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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4554

Last change on this file since 4554 was 4535, checked in by raasch, 5 years ago
bugfix for restart data format query
Property svn:keywords set to `Id`
File size: 110.6 KB

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[2259]	1	!> @synthetic_turbulence_generator_mod.f90
	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[2259]	4	!
[2696]	5	! PALM is free software: you can redistribute it and/or modify it under the
[2259]	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
	9	!
[2696]	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
[2259]	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[4481]	17	! Copyright 2017-2020 Leibniz Universitaet Hannover
[2259]	18	!------------------------------------------------------------------------------!
	19	!
	20	! Current revisions:
	21	! -----------------
	22	!
[4442]	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4535 2020-05-15 12:07:23Z eckhard $
[4535]	27	! bugfix for restart data format query
	28	!
	29	! 4495 2020-04-13 20:11:20Z raasch
[4495]	30	! restart data handling with MPI-IO added
	31	!
	32	! 4481 2020-03-31 18:55:54Z maronga
[4444]	33	! bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
	34	!
	35	! 4442 2020-03-04 19:21:13Z suehring
[4442]	36	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	37	! (was accidantly changed).
	38	!
	39	! 4441 2020-03-04 19:20:35Z suehring
[4440]	40	! Correct misplaced preprocessor directive
	41	!
	42	! 4438 2020-03-03 20:49:28Z suehring
[4438]	43	! Performance optimizations in velocity-seed calculation:
	44	! - random number array is only defined and computed locally (except for
	45	! normalization to zero mean and unit variance)
	46	! - parallel random number generator is applied independent on the 2D random
	47	! numbers in other routines
	48	! - option to decide wheter velocity seeds are computed locally without any
	49	! further communication or are computed by all processes along the
	50	! communicator
	51	!
	52	! 4346 2019-12-18 11:55:56Z motisi
[4346]	53	! Introduction of wall_flags_total_0, which currently sets bits based on static
	54	! topography information used in wall_flags_static_0
	55	!
	56	! 4335 2019-12-12 16:39:05Z suehring
[4335]	57	! Commentation of last commit
	58	!
	59	! 4332 2019-12-10 19:44:12Z suehring
[4332]	60	! Limit initial velocity seeds in restart runs, if not the seed calculation
	61	! may become unstable. Further, minor bugfix in initial velocity seed
	62	! calculation.
	63	!
	64	! 4329 2019-12-10 15:46:36Z motisi
[4329]	65	! Renamed wall_flags_0 to wall_flags_static_0
	66	!
	67	! 4309 2019-11-26 18:49:59Z suehring
[4309]	68	! Computation of velocity seeds optimized. This implies that random numbers
	69	! are computed now using the parallel random number generator. Random numbers
	70	! are now only computed and normalized locally, while distributed over all
	71	! mpi ranks afterwards, instead of computing random numbers on a global array.
	72	! Further, the number of calls for the time-consuming velocity-seed generation
	73	! is reduced - now the left and right, as well as the north and south boundary
	74	! share the same velocity-seed matrices.
	75	!
	76	! 4182 2019-08-22 15:20:23Z scharf
[4182]	77	! Corrected "Former revisions" section
	78	!
	79	! 4148 2019-08-08 11:26:00Z suehring
[4148]	80	! Remove unused variable
	81	!
	82	! 4144 2019-08-06 09:11:47Z raasch
[4144]	83	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	84	!
	85	! 4071 2019-07-03 20:02:00Z suehring
[4071]	86	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	87	! information is not read from file.
	88	!
	89	! 4022 2019-06-12 11:52:39Z suehring
[4022]	90	! Several bugfixes and improvements
	91	! - revise bias correction of the imposed perturbations (correction via volume
	92	! flow can create instabilities in case the mean volume flow is close to zero)
	93	! - introduce lower limits in calculation of coefficient matrix, else the
	94	! calculation may become numerically unstable
	95	! - impose perturbations every timestep, even though no new set of perturbations
	96	! is generated in case dt_stg_call /= dt_3d
	97	! - Implement a gradual decrease of Reynolds stress and length scales above
	98	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	99	! discontinuous decrease
	100	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	101	!
	102	! 3987 2019-05-22 09:52:13Z kanani
[3987]	103	! Introduce alternative switch for debug output during timestepping
	104	!
	105	! 3938 2019-04-29 16:06:25Z suehring
[3938]	106	! Remove unused variables
	107	!
	108	! 3937 2019-04-29 15:09:07Z suehring
[3937]	109	! Minor bugfix in case of a very early restart where mc_factor is sill not
	110	! present.
	111	! Some modification and fixing of potential bugs in the calculation of scaling
	112	! parameters used for synthetic turbulence parametrization.
	113	!
	114	! 3909 2019-04-17 09:13:25Z suehring
[3909]	115	! Minor bugfix for last commit
	116	!
	117	! 3900 2019-04-16 15:17:43Z suehring
[3900]	118	! Missing re-calculation of perturbation seeds in case of restarts
	119	!
	120	! 3891 2019-04-12 17:52:01Z suehring
[3891]	121	! Bugfix in initialization in case of restart runs.
	122	!
	123	! 3885 2019-04-11 11:29:34Z kanani
[3885]	124	! Changes related to global restructuring of location messages and introduction
	125	! of additional debug messages
	126	!
	127	!
[3775]	128	! removed unused variables
	129	!
	130	! 3719 2019-02-06 13:10:18Z kanani
[3719]	131	! Removed log_point measurement from stg_init, since this part is counted to
	132	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	133	! the subroutines in time_integration for better overview.
	134	!
[4182]	135	! 2259 2017-06-08 09:09:11Z gronemeier
	136	! Initial revision
[3044]	137	!
[4182]	138	! Authors:
	139	! --------
	140	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	141	!
	142	!
[2259]	143	! Description:
	144	! ------------
	145	!> The module generates turbulence at the inflow boundary based on a method by
	146	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	147	!> correction by Kim et al. (2013).
	148	!> The turbulence is correlated based on length scales in y- and z-direction and
	149	!> a time scale for each velocity component. The profiles of length and time
	150	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	151	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	152	!> within the boundary layer.
[2259]	153	!>
	154	!> @todo test restart
	155	!> enable cyclic_fill
	156	!> implement turbulence generation for e and pt
[2945]	157	!> @todo Input of height-constant length scales via namelist
[2259]	158	!> @note <Enter notes on the module>
	159	!> @bug Height information from input file is not used. Profiles from input
	160	!> must match with current PALM grid.
	161	!> In case of restart, velocity seeds differ from precursor run if a11,
	162	!> a22, or a33 are zero.
	163	!------------------------------------------------------------------------------!
	164	MODULE synthetic_turbulence_generator_mod
	165
	166
	167	USE arrays_3d, &
[4022]	168	ONLY: dzw, &
	169	ddzw, &
	170	drho_air, &
	171	mean_inflow_profiles, &
	172	q, &
[4071]	173	q_init, &
	174	pt, &
	175	pt_init, &
[4022]	176	u, &
	177	u_init, &
	178	v, &
	179	v_init, &
	180	w, &
	181	zu, &
	182	zw
[2259]	183
[3274]	184	USE basic_constants_and_equations_mod, &
[4022]	185	ONLY: g, &
	186	kappa, &
	187	pi
[2259]	188
	189	USE control_parameters, &
[4022]	190	ONLY: bc_lr, &
	191	bc_ns, &
	192	child_domain, &
	193	coupling_char, &
	194	debug_output_timestep, &
	195	dt_3d, &
	196	e_init, &
[4071]	197	humidity, &
[3885]	198	initializing_actions, &
[4022]	199	intermediate_timestep_count, &
	200	intermediate_timestep_count_max, &
	201	length, &
[3885]	202	message_string, &
[4022]	203	nesting_offline, &
[4071]	204	neutral, &
[3885]	205	num_mean_inflow_profiles, &
[4309]	206	random_generator, &
[4022]	207	rans_mode, &
[4495]	208	restart_data_format_output, &
[4022]	209	restart_string, &
	210	syn_turb_gen, &
	211	time_since_reference_point, &
	212	turbulent_inflow
[4438]	213
	214	USE cpulog, &
	215	ONLY: cpu_log, &
	216	log_point_s
	217
[4022]	218	USE grid_variables, &
	219	ONLY: ddx, &
	220	ddy, &
	221	dx, &
	222	dy
[2259]	223
	224	USE indices, &
[4022]	225	ONLY: nbgp, &
	226	nz, &
	227	nzb, &
	228	nzt, &
	229	nx, &
	230	nxl, &
	231	nxlu, &
	232	nxr, &
	233	ny, &
	234	nys, &
	235	nysv, &
	236	nyn, &
[4346]	237	wall_flags_total_0
[2259]	238
	239	USE kinds
	240
[2967]	241	#if defined( __parallel ) && !defined( __mpifh )
[2259]	242	USE MPI
[2841]	243	#endif
[2259]	244
[3347]	245	USE nesting_offl_mod, &
[4022]	246	ONLY: nesting_offl_calc_zi, &
	247	zi_ribulk
[3347]	248
[2259]	249	USE pegrid, &
[4022]	250	ONLY: comm1dx, &
	251	comm1dy, &
	252	comm2d, &
	253	ierr, &
	254	myidx, &
	255	myidy, &
	256	pdims
[4438]	257
[4022]	258	USE pmc_interface, &
	259	ONLY : rans_mode_parent
[4438]	260
	261	USE random_generator_parallel, &
	262	ONLY: init_parallel_random_generator, &
	263	random_dummy, &
[4309]	264	random_number_parallel, &
[4438]	265	random_seed_parallel
[2259]	266
[4495]	267	USE restart_data_mpi_io_mod, &
	268	ONLY: rrd_mpi_io, &
	269	wrd_mpi_io
	270
[2259]	271	USE transpose_indices, &
[4022]	272	ONLY: nzb_x, &
	273	nzt_x
[2259]	274
[4438]	275	USE surface_mod, &
	276	ONLY: surf_def_h, &
	277	surf_lsm_h, &
	278	surf_usm_h
[2259]	279
	280	IMPLICIT NONE
	281
[2967]	282	#if defined( __parallel ) && defined( __mpifh )
[2841]	283	INCLUDE "mpif.h"
	284	#endif
	285
[3182]	286
[3347]	287	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	288	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	289	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[4438]	290	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
	291	!< is distributed over several processes
[2259]	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
[4438]	297	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
[3038]	298	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	299	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	300	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	301	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4444]	302	#if defined( __parallel )
[4309]	303	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	304	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	305	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	306	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[4444]	307	#endif
[2259]	308
[4022]	309	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	310	!< required for bias correction of imposed perturbations
	311	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	312	!< required for bias correction of imposed perturbations
	313
[4444]	314	#if defined( __parallel )
[3347]	315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	318	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
[4444]	319	#endif
[3347]	320	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	321	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	322	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	323	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	324	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	325	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	326	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	327	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	328	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	329
[4438]	330	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	331	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	332	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	333	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
	334
[4022]	335	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	336	!< scales above the boundary layer
	337	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	338	!< one length scale above ABL top
	339	REAL(wp) :: d_l !< blend_coeff/length_scale
	340	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	341	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
[4438]	342	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
[3347]	343	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	344	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	345	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	346	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	347	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	348
[4022]	349	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	350
[4022]	351
[3347]	352	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	353	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	354	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	355	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	356	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	357	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	358
	359	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	360	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	361	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	362	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	363	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	364	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	365	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	366	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	367	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	368
[3347]	369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	379	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	380	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	383	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	384	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	385	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	386	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	387	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	388	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	389	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	390
	391	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	392	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	393
	394	!
	395	!-- PALM interfaces:
[3347]	396	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	397	INTERFACE stg_adjust
	398	MODULE PROCEDURE stg_adjust
	399	END INTERFACE stg_adjust
	400	!
[2259]	401	!-- Input parameter checks to be done in check_parameters
	402	INTERFACE stg_check_parameters
	403	MODULE PROCEDURE stg_check_parameters
	404	END INTERFACE stg_check_parameters
	405
	406	!
	407	!-- Calculate filter functions
	408	INTERFACE stg_filter_func
	409	MODULE PROCEDURE stg_filter_func
	410	END INTERFACE stg_filter_func
	411
	412	!
[2938]	413	!-- Generate velocity seeds at south and north domain boundary
	414	INTERFACE stg_generate_seed_xz
	415	MODULE PROCEDURE stg_generate_seed_xz
	416	END INTERFACE stg_generate_seed_xz
	417	!
	418	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	419	INTERFACE stg_generate_seed_yz
	420	MODULE PROCEDURE stg_generate_seed_yz
	421	END INTERFACE stg_generate_seed_yz
	422
	423	!
	424	!-- Output of information to the header file
	425	INTERFACE stg_header
	426	MODULE PROCEDURE stg_header
	427	END INTERFACE stg_header
	428
	429	!
	430	!-- Initialization actions
	431	INTERFACE stg_init
	432	MODULE PROCEDURE stg_init
	433	END INTERFACE stg_init
	434
	435	!
	436	!-- Main procedure of synth. turb. gen.
	437	INTERFACE stg_main
	438	MODULE PROCEDURE stg_main
	439	END INTERFACE stg_main
	440
	441	!
	442	!-- Reading of NAMELIST parameters
	443	INTERFACE stg_parin
	444	MODULE PROCEDURE stg_parin
	445	END INTERFACE stg_parin
	446
	447	!
	448	!-- Reading of parameters for restart runs
[2894]	449	INTERFACE stg_rrd_global
[4495]	450	MODULE PROCEDURE stg_rrd_global_ftn
	451	MODULE PROCEDURE stg_rrd_global_mpi
[2894]	452	END INTERFACE stg_rrd_global
[2259]	453
	454	!
	455	!-- Writing of binary output for restart runs
[2894]	456	INTERFACE stg_wrd_global
	457	MODULE PROCEDURE stg_wrd_global
	458	END INTERFACE stg_wrd_global
[2259]	459
	460	SAVE
	461
	462	PRIVATE
	463
	464	!
	465	!-- Public interfaces
[3347]	466	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	467	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	468
	469	!
	470	!-- Public variables
[3347]	471	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	472	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	473	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	474
	475
	476	CONTAINS
	477
	478
	479	!------------------------------------------------------------------------------!
	480	! Description:
	481	! ------------
	482	!> Check parameters routine for synthetic turbulence generator
	483	!------------------------------------------------------------------------------!
	484	SUBROUTINE stg_check_parameters
	485
[3182]	486	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	487	nesting_offline ) THEN
[3376]	488	message_string = 'Synthetic turbulence generator is required ' // &
	489	'if offline nesting is applied and PALM operates ' // &
	490	'in LES mode.'
	491	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	492	ENDIF
	493
[3182]	494	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	495	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	496	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	497	'when nesting is applied and parent operates in ' // &
	498	'RANS-mode but current child in LES mode.'
[3376]	499	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	500	ENDIF
	501
[2776]	502	IF ( use_syn_turb_gen ) THEN
[2259]	503
[3579]	504	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	505	.NOT. rans_mode_parent ) THEN
	506	message_string = 'Using synthetic turbulence generator ' // &
	507	'is not allowed in LES-LES nesting.'
	508	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	509
	510	ENDIF
	511
	512	IF ( child_domain .AND. rans_mode .AND. &
	513	rans_mode_parent ) THEN
	514	message_string = 'Using synthetic turbulence generator ' // &
	515	'is not allowed in RANS-RANS nesting.'
	516	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	517
	518	ENDIF
	519
[3182]	520	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	521
[2938]	522	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	523	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	524	message_string = 'Using synthetic turbulence generator ' // &
[3579]	525	'requires %initializing_actions = ' // &
	526	'"set_constant_profiles" or "read_restart_data"' //&
	527	', if not offline nesting is applied.'
[2938]	528	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	529	ENDIF
	530
	531	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	532	message_string = 'Using synthetic turbulence generator ' // &
[3347]	533	'requires &bc_lr = "dirichlet/radiation", ' // &
	534	'if not offline nesting is applied.'
[2938]	535	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	536	ENDIF
	537	IF ( bc_ns /= 'cyclic' ) THEN
	538	message_string = 'Using synthetic turbulence generator ' // &
[3579]	539	'requires &bc_ns = "cyclic", ' // &
[3347]	540	'if not offline nesting is applied.'
[2938]	541	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	542	ENDIF
	543
[2259]	544	ENDIF
	545
	546	IF ( turbulent_inflow ) THEN
	547	message_string = 'Using synthetic turbulence generator ' // &
[2938]	548	'in combination &with turbulent_inflow = .T. '// &
	549	'is not allowed'
[2259]	550	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	551	ENDIF
[4309]	552	!
	553	!-- Synthetic turbulence generator requires the parallel random generator
	554	IF ( random_generator /= 'random-parallel' ) THEN
	555	message_string = 'Using synthetic turbulence generator ' // &
	556	'requires random_generator = random-parallel.'
	557	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	558	ENDIF
[2259]	559
	560	ENDIF
	561
	562	END SUBROUTINE stg_check_parameters
	563
	564
	565	!------------------------------------------------------------------------------!
	566	! Description:
	567	! ------------
	568	!> Header output for synthetic turbulence generator
	569	!------------------------------------------------------------------------------!
	570	SUBROUTINE stg_header ( io )
	571
	572	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	573
	574	!
	575	!-- Write synthetic turbulence generator Header
	576	WRITE( io, 1 )
[2776]	577	IF ( use_syn_turb_gen ) THEN
[2259]	578	WRITE( io, 2 )
	579	ELSE
	580	WRITE( io, 3 )
	581	ENDIF
[3347]	582
	583	IF ( parametrize_inflow_turbulence ) THEN
	584	WRITE( io, 4 ) dt_stg_adjust
	585	ELSE
	586	WRITE( io, 5 )
	587	ENDIF
[2259]	588
	589	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	590	' ------------------------------------------'/)
[3347]	591	2 FORMAT (' synthetic turbulence generator is switched on')
	592	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	593	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	594	5 FORMAT (' imposed turbulence is read from file' )
[2259]	595
	596	END SUBROUTINE stg_header
	597
	598
	599	!------------------------------------------------------------------------------!
	600	! Description:
	601	! ------------
	602	!> Initialization of the synthetic turbulence generator
	603	!------------------------------------------------------------------------------!
	604	SUBROUTINE stg_init
	605
[3347]	606	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	607
[2669]	608	#if defined( __parallel )
[2259]	609	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	610	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	611	#endif
[2259]	612
[2938]	613	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	614	INTEGER(iwp) :: j !> loop index
	615	INTEGER(iwp) :: k !< index
[4444]	616	#if defined( __parallel )
[2259]	617	INTEGER(iwp) :: newtype !< dummy MPI type
	618	INTEGER(iwp) :: realsize !< size of REAL variables
[4444]	619	#endif
[4309]	620
[4022]	621	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	622	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	623	!
	624	!-- Dummy variables used for reading profiles
	625	REAL(wp) :: d1 !< u profile
	626	REAL(wp) :: d2 !< v profile
	627	REAL(wp) :: d3 !< w profile
	628	REAL(wp) :: d5 !< e profile
	629	REAL(wp) :: luy !< length scale for u in y direction
	630	REAL(wp) :: luz !< length scale for u in z direction
	631	REAL(wp) :: lvy !< length scale for v in y direction
	632	REAL(wp) :: lvz !< length scale for v in z direction
	633	REAL(wp) :: lwy !< length scale for w in y direction
	634	REAL(wp) :: lwz !< length scale for w in z direction
[4444]	635	#if defined( __parallel )
[3038]	636	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[4444]	637	#endif
[2259]	638	REAL(wp) :: zz !< height
	639
[2938]	640
[2259]	641	#if defined( __parallel )
	642	CALL MPI_BARRIER( comm2d, ierr )
	643	#endif
[4438]	644	!
	645	!-- Create mpi-datatypes for exchange in case of non-local but distributed
	646	!-- computation of the velocity seeds. This option is useful in
[4444]	647	!-- case large turbulent length scales are present, where the computational
	648	!-- effort becomes large and need to be parallelized. For parameterized
[4438]	649	!-- turbulence the length scales are small and computing the velocity seeds
	650	!-- locally is faster (no overhead by communication).
	651	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	652	#if defined( __parallel )
[4438]	653	!
	654	!-- Determine processor decomposition of z-axis along x- and y-direction
	655	nnz = nz / pdims(1)
	656	nzb_x_stg = 1 + myidx * INT( nnz )
	657	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
	658
	659	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
	660	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
	661
	662	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	663	.AND. .NOT. rans_mode ) ) THEN
	664	nnz = nz / pdims(2)
	665	nzb_y_stg = 1 + myidy * INT( nnz )
	666	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
	667
	668	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
	669	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	670	ENDIF
	671
	672	!
	673	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	674	!-- velocity seeds
	675	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	676	extent = 1 * realsize
	677	!
	678	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	679	!-- layer
	680	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
	681	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
	682	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	683	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	684	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	685	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	686
	687	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	688	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
	689	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	690	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	691	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	692	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	693
[2938]	694	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	695	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
	696
	697	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	698	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
	699
	700	DO j = 1, pdims(1)
	701	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	702	ENDDO
[4438]	703	!
	704	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	705	!-- layer
	706	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	707	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	708	.AND. .NOT. rans_mode ) ) THEN
	709	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	710	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	711	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	712	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	713	CALL MPI_TYPE_FREE( newtype, ierr )
	714
	715	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	716	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	717	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	718	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	719	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	720	CALL MPI_TYPE_FREE( newtype, ierr )
	721
	722	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	723	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	724
	725	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	726	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	727
	728	DO j = 1, pdims(2)
	729	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	730	ENDDO
	731
	732	ENDIF
[4440]	733	#endif
[2938]	734	ENDIF
[2259]	735	!
[4071]	736	!-- Allocate required arrays.
	737	!-- In case no offline nesting or self nesting is used, the arrary
	738	!-- mean_inflow profiles is required. Check if it is already allocated, else
	739	!-- allocate and initialize it appropriately. Note, in case turbulence and
	740	!-- inflow information is read from file, mean_inflow_profiles is already
	741	!-- allocated and initialized appropriately.
[3347]	742	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	743	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	744	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	745	mean_inflow_profiles = 0.0_wp
	746	mean_inflow_profiles(:,1) = u_init
	747	mean_inflow_profiles(:,2) = v_init
	748	!
	749	!-- Even though potential temperature and humidity are not perturbed,
	750	!-- they need to be initialized appropriately.
	751	IF ( .NOT. neutral ) &
	752	mean_inflow_profiles(:,4) = pt_init
	753	IF ( humidity ) &
	754	mean_inflow_profiles(:,6) = q_init
	755	ENDIF
[3347]	756	ENDIF
[2259]	757
[3347]	758	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	759	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	760	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	761	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	762	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	763	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	764	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	765	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	766
[4438]	767	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	768	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	769	dist_xz = 0.0_wp
	770	dist_yz = 0.0_wp
	771	!
[2259]	772	!-- Read inflow profile
	773	!-- Height levels of profiles in input profile is as follows:
	774	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	775	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	776	!-- WARNING: zz is not used at the moment
[2938]	777	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	778	EXIST = file_stg_exist )
[2259]	779
[2938]	780	IF ( file_stg_exist ) THEN
[2259]	781
[2938]	782	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	783	FORM='FORMATTED')
	784	!
	785	!-- Skip header
	786	READ( 90, * )
[2259]	787
[3182]	788	DO k = nzb+1, nzt+1
[2938]	789	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	790	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	791	d1, d2, d3, d5
	792
[2259]	793	!
[3182]	794	!-- Convert length scales from meter to number of grid points.
[2938]	795	nuy(k) = INT( luy * ddy )
[3182]	796	nuz(k) = INT( luz * ddzw(k) )
[2938]	797	nvy(k) = INT( lvy * ddy )
[3182]	798	nvz(k) = INT( lvz * ddzw(k) )
[2938]	799	nwy(k) = INT( lwy * ddy )
[3182]	800	nwz(k) = INT( lwz * ddzw(k) )
[2938]	801	!
	802	!-- Workaround, assume isotropic turbulence
	803	nwx(k) = nwy(k)
	804	nvx(k) = nvy(k)
	805	nux(k) = nuy(k)
	806	!
	807	!-- Save Mean inflow profiles
	808	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	809	mean_inflow_profiles(k,1) = d1
	810	mean_inflow_profiles(k,2) = d2
	811	! mean_inflow_profiles(k,4) = d4
	812	mean_inflow_profiles(k,5) = d5
	813	ENDIF
	814	ENDDO
[3182]	815	!
	816	!-- Set lenght scales at surface grid point
	817	nuy(nzb) = nuy(nzb+1)
	818	nuz(nzb) = nuz(nzb+1)
	819	nvy(nzb) = nvy(nzb+1)
	820	nvz(nzb) = nvz(nzb+1)
	821	nwy(nzb) = nwy(nzb+1)
	822	nwz(nzb) = nwz(nzb+1)
	823
[2938]	824	CLOSE( 90 )
[3347]	825	!
	826	!-- Calculate coefficient matrix from Reynolds stress tensor
	827	!-- (Lund rotation)
	828	CALL calc_coeff_matrix
	829	!
	830	!-- No information about turbulence and its length scales are available.
	831	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	832	!-- Set flag which indicates that turbulence is parametrized, which is done
	833	!-- later when energy-balance models are already initialized. This is
	834	!-- because the STG needs information about surface properties such as
	835	!-- roughness to build 'realistic' turbulence profiles.
[2938]	836	ELSE
[2259]	837	!
[4022]	838	!-- Define length scale for the imposed turbulence, which is defined as
	839	!-- 8 times the minimum grid spacing
[4441]	840	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
[4022]	841	!
	842	!-- Define constant to gradually decrease length scales and Reynolds stress
	843	!-- above ABL top. Assure that no zero length scales are used.
	844	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	845	!
[3347]	846	!-- Set flag indicating that turbulence is parametrized
	847	parametrize_inflow_turbulence = .TRUE.
	848	!
[4022]	849	!-- In case of dirichlet inflow boundary conditions only at one lateral
	850	!-- boundary, i.e. in the case no offline or self nesting is applied but
	851	!-- synthetic turbulence shall be parametrized nevertheless, the
	852	!-- boundary-layer depth need to determined first.
	853	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	854	CALL nesting_offl_calc_zi
	855	!
[3347]	856	!-- Determine boundary-layer depth, which is used to initialize lenght
	857	!-- scales
	858	CALL calc_scaling_variables
	859	!
	860	!-- Initialize lenght and time scales, which in turn are used
	861	!-- to initialize the filter functions.
	862	CALL calc_length_and_time_scale
[3891]	863	!
	864	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	865	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	866	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	867	!-- friction velocity and velocity scale.
	868	CALL parametrize_reynolds_stress
	869	!
	870	!-- Calculate coefficient matrix from Reynolds stress tensor
	871	!-- (Lund rotation)
	872	CALL calc_coeff_matrix
[3347]	873
[2938]	874	ENDIF
	875
[2259]	876	!
[3347]	877	!-- Assign initial profiles. Note, this is only required if turbulent
	878	!-- inflow from the left is desired, not in case of any of the
	879	!-- nesting (offline or self nesting) approaches.
[3182]	880	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	881	u_init = mean_inflow_profiles(:,1)
	882	v_init = mean_inflow_profiles(:,2)
	883	!pt_init = mean_inflow_profiles(:,4)
	884	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	885	ENDIF
[3347]	886
[2938]	887	!
[2259]	888	!-- Define the size of the filter functions and allocate them.
[4438]	889	mergp = 0
[2259]	890
	891	! arrays must be large enough to cover the largest length scale
	892	DO k = nzb, nzt+1
[2938]	893	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	894	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	895	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[4438]	896	IF ( j > mergp ) mergp = j
[2259]	897	ENDDO
	898
[4438]	899	! mergp = 2 * mergp
	900	! mergp = mergp
[2259]	901
[4438]	902	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
	903	buy(-mergp:mergp,nzb:nzt+1), &
	904	buz(-mergp:mergp,nzb:nzt+1), &
	905	bvx(-mergp:mergp,nzb:nzt+1), &
	906	bvy(-mergp:mergp,nzb:nzt+1), &
	907	bvz(-mergp:mergp,nzb:nzt+1), &
	908	bwx(-mergp:mergp,nzb:nzt+1), &
	909	bwy(-mergp:mergp,nzb:nzt+1), &
	910	bwz(-mergp:mergp,nzb:nzt+1) )
[2259]	911
	912	!
[2938]	913	!-- Allocate velocity seeds for turbulence at xz-layer
[4438]	914	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	915	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	916	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	917
[2938]	918	!
	919	!-- Allocate velocity seeds for turbulence at yz-layer
[4438]	920	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	921	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	922	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	923
[2938]	924	fu_xz = 0.0_wp
	925	fuo_xz = 0.0_wp
	926	fv_xz = 0.0_wp
	927	fvo_xz = 0.0_wp
	928	fw_xz = 0.0_wp
	929	fwo_xz = 0.0_wp
	930
	931	fu_yz = 0.0_wp
	932	fuo_yz = 0.0_wp
	933	fv_yz = 0.0_wp
	934	fvo_yz = 0.0_wp
	935	fw_yz = 0.0_wp
	936	fwo_yz = 0.0_wp
	937
[2259]	938	!
	939	!-- Create filter functions
[2938]	940	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	941	CALL stg_filter_func( nuy, buy ) !filter uy
	942	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	943	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	944	CALL stg_filter_func( nvy, bvy ) !filter vy
	945	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	946	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	947	CALL stg_filter_func( nwy, bwy ) !filter wy
	948	CALL stg_filter_func( nwz, bwz ) !filter wz
	949
	950	#if defined( __parallel )
	951	CALL MPI_BARRIER( comm2d, ierr )
	952	#endif
	953
	954	!
[2938]	955	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	956	! time step.
	957	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	958	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	959	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	960	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	961
	962	IF ( myidx == id_stg_left ) i = -1
	963	IF ( myidx == id_stg_right ) i = nxr+1
	964
[4438]	965	DO j = nys, nyn
[2259]	966	DO k = nzb, nzt+1
[4332]	967	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	968	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	969	ELSE
[4332]	970	fu_yz(k,j) = 10E-8_wp
[2259]	971	ENDIF
	972
[4332]	973	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	974	fv_yz(k,j) = ( v(k,j,i) - &
	975	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	976	ELSE
[4332]	977	fv_yz(k,j) = 10E-8_wp
[2259]	978	ENDIF
	979
[4332]	980	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	981	fw_yz(k,j) = ( w(k,j,i) - &
	982	a31(k) * fu_yz(k,j) - a32(k) * &
	983	fv_yz(k,j) ) / a33(k)
[2259]	984	ELSE
[4332]	985	fw_yz(k,j) = 10E-8_wp
[2259]	986	ENDIF
	987	ENDDO
	988	ENDDO
	989	ENDIF
[3900]	990
	991	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	992
	993	IF ( myidy == id_stg_south ) j = -1
	994	IF ( myidy == id_stg_north ) j = nyn+1
	995
[4438]	996	DO i = nxl, nxr
[3900]	997	DO k = nzb, nzt+1
[4335]	998	!
	999	!-- In case the correlation coefficients are very small, the
	1000	!-- velocity seeds may become very large finally creating
	1001	!-- numerical instabilities in the synthetic turbulence generator.
	1002	!-- Empirically, a value of 10E-8 seems to be sufficient.
[4332]	1003	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	1004	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	1005	ELSE
[4332]	1006	fu_xz(k,i) = 10E-8_wp
[3900]	1007	ENDIF
	1008
[4332]	1009	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	1010	fv_xz(k,i) = ( v(k,j,i) - &
	1011	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	1012	ELSE
[4332]	1013	fv_xz(k,i) = 10E-8_wp
[3900]	1014	ENDIF
	1015
[4332]	1016	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	1017	fw_xz(k,i) = ( w(k,j,i) - &
	1018	a31(k) * fu_xz(k,i) - &
	1019	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	1020	ELSE
[4332]	1021	fw_xz(k,i) = 10E-8_wp
[3900]	1022	ENDIF
	1023
	1024	ENDDO
	1025	ENDDO
	1026	ENDIF
[2259]	1027	ENDIF
[4022]	1028	!
	1029	!-- Count the number of non-topography grid points at the boundaries where
	1030	!-- perturbations are imposed. This number is later used for bias corrections
	1031	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	1032	!-- due to the asymetry of u and v along x and y direction, respectively,
	1033	!-- different cases must be distinguished.
	1034	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1035	!
	1036	!-- Number of grid points where perturbations are imposed on u
	1037	IF ( myidx == id_stg_left ) i = nxl
	1038	IF ( myidx == id_stg_right ) i = nxr+1
	1039
	1040	nr_non_topo_yz_l(1) = SUM( &
	1041	MERGE( 1, 0, &
[4346]	1042	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1043	!
	1044	!-- Number of grid points where perturbations are imposed on v and w
	1045	IF ( myidx == id_stg_left ) i = nxl-1
	1046	IF ( myidx == id_stg_right ) i = nxr+1
	1047
	1048	nr_non_topo_yz_l(2) = SUM( &
	1049	MERGE( 1, 0, &
[4346]	1050	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1051	nr_non_topo_yz_l(3) = SUM( &
	1052	MERGE( 1, 0, &
[4346]	1053	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1054
	1055	#if defined( __parallel )
	1056	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	1057	MPI_SUM, comm1dy, ierr )
	1058	#else
	1059	nr_non_topo_yz = nr_non_topo_yz_l
	1060	#endif
	1061	ENDIF
	1062
	1063	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1064	!
	1065	!-- Number of grid points where perturbations are imposed on v
	1066	IF ( myidy == id_stg_south ) j = nys
	1067	IF ( myidy == id_stg_north ) j = nyn+1
	1068
	1069	nr_non_topo_xz_l(2) = SUM( &
	1070	MERGE( 1, 0, &
[4346]	1071	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1072	!
	1073	!-- Number of grid points where perturbations are imposed on u and w
	1074	IF ( myidy == id_stg_south ) j = nys-1
	1075	IF ( myidy == id_stg_north ) j = nyn+1
	1076
	1077	nr_non_topo_xz_l(1) = SUM( &
	1078	MERGE( 1, 0, &
[4346]	1079	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1080	nr_non_topo_xz_l(3) = SUM( &
	1081	MERGE( 1, 0, &
[4346]	1082	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1083
	1084	#if defined( __parallel )
	1085	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1086	MPI_SUM, comm1dx, ierr )
	1087	#else
	1088	nr_non_topo_xz = nr_non_topo_xz_l
	1089	#endif
	1090	ENDIF
[4438]	1091	!
	1092	!-- Initialize random number generator at xz- and yz-layers. Random numbers
	1093	!-- are initialized at each core. In case there is only inflow from the left,
	1094	!-- it is sufficient to generate only random numbers for the yz-layer, else
	1095	!-- random numbers for the xz-layer are also required.
	1096	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
	1097	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
	1098	id_rand_yz = 0
	1099	seq_rand_yz = 0
[2259]	1100
[4438]	1101	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
	1102	id_rand_yz, seq_rand_yz )
[4022]	1103
[4438]	1104	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1105	.AND. .NOT. rans_mode ) ) THEN
	1106	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
	1107	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
	1108	id_rand_xz = 0
	1109	seq_rand_xz = 0
	1110
	1111	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
	1112	id_rand_xz, seq_rand_xz )
	1113	ENDIF
	1114
	1115
	1116
[2259]	1117	END SUBROUTINE stg_init
	1118
	1119
	1120	!------------------------------------------------------------------------------!
	1121	! Description:
	1122	! ------------
	1123	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1124	!> (Xie and Castro, 2008)
	1125	!------------------------------------------------------------------------------!
	1126	SUBROUTINE stg_filter_func( nxx, bxx )
	1127
	1128	INTEGER(iwp) :: k !< loop index
	1129	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1130	INTEGER(iwp) :: nf !< index for length scales
	1131
	1132	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1133	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1134
[4438]	1135	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
[2259]	1136
[4438]	1137	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1138
	1139
	1140	bxx = 0.0_wp
	1141
	1142	DO k = nzb, nzt+1
	1143	bdenom = 0.0_wp
	1144	n_k = nxx(k)
	1145	IF ( n_k /= 0 ) THEN
	1146
	1147	!
	1148	!-- ( Eq.10 )^2
[4438]	1149	DO nf = -n_k, n_k
[2259]	1150	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1151	ENDDO
	1152
	1153	!
	1154	!-- ( Eq.9 )
	1155	bdenom = SQRT( bdenom )
[4438]	1156	DO nf = -n_k, n_k
[2259]	1157	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1158	ENDDO
	1159	ENDIF
	1160	ENDDO
	1161
[3347]	1162	END SUBROUTINE stg_filter_func
[2259]	1163
	1164
	1165	!------------------------------------------------------------------------------!
	1166	! Description:
	1167	! ------------
	1168	!> Parin for &stg_par for synthetic turbulence generator
	1169	!------------------------------------------------------------------------------!
	1170	SUBROUTINE stg_parin
	1171
	1172	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1173
	1174
[4438]	1175	NAMELIST /stg_par/ dt_stg_adjust, &
	1176	dt_stg_call, &
	1177	use_syn_turb_gen, &
	1178	compute_velocity_seeds_local
[2259]	1179
	1180	line = ' '
	1181	!
	1182	!-- Try to find stg package
	1183	REWIND ( 11 )
	1184	line = ' '
	1185	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1186	READ ( 11, '(A)', END=20 ) line
[2259]	1187	ENDDO
	1188	BACKSPACE ( 11 )
	1189
	1190	!
	1191	!-- Read namelist
[3246]	1192	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1193
	1194	!
	1195	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1196	!-- on
[2776]	1197	syn_turb_gen = .TRUE.
[3246]	1198	GOTO 20
[2259]	1199
[3246]	1200	10 BACKSPACE( 11 )
[3248]	1201	READ( 11 , '(A)') line
	1202	CALL parin_fail_message( 'stg_par', line )
[2563]	1203
[3246]	1204	20 CONTINUE
[2259]	1205
	1206	END SUBROUTINE stg_parin
	1207
	1208
	1209	!------------------------------------------------------------------------------!
	1210	! Description:
	1211	! ------------
[4495]	1212	!> Read module-specific global restart data (Fortran binary format).
[2576]	1213	!------------------------------------------------------------------------------!
[4495]	1214	SUBROUTINE stg_rrd_global_ftn( found )
[2576]	1215
[3044]	1216	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1217
[2894]	1218	found = .TRUE.
[2259]	1219
[3038]	1220
[2894]	1221	SELECT CASE ( restart_string(1:length) )
[4022]	1222
	1223	CASE ( 'time_stg_adjust' )
	1224	READ ( 13 ) time_stg_adjust
	1225
	1226	CASE ( 'time_stg_call' )
	1227	READ ( 13 ) time_stg_call
	1228
[2894]	1229	CASE ( 'use_syn_turb_gen' )
	1230	READ ( 13 ) use_syn_turb_gen
[2259]	1231
[2894]	1232	CASE DEFAULT
[2259]	1233
[3038]	1234	found = .FALSE.
[2259]	1235
[2894]	1236	END SELECT
[2259]	1237
	1238
[4495]	1239	END SUBROUTINE stg_rrd_global_ftn
[2259]	1240
	1241
	1242	!------------------------------------------------------------------------------!
	1243	! Description:
	1244	! ------------
[4495]	1245	!> Read module-specific global restart data (MPI-IO).
	1246	!------------------------------------------------------------------------------!
	1247	SUBROUTINE stg_rrd_global_mpi
	1248
	1249	CALL rrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1250	CALL rrd_mpi_io( 'time_stg_call', time_stg_call )
	1251	CALL rrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1252
	1253	END SUBROUTINE stg_rrd_global_mpi
	1254
	1255
	1256	!------------------------------------------------------------------------------!
	1257	! Description:
	1258	! ------------
[2259]	1259	!> This routine writes the respective restart data.
	1260	!------------------------------------------------------------------------------!
[2894]	1261	SUBROUTINE stg_wrd_global
[2259]	1262
[4495]	1263	IF ( TRIM( restart_data_format_output ) == 'fortran_binary' ) THEN
	1264
	1265	CALL wrd_write_string( 'time_stg_adjust' )
	1266	WRITE ( 14 ) time_stg_adjust
[4022]	1267
[4495]	1268	CALL wrd_write_string( 'time_stg_call' )
	1269	WRITE ( 14 ) time_stg_call
[2259]	1270
[4495]	1271	CALL wrd_write_string( 'use_syn_turb_gen' )
	1272	WRITE ( 14 ) use_syn_turb_gen
[2259]	1273
[4535]	1274	ELSEIF ( restart_data_format_output(1:3) == 'mpi' ) THEN
[2259]	1275
[4495]	1276	CALL wrd_mpi_io( 'time_stg_adjust', time_stg_adjust )
	1277	CALL wrd_mpi_io( 'time_stg_call', time_stg_call )
	1278	CALL wrd_mpi_io( 'use_syn_turb_gen', use_syn_turb_gen )
	1279
	1280	ENDIF
	1281
[2894]	1282	END SUBROUTINE stg_wrd_global
[2259]	1283
[2894]	1284
[2259]	1285	!------------------------------------------------------------------------------!
	1286	! Description:
	1287	! ------------
	1288	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1289	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1290	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1291	!> (Lund, 1998).
	1292	!------------------------------------------------------------------------------!
	1293	SUBROUTINE stg_main
	1294
[4457]	1295	USE exchange_horiz_mod, &
	1296	ONLY: exchange_horiz
	1297
[2938]	1298	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1299	INTEGER(iwp) :: j !< loop index in y-direction
	1300	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1301
	1302	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1303
	1304	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1305
	1306	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1307
[3987]	1308	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1309	!
	1310	!-- Calculate time step which is needed for filter functions
[3775]	1311	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1312	!
[4022]	1313	!-- Check if synthetic turbulence generator needs to be called and new
	1314	!-- perturbations need to be created or if old disturbances can be imposed
	1315	!-- again.
	1316	IF ( time_stg_call >= dt_stg_call .AND. &
	1317	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1318	stg_call = .TRUE.
	1319	ELSE
	1320	stg_call = .FALSE.
	1321	ENDIF
	1322	!
[2259]	1323	!-- Initial value of fu, fv, fw
[3646]	1324	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1325	!
	1326	!-- Generate turbulence at the left and right boundary. Random numbers
	1327	!-- for the yz-planes at the left/right boundary are generated by the
	1328	!-- left-sided mpi ranks only. After random numbers are calculated, they
	1329	!-- are distributed to all other mpi ranks in the model, so that the
	1330	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
	1331	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
	1332	!-- that the left- and the right-sided lateral boundary have the same initial
	1333	!-- seeds.
	1334	!-- Note, in case of inflow from the right only, only turbulence at the left
	1335	!-- boundary is required.
	1336	IF ( .NOT. ( nesting_offline .OR. &
	1337	( child_domain .AND. rans_mode_parent &
	1338	.AND. .NOT. rans_mode ) ) ) THEN
	1339	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1340	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1341	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1342	ELSE
	1343	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
	1344	id_stg_left, id_stg_right )
	1345	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
	1346	id_stg_left, id_stg_right )
	1347	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
	1348	id_stg_left, id_stg_right )
[2938]	1349	!
[4309]	1350	!-- Generate turbulence at the south and north boundary. Random numbers
	1351	!-- for the xz-planes at the south/north boundary are generated by the
	1352	!-- south-sided mpi ranks only. Please see also comment above.
	1353	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
	1354	id_stg_south, id_stg_north )
	1355	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
	1356	id_stg_south, id_stg_north )
	1357	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
	1358	id_stg_south, id_stg_north )
[2938]	1359	ENDIF
[2259]	1360	velocity_seed_initialized = .TRUE.
	1361	ENDIF
	1362	!
[4309]	1363	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
	1364	!-- seeds are only required at the left boundary, while in case of offline
	1365	!-- nesting or RANS-LES nesting velocity seeds are required also at the
	1366	!-- right, south and north boundaries.
[4022]	1367	IF ( stg_call ) THEN
[4309]	1368	IF ( .NOT. ( nesting_offline .OR. &
	1369	( child_domain .AND. rans_mode_parent &
	1370	.AND. .NOT. rans_mode ) ) ) THEN
	1371	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1372	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1373	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1374
	1375	ELSE
	1376	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
	1377	id_stg_left, id_stg_right )
	1378	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
	1379	id_stg_left, id_stg_right )
	1380	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
	1381	id_stg_left, id_stg_right )
	1382
	1383	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
	1384	id_stg_south, id_stg_north )
	1385	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
	1386	id_stg_south, id_stg_north )
	1387	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
	1388	id_stg_south, id_stg_north )
[4022]	1389	ENDIF
[2938]	1390	ENDIF
[3347]	1391
[2938]	1392	!
[4309]	1393	!-- Turbulence generation at left and/or right boundary
[2938]	1394	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1395	!
[4022]	1396	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1397	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1398	!-- imposed
	1399	IF ( stg_call ) THEN
	1400
[4438]	1401	DO j = nys, nyn
[4022]	1402	DO k = nzb, nzt + 1
	1403	!
	1404	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1405	IF ( tu(k) == 0.0_wp ) THEN
	1406	fu_yz(k,j) = fuo_yz(k,j)
	1407	ELSE
	1408	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1409	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1410	ENDIF
	1411
	1412	IF ( tv(k) == 0.0_wp ) THEN
	1413	fv_yz(k,j) = fvo_yz(k,j)
	1414	ELSE
	1415	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1416	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1417	ENDIF
	1418
	1419	IF ( tw(k) == 0.0_wp ) THEN
	1420	fw_yz(k,j) = fwo_yz(k,j)
	1421	ELSE
	1422	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1423	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1424	ENDIF
	1425	ENDDO
	1426	ENDDO
	1427
	1428	dist_yz(nzb,:,1) = 0.0_wp
	1429	dist_yz(nzb,:,2) = 0.0_wp
	1430	dist_yz(nzb,:,3) = 0.0_wp
	1431
	1432	IF ( myidx == id_stg_left ) i = nxl
	1433	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1434	DO j = nys, nyn
[4022]	1435	DO k = nzb+1, nzt + 1
	1436	!
	1437	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1438	!-- Additional factors are added to improve the variance of v and w
	1439	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1440	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1441	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1442	ENDDO
	1443	ENDDO
[4309]	1444
[4022]	1445	IF ( myidx == id_stg_left ) i = nxl-1
	1446	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1447	DO j = nys, nyn
[4022]	1448	DO k = nzb+1, nzt + 1
	1449	!
	1450	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1451	!-- Additional factors are added to improve the variance of v and w
	1452	!-- experimental test of 1.2
[3347]	1453	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1454	* 1.2_wp ) &
	1455	* ( a21(k) * fu_yz(k,j) &
[4022]	1456	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1457	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1458	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[3347]	1459	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1460	* 1.3_wp ) &
	1461	* ( a31(k) * fu_yz(k,j) &
	1462	+ a32(k) * fv_yz(k,j) &
[4022]	1463	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1464	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1465	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1466	ENDDO
[2259]	1467	ENDDO
[4022]	1468	ENDIF
[2259]	1469	!
	1470	!-- Mass flux correction following Kim et al. (2013)
	1471	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1472	!-- inflow boundary. First, calculate mean value of the imposed
	1473	!-- perturbations at yz boundary.
	1474	!-- Note, this needs to be done only after the last RK3-substep, else
	1475	!-- the boundary values won't be accessed.
	1476	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1477	mc_factor_l = 0.0_wp
	1478	mc_factor = 0.0_wp
	1479	!
	1480	!-- Sum up the original volume flows (with and without perturbations).
	1481	!-- Note, for non-normal components (here v and w) it is actually no
	1482	!-- volume flow.
[2938]	1483	IF ( myidx == id_stg_left ) i = nxl
	1484	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1485
	1486	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1487	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1488	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1489
	1490	IF ( myidx == id_stg_left ) i = nxl-1
	1491	IF ( myidx == id_stg_right ) i = nxr+1
	1492
	1493	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1494	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1495	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1496	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1497	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1498	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1499
[2938]	1500	#if defined( __parallel )
	1501	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1502	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1503	#else
	1504	mc_factor = mc_factor_l
[2938]	1505	#endif
[4022]	1506	!
	1507	!-- Calculate correction factor and force zero mean perturbations.
	1508	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1509
	1510	IF ( myidx == id_stg_left ) i = nxl
	1511	IF ( myidx == id_stg_right ) i = nxr+1
	1512
[4438]	1513	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
[4022]	1514	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1515	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4022]	1516
	1517
	1518	IF ( myidx == id_stg_left ) i = nxl-1
	1519	IF ( myidx == id_stg_right ) i = nxr+1
	1520
[4438]	1521	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
[4022]	1522	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1523	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4022]	1524
[4438]	1525	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
[4022]	1526	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1527	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4022]	1528	!
[2938]	1529	!-- Add disturbances
	1530	IF ( myidx == id_stg_left ) THEN
[4022]	1531	!
	1532	!-- For the left boundary distinguish between mesoscale offline / self
	1533	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1534	!-- case turbulence is imposed on the mean inflow profiles.
	1535	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1536	!
	1537	!-- Add disturbance at the inflow
[4438]	1538	DO j = nys, nyn
[4022]	1539	DO k = nzb, nzt+1
	1540	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1541	dist_yz(k,j,1) ) &
	1542	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1543	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1544	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1545	dist_yz(k,j,2) ) &
	1546	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1547	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1548	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1549	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1550	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1551	ENDDO
[2938]	1552	ENDDO
[4022]	1553	ELSE
	1554
	1555	DO j = nys, nyn
	1556	DO k = nzb+1, nzt
	1557	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1558	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1559	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1560	u(k,j,-1) = u(k,j,0)
	1561	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1562	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1563	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1564	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1565	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1566	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1567	ENDDO
	1568	ENDDO
	1569	ENDIF
[2938]	1570	ENDIF
	1571	IF ( myidx == id_stg_right ) THEN
[3186]	1572	DO j = nys, nyn
[3347]	1573	DO k = nzb+1, nzt
[3186]	1574	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1575	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1576	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
[3186]	1577	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1578	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1579	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
[3186]	1580	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1581	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1582	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1583	ENDDO
	1584	ENDDO
	1585	ENDIF
	1586	ENDIF
	1587	ENDIF
	1588	!
	1589	!-- Turbulence generation at north and south boundary
	1590	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1591	!
[4022]	1592	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1593	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1594	!-- imposed
	1595	IF ( stg_call ) THEN
[4438]	1596	DO i = nxl, nxr
[4022]	1597	DO k = nzb, nzt + 1
	1598	!
	1599	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1600	IF ( tu(k) == 0.0_wp ) THEN
	1601	fu_xz(k,i) = fuo_xz(k,i)
	1602	ELSE
	1603	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1604	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1605	ENDIF
	1606
	1607	IF ( tv(k) == 0.0_wp ) THEN
	1608	fv_xz(k,i) = fvo_xz(k,i)
	1609	ELSE
	1610	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1611	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1612	ENDIF
	1613
	1614	IF ( tw(k) == 0.0_wp ) THEN
	1615	fw_xz(k,i) = fwo_xz(k,i)
	1616	ELSE
	1617	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1618	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1619	ENDIF
	1620	ENDDO
	1621	ENDDO
	1622
	1623
	1624	dist_xz(nzb,:,1) = 0.0_wp
	1625	dist_xz(nzb,:,2) = 0.0_wp
	1626	dist_xz(nzb,:,3) = 0.0_wp
	1627
	1628	IF ( myidy == id_stg_south ) j = nys
	1629	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1630	DO i = nxl, nxr
[4022]	1631	DO k = nzb+1, nzt + 1
	1632	!
	1633	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1634	!-- Additional factors are added to improve the variance of v and w
	1635	!experimental test of 1.2
[3347]	1636	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1637	* 1.2_wp ) &
	1638	* ( a21(k) * fu_xz(k,i) &
[4022]	1639	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1640	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1641	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1642	ENDDO
	1643	ENDDO
	1644
	1645	IF ( myidy == id_stg_south ) j = nys-1
	1646	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1647	DO i = nxl, nxr
[4022]	1648	DO k = nzb+1, nzt + 1
	1649	!
	1650	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1651	!-- Additional factors are added to improve the variance of v and w
	1652	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1653	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1654	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1655
[3347]	1656	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1657	* 1.3_wp ) &
	1658	* ( a31(k) * fu_xz(k,i) &
	1659	+ a32(k) * fv_xz(k,i) &
[4022]	1660	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1661	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1662	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1663	ENDDO
[2938]	1664	ENDDO
[4022]	1665	ENDIF
[3347]	1666
[2938]	1667	!
	1668	!-- Mass flux correction following Kim et al. (2013)
	1669	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1670	!-- inflow boundary. First, calculate mean value of the imposed
	1671	!-- perturbations at yz boundary.
	1672	!-- Note, this needs to be done only after the last RK3-substep, else
	1673	!-- the boundary values won't be accessed.
	1674	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1675	mc_factor_l = 0.0_wp
	1676	mc_factor = 0.0_wp
	1677
	1678	IF ( myidy == id_stg_south ) j = nys
	1679	IF ( myidy == id_stg_north ) j = nyn+1
	1680
	1681	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1682	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1683	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1684
	1685	IF ( myidy == id_stg_south ) j = nys-1
	1686	IF ( myidy == id_stg_north ) j = nyn+1
	1687
	1688	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1689	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1690	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1691	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1692	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1693	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1694
[2938]	1695	#if defined( __parallel )
[4022]	1696	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1697	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1698	#else
	1699	mc_factor = mc_factor_l
[2938]	1700	#endif
[4022]	1701
	1702	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1703
	1704	IF ( myidy == id_stg_south ) j = nys
	1705	IF ( myidy == id_stg_north ) j = nyn+1
	1706
[4438]	1707	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
[4022]	1708	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1709	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4022]	1710
	1711
	1712	IF ( myidy == id_stg_south ) j = nys-1
	1713	IF ( myidy == id_stg_north ) j = nyn+1
	1714
[4438]	1715	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
[4022]	1716	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1717	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4022]	1718
[4438]	1719	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
[4022]	1720	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1721	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4022]	1722	!
	1723	!-- Add disturbances
	1724	IF ( myidy == id_stg_south ) THEN
	1725	DO i = nxl, nxr
	1726	DO k = nzb+1, nzt
	1727	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1728	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1729	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
[4022]	1730	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1731	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1732	BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1733	v(k,-1,i) = v(k,0,i)
	1734	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1735	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1736	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1737	ENDDO
[2938]	1738	ENDDO
[4022]	1739	ENDIF
	1740	IF ( myidy == id_stg_north ) THEN
	1741
	1742	DO i = nxl, nxr
	1743	DO k = nzb+1, nzt
	1744	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1745	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1746	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
[4022]	1747	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1748	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1749	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
[4022]	1750	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1751	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1752	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1753	ENDDO
[2938]	1754	ENDDO
[4022]	1755	ENDIF
[2938]	1756	ENDIF
[2259]	1757	ENDIF
[3347]	1758	!
[4438]	1759	!-- Exchange ghost points.
	1760	CALL exchange_horiz( u, nbgp )
	1761	CALL exchange_horiz( v, nbgp )
	1762	CALL exchange_horiz( w, nbgp )
	1763	!
[3347]	1764	!-- Finally, set time counter for calling STG to zero
[4022]	1765	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1766
[3987]	1767	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1768
[2259]	1769	END SUBROUTINE stg_main
	1770
	1771	!------------------------------------------------------------------------------!
	1772	! Description:
	1773	! ------------
	1774	!> Generate a set of random number rand_it wich is equal on each PE
	1775	!> and calculate the velocity seed f_n.
	1776	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1777	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1778	!> parts are collected to form the full array.
	1779	!------------------------------------------------------------------------------!
[4309]	1780	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1781
[4309]	1782	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1783	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1784	INTEGER(iwp) :: j !< loop index in y-direction
	1785	INTEGER(iwp) :: jj !< loop index in y-direction
	1786	INTEGER(iwp) :: k !< loop index in z-direction
	1787	INTEGER(iwp) :: kk !< loop index in z-direction
	1788	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1789
	1790	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1791	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1792
	1793	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1794	REAL(wp) :: rand_av !< average of random number
	1795	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1796
[4438]	1797	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
	1798	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1799
[4438]	1800	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1801	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
[4309]	1802
	1803	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1804	!
[4309]	1805	!-- Generate random numbers using the parallel random generator.
[2259]	1806	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1807	!-- unit variance. Note, at the end the random number array must be defined
	1808	!-- globally in order to compute the correlation matrices. However,
	1809	!-- the calculation and normalization of random numbers is done locally,
	1810	!-- while the result is later distributed to all processes. Further,
	1811	!-- please note, a set of random numbers is only calculated for the
	1812	!-- left boundary, while the right boundary uses the same random numbers
	1813	!-- and thus also computes the same correlation matrix.
[4438]	1814	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
	1815	rand_it = 0.0_wp
[2259]	1816
	1817	rand_av = 0.0_wp
	1818	rand_sigma_inv = 0.0_wp
[4438]	1819	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1820	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
	1821	KIND=wp )
[4309]	1822	!
[4438]	1823	!-- Compute and normalize random numbers.
	1824	DO j = nys - mergp, nyn + mergp
[4309]	1825	!
[4438]	1826	!-- Put the random seeds at grid point j
	1827	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
	1828	DO k = nzb - mergp, nzt + 1 + mergp
	1829	CALL random_number_parallel( random_dummy )
	1830	rand_it(k,j) = random_dummy
	1831	ENDDO
[4309]	1832	!
[4438]	1833	!-- Get the new random seeds from last call at grid point j
	1834	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1835	ENDDO
[4309]	1836	!
[4438]	1837	!-- For normalization to zero mean, sum-up the global random numers.
	1838	!-- To normalize the global set of random numbers,
	1839	!-- the inner ghost layers mergp must not be summed-up, else
	1840	!-- the random numbers on the ghost layers will be stronger weighted as they
	1841	!-- also occur on the inner subdomains.
	1842	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1843	MERGE( nyn, nyn + mergp, nyn /= ny )
	1844	DO k = nzb - mergp, nzt + 1 + mergp
	1845	rand_av = rand_av + rand_it(k,j)
[2259]	1846	ENDDO
[4438]	1847	ENDDO
	1848
[4309]	1849	#if defined( __parallel )
	1850	!
[4438]	1851	!-- Sum-up the local averages of the random numbers
	1852	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1853	MPI_SUM, comm1dy, ierr )
[4309]	1854	#endif
[4438]	1855	rand_av = rand_av * nyz_inv
[4309]	1856	!
[4438]	1857	!-- Obtain zero mean
	1858	rand_it= rand_it - rand_av
[4309]	1859	!
[4438]	1860	!-- Now, compute the variance
	1861	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1862	MERGE( nyn, nyn + mergp, nyn /= ny )
	1863	DO k = nzb - mergp, nzt + 1 + mergp
	1864	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1865	ENDDO
[4438]	1866	ENDDO
[2259]	1867
[4309]	1868	#if defined( __parallel )
[2259]	1869	!
[4438]	1870	!-- Sum-up the local quadratic averages of the random numbers
	1871	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1872	MPI_SUM, comm1dy, ierr )
[4309]	1873	#endif
	1874	!
[4438]	1875	!-- Compute standard deviation
	1876	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1877	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1878	ELSE
	1879	rand_sigma_inv = 1.0_wp
[4309]	1880	ENDIF
	1881	!
[4438]	1882	!-- Normalize with standard deviation to obtain unit variance
	1883	rand_it = rand_it * rand_sigma_inv
	1884
	1885	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1886	!
[4438]	1887	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	1888	!-- are two options. In the first one, the computation of the seeds is
	1889	!-- distributed to all processes along the communicator comm1dy and
	1890	!-- gathered on the leftmost and, if necessary, on the rightmost process.
	1891	!-- For huge length scales the computational effort can become quite huge
	1892	!-- (it scales with the turbulent length scales), so that gain by parallelization
	1893	!-- exceeds the costs by the subsequent communication.
	1894	!-- In the second option, which performs better when the turbulent length scales
	1895	!-- are parametrized and thus the loops are smaller, the seeds are computed
	1896	!-- locally and no communication is necessary.
	1897	IF ( compute_velocity_seeds_local ) THEN
	1898
	1899	f_n = 0.0_wp
	1900	DO j = nys, nyn
	1901	DO k = nzb, nzt+1
	1902	DO jj = -n_y(k), n_y(k)
	1903	DO kk = -n_z(k), n_z(k)
	1904	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1905	ENDDO
	1906	ENDDO
	1907	ENDDO
[2259]	1908	ENDDO
	1909
[4438]	1910	ELSE
[2259]	1911
[4438]	1912	f_n_l = 0.0_wp
	1913	DO j = nys, nyn
	1914	DO k = nzb_x_stg, nzt_x_stg+1
	1915	DO jj = -n_y(k), n_y(k)
	1916	DO kk = -n_z(k), n_z(k)
	1917	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1918	ENDDO
[2259]	1919	ENDDO
	1920	ENDDO
	1921	ENDDO
	1922	!
[4438]	1923	!-- Gather velocity seeds of full subdomain
	1924	send_count = nzt_x_stg - nzb_x_stg + 1
	1925	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1926
	1927	#if defined( __parallel )
[4309]	1928	!
[4438]	1929	!-- Gather the velocity seed matrix on left boundary mpi ranks.
	1930	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1931	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1932	id_left, comm1dx, ierr )
[4309]	1933	!
[4438]	1934	!-- If required, gather the same velocity seed matrix on right boundary
	1935	!-- mpi ranks (in offline nesting for example).
	1936	IF ( PRESENT( id_right ) ) THEN
	1937	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1938	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1939	id_right, comm1dx, ierr )
	1940	ENDIF
[2259]	1941	#else
[4438]	1942	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[4444]	1943	!
	1944	!-- Next line required to avoid compile errors because of unused dummy arguments
	1945	IF ( id_left == 0 ) id_right = 0
[2259]	1946	#endif
	1947
[4438]	1948	ENDIF
[2259]	1949
[4438]	1950	DEALLOCATE( rand_it )
	1951
	1952	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1953
[2259]	1954	END SUBROUTINE stg_generate_seed_yz
	1955
[2938]	1956
	1957	!------------------------------------------------------------------------------!
	1958	! Description:
	1959	! ------------
	1960	!> Generate a set of random number rand_it wich is equal on each PE
	1961	!> and calculate the velocity seed f_n.
	1962	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1963	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1964	!> parts are collected to form the full array.
	1965	!------------------------------------------------------------------------------!
[4309]	1966	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1967
	1968	INTEGER(iwp) :: i !< loop index in x-direction
[4309]	1969	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1970	INTEGER(iwp) :: id_south !< core ids at respective boundaries
[2938]	1971	INTEGER(iwp) :: ii !< loop index in x-direction
	1972	INTEGER(iwp) :: k !< loop index in z-direction
	1973	INTEGER(iwp) :: kk !< loop index in z-direction
	1974	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1975
	1976	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1977	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1978
	1979	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1980	REAL(wp) :: rand_av !< average of random number
	1981	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1982
[4438]	1983	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
	1984	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1985
[4438]	1986	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1987	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1988
[4309]	1989	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1990
	1991	!
[4309]	1992	!-- Generate random numbers using the parallel random generator.
[2938]	1993	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1994	!-- unit variance. Note, at the end the random number array must be defined
	1995	!-- globally in order to compute the correlation matrices. However,
	1996	!-- the calculation and normalization of random numbers is done locally,
	1997	!-- while the result is later distributed to all processes. Further,
	1998	!-- please note, a set of random numbers is only calculated for the
	1999	!-- left boundary, while the right boundary uses the same random numbers
	2000	!-- and thus also computes the same correlation matrix.
[4438]	2001	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
	2002	rand_it = 0.0_wp
[2938]	2003
	2004	rand_av = 0.0_wp
	2005	rand_sigma_inv = 0.0_wp
[4438]	2006	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	2007	* ( nx + mergp - ( 0 - mergp ) +1 ), &
	2008	KIND=wp )
[4309]	2009	!
[4438]	2010	!-- Compute and normalize random numbers.
	2011	DO i = nxl - mergp, nxr + mergp
[4309]	2012	!
[4438]	2013	!-- Put the random seeds at grid point ii
	2014	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
	2015	DO k = nzb - mergp, nzt + 1 + mergp
	2016	CALL random_number_parallel( random_dummy )
	2017	rand_it(k,i) = random_dummy
	2018	ENDDO
[4309]	2019	!
[4438]	2020	!-- Get the new random seeds from last call at grid point ii
	2021	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	2022	ENDDO
[4309]	2023	!
[4438]	2024	!-- For normalization to zero mean, sum-up the global random numers.
	2025	!-- To normalize the global set of random numbers,
	2026	!-- the inner ghost layers mergp must not be summed-up, else
	2027	!-- the random numbers on the ghost layers will be stronger weighted as they
	2028	!-- also occur on the inner subdomains.
	2029	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	2030	MERGE( nxr, nxr + mergp, nxr /= nx )
	2031	DO k = nzb - mergp, nzt + 1 + mergp
	2032	rand_av = rand_av + rand_it(k,i)
[2938]	2033	ENDDO
[4438]	2034	ENDDO
	2035
[4309]	2036	#if defined( __parallel )
[4438]	2037	!
	2038	!-- Sum-up the local averages of the random numbers
	2039	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	2040	MPI_SUM, comm1dx, ierr )
[4309]	2041	#endif
[4438]	2042	rand_av = rand_av * nxz_inv
[4309]	2043	!
[4438]	2044	!-- Obtain zero mean
	2045	rand_it= rand_it - rand_av
[4309]	2046	!
[4438]	2047	!-- Now, compute the variance
	2048	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	2049	MERGE( nxr, nxr + mergp, nxr /= nx )
	2050	DO k = nzb - mergp, nzt + 1 + mergp
	2051	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	2052	ENDDO
[4438]	2053	ENDDO
[2938]	2054
[4309]	2055	#if defined( __parallel )
[4438]	2056	!
	2057	!-- Sum-up the local quadratic averages of the random numbers
	2058	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	2059	MPI_SUM, comm1dx, ierr )
[4309]	2060	#endif
[2938]	2061	!
[4438]	2062	!-- Compute standard deviation
	2063	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	2064	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	2065	ELSE
	2066	rand_sigma_inv = 1.0_wp
[4309]	2067	ENDIF
	2068	!
[4438]	2069	!-- Normalize with standard deviation to obtain unit variance
	2070	rand_it = rand_it * rand_sigma_inv
	2071
	2072	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2073	!
[4438]	2074	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	2075	!-- are two options. In the first one, the computation of the seeds is
	2076	!-- distributed to all processes along the communicator comm1dx and
	2077	!-- gathered on the southmost and, if necessary, on the northmost process.
	2078	!-- For huge length scales the computational effort can become quite huge
	2079	!-- (it scales with the turbulent length scales), so that gain by parallelization
	2080	!-- exceeds the costs by the subsequent communication.
	2081	!-- In the second option, which performs better when the turbulent length scales
	2082	!-- are parametrized and thus the loops are smaller, the seeds are computed
	2083	!-- locally and no communication is necessary.
	2084	IF ( compute_velocity_seeds_local ) THEN
[2938]	2085
[4438]	2086	f_n = 0.0_wp
	2087	DO i = nxl, nxr
	2088	DO k = nzb, nzt+1
	2089	DO ii = -n_x(k), n_x(k)
	2090	DO kk = -n_z(k), n_z(k)
	2091	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2092	ENDDO
[2938]	2093	ENDDO
	2094	ENDDO
	2095	ENDDO
	2096
[4438]	2097	ELSE
[2938]	2098
[4438]	2099	f_n_l = 0.0_wp
	2100	DO i = nxl, nxr
	2101	DO k = nzb_y_stg, nzt_y_stg+1
	2102	DO ii = -n_x(k), n_x(k)
	2103	DO kk = -n_z(k), n_z(k)
	2104	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2105	ENDDO
	2106	ENDDO
	2107	ENDDO
	2108	ENDDO
[2938]	2109	!
[4438]	2110	!-- Gather velocity seeds of full subdomain
	2111	send_count = nzt_y_stg - nzb_y_stg + 1
	2112	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2113
	2114	#if defined( __parallel )
[4309]	2115	!
[4438]	2116	!-- Gather the processed velocity seed on south boundary mpi ranks.
	2117	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2118	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2119	id_south, comm1dy, ierr )
[4309]	2120	!
[4438]	2121	!-- Gather the processed velocity seed on north boundary mpi ranks.
	2122	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2123	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2124	id_north, comm1dy, ierr )
[2938]	2125	#else
[4438]	2126	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[4444]	2127	!
	2128	!-- Next line required to avoid compile errors because of unused dummy arguments
	2129	IF ( id_north == 0 ) id_south = 0
[2938]	2130	#endif
	2131
[4438]	2132	ENDIF
	2133
	2134	DEALLOCATE( rand_it )
	2135
	2136	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2137
[2938]	2138	END SUBROUTINE stg_generate_seed_xz
	2139
[3347]	2140	!------------------------------------------------------------------------------!
	2141	! Description:
	2142	! ------------
	2143	!> Parametrization of the Reynolds stress tensor, following the parametrization
	2144	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	2145	!> dispserion modelling. Please note, the parametrization does not distinguish
	2146	!> between along-wind and cross-wind turbulence.
	2147	!------------------------------------------------------------------------------!
	2148	SUBROUTINE parametrize_reynolds_stress
	2149
	2150	INTEGER(iwp) :: k !< loop index in z-direction
	2151
	2152	REAL(wp) :: zzi !< ratio of z/zi
	2153
	2154	DO k = nzb+1, nzt+1
	2155	!
[4022]	2156	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2157	!-- The function decreases to 1/10 after one length scale above the
	2158	!-- ABL top.
	2159	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2160	!
[4022]	2161	!-- Determine normalized height coordinate
	2162	zzi = zu(k) / zi_ribulk
[3347]	2163	!
[4022]	2164	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
[4438]	2165	!-- to the denominator, else the mergpe-function can crash if scale_l is
[4022]	2166	!-- zero.
	2167	r11(k) = scale_us*2 ( &
	2168	MERGE( 0.35_wp * ABS( &
	2169	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2170	)**( 2.0_wp / 3.0_wp ), &
	2171	0.0_wp, &
	2172	scale_l < 0.0_wp ) &
	2173	+ 5.0_wp - 4.0_wp * zzi &
	2174	) * blend
	2175
	2176	r22(k) = r11(k)
	2177	!
	2178	!-- w'w'
	2179	r33(k) = scale_wm*2 ( &
	2180	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2181	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2182	) * blend
	2183	!
	2184	!-- u'w' and v'w'. Assume isotropy.
	2185	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	2186	r32(k) = r31(k)
[3347]	2187	!
[4022]	2188	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	2189	!-- a similar profile as for u'w'.
	2190	r21(k) = r31(k)
[3347]	2191	ENDDO
	2192
	2193	!
	2194	!-- Set bottom boundary condition
	2195	r11(nzb) = r11(nzb+1)
	2196	r22(nzb) = r22(nzb+1)
	2197	r33(nzb) = r33(nzb+1)
	2198
	2199	r21(nzb) = r11(nzb+1)
	2200	r31(nzb) = r31(nzb+1)
	2201	r32(nzb) = r32(nzb+1)
	2202
	2203
	2204	END SUBROUTINE parametrize_reynolds_stress
	2205
	2206	!------------------------------------------------------------------------------!
	2207	! Description:
	2208	! ------------
	2209	!> Calculate the coefficient matrix from the Lund rotation.
	2210	!------------------------------------------------------------------------------!
	2211	SUBROUTINE calc_coeff_matrix
	2212
	2213	INTEGER(iwp) :: k !< loop index in z-direction
	2214
	2215	!
	2216	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2217	DO k = nzb+1, nzt+1
[4022]	2218	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	2219	a11(k) = SQRT( r11(k) )
	2220	a21(k) = r21(k) / a11(k)
	2221	a31(k) = r31(k) / a11(k)
	2222	ELSE
	2223	a11(k) = 10E-8_wp
	2224	a21(k) = 10E-8_wp
	2225	a31(k) = 10E-8_wp
	2226	ENDIF
	2227	ENDDO
	2228	DO k = nzb+1, nzt+1
	2229	a22(k) = r22(k) - a21(k)**2
[4022]	2230	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2231	a22(k) = SQRT( a22(k) )
	2232	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	2233	ELSE
	2234	a22(k) = 10E-8_wp
	2235	a32(k) = 10E-8_wp
	2236	ENDIF
	2237	ENDDO
	2238	DO k = nzb+1, nzt+1
	2239	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2240	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2241	a33(k) = SQRT( a33(k) )
	2242	ELSE
	2243	a33(k) = 10E-8_wp
	2244	ENDIF
	2245	ENDDO
	2246	!
	2247	!-- Set bottom boundary condition
	2248	a11(nzb) = a11(nzb+1)
	2249	a22(nzb) = a22(nzb+1)
	2250	a21(nzb) = a21(nzb+1)
	2251	a33(nzb) = a33(nzb+1)
	2252	a31(nzb) = a31(nzb+1)
	2253	a32(nzb) = a32(nzb+1)
	2254
	2255	END SUBROUTINE calc_coeff_matrix
	2256
	2257	!------------------------------------------------------------------------------!
	2258	! Description:
	2259	! ------------
	2260	!> This routine controls the re-adjustment of the turbulence statistics used
	2261	!> for generating turbulence at the lateral boundaries.
	2262	!------------------------------------------------------------------------------!
	2263	SUBROUTINE stg_adjust
	2264
[3987]	2265	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2266	!
[4022]	2267	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2268	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2269	!-- synthetic turbulence shall be parametrized nevertheless, the
	2270	!-- boundary-layer depth need to determined first.
	2271	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2272	CALL nesting_offl_calc_zi
	2273	!
	2274	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2275	!-- are calculated.
[3347]	2276	CALL calc_scaling_variables
	2277	!
	2278	!-- Set length and time scales depending on boundary-layer height
	2279	CALL calc_length_and_time_scale
	2280	!
	2281	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2282	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2283	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2284	!-- friction velocity and velocity scale.
	2285	CALL parametrize_reynolds_stress
	2286	!
	2287	!-- Calculate coefficient matrix from Reynolds stress tensor
	2288	!-- (Lund rotation)
	2289	CALL calc_coeff_matrix
	2290	!
	2291	!-- Determine filter functions on basis of updated length scales
	2292	CALL stg_filter_func( nux, bux ) !filter ux
	2293	CALL stg_filter_func( nuy, buy ) !filter uy
	2294	CALL stg_filter_func( nuz, buz ) !filter uz
	2295	CALL stg_filter_func( nvx, bvx ) !filter vx
	2296	CALL stg_filter_func( nvy, bvy ) !filter vy
	2297	CALL stg_filter_func( nvz, bvz ) !filter vz
	2298	CALL stg_filter_func( nwx, bwx ) !filter wx
	2299	CALL stg_filter_func( nwy, bwy ) !filter wy
	2300	CALL stg_filter_func( nwz, bwz ) !filter wz
	2301	!
	2302	!-- Reset time counter for controlling next adjustment to zero
	2303	time_stg_adjust = 0.0_wp
[3987]	2304
	2305	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2306
	2307	END SUBROUTINE stg_adjust
	2308
	2309
	2310	!------------------------------------------------------------------------------!
	2311	! Description:
	2312	! ------------
	2313	!> Calculates turbuluent length and time scales if these are not available
	2314	!> from measurements.
	2315	!------------------------------------------------------------------------------!
	2316	SUBROUTINE calc_length_and_time_scale
	2317
[4022]	2318	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2319
[4022]	2320	REAL(wp) :: length_scale_dum !< effectively used length scale
	2321
[3347]	2322	!
	2323	!-- In initial call the boundary-layer depth can be zero. This case, set
	2324	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2325	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2326	!
	2327	!-- Set-up default turbulent length scales. From the numerical point of
	2328	!-- view the imposed perturbations should not be immediately dissipated
	2329	!-- by the numerics. The numerical dissipation, however, acts on scales
	2330	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2331	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2332	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2333	!-- imposing any perturbations) in order to save computational costs.
	2334	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2335	!-- using the length scales and the mean profiles of u- and v-component.
	2336	DO k = nzb+1, nzt+1
	2337	!
[4022]	2338	!-- Determine blending parameter. Within the boundary layer length scales
	2339	!-- are constant, while above lengths scales approach gradully zero,
	2340	!-- i.e. imposed turbulence is not correlated in space and time,
	2341	!-- just white noise, which saves computations power as the loops for the
	2342	!-- computation of the filter functions depend on the length scales.
	2343	!-- The value decreases to 1/10 after one length scale above the
	2344	!-- ABL top.
	2345	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2346	!
[4022]	2347	!-- Assume isotropic turbulence length scales
	2348	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2349	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2350	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2351	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2352	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2353	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2354	!
[4022]	2355	!-- Along the vertical direction limit the length scale further by the
	2356	!-- boundary-layer depth to assure that no length scales larger than
	2357	!-- the boundary-layer depth are used
	2358	length_scale_dum = MIN( length_scale, zi_ribulk )
	2359
	2360	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2361	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2362	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2363	!
[4022]	2364	!-- Limit time scales, else they become very larger for low wind speed,
	2365	!-- imposing long-living inflow perturbations which in turn propagate
	2366	!-- further into the model domain. Use u_init and v_init to calculate
	2367	!-- the time scales, which will be equal to the inflow profiles, both,
	2368	!-- in offline nesting mode or in dirichlet/radiation mode.
	2369	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2370	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2371	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2372	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2373	!
	2374	!-- Time scale of w-component is a mixture from u- and v-component.
	2375	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2376
[3347]	2377	ENDDO
	2378	!
	2379	!-- Set bottom boundary condition for the length and time scales
	2380	nux(nzb) = nux(nzb+1)
	2381	nuy(nzb) = nuy(nzb+1)
	2382	nuz(nzb) = nuz(nzb+1)
	2383	nvx(nzb) = nvx(nzb+1)
	2384	nvy(nzb) = nvy(nzb+1)
	2385	nvz(nzb) = nvz(nzb+1)
	2386	nwx(nzb) = nwx(nzb+1)
	2387	nwy(nzb) = nwy(nzb+1)
	2388	nwz(nzb) = nwz(nzb+1)
	2389
	2390	tu(nzb) = tu(nzb+1)
	2391	tv(nzb) = tv(nzb+1)
	2392	tw(nzb) = tw(nzb+1)
	2393
	2394
	2395	END SUBROUTINE calc_length_and_time_scale
	2396
	2397	!------------------------------------------------------------------------------!
	2398	! Description:
	2399	! ------------
	2400	!> Calculate scaling variables which are used for turbulence parametrization
	2401	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2402	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2403	!------------------------------------------------------------------------------!
	2404	SUBROUTINE calc_scaling_variables
	2405
	2406	INTEGER(iwp) :: i !< loop index in x-direction
	2407	INTEGER(iwp) :: j !< loop index in y-direction
	2408	INTEGER(iwp) :: k !< loop index in z-direction
	2409	INTEGER(iwp) :: m !< surface element index
	2410
	2411	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2412	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2413	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2414	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2415	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2416	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2417	REAL(wp) :: w_convective !< convective velocity scale
	2418
	2419	!
[3937]	2420	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2421	!-- near-surface temperature in the model domain.
	2422	pt_surf_mean_l = 0.0_wp
	2423	shf_mean_l = 0.0_wp
	2424	scale_l_l = 0.0_wp
	2425	friction_vel_l = 0.0_wp
[3347]	2426	DO m = 1, surf_def_h(0)%ns
[3937]	2427	i = surf_def_h(0)%i(m)
	2428	j = surf_def_h(0)%j(m)
	2429	k = surf_def_h(0)%k(m)
	2430	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2431	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2432	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2433	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2434	ENDDO
	2435	DO m = 1, surf_lsm_h%ns
[3937]	2436	i = surf_lsm_h%i(m)
	2437	j = surf_lsm_h%j(m)
	2438	k = surf_lsm_h%k(m)
	2439	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2440	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2441	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2442	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2443	ENDDO
	2444	DO m = 1, surf_usm_h%ns
[3937]	2445	i = surf_usm_h%i(m)
	2446	j = surf_usm_h%j(m)
	2447	k = surf_usm_h%k(m)
	2448	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2449	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2450	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2451	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2452	ENDDO
	2453
	2454	#if defined( __parallel )
[3937]	2455	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2456	comm2d, ierr )
[3937]	2457	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2458	comm2d, ierr )
[3937]	2459	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2460	comm2d, ierr )
	2461	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2462	comm2d, ierr )
[3347]	2463	#else
[3937]	2464	scale_us = friction_vel_l
	2465	shf_mean = shf_mean_l
	2466	scale_l = scale_l_l
	2467	pt_surf_mean = pt_surf_mean_l
[3347]	2468	#endif
	2469
[3937]	2470	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2471	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2472	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2473	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2474	!
	2475	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2476	!-- is negative, set convective velocity scale to zero.
	2477	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2478	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2479	ELSE
	2480	w_convective = 0.0_wp
	2481	ENDIF
	2482	!
	2483	!-- Finally, in order to consider also neutral or stable stratification,
	2484	!-- compute momentum velocity scale from u* and convective velocity scale,
	2485	!-- according to Rotach et al. (1996).
	2486	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2487
	2488	END SUBROUTINE calc_scaling_variables
	2489
[2259]	2490	END MODULE synthetic_turbulence_generator_mod

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