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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4469

Last change on this file since 4469 was 4457, checked in by raasch, 5 years ago
ghost point exchange modularized, bugfix for wrong 2d-exchange
Property svn:keywords set to `Id`
File size: 109.3 KB

Rev	Line
[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 4457 2020-03-11 14:20:43Z suehring $
[4444]	27	! bugfix: cpp-directives for serial mode added, dummy statements to prevent compile errors added
	28	!
	29	! 4442 2020-03-04 19:21:13Z suehring
[4442]	30	! Set back turbulent length scale to 8 x grid spacing in the parametrized mode
	31	! (was accidantly changed).
	32	!
	33	! 4441 2020-03-04 19:20:35Z suehring
[4440]	34	! Correct misplaced preprocessor directive
	35	!
	36	! 4438 2020-03-03 20:49:28Z suehring
[4438]	37	! Performance optimizations in velocity-seed calculation:
	38	! - random number array is only defined and computed locally (except for
	39	! normalization to zero mean and unit variance)
	40	! - parallel random number generator is applied independent on the 2D random
	41	! numbers in other routines
	42	! - option to decide wheter velocity seeds are computed locally without any
	43	! further communication or are computed by all processes along the
	44	! communicator
	45	!
	46	! 4346 2019-12-18 11:55:56Z motisi
[4346]	47	! Introduction of wall_flags_total_0, which currently sets bits based on static
	48	! topography information used in wall_flags_static_0
	49	!
	50	! 4335 2019-12-12 16:39:05Z suehring
[4335]	51	! Commentation of last commit
	52	!
	53	! 4332 2019-12-10 19:44:12Z suehring
[4332]	54	! Limit initial velocity seeds in restart runs, if not the seed calculation
	55	! may become unstable. Further, minor bugfix in initial velocity seed
	56	! calculation.
	57	!
	58	! 4329 2019-12-10 15:46:36Z motisi
[4329]	59	! Renamed wall_flags_0 to wall_flags_static_0
	60	!
	61	! 4309 2019-11-26 18:49:59Z suehring
[4309]	62	! Computation of velocity seeds optimized. This implies that random numbers
	63	! are computed now using the parallel random number generator. Random numbers
	64	! are now only computed and normalized locally, while distributed over all
	65	! mpi ranks afterwards, instead of computing random numbers on a global array.
	66	! Further, the number of calls for the time-consuming velocity-seed generation
	67	! is reduced - now the left and right, as well as the north and south boundary
	68	! share the same velocity-seed matrices.
	69	!
	70	! 4182 2019-08-22 15:20:23Z scharf
[4182]	71	! Corrected "Former revisions" section
	72	!
	73	! 4148 2019-08-08 11:26:00Z suehring
[4148]	74	! Remove unused variable
	75	!
	76	! 4144 2019-08-06 09:11:47Z raasch
[4144]	77	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	78	!
	79	! 4071 2019-07-03 20:02:00Z suehring
[4071]	80	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	81	! information is not read from file.
	82	!
	83	! 4022 2019-06-12 11:52:39Z suehring
[4022]	84	! Several bugfixes and improvements
	85	! - revise bias correction of the imposed perturbations (correction via volume
	86	! flow can create instabilities in case the mean volume flow is close to zero)
	87	! - introduce lower limits in calculation of coefficient matrix, else the
	88	! calculation may become numerically unstable
	89	! - impose perturbations every timestep, even though no new set of perturbations
	90	! is generated in case dt_stg_call /= dt_3d
	91	! - Implement a gradual decrease of Reynolds stress and length scales above
	92	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	93	! discontinuous decrease
	94	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	95	!
	96	! 3987 2019-05-22 09:52:13Z kanani
[3987]	97	! Introduce alternative switch for debug output during timestepping
	98	!
	99	! 3938 2019-04-29 16:06:25Z suehring
[3938]	100	! Remove unused variables
	101	!
	102	! 3937 2019-04-29 15:09:07Z suehring
[3937]	103	! Minor bugfix in case of a very early restart where mc_factor is sill not
	104	! present.
	105	! Some modification and fixing of potential bugs in the calculation of scaling
	106	! parameters used for synthetic turbulence parametrization.
	107	!
	108	! 3909 2019-04-17 09:13:25Z suehring
[3909]	109	! Minor bugfix for last commit
	110	!
	111	! 3900 2019-04-16 15:17:43Z suehring
[3900]	112	! Missing re-calculation of perturbation seeds in case of restarts
	113	!
	114	! 3891 2019-04-12 17:52:01Z suehring
[3891]	115	! Bugfix in initialization in case of restart runs.
	116	!
	117	! 3885 2019-04-11 11:29:34Z kanani
[3885]	118	! Changes related to global restructuring of location messages and introduction
	119	! of additional debug messages
	120	!
	121	!
[3775]	122	! removed unused variables
	123	!
	124	! 3719 2019-02-06 13:10:18Z kanani
[3719]	125	! Removed log_point measurement from stg_init, since this part is counted to
	126	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	127	! the subroutines in time_integration for better overview.
	128	!
[4182]	129	! 2259 2017-06-08 09:09:11Z gronemeier
	130	! Initial revision
[3044]	131	!
[4182]	132	! Authors:
	133	! --------
	134	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	135	!
	136	!
[2259]	137	! Description:
	138	! ------------
	139	!> The module generates turbulence at the inflow boundary based on a method by
	140	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	141	!> correction by Kim et al. (2013).
	142	!> The turbulence is correlated based on length scales in y- and z-direction and
	143	!> a time scale for each velocity component. The profiles of length and time
	144	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	145	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	146	!> within the boundary layer.
[2259]	147	!>
	148	!> @todo test restart
	149	!> enable cyclic_fill
	150	!> implement turbulence generation for e and pt
[2945]	151	!> @todo Input of height-constant length scales via namelist
[2259]	152	!> @note <Enter notes on the module>
	153	!> @bug Height information from input file is not used. Profiles from input
	154	!> must match with current PALM grid.
	155	!> In case of restart, velocity seeds differ from precursor run if a11,
	156	!> a22, or a33 are zero.
	157	!------------------------------------------------------------------------------!
	158	MODULE synthetic_turbulence_generator_mod
	159
	160
	161	USE arrays_3d, &
[4022]	162	ONLY: dzw, &
	163	ddzw, &
	164	drho_air, &
	165	mean_inflow_profiles, &
	166	q, &
[4071]	167	q_init, &
	168	pt, &
	169	pt_init, &
[4022]	170	u, &
	171	u_init, &
	172	v, &
	173	v_init, &
	174	w, &
	175	zu, &
	176	zw
[2259]	177
[3274]	178	USE basic_constants_and_equations_mod, &
[4022]	179	ONLY: g, &
	180	kappa, &
	181	pi
[2259]	182
	183	USE control_parameters, &
[4022]	184	ONLY: bc_lr, &
	185	bc_ns, &
	186	child_domain, &
	187	coupling_char, &
	188	debug_output_timestep, &
	189	dt_3d, &
	190	e_init, &
[4071]	191	humidity, &
[3885]	192	initializing_actions, &
[4022]	193	intermediate_timestep_count, &
	194	intermediate_timestep_count_max, &
	195	length, &
[3885]	196	message_string, &
[4022]	197	nesting_offline, &
[4071]	198	neutral, &
[3885]	199	num_mean_inflow_profiles, &
[4309]	200	random_generator, &
[4022]	201	rans_mode, &
	202	restart_string, &
	203	syn_turb_gen, &
	204	time_since_reference_point, &
	205	turbulent_inflow
[4438]	206
	207	USE cpulog, &
	208	ONLY: cpu_log, &
	209	log_point_s
	210
[4022]	211	USE grid_variables, &
	212	ONLY: ddx, &
	213	ddy, &
	214	dx, &
	215	dy
[2259]	216
	217	USE indices, &
[4022]	218	ONLY: nbgp, &
	219	nz, &
	220	nzb, &
	221	nzt, &
	222	nx, &
	223	nxl, &
	224	nxlu, &
	225	nxr, &
	226	ny, &
	227	nys, &
	228	nysv, &
	229	nyn, &
[4346]	230	wall_flags_total_0
[2259]	231
	232	USE kinds
	233
[2967]	234	#if defined( __parallel ) && !defined( __mpifh )
[2259]	235	USE MPI
[2841]	236	#endif
[2259]	237
[3347]	238	USE nesting_offl_mod, &
[4022]	239	ONLY: nesting_offl_calc_zi, &
	240	zi_ribulk
[3347]	241
[2259]	242	USE pegrid, &
[4022]	243	ONLY: comm1dx, &
	244	comm1dy, &
	245	comm2d, &
	246	ierr, &
	247	myidx, &
	248	myidy, &
	249	pdims
[4438]	250
[4022]	251	USE pmc_interface, &
	252	ONLY : rans_mode_parent
[4438]	253
	254	USE random_generator_parallel, &
	255	ONLY: init_parallel_random_generator, &
	256	random_dummy, &
[4309]	257	random_number_parallel, &
[4438]	258	random_seed_parallel
[2259]	259
	260	USE transpose_indices, &
[4022]	261	ONLY: nzb_x, &
	262	nzt_x
[2259]	263
[4438]	264	USE surface_mod, &
	265	ONLY: surf_def_h, &
	266	surf_lsm_h, &
	267	surf_usm_h
[2259]	268
	269	IMPLICIT NONE
	270
[2967]	271	#if defined( __parallel ) && defined( __mpifh )
[2841]	272	INCLUDE "mpif.h"
	273	#endif
	274
[3182]	275
[3347]	276	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	277	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	278	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[4438]	279	LOGICAL :: compute_velocity_seeds_local = .TRUE. !< switch to decide whether velocity seeds are computed locally or if computation
	280	!< is distributed over several processes
[2259]	281
[3038]	282	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	283	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	284	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	285	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[4438]	286	INTEGER(iwp) :: mergp !< maximum length scale (in gp)
[3038]	287	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	288	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	289	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	290	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[4444]	291	#if defined( __parallel )
[4309]	292	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	293	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	294	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	295	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
[4444]	296	#endif
[2259]	297
[4022]	298	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	299	!< required for bias correction of imposed perturbations
	300	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	301	!< required for bias correction of imposed perturbations
	302
[4444]	303	#if defined( __parallel )
[3347]	304	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	305	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	306	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	307	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
[4444]	308	#endif
[3347]	309	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	310	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	311	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	312	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	313	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	314	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	315	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	316	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	317	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
[2259]	318
[4438]	319	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_xz !< initial random IDs at xz inflow boundary
	320	INTEGER(isp), DIMENSION(:), ALLOCATABLE :: id_rand_yz !< initial random IDs at yz inflow boundary
	321	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_xz !< initial random seeds at xz inflow boundary
	322	INTEGER(isp), DIMENSION(:,:), ALLOCATABLE :: seq_rand_yz !< initial random seeds at yz inflow boundary
	323
[4022]	324	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	325	!< scales above the boundary layer
	326	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	327	!< one length scale above ABL top
	328	REAL(wp) :: d_l !< blend_coeff/length_scale
	329	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	330	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
[4438]	331	REAL(wp) :: dt_stg_call = 0.0_wp !< time interval for calling synthetic turbulence generator
[3347]	332	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	333	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	334	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	335	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	336	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	337
[4022]	338	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	339
[4022]	340
[3347]	341	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	342	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	343	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	344	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	345	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	346	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	347
	348	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	349	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	350	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	351	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	352	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	353	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	354	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	355	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	356	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	357
[3347]	358	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	359	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	360	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	361	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	362	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	363	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	364	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	365	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	366	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	367	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	368	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	369	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	370	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	371	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	377	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	379
	380	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	381	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	382
	383	!
	384	!-- PALM interfaces:
[3347]	385	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	386	INTERFACE stg_adjust
	387	MODULE PROCEDURE stg_adjust
	388	END INTERFACE stg_adjust
	389	!
[2259]	390	!-- Input parameter checks to be done in check_parameters
	391	INTERFACE stg_check_parameters
	392	MODULE PROCEDURE stg_check_parameters
	393	END INTERFACE stg_check_parameters
	394
	395	!
	396	!-- Calculate filter functions
	397	INTERFACE stg_filter_func
	398	MODULE PROCEDURE stg_filter_func
	399	END INTERFACE stg_filter_func
	400
	401	!
[2938]	402	!-- Generate velocity seeds at south and north domain boundary
	403	INTERFACE stg_generate_seed_xz
	404	MODULE PROCEDURE stg_generate_seed_xz
	405	END INTERFACE stg_generate_seed_xz
	406	!
	407	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	408	INTERFACE stg_generate_seed_yz
	409	MODULE PROCEDURE stg_generate_seed_yz
	410	END INTERFACE stg_generate_seed_yz
	411
	412	!
	413	!-- Output of information to the header file
	414	INTERFACE stg_header
	415	MODULE PROCEDURE stg_header
	416	END INTERFACE stg_header
	417
	418	!
	419	!-- Initialization actions
	420	INTERFACE stg_init
	421	MODULE PROCEDURE stg_init
	422	END INTERFACE stg_init
	423
	424	!
	425	!-- Main procedure of synth. turb. gen.
	426	INTERFACE stg_main
	427	MODULE PROCEDURE stg_main
	428	END INTERFACE stg_main
	429
	430	!
	431	!-- Reading of NAMELIST parameters
	432	INTERFACE stg_parin
	433	MODULE PROCEDURE stg_parin
	434	END INTERFACE stg_parin
	435
	436	!
	437	!-- Reading of parameters for restart runs
[2894]	438	INTERFACE stg_rrd_global
	439	MODULE PROCEDURE stg_rrd_global
	440	END INTERFACE stg_rrd_global
[2259]	441
	442	!
	443	!-- Writing of binary output for restart runs
[2894]	444	INTERFACE stg_wrd_global
	445	MODULE PROCEDURE stg_wrd_global
	446	END INTERFACE stg_wrd_global
[2259]	447
	448	SAVE
	449
	450	PRIVATE
	451
	452	!
	453	!-- Public interfaces
[3347]	454	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	455	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	456
	457	!
	458	!-- Public variables
[3347]	459	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	460	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	461	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	462
	463
	464	CONTAINS
	465
	466
	467	!------------------------------------------------------------------------------!
	468	! Description:
	469	! ------------
	470	!> Check parameters routine for synthetic turbulence generator
	471	!------------------------------------------------------------------------------!
	472	SUBROUTINE stg_check_parameters
	473
[3182]	474	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	475	nesting_offline ) THEN
[3376]	476	message_string = 'Synthetic turbulence generator is required ' // &
	477	'if offline nesting is applied and PALM operates ' // &
	478	'in LES mode.'
	479	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	480	ENDIF
	481
[3182]	482	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	483	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	484	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	485	'when nesting is applied and parent operates in ' // &
	486	'RANS-mode but current child in LES mode.'
[3376]	487	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	488	ENDIF
	489
[2776]	490	IF ( use_syn_turb_gen ) THEN
[2259]	491
[3579]	492	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	493	.NOT. rans_mode_parent ) THEN
	494	message_string = 'Using synthetic turbulence generator ' // &
	495	'is not allowed in LES-LES nesting.'
	496	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	497
	498	ENDIF
	499
	500	IF ( child_domain .AND. rans_mode .AND. &
	501	rans_mode_parent ) THEN
	502	message_string = 'Using synthetic turbulence generator ' // &
	503	'is not allowed in RANS-RANS nesting.'
	504	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	505
	506	ENDIF
	507
[3182]	508	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	509
[2938]	510	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	511	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	512	message_string = 'Using synthetic turbulence generator ' // &
[3579]	513	'requires %initializing_actions = ' // &
	514	'"set_constant_profiles" or "read_restart_data"' //&
	515	', if not offline nesting is applied.'
[2938]	516	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	517	ENDIF
	518
	519	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	520	message_string = 'Using synthetic turbulence generator ' // &
[3347]	521	'requires &bc_lr = "dirichlet/radiation", ' // &
	522	'if not offline nesting is applied.'
[2938]	523	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	524	ENDIF
	525	IF ( bc_ns /= 'cyclic' ) THEN
	526	message_string = 'Using synthetic turbulence generator ' // &
[3579]	527	'requires &bc_ns = "cyclic", ' // &
[3347]	528	'if not offline nesting is applied.'
[2938]	529	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	530	ENDIF
	531
[2259]	532	ENDIF
	533
	534	IF ( turbulent_inflow ) THEN
	535	message_string = 'Using synthetic turbulence generator ' // &
[2938]	536	'in combination &with turbulent_inflow = .T. '// &
	537	'is not allowed'
[2259]	538	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	539	ENDIF
[4309]	540	!
	541	!-- Synthetic turbulence generator requires the parallel random generator
	542	IF ( random_generator /= 'random-parallel' ) THEN
	543	message_string = 'Using synthetic turbulence generator ' // &
	544	'requires random_generator = random-parallel.'
	545	CALL message( 'stg_check_parameters', 'PA0421', 1, 2, 0, 6, 0 )
	546	ENDIF
[2259]	547
	548	ENDIF
	549
	550	END SUBROUTINE stg_check_parameters
	551
	552
	553	!------------------------------------------------------------------------------!
	554	! Description:
	555	! ------------
	556	!> Header output for synthetic turbulence generator
	557	!------------------------------------------------------------------------------!
	558	SUBROUTINE stg_header ( io )
	559
	560	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	561
	562	!
	563	!-- Write synthetic turbulence generator Header
	564	WRITE( io, 1 )
[2776]	565	IF ( use_syn_turb_gen ) THEN
[2259]	566	WRITE( io, 2 )
	567	ELSE
	568	WRITE( io, 3 )
	569	ENDIF
[3347]	570
	571	IF ( parametrize_inflow_turbulence ) THEN
	572	WRITE( io, 4 ) dt_stg_adjust
	573	ELSE
	574	WRITE( io, 5 )
	575	ENDIF
[2259]	576
	577	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	578	' ------------------------------------------'/)
[3347]	579	2 FORMAT (' synthetic turbulence generator is switched on')
	580	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	581	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	582	5 FORMAT (' imposed turbulence is read from file' )
[2259]	583
	584	END SUBROUTINE stg_header
	585
	586
	587	!------------------------------------------------------------------------------!
	588	! Description:
	589	! ------------
	590	!> Initialization of the synthetic turbulence generator
	591	!------------------------------------------------------------------------------!
	592	SUBROUTINE stg_init
	593
[3347]	594	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	595
[2669]	596	#if defined( __parallel )
[2259]	597	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	598	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	599	#endif
[2259]	600
[2938]	601	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	602	INTEGER(iwp) :: j !> loop index
	603	INTEGER(iwp) :: k !< index
[4444]	604	#if defined( __parallel )
[2259]	605	INTEGER(iwp) :: newtype !< dummy MPI type
	606	INTEGER(iwp) :: realsize !< size of REAL variables
[4444]	607	#endif
[4309]	608
[4022]	609	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	610	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	611	!
	612	!-- Dummy variables used for reading profiles
	613	REAL(wp) :: d1 !< u profile
	614	REAL(wp) :: d2 !< v profile
	615	REAL(wp) :: d3 !< w profile
	616	REAL(wp) :: d5 !< e profile
	617	REAL(wp) :: luy !< length scale for u in y direction
	618	REAL(wp) :: luz !< length scale for u in z direction
	619	REAL(wp) :: lvy !< length scale for v in y direction
	620	REAL(wp) :: lvz !< length scale for v in z direction
	621	REAL(wp) :: lwy !< length scale for w in y direction
	622	REAL(wp) :: lwz !< length scale for w in z direction
[4444]	623	#if defined( __parallel )
[3038]	624	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[4444]	625	#endif
[2259]	626	REAL(wp) :: zz !< height
	627
[2938]	628
[2259]	629	#if defined( __parallel )
	630	CALL MPI_BARRIER( comm2d, ierr )
	631	#endif
[4438]	632	!
	633	!-- Create mpi-datatypes for exchange in case of non-local but distributed
	634	!-- computation of the velocity seeds. This option is useful in
[4444]	635	!-- case large turbulent length scales are present, where the computational
	636	!-- effort becomes large and need to be parallelized. For parameterized
[4438]	637	!-- turbulence the length scales are small and computing the velocity seeds
	638	!-- locally is faster (no overhead by communication).
	639	IF ( .NOT. compute_velocity_seeds_local ) THEN
[2669]	640	#if defined( __parallel )
[4438]	641	!
	642	!-- Determine processor decomposition of z-axis along x- and y-direction
	643	nnz = nz / pdims(1)
	644	nzb_x_stg = 1 + myidx * INT( nnz )
	645	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
	646
	647	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
	648	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
	649
	650	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	651	.AND. .NOT. rans_mode ) ) THEN
	652	nnz = nz / pdims(2)
	653	nzb_y_stg = 1 + myidy * INT( nnz )
	654	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
	655
	656	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
	657	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
	658	ENDIF
	659
	660	!
	661	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	662	!-- velocity seeds
	663	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	664	extent = 1 * realsize
	665	!
	666	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	667	!-- layer
	668	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
	669	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyn-nys+1], &
	670	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	671	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	672	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
[2938]	673	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	674
	675	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	676	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyn-nys+1], &
	677	[1,nyn-nys+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	678	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	679	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
[2938]	680	CALL MPI_TYPE_FREE( newtype, ierr )
[4438]	681
[2938]	682	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[4438]	683	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
	684
	685	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	686	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
	687
	688	DO j = 1, pdims(1)
	689	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2938]	690	ENDDO
[4438]	691	!
	692	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	693	!-- layer
	694	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
	695	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	696	.AND. .NOT. rans_mode ) ) THEN
	697	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxr-nxl+1], &
	698	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	699	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	700	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	701	CALL MPI_TYPE_FREE( newtype, ierr )
	702
	703	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
	704	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxr-nxl+1], &
	705	[1,nxr-nxl+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	706	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	707	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	708	CALL MPI_TYPE_FREE( newtype, ierr )
	709
	710	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	711	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	712
	713	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	714	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	715
	716	DO j = 1, pdims(2)
	717	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	718	ENDDO
	719
	720	ENDIF
[4440]	721	#endif
[2938]	722	ENDIF
[2259]	723	!
[4071]	724	!-- Allocate required arrays.
	725	!-- In case no offline nesting or self nesting is used, the arrary
	726	!-- mean_inflow profiles is required. Check if it is already allocated, else
	727	!-- allocate and initialize it appropriately. Note, in case turbulence and
	728	!-- inflow information is read from file, mean_inflow_profiles is already
	729	!-- allocated and initialized appropriately.
[3347]	730	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	731	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	732	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	733	mean_inflow_profiles = 0.0_wp
	734	mean_inflow_profiles(:,1) = u_init
	735	mean_inflow_profiles(:,2) = v_init
	736	!
	737	!-- Even though potential temperature and humidity are not perturbed,
	738	!-- they need to be initialized appropriately.
	739	IF ( .NOT. neutral ) &
	740	mean_inflow_profiles(:,4) = pt_init
	741	IF ( humidity ) &
	742	mean_inflow_profiles(:,6) = q_init
	743	ENDIF
[3347]	744	ENDIF
[2259]	745
[3347]	746	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	747	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	748	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	749	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	750	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	751	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	752	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	753	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	754
[4438]	755	ALLOCATE ( dist_xz(nzb:nzt+1,nxl:nxr,3) )
	756	ALLOCATE ( dist_yz(nzb:nzt+1,nys:nyn,3) )
[3347]	757	dist_xz = 0.0_wp
	758	dist_yz = 0.0_wp
	759	!
[2259]	760	!-- Read inflow profile
	761	!-- Height levels of profiles in input profile is as follows:
	762	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	763	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	764	!-- WARNING: zz is not used at the moment
[2938]	765	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	766	EXIST = file_stg_exist )
[2259]	767
[2938]	768	IF ( file_stg_exist ) THEN
[2259]	769
[2938]	770	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	771	FORM='FORMATTED')
	772	!
	773	!-- Skip header
	774	READ( 90, * )
[2259]	775
[3182]	776	DO k = nzb+1, nzt+1
[2938]	777	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	778	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	779	d1, d2, d3, d5
	780
[2259]	781	!
[3182]	782	!-- Convert length scales from meter to number of grid points.
[2938]	783	nuy(k) = INT( luy * ddy )
[3182]	784	nuz(k) = INT( luz * ddzw(k) )
[2938]	785	nvy(k) = INT( lvy * ddy )
[3182]	786	nvz(k) = INT( lvz * ddzw(k) )
[2938]	787	nwy(k) = INT( lwy * ddy )
[3182]	788	nwz(k) = INT( lwz * ddzw(k) )
[2938]	789	!
	790	!-- Workaround, assume isotropic turbulence
	791	nwx(k) = nwy(k)
	792	nvx(k) = nvy(k)
	793	nux(k) = nuy(k)
	794	!
	795	!-- Save Mean inflow profiles
	796	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	797	mean_inflow_profiles(k,1) = d1
	798	mean_inflow_profiles(k,2) = d2
	799	! mean_inflow_profiles(k,4) = d4
	800	mean_inflow_profiles(k,5) = d5
	801	ENDIF
	802	ENDDO
[3182]	803	!
	804	!-- Set lenght scales at surface grid point
	805	nuy(nzb) = nuy(nzb+1)
	806	nuz(nzb) = nuz(nzb+1)
	807	nvy(nzb) = nvy(nzb+1)
	808	nvz(nzb) = nvz(nzb+1)
	809	nwy(nzb) = nwy(nzb+1)
	810	nwz(nzb) = nwz(nzb+1)
	811
[2938]	812	CLOSE( 90 )
[3347]	813	!
	814	!-- Calculate coefficient matrix from Reynolds stress tensor
	815	!-- (Lund rotation)
	816	CALL calc_coeff_matrix
	817	!
	818	!-- No information about turbulence and its length scales are available.
	819	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	820	!-- Set flag which indicates that turbulence is parametrized, which is done
	821	!-- later when energy-balance models are already initialized. This is
	822	!-- because the STG needs information about surface properties such as
	823	!-- roughness to build 'realistic' turbulence profiles.
[2938]	824	ELSE
[2259]	825	!
[4022]	826	!-- Define length scale for the imposed turbulence, which is defined as
	827	!-- 8 times the minimum grid spacing
[4441]	828	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
[4022]	829	!
	830	!-- Define constant to gradually decrease length scales and Reynolds stress
	831	!-- above ABL top. Assure that no zero length scales are used.
	832	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	833	!
[3347]	834	!-- Set flag indicating that turbulence is parametrized
	835	parametrize_inflow_turbulence = .TRUE.
	836	!
[4022]	837	!-- In case of dirichlet inflow boundary conditions only at one lateral
	838	!-- boundary, i.e. in the case no offline or self nesting is applied but
	839	!-- synthetic turbulence shall be parametrized nevertheless, the
	840	!-- boundary-layer depth need to determined first.
	841	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	842	CALL nesting_offl_calc_zi
	843	!
[3347]	844	!-- Determine boundary-layer depth, which is used to initialize lenght
	845	!-- scales
	846	CALL calc_scaling_variables
	847	!
	848	!-- Initialize lenght and time scales, which in turn are used
	849	!-- to initialize the filter functions.
	850	CALL calc_length_and_time_scale
[3891]	851	!
	852	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	853	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	854	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	855	!-- friction velocity and velocity scale.
	856	CALL parametrize_reynolds_stress
	857	!
	858	!-- Calculate coefficient matrix from Reynolds stress tensor
	859	!-- (Lund rotation)
	860	CALL calc_coeff_matrix
[3347]	861
[2938]	862	ENDIF
	863
[2259]	864	!
[3347]	865	!-- Assign initial profiles. Note, this is only required if turbulent
	866	!-- inflow from the left is desired, not in case of any of the
	867	!-- nesting (offline or self nesting) approaches.
[3182]	868	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	869	u_init = mean_inflow_profiles(:,1)
	870	v_init = mean_inflow_profiles(:,2)
	871	!pt_init = mean_inflow_profiles(:,4)
	872	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	873	ENDIF
[3347]	874
[2938]	875	!
[2259]	876	!-- Define the size of the filter functions and allocate them.
[4438]	877	mergp = 0
[2259]	878
	879	! arrays must be large enough to cover the largest length scale
	880	DO k = nzb, nzt+1
[2938]	881	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	882	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	883	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[4438]	884	IF ( j > mergp ) mergp = j
[2259]	885	ENDDO
	886
[4438]	887	! mergp = 2 * mergp
	888	! mergp = mergp
[2259]	889
[4438]	890	ALLOCATE ( bux(-mergp:mergp,nzb:nzt+1), &
	891	buy(-mergp:mergp,nzb:nzt+1), &
	892	buz(-mergp:mergp,nzb:nzt+1), &
	893	bvx(-mergp:mergp,nzb:nzt+1), &
	894	bvy(-mergp:mergp,nzb:nzt+1), &
	895	bvz(-mergp:mergp,nzb:nzt+1), &
	896	bwx(-mergp:mergp,nzb:nzt+1), &
	897	bwy(-mergp:mergp,nzb:nzt+1), &
	898	bwz(-mergp:mergp,nzb:nzt+1) )
[2259]	899
	900	!
[2938]	901	!-- Allocate velocity seeds for turbulence at xz-layer
[4438]	902	ALLOCATE ( fu_xz( nzb:nzt+1,nxl:nxr), fuo_xz(nzb:nzt+1,nxl:nxr), &
	903	fv_xz( nzb:nzt+1,nxl:nxr), fvo_xz(nzb:nzt+1,nxl:nxr), &
	904	fw_xz( nzb:nzt+1,nxl:nxr), fwo_xz(nzb:nzt+1,nxl:nxr) )
[2259]	905
[2938]	906	!
	907	!-- Allocate velocity seeds for turbulence at yz-layer
[4438]	908	ALLOCATE ( fu_yz( nzb:nzt+1,nys:nyn), fuo_yz(nzb:nzt+1,nys:nyn), &
	909	fv_yz( nzb:nzt+1,nys:nyn), fvo_yz(nzb:nzt+1,nys:nyn), &
	910	fw_yz( nzb:nzt+1,nys:nyn), fwo_yz(nzb:nzt+1,nys:nyn) )
[2259]	911
[2938]	912	fu_xz = 0.0_wp
	913	fuo_xz = 0.0_wp
	914	fv_xz = 0.0_wp
	915	fvo_xz = 0.0_wp
	916	fw_xz = 0.0_wp
	917	fwo_xz = 0.0_wp
	918
	919	fu_yz = 0.0_wp
	920	fuo_yz = 0.0_wp
	921	fv_yz = 0.0_wp
	922	fvo_yz = 0.0_wp
	923	fw_yz = 0.0_wp
	924	fwo_yz = 0.0_wp
	925
[2259]	926	!
	927	!-- Create filter functions
[2938]	928	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	929	CALL stg_filter_func( nuy, buy ) !filter uy
	930	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	931	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	932	CALL stg_filter_func( nvy, bvy ) !filter vy
	933	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	934	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	935	CALL stg_filter_func( nwy, bwy ) !filter wy
	936	CALL stg_filter_func( nwz, bwz ) !filter wz
	937
	938	#if defined( __parallel )
	939	CALL MPI_BARRIER( comm2d, ierr )
	940	#endif
	941
	942	!
[2938]	943	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	944	! time step.
	945	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	946	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	947	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	948	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	949
	950	IF ( myidx == id_stg_left ) i = -1
	951	IF ( myidx == id_stg_right ) i = nxr+1
	952
[4438]	953	DO j = nys, nyn
[2259]	954	DO k = nzb, nzt+1
[4332]	955	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	956	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	957	ELSE
[4332]	958	fu_yz(k,j) = 10E-8_wp
[2259]	959	ENDIF
	960
[4332]	961	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	962	fv_yz(k,j) = ( v(k,j,i) - &
	963	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	964	ELSE
[4332]	965	fv_yz(k,j) = 10E-8_wp
[2259]	966	ENDIF
	967
[4332]	968	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	969	fw_yz(k,j) = ( w(k,j,i) - &
	970	a31(k) * fu_yz(k,j) - a32(k) * &
	971	fv_yz(k,j) ) / a33(k)
[2259]	972	ELSE
[4332]	973	fw_yz(k,j) = 10E-8_wp
[2259]	974	ENDIF
	975	ENDDO
	976	ENDDO
	977	ENDIF
[3900]	978
	979	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	980
	981	IF ( myidy == id_stg_south ) j = -1
	982	IF ( myidy == id_stg_north ) j = nyn+1
	983
[4438]	984	DO i = nxl, nxr
[3900]	985	DO k = nzb, nzt+1
[4335]	986	!
	987	!-- In case the correlation coefficients are very small, the
	988	!-- velocity seeds may become very large finally creating
	989	!-- numerical instabilities in the synthetic turbulence generator.
	990	!-- Empirically, a value of 10E-8 seems to be sufficient.
[4332]	991	IF ( a11(k) > 10E-8_wp ) THEN
[4022]	992	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	993	ELSE
[4332]	994	fu_xz(k,i) = 10E-8_wp
[3900]	995	ENDIF
	996
[4332]	997	IF ( a22(k) > 10E-8_wp ) THEN
[4022]	998	fv_xz(k,i) = ( v(k,j,i) - &
	999	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	1000	ELSE
[4332]	1001	fv_xz(k,i) = 10E-8_wp
[3900]	1002	ENDIF
	1003
[4332]	1004	IF ( a33(k) > 10E-8_wp ) THEN
[4022]	1005	fw_xz(k,i) = ( w(k,j,i) - &
	1006	a31(k) * fu_xz(k,i) - &
	1007	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	1008	ELSE
[4332]	1009	fw_xz(k,i) = 10E-8_wp
[3900]	1010	ENDIF
	1011
	1012	ENDDO
	1013	ENDDO
	1014	ENDIF
[2259]	1015	ENDIF
[4022]	1016	!
	1017	!-- Count the number of non-topography grid points at the boundaries where
	1018	!-- perturbations are imposed. This number is later used for bias corrections
	1019	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	1020	!-- due to the asymetry of u and v along x and y direction, respectively,
	1021	!-- different cases must be distinguished.
	1022	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	1023	!
	1024	!-- Number of grid points where perturbations are imposed on u
	1025	IF ( myidx == id_stg_left ) i = nxl
	1026	IF ( myidx == id_stg_right ) i = nxr+1
	1027
	1028	nr_non_topo_yz_l(1) = SUM( &
	1029	MERGE( 1, 0, &
[4346]	1030	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1031	!
	1032	!-- Number of grid points where perturbations are imposed on v and w
	1033	IF ( myidx == id_stg_left ) i = nxl-1
	1034	IF ( myidx == id_stg_right ) i = nxr+1
	1035
	1036	nr_non_topo_yz_l(2) = SUM( &
	1037	MERGE( 1, 0, &
[4346]	1038	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1039	nr_non_topo_yz_l(3) = SUM( &
	1040	MERGE( 1, 0, &
[4346]	1041	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1042
	1043	#if defined( __parallel )
	1044	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	1045	MPI_SUM, comm1dy, ierr )
	1046	#else
	1047	nr_non_topo_yz = nr_non_topo_yz_l
	1048	#endif
	1049	ENDIF
	1050
	1051	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	1052	!
	1053	!-- Number of grid points where perturbations are imposed on v
	1054	IF ( myidy == id_stg_south ) j = nys
	1055	IF ( myidy == id_stg_north ) j = nyn+1
	1056
	1057	nr_non_topo_xz_l(2) = SUM( &
	1058	MERGE( 1, 0, &
[4346]	1059	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1060	!
	1061	!-- Number of grid points where perturbations are imposed on u and w
	1062	IF ( myidy == id_stg_south ) j = nys-1
	1063	IF ( myidy == id_stg_north ) j = nyn+1
	1064
	1065	nr_non_topo_xz_l(1) = SUM( &
	1066	MERGE( 1, 0, &
[4346]	1067	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1068	nr_non_topo_xz_l(3) = SUM( &
	1069	MERGE( 1, 0, &
[4346]	1070	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1071
	1072	#if defined( __parallel )
	1073	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1074	MPI_SUM, comm1dx, ierr )
	1075	#else
	1076	nr_non_topo_xz = nr_non_topo_xz_l
	1077	#endif
	1078	ENDIF
[4438]	1079	!
	1080	!-- Initialize random number generator at xz- and yz-layers. Random numbers
	1081	!-- are initialized at each core. In case there is only inflow from the left,
	1082	!-- it is sufficient to generate only random numbers for the yz-layer, else
	1083	!-- random numbers for the xz-layer are also required.
	1084	ALLOCATE ( id_rand_yz(-mergp+nys:nyn+mergp) )
	1085	ALLOCATE ( seq_rand_yz(5,-mergp+nys:nyn+mergp) )
	1086	id_rand_yz = 0
	1087	seq_rand_yz = 0
[2259]	1088
[4438]	1089	CALL init_parallel_random_generator( ny, -mergp+nys, nyn+mergp, &
	1090	id_rand_yz, seq_rand_yz )
[4022]	1091
[4438]	1092	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1093	.AND. .NOT. rans_mode ) ) THEN
	1094	ALLOCATE ( id_rand_xz(-mergp+nxl:nxr+mergp) )
	1095	ALLOCATE ( seq_rand_xz(5,-mergp+nxl:nxr+mergp) )
	1096	id_rand_xz = 0
	1097	seq_rand_xz = 0
	1098
	1099	CALL init_parallel_random_generator( nx, -mergp+nxl, nxr+mergp, &
	1100	id_rand_xz, seq_rand_xz )
	1101	ENDIF
	1102
	1103
	1104
[2259]	1105	END SUBROUTINE stg_init
	1106
	1107
	1108	!------------------------------------------------------------------------------!
	1109	! Description:
	1110	! ------------
	1111	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1112	!> (Xie and Castro, 2008)
	1113	!------------------------------------------------------------------------------!
	1114	SUBROUTINE stg_filter_func( nxx, bxx )
	1115
	1116	INTEGER(iwp) :: k !< loop index
	1117	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1118	INTEGER(iwp) :: nf !< index for length scales
	1119
	1120	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1121	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1122
[4438]	1123	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: nxx !< length scale (in gp)
[2259]	1124
[4438]	1125	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: bxx !< filter function
[2259]	1126
	1127
	1128	bxx = 0.0_wp
	1129
	1130	DO k = nzb, nzt+1
	1131	bdenom = 0.0_wp
	1132	n_k = nxx(k)
	1133	IF ( n_k /= 0 ) THEN
	1134
	1135	!
	1136	!-- ( Eq.10 )^2
[4438]	1137	DO nf = -n_k, n_k
[2259]	1138	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1139	ENDDO
	1140
	1141	!
	1142	!-- ( Eq.9 )
	1143	bdenom = SQRT( bdenom )
[4438]	1144	DO nf = -n_k, n_k
[2259]	1145	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1146	ENDDO
	1147	ENDIF
	1148	ENDDO
	1149
[3347]	1150	END SUBROUTINE stg_filter_func
[2259]	1151
	1152
	1153	!------------------------------------------------------------------------------!
	1154	! Description:
	1155	! ------------
	1156	!> Parin for &stg_par for synthetic turbulence generator
	1157	!------------------------------------------------------------------------------!
	1158	SUBROUTINE stg_parin
	1159
	1160	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1161
	1162
[4438]	1163	NAMELIST /stg_par/ dt_stg_adjust, &
	1164	dt_stg_call, &
	1165	use_syn_turb_gen, &
	1166	compute_velocity_seeds_local
[2259]	1167
	1168	line = ' '
	1169	!
	1170	!-- Try to find stg package
	1171	REWIND ( 11 )
	1172	line = ' '
	1173	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1174	READ ( 11, '(A)', END=20 ) line
[2259]	1175	ENDDO
	1176	BACKSPACE ( 11 )
	1177
	1178	!
	1179	!-- Read namelist
[3246]	1180	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1181
	1182	!
	1183	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1184	!-- on
[2776]	1185	syn_turb_gen = .TRUE.
[3246]	1186	GOTO 20
[2259]	1187
[3246]	1188	10 BACKSPACE( 11 )
[3248]	1189	READ( 11 , '(A)') line
	1190	CALL parin_fail_message( 'stg_par', line )
[2563]	1191
[3246]	1192	20 CONTINUE
[2259]	1193
	1194	END SUBROUTINE stg_parin
	1195
	1196
	1197	!------------------------------------------------------------------------------!
	1198	! Description:
	1199	! ------------
[2894]	1200	!> This routine reads the respective restart data.
[2576]	1201	!------------------------------------------------------------------------------!
[2894]	1202	SUBROUTINE stg_rrd_global( found )
[2576]	1203
[3044]	1204	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1205
[2894]	1206	found = .TRUE.
[2259]	1207
[3038]	1208
[2894]	1209	SELECT CASE ( restart_string(1:length) )
[4022]	1210
	1211	CASE ( 'time_stg_adjust' )
	1212	READ ( 13 ) time_stg_adjust
	1213
	1214	CASE ( 'time_stg_call' )
	1215	READ ( 13 ) time_stg_call
	1216
[2894]	1217	CASE ( 'use_syn_turb_gen' )
	1218	READ ( 13 ) use_syn_turb_gen
[2259]	1219
[2894]	1220	CASE DEFAULT
[2259]	1221
[3038]	1222	found = .FALSE.
[2259]	1223
[2894]	1224	END SELECT
[2259]	1225
	1226
[2894]	1227	END SUBROUTINE stg_rrd_global
[2259]	1228
	1229
	1230	!------------------------------------------------------------------------------!
	1231	! Description:
	1232	! ------------
	1233	!> This routine writes the respective restart data.
	1234	!------------------------------------------------------------------------------!
[2894]	1235	SUBROUTINE stg_wrd_global
[2259]	1236
[4022]	1237	CALL wrd_write_string( 'time_stg_adjust' )
	1238	WRITE ( 14 ) time_stg_adjust
	1239
	1240	CALL wrd_write_string( 'time_stg_call' )
	1241	WRITE ( 14 ) time_stg_call
[2259]	1242
[2894]	1243	CALL wrd_write_string( 'use_syn_turb_gen' )
	1244	WRITE ( 14 ) use_syn_turb_gen
[2259]	1245
	1246
[2894]	1247	END SUBROUTINE stg_wrd_global
[2259]	1248
[2894]	1249
[2259]	1250	!------------------------------------------------------------------------------!
	1251	! Description:
	1252	! ------------
	1253	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1254	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1255	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1256	!> (Lund, 1998).
	1257	!------------------------------------------------------------------------------!
	1258	SUBROUTINE stg_main
	1259
[4457]	1260	USE exchange_horiz_mod, &
	1261	ONLY: exchange_horiz
	1262
[2938]	1263	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1264	INTEGER(iwp) :: j !< loop index in y-direction
	1265	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1266
	1267	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1268
	1269	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1270
	1271	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1272
[3987]	1273	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1274	!
	1275	!-- Calculate time step which is needed for filter functions
[3775]	1276	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1277	!
[4022]	1278	!-- Check if synthetic turbulence generator needs to be called and new
	1279	!-- perturbations need to be created or if old disturbances can be imposed
	1280	!-- again.
	1281	IF ( time_stg_call >= dt_stg_call .AND. &
	1282	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1283	stg_call = .TRUE.
	1284	ELSE
	1285	stg_call = .FALSE.
	1286	ENDIF
	1287	!
[2259]	1288	!-- Initial value of fu, fv, fw
[3646]	1289	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[4309]	1290	!
	1291	!-- Generate turbulence at the left and right boundary. Random numbers
	1292	!-- for the yz-planes at the left/right boundary are generated by the
	1293	!-- left-sided mpi ranks only. After random numbers are calculated, they
	1294	!-- are distributed to all other mpi ranks in the model, so that the
	1295	!-- velocity seed matrices are available on all mpi ranks (i.e. also on the
	1296	!-- right-sided boundary mpi ranks). In case of offline nesting, this implies,
	1297	!-- that the left- and the right-sided lateral boundary have the same initial
	1298	!-- seeds.
	1299	!-- Note, in case of inflow from the right only, only turbulence at the left
	1300	!-- boundary is required.
	1301	IF ( .NOT. ( nesting_offline .OR. &
	1302	( child_domain .AND. rans_mode_parent &
	1303	.AND. .NOT. rans_mode ) ) ) THEN
	1304	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1305	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1306	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1307	ELSE
	1308	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, &
	1309	id_stg_left, id_stg_right )
	1310	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, &
	1311	id_stg_left, id_stg_right )
	1312	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, &
	1313	id_stg_left, id_stg_right )
[2938]	1314	!
[4309]	1315	!-- Generate turbulence at the south and north boundary. Random numbers
	1316	!-- for the xz-planes at the south/north boundary are generated by the
	1317	!-- south-sided mpi ranks only. Please see also comment above.
	1318	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, &
	1319	id_stg_south, id_stg_north )
	1320	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, &
	1321	id_stg_south, id_stg_north )
	1322	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, &
	1323	id_stg_south, id_stg_north )
[2938]	1324	ENDIF
[2259]	1325	velocity_seed_initialized = .TRUE.
	1326	ENDIF
	1327	!
[4309]	1328	!-- New set of fu, fv, fw. Note, for inflow from the left side only, velocity
	1329	!-- seeds are only required at the left boundary, while in case of offline
	1330	!-- nesting or RANS-LES nesting velocity seeds are required also at the
	1331	!-- right, south and north boundaries.
[4022]	1332	IF ( stg_call ) THEN
[4309]	1333	IF ( .NOT. ( nesting_offline .OR. &
	1334	( child_domain .AND. rans_mode_parent &
	1335	.AND. .NOT. rans_mode ) ) ) THEN
	1336	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1337	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1338	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1339
	1340	ELSE
	1341	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, &
	1342	id_stg_left, id_stg_right )
	1343	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, &
	1344	id_stg_left, id_stg_right )
	1345	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, &
	1346	id_stg_left, id_stg_right )
	1347
	1348	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, &
	1349	id_stg_south, id_stg_north )
	1350	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, &
	1351	id_stg_south, id_stg_north )
	1352	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, &
	1353	id_stg_south, id_stg_north )
[4022]	1354	ENDIF
[2938]	1355	ENDIF
[3347]	1356
[2938]	1357	!
[4309]	1358	!-- Turbulence generation at left and/or right boundary
[2938]	1359	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1360	!
[4022]	1361	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1362	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1363	!-- imposed
	1364	IF ( stg_call ) THEN
	1365
[4438]	1366	DO j = nys, nyn
[4022]	1367	DO k = nzb, nzt + 1
	1368	!
	1369	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1370	IF ( tu(k) == 0.0_wp ) THEN
	1371	fu_yz(k,j) = fuo_yz(k,j)
	1372	ELSE
	1373	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1374	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1375	ENDIF
	1376
	1377	IF ( tv(k) == 0.0_wp ) THEN
	1378	fv_yz(k,j) = fvo_yz(k,j)
	1379	ELSE
	1380	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1381	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1382	ENDIF
	1383
	1384	IF ( tw(k) == 0.0_wp ) THEN
	1385	fw_yz(k,j) = fwo_yz(k,j)
	1386	ELSE
	1387	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1388	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1389	ENDIF
	1390	ENDDO
	1391	ENDDO
	1392
	1393	dist_yz(nzb,:,1) = 0.0_wp
	1394	dist_yz(nzb,:,2) = 0.0_wp
	1395	dist_yz(nzb,:,3) = 0.0_wp
	1396
	1397	IF ( myidx == id_stg_left ) i = nxl
	1398	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1399	DO j = nys, nyn
[4022]	1400	DO k = nzb+1, nzt + 1
	1401	!
	1402	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1403	!-- Additional factors are added to improve the variance of v and w
	1404	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1405	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1406	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1407	ENDDO
	1408	ENDDO
[4309]	1409
[4022]	1410	IF ( myidx == id_stg_left ) i = nxl-1
	1411	IF ( myidx == id_stg_right ) i = nxr+1
[4438]	1412	DO j = nys, nyn
[4022]	1413	DO k = nzb+1, nzt + 1
	1414	!
	1415	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1416	!-- Additional factors are added to improve the variance of v and w
	1417	!-- experimental test of 1.2
[3347]	1418	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1419	* 1.2_wp ) &
	1420	* ( a21(k) * fu_yz(k,j) &
[4022]	1421	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1422	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1423	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[3347]	1424	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1425	* 1.3_wp ) &
	1426	* ( a31(k) * fu_yz(k,j) &
	1427	+ a32(k) * fv_yz(k,j) &
[4022]	1428	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1429	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1430	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1431	ENDDO
[2259]	1432	ENDDO
[4022]	1433	ENDIF
[2259]	1434	!
	1435	!-- Mass flux correction following Kim et al. (2013)
	1436	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1437	!-- inflow boundary. First, calculate mean value of the imposed
	1438	!-- perturbations at yz boundary.
	1439	!-- Note, this needs to be done only after the last RK3-substep, else
	1440	!-- the boundary values won't be accessed.
	1441	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1442	mc_factor_l = 0.0_wp
	1443	mc_factor = 0.0_wp
	1444	!
	1445	!-- Sum up the original volume flows (with and without perturbations).
	1446	!-- Note, for non-normal components (here v and w) it is actually no
	1447	!-- volume flow.
[2938]	1448	IF ( myidx == id_stg_left ) i = nxl
	1449	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1450
	1451	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1452	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1453	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 1 ) ) )
[4022]	1454
	1455	IF ( myidx == id_stg_left ) i = nxl-1
	1456	IF ( myidx == id_stg_right ) i = nxr+1
	1457
	1458	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1459	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1460	BTEST( wall_flags_total_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
[4022]	1461	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1462	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1463	BTEST( wall_flags_total_0(nzb:nzt,nys:nyn,i), 3 ) ) )
[4022]	1464
[2938]	1465	#if defined( __parallel )
	1466	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1467	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1468	#else
	1469	mc_factor = mc_factor_l
[2938]	1470	#endif
[4022]	1471	!
	1472	!-- Calculate correction factor and force zero mean perturbations.
	1473	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1474
	1475	IF ( myidx == id_stg_left ) i = nxl
	1476	IF ( myidx == id_stg_right ) i = nxr+1
	1477
[4438]	1478	dist_yz(:,nys:nyn,1) = ( dist_yz(:,nys:nyn,1) - mc_factor(1) ) &
[4022]	1479	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1480	BTEST( wall_flags_total_0(:,nys:nyn,i), 1 ) )
[4022]	1481
	1482
	1483	IF ( myidx == id_stg_left ) i = nxl-1
	1484	IF ( myidx == id_stg_right ) i = nxr+1
	1485
[4438]	1486	dist_yz(:,nys:nyn,2) = ( dist_yz(:,nys:nyn,2) - mc_factor(2) ) &
[4022]	1487	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1488	BTEST( wall_flags_total_0(:,nys:nyn,i), 2 ) )
[4022]	1489
[4438]	1490	dist_yz(:,nys:nyn,3) = ( dist_yz(:,nys:nyn,3) - mc_factor(3) ) &
[4022]	1491	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1492	BTEST( wall_flags_total_0(:,nys:nyn,i), 3 ) )
[4022]	1493	!
[2938]	1494	!-- Add disturbances
	1495	IF ( myidx == id_stg_left ) THEN
[4022]	1496	!
	1497	!-- For the left boundary distinguish between mesoscale offline / self
	1498	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1499	!-- case turbulence is imposed on the mean inflow profiles.
	1500	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1501	!
	1502	!-- Add disturbance at the inflow
[4438]	1503	DO j = nys, nyn
[4022]	1504	DO k = nzb, nzt+1
	1505	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1506	dist_yz(k,j,1) ) &
	1507	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1508	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1509	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1510	dist_yz(k,j,2) ) &
	1511	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1512	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1513	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1514	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1515	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1516	ENDDO
[2938]	1517	ENDDO
[4022]	1518	ELSE
	1519
	1520	DO j = nys, nyn
	1521	DO k = nzb+1, nzt
	1522	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1523	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1524	BTEST( wall_flags_total_0(k,j,0), 1 ) )
[4022]	1525	u(k,j,-1) = u(k,j,0)
	1526	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1527	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1528	BTEST( wall_flags_total_0(k,j,-1), 2 ) )
[4022]	1529	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1530	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1531	BTEST( wall_flags_total_0(k,j,-1), 3 ) )
[4022]	1532	ENDDO
	1533	ENDDO
	1534	ENDIF
[2938]	1535	ENDIF
	1536	IF ( myidx == id_stg_right ) THEN
[3186]	1537	DO j = nys, nyn
[3347]	1538	DO k = nzb+1, nzt
[3186]	1539	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1540	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1541	BTEST( wall_flags_total_0(k,j,nxr+1), 1 ) )
[3186]	1542	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1543	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1544	BTEST( wall_flags_total_0(k,j,nxr+1), 2 ) )
[3186]	1545	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1546	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1547	BTEST( wall_flags_total_0(k,j,nxr+1), 3 ) )
[2938]	1548	ENDDO
	1549	ENDDO
	1550	ENDIF
	1551	ENDIF
	1552	ENDIF
	1553	!
	1554	!-- Turbulence generation at north and south boundary
	1555	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1556	!
[4022]	1557	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1558	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1559	!-- imposed
	1560	IF ( stg_call ) THEN
[4438]	1561	DO i = nxl, nxr
[4022]	1562	DO k = nzb, nzt + 1
	1563	!
	1564	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1565	IF ( tu(k) == 0.0_wp ) THEN
	1566	fu_xz(k,i) = fuo_xz(k,i)
	1567	ELSE
	1568	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1569	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1570	ENDIF
	1571
	1572	IF ( tv(k) == 0.0_wp ) THEN
	1573	fv_xz(k,i) = fvo_xz(k,i)
	1574	ELSE
	1575	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1576	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1577	ENDIF
	1578
	1579	IF ( tw(k) == 0.0_wp ) THEN
	1580	fw_xz(k,i) = fwo_xz(k,i)
	1581	ELSE
	1582	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1583	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1584	ENDIF
	1585	ENDDO
	1586	ENDDO
	1587
	1588
	1589	dist_xz(nzb,:,1) = 0.0_wp
	1590	dist_xz(nzb,:,2) = 0.0_wp
	1591	dist_xz(nzb,:,3) = 0.0_wp
	1592
	1593	IF ( myidy == id_stg_south ) j = nys
	1594	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1595	DO i = nxl, nxr
[4022]	1596	DO k = nzb+1, nzt + 1
	1597	!
	1598	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1599	!-- Additional factors are added to improve the variance of v and w
	1600	!experimental test of 1.2
[3347]	1601	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1602	* 1.2_wp ) &
	1603	* ( a21(k) * fu_xz(k,i) &
[4022]	1604	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1605	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1606	BTEST( wall_flags_total_0(k,j,i), 2 ) )
[4022]	1607	ENDDO
	1608	ENDDO
	1609
	1610	IF ( myidy == id_stg_south ) j = nys-1
	1611	IF ( myidy == id_stg_north ) j = nyn+1
[4438]	1612	DO i = nxl, nxr
[4022]	1613	DO k = nzb+1, nzt + 1
	1614	!
	1615	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1616	!-- Additional factors are added to improve the variance of v and w
	1617	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1618	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1619	BTEST( wall_flags_total_0(k,j,i), 1 ) )
[4022]	1620
[3347]	1621	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1622	* 1.3_wp ) &
	1623	* ( a31(k) * fu_xz(k,i) &
	1624	+ a32(k) * fv_xz(k,i) &
[4022]	1625	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1626	MERGE( 1.0_wp, 0.0_wp, &
[4346]	1627	BTEST( wall_flags_total_0(k,j,i), 3 ) )
[4022]	1628	ENDDO
[2938]	1629	ENDDO
[4022]	1630	ENDIF
[3347]	1631
[2938]	1632	!
	1633	!-- Mass flux correction following Kim et al. (2013)
	1634	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1635	!-- inflow boundary. First, calculate mean value of the imposed
	1636	!-- perturbations at yz boundary.
	1637	!-- Note, this needs to be done only after the last RK3-substep, else
	1638	!-- the boundary values won't be accessed.
	1639	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1640	mc_factor_l = 0.0_wp
	1641	mc_factor = 0.0_wp
	1642
	1643	IF ( myidy == id_stg_south ) j = nys
	1644	IF ( myidy == id_stg_north ) j = nyn+1
	1645
	1646	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1647	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1648	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
[4022]	1649
	1650	IF ( myidy == id_stg_south ) j = nys-1
	1651	IF ( myidy == id_stg_north ) j = nyn+1
	1652
	1653	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1654	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1655	BTEST( wall_flags_total_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
[4022]	1656	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1657	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1658	BTEST( wall_flags_total_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
[4022]	1659
[2938]	1660	#if defined( __parallel )
[4022]	1661	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1662	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1663	#else
	1664	mc_factor = mc_factor_l
[2938]	1665	#endif
[4022]	1666
	1667	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1668
	1669	IF ( myidy == id_stg_south ) j = nys
	1670	IF ( myidy == id_stg_north ) j = nyn+1
	1671
[4438]	1672	dist_xz(:,nxl:nxr,2) = ( dist_xz(:,nxl:nxr,2) - mc_factor(2) ) &
[4022]	1673	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1674	BTEST( wall_flags_total_0(:,j,nxl:nxr), 2 ) )
[4022]	1675
	1676
	1677	IF ( myidy == id_stg_south ) j = nys-1
	1678	IF ( myidy == id_stg_north ) j = nyn+1
	1679
[4438]	1680	dist_xz(:,nxl:nxr,1) = ( dist_xz(:,nxl:nxr,1) - mc_factor(1) ) &
[4022]	1681	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1682	BTEST( wall_flags_total_0(:,j,nxl:nxr), 1 ) )
[4022]	1683
[4438]	1684	dist_xz(:,nxl:nxr,3) = ( dist_xz(:,nxl:nxr,3) - mc_factor(3) ) &
[4022]	1685	* MERGE( 1.0_wp, 0.0_wp, &
[4438]	1686	BTEST( wall_flags_total_0(:,j,nxl:nxr), 3 ) )
[4022]	1687	!
	1688	!-- Add disturbances
	1689	IF ( myidy == id_stg_south ) THEN
	1690	DO i = nxl, nxr
	1691	DO k = nzb+1, nzt
	1692	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1693	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1694	BTEST( wall_flags_total_0(k,-1,i), 1 ) )
[4022]	1695	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1696	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1697	BTEST( wall_flags_total_0(k,0,i), 2 ) )
[4022]	1698	v(k,-1,i) = v(k,0,i)
	1699	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1700	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1701	BTEST( wall_flags_total_0(k,-1,i), 3 ) )
[4022]	1702	ENDDO
[2938]	1703	ENDDO
[4022]	1704	ENDIF
	1705	IF ( myidy == id_stg_north ) THEN
	1706
	1707	DO i = nxl, nxr
	1708	DO k = nzb+1, nzt
	1709	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1710	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1711	BTEST( wall_flags_total_0(k,nyn+1,i), 1 ) )
[4022]	1712	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1713	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1714	BTEST( wall_flags_total_0(k,nyn+1,i), 2 ) )
[4022]	1715	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1716	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	1717	BTEST( wall_flags_total_0(k,nyn+1,i), 3 ) )
[4022]	1718	ENDDO
[2938]	1719	ENDDO
[4022]	1720	ENDIF
[2938]	1721	ENDIF
[2259]	1722	ENDIF
[3347]	1723	!
[4438]	1724	!-- Exchange ghost points.
	1725	CALL exchange_horiz( u, nbgp )
	1726	CALL exchange_horiz( v, nbgp )
	1727	CALL exchange_horiz( w, nbgp )
	1728	!
[3347]	1729	!-- Finally, set time counter for calling STG to zero
[4022]	1730	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1731
[3987]	1732	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1733
[2259]	1734	END SUBROUTINE stg_main
	1735
	1736	!------------------------------------------------------------------------------!
	1737	! Description:
	1738	! ------------
	1739	!> Generate a set of random number rand_it wich is equal on each PE
	1740	!> and calculate the velocity seed f_n.
	1741	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1742	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1743	!> parts are collected to form the full array.
	1744	!------------------------------------------------------------------------------!
[4309]	1745	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id_left, id_right )
[2259]	1746
[4309]	1747	INTEGER(iwp) :: id_left !< core ids at respective boundaries
	1748	INTEGER(iwp), OPTIONAL :: id_right !< core ids at respective boundaries
	1749	INTEGER(iwp) :: j !< loop index in y-direction
	1750	INTEGER(iwp) :: jj !< loop index in y-direction
	1751	INTEGER(iwp) :: k !< loop index in z-direction
	1752	INTEGER(iwp) :: kk !< loop index in z-direction
	1753	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
[2259]	1754
	1755	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1756	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1757
	1758	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1759	REAL(wp) :: rand_av !< average of random number
	1760	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1761
[4438]	1762	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_y !< filter function in y-direction
	1763	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1764
[4438]	1765	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nys:nyn) :: f_n_l !< local velocity seed
	1766	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn) :: f_n !< velocity seed
[4309]	1767
	1768	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2259]	1769	!
[4309]	1770	!-- Generate random numbers using the parallel random generator.
[2259]	1771	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1772	!-- unit variance. Note, at the end the random number array must be defined
	1773	!-- globally in order to compute the correlation matrices. However,
	1774	!-- the calculation and normalization of random numbers is done locally,
	1775	!-- while the result is later distributed to all processes. Further,
	1776	!-- please note, a set of random numbers is only calculated for the
	1777	!-- left boundary, while the right boundary uses the same random numbers
	1778	!-- and thus also computes the same correlation matrix.
[4438]	1779	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nys:nyn+mergp) )
	1780	rand_it = 0.0_wp
[2259]	1781
	1782	rand_av = 0.0_wp
	1783	rand_sigma_inv = 0.0_wp
[4438]	1784	nyz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1785	* ( ny + mergp - ( 0 - mergp ) + 1 ), &
	1786	KIND=wp )
[4309]	1787	!
[4438]	1788	!-- Compute and normalize random numbers.
	1789	DO j = nys - mergp, nyn + mergp
[4309]	1790	!
[4438]	1791	!-- Put the random seeds at grid point j
	1792	CALL random_seed_parallel( put=seq_rand_yz(:,j) )
	1793	DO k = nzb - mergp, nzt + 1 + mergp
	1794	CALL random_number_parallel( random_dummy )
	1795	rand_it(k,j) = random_dummy
	1796	ENDDO
[4309]	1797	!
[4438]	1798	!-- Get the new random seeds from last call at grid point j
	1799	CALL random_seed_parallel( get=seq_rand_yz(:,j) )
	1800	ENDDO
[4309]	1801	!
[4438]	1802	!-- For normalization to zero mean, sum-up the global random numers.
	1803	!-- To normalize the global set of random numbers,
	1804	!-- the inner ghost layers mergp must not be summed-up, else
	1805	!-- the random numbers on the ghost layers will be stronger weighted as they
	1806	!-- also occur on the inner subdomains.
	1807	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1808	MERGE( nyn, nyn + mergp, nyn /= ny )
	1809	DO k = nzb - mergp, nzt + 1 + mergp
	1810	rand_av = rand_av + rand_it(k,j)
[2259]	1811	ENDDO
[4438]	1812	ENDDO
	1813
[4309]	1814	#if defined( __parallel )
	1815	!
[4438]	1816	!-- Sum-up the local averages of the random numbers
	1817	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	1818	MPI_SUM, comm1dy, ierr )
[4309]	1819	#endif
[4438]	1820	rand_av = rand_av * nyz_inv
[4309]	1821	!
[4438]	1822	!-- Obtain zero mean
	1823	rand_it= rand_it - rand_av
[4309]	1824	!
[4438]	1825	!-- Now, compute the variance
	1826	DO j = MERGE( nys, nys - mergp, nys /= 0 ), &
	1827	MERGE( nyn, nyn + mergp, nyn /= ny )
	1828	DO k = nzb - mergp, nzt + 1 + mergp
	1829	rand_sigma_inv = rand_sigma_inv + rand_it(k,j)**2
[2259]	1830	ENDDO
[4438]	1831	ENDDO
[2259]	1832
[4309]	1833	#if defined( __parallel )
[2259]	1834	!
[4438]	1835	!-- Sum-up the local quadratic averages of the random numbers
	1836	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	1837	MPI_SUM, comm1dy, ierr )
[4309]	1838	#endif
	1839	!
[4438]	1840	!-- Compute standard deviation
	1841	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	1842	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nyz_inv )
	1843	ELSE
	1844	rand_sigma_inv = 1.0_wp
[4309]	1845	ENDIF
	1846	!
[4438]	1847	!-- Normalize with standard deviation to obtain unit variance
	1848	rand_it = rand_it * rand_sigma_inv
	1849
	1850	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	1851	!
[4438]	1852	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	1853	!-- are two options. In the first one, the computation of the seeds is
	1854	!-- distributed to all processes along the communicator comm1dy and
	1855	!-- gathered on the leftmost and, if necessary, on the rightmost process.
	1856	!-- For huge length scales the computational effort can become quite huge
	1857	!-- (it scales with the turbulent length scales), so that gain by parallelization
	1858	!-- exceeds the costs by the subsequent communication.
	1859	!-- In the second option, which performs better when the turbulent length scales
	1860	!-- are parametrized and thus the loops are smaller, the seeds are computed
	1861	!-- locally and no communication is necessary.
	1862	IF ( compute_velocity_seeds_local ) THEN
	1863
	1864	f_n = 0.0_wp
	1865	DO j = nys, nyn
	1866	DO k = nzb, nzt+1
	1867	DO jj = -n_y(k), n_y(k)
	1868	DO kk = -n_z(k), n_z(k)
	1869	f_n(k,j) = f_n(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1870	ENDDO
	1871	ENDDO
	1872	ENDDO
[2259]	1873	ENDDO
	1874
[4438]	1875	ELSE
[2259]	1876
[4438]	1877	f_n_l = 0.0_wp
	1878	DO j = nys, nyn
	1879	DO k = nzb_x_stg, nzt_x_stg+1
	1880	DO jj = -n_y(k), n_y(k)
	1881	DO kk = -n_z(k), n_z(k)
	1882	f_n_l(k,j) = f_n_l(k,j) + b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1883	ENDDO
[2259]	1884	ENDDO
	1885	ENDDO
	1886	ENDDO
	1887	!
[4438]	1888	!-- Gather velocity seeds of full subdomain
	1889	send_count = nzt_x_stg - nzb_x_stg + 1
	1890	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1891
	1892	#if defined( __parallel )
[4309]	1893	!
[4438]	1894	!-- Gather the velocity seed matrix on left boundary mpi ranks.
	1895	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1896	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1897	id_left, comm1dx, ierr )
[4309]	1898	!
[4438]	1899	!-- If required, gather the same velocity seed matrix on right boundary
	1900	!-- mpi ranks (in offline nesting for example).
	1901	IF ( PRESENT( id_right ) ) THEN
	1902	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nys), send_count, stg_type_yz_small, &
	1903	f_n(nzb+1,nys), recv_count_yz, displs_yz, stg_type_yz,&
	1904	id_right, comm1dx, ierr )
	1905	ENDIF
[2259]	1906	#else
[4438]	1907	f_n(nzb+1:nzt+1,nys:nyn) = f_n_l(nzb_x_stg:nzt_x_stg+1,nys:nyn)
[4444]	1908	!
	1909	!-- Next line required to avoid compile errors because of unused dummy arguments
	1910	IF ( id_left == 0 ) id_right = 0
[2259]	1911	#endif
	1912
[4438]	1913	ENDIF
[2259]	1914
[4438]	1915	DEALLOCATE( rand_it )
	1916
	1917	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	1918
[2259]	1919	END SUBROUTINE stg_generate_seed_yz
	1920
[2938]	1921
	1922	!------------------------------------------------------------------------------!
	1923	! Description:
	1924	! ------------
	1925	!> Generate a set of random number rand_it wich is equal on each PE
	1926	!> and calculate the velocity seed f_n.
	1927	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1928	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1929	!> parts are collected to form the full array.
	1930	!------------------------------------------------------------------------------!
[4309]	1931	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id_south, id_north )
[2938]	1932
	1933	INTEGER(iwp) :: i !< loop index in x-direction
[4309]	1934	INTEGER(iwp) :: id_north !< core ids at respective boundaries
	1935	INTEGER(iwp) :: id_south !< core ids at respective boundaries
[2938]	1936	INTEGER(iwp) :: ii !< loop index in x-direction
	1937	INTEGER(iwp) :: k !< loop index in z-direction
	1938	INTEGER(iwp) :: kk !< loop index in z-direction
	1939	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1940
	1941	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1942	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1943
	1944	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1945	REAL(wp) :: rand_av !< average of random number
	1946	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1947
[4438]	1948	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_x !< filter function in x-direction
	1949	REAL(wp), DIMENSION(-mergp:mergp,nzb:nzt+1) :: b_z !< filter function in z-direction
[4309]	1950
[4438]	1951	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxl:nxr) :: f_n_l !< local velocity seed
	1952	REAL(wp), DIMENSION(nzb:nzt+1,nxl:nxr) :: f_n !< velocity seed
[2938]	1953
[4309]	1954	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< global array of random numbers
[2938]	1955
	1956	!
[4309]	1957	!-- Generate random numbers using the parallel random generator.
[2938]	1958	!-- The set of random numbers are modified to have an average of 0 and
[4309]	1959	!-- unit variance. Note, at the end the random number array must be defined
	1960	!-- globally in order to compute the correlation matrices. However,
	1961	!-- the calculation and normalization of random numbers is done locally,
	1962	!-- while the result is later distributed to all processes. Further,
	1963	!-- please note, a set of random numbers is only calculated for the
	1964	!-- left boundary, while the right boundary uses the same random numbers
	1965	!-- and thus also computes the same correlation matrix.
[4438]	1966	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp+nxl:nxr+mergp) )
	1967	rand_it = 0.0_wp
[2938]	1968
	1969	rand_av = 0.0_wp
	1970	rand_sigma_inv = 0.0_wp
[4438]	1971	nxz_inv = 1.0_wp / REAL( ( nzt + 1 + mergp - ( nzb - mergp ) + 1 ) &
	1972	* ( nx + mergp - ( 0 - mergp ) +1 ), &
	1973	KIND=wp )
[4309]	1974	!
[4438]	1975	!-- Compute and normalize random numbers.
	1976	DO i = nxl - mergp, nxr + mergp
[4309]	1977	!
[4438]	1978	!-- Put the random seeds at grid point ii
	1979	CALL random_seed_parallel( put=seq_rand_xz(:,i) )
	1980	DO k = nzb - mergp, nzt + 1 + mergp
	1981	CALL random_number_parallel( random_dummy )
	1982	rand_it(k,i) = random_dummy
	1983	ENDDO
[4309]	1984	!
[4438]	1985	!-- Get the new random seeds from last call at grid point ii
	1986	CALL random_seed_parallel( get=seq_rand_xz(:,i) )
	1987	ENDDO
[4309]	1988	!
[4438]	1989	!-- For normalization to zero mean, sum-up the global random numers.
	1990	!-- To normalize the global set of random numbers,
	1991	!-- the inner ghost layers mergp must not be summed-up, else
	1992	!-- the random numbers on the ghost layers will be stronger weighted as they
	1993	!-- also occur on the inner subdomains.
	1994	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	1995	MERGE( nxr, nxr + mergp, nxr /= nx )
	1996	DO k = nzb - mergp, nzt + 1 + mergp
	1997	rand_av = rand_av + rand_it(k,i)
[2938]	1998	ENDDO
[4438]	1999	ENDDO
	2000
[4309]	2001	#if defined( __parallel )
[4438]	2002	!
	2003	!-- Sum-up the local averages of the random numbers
	2004	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_av, 1, MPI_REAL, &
	2005	MPI_SUM, comm1dx, ierr )
[4309]	2006	#endif
[4438]	2007	rand_av = rand_av * nxz_inv
[4309]	2008	!
[4438]	2009	!-- Obtain zero mean
	2010	rand_it= rand_it - rand_av
[4309]	2011	!
[4438]	2012	!-- Now, compute the variance
	2013	DO i = MERGE( nxl, nxl - mergp, nxl /= 0 ), &
	2014	MERGE( nxr, nxr + mergp, nxr /= nx )
	2015	DO k = nzb - mergp, nzt + 1 + mergp
	2016	rand_sigma_inv = rand_sigma_inv + rand_it(k,i)**2
[2938]	2017	ENDDO
[4438]	2018	ENDDO
[2938]	2019
[4309]	2020	#if defined( __parallel )
[4438]	2021	!
	2022	!-- Sum-up the local quadratic averages of the random numbers
	2023	CALL MPI_ALLREDUCE( MPI_IN_PLACE, rand_sigma_inv, 1, MPI_REAL, &
	2024	MPI_SUM, comm1dx, ierr )
[4309]	2025	#endif
[2938]	2026	!
[4438]	2027	!-- Compute standard deviation
	2028	IF ( rand_sigma_inv /= 0.0_wp ) THEN
	2029	rand_sigma_inv = 1.0_wp / SQRT( rand_sigma_inv * nxz_inv )
	2030	ELSE
	2031	rand_sigma_inv = 1.0_wp
[4309]	2032	ENDIF
	2033	!
[4438]	2034	!-- Normalize with standard deviation to obtain unit variance
	2035	rand_it = rand_it * rand_sigma_inv
	2036
	2037	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'start' )
[4309]	2038	!
[4438]	2039	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008). There
	2040	!-- are two options. In the first one, the computation of the seeds is
	2041	!-- distributed to all processes along the communicator comm1dx and
	2042	!-- gathered on the southmost and, if necessary, on the northmost process.
	2043	!-- For huge length scales the computational effort can become quite huge
	2044	!-- (it scales with the turbulent length scales), so that gain by parallelization
	2045	!-- exceeds the costs by the subsequent communication.
	2046	!-- In the second option, which performs better when the turbulent length scales
	2047	!-- are parametrized and thus the loops are smaller, the seeds are computed
	2048	!-- locally and no communication is necessary.
	2049	IF ( compute_velocity_seeds_local ) THEN
[2938]	2050
[4438]	2051	f_n = 0.0_wp
	2052	DO i = nxl, nxr
	2053	DO k = nzb, nzt+1
	2054	DO ii = -n_x(k), n_x(k)
	2055	DO kk = -n_z(k), n_z(k)
	2056	f_n(k,i) = f_n(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2057	ENDDO
[2938]	2058	ENDDO
	2059	ENDDO
	2060	ENDDO
	2061
[4438]	2062	ELSE
[2938]	2063
[4438]	2064	f_n_l = 0.0_wp
	2065	DO i = nxl, nxr
	2066	DO k = nzb_y_stg, nzt_y_stg+1
	2067	DO ii = -n_x(k), n_x(k)
	2068	DO kk = -n_z(k), n_z(k)
	2069	f_n_l(k,i) = f_n_l(k,i) + b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	2070	ENDDO
	2071	ENDDO
	2072	ENDDO
	2073	ENDDO
[2938]	2074	!
[4438]	2075	!-- Gather velocity seeds of full subdomain
	2076	send_count = nzt_y_stg - nzb_y_stg + 1
	2077	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
[2938]	2078
	2079	#if defined( __parallel )
[4309]	2080	!
[4438]	2081	!-- Gather the processed velocity seed on south boundary mpi ranks.
	2082	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2083	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2084	id_south, comm1dy, ierr )
[4309]	2085	!
[4438]	2086	!-- Gather the processed velocity seed on north boundary mpi ranks.
	2087	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxl), send_count, stg_type_xz_small, &
	2088	f_n(nzb+1,nxl), recv_count_xz, displs_xz, stg_type_xz, &
	2089	id_north, comm1dy, ierr )
[2938]	2090	#else
[4438]	2091	f_n(nzb+1:nzt+1,nxl:nxr) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxl:nxr)
[4444]	2092	!
	2093	!-- Next line required to avoid compile errors because of unused dummy arguments
	2094	IF ( id_north == 0 ) id_south = 0
[2938]	2095	#endif
	2096
[4438]	2097	ENDIF
	2098
	2099	DEALLOCATE( rand_it )
	2100
	2101	CALL cpu_log( log_point_s(31), 'STG f_n factors', 'stop' )
	2102
[2938]	2103	END SUBROUTINE stg_generate_seed_xz
	2104
[3347]	2105	!------------------------------------------------------------------------------!
	2106	! Description:
	2107	! ------------
	2108	!> Parametrization of the Reynolds stress tensor, following the parametrization
	2109	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	2110	!> dispserion modelling. Please note, the parametrization does not distinguish
	2111	!> between along-wind and cross-wind turbulence.
	2112	!------------------------------------------------------------------------------!
	2113	SUBROUTINE parametrize_reynolds_stress
	2114
	2115	INTEGER(iwp) :: k !< loop index in z-direction
	2116
	2117	REAL(wp) :: zzi !< ratio of z/zi
	2118
	2119	DO k = nzb+1, nzt+1
	2120	!
[4022]	2121	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	2122	!-- The function decreases to 1/10 after one length scale above the
	2123	!-- ABL top.
	2124	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2125	!
[4022]	2126	!-- Determine normalized height coordinate
	2127	zzi = zu(k) / zi_ribulk
[3347]	2128	!
[4022]	2129	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
[4438]	2130	!-- to the denominator, else the mergpe-function can crash if scale_l is
[4022]	2131	!-- zero.
	2132	r11(k) = scale_us*2 ( &
	2133	MERGE( 0.35_wp * ABS( &
	2134	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	2135	)**( 2.0_wp / 3.0_wp ), &
	2136	0.0_wp, &
	2137	scale_l < 0.0_wp ) &
	2138	+ 5.0_wp - 4.0_wp * zzi &
	2139	) * blend
	2140
	2141	r22(k) = r11(k)
	2142	!
	2143	!-- w'w'
	2144	r33(k) = scale_wm*2 ( &
	2145	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	2146	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	2147	) * blend
	2148	!
	2149	!-- u'w' and v'w'. Assume isotropy.
	2150	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	2151	r32(k) = r31(k)
[3347]	2152	!
[4022]	2153	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	2154	!-- a similar profile as for u'w'.
	2155	r21(k) = r31(k)
[3347]	2156	ENDDO
	2157
	2158	!
	2159	!-- Set bottom boundary condition
	2160	r11(nzb) = r11(nzb+1)
	2161	r22(nzb) = r22(nzb+1)
	2162	r33(nzb) = r33(nzb+1)
	2163
	2164	r21(nzb) = r11(nzb+1)
	2165	r31(nzb) = r31(nzb+1)
	2166	r32(nzb) = r32(nzb+1)
	2167
	2168
	2169	END SUBROUTINE parametrize_reynolds_stress
	2170
	2171	!------------------------------------------------------------------------------!
	2172	! Description:
	2173	! ------------
	2174	!> Calculate the coefficient matrix from the Lund rotation.
	2175	!------------------------------------------------------------------------------!
	2176	SUBROUTINE calc_coeff_matrix
	2177
	2178	INTEGER(iwp) :: k !< loop index in z-direction
	2179
	2180	!
	2181	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	2182	DO k = nzb+1, nzt+1
[4022]	2183	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	2184	a11(k) = SQRT( r11(k) )
	2185	a21(k) = r21(k) / a11(k)
	2186	a31(k) = r31(k) / a11(k)
	2187	ELSE
	2188	a11(k) = 10E-8_wp
	2189	a21(k) = 10E-8_wp
	2190	a31(k) = 10E-8_wp
	2191	ENDIF
	2192	ENDDO
	2193	DO k = nzb+1, nzt+1
	2194	a22(k) = r22(k) - a21(k)**2
[4022]	2195	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	2196	a22(k) = SQRT( a22(k) )
	2197	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	2198	ELSE
	2199	a22(k) = 10E-8_wp
	2200	a32(k) = 10E-8_wp
	2201	ENDIF
	2202	ENDDO
	2203	DO k = nzb+1, nzt+1
	2204	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	2205	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	2206	a33(k) = SQRT( a33(k) )
	2207	ELSE
	2208	a33(k) = 10E-8_wp
	2209	ENDIF
	2210	ENDDO
	2211	!
	2212	!-- Set bottom boundary condition
	2213	a11(nzb) = a11(nzb+1)
	2214	a22(nzb) = a22(nzb+1)
	2215	a21(nzb) = a21(nzb+1)
	2216	a33(nzb) = a33(nzb+1)
	2217	a31(nzb) = a31(nzb+1)
	2218	a32(nzb) = a32(nzb+1)
	2219
	2220	END SUBROUTINE calc_coeff_matrix
	2221
	2222	!------------------------------------------------------------------------------!
	2223	! Description:
	2224	! ------------
	2225	!> This routine controls the re-adjustment of the turbulence statistics used
	2226	!> for generating turbulence at the lateral boundaries.
	2227	!------------------------------------------------------------------------------!
	2228	SUBROUTINE stg_adjust
	2229
[3987]	2230	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2231	!
[4022]	2232	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2233	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2234	!-- synthetic turbulence shall be parametrized nevertheless, the
	2235	!-- boundary-layer depth need to determined first.
	2236	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2237	CALL nesting_offl_calc_zi
	2238	!
	2239	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2240	!-- are calculated.
[3347]	2241	CALL calc_scaling_variables
	2242	!
	2243	!-- Set length and time scales depending on boundary-layer height
	2244	CALL calc_length_and_time_scale
	2245	!
	2246	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2247	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2248	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2249	!-- friction velocity and velocity scale.
	2250	CALL parametrize_reynolds_stress
	2251	!
	2252	!-- Calculate coefficient matrix from Reynolds stress tensor
	2253	!-- (Lund rotation)
	2254	CALL calc_coeff_matrix
	2255	!
	2256	!-- Determine filter functions on basis of updated length scales
	2257	CALL stg_filter_func( nux, bux ) !filter ux
	2258	CALL stg_filter_func( nuy, buy ) !filter uy
	2259	CALL stg_filter_func( nuz, buz ) !filter uz
	2260	CALL stg_filter_func( nvx, bvx ) !filter vx
	2261	CALL stg_filter_func( nvy, bvy ) !filter vy
	2262	CALL stg_filter_func( nvz, bvz ) !filter vz
	2263	CALL stg_filter_func( nwx, bwx ) !filter wx
	2264	CALL stg_filter_func( nwy, bwy ) !filter wy
	2265	CALL stg_filter_func( nwz, bwz ) !filter wz
	2266	!
	2267	!-- Reset time counter for controlling next adjustment to zero
	2268	time_stg_adjust = 0.0_wp
[3987]	2269
	2270	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2271
	2272	END SUBROUTINE stg_adjust
	2273
	2274
	2275	!------------------------------------------------------------------------------!
	2276	! Description:
	2277	! ------------
	2278	!> Calculates turbuluent length and time scales if these are not available
	2279	!> from measurements.
	2280	!------------------------------------------------------------------------------!
	2281	SUBROUTINE calc_length_and_time_scale
	2282
[4022]	2283	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2284
[4022]	2285	REAL(wp) :: length_scale_dum !< effectively used length scale
	2286
[3347]	2287	!
	2288	!-- In initial call the boundary-layer depth can be zero. This case, set
	2289	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2290	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2291	!
	2292	!-- Set-up default turbulent length scales. From the numerical point of
	2293	!-- view the imposed perturbations should not be immediately dissipated
	2294	!-- by the numerics. The numerical dissipation, however, acts on scales
	2295	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2296	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2297	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2298	!-- imposing any perturbations) in order to save computational costs.
	2299	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2300	!-- using the length scales and the mean profiles of u- and v-component.
	2301	DO k = nzb+1, nzt+1
	2302	!
[4022]	2303	!-- Determine blending parameter. Within the boundary layer length scales
	2304	!-- are constant, while above lengths scales approach gradully zero,
	2305	!-- i.e. imposed turbulence is not correlated in space and time,
	2306	!-- just white noise, which saves computations power as the loops for the
	2307	!-- computation of the filter functions depend on the length scales.
	2308	!-- The value decreases to 1/10 after one length scale above the
	2309	!-- ABL top.
	2310	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2311	!
[4022]	2312	!-- Assume isotropic turbulence length scales
	2313	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2314	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2315	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2316	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[4022]	2317	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
[4438]	2318	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2319	!
[4022]	2320	!-- Along the vertical direction limit the length scale further by the
	2321	!-- boundary-layer depth to assure that no length scales larger than
	2322	!-- the boundary-layer depth are used
	2323	length_scale_dum = MIN( length_scale, zi_ribulk )
	2324
	2325	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2326	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2327	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2328	!
[4022]	2329	!-- Limit time scales, else they become very larger for low wind speed,
	2330	!-- imposing long-living inflow perturbations which in turn propagate
	2331	!-- further into the model domain. Use u_init and v_init to calculate
	2332	!-- the time scales, which will be equal to the inflow profiles, both,
	2333	!-- in offline nesting mode or in dirichlet/radiation mode.
	2334	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2335	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2336	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2337	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2338	!
	2339	!-- Time scale of w-component is a mixture from u- and v-component.
	2340	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2341
[3347]	2342	ENDDO
	2343	!
	2344	!-- Set bottom boundary condition for the length and time scales
	2345	nux(nzb) = nux(nzb+1)
	2346	nuy(nzb) = nuy(nzb+1)
	2347	nuz(nzb) = nuz(nzb+1)
	2348	nvx(nzb) = nvx(nzb+1)
	2349	nvy(nzb) = nvy(nzb+1)
	2350	nvz(nzb) = nvz(nzb+1)
	2351	nwx(nzb) = nwx(nzb+1)
	2352	nwy(nzb) = nwy(nzb+1)
	2353	nwz(nzb) = nwz(nzb+1)
	2354
	2355	tu(nzb) = tu(nzb+1)
	2356	tv(nzb) = tv(nzb+1)
	2357	tw(nzb) = tw(nzb+1)
	2358
	2359
	2360	END SUBROUTINE calc_length_and_time_scale
	2361
	2362	!------------------------------------------------------------------------------!
	2363	! Description:
	2364	! ------------
	2365	!> Calculate scaling variables which are used for turbulence parametrization
	2366	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2367	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2368	!------------------------------------------------------------------------------!
	2369	SUBROUTINE calc_scaling_variables
	2370
	2371	INTEGER(iwp) :: i !< loop index in x-direction
	2372	INTEGER(iwp) :: j !< loop index in y-direction
	2373	INTEGER(iwp) :: k !< loop index in z-direction
	2374	INTEGER(iwp) :: m !< surface element index
	2375
	2376	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2377	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2378	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2379	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2380	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2381	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2382	REAL(wp) :: w_convective !< convective velocity scale
	2383
	2384	!
[3937]	2385	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2386	!-- near-surface temperature in the model domain.
	2387	pt_surf_mean_l = 0.0_wp
	2388	shf_mean_l = 0.0_wp
	2389	scale_l_l = 0.0_wp
	2390	friction_vel_l = 0.0_wp
[3347]	2391	DO m = 1, surf_def_h(0)%ns
[3937]	2392	i = surf_def_h(0)%i(m)
	2393	j = surf_def_h(0)%j(m)
	2394	k = surf_def_h(0)%k(m)
	2395	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2396	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2397	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2398	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2399	ENDDO
	2400	DO m = 1, surf_lsm_h%ns
[3937]	2401	i = surf_lsm_h%i(m)
	2402	j = surf_lsm_h%j(m)
	2403	k = surf_lsm_h%k(m)
	2404	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2405	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2406	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2407	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2408	ENDDO
	2409	DO m = 1, surf_usm_h%ns
[3937]	2410	i = surf_usm_h%i(m)
	2411	j = surf_usm_h%j(m)
	2412	k = surf_usm_h%k(m)
	2413	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2414	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2415	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2416	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2417	ENDDO
	2418
	2419	#if defined( __parallel )
[3937]	2420	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2421	comm2d, ierr )
[3937]	2422	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2423	comm2d, ierr )
[3937]	2424	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2425	comm2d, ierr )
	2426	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2427	comm2d, ierr )
[3347]	2428	#else
[3937]	2429	scale_us = friction_vel_l
	2430	shf_mean = shf_mean_l
	2431	scale_l = scale_l_l
	2432	pt_surf_mean = pt_surf_mean_l
[3347]	2433	#endif
	2434
[3937]	2435	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2436	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2437	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2438	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2439	!
	2440	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2441	!-- is negative, set convective velocity scale to zero.
	2442	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2443	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2444	ELSE
	2445	w_convective = 0.0_wp
	2446	ENDIF
	2447	!
	2448	!-- Finally, in order to consider also neutral or stable stratification,
	2449	!-- compute momentum velocity scale from u* and convective velocity scale,
	2450	!-- according to Rotach et al. (1996).
	2451	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2452
	2453	END SUBROUTINE calc_scaling_variables
	2454
[2259]	2455	END MODULE synthetic_turbulence_generator_mod

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