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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4283

Last change on this file since 4283 was 4182, checked in by scharf, 5 years ago
corrected "Former revisions" section minor formatting in "Former revisions" section added "Author" section
Property svn:keywords set to `Id`
File size: 96.4 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	!
[3349]	23	!
[2259]	24	! Former revisions:
	25	! -----------------
	26	! $Id: synthetic_turbulence_generator_mod.f90 4182 2019-08-22 15:20:23Z resler $
[4182]	27	! Corrected "Former revisions" section
	28	!
	29	! 4148 2019-08-08 11:26:00Z suehring
[4148]	30	! Remove unused variable
	31	!
	32	! 4144 2019-08-06 09:11:47Z raasch
[4144]	33	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	34	!
	35	! 4071 2019-07-03 20:02:00Z suehring
[4071]	36	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	37	! information is not read from file.
	38	!
	39	! 4022 2019-06-12 11:52:39Z suehring
[4022]	40	! Several bugfixes and improvements
	41	! - revise bias correction of the imposed perturbations (correction via volume
	42	! flow can create instabilities in case the mean volume flow is close to zero)
	43	! - introduce lower limits in calculation of coefficient matrix, else the
	44	! calculation may become numerically unstable
	45	! - impose perturbations every timestep, even though no new set of perturbations
	46	! is generated in case dt_stg_call /= dt_3d
	47	! - Implement a gradual decrease of Reynolds stress and length scales above
	48	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	49	! discontinuous decrease
	50	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	51	!
	52	! 3987 2019-05-22 09:52:13Z kanani
[3987]	53	! Introduce alternative switch for debug output during timestepping
	54	!
	55	! 3938 2019-04-29 16:06:25Z suehring
[3938]	56	! Remove unused variables
	57	!
	58	! 3937 2019-04-29 15:09:07Z suehring
[3937]	59	! Minor bugfix in case of a very early restart where mc_factor is sill not
	60	! present.
	61	! Some modification and fixing of potential bugs in the calculation of scaling
	62	! parameters used for synthetic turbulence parametrization.
	63	!
	64	! 3909 2019-04-17 09:13:25Z suehring
[3909]	65	! Minor bugfix for last commit
	66	!
	67	! 3900 2019-04-16 15:17:43Z suehring
[3900]	68	! Missing re-calculation of perturbation seeds in case of restarts
	69	!
	70	! 3891 2019-04-12 17:52:01Z suehring
[3891]	71	! Bugfix in initialization in case of restart runs.
	72	!
	73	! 3885 2019-04-11 11:29:34Z kanani
[3885]	74	! Changes related to global restructuring of location messages and introduction
	75	! of additional debug messages
	76	!
	77	!
[3775]	78	! removed unused variables
	79	!
	80	! 3719 2019-02-06 13:10:18Z kanani
[3719]	81	! Removed log_point measurement from stg_init, since this part is counted to
	82	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	83	! the subroutines in time_integration for better overview.
	84	!
[4182]	85	! 2259 2017-06-08 09:09:11Z gronemeier
	86	! Initial revision
[3044]	87	!
[4182]	88	! Authors:
	89	! --------
	90	! @author Tobias Gronemeier, Matthias Suehring, Atsushi Inagaki, Micha Gryschka, Christoph Knigge
	91	!
	92	!
[2259]	93	! Description:
	94	! ------------
	95	!> The module generates turbulence at the inflow boundary based on a method by
	96	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	97	!> correction by Kim et al. (2013).
	98	!> The turbulence is correlated based on length scales in y- and z-direction and
	99	!> a time scale for each velocity component. The profiles of length and time
	100	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	101	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	102	!> within the boundary layer.
[2259]	103	!>
	104	!> @todo test restart
	105	!> enable cyclic_fill
	106	!> implement turbulence generation for e and pt
[2945]	107	!> @todo Input of height-constant length scales via namelist
[2259]	108	!> @note <Enter notes on the module>
	109	!> @bug Height information from input file is not used. Profiles from input
	110	!> must match with current PALM grid.
	111	!> In case of restart, velocity seeds differ from precursor run if a11,
	112	!> a22, or a33 are zero.
	113	!------------------------------------------------------------------------------!
	114	MODULE synthetic_turbulence_generator_mod
	115
	116
	117	USE arrays_3d, &
[4022]	118	ONLY: dzw, &
	119	ddzw, &
	120	drho_air, &
	121	mean_inflow_profiles, &
	122	q, &
[4071]	123	q_init, &
	124	pt, &
	125	pt_init, &
[4022]	126	u, &
	127	u_init, &
	128	v, &
	129	v_init, &
	130	w, &
	131	zu, &
	132	zw
[2259]	133
[3274]	134	USE basic_constants_and_equations_mod, &
[4022]	135	ONLY: g, &
	136	kappa, &
	137	pi
[2259]	138
	139	USE control_parameters, &
[4022]	140	ONLY: bc_lr, &
	141	bc_ns, &
	142	child_domain, &
	143	coupling_char, &
	144	debug_output_timestep, &
	145	dt_3d, &
	146	e_init, &
[4071]	147	humidity, &
[3885]	148	initializing_actions, &
[4022]	149	intermediate_timestep_count, &
	150	intermediate_timestep_count_max, &
	151	length, &
[3885]	152	message_string, &
[4022]	153	nesting_offline, &
[4071]	154	neutral, &
[3885]	155	num_mean_inflow_profiles, &
[4022]	156	rans_mode, &
	157	restart_string, &
	158	syn_turb_gen, &
	159	time_since_reference_point, &
	160	turbulent_inflow
	161
	162	USE grid_variables, &
	163	ONLY: ddx, &
	164	ddy, &
	165	dx, &
	166	dy
[2259]	167
	168	USE indices, &
[4022]	169	ONLY: nbgp, &
	170	nz, &
	171	nzb, &
	172	nzt, &
	173	nx, &
	174	nxl, &
	175	nxlu, &
	176	nxlg, &
	177	nxr, &
	178	nxrg, &
	179	ny, &
	180	nys, &
	181	nysv, &
	182	nyn, &
	183	nyng, &
	184	nysg, &
	185	wall_flags_0
[2259]	186
	187	USE kinds
	188
[2967]	189	#if defined( __parallel ) && !defined( __mpifh )
[2259]	190	USE MPI
[2841]	191	#endif
[2259]	192
[3347]	193	USE nesting_offl_mod, &
[4022]	194	ONLY: nesting_offl_calc_zi, &
	195	zi_ribulk
[3347]	196
[2259]	197	USE pegrid, &
[4022]	198	ONLY: comm1dx, &
	199	comm1dy, &
	200	comm2d, &
	201	ierr, &
	202	myidx, &
	203	myidy, &
	204	pdims
	205
	206	USE pmc_interface, &
	207	ONLY : rans_mode_parent
[2259]	208
	209	USE transpose_indices, &
[4022]	210	ONLY: nzb_x, &
	211	nzt_x
[2259]	212
	213
	214	IMPLICIT NONE
	215
[2967]	216	#if defined( __parallel ) && defined( __mpifh )
[2841]	217	INCLUDE "mpif.h"
	218	#endif
	219
[3182]	220
[3347]	221	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	222	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	223	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[2259]	224
[3038]	225	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	226	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	227	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	228	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[2938]	229	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	230	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	231	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	232	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
	233	INTEGER(iwp) :: merg !< maximum length scale (in gp)
	234	INTEGER(iwp) :: mergp !< merg + nbgp
[3038]	235	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	236	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	237	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	238	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[2259]	239
[4022]	240	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	241	!< required for bias correction of imposed perturbations
	242	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	243	!< required for bias correction of imposed perturbations
	244
[3347]	245	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	246	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	247	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	248	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
	249	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	250	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	251	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	252	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	253	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	254	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	255	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	256	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	257	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
	258	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed !< seed of random number for rn-generator
[2259]	259
[4022]	260	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	261	!< scales above the boundary layer
	262	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	263	!< one length scale above ABL top
	264	REAL(wp) :: d_l !< blend_coeff/length_scale
	265	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	266	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
	267	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
	268	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	269	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	270	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	271	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	272	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	273
[4022]	274	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	275
[4022]	276
[3347]	277	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	278	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	279	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	280	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	281	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	282	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	283
	284	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	285	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	286	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	287	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	288	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	289	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	290	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	291	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	292	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	293
[3347]	294	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	295	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	296	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	297	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	298	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	299	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	300	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	301	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	302	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	303	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	304	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	305	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	306	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	307	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	308	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	309	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	310	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	311	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	312	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	313	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	314	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	315
	316	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	317	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	318
	319	!
	320	!-- PALM interfaces:
[3347]	321	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	322	INTERFACE stg_adjust
	323	MODULE PROCEDURE stg_adjust
	324	END INTERFACE stg_adjust
	325	!
[2259]	326	!-- Input parameter checks to be done in check_parameters
	327	INTERFACE stg_check_parameters
	328	MODULE PROCEDURE stg_check_parameters
	329	END INTERFACE stg_check_parameters
	330
	331	!
	332	!-- Calculate filter functions
	333	INTERFACE stg_filter_func
	334	MODULE PROCEDURE stg_filter_func
	335	END INTERFACE stg_filter_func
	336
	337	!
[2938]	338	!-- Generate velocity seeds at south and north domain boundary
	339	INTERFACE stg_generate_seed_xz
	340	MODULE PROCEDURE stg_generate_seed_xz
	341	END INTERFACE stg_generate_seed_xz
	342	!
	343	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	344	INTERFACE stg_generate_seed_yz
	345	MODULE PROCEDURE stg_generate_seed_yz
	346	END INTERFACE stg_generate_seed_yz
	347
	348	!
	349	!-- Output of information to the header file
	350	INTERFACE stg_header
	351	MODULE PROCEDURE stg_header
	352	END INTERFACE stg_header
	353
	354	!
	355	!-- Initialization actions
	356	INTERFACE stg_init
	357	MODULE PROCEDURE stg_init
	358	END INTERFACE stg_init
	359
	360	!
	361	!-- Main procedure of synth. turb. gen.
	362	INTERFACE stg_main
	363	MODULE PROCEDURE stg_main
	364	END INTERFACE stg_main
	365
	366	!
	367	!-- Reading of NAMELIST parameters
	368	INTERFACE stg_parin
	369	MODULE PROCEDURE stg_parin
	370	END INTERFACE stg_parin
	371
	372	!
	373	!-- Reading of parameters for restart runs
[2894]	374	INTERFACE stg_rrd_global
	375	MODULE PROCEDURE stg_rrd_global
	376	END INTERFACE stg_rrd_global
[2259]	377
	378	!
	379	!-- Writing of binary output for restart runs
[2894]	380	INTERFACE stg_wrd_global
	381	MODULE PROCEDURE stg_wrd_global
	382	END INTERFACE stg_wrd_global
[2259]	383
	384	SAVE
	385
	386	PRIVATE
	387
	388	!
	389	!-- Public interfaces
[3347]	390	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	391	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	392
	393	!
	394	!-- Public variables
[3347]	395	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	396	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	397	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	398
	399
	400	CONTAINS
	401
	402
	403	!------------------------------------------------------------------------------!
	404	! Description:
	405	! ------------
	406	!> Check parameters routine for synthetic turbulence generator
	407	!------------------------------------------------------------------------------!
	408	SUBROUTINE stg_check_parameters
	409
	410	IMPLICIT NONE
	411
[3182]	412	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	413	nesting_offline ) THEN
[3376]	414	message_string = 'Synthetic turbulence generator is required ' // &
	415	'if offline nesting is applied and PALM operates ' // &
	416	'in LES mode.'
	417	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	418	ENDIF
	419
[3182]	420	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	421	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	422	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	423	'when nesting is applied and parent operates in ' // &
	424	'RANS-mode but current child in LES mode.'
[3376]	425	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	426	ENDIF
	427
[2776]	428	IF ( use_syn_turb_gen ) THEN
[2259]	429
[3579]	430	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	431	.NOT. rans_mode_parent ) THEN
	432	message_string = 'Using synthetic turbulence generator ' // &
	433	'is not allowed in LES-LES nesting.'
	434	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	435
	436	ENDIF
	437
	438	IF ( child_domain .AND. rans_mode .AND. &
	439	rans_mode_parent ) THEN
	440	message_string = 'Using synthetic turbulence generator ' // &
	441	'is not allowed in RANS-RANS nesting.'
	442	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	443
	444	ENDIF
	445
[3182]	446	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	447
[2938]	448	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	449	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	450	message_string = 'Using synthetic turbulence generator ' // &
[3579]	451	'requires %initializing_actions = ' // &
	452	'"set_constant_profiles" or "read_restart_data"' //&
	453	', if not offline nesting is applied.'
[2938]	454	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	455	ENDIF
	456
	457	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	458	message_string = 'Using synthetic turbulence generator ' // &
[3347]	459	'requires &bc_lr = "dirichlet/radiation", ' // &
	460	'if not offline nesting is applied.'
[2938]	461	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	462	ENDIF
	463	IF ( bc_ns /= 'cyclic' ) THEN
	464	message_string = 'Using synthetic turbulence generator ' // &
[3579]	465	'requires &bc_ns = "cyclic", ' // &
[3347]	466	'if not offline nesting is applied.'
[2938]	467	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	468	ENDIF
	469
[2259]	470	ENDIF
	471
	472	IF ( turbulent_inflow ) THEN
	473	message_string = 'Using synthetic turbulence generator ' // &
[2938]	474	'in combination &with turbulent_inflow = .T. '// &
	475	'is not allowed'
[2259]	476	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	477	ENDIF
	478
	479	ENDIF
	480
	481	END SUBROUTINE stg_check_parameters
	482
	483
	484	!------------------------------------------------------------------------------!
	485	! Description:
	486	! ------------
	487	!> Header output for synthetic turbulence generator
	488	!------------------------------------------------------------------------------!
	489	SUBROUTINE stg_header ( io )
	490
	491
	492	IMPLICIT NONE
	493
	494	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	495
	496	!
	497	!-- Write synthetic turbulence generator Header
	498	WRITE( io, 1 )
[2776]	499	IF ( use_syn_turb_gen ) THEN
[2259]	500	WRITE( io, 2 )
	501	ELSE
	502	WRITE( io, 3 )
	503	ENDIF
[3347]	504
	505	IF ( parametrize_inflow_turbulence ) THEN
	506	WRITE( io, 4 ) dt_stg_adjust
	507	ELSE
	508	WRITE( io, 5 )
	509	ENDIF
[2259]	510
	511	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	512	' ------------------------------------------'/)
[3347]	513	2 FORMAT (' synthetic turbulence generator is switched on')
	514	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	515	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	516	5 FORMAT (' imposed turbulence is read from file' )
[2259]	517
	518	END SUBROUTINE stg_header
	519
	520
	521	!------------------------------------------------------------------------------!
	522	! Description:
	523	! ------------
	524	!> Initialization of the synthetic turbulence generator
	525	!------------------------------------------------------------------------------!
	526	SUBROUTINE stg_init
	527
	528	IMPLICIT NONE
	529
[3347]	530	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	531
[2669]	532	#if defined( __parallel )
[2259]	533	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	534	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	535	#endif
[2259]	536
[2938]	537	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	538	INTEGER(iwp) :: j !> loop index
	539	INTEGER(iwp) :: k !< index
	540	INTEGER(iwp) :: newtype !< dummy MPI type
	541	INTEGER(iwp) :: realsize !< size of REAL variables
	542	INTEGER(iwp) :: nseed !< dimension of random number seed
	543	INTEGER(iwp) :: startseed = 1234567890 !< start seed for random number generator
[4022]	544
	545	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	546	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	547	!
	548	!-- Dummy variables used for reading profiles
	549	REAL(wp) :: d1 !< u profile
	550	REAL(wp) :: d2 !< v profile
	551	REAL(wp) :: d3 !< w profile
	552	REAL(wp) :: d5 !< e profile
	553	REAL(wp) :: luy !< length scale for u in y direction
	554	REAL(wp) :: luz !< length scale for u in z direction
	555	REAL(wp) :: lvy !< length scale for v in y direction
	556	REAL(wp) :: lvz !< length scale for v in z direction
	557	REAL(wp) :: lwy !< length scale for w in y direction
	558	REAL(wp) :: lwz !< length scale for w in z direction
[3038]	559	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[2259]	560	REAL(wp) :: zz !< height
	561
[2938]	562
[2259]	563	#if defined( __parallel )
	564	CALL MPI_BARRIER( comm2d, ierr )
	565	#endif
	566
[2669]	567	#if defined( __parallel )
[2259]	568	!
[2938]	569	!-- Determine processor decomposition of z-axis along x- and y-direction
	570	nnz = nz / pdims(1)
[2945]	571	nzb_x_stg = 1 + myidx * INT( nnz )
	572	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[2938]	573
[3038]	574	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[2945]	575	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[2938]	576
[3182]	577	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	578	.AND. .NOT. rans_mode ) ) THEN
[2938]	579	nnz = nz / pdims(2)
[2945]	580	nzb_y_stg = 1 + myidy * INT( nnz )
	581	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[2938]	582
[2945]	583	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[3038]	584	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
[2938]	585	ENDIF
	586
	587	!
[2259]	588	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	589	!-- velocity seeds
	590	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	591	extent = 1 * realsize
[2938]	592	!
[3038]	593	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	594	!-- layer
[2938]	595	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[2259]	596	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
	597	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	598	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	599	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
	600	CALL MPI_TYPE_FREE( newtype, ierr )
	601
[2938]	602	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	603	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
[2259]	604	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	605	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	606	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
	607	CALL MPI_TYPE_FREE( newtype, ierr )
	608
	609	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[2938]	610	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[2259]	611
[2938]	612	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	613	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[2259]	614
	615	DO j = 1, pdims(1)
[2938]	616	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2259]	617	ENDDO
[2938]	618	!
[3038]	619	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	620	!-- layer
[2938]	621	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
[3182]	622	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	623	.AND. .NOT. rans_mode ) ) THEN
[2945]	624	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
[2938]	625	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	626	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	627	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	628	CALL MPI_TYPE_FREE( newtype, ierr )
	629
	630	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	631	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
[2938]	632	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	633	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	634	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	635	CALL MPI_TYPE_FREE( newtype, ierr )
	636
	637	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	638	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	639
	640	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	641	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	642
	643	DO j = 1, pdims(2)
	644	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	645	ENDDO
	646
	647	ENDIF
	648
[2669]	649	#endif
[2259]	650	!
	651	!-- Define seed of random number
	652	CALL RANDOM_SEED()
	653	CALL RANDOM_SEED( size=nseed )
	654	ALLOCATE( seed(1:nseed) )
	655	DO j = 1, nseed
	656	seed(j) = startseed + j
	657	ENDDO
	658	CALL RANDOM_SEED(put=seed)
[3347]	659	!
[4071]	660	!-- Allocate required arrays.
	661	!-- In case no offline nesting or self nesting is used, the arrary
	662	!-- mean_inflow profiles is required. Check if it is already allocated, else
	663	!-- allocate and initialize it appropriately. Note, in case turbulence and
	664	!-- inflow information is read from file, mean_inflow_profiles is already
	665	!-- allocated and initialized appropriately.
[3347]	666	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	667	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	668	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	669	mean_inflow_profiles = 0.0_wp
	670	mean_inflow_profiles(:,1) = u_init
	671	mean_inflow_profiles(:,2) = v_init
	672	!
	673	!-- Even though potential temperature and humidity are not perturbed,
	674	!-- they need to be initialized appropriately.
	675	IF ( .NOT. neutral ) &
	676	mean_inflow_profiles(:,4) = pt_init
	677	IF ( humidity ) &
	678	mean_inflow_profiles(:,6) = q_init
	679	ENDIF
[3347]	680	ENDIF
[2259]	681
[3347]	682	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	683	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	684	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	685	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	686	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	687	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	688	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	689	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	690
	691	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
	692	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
	693	dist_xz = 0.0_wp
	694	dist_yz = 0.0_wp
	695	!
[2259]	696	!-- Read inflow profile
	697	!-- Height levels of profiles in input profile is as follows:
	698	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	699	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	700	!-- WARNING: zz is not used at the moment
[2938]	701	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	702	EXIST = file_stg_exist )
[2259]	703
[2938]	704	IF ( file_stg_exist ) THEN
[2259]	705
[2938]	706	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	707	FORM='FORMATTED')
	708	!
	709	!-- Skip header
	710	READ( 90, * )
[2259]	711
[3182]	712	DO k = nzb+1, nzt+1
[2938]	713	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	714	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	715	d1, d2, d3, d5
	716
[2259]	717	!
[3182]	718	!-- Convert length scales from meter to number of grid points.
[2938]	719	nuy(k) = INT( luy * ddy )
[3182]	720	nuz(k) = INT( luz * ddzw(k) )
[2938]	721	nvy(k) = INT( lvy * ddy )
[3182]	722	nvz(k) = INT( lvz * ddzw(k) )
[2938]	723	nwy(k) = INT( lwy * ddy )
[3182]	724	nwz(k) = INT( lwz * ddzw(k) )
[2938]	725	!
	726	!-- Workaround, assume isotropic turbulence
	727	nwx(k) = nwy(k)
	728	nvx(k) = nvy(k)
	729	nux(k) = nuy(k)
	730	!
	731	!-- Save Mean inflow profiles
	732	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	733	mean_inflow_profiles(k,1) = d1
	734	mean_inflow_profiles(k,2) = d2
	735	! mean_inflow_profiles(k,4) = d4
	736	mean_inflow_profiles(k,5) = d5
	737	ENDIF
	738	ENDDO
[3182]	739	!
	740	!-- Set lenght scales at surface grid point
	741	nuy(nzb) = nuy(nzb+1)
	742	nuz(nzb) = nuz(nzb+1)
	743	nvy(nzb) = nvy(nzb+1)
	744	nvz(nzb) = nvz(nzb+1)
	745	nwy(nzb) = nwy(nzb+1)
	746	nwz(nzb) = nwz(nzb+1)
	747
[2938]	748	CLOSE( 90 )
[3347]	749	!
	750	!-- Calculate coefficient matrix from Reynolds stress tensor
	751	!-- (Lund rotation)
	752	CALL calc_coeff_matrix
	753	!
	754	!-- No information about turbulence and its length scales are available.
	755	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	756	!-- Set flag which indicates that turbulence is parametrized, which is done
	757	!-- later when energy-balance models are already initialized. This is
	758	!-- because the STG needs information about surface properties such as
	759	!-- roughness to build 'realistic' turbulence profiles.
[2938]	760	ELSE
[2259]	761	!
[4022]	762	!-- Define length scale for the imposed turbulence, which is defined as
	763	!-- 8 times the minimum grid spacing
	764	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
	765	!
	766	!-- Define constant to gradually decrease length scales and Reynolds stress
	767	!-- above ABL top. Assure that no zero length scales are used.
	768	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	769	!
[3347]	770	!-- Set flag indicating that turbulence is parametrized
	771	parametrize_inflow_turbulence = .TRUE.
	772	!
[4022]	773	!-- In case of dirichlet inflow boundary conditions only at one lateral
	774	!-- boundary, i.e. in the case no offline or self nesting is applied but
	775	!-- synthetic turbulence shall be parametrized nevertheless, the
	776	!-- boundary-layer depth need to determined first.
	777	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	778	CALL nesting_offl_calc_zi
	779	!
[3347]	780	!-- Determine boundary-layer depth, which is used to initialize lenght
	781	!-- scales
	782	CALL calc_scaling_variables
	783	!
	784	!-- Initialize lenght and time scales, which in turn are used
	785	!-- to initialize the filter functions.
	786	CALL calc_length_and_time_scale
[3891]	787	!
	788	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	789	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	790	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	791	!-- friction velocity and velocity scale.
	792	CALL parametrize_reynolds_stress
	793	!
	794	!-- Calculate coefficient matrix from Reynolds stress tensor
	795	!-- (Lund rotation)
	796	CALL calc_coeff_matrix
[3347]	797
[2938]	798	ENDIF
	799
[2259]	800	!
[3347]	801	!-- Assign initial profiles. Note, this is only required if turbulent
	802	!-- inflow from the left is desired, not in case of any of the
	803	!-- nesting (offline or self nesting) approaches.
[3182]	804	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	805	u_init = mean_inflow_profiles(:,1)
	806	v_init = mean_inflow_profiles(:,2)
	807	!pt_init = mean_inflow_profiles(:,4)
	808	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	809	ENDIF
[3347]	810
[2938]	811	!
[2259]	812	!-- Define the size of the filter functions and allocate them.
	813	merg = 0
	814
	815	! arrays must be large enough to cover the largest length scale
	816	DO k = nzb, nzt+1
[2938]	817	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	818	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	819	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[2259]	820	IF ( j > merg ) merg = j
	821	ENDDO
	822
	823	merg = 2 * merg
	824	mergp = merg + nbgp
	825
[2938]	826	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
	827	buy(-merg:merg,nzb:nzt+1), &
	828	buz(-merg:merg,nzb:nzt+1), &
	829	bvx(-merg:merg,nzb:nzt+1), &
	830	bvy(-merg:merg,nzb:nzt+1), &
	831	bvz(-merg:merg,nzb:nzt+1), &
	832	bwx(-merg:merg,nzb:nzt+1), &
	833	bwy(-merg:merg,nzb:nzt+1), &
	834	bwz(-merg:merg,nzb:nzt+1) )
[2259]	835
	836	!
[2938]	837	!-- Allocate velocity seeds for turbulence at xz-layer
	838	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
	839	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
	840	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
[2259]	841
[2938]	842	!
	843	!-- Allocate velocity seeds for turbulence at yz-layer
	844	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
	845	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
	846	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
[2259]	847
[2938]	848	fu_xz = 0.0_wp
	849	fuo_xz = 0.0_wp
	850	fv_xz = 0.0_wp
	851	fvo_xz = 0.0_wp
	852	fw_xz = 0.0_wp
	853	fwo_xz = 0.0_wp
	854
	855	fu_yz = 0.0_wp
	856	fuo_yz = 0.0_wp
	857	fv_yz = 0.0_wp
	858	fvo_yz = 0.0_wp
	859	fw_yz = 0.0_wp
	860	fwo_yz = 0.0_wp
	861
[2259]	862	!
	863	!-- Create filter functions
[2938]	864	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	865	CALL stg_filter_func( nuy, buy ) !filter uy
	866	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	867	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	868	CALL stg_filter_func( nvy, bvy ) !filter vy
	869	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	870	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	871	CALL stg_filter_func( nwy, bwy ) !filter wy
	872	CALL stg_filter_func( nwz, bwz ) !filter wz
	873
	874	#if defined( __parallel )
	875	CALL MPI_BARRIER( comm2d, ierr )
	876	#endif
	877
	878	!
[2938]	879	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	880	! time step.
	881	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	882	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	883	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	884	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	885
	886	IF ( myidx == id_stg_left ) i = -1
	887	IF ( myidx == id_stg_right ) i = nxr+1
	888
[2259]	889	DO j = nysg, nyng
	890	DO k = nzb, nzt+1
[4144]	891	IF ( a11(k) /= 0.0_wp ) THEN
[4022]	892	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	893	ELSE
[4144]	894	fu_yz(k,j) = 0.0_wp
[2259]	895	ENDIF
	896
[4144]	897	IF ( a22(k) /= 0.0_wp ) THEN
[4022]	898	fv_yz(k,j) = ( v(k,j,i) - &
	899	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	900	ELSE
[4144]	901	fv_yz(k,j) = 0.0_wp
[2259]	902	ENDIF
	903
[4144]	904	IF ( a33(k) /= 0.0_wp ) THEN
[4022]	905	fw_yz(k,j) = ( w(k,j,i) - &
	906	a31(k) * fu_yz(k,j) - a32(k) * &
	907	fv_yz(k,j) ) / a33(k)
[2259]	908	ELSE
[2938]	909	fw_yz = 0._wp
[2259]	910	ENDIF
	911
	912	ENDDO
	913	ENDDO
	914	ENDIF
[3900]	915
	916	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	917
	918	IF ( myidy == id_stg_south ) j = -1
	919	IF ( myidy == id_stg_north ) j = nyn+1
	920
	921	DO i = nxlg, nxrg
	922	DO k = nzb, nzt+1
	923
[4144]	924	IF ( a11(k) /= 0.0_wp ) THEN
[4022]	925	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	926	ELSE
[4144]	927	fu_xz(k,i) = 0.0_wp
[3900]	928	ENDIF
	929
[4144]	930	IF ( a22(k) /= 0.0_wp ) THEN
[4022]	931	fv_xz(k,i) = ( v(k,j,i) - &
	932	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	933	ELSE
[4144]	934	fv_xz(k,i) = 0.0_wp
[3900]	935	ENDIF
	936
[4144]	937	IF ( a33(k) /= 0.0_wp ) THEN
[4022]	938	fw_xz(k,i) = ( w(k,j,i) - &
	939	a31(k) * fu_xz(k,i) - &
	940	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	941	ELSE
	942	fw_xz = 0._wp
	943	ENDIF
	944
	945	ENDDO
	946	ENDDO
	947	ENDIF
[2259]	948	ENDIF
[4022]	949	!
	950	!-- Count the number of non-topography grid points at the boundaries where
	951	!-- perturbations are imposed. This number is later used for bias corrections
	952	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	953	!-- due to the asymetry of u and v along x and y direction, respectively,
	954	!-- different cases must be distinguished.
	955	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	956	!
	957	!-- Number of grid points where perturbations are imposed on u
	958	IF ( myidx == id_stg_left ) i = nxl
	959	IF ( myidx == id_stg_right ) i = nxr+1
	960
	961	nr_non_topo_yz_l(1) = SUM( &
	962	MERGE( 1, 0, &
	963	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
	964	!
	965	!-- Number of grid points where perturbations are imposed on v and w
	966	IF ( myidx == id_stg_left ) i = nxl-1
	967	IF ( myidx == id_stg_right ) i = nxr+1
	968
	969	nr_non_topo_yz_l(2) = SUM( &
	970	MERGE( 1, 0, &
	971	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	972	nr_non_topo_yz_l(3) = SUM( &
	973	MERGE( 1, 0, &
	974	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	975
	976	#if defined( __parallel )
	977	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	978	MPI_SUM, comm1dy, ierr )
	979	#else
	980	nr_non_topo_yz = nr_non_topo_yz_l
	981	#endif
	982	ENDIF
	983
	984	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	985	!
	986	!-- Number of grid points where perturbations are imposed on v
	987	IF ( myidy == id_stg_south ) j = nys
	988	IF ( myidy == id_stg_north ) j = nyn+1
	989
	990	nr_non_topo_xz_l(2) = SUM( &
	991	MERGE( 1, 0, &
	992	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
	993	!
	994	!-- Number of grid points where perturbations are imposed on u and w
	995	IF ( myidy == id_stg_south ) j = nys-1
	996	IF ( myidy == id_stg_north ) j = nyn+1
	997
	998	nr_non_topo_xz_l(1) = SUM( &
	999	MERGE( 1, 0, &
	1000	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1001	nr_non_topo_xz_l(3) = SUM( &
	1002	MERGE( 1, 0, &
	1003	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1004
	1005	#if defined( __parallel )
	1006	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	1007	MPI_SUM, comm1dx, ierr )
	1008	#else
	1009	nr_non_topo_xz = nr_non_topo_xz_l
	1010	#endif
	1011	ENDIF
[2259]	1012
[4022]	1013
[2259]	1014	END SUBROUTINE stg_init
	1015
	1016
	1017	!------------------------------------------------------------------------------!
	1018	! Description:
	1019	! ------------
	1020	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1021	!> (Xie and Castro, 2008)
	1022	!------------------------------------------------------------------------------!
	1023	SUBROUTINE stg_filter_func( nxx, bxx )
	1024
	1025
	1026	IMPLICIT NONE
	1027
	1028	INTEGER(iwp) :: k !< loop index
	1029	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1030	INTEGER(iwp) :: n_k2 !< n_k * 2
	1031	INTEGER(iwp) :: nf !< index for length scales
	1032
	1033	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1034	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1035
	1036	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
	1037
	1038	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
	1039
	1040
	1041	bxx = 0.0_wp
	1042
	1043	DO k = nzb, nzt+1
	1044	bdenom = 0.0_wp
	1045	n_k = nxx(k)
	1046	IF ( n_k /= 0 ) THEN
	1047	n_k2 = n_k * 2
	1048
	1049	!
	1050	!-- ( Eq.10 )^2
	1051	DO nf = -n_k2, n_k2
	1052	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1053	ENDDO
	1054
	1055	!
	1056	!-- ( Eq.9 )
	1057	bdenom = SQRT( bdenom )
	1058	DO nf = -n_k2, n_k2
	1059	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1060	ENDDO
	1061	ENDIF
	1062	ENDDO
	1063
[3347]	1064	END SUBROUTINE stg_filter_func
[2259]	1065
	1066
	1067	!------------------------------------------------------------------------------!
	1068	! Description:
	1069	! ------------
	1070	!> Parin for &stg_par for synthetic turbulence generator
	1071	!------------------------------------------------------------------------------!
	1072	SUBROUTINE stg_parin
	1073
	1074
	1075	IMPLICIT NONE
	1076
	1077	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1078
	1079
[3347]	1080	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
[2259]	1081
	1082	line = ' '
	1083
	1084	!
	1085	!-- Try to find stg package
	1086	REWIND ( 11 )
	1087	line = ' '
	1088	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1089	READ ( 11, '(A)', END=20 ) line
[2259]	1090	ENDDO
	1091	BACKSPACE ( 11 )
	1092
	1093	!
	1094	!-- Read namelist
[3246]	1095	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1096
	1097	!
	1098	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1099	!-- on
[2776]	1100	syn_turb_gen = .TRUE.
[3246]	1101	GOTO 20
[2259]	1102
[3246]	1103	10 BACKSPACE( 11 )
[3248]	1104	READ( 11 , '(A)') line
	1105	CALL parin_fail_message( 'stg_par', line )
[2563]	1106
[3246]	1107	20 CONTINUE
[2259]	1108
	1109	END SUBROUTINE stg_parin
	1110
	1111
	1112	!------------------------------------------------------------------------------!
	1113	! Description:
	1114	! ------------
[2894]	1115	!> This routine reads the respective restart data.
[2576]	1116	!------------------------------------------------------------------------------!
[2894]	1117	SUBROUTINE stg_rrd_global( found )
[2576]	1118
	1119
[2894]	1120	IMPLICIT NONE
[2576]	1121
[3044]	1122	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1123
	1124
[2894]	1125	found = .TRUE.
[2259]	1126
[3038]	1127
[2894]	1128	SELECT CASE ( restart_string(1:length) )
[4022]	1129
	1130	CASE ( 'time_stg_adjust' )
	1131	READ ( 13 ) time_stg_adjust
	1132
	1133	CASE ( 'time_stg_call' )
	1134	READ ( 13 ) time_stg_call
	1135
[2894]	1136	CASE ( 'use_syn_turb_gen' )
	1137	READ ( 13 ) use_syn_turb_gen
[2259]	1138
[2894]	1139	CASE DEFAULT
[2259]	1140
[3038]	1141	found = .FALSE.
[2259]	1142
[2894]	1143	END SELECT
[2259]	1144
	1145
[2894]	1146	END SUBROUTINE stg_rrd_global
[2259]	1147
	1148
	1149	!------------------------------------------------------------------------------!
	1150	! Description:
	1151	! ------------
	1152	!> This routine writes the respective restart data.
	1153	!------------------------------------------------------------------------------!
[2894]	1154	SUBROUTINE stg_wrd_global
[2259]	1155
	1156
	1157	IMPLICIT NONE
[4022]	1158
	1159	CALL wrd_write_string( 'time_stg_adjust' )
	1160	WRITE ( 14 ) time_stg_adjust
	1161
	1162	CALL wrd_write_string( 'time_stg_call' )
	1163	WRITE ( 14 ) time_stg_call
[2259]	1164
[2894]	1165	CALL wrd_write_string( 'use_syn_turb_gen' )
	1166	WRITE ( 14 ) use_syn_turb_gen
[2259]	1167
	1168
[2894]	1169	END SUBROUTINE stg_wrd_global
[2259]	1170
[2894]	1171
[2259]	1172	!------------------------------------------------------------------------------!
	1173	! Description:
	1174	! ------------
	1175	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1176	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1177	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1178	!> (Lund, 1998).
	1179	!------------------------------------------------------------------------------!
	1180	SUBROUTINE stg_main
	1181
	1182	IMPLICIT NONE
	1183
[2938]	1184	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1185	INTEGER(iwp) :: j !< loop index in y-direction
	1186	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1187
	1188	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1189
	1190	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1191
	1192	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1193
[3987]	1194	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1195	!
	1196	!-- Calculate time step which is needed for filter functions
[3775]	1197	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1198	!
[4022]	1199	!-- Check if synthetic turbulence generator needs to be called and new
	1200	!-- perturbations need to be created or if old disturbances can be imposed
	1201	!-- again.
	1202	IF ( time_stg_call >= dt_stg_call .AND. &
	1203	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1204	stg_call = .TRUE.
	1205	ELSE
	1206	stg_call = .FALSE.
	1207	ENDIF
	1208	!
[2259]	1209	!-- Initial value of fu, fv, fw
[3646]	1210	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[2938]	1211	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1212	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1213	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1214
[3182]	1215	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1216	.AND. .NOT. rans_mode ) ) THEN
[2938]	1217	!
	1218	!-- Generate turbulence at right boundary
	1219	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_right )
	1220	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_right )
	1221	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_right )
	1222	!
	1223	!-- Generate turbulence at north boundary
	1224	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_north )
	1225	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_north )
	1226	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_north )
	1227	!
	1228	!-- Generate turbulence at south boundary
	1229	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south )
	1230	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south )
	1231	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south )
	1232	ENDIF
[2259]	1233	velocity_seed_initialized = .TRUE.
	1234	ENDIF
[3347]	1235
[2259]	1236	!
	1237	!-- New set of fu, fv, fw
[4022]	1238	IF ( stg_call ) THEN
	1239	!
	1240	!-- Generate turbulence at left boundary (required in all applications,
	1241	!-- i.e. offline nesting and turbulent inflow from the left)
	1242	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1243	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1244	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1245
	1246	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1247	.AND. .NOT. rans_mode ) ) THEN
	1248	!
	1249	!-- Generate turbulence at right boundary
	1250	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_right )
	1251	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_right )
	1252	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_right )
	1253	!
	1254	!-- Generate turbulence at north boundary
	1255	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_north )
	1256	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_north )
	1257	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_north )
	1258	!
	1259	!-- Generate turbulence at south boundary
	1260	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south )
	1261	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south )
	1262	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south )
	1263	ENDIF
[2938]	1264	ENDIF
[3347]	1265
[2938]	1266	!
	1267	!-- Turbulence generation at left and or right boundary
	1268	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1269	!
[4022]	1270	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1271	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1272	!-- imposed
	1273	IF ( stg_call ) THEN
	1274
	1275	DO j = nysg, nyng
	1276	DO k = nzb, nzt + 1
	1277	!
	1278	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1279	IF ( tu(k) == 0.0_wp ) THEN
	1280	fu_yz(k,j) = fuo_yz(k,j)
	1281	ELSE
	1282	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1283	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1284	ENDIF
	1285
	1286	IF ( tv(k) == 0.0_wp ) THEN
	1287	fv_yz(k,j) = fvo_yz(k,j)
	1288	ELSE
	1289	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1290	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1291	ENDIF
	1292
	1293	IF ( tw(k) == 0.0_wp ) THEN
	1294	fw_yz(k,j) = fwo_yz(k,j)
	1295	ELSE
	1296	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1297	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1298	ENDIF
	1299	ENDDO
	1300	ENDDO
	1301
	1302	dist_yz(nzb,:,1) = 0.0_wp
	1303	dist_yz(nzb,:,2) = 0.0_wp
	1304	dist_yz(nzb,:,3) = 0.0_wp
	1305
	1306	IF ( myidx == id_stg_left ) i = nxl
	1307	IF ( myidx == id_stg_right ) i = nxr+1
	1308	DO j = nysg, nyng
	1309	DO k = nzb+1, nzt + 1
	1310	!
	1311	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1312	!-- Additional factors are added to improve the variance of v and w
	1313	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1314	MERGE( 1.0_wp, 0.0_wp, &
	1315	BTEST( wall_flags_0(k,j,i), 1 ) )
	1316	ENDDO
	1317	ENDDO
	1318
	1319	IF ( myidx == id_stg_left ) i = nxl-1
	1320	IF ( myidx == id_stg_right ) i = nxr+1
	1321	DO j = nysg, nyng
	1322	DO k = nzb+1, nzt + 1
	1323	!
	1324	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1325	!-- Additional factors are added to improve the variance of v and w
	1326	!-- experimental test of 1.2
[3347]	1327	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1328	* 1.2_wp ) &
	1329	* ( a21(k) * fu_yz(k,j) &
[4022]	1330	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1331	MERGE( 1.0_wp, 0.0_wp, &
	1332	BTEST( wall_flags_0(k,j,i), 2 ) )
[3347]	1333	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1334	* 1.3_wp ) &
	1335	* ( a31(k) * fu_yz(k,j) &
	1336	+ a32(k) * fv_yz(k,j) &
[4022]	1337	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1338	MERGE( 1.0_wp, 0.0_wp, &
	1339	BTEST( wall_flags_0(k,j,i), 3 ) )
	1340	ENDDO
[2259]	1341	ENDDO
[4022]	1342	ENDIF
[2259]	1343
	1344	!
	1345	!-- Mass flux correction following Kim et al. (2013)
	1346	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1347	!-- inflow boundary. First, calculate mean value of the imposed
	1348	!-- perturbations at yz boundary.
	1349	!-- Note, this needs to be done only after the last RK3-substep, else
	1350	!-- the boundary values won't be accessed.
	1351	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1352	mc_factor_l = 0.0_wp
	1353	mc_factor = 0.0_wp
	1354	!
	1355	!-- Sum up the original volume flows (with and without perturbations).
	1356	!-- Note, for non-normal components (here v and w) it is actually no
	1357	!-- volume flow.
[2938]	1358	IF ( myidx == id_stg_left ) i = nxl
	1359	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1360
	1361	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1362	* MERGE( 1.0_wp, 0.0_wp, &
	1363	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
	1364
	1365	IF ( myidx == id_stg_left ) i = nxl-1
	1366	IF ( myidx == id_stg_right ) i = nxr+1
	1367
	1368	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1369	* MERGE( 1.0_wp, 0.0_wp, &
	1370	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1371	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1372	* MERGE( 1.0_wp, 0.0_wp, &
	1373	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	1374
[2938]	1375	#if defined( __parallel )
	1376	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1377	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1378	#else
	1379	mc_factor = mc_factor_l
[2938]	1380	#endif
[4022]	1381	!
	1382	!-- Calculate correction factor and force zero mean perturbations.
	1383	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1384
	1385	IF ( myidx == id_stg_left ) i = nxl
	1386	IF ( myidx == id_stg_right ) i = nxr+1
	1387
	1388	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
	1389	* MERGE( 1.0_wp, 0.0_wp, &
	1390	BTEST( wall_flags_0(:,:,i), 1 ) )
	1391
	1392
	1393	IF ( myidx == id_stg_left ) i = nxl-1
	1394	IF ( myidx == id_stg_right ) i = nxr+1
	1395
	1396	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
	1397	* MERGE( 1.0_wp, 0.0_wp, &
	1398	BTEST( wall_flags_0(:,:,i), 2 ) )
	1399
	1400	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
	1401	* MERGE( 1.0_wp, 0.0_wp, &
	1402	BTEST( wall_flags_0(:,:,i), 3 ) )
	1403	!
[2938]	1404	!-- Add disturbances
	1405	IF ( myidx == id_stg_left ) THEN
[4022]	1406	!
	1407	!-- For the left boundary distinguish between mesoscale offline / self
	1408	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1409	!-- case turbulence is imposed on the mean inflow profiles.
	1410	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1411	!
	1412	!-- Add disturbance at the inflow
	1413	DO j = nysg, nyng
	1414	DO k = nzb, nzt+1
	1415	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1416	dist_yz(k,j,1) ) &
	1417	* MERGE( 1.0_wp, 0.0_wp, &
	1418	BTEST( wall_flags_0(k,j,0), 1 ) )
	1419	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1420	dist_yz(k,j,2) ) &
	1421	* MERGE( 1.0_wp, 0.0_wp, &
	1422	BTEST( wall_flags_0(k,j,-1), 2 ) )
	1423	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1424	* MERGE( 1.0_wp, 0.0_wp, &
[3186]	1425	BTEST( wall_flags_0(k,j,-1), 3 ) )
[4022]	1426	ENDDO
[2938]	1427	ENDDO
[4022]	1428	ELSE
	1429
	1430	DO j = nys, nyn
	1431	DO k = nzb+1, nzt
	1432	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1433	* MERGE( 1.0_wp, 0.0_wp, &
	1434	BTEST( wall_flags_0(k,j,0), 1 ) )
	1435	u(k,j,-1) = u(k,j,0)
	1436	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1437	* MERGE( 1.0_wp, 0.0_wp, &
	1438	BTEST( wall_flags_0(k,j,-1), 2 ) )
	1439	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1440	* MERGE( 1.0_wp, 0.0_wp, &
	1441	BTEST( wall_flags_0(k,j,-1), 3 ) )
	1442	ENDDO
	1443	ENDDO
	1444	ENDIF
[2938]	1445	ENDIF
	1446	IF ( myidx == id_stg_right ) THEN
[3186]	1447	DO j = nys, nyn
[3347]	1448	DO k = nzb+1, nzt
[3186]	1449	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1450	* MERGE( 1.0_wp, 0.0_wp, &
	1451	BTEST( wall_flags_0(k,j,nxr+1), 1 ) )
[3186]	1452	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1453	* MERGE( 1.0_wp, 0.0_wp, &
	1454	BTEST( wall_flags_0(k,j,nxr+1), 2 ) )
[3186]	1455	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1456	* MERGE( 1.0_wp, 0.0_wp, &
	1457	BTEST( wall_flags_0(k,j,nxr+1), 3 ) )
[2938]	1458	ENDDO
	1459	ENDDO
	1460	ENDIF
	1461	ENDIF
	1462	ENDIF
	1463	!
	1464	!-- Turbulence generation at north and south boundary
	1465	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1466	!
[4022]	1467	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1468	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1469	!-- imposed
	1470	IF ( stg_call ) THEN
	1471	DO i = nxlg, nxrg
	1472	DO k = nzb, nzt + 1
	1473	!
	1474	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1475	IF ( tu(k) == 0.0_wp ) THEN
	1476	fu_xz(k,i) = fuo_xz(k,i)
	1477	ELSE
	1478	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1479	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1480	ENDIF
	1481
	1482	IF ( tv(k) == 0.0_wp ) THEN
	1483	fv_xz(k,i) = fvo_xz(k,i)
	1484	ELSE
	1485	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1486	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1487	ENDIF
	1488
	1489	IF ( tw(k) == 0.0_wp ) THEN
	1490	fw_xz(k,i) = fwo_xz(k,i)
	1491	ELSE
	1492	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1493	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1494	ENDIF
	1495	ENDDO
	1496	ENDDO
	1497
	1498
	1499	dist_xz(nzb,:,1) = 0.0_wp
	1500	dist_xz(nzb,:,2) = 0.0_wp
	1501	dist_xz(nzb,:,3) = 0.0_wp
	1502
	1503	IF ( myidy == id_stg_south ) j = nys
	1504	IF ( myidy == id_stg_north ) j = nyn+1
	1505	DO i = nxlg, nxrg
	1506	DO k = nzb+1, nzt + 1
	1507	!
	1508	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1509	!-- Additional factors are added to improve the variance of v and w
	1510	!experimental test of 1.2
[3347]	1511	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1512	* 1.2_wp ) &
	1513	* ( a21(k) * fu_xz(k,i) &
[4022]	1514	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1515	MERGE( 1.0_wp, 0.0_wp, &
	1516	BTEST( wall_flags_0(k,j,i), 2 ) )
	1517	ENDDO
	1518	ENDDO
	1519
	1520	IF ( myidy == id_stg_south ) j = nys-1
	1521	IF ( myidy == id_stg_north ) j = nyn+1
	1522	DO i = nxlg, nxrg
	1523	DO k = nzb+1, nzt + 1
	1524	!
	1525	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1526	!-- Additional factors are added to improve the variance of v and w
	1527	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1528	MERGE( 1.0_wp, 0.0_wp, &
	1529	BTEST( wall_flags_0(k,j,i), 1 ) )
	1530
[3347]	1531	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1532	* 1.3_wp ) &
	1533	* ( a31(k) * fu_xz(k,i) &
	1534	+ a32(k) * fv_xz(k,i) &
[4022]	1535	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1536	MERGE( 1.0_wp, 0.0_wp, &
	1537	BTEST( wall_flags_0(k,j,i), 3 ) )
	1538	ENDDO
[2938]	1539	ENDDO
[4022]	1540	ENDIF
[3347]	1541
[2938]	1542	!
	1543	!-- Mass flux correction following Kim et al. (2013)
	1544	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1545	!-- inflow boundary. First, calculate mean value of the imposed
	1546	!-- perturbations at yz boundary.
	1547	!-- Note, this needs to be done only after the last RK3-substep, else
	1548	!-- the boundary values won't be accessed.
	1549	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1550	mc_factor_l = 0.0_wp
	1551	mc_factor = 0.0_wp
	1552
	1553	IF ( myidy == id_stg_south ) j = nys
	1554	IF ( myidy == id_stg_north ) j = nyn+1
	1555
	1556	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1557	* MERGE( 1.0_wp, 0.0_wp, &
	1558	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
	1559
	1560	IF ( myidy == id_stg_south ) j = nys-1
	1561	IF ( myidy == id_stg_north ) j = nyn+1
	1562
	1563	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1564	* MERGE( 1.0_wp, 0.0_wp, &
	1565	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1566	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1567	* MERGE( 1.0_wp, 0.0_wp, &
	1568	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1569
[2938]	1570	#if defined( __parallel )
[4022]	1571	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1572	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1573	#else
	1574	mc_factor = mc_factor_l
[2938]	1575	#endif
[4022]	1576
	1577	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1578
	1579	IF ( myidy == id_stg_south ) j = nys
	1580	IF ( myidy == id_stg_north ) j = nyn+1
	1581
	1582	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
	1583	* MERGE( 1.0_wp, 0.0_wp, &
	1584	BTEST( wall_flags_0(:,j,:), 2 ) )
	1585
	1586
	1587	IF ( myidy == id_stg_south ) j = nys-1
	1588	IF ( myidy == id_stg_north ) j = nyn+1
	1589
	1590	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
	1591	* MERGE( 1.0_wp, 0.0_wp, &
	1592	BTEST( wall_flags_0(:,j,:), 1 ) )
	1593
	1594	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
	1595	* MERGE( 1.0_wp, 0.0_wp, &
	1596	BTEST( wall_flags_0(:,j,:), 3 ) )
	1597	!
	1598	!-- Add disturbances
	1599	IF ( myidy == id_stg_south ) THEN
	1600	DO i = nxl, nxr
	1601	DO k = nzb+1, nzt
	1602	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1603	* MERGE( 1.0_wp, 0.0_wp, &
	1604	BTEST( wall_flags_0(k,-1,i), 1 ) )
	1605	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1606	* MERGE( 1.0_wp, 0.0_wp, &
	1607	BTEST( wall_flags_0(k,0,i), 2 ) )
	1608	v(k,-1,i) = v(k,0,i)
	1609	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1610	* MERGE( 1.0_wp, 0.0_wp, &
	1611	BTEST( wall_flags_0(k,-1,i), 3 ) )
	1612	ENDDO
[2938]	1613	ENDDO
[4022]	1614	ENDIF
	1615	IF ( myidy == id_stg_north ) THEN
	1616
	1617	DO i = nxl, nxr
	1618	DO k = nzb+1, nzt
	1619	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1620	* MERGE( 1.0_wp, 0.0_wp, &
	1621	BTEST( wall_flags_0(k,nyn+1,i), 1 ) )
	1622	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1623	* MERGE( 1.0_wp, 0.0_wp, &
	1624	BTEST( wall_flags_0(k,nyn+1,i), 2 ) )
	1625	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1626	* MERGE( 1.0_wp, 0.0_wp, &
	1627	BTEST( wall_flags_0(k,nyn+1,i), 3 ) )
	1628	ENDDO
[2938]	1629	ENDDO
[4022]	1630	ENDIF
[2938]	1631	ENDIF
[2259]	1632	ENDIF
[3347]	1633	!
	1634	!-- Finally, set time counter for calling STG to zero
[4022]	1635	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1636
[3987]	1637	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1638
[2259]	1639	END SUBROUTINE stg_main
	1640
	1641	!------------------------------------------------------------------------------!
	1642	! Description:
	1643	! ------------
	1644	!> Generate a set of random number rand_it wich is equal on each PE
	1645	!> and calculate the velocity seed f_n.
	1646	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1647	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1648	!> parts are collected to form the full array.
	1649	!------------------------------------------------------------------------------!
[2938]	1650	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id )
[2259]	1651
	1652	IMPLICIT NONE
	1653
[2938]	1654	INTEGER(iwp) :: id !< core ids at respective boundaries
[2259]	1655	INTEGER(iwp) :: j !< loop index in y-direction
	1656	INTEGER(iwp) :: jj !< loop index in y-direction
	1657	INTEGER(iwp) :: k !< loop index in z-direction
	1658	INTEGER(iwp) :: kk !< loop index in z-direction
	1659	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1660
	1661	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1662	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1663	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
	1664	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1665
	1666	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1667	REAL(wp) :: rand_av !< average of random number
	1668	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1669
[3347]	1670	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
	1671	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[2938]	1672	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
[2259]	1673	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
	1674	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
	1675
	1676
	1677	!
	1678	!-- Generate random numbers using a seed generated in stg_init.
	1679	!-- The set of random numbers are modified to have an average of 0 and
	1680	!-- unit variance.
	1681	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
	1682
	1683	rand_av = 0.0_wp
	1684	rand_sigma_inv = 0.0_wp
	1685	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
	1686
	1687	DO j = 0, ny
	1688	DO k = nzb, nzt+1
	1689	CALL RANDOM_NUMBER( rand_it(k,j) )
	1690	rand_av = rand_av + rand_it(k,j)
	1691	ENDDO
	1692	ENDDO
	1693
	1694	rand_av = rand_av * nyz_inv
	1695
	1696	DO j = 0, ny
	1697	DO k = nzb, nzt+1
	1698	rand_it(k,j) = rand_it(k,j) - rand_av
	1699	rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
	1700	ENDDO
	1701	ENDDO
	1702
	1703	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)
	1704
	1705	DO j = 0, ny
	1706	DO k = nzb, nzt+1
	1707	rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
	1708	ENDDO
	1709	ENDDO
	1710
	1711	!
	1712	!-- Periodic fill of random number in space
	1713	DO j = 0, ny
	1714	DO k = 1, mergp
	1715	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
	1716	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
	1717	ENDDO
	1718	ENDDO
	1719	DO j = 1, mergp
	1720	DO k = nzb-mergp, nzt+1+mergp
	1721	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
	1722	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
	1723	ENDDO
	1724	ENDDO
	1725
	1726	!
	1727	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	1728	n_y2 = n_y * 2
	1729	n_z2 = n_z * 2
	1730	f_n_l = 0.0_wp
	1731
	1732	DO j = nysg, nyng
[2938]	1733	DO k = nzb_x_stg, nzt_x_stg+1
[2259]	1734	DO jj = -n_y2(k), n_y2(k)
	1735	DO kk = -n_z2(k), n_z2(k)
	1736	f_n_l(k,j) = f_n_l(k,j) &
	1737	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1738	ENDDO
	1739	ENDDO
	1740	ENDDO
	1741	ENDDO
	1742
	1743	DEALLOCATE( rand_it )
	1744	!
	1745	!-- Gather velocity seeds of full subdomain
[2938]	1746	send_count = nzt_x_stg - nzb_x_stg + 1
	1747	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1748
	1749	#if defined( __parallel )
[2945]	1750	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
	1751	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
[2938]	1752	id, comm1dx, ierr )
[2259]	1753	#else
[2938]	1754	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
[2259]	1755	#endif
	1756
	1757
	1758	END SUBROUTINE stg_generate_seed_yz
	1759
[2938]	1760
	1761
	1762
	1763	!------------------------------------------------------------------------------!
	1764	! Description:
	1765	! ------------
	1766	!> Generate a set of random number rand_it wich is equal on each PE
	1767	!> and calculate the velocity seed f_n.
	1768	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1769	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1770	!> parts are collected to form the full array.
	1771	!------------------------------------------------------------------------------!
	1772	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id )
	1773
	1774	IMPLICIT NONE
	1775
	1776	INTEGER(iwp) :: id !< core ids at respective boundaries
	1777	INTEGER(iwp) :: i !< loop index in x-direction
	1778	INTEGER(iwp) :: ii !< loop index in x-direction
	1779	INTEGER(iwp) :: k !< loop index in z-direction
	1780	INTEGER(iwp) :: kk !< loop index in z-direction
	1781	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1782
	1783	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1784	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[3347]	1785	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
[2938]	1786	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1787
	1788	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1789	REAL(wp) :: rand_av !< average of random number
	1790	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1791
[3347]	1792	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
	1793	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[2938]	1794	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
	1795	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
	1796	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
	1797
	1798
	1799	!
	1800	!-- Generate random numbers using a seed generated in stg_init.
	1801	!-- The set of random numbers are modified to have an average of 0 and
	1802	!-- unit variance.
	1803	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
	1804
	1805	rand_av = 0.0_wp
	1806	rand_sigma_inv = 0.0_wp
	1807	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
	1808
	1809	DO i = 0, nx
	1810	DO k = nzb, nzt+1
	1811	CALL RANDOM_NUMBER( rand_it(k,i) )
	1812	rand_av = rand_av + rand_it(k,i)
	1813	ENDDO
	1814	ENDDO
	1815
	1816	rand_av = rand_av * nxz_inv
	1817
	1818	DO i = 0, nx
	1819	DO k = nzb, nzt+1
	1820	rand_it(k,i) = rand_it(k,i) - rand_av
	1821	rand_sigma_inv = rand_sigma_inv + rand_it(k,i) ** 2
	1822	ENDDO
	1823	ENDDO
	1824
	1825	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nxz_inv)
	1826
	1827	DO i = 0, nx
	1828	DO k = nzb, nzt+1
	1829	rand_it(k,i) = rand_it(k,i) * rand_sigma_inv
	1830	ENDDO
	1831	ENDDO
	1832
	1833	!
	1834	!-- Periodic fill of random number in space
	1835	DO i = 0, nx
	1836	DO k = 1, mergp
	1837	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
	1838	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
	1839	ENDDO
	1840	ENDDO
	1841	DO i = 1, mergp
	1842	DO k = nzb-mergp, nzt+1+mergp
	1843	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
	1844	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
	1845	ENDDO
	1846	ENDDO
	1847
	1848	!
	1849	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	1850	n_x2 = n_x * 2
	1851	n_z2 = n_z * 2
	1852	f_n_l = 0.0_wp
	1853
	1854	DO i = nxlg, nxrg
	1855	DO k = nzb_y_stg, nzt_y_stg+1
	1856	DO ii = -n_x2(k), n_x2(k)
	1857	DO kk = -n_z2(k), n_z2(k)
	1858	f_n_l(k,i) = f_n_l(k,i) &
	1859	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	1860	ENDDO
	1861	ENDDO
	1862	ENDDO
	1863	ENDDO
	1864
	1865	DEALLOCATE( rand_it )
	1866
	1867	!
	1868	!-- Gather velocity seeds of full subdomain
	1869	send_count = nzt_y_stg - nzb_y_stg + 1
	1870	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
	1871
	1872
	1873	#if defined( __parallel )
[2945]	1874	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
[2938]	1875	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
	1876	id, comm1dy, ierr )
	1877	#else
	1878	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
	1879	#endif
	1880
	1881
	1882	END SUBROUTINE stg_generate_seed_xz
	1883
[3347]	1884	!------------------------------------------------------------------------------!
	1885	! Description:
	1886	! ------------
	1887	!> Parametrization of the Reynolds stress tensor, following the parametrization
	1888	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	1889	!> dispserion modelling. Please note, the parametrization does not distinguish
	1890	!> between along-wind and cross-wind turbulence.
	1891	!------------------------------------------------------------------------------!
	1892	SUBROUTINE parametrize_reynolds_stress
	1893
	1894	IMPLICIT NONE
	1895
	1896	INTEGER(iwp) :: k !< loop index in z-direction
	1897
	1898	REAL(wp) :: zzi !< ratio of z/zi
	1899
	1900	DO k = nzb+1, nzt+1
	1901	!
[4022]	1902	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	1903	!-- The function decreases to 1/10 after one length scale above the
	1904	!-- ABL top.
	1905	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	1906	!
[4022]	1907	!-- Determine normalized height coordinate
	1908	zzi = zu(k) / zi_ribulk
[3347]	1909	!
[4022]	1910	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
	1911	!-- to the denominator, else the merge-function can crash if scale_l is
	1912	!-- zero.
	1913	r11(k) = scale_us*2 ( &
	1914	MERGE( 0.35_wp * ABS( &
	1915	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	1916	)**( 2.0_wp / 3.0_wp ), &
	1917	0.0_wp, &
	1918	scale_l < 0.0_wp ) &
	1919	+ 5.0_wp - 4.0_wp * zzi &
	1920	) * blend
	1921
	1922	r22(k) = r11(k)
	1923	!
	1924	!-- w'w'
	1925	r33(k) = scale_wm*2 ( &
	1926	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	1927	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	1928	) * blend
	1929	!
	1930	!-- u'w' and v'w'. Assume isotropy.
	1931	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	1932	r32(k) = r31(k)
[3347]	1933	!
[4022]	1934	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	1935	!-- a similar profile as for u'w'.
	1936	r21(k) = r31(k)
[3347]	1937	ENDDO
	1938
	1939	!
	1940	!-- Set bottom boundary condition
	1941	r11(nzb) = r11(nzb+1)
	1942	r22(nzb) = r22(nzb+1)
	1943	r33(nzb) = r33(nzb+1)
	1944
	1945	r21(nzb) = r11(nzb+1)
	1946	r31(nzb) = r31(nzb+1)
	1947	r32(nzb) = r32(nzb+1)
	1948
	1949
	1950	END SUBROUTINE parametrize_reynolds_stress
	1951
	1952	!------------------------------------------------------------------------------!
	1953	! Description:
	1954	! ------------
	1955	!> Calculate the coefficient matrix from the Lund rotation.
	1956	!------------------------------------------------------------------------------!
	1957	SUBROUTINE calc_coeff_matrix
	1958
	1959	IMPLICIT NONE
	1960
	1961	INTEGER(iwp) :: k !< loop index in z-direction
	1962
	1963	!
	1964	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	1965	DO k = nzb+1, nzt+1
[4022]	1966	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	1967	a11(k) = SQRT( r11(k) )
	1968	a21(k) = r21(k) / a11(k)
	1969	a31(k) = r31(k) / a11(k)
	1970	ELSE
	1971	a11(k) = 10E-8_wp
	1972	a21(k) = 10E-8_wp
	1973	a31(k) = 10E-8_wp
	1974	ENDIF
	1975	ENDDO
	1976	DO k = nzb+1, nzt+1
	1977	a22(k) = r22(k) - a21(k)**2
[4022]	1978	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	1979	a22(k) = SQRT( a22(k) )
	1980	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	1981	ELSE
	1982	a22(k) = 10E-8_wp
	1983	a32(k) = 10E-8_wp
	1984	ENDIF
	1985	ENDDO
	1986	DO k = nzb+1, nzt+1
	1987	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	1988	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	1989	a33(k) = SQRT( a33(k) )
	1990	ELSE
	1991	a33(k) = 10E-8_wp
	1992	ENDIF
	1993	ENDDO
	1994	!
	1995	!-- Set bottom boundary condition
	1996	a11(nzb) = a11(nzb+1)
	1997	a22(nzb) = a22(nzb+1)
	1998	a21(nzb) = a21(nzb+1)
	1999	a33(nzb) = a33(nzb+1)
	2000	a31(nzb) = a31(nzb+1)
	2001	a32(nzb) = a32(nzb+1)
	2002
	2003	END SUBROUTINE calc_coeff_matrix
	2004
	2005	!------------------------------------------------------------------------------!
	2006	! Description:
	2007	! ------------
	2008	!> This routine controls the re-adjustment of the turbulence statistics used
	2009	!> for generating turbulence at the lateral boundaries.
	2010	!------------------------------------------------------------------------------!
	2011	SUBROUTINE stg_adjust
	2012
	2013	IMPLICIT NONE
	2014
[3987]	2015
	2016	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2017	!
[4022]	2018	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2019	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2020	!-- synthetic turbulence shall be parametrized nevertheless, the
	2021	!-- boundary-layer depth need to determined first.
	2022	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2023	CALL nesting_offl_calc_zi
	2024	!
	2025	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2026	!-- are calculated.
[3347]	2027	CALL calc_scaling_variables
	2028	!
	2029	!-- Set length and time scales depending on boundary-layer height
	2030	CALL calc_length_and_time_scale
	2031	!
	2032	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2033	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2034	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2035	!-- friction velocity and velocity scale.
	2036	CALL parametrize_reynolds_stress
	2037	!
	2038	!-- Calculate coefficient matrix from Reynolds stress tensor
	2039	!-- (Lund rotation)
	2040	CALL calc_coeff_matrix
	2041	!
	2042	!-- Determine filter functions on basis of updated length scales
	2043	CALL stg_filter_func( nux, bux ) !filter ux
	2044	CALL stg_filter_func( nuy, buy ) !filter uy
	2045	CALL stg_filter_func( nuz, buz ) !filter uz
	2046	CALL stg_filter_func( nvx, bvx ) !filter vx
	2047	CALL stg_filter_func( nvy, bvy ) !filter vy
	2048	CALL stg_filter_func( nvz, bvz ) !filter vz
	2049	CALL stg_filter_func( nwx, bwx ) !filter wx
	2050	CALL stg_filter_func( nwy, bwy ) !filter wy
	2051	CALL stg_filter_func( nwz, bwz ) !filter wz
	2052	!
	2053	!-- Reset time counter for controlling next adjustment to zero
	2054	time_stg_adjust = 0.0_wp
[3987]	2055
	2056	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2057
	2058	END SUBROUTINE stg_adjust
	2059
	2060
	2061	!------------------------------------------------------------------------------!
	2062	! Description:
	2063	! ------------
	2064	!> Calculates turbuluent length and time scales if these are not available
	2065	!> from measurements.
	2066	!------------------------------------------------------------------------------!
	2067	SUBROUTINE calc_length_and_time_scale
	2068
	2069	IMPLICIT NONE
	2070
	2071
[4022]	2072	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2073
[4022]	2074	REAL(wp) :: length_scale_dum !< effectively used length scale
	2075
[3347]	2076	!
	2077	!-- In initial call the boundary-layer depth can be zero. This case, set
	2078	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2079	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2080	!
	2081	!-- Set-up default turbulent length scales. From the numerical point of
	2082	!-- view the imposed perturbations should not be immediately dissipated
	2083	!-- by the numerics. The numerical dissipation, however, acts on scales
	2084	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2085	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2086	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2087	!-- imposing any perturbations) in order to save computational costs.
	2088	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2089	!-- using the length scales and the mean profiles of u- and v-component.
	2090	DO k = nzb+1, nzt+1
	2091	!
[4022]	2092	!-- Determine blending parameter. Within the boundary layer length scales
	2093	!-- are constant, while above lengths scales approach gradully zero,
	2094	!-- i.e. imposed turbulence is not correlated in space and time,
	2095	!-- just white noise, which saves computations power as the loops for the
	2096	!-- computation of the filter functions depend on the length scales.
	2097	!-- The value decreases to 1/10 after one length scale above the
	2098	!-- ABL top.
	2099	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2100	!
[4022]	2101	!-- Assume isotropic turbulence length scales
	2102	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2103	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2104	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2105	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2106	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2107	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2108	!
[4022]	2109	!-- Along the vertical direction limit the length scale further by the
	2110	!-- boundary-layer depth to assure that no length scales larger than
	2111	!-- the boundary-layer depth are used
	2112	length_scale_dum = MIN( length_scale, zi_ribulk )
	2113
	2114	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2115	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2116	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2117	!
[4022]	2118	!-- Limit time scales, else they become very larger for low wind speed,
	2119	!-- imposing long-living inflow perturbations which in turn propagate
	2120	!-- further into the model domain. Use u_init and v_init to calculate
	2121	!-- the time scales, which will be equal to the inflow profiles, both,
	2122	!-- in offline nesting mode or in dirichlet/radiation mode.
	2123	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2124	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2125	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2126	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2127	!
	2128	!-- Time scale of w-component is a mixture from u- and v-component.
	2129	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2130
[3347]	2131	ENDDO
	2132	!
	2133	!-- Set bottom boundary condition for the length and time scales
	2134	nux(nzb) = nux(nzb+1)
	2135	nuy(nzb) = nuy(nzb+1)
	2136	nuz(nzb) = nuz(nzb+1)
	2137	nvx(nzb) = nvx(nzb+1)
	2138	nvy(nzb) = nvy(nzb+1)
	2139	nvz(nzb) = nvz(nzb+1)
	2140	nwx(nzb) = nwx(nzb+1)
	2141	nwy(nzb) = nwy(nzb+1)
	2142	nwz(nzb) = nwz(nzb+1)
	2143
	2144	tu(nzb) = tu(nzb+1)
	2145	tv(nzb) = tv(nzb+1)
	2146	tw(nzb) = tw(nzb+1)
	2147
	2148
	2149	END SUBROUTINE calc_length_and_time_scale
	2150
	2151	!------------------------------------------------------------------------------!
	2152	! Description:
	2153	! ------------
	2154	!> Calculate scaling variables which are used for turbulence parametrization
	2155	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2156	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2157	!------------------------------------------------------------------------------!
	2158	SUBROUTINE calc_scaling_variables
	2159
	2160	USE surface_mod, &
[4148]	2161	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
[3347]	2162
	2163	IMPLICIT NONE
	2164
	2165	INTEGER(iwp) :: i !< loop index in x-direction
	2166	INTEGER(iwp) :: j !< loop index in y-direction
	2167	INTEGER(iwp) :: k !< loop index in z-direction
	2168	INTEGER(iwp) :: m !< surface element index
	2169
	2170	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2171	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2172	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2173	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2174	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2175	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2176	REAL(wp) :: w_convective !< convective velocity scale
	2177
	2178	!
[3937]	2179	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2180	!-- near-surface temperature in the model domain.
	2181	pt_surf_mean_l = 0.0_wp
	2182	shf_mean_l = 0.0_wp
	2183	scale_l_l = 0.0_wp
	2184	friction_vel_l = 0.0_wp
[3347]	2185	DO m = 1, surf_def_h(0)%ns
[3937]	2186	i = surf_def_h(0)%i(m)
	2187	j = surf_def_h(0)%j(m)
	2188	k = surf_def_h(0)%k(m)
	2189	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2190	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2191	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2192	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2193	ENDDO
	2194	DO m = 1, surf_lsm_h%ns
[3937]	2195	i = surf_lsm_h%i(m)
	2196	j = surf_lsm_h%j(m)
	2197	k = surf_lsm_h%k(m)
	2198	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2199	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2200	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2201	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2202	ENDDO
	2203	DO m = 1, surf_usm_h%ns
[3937]	2204	i = surf_usm_h%i(m)
	2205	j = surf_usm_h%j(m)
	2206	k = surf_usm_h%k(m)
	2207	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2208	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2209	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2210	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2211	ENDDO
	2212
	2213	#if defined( __parallel )
[3937]	2214	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2215	comm2d, ierr )
[3937]	2216	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2217	comm2d, ierr )
[3937]	2218	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2219	comm2d, ierr )
	2220	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2221	comm2d, ierr )
[3347]	2222	#else
[3937]	2223	scale_us = friction_vel_l
	2224	shf_mean = shf_mean_l
	2225	scale_l = scale_l_l
	2226	pt_surf_mean = pt_surf_mean_l
[3347]	2227	#endif
	2228
[3937]	2229	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2230	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2231	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2232	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2233	!
	2234	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2235	!-- is negative, set convective velocity scale to zero.
	2236	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2237	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2238	ELSE
	2239	w_convective = 0.0_wp
	2240	ENDIF
	2241	!
	2242	!-- Finally, in order to consider also neutral or stable stratification,
	2243	!-- compute momentum velocity scale from u* and convective velocity scale,
	2244	!-- according to Rotach et al. (1996).
	2245	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2246
	2247	END SUBROUTINE calc_scaling_variables
	2248
[2259]	2249	END MODULE synthetic_turbulence_generator_mod

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