-29 16:06:25Z suehring
[3938]	118	! Remove unused variables
[4559]	119	!
[3938]	120	! 3937 2019-04-29 15:09:07Z suehring
[4559]	121	! Minor bugfix in case of a very early restart where mc_factor is sill not present.
	122	! Some modification and fixing of potential bugs in the calculation of scaling parameters used for
	123	! synthetic turbulence parametrization.
	124	!
[3937]	125	! 3909 2019-04-17 09:13:25Z suehring
[3909]	126	! Minor bugfix for last commit
[4559]	127	!
[3909]	128	! 3900 2019-04-16 15:17:43Z suehring
[3900]	129	! Missing re-calculation of perturbation seeds in case of restarts
[4559]	130	!
[3900]	131	! 3891 2019-04-12 17:52:01Z suehring
[4559]	132	! Bugfix in initialization in case of restart runs.
	133	!
[3891]	134	! 3885 2019-04-11 11:29:34Z kanani
[4559]	135	! Changes related to global restructuring of location messages and introduction of additional debug
	136	! messages
	137	!
	138	!
	139	! Removed unused variables
	140	!
[3775]	141	! 3719 2019-02-06 13:10:18Z kanani
[4559]	142	! Removed log_point measurement from stg_init, since this part is counted to log_point(2)
	143	! 'initialization' already. Moved other log_points to calls of the subroutines in time_integration
	144	! for better overview.
	145	!
[4182]	146	! 2259 2017-06-08 09:09:11Z gronemeier
	147	! Initial revision
[3044]	148	!
[4182]	149	! Authors:
	150	! --------
	151	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	152	!
	153	!
[2259]	154	! Description:
	155	! ------------
[4559]	156	!> The module generates turbulence at the inflow boundary based on a method by Xie and Castro (2008)
	157	!> utilizing a Lund rotation (Lund, 1998) and a mass-flux correction by Kim et al. (2013).
	158	!> The turbulence is correlated based on length scales in y- and z-direction and a time scale for
	159	!> each velocity component. The profiles of length and time scales, mean u, v, w, e and pt, and all
	160	!> components of the Reynolds stress tensor can be either read from file STG_PROFILES, or will be
	161	!> parametrized within the boundary layer.
[2259]	162	!>
[4566]	163	!> @todo Enable cyclic_fill
[4559]	164	!> Implement turbulence generation for e and pt
[2259]	165	!> @note <Enter notes on the module>
[4559]	166	!> @bug Height information from input file is not used. Profiles from input must match with current
	167	!> PALM grid.
	168	!> In case of restart, velocity seeds differ from precursor run if a11, a22, or a33 are zero.
	169	!--------------------------------------------------------------------------------------------------!
[2259]	170	MODULE synthetic_turbulence_generator_mod
	171
	172
[4559]	173	USE arrays_3d, &
	174	ONLY: dzw, &
	175	ddzw, &
	176	drho_air, &
	177	mean_inflow_profiles, &
	178	pt, &
	179	pt_init, &
	180	q, &
	181	q_init, &
	182	u, &
	183	u_init, &
	184	v, &
	185	v_init, &
	186	w, &
	187	zu, &
[4022]	188	zw
[2259]	189
[4559]	190	USE basic_constants_and_equations_mod, &
	191	ONLY: g, &
	192	kappa, &
[4022]	193	pi
[2259]	194
[4559]	195	USE control_parameters, &
	196	ONLY: bc_lr, &
	197	bc_ns, &
	198	child_domain, &
	199	coupling_char, &
	200	debug_output_timestep, &
	201	dt_3d, &
	202	e_init, &
	203	humidity, &
	204	initializing_actions, &
	205	intermediate_timestep_count, &
	206	intermediate_timestep_count_max, &
	207	length, &
	208	message_string, &
	209	nesting_offline, &
	210	neutral, &
	211	num_mean_inflow_profiles, &
	212	random_generator, &
	213	rans_mode, &
	214	restart_data_format_output, &
	215	restart_string, &
	216	syn_turb_gen, &
	217	time_since_reference_point, &
[4022]	218	turbulent_inflow
[4438]	219
[4559]	220	USE cpulog, &
	221	ONLY: cpu_log, &
[4438]	222	log_point_s
	223
[4559]	224	USE grid_variables, &
	225	ONLY: ddx, &
	226	ddy, &
	227	dx, &
[4022]	228	dy
[2259]	229
[4559]	230	USE indices, &
	231	ONLY: nbgp, &
	232	nz, &
	233	nzb, &
	234	nzt, &
	235	nx, &
	236	nxl, &
	237	nxlu, &
	238	nxr, &
	239	ny, &
	240	nys, &
	241	nysv, &
	242	nyn, &
[4346]	243	wall_flags_total_0
[2259]	244
	245	USE kinds
	246
[2967]	247	#if defined( __parallel ) && !defined( __mpifh )
[2259]	248	USE MPI
[2841]	249	#endif
[2259]	250
[4559]	251	USE nesting_offl_mod, &
	252	ONLY: nesting_offl_calc_zi, &
[4022]	253	zi_ribulk
[3347]	254
[4559]	255	USE pegrid, &
	256	ONLY: comm1dx, &
	257	comm1dy, &
	258	comm2d, &
	259	ierr, &
	260	myidx, &
	261	myidy, &
[4022]	262	pdims
[4438]	263
[4559]	264	USE pmc_interface, &
[4022]	265	ONLY : rans_mode_parent
[4438]	266
[4559]	267	USE random_generator_parallel, &
	268	ONLY: init_parallel_random_generator, &
	269	random_dummy, &
	270	random_number_parallel, &
[4438]	271	random_seed_parallel
[2259]	272
[4495]	273	USE restart_data_mpi_io_mod, &
	274	ONLY: rrd_mpi_io, &
	275	wrd_mpi_io
	276
[4559]	277	USE transpose_indices, &
	278	ONLY: nzb_x, &
	279	nzt_x
[2259]	280
[4559]	281	USE surface_mod, &
	282	ONLY: surf_def_h, &
	283	surf_lsm_h, &
[4438]	284	surf_usm_h
[2259]	285
	286	IMPLICIT NONE
	287
[2967]	288	#if defined( __parallel ) && defined( __mpifh )
[2841]	289	INCLUDE "mpif.h"
	290	#endif
	291
[3182]	292
[3038]	293	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	294	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	295	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	296	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4566]	297	INTEGER(iwp) :: k_zi !< vertical index of boundary-layer top
	298	INTEGER(iwp) :: mergp_limit = 1000 !< maximum length scale (in gp)
	299	INTEGER(iwp) :: mergp_x !< maximum length scale in x (in gp)
	300	INTEGER(iwp) :: mergp_xy !< maximum horizontal length scale (in gp)
	301	INTEGER(iwp) :: mergp_y !< maximum length scale in y (in gp)
	302	INTEGER(iwp) :: mergp_z !< maximum length scale in z (in gp)
[3038]	303	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	304	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	305	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	306	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4444]	307	#if defined( __parallel )
[4309]	308	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	309	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	310	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	311	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[4444]	312	#endif
[2259]	313
[4559]	314	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	315	!< required for bias correction of imposed perturbations
	316	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	317	!< required for bias correction of imposed perturbations
	318
[4444]	319	#if defined( __parallel )
[3347]	320	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
[4444]	324	#endif
[3347]	325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	329	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	330	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	331	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	332	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	333	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	334
[4559]	335	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	336	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	337	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	338	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
[4438]	339
[2259]	340
[4566]	341	LOGICAL :: adjustment_step = .FALSE. !< control flag indicating that time and lenght scales have been updated and
	342	!< no time correlation to the timestep before should be considered
[4559]	343	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally
	344	!< or if computation is distributed over several processes
	345	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file
	346	!< (.FALSE.) or if it parametrized
	347	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
	348	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
[2259]	349
[4559]	350
	351	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	352	!< scales above the boundary layer
[4566]	353	REAL(wp) :: blend_coeff = -9.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
[4559]	354	!< one length scale above ABL top
	355	REAL(wp) :: d_l !< blend_coeff/length_scale
[4566]	356	REAL(wp) :: d_nxy !< inverse of the total number of xy-grid points
	357	REAL(wp) :: dt_stg_adjust = 1800.0_wp !< time interval for adjusting turbulence statistics
[4559]	358	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
	359	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	360	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	361	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	362	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	363	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	364
	365	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
	366
	367
	368	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	369	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	370	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	371	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	372	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	373	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	374
	375	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	376	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	377	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	378	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	379	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	380	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	381	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	382	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	383	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
	384
	385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	390	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	391	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	392	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	393	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	394	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	395	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	396	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	397	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	398	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	399	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	400	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	401	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	402	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	403	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	404	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	405	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	406
[4566]	407	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< disturbances for parallel/crosswind/vertical component at north/south boundary
	408	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< disturbances for parallel/crosswind/vertical component at north/south boundary
[4559]	409
[2259]	410	!
	411	!-- PALM interfaces:
[3347]	412	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	413	INTERFACE stg_adjust
	414	MODULE PROCEDURE stg_adjust
	415	END INTERFACE stg_adjust
	416	!
[2259]	417	!-- Input parameter checks to be done in check_parameters
	418	INTERFACE stg_check_parameters
	419	MODULE PROCEDURE stg_check_parameters
	420	END INTERFACE stg_check_parameters
	421
	422	!
	423	!-- Calculate filter functions
	424	INTERFACE stg_filter_func
	425	MODULE PROCEDURE stg_filter_func
	426	END INTERFACE stg_filter_func
	427
	428	!
[2938]	429	!-- Generate velocity seeds at south and north domain boundary
	430	INTERFACE stg_generate_seed_xz
	431	MODULE PROCEDURE stg_generate_seed_xz
	432	END INTERFACE stg_generate_seed_xz
	433	!
	434	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	435	INTERFACE stg_generate_seed_yz
	436	MODULE PROCEDURE stg_generate_seed_yz
	437	END INTERFACE stg_generate_seed_yz
	438
	439	!
	440	!-- Output of information to the header file
	441	INTERFACE stg_header
	442	MODULE PROCEDURE stg_header
	443	END INTERFACE stg_header
	444
	445	!
	446	!-- Initialization actions
	447	INTERFACE stg_init
	448	MODULE PROCEDURE stg_init
	449	END INTERFACE stg_init
	450
	451	!
	452	!-- Main procedure of synth. turb. gen.
	453	INTERFACE stg_main
	454	MODULE PROCEDURE stg_main
	455	END INTERFACE stg_main
	456
	457	!
	458	!-- Reading of NAMELIST parameters
	459	INTERFACE stg_parin
	460	MODULE PROCEDURE stg_parin
	461	END INTERFACE stg_parin
	462
	463	!
	464	!-- Reading of parameters for restart runs
[2894]	465	INTERFACE stg_rrd_global
[4495]	466	MODULE PROCEDURE stg_rrd_global_ftn
	467	MODULE PROCEDURE stg_rrd_global_mpi
[2894]	468	END INTERFACE stg_rrd_global
[2259]	469
	470	!
	471	!-- Writing of binary output for restart runs
[2894]	472	INTERFACE stg_wrd_global
	473	MODULE PROCEDURE stg_wrd_global
	474	END INTERFACE stg_wrd_global
[2259]	475
	476	SAVE
	477
	478	PRIVATE
	479
	480	!
	481	!-- Public interfaces
[4559]	482	PUBLIC stg_adjust, &
	483	stg_check_parameters, &
	484	stg_header, &
	485	stg_init, &
	486	stg_main, &
	487	stg_parin, &
	488	stg_rrd_global, &
	489	stg_wrd_global
[2259]	490
	491	!
	492	!-- Public variables
[4559]	493	PUBLIC dt_stg_call, &
	494	dt_stg_adjust, &
	495	id_stg_left, &
	496	id_stg_north, &
	497	id_stg_right, &
	498	id_stg_south, &
	499	parametrize_inflow_turbulence, &
	500	time_stg_adjust, &
	501	time_stg_call, &
	502	use_syn_turb_gen
[2259]	503
	504
	505	CONTAINS
	506
	507
[4559]	508	!--------------------------------------------------------------------------------------------------!
[2259]	509	! Description:
	510	! ------------
	511	!> Check parameters routine for synthetic turbulence generator
[4559]	512	!--------------------------------------------------------------------------------------------------!
[2259]	513	SUBROUTINE stg_check_parameters
	514
[4559]	515	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
[3182]	516	nesting_offline ) THEN
[4559]	517	message_string = 'Synthetic turbulence generator is required ' // &
	518	'if offline nesting is applied and PALM operates in LES mode.'
[3376]	519	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	520	ENDIF
	521
[4559]	522	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	523	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[4559]	524	message_string = 'Synthetic turbulence generator is required when nesting is applied ' // &
	525	'and parent operates in RANS-mode but current child in LES mode.'
[3376]	526	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	527	ENDIF
	528
[2776]	529	IF ( use_syn_turb_gen ) THEN
[2259]	530
[4559]	531	IF ( child_domain .AND. .NOT. rans_mode .AND. .NOT. rans_mode_parent ) THEN
	532	message_string = 'Using synthetic turbulence generator is not allowed in LES-LES nesting.'
[3579]	533	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
[4559]	534
[3579]	535	ENDIF
[4559]	536
	537	IF ( child_domain .AND. rans_mode .AND. rans_mode_parent ) THEN
	538	message_string = 'Using synthetic turbulence generator is not allowed in RANS-RANS nesting.'
[3579]	539	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
[4559]	540
[3579]	541	ENDIF
[4559]	542
	543	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	544
	545	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	546	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	547	message_string = 'Using synthetic turbulence generator requires ' // &
	548	'%initializing_actions = "set_constant_profiles" or ' // &
	549	' "read_restart_data", if not offline nesting is applied.'
[2938]	550	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	551	ENDIF
	552
	553	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
[4559]	554	message_string = 'Using synthetic turbulence generator requires &bc_lr = ' // &
	555	' "dirichlet/radiation", if not offline nesting is applied.'
[2938]	556	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	557	ENDIF
	558	IF ( bc_ns /= 'cyclic' ) THEN
[4559]	559	message_string = 'Using synthetic turbulence generator requires &bc_ns = ' // &
	560	' "cyclic", if not offline nesting is applied.'
[2938]	561	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	562	ENDIF
	563
[2259]	564	ENDIF
	565
	566	IF ( turbulent_inflow ) THEN
[4559]	567	message_string = 'Using synthetic turbulence generator in combination ' // &
	568	'&with turbulent_inflow = .T. is not allowed'
[2259]	569	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	570	ENDIF
[4309]	571	!
	572	!-- Synthetic turbulence generator requires the parallel random generator
	573	IF ( random_generator /= 'random-parallel' ) THEN
[4559]	574	message_string = 'Using synthetic turbulence generator requires random_generator = ' // &
	575	'random-parallel.'
[4309]	576	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	577	ENDIF
[2259]	578
	579	ENDIF
	580
	581	END SUBROUTINE stg_check_parameters
	582
	583
[4559]	584	!--------------------------------------------------------------------------------------------------!
[2259]	585	! Description:
	586	! ------------
	587	!> Header output for synthetic turbulence generator
[4559]	588	!--------------------------------------------------------------------------------------------------!
[2259]	589	SUBROUTINE stg_header ( io )
	590
[4559]	591	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
[2259]	592
	593	!
	594	!-- Write synthetic turbulence generator Header
	595	WRITE( io, 1 )
[2776]	596	IF ( use_syn_turb_gen ) THEN
[2259]	597	WRITE( io, 2 )
	598	ELSE
	599	WRITE( io, 3 )
	600	ENDIF
[4559]	601
[3347]	602	IF ( parametrize_inflow_turbulence ) THEN
	603	WRITE( io, 4 ) dt_stg_adjust
	604	ELSE
	605	WRITE( io, 5 )
	606	ENDIF
[2259]	607
[4559]	608	1 FORMAT (//' Synthetic turbulence generator information:'/ &
[2259]	609	' ------------------------------------------'/)
[3347]	610	2 FORMAT (' synthetic turbulence generator is switched on')
	611	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	612	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	613	5 FORMAT (' imposed turbulence is read from file' )
[2259]	614
	615	END SUBROUTINE stg_header
	616
	617
[4559]	618	!--------------------------------------------------------------------------------------------------!
[2259]	619	! Description:
	620	! ------------
	621	!> Initialization of the synthetic turbulence generator
[4559]	622	!--------------------------------------------------------------------------------------------------!
[2259]	623	SUBROUTINE stg_init
	624
[2669]	625	#if defined( __parallel )
[4559]	626	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	627	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob = 0 !< dummy variable
[2669]	628	#endif
[2259]	629
[4559]	630	INTEGER(iwp) :: i !> grid index in x-direction
	631	INTEGER(iwp) :: j !> loop index
	632	INTEGER(iwp) :: k !< index
[4444]	633	#if defined( __parallel )
[4559]	634	INTEGER(iwp) :: newtype !< dummy MPI type
	635	INTEGER(iwp) :: realsize !< size of REAL variables
[4444]	636	#endif
[4309]	637
[4022]	638	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	639	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[4559]	640
	641
	642	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
	643
[2259]	644	!
	645	!-- Dummy variables used for reading profiles
[4559]	646	REAL(wp) :: d1 !< u profile
	647	REAL(wp) :: d2 !< v profile
	648	REAL(wp) :: d3 !< w profile
	649	REAL(wp) :: d5 !< e profile
	650	REAL(wp) :: luy !< length scale for u in y direction
	651	REAL(wp) :: luz !< length scale for u in z direction
	652	REAL(wp) :: lvy !< length scale for v in y direction
	653	REAL(wp) :: lvz !< length scale for v in z direction
	654	REAL(wp) :: lwy !< length scale for w in y direction
	655	REAL(wp) :: lwz !< length scale for w in z direction
[4444]	656	#if defined( __parallel )
[4559]	657	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[4444]	658	#endif
[4559]	659	REAL(wp) :: zz !< height
[2259]	660
[2938]	661
[2259]	662	#if defined( __parallel )
	663	CALL MPI_BARRIER( comm2d, ierr )
	664	#endif
[4438]	665	!
[4559]	666	!-- Create mpi-datatypes for exchange in case of non-local but distributed computation of the
	667	!-- velocity seeds. This option is useful in case large turbulent length scales are present, where
	668	!-- the computational effort becomes large and needs to be parallelized. For parameterized turbulence
	669	!-- the length scales are small and computing the velocity seeds locally is faster (no overhead by
	670	!-- communication).
[4438]	671	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	672	#if defined( __parallel )
[4559]	673	!
[4438]	674	!-- Determine processor decomposition of z-axis along x- and y-direction
	675	nnz = nz / pdims(1)
	676	nzb_x_stg = 1 + myidx * INT( nnz )
	677	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[4559]	678
	679	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[4438]	680	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[4559]	681
	682	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
[4438]	683	.AND. .NOT. rans_mode ) ) THEN
	684	nnz = nz / pdims(2)
	685	nzb_y_stg = 1 + myidy * INT( nnz )
	686	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[4559]	687
	688	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[4438]	689	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	690	ENDIF
[4559]	691
	692	!
	693	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted velocity seeds
[4438]	694	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	695	extent = 1 * realsize
[4559]	696	!
	697	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz layer
[4438]	698	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[4559]	699	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
[4438]	700	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	701	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	702	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	703	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	704
[4438]	705	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[4559]	706	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
[4438]	707	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	708	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	709	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	710	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	711
	712	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	713	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[4559]	714
[4438]	715	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	716	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[4559]	717
[4438]	718	DO j = 1, pdims(1)
	719	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	720	ENDDO
[4559]	721	!
	722	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz layer
[4438]	723	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	724	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	725	.AND. .NOT. rans_mode ) ) THEN
	726	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	727	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	728	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	729	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	730	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	731
[4438]	732	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	733	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	734	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	735	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	736	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	737	CALL MPI_TYPE_FREE( newtype, ierr )
[4559]	738
	739	! Receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	740	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
[4559]	741
[4438]	742	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	743	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
[4559]	744
[4438]	745	DO j = 1, pdims(2)
	746	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	747	ENDDO
[4559]	748
[4438]	749	ENDIF
[4440]	750	#endif
[2938]	751	ENDIF
[2259]	752	!
[4071]	753	!-- Allocate required arrays.
[4559]	754	!-- In case no offline nesting or self nesting is used, the arrary mean_inflow profiles is required.
	755	!-- Check if it is already allocated, else allocate and initialize it appropriately. Note, in case
	756	!-- turbulence and inflow information is read from file, mean_inflow_profiles is already allocated
	757	!-- and initialized appropriately.
	758	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	759	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	760	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	761	mean_inflow_profiles = 0.0_wp
	762	mean_inflow_profiles(:,1) = u_init
	763	mean_inflow_profiles(:,2) = v_init
	764	!
[4559]	765	!-- Even though potential temperature and humidity are not perturbed, they need to be
	766	!-- initialized appropriately.
	767	IF ( .NOT. neutral ) &
[4071]	768	mean_inflow_profiles(:,4) = pt_init
[4559]	769	IF ( humidity ) &
	770	mean_inflow_profiles(:,6) = q_init
	771	ENDIF
[3347]	772	ENDIF
[4566]	773	!
	774	!-- Assign initial profiles. Note, this is only required if turbulent inflow from the left is
	775	!-- desired, not in case of any of the nesting (offline or self nesting) approaches.
	776	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	777	u_init = mean_inflow_profiles(:,1)
	778	v_init = mean_inflow_profiles(:,2)
	779	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	780	ENDIF
[2259]	781
[4559]	782	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	783	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	784	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	785	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	786	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	787	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	788	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	789	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	790
[4566]	791	r11 = 0.0_wp
	792	r21 = 0.0_wp
	793	r22 = 0.0_wp
	794	r31 = 0.0_wp
	795	r32 = 0.0_wp
	796	r33 = 0.0_wp
	797	tu = 0.0_wp
	798	tv = 0.0_wp
	799	tw = 0.0_wp
	800
[4438]	801	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	802	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	803	dist_xz = 0.0_wp
	804	dist_yz = 0.0_wp
	805	!
[2259]	806	!-- Read inflow profile
	807	!-- Height levels of profiles in input profile is as follows:
[4559]	808	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5 zw: lwy, lwz, tw, r31, r32, r33, d3
[2259]	809	!-- WARNING: zz is not used at the moment
[4559]	810	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), EXIST = file_stg_exist )
[2259]	811
[2938]	812	IF ( file_stg_exist ) THEN
[2259]	813
[4559]	814	OPEN( 90, FILE = 'STG_PROFILES' // TRIM( coupling_char ), STATUS = 'OLD', FORM = 'FORMATTED' )
[2938]	815	!
	816	!-- Skip header
	817	READ( 90, * )
[2259]	818
[4603]	819	DO k = nzb, nzt
[4559]	820	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), r11(k), r21(k), &
	821	r22(k), r31(k), r32(k), r33(k), d1, d2, d3, d5
[2938]	822
[2259]	823	!
[4559]	824	!-- Convert length scales from meter to number of grid points.
[4603]	825	IF ( k /= nzb ) THEN
	826	nuz(k) = INT( luz * ddzw(k) )
	827	nvz(k) = INT( lvz * ddzw(k) )
	828	nwz(k) = INT( lwz * ddzw(k) )
	829	ELSE
	830	nuz(k) = INT( luz * ddzw(k+1) )
	831	nvz(k) = INT( lvz * ddzw(k+1) )
	832	nwz(k) = INT( lwz * ddzw(k+1) )
	833	ENDIF
	834
[2938]	835	nuy(k) = INT( luy * ddy )
	836	nvy(k) = INT( lvy * ddy )
	837	nwy(k) = INT( lwy * ddy )
	838	!
[4603]	839	!-- Set length scales in x-direction. As a workaround assume isotropic turbulence in x- and
	840	!-- y-direction.
[2938]	841	nwx(k) = nwy(k)
	842	nvx(k) = nvy(k)
	843	nux(k) = nuy(k)
	844	!
	845	!-- Save Mean inflow profiles
	846	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	847	mean_inflow_profiles(k,1) = d1
	848	mean_inflow_profiles(k,2) = d2
	849	! mean_inflow_profiles(k,4) = d4
	850	mean_inflow_profiles(k,5) = d5
	851	ENDIF
	852	ENDDO
[3182]	853	!
[4603]	854	!-- Set length scales at the surface and top boundary. At the surface the lengths scales are
	855	!-- simply overwritten.
	856	nwx(nzb) = nwy(nzb+1)
	857	nvx(nzb) = nvy(nzb+1)
	858	nux(nzb) = nuy(nzb+1)
[4559]	859	nuy(nzb) = nuy(nzb+1)
[3182]	860	nuz(nzb) = nuz(nzb+1)
	861	nvy(nzb) = nvy(nzb+1)
	862	nvz(nzb) = nvz(nzb+1)
	863	nwy(nzb) = nwy(nzb+1)
	864	nwz(nzb) = nwz(nzb+1)
[4559]	865
[4603]	866	nwx(nzt+1) = nwy(nzt)
	867	nvx(nzt+1) = nvy(nzt)
	868	nux(nzt+1) = nuy(nzt)
	869	nuy(nzt+1) = nuy(nzt)
	870	nuz(nzt+1) = nuz(nzt)
	871	nvy(nzt+1) = nvy(nzt)
	872	nvz(nzt+1) = nvz(nzt)
	873	nwy(nzt+1) = nwy(nzt)
	874	nwz(nzt+1) = nwz(nzt)
	875
[2938]	876	CLOSE( 90 )
[3347]	877	!
[4559]	878	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3347]	879	CALL calc_coeff_matrix
	880	!
[4559]	881	!-- No information about turbulence and its length scales are available. Instead, parametrize
	882	!-- turbulence which is imposed at the boundaries. Set flag which indicates that turbulence is
	883	!-- parametrized, which is done later when energy-balance models are already initialized. This is
	884	!-- because the STG needs information about surface properties such as roughness to build
	885	!-- 'realistic' turbulence profiles.
[2938]	886	ELSE
[2259]	887	!
[4566]	888	!-- Precalulate the inversion number of xy-grid points - later used for mass conservation
	889	d_nxy = 1.0_wp / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[4022]	890	!
[3347]	891	!-- Set flag indicating that turbulence is parametrized
	892	parametrize_inflow_turbulence = .TRUE.
	893	!
[4559]	894	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the
	895	!-- case no offline or self nesting is applied but synthetic turbulence shall be parametrized
	896	!-- nevertheless, the boundary-layer depth needs to be determined first.
	897	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
[4022]	898	CALL nesting_offl_calc_zi
	899	!
[4559]	900	!-- Determine boundary-layer depth, which is used to initialize lenght scales
[3347]	901	CALL calc_scaling_variables
	902	!
[4559]	903	!-- Parametrize Reynolds-stress tensor, diagonal elements as well as r21 (v'u'), r31 (w'u'),
	904	!-- r32 (w'v'). Parametrization follows Rotach et al. (1996) and is based on boundary-layer depth,
	905	!-- friction velocity and velocity scale.
[4566]	906	CALL parametrize_turbulence
[4559]	907	!
	908	!-- Calculate coefficient matrix from Reynolds stress tensor (Lund rotation)
[3891]	909	CALL calc_coeff_matrix
[4559]	910
[2938]	911	ENDIF
[2259]	912	!
[4566]	913	!-- Initial filter functions
	914	CALL stg_setup_filter_function
[2938]	915	!
	916	!-- Allocate velocity seeds for turbulence at xz-layer
[4559]	917	ALLOCATE ( fu_xz(nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	918	fv_xz(nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	919	fw_xz(nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	920
[2938]	921	!
	922	!-- Allocate velocity seeds for turbulence at yz-layer
[4559]	923	ALLOCATE ( fu_yz(nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	924	fv_yz(nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	925	fw_yz(nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	926
[2938]	927	fu_xz = 0.0_wp
	928	fuo_xz = 0.0_wp
	929	fv_xz = 0.0_wp
	930	fvo_xz = 0.0_wp
	931	fw_xz = 0.0_wp
	932	fwo_xz = 0.0_wp
	933
	934	fu_yz = 0.0_wp
	935	fuo_yz = 0.0_wp
	936	fv_yz = 0.0_wp
	937	fvo_yz = 0.0_wp
	938	fw_yz = 0.0_wp
	939	fwo_yz = 0.0_wp
	940
[2259]	941	#if defined( __parallel )
	942	CALL MPI_BARRIER( comm2d, ierr )
	943	#endif
	944
	945	!
[4559]	946	!-- In case of restart, calculate velocity seeds fu, fv, fw from former time step.
	947	! Bug: fu, fv, fw are different in those heights where a11, a22, a33 are 0 compared to the prerun.
	948	!-- This is mostly for k=nzt+1.
[2259]	949	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	950	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	951
	952	IF ( myidx == id_stg_left ) i = -1
	953	IF ( myidx == id_stg_right ) i = nxr+1
	954
[4438]	955	DO j = nys, nyn
[2259]	956	DO k = nzb, nzt+1
[4332]	957	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	958	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	959	ELSE
[4332]	960	fu_yz(k,j) = 10E-8_wp
[2259]	961	ENDIF
	962
[4332]	963	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	964	fv_yz(k,j) = ( v(k,j,i) - a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	965	ELSE
[4332]	966	fv_yz(k,j) = 10E-8_wp
[2259]	967	ENDIF
	968
[4332]	969	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	970	fw_yz(k,j) = ( w(k,j,i) - a31(k) * fu_yz(k,j) - a32(k) * fv_yz(k,j) ) / a33(k)
[2259]	971	ELSE
[4332]	972	fw_yz(k,j) = 10E-8_wp
[2259]	973	ENDIF
	974	ENDDO
	975	ENDDO
	976	ENDIF
[4559]	977
[3900]	978	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	979
	980	IF ( myidy == id_stg_south ) j = -1
	981	IF ( myidy == id_stg_north ) j = nyn+1
	982
[4438]	983	DO i = nxl, nxr
[3900]	984	DO k = nzb, nzt+1
[4335]	985	!
[4559]	986	!-- In case the correlation coefficients are very small, the velocity seeds may become
	987	!-- very large finally creating numerical instabilities in the synthetic turbulence
	988	!-- generator. Empirically, a value of 10E-8 seems to be sufficient.
[4332]	989	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	990	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	991	ELSE
[4332]	992	fu_xz(k,i) = 10E-8_wp
[3900]	993	ENDIF
	994
[4332]	995	IF ( a22(k) > 10E-8_wp ) THEN
[4559]	996	fv_xz(k,i) = ( v(k,j,i) - a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	997	ELSE
[4332]	998	fv_xz(k,i) = 10E-8_wp
[3900]	999	ENDIF
	1000
[4332]	1001	IF ( a33(k) > 10E-8_wp ) THEN
[4559]	1002	fw_xz(k,i) = ( w(k,j,i) - a31(k) * fu_xz(k,i) - a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	1003	ELSE
[4332]	1004	fw_xz(k,i) = 10E-8_wp
[3900]	1005	ENDIF
	1006
	1007	ENDDO
	1008	ENDDO
	1009	ENDIF
[2259]	1010	ENDIF
[4022]	1011	!
[4559]	1012	!-- Count the number of non-topography grid points at the boundaries where perturbations are imposed.
	1013	!-- This number is later used for bias corrections of the perturbations, i.e. to force their mean to
	1014	!-- be zero. Please note, due to the asymetry of u and v along x and y direction, respectively,
	1015	!-- different cases must be distinguished.
[4022]	1016	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1017	!
	1018	!-- Number of grid points where perturbations are imposed on u
	1019	IF ( myidx == id_stg_left ) i = nxl
	1020	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1021
	1022	nr_non_topo_yz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1023	!
[4559]	1024	!-- Number of grid points where perturbations are imposed on v and w
[4022]	1025	IF ( myidx == id_stg_left ) i = nxl-1
	1026	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1027
	1028	nr_non_topo_yz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1029	nr_non_topo_yz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	1030
[4022]	1031	#if defined( __parallel )
[4559]	1032	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, MPI_SUM, comm1dy, ierr )
[4022]	1033	#else
	1034	nr_non_topo_yz = nr_non_topo_yz_l
[4559]	1035	#endif
[4022]	1036	ENDIF
[4559]	1037
[4022]	1038	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1039	!
	1040	!-- Number of grid points where perturbations are imposed on v
	1041	IF ( myidy == id_stg_south ) j = nys
	1042	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1043
	1044	nr_non_topo_xz_l(2) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1045	!
[4559]	1046	!-- Number of grid points where perturbations are imposed on u and w
[4022]	1047	IF ( myidy == id_stg_south ) j = nys-1
	1048	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1049
	1050	nr_non_topo_xz_l(1) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1051	nr_non_topo_xz_l(3) = SUM( MERGE( 1, 0, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1052
[4022]	1053	#if defined( __parallel )
[4559]	1054	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, MPI_SUM, comm1dx, ierr )
[4022]	1055	#else
	1056	nr_non_topo_xz = nr_non_topo_xz_l
[4559]	1057	#endif
[4022]	1058	ENDIF
[4438]	1059	!
[4559]	1060	!-- Initialize random number generator at xz- and yz-layers. Random numbers are initialized at each
	1061	!-- core. In case there is only inflow from the left, it is sufficient to generate only random
	1062	!-- numbers for the yz-layer, else random numbers for the xz-layer are also required.
[4566]	1063	ALLOCATE ( id_rand_yz(-mergp_limit+nys:nyn+mergp_limit) )
	1064	ALLOCATE ( seq_rand_yz(5,-mergp_limit+nys:nyn+mergp_limit) )
[4438]	1065	id_rand_yz = 0
	1066	seq_rand_yz = 0
[2259]	1067
[4566]	1068	CALL init_parallel_random_generator( ny, -mergp_limit+nys, nyn+mergp_limit, id_rand_yz, seq_rand_yz )
[4022]	1069
[4559]	1070	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1071	.AND. .NOT. rans_mode ) ) THEN
[4566]	1072	ALLOCATE ( id_rand_xz(-mergp_limit+nxl:nxr+mergp_limit) )
	1073	ALLOCATE ( seq_rand_xz(5,-mergp_limit+nxl:nxr+mergp_limit) )
[4438]	1074	id_rand_xz = 0
	1075	seq_rand_xz = 0
	1076
[4566]	1077	CALL init_parallel_random_generator( nx, -mergp_limit+nxl, nxr+mergp_limit, id_rand_xz, seq_rand_xz )
[4438]	1078	ENDIF
	1079
[2259]	1080	END SUBROUTINE stg_init
	1081
	1082
[4559]	1083	!--------------------------------------------------------------------------------------------------!
[2259]	1084	! Description:
	1085	! ------------
[4559]	1086	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10 (Xie and Castro, 2008)
	1087	!--------------------------------------------------------------------------------------------------!
[4566]	1088	SUBROUTINE stg_filter_func( nxx, bxx, mergp )
[2259]	1089
[4566]	1090	INTEGER(iwp) :: k !< loop index
	1091	INTEGER(iwp) :: mergp !< passed length scale in grid points
	1092	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1093	INTEGER(iwp) :: nf !< index for length scales
[2259]	1094
[4559]	1095	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
	1096
[2259]	1097	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1098	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1099
[4438]	1100	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1101
	1102
	1103	bxx = 0.0_wp
	1104
	1105	DO k = nzb, nzt+1
	1106	bdenom = 0.0_wp
	1107	n_k = nxx(k)
	1108	IF ( n_k /= 0 ) THEN
	1109
	1110	!
	1111	!-- ( Eq.10 )^2
[4438]	1112	DO nf = -n_k, n_k
[4559]	1113	bdenom = bdenom + EXP( -qsi * pi * ABS( nf ) / n_k )**2
[2259]	1114	ENDDO
	1115
	1116	!
	1117	!-- ( Eq.9 )
	1118	bdenom = SQRT( bdenom )
[4438]	1119	DO nf = -n_k, n_k
[4559]	1120	bxx(nf,k) = EXP( -qsi * pi * ABS( nf ) / n_k ) / bdenom
[2259]	1121	ENDDO
	1122	ENDIF
	1123	ENDDO
	1124
[3347]	1125	END SUBROUTINE stg_filter_func
[2259]	1126
	1127
[4566]	1128	!------------------------------------------------------------------------------!
	1129	! Description:
	1130	! ------------
	1131	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1132	!> (Xie and Castro, 2008)
	1133	!------------------------------------------------------------------------------!
	1134	SUBROUTINE stg_setup_filter_function
	1135
	1136	INTEGER(iwp) :: j !< dummy value to calculate maximum length scale index
	1137	INTEGER(iwp) :: k !< loop index along vertical direction
	1138	!
	1139	!-- Define the size of the filter functions and allocate them.
	1140	mergp_x = 0
	1141	mergp_y = 0
	1142	mergp_z = 0
	1143
	1144	DO k = nzb, nzt+1
	1145	j = MAX( ABS(nux(k)), ABS(nvx(k)), ABS(nwx(k)) )
	1146	IF ( j > mergp_x ) mergp_x = j
	1147	ENDDO
	1148	DO k = nzb, nzt+1
	1149	j = MAX( ABS(nuy(k)), ABS(nvy(k)), ABS(nwy(k)) )
	1150	IF ( j > mergp_y ) mergp_y = j
	1151	ENDDO
	1152	DO k = nzb, nzt+1
	1153	j = MAX( ABS(nuz(k)), ABS(nvz(k)), ABS(nwz(k)) )
	1154	IF ( j > mergp_z ) mergp_z = j
	1155	ENDDO
	1156
	1157	mergp_xy = MAX( mergp_x, mergp_y )
	1158
	1159	IF ( ALLOCATED( bux ) ) DEALLOCATE( bux )
	1160	IF ( ALLOCATED( bvx ) ) DEALLOCATE( bvx )
	1161	IF ( ALLOCATED( bwx ) ) DEALLOCATE( bwx )
	1162	IF ( ALLOCATED( buy ) ) DEALLOCATE( buy )
	1163	IF ( ALLOCATED( bvy ) ) DEALLOCATE( bvy )
	1164	IF ( ALLOCATED( bwy ) ) DEALLOCATE( bwy )
	1165	IF ( ALLOCATED( buz ) ) DEALLOCATE( buz )
	1166	IF ( ALLOCATED( bvz ) ) DEALLOCATE( bvz )
	1167	IF ( ALLOCATED( bwz ) ) DEALLOCATE( bwz )
	1168
	1169	ALLOCATE ( bux(-mergp_x:mergp_x,nzb:nzt+1), &
	1170	buy(-mergp_y:mergp_y,nzb:nzt+1), &
	1171	buz(-mergp_z:mergp_z,nzb:nzt+1), &
	1172	bvx(-mergp_x:mergp_x,nzb:nzt+1), &
	1173	bvy(-mergp_y:mergp_y,nzb:nzt+1), &
	1174	bvz(-mergp_z:mergp_z,nzb:nzt+1), &
	1175	bwx(-mergp_x:mergp_x,nzb:nzt+1), &
	1176	bwy(-mergp_y:mergp_y,nzb:nzt+1), &
	1177	bwz(-mergp_z:mergp_z,nzb:nzt+1) )
	1178	!
	1179	!-- Create filter functions
	1180	CALL stg_filter_func( nux, bux, mergp_x ) !filter ux
	1181	CALL stg_filter_func( nuy, buy, mergp_y ) !filter uy
	1182	CALL stg_filter_func( nuz, buz, mergp_z ) !filter uz
	1183	CALL stg_filter_func( nvx, bvx, mergp_x ) !filter vx
	1184	CALL stg_filter_func( nvy, bvy, mergp_y ) !filter vy
	1185	CALL stg_filter_func( nvz, bvz, mergp_z ) !filter vz
	1186	CALL stg_filter_func( nwx, bwx, mergp_x ) !filter wx
	1187	CALL stg_filter_func( nwy, bwy, mergp_y ) !filter wy
	1188	CALL stg_filter_func( nwz, bwz, mergp_z ) !filter wz
	1189
	1190	END SUBROUTINE stg_setup_filter_function
	1191
[4559]	1192	!--------------------------------------------------------------------------------------------------!
[2259]	1193	! Description:
	1194	! ------------
	1195	!> Parin for &stg_par for synthetic turbulence generator
[4559]	1196	!--------------------------------------------------------------------------------------------------!
[2259]	1197	SUBROUTINE stg_parin
	1198
[4559]	1199	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
[2259]	1200
	1201
[4559]	1202	NAMELIST /stg_par/ dt_stg_adjust, &
	1203	dt_stg_call, &
	1204	use_syn_turb_gen, &
[4438]	1205	compute_velocity_seeds_local
[2259]	1206
	1207	line = ' '
	1208	!
	1209	!-- Try to find stg package
	1210	REWIND ( 11 )
	1211	line = ' '
	1212	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[4559]	1213	READ ( 11, '(A)', END = 20 ) line
[2259]	1214	ENDDO
	1215	BACKSPACE ( 11 )
	1216
	1217	!
	1218	!-- Read namelist
[3246]	1219	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1220
	1221	!
[4559]	1222	!-- Set flag that indicates that the synthetic turbulence generator is switched on
[2776]	1223	syn_turb_gen = .TRUE.
[3246]	1224	GOTO 20
[2259]	1225
[3246]	1226	10 BACKSPACE( 11 )
[3248]	1227	READ( 11 , '(A)') line
	1228	CALL parin_fail_message( 'stg_par', line )
[2563]	1229
[3246]	1230	20 CONTINUE
[2259]	1231
	1232	END SUBROUTINE stg_parin
	1233
	1234
[4559]	1235	!--------------------------------------------------------------------------------------------------!
[2259]	1236	! Description:
	1237	! ------------
[4495]	1238	!> Read module-specific global restart data (Fortran binary format).
[4559]	1239	!--------------------------------------------------------------------------------------------------!
[4495]	1240	SUBROUTINE stg_rrd_global_ftn( found )
[2576]	1241
[4559]	1242	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1243
[2894]	1244	found = .TRUE.
[2259]	1245
[3038]	1246
[2894]	1247	SELECT CASE ( restart_string(1:length) )
[4559]	1248
[4022]	1249	CASE ( 'time_stg_adjust' )
	1250	READ ( 13 ) time_stg_adjust
[4559]	1251
[4022]	1252	CASE ( 'time_stg_call' )
	1253	READ ( 13 ) time_stg_call
[4559]	1254
[2894]	1255	CASE ( 'use_syn_turb_gen' )
	1256	READ ( 13 ) use_syn_turb_gen
[2259]	1257
[2894]	1258	CASE DEFAULT
[2259]	1259
[3038]	1260	found = .FALSE.
[2259]	1261
[2894]	1262	END SELECT
[2259]	1263
	1264
[4495]	1265	END SUBROUTINE stg_rrd_global_ftn
[2259]	1266
	1267
[4559]	1268	!--------------------------------------------------------------------------------------------------!
[2259]	1269	! Description:
	1270	! ------------
[4495]	1271	!> Read module-specific global restart data (MPI-IO).
[4559]	1272	!--------------------------------------------------------------------------------------------------!
[4495]	1273	SUBROUTINE stg_rrd_global_mpi
	1274
	1275	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1276	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
	1277	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1278
	1279	END SUBROUTINE stg_rrd_global_mpi
	1280
	1281
[4559]	1282	!--------------------------------------------------------------------------------------------------!
[4495]	1283	! Description:
	1284	! ------------
[2259]	1285	!> This routine writes the respective restart data.
[4559]	1286	!--------------------------------------------------------------------------------------------------!
[2894]	1287	SUBROUTINE stg_wrd_global
[2259]	1288
[4495]	1289	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
	1290
	1291	CALL wrd_write_string( 'time_stg_adjust' )
	1292	WRITE ( 14 ) time_stg_adjust
[4559]	1293
[4495]	1294	CALL wrd_write_string( 'time_stg_call' )
	1295	WRITE ( 14 ) time_stg_call
[2259]	1296
[4495]	1297	CALL wrd_write_string( 'use_syn_turb_gen' )
	1298	WRITE ( 14 ) use_syn_turb_gen
[2259]	1299
[4535]	1300	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
[2259]	1301
[4495]	1302	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1303	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
	1304	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1305
	1306	ENDIF
	1307
[2894]	1308	END SUBROUTINE stg_wrd_global
[2259]	1309
[2894]	1310
[4559]	1311	!--------------------------------------------------------------------------------------------------!
[2259]	1312	! Description:
	1313	! ------------
[4559]	1314	!> Create turbulent inflow fields for u, v, w with prescribed length scales and Reynolds stress
	1315	!> tensor after a method of Xie and Castro (2008), modified following suggestions of Kim et al.
	1316	!> (2013), and using a Lund rotation (Lund, 1998).
	1317	!--------------------------------------------------------------------------------------------------!
[2259]	1318	SUBROUTINE stg_main
	1319
[4559]	1320	USE exchange_horiz_mod, &
[4457]	1321	ONLY: exchange_horiz
	1322
[4559]	1323	INTEGER(iwp) :: i !< grid index in x-direction
	1324	INTEGER(iwp) :: j !< loop index in y-direction
	1325	INTEGER(iwp) :: k !< loop index in z-direction
[2259]	1326
[4559]	1327	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1328
[4566]	1329	REAL(wp) :: dt_stg !< time interval the STG is called
[4559]	1330
	1331	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
	1332
[3987]	1333	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1334	!
	1335	!-- Calculate time step which is needed for filter functions
[3775]	1336	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1337	!
[4559]	1338	!-- Check if synthetic turbulence generator needs to be called and new perturbations need to be
	1339	!-- created or if old disturbances can be imposed again.
	1340	IF ( time_stg_call >= dt_stg_call .AND. &
[4022]	1341	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1342	stg_call = .TRUE.
	1343	ELSE
	1344	stg_call = .FALSE.
	1345	ENDIF
	1346	!
[2259]	1347	!-- Initial value of fu, fv, fw
[3646]	1348	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1349	!
[4559]	1350	!-- Generate turbulence at the left and right boundary. Random numbers for the yz-planes at the
	1351	!-- left/right boundary are generated by the left-sided mpi ranks only. After random numbers are
	1352	!-- calculated, they are distributed to all other mpi ranks in the model, so that the velocity
	1353	!-- seed matrices are available on all mpi ranks (i.e. also on the right-sided boundary mpi ranks).
	1354	!-- In case of offline nesting, this implies, that the left- and the right-sided lateral boundary
	1355	!-- have the same initial seeds.
	1356	!-- Note, in case of inflow from the right only, only turbulence at the left boundary is required.
	1357	IF ( .NOT. ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1358	.AND. .NOT. rans_mode ) ) ) THEN
[4309]	1359	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1360	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1361	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1362	ELSE
[4559]	1363	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left, id_stg_right )
	1364	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left, id_stg_right )
	1365	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left, id_stg_right )
[2938]	1366	!
[4559]	1367	!-- Generate turbulence at the south and north boundary. Random numbers for the xz-planes at
	1368	!-- the south/north boundary are generated by the south-sided mpi ranks only. Please see also
	1369	!-- comment above.
	1370	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south, id_stg_north )
	1371	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south, id_stg_north )
	1372	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south, id_stg_north )
[2938]	1373	ENDIF
[2259]	1374	velocity_seed_initialized = .TRUE.
	1375	ENDIF
	1376	!
[4559]	1377	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity seeds are only
	1378	!-- required at the left boundary, while in case of offline nesting or RANS-LES nesting velocity
	1379	!-- seeds are required also at the right, south and north boundaries.
[4022]	1380	IF ( stg_call ) THEN
[4559]	1381	IF ( .NOT. ( nesting_offline .OR. &
	1382	( child_domain .AND. rans_mode_parent &
[4309]	1383	.AND. .NOT. rans_mode ) ) ) THEN
	1384	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1385	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1386	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1387
	1388	ELSE
[4559]	1389	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left, id_stg_right )
	1390	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left, id_stg_right )
	1391	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left, id_stg_right )
[4309]	1392
[4559]	1393	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south, id_stg_north )
	1394	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south, id_stg_north )
	1395	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south, id_stg_north )
[4022]	1396	ENDIF
[2938]	1397	ENDIF
[4559]	1398
[2938]	1399	!
[4309]	1400	!-- Turbulence generation at left and/or right boundary
[2938]	1401	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1402	!
[4559]	1403	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1404	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1405	IF ( stg_call ) THEN
[4559]	1406
[4438]	1407	DO j = nys, nyn
[4022]	1408	DO k = nzb, nzt + 1
[4559]	1409	!
[4022]	1410	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1411	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1412	fu_yz(k,j) = fuo_yz(k,j)
	1413	ELSE
[4559]	1414	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1415	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
[4022]	1416	ENDIF
[4559]	1417
[4566]	1418	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1419	fv_yz(k,j) = fvo_yz(k,j)
	1420	ELSE
[4559]	1421	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1422	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
[4022]	1423	ENDIF
[4559]	1424
[4566]	1425	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1426	fw_yz(k,j) = fwo_yz(k,j)
	1427	ELSE
[4559]	1428	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1429	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
[4022]	1430	ENDIF
	1431	ENDDO
	1432	ENDDO
[4559]	1433
[4022]	1434	dist_yz(nzb,:,1) = 0.0_wp
	1435	dist_yz(nzb,:,2) = 0.0_wp
	1436	dist_yz(nzb,:,3) = 0.0_wp
[4559]	1437
[4022]	1438	IF ( myidx == id_stg_left ) i = nxl
[4559]	1439	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1440	DO j = nys, nyn
[4022]	1441	DO k = nzb+1, nzt + 1
[4559]	1442	!
[4022]	1443	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4566]	1444	dist_yz(k,j,1) = a11(k) * fu_yz(k,j) * &
[4562]	1445	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4566]	1446
[4022]	1447	ENDDO
	1448	ENDDO
[4309]	1449
[4022]	1450	IF ( myidx == id_stg_left ) i = nxl-1
	1451	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1452	DO j = nys, nyn
[4022]	1453	DO k = nzb+1, nzt + 1
[4559]	1454	!
[4022]	1455	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1456	!-- Additional factors are added to improve the variance of v and w experimental test
	1457	!-- of 1.2
[4566]	1458	dist_yz(k,j,2) = ( a21(k) * fu_yz(k,j) + a22(k) * fv_yz(k,j) ) * &
[4559]	1459	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4566]	1460	dist_yz(k,j,3) = ( a31(k) * fu_yz(k,j) + a32(k) * fv_yz(k,j) + &
	1461	a33(k) * fw_yz(k,j) ) * &
	1462	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
	1463
[4022]	1464	ENDDO
[2259]	1465	ENDDO
[4022]	1466	ENDIF
[2259]	1467	!
	1468	!-- Mass flux correction following Kim et al. (2013)
[4559]	1469	!-- This correction factor ensures that the mass flux is preserved at the inflow boundary. First,
	1470	!-- calculate mean value of the imposed perturbations at yz boundary. Note, this needs to be done
	1471	!-- only after the last RK3-substep, else the boundary values won't be accessed.
[4022]	1472	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1473	mc_factor_l = 0.0_wp
	1474	mc_factor = 0.0_wp
	1475	!
	1476	!-- Sum up the original volume flows (with and without perturbations).
	1477	!-- Note, for non-normal components (here v and w) it is actually no volume flow.
[2938]	1478	IF ( myidx == id_stg_left ) i = nxl
	1479	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1480
[4562]	1481	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) * &
	1482	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4559]	1483
[4022]	1484	IF ( myidx == id_stg_left ) i = nxl-1
	1485	IF ( myidx == id_stg_right ) i = nxr+1
[4559]	1486
[4562]	1487	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) * &
	1488	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1489	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) * &
	1490	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4559]	1491
[2938]	1492	#if defined( __parallel )
[4559]	1493	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1494	#else
	1495	mc_factor = mc_factor_l
[2938]	1496	#endif
[4559]	1497	!
	1498	!-- Calculate correction factor and force zero mean perturbations.
	1499	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1500
	1501	IF ( myidx == id_stg_left ) i = nxl
	1502	IF ( myidx == id_stg_right ) i = nxr+1
	1503
[4562]	1504	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) * &
	1505	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4559]	1506
	1507
	1508	IF ( myidx == id_stg_left ) i = nxl-1
	1509	IF ( myidx == id_stg_right ) i = nxr+1
	1510
[4562]	1511	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) * &
	1512	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4559]	1513
[4562]	1514	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) * &
	1515	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4559]	1516	!
[2938]	1517	!-- Add disturbances
	1518	IF ( myidx == id_stg_left ) THEN
[4559]	1519	!
	1520	!-- For the left boundary distinguish between mesoscale offline / self nesting and
	1521	!-- turbulent inflow at the left boundary only. In the latter case turbulence is imposed on
	1522	!-- the mean inflow profiles.
	1523	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1524	!
[4022]	1525	!-- Add disturbance at the inflow
[4438]	1526	DO j = nys, nyn
[4022]	1527	DO k = nzb, nzt+1
[4562]	1528	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + dist_yz(k,j,1) ) * &
	1529	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
	1530	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + dist_yz(k,j,2) ) * &
	1531	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1532	w(k,j,-nbgp:-1) = dist_yz(k,j,3) * &
	1533	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1534	ENDDO
[2938]	1535	ENDDO
[4022]	1536	ELSE
[4559]	1537
[4022]	1538	DO j = nys, nyn
	1539	DO k = nzb+1, nzt
[4562]	1540	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) * &
	1541	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1542	u(k,j,-1) = u(k,j,0)
[4562]	1543	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) * &
	1544	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 2 ) )
	1545	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) * &
	1546	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1547	ENDDO
	1548	ENDDO
	1549	ENDIF
[2938]	1550	ENDIF
	1551	IF ( myidx == id_stg_right ) THEN
[3186]	1552	DO j = nys, nyn
[3347]	1553	DO k = nzb+1, nzt
[4562]	1554	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) * &
	1555	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
	1556	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) * &
	1557	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
	1558	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) * &
	1559	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1560	ENDDO
	1561	ENDDO
	1562	ENDIF
	1563	ENDIF
	1564	ENDIF
	1565	!
	1566	!-- Turbulence generation at north and south boundary
	1567	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1568	!
[4559]	1569	!-- Calculate new set of perturbations. Do this only at last RK3-substep and when dt_stg_call is
	1570	!-- exceeded. Else the old set of perturbations is imposed
[4022]	1571	IF ( stg_call ) THEN
[4438]	1572	DO i = nxl, nxr
[4022]	1573	DO k = nzb, nzt + 1
[4559]	1574	!
[4022]	1575	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
[4566]	1576	IF ( tu(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1577	fu_xz(k,i) = fuo_xz(k,i)
	1578	ELSE
[4559]	1579	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1580	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
[4022]	1581	ENDIF
[4559]	1582
[4566]	1583	IF ( tv(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1584	fv_xz(k,i) = fvo_xz(k,i)
	1585	ELSE
[4559]	1586	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1587	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
[4022]	1588	ENDIF
[4559]	1589
[4566]	1590	IF ( tw(k) == 0.0_wp .OR. adjustment_step ) THEN
[4022]	1591	fw_xz(k,i) = fwo_xz(k,i)
	1592	ELSE
[4559]	1593	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1594	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
[4022]	1595	ENDIF
	1596	ENDDO
	1597	ENDDO
[4559]	1598
	1599
[4022]	1600	dist_xz(nzb,:,1) = 0.0_wp
	1601	dist_xz(nzb,:,2) = 0.0_wp
	1602	dist_xz(nzb,:,3) = 0.0_wp
[4559]	1603
[4022]	1604	IF ( myidy == id_stg_south ) j = nys
	1605	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1606	DO i = nxl, nxr
[4022]	1607	DO k = nzb+1, nzt + 1
[4559]	1608	!
[4022]	1609	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
[4559]	1610	!-- Additional factors are added to improve the variance of v and w
	1611	!experimental test of 1.2
[4566]	1612	dist_xz(k,i,2) = ( a21(k) * fu_xz(k,i) + a22(k) * fv_xz(k,i) ) * &
[4559]	1613	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1614	ENDDO
	1615	ENDDO
[4559]	1616
[4022]	1617	IF ( myidy == id_stg_south ) j = nys-1
	1618	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1619	DO i = nxl, nxr
[4022]	1620	DO k = nzb+1, nzt + 1
[4559]	1621	!
[4022]	1622	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1623	!-- Additional factors are added to improve the variance of v and w
[4566]	1624	dist_xz(k,i,1) = a11(k) * fu_xz(k,i) * &
[4562]	1625	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4559]	1626
[4566]	1627	dist_xz(k,i,3) = ( a31(k) * fu_xz(k,i) + a32(k) * fv_xz(k,i) + &
	1628	a33(k) * fw_xz(k,i) ) * &
[4562]	1629	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1630	ENDDO
[2938]	1631	ENDDO
[4022]	1632	ENDIF
[3347]	1633
[2938]	1634	!
[4559]	1635	!-- Mass flux correction following Kim et al. (2013). This correction factor ensures that the
	1636	!-- mass flux is preserved at the inflow boundary. First, calculate mean value of the imposed
	1637	!-- perturbations at yz boundary. Note, this needs to be done only after the last RK3-substep,
	1638	!-- else the boundary values won't be accessed.
[4022]	1639	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
[4559]	1640	mc_factor_l = 0.0_wp
	1641	mc_factor = 0.0_wp
	1642
[4022]	1643	IF ( myidy == id_stg_south ) j = nys
	1644	IF ( myidy == id_stg_north ) j = nyn+1
[4559]	1645
[4562]	1646	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) * &
	1647	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4559]	1648
	1649	IF ( myidy == id_stg_south ) j = nys-1
	1650	IF ( myidy == id_stg_north ) j = nyn+1
	1651
[4562]	1652	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) * &
	1653	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1654	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) * &
	1655	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4559]	1656
[2938]	1657	#if defined( __parallel )
[4559]	1658	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, 3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1659	#else
[4022]	1660	mc_factor = mc_factor_l
[2938]	1661	#endif
[4559]	1662
[4022]	1663	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
[4559]	1664
	1665	IF ( myidy == id_stg_south ) j = nys
	1666	IF ( myidy == id_stg_north ) j = nyn+1
	1667
[4562]	1668	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) * &
	1669	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4559]	1670
	1671
	1672	IF ( myidy == id_stg_south ) j = nys-1
	1673	IF ( myidy == id_stg_north ) j = nyn+1
	1674
[4562]	1675	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) * &
	1676	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4559]	1677
[4562]	1678	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) * &
	1679	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4559]	1680	!
[4022]	1681	!-- Add disturbances
[4559]	1682	IF ( myidy == id_stg_south ) THEN
[4022]	1683	DO i = nxl, nxr
	1684	DO k = nzb+1, nzt
[4559]	1685	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1686	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 1 ) )
	1687	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1688	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1689	v(k,-1,i) = v(k,0,i)
[4559]	1690	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1691	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1692	ENDDO
[2938]	1693	ENDDO
[4022]	1694	ENDIF
	1695	IF ( myidy == id_stg_north ) THEN
[4559]	1696
[4022]	1697	DO i = nxl, nxr
	1698	DO k = nzb+1, nzt
[4562]	1699	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) * &
	1700	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
	1701	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) * &
	1702	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
	1703	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) * &
	1704	MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1705	ENDDO
[2938]	1706	ENDDO
[4022]	1707	ENDIF
[2938]	1708	ENDIF
[2259]	1709	ENDIF
[3347]	1710	!
[4438]	1711	!-- Exchange ghost points.
	1712	CALL exchange_horiz( u, nbgp )
	1713	CALL exchange_horiz( v, nbgp )
	1714	CALL exchange_horiz( w, nbgp )
	1715	!
[3347]	1716	!-- Finally, set time counter for calling STG to zero
[4022]	1717	IF ( stg_call ) time_stg_call = 0.0_wp
[4566]	1718	!
	1719	!-- Set adjustment step to False to indicate that time correlation can be
	1720	!-- switched-on again.
	1721	adjustment_step = .FALSE.
[2259]	1722
[3987]	1723	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1724
[2259]	1725	END SUBROUTINE stg_main
	1726
[4559]	1727	!--------------------------------------------------------------------------------------------------!
[2259]	1728	! Description:
	1729	! ------------
[4559]	1730	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1731	!> f_n. f_n is splitted in vertical direction by the number of PEs in x-direction and each PE
	1732	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the full
	1733	!> array.
	1734	!--------------------------------------------------------------------------------------------------!
[4309]	1735	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1736
[4559]	1737	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1738	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1739	INTEGER(iwp) :: j !< loop index in y-direction
	1740	INTEGER(iwp) :: jj !< loop index in y-direction
	1741	INTEGER(iwp) :: k !< loop index in z-direction
	1742	INTEGER(iwp) :: kk !< loop index in z-direction
	1743	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1744
[4559]	1745	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1746	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2259]	1747
[4559]	1748	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1749	REAL(wp) :: rand_av !< average of random number
	1750	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2259]	1751
[4566]	1752	REAL(wp), DIMENSION(-mergp_y:mergp_y,nzb:nzt+1) :: b_y !< filter function in y-direction
	1753	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
[4559]	1754
	1755	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1756	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
	1757
	1758	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1759	!
[4559]	1760	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1761	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1762	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1763	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1764	!-- all processes. Further, please note, a set of random numbers is only calculated for the west
	1765	!-- boundary, while the east boundary uses the same random numbers and thus also computes the same
[4559]	1766	!-- correlation matrix.
[4566]	1767	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_y+nys:nyn+mergp_y) )
[4438]	1768	rand_it = 0.0_wp
[2259]	1769
	1770	rand_av = 0.0_wp
	1771	rand_sigma_inv = 0.0_wp
[4566]	1772	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1773	* ( ny + mergp_y - ( 0 - mergp_y ) + 1 ), KIND = wp )
[4309]	1774	!
[4438]	1775	!-- Compute and normalize random numbers.
[4566]	1776	DO j = nys - mergp_y, nyn + mergp_y
[4309]	1777	!
[4438]	1778	!-- Put the random seeds at grid point j
	1779	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
[4566]	1780	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1781	CALL random_number_parallel( random_dummy )
	1782	rand_it(k,j) = random_dummy
	1783	ENDDO
[4309]	1784	!
[4438]	1785	!-- Get the new random seeds from last call at grid point j
	1786	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1787	ENDDO
[4309]	1788	!
[4559]	1789	!-- For normalization to zero mean, sum-up the global random numers. To normalize the global set of
	1790	!-- random numbers, the inner ghost layers mergp must not be summed-up, else the random numbers on
	1791	!-- the ghost layers will be stronger weighted as they also occur on the inner subdomains.
[4566]	1792	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1793	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1794	rand_av = rand_av + rand_it(k,j)
[2259]	1795	ENDDO
[4438]	1796	ENDDO
[4566]	1797
[4309]	1798	#if defined( __parallel )
	1799	!
[4438]	1800	!-- Sum-up the local averages of the random numbers
[4559]	1801	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1802	#endif
[4438]	1803	rand_av = rand_av * nyz_inv
[4309]	1804	!
[4438]	1805	!-- Obtain zero mean
	1806	rand_it= rand_it - rand_av
[4309]	1807	!
[4438]	1808	!-- Now, compute the variance
[4566]	1809	DO j = MERGE( nys, nys - mergp_y, nys /= 0 ), MERGE( nyn, nyn + mergp_y, nyn /= ny )
	1810	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1811	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1812	ENDDO
[4438]	1813	ENDDO
[2259]	1814
[4309]	1815	#if defined( __parallel )
[2259]	1816	!
[4438]	1817	!-- Sum-up the local quadratic averages of the random numbers
[4559]	1818	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
[4309]	1819	#endif
	1820	!
[4438]	1821	!-- Compute standard deviation
	1822	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1823	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1824	ELSE
	1825	rand_sigma_inv = 1.0_wp
[4309]	1826	ENDIF
	1827	!
[4438]	1828	!-- Normalize with standard deviation to obtain unit variance
	1829	rand_it = rand_it * rand_sigma_inv
	1830
	1831	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1832	!
[4559]	1833	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	1834	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	1835	!-- comm1dy and gathered on the leftmost and, if necessary, on the rightmost process. For huge
	1836	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	1837	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent
	1838	!-- communication. In the second option, which performs better when the turbulent length scales
	1839	!-- are parametrized and thus the loops are smaller, the seeds are computed locally and no
	1840	!-- communication is necessary.
[4438]	1841	IF ( compute_velocity_seeds_local ) THEN
	1842
	1843	f_n = 0.0_wp
	1844	DO j = nys, nyn
	1845	DO k = nzb, nzt+1
	1846	DO jj = -n_y(k), n_y(k)
	1847	DO kk = -n_z(k), n_z(k)
	1848	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1849	ENDDO
	1850	ENDDO
	1851	ENDDO
[2259]	1852	ENDDO
	1853
[4438]	1854	ELSE
[2259]	1855
[4438]	1856	f_n_l = 0.0_wp
	1857	DO j = nys, nyn
	1858	DO k = nzb_x_stg, nzt_x_stg+1
	1859	DO jj = -n_y(k), n_y(k)
	1860	DO kk = -n_z(k), n_z(k)
	1861	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1862	ENDDO
[2259]	1863	ENDDO
	1864	ENDDO
	1865	ENDDO
	1866	!
[4438]	1867	!-- Gather velocity seeds of full subdomain
	1868	send_count = nzt_x_stg - nzb_x_stg + 1
	1869	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1870
	1871	#if defined( __parallel )
[4309]	1872	!
[4438]	1873	!-- Gather the velocity seed matrix on left boundary mpi ranks.
[4559]	1874	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1875	recv_count_yz, displs_yz, stg_type_yz, id_left, comm1dx, ierr )
[4309]	1876	!
[4559]	1877	!-- If required, gather the same velocity seed matrix on right boundary mpi ranks (in offline
	1878	!-- nesting for example).
[4438]	1879	IF ( PRESENT( id_right ) ) THEN
[4559]	1880	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, f_n(nzb+1,nys), &
	1881	recv_count_yz, displs_yz, stg_type_yz, id_right, comm1dx, ierr )
[4438]	1882	ENDIF
[2259]	1883	#else
[4438]	1884	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[4444]	1885	!
	1886	!-- Next line required to avoid compile errors because of unused dummy arguments
	1887	IF ( id_left == 0 ) id_right = 0
[2259]	1888	#endif
	1889
[4438]	1890	ENDIF
[2259]	1891
[4438]	1892	DEALLOCATE( rand_it )
	1893
	1894	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1895
[2259]	1896	END SUBROUTINE stg_generate_seed_yz
	1897
[2938]	1898
[4559]	1899	!--------------------------------------------------------------------------------------------------!
[2938]	1900	! Description:
	1901	! ------------
[4559]	1902	!> Generate a set of random number rand_it wich is equal on each PE and calculate the velocity seed
	1903	!> f_n.
	1904	!> f_n is splitted in vertical direction by the number of PEs in y-direction and and each PE
	1905	!> calculates a vertical subsection of f_n. At the the end, all parts are collected to form the
	1906	!> full array.
	1907	!--------------------------------------------------------------------------------------------------!
[4309]	1908	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1909
[4566]	1910	INTEGER(iwp) :: i !< loop index in x-direction
	1911	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1912	INTEGER(iwp) :: id_south !< core ids at respective boundaries
	1913	INTEGER(iwp) :: ii !< loop index in x-direction
	1914	INTEGER(iwp) :: k !< loop index in z-direction
	1915	INTEGER(iwp) :: kk !< loop index in z-direction
	1916	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2938]	1917
[4566]	1918	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1919	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[2938]	1920
[4566]	1921	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1922	REAL(wp) :: rand_av !< average of random number
	1923	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
[2938]	1924
[4566]	1925	REAL(wp), DIMENSION(-mergp_x:mergp_x,nzb:nzt+1) :: b_x !< filter function in x-direction
	1926	REAL(wp), DIMENSION(-mergp_z:mergp_z,nzb:nzt+1) :: b_z !< filter function in z-direction
	1927
	1928	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1929	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1930
[4566]	1931	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1932
	1933	!
[4559]	1934	!-- Generate random numbers using the parallel random generator. The set of random numbers are
	1935	!-- modified to have an average of 0 and unit variance. Note, at the end the random number array
	1936	!-- must be defined globally in order to compute the correlation matrices. However, the calculation
	1937	!-- and normalization of random numbers is done locally, while the result is later distributed to
[4566]	1938	!-- all processes. Further, please note, a set of random numbers is only calculated for the south
	1939	!-- boundary, while the north boundary uses the same random numbers and thus also computes the same
[4559]	1940	!-- correlation matrix.
[4566]	1941	ALLOCATE( rand_it(nzb-mergp_z:nzt+1+mergp_z,-mergp_x+nxl:nxr+mergp_x) )
[4438]	1942	rand_it = 0.0_wp
[2938]	1943
	1944	rand_av = 0.0_wp
	1945	rand_sigma_inv = 0.0_wp
[4566]	1946	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp_z - ( nzb - mergp_z ) + 1 ) &
	1947	* ( nx + mergp_x - ( 0 - mergp_x ) +1 ), KIND = wp )
[4309]	1948	!
[4438]	1949	!-- Compute and normalize random numbers.
[4566]	1950	DO i = nxl - mergp_x, nxr + mergp_x
[4309]	1951	!
[4438]	1952	!-- Put the random seeds at grid point ii
	1953	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
[4566]	1954	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1955	CALL random_number_parallel( random_dummy )
	1956	rand_it(k,i) = random_dummy
	1957	ENDDO
[4309]	1958	!
[4438]	1959	!-- Get the new random seeds from last call at grid point ii
	1960	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1961	ENDDO
[4309]	1962	!
[4438]	1963	!-- For normalization to zero mean, sum-up the global random numers.
[4559]	1964	!-- To normalize the global set of random numbers, the inner ghost layers mergp must not be
	1965	!-- summed-up, else the random numbers on the ghost layers will be stronger weighted as they
[4438]	1966	!-- also occur on the inner subdomains.
[4566]	1967	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1968	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1969	rand_av = rand_av + rand_it(k,i)
[2938]	1970	ENDDO
[4438]	1971	ENDDO
[4566]	1972
[4309]	1973	#if defined( __parallel )
[4438]	1974	!
	1975	!-- Sum-up the local averages of the random numbers
[4559]	1976	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	1977	#endif
[4438]	1978	rand_av = rand_av * nxz_inv
[4309]	1979	!
[4438]	1980	!-- Obtain zero mean
	1981	rand_it= rand_it - rand_av
[4309]	1982	!
[4438]	1983	!-- Now, compute the variance
[4566]	1984	DO i = MERGE( nxl, nxl - mergp_x, nxl /= 0 ), MERGE( nxr, nxr + mergp_x, nxr /= nx )
	1985	DO k = nzb - mergp_z, nzt + 1 + mergp_z
[4438]	1986	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	1987	ENDDO
[4438]	1988	ENDDO
[2938]	1989
[4309]	1990	#if defined( __parallel )
[4438]	1991	!
	1992	!-- Sum-up the local quadratic averages of the random numbers
[4559]	1993	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
[4309]	1994	#endif
[2938]	1995	!
[4438]	1996	!-- Compute standard deviation
	1997	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1998	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	1999	ELSE
	2000	rand_sigma_inv = 1.0_wp
[4309]	2001	ENDIF
	2002	!
[4438]	2003	!-- Normalize with standard deviation to obtain unit variance
	2004	rand_it = rand_it * rand_sigma_inv
	2005
	2006	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2007	!
[4559]	2008	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There are two options. In the
	2009	!-- first one, the computation of the seeds is distributed to all processes along the communicator
	2010	!-- comm1dx and gathered on the southmost and, if necessary, on the northmost process. For huge
	2011	!-- length scales the computational effort can become quite huge (it scales with the turbulent
	2012	!-- length scales), so that gain by parallelization exceeds the costs by the subsequent communication.
	2013	!-- In the second option, which performs better when the turbulent length scales are parametrized
	2014	!-- and thus the loops are smaller, the seeds are computed locally and no communication is necessary.
[4438]	2015	IF ( compute_velocity_seeds_local ) THEN
[2938]	2016
[4438]	2017	f_n = 0.0_wp
	2018	DO i = nxl, nxr
	2019	DO k = nzb, nzt+1
	2020	DO ii = -n_x(k), n_x(k)
	2021	DO kk = -n_z(k), n_z(k)
	2022	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2023	ENDDO
[2938]	2024	ENDDO
	2025	ENDDO
	2026	ENDDO
	2027
[4438]	2028	ELSE
[2938]	2029
[4438]	2030	f_n_l = 0.0_wp
	2031	DO i = nxl, nxr
	2032	DO k = nzb_y_stg, nzt_y_stg+1
	2033	DO ii = -n_x(k), n_x(k)
	2034	DO kk = -n_z(k), n_z(k)
	2035	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2036	ENDDO
	2037	ENDDO
	2038	ENDDO
	2039	ENDDO
[2938]	2040	!
[4438]	2041	!-- Gather velocity seeds of full subdomain
	2042	send_count = nzt_y_stg - nzb_y_stg + 1
	2043	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2044
	2045	#if defined( __parallel )
[4309]	2046	!
[4438]	2047	!-- Gather the processed velocity seed on south boundary mpi ranks.
[4559]	2048	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2049	recv_count_xz, displs_xz, stg_type_xz, id_south, comm1dy, ierr )
[4309]	2050	!
[4438]	2051	!-- Gather the processed velocity seed on north boundary mpi ranks.
[4559]	2052	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, f_n(nzb+1,nxl), &
	2053	recv_count_xz, displs_xz, stg_type_xz, id_north, comm1dy, ierr )
[2938]	2054	#else
[4438]	2055	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[4444]	2056	!
	2057	!-- Next line required to avoid compile errors because of unused dummy arguments
	2058	IF ( id_north == 0 ) id_south = 0
[2938]	2059	#endif
	2060
[4438]	2061	ENDIF
	2062
	2063	DEALLOCATE( rand_it )
	2064
	2065	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2066
[2938]	2067	END SUBROUTINE stg_generate_seed_xz
	2068
[4559]	2069	!--------------------------------------------------------------------------------------------------!
[3347]	2070	! Description:
	2071	! ------------
[4566]	2072	!> Parametrization of the Reynolds-stress componentes, turbulent length- and time scales. The
	2073	!> parametrization follows Brost et al. (1982) with modifications described in Rotach et al. (1996),
	2074	!> which is applied in state-of-the-art dispserion modelling.
[4559]	2075	!--------------------------------------------------------------------------------------------------!
[4566]	2076	SUBROUTINE parametrize_turbulence
[3347]	2077
[4566]	2078	INTEGER(iwp) :: k !< loop index in z-direction
[4559]	2079
[4566]	2080	REAL(wp) :: corr_term_uh !< correction term in parametrization of horizontal variances for unstable stratification
	2081	REAL(wp) :: d_zi !< inverse boundary-layer depth
	2082	REAL(wp) :: length_scale_lon !< length scale in flow direction
	2083	REAL(wp) :: length_scale_lon_zi !< length scale in flow direction at boundary-layer top
	2084	REAL(wp) :: length_scale_lat !< length scale in crosswind direction
	2085	REAL(wp) :: length_scale_lat_zi !< length scale in crosswind direction at boundary-layer top
	2086	REAL(wp) :: length_scale_vert !< length scale in vertical direction
	2087	REAL(wp) :: length_scale_vert_zi !< length scale in vertical direction at boundary-layer top
	2088	REAL(wp) :: time_scale_zi !< time scale at boundary-layer top
	2089	REAL(wp) :: r11_zi !< longitudinal variance at boundary-layer top
	2090	REAL(wp) :: r22_zi !< crosswind variance at boundary-layer top
	2091	REAL(wp) :: r33_zi !< vertical variance at boundary-layer top
	2092	REAL(wp) :: r31_zi !< r31 at boundary-layer top
	2093	REAL(wp) :: r32_zi !< r32 at boundary-layer top
	2094	REAL(wp) :: rlat1 !< first dummy argument for crosswind compoment of reynolds stress
	2095	REAL(wp) :: rlat2 !< second dummy argument for crosswind compoment of reynolds stress
	2096	REAL(wp) :: rlon1 !< first dummy argument for longitudinal compoment of reynolds stress
	2097	REAL(wp) :: rlon2 !< second dummy argument for longitudinal compoment of reynolds stress
	2098	REAL(wp) :: zzi !< ratio of z/zi
[4559]	2099
[4566]	2100	REAL(wp), DIMENSION(nzb+1:nzt+1) :: cos_phi !< cosine of angle between mean flow direction and x-axis
	2101	REAL(wp), DIMENSION(nzb+1:nzt+1) :: phi !< angle between mean flow direction and x-axis
	2102	REAL(wp), DIMENSION(nzb+1:nzt+1) :: sin_phi !< sine of angle between mean flow direction and x-axis
	2103
[3347]	2104	!
[4566]	2105	!-- Calculate the boundary-layer top index. Boundary-layer top is calculated by Richardson-bulk
	2106	!-- criterion according to Heinze et al. (2017).
	2107	k_zi = MAX( 1, MINLOC( ABS( zu - zi_ribulk ), DIM = 1 ) )
	2108	IF ( zu(k_zi) > zi_ribulk ) k_zi = k_zi - 1
	2109	k_zi = MIN( k_zi, nzt )
[3347]	2110	!
[4566]	2111	!-- Calculate angle between flow direction and x-axis.
	2112	DO k = nzb+1, nzt + 1
	2113	IF ( u_init(k) /= 0.0_wp ) THEN
	2114	phi(k) = ATAN( v_init(k) / u_init(k) )
	2115	ELSE
	2116	phi(k) = 0.5 * pi
	2117	ENDIF
	2118	!
	2119	!-- Pre-calculate sine and cosine.
	2120	cos_phi(k) = COS( phi(k) )
	2121	sin_phi(k) = SIN( phi(k) )
	2122	ENDDO
	2123	!
	2124	!-- Parametrize Reynolds-stress components. Please note, parametrization is formulated for the
	2125	!-- stream- and spanwise components, while stream- and spanwise direction do not necessarily
	2126	!-- coincide with the grid axis. Hence, components are rotated after computation.
	2127	d_zi = 1.0_wp / zi_ribulk
	2128	DO k = nzb+1, k_zi
	2129
	2130	corr_term_uh = MERGE( 0.35_wp * ABS( &
	2131	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2132	)**( 2.0_wp / 3.0_wp ), &
	2133	0.0_wp, &
	2134	scale_l < 0.0_wp )
	2135	!
[4022]	2136	!-- Determine normalized height coordinate
[4566]	2137	zzi = zu(k) * d_zi
[3347]	2138	!
[4566]	2139	!-- Compute longitudinal and crosswind component of reynolds stress. Rotate these components by
	2140	!-- the wind direction to map onto the u- and v-component. Note, since reynolds stress for
	2141	!-- variances cannot become negative, take the absolute values.
	2142	rlon1 = scale_us*2 ( corr_term_uh + 5.0_wp - 4.0_wp * zzi )
	2143	rlat1 = scale_us*2 ( corr_term_uh + 2.0_wp - zzi )
[4559]	2144
[4566]	2145	r11(k) = ABS( cos_phi(k) * rlon1 + sin_phi(k) * rlat1 )
	2146	r22(k) = ABS( - sin_phi(k) * rlon1 + cos_phi(k) * rlat1 )
[4559]	2147	!
[4566]	2148	!-- For u'v' no parametrization exist so far - ?. For simplicity assume a similar profile as
	2149	!-- for u'w'.
	2150	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
	2151	!
[4559]	2152	!-- w'w'
[4566]	2153	r33(k) = scale_wm*2 ( &
	2154	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2155	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2156	)
[4559]	2157	!
[4566]	2158	!-- u'w' and v'w'. After calculation of the longitudinal and crosswind component
	2159	!-- these are projected along the x- and y-direction. Note, it is assumed that
	2160	!-- the flux within the boundary points opposite to the vertical gradient.
	2161	rlon2 = scale_us*2 ( zzi - 1.0_wp )
	2162	rlat2 = scale_us*2 ( 0.4 * zzi * ( 1.0_wp - zzi ) )
	2163
	2164	r31(k) = SIGN( ABS( cos_phi(k) * rlon2 + sin_phi(k) * rlat2 ), &
	2165	- ( u_init(k+1) - u_init(k-1) ) )
	2166	r32(k) = SIGN( ABS( - sin_phi(k) * rlon2 + cos_phi(k) * rlat2 ), &
	2167	- ( v_init(k+1) - v_init(k-1) ) )
[3347]	2168	!
[4566]	2169	!-- Compute turbulent time scales according to Brost et al. (1982). Note, time scales are
	2170	!-- limited to the adjustment time scales.
	2171	tu(k) = MIN( dt_stg_adjust, &
	2172	3.33_wp * zzi * ( 1.0 - 0.67_wp * zzi ) / scale_wm * zi_ribulk )
	2173
	2174	tv(k) = tu(k)
	2175	tw(k) = tu(k)
	2176
	2177	length_scale_lon = MIN( SQRT( r11(k) ) * tu(k), zi_ribulk )
	2178	length_scale_lat = MIN( SQRT( r22(k) ) * tv(k), zi_ribulk )
	2179	length_scale_vert = MIN( SQRT( r33(k) ) * tw(k), zi_ribulk )
	2180	!
	2181	!-- Assume isotropic turbulence length scales
	2182	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2183	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2184	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2185	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2186	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2187	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2188	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2189	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2190	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2191
[3347]	2192	ENDDO
[4566]	2193	!
	2194	!-- Above boundary-layer top length- and timescales as well as reynolds-stress components are
	2195	!-- reduced to zero by a blending function.
	2196	length_scale_lon_zi = SQRT( r11(k_zi) ) * tu(k_zi)
	2197	length_scale_lat_zi = SQRT( r22(k_zi) ) * tv(k_zi)
	2198	length_scale_vert_zi = SQRT( r33(k_zi) ) * tu(k_zi)
[3347]	2199
[4566]	2200	time_scale_zi = tu(k_zi)
	2201	r11_zi = r11(k_zi)
	2202	r22_zi = r22(k_zi)
	2203	r33_zi = r33(k_zi)
	2204	r31_zi = r31(k_zi)
	2205	r32_zi = r32(k_zi)
	2206
	2207	d_l = blend_coeff / MAX( length_scale_vert_zi, dx, dy, MINVAL( dzw ) )
	2208
	2209	DO k = k_zi+1, nzt+1
[3347]	2210	!
[4566]	2211	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2212	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
	2213	!
	2214	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number to the denominator, else
	2215	!-- the mergpe-function can crash if scale_l is zero.
	2216	r11(k) = r11_zi * blend
	2217	r22(k) = r22_zi * blend
	2218	r33(k) = r33_zi * blend
	2219	r31(k) = r31_zi * blend
	2220	r32(k) = r32_zi * blend
	2221	r21(k) = 0.5_wp * ( r11(k) + r22(k) )
	2222
	2223	!
	2224	!-- Compute turbulent time scales according to Brost et al. (1982).
	2225	!-- Note, time scales are limited to the adjustment time scales.
	2226	tu(k) = time_scale_zi * blend
	2227	tv(k) = time_scale_zi * blend
	2228	tw(k) = time_scale_zi * blend
	2229
	2230	length_scale_lon = length_scale_lon_zi * blend
	2231	length_scale_lat = length_scale_lat_zi * blend
	2232	length_scale_vert = length_scale_vert_zi * blend
	2233	!
	2234	!-- Assume isotropic turbulence length scales
	2235	nux(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2236	nuy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2237	nvx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2238	nvy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2239	nwx(k) = MAX( INT( length_scale_lon * ddx ), 1 )
	2240	nwy(k) = MAX( INT( length_scale_lat * ddy ), 1 )
	2241	nuz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2242	nvz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2243	nwz(k) = MAX( INT( length_scale_vert * ddzw(k) ), 1 )
	2244	ENDDO
	2245	!
	2246	!-- Set bottom boundary condition for reynolds stresses
[3347]	2247	r11(nzb) = r11(nzb+1)
	2248	r22(nzb) = r22(nzb+1)
	2249	r33(nzb) = r33(nzb+1)
	2250
	2251	r21(nzb) = r11(nzb+1)
	2252	r31(nzb) = r31(nzb+1)
	2253	r32(nzb) = r32(nzb+1)
	2254
[4566]	2255	!
	2256	!-- Set bottom boundary condition for the length and time scales
	2257	nux(nzb) = nux(nzb+1)
	2258	nuy(nzb) = nuy(nzb+1)
	2259	nuz(nzb) = nuz(nzb+1)
	2260	nvx(nzb) = nvx(nzb+1)
	2261	nvy(nzb) = nvy(nzb+1)
	2262	nvz(nzb) = nvz(nzb+1)
	2263	nwx(nzb) = nwx(nzb+1)
	2264	nwy(nzb) = nwy(nzb+1)
	2265	nwz(nzb) = nwz(nzb+1)
[4559]	2266
[4566]	2267	tu(nzb) = tu(nzb+1)
	2268	tv(nzb) = tv(nzb+1)
	2269	tw(nzb) = tw(nzb+1)
[4559]	2270
[4566]	2271	adjustment_step = .TRUE.
	2272
	2273	END SUBROUTINE parametrize_turbulence
	2274
[4559]	2275	!--------------------------------------------------------------------------------------------------!
[3347]	2276	! Description:
	2277	! ------------
[4559]	2278	!> Calculate the coefficient matrix from the Lund rotation.
	2279	!--------------------------------------------------------------------------------------------------!
[3347]	2280	SUBROUTINE calc_coeff_matrix
	2281
[4559]	2282	INTEGER(iwp) :: k !< loop index in z-direction
	2283
[3347]	2284	!
	2285	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2286	DO k = nzb+1, nzt+1
[4022]	2287	IF ( r11(k) > 10E-6_wp ) THEN
[4566]	2288	a11(k) = SQRT( r11(k) )
[3347]	2289	a21(k) = r21(k) / a11(k)
	2290	a31(k) = r31(k) / a11(k)
	2291	ELSE
	2292	a11(k) = 10E-8_wp
	2293	a21(k) = 10E-8_wp
	2294	a31(k) = 10E-8_wp
	2295	ENDIF
	2296	ENDDO
	2297	DO k = nzb+1, nzt+1
[4566]	2298	a22(k) = r22(k) - a21(k)**2
[4022]	2299	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2300	a22(k) = SQRT( a22(k) )
[4566]	2301	a32(k) = ( r32(k) - a21(k) * a31(k) ) / a22(k)
	2302	ELSE
[3347]	2303	a22(k) = 10E-8_wp
	2304	a32(k) = 10E-8_wp
	2305	ENDIF
	2306	ENDDO
	2307	DO k = nzb+1, nzt+1
	2308	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2309	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2310	a33(k) = SQRT( a33(k) )
	2311	ELSE
	2312	a33(k) = 10E-8_wp
	2313	ENDIF
[4559]	2314	ENDDO
[3347]	2315	!
	2316	!-- Set bottom boundary condition
	2317	a11(nzb) = a11(nzb+1)
	2318	a22(nzb) = a22(nzb+1)
	2319	a21(nzb) = a21(nzb+1)
[4559]	2320	a33(nzb) = a33(nzb+1)
[3347]	2321	a31(nzb) = a31(nzb+1)
[4559]	2322	a32(nzb) = a32(nzb+1)
[3347]	2323
	2324	END SUBROUTINE calc_coeff_matrix
[4559]	2325
	2326	!--------------------------------------------------------------------------------------------------!
[3347]	2327	! Description:
	2328	! ------------
[4559]	2329	!> This routine controls the re-adjustment of the turbulence statistics used for generating
	2330	!> turbulence at the lateral boundaries.
	2331	!--------------------------------------------------------------------------------------------------!
[3347]	2332	SUBROUTINE stg_adjust
	2333
[3987]	2334	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2335	!
[4559]	2336	!-- In case of dirichlet inflow boundary conditions only at one lateral boundary, i.e. in the case
	2337	!-- no offline or self nesting is applied but synthetic turbulence shall be parametrized
	2338	!-- nevertheless, the boundary-layer depth need to determined first.
	2339	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2340	CALL nesting_offl_calc_zi
[4022]	2341	!
[4559]	2342	!-- Compute scaling parameters (domain-averaged), such as friction velocity are calculated.
[3347]	2343	CALL calc_scaling_variables
	2344	!
[4566]	2345	!-- Parametrize Reynolds-stress tensor. Parametrization follows Brost et al. (1982) with
	2346	!-- modifications described in Rotach et al. (1996) and is based on boundary-layer depth, friction
	2347	!-- velocity and velocity scale.
	2348	CALL parametrize_turbulence
[3347]	2349	!
[4566]	2350	!-- Calculate coefficient matrix from Reynolds stress tensor
	2351	!-- (Lund rotation)
[3347]	2352	CALL calc_coeff_matrix
	2353	!
[4566]	2354	!-- Setup filter functions according to updated length scales.
	2355	CALL stg_setup_filter_function
[3347]	2356	!
	2357	!-- Reset time counter for controlling next adjustment to zero
	2358	time_stg_adjust = 0.0_wp
[3987]	2359
	2360	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[4559]	2361
	2362	END SUBROUTINE stg_adjust
	2363
	2364
	2365	!--------------------------------------------------------------------------------------------------!
[3347]	2366	! Description:
	2367	! ------------
[4559]	2368	!> Calculate scaling variables which are used for turbulence parametrization according to Rotach
	2369	!> et al. (1996). Scaling variables are: friction velocity, boundary-layer depth, momentum velocity
	2370	!> scale, and Obukhov length.
	2371	!--------------------------------------------------------------------------------------------------!
[3347]	2372	SUBROUTINE calc_scaling_variables
	2373
[4559]	2374	INTEGER(iwp) :: i !< loop index in x-direction
	2375	INTEGER(iwp) :: j !< loop index in y-direction
	2376	INTEGER(iwp) :: k !< loop index in z-direction
	2377	INTEGER(iwp) :: m !< surface element index
[3347]	2378
[4559]	2379	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
	2380	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2381	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2382	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
	2383	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2384	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2385	REAL(wp) :: w_convective !< convective velocity scale
	2386
[3347]	2387	!
[4559]	2388	!-- Calculate mean friction velocity, velocity scale, heat flux and near-surface temperature in the
	2389	!-- model domain.
[3937]	2390	pt_surf_mean_l = 0.0_wp
	2391	shf_mean_l = 0.0_wp
	2392	scale_l_l = 0.0_wp
	2393	friction_vel_l = 0.0_wp
[3347]	2394	DO m = 1, surf_def_h(0)%ns
[3937]	2395	i = surf_def_h(0)%i(m)
	2396	j = surf_def_h(0)%j(m)
	2397	k = surf_def_h(0)%k(m)
	2398	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2399	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2400	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2401	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[4559]	2402	ENDDO
[3347]	2403	DO m = 1, surf_lsm_h%ns
[3937]	2404	i = surf_lsm_h%i(m)
	2405	j = surf_lsm_h%j(m)
	2406	k = surf_lsm_h%k(m)
	2407	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2408	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2409	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2410	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2411	ENDDO
	2412	DO m = 1, surf_usm_h%ns
[3937]	2413	i = surf_usm_h%i(m)
	2414	j = surf_usm_h%j(m)
	2415	k = surf_usm_h%k(m)
	2416	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2417	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2418	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2419	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2420	ENDDO
[4559]	2421
[3347]	2422	#if defined( __parallel )
[4559]	2423	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2424	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2425	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
	2426	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, comm2d, ierr )
[3347]	2427	#else
[3937]	2428	scale_us = friction_vel_l
	2429	shf_mean = shf_mean_l
	2430	scale_l = scale_l_l
	2431	pt_surf_mean = pt_surf_mean_l
[3347]	2432	#endif
	2433
[4566]	2434	scale_us = scale_us * d_nxy
	2435	shf_mean = shf_mean * d_nxy
	2436	scale_l = scale_l * d_nxy
	2437	pt_surf_mean = pt_surf_mean * d_nxy
[3347]	2438	!
[4559]	2439	!-- Compute mean convective velocity scale. Note, in case the mean heat flux is negative, set
	2440	!-- convective velocity scale to zero.
[3347]	2441	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2442	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2443	ELSE
	2444	w_convective = 0.0_wp
	2445	ENDIF
	2446	!
[4566]	2447	!-- At the initial run the friction velocity is initialized close to zero, leading to almost zero
	2448	!-- disturbances at the boundaries. In order to obtain disturbances nevertheless, set a minium
	2449	!-- value of friction velocity for the reynolds-stress parametrization.
	2450	IF ( time_since_reference_point <= 0.0_wp ) scale_us = MAX( scale_us, 0.05_wp )
	2451	!
[4559]	2452	!-- Finally, in order to consider also neutral or stable stratification, compute momentum velocity
	2453	!-- scale from u* and convective velocity scale, according to Rotach et al. (1996).
[3347]	2454	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
[4559]	2455
[3347]	2456	END SUBROUTINE calc_scaling_variables
	2457
[2259]	2458	END MODULE synthetic_turbulence_generator_mod

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