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source: palm/trunk/SOURCE/synthetic_turbulence_generator_mod.f90 @ 4180

Last change on this file since 4180 was 4180, checked in by scharf, 5 years ago
removed comments in 'Former revisions' section that are older than 01.01.2019
Property svn:keywords set to `Id`
File size: 96.1 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 4180 2019-08-21 14:37:54Z scharf $
[4148]	27	! Remove unused variable
	28	!
	29	! 4144 2019-08-06 09:11:47Z raasch
[4144]	30	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
	31	!
	32	! 4071 2019-07-03 20:02:00Z suehring
[4071]	33	! Bugfix, initialize mean_inflow_profiles in case turbulence and inflow
	34	! information is not read from file.
	35	!
	36	! 4022 2019-06-12 11:52:39Z suehring
[4022]	37	! Several bugfixes and improvements
	38	! - revise bias correction of the imposed perturbations (correction via volume
	39	! flow can create instabilities in case the mean volume flow is close to zero)
	40	! - introduce lower limits in calculation of coefficient matrix, else the
	41	! calculation may become numerically unstable
	42	! - impose perturbations every timestep, even though no new set of perturbations
	43	! is generated in case dt_stg_call /= dt_3d
	44	! - Implement a gradual decrease of Reynolds stress and length scales above
	45	! ABL height (within 1 length scale above ABL depth to 1/10) rather than a
	46	! discontinuous decrease
	47	! - Bugfix in non-nested case: use ABL height for parametrized turbulence
	48	!
	49	! 3987 2019-05-22 09:52:13Z kanani
[3987]	50	! Introduce alternative switch for debug output during timestepping
	51	!
	52	! 3938 2019-04-29 16:06:25Z suehring
[3938]	53	! Remove unused variables
	54	!
	55	! 3937 2019-04-29 15:09:07Z suehring
[3937]	56	! Minor bugfix in case of a very early restart where mc_factor is sill not
	57	! present.
	58	! Some modification and fixing of potential bugs in the calculation of scaling
	59	! parameters used for synthetic turbulence parametrization.
	60	!
	61	! 3909 2019-04-17 09:13:25Z suehring
[3909]	62	! Minor bugfix for last commit
	63	!
	64	! 3900 2019-04-16 15:17:43Z suehring
[3900]	65	! Missing re-calculation of perturbation seeds in case of restarts
	66	!
	67	! 3891 2019-04-12 17:52:01Z suehring
[3891]	68	! Bugfix in initialization in case of restart runs.
	69	!
	70	! 3885 2019-04-11 11:29:34Z kanani
[3885]	71	! Changes related to global restructuring of location messages and introduction
	72	! of additional debug messages
	73	!
	74	!
[3775]	75	! removed unused variables
	76	!
	77	! 3719 2019-02-06 13:10:18Z kanani
[3719]	78	! Removed log_point measurement from stg_init, since this part is counted to
	79	! log_point(2) 'initialisation' already. Moved other log_points to calls of
	80	! the subroutines in time_integration for better overview.
	81	!
[3044]	82	!
[2259]	83	! Description:
	84	! ------------
	85	!> The module generates turbulence at the inflow boundary based on a method by
	86	!> Xie and Castro (2008) utilizing a Lund rotation (Lund, 1998) and a mass-flux
	87	!> correction by Kim et al. (2013).
	88	!> The turbulence is correlated based on length scales in y- and z-direction and
	89	!> a time scale for each velocity component. The profiles of length and time
	90	!> scales, mean u, v, w, e and pt, and all components of the Reynolds stress
[3347]	91	!> tensor can be either read from file STG_PROFILES, or will be parametrized
	92	!> within the boundary layer.
[2259]	93	!>
	94	!> @todo test restart
	95	!> enable cyclic_fill
	96	!> implement turbulence generation for e and pt
[2945]	97	!> @todo Input of height-constant length scales via namelist
[2259]	98	!> @note <Enter notes on the module>
	99	!> @bug Height information from input file is not used. Profiles from input
	100	!> must match with current PALM grid.
	101	!> In case of restart, velocity seeds differ from precursor run if a11,
	102	!> a22, or a33 are zero.
	103	!------------------------------------------------------------------------------!
	104	MODULE synthetic_turbulence_generator_mod
	105
	106
	107	USE arrays_3d, &
[4022]	108	ONLY: dzw, &
	109	ddzw, &
	110	drho_air, &
	111	mean_inflow_profiles, &
	112	q, &
[4071]	113	q_init, &
	114	pt, &
	115	pt_init, &
[4022]	116	u, &
	117	u_init, &
	118	v, &
	119	v_init, &
	120	w, &
	121	zu, &
	122	zw
[2259]	123
[3274]	124	USE basic_constants_and_equations_mod, &
[4022]	125	ONLY: g, &
	126	kappa, &
	127	pi
[2259]	128
	129	USE control_parameters, &
[4022]	130	ONLY: bc_lr, &
	131	bc_ns, &
	132	child_domain, &
	133	coupling_char, &
	134	debug_output_timestep, &
	135	dt_3d, &
	136	e_init, &
[4071]	137	humidity, &
[3885]	138	initializing_actions, &
[4022]	139	intermediate_timestep_count, &
	140	intermediate_timestep_count_max, &
	141	length, &
[3885]	142	message_string, &
[4022]	143	nesting_offline, &
[4071]	144	neutral, &
[3885]	145	num_mean_inflow_profiles, &
[4022]	146	rans_mode, &
	147	restart_string, &
	148	syn_turb_gen, &
	149	time_since_reference_point, &
	150	turbulent_inflow
	151
	152	USE grid_variables, &
	153	ONLY: ddx, &
	154	ddy, &
	155	dx, &
	156	dy
[2259]	157
	158	USE indices, &
[4022]	159	ONLY: nbgp, &
	160	nz, &
	161	nzb, &
	162	nzt, &
	163	nx, &
	164	nxl, &
	165	nxlu, &
	166	nxlg, &
	167	nxr, &
	168	nxrg, &
	169	ny, &
	170	nys, &
	171	nysv, &
	172	nyn, &
	173	nyng, &
	174	nysg, &
	175	wall_flags_0
[2259]	176
	177	USE kinds
	178
[2967]	179	#if defined( __parallel ) && !defined( __mpifh )
[2259]	180	USE MPI
[2841]	181	#endif
[2259]	182
[3347]	183	USE nesting_offl_mod, &
[4022]	184	ONLY: nesting_offl_calc_zi, &
	185	zi_ribulk
[3347]	186
[2259]	187	USE pegrid, &
[4022]	188	ONLY: comm1dx, &
	189	comm1dy, &
	190	comm2d, &
	191	ierr, &
	192	myidx, &
	193	myidy, &
	194	pdims
	195
	196	USE pmc_interface, &
	197	ONLY : rans_mode_parent
[2259]	198
	199	USE transpose_indices, &
[4022]	200	ONLY: nzb_x, &
	201	nzt_x
[2259]	202
	203
	204	IMPLICIT NONE
	205
[2967]	206	#if defined( __parallel ) && defined( __mpifh )
[2841]	207	INCLUDE "mpif.h"
	208	#endif
	209
[3182]	210
[3347]	211	LOGICAL :: velocity_seed_initialized = .FALSE. !< true after first call of stg_main
	212	LOGICAL :: parametrize_inflow_turbulence = .FALSE. !< flag indicating that inflow turbulence is either read from file (.FALSE.) or if it parametrized
	213	LOGICAL :: use_syn_turb_gen = .FALSE. !< switch to use synthetic turbulence generator
[2259]	214
[3038]	215	INTEGER(iwp) :: id_stg_left !< left lateral boundary core id in case of turbulence generator
	216	INTEGER(iwp) :: id_stg_north !< north lateral boundary core id in case of turbulence generator
	217	INTEGER(iwp) :: id_stg_right !< right lateral boundary core id in case of turbulence generator
	218	INTEGER(iwp) :: id_stg_south !< south lateral boundary core id in case of turbulence generator
[2938]	219	INTEGER(iwp) :: stg_type_xz !< MPI type for full z range
	220	INTEGER(iwp) :: stg_type_xz_small !< MPI type for small z range
	221	INTEGER(iwp) :: stg_type_yz !< MPI type for full z range
	222	INTEGER(iwp) :: stg_type_yz_small !< MPI type for small z range
	223	INTEGER(iwp) :: merg !< maximum length scale (in gp)
	224	INTEGER(iwp) :: mergp !< merg + nbgp
[3038]	225	INTEGER(iwp) :: nzb_x_stg !< lower bound of z coordinate (required for transposing z on PEs along x)
	226	INTEGER(iwp) :: nzt_x_stg !< upper bound of z coordinate (required for transposing z on PEs along x)
	227	INTEGER(iwp) :: nzb_y_stg !< lower bound of z coordinate (required for transposing z on PEs along y)
	228	INTEGER(iwp) :: nzt_y_stg !< upper bound of z coordinate (required for transposing z on PEs along y)
[2259]	229
[4022]	230	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz = 0 !< number of non-topography grid points at xz cross-sections,
	231	!< required for bias correction of imposed perturbations
	232	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz = 0 !< number of non-topography grid points at yz cross-sections,
	233	!< required for bias correction of imposed perturbations
	234
[3347]	235	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_xz !< displacement for MPI_GATHERV
	236	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_xz !< receive count for MPI_GATHERV
	237	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: displs_yz !< displacement for MPI_GATHERV
	238	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: recv_count_yz !< receive count for MPI_GATHERV
	239	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nux !< length scale of u in x direction (in gp)
	240	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuy !< length scale of u in y direction (in gp)
	241	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nuz !< length scale of u in z direction (in gp)
	242	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvx !< length scale of v in x direction (in gp)
	243	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvy !< length scale of v in y direction (in gp)
	244	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nvz !< length scale of v in z direction (in gp)
	245	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwx !< length scale of w in x direction (in gp)
	246	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwy !< length scale of w in y direction (in gp)
	247	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: nwz !< length scale of w in z direction (in gp)
	248	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: seed !< seed of random number for rn-generator
[2259]	249
[4022]	250	REAL(wp) :: blend !< value to create gradually and smooth blending of Reynolds stress and length
	251	!< scales above the boundary layer
	252	REAL(wp) :: blend_coeff = -2.3_wp !< coefficient used to ensure that blending functions decreases to 1/10 after
	253	!< one length scale above ABL top
	254	REAL(wp) :: d_l !< blend_coeff/length_scale
	255	REAL(wp) :: length_scale !< length scale, default is 8 x minimum grid spacing
[3347]	256	REAL(wp) :: dt_stg_adjust = 300.0_wp !< time interval for adjusting turbulence statistics
	257	REAL(wp) :: dt_stg_call = 5.0_wp !< time interval for calling synthetic turbulence generator
	258	REAL(wp) :: scale_l !< scaling parameter used for turbulence parametrization - Obukhov length
	259	REAL(wp) :: scale_us !< scaling parameter used for turbulence parametrization - friction velocity
	260	REAL(wp) :: scale_wm !< scaling parameter used for turbulence parametrization - momentum scale
	261	REAL(wp) :: time_stg_adjust = 0.0_wp !< time counter for adjusting turbulence information
	262	REAL(wp) :: time_stg_call = 0.0_wp !< time counter for calling generator
	263
[4022]	264	REAL(wp), DIMENSION(3) :: mc_factor = 1.0_wp !< correction factor for the u,v,w-components to maintain original mass flux
[3347]	265
[4022]	266
[3347]	267	REAL(wp),DIMENSION(:), ALLOCATABLE :: r11 !< Reynolds parameter
	268	REAL(wp),DIMENSION(:), ALLOCATABLE :: r21 !< Reynolds parameter
	269	REAL(wp),DIMENSION(:), ALLOCATABLE :: r22 !< Reynolds parameter
	270	REAL(wp),DIMENSION(:), ALLOCATABLE :: r31 !< Reynolds parameter
	271	REAL(wp),DIMENSION(:), ALLOCATABLE :: r32 !< Reynolds parameter
	272	REAL(wp),DIMENSION(:), ALLOCATABLE :: r33 !< Reynolds parameter
	273
	274	REAL(wp), DIMENSION(:), ALLOCATABLE :: a11 !< coefficient for Lund rotation
	275	REAL(wp), DIMENSION(:), ALLOCATABLE :: a21 !< coefficient for Lund rotation
	276	REAL(wp), DIMENSION(:), ALLOCATABLE :: a22 !< coefficient for Lund rotation
	277	REAL(wp), DIMENSION(:), ALLOCATABLE :: a31 !< coefficient for Lund rotation
	278	REAL(wp), DIMENSION(:), ALLOCATABLE :: a32 !< coefficient for Lund rotation
	279	REAL(wp), DIMENSION(:), ALLOCATABLE :: a33 !< coefficient for Lund rotation
	280	REAL(wp), DIMENSION(:), ALLOCATABLE :: tu !< Lagrangian time scale of u
	281	REAL(wp), DIMENSION(:), ALLOCATABLE :: tv !< Lagrangian time scale of v
	282	REAL(wp), DIMENSION(:), ALLOCATABLE :: tw !< Lagrangian time scale of w
[2259]	283
[3347]	284	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bux !< filter function for u in x direction
	285	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buy !< filter function for u in y direction
	286	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: buz !< filter function for u in z direction
	287	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvx !< filter function for v in x direction
	288	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvy !< filter function for v in y direction
	289	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bvz !< filter function for v in z direction
	290	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwx !< filter function for w in y direction
	291	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwy !< filter function for w in y direction
	292	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: bwz !< filter function for w in z direction
	293	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_xz !< velocity seed for u at xz plane
	294	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_xz !< velocity seed for u at xz plane with new random number
	295	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fu_yz !< velocity seed for u at yz plane
	296	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fuo_yz !< velocity seed for u at yz plane with new random number
	297	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_xz !< velocity seed for v at xz plane
	298	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_xz !< velocity seed for v at xz plane with new random number
	299	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fv_yz !< velocity seed for v at yz plane
	300	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fvo_yz !< velocity seed for v at yz plane with new random number
	301	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_xz !< velocity seed for w at xz plane
	302	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_xz !< velocity seed for w at xz plane with new random number
	303	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fw_yz !< velocity seed for w at yz plane
	304	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fwo_yz !< velocity seed for w at yz plane with new random number
	305
	306	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_xz !< imposed disturbances at north/south boundary
	307	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: dist_yz !< imposed disturbances at north/south boundary
[2259]	308
	309	!
	310	!-- PALM interfaces:
[3347]	311	!-- Adjust time and lenght scales, Reynolds stress, and filter functions
	312	INTERFACE stg_adjust
	313	MODULE PROCEDURE stg_adjust
	314	END INTERFACE stg_adjust
	315	!
[2259]	316	!-- Input parameter checks to be done in check_parameters
	317	INTERFACE stg_check_parameters
	318	MODULE PROCEDURE stg_check_parameters
	319	END INTERFACE stg_check_parameters
	320
	321	!
	322	!-- Calculate filter functions
	323	INTERFACE stg_filter_func
	324	MODULE PROCEDURE stg_filter_func
	325	END INTERFACE stg_filter_func
	326
	327	!
[2938]	328	!-- Generate velocity seeds at south and north domain boundary
	329	INTERFACE stg_generate_seed_xz
	330	MODULE PROCEDURE stg_generate_seed_xz
	331	END INTERFACE stg_generate_seed_xz
	332	!
	333	!-- Generate velocity seeds at left and/or right domain boundary
[2259]	334	INTERFACE stg_generate_seed_yz
	335	MODULE PROCEDURE stg_generate_seed_yz
	336	END INTERFACE stg_generate_seed_yz
	337
	338	!
	339	!-- Output of information to the header file
	340	INTERFACE stg_header
	341	MODULE PROCEDURE stg_header
	342	END INTERFACE stg_header
	343
	344	!
	345	!-- Initialization actions
	346	INTERFACE stg_init
	347	MODULE PROCEDURE stg_init
	348	END INTERFACE stg_init
	349
	350	!
	351	!-- Main procedure of synth. turb. gen.
	352	INTERFACE stg_main
	353	MODULE PROCEDURE stg_main
	354	END INTERFACE stg_main
	355
	356	!
	357	!-- Reading of NAMELIST parameters
	358	INTERFACE stg_parin
	359	MODULE PROCEDURE stg_parin
	360	END INTERFACE stg_parin
	361
	362	!
	363	!-- Reading of parameters for restart runs
[2894]	364	INTERFACE stg_rrd_global
	365	MODULE PROCEDURE stg_rrd_global
	366	END INTERFACE stg_rrd_global
[2259]	367
	368	!
	369	!-- Writing of binary output for restart runs
[2894]	370	INTERFACE stg_wrd_global
	371	MODULE PROCEDURE stg_wrd_global
	372	END INTERFACE stg_wrd_global
[2259]	373
	374	SAVE
	375
	376	PRIVATE
	377
	378	!
	379	!-- Public interfaces
[3347]	380	PUBLIC stg_adjust, stg_check_parameters, stg_header, stg_init, stg_main, &
	381	stg_parin, stg_rrd_global, stg_wrd_global
[2259]	382
	383	!
	384	!-- Public variables
[3347]	385	PUBLIC dt_stg_call, dt_stg_adjust, id_stg_left, id_stg_north, &
	386	id_stg_right, id_stg_south, parametrize_inflow_turbulence, &
	387	time_stg_adjust, time_stg_call, use_syn_turb_gen
[2259]	388
	389
	390	CONTAINS
	391
	392
	393	!------------------------------------------------------------------------------!
	394	! Description:
	395	! ------------
	396	!> Check parameters routine for synthetic turbulence generator
	397	!------------------------------------------------------------------------------!
	398	SUBROUTINE stg_check_parameters
	399
	400	IMPLICIT NONE
	401
[3182]	402	IF ( .NOT. use_syn_turb_gen .AND. .NOT. rans_mode .AND. &
	403	nesting_offline ) THEN
[3376]	404	message_string = 'Synthetic turbulence generator is required ' // &
	405	'if offline nesting is applied and PALM operates ' // &
	406	'in LES mode.'
	407	CALL message( 'stg_check_parameters', 'PA0520', 0, 0, 0, 6, 0 )
[2938]	408	ENDIF
	409
[3182]	410	IF ( .NOT. use_syn_turb_gen .AND. child_domain &
[2938]	411	.AND. rans_mode_parent .AND. .NOT. rans_mode ) THEN
[3376]	412	message_string = 'Synthetic turbulence generator is required ' // &
[2938]	413	'when nesting is applied and parent operates in ' // &
	414	'RANS-mode but current child in LES mode.'
[3376]	415	CALL message( 'stg_check_parameters', 'PA0524', 1, 2, 0, 6, 0 )
[2938]	416	ENDIF
	417
[2776]	418	IF ( use_syn_turb_gen ) THEN
[2259]	419
[3579]	420	IF ( child_domain .AND. .NOT. rans_mode .AND. &
	421	.NOT. rans_mode_parent ) THEN
	422	message_string = 'Using synthetic turbulence generator ' // &
	423	'is not allowed in LES-LES nesting.'
	424	CALL message( 'stg_check_parameters', 'PA0620', 1, 2, 0, 6, 0 )
	425
	426	ENDIF
	427
	428	IF ( child_domain .AND. rans_mode .AND. &
	429	rans_mode_parent ) THEN
	430	message_string = 'Using synthetic turbulence generator ' // &
	431	'is not allowed in RANS-RANS nesting.'
	432	CALL message( 'stg_check_parameters', 'PA0621', 1, 2, 0, 6, 0 )
	433
	434	ENDIF
	435
[3182]	436	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	437
[2938]	438	IF ( INDEX( initializing_actions, 'set_constant_profiles' ) == 0 &
	439	.AND. INDEX( initializing_actions, 'read_restart_data' ) == 0 ) THEN
	440	message_string = 'Using synthetic turbulence generator ' // &
[3579]	441	'requires %initializing_actions = ' // &
	442	'"set_constant_profiles" or "read_restart_data"' //&
	443	', if not offline nesting is applied.'
[2938]	444	CALL message( 'stg_check_parameters', 'PA0015', 1, 2, 0, 6, 0 )
	445	ENDIF
	446
	447	IF ( bc_lr /= 'dirichlet/radiation' ) THEN
	448	message_string = 'Using synthetic turbulence generator ' // &
[3347]	449	'requires &bc_lr = "dirichlet/radiation", ' // &
	450	'if not offline nesting is applied.'
[2938]	451	CALL message( 'stg_check_parameters', 'PA0035', 1, 2, 0, 6, 0 )
	452	ENDIF
	453	IF ( bc_ns /= 'cyclic' ) THEN
	454	message_string = 'Using synthetic turbulence generator ' // &
[3579]	455	'requires &bc_ns = "cyclic", ' // &
[3347]	456	'if not offline nesting is applied.'
[2938]	457	CALL message( 'stg_check_parameters', 'PA0037', 1, 2, 0, 6, 0 )
	458	ENDIF
	459
[2259]	460	ENDIF
	461
	462	IF ( turbulent_inflow ) THEN
	463	message_string = 'Using synthetic turbulence generator ' // &
[2938]	464	'in combination &with turbulent_inflow = .T. '// &
	465	'is not allowed'
[2259]	466	CALL message( 'stg_check_parameters', 'PA0039', 1, 2, 0, 6, 0 )
	467	ENDIF
	468
	469	ENDIF
	470
	471	END SUBROUTINE stg_check_parameters
	472
	473
	474	!------------------------------------------------------------------------------!
	475	! Description:
	476	! ------------
	477	!> Header output for synthetic turbulence generator
	478	!------------------------------------------------------------------------------!
	479	SUBROUTINE stg_header ( io )
	480
	481
	482	IMPLICIT NONE
	483
	484	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
	485
	486	!
	487	!-- Write synthetic turbulence generator Header
	488	WRITE( io, 1 )
[2776]	489	IF ( use_syn_turb_gen ) THEN
[2259]	490	WRITE( io, 2 )
	491	ELSE
	492	WRITE( io, 3 )
	493	ENDIF
[3347]	494
	495	IF ( parametrize_inflow_turbulence ) THEN
	496	WRITE( io, 4 ) dt_stg_adjust
	497	ELSE
	498	WRITE( io, 5 )
	499	ENDIF
[2259]	500
	501	1 FORMAT (//' Synthetic turbulence generator information:'/ &
	502	' ------------------------------------------'/)
[3347]	503	2 FORMAT (' synthetic turbulence generator is switched on')
	504	3 FORMAT (' synthetic turbulence generator is switched off')
[3348]	505	4 FORMAT (' imposed turbulence statistics are parametrized and ajdusted to boundary-layer development each ', F8.2, ' s' )
[3347]	506	5 FORMAT (' imposed turbulence is read from file' )
[2259]	507
	508	END SUBROUTINE stg_header
	509
	510
	511	!------------------------------------------------------------------------------!
	512	! Description:
	513	! ------------
	514	!> Initialization of the synthetic turbulence generator
	515	!------------------------------------------------------------------------------!
	516	SUBROUTINE stg_init
	517
	518	IMPLICIT NONE
	519
[3347]	520	LOGICAL :: file_stg_exist = .FALSE. !< flag indicating whether parameter file for Reynolds stress and length scales exist
[2938]	521
[2669]	522	#if defined( __parallel )
[2259]	523	INTEGER(KIND=MPI_ADDRESS_KIND) :: extent !< extent of new MPI type
	524	INTEGER(KIND=MPI_ADDRESS_KIND) :: tob=0 !< dummy variable
[2669]	525	#endif
[2259]	526
[2938]	527	INTEGER(iwp) :: i !> grid index in x-direction
[2259]	528	INTEGER(iwp) :: j !> loop index
	529	INTEGER(iwp) :: k !< index
	530	INTEGER(iwp) :: newtype !< dummy MPI type
	531	INTEGER(iwp) :: realsize !< size of REAL variables
	532	INTEGER(iwp) :: nseed !< dimension of random number seed
	533	INTEGER(iwp) :: startseed = 1234567890 !< start seed for random number generator
[4022]	534
	535	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_xz_l = 0 !< number of non-topography grid points at xz-cross-section on subdomain
	536	INTEGER(iwp), DIMENSION(3) :: nr_non_topo_yz_l = 0 !< number of non-topography grid points at yz-cross-section on subdomain
[2259]	537	!
	538	!-- Dummy variables used for reading profiles
	539	REAL(wp) :: d1 !< u profile
	540	REAL(wp) :: d2 !< v profile
	541	REAL(wp) :: d3 !< w profile
	542	REAL(wp) :: d5 !< e profile
	543	REAL(wp) :: luy !< length scale for u in y direction
	544	REAL(wp) :: luz !< length scale for u in z direction
	545	REAL(wp) :: lvy !< length scale for v in y direction
	546	REAL(wp) :: lvz !< length scale for v in z direction
	547	REAL(wp) :: lwy !< length scale for w in y direction
	548	REAL(wp) :: lwz !< length scale for w in z direction
[3038]	549	REAL(wp) :: nnz !< increment used to determine processor decomposition of z-axis along x and y direction
[2259]	550	REAL(wp) :: zz !< height
	551
[2938]	552
[2259]	553	#if defined( __parallel )
	554	CALL MPI_BARRIER( comm2d, ierr )
	555	#endif
	556
[2669]	557	#if defined( __parallel )
[2259]	558	!
[2938]	559	!-- Determine processor decomposition of z-axis along x- and y-direction
	560	nnz = nz / pdims(1)
[2945]	561	nzb_x_stg = 1 + myidx * INT( nnz )
	562	nzt_x_stg = ( myidx + 1 ) * INT( nnz )
[2938]	563
[3038]	564	IF ( MOD( nz , pdims(1) ) /= 0 .AND. myidx == id_stg_right ) &
[2945]	565	nzt_x_stg = nzt_x_stg + myidx * ( nnz - INT( nnz ) )
[2938]	566
[3182]	567	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	568	.AND. .NOT. rans_mode ) ) THEN
[2938]	569	nnz = nz / pdims(2)
[2945]	570	nzb_y_stg = 1 + myidy * INT( nnz )
	571	nzt_y_stg = ( myidy + 1 ) * INT( nnz )
[2938]	572
[2945]	573	IF ( MOD( nz , pdims(2) ) /= 0 .AND. myidy == id_stg_north ) &
[3038]	574	nzt_y_stg = nzt_y_stg + myidy * ( nnz - INT( nnz ) )
[2938]	575	ENDIF
	576
	577	!
[2259]	578	!-- Define MPI type used in stg_generate_seed_yz to gather vertical splitted
	579	!-- velocity seeds
	580	CALL MPI_TYPE_SIZE( MPI_REAL, realsize, ierr )
	581	extent = 1 * realsize
[2938]	582	!
[3038]	583	!-- Set-up MPI datatyp to involve all cores for turbulence generation at yz
	584	!-- layer
[2938]	585	!-- stg_type_yz: yz-slice with vertical bounds nzb:nzt+1
[2259]	586	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nyng-nysg+1], &
	587	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	588	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz, ierr )
	589	CALL MPI_TYPE_COMMIT( stg_type_yz, ierr )
	590	CALL MPI_TYPE_FREE( newtype, ierr )
	591
[2938]	592	! stg_type_yz_small: yz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	593	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_x_stg-nzb_x_stg+2,nyng-nysg+1], &
[2259]	594	[1,nyng-nysg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	595	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_yz_small, ierr )
	596	CALL MPI_TYPE_COMMIT( stg_type_yz_small, ierr )
	597	CALL MPI_TYPE_FREE( newtype, ierr )
	598
	599	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
[2938]	600	ALLOCATE( recv_count_yz(pdims(1)), displs_yz(pdims(1)) )
[2259]	601
[2938]	602	recv_count_yz = nzt_x_stg-nzb_x_stg + 1
	603	recv_count_yz(pdims(1)) = recv_count_yz(pdims(1)) + 1
[2259]	604
	605	DO j = 1, pdims(1)
[2938]	606	displs_yz(j) = 0 + (nzt_x_stg-nzb_x_stg+1) * (j-1)
[2259]	607	ENDDO
[2938]	608	!
[3038]	609	!-- Set-up MPI datatyp to involve all cores for turbulence generation at xz
	610	!-- layer
[2938]	611	!-- stg_type_xz: xz-slice with vertical bounds nzb:nzt+1
[3182]	612	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	613	.AND. .NOT. rans_mode ) ) THEN
[2945]	614	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt-nzb+2,nxrg-nxlg+1], &
[2938]	615	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	616	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz, ierr )
	617	CALL MPI_TYPE_COMMIT( stg_type_xz, ierr )
	618	CALL MPI_TYPE_FREE( newtype, ierr )
	619
	620	! stg_type_yz_small: xz-slice with vertical bounds nzb_x_stg:nzt_x_stg+1
[2945]	621	CALL MPI_TYPE_CREATE_SUBARRAY( 2, [nzt_y_stg-nzb_y_stg+2,nxrg-nxlg+1], &
[2938]	622	[1,nxrg-nxlg+1], [0,0], MPI_ORDER_FORTRAN, MPI_REAL, newtype, ierr )
	623	CALL MPI_TYPE_CREATE_RESIZED( newtype, tob, extent, stg_type_xz_small, ierr )
	624	CALL MPI_TYPE_COMMIT( stg_type_xz_small, ierr )
	625	CALL MPI_TYPE_FREE( newtype, ierr )
	626
	627	! receive count and displacement for MPI_GATHERV in stg_generate_seed_yz
	628	ALLOCATE( recv_count_xz(pdims(2)), displs_xz(pdims(2)) )
	629
	630	recv_count_xz = nzt_y_stg-nzb_y_stg + 1
	631	recv_count_xz(pdims(2)) = recv_count_xz(pdims(2)) + 1
	632
	633	DO j = 1, pdims(2)
	634	displs_xz(j) = 0 + (nzt_y_stg-nzb_y_stg+1) * (j-1)
	635	ENDDO
	636
	637	ENDIF
	638
[2669]	639	#endif
[2259]	640	!
	641	!-- Define seed of random number
	642	CALL RANDOM_SEED()
	643	CALL RANDOM_SEED( size=nseed )
	644	ALLOCATE( seed(1:nseed) )
	645	DO j = 1, nseed
	646	seed(j) = startseed + j
	647	ENDDO
	648	CALL RANDOM_SEED(put=seed)
[3347]	649	!
[4071]	650	!-- Allocate required arrays.
	651	!-- In case no offline nesting or self nesting is used, the arrary
	652	!-- mean_inflow profiles is required. Check if it is already allocated, else
	653	!-- allocate and initialize it appropriately. Note, in case turbulence and
	654	!-- inflow information is read from file, mean_inflow_profiles is already
	655	!-- allocated and initialized appropriately.
[3347]	656	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[4071]	657	IF ( .NOT. ALLOCATED( mean_inflow_profiles ) ) THEN
[3347]	658	ALLOCATE( mean_inflow_profiles(nzb:nzt+1,1:num_mean_inflow_profiles) )
[4071]	659	mean_inflow_profiles = 0.0_wp
	660	mean_inflow_profiles(:,1) = u_init
	661	mean_inflow_profiles(:,2) = v_init
	662	!
	663	!-- Even though potential temperature and humidity are not perturbed,
	664	!-- they need to be initialized appropriately.
	665	IF ( .NOT. neutral ) &
	666	mean_inflow_profiles(:,4) = pt_init
	667	IF ( humidity ) &
	668	mean_inflow_profiles(:,6) = q_init
	669	ENDIF
[3347]	670	ENDIF
[2259]	671
[3347]	672	ALLOCATE ( a11(nzb:nzt+1), a21(nzb:nzt+1), a22(nzb:nzt+1), &
	673	a31(nzb:nzt+1), a32(nzb:nzt+1), a33(nzb:nzt+1), &
	674	nux(nzb:nzt+1), nuy(nzb:nzt+1), nuz(nzb:nzt+1), &
	675	nvx(nzb:nzt+1), nvy(nzb:nzt+1), nvz(nzb:nzt+1), &
	676	nwx(nzb:nzt+1), nwy(nzb:nzt+1), nwz(nzb:nzt+1), &
	677	r11(nzb:nzt+1), r21(nzb:nzt+1), r22(nzb:nzt+1), &
	678	r31(nzb:nzt+1), r32(nzb:nzt+1), r33(nzb:nzt+1), &
	679	tu(nzb:nzt+1), tv(nzb:nzt+1), tw(nzb:nzt+1) )
	680
	681	ALLOCATE ( dist_xz(nzb:nzt+1,nxlg:nxrg,3) )
	682	ALLOCATE ( dist_yz(nzb:nzt+1,nysg:nyng,3) )
	683	dist_xz = 0.0_wp
	684	dist_yz = 0.0_wp
	685	!
[2259]	686	!-- Read inflow profile
	687	!-- Height levels of profiles in input profile is as follows:
	688	!-- zu: luy, luz, tu, lvy, lvz, tv, r11, r21, r22, d1, d2, d5
	689	!-- zw: lwy, lwz, tw, r31, r32, r33, d3
	690	!-- WARNING: zz is not used at the moment
[2938]	691	INQUIRE( FILE = 'STG_PROFILES' // TRIM( coupling_char ), &
	692	EXIST = file_stg_exist )
[2259]	693
[2938]	694	IF ( file_stg_exist ) THEN
[2259]	695
[2938]	696	OPEN( 90, FILE='STG_PROFILES'//TRIM( coupling_char ), STATUS='OLD', &
	697	FORM='FORMATTED')
	698	!
	699	!-- Skip header
	700	READ( 90, * )
[2259]	701
[3182]	702	DO k = nzb+1, nzt+1
[2938]	703	READ( 90, * ) zz, luy, luz, tu(k), lvy, lvz, tv(k), lwy, lwz, tw(k), &
	704	r11(k), r21(k), r22(k), r31(k), r32(k), r33(k), &
	705	d1, d2, d3, d5
	706
[2259]	707	!
[3182]	708	!-- Convert length scales from meter to number of grid points.
[2938]	709	nuy(k) = INT( luy * ddy )
[3182]	710	nuz(k) = INT( luz * ddzw(k) )
[2938]	711	nvy(k) = INT( lvy * ddy )
[3182]	712	nvz(k) = INT( lvz * ddzw(k) )
[2938]	713	nwy(k) = INT( lwy * ddy )
[3182]	714	nwz(k) = INT( lwz * ddzw(k) )
[2938]	715	!
	716	!-- Workaround, assume isotropic turbulence
	717	nwx(k) = nwy(k)
	718	nvx(k) = nvy(k)
	719	nux(k) = nuy(k)
	720	!
	721	!-- Save Mean inflow profiles
	722	IF ( TRIM( initializing_actions ) /= 'read_restart_data' ) THEN
	723	mean_inflow_profiles(k,1) = d1
	724	mean_inflow_profiles(k,2) = d2
	725	! mean_inflow_profiles(k,4) = d4
	726	mean_inflow_profiles(k,5) = d5
	727	ENDIF
	728	ENDDO
[3182]	729	!
	730	!-- Set lenght scales at surface grid point
	731	nuy(nzb) = nuy(nzb+1)
	732	nuz(nzb) = nuz(nzb+1)
	733	nvy(nzb) = nvy(nzb+1)
	734	nvz(nzb) = nvz(nzb+1)
	735	nwy(nzb) = nwy(nzb+1)
	736	nwz(nzb) = nwz(nzb+1)
	737
[2938]	738	CLOSE( 90 )
[3347]	739	!
	740	!-- Calculate coefficient matrix from Reynolds stress tensor
	741	!-- (Lund rotation)
	742	CALL calc_coeff_matrix
	743	!
	744	!-- No information about turbulence and its length scales are available.
	745	!-- Instead, parametrize turbulence which is imposed at the boundaries.
	746	!-- Set flag which indicates that turbulence is parametrized, which is done
	747	!-- later when energy-balance models are already initialized. This is
	748	!-- because the STG needs information about surface properties such as
	749	!-- roughness to build 'realistic' turbulence profiles.
[2938]	750	ELSE
[2259]	751	!
[4022]	752	!-- Define length scale for the imposed turbulence, which is defined as
	753	!-- 8 times the minimum grid spacing
	754	length_scale = 8.0_wp * MIN( dx, dy, MINVAL( dzw ) )
	755	!
	756	!-- Define constant to gradually decrease length scales and Reynolds stress
	757	!-- above ABL top. Assure that no zero length scales are used.
	758	d_l = blend_coeff / MAX( length_scale, dx, dy, MINVAL( dzw ) )
	759	!
[3347]	760	!-- Set flag indicating that turbulence is parametrized
	761	parametrize_inflow_turbulence = .TRUE.
	762	!
[4022]	763	!-- In case of dirichlet inflow boundary conditions only at one lateral
	764	!-- boundary, i.e. in the case no offline or self nesting is applied but
	765	!-- synthetic turbulence shall be parametrized nevertheless, the
	766	!-- boundary-layer depth need to determined first.
	767	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	768	CALL nesting_offl_calc_zi
	769	!
[3347]	770	!-- Determine boundary-layer depth, which is used to initialize lenght
	771	!-- scales
	772	CALL calc_scaling_variables
	773	!
	774	!-- Initialize lenght and time scales, which in turn are used
	775	!-- to initialize the filter functions.
	776	CALL calc_length_and_time_scale
[3891]	777	!
	778	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	779	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	780	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	781	!-- friction velocity and velocity scale.
	782	CALL parametrize_reynolds_stress
	783	!
	784	!-- Calculate coefficient matrix from Reynolds stress tensor
	785	!-- (Lund rotation)
	786	CALL calc_coeff_matrix
[3347]	787
[2938]	788	ENDIF
	789
[2259]	790	!
[3347]	791	!-- Assign initial profiles. Note, this is only required if turbulent
	792	!-- inflow from the left is desired, not in case of any of the
	793	!-- nesting (offline or self nesting) approaches.
[3182]	794	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
[2938]	795	u_init = mean_inflow_profiles(:,1)
	796	v_init = mean_inflow_profiles(:,2)
	797	!pt_init = mean_inflow_profiles(:,4)
	798	e_init = MAXVAL( mean_inflow_profiles(:,5) )
	799	ENDIF
[3347]	800
[2938]	801	!
[2259]	802	!-- Define the size of the filter functions and allocate them.
	803	merg = 0
	804
	805	! arrays must be large enough to cover the largest length scale
	806	DO k = nzb, nzt+1
[2938]	807	j = MAX( ABS(nux(k)), ABS(nuy(k)), ABS(nuz(k)), &
	808	ABS(nvx(k)), ABS(nvy(k)), ABS(nvz(k)), &
	809	ABS(nwx(k)), ABS(nwy(k)), ABS(nwz(k)) )
[2259]	810	IF ( j > merg ) merg = j
	811	ENDDO
	812
	813	merg = 2 * merg
	814	mergp = merg + nbgp
	815
[2938]	816	ALLOCATE ( bux(-merg:merg,nzb:nzt+1), &
	817	buy(-merg:merg,nzb:nzt+1), &
	818	buz(-merg:merg,nzb:nzt+1), &
	819	bvx(-merg:merg,nzb:nzt+1), &
	820	bvy(-merg:merg,nzb:nzt+1), &
	821	bvz(-merg:merg,nzb:nzt+1), &
	822	bwx(-merg:merg,nzb:nzt+1), &
	823	bwy(-merg:merg,nzb:nzt+1), &
	824	bwz(-merg:merg,nzb:nzt+1) )
[2259]	825
	826	!
[2938]	827	!-- Allocate velocity seeds for turbulence at xz-layer
	828	ALLOCATE ( fu_xz( nzb:nzt+1,nxlg:nxrg), fuo_xz(nzb:nzt+1,nxlg:nxrg), &
	829	fv_xz( nzb:nzt+1,nxlg:nxrg), fvo_xz(nzb:nzt+1,nxlg:nxrg), &
	830	fw_xz( nzb:nzt+1,nxlg:nxrg), fwo_xz(nzb:nzt+1,nxlg:nxrg) )
[2259]	831
[2938]	832	!
	833	!-- Allocate velocity seeds for turbulence at yz-layer
	834	ALLOCATE ( fu_yz( nzb:nzt+1,nysg:nyng), fuo_yz(nzb:nzt+1,nysg:nyng), &
	835	fv_yz( nzb:nzt+1,nysg:nyng), fvo_yz(nzb:nzt+1,nysg:nyng), &
	836	fw_yz( nzb:nzt+1,nysg:nyng), fwo_yz(nzb:nzt+1,nysg:nyng) )
[2259]	837
[2938]	838	fu_xz = 0.0_wp
	839	fuo_xz = 0.0_wp
	840	fv_xz = 0.0_wp
	841	fvo_xz = 0.0_wp
	842	fw_xz = 0.0_wp
	843	fwo_xz = 0.0_wp
	844
	845	fu_yz = 0.0_wp
	846	fuo_yz = 0.0_wp
	847	fv_yz = 0.0_wp
	848	fvo_yz = 0.0_wp
	849	fw_yz = 0.0_wp
	850	fwo_yz = 0.0_wp
	851
[2259]	852	!
	853	!-- Create filter functions
[2938]	854	CALL stg_filter_func( nux, bux ) !filter ux
[2259]	855	CALL stg_filter_func( nuy, buy ) !filter uy
	856	CALL stg_filter_func( nuz, buz ) !filter uz
[2938]	857	CALL stg_filter_func( nvx, bvx ) !filter vx
[2259]	858	CALL stg_filter_func( nvy, bvy ) !filter vy
	859	CALL stg_filter_func( nvz, bvz ) !filter vz
[2938]	860	CALL stg_filter_func( nwx, bwx ) !filter wx
[2259]	861	CALL stg_filter_func( nwy, bwy ) !filter wy
	862	CALL stg_filter_func( nwz, bwz ) !filter wz
	863
	864	#if defined( __parallel )
	865	CALL MPI_BARRIER( comm2d, ierr )
	866	#endif
	867
	868	!
[2938]	869	!-- In case of restart, calculate velocity seeds fu, fv, fw from former
	870	! time step.
	871	! Bug: fu, fv, fw are different in those heights where a11, a22, a33
	872	! are 0 compared to the prerun. This is mostly for k=nzt+1.
[2259]	873	IF ( TRIM( initializing_actions ) == 'read_restart_data' ) THEN
[2938]	874	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	875
	876	IF ( myidx == id_stg_left ) i = -1
	877	IF ( myidx == id_stg_right ) i = nxr+1
	878
[2259]	879	DO j = nysg, nyng
	880	DO k = nzb, nzt+1
[4144]	881	IF ( a11(k) /= 0.0_wp ) THEN
[4022]	882	fu_yz(k,j) = ( u(k,j,i) - u_init(k) ) / a11(k)
[2259]	883	ELSE
[4144]	884	fu_yz(k,j) = 0.0_wp
[2259]	885	ENDIF
	886
[4144]	887	IF ( a22(k) /= 0.0_wp ) THEN
[4022]	888	fv_yz(k,j) = ( v(k,j,i) - &
	889	a21(k) * fu_yz(k,j) - v_init(k) ) / a22(k)
[2259]	890	ELSE
[4144]	891	fv_yz(k,j) = 0.0_wp
[2259]	892	ENDIF
	893
[4144]	894	IF ( a33(k) /= 0.0_wp ) THEN
[4022]	895	fw_yz(k,j) = ( w(k,j,i) - &
	896	a31(k) * fu_yz(k,j) - a32(k) * &
	897	fv_yz(k,j) ) / a33(k)
[2259]	898	ELSE
[2938]	899	fw_yz = 0._wp
[2259]	900	ENDIF
	901
	902	ENDDO
	903	ENDDO
	904	ENDIF
[3900]	905
	906	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	907
	908	IF ( myidy == id_stg_south ) j = -1
	909	IF ( myidy == id_stg_north ) j = nyn+1
	910
	911	DO i = nxlg, nxrg
	912	DO k = nzb, nzt+1
	913
[4144]	914	IF ( a11(k) /= 0.0_wp ) THEN
[4022]	915	fu_xz(k,i) = ( u(k,j,i) - u_init(k) ) / a11(k)
[3900]	916	ELSE
[4144]	917	fu_xz(k,i) = 0.0_wp
[3900]	918	ENDIF
	919
[4144]	920	IF ( a22(k) /= 0.0_wp ) THEN
[4022]	921	fv_xz(k,i) = ( v(k,j,i) - &
	922	a21(k) * fu_xz(k,i) - v_init(k) ) / a22(k)
[3900]	923	ELSE
[4144]	924	fv_xz(k,i) = 0.0_wp
[3900]	925	ENDIF
	926
[4144]	927	IF ( a33(k) /= 0.0_wp ) THEN
[4022]	928	fw_xz(k,i) = ( w(k,j,i) - &
	929	a31(k) * fu_xz(k,i) - &
	930	a32(k) * fv_xz(k,i) ) / a33(k)
[3900]	931	ELSE
	932	fw_xz = 0._wp
	933	ENDIF
	934
	935	ENDDO
	936	ENDDO
	937	ENDIF
[2259]	938	ENDIF
[4022]	939	!
	940	!-- Count the number of non-topography grid points at the boundaries where
	941	!-- perturbations are imposed. This number is later used for bias corrections
	942	!-- of the perturbations, i.e. to force that their mean is zero. Please note,
	943	!-- due to the asymetry of u and v along x and y direction, respectively,
	944	!-- different cases must be distinguished.
	945	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
	946	!
	947	!-- Number of grid points where perturbations are imposed on u
	948	IF ( myidx == id_stg_left ) i = nxl
	949	IF ( myidx == id_stg_right ) i = nxr+1
	950
	951	nr_non_topo_yz_l(1) = SUM( &
	952	MERGE( 1, 0, &
	953	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
	954	!
	955	!-- Number of grid points where perturbations are imposed on v and w
	956	IF ( myidx == id_stg_left ) i = nxl-1
	957	IF ( myidx == id_stg_right ) i = nxr+1
	958
	959	nr_non_topo_yz_l(2) = SUM( &
	960	MERGE( 1, 0, &
	961	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	962	nr_non_topo_yz_l(3) = SUM( &
	963	MERGE( 1, 0, &
	964	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	965
	966	#if defined( __parallel )
	967	CALL MPI_ALLREDUCE( nr_non_topo_yz_l, nr_non_topo_yz, 3, MPI_INTEGER, &
	968	MPI_SUM, comm1dy, ierr )
	969	#else
	970	nr_non_topo_yz = nr_non_topo_yz_l
	971	#endif
	972	ENDIF
	973
	974	IF ( myidy == id_stg_south .OR. myidy == id_stg_north ) THEN
	975	!
	976	!-- Number of grid points where perturbations are imposed on v
	977	IF ( myidy == id_stg_south ) j = nys
	978	IF ( myidy == id_stg_north ) j = nyn+1
	979
	980	nr_non_topo_xz_l(2) = SUM( &
	981	MERGE( 1, 0, &
	982	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
	983	!
	984	!-- Number of grid points where perturbations are imposed on u and w
	985	IF ( myidy == id_stg_south ) j = nys-1
	986	IF ( myidy == id_stg_north ) j = nyn+1
	987
	988	nr_non_topo_xz_l(1) = SUM( &
	989	MERGE( 1, 0, &
	990	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	991	nr_non_topo_xz_l(3) = SUM( &
	992	MERGE( 1, 0, &
	993	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	994
	995	#if defined( __parallel )
	996	CALL MPI_ALLREDUCE( nr_non_topo_xz_l, nr_non_topo_xz, 3, MPI_INTEGER, &
	997	MPI_SUM, comm1dx, ierr )
	998	#else
	999	nr_non_topo_xz = nr_non_topo_xz_l
	1000	#endif
	1001	ENDIF
[2259]	1002
[4022]	1003
[2259]	1004	END SUBROUTINE stg_init
	1005
	1006
	1007	!------------------------------------------------------------------------------!
	1008	! Description:
	1009	! ------------
	1010	!> Calculate filter function bxx from length scale nxx following Eg.9 and 10
	1011	!> (Xie and Castro, 2008)
	1012	!------------------------------------------------------------------------------!
	1013	SUBROUTINE stg_filter_func( nxx, bxx )
	1014
	1015
	1016	IMPLICIT NONE
	1017
	1018	INTEGER(iwp) :: k !< loop index
	1019	INTEGER(iwp) :: n_k !< length scale nXX in height k
	1020	INTEGER(iwp) :: n_k2 !< n_k * 2
	1021	INTEGER(iwp) :: nf !< index for length scales
	1022
	1023	REAL(wp) :: bdenom !< denominator for filter functions bXX
	1024	REAL(wp) :: qsi = 1.0_wp !< minimization factor
	1025
	1026	INTEGER(iwp), DIMENSION(:) :: nxx(nzb:nzt+1) !< length scale (in gp)
	1027
	1028	REAL(wp), DIMENSION(:,:) :: bxx(-merg:merg,nzb:nzt+1) !< filter function
	1029
	1030
	1031	bxx = 0.0_wp
	1032
	1033	DO k = nzb, nzt+1
	1034	bdenom = 0.0_wp
	1035	n_k = nxx(k)
	1036	IF ( n_k /= 0 ) THEN
	1037	n_k2 = n_k * 2
	1038
	1039	!
	1040	!-- ( Eq.10 )^2
	1041	DO nf = -n_k2, n_k2
	1042	bdenom = bdenom + EXP( -qsi * pi * ABS(nf) / n_k )**2
	1043	ENDDO
	1044
	1045	!
	1046	!-- ( Eq.9 )
	1047	bdenom = SQRT( bdenom )
	1048	DO nf = -n_k2, n_k2
	1049	bxx(nf,k) = EXP( -qsi * pi * ABS(nf) / n_k ) / bdenom
	1050	ENDDO
	1051	ENDIF
	1052	ENDDO
	1053
[3347]	1054	END SUBROUTINE stg_filter_func
[2259]	1055
	1056
	1057	!------------------------------------------------------------------------------!
	1058	! Description:
	1059	! ------------
	1060	!> Parin for &stg_par for synthetic turbulence generator
	1061	!------------------------------------------------------------------------------!
	1062	SUBROUTINE stg_parin
	1063
	1064
	1065	IMPLICIT NONE
	1066
	1067	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
	1068
	1069
[3347]	1070	NAMELIST /stg_par/ dt_stg_adjust, dt_stg_call, use_syn_turb_gen
[2259]	1071
	1072	line = ' '
	1073
	1074	!
	1075	!-- Try to find stg package
	1076	REWIND ( 11 )
	1077	line = ' '
	1078	DO WHILE ( INDEX( line, '&stg_par' ) == 0 )
[3246]	1079	READ ( 11, '(A)', END=20 ) line
[2259]	1080	ENDDO
	1081	BACKSPACE ( 11 )
	1082
	1083	!
	1084	!-- Read namelist
[3246]	1085	READ ( 11, stg_par, ERR = 10, END = 20 )
[2259]	1086
	1087	!
	1088	!-- Set flag that indicates that the synthetic turbulence generator is switched
	1089	!-- on
[2776]	1090	syn_turb_gen = .TRUE.
[3246]	1091	GOTO 20
[2259]	1092
[3246]	1093	10 BACKSPACE( 11 )
[3248]	1094	READ( 11 , '(A)') line
	1095	CALL parin_fail_message( 'stg_par', line )
[2563]	1096
[3246]	1097	20 CONTINUE
[2259]	1098
	1099	END SUBROUTINE stg_parin
	1100
	1101
	1102	!------------------------------------------------------------------------------!
	1103	! Description:
	1104	! ------------
[2894]	1105	!> This routine reads the respective restart data.
[2576]	1106	!------------------------------------------------------------------------------!
[2894]	1107	SUBROUTINE stg_rrd_global( found )
[2576]	1108
	1109
[2894]	1110	IMPLICIT NONE
[2576]	1111
[3044]	1112	LOGICAL, INTENT(OUT) :: found !< flag indicating if variable was found
[2259]	1113
	1114
[2894]	1115	found = .TRUE.
[2259]	1116
[3038]	1117
[2894]	1118	SELECT CASE ( restart_string(1:length) )
[4022]	1119
	1120	CASE ( 'time_stg_adjust' )
	1121	READ ( 13 ) time_stg_adjust
	1122
	1123	CASE ( 'time_stg_call' )
	1124	READ ( 13 ) time_stg_call
	1125
[2894]	1126	CASE ( 'use_syn_turb_gen' )
	1127	READ ( 13 ) use_syn_turb_gen
[2259]	1128
[2894]	1129	CASE DEFAULT
[2259]	1130
[3038]	1131	found = .FALSE.
[2259]	1132
[2894]	1133	END SELECT
[2259]	1134
	1135
[2894]	1136	END SUBROUTINE stg_rrd_global
[2259]	1137
	1138
	1139	!------------------------------------------------------------------------------!
	1140	! Description:
	1141	! ------------
	1142	!> This routine writes the respective restart data.
	1143	!------------------------------------------------------------------------------!
[2894]	1144	SUBROUTINE stg_wrd_global
[2259]	1145
	1146
	1147	IMPLICIT NONE
[4022]	1148
	1149	CALL wrd_write_string( 'time_stg_adjust' )
	1150	WRITE ( 14 ) time_stg_adjust
	1151
	1152	CALL wrd_write_string( 'time_stg_call' )
	1153	WRITE ( 14 ) time_stg_call
[2259]	1154
[2894]	1155	CALL wrd_write_string( 'use_syn_turb_gen' )
	1156	WRITE ( 14 ) use_syn_turb_gen
[2259]	1157
	1158
[2894]	1159	END SUBROUTINE stg_wrd_global
[2259]	1160
[2894]	1161
[2259]	1162	!------------------------------------------------------------------------------!
	1163	! Description:
	1164	! ------------
	1165	!> Create turbulent inflow fields for u, v, w with prescribed length scales and
	1166	!> Reynolds stress tensor after a method of Xie and Castro (2008), modified
	1167	!> following suggestions of Kim et al. (2013), and using a Lund rotation
	1168	!> (Lund, 1998).
	1169	!------------------------------------------------------------------------------!
	1170	SUBROUTINE stg_main
	1171
	1172	IMPLICIT NONE
	1173
[2938]	1174	INTEGER(iwp) :: i !< grid index in x-direction
[2259]	1175	INTEGER(iwp) :: j !< loop index in y-direction
	1176	INTEGER(iwp) :: k !< loop index in z-direction
[4022]	1177
	1178	LOGICAL :: stg_call = .FALSE. !< control flag indicating whether turbulence was updated or only restored from last call
[2259]	1179
	1180	REAL(wp) :: dt_stg !< wheighted subtimestep
[4022]	1181
	1182	REAL(wp), DIMENSION(3) :: mc_factor_l !< local mass flux correction factor
[2259]	1183
[3987]	1184	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'start' )
[2259]	1185	!
	1186	!-- Calculate time step which is needed for filter functions
[3775]	1187	dt_stg = MAX( dt_3d, dt_stg_call )
[2259]	1188	!
[4022]	1189	!-- Check if synthetic turbulence generator needs to be called and new
	1190	!-- perturbations need to be created or if old disturbances can be imposed
	1191	!-- again.
	1192	IF ( time_stg_call >= dt_stg_call .AND. &
	1193	intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1194	stg_call = .TRUE.
	1195	ELSE
	1196	stg_call = .FALSE.
	1197	ENDIF
	1198	!
[2259]	1199	!-- Initial value of fu, fv, fw
[3646]	1200	IF ( time_since_reference_point == 0.0_wp .AND. .NOT. velocity_seed_initialized ) THEN
[2938]	1201	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_left )
	1202	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_left )
	1203	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_left )
	1204
[3182]	1205	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1206	.AND. .NOT. rans_mode ) ) THEN
[2938]	1207	!
	1208	!-- Generate turbulence at right boundary
	1209	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fu_yz, id_stg_right )
	1210	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fv_yz, id_stg_right )
	1211	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fw_yz, id_stg_right )
	1212	!
	1213	!-- Generate turbulence at north boundary
	1214	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_north )
	1215	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_north )
	1216	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_north )
	1217	!
	1218	!-- Generate turbulence at south boundary
	1219	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fu_xz, id_stg_south )
	1220	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fv_xz, id_stg_south )
	1221	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fw_xz, id_stg_south )
	1222	ENDIF
[2259]	1223	velocity_seed_initialized = .TRUE.
	1224	ENDIF
[3347]	1225
[2259]	1226	!
	1227	!-- New set of fu, fv, fw
[4022]	1228	IF ( stg_call ) THEN
	1229	!
	1230	!-- Generate turbulence at left boundary (required in all applications,
	1231	!-- i.e. offline nesting and turbulent inflow from the left)
	1232	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_left )
	1233	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_left )
	1234	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_left )
	1235
	1236	IF ( nesting_offline .OR. ( child_domain .AND. rans_mode_parent &
	1237	.AND. .NOT. rans_mode ) ) THEN
	1238	!
	1239	!-- Generate turbulence at right boundary
	1240	CALL stg_generate_seed_yz( nuy, nuz, buy, buz, fuo_yz, id_stg_right )
	1241	CALL stg_generate_seed_yz( nvy, nvz, bvy, bvz, fvo_yz, id_stg_right )
	1242	CALL stg_generate_seed_yz( nwy, nwz, bwy, bwz, fwo_yz, id_stg_right )
	1243	!
	1244	!-- Generate turbulence at north boundary
	1245	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_north )
	1246	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_north )
	1247	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_north )
	1248	!
	1249	!-- Generate turbulence at south boundary
	1250	CALL stg_generate_seed_xz( nux, nuz, bux, buz, fuo_xz, id_stg_south )
	1251	CALL stg_generate_seed_xz( nvx, nvz, bvx, bvz, fvo_xz, id_stg_south )
	1252	CALL stg_generate_seed_xz( nwx, nwz, bwx, bwz, fwo_xz, id_stg_south )
	1253	ENDIF
[2938]	1254	ENDIF
[3347]	1255
[2938]	1256	!
	1257	!-- Turbulence generation at left and or right boundary
	1258	IF ( myidx == id_stg_left .OR. myidx == id_stg_right ) THEN
[2259]	1259	!
[4022]	1260	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1261	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1262	!-- imposed
	1263	IF ( stg_call ) THEN
	1264
	1265	DO j = nysg, nyng
	1266	DO k = nzb, nzt + 1
	1267	!
	1268	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1269	IF ( tu(k) == 0.0_wp ) THEN
	1270	fu_yz(k,j) = fuo_yz(k,j)
	1271	ELSE
	1272	fu_yz(k,j) = fu_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1273	fuo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1274	ENDIF
	1275
	1276	IF ( tv(k) == 0.0_wp ) THEN
	1277	fv_yz(k,j) = fvo_yz(k,j)
	1278	ELSE
	1279	fv_yz(k,j) = fv_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1280	fvo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1281	ENDIF
	1282
	1283	IF ( tw(k) == 0.0_wp ) THEN
	1284	fw_yz(k,j) = fwo_yz(k,j)
	1285	ELSE
	1286	fw_yz(k,j) = fw_yz(k,j) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1287	fwo_yz(k,j) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1288	ENDIF
	1289	ENDDO
	1290	ENDDO
	1291
	1292	dist_yz(nzb,:,1) = 0.0_wp
	1293	dist_yz(nzb,:,2) = 0.0_wp
	1294	dist_yz(nzb,:,3) = 0.0_wp
	1295
	1296	IF ( myidx == id_stg_left ) i = nxl
	1297	IF ( myidx == id_stg_right ) i = nxr+1
	1298	DO j = nysg, nyng
	1299	DO k = nzb+1, nzt + 1
	1300	!
	1301	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1302	!-- Additional factors are added to improve the variance of v and w
	1303	dist_yz(k,j,1) = MIN( a11(k) * fu_yz(k,j), 3.0_wp ) * &
	1304	MERGE( 1.0_wp, 0.0_wp, &
	1305	BTEST( wall_flags_0(k,j,i), 1 ) )
	1306	ENDDO
	1307	ENDDO
	1308
	1309	IF ( myidx == id_stg_left ) i = nxl-1
	1310	IF ( myidx == id_stg_right ) i = nxr+1
	1311	DO j = nysg, nyng
	1312	DO k = nzb+1, nzt + 1
	1313	!
	1314	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1315	!-- Additional factors are added to improve the variance of v and w
	1316	!-- experimental test of 1.2
[3347]	1317	dist_yz(k,j,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1318	* 1.2_wp ) &
	1319	* ( a21(k) * fu_yz(k,j) &
[4022]	1320	+ a22(k) * fv_yz(k,j) ), 3.0_wp ) * &
	1321	MERGE( 1.0_wp, 0.0_wp, &
	1322	BTEST( wall_flags_0(k,j,i), 2 ) )
[3347]	1323	dist_yz(k,j,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1324	* 1.3_wp ) &
	1325	* ( a31(k) * fu_yz(k,j) &
	1326	+ a32(k) * fv_yz(k,j) &
[4022]	1327	+ a33(k) * fw_yz(k,j) ), 3.0_wp ) * &
	1328	MERGE( 1.0_wp, 0.0_wp, &
	1329	BTEST( wall_flags_0(k,j,i), 3 ) )
	1330	ENDDO
[2259]	1331	ENDDO
[4022]	1332	ENDIF
[2259]	1333
	1334	!
	1335	!-- Mass flux correction following Kim et al. (2013)
	1336	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1337	!-- inflow boundary. First, calculate mean value of the imposed
	1338	!-- perturbations at yz boundary.
	1339	!-- Note, this needs to be done only after the last RK3-substep, else
	1340	!-- the boundary values won't be accessed.
	1341	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1342	mc_factor_l = 0.0_wp
	1343	mc_factor = 0.0_wp
	1344	!
	1345	!-- Sum up the original volume flows (with and without perturbations).
	1346	!-- Note, for non-normal components (here v and w) it is actually no
	1347	!-- volume flow.
[2938]	1348	IF ( myidx == id_stg_left ) i = nxl
	1349	IF ( myidx == id_stg_right ) i = nxr+1
[4022]	1350
	1351	mc_factor_l(1) = SUM( dist_yz(nzb:nzt,nys:nyn,1) &
	1352	* MERGE( 1.0_wp, 0.0_wp, &
	1353	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 1 ) ) )
	1354
	1355	IF ( myidx == id_stg_left ) i = nxl-1
	1356	IF ( myidx == id_stg_right ) i = nxr+1
	1357
	1358	mc_factor_l(2) = SUM( dist_yz(nzb:nzt,nysv:nyn,2) &
	1359	* MERGE( 1.0_wp, 0.0_wp, &
	1360	BTEST( wall_flags_0(nzb:nzt,nysv:nyn,i), 2 ) ) )
	1361	mc_factor_l(3) = SUM( dist_yz(nzb:nzt,nys:nyn,3) &
	1362	* MERGE( 1.0_wp, 0.0_wp, &
	1363	BTEST( wall_flags_0(nzb:nzt,nys:nyn,i), 3 ) ) )
	1364
[2938]	1365	#if defined( __parallel )
	1366	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
[4022]	1367	3, MPI_REAL, MPI_SUM, comm1dy, ierr )
	1368	#else
	1369	mc_factor = mc_factor_l
[2938]	1370	#endif
[4022]	1371	!
	1372	!-- Calculate correction factor and force zero mean perturbations.
	1373	mc_factor = mc_factor / REAL( nr_non_topo_yz, KIND = wp )
	1374
	1375	IF ( myidx == id_stg_left ) i = nxl
	1376	IF ( myidx == id_stg_right ) i = nxr+1
	1377
	1378	dist_yz(:,:,1) = ( dist_yz(:,:,1) - mc_factor(1) ) &
	1379	* MERGE( 1.0_wp, 0.0_wp, &
	1380	BTEST( wall_flags_0(:,:,i), 1 ) )
	1381
	1382
	1383	IF ( myidx == id_stg_left ) i = nxl-1
	1384	IF ( myidx == id_stg_right ) i = nxr+1
	1385
	1386	dist_yz(:,:,2) = ( dist_yz(:,:,2) - mc_factor(2) ) &
	1387	* MERGE( 1.0_wp, 0.0_wp, &
	1388	BTEST( wall_flags_0(:,:,i), 2 ) )
	1389
	1390	dist_yz(:,:,3) = ( dist_yz(:,:,3) - mc_factor(3) ) &
	1391	* MERGE( 1.0_wp, 0.0_wp, &
	1392	BTEST( wall_flags_0(:,:,i), 3 ) )
	1393	!
[2938]	1394	!-- Add disturbances
	1395	IF ( myidx == id_stg_left ) THEN
[4022]	1396	!
	1397	!-- For the left boundary distinguish between mesoscale offline / self
	1398	!-- nesting and turbulent inflow at the left boundary only. In the latter
	1399	!-- case turbulence is imposed on the mean inflow profiles.
	1400	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) THEN
	1401	!
	1402	!-- Add disturbance at the inflow
	1403	DO j = nysg, nyng
	1404	DO k = nzb, nzt+1
	1405	u(k,j,-nbgp+1:0) = ( mean_inflow_profiles(k,1) + &
	1406	dist_yz(k,j,1) ) &
	1407	* MERGE( 1.0_wp, 0.0_wp, &
	1408	BTEST( wall_flags_0(k,j,0), 1 ) )
	1409	v(k,j,-nbgp:-1) = ( mean_inflow_profiles(k,2) + &
	1410	dist_yz(k,j,2) ) &
	1411	* MERGE( 1.0_wp, 0.0_wp, &
	1412	BTEST( wall_flags_0(k,j,-1), 2 ) )
	1413	w(k,j,-nbgp:-1) = dist_yz(k,j,3) &
	1414	* MERGE( 1.0_wp, 0.0_wp, &
[3186]	1415	BTEST( wall_flags_0(k,j,-1), 3 ) )
[4022]	1416	ENDDO
[2938]	1417	ENDDO
[4022]	1418	ELSE
	1419
	1420	DO j = nys, nyn
	1421	DO k = nzb+1, nzt
	1422	u(k,j,0) = ( u(k,j,0) + dist_yz(k,j,1) ) &
	1423	* MERGE( 1.0_wp, 0.0_wp, &
	1424	BTEST( wall_flags_0(k,j,0), 1 ) )
	1425	u(k,j,-1) = u(k,j,0)
	1426	v(k,j,-1) = ( v(k,j,-1) + dist_yz(k,j,2) ) &
	1427	* MERGE( 1.0_wp, 0.0_wp, &
	1428	BTEST( wall_flags_0(k,j,-1), 2 ) )
	1429	w(k,j,-1) = ( w(k,j,-1) + dist_yz(k,j,3) ) &
	1430	* MERGE( 1.0_wp, 0.0_wp, &
	1431	BTEST( wall_flags_0(k,j,-1), 3 ) )
	1432	ENDDO
	1433	ENDDO
	1434	ENDIF
[2938]	1435	ENDIF
	1436	IF ( myidx == id_stg_right ) THEN
[3186]	1437	DO j = nys, nyn
[3347]	1438	DO k = nzb+1, nzt
[3186]	1439	u(k,j,nxr+1) = ( u(k,j,nxr+1) + dist_yz(k,j,1) ) &
[4022]	1440	* MERGE( 1.0_wp, 0.0_wp, &
	1441	BTEST( wall_flags_0(k,j,nxr+1), 1 ) )
[3186]	1442	v(k,j,nxr+1) = ( v(k,j,nxr+1) + dist_yz(k,j,2) ) &
[4022]	1443	* MERGE( 1.0_wp, 0.0_wp, &
	1444	BTEST( wall_flags_0(k,j,nxr+1), 2 ) )
[3186]	1445	w(k,j,nxr+1) = ( w(k,j,nxr+1) + dist_yz(k,j,3) ) &
[4022]	1446	* MERGE( 1.0_wp, 0.0_wp, &
	1447	BTEST( wall_flags_0(k,j,nxr+1), 3 ) )
[2938]	1448	ENDDO
	1449	ENDDO
	1450	ENDIF
	1451	ENDIF
	1452	ENDIF
	1453	!
	1454	!-- Turbulence generation at north and south boundary
	1455	IF ( myidy == id_stg_north .OR. myidy == id_stg_south ) THEN
	1456	!
[4022]	1457	!-- Calculate new set of perturbations. Do this only at last RK3-substep and
	1458	!-- when dt_stg_call is exceeded. Else the old set of perturbations is
	1459	!-- imposed
	1460	IF ( stg_call ) THEN
	1461	DO i = nxlg, nxrg
	1462	DO k = nzb, nzt + 1
	1463	!
	1464	!-- Update fu, fv, fw following Eq. 14 of Xie and Castro (2008)
	1465	IF ( tu(k) == 0.0_wp ) THEN
	1466	fu_xz(k,i) = fuo_xz(k,i)
	1467	ELSE
	1468	fu_xz(k,i) = fu_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tu(k) ) + &
	1469	fuo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tu(k) ) )
	1470	ENDIF
	1471
	1472	IF ( tv(k) == 0.0_wp ) THEN
	1473	fv_xz(k,i) = fvo_xz(k,i)
	1474	ELSE
	1475	fv_xz(k,i) = fv_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tv(k) ) + &
	1476	fvo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tv(k) ) )
	1477	ENDIF
	1478
	1479	IF ( tw(k) == 0.0_wp ) THEN
	1480	fw_xz(k,i) = fwo_xz(k,i)
	1481	ELSE
	1482	fw_xz(k,i) = fw_xz(k,i) * EXP( -pi * dt_stg * 0.5_wp / tw(k) ) + &
	1483	fwo_xz(k,i) * SQRT( 1.0_wp - EXP( -pi * dt_stg / tw(k) ) )
	1484	ENDIF
	1485	ENDDO
	1486	ENDDO
	1487
	1488
	1489	dist_xz(nzb,:,1) = 0.0_wp
	1490	dist_xz(nzb,:,2) = 0.0_wp
	1491	dist_xz(nzb,:,3) = 0.0_wp
	1492
	1493	IF ( myidy == id_stg_south ) j = nys
	1494	IF ( myidy == id_stg_north ) j = nyn+1
	1495	DO i = nxlg, nxrg
	1496	DO k = nzb+1, nzt + 1
	1497	!
	1498	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1499	!-- Additional factors are added to improve the variance of v and w
	1500	!experimental test of 1.2
[3347]	1501	dist_xz(k,i,2) = MIN( ( SQRT( a22(k) / MAXVAL(a22) ) &
	1502	* 1.2_wp ) &
	1503	* ( a21(k) * fu_xz(k,i) &
[4022]	1504	+ a22(k) * fv_xz(k,i) ), 3.0_wp ) * &
	1505	MERGE( 1.0_wp, 0.0_wp, &
	1506	BTEST( wall_flags_0(k,j,i), 2 ) )
	1507	ENDDO
	1508	ENDDO
	1509
	1510	IF ( myidy == id_stg_south ) j = nys-1
	1511	IF ( myidy == id_stg_north ) j = nyn+1
	1512	DO i = nxlg, nxrg
	1513	DO k = nzb+1, nzt + 1
	1514	!
	1515	!-- Lund rotation following Eq. 17 in Xie and Castro (2008).
	1516	!-- Additional factors are added to improve the variance of v and w
	1517	dist_xz(k,i,1) = MIN( a11(k) * fu_xz(k,i), 3.0_wp ) * &
	1518	MERGE( 1.0_wp, 0.0_wp, &
	1519	BTEST( wall_flags_0(k,j,i), 1 ) )
	1520
[3347]	1521	dist_xz(k,i,3) = MIN( ( SQRT(a33(k) / MAXVAL(a33) ) &
	1522	* 1.3_wp ) &
	1523	* ( a31(k) * fu_xz(k,i) &
	1524	+ a32(k) * fv_xz(k,i) &
[4022]	1525	+ a33(k) * fw_xz(k,i) ), 3.0_wp ) * &
	1526	MERGE( 1.0_wp, 0.0_wp, &
	1527	BTEST( wall_flags_0(k,j,i), 3 ) )
	1528	ENDDO
[2938]	1529	ENDDO
[4022]	1530	ENDIF
[3347]	1531
[2938]	1532	!
	1533	!-- Mass flux correction following Kim et al. (2013)
	1534	!-- This correction factor insures that the mass flux is preserved at the
[4022]	1535	!-- inflow boundary. First, calculate mean value of the imposed
	1536	!-- perturbations at yz boundary.
	1537	!-- Note, this needs to be done only after the last RK3-substep, else
	1538	!-- the boundary values won't be accessed.
	1539	IF ( intermediate_timestep_count == intermediate_timestep_count_max ) THEN
	1540	mc_factor_l = 0.0_wp
	1541	mc_factor = 0.0_wp
	1542
	1543	IF ( myidy == id_stg_south ) j = nys
	1544	IF ( myidy == id_stg_north ) j = nyn+1
	1545
	1546	mc_factor_l(2) = SUM( dist_xz(nzb:nzt,nxl:nxr,2) &
	1547	* MERGE( 1.0_wp, 0.0_wp, &
	1548	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 2 ) ) )
	1549
	1550	IF ( myidy == id_stg_south ) j = nys-1
	1551	IF ( myidy == id_stg_north ) j = nyn+1
	1552
	1553	mc_factor_l(1) = SUM( dist_xz(nzb:nzt,nxlu:nxr,1) &
	1554	* MERGE( 1.0_wp, 0.0_wp, &
	1555	BTEST( wall_flags_0(nzb:nzt,j,nxlu:nxr), 1 ) ) )
	1556	mc_factor_l(3) = SUM( dist_xz(nzb:nzt,nxl:nxr,3) &
	1557	* MERGE( 1.0_wp, 0.0_wp, &
	1558	BTEST( wall_flags_0(nzb:nzt,j,nxl:nxr), 3 ) ) )
	1559
[2938]	1560	#if defined( __parallel )
[4022]	1561	CALL MPI_ALLREDUCE( mc_factor_l, mc_factor, &
	1562	3, MPI_REAL, MPI_SUM, comm1dx, ierr )
	1563	#else
	1564	mc_factor = mc_factor_l
[2938]	1565	#endif
[4022]	1566
	1567	mc_factor = mc_factor / REAL( nr_non_topo_xz, KIND = wp )
	1568
	1569	IF ( myidy == id_stg_south ) j = nys
	1570	IF ( myidy == id_stg_north ) j = nyn+1
	1571
	1572	dist_xz(:,:,2) = ( dist_xz(:,:,2) - mc_factor(2) ) &
	1573	* MERGE( 1.0_wp, 0.0_wp, &
	1574	BTEST( wall_flags_0(:,j,:), 2 ) )
	1575
	1576
	1577	IF ( myidy == id_stg_south ) j = nys-1
	1578	IF ( myidy == id_stg_north ) j = nyn+1
	1579
	1580	dist_xz(:,:,1) = ( dist_xz(:,:,1) - mc_factor(1) ) &
	1581	* MERGE( 1.0_wp, 0.0_wp, &
	1582	BTEST( wall_flags_0(:,j,:), 1 ) )
	1583
	1584	dist_xz(:,:,3) = ( dist_xz(:,:,3) - mc_factor(3) ) &
	1585	* MERGE( 1.0_wp, 0.0_wp, &
	1586	BTEST( wall_flags_0(:,j,:), 3 ) )
	1587	!
	1588	!-- Add disturbances
	1589	IF ( myidy == id_stg_south ) THEN
	1590	DO i = nxl, nxr
	1591	DO k = nzb+1, nzt
	1592	u(k,-1,i) = ( u(k,-1,i) + dist_xz(k,i,1) ) &
	1593	* MERGE( 1.0_wp, 0.0_wp, &
	1594	BTEST( wall_flags_0(k,-1,i), 1 ) )
	1595	v(k,0,i) = ( v(k,0,i) + dist_xz(k,i,2) ) &
	1596	* MERGE( 1.0_wp, 0.0_wp, &
	1597	BTEST( wall_flags_0(k,0,i), 2 ) )
	1598	v(k,-1,i) = v(k,0,i)
	1599	w(k,-1,i) = ( w(k,-1,i) + dist_xz(k,i,3) ) &
	1600	* MERGE( 1.0_wp, 0.0_wp, &
	1601	BTEST( wall_flags_0(k,-1,i), 3 ) )
	1602	ENDDO
[2938]	1603	ENDDO
[4022]	1604	ENDIF
	1605	IF ( myidy == id_stg_north ) THEN
	1606
	1607	DO i = nxl, nxr
	1608	DO k = nzb+1, nzt
	1609	u(k,nyn+1,i) = ( u(k,nyn+1,i) + dist_xz(k,i,1) ) &
	1610	* MERGE( 1.0_wp, 0.0_wp, &
	1611	BTEST( wall_flags_0(k,nyn+1,i), 1 ) )
	1612	v(k,nyn+1,i) = ( v(k,nyn+1,i) + dist_xz(k,i,2) ) &
	1613	* MERGE( 1.0_wp, 0.0_wp, &
	1614	BTEST( wall_flags_0(k,nyn+1,i), 2 ) )
	1615	w(k,nyn+1,i) = ( w(k,nyn+1,i) + dist_xz(k,i,3) ) &
	1616	* MERGE( 1.0_wp, 0.0_wp, &
	1617	BTEST( wall_flags_0(k,nyn+1,i), 3 ) )
	1618	ENDDO
[2938]	1619	ENDDO
[4022]	1620	ENDIF
[2938]	1621	ENDIF
[2259]	1622	ENDIF
[3347]	1623	!
	1624	!-- Finally, set time counter for calling STG to zero
[4022]	1625	IF ( stg_call ) time_stg_call = 0.0_wp
[2259]	1626
[3987]	1627	IF ( debug_output_timestep ) CALL debug_message( 'stg_main', 'end' )
	1628
[2259]	1629	END SUBROUTINE stg_main
	1630
	1631	!------------------------------------------------------------------------------!
	1632	! Description:
	1633	! ------------
	1634	!> Generate a set of random number rand_it wich is equal on each PE
	1635	!> and calculate the velocity seed f_n.
	1636	!> f_n is splitted in vertical direction by the number of PEs in x-direction and
	1637	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1638	!> parts are collected to form the full array.
	1639	!------------------------------------------------------------------------------!
[2938]	1640	SUBROUTINE stg_generate_seed_yz( n_y, n_z, b_y, b_z, f_n, id )
[2259]	1641
	1642	IMPLICIT NONE
	1643
[2938]	1644	INTEGER(iwp) :: id !< core ids at respective boundaries
[2259]	1645	INTEGER(iwp) :: j !< loop index in y-direction
	1646	INTEGER(iwp) :: jj !< loop index in y-direction
	1647	INTEGER(iwp) :: k !< loop index in z-direction
	1648	INTEGER(iwp) :: kk !< loop index in z-direction
	1649	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1650
	1651	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y !< length scale in y-direction
	1652	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
	1653	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_y2 !< n_y*2
	1654	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1655
	1656	REAL(wp) :: nyz_inv !< inverse of number of grid points in yz-slice
	1657	REAL(wp) :: rand_av !< average of random number
	1658	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1659
[3347]	1660	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_y !< filter function in y-direction
	1661	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[2938]	1662	REAL(wp), DIMENSION(nzb_x_stg:nzt_x_stg+1,nysg:nyng) :: f_n_l !< local velocity seed
[2259]	1663	REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng) :: f_n !< velocity seed
	1664	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
	1665
	1666
	1667	!
	1668	!-- Generate random numbers using a seed generated in stg_init.
	1669	!-- The set of random numbers are modified to have an average of 0 and
	1670	!-- unit variance.
	1671	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:ny+mergp) )
	1672
	1673	rand_av = 0.0_wp
	1674	rand_sigma_inv = 0.0_wp
	1675	nyz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( ny+1 ), KIND=wp )
	1676
	1677	DO j = 0, ny
	1678	DO k = nzb, nzt+1
	1679	CALL RANDOM_NUMBER( rand_it(k,j) )
	1680	rand_av = rand_av + rand_it(k,j)
	1681	ENDDO
	1682	ENDDO
	1683
	1684	rand_av = rand_av * nyz_inv
	1685
	1686	DO j = 0, ny
	1687	DO k = nzb, nzt+1
	1688	rand_it(k,j) = rand_it(k,j) - rand_av
	1689	rand_sigma_inv = rand_sigma_inv + rand_it(k,j) ** 2
	1690	ENDDO
	1691	ENDDO
	1692
	1693	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nyz_inv)
	1694
	1695	DO j = 0, ny
	1696	DO k = nzb, nzt+1
	1697	rand_it(k,j) = rand_it(k,j) * rand_sigma_inv
	1698	ENDDO
	1699	ENDDO
	1700
	1701	!
	1702	!-- Periodic fill of random number in space
	1703	DO j = 0, ny
	1704	DO k = 1, mergp
	1705	rand_it(nzb -k,j) = rand_it(nzt+2-k,j) ! bottom margin
	1706	rand_it(nzt+1+k,j) = rand_it(nzb+k-1,j) ! top margin
	1707	ENDDO
	1708	ENDDO
	1709	DO j = 1, mergp
	1710	DO k = nzb-mergp, nzt+1+mergp
	1711	rand_it(k, -j) = rand_it(k,ny-j+1) ! south margin
	1712	rand_it(k,ny+j) = rand_it(k, j-1) ! north margin
	1713	ENDDO
	1714	ENDDO
	1715
	1716	!
	1717	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	1718	n_y2 = n_y * 2
	1719	n_z2 = n_z * 2
	1720	f_n_l = 0.0_wp
	1721
	1722	DO j = nysg, nyng
[2938]	1723	DO k = nzb_x_stg, nzt_x_stg+1
[2259]	1724	DO jj = -n_y2(k), n_y2(k)
	1725	DO kk = -n_z2(k), n_z2(k)
	1726	f_n_l(k,j) = f_n_l(k,j) &
	1727	+ b_y(jj,k) * b_z(kk,k) * rand_it(k+kk,j+jj)
	1728	ENDDO
	1729	ENDDO
	1730	ENDDO
	1731	ENDDO
	1732
	1733	DEALLOCATE( rand_it )
	1734	!
	1735	!-- Gather velocity seeds of full subdomain
[2938]	1736	send_count = nzt_x_stg - nzb_x_stg + 1
	1737	IF ( nzt_x_stg == nzt ) send_count = send_count + 1
[2259]	1738
	1739	#if defined( __parallel )
[2945]	1740	CALL MPI_GATHERV( f_n_l(nzb_x_stg,nysg), send_count, stg_type_yz_small, &
	1741	f_n(nzb+1,nysg), recv_count_yz, displs_yz, stg_type_yz, &
[2938]	1742	id, comm1dx, ierr )
[2259]	1743	#else
[2938]	1744	f_n(nzb+1:nzt+1,nysg:nyng) = f_n_l(nzb_x_stg:nzt_x_stg+1,nysg:nyng)
[2259]	1745	#endif
	1746
	1747
	1748	END SUBROUTINE stg_generate_seed_yz
	1749
[2938]	1750
	1751
	1752
	1753	!------------------------------------------------------------------------------!
	1754	! Description:
	1755	! ------------
	1756	!> Generate a set of random number rand_it wich is equal on each PE
	1757	!> and calculate the velocity seed f_n.
	1758	!> f_n is splitted in vertical direction by the number of PEs in y-direction and
	1759	!> and each PE calculates a vertical subsection of f_n. At the the end, all
	1760	!> parts are collected to form the full array.
	1761	!------------------------------------------------------------------------------!
	1762	SUBROUTINE stg_generate_seed_xz( n_x, n_z, b_x, b_z, f_n, id )
	1763
	1764	IMPLICIT NONE
	1765
	1766	INTEGER(iwp) :: id !< core ids at respective boundaries
	1767	INTEGER(iwp) :: i !< loop index in x-direction
	1768	INTEGER(iwp) :: ii !< loop index in x-direction
	1769	INTEGER(iwp) :: k !< loop index in z-direction
	1770	INTEGER(iwp) :: kk !< loop index in z-direction
	1771	INTEGER(iwp) :: send_count !< send count for MPI_GATHERV
	1772
	1773	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x !< length scale in x-direction
	1774	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z !< length scale in z-direction
[3347]	1775	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_x2 !< n_x*2
[2938]	1776	INTEGER(iwp), DIMENSION(nzb:nzt+1) :: n_z2 !< n_z*2
	1777
	1778	REAL(wp) :: nxz_inv !< inverse of number of grid points in xz-slice
	1779	REAL(wp) :: rand_av !< average of random number
	1780	REAL(wp) :: rand_sigma_inv !< inverse of stdev of random number
	1781
[3347]	1782	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_x !< filter function in x-direction
	1783	REAL(wp), DIMENSION(-merg:merg,nzb:nzt+1) :: b_z !< filter function in z-direction
[2938]	1784	REAL(wp), DIMENSION(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg) :: f_n_l !< local velocity seed
	1785	REAL(wp), DIMENSION(nzb:nzt+1,nxlg:nxrg) :: f_n !< velocity seed
	1786	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: rand_it !< random number
	1787
	1788
	1789	!
	1790	!-- Generate random numbers using a seed generated in stg_init.
	1791	!-- The set of random numbers are modified to have an average of 0 and
	1792	!-- unit variance.
	1793	ALLOCATE( rand_it(nzb-mergp:nzt+1+mergp,-mergp:nx+mergp) )
	1794
	1795	rand_av = 0.0_wp
	1796	rand_sigma_inv = 0.0_wp
	1797	nxz_inv = 1.0_wp / REAL( ( nzt+1 - nzb+1 ) * ( nx+1 ), KIND=wp )
	1798
	1799	DO i = 0, nx
	1800	DO k = nzb, nzt+1
	1801	CALL RANDOM_NUMBER( rand_it(k,i) )
	1802	rand_av = rand_av + rand_it(k,i)
	1803	ENDDO
	1804	ENDDO
	1805
	1806	rand_av = rand_av * nxz_inv
	1807
	1808	DO i = 0, nx
	1809	DO k = nzb, nzt+1
	1810	rand_it(k,i) = rand_it(k,i) - rand_av
	1811	rand_sigma_inv = rand_sigma_inv + rand_it(k,i) ** 2
	1812	ENDDO
	1813	ENDDO
	1814
	1815	rand_sigma_inv = 1.0_wp / SQRT(rand_sigma_inv * nxz_inv)
	1816
	1817	DO i = 0, nx
	1818	DO k = nzb, nzt+1
	1819	rand_it(k,i) = rand_it(k,i) * rand_sigma_inv
	1820	ENDDO
	1821	ENDDO
	1822
	1823	!
	1824	!-- Periodic fill of random number in space
	1825	DO i = 0, nx
	1826	DO k = 1, mergp
	1827	rand_it(nzb-k,i) = rand_it(nzt+2-k,i) ! bottom margin
	1828	rand_it(nzt+1+k,i) = rand_it(nzb+k-1,i) ! top margin
	1829	ENDDO
	1830	ENDDO
	1831	DO i = 1, mergp
	1832	DO k = nzb-mergp, nzt+1+mergp
	1833	rand_it(k,-i) = rand_it(k,nx-i+1) ! left margin
	1834	rand_it(k,nx+i) = rand_it(k,i-1) ! right margin
	1835	ENDDO
	1836	ENDDO
	1837
	1838	!
	1839	!-- Generate velocity seed following Eq.6 of Xie and Castro (2008)
	1840	n_x2 = n_x * 2
	1841	n_z2 = n_z * 2
	1842	f_n_l = 0.0_wp
	1843
	1844	DO i = nxlg, nxrg
	1845	DO k = nzb_y_stg, nzt_y_stg+1
	1846	DO ii = -n_x2(k), n_x2(k)
	1847	DO kk = -n_z2(k), n_z2(k)
	1848	f_n_l(k,i) = f_n_l(k,i) &
	1849	+ b_x(ii,k) * b_z(kk,k) * rand_it(k+kk,i+ii)
	1850	ENDDO
	1851	ENDDO
	1852	ENDDO
	1853	ENDDO
	1854
	1855	DEALLOCATE( rand_it )
	1856
	1857	!
	1858	!-- Gather velocity seeds of full subdomain
	1859	send_count = nzt_y_stg - nzb_y_stg + 1
	1860	IF ( nzt_y_stg == nzt ) send_count = send_count + 1
	1861
	1862
	1863	#if defined( __parallel )
[2945]	1864	CALL MPI_GATHERV( f_n_l(nzb_y_stg,nxlg), send_count, stg_type_xz_small, &
[2938]	1865	f_n(nzb+1,nxlg), recv_count_xz, displs_xz, stg_type_xz, &
	1866	id, comm1dy, ierr )
	1867	#else
	1868	f_n(nzb+1:nzt+1,nxlg:nxrg) = f_n_l(nzb_y_stg:nzt_y_stg+1,nxlg:nxrg)
	1869	#endif
	1870
	1871
	1872	END SUBROUTINE stg_generate_seed_xz
	1873
[3347]	1874	!------------------------------------------------------------------------------!
	1875	! Description:
	1876	! ------------
	1877	!> Parametrization of the Reynolds stress tensor, following the parametrization
	1878	!> described in Rotach et al. (1996), which is applied in state-of-the-art
	1879	!> dispserion modelling. Please note, the parametrization does not distinguish
	1880	!> between along-wind and cross-wind turbulence.
	1881	!------------------------------------------------------------------------------!
	1882	SUBROUTINE parametrize_reynolds_stress
	1883
	1884	IMPLICIT NONE
	1885
	1886	INTEGER(iwp) :: k !< loop index in z-direction
	1887
	1888	REAL(wp) :: zzi !< ratio of z/zi
	1889
	1890	DO k = nzb+1, nzt+1
	1891	!
[4022]	1892	!-- Calculate function to gradually decrease Reynolds stress above ABL top.
	1893	!-- The function decreases to 1/10 after one length scale above the
	1894	!-- ABL top.
	1895	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	1896	!
[4022]	1897	!-- Determine normalized height coordinate
	1898	zzi = zu(k) / zi_ribulk
[3347]	1899	!
[4022]	1900	!-- u'u' and v'v'. Assume isotropy. Note, add a small negative number
	1901	!-- to the denominator, else the merge-function can crash if scale_l is
	1902	!-- zero.
	1903	r11(k) = scale_us*2 ( &
	1904	MERGE( 0.35_wp * ABS( &
	1905	- zi_ribulk / ( kappa * scale_l - 10E-4_wp ) &
	1906	)**( 2.0_wp / 3.0_wp ), &
	1907	0.0_wp, &
	1908	scale_l < 0.0_wp ) &
	1909	+ 5.0_wp - 4.0_wp * zzi &
	1910	) * blend
	1911
	1912	r22(k) = r11(k)
	1913	!
	1914	!-- w'w'
	1915	r33(k) = scale_wm*2 ( &
	1916	1.5_wp * zzi*( 2.0_wp / 3.0_wp ) EXP( -2.0_wp * zzi ) &
	1917	+ ( 1.7_wp - zzi ) * ( scale_us / scale_wm )**2 &
	1918	) * blend
	1919	!
	1920	!-- u'w' and v'w'. Assume isotropy.
	1921	r31(k) = - scale_us*2 ( 1.01_wp - MIN( zzi, 1.0_wp ) ) * blend
	1922	r32(k) = r31(k)
[3347]	1923	!
[4022]	1924	!-- For u'v' no parametrization exist so far - ?. For simplicity assume
	1925	!-- a similar profile as for u'w'.
	1926	r21(k) = r31(k)
[3347]	1927	ENDDO
	1928
	1929	!
	1930	!-- Set bottom boundary condition
	1931	r11(nzb) = r11(nzb+1)
	1932	r22(nzb) = r22(nzb+1)
	1933	r33(nzb) = r33(nzb+1)
	1934
	1935	r21(nzb) = r11(nzb+1)
	1936	r31(nzb) = r31(nzb+1)
	1937	r32(nzb) = r32(nzb+1)
	1938
	1939
	1940	END SUBROUTINE parametrize_reynolds_stress
	1941
	1942	!------------------------------------------------------------------------------!
	1943	! Description:
	1944	! ------------
	1945	!> Calculate the coefficient matrix from the Lund rotation.
	1946	!------------------------------------------------------------------------------!
	1947	SUBROUTINE calc_coeff_matrix
	1948
	1949	IMPLICIT NONE
	1950
	1951	INTEGER(iwp) :: k !< loop index in z-direction
	1952
	1953	!
	1954	!-- Calculate coefficient matrix. Split loops to allow for loop vectorization.
	1955	DO k = nzb+1, nzt+1
[4022]	1956	IF ( r11(k) > 10E-6_wp ) THEN
[3347]	1957	a11(k) = SQRT( r11(k) )
	1958	a21(k) = r21(k) / a11(k)
	1959	a31(k) = r31(k) / a11(k)
	1960	ELSE
	1961	a11(k) = 10E-8_wp
	1962	a21(k) = 10E-8_wp
	1963	a31(k) = 10E-8_wp
	1964	ENDIF
	1965	ENDDO
	1966	DO k = nzb+1, nzt+1
	1967	a22(k) = r22(k) - a21(k)**2
[4022]	1968	IF ( a22(k) > 10E-6_wp ) THEN
[3347]	1969	a22(k) = SQRT( a22(k) )
	1970	a32(k) = r32(k) - a21(k) * a31(k) / a22(k)
	1971	ELSE
	1972	a22(k) = 10E-8_wp
	1973	a32(k) = 10E-8_wp
	1974	ENDIF
	1975	ENDDO
	1976	DO k = nzb+1, nzt+1
	1977	a33(k) = r33(k) - a31(k)2 - a32(k)2
[4022]	1978	IF ( a33(k) > 10E-6_wp ) THEN
[3347]	1979	a33(k) = SQRT( a33(k) )
	1980	ELSE
	1981	a33(k) = 10E-8_wp
	1982	ENDIF
	1983	ENDDO
	1984	!
	1985	!-- Set bottom boundary condition
	1986	a11(nzb) = a11(nzb+1)
	1987	a22(nzb) = a22(nzb+1)
	1988	a21(nzb) = a21(nzb+1)
	1989	a33(nzb) = a33(nzb+1)
	1990	a31(nzb) = a31(nzb+1)
	1991	a32(nzb) = a32(nzb+1)
	1992
	1993	END SUBROUTINE calc_coeff_matrix
	1994
	1995	!------------------------------------------------------------------------------!
	1996	! Description:
	1997	! ------------
	1998	!> This routine controls the re-adjustment of the turbulence statistics used
	1999	!> for generating turbulence at the lateral boundaries.
	2000	!------------------------------------------------------------------------------!
	2001	SUBROUTINE stg_adjust
	2002
	2003	IMPLICIT NONE
	2004
[3987]	2005
	2006	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'start' )
[3347]	2007	!
[4022]	2008	!-- In case of dirichlet inflow boundary conditions only at one lateral
	2009	!-- boundary, i.e. in the case no offline or self nesting is applied but
	2010	!-- synthetic turbulence shall be parametrized nevertheless, the
	2011	!-- boundary-layer depth need to determined first.
	2012	IF ( .NOT. nesting_offline .AND. .NOT. child_domain ) &
	2013	CALL nesting_offl_calc_zi
	2014	!
	2015	!-- Compute scaling parameters (domain-averaged), such as friction velocity
	2016	!-- are calculated.
[3347]	2017	CALL calc_scaling_variables
	2018	!
	2019	!-- Set length and time scales depending on boundary-layer height
	2020	CALL calc_length_and_time_scale
	2021	!
	2022	!-- Parametrize Reynolds-stress tensor, diagonal elements as well
	2023	!-- as r21 (v'u'), r31 (w'u'), r32 (w'v'). Parametrization follows
	2024	!-- Rotach et al. (1996) and is based on boundary-layer depth,
	2025	!-- friction velocity and velocity scale.
	2026	CALL parametrize_reynolds_stress
	2027	!
	2028	!-- Calculate coefficient matrix from Reynolds stress tensor
	2029	!-- (Lund rotation)
	2030	CALL calc_coeff_matrix
	2031	!
	2032	!-- Determine filter functions on basis of updated length scales
	2033	CALL stg_filter_func( nux, bux ) !filter ux
	2034	CALL stg_filter_func( nuy, buy ) !filter uy
	2035	CALL stg_filter_func( nuz, buz ) !filter uz
	2036	CALL stg_filter_func( nvx, bvx ) !filter vx
	2037	CALL stg_filter_func( nvy, bvy ) !filter vy
	2038	CALL stg_filter_func( nvz, bvz ) !filter vz
	2039	CALL stg_filter_func( nwx, bwx ) !filter wx
	2040	CALL stg_filter_func( nwy, bwy ) !filter wy
	2041	CALL stg_filter_func( nwz, bwz ) !filter wz
	2042	!
	2043	!-- Reset time counter for controlling next adjustment to zero
	2044	time_stg_adjust = 0.0_wp
[3987]	2045
	2046	IF ( debug_output_timestep ) CALL debug_message( 'stg_adjust', 'end' )
[3347]	2047
	2048	END SUBROUTINE stg_adjust
	2049
	2050
	2051	!------------------------------------------------------------------------------!
	2052	! Description:
	2053	! ------------
	2054	!> Calculates turbuluent length and time scales if these are not available
	2055	!> from measurements.
	2056	!------------------------------------------------------------------------------!
	2057	SUBROUTINE calc_length_and_time_scale
	2058
	2059	IMPLICIT NONE
	2060
	2061
[4022]	2062	INTEGER(iwp) :: k !< loop index in z-direction
[3347]	2063
[4022]	2064	REAL(wp) :: length_scale_dum !< effectively used length scale
	2065
[3347]	2066	!
	2067	!-- In initial call the boundary-layer depth can be zero. This case, set
	2068	!-- minimum value for boundary-layer depth, to setup length scales correctly.
	2069	zi_ribulk = MAX( zi_ribulk, zw(nzb+2) )
	2070	!
	2071	!-- Set-up default turbulent length scales. From the numerical point of
	2072	!-- view the imposed perturbations should not be immediately dissipated
	2073	!-- by the numerics. The numerical dissipation, however, acts on scales
	2074	!-- up to 8 x the grid spacing. For this reason, set the turbulence
	2075	!-- length scale to 8 time the grid spacing. Further, above the boundary
	2076	!-- layer height, set turbulence lenght scales to zero (equivalent to not
	2077	!-- imposing any perturbations) in order to save computational costs.
	2078	!-- Typical time scales are derived by assuming Taylors's hypothesis,
	2079	!-- using the length scales and the mean profiles of u- and v-component.
	2080	DO k = nzb+1, nzt+1
	2081	!
[4022]	2082	!-- Determine blending parameter. Within the boundary layer length scales
	2083	!-- are constant, while above lengths scales approach gradully zero,
	2084	!-- i.e. imposed turbulence is not correlated in space and time,
	2085	!-- just white noise, which saves computations power as the loops for the
	2086	!-- computation of the filter functions depend on the length scales.
	2087	!-- The value decreases to 1/10 after one length scale above the
	2088	!-- ABL top.
	2089	blend = MIN( 1.0_wp, EXP( d_l * zu(k) - d_l * zi_ribulk ) )
[3347]	2090	!
[4022]	2091	!-- Assume isotropic turbulence length scales
	2092	nux(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2093	nuy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2094	nvx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2095	nvy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
	2096	nwx(k) = MAX( INT( length_scale * ddx ), 1 ) * blend
	2097	nwy(k) = MAX( INT( length_scale * ddy ), 1 ) * blend
[3347]	2098	!
[4022]	2099	!-- Along the vertical direction limit the length scale further by the
	2100	!-- boundary-layer depth to assure that no length scales larger than
	2101	!-- the boundary-layer depth are used
	2102	length_scale_dum = MIN( length_scale, zi_ribulk )
	2103
	2104	nuz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2105	nvz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
	2106	nwz(k) = MAX( INT( length_scale_dum * ddzw(k) ), 1 ) * blend
[3347]	2107	!
[4022]	2108	!-- Limit time scales, else they become very larger for low wind speed,
	2109	!-- imposing long-living inflow perturbations which in turn propagate
	2110	!-- further into the model domain. Use u_init and v_init to calculate
	2111	!-- the time scales, which will be equal to the inflow profiles, both,
	2112	!-- in offline nesting mode or in dirichlet/radiation mode.
	2113	tu(k) = MIN( dt_stg_adjust, length_scale / &
	2114	( ABS( u_init(k) ) + 0.1_wp ) ) * blend
	2115	tv(k) = MIN( dt_stg_adjust, length_scale / &
	2116	( ABS( v_init(k) ) + 0.1_wp ) ) * blend
	2117	!
	2118	!-- Time scale of w-component is a mixture from u- and v-component.
	2119	tw(k) = SQRT( tu(k)2 + tv(k)2 ) * blend
	2120
[3347]	2121	ENDDO
	2122	!
	2123	!-- Set bottom boundary condition for the length and time scales
	2124	nux(nzb) = nux(nzb+1)
	2125	nuy(nzb) = nuy(nzb+1)
	2126	nuz(nzb) = nuz(nzb+1)
	2127	nvx(nzb) = nvx(nzb+1)
	2128	nvy(nzb) = nvy(nzb+1)
	2129	nvz(nzb) = nvz(nzb+1)
	2130	nwx(nzb) = nwx(nzb+1)
	2131	nwy(nzb) = nwy(nzb+1)
	2132	nwz(nzb) = nwz(nzb+1)
	2133
	2134	tu(nzb) = tu(nzb+1)
	2135	tv(nzb) = tv(nzb+1)
	2136	tw(nzb) = tw(nzb+1)
	2137
	2138
	2139	END SUBROUTINE calc_length_and_time_scale
	2140
	2141	!------------------------------------------------------------------------------!
	2142	! Description:
	2143	! ------------
	2144	!> Calculate scaling variables which are used for turbulence parametrization
	2145	!> according to Rotach et al. (1996). Scaling variables are: friction velocity,
	2146	!> boundary-layer depth, momentum velocity scale, and Obukhov length.
	2147	!------------------------------------------------------------------------------!
	2148	SUBROUTINE calc_scaling_variables
	2149
	2150	USE surface_mod, &
[4148]	2151	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
[3347]	2152
	2153	IMPLICIT NONE
	2154
	2155	INTEGER(iwp) :: i !< loop index in x-direction
	2156	INTEGER(iwp) :: j !< loop index in y-direction
	2157	INTEGER(iwp) :: k !< loop index in z-direction
	2158	INTEGER(iwp) :: m !< surface element index
	2159
	2160	REAL(wp) :: friction_vel_l !< mean friction veloctiy on subdomain
[3937]	2161	REAL(wp) :: pt_surf_mean !< mean near surface temperature (at 1st grid point)
	2162	REAL(wp) :: pt_surf_mean_l !< mean near surface temperature (at 1st grid point) on subdomain
	2163	REAL(wp) :: scale_l_l !< mean Obukhov lenght on subdomain
[3347]	2164	REAL(wp) :: shf_mean !< mean surface sensible heat flux
	2165	REAL(wp) :: shf_mean_l !< mean surface sensible heat flux on subdomain
	2166	REAL(wp) :: w_convective !< convective velocity scale
	2167
	2168	!
[3937]	2169	!-- Calculate mean friction velocity, velocity scale, heat flux and
	2170	!-- near-surface temperature in the model domain.
	2171	pt_surf_mean_l = 0.0_wp
	2172	shf_mean_l = 0.0_wp
	2173	scale_l_l = 0.0_wp
	2174	friction_vel_l = 0.0_wp
[3347]	2175	DO m = 1, surf_def_h(0)%ns
[3937]	2176	i = surf_def_h(0)%i(m)
	2177	j = surf_def_h(0)%j(m)
	2178	k = surf_def_h(0)%k(m)
	2179	friction_vel_l = friction_vel_l + surf_def_h(0)%us(m)
	2180	shf_mean_l = shf_mean_l + surf_def_h(0)%shf(m) * drho_air(k)
	2181	scale_l_l = scale_l_l + surf_def_h(0)%ol(m)
	2182	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2183	ENDDO
	2184	DO m = 1, surf_lsm_h%ns
[3937]	2185	i = surf_lsm_h%i(m)
	2186	j = surf_lsm_h%j(m)
	2187	k = surf_lsm_h%k(m)
	2188	friction_vel_l = friction_vel_l + surf_lsm_h%us(m)
	2189	shf_mean_l = shf_mean_l + surf_lsm_h%shf(m) * drho_air(k)
	2190	scale_l_l = scale_l_l + surf_lsm_h%ol(m)
	2191	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2192	ENDDO
	2193	DO m = 1, surf_usm_h%ns
[3937]	2194	i = surf_usm_h%i(m)
	2195	j = surf_usm_h%j(m)
	2196	k = surf_usm_h%k(m)
	2197	friction_vel_l = friction_vel_l + surf_usm_h%us(m)
	2198	shf_mean_l = shf_mean_l + surf_usm_h%shf(m) * drho_air(k)
	2199	scale_l_l = scale_l_l + surf_usm_h%ol(m)
	2200	pt_surf_mean_l = pt_surf_mean_l + pt(k,j,i)
[3347]	2201	ENDDO
	2202
	2203	#if defined( __parallel )
[3937]	2204	CALL MPI_ALLREDUCE( friction_vel_l, scale_us, 1, MPI_REAL, MPI_SUM, &
[3347]	2205	comm2d, ierr )
[3937]	2206	CALL MPI_ALLREDUCE( shf_mean_l, shf_mean, 1, MPI_REAL, MPI_SUM, &
[3347]	2207	comm2d, ierr )
[3937]	2208	CALL MPI_ALLREDUCE( scale_l_l, scale_l, 1, MPI_REAL, MPI_SUM, &
	2209	comm2d, ierr )
	2210	CALL MPI_ALLREDUCE( pt_surf_mean_l, pt_surf_mean, 1, MPI_REAL, MPI_SUM, &
	2211	comm2d, ierr )
[3347]	2212	#else
[3937]	2213	scale_us = friction_vel_l
	2214	shf_mean = shf_mean_l
	2215	scale_l = scale_l_l
	2216	pt_surf_mean = pt_surf_mean_l
[3347]	2217	#endif
	2218
[3937]	2219	scale_us = scale_us / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2220	shf_mean = shf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2221	scale_l = scale_l / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
	2222	pt_surf_mean = pt_surf_mean / REAL( ( nx + 1 ) * ( ny + 1 ), KIND = wp )
[3347]	2223	!
	2224	!-- Compute mean convective velocity scale. Note, in case the mean heat flux
	2225	!-- is negative, set convective velocity scale to zero.
	2226	IF ( shf_mean > 0.0_wp ) THEN
[3937]	2227	w_convective = ( g * shf_mean * zi_ribulk / pt_surf_mean )**( 1.0_wp / 3.0_wp )
[3347]	2228	ELSE
	2229	w_convective = 0.0_wp
	2230	ENDIF
	2231	!
	2232	!-- Finally, in order to consider also neutral or stable stratification,
	2233	!-- compute momentum velocity scale from u* and convective velocity scale,
	2234	!-- according to Rotach et al. (1996).
	2235	scale_wm = ( scale_us*3 + 0.6_wp w_convective3 )( 1.0_wp / 3.0_wp )
	2236
	2237	END SUBROUTINE calc_scaling_variables
	2238
[2259]	2239	END MODULE synthetic_turbulence_generator_mod

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