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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4442

Last change on this file since 4442 was 4442, checked in by suehring, 4 years ago
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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	!
[3885]	17	! Copyright 2017-2019 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 4442 2020-03-04 19:21:13Z suehring $
[4442]	27	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	28	! (was accidantly changed).
	29	!
	30	! 4441 2020-03-04 19:20:35Z suehring
[4440]	31	! Correct misplaced preprocessor directive
	32	!
	33	! 4438 2020-03-03 20:49:28Z suehring
[4438]	34	! Performance optimizations in velocity-seed calculation:
	35	! - random number array is only defined and computed locally (except for
	36	! normalization to zero mean and unit variance)
	37	! - parallel random number generator is applied independent on the 2D random
	38	! numbers in other routines
	39	! - option to decide wheter velocity seeds are computed locally without any
	40	! further communication or are computed by all processes along the
	41	! communicator
	42	!
	43	! 4346 2019-12-18 11:55:56Z motisi
[4346]	44	! Introduction of wall_flags_total_0, which currently sets bits based on static
	45	! topography information used in wall_flags_static_0
	46	!
	47	! 4335 2019-12-12 16:39:05Z suehring
[4335]	48	! Commentation of last commit
	49	!
	50	! 4332 2019-12-10 19:44:12Z suehring
[4332]	51	! Limit initial velocity seeds in restart runs, if not the seed calculation
	52	! may become unstable. Further, minor bugfix in initial velocity seed
	53	! calculation.
	54	!
	55	! 4329 2019-12-10 15:46:36Z motisi
[4329]	56	! Renamed wall_flags_0 to wall_flags_static_0
	57	!
	58	! 4309 2019-11-26 18:49:59Z suehring
[4309]	59	! Computation of velocity seeds optimized. This implies that random numbers
	60	! are computed now using the parallel random number generator. Random numbers
	61	! are now only computed and normalized locally, while distributed over all
	62	! mpi ranks afterwards, instead of computing random numbers on a global array.
	63	! Further, the number of calls for the time-consuming velocity-seed generation
	64	! is reduced - now the left and right, as well as the north and south boundary
	65	! share the same velocity-seed matrices.
	66	!
	67	! 4182 2019-08-22 15:20:23Z scharf
[4182]	68	! Corrected "Former revisions" section
	69	!
	70	! 4148 2019-08-08 11:26:00Z suehring
[4148]	71	! Remove unused variable
	72	!
	73	! 4144 2019-08-06 09:11:47Z raasch
[4144]	74	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	75	!
	76	! 4071 2019-07-03 20:02:00Z suehring
[4071]	77	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	78	! information is not read from file.
	79	!
	80	! 4022 2019-06-12 11:52:39Z suehring
[4022]	81	! Several bugfixes and improvements
	82	! - revise bias correction of the imposed perturbations (correction via volume
	83	! flow can create instabilities in case the mean volume flow is close to zero)
	84	! - introduce lower limits in calculation of coefficient matrix, else the
	85	! calculation may become numerically unstable
	86	! - impose perturbations every timestep, even though no new set of perturbations
	87	! is generated in case dt_stg_call /= dt_3d
	88	! - Implement a gradual decrease of Reynolds stress and length scales above
	89	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	90	! discontinuous decrease
	91	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	92	!
	93	! 3987 2019-05-22 09:52:13Z kanani
[3987]	94	! Introduce alternative switch for debug output during timestepping
	95	!
	96	! 3938 2019-04-29 16:06:25Z suehring
[3938]	97	! Remove unused variables
	98	!
	99	! 3937 2019-04-29 15:09:07Z suehring
[3937]	100	! Minor bugfix in case of a very early restart where mc_factor is sill not
	101	! present.
	102	! Some modification and fixing of potential bugs in the calculation of scaling
	103	! parameters used for synthetic turbulence parametrization.
	104	!
	105	! 3909 2019-04-17 09:13:25Z suehring
[3909]	106	! Minor bugfix for last commit
	107	!
	108	! 3900 2019-04-16 15:17:43Z suehring
[3900]	109	! Missing re-calculation of perturbation seeds in case of restarts
	110	!
	111	! 3891 2019-04-12 17:52:01Z suehring
[3891]	112	! Bugfix in initialization in case of restart runs.
	113	!
	114	! 3885 2019-04-11 11:29:34Z kanani
[3885]	115	! Changes related to global restructuring of location messages and introduction
	116	! of additional debug messages
	117	!
	118	!
[3775]	119	! removed unused variables
	120	!
	121	! 3719 2019-02-06 13:10:18Z kanani
[3719]	122	! Removed log_point measurement from stg_init, since this part is counted to
	123	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	124	! the subroutines in time_integration for better overview.
	125	!
[4182]	126	! 2259 2017-06-08 09:09:11Z gronemeier
	127	! Initial revision
[3044]	128	!
[4182]	129	! Authors:
	130	! --------
	131	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	132	!
	133	!
[2259]	134	! Description:
	135	! ------------
	136	!> The module generates turbulence at the inflow boundary based on a method by
	137	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	138	!> correction by Kim et al. (2013).
	139	!> The turbulence is correlated based on length scales in y- and z-direction and
	140	!> a time scale for each velocity component. The profiles of length and time
	141	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	142	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	143	!> within the boundary layer.
[2259]	144	!>
	145	!> @todo test restart
	146	!> enable cyclic_fill
	147	!> implement turbulence generation for e and pt
[2945]	148	!> @todo Input of height-constant length scales via namelist
[2259]	149	!> @note <Enter notes on the module>
	150	!> @bug Height information from input file is not used. Profiles from input
	151	!> must match with current PALM grid.
	152	!> In case of restart, velocity seeds differ from precursor run if a11,
	153	!> a22, or a33 are zero.
	154	!------------------------------------------------------------------------------!
	155	MODULE synthetic_turbulence_generator_mod
	156
	157
	158	USE arrays_3d, &
[4022]	159	ONLY: dzw, &
	160	ddzw, &
	161	drho_air, &
	162	mean_inflow_profiles, &
	163	q, &
[4071]	164	q_init, &
	165	pt, &
	166	pt_init, &
[4022]	167	u, &
	168	u_init, &
	169	v, &
	170	v_init, &
	171	w, &
	172	zu, &
	173	zw
[2259]	174
[3274]	175	USE basic_constants_and_equations_mod, &
[4022]	176	ONLY: g, &
	177	kappa, &
	178	pi
[2259]	179
	180	USE control_parameters, &
[4022]	181	ONLY: bc_lr, &
	182	bc_ns, &
	183	child_domain, &
	184	coupling_char, &
	185	debug_output_timestep, &
	186	dt_3d, &
	187	e_init, &
[4071]	188	humidity, &
[3885]	189	initializing_actions, &
[4022]	190	intermediate_timestep_count, &
	191	intermediate_timestep_count_max, &
	192	length, &
[3885]	193	message_string, &
[4022]	194	nesting_offline, &
[4071]	195	neutral, &
[3885]	196	num_mean_inflow_profiles, &
[4309]	197	random_generator, &
[4022]	198	rans_mode, &
	199	restart_string, &
	200	syn_turb_gen, &
	201	time_since_reference_point, &
	202	turbulent_inflow
[4438]	203
	204	USE cpulog, &
	205	ONLY: cpu_log, &
	206	log_point_s
	207
[4022]	208	USE grid_variables, &
	209	ONLY: ddx, &
	210	ddy, &
	211	dx, &
	212	dy
[2259]	213
	214	USE indices, &
[4022]	215	ONLY: nbgp, &
	216	nz, &
	217	nzb, &
	218	nzt, &
	219	nx, &
	220	nxl, &
	221	nxlu, &
	222	nxr, &
	223	ny, &
	224	nys, &
	225	nysv, &
	226	nyn, &
[4346]	227	wall_flags_total_0
[2259]	228
	229	USE kinds
	230
[2967]	231	#if defined( __parallel ) && !defined( __mpifh )
[2259]	232	USE MPI
[2841]	233	#endif
[2259]	234
[3347]	235	USE nesting_offl_mod, &
[4022]	236	ONLY: nesting_offl_calc_zi, &
	237	zi_ribulk
[3347]	238
[2259]	239	USE pegrid, &
[4022]	240	ONLY: comm1dx, &
	241	comm1dy, &
	242	comm2d, &
	243	ierr, &
	244	myidx, &
	245	myidy, &
	246	pdims
[4438]	247
[4022]	248	USE pmc_interface, &
	249	ONLY : rans_mode_parent
[4438]	250
	251	USE random_generator_parallel, &
	252	ONLY: init_parallel_random_generator, &
	253	random_dummy, &
[4309]	254	random_number_parallel, &
[4438]	255	random_seed_parallel
[2259]	256
	257	USE transpose_indices, &
[4022]	258	ONLY: nzb_x, &
	259	nzt_x
[2259]	260
[4438]	261	USE surface_mod, &
	262	ONLY: surf_def_h, &
	263	surf_lsm_h, &
	264	surf_usm_h
[2259]	265
	266	IMPLICIT NONE
	267
[2967]	268	#if defined( __parallel ) && defined( __mpifh )
[2841]	269	INCLUDE "mpif.h"
	270	#endif
	271
[3182]	272
[3347]	273	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	274	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	275	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[4438]	276	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
	277	!< is distributed over several processes
[2259]	278
[3038]	279	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	280	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	281	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	282	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4438]	283	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
[3038]	284	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	285	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	286	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	287	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4309]	288	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	289	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	290	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	291	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[2259]	292
[4022]	293	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	294	!< required for bias correction of imposed perturbations
	295	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	296	!< required for bias correction of imposed perturbations
	297
[3347]	298	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	299	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	300	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	301	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
	302	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	303	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	308	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	311
[4438]	312	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	313	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	314	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	315	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
	316
[4022]	317	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	318	!< scales above the boundary layer
	319	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	320	!< one length scale above ABL top
	321	REAL(wp) :: d_l !< blend_coeff/length_scale
	322	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	323	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
[4438]	324	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
[3347]	325	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	326	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	327	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	328	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	329	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	330
[4022]	331	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	332
[4022]	333
[3347]	334	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	335	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	336	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	337	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	338	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	339	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	340
	341	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	342	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	343	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	344	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	345	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	346	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	347	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	348	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	349	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	350
[3347]	351	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	352	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	353	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	354	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	355	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	356	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	357	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	372
	373	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	374	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	375
	376	!
	377	!-- PALM interfaces:
[3347]	378	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	379	INTERFACE stg_adjust
	380	MODULE PROCEDURE stg_adjust
	381	END INTERFACE stg_adjust
	382	!
[2259]	383	!-- Input parameter checks to be done in check_parameters
	384	INTERFACE stg_check_parameters
	385	MODULE PROCEDURE stg_check_parameters
	386	END INTERFACE stg_check_parameters
	387
	388	!
	389	!-- Calculate filter functions
	390	INTERFACE stg_filter_func
	391	MODULE PROCEDURE stg_filter_func
	392	END INTERFACE stg_filter_func
	393
	394	!
[2938]	395	!-- Generate velocity seeds at south and north domain boundary
	396	INTERFACE stg_generate_seed_xz
	397	MODULE PROCEDURE stg_generate_seed_xz
	398	END INTERFACE stg_generate_seed_xz
	399	!
	400	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	401	INTERFACE stg_generate_seed_yz
	402	MODULE PROCEDURE stg_generate_seed_yz
	403	END INTERFACE stg_generate_seed_yz
	404
	405	!
	406	!-- Output of information to the header file
	407	INTERFACE stg_header
	408	MODULE PROCEDURE stg_header
	409	END INTERFACE stg_header
	410
	411	!
	412	!-- Initialization actions
	413	INTERFACE stg_init
	414	MODULE PROCEDURE stg_init
	415	END INTERFACE stg_init
	416
	417	!
	418	!-- Main procedure of synth. turb. gen.
	419	INTERFACE stg_main
	420	MODULE PROCEDURE stg_main
	421	END INTERFACE stg_main
	422
	423	!
	424	!-- Reading of NAMELIST parameters
	425	INTERFACE stg_parin
	426	MODULE PROCEDURE stg_parin
	427	END INTERFACE stg_parin
	428
	429	!
	430	!-- Reading of parameters for restart runs
[2894]	431	INTERFACE stg_rrd_global
	432	MODULE PROCEDURE stg_rrd_global
	433	END INTERFACE stg_rrd_global
[2259]	434
	435	!
	436	!-- Writing of binary output for restart runs
[2894]	437	INTERFACE stg_wrd_global
	438	MODULE PROCEDURE stg_wrd_global
	439	END INTERFACE stg_wrd_global
[2259]	440
	441	SAVE
	442
	443	PRIVATE
	444
	445	!
	446	!-- Public interfaces
[3347]	447	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	448	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	449
	450	!
	451	!-- Public variables
[3347]	452	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	453	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	454	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	455
	456
	457	CONTAINS
	458
	459
	460	!------------------------------------------------------------------------------!
	461	! Description:
	462	! ------------
	463	!> Check parameters routine for synthetic turbulence generator
	464	!------------------------------------------------------------------------------!
	465	SUBROUTINE stg_check_parameters
	466
[3182]	467	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	468	nesting_offline ) THEN
[3376]	469	message_string = 'Synthetic turbulence generator is required ' // &
	470	'if offline nesting is applied and PALM operates ' // &
	471	'in LES mode.'
	472	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	473	ENDIF
	474
[3182]	475	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	476	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	477	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	478	'when nesting is applied and parent operates in ' // &
	479	'RANS-mode but current child in LES mode.'
[3376]	480	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	481	ENDIF
	482
[2776]	483	IF ( use_syn_turb_gen ) THEN
[2259]	484
[3579]	485	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	486	.NOT. rans_mode_parent ) THEN
	487	message_string = 'Using synthetic turbulence generator ' // &
	488	'is not allowed in LES-LES nesting.'
	489	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	490
	491	ENDIF
	492
	493	IF ( child_domain .AND. rans_mode .AND. &
	494	rans_mode_parent ) THEN
	495	message_string = 'Using synthetic turbulence generator ' // &
	496	'is not allowed in RANS-RANS nesting.'
	497	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	498
	499	ENDIF
	500
[3182]	501	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	502
[2938]	503	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	504	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	505	message_string = 'Using synthetic turbulence generator ' // &
[3579]	506	'requires %initializing_actions = ' // &
	507	'"set_constant_profiles" or "read_restart_data"' //&
	508	', if not offline nesting is applied.'
[2938]	509	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	510	ENDIF
	511
	512	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	513	message_string = 'Using synthetic turbulence generator ' // &
[3347]	514	'requires &bc_lr = "dirichlet/radiation", ' // &
	515	'if not offline nesting is applied.'
[2938]	516	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	517	ENDIF
	518	IF ( bc_ns /= 'cyclic' ) THEN
	519	message_string = 'Using synthetic turbulence generator ' // &
[3579]	520	'requires &bc_ns = "cyclic", ' // &
[3347]	521	'if not offline nesting is applied.'
[2938]	522	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	523	ENDIF
	524
[2259]	525	ENDIF
	526
	527	IF ( turbulent_inflow ) THEN
	528	message_string = 'Using synthetic turbulence generator ' // &
[2938]	529	'in combination &with turbulent_inflow = .T. '// &
	530	'is not allowed'
[2259]	531	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	532	ENDIF
[4309]	533	!
	534	!-- Synthetic turbulence generator requires the parallel random generator
	535	IF ( random_generator /= 'random-parallel' ) THEN
	536	message_string = 'Using synthetic turbulence generator ' // &
	537	'requires random_generator = random-parallel.'
	538	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	539	ENDIF
[2259]	540
	541	ENDIF
	542
	543	END SUBROUTINE stg_check_parameters
	544
	545
	546	!------------------------------------------------------------------------------!
	547	! Description:
	548	! ------------
	549	!> Header output for synthetic turbulence generator
	550	!------------------------------------------------------------------------------!
	551	SUBROUTINE stg_header ( io )
	552
	553	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	554
	555	!
	556	!-- Write synthetic turbulence generator Header
	557	WRITE( io, 1 )
[2776]	558	IF ( use_syn_turb_gen ) THEN
[2259]	559	WRITE( io, 2 )
	560	ELSE
	561	WRITE( io, 3 )
	562	ENDIF
[3347]	563
	564	IF ( parametrize_inflow_turbulence ) THEN
	565	WRITE( io, 4 ) dt_stg_adjust
	566	ELSE
	567	WRITE( io, 5 )
	568	ENDIF
[2259]	569
	570	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	571	' ------------------------------------------'/)
[3347]	572	2 FORMAT (' synthetic turbulence generator is switched on')
	573	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	574	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	575	5 FORMAT (' imposed turbulence is read from file' )
[2259]	576
	577	END SUBROUTINE stg_header
	578
	579
	580	!------------------------------------------------------------------------------!
	581	! Description:
	582	! ------------
	583	!> Initialization of the synthetic turbulence generator
	584	!------------------------------------------------------------------------------!
	585	SUBROUTINE stg_init
	586
[3347]	587	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	588
[2669]	589	#if defined( __parallel )
[2259]	590	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	591	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	592	#endif
[2259]	593
[2938]	594	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	595	INTEGER(iwp) :: j !> loop index
	596	INTEGER(iwp) :: k !< index
	597	INTEGER(iwp) :: newtype !< dummy MPI type
	598	INTEGER(iwp) :: realsize !< size of REAL variables
[4309]	599
[4022]	600	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	601	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	602	!
	603	!-- Dummy variables used for reading profiles
	604	REAL(wp) :: d1 !< u profile
	605	REAL(wp) :: d2 !< v profile
	606	REAL(wp) :: d3 !< w profile
	607	REAL(wp) :: d5 !< e profile
	608	REAL(wp) :: luy !< length scale for u in y direction
	609	REAL(wp) :: luz !< length scale for u in z direction
	610	REAL(wp) :: lvy !< length scale for v in y direction
	611	REAL(wp) :: lvz !< length scale for v in z direction
	612	REAL(wp) :: lwy !< length scale for w in y direction
	613	REAL(wp) :: lwz !< length scale for w in z direction
[3038]	614	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[2259]	615	REAL(wp) :: zz !< height
	616
[2938]	617
[2259]	618	#if defined( __parallel )
	619	CALL MPI_BARRIER( comm2d, ierr )
	620	#endif
[4438]	621	!
	622	!-- Create mpi-datatypes for exchange in case of non-local but distributed
	623	!-- computation of the velocity seeds. This option is useful in
	624	!-- case large turbulent length scales are presentm, where the computational
	625	!-- effort becomes large and need to be parallelized. For parametrized
	626	!-- turbulence the length scales are small and computing the velocity seeds
	627	!-- locally is faster (no overhead by communication).
	628	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	629	#if defined( __parallel )
[4438]	630	!
	631	!-- Determine processor decomposition of z-axis along x- and y-direction
	632	nnz = nz / pdims(1)
	633	nzb_x_stg = 1 + myidx * INT( nnz )
	634	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
	635
	636	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
	637	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
	638
	639	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	640	.AND. .NOT. rans_mode ) ) THEN
	641	nnz = nz / pdims(2)
	642	nzb_y_stg = 1 + myidy * INT( nnz )
	643	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
	644
	645	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
	646	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	647	ENDIF
	648
	649	!
	650	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	651	!-- velocity seeds
	652	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	653	extent = 1 * realsize
	654	!
	655	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	656	!-- layer
	657	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
	658	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
	659	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	660	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	661	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	662	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	663
	664	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	665	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
	666	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	667	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	668	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	669	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	670
[2938]	671	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	672	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
	673
	674	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	675	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
	676
	677	DO j = 1, pdims(1)
	678	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	679	ENDDO
[4438]	680	!
	681	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	682	!-- layer
	683	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	684	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	685	.AND. .NOT. rans_mode ) ) THEN
	686	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	687	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	688	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	689	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	690	CALL MPI_TYPE_FREE( newtype, ierr )
	691
	692	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	693	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	694	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	695	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	696	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	697	CALL MPI_TYPE_FREE( newtype, ierr )
	698
	699	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	700	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	701
	702	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	703	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	704
	705	DO j = 1, pdims(2)
	706	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	707	ENDDO
	708
	709	ENDIF
[4440]	710	#endif
[2938]	711	ENDIF
[2259]	712	!
[4071]	713	!-- Allocate required arrays.
	714	!-- In case no offline nesting or self nesting is used, the arrary
	715	!-- mean_inflow profiles is required. Check if it is already allocated, else
	716	!-- allocate and initialize it appropriately. Note, in case turbulence and
	717	!-- inflow information is read from file, mean_inflow_profiles is already
	718	!-- allocated and initialized appropriately.
[3347]	719	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	720	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	721	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	722	mean_inflow_profiles = 0.0_wp
	723	mean_inflow_profiles(:,1) = u_init
	724	mean_inflow_profiles(:,2) = v_init
	725	!
	726	!-- Even though potential temperature and humidity are not perturbed,
	727	!-- they need to be initialized appropriately.
	728	IF ( .NOT. neutral ) &
	729	mean_inflow_profiles(:,4) = pt_init
	730	IF ( humidity ) &
	731	mean_inflow_profiles(:,6) = q_init
	732	ENDIF
[3347]	733	ENDIF
[2259]	734
[3347]	735	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	736	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	737	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	738	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	739	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	740	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	741	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	742	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	743
[4438]	744	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	745	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	746	dist_xz = 0.0_wp
	747	dist_yz = 0.0_wp
	748	!
[2259]	749	!-- Read inflow profile
	750	!-- Height levels of profiles in input profile is as follows:
	751	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	752	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	753	!-- WARNING: zz is not used at the moment
[2938]	754	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	755	EXIST = file_stg_exist )
[2259]	756
[2938]	757	IF ( file_stg_exist ) THEN
[2259]	758
[2938]	759	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	760	FORM='FORMATTED')
	761	!
	762	!-- Skip header
	763	READ( 90, * )
[2259]	764
[3182]	765	DO k = nzb+1, nzt+1
[2938]	766	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	767	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	768	d1, d2, d3, d5
	769
[2259]	770	!
[3182]	771	!-- Convert length scales from meter to number of grid points.
[2938]	772	nuy(k) = INT( luy * ddy )
[3182]	773	nuz(k) = INT( luz * ddzw(k) )
[2938]	774	nvy(k) = INT( lvy * ddy )
[3182]	775	nvz(k) = INT( lvz * ddzw(k) )
[2938]	776	nwy(k) = INT( lwy * ddy )
[3182]	777	nwz(k) = INT( lwz * ddzw(k) )
[2938]	778	!
	779	!-- Workaround, assume isotropic turbulence
	780	nwx(k) = nwy(k)
	781	nvx(k) = nvy(k)
	782	nux(k) = nuy(k)
	783	!
	784	!-- Save Mean inflow profiles
	785	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	786	mean_inflow_profiles(k,1) = d1
	787	mean_inflow_profiles(k,2) = d2
	788	! mean_inflow_profiles(k,4) = d4
	789	mean_inflow_profiles(k,5) = d5
	790	ENDIF
	791	ENDDO
[3182]	792	!
	793	!-- Set lenght scales at surface grid point
	794	nuy(nzb) = nuy(nzb+1)
	795	nuz(nzb) = nuz(nzb+1)
	796	nvy(nzb) = nvy(nzb+1)
	797	nvz(nzb) = nvz(nzb+1)
	798	nwy(nzb) = nwy(nzb+1)
	799	nwz(nzb) = nwz(nzb+1)
	800
[2938]	801	CLOSE( 90 )
[3347]	802	!
	803	!-- Calculate coefficient matrix from Reynolds stress tensor
	804	!-- (Lund rotation)
	805	CALL calc_coeff_matrix
	806	!
	807	!-- No information about turbulence and its length scales are available.
	808	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	809	!-- Set flag which indicates that turbulence is parametrized, which is done
	810	!-- later when energy-balance models are already initialized. This is
	811	!-- because the STG needs information about surface properties such as
	812	!-- roughness to build 'realistic' turbulence profiles.
[2938]	813	ELSE
[2259]	814	!
[4022]	815	!-- Define length scale for the imposed turbulence, which is defined as
	816	!-- 8 times the minimum grid spacing
[4441]	817	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
[4022]	818	!
	819	!-- Define constant to gradually decrease length scales and Reynolds stress
	820	!-- above ABL top. Assure that no zero length scales are used.
	821	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	822	!
[3347]	823	!-- Set flag indicating that turbulence is parametrized
	824	parametrize_inflow_turbulence = .TRUE.
	825	!
[4022]	826	!-- In case of dirichlet inflow boundary conditions only at one lateral
	827	!-- boundary, i.e. in the case no offline or self nesting is applied but
	828	!-- synthetic turbulence shall be parametrized nevertheless, the
	829	!-- boundary-layer depth need to determined first.
	830	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	831	CALL nesting_offl_calc_zi
	832	!
[3347]	833	!-- Determine boundary-layer depth, which is used to initialize lenght
	834	!-- scales
	835	CALL calc_scaling_variables
	836	!
	837	!-- Initialize lenght and time scales, which in turn are used
	838	!-- to initialize the filter functions.
	839	CALL calc_length_and_time_scale
[3891]	840	!
	841	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	842	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	843	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	844	!-- friction velocity and velocity scale.
	845	CALL parametrize_reynolds_stress
	846	!
	847	!-- Calculate coefficient matrix from Reynolds stress tensor
	848	!-- (Lund rotation)
	849	CALL calc_coeff_matrix
[3347]	850
[2938]	851	ENDIF
	852
[2259]	853	!
[3347]	854	!-- Assign initial profiles. Note, this is only required if turbulent
	855	!-- inflow from the left is desired, not in case of any of the
	856	!-- nesting (offline or self nesting) approaches.
[3182]	857	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	858	u_init = mean_inflow_profiles(:,1)
	859	v_init = mean_inflow_profiles(:,2)
	860	!pt_init = mean_inflow_profiles(:,4)
	861	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	862	ENDIF
[3347]	863
[2938]	864	!
[2259]	865	!-- Define the size of the filter functions and allocate them.
[4438]	866	mergp = 0
[2259]	867
	868	! arrays must be large enough to cover the largest length scale
	869	DO k = nzb, nzt+1
[2938]	870	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	871	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	872	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[4438]	873	IF ( j > mergp ) mergp = j
[2259]	874	ENDDO
	875
[4438]	876	! mergp = 2 * mergp
	877	! mergp = mergp
[2259]	878
[4438]	879	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
	880	buy(-mergp:mergp,nzb:nzt+1), &
	881	buz(-mergp:mergp,nzb:nzt+1), &
	882	bvx(-mergp:mergp,nzb:nzt+1), &
	883	bvy(-mergp:mergp,nzb:nzt+1), &
	884	bvz(-mergp:mergp,nzb:nzt+1), &
	885	bwx(-mergp:mergp,nzb:nzt+1), &
	886	bwy(-mergp:mergp,nzb:nzt+1), &
	887	bwz(-mergp:mergp,nzb:nzt+1) )
[2259]	888
	889	!
[2938]	890	!-- Allocate velocity seeds for turbulence at xz-layer
[4438]	891	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	892	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	893	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	894
[2938]	895	!
	896	!-- Allocate velocity seeds for turbulence at yz-layer
[4438]	897	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	898	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	899	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	900
[2938]	901	fu_xz = 0.0_wp
	902	fuo_xz = 0.0_wp
	903	fv_xz = 0.0_wp
	904	fvo_xz = 0.0_wp
	905	fw_xz = 0.0_wp
	906	fwo_xz = 0.0_wp
	907
	908	fu_yz = 0.0_wp
	909	fuo_yz = 0.0_wp
	910	fv_yz = 0.0_wp
	911	fvo_yz = 0.0_wp
	912	fw_yz = 0.0_wp
	913	fwo_yz = 0.0_wp
	914
[2259]	915	!
	916	!-- Create filter functions
[2938]	917	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	918	CALL stg_filter_func( nuy, buy ) !filter uy
	919	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	920	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	921	CALL stg_filter_func( nvy, bvy ) !filter vy
	922	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	923	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	924	CALL stg_filter_func( nwy, bwy ) !filter wy
	925	CALL stg_filter_func( nwz, bwz ) !filter wz
	926
	927	#if defined( __parallel )
	928	CALL MPI_BARRIER( comm2d, ierr )
	929	#endif
	930
	931	!
[2938]	932	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	933	! time step.
	934	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	935	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	936	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	937	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	938
	939	IF ( myidx == id_stg_left ) i = -1
	940	IF ( myidx == id_stg_right ) i = nxr+1
	941
[4438]	942	DO j = nys, nyn
[2259]	943	DO k = nzb, nzt+1
[4332]	944	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	945	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	946	ELSE
[4332]	947	fu_yz(k,j) = 10E-8_wp
[2259]	948	ENDIF
	949
[4332]	950	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	951	fv_yz(k,j) = ( v(k,j,i) - &
	952	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	953	ELSE
[4332]	954	fv_yz(k,j) = 10E-8_wp
[2259]	955	ENDIF
	956
[4332]	957	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	958	fw_yz(k,j) = ( w(k,j,i) - &
	959	a31(k) * fu_yz(k,j) - a32(k) * &
	960	fv_yz(k,j) ) / a33(k)
[2259]	961	ELSE
[4332]	962	fw_yz(k,j) = 10E-8_wp
[2259]	963	ENDIF
	964	ENDDO
	965	ENDDO
	966	ENDIF
[3900]	967
	968	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	969
	970	IF ( myidy == id_stg_south ) j = -1
	971	IF ( myidy == id_stg_north ) j = nyn+1
	972
[4438]	973	DO i = nxl, nxr
[3900]	974	DO k = nzb, nzt+1
[4335]	975	!
	976	!-- In case the correlation coefficients are very small, the
	977	!-- velocity seeds may become very large finally creating
	978	!-- numerical instabilities in the synthetic turbulence generator.
	979	!-- Empirically, a value of 10E-8 seems to be sufficient.
[4332]	980	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	981	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	982	ELSE
[4332]	983	fu_xz(k,i) = 10E-8_wp
[3900]	984	ENDIF
	985
[4332]	986	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	987	fv_xz(k,i) = ( v(k,j,i) - &
	988	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	989	ELSE
[4332]	990	fv_xz(k,i) = 10E-8_wp
[3900]	991	ENDIF
	992
[4332]	993	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	994	fw_xz(k,i) = ( w(k,j,i) - &
	995	a31(k) * fu_xz(k,i) - &
	996	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	997	ELSE
[4332]	998	fw_xz(k,i) = 10E-8_wp
[3900]	999	ENDIF
	1000
	1001	ENDDO
	1002	ENDDO
	1003	ENDIF
[2259]	1004	ENDIF
[4022]	1005	!
	1006	!-- Count the number of non-topography grid points at the boundaries where
	1007	!-- perturbations are imposed. This number is later used for bias corrections
	1008	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	1009	!-- due to the asymetry of u and v along x and y direction, respectively,
	1010	!-- different cases must be distinguished.
	1011	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1012	!
	1013	!-- Number of grid points where perturbations are imposed on u
	1014	IF ( myidx == id_stg_left ) i = nxl
	1015	IF ( myidx == id_stg_right ) i = nxr+1
	1016
	1017	nr_non_topo_yz_l(1) = SUM( &
	1018	MERGE( 1, 0, &
[4346]	1019	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1020	!
	1021	!-- Number of grid points where perturbations are imposed on v and w
	1022	IF ( myidx == id_stg_left ) i = nxl-1
	1023	IF ( myidx == id_stg_right ) i = nxr+1
	1024
	1025	nr_non_topo_yz_l(2) = SUM( &
	1026	MERGE( 1, 0, &
[4346]	1027	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1028	nr_non_topo_yz_l(3) = SUM( &
	1029	MERGE( 1, 0, &
[4346]	1030	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1031
	1032	#if defined( __parallel )
	1033	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	1034	MPI_SUM, comm1dy, ierr )
	1035	#else
	1036	nr_non_topo_yz = nr_non_topo_yz_l
	1037	#endif
	1038	ENDIF
	1039
	1040	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1041	!
	1042	!-- Number of grid points where perturbations are imposed on v
	1043	IF ( myidy == id_stg_south ) j = nys
	1044	IF ( myidy == id_stg_north ) j = nyn+1
	1045
	1046	nr_non_topo_xz_l(2) = SUM( &
	1047	MERGE( 1, 0, &
[4346]	1048	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1049	!
	1050	!-- Number of grid points where perturbations are imposed on u and w
	1051	IF ( myidy == id_stg_south ) j = nys-1
	1052	IF ( myidy == id_stg_north ) j = nyn+1
	1053
	1054	nr_non_topo_xz_l(1) = SUM( &
	1055	MERGE( 1, 0, &
[4346]	1056	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1057	nr_non_topo_xz_l(3) = SUM( &
	1058	MERGE( 1, 0, &
[4346]	1059	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1060
	1061	#if defined( __parallel )
	1062	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1063	MPI_SUM, comm1dx, ierr )
	1064	#else
	1065	nr_non_topo_xz = nr_non_topo_xz_l
	1066	#endif
	1067	ENDIF
[4438]	1068	!
	1069	!-- Initialize random number generator at xz- and yz-layers. Random numbers
	1070	!-- are initialized at each core. In case there is only inflow from the left,
	1071	!-- it is sufficient to generate only random numbers for the yz-layer, else
	1072	!-- random numbers for the xz-layer are also required.
	1073	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
	1074	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
	1075	id_rand_yz = 0
	1076	seq_rand_yz = 0
[2259]	1077
[4438]	1078	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
	1079	id_rand_yz, seq_rand_yz )
[4022]	1080
[4438]	1081	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1082	.AND. .NOT. rans_mode ) ) THEN
	1083	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
	1084	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
	1085	id_rand_xz = 0
	1086	seq_rand_xz = 0
	1087
	1088	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
	1089	id_rand_xz, seq_rand_xz )
	1090	ENDIF
	1091
	1092
	1093
[2259]	1094	END SUBROUTINE stg_init
	1095
	1096
	1097	!------------------------------------------------------------------------------!
	1098	! Description:
	1099	! ------------
	1100	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1101	!> (Xie and Castro, 2008)
	1102	!------------------------------------------------------------------------------!
	1103	SUBROUTINE stg_filter_func( nxx, bxx )
	1104
	1105	INTEGER(iwp) :: k !< loop index
	1106	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1107	INTEGER(iwp) :: nf !< index for length scales
	1108
	1109	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1110	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1111
[4438]	1112	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
[2259]	1113
[4438]	1114	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1115
	1116
	1117	bxx = 0.0_wp
	1118
	1119	DO k = nzb, nzt+1
	1120	bdenom = 0.0_wp
	1121	n_k = nxx(k)
	1122	IF ( n_k /= 0 ) THEN
	1123
	1124	!
	1125	!-- ( Eq.10 )^2
[4438]	1126	DO nf = -n_k, n_k
[2259]	1127	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1128	ENDDO
	1129
	1130	!
	1131	!-- ( Eq.9 )
	1132	bdenom = SQRT( bdenom )
[4438]	1133	DO nf = -n_k, n_k
[2259]	1134	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1135	ENDDO
	1136	ENDIF
	1137	ENDDO
	1138
[3347]	1139	END SUBROUTINE stg_filter_func
[2259]	1140
	1141
	1142	!------------------------------------------------------------------------------!
	1143	! Description:
	1144	! ------------
	1145	!> Parin for &stg_par for synthetic turbulence generator
	1146	!------------------------------------------------------------------------------!
	1147	SUBROUTINE stg_parin
	1148
	1149	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1150
	1151
[4438]	1152	NAMELIST /stg_par/ dt_stg_adjust, &
	1153	dt_stg_call, &
	1154	use_syn_turb_gen, &
	1155	compute_velocity_seeds_local
[2259]	1156
	1157	line = ' '
	1158	!
	1159	!-- Try to find stg package
	1160	REWIND ( 11 )
	1161	line = ' '
	1162	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1163	READ ( 11, '(A)', END=20 ) line
[2259]	1164	ENDDO
	1165	BACKSPACE ( 11 )
	1166
	1167	!
	1168	!-- Read namelist
[3246]	1169	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1170
	1171	!
	1172	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1173	!-- on
[2776]	1174	syn_turb_gen = .TRUE.
[3246]	1175	GOTO 20
[2259]	1176
[3246]	1177	10 BACKSPACE( 11 )
[3248]	1178	READ( 11 , '(A)') line
	1179	CALL parin_fail_message( 'stg_par', line )
[2563]	1180
[3246]	1181	20 CONTINUE
[2259]	1182
	1183	END SUBROUTINE stg_parin
	1184
	1185
	1186	!------------------------------------------------------------------------------!
	1187	! Description:
	1188	! ------------
[2894]	1189	!> This routine reads the respective restart data.
[2576]	1190	!------------------------------------------------------------------------------!
[2894]	1191	SUBROUTINE stg_rrd_global( found )
[2576]	1192
[3044]	1193	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1194
[2894]	1195	found = .TRUE.
[2259]	1196
[3038]	1197
[2894]	1198	SELECT CASE ( restart_string(1:length) )
[4022]	1199
	1200	CASE ( 'time_stg_adjust' )
	1201	READ ( 13 ) time_stg_adjust
	1202
	1203	CASE ( 'time_stg_call' )
	1204	READ ( 13 ) time_stg_call
	1205
[2894]	1206	CASE ( 'use_syn_turb_gen' )
	1207	READ ( 13 ) use_syn_turb_gen
[2259]	1208
[2894]	1209	CASE DEFAULT
[2259]	1210
[3038]	1211	found = .FALSE.
[2259]	1212
[2894]	1213	END SELECT
[2259]	1214
	1215
[2894]	1216	END SUBROUTINE stg_rrd_global
[2259]	1217
	1218
	1219	!------------------------------------------------------------------------------!
	1220	! Description:
	1221	! ------------
	1222	!> This routine writes the respective restart data.
	1223	!------------------------------------------------------------------------------!
[2894]	1224	SUBROUTINE stg_wrd_global
[2259]	1225
[4022]	1226	CALL wrd_write_string( 'time_stg_adjust' )
	1227	WRITE ( 14 ) time_stg_adjust
	1228
	1229	CALL wrd_write_string( 'time_stg_call' )
	1230	WRITE ( 14 ) time_stg_call
[2259]	1231
[2894]	1232	CALL wrd_write_string( 'use_syn_turb_gen' )
	1233	WRITE ( 14 ) use_syn_turb_gen
[2259]	1234
	1235
[2894]	1236	END SUBROUTINE stg_wrd_global
[2259]	1237
[2894]	1238
[2259]	1239	!------------------------------------------------------------------------------!
	1240	! Description:
	1241	! ------------
	1242	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1243	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1244	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1245	!> (Lund, 1998).
	1246	!------------------------------------------------------------------------------!
	1247	SUBROUTINE stg_main
	1248
[2938]	1249	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1250	INTEGER(iwp) :: j !< loop index in y-direction
	1251	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1252
	1253	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1254
	1255	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1256
	1257	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1258
[3987]	1259	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1260	!
	1261	!-- Calculate time step which is needed for filter functions
[3775]	1262	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1263	!
[4022]	1264	!-- Check if synthetic turbulence generator needs to be called and new
	1265	!-- perturbations need to be created or if old disturbances can be imposed
	1266	!-- again.
	1267	IF ( time_stg_call >= dt_stg_call .AND. &
	1268	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1269	stg_call = .TRUE.
	1270	ELSE
	1271	stg_call = .FALSE.
	1272	ENDIF
	1273	!
[2259]	1274	!-- Initial value of fu, fv, fw
[3646]	1275	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1276	!
	1277	!-- Generate turbulence at the left and right boundary. Random numbers
	1278	!-- for the yz-planes at the left/right boundary are generated by the
	1279	!-- left-sided mpi ranks only. After random numbers are calculated, they
	1280	!-- are distributed to all other mpi ranks in the model, so that the
	1281	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
	1282	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
	1283	!-- that the left- and the right-sided lateral boundary have the same initial
	1284	!-- seeds.
	1285	!-- Note, in case of inflow from the right only, only turbulence at the left
	1286	!-- boundary is required.
	1287	IF ( .NOT. ( nesting_offline .OR. &
	1288	( child_domain .AND. rans_mode_parent &
	1289	.AND. .NOT. rans_mode ) ) ) THEN
	1290	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1291	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1292	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1293	ELSE
	1294	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
	1295	id_stg_left, id_stg_right )
	1296	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
	1297	id_stg_left, id_stg_right )
	1298	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
	1299	id_stg_left, id_stg_right )
[2938]	1300	!
[4309]	1301	!-- Generate turbulence at the south and north boundary. Random numbers
	1302	!-- for the xz-planes at the south/north boundary are generated by the
	1303	!-- south-sided mpi ranks only. Please see also comment above.
	1304	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
	1305	id_stg_south, id_stg_north )
	1306	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
	1307	id_stg_south, id_stg_north )
	1308	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
	1309	id_stg_south, id_stg_north )
[2938]	1310	ENDIF
[2259]	1311	velocity_seed_initialized = .TRUE.
	1312	ENDIF
	1313	!
[4309]	1314	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
	1315	!-- seeds are only required at the left boundary, while in case of offline
	1316	!-- nesting or RANS-LES nesting velocity seeds are required also at the
	1317	!-- right, south and north boundaries.
[4022]	1318	IF ( stg_call ) THEN
[4309]	1319	IF ( .NOT. ( nesting_offline .OR. &
	1320	( child_domain .AND. rans_mode_parent &
	1321	.AND. .NOT. rans_mode ) ) ) THEN
	1322	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1323	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1324	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1325
	1326	ELSE
	1327	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
	1328	id_stg_left, id_stg_right )
	1329	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
	1330	id_stg_left, id_stg_right )
	1331	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
	1332	id_stg_left, id_stg_right )
	1333
	1334	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
	1335	id_stg_south, id_stg_north )
	1336	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
	1337	id_stg_south, id_stg_north )
	1338	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
	1339	id_stg_south, id_stg_north )
[4022]	1340	ENDIF
[2938]	1341	ENDIF
[3347]	1342
[2938]	1343	!
[4309]	1344	!-- Turbulence generation at left and/or right boundary
[2938]	1345	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1346	!
[4022]	1347	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1348	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1349	!-- imposed
	1350	IF ( stg_call ) THEN
	1351
[4438]	1352	DO j = nys, nyn
[4022]	1353	DO k = nzb, nzt + 1
	1354	!
	1355	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1356	IF ( tu(k) == 0.0_wp ) THEN
	1357	fu_yz(k,j) = fuo_yz(k,j)
	1358	ELSE
	1359	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1360	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1361	ENDIF
	1362
	1363	IF ( tv(k) == 0.0_wp ) THEN
	1364	fv_yz(k,j) = fvo_yz(k,j)
	1365	ELSE
	1366	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1367	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1368	ENDIF
	1369
	1370	IF ( tw(k) == 0.0_wp ) THEN
	1371	fw_yz(k,j) = fwo_yz(k,j)
	1372	ELSE
	1373	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1374	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1375	ENDIF
	1376	ENDDO
	1377	ENDDO
	1378
	1379	dist_yz(nzb,:,1) = 0.0_wp
	1380	dist_yz(nzb,:,2) = 0.0_wp
	1381	dist_yz(nzb,:,3) = 0.0_wp
	1382
	1383	IF ( myidx == id_stg_left ) i = nxl
	1384	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1385	DO j = nys, nyn
[4022]	1386	DO k = nzb+1, nzt + 1
	1387	!
	1388	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1389	!-- Additional factors are added to improve the variance of v and w
	1390	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1391	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1392	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1393	ENDDO
	1394	ENDDO
[4309]	1395
[4022]	1396	IF ( myidx == id_stg_left ) i = nxl-1
	1397	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1398	DO j = nys, nyn
[4022]	1399	DO k = nzb+1, nzt + 1
	1400	!
	1401	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1402	!-- Additional factors are added to improve the variance of v and w
	1403	!-- experimental test of 1.2
[3347]	1404	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1405	* 1.2_wp ) &
	1406	* ( a21(k) * fu_yz(k,j) &
[4022]	1407	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1408	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1409	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[3347]	1410	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1411	* 1.3_wp ) &
	1412	* ( a31(k) * fu_yz(k,j) &
	1413	+ a32(k) * fv_yz(k,j) &
[4022]	1414	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1415	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1416	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1417	ENDDO
[2259]	1418	ENDDO
[4022]	1419	ENDIF
[2259]	1420	!
	1421	!-- Mass flux correction following Kim et al. (2013)
	1422	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1423	!-- inflow boundary. First, calculate mean value of the imposed
	1424	!-- perturbations at yz boundary.
	1425	!-- Note, this needs to be done only after the last RK3-substep, else
	1426	!-- the boundary values won't be accessed.
	1427	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1428	mc_factor_l = 0.0_wp
	1429	mc_factor = 0.0_wp
	1430	!
	1431	!-- Sum up the original volume flows (with and without perturbations).
	1432	!-- Note, for non-normal components (here v and w) it is actually no
	1433	!-- volume flow.
[2938]	1434	IF ( myidx == id_stg_left ) i = nxl
	1435	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1436
	1437	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1438	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1439	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1440
	1441	IF ( myidx == id_stg_left ) i = nxl-1
	1442	IF ( myidx == id_stg_right ) i = nxr+1
	1443
	1444	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1445	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1446	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1447	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1448	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1449	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1450
[2938]	1451	#if defined( __parallel )
	1452	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1453	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1454	#else
	1455	mc_factor = mc_factor_l
[2938]	1456	#endif
[4022]	1457	!
	1458	!-- Calculate correction factor and force zero mean perturbations.
	1459	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1460
	1461	IF ( myidx == id_stg_left ) i = nxl
	1462	IF ( myidx == id_stg_right ) i = nxr+1
	1463
[4438]	1464	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
[4022]	1465	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1466	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4022]	1467
	1468
	1469	IF ( myidx == id_stg_left ) i = nxl-1
	1470	IF ( myidx == id_stg_right ) i = nxr+1
	1471
[4438]	1472	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
[4022]	1473	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1474	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4022]	1475
[4438]	1476	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
[4022]	1477	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1478	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4022]	1479	!
[2938]	1480	!-- Add disturbances
	1481	IF ( myidx == id_stg_left ) THEN
[4022]	1482	!
	1483	!-- For the left boundary distinguish between mesoscale offline / self
	1484	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1485	!-- case turbulence is imposed on the mean inflow profiles.
	1486	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1487	!
	1488	!-- Add disturbance at the inflow
[4438]	1489	DO j = nys, nyn
[4022]	1490	DO k = nzb, nzt+1
	1491	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1492	dist_yz(k,j,1) ) &
	1493	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1494	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1495	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1496	dist_yz(k,j,2) ) &
	1497	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1498	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1499	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1500	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1501	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1502	ENDDO
[2938]	1503	ENDDO
[4022]	1504	ELSE
	1505
	1506	DO j = nys, nyn
	1507	DO k = nzb+1, nzt
	1508	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1509	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1510	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1511	u(k,j,-1) = u(k,j,0)
	1512	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1513	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1514	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1515	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1516	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1517	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1518	ENDDO
	1519	ENDDO
	1520	ENDIF
[2938]	1521	ENDIF
	1522	IF ( myidx == id_stg_right ) THEN
[3186]	1523	DO j = nys, nyn
[3347]	1524	DO k = nzb+1, nzt
[3186]	1525	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1526	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1527	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
[3186]	1528	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1529	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1530	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
[3186]	1531	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1532	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1533	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1534	ENDDO
	1535	ENDDO
	1536	ENDIF
	1537	ENDIF
	1538	ENDIF
	1539	!
	1540	!-- Turbulence generation at north and south boundary
	1541	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1542	!
[4022]	1543	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1544	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1545	!-- imposed
	1546	IF ( stg_call ) THEN
[4438]	1547	DO i = nxl, nxr
[4022]	1548	DO k = nzb, nzt + 1
	1549	!
	1550	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1551	IF ( tu(k) == 0.0_wp ) THEN
	1552	fu_xz(k,i) = fuo_xz(k,i)
	1553	ELSE
	1554	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1555	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1556	ENDIF
	1557
	1558	IF ( tv(k) == 0.0_wp ) THEN
	1559	fv_xz(k,i) = fvo_xz(k,i)
	1560	ELSE
	1561	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1562	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1563	ENDIF
	1564
	1565	IF ( tw(k) == 0.0_wp ) THEN
	1566	fw_xz(k,i) = fwo_xz(k,i)
	1567	ELSE
	1568	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1569	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1570	ENDIF
	1571	ENDDO
	1572	ENDDO
	1573
	1574
	1575	dist_xz(nzb,:,1) = 0.0_wp
	1576	dist_xz(nzb,:,2) = 0.0_wp
	1577	dist_xz(nzb,:,3) = 0.0_wp
	1578
	1579	IF ( myidy == id_stg_south ) j = nys
	1580	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1581	DO i = nxl, nxr
[4022]	1582	DO k = nzb+1, nzt + 1
	1583	!
	1584	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1585	!-- Additional factors are added to improve the variance of v and w
	1586	!experimental test of 1.2
[3347]	1587	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1588	* 1.2_wp ) &
	1589	* ( a21(k) * fu_xz(k,i) &
[4022]	1590	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1591	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1592	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1593	ENDDO
	1594	ENDDO
	1595
	1596	IF ( myidy == id_stg_south ) j = nys-1
	1597	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1598	DO i = nxl, nxr
[4022]	1599	DO k = nzb+1, nzt + 1
	1600	!
	1601	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1602	!-- Additional factors are added to improve the variance of v and w
	1603	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1604	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1605	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1606
[3347]	1607	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1608	* 1.3_wp ) &
	1609	* ( a31(k) * fu_xz(k,i) &
	1610	+ a32(k) * fv_xz(k,i) &
[4022]	1611	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1612	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1613	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1614	ENDDO
[2938]	1615	ENDDO
[4022]	1616	ENDIF
[3347]	1617
[2938]	1618	!
	1619	!-- Mass flux correction following Kim et al. (2013)
	1620	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1621	!-- inflow boundary. First, calculate mean value of the imposed
	1622	!-- perturbations at yz boundary.
	1623	!-- Note, this needs to be done only after the last RK3-substep, else
	1624	!-- the boundary values won't be accessed.
	1625	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1626	mc_factor_l = 0.0_wp
	1627	mc_factor = 0.0_wp
	1628
	1629	IF ( myidy == id_stg_south ) j = nys
	1630	IF ( myidy == id_stg_north ) j = nyn+1
	1631
	1632	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1633	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1634	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1635
	1636	IF ( myidy == id_stg_south ) j = nys-1
	1637	IF ( myidy == id_stg_north ) j = nyn+1
	1638
	1639	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1640	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1641	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1642	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1643	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1644	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1645
[2938]	1646	#if defined( __parallel )
[4022]	1647	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1648	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1649	#else
	1650	mc_factor = mc_factor_l
[2938]	1651	#endif
[4022]	1652
	1653	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1654
	1655	IF ( myidy == id_stg_south ) j = nys
	1656	IF ( myidy == id_stg_north ) j = nyn+1
	1657
[4438]	1658	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
[4022]	1659	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1660	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4022]	1661
	1662
	1663	IF ( myidy == id_stg_south ) j = nys-1
	1664	IF ( myidy == id_stg_north ) j = nyn+1
	1665
[4438]	1666	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
[4022]	1667	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1668	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4022]	1669
[4438]	1670	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
[4022]	1671	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1672	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4022]	1673	!
	1674	!-- Add disturbances
	1675	IF ( myidy == id_stg_south ) THEN
	1676	DO i = nxl, nxr
	1677	DO k = nzb+1, nzt
	1678	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1679	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1680	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
[4022]	1681	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1682	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1683	BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1684	v(k,-1,i) = v(k,0,i)
	1685	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1686	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1687	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1688	ENDDO
[2938]	1689	ENDDO
[4022]	1690	ENDIF
	1691	IF ( myidy == id_stg_north ) THEN
	1692
	1693	DO i = nxl, nxr
	1694	DO k = nzb+1, nzt
	1695	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1696	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1697	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
[4022]	1698	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1699	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1700	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
[4022]	1701	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1702	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1703	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1704	ENDDO
[2938]	1705	ENDDO
[4022]	1706	ENDIF
[2938]	1707	ENDIF
[2259]	1708	ENDIF
[3347]	1709	!
[4438]	1710	!-- Exchange ghost points.
	1711	CALL exchange_horiz( u, nbgp )
	1712	CALL exchange_horiz( v, nbgp )
	1713	CALL exchange_horiz( w, nbgp )
	1714	!
[3347]	1715	!-- Finally, set time counter for calling STG to zero
[4022]	1716	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1717
[3987]	1718	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1719
[2259]	1720	END SUBROUTINE stg_main
	1721
	1722	!------------------------------------------------------------------------------!
	1723	! Description:
	1724	! ------------
	1725	!> Generate a set of random number rand_it wich is equal on each PE
	1726	!> and calculate the velocity seed f_n.
	1727	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1728	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1729	!> parts are collected to form the full array.
	1730	!------------------------------------------------------------------------------!
[4309]	1731	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1732
[4309]	1733	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1734	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1735	INTEGER(iwp) :: j !< loop index in y-direction
	1736	INTEGER(iwp) :: jj !< loop index in y-direction
	1737	INTEGER(iwp) :: k !< loop index in z-direction
	1738	INTEGER(iwp) :: kk !< loop index in z-direction
	1739	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1740
	1741	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1742	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1743
	1744	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1745	REAL(wp) :: rand_av !< average of random number
	1746	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1747
[4438]	1748	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
	1749	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1750
[4438]	1751	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1752	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
[4309]	1753
	1754	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1755	!
[4309]	1756	!-- Generate random numbers using the parallel random generator.
[2259]	1757	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1758	!-- unit variance. Note, at the end the random number array must be defined
	1759	!-- globally in order to compute the correlation matrices. However,
	1760	!-- the calculation and normalization of random numbers is done locally,
	1761	!-- while the result is later distributed to all processes. Further,
	1762	!-- please note, a set of random numbers is only calculated for the
	1763	!-- left boundary, while the right boundary uses the same random numbers
	1764	!-- and thus also computes the same correlation matrix.
[4438]	1765	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
	1766	rand_it = 0.0_wp
[2259]	1767
	1768	rand_av = 0.0_wp
	1769	rand_sigma_inv = 0.0_wp
[4438]	1770	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1771	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
	1772	KIND=wp )
[4309]	1773	!
[4438]	1774	!-- Compute and normalize random numbers.
	1775	DO j = nys - mergp, nyn + mergp
[4309]	1776	!
[4438]	1777	!-- Put the random seeds at grid point j
	1778	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
	1779	DO k = nzb - mergp, nzt + 1 + mergp
	1780	CALL random_number_parallel( random_dummy )
	1781	rand_it(k,j) = random_dummy
	1782	ENDDO
[4309]	1783	!
[4438]	1784	!-- Get the new random seeds from last call at grid point j
	1785	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1786	ENDDO
[4309]	1787	!
[4438]	1788	!-- For normalization to zero mean, sum-up the global random numers.
	1789	!-- To normalize the global set of random numbers,
	1790	!-- the inner ghost layers mergp must not be summed-up, else
	1791	!-- the random numbers on the ghost layers will be stronger weighted as they
	1792	!-- also occur on the inner subdomains.
	1793	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1794	MERGE( nyn, nyn + mergp, nyn /= ny )
	1795	DO k = nzb - mergp, nzt + 1 + mergp
	1796	rand_av = rand_av + rand_it(k,j)
[2259]	1797	ENDDO
[4438]	1798	ENDDO
	1799
[4309]	1800	#if defined( __parallel )
	1801	!
[4438]	1802	!-- Sum-up the local averages of the random numbers
	1803	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1804	MPI_SUM, comm1dy, ierr )
[4309]	1805	#endif
[4438]	1806	rand_av = rand_av * nyz_inv
[4309]	1807	!
[4438]	1808	!-- Obtain zero mean
	1809	rand_it= rand_it - rand_av
[4309]	1810	!
[4438]	1811	!-- Now, compute the variance
	1812	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1813	MERGE( nyn, nyn + mergp, nyn /= ny )
	1814	DO k = nzb - mergp, nzt + 1 + mergp
	1815	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1816	ENDDO
[4438]	1817	ENDDO
[2259]	1818
[4309]	1819	#if defined( __parallel )
[2259]	1820	!
[4438]	1821	!-- Sum-up the local quadratic averages of the random numbers
	1822	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1823	MPI_SUM, comm1dy, ierr )
[4309]	1824	#endif
	1825	!
[4438]	1826	!-- Compute standard deviation
	1827	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1828	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1829	ELSE
	1830	rand_sigma_inv = 1.0_wp
[4309]	1831	ENDIF
	1832	!
[4438]	1833	!-- Normalize with standard deviation to obtain unit variance
	1834	rand_it = rand_it * rand_sigma_inv
	1835
	1836	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1837	!
[4438]	1838	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	1839	!-- are two options. In the first one, the computation of the seeds is
	1840	!-- distributed to all processes along the communicator comm1dy and
	1841	!-- gathered on the leftmost and, if necessary, on the rightmost process.
	1842	!-- For huge length scales the computational effort can become quite huge
	1843	!-- (it scales with the turbulent length scales), so that gain by parallelization
	1844	!-- exceeds the costs by the subsequent communication.
	1845	!-- In the second option, which performs better when the turbulent length scales
	1846	!-- are parametrized and thus the loops are smaller, the seeds are computed
	1847	!-- locally and no communication is necessary.
	1848	IF ( compute_velocity_seeds_local ) THEN
	1849
	1850	f_n = 0.0_wp
	1851	DO j = nys, nyn
	1852	DO k = nzb, nzt+1
	1853	DO jj = -n_y(k), n_y(k)
	1854	DO kk = -n_z(k), n_z(k)
	1855	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1856	ENDDO
	1857	ENDDO
	1858	ENDDO
[2259]	1859	ENDDO
	1860
[4438]	1861	ELSE
[2259]	1862
[4438]	1863	f_n_l = 0.0_wp
	1864	DO j = nys, nyn
	1865	DO k = nzb_x_stg, nzt_x_stg+1
	1866	DO jj = -n_y(k), n_y(k)
	1867	DO kk = -n_z(k), n_z(k)
	1868	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1869	ENDDO
[2259]	1870	ENDDO
	1871	ENDDO
	1872	ENDDO
	1873	!
[4438]	1874	!-- Gather velocity seeds of full subdomain
	1875	send_count = nzt_x_stg - nzb_x_stg + 1
	1876	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1877
	1878	#if defined( __parallel )
[4309]	1879	!
[4438]	1880	!-- Gather the velocity seed matrix on left boundary mpi ranks.
	1881	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1882	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1883	id_left, comm1dx, ierr )
[4309]	1884	!
[4438]	1885	!-- If required, gather the same velocity seed matrix on right boundary
	1886	!-- mpi ranks (in offline nesting for example).
	1887	IF ( PRESENT( id_right ) ) THEN
	1888	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1889	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1890	id_right, comm1dx, ierr )
	1891	ENDIF
[2259]	1892	#else
[4438]	1893	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[2259]	1894	#endif
	1895
[4438]	1896	ENDIF
[2259]	1897
[4438]	1898	DEALLOCATE( rand_it )
	1899
	1900	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1901
[2259]	1902	END SUBROUTINE stg_generate_seed_yz
	1903
[2938]	1904
	1905	!------------------------------------------------------------------------------!
	1906	! Description:
	1907	! ------------
	1908	!> Generate a set of random number rand_it wich is equal on each PE
	1909	!> and calculate the velocity seed f_n.
	1910	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1911	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1912	!> parts are collected to form the full array.
	1913	!------------------------------------------------------------------------------!
[4309]	1914	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1915
	1916	INTEGER(iwp) :: i !< loop index in x-direction
[4309]	1917	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1918	INTEGER(iwp) :: id_south !< core ids at respective boundaries
[2938]	1919	INTEGER(iwp) :: ii !< loop index in x-direction
	1920	INTEGER(iwp) :: k !< loop index in z-direction
	1921	INTEGER(iwp) :: kk !< loop index in z-direction
	1922	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1923
	1924	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1925	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1926
	1927	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1928	REAL(wp) :: rand_av !< average of random number
	1929	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1930
[4438]	1931	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
	1932	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1933
[4438]	1934	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1935	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1936
[4309]	1937	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1938
	1939	!
[4309]	1940	!-- Generate random numbers using the parallel random generator.
[2938]	1941	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1942	!-- unit variance. Note, at the end the random number array must be defined
	1943	!-- globally in order to compute the correlation matrices. However,
	1944	!-- the calculation and normalization of random numbers is done locally,
	1945	!-- while the result is later distributed to all processes. Further,
	1946	!-- please note, a set of random numbers is only calculated for the
	1947	!-- left boundary, while the right boundary uses the same random numbers
	1948	!-- and thus also computes the same correlation matrix.
[4438]	1949	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
	1950	rand_it = 0.0_wp
[2938]	1951
	1952	rand_av = 0.0_wp
	1953	rand_sigma_inv = 0.0_wp
[4438]	1954	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1955	* ( nx + mergp - ( 0 - mergp ) +1 ), &
	1956	KIND=wp )
[4309]	1957	!
[4438]	1958	!-- Compute and normalize random numbers.
	1959	DO i = nxl - mergp, nxr + mergp
[4309]	1960	!
[4438]	1961	!-- Put the random seeds at grid point ii
	1962	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
	1963	DO k = nzb - mergp, nzt + 1 + mergp
	1964	CALL random_number_parallel( random_dummy )
	1965	rand_it(k,i) = random_dummy
	1966	ENDDO
[4309]	1967	!
[4438]	1968	!-- Get the new random seeds from last call at grid point ii
	1969	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1970	ENDDO
[4309]	1971	!
[4438]	1972	!-- For normalization to zero mean, sum-up the global random numers.
	1973	!-- To normalize the global set of random numbers,
	1974	!-- the inner ghost layers mergp must not be summed-up, else
	1975	!-- the random numbers on the ghost layers will be stronger weighted as they
	1976	!-- also occur on the inner subdomains.
	1977	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	1978	MERGE( nxr, nxr + mergp, nxr /= nx )
	1979	DO k = nzb - mergp, nzt + 1 + mergp
	1980	rand_av = rand_av + rand_it(k,i)
[2938]	1981	ENDDO
[4438]	1982	ENDDO
	1983
[4309]	1984	#if defined( __parallel )
[4438]	1985	!
	1986	!-- Sum-up the local averages of the random numbers
	1987	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1988	MPI_SUM, comm1dx, ierr )
[4309]	1989	#endif
[4438]	1990	rand_av = rand_av * nxz_inv
[4309]	1991	!
[4438]	1992	!-- Obtain zero mean
	1993	rand_it= rand_it - rand_av
[4309]	1994	!
[4438]	1995	!-- Now, compute the variance
	1996	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	1997	MERGE( nxr, nxr + mergp, nxr /= nx )
	1998	DO k = nzb - mergp, nzt + 1 + mergp
	1999	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	2000	ENDDO
[4438]	2001	ENDDO
[2938]	2002
[4309]	2003	#if defined( __parallel )
[4438]	2004	!
	2005	!-- Sum-up the local quadratic averages of the random numbers
	2006	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	2007	MPI_SUM, comm1dx, ierr )
[4309]	2008	#endif
[2938]	2009	!
[4438]	2010	!-- Compute standard deviation
	2011	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	2012	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	2013	ELSE
	2014	rand_sigma_inv = 1.0_wp
[4309]	2015	ENDIF
	2016	!
[4438]	2017	!-- Normalize with standard deviation to obtain unit variance
	2018	rand_it = rand_it * rand_sigma_inv
	2019
	2020	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2021	!
[4438]	2022	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	2023	!-- are two options. In the first one, the computation of the seeds is
	2024	!-- distributed to all processes along the communicator comm1dx and
	2025	!-- gathered on the southmost and, if necessary, on the northmost process.
	2026	!-- For huge length scales the computational effort can become quite huge
	2027	!-- (it scales with the turbulent length scales), so that gain by parallelization
	2028	!-- exceeds the costs by the subsequent communication.
	2029	!-- In the second option, which performs better when the turbulent length scales
	2030	!-- are parametrized and thus the loops are smaller, the seeds are computed
	2031	!-- locally and no communication is necessary.
	2032	IF ( compute_velocity_seeds_local ) THEN
[2938]	2033
[4438]	2034	f_n = 0.0_wp
	2035	DO i = nxl, nxr
	2036	DO k = nzb, nzt+1
	2037	DO ii = -n_x(k), n_x(k)
	2038	DO kk = -n_z(k), n_z(k)
	2039	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2040	ENDDO
[2938]	2041	ENDDO
	2042	ENDDO
	2043	ENDDO
	2044
[4438]	2045	ELSE
[2938]	2046
[4438]	2047	f_n_l = 0.0_wp
	2048	DO i = nxl, nxr
	2049	DO k = nzb_y_stg, nzt_y_stg+1
	2050	DO ii = -n_x(k), n_x(k)
	2051	DO kk = -n_z(k), n_z(k)
	2052	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2053	ENDDO
	2054	ENDDO
	2055	ENDDO
	2056	ENDDO
[2938]	2057	!
[4438]	2058	!-- Gather velocity seeds of full subdomain
	2059	send_count = nzt_y_stg - nzb_y_stg + 1
	2060	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2061
	2062	#if defined( __parallel )
[4309]	2063	!
[4438]	2064	!-- Gather the processed velocity seed on south boundary mpi ranks.
	2065	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2066	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2067	id_south, comm1dy, ierr )
[4309]	2068	!
[4438]	2069	!-- Gather the processed velocity seed on north boundary mpi ranks.
	2070	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2071	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2072	id_north, comm1dy, ierr )
[2938]	2073	#else
[4438]	2074	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[2938]	2075	#endif
	2076
[4438]	2077	ENDIF
	2078
	2079	DEALLOCATE( rand_it )
	2080
	2081	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2082
[2938]	2083	END SUBROUTINE stg_generate_seed_xz
	2084
[3347]	2085	!------------------------------------------------------------------------------!
	2086	! Description:
	2087	! ------------
	2088	!> Parametrization of the Reynolds stress tensor, following the parametrization
	2089	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	2090	!> dispserion modelling. Please note, the parametrization does not distinguish
	2091	!> between along-wind and cross-wind turbulence.
	2092	!------------------------------------------------------------------------------!
	2093	SUBROUTINE parametrize_reynolds_stress
	2094
	2095	INTEGER(iwp) :: k !< loop index in z-direction
	2096
	2097	REAL(wp) :: zzi !< ratio of z/zi
	2098
	2099	DO k = nzb+1, nzt+1
	2100	!
[4022]	2101	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2102	!-- The function decreases to 1/10 after one length scale above the
	2103	!-- ABL top.
	2104	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2105	!
[4022]	2106	!-- Determine normalized height coordinate
	2107	zzi = zu(k) / zi_ribulk
[3347]	2108	!
[4022]	2109	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
[4438]	2110	!-- to the denominator, else the mergpe-function can crash if scale_l is
[4022]	2111	!-- zero.
	2112	r11(k) = scale_us*2 ( &
	2113	MERGE( 0.35_wp * ABS( &
	2114	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2115	)**( 2.0_wp / 3.0_wp ), &
	2116	0.0_wp, &
	2117	scale_l < 0.0_wp ) &
	2118	+ 5.0_wp - 4.0_wp * zzi &
	2119	) * blend
	2120
	2121	r22(k) = r11(k)
	2122	!
	2123	!-- w'w'
	2124	r33(k) = scale_wm*2 ( &
	2125	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2126	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2127	) * blend
	2128	!
	2129	!-- u'w' and v'w'. Assume isotropy.
	2130	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	2131	r32(k) = r31(k)
[3347]	2132	!
[4022]	2133	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	2134	!-- a similar profile as for u'w'.
	2135	r21(k) = r31(k)
[3347]	2136	ENDDO
	2137
	2138	!
	2139	!-- Set bottom boundary condition
	2140	r11(nzb) = r11(nzb+1)
	2141	r22(nzb) = r22(nzb+1)
	2142	r33(nzb) = r33(nzb+1)
	2143
	2144	r21(nzb) = r11(nzb+1)
	2145	r31(nzb) = r31(nzb+1)
	2146	r32(nzb) = r32(nzb+1)
	2147
	2148
	2149	END SUBROUTINE parametrize_reynolds_stress
	2150
	2151	!------------------------------------------------------------------------------!
	2152	! Description:
	2153	! ------------
	2154	!> Calculate the coefficient matrix from the Lund rotation.
	2155	!------------------------------------------------------------------------------!
	2156	SUBROUTINE calc_coeff_matrix
	2157
	2158	INTEGER(iwp) :: k !< loop index in z-direction
	2159
	2160	!
	2161	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2162	DO k = nzb+1, nzt+1
[4022]	2163	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	2164	a11(k) = SQRT( r11(k) )
	2165	a21(k) = r21(k) / a11(k)
	2166	a31(k) = r31(k) / a11(k)
	2167	ELSE
	2168	a11(k) = 10E-8_wp
	2169	a21(k) = 10E-8_wp
	2170	a31(k) = 10E-8_wp
	2171	ENDIF
	2172	ENDDO
	2173	DO k = nzb+1, nzt+1
	2174	a22(k) = r22(k) - a21(k)**2
[4022]	2175	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2176	a22(k) = SQRT( a22(k) )
	2177	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	2178	ELSE
	2179	a22(k) = 10E-8_wp
	2180	a32(k) = 10E-8_wp
	2181	ENDIF
	2182	ENDDO
	2183	DO k = nzb+1, nzt+1
	2184	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2185	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2186	a33(k) = SQRT( a33(k) )
	2187	ELSE
	2188	a33(k) = 10E-8_wp
	2189	ENDIF
	2190	ENDDO
	2191	!
	2192	!-- Set bottom boundary condition
	2193	a11(nzb) = a11(nzb+1)
	2194	a22(nzb) = a22(nzb+1)
	2195	a21(nzb) = a21(nzb+1)
	2196	a33(nzb) = a33(nzb+1)
	2197	a31(nzb) = a31(nzb+1)
	2198	a32(nzb) = a32(nzb+1)
	2199
	2200	END SUBROUTINE calc_coeff_matrix
	2201
	2202	!------------------------------------------------------------------------------!
	2203	! Description:
	2204	! ------------
	2205	!> This routine controls the re-adjustment of the turbulence statistics used
	2206	!> for generating turbulence at the lateral boundaries.
	2207	!------------------------------------------------------------------------------!
	2208	SUBROUTINE stg_adjust
	2209
[3987]	2210	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2211	!
[4022]	2212	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2213	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2214	!-- synthetic turbulence shall be parametrized nevertheless, the
	2215	!-- boundary-layer depth need to determined first.
	2216	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2217	CALL nesting_offl_calc_zi
	2218	!
	2219	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2220	!-- are calculated.
[3347]	2221	CALL calc_scaling_variables
	2222	!
	2223	!-- Set length and time scales depending on boundary-layer height
	2224	CALL calc_length_and_time_scale
	2225	!
	2226	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2227	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2228	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2229	!-- friction velocity and velocity scale.
	2230	CALL parametrize_reynolds_stress
	2231	!
	2232	!-- Calculate coefficient matrix from Reynolds stress tensor
	2233	!-- (Lund rotation)
	2234	CALL calc_coeff_matrix
	2235	!
	2236	!-- Determine filter functions on basis of updated length scales
	2237	CALL stg_filter_func( nux, bux ) !filter ux
	2238	CALL stg_filter_func( nuy, buy ) !filter uy
	2239	CALL stg_filter_func( nuz, buz ) !filter uz
	2240	CALL stg_filter_func( nvx, bvx ) !filter vx
	2241	CALL stg_filter_func( nvy, bvy ) !filter vy
	2242	CALL stg_filter_func( nvz, bvz ) !filter vz
	2243	CALL stg_filter_func( nwx, bwx ) !filter wx
	2244	CALL stg_filter_func( nwy, bwy ) !filter wy
	2245	CALL stg_filter_func( nwz, bwz ) !filter wz
	2246	!
	2247	!-- Reset time counter for controlling next adjustment to zero
	2248	time_stg_adjust = 0.0_wp
[3987]	2249
	2250	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2251
	2252	END SUBROUTINE stg_adjust
	2253
	2254
	2255	!------------------------------------------------------------------------------!
	2256	! Description:
	2257	! ------------
	2258	!> Calculates turbuluent length and time scales if these are not available
	2259	!> from measurements.
	2260	!------------------------------------------------------------------------------!
	2261	SUBROUTINE calc_length_and_time_scale
	2262
[4022]	2263	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2264
[4022]	2265	REAL(wp) :: length_scale_dum !< effectively used length scale
	2266
[3347]	2267	!
	2268	!-- In initial call the boundary-layer depth can be zero. This case, set
	2269	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2270	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2271	!
	2272	!-- Set-up default turbulent length scales. From the numerical point of
	2273	!-- view the imposed perturbations should not be immediately dissipated
	2274	!-- by the numerics. The numerical dissipation, however, acts on scales
	2275	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2276	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2277	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2278	!-- imposing any perturbations) in order to save computational costs.
	2279	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2280	!-- using the length scales and the mean profiles of u- and v-component.
	2281	DO k = nzb+1, nzt+1
	2282	!
[4022]	2283	!-- Determine blending parameter. Within the boundary layer length scales
	2284	!-- are constant, while above lengths scales approach gradully zero,
	2285	!-- i.e. imposed turbulence is not correlated in space and time,
	2286	!-- just white noise, which saves computations power as the loops for the
	2287	!-- computation of the filter functions depend on the length scales.
	2288	!-- The value decreases to 1/10 after one length scale above the
	2289	!-- ABL top.
	2290	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2291	!
[4022]	2292	!-- Assume isotropic turbulence length scales
	2293	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2294	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2295	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2296	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2297	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2298	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2299	!
[4022]	2300	!-- Along the vertical direction limit the length scale further by the
	2301	!-- boundary-layer depth to assure that no length scales larger than
	2302	!-- the boundary-layer depth are used
	2303	length_scale_dum = MIN( length_scale, zi_ribulk )
	2304
	2305	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2306	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2307	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2308	!
[4022]	2309	!-- Limit time scales, else they become very larger for low wind speed,
	2310	!-- imposing long-living inflow perturbations which in turn propagate
	2311	!-- further into the model domain. Use u_init and v_init to calculate
	2312	!-- the time scales, which will be equal to the inflow profiles, both,
	2313	!-- in offline nesting mode or in dirichlet/radiation mode.
	2314	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2315	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2316	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2317	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2318	!
	2319	!-- Time scale of w-component is a mixture from u- and v-component.
	2320	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2321
[3347]	2322	ENDDO
	2323	!
	2324	!-- Set bottom boundary condition for the length and time scales
	2325	nux(nzb) = nux(nzb+1)
	2326	nuy(nzb) = nuy(nzb+1)
	2327	nuz(nzb) = nuz(nzb+1)
	2328	nvx(nzb) = nvx(nzb+1)
	2329	nvy(nzb) = nvy(nzb+1)
	2330	nvz(nzb) = nvz(nzb+1)
	2331	nwx(nzb) = nwx(nzb+1)
	2332	nwy(nzb) = nwy(nzb+1)
	2333	nwz(nzb) = nwz(nzb+1)
	2334
	2335	tu(nzb) = tu(nzb+1)
	2336	tv(nzb) = tv(nzb+1)
	2337	tw(nzb) = tw(nzb+1)
	2338
	2339
	2340	END SUBROUTINE calc_length_and_time_scale
	2341
	2342	!------------------------------------------------------------------------------!
	2343	! Description:
	2344	! ------------
	2345	!> Calculate scaling variables which are used for turbulence parametrization
	2346	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2347	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2348	!------------------------------------------------------------------------------!
	2349	SUBROUTINE calc_scaling_variables
	2350
	2351	INTEGER(iwp) :: i !< loop index in x-direction
	2352	INTEGER(iwp) :: j !< loop index in y-direction
	2353	INTEGER(iwp) :: k !< loop index in z-direction
	2354	INTEGER(iwp) :: m !< surface element index
	2355
	2356	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2357	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2358	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2359	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2360	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2361	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2362	REAL(wp) :: w_convective !< convective velocity scale
	2363
	2364	!
[3937]	2365	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2366	!-- near-surface temperature in the model domain.
	2367	pt_surf_mean_l = 0.0_wp
	2368	shf_mean_l = 0.0_wp
	2369	scale_l_l = 0.0_wp
	2370	friction_vel_l = 0.0_wp
[3347]	2371	DO m = 1, surf_def_h(0)%ns
[3937]	2372	i = surf_def_h(0)%i(m)
	2373	j = surf_def_h(0)%j(m)
	2374	k = surf_def_h(0)%k(m)
	2375	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2376	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2377	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2378	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2379	ENDDO
	2380	DO m = 1, surf_lsm_h%ns
[3937]	2381	i = surf_lsm_h%i(m)
	2382	j = surf_lsm_h%j(m)
	2383	k = surf_lsm_h%k(m)
	2384	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2385	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2386	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2387	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2388	ENDDO
	2389	DO m = 1, surf_usm_h%ns
[3937]	2390	i = surf_usm_h%i(m)
	2391	j = surf_usm_h%j(m)
	2392	k = surf_usm_h%k(m)
	2393	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2394	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2395	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2396	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2397	ENDDO
	2398
	2399	#if defined( __parallel )
[3937]	2400	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2401	comm2d, ierr )
[3937]	2402	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2403	comm2d, ierr )
[3937]	2404	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2405	comm2d, ierr )
	2406	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2407	comm2d, ierr )
[3347]	2408	#else
[3937]	2409	scale_us = friction_vel_l
	2410	shf_mean = shf_mean_l
	2411	scale_l = scale_l_l
	2412	pt_surf_mean = pt_surf_mean_l
[3347]	2413	#endif
	2414
[3937]	2415	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2416	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2417	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2418	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2419	!
	2420	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2421	!-- is negative, set convective velocity scale to zero.
	2422	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2423	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2424	ELSE
	2425	w_convective = 0.0_wp
	2426	ENDIF
	2427	!
	2428	!-- Finally, in order to consider also neutral or stable stratification,
	2429	!-- compute momentum velocity scale from u* and convective velocity scale,
	2430	!-- according to Rotach et al. (1996).
	2431	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2432
	2433	END SUBROUTINE calc_scaling_variables
	2434
[2259]	2435	END MODULE synthetic_turbulence_generator_mod

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