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lagrangian_particle_model_mod.f90 @ 4329

Last change on this file since 4329 was 4329, checked in by motisi, 4 years ago
Renamed wall_flags_0 to wall_flags_static_0
Property svn:keywords set to `Id`
File size: 353.9 KB

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1	!> @file lagrangian_particle_model_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
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	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
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	!
17	! Copyright 1997-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lagrangian_particle_model_mod.f90 4329 2019-12-10 15:46:36Z motisi $
27	! Renamed wall_flags_0 to wall_flags_static_0
28	!
29	! 4282 2019-10-29 16:18:46Z schwenkel
30	! Bugfix of particle timeseries in case of more than one particle group
31	!
32	! 4277 2019-10-28 16:53:23Z schwenkel
33	! Bugfix: Added first_call_lpm in use statement
34	!
35	! 4276 2019-10-28 16:03:29Z schwenkel
36	! Modularize lpm: Move conditions in time intergration to module
37	!
38	! 4275 2019-10-28 15:34:55Z schwenkel
39	! Change call of simple predictor corrector method, i.e. two divergence free
40	! velocitiy fields are now used.
41	!
42	! 4232 2019-09-20 09:34:22Z knoop
43	! Removed INCLUDE "mpif.h", as it is not needed because of USE pegrid
44	!
45	! 4195 2019-08-28 13:44:27Z schwenkel
46	! Bugfix for simple_corrector interpolation method in case of ocean runs and
47	! output particle advection interpolation method into header
48	!
49	! 4182 2019-08-22 15:20:23Z scharf
50	! Corrected "Former revisions" section
51	!
52	! 4168 2019-08-16 13:50:17Z suehring
53	! Replace function get_topography_top_index by topo_top_ind
54	!
55	! 4145 2019-08-06 09:55:22Z schwenkel
56	! Some reformatting
57	!
58	! 4144 2019-08-06 09:11:47Z raasch
59	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
60	!
61	! 4143 2019-08-05 15:14:53Z schwenkel
62	! Rename variable and change select case to if statement
63	!
64	! 4122 2019-07-26 13:11:56Z schwenkel
65	! Implement reset method as bottom boundary condition
66	!
67	! 4121 2019-07-26 10:01:22Z schwenkel
68	! Implementation of an simple method for interpolating the velocities to
69	! particle position
70	!
71	! 4114 2019-07-23 14:09:27Z schwenkel
72	! Bugfix: Added working precision for if statement
73	!
74	! 4054 2019-06-27 07:42:18Z raasch
75	! bugfix for calculating the minimum particle time step
76	!
77	! 4044 2019-06-19 12:28:27Z schwenkel
78	! Bugfix in case of grid strecting: corrected calculation of k-Index
79	!
80	! 4043 2019-06-18 16:59:00Z schwenkel
81	! Remove min_nr_particle, Add lpm_droplet_interactions_ptq into module
82	!
83	! 4028 2019-06-13 12:21:37Z schwenkel
84	! Further modularization of particle code components
85	!
86	! 4020 2019-06-06 14:57:48Z schwenkel
87	! Removing submodules
88	!
89	! 4018 2019-06-06 13:41:50Z eckhard
90	! Bugfix for former revision
91	!
92	! 4017 2019-06-06 12:16:46Z schwenkel
93	! Modularization of all lagrangian particle model code components
94	!
95	! 3655 2019-01-07 16:51:22Z knoop
96	! bugfix to guarantee correct particle releases in case that the release
97	! interval is smaller than the model timestep
98	!
99	! Revision 1.1 1999/11/25 16:16:06 raasch
100	! Initial revision
101	!
102	!
103	! Description:
104	! ------------
105	!> The embedded LPM allows for studying transport and dispersion processes within
106	!> turbulent flows. This model including passive particles that do not show any
107	!> feedback on the turbulent flow. Further also particles with inertia and
108	!> cloud droplets ca be simulated explicitly.
109	!>
110	!> @todo test lcm
111	!> implement simple interpolation method for subgrid scale velocites
112	!> @note <Enter notes on the module>
113	!> @bug <Enter bug on the module>
114	!------------------------------------------------------------------------------!
115	MODULE lagrangian_particle_model_mod
116
117	USE, INTRINSIC :: ISO_C_BINDING
118
119	USE arrays_3d, &
120	ONLY: de_dx, de_dy, de_dz, dzw, zu, zw, ql_c, ql_v, ql_vp, hyp, &
121	pt, q, exner, ql, diss, e, u, v, w, km, ql_1, ql_2, pt_p, q_p, &
122	d_exner
123
124	USE averaging, &
125	ONLY: ql_c_av, pr_av, pc_av, ql_vp_av, ql_v_av
126
127	USE basic_constants_and_equations_mod, &
128	ONLY: molecular_weight_of_solute, molecular_weight_of_water, magnus, &
129	pi, rd_d_rv, rho_l, r_v, rho_s, vanthoff, l_v, kappa, g, lv_d_cp
130
131	USE control_parameters, &
132	ONLY: bc_dirichlet_l, bc_dirichlet_n, bc_dirichlet_r, bc_dirichlet_s, &
133	cloud_droplets, constant_flux_layer, current_timestep_number, &
134	dt_3d, dt_3d_reached, first_call_lpm, humidity, &
135	dt_3d_reached_l, dt_dopts, dz, initializing_actions, &
136	intermediate_timestep_count, intermediate_timestep_count_max, &
137	message_string, molecular_viscosity, ocean_mode, &
138	particle_maximum_age, iran, &
139	simulated_time, topography, dopts_time_count, &
140	time_since_reference_point, rho_surface, u_gtrans, v_gtrans, &
141	dz_stretch_level, dz_stretch_level_start
142
143	USE cpulog, &
144	ONLY: cpu_log, log_point, log_point_s
145
146	USE indices, &
147	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
148	nzb_max, nzt,nbgp, ngp_2dh_outer, &
149	topo_top_ind, &
150	wall_flags_static_0
151
152	USE kinds
153
154	USE pegrid
155
156	USE particle_attributes
157
158	USE pmc_particle_interface, &
159	ONLY: pmcp_c_get_particle_from_parent, pmcp_p_fill_particle_win, &
160	pmcp_c_send_particle_to_parent, pmcp_p_empty_particle_win, &
161	pmcp_p_delete_particles_in_fine_grid_area, pmcp_g_init, &
162	pmcp_g_print_number_of_particles
163
164	USE pmc_interface, &
165	ONLY: nested_run
166
167	USE grid_variables, &
168	ONLY: ddx, dx, ddy, dy
169
170	USE netcdf_interface, &
171	ONLY: netcdf_data_format, netcdf_deflate, dopts_num, id_set_pts, &
172	id_var_dopts, id_var_time_pts, nc_stat, &
173	netcdf_handle_error
174
175	USE random_function_mod, &
176	ONLY: random_function
177
178	USE statistics, &
179	ONLY: hom
180
181	USE surface_mod, &
182	ONLY: bc_h, &
183	surf_def_h, &
184	surf_lsm_h, &
185	surf_usm_h
186
187	#if defined( __parallel ) && !defined( __mpifh )
188	USE MPI
189	#endif
190
191	#if defined( __netcdf )
192	USE NETCDF
193	#endif
194
195	IMPLICIT NONE
196
197	CHARACTER(LEN=15) :: aero_species = 'nacl' !< aerosol species
198	CHARACTER(LEN=15) :: aero_type = 'maritime' !< aerosol type
199	CHARACTER(LEN=15) :: bc_par_lr = 'cyclic' !< left/right boundary condition
200	CHARACTER(LEN=15) :: bc_par_ns = 'cyclic' !< north/south boundary condition
201	CHARACTER(LEN=15) :: bc_par_b = 'reflect' !< bottom boundary condition
202	CHARACTER(LEN=15) :: bc_par_t = 'absorb' !< top boundary condition
203	CHARACTER(LEN=15) :: collision_kernel = 'none' !< collision kernel
204
205	CHARACTER(LEN=5) :: splitting_function = 'gamma' !< function for calculation critical weighting factor
206	CHARACTER(LEN=5) :: splitting_mode = 'const' !< splitting mode
207
208	CHARACTER(LEN=25) :: particle_advection_interpolation = 'trilinear' !< interpolation method for calculatin the particle
209
210	INTEGER(iwp) :: deleted_particles = 0 !< number of deleted particles per time step
211	INTEGER(iwp) :: i_splitting_mode !< dummy for splitting mode
212	INTEGER(iwp) :: iran_part = -1234567 !< number for random generator
213	INTEGER(iwp) :: max_number_particles_per_gridbox = 100 !< namelist parameter (see documentation)
214	INTEGER(iwp) :: isf !< dummy for splitting function
215	INTEGER(iwp) :: number_particles_per_gridbox = -1 !< namelist parameter (see documentation)
216	INTEGER(iwp) :: number_of_sublayers = 20 !< number of sublayers for particle velocities betwenn surface and first grid level
217	INTEGER(iwp) :: offset_ocean_nzt = 0 !< in case of oceans runs, the vertical index calculations need an offset
218	INTEGER(iwp) :: offset_ocean_nzt_m1 = 0 !< in case of oceans runs, the vertical index calculations need an offset
219	INTEGER(iwp) :: particles_per_point = 1 !< namelist parameter (see documentation)
220	INTEGER(iwp) :: radius_classes = 20 !< namelist parameter (see documentation)
221	INTEGER(iwp) :: splitting_factor = 2 !< namelist parameter (see documentation)
222	INTEGER(iwp) :: splitting_factor_max = 5 !< namelist parameter (see documentation)
223	INTEGER(iwp) :: step_dealloc = 100 !< namelist parameter (see documentation)
224	INTEGER(iwp) :: total_number_of_particles !< total number of particles in the whole model domain
225	INTEGER(iwp) :: trlp_count_sum !< parameter for particle exchange of PEs
226	INTEGER(iwp) :: trlp_count_recv_sum !< parameter for particle exchange of PEs
227	INTEGER(iwp) :: trrp_count_sum !< parameter for particle exchange of PEs
228	INTEGER(iwp) :: trrp_count_recv_sum !< parameter for particle exchange of PEs
229	INTEGER(iwp) :: trsp_count_sum !< parameter for particle exchange of PEs
230	INTEGER(iwp) :: trsp_count_recv_sum !< parameter for particle exchange of PEs
231	INTEGER(iwp) :: trnp_count_sum !< parameter for particle exchange of PEs
232	INTEGER(iwp) :: trnp_count_recv_sum !< parameter for particle exchange of PEs
233
234	LOGICAL :: lagrangian_particle_model = .FALSE. !< namelist parameter (see documentation)
235	LOGICAL :: curvature_solution_effects = .FALSE. !< namelist parameter (see documentation)
236	LOGICAL :: deallocate_memory = .TRUE. !< namelist parameter (see documentation)
237	LOGICAL :: hall_kernel = .FALSE. !< flag for collision kernel
238	LOGICAL :: merging = .FALSE. !< namelist parameter (see documentation)
239	LOGICAL :: random_start_position = .FALSE. !< namelist parameter (see documentation)
240	LOGICAL :: read_particles_from_restartfile = .TRUE. !< namelist parameter (see documentation)
241	LOGICAL :: seed_follows_topography = .FALSE. !< namelist parameter (see documentation)
242	LOGICAL :: splitting = .FALSE. !< namelist parameter (see documentation)
243	LOGICAL :: use_kernel_tables = .FALSE. !< parameter, which turns on the use of precalculated collision kernels
244	LOGICAL :: write_particle_statistics = .FALSE. !< namelist parameter (see documentation)
245	LOGICAL :: interpolation_simple_predictor = .FALSE. !< flag for simple particle advection interpolation with predictor step
246	LOGICAL :: interpolation_simple_corrector = .FALSE. !< flag for simple particle advection interpolation with corrector step
247	LOGICAL :: interpolation_trilinear = .FALSE. !< flag for trilinear particle advection interpolation
248
249	LOGICAL, DIMENSION(max_number_of_particle_groups) :: vertical_particle_advection = .TRUE. !< Switch for vertical particle transport
250
251	REAL(wp) :: aero_weight = 1.0_wp !< namelist parameter (see documentation)
252	REAL(wp) :: dt_min_part = 0.0002_wp !< minimum particle time step when SGS velocities are used (s)
253	REAL(wp) :: dt_prel = 9999999.9_wp !< namelist parameter (see documentation)
254	REAL(wp) :: dt_write_particle_data = 9999999.9_wp !< namelist parameter (see documentation)
255	REAL(wp) :: end_time_prel = 9999999.9_wp !< namelist parameter (see documentation)
256	REAL(wp) :: initial_weighting_factor = 1.0_wp !< namelist parameter (see documentation)
257	REAL(wp) :: last_particle_release_time = 0.0_wp !< last time of particle release
258	REAL(wp) :: log_sigma(3) = 1.0_wp !< namelist parameter (see documentation)
259	REAL(wp) :: na(3) = 0.0_wp !< namelist parameter (see documentation)
260	REAL(wp) :: number_concentration = -1.0_wp !< namelist parameter (see documentation)
261	REAL(wp) :: radius_merge = 1.0E-7_wp !< namelist parameter (see documentation)
262	REAL(wp) :: radius_split = 40.0E-6_wp !< namelist parameter (see documentation)
263	REAL(wp) :: rm(3) = 1.0E-6_wp !< namelist parameter (see documentation)
264	REAL(wp) :: sgs_wf_part !< parameter for sgs
265	REAL(wp) :: time_write_particle_data = 0.0_wp !< write particle data at current time on file
266	REAL(wp) :: weight_factor_merge = -1.0_wp !< namelist parameter (see documentation)
267	REAL(wp) :: weight_factor_split = -1.0_wp !< namelist parameter (see documentation)
268	REAL(wp) :: z0_av_global !< horizontal mean value of z0
269
270	REAL(wp) :: rclass_lbound !<
271	REAL(wp) :: rclass_ubound !<
272
273	REAL(wp), PARAMETER :: c_0 = 3.0_wp !< parameter for lagrangian timescale
274
275	REAL(wp), DIMENSION(max_number_of_particle_groups) :: density_ratio = 9999999.9_wp !< namelist parameter (see documentation)
276	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdx = 9999999.9_wp !< namelist parameter (see documentation)
277	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdy = 9999999.9_wp !< namelist parameter (see documentation)
278	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdz = 9999999.9_wp !< namelist parameter (see documentation)
279	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psb = 9999999.9_wp !< namelist parameter (see documentation)
280	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psl = 9999999.9_wp !< namelist parameter (see documentation)
281	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psn = 9999999.9_wp !< namelist parameter (see documentation)
282	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psr = 9999999.9_wp !< namelist parameter (see documentation)
283	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pss = 9999999.9_wp !< namelist parameter (see documentation)
284	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pst = 9999999.9_wp !< namelist parameter (see documentation).
285	REAL(wp), DIMENSION(max_number_of_particle_groups) :: radius = 9999999.9_wp !< namelist parameter (see documentation)
286
287	REAL(wp), DIMENSION(:), ALLOCATABLE :: log_z_z0 !< Precalculate LOG(z/z0)
288
289	INTEGER(iwp), PARAMETER :: NR_2_direction_move = 10000 !<
290	INTEGER(iwp) :: nr_move_north !<
291	INTEGER(iwp) :: nr_move_south !<
292
293	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_north
294	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_south
295
296	REAL(wp) :: epsilon_collision !<
297	REAL(wp) :: urms !<
298
299	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
300	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
301	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
302
303	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
304	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
305	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
306	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
307	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
308
309	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
310	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: u_t !< u value of old timelevel t
311	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: v_t !< v value of old timelevel t
312	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: w_t !< w value of old timelevel t
313
314
315	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
316	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
317
318	SAVE
319
320	PRIVATE
321
322	PUBLIC lpm_parin, &
323	lpm_header, &
324	lpm_init_arrays,&
325	lpm_init, &
326	lpm_actions, &
327	lpm_data_output_ptseries, &
328	lpm_interaction_droplets_ptq, &
329	lpm_rrd_local_particles, &
330	lpm_wrd_local, &
331	lpm_rrd_global, &
332	lpm_wrd_global, &
333	lpm_rrd_local, &
334	lpm_check_parameters
335
336	PUBLIC lagrangian_particle_model
337
338	INTERFACE lpm_check_parameters
339	MODULE PROCEDURE lpm_check_parameters
340	END INTERFACE lpm_check_parameters
341
342	INTERFACE lpm_parin
343	MODULE PROCEDURE lpm_parin
344	END INTERFACE lpm_parin
345
346	INTERFACE lpm_header
347	MODULE PROCEDURE lpm_header
348	END INTERFACE lpm_header
349
350	INTERFACE lpm_init_arrays
351	MODULE PROCEDURE lpm_init_arrays
352	END INTERFACE lpm_init_arrays
353
354	INTERFACE lpm_init
355	MODULE PROCEDURE lpm_init
356	END INTERFACE lpm_init
357
358	INTERFACE lpm_actions
359	MODULE PROCEDURE lpm_actions
360	END INTERFACE lpm_actions
361
362	INTERFACE lpm_data_output_ptseries
363	MODULE PROCEDURE lpm_data_output_ptseries
364	END INTERFACE
365
366	INTERFACE lpm_rrd_local_particles
367	MODULE PROCEDURE lpm_rrd_local_particles
368	END INTERFACE lpm_rrd_local_particles
369
370	INTERFACE lpm_rrd_global
371	MODULE PROCEDURE lpm_rrd_global
372	END INTERFACE lpm_rrd_global
373
374	INTERFACE lpm_rrd_local
375	MODULE PROCEDURE lpm_rrd_local
376	END INTERFACE lpm_rrd_local
377
378	INTERFACE lpm_wrd_local
379	MODULE PROCEDURE lpm_wrd_local
380	END INTERFACE lpm_wrd_local
381
382	INTERFACE lpm_wrd_global
383	MODULE PROCEDURE lpm_wrd_global
384	END INTERFACE lpm_wrd_global
385
386	INTERFACE lpm_advec
387	MODULE PROCEDURE lpm_advec
388	END INTERFACE lpm_advec
389
390	INTERFACE lpm_calc_liquid_water_content
391	MODULE PROCEDURE lpm_calc_liquid_water_content
392	END INTERFACE
393
394	INTERFACE lpm_interaction_droplets_ptq
395	MODULE PROCEDURE lpm_interaction_droplets_ptq
396	MODULE PROCEDURE lpm_interaction_droplets_ptq_ij
397	END INTERFACE lpm_interaction_droplets_ptq
398
399	INTERFACE lpm_boundary_conds
400	MODULE PROCEDURE lpm_boundary_conds
401	END INTERFACE lpm_boundary_conds
402
403	INTERFACE lpm_droplet_condensation
404	MODULE PROCEDURE lpm_droplet_condensation
405	END INTERFACE
406
407	INTERFACE lpm_droplet_collision
408	MODULE PROCEDURE lpm_droplet_collision
409	END INTERFACE lpm_droplet_collision
410
411	INTERFACE lpm_init_kernels
412	MODULE PROCEDURE lpm_init_kernels
413	END INTERFACE lpm_init_kernels
414
415	INTERFACE lpm_splitting
416	MODULE PROCEDURE lpm_splitting
417	END INTERFACE lpm_splitting
418
419	INTERFACE lpm_merging
420	MODULE PROCEDURE lpm_merging
421	END INTERFACE lpm_merging
422
423	INTERFACE lpm_exchange_horiz
424	MODULE PROCEDURE lpm_exchange_horiz
425	END INTERFACE lpm_exchange_horiz
426
427	INTERFACE lpm_move_particle
428	MODULE PROCEDURE lpm_move_particle
429	END INTERFACE lpm_move_particle
430
431	INTERFACE realloc_particles_array
432	MODULE PROCEDURE realloc_particles_array
433	END INTERFACE realloc_particles_array
434
435	INTERFACE dealloc_particles_array
436	MODULE PROCEDURE dealloc_particles_array
437	END INTERFACE dealloc_particles_array
438
439	INTERFACE lpm_sort_and_delete
440	MODULE PROCEDURE lpm_sort_and_delete
441	END INTERFACE lpm_sort_and_delete
442
443	INTERFACE lpm_sort_timeloop_done
444	MODULE PROCEDURE lpm_sort_timeloop_done
445	END INTERFACE lpm_sort_timeloop_done
446
447	INTERFACE lpm_pack
448	MODULE PROCEDURE lpm_pack
449	END INTERFACE lpm_pack
450
451	CONTAINS
452
453
454	!------------------------------------------------------------------------------!
455	! Description:
456	! ------------
457	!> Parin for &particle_parameters for the Lagrangian particle model
458	!------------------------------------------------------------------------------!
459	SUBROUTINE lpm_parin
460
461	CHARACTER (LEN=80) :: line !<
462
463	NAMELIST /particles_par/ &
464	aero_species, &
465	aero_type, &
466	aero_weight, &
467	alloc_factor, &
468	bc_par_b, &
469	bc_par_lr, &
470	bc_par_ns, &
471	bc_par_t, &
472	collision_kernel, &
473	curvature_solution_effects, &
474	deallocate_memory, &
475	density_ratio, &
476	dissipation_classes, &
477	dt_dopts, &
478	dt_min_part, &
479	dt_prel, &
480	dt_write_particle_data, &
481	end_time_prel, &
482	initial_weighting_factor, &
483	log_sigma, &
484	max_number_particles_per_gridbox, &
485	merging, &
486	na, &
487	number_concentration, &
488	number_of_particle_groups, &
489	number_particles_per_gridbox, &
490	particles_per_point, &
491	particle_advection_start, &
492	particle_advection_interpolation, &
493	particle_maximum_age, &
494	pdx, &
495	pdy, &
496	pdz, &
497	psb, &
498	psl, &
499	psn, &
500	psr, &
501	pss, &
502	pst, &
503	radius, &
504	radius_classes, &
505	radius_merge, &
506	radius_split, &
507	random_start_position, &
508	read_particles_from_restartfile, &
509	rm, &
510	seed_follows_topography, &
511	splitting, &
512	splitting_factor, &
513	splitting_factor_max, &
514	splitting_function, &
515	splitting_mode, &
516	step_dealloc, &
517	use_sgs_for_particles, &
518	vertical_particle_advection, &
519	weight_factor_merge, &
520	weight_factor_split, &
521	write_particle_statistics
522
523	NAMELIST /particle_parameters/ &
524	aero_species, &
525	aero_type, &
526	aero_weight, &
527	alloc_factor, &
528	bc_par_b, &
529	bc_par_lr, &
530	bc_par_ns, &
531	bc_par_t, &
532	collision_kernel, &
533	curvature_solution_effects, &
534	deallocate_memory, &
535	density_ratio, &
536	dissipation_classes, &
537	dt_dopts, &
538	dt_min_part, &
539	dt_prel, &
540	dt_write_particle_data, &
541	end_time_prel, &
542	initial_weighting_factor, &
543	log_sigma, &
544	max_number_particles_per_gridbox, &
545	merging, &
546	na, &
547	number_concentration, &
548	number_of_particle_groups, &
549	number_particles_per_gridbox, &
550	particles_per_point, &
551	particle_advection_start, &
552	particle_advection_interpolation, &
553	particle_maximum_age, &
554	pdx, &
555	pdy, &
556	pdz, &
557	psb, &
558	psl, &
559	psn, &
560	psr, &
561	pss, &
562	pst, &
563	radius, &
564	radius_classes, &
565	radius_merge, &
566	radius_split, &
567	random_start_position, &
568	read_particles_from_restartfile, &
569	rm, &
570	seed_follows_topography, &
571	splitting, &
572	splitting_factor, &
573	splitting_factor_max, &
574	splitting_function, &
575	splitting_mode, &
576	step_dealloc, &
577	use_sgs_for_particles, &
578	vertical_particle_advection, &
579	weight_factor_merge, &
580	weight_factor_split, &
581	write_particle_statistics
582
583	!
584	!-- Position the namelist-file at the beginning (it was already opened in
585	!-- parin), search for the namelist-group of the package and position the
586	!-- file at this line. Do the same for each optionally used package.
587	line = ' '
588
589	!
590	!-- Try to find particles package
591	REWIND ( 11 )
592	line = ' '
593	DO WHILE ( INDEX( line, '&particle_parameters' ) == 0 )
594	READ ( 11, '(A)', END=12 ) line
595	ENDDO
596	BACKSPACE ( 11 )
597	!
598	!-- Read user-defined namelist
599	READ ( 11, particle_parameters, ERR = 10 )
600	!
601	!-- Set flag that indicates that particles are switched on
602	particle_advection = .TRUE.
603
604	GOTO 14
605
606	10 BACKSPACE( 11 )
607	READ( 11 , '(A)') line
608	CALL parin_fail_message( 'particle_parameters', line )
609	!
610	!-- Try to find particles package (old namelist)
611	12 REWIND ( 11 )
612	line = ' '
613	DO WHILE ( INDEX( line, '&particles_par' ) == 0 )
614	READ ( 11, '(A)', END=14 ) line
615	ENDDO
616	BACKSPACE ( 11 )
617	!
618	!-- Read user-defined namelist
619	READ ( 11, particles_par, ERR = 13, END = 14 )
620
621	message_string = 'namelist particles_par is deprecated and will be ' // &
622	'removed in near future. Please use namelist ' // &
623	'particle_parameters instead'
624	CALL message( 'package_parin', 'PA0487', 0, 1, 0, 6, 0 )
625
626	!
627	!-- Set flag that indicates that particles are switched on
628	particle_advection = .TRUE.
629
630	GOTO 14
631
632	13 BACKSPACE( 11 )
633	READ( 11 , '(A)') line
634	CALL parin_fail_message( 'particles_par', line )
635
636	14 CONTINUE
637
638	END SUBROUTINE lpm_parin
639
640	!------------------------------------------------------------------------------!
641	! Description:
642	! ------------
643	!> Writes used particle attributes in header file.
644	!------------------------------------------------------------------------------!
645	SUBROUTINE lpm_header ( io )
646
647	CHARACTER (LEN=40) :: output_format !< netcdf format
648
649	INTEGER(iwp) :: i !<
650	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
651
652
653	IF ( humidity .AND. cloud_droplets ) THEN
654	WRITE ( io, 433 )
655	IF ( curvature_solution_effects ) WRITE ( io, 434 )
656	IF ( collision_kernel /= 'none' ) THEN
657	WRITE ( io, 435 ) TRIM( collision_kernel )
658	IF ( collision_kernel(6:9) == 'fast' ) THEN
659	WRITE ( io, 436 ) radius_classes, dissipation_classes
660	ENDIF
661	ELSE
662	WRITE ( io, 437 )
663	ENDIF
664	ENDIF
665
666	IF ( particle_advection ) THEN
667	!
668	!-- Particle attributes
669	WRITE ( io, 480 ) particle_advection_start, TRIM(particle_advection_interpolation), &
670	dt_prel, bc_par_lr, &
671	bc_par_ns, bc_par_b, bc_par_t, particle_maximum_age, &
672	end_time_prel
673	IF ( use_sgs_for_particles ) WRITE ( io, 488 ) dt_min_part
674	IF ( random_start_position ) WRITE ( io, 481 )
675	IF ( seed_follows_topography ) WRITE ( io, 496 )
676	IF ( particles_per_point > 1 ) WRITE ( io, 489 ) particles_per_point
677	WRITE ( io, 495 ) total_number_of_particles
678	IF ( dt_write_particle_data /= 9999999.9_wp ) THEN
679	WRITE ( io, 485 ) dt_write_particle_data
680	IF ( netcdf_data_format > 1 ) THEN
681	output_format = 'netcdf (64 bit offset) and binary'
682	ELSE
683	output_format = 'netcdf and binary'
684	ENDIF
685	IF ( netcdf_deflate == 0 ) THEN
686	WRITE ( io, 344 ) output_format
687	ELSE
688	WRITE ( io, 354 ) TRIM( output_format ), netcdf_deflate
689	ENDIF
690	ENDIF
691	IF ( dt_dopts /= 9999999.9_wp ) WRITE ( io, 494 ) dt_dopts
692	IF ( write_particle_statistics ) WRITE ( io, 486 )
693
694	WRITE ( io, 487 ) number_of_particle_groups
695
696	DO i = 1, number_of_particle_groups
697	IF ( i == 1 .AND. density_ratio(i) == 9999999.9_wp ) THEN
698	WRITE ( io, 490 ) i, 0.0_wp
699	WRITE ( io, 492 )
700	ELSE
701	WRITE ( io, 490 ) i, radius(i)
702	IF ( density_ratio(i) /= 0.0_wp ) THEN
703	WRITE ( io, 491 ) density_ratio(i)
704	ELSE
705	WRITE ( io, 492 )
706	ENDIF
707	ENDIF
708	WRITE ( io, 493 ) psl(i), psr(i), pss(i), psn(i), psb(i), pst(i), &
709	pdx(i), pdy(i), pdz(i)
710	IF ( .NOT. vertical_particle_advection(i) ) WRITE ( io, 482 )
711	ENDDO
712
713	ENDIF
714
715	344 FORMAT (' Output format: ',A/)
716	354 FORMAT (' Output format: ',A, ' compressed with level: ',I1/)
717
718	433 FORMAT (' Cloud droplets treated explicitly using the Lagrangian part', &
719	'icle model')
720	434 FORMAT (' Curvature and solution effecs are considered for growth of', &
721	' droplets < 1.0E-6 m')
722	435 FORMAT (' Droplet collision is handled by ',A,'-kernel')
723	436 FORMAT (' Fast kernel with fixed radius- and dissipation classes ', &
724	'are used'/ &
725	' number of radius classes: ',I3,' interval ', &
726	'[1.0E-6,2.0E-4] m'/ &
727	' number of dissipation classes: ',I2,' interval ', &
728	'[0,1000] cm2/s3')
729	437 FORMAT (' Droplet collision is switched off')
730
731	480 FORMAT (' Particles:'/ &
732	' ---------'// &
733	' Particle advection is active (switched on at t = ', F7.1, &
734	' s)'/ &
735	' Interpolation of particle velocities is done by using ', A, &
736	' method'/ &
737	' Start of new particle generations every ',F6.1,' s'/ &
738	' Boundary conditions: left/right: ', A, ' north/south: ', A/&
739	' bottom: ', A, ' top: ', A/&
740	' Maximum particle age: ',F9.1,' s'/ &
741	' Advection stopped at t = ',F9.1,' s'/)
742	481 FORMAT (' Particles have random start positions'/)
743	482 FORMAT (' Particles are advected only horizontally'/)
744	485 FORMAT (' Particle data are written on file every ', F9.1, ' s')
745	486 FORMAT (' Particle statistics are written on file'/)
746	487 FORMAT (' Number of particle groups: ',I2/)
747	488 FORMAT (' SGS velocity components are used for particle advection'/ &
748	' minimum timestep for advection:', F8.5/)
749	489 FORMAT (' Number of particles simultaneously released at each ', &
750	'point: ', I5/)
751	490 FORMAT (' Particle group ',I2,':'/ &
752	' Particle radius: ',E10.3, 'm')
753	491 FORMAT (' Particle inertia is activated'/ &
754	' density_ratio (rho_fluid/rho_particle) =',F6.3/)
755	492 FORMAT (' Particles are advected only passively (no inertia)'/)
756	493 FORMAT (' Boundaries of particle source: x:',F8.1,' - ',F8.1,' m'/&
757	' y:',F8.1,' - ',F8.1,' m'/&
758	' z:',F8.1,' - ',F8.1,' m'/&
759	' Particle distances: dx = ',F8.1,' m dy = ',F8.1, &
760	' m dz = ',F8.1,' m'/)
761	494 FORMAT (' Output of particle time series in NetCDF format every ', &
762	F8.2,' s'/)
763	495 FORMAT (' Number of particles in total domain: ',I10/)
764	496 FORMAT (' Initial vertical particle positions are interpreted ', &
765	'as relative to the given topography')
766
767	END SUBROUTINE lpm_header
768
769	!------------------------------------------------------------------------------!
770	! Description:
771	! ------------
772	!> Writes used particle attributes in header file.
773	!------------------------------------------------------------------------------!
774	SUBROUTINE lpm_check_parameters
775
776	!
777	!-- Collision kernels:
778	SELECT CASE ( TRIM( collision_kernel ) )
779
780	CASE ( 'hall', 'hall_fast' )
781	hall_kernel = .TRUE.
782
783	CASE ( 'wang', 'wang_fast' )
784	wang_kernel = .TRUE.
785
786	CASE ( 'none' )
787
788
789	CASE DEFAULT
790	message_string = 'unknown collision kernel: collision_kernel = "' // &
791	TRIM( collision_kernel ) // '"'
792	CALL message( 'lpm_check_parameters', 'PA0350', 1, 2, 0, 6, 0 )
793
794	END SELECT
795	IF ( collision_kernel(6:9) == 'fast' ) use_kernel_tables = .TRUE.
796
797	!
798	!-- Subgrid scale velocites with the simple interpolation method for resolved
799	!-- velocites is not implemented for passive particles. However, for cloud
800	!-- it can be combined as the sgs-velocites for active particles are
801	!-- calculated differently, i.e. no subboxes are needed.
802	IF ( .NOT. TRIM( particle_advection_interpolation ) == 'trilinear' .AND. &
803	use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
804	message_string = 'subrgrid scale velocities in combination with ' // &
805	'simple interpolation method is not ' // &
806	'implemented'
807	CALL message( 'lpm_check_parameters', 'PA0659', 1, 2, 0, 6, 0 )
808	ENDIF
809
810	IF ( nested_run .AND. cloud_droplets ) THEN
811	message_string = 'nested runs in combination with cloud droplets ' // &
812	'is not implemented'
813	CALL message( 'lpm_check_parameters', 'PA0687', 1, 2, 0, 6, 0 )
814	ENDIF
815
816
817	END SUBROUTINE lpm_check_parameters
818
819	!------------------------------------------------------------------------------!
820	! Description:
821	! ------------
822	!> Initialize arrays for lpm
823	!------------------------------------------------------------------------------!
824	SUBROUTINE lpm_init_arrays
825
826	IF ( cloud_droplets ) THEN
827	!
828	!-- Liquid water content, change in liquid water content
829	ALLOCATE ( ql_1(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
830	ql_2(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
831	!
832	!-- Real volume of particles (with weighting), volume of particles
833	ALLOCATE ( ql_v(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
834	ql_vp(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
835	ENDIF
836
837
838	ALLOCATE( u_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
839	v_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
840	w_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
841	!
842	!-- Initialize values with current time step
843	u_t = u
844	v_t = v
845	w_t = w
846	!
847	!-- Initial assignment of the pointers
848	IF ( cloud_droplets ) THEN
849	ql => ql_1
850	ql_c => ql_2
851	ENDIF
852
853	END SUBROUTINE lpm_init_arrays
854
855	!------------------------------------------------------------------------------!
856	! Description:
857	! ------------
858	!> Initialize Lagrangian particle model
859	!------------------------------------------------------------------------------!
860	SUBROUTINE lpm_init
861
862	INTEGER(iwp) :: i !<
863	INTEGER(iwp) :: j !<
864	INTEGER(iwp) :: k !<
865
866	REAL(wp) :: div !<
867	REAL(wp) :: height_int !<
868	REAL(wp) :: height_p !<
869	REAL(wp) :: z_p !<
870	REAL(wp) :: z0_av_local !<
871
872	!
873	!-- In case of oceans runs, the vertical index calculations need an offset,
874	!-- because otherwise the k indices will become negative
875	IF ( ocean_mode ) THEN
876	offset_ocean_nzt = nzt
877	offset_ocean_nzt_m1 = nzt - 1
878	ENDIF
879
880	!
881	!-- Define block offsets for dividing a gridcell in 8 sub cells
882	!-- See documentation for List of subgrid boxes
883	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
884	block_offset(0) = block_offset_def ( 0, 0, 0)
885	block_offset(1) = block_offset_def ( 0, 0,-1)
886	block_offset(2) = block_offset_def ( 0,-1, 0)
887	block_offset(3) = block_offset_def ( 0,-1,-1)
888	block_offset(4) = block_offset_def (-1, 0, 0)
889	block_offset(5) = block_offset_def (-1, 0,-1)
890	block_offset(6) = block_offset_def (-1,-1, 0)
891	block_offset(7) = block_offset_def (-1,-1,-1)
892	!
893	!-- Check the number of particle groups.
894	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
895	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
896	max_number_of_particle_groups , &
897	'&number_of_particle_groups reset to ', &
898	max_number_of_particle_groups
899	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
900	number_of_particle_groups = max_number_of_particle_groups
901	ENDIF
902	!
903	!-- Check if downward-facing walls exist. This case, reflection boundary
904	!-- conditions (as well as subgrid-scale velocities) may do not work
905	!-- propably (not realized so far).
906	IF ( surf_def_h(1)%ns >= 1 ) THEN
907	WRITE( message_string, * ) 'Overhanging topography do not work '// &
908	'with particles'
909	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
910
911	ENDIF
912
913	!
914	!-- Set default start positions, if necessary
915	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
916	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
917	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
918	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
919	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
920	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
921
922	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
923	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
924	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
925
926	!
927	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
928	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
929	IF ( number_particles_per_gridbox /= -1 .AND. &
930	number_particles_per_gridbox >= 1 ) THEN
931	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
932	REAL(number_particles_per_gridbox))**0.3333333_wp
933	!
934	!-- Ensure a smooth value (two significant digits) of distance between
935	!-- particles (pdx, pdy, pdz).
936	div = 1000.0_wp
937	DO WHILE ( pdx(1) < div )
938	div = div / 10.0_wp
939	ENDDO
940	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
941	pdy(1) = pdx(1)
942	pdz(1) = pdx(1)
943
944	ENDIF
945
946	DO j = 2, number_of_particle_groups
947	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
948	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
949	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
950	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
951	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
952	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
953	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
954	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
955	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
956	ENDDO
957
958	!
959	!-- Allocate arrays required for calculating particle SGS velocities.
960	!-- Initialize prefactor required for stoachastic Weil equation.
961	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
962	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
963	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
964	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
965
966	de_dx = 0.0_wp
967	de_dy = 0.0_wp
968	de_dz = 0.0_wp
969
970	sgs_wf_part = 1.0_wp / 3.0_wp
971	ENDIF
972
973	!
974	!-- Allocate array required for logarithmic vertical interpolation of
975	!-- horizontal particle velocities between the surface and the first vertical
976	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
977	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
978	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
979	!-- To obtain exact height levels of particles, linear interpolation is applied
980	!-- (see lpm_advec.f90).
981	IF ( constant_flux_layer ) THEN
982
983	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
984	z_p = zu(nzb+1) - zw(nzb)
985
986	!
987	!-- Calculate horizontal mean value of z0 used for logartihmic
988	!-- interpolation. Note: this is not exact for heterogeneous z0.
989	!-- However, sensitivity studies showed that the effect is
990	!-- negligible.
991	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
992	SUM( surf_usm_h%z0 )
993	z0_av_global = 0.0_wp
994
995	#if defined( __parallel )
996	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
997	comm2d, ierr )
998	#else
999	z0_av_global = z0_av_local
1000	#endif
1001
1002	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
1003	!
1004	!-- Horizontal wind speed is zero below and at z0
1005	log_z_z0(0) = 0.0_wp
1006	!
1007	!-- Calculate vertical depth of the sublayers
1008	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
1009	!
1010	!-- Precalculate LOG(z/z0)
1011	height_p = z0_av_global
1012	DO k = 1, number_of_sublayers
1013
1014	height_p = height_p + height_int
1015	log_z_z0(k) = LOG( height_p / z0_av_global )
1016
1017	ENDDO
1018
1019	ENDIF
1020
1021	!
1022	!-- Check which particle interpolation method should be used
1023	IF ( TRIM( particle_advection_interpolation ) == 'trilinear' ) THEN
1024	interpolation_simple_corrector = .FALSE.
1025	interpolation_simple_predictor = .FALSE.
1026	interpolation_trilinear = .TRUE.
1027	ELSEIF ( TRIM( particle_advection_interpolation ) == 'simple_corrector' ) THEN
1028	interpolation_simple_corrector = .TRUE.
1029	interpolation_simple_predictor = .FALSE.
1030	interpolation_trilinear = .FALSE.
1031	ELSEIF ( TRIM( particle_advection_interpolation ) == 'simple_predictor' ) THEN
1032	interpolation_simple_corrector = .FALSE.
1033	interpolation_simple_predictor = .TRUE.
1034	interpolation_trilinear = .FALSE.
1035	ENDIF
1036
1037	!
1038	!-- Check boundary condition and set internal variables
1039	SELECT CASE ( bc_par_b )
1040
1041	CASE ( 'absorb' )
1042	ibc_par_b = 1
1043
1044	CASE ( 'reflect' )
1045	ibc_par_b = 2
1046
1047	CASE ( 'reset' )
1048	ibc_par_b = 3
1049
1050	CASE DEFAULT
1051	WRITE( message_string, * ) 'unknown boundary condition ', &
1052	'bc_par_b = "', TRIM( bc_par_b ), '"'
1053	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
1054
1055	END SELECT
1056	SELECT CASE ( bc_par_t )
1057
1058	CASE ( 'absorb' )
1059	ibc_par_t = 1
1060
1061	CASE ( 'reflect' )
1062	ibc_par_t = 2
1063
1064	CASE ( 'nested' )
1065	ibc_par_t = 3
1066
1067	CASE DEFAULT
1068	WRITE( message_string, * ) 'unknown boundary condition ', &
1069	'bc_par_t = "', TRIM( bc_par_t ), '"'
1070	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
1071
1072	END SELECT
1073	SELECT CASE ( bc_par_lr )
1074
1075	CASE ( 'cyclic' )
1076	ibc_par_lr = 0
1077
1078	CASE ( 'absorb' )
1079	ibc_par_lr = 1
1080
1081	CASE ( 'reflect' )
1082	ibc_par_lr = 2
1083
1084	CASE ( 'nested' )
1085	ibc_par_lr = 3
1086
1087	CASE DEFAULT
1088	WRITE( message_string, * ) 'unknown boundary condition ', &
1089	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
1090	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
1091
1092	END SELECT
1093	SELECT CASE ( bc_par_ns )
1094
1095	CASE ( 'cyclic' )
1096	ibc_par_ns = 0
1097
1098	CASE ( 'absorb' )
1099	ibc_par_ns = 1
1100
1101	CASE ( 'reflect' )
1102	ibc_par_ns = 2
1103
1104	CASE ( 'nested' )
1105	ibc_par_ns = 3
1106
1107	CASE DEFAULT
1108	WRITE( message_string, * ) 'unknown boundary condition ', &
1109	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
1110	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
1111
1112	END SELECT
1113	SELECT CASE ( splitting_mode )
1114
1115	CASE ( 'const' )
1116	i_splitting_mode = 1
1117
1118	CASE ( 'cl_av' )
1119	i_splitting_mode = 2
1120
1121	CASE ( 'gb_av' )
1122	i_splitting_mode = 3
1123
1124	CASE DEFAULT
1125	WRITE( message_string, * ) 'unknown splitting_mode = "', &
1126	TRIM( splitting_mode ), '"'
1127	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
1128
1129	END SELECT
1130	SELECT CASE ( splitting_function )
1131
1132	CASE ( 'gamma' )
1133	isf = 1
1134
1135	CASE ( 'log' )
1136	isf = 2
1137
1138	CASE ( 'exp' )
1139	isf = 3
1140
1141	CASE DEFAULT
1142	WRITE( message_string, * ) 'unknown splitting function = "', &
1143	TRIM( splitting_function ), '"'
1144	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
1145
1146	END SELECT
1147	!
1148	!-- Initialize collision kernels
1149	IF ( collision_kernel /= 'none' ) CALL lpm_init_kernels
1150	!
1151	!-- For the first model run of a possible job chain initialize the
1152	!-- particles, otherwise read the particle data from restart file.
1153	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
1154	.AND. read_particles_from_restartfile ) THEN
1155	CALL lpm_rrd_local_particles
1156	ELSE
1157	!
1158	!-- Allocate particle arrays and set attributes of the initial set of
1159	!-- particles, which can be also periodically released at later times.
1160	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1161	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
1162
1163	number_of_particles = 0
1164	prt_count = 0
1165	!
1166	!-- initialize counter for particle IDs
1167	grid_particles%id_counter = 1
1168	!
1169	!-- Initialize all particles with dummy values (otherwise errors may
1170	!-- occur within restart runs). The reason for this is still not clear
1171	!-- and may be presumably caused by errors in the respective user-interface.
1172	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1173	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1174	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1175	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1176	0, 0, 0_idp, .FALSE., -1 )
1177
1178	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
1179	!
1180	!-- Set values for the density ratio and radius for all particle
1181	!-- groups, if necessary
1182	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
1183	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
1184	DO i = 2, number_of_particle_groups
1185	IF ( density_ratio(i) == 9999999.9_wp ) THEN
1186	density_ratio(i) = density_ratio(i-1)
1187	ENDIF
1188	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
1189	ENDDO
1190
1191	DO i = 1, number_of_particle_groups
1192	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
1193	WRITE( message_string, * ) 'particle group #', i, ' has a', &
1194	'density ratio /= 0 but radius = 0'
1195	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
1196	ENDIF
1197	particle_groups(i)%density_ratio = density_ratio(i)
1198	particle_groups(i)%radius = radius(i)
1199	ENDDO
1200	!
1201	!-- Set a seed value for the random number generator to be exclusively
1202	!-- used for the particle code. The generated random numbers should be
1203	!-- different on the different PEs.
1204	iran_part = iran_part + myid
1205	!
1206	!-- Create the particle set, and set the initial particles
1207	CALL lpm_create_particle( phase_init )
1208	last_particle_release_time = particle_advection_start
1209	!
1210	!-- User modification of initial particles
1211	CALL user_lpm_init
1212	!
1213	!-- Open file for statistical informations about particle conditions
1214	IF ( write_particle_statistics ) THEN
1215	CALL check_open( 80 )
1216	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
1217	number_of_particles
1218	CALL close_file( 80 )
1219	ENDIF
1220
1221	ENDIF
1222
1223	IF ( nested_run ) CALL pmcp_g_init
1224	!
1225	!-- To avoid programm abort, assign particles array to the local version of
1226	!-- first grid cell
1227	number_of_particles = prt_count(nzb+1,nys,nxl)
1228	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
1229	!
1230	!-- Formats
1231	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
1232
1233	END SUBROUTINE lpm_init
1234
1235	!------------------------------------------------------------------------------!
1236	! Description:
1237	! ------------
1238	!> Create Lagrangian particles
1239	!------------------------------------------------------------------------------!
1240	SUBROUTINE lpm_create_particle (phase)
1241
1242	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
1243	INTEGER(iwp) :: i !< loop variable ( particle groups )
1244	INTEGER(iwp) :: ip !< index variable along x
1245	INTEGER(iwp) :: j !< loop variable ( particles per point )
1246	INTEGER(iwp) :: jp !< index variable along y
1247	INTEGER(iwp) :: k !< index variable along z
1248	INTEGER(iwp) :: k_surf !< index of surface grid point
1249	INTEGER(iwp) :: kp !< index variable along z
1250	INTEGER(iwp) :: loop_stride !< loop variable for initialization
1251	INTEGER(iwp) :: n !< loop variable ( number of particles )
1252	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
1253
1254	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
1255
1256	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
1257	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
1258
1259	LOGICAL :: first_stride !< flag for initialization
1260
1261	REAL(wp) :: pos_x !< increment for particle position in x
1262	REAL(wp) :: pos_y !< increment for particle position in y
1263	REAL(wp) :: pos_z !< increment for particle position in z
1264	REAL(wp) :: rand_contr !< dummy argument for random position
1265
1266	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
1267
1268
1269	!
1270	!-- Calculate particle positions and store particle attributes, if
1271	!-- particle is situated on this PE
1272	DO loop_stride = 1, 2
1273	first_stride = (loop_stride == 1)
1274	IF ( first_stride ) THEN
1275	local_count = 0 ! count number of particles
1276	ELSE
1277	local_count = prt_count ! Start address of new particles
1278	ENDIF
1279
1280	!
1281	!-- Calculate initial_weighting_factor diagnostically
1282	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
1283	initial_weighting_factor = number_concentration * &
1284	pdx(1) * pdy(1) * pdz(1)
1285	END IF
1286
1287	n = 0
1288	DO i = 1, number_of_particle_groups
1289	pos_z = psb(i)
1290	DO WHILE ( pos_z <= pst(i) )
1291	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
1292	pos_y = pss(i)
1293	DO WHILE ( pos_y <= psn(i) )
1294	IF ( pos_y >= nys * dy .AND. &
1295	pos_y < ( nyn + 1 ) * dy ) THEN
1296	pos_x = psl(i)
1297	xloop: DO WHILE ( pos_x <= psr(i) )
1298	IF ( pos_x >= nxl * dx .AND. &
1299	pos_x < ( nxr + 1) * dx ) THEN
1300	DO j = 1, particles_per_point
1301	n = n + 1
1302	tmp_particle%x = pos_x
1303	tmp_particle%y = pos_y
1304	tmp_particle%z = pos_z
1305	tmp_particle%age = 0.0_wp
1306	tmp_particle%age_m = 0.0_wp
1307	tmp_particle%dt_sum = 0.0_wp
1308	tmp_particle%e_m = 0.0_wp
1309	tmp_particle%rvar1 = 0.0_wp
1310	tmp_particle%rvar2 = 0.0_wp
1311	tmp_particle%rvar3 = 0.0_wp
1312	tmp_particle%speed_x = 0.0_wp
1313	tmp_particle%speed_y = 0.0_wp
1314	tmp_particle%speed_z = 0.0_wp
1315	tmp_particle%origin_x = pos_x
1316	tmp_particle%origin_y = pos_y
1317	tmp_particle%origin_z = pos_z
1318	IF ( curvature_solution_effects ) THEN
1319	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
1320	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
1321	ELSE
1322	tmp_particle%aux1 = 0.0_wp ! free to use
1323	tmp_particle%aux2 = 0.0_wp ! free to use
1324	ENDIF
1325	tmp_particle%radius = particle_groups(i)%radius
1326	tmp_particle%weight_factor = initial_weighting_factor
1327	tmp_particle%class = 1
1328	tmp_particle%group = i
1329	tmp_particle%id = 0_idp
1330	tmp_particle%particle_mask = .TRUE.
1331	tmp_particle%block_nr = -1
1332	!
1333	!-- Determine the grid indices of the particle position
1334	ip = INT( tmp_particle%x * ddx )
1335	jp = INT( tmp_particle%y * ddy )
1336	!
1337	!-- In case of stretching the actual k index is found iteratively
1338	IF ( dz_stretch_level /= -9999999.9_wp .OR. &
1339	dz_stretch_level_start(1) /= -9999999.9_wp ) THEN
1340	kp = MINLOC( ABS( tmp_particle%z - zu ), DIM = 1 ) - 1
1341	ELSE
1342	kp = INT( tmp_particle%z / dz(1) + 1 + offset_ocean_nzt )
1343	ENDIF
1344	!
1345	!-- Determine surface level. Therefore, check for
1346	!-- upward-facing wall on w-grid.
1347	k_surf = topo_top_ind(jp,ip,3)
1348	IF ( seed_follows_topography ) THEN
1349	!
1350	!-- Particle height is given relative to topography
1351	kp = kp + k_surf
1352	tmp_particle%z = tmp_particle%z + zw(k_surf)
1353	!-- Skip particle release if particle position is
1354	!-- above model top, or within topography in case
1355	!-- of overhanging structures.
1356	IF ( kp > nzt .OR. &
1357	.NOT. BTEST( wall_flags_static_0(kp,jp,ip), 0 ) ) THEN
1358	pos_x = pos_x + pdx(i)
1359	CYCLE xloop
1360	ENDIF
1361	!
1362	!-- Skip particle release if particle position is
1363	!-- below surface, or within topography in case
1364	!-- of overhanging structures.
1365	ELSEIF ( .NOT. seed_follows_topography .AND. &
1366	tmp_particle%z <= zw(k_surf) .OR. &
1367	.NOT. BTEST( wall_flags_static_0(kp,jp,ip), 0 ) )&
1368	THEN
1369	pos_x = pos_x + pdx(i)
1370	CYCLE xloop
1371	ENDIF
1372
1373	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
1374
1375	IF ( .NOT. first_stride ) THEN
1376	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
1377	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
1378	ENDIF
1379	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
1380	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
1381	ENDIF
1382	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
1383	ENDIF
1384	ENDDO
1385	ENDIF
1386	pos_x = pos_x + pdx(i)
1387	ENDDO xloop
1388	ENDIF
1389	pos_y = pos_y + pdy(i)
1390	ENDDO
1391	ENDIF
1392
1393	pos_z = pos_z + pdz(i)
1394	ENDDO
1395	ENDDO
1396
1397	IF ( first_stride ) THEN
1398	DO ip = nxl, nxr
1399	DO jp = nys, nyn
1400	DO kp = nzb+1, nzt
1401	IF ( phase == PHASE_INIT ) THEN
1402	IF ( local_count(kp,jp,ip) > 0 ) THEN
1403	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
1404	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
1405	1 )
1406	ELSE
1407	alloc_size = 1
1408	ENDIF
1409	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
1410	DO n = 1, alloc_size
1411	grid_particles(kp,jp,ip)%particles(n) = zero_particle
1412	ENDDO
1413	ELSEIF ( phase == PHASE_RELEASE ) THEN
1414	IF ( local_count(kp,jp,ip) > 0 ) THEN
1415	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
1416	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
1417	alloc_factor / 100.0_wp ) ), 1 )
1418	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
1419	CALL realloc_particles_array( ip, jp, kp, alloc_size )
1420	ENDIF
1421	ENDIF
1422	ENDIF
1423	ENDDO
1424	ENDDO
1425	ENDDO
1426	ENDIF
1427
1428	ENDDO
1429
1430	local_start = prt_count+1
1431	prt_count = local_count
1432	!
1433	!-- Calculate particle IDs
1434	DO ip = nxl, nxr
1435	DO jp = nys, nyn
1436	DO kp = nzb+1, nzt
1437	number_of_particles = prt_count(kp,jp,ip)
1438	IF ( number_of_particles <= 0 ) CYCLE
1439	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1440
1441	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1442
1443	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
1444	10000_idp*2 kp + 10000_idp * jp + ip
1445	!
1446	!-- Count the number of particles that have been released before
1447	grid_particles(kp,jp,ip)%id_counter = &
1448	grid_particles(kp,jp,ip)%id_counter + 1
1449
1450	ENDDO
1451
1452	ENDDO
1453	ENDDO
1454	ENDDO
1455	!
1456	!-- Initialize aerosol background spectrum
1457	IF ( curvature_solution_effects ) THEN
1458	CALL lpm_init_aerosols( local_start )
1459	ENDIF
1460	!
1461	!-- Add random fluctuation to particle positions.
1462	IF ( random_start_position ) THEN
1463	DO ip = nxl, nxr
1464	DO jp = nys, nyn
1465	DO kp = nzb+1, nzt
1466	number_of_particles = prt_count(kp,jp,ip)
1467	IF ( number_of_particles <= 0 ) CYCLE
1468	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1469	!
1470	!-- Move only new particles. Moreover, limit random fluctuation
1471	!-- in order to prevent that particles move more than one grid box,
1472	!-- which would lead to problems concerning particle exchange
1473	!-- between processors in case pdx/pdy are larger than dx/dy,
1474	!-- respectively.
1475	DO n = local_start(kp,jp,ip), number_of_particles
1476	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
1477	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1478	pdx(particles(n)%group)
1479	particles(n)%x = particles(n)%x + &
1480	MERGE( rand_contr, SIGN( dx, rand_contr ), &
1481	ABS( rand_contr ) < dx &
1482	)
1483	ENDIF
1484	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
1485	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1486	pdy(particles(n)%group)
1487	particles(n)%y = particles(n)%y + &
1488	MERGE( rand_contr, SIGN( dy, rand_contr ), &
1489	ABS( rand_contr ) < dy &
1490	)
1491	ENDIF
1492	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
1493	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1494	pdz(particles(n)%group)
1495	particles(n)%z = particles(n)%z + &
1496	MERGE( rand_contr, SIGN( dzw(kp), rand_contr ), &
1497	ABS( rand_contr ) < dzw(kp) &
1498	)
1499	ENDIF
1500	ENDDO
1501	!
1502	!-- Identify particles located outside the model domain and reflect
1503	!-- or absorb them if necessary.
1504	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
1505	!
1506	!-- Furthermore, remove particles located in topography. Note, as
1507	!-- the particle speed is still zero at this point, wall
1508	!-- reflection boundary conditions will not work in this case.
1509	particles => &
1510	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1511	DO n = local_start(kp,jp,ip), number_of_particles
1512	i = particles(n)%x * ddx
1513	j = particles(n)%y * ddy
1514	k = particles(n)%z / dz(1) + 1 + offset_ocean_nzt
1515	DO WHILE( zw(k) < particles(n)%z )
1516	k = k + 1
1517	ENDDO
1518	DO WHILE( zw(k-1) > particles(n)%z )
1519	k = k - 1
1520	ENDDO
1521	!
1522	!-- Check if particle is within topography
1523	IF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 0 ) ) THEN
1524	particles(n)%particle_mask = .FALSE.
1525	deleted_particles = deleted_particles + 1
1526	ENDIF
1527
1528	ENDDO
1529	ENDDO
1530	ENDDO
1531	ENDDO
1532	!
1533	!-- Exchange particles between grid cells and processors
1534	CALL lpm_move_particle
1535	CALL lpm_exchange_horiz
1536
1537	ENDIF
1538	!
1539	!-- In case of random_start_position, delete particles identified by
1540	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1541	!-- which is needed for a fast interpolation of the LES fields on the particle
1542	!-- position.
1543	CALL lpm_sort_and_delete
1544	!
1545	!-- Determine the current number of particles
1546	DO ip = nxl, nxr
1547	DO jp = nys, nyn
1548	DO kp = nzb+1, nzt
1549	number_of_particles = number_of_particles &
1550	+ prt_count(kp,jp,ip)
1551	ENDDO
1552	ENDDO
1553	ENDDO
1554	!
1555	!-- Calculate the number of particles of the total domain
1556	#if defined( __parallel )
1557	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1558	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1559	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1560	#else
1561	total_number_of_particles = number_of_particles
1562	#endif
1563
1564	RETURN
1565
1566	END SUBROUTINE lpm_create_particle
1567
1568
1569	!------------------------------------------------------------------------------!
1570	! Description:
1571	! ------------
1572	!> This routine initialize the particles as aerosols with physio-chemical
1573	!> properties.
1574	!------------------------------------------------------------------------------!
1575	SUBROUTINE lpm_init_aerosols(local_start)
1576
1577	REAL(wp) :: afactor !< curvature effects
1578	REAL(wp) :: bfactor !< solute effects
1579	REAL(wp) :: dlogr !< logarithmic width of radius bin
1580	REAL(wp) :: e_a !< vapor pressure
1581	REAL(wp) :: e_s !< saturation vapor pressure
1582	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1583	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1584	REAL(wp) :: r_mid !< mean radius of bin
1585	REAL(wp) :: r_l !< left radius of bin
1586	REAL(wp) :: r_r !< right radius of bin
1587	REAL(wp) :: sigma !< surface tension
1588	REAL(wp) :: t_int !< temperature
1589
1590	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1591
1592	INTEGER(iwp) :: n !<
1593	INTEGER(iwp) :: ip !<
1594	INTEGER(iwp) :: jp !<
1595	INTEGER(iwp) :: kp !<
1596
1597	!
1598	!-- Set constants for different aerosol species
1599	IF ( TRIM( aero_species ) == 'nacl' ) THEN
1600	molecular_weight_of_solute = 0.05844_wp
1601	rho_s = 2165.0_wp
1602	vanthoff = 2.0_wp
1603	ELSEIF ( TRIM( aero_species ) == 'c3h4o4' ) THEN
1604	molecular_weight_of_solute = 0.10406_wp
1605	rho_s = 1600.0_wp
1606	vanthoff = 1.37_wp
1607	ELSEIF ( TRIM( aero_species ) == 'nh4o3' ) THEN
1608	molecular_weight_of_solute = 0.08004_wp
1609	rho_s = 1720.0_wp
1610	vanthoff = 2.31_wp
1611	ELSE
1612	WRITE( message_string, * ) 'unknown aerosol species ', &
1613	'aero_species = "', TRIM( aero_species ), '"'
1614	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1615	ENDIF
1616	!
1617	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1618	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1619	IF ( TRIM( aero_type ) == 'polar' ) THEN
1620	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6_wp
1621	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6_wp
1622	log_sigma = (/ 0.245, 0.300, 0.291 /)
1623	ELSEIF ( TRIM( aero_type ) == 'background' ) THEN
1624	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6_wp
1625	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6_wp
1626	log_sigma = (/ 0.645, 0.253, 0.425 /)
1627	ELSEIF ( TRIM( aero_type ) == 'maritime' ) THEN
1628	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6_wp
1629	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6_wp
1630	log_sigma = (/ 0.657, 0.210, 0.396 /)
1631	ELSEIF ( TRIM( aero_type ) == 'continental' ) THEN
1632	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6_wp
1633	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6_wp
1634	log_sigma = (/ 0.161, 0.217, 0.380 /)
1635	ELSEIF ( TRIM( aero_type ) == 'desert' ) THEN
1636	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6_wp
1637	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6_wp
1638	log_sigma = (/ 0.247, 0.770, 0.438 /)
1639	ELSEIF ( TRIM( aero_type ) == 'rural' ) THEN
1640	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6_wp
1641	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6_wp
1642	log_sigma = (/ 0.225, 0.557, 0.266 /)
1643	ELSEIF ( TRIM( aero_type ) == 'urban' ) THEN
1644	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6_wp
1645	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6_wp
1646	log_sigma = (/ 0.245, 0.666, 0.337 /)
1647	ELSEIF ( TRIM( aero_type ) == 'user' ) THEN
1648	CONTINUE
1649	ELSE
1650	WRITE( message_string, * ) 'unknown aerosol type ', &
1651	'aero_type = "', TRIM( aero_type ), '"'
1652	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1653	ENDIF
1654
1655	DO ip = nxl, nxr
1656	DO jp = nys, nyn
1657	DO kp = nzb+1, nzt
1658
1659	number_of_particles = prt_count(kp,jp,ip)
1660	IF ( number_of_particles <= 0 ) CYCLE
1661	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1662
1663	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1664	!
1665	!-- Initialize the aerosols with a predefined spectral distribution
1666	!-- of the dry radius (logarithmically increasing bins) and a varying
1667	!-- weighting factor
1668	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1669
1670	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1671	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1672	r_mid = SQRT( r_l * r_r )
1673
1674	particles(n)%aux1 = r_mid
1675	particles(n)%weight_factor = &
1676	( na(1) / ( SQRT( 2.0_wp * pi ) * log_sigma(1) ) * &
1677	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0_wp log_sigma(1)**2 ) ) + &
1678	na(2) / ( SQRT( 2.0_wp * pi ) * log_sigma(2) ) * &
1679	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0_wp log_sigma(2)**2 ) ) + &
1680	na(3) / ( SQRT( 2.0_wp * pi ) * log_sigma(3) ) * &
1681	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0_wp log_sigma(3)**2 ) ) &
1682	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dzw(kp) )
1683
1684	!
1685	!-- Multiply weight_factor with the namelist parameter aero_weight
1686	!-- to increase or decrease the number of simulated aerosols
1687	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1688
1689	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1690	> random_function( iran_part ) ) THEN
1691	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0_wp
1692	ELSE
1693	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1694	ENDIF
1695	!
1696	!-- Unnecessary particles will be deleted
1697	IF ( particles(n)%weight_factor <= 0.0_wp ) particles(n)%particle_mask = .FALSE.
1698
1699	ENDDO
1700	!
1701	!-- Set particle radius to equilibrium radius based on the environmental
1702	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1703	!-- the sometimes lengthy growth toward their equilibrium radius within
1704	!-- the simulation.
1705	t_int = pt(kp,jp,ip) * exner(kp)
1706
1707	e_s = magnus( t_int )
1708	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + rd_d_rv )
1709
1710	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1711	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1712
1713	bfactor = vanthoff * molecular_weight_of_water * &
1714	rho_s / ( molecular_weight_of_solute * rho_l )
1715	!
1716	!-- The formula is only valid for subsaturated environments. For
1717	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1718	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1719
1720	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1721	!
1722	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1723	!-- Curry (2007, JGR)
1724	particles(n)%radius = bfactor*0.3333333_wp &
1725	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1726	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1727	particles(n)%aux1 ) ) / &
1728	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1729	)
1730
1731	ENDDO
1732
1733	ENDDO
1734	ENDDO
1735	ENDDO
1736
1737	END SUBROUTINE lpm_init_aerosols
1738
1739
1740	!------------------------------------------------------------------------------!
1741	! Description:
1742	! ------------
1743	!> Calculates quantities required for considering the SGS velocity fluctuations
1744	!> in the particle transport by a stochastic approach. The respective
1745	!> quantities are: SGS-TKE gradients and horizontally averaged profiles of the
1746	!> SGS TKE and the resolved-scale velocity variances.
1747	!------------------------------------------------------------------------------!
1748	SUBROUTINE lpm_init_sgs_tke
1749
1750	USE statistics, &
1751	ONLY: flow_statistics_called, hom, sums, sums_l
1752
1753	INTEGER(iwp) :: i !< index variable along x
1754	INTEGER(iwp) :: j !< index variable along y
1755	INTEGER(iwp) :: k !< index variable along z
1756	INTEGER(iwp) :: m !< running index for the surface elements
1757
1758	REAL(wp) :: flag1 !< flag to mask topography
1759
1760	!
1761	!-- TKE gradient along x and y
1762	DO i = nxl, nxr
1763	DO j = nys, nyn
1764	DO k = nzb, nzt+1
1765
1766	IF ( .NOT. BTEST( wall_flags_static_0(k,j,i-1), 0 ) .AND. &
1767	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1768	BTEST( wall_flags_static_0(k,j,i+1), 0 ) ) &
1769	THEN
1770	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1771	( e(k,j,i+1) - e(k,j,i) ) * ddx
1772	ELSEIF ( BTEST( wall_flags_static_0(k,j,i-1), 0 ) .AND. &
1773	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1774	.NOT. BTEST( wall_flags_static_0(k,j,i+1), 0 ) ) &
1775	THEN
1776	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1777	( e(k,j,i) - e(k,j,i-1) ) * ddx
1778	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) .AND. &
1779	.NOT. BTEST( wall_flags_static_0(k,j,i+1), 22 ) ) &
1780	THEN
1781	de_dx(k,j,i) = 0.0_wp
1782	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i-1), 22 ) .AND. &
1783	.NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) ) &
1784	THEN
1785	de_dx(k,j,i) = 0.0_wp
1786	ELSE
1787	de_dx(k,j,i) = sgs_wf_part * ( e(k,j,i+1) - e(k,j,i-1) ) * ddx
1788	ENDIF
1789
1790	IF ( .NOT. BTEST( wall_flags_static_0(k,j-1,i), 0 ) .AND. &
1791	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1792	BTEST( wall_flags_static_0(k,j+1,i), 0 ) ) &
1793	THEN
1794	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1795	( e(k,j+1,i) - e(k,j,i) ) * ddy
1796	ELSEIF ( BTEST( wall_flags_static_0(k,j-1,i), 0 ) .AND. &
1797	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1798	.NOT. BTEST( wall_flags_static_0(k,j+1,i), 0 ) ) &
1799	THEN
1800	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1801	( e(k,j,i) - e(k,j-1,i) ) * ddy
1802	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) .AND. &
1803	.NOT. BTEST( wall_flags_static_0(k,j+1,i), 22 ) ) &
1804	THEN
1805	de_dy(k,j,i) = 0.0_wp
1806	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j-1,i), 22 ) .AND. &
1807	.NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) ) &
1808	THEN
1809	de_dy(k,j,i) = 0.0_wp
1810	ELSE
1811	de_dy(k,j,i) = sgs_wf_part * ( e(k,j+1,i) - e(k,j-1,i) ) * ddy
1812	ENDIF
1813
1814	ENDDO
1815	ENDDO
1816	ENDDO
1817
1818	!
1819	!-- TKE gradient along z at topograhy and including bottom and top boundary conditions
1820	DO i = nxl, nxr
1821	DO j = nys, nyn
1822	DO k = nzb+1, nzt-1
1823	!
1824	!-- Flag to mask topography
1825	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 0 ) )
1826
1827	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1828	( e(k+1,j,i) - e(k-1,j,i) ) / ( zu(k+1) - zu(k-1) ) &
1829	* flag1
1830	ENDDO
1831	!
1832	!-- upward-facing surfaces
1833	DO m = bc_h(0)%start_index(j,i), bc_h(0)%end_index(j,i)
1834	k = bc_h(0)%k(m)
1835	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1836	( e(k+1,j,i) - e(k,j,i) ) / ( zu(k+1) - zu(k) )
1837	ENDDO
1838	!
1839	!-- downward-facing surfaces
1840	DO m = bc_h(1)%start_index(j,i), bc_h(1)%end_index(j,i)
1841	k = bc_h(1)%k(m)
1842	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1843	( e(k,j,i) - e(k-1,j,i) ) / ( zu(k) - zu(k-1) )
1844	ENDDO
1845
1846	de_dz(nzb,j,i) = 0.0_wp
1847	de_dz(nzt,j,i) = 0.0_wp
1848	de_dz(nzt+1,j,i) = 0.0_wp
1849	ENDDO
1850	ENDDO
1851	!
1852	!-- Ghost point exchange
1853	CALL exchange_horiz( de_dx, nbgp )
1854	CALL exchange_horiz( de_dy, nbgp )
1855	CALL exchange_horiz( de_dz, nbgp )
1856	CALL exchange_horiz( diss, nbgp )
1857	!
1858	!-- Set boundary conditions at non-periodic boundaries. Note, at non-period
1859	!-- boundaries zero-gradient boundary conditions are set for the subgrid TKE.
1860	!-- Thus, TKE gradients normal to the respective lateral boundaries are zero,
1861	!-- while tangetial TKE gradients then must be the same as within the prognostic
1862	!-- domain.
1863	IF ( bc_dirichlet_l ) THEN
1864	de_dx(:,:,-1) = 0.0_wp
1865	de_dy(:,:,-1) = de_dy(:,:,0)
1866	de_dz(:,:,-1) = de_dz(:,:,0)
1867	ENDIF
1868	IF ( bc_dirichlet_r ) THEN
1869	de_dx(:,:,nxr+1) = 0.0_wp
1870	de_dy(:,:,nxr+1) = de_dy(:,:,nxr)
1871	de_dz(:,:,nxr+1) = de_dz(:,:,nxr)
1872	ENDIF
1873	IF ( bc_dirichlet_n ) THEN
1874	de_dx(:,nyn+1,:) = de_dx(:,nyn,:)
1875	de_dy(:,nyn+1,:) = 0.0_wp
1876	de_dz(:,nyn+1,:) = de_dz(:,nyn,:)
1877	ENDIF
1878	IF ( bc_dirichlet_s ) THEN
1879	de_dx(:,nys-1,:) = de_dx(:,nys,:)
1880	de_dy(:,nys-1,:) = 0.0_wp
1881	de_dz(:,nys-1,:) = de_dz(:,nys,:)
1882	ENDIF
1883	!
1884	!-- Calculate the horizontally averaged profiles of SGS TKE and resolved
1885	!-- velocity variances (they may have been already calculated in routine
1886	!-- flow_statistics).
1887	IF ( .NOT. flow_statistics_called ) THEN
1888
1889	!
1890	!-- First calculate horizontally averaged profiles of the horizontal
1891	!-- velocities.
1892	sums_l(:,1,0) = 0.0_wp
1893	sums_l(:,2,0) = 0.0_wp
1894
1895	DO i = nxl, nxr
1896	DO j = nys, nyn
1897	DO k = nzb, nzt+1
1898	!
1899	!-- Flag indicating vicinity of wall
1900	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 24 ) )
1901
1902	sums_l(k,1,0) = sums_l(k,1,0) + u(k,j,i) * flag1
1903	sums_l(k,2,0) = sums_l(k,2,0) + v(k,j,i) * flag1
1904	ENDDO
1905	ENDDO
1906	ENDDO
1907
1908	#if defined( __parallel )
1909	!
1910	!-- Compute total sum from local sums
1911	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1912	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, &
1913	MPI_REAL, MPI_SUM, comm2d, ierr )
1914	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1915	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, &
1916	MPI_REAL, MPI_SUM, comm2d, ierr )
1917	#else
1918	sums(:,1) = sums_l(:,1,0)
1919	sums(:,2) = sums_l(:,2,0)
1920	#endif
1921
1922	!
1923	!-- Final values are obtained by division by the total number of grid
1924	!-- points used for the summation.
1925	hom(:,1,1,0) = sums(:,1) / ngp_2dh_outer(:,0) ! u
1926	hom(:,1,2,0) = sums(:,2) / ngp_2dh_outer(:,0) ! v
1927
1928	!
1929	!-- Now calculate the profiles of SGS TKE and the resolved-scale
1930	!-- velocity variances
1931	sums_l(:,8,0) = 0.0_wp
1932	sums_l(:,30,0) = 0.0_wp
1933	sums_l(:,31,0) = 0.0_wp
1934	sums_l(:,32,0) = 0.0_wp
1935	DO i = nxl, nxr
1936	DO j = nys, nyn
1937	DO k = nzb, nzt+1
1938	!
1939	!-- Flag indicating vicinity of wall
1940	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 24 ) )
1941
1942	sums_l(k,8,0) = sums_l(k,8,0) + e(k,j,i) * flag1
1943	sums_l(k,30,0) = sums_l(k,30,0) + ( u(k,j,i) - hom(k,1,1,0) )*2 flag1
1944	sums_l(k,31,0) = sums_l(k,31,0) + ( v(k,j,i) - hom(k,1,2,0) )*2 flag1
1945	sums_l(k,32,0) = sums_l(k,32,0) + w(k,j,i)*2 flag1
1946	ENDDO
1947	ENDDO
1948	ENDDO
1949
1950	#if defined( __parallel )
1951	!
1952	!-- Compute total sum from local sums
1953	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1954	CALL MPI_ALLREDUCE( sums_l(nzb,8,0), sums(nzb,8), nzt+2-nzb, &
1955	MPI_REAL, MPI_SUM, comm2d, ierr )
1956	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1957	CALL MPI_ALLREDUCE( sums_l(nzb,30,0), sums(nzb,30), nzt+2-nzb, &
1958	MPI_REAL, MPI_SUM, comm2d, ierr )
1959	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1960	CALL MPI_ALLREDUCE( sums_l(nzb,31,0), sums(nzb,31), nzt+2-nzb, &
1961	MPI_REAL, MPI_SUM, comm2d, ierr )
1962	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1963	CALL MPI_ALLREDUCE( sums_l(nzb,32,0), sums(nzb,32), nzt+2-nzb, &
1964	MPI_REAL, MPI_SUM, comm2d, ierr )
1965
1966	#else
1967	sums(:,8) = sums_l(:,8,0)
1968	sums(:,30) = sums_l(:,30,0)
1969	sums(:,31) = sums_l(:,31,0)
1970	sums(:,32) = sums_l(:,32,0)
1971	#endif
1972
1973	!
1974	!-- Final values are obtained by division by the total number of grid
1975	!-- points used for the summation.
1976	hom(:,1,8,0) = sums(:,8) / ngp_2dh_outer(:,0) ! e
1977	hom(:,1,30,0) = sums(:,30) / ngp_2dh_outer(:,0) ! u*2
1978	hom(:,1,31,0) = sums(:,31) / ngp_2dh_outer(:,0) ! v*2
1979	hom(:,1,32,0) = sums(:,32) / ngp_2dh_outer(:,0) ! w*2
1980
1981	ENDIF
1982
1983	END SUBROUTINE lpm_init_sgs_tke
1984
1985
1986	!------------------------------------------------------------------------------!
1987	! Description:
1988	! ------------
1989	!> Sobroutine control lpm actions, i.e. all actions during one time step.
1990	!------------------------------------------------------------------------------!
1991	SUBROUTINE lpm_actions( location )
1992
1993	CHARACTER (LEN=*), INTENT(IN) :: location !< call location string
1994
1995	INTEGER(iwp) :: i !<
1996	INTEGER(iwp) :: ie !<
1997	INTEGER(iwp) :: is !<
1998	INTEGER(iwp) :: j !<
1999	INTEGER(iwp) :: je !<
2000	INTEGER(iwp) :: js !<
2001	INTEGER(iwp), SAVE :: lpm_count = 0 !<
2002	INTEGER(iwp) :: k !<
2003	INTEGER(iwp) :: ke !<
2004	INTEGER(iwp) :: ks !<
2005	INTEGER(iwp) :: m !<
2006	INTEGER(iwp), SAVE :: steps = 0 !<
2007
2008	LOGICAL :: first_loop_stride !<
2009
2010
2011	SELECT CASE ( location )
2012
2013	CASE ( 'after_pressure_solver' )
2014	!
2015	!-- The particle model is executed if particle advection start is reached and only at the end
2016	!-- of the intermediate time step loop.
2017	IF ( time_since_reference_point >= particle_advection_start &
2018	.AND. intermediate_timestep_count == intermediate_timestep_count_max ) &
2019	THEN
2020	CALL cpu_log( log_point(25), 'lpm', 'start' )
2021	!
2022	!-- Write particle data at current time on file.
2023	!-- This has to be done here, before particles are further processed,
2024	!-- because they may be deleted within this timestep (in case that
2025	!-- dt_write_particle_data = dt_prel = particle_maximum_age).
2026	time_write_particle_data = time_write_particle_data + dt_3d
2027	IF ( time_write_particle_data >= dt_write_particle_data ) THEN
2028
2029	CALL lpm_data_output_particles
2030	!
2031	!-- The MOD function allows for changes in the output interval with restart
2032	!-- runs.
2033	time_write_particle_data = MOD( time_write_particle_data, &
2034	MAX( dt_write_particle_data, dt_3d ) )
2035	ENDIF
2036
2037	!
2038	!-- Initialize arrays for marking those particles to be deleted after the
2039	!-- (sub-) timestep
2040	deleted_particles = 0
2041
2042	!
2043	!-- Initialize variables used for accumulating the number of particles
2044	!-- xchanged between the subdomains during all sub-timesteps (if sgs
2045	!-- velocities are included). These data are output further below on the
2046	!-- particle statistics file.
2047	trlp_count_sum = 0
2048	trlp_count_recv_sum = 0
2049	trrp_count_sum = 0
2050	trrp_count_recv_sum = 0
2051	trsp_count_sum = 0
2052	trsp_count_recv_sum = 0
2053	trnp_count_sum = 0
2054	trnp_count_recv_sum = 0
2055	!
2056	!-- Calculate exponential term used in case of particle inertia for each
2057	!-- of the particle groups
2058	DO m = 1, number_of_particle_groups
2059	IF ( particle_groups(m)%density_ratio /= 0.0_wp ) THEN
2060	particle_groups(m)%exp_arg = &
2061	4.5_wp * particle_groups(m)%density_ratio * &
2062	molecular_viscosity / ( particle_groups(m)%radius )**2
2063
2064	particle_groups(m)%exp_term = EXP( -particle_groups(m)%exp_arg * &
2065	dt_3d )
2066	ENDIF
2067	ENDDO
2068	!
2069	!-- If necessary, release new set of particles
2070	IF ( ( simulated_time - last_particle_release_time ) >= dt_prel .AND. &
2071	end_time_prel > simulated_time ) THEN
2072	DO WHILE ( ( simulated_time - last_particle_release_time ) >= dt_prel )
2073	CALL lpm_create_particle( PHASE_RELEASE )
2074	last_particle_release_time = last_particle_release_time + dt_prel
2075	ENDDO
2076	ENDIF
2077	!
2078	!-- Reset summation arrays
2079	IF ( cloud_droplets ) THEN
2080	ql_c = 0.0_wp
2081	ql_v = 0.0_wp
2082	ql_vp = 0.0_wp
2083	ENDIF
2084
2085	first_loop_stride = .TRUE.
2086	grid_particles(:,:,:)%time_loop_done = .TRUE.
2087	!
2088	!-- Timestep loop for particle advection.
2089	!-- This loop has to be repeated until the advection time of every particle
2090	!-- (within the total domain!) has reached the LES timestep (dt_3d).
2091	!-- In case of including the SGS velocities, the particle timestep may be
2092	!-- smaller than the LES timestep (because of the Lagrangian timescale
2093	!-- restriction) and particles may require to undergo several particle
2094	!-- timesteps, before the LES timestep is reached. Because the number of these
2095	!-- particle timesteps to be carried out is unknown at first, these steps are
2096	!-- carried out in the following infinite loop with exit condition.
2097	DO
2098	CALL cpu_log( log_point_s(44), 'lpm_advec', 'start' )
2099	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
2100
2101	!
2102	!-- If particle advection includes SGS velocity components, calculate the
2103	!-- required SGS quantities (i.e. gradients of the TKE, as well as
2104	!-- horizontally averaged profiles of the SGS TKE and the resolved-scale
2105	!-- velocity variances)
2106	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
2107	CALL lpm_init_sgs_tke
2108	ENDIF
2109	!
2110	!-- In case SGS-particle speed is considered, particles may carry out
2111	!-- several particle timesteps. In order to prevent unnecessary
2112	!-- treatment of particles that already reached the final time level,
2113	!-- particles are sorted into contiguous blocks of finished and
2114	!-- not-finished particles, in addition to their already sorting
2115	!-- according to their sub-boxes.
2116	IF ( .NOT. first_loop_stride .AND. use_sgs_for_particles ) &
2117	CALL lpm_sort_timeloop_done
2118	DO i = nxl, nxr
2119	DO j = nys, nyn
2120	DO k = nzb+1, nzt
2121
2122	number_of_particles = prt_count(k,j,i)
2123	!
2124	!-- If grid cell gets empty, flag must be true
2125	IF ( number_of_particles <= 0 ) THEN
2126	grid_particles(k,j,i)%time_loop_done = .TRUE.
2127	CYCLE
2128	ENDIF
2129
2130	IF ( .NOT. first_loop_stride .AND. &
2131	grid_particles(k,j,i)%time_loop_done ) CYCLE
2132
2133	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2134
2135	particles(1:number_of_particles)%particle_mask = .TRUE.
2136	!
2137	!-- Initialize the variable storing the total time that a particle
2138	!-- has advanced within the timestep procedure
2139	IF ( first_loop_stride ) THEN
2140	particles(1:number_of_particles)%dt_sum = 0.0_wp
2141	ENDIF
2142	!
2143	!-- Particle (droplet) growth by condensation/evaporation and
2144	!-- collision
2145	IF ( cloud_droplets .AND. first_loop_stride) THEN
2146	!
2147	!-- Droplet growth by condensation / evaporation
2148	CALL lpm_droplet_condensation(i,j,k)
2149	!
2150	!-- Particle growth by collision
2151	IF ( collision_kernel /= 'none' ) THEN
2152	CALL lpm_droplet_collision(i,j,k)
2153	ENDIF
2154
2155	ENDIF
2156	!
2157	!-- Initialize the switch used for the loop exit condition checked
2158	!-- at the end of this loop. If at least one particle has failed to
2159	!-- reach the LES timestep, this switch will be set false in
2160	!-- lpm_advec.
2161	dt_3d_reached_l = .TRUE.
2162
2163	!
2164	!-- Particle advection
2165	CALL lpm_advec( i, j, k )
2166	!
2167	!-- Particle reflection from walls. Only applied if the particles
2168	!-- are in the vertical range of the topography. (Here, some
2169	!-- optimization is still possible.)
2170	IF ( topography /= 'flat' .AND. k < nzb_max + 2 ) THEN
2171	CALL lpm_boundary_conds( 'walls', i, j, k )
2172	ENDIF
2173	!
2174	!-- User-defined actions after the calculation of the new particle
2175	!-- position
2176	CALL user_lpm_advec( i, j, k )
2177	!
2178	!-- Apply boundary conditions to those particles that have crossed
2179	!-- the top or bottom boundary and delete those particles, which are
2180	!-- older than allowed
2181	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
2182	!
2183	!--- If not all particles of the actual grid cell have reached the
2184	!-- LES timestep, this cell has to do another loop iteration. Due to
2185	!-- the fact that particles can move into neighboring grid cells,
2186	!-- these neighbor cells also have to perform another loop iteration.
2187	!-- Please note, this realization does not work properly if
2188	!-- particles move into another subdomain.
2189	IF ( .NOT. dt_3d_reached_l ) THEN
2190	ks = MAX(nzb+1,k-1)
2191	ke = MIN(nzt,k+1)
2192	js = MAX(nys,j-1)
2193	je = MIN(nyn,j+1)
2194	is = MAX(nxl,i-1)
2195	ie = MIN(nxr,i+1)
2196	grid_particles(ks:ke,js:je,is:ie)%time_loop_done = .FALSE.
2197	ELSE
2198	grid_particles(k,j,i)%time_loop_done = .TRUE.
2199	ENDIF
2200
2201	ENDDO
2202	ENDDO
2203	ENDDO
2204	steps = steps + 1
2205	dt_3d_reached_l = ALL(grid_particles(:,:,:)%time_loop_done)
2206	!
2207	!-- Find out, if all particles on every PE have completed the LES timestep
2208	!-- and set the switch corespondingly
2209	#if defined( __parallel )
2210	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2211	CALL MPI_ALLREDUCE( dt_3d_reached_l, dt_3d_reached, 1, MPI_LOGICAL, &
2212	MPI_LAND, comm2d, ierr )
2213	#else
2214	dt_3d_reached = dt_3d_reached_l
2215	#endif
2216	CALL cpu_log( log_point_s(44), 'lpm_advec', 'stop' )
2217
2218	!
2219	!-- Apply splitting and merging algorithm
2220	IF ( cloud_droplets ) THEN
2221	IF ( splitting ) THEN
2222	CALL lpm_splitting
2223	ENDIF
2224	IF ( merging ) THEN
2225	CALL lpm_merging
2226	ENDIF
2227	ENDIF
2228	!
2229	!-- Move Particles local to PE to a different grid cell
2230	CALL lpm_move_particle
2231	!
2232	!-- Horizontal boundary conditions including exchange between subdmains
2233	CALL lpm_exchange_horiz
2234
2235	!
2236	!-- IF .FALSE., lpm_sort_and_delete is done inside pcmp
2237	IF ( .NOT. dt_3d_reached .OR. .NOT. nested_run ) THEN
2238	!
2239	!-- Pack particles (eliminate those marked for deletion),
2240	!-- determine new number of particles
2241	CALL lpm_sort_and_delete
2242
2243	!-- Initialize variables for the next (sub-) timestep, i.e., for marking
2244	!-- those particles to be deleted after the timestep
2245	deleted_particles = 0
2246	ENDIF
2247
2248	IF ( dt_3d_reached ) EXIT
2249
2250	first_loop_stride = .FALSE.
2251	ENDDO ! timestep loop
2252	!
2253	!-- in case of nested runs do the transfer of particles after every full model time step
2254	IF ( nested_run ) THEN
2255	CALL particles_from_parent_to_child
2256	CALL particles_from_child_to_parent
2257	CALL pmcp_p_delete_particles_in_fine_grid_area
2258
2259	CALL lpm_sort_and_delete
2260
2261	deleted_particles = 0
2262	ENDIF
2263
2264	!
2265	!-- Calculate the new liquid water content for each grid box
2266	IF ( cloud_droplets ) CALL lpm_calc_liquid_water_content
2267
2268	!
2269	!-- At the end all arrays are exchanged
2270	IF ( cloud_droplets ) THEN
2271	CALL exchange_horiz( ql, nbgp )
2272	CALL exchange_horiz( ql_c, nbgp )
2273	CALL exchange_horiz( ql_v, nbgp )
2274	CALL exchange_horiz( ql_vp, nbgp )
2275	ENDIF
2276
2277	!
2278	!-- Deallocate unused memory
2279	IF ( deallocate_memory .AND. lpm_count == step_dealloc ) THEN
2280	CALL dealloc_particles_array
2281	lpm_count = 0
2282	ELSEIF ( deallocate_memory ) THEN
2283	lpm_count = lpm_count + 1
2284	ENDIF
2285
2286	!
2287	!-- Write particle statistics (in particular the number of particles
2288	!-- exchanged between the subdomains) on file
2289	IF ( write_particle_statistics ) CALL lpm_write_exchange_statistics
2290	!
2291	!-- Execute Interactions of condnesation and evaporation to humidity and
2292	!-- temperature field
2293	IF ( cloud_droplets ) THEN
2294	CALL lpm_interaction_droplets_ptq
2295	CALL exchange_horiz( pt, nbgp )
2296	CALL exchange_horiz( q, nbgp )
2297	ENDIF
2298
2299	CALL cpu_log( log_point(25), 'lpm', 'stop' )
2300
2301	! !
2302	! !-- Output of particle time series
2303	! IF ( particle_advection ) THEN
2304	! IF ( time_dopts >= dt_dopts .OR. &
2305	! ( time_since_reference_point >= particle_advection_start .AND. &
2306	! first_call_lpm ) ) THEN
2307	! CALL lpm_data_output_ptseries
2308	! time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
2309	! ENDIF
2310	! ENDIF
2311
2312	!
2313	!-- Set this switch to .false. @todo: maybe find better solution.
2314	first_call_lpm = .FALSE.
2315	ENDIF! ENDIF statement of lpm_actions('after_pressure_solver')
2316
2317	CASE ( 'after_integration' )
2318	!
2319	!-- Call at the end of timestep routine to save particle velocities fields
2320	!-- for the next timestep
2321	CALL lpm_swap_timelevel_for_particle_advection
2322
2323	CASE DEFAULT
2324	CONTINUE
2325
2326	END SELECT
2327
2328	END SUBROUTINE lpm_actions
2329
2330
2331	!------------------------------------------------------------------------------!
2332	! Description:
2333	! ------------
2334	!
2335	!------------------------------------------------------------------------------!
2336	SUBROUTINE particles_from_parent_to_child
2337	IMPLICIT NONE
2338
2339	CALL pmcp_c_get_particle_from_parent ! Child actions
2340	CALL pmcp_p_fill_particle_win ! Parent actions
2341
2342	RETURN
2343	END SUBROUTINE particles_from_parent_to_child
2344
2345
2346	!------------------------------------------------------------------------------!
2347	! Description:
2348	! ------------
2349	!
2350	!------------------------------------------------------------------------------!
2351	SUBROUTINE particles_from_child_to_parent
2352	IMPLICIT NONE
2353
2354	CALL pmcp_c_send_particle_to_parent ! Child actions
2355	CALL pmcp_p_empty_particle_win ! Parent actions
2356
2357	RETURN
2358	END SUBROUTINE particles_from_child_to_parent
2359
2360	!------------------------------------------------------------------------------!
2361	! Description:
2362	! ------------
2363	!> This routine write exchange statistics of the lpm in a ascii file.
2364	!------------------------------------------------------------------------------!
2365	SUBROUTINE lpm_write_exchange_statistics
2366
2367	INTEGER(iwp) :: ip !<
2368	INTEGER(iwp) :: jp !<
2369	INTEGER(iwp) :: kp !<
2370	INTEGER(iwp) :: tot_number_of_particles !<
2371
2372	!
2373	!-- Determine the current number of particles
2374	number_of_particles = 0
2375	DO ip = nxl, nxr
2376	DO jp = nys, nyn
2377	DO kp = nzb+1, nzt
2378	number_of_particles = number_of_particles &
2379	+ prt_count(kp,jp,ip)
2380	ENDDO
2381	ENDDO
2382	ENDDO
2383
2384	CALL check_open( 80 )
2385	#if defined( __parallel )
2386	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2387	number_of_particles, pleft, trlp_count_sum, &
2388	trlp_count_recv_sum, pright, trrp_count_sum, &
2389	trrp_count_recv_sum, psouth, trsp_count_sum, &
2390	trsp_count_recv_sum, pnorth, trnp_count_sum, &
2391	trnp_count_recv_sum
2392	#else
2393	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2394	number_of_particles
2395	#endif
2396	CALL close_file( 80 )
2397
2398	IF ( number_of_particles > 0 ) THEN
2399	WRITE(9,*) 'number_of_particles ', number_of_particles, &
2400	current_timestep_number + 1, simulated_time + dt_3d
2401	ENDIF
2402
2403	#if defined( __parallel )
2404	CALL MPI_ALLREDUCE( number_of_particles, tot_number_of_particles, 1, &
2405	MPI_INTEGER, MPI_SUM, comm2d, ierr )
2406	#else
2407	tot_number_of_particles = number_of_particles
2408	#endif
2409
2410	IF ( nested_run ) THEN
2411	CALL pmcp_g_print_number_of_particles( simulated_time+dt_3d, &
2412	tot_number_of_particles)
2413	ENDIF
2414
2415	!
2416	!-- Formats
2417	8000 FORMAT (I6,1X,F7.2,4X,I10,5X,4(I3,1X,I4,'/',I4,2X),6X,I10)
2418
2419
2420	END SUBROUTINE lpm_write_exchange_statistics
2421
2422
2423	!------------------------------------------------------------------------------!
2424	! Description:
2425	! ------------
2426	!> Write particle data in FORTRAN binary and/or netCDF format
2427	!------------------------------------------------------------------------------!
2428	SUBROUTINE lpm_data_output_particles
2429
2430	INTEGER(iwp) :: ip !<
2431	INTEGER(iwp) :: jp !<
2432	INTEGER(iwp) :: kp !<
2433
2434	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'start' )
2435
2436	!
2437	!-- Attention: change version number for unit 85 (in routine check_open)
2438	!-- whenever the output format for this unit is changed!
2439	CALL check_open( 85 )
2440
2441	WRITE ( 85 ) simulated_time
2442	WRITE ( 85 ) prt_count
2443
2444	DO ip = nxl, nxr
2445	DO jp = nys, nyn
2446	DO kp = nzb+1, nzt
2447	number_of_particles = prt_count(kp,jp,ip)
2448	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
2449	IF ( number_of_particles <= 0 ) CYCLE
2450	WRITE ( 85 ) particles
2451	ENDDO
2452	ENDDO
2453	ENDDO
2454
2455	CALL close_file( 85 )
2456
2457
2458	#if defined( __netcdf )
2459	! !
2460	! !-- Output in netCDF format
2461	! CALL check_open( 108 )
2462	!
2463	! !
2464	! !-- Update the NetCDF time axis
2465	! prt_time_count = prt_time_count + 1
2466	!
2467	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_time_prt, &
2468	! (/ simulated_time /), &
2469	! start = (/ prt_time_count /), count = (/ 1 /) )
2470	! CALL netcdf_handle_error( 'lpm_data_output_particles', 1 )
2471	!
2472	! !
2473	! !-- Output the real number of particles used
2474	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_rnop_prt, &
2475	! (/ number_of_particles /), &
2476	! start = (/ prt_time_count /), count = (/ 1 /) )
2477	! CALL netcdf_handle_error( 'lpm_data_output_particles', 2 )
2478	!
2479	! !
2480	! !-- Output all particle attributes
2481	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(1), particles%age, &
2482	! start = (/ 1, prt_time_count /), &
2483	! count = (/ maximum_number_of_particles /) )
2484	! CALL netcdf_handle_error( 'lpm_data_output_particles', 3 )
2485	!
2486	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(2), particles%user, &
2487	! start = (/ 1, prt_time_count /), &
2488	! count = (/ maximum_number_of_particles /) )
2489	! CALL netcdf_handle_error( 'lpm_data_output_particles', 4 )
2490	!
2491	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(3), particles%origin_x, &
2492	! start = (/ 1, prt_time_count /), &
2493	! count = (/ maximum_number_of_particles /) )
2494	! CALL netcdf_handle_error( 'lpm_data_output_particles', 5 )
2495	!
2496	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(4), particles%origin_y, &
2497	! start = (/ 1, prt_time_count /), &
2498	! count = (/ maximum_number_of_particles /) )
2499	! CALL netcdf_handle_error( 'lpm_data_output_particles', 6 )
2500	!
2501	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(5), particles%origin_z, &
2502	! start = (/ 1, prt_time_count /), &
2503	! count = (/ maximum_number_of_particles /) )
2504	! CALL netcdf_handle_error( 'lpm_data_output_particles', 7 )
2505	!
2506	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(6), particles%radius, &
2507	! start = (/ 1, prt_time_count /), &
2508	! count = (/ maximum_number_of_particles /) )
2509	! CALL netcdf_handle_error( 'lpm_data_output_particles', 8 )
2510	!
2511	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(7), particles%speed_x, &
2512	! start = (/ 1, prt_time_count /), &
2513	! count = (/ maximum_number_of_particles /) )
2514	! CALL netcdf_handle_error( 'lpm_data_output_particles', 9 )
2515	!
2516	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(8), particles%speed_y, &
2517	! start = (/ 1, prt_time_count /), &
2518	! count = (/ maximum_number_of_particles /) )
2519	! CALL netcdf_handle_error( 'lpm_data_output_particles', 10 )
2520	!
2521	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(9), particles%speed_z, &
2522	! start = (/ 1, prt_time_count /), &
2523	! count = (/ maximum_number_of_particles /) )
2524	! CALL netcdf_handle_error( 'lpm_data_output_particles', 11 )
2525	!
2526	! nc_stat = NF90_PUT_VAR( id_set_prt,id_var_prt(10), &
2527	! particles%weight_factor, &
2528	! start = (/ 1, prt_time_count /), &
2529	! count = (/ maximum_number_of_particles /) )
2530	! CALL netcdf_handle_error( 'lpm_data_output_particles', 12 )
2531	!
2532	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(11), particles%x, &
2533	! start = (/ 1, prt_time_count /), &
2534	! count = (/ maximum_number_of_particles /) )
2535	! CALL netcdf_handle_error( 'lpm_data_output_particles', 13 )
2536	!
2537	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(12), particles%y, &
2538	! start = (/ 1, prt_time_count /), &
2539	! count = (/ maximum_number_of_particles /) )
2540	! CALL netcdf_handle_error( 'lpm_data_output_particles', 14 )
2541	!
2542	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(13), particles%z, &
2543	! start = (/ 1, prt_time_count /), &
2544	! count = (/ maximum_number_of_particles /) )
2545	! CALL netcdf_handle_error( 'lpm_data_output_particles', 15 )
2546	!
2547	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(14), particles%class, &
2548	! start = (/ 1, prt_time_count /), &
2549	! count = (/ maximum_number_of_particles /) )
2550	! CALL netcdf_handle_error( 'lpm_data_output_particles', 16 )
2551	!
2552	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(15), particles%group, &
2553	! start = (/ 1, prt_time_count /), &
2554	! count = (/ maximum_number_of_particles /) )
2555	! CALL netcdf_handle_error( 'lpm_data_output_particles', 17 )
2556	!
2557	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(16), &
2558	! particles%id2, &
2559	! start = (/ 1, prt_time_count /), &
2560	! count = (/ maximum_number_of_particles /) )
2561	! CALL netcdf_handle_error( 'lpm_data_output_particles', 18 )
2562	!
2563	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(17), particles%id1, &
2564	! start = (/ 1, prt_time_count /), &
2565	! count = (/ maximum_number_of_particles /) )
2566	! CALL netcdf_handle_error( 'lpm_data_output_particles', 19 )
2567	!
2568	#endif
2569
2570	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'stop' )
2571
2572	END SUBROUTINE lpm_data_output_particles
2573
2574	!------------------------------------------------------------------------------!
2575	! Description:
2576	! ------------
2577	!> This routine calculates and provide particle timeseries output.
2578	!------------------------------------------------------------------------------!
2579	SUBROUTINE lpm_data_output_ptseries
2580
2581	INTEGER(iwp) :: i !<
2582	INTEGER(iwp) :: inum !<
2583	INTEGER(iwp) :: j !<
2584	INTEGER(iwp) :: jg !<
2585	INTEGER(iwp) :: k !<
2586	INTEGER(iwp) :: n !<
2587
2588	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value !<
2589	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value_l !<
2590
2591
2592	CALL cpu_log( log_point(36), 'data_output_ptseries', 'start' )
2593
2594	IF ( myid == 0 ) THEN
2595	!
2596	!-- Open file for time series output in NetCDF format
2597	dopts_time_count = dopts_time_count + 1
2598	CALL check_open( 109 )
2599	#if defined( __netcdf )
2600	!
2601	!-- Update the particle time series time axis
2602	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_time_pts, &
2603	(/ time_since_reference_point /), &
2604	start = (/ dopts_time_count /), count = (/ 1 /) )
2605	CALL netcdf_handle_error( 'data_output_ptseries', 391 )
2606	#endif
2607
2608	ENDIF
2609
2610	ALLOCATE( pts_value(0:number_of_particle_groups,dopts_num), &
2611	pts_value_l(0:number_of_particle_groups,dopts_num) )
2612
2613	pts_value_l = 0.0_wp
2614	pts_value_l(:,16) = 9999999.9_wp ! for calculation of minimum radius
2615
2616	!
2617	!-- Calculate or collect the particle time series quantities for all particles
2618	!-- and seperately for each particle group (if there is more than one group)
2619	DO i = nxl, nxr
2620	DO j = nys, nyn
2621	DO k = nzb, nzt
2622	number_of_particles = prt_count(k,j,i)
2623	IF (number_of_particles <= 0) CYCLE
2624	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2625	DO n = 1, number_of_particles
2626
2627	IF ( particles(n)%particle_mask ) THEN ! Restrict analysis to active particles
2628
2629	pts_value_l(0,1) = pts_value_l(0,1) + 1.0_wp ! total # of particles
2630	pts_value_l(0,2) = pts_value_l(0,2) + &
2631	( particles(n)%x - particles(n)%origin_x ) ! mean x
2632	pts_value_l(0,3) = pts_value_l(0,3) + &
2633	( particles(n)%y - particles(n)%origin_y ) ! mean y
2634	pts_value_l(0,4) = pts_value_l(0,4) + &
2635	( particles(n)%z - particles(n)%origin_z ) ! mean z
2636	pts_value_l(0,5) = pts_value_l(0,5) + particles(n)%z ! mean z (absolute)
2637	pts_value_l(0,6) = pts_value_l(0,6) + particles(n)%speed_x ! mean u
2638	pts_value_l(0,7) = pts_value_l(0,7) + particles(n)%speed_y ! mean v
2639	pts_value_l(0,8) = pts_value_l(0,8) + particles(n)%speed_z ! mean w
2640	pts_value_l(0,9) = pts_value_l(0,9) + particles(n)%rvar1 ! mean sgsu
2641	pts_value_l(0,10) = pts_value_l(0,10) + particles(n)%rvar2 ! mean sgsv
2642	pts_value_l(0,11) = pts_value_l(0,11) + particles(n)%rvar3 ! mean sgsw
2643	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2644	pts_value_l(0,12) = pts_value_l(0,12) + 1.0_wp ! # of upward moving prts
2645	pts_value_l(0,13) = pts_value_l(0,13) + &
2646	particles(n)%speed_z ! mean w upw.
2647	ELSE
2648	pts_value_l(0,14) = pts_value_l(0,14) + &
2649	particles(n)%speed_z ! mean w down
2650	ENDIF
2651	pts_value_l(0,15) = pts_value_l(0,15) + particles(n)%radius ! mean rad
2652	pts_value_l(0,16) = MIN( pts_value_l(0,16), particles(n)%radius ) ! minrad
2653	pts_value_l(0,17) = MAX( pts_value_l(0,17), particles(n)%radius ) ! maxrad
2654	pts_value_l(0,18) = pts_value_l(0,18) + 1.0_wp
2655	pts_value_l(0,19) = pts_value_l(0,18) + 1.0_wp
2656	!
2657	!-- Repeat the same for the respective particle group
2658	IF ( number_of_particle_groups > 1 ) THEN
2659	jg = particles(n)%group
2660
2661	pts_value_l(jg,1) = pts_value_l(jg,1) + 1.0_wp
2662	pts_value_l(jg,2) = pts_value_l(jg,2) + &
2663	( particles(n)%x - particles(n)%origin_x )
2664	pts_value_l(jg,3) = pts_value_l(jg,3) + &
2665	( particles(n)%y - particles(n)%origin_y )
2666	pts_value_l(jg,4) = pts_value_l(jg,4) + &
2667	( particles(n)%z - particles(n)%origin_z )
2668	pts_value_l(jg,5) = pts_value_l(jg,5) + particles(n)%z
2669	pts_value_l(jg,6) = pts_value_l(jg,6) + particles(n)%speed_x
2670	pts_value_l(jg,7) = pts_value_l(jg,7) + particles(n)%speed_y
2671	pts_value_l(jg,8) = pts_value_l(jg,8) + particles(n)%speed_z
2672	pts_value_l(jg,9) = pts_value_l(jg,9) + particles(n)%rvar1
2673	pts_value_l(jg,10) = pts_value_l(jg,10) + particles(n)%rvar2
2674	pts_value_l(jg,11) = pts_value_l(jg,11) + particles(n)%rvar3
2675	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2676	pts_value_l(jg,12) = pts_value_l(jg,12) + 1.0_wp
2677	pts_value_l(jg,13) = pts_value_l(jg,13) + particles(n)%speed_z
2678	ELSE
2679	pts_value_l(jg,14) = pts_value_l(jg,14) + particles(n)%speed_z
2680	ENDIF
2681	pts_value_l(jg,15) = pts_value_l(jg,15) + particles(n)%radius
2682	pts_value_l(jg,16) = MIN( pts_value_l(jg,16), particles(n)%radius )
2683	pts_value_l(jg,17) = MAX( pts_value_l(jg,17), particles(n)%radius )
2684	pts_value_l(jg,18) = pts_value_l(jg,18) + 1.0_wp
2685	pts_value_l(jg,19) = pts_value_l(jg,19) + 1.0_wp
2686	ENDIF
2687
2688	ENDIF
2689
2690	ENDDO
2691
2692	ENDDO
2693	ENDDO
2694	ENDDO
2695
2696
2697	#if defined( __parallel )
2698	!
2699	!-- Sum values of the subdomains
2700	inum = number_of_particle_groups + 1
2701
2702	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2703	CALL MPI_ALLREDUCE( pts_value_l(0,1), pts_value(0,1), 15*inum, MPI_REAL, &
2704	MPI_SUM, comm2d, ierr )
2705	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2706	CALL MPI_ALLREDUCE( pts_value_l(0,16), pts_value(0,16), inum, MPI_REAL, &
2707	MPI_MIN, comm2d, ierr )
2708	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2709	CALL MPI_ALLREDUCE( pts_value_l(0,17), pts_value(0,17), inum, MPI_REAL, &
2710	MPI_MAX, comm2d, ierr )
2711	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2712	CALL MPI_ALLREDUCE( pts_value_l(0,18), pts_value(0,18), inum, MPI_REAL, &
2713	MPI_MAX, comm2d, ierr )
2714	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2715	CALL MPI_ALLREDUCE( pts_value_l(0,19), pts_value(0,19), inum, MPI_REAL, &
2716	MPI_MIN, comm2d, ierr )
2717	#else
2718	pts_value(:,1:19) = pts_value_l(:,1:19)
2719	#endif
2720
2721	!
2722	!-- Normalize the above calculated quantities (except min/max values) with the
2723	!-- total number of particles
2724	IF ( number_of_particle_groups > 1 ) THEN
2725	inum = number_of_particle_groups
2726	ELSE
2727	inum = 0
2728	ENDIF
2729
2730	DO j = 0, inum
2731
2732	IF ( pts_value(j,1) > 0.0_wp ) THEN
2733
2734	pts_value(j,2:15) = pts_value(j,2:15) / pts_value(j,1)
2735	IF ( pts_value(j,12) > 0.0_wp .AND. pts_value(j,12) < 1.0_wp ) THEN
2736	pts_value(j,13) = pts_value(j,13) / pts_value(j,12)
2737	pts_value(j,14) = pts_value(j,14) / ( 1.0_wp - pts_value(j,12) )
2738	ELSEIF ( pts_value(j,12) == 0.0_wp ) THEN
2739	pts_value(j,13) = -1.0_wp
2740	ELSE
2741	pts_value(j,14) = -1.0_wp
2742	ENDIF
2743
2744	ENDIF
2745
2746	ENDDO
2747
2748	!
2749	!-- Calculate higher order moments of particle time series quantities,
2750	!-- seperately for each particle group (if there is more than one group)
2751	DO i = nxl, nxr
2752	DO j = nys, nyn
2753	DO k = nzb, nzt
2754	number_of_particles = prt_count(k,j,i)
2755	IF (number_of_particles <= 0) CYCLE
2756	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2757	DO n = 1, number_of_particles
2758
2759	pts_value_l(0,20) = pts_value_l(0,20) + ( particles(n)%x - &
2760	particles(n)%origin_x - pts_value(0,2) )*2 ! x2
2761	pts_value_l(0,21) = pts_value_l(0,21) + ( particles(n)%y - &
2762	particles(n)%origin_y - pts_value(0,3) )*2 ! y2
2763	pts_value_l(0,22) = pts_value_l(0,22) + ( particles(n)%z - &
2764	particles(n)%origin_z - pts_value(0,4) )*2 ! z2
2765	pts_value_l(0,23) = pts_value_l(0,23) + ( particles(n)%speed_x - &
2766	pts_value(0,6) )*2 ! u2
2767	pts_value_l(0,24) = pts_value_l(0,24) + ( particles(n)%speed_y - &
2768	pts_value(0,7) )*2 ! v2
2769	pts_value_l(0,25) = pts_value_l(0,25) + ( particles(n)%speed_z - &
2770	pts_value(0,8) )*2 ! w2
2771	pts_value_l(0,26) = pts_value_l(0,26) + ( particles(n)%rvar1 - &
2772	pts_value(0,9) )**2 ! u"2
2773	pts_value_l(0,27) = pts_value_l(0,27) + ( particles(n)%rvar2 - &
2774	pts_value(0,10) )**2 ! v"2
2775	pts_value_l(0,28) = pts_value_l(0,28) + ( particles(n)%rvar3 - &
2776	pts_value(0,11) )**2 ! w"2
2777	!
2778	!-- Repeat the same for the respective particle group
2779	IF ( number_of_particle_groups > 1 ) THEN
2780	jg = particles(n)%group
2781
2782	pts_value_l(jg,20) = pts_value_l(jg,20) + ( particles(n)%x - &
2783	particles(n)%origin_x - pts_value(jg,2) )**2
2784	pts_value_l(jg,21) = pts_value_l(jg,21) + ( particles(n)%y - &
2785	particles(n)%origin_y - pts_value(jg,3) )**2
2786	pts_value_l(jg,22) = pts_value_l(jg,22) + ( particles(n)%z - &
2787	particles(n)%origin_z - pts_value(jg,4) )**2
2788	pts_value_l(jg,23) = pts_value_l(jg,23) + ( particles(n)%speed_x - &
2789	pts_value(jg,6) )**2
2790	pts_value_l(jg,24) = pts_value_l(jg,24) + ( particles(n)%speed_y - &
2791	pts_value(jg,7) )**2
2792	pts_value_l(jg,25) = pts_value_l(jg,25) + ( particles(n)%speed_z - &
2793	pts_value(jg,8) )**2
2794	pts_value_l(jg,26) = pts_value_l(jg,26) + ( particles(n)%rvar1 - &
2795	pts_value(jg,9) )**2
2796	pts_value_l(jg,27) = pts_value_l(jg,27) + ( particles(n)%rvar2 - &
2797	pts_value(jg,10) )**2
2798	pts_value_l(jg,28) = pts_value_l(jg,28) + ( particles(n)%rvar3 - &
2799	pts_value(jg,11) )**2
2800	ENDIF
2801
2802	ENDDO
2803	ENDDO
2804	ENDDO
2805	ENDDO
2806
2807	pts_value_l(0,29) = ( number_of_particles - pts_value(0,1) / numprocs )**2
2808	! variance of particle numbers
2809	IF ( number_of_particle_groups > 1 ) THEN
2810	DO j = 1, number_of_particle_groups
2811	pts_value_l(j,29) = ( pts_value_l(j,1) - &
2812	pts_value(j,1) / numprocs )**2
2813	ENDDO
2814	ENDIF
2815
2816	#if defined( __parallel )
2817	!
2818	!-- Sum values of the subdomains
2819	inum = number_of_particle_groups + 1
2820
2821	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2822	CALL MPI_ALLREDUCE( pts_value_l(0,20), pts_value(0,20), inum*10, MPI_REAL, &
2823	MPI_SUM, comm2d, ierr )
2824	#else
2825	pts_value(:,20:29) = pts_value_l(:,20:29)
2826	#endif
2827
2828	!
2829	!-- Normalize the above calculated quantities with the total number of
2830	!-- particles
2831	IF ( number_of_particle_groups > 1 ) THEN
2832	inum = number_of_particle_groups
2833	ELSE
2834	inum = 0
2835	ENDIF
2836
2837	DO j = 0, inum
2838
2839	IF ( pts_value(j,1) > 0.0_wp ) THEN
2840	pts_value(j,20:28) = pts_value(j,20:28) / pts_value(j,1)
2841	ENDIF
2842	pts_value(j,29) = pts_value(j,29) / numprocs
2843
2844	ENDDO
2845
2846	#if defined( __netcdf )
2847	!
2848	!-- Output particle time series quantities in NetCDF format
2849	IF ( myid == 0 ) THEN
2850	DO j = 0, inum
2851	DO i = 1, dopts_num
2852	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_dopts(i,j), &
2853	(/ pts_value(j,i) /), &
2854	start = (/ dopts_time_count /), &
2855	count = (/ 1 /) )
2856	CALL netcdf_handle_error( 'data_output_ptseries', 392 )
2857	ENDDO
2858	ENDDO
2859	ENDIF
2860	#endif
2861
2862	DEALLOCATE( pts_value, pts_value_l )
2863
2864	CALL cpu_log( log_point(36), 'data_output_ptseries', 'stop' )
2865
2866	END SUBROUTINE lpm_data_output_ptseries
2867
2868
2869	!------------------------------------------------------------------------------!
2870	! Description:
2871	! ------------
2872	!> This routine reads the respective restart data for the lpm.
2873	!------------------------------------------------------------------------------!
2874	SUBROUTINE lpm_rrd_local_particles
2875
2876	CHARACTER (LEN=10) :: particle_binary_version !<
2877	CHARACTER (LEN=10) :: version_on_file !<
2878
2879	INTEGER(iwp) :: alloc_size !<
2880	INTEGER(iwp) :: ip !<
2881	INTEGER(iwp) :: jp !<
2882	INTEGER(iwp) :: kp !<
2883
2884	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles !<
2885
2886	!
2887	!-- Read particle data from previous model run.
2888	!-- First open the input unit.
2889	IF ( myid_char == '' ) THEN
2890	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN'//myid_char, &
2891	FORM='UNFORMATTED' )
2892	ELSE
2893	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN/'//myid_char, &
2894	FORM='UNFORMATTED' )
2895	ENDIF
2896
2897	!
2898	!-- First compare the version numbers
2899	READ ( 90 ) version_on_file
2900	particle_binary_version = '4.0'
2901	IF ( TRIM( version_on_file ) /= TRIM( particle_binary_version ) ) THEN
2902	message_string = 'version mismatch concerning data from prior ' // &
2903	'run &version on file = "' // &
2904	TRIM( version_on_file ) // &
2905	'&version in program = "' // &
2906	TRIM( particle_binary_version ) // '"'
2907	CALL message( 'lpm_read_restart_file', 'PA0214', 1, 2, 0, 6, 0 )
2908	ENDIF
2909
2910	!
2911	!-- If less particles are stored on the restart file than prescribed by
2912	!-- 1, the remainder is initialized by zero_particle to avoid
2913	!-- errors.
2914	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2915	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2916	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2917	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2918	0, 0, 0_idp, .FALSE., -1 )
2919	!
2920	!-- Read some particle parameters and the size of the particle arrays,
2921	!-- allocate them and read their contents.
2922	READ ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
2923	last_particle_release_time, number_of_particle_groups, &
2924	particle_groups, time_write_particle_data
2925
2926	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
2927	grid_particles(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
2928
2929	READ ( 90 ) prt_count
2930
2931	DO ip = nxl, nxr
2932	DO jp = nys, nyn
2933	DO kp = nzb+1, nzt
2934
2935	number_of_particles = prt_count(kp,jp,ip)
2936	IF ( number_of_particles > 0 ) THEN
2937	alloc_size = MAX( INT( number_of_particles * &
2938	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
2939	1 )
2940	ELSE
2941	alloc_size = 1
2942	ENDIF
2943
2944	ALLOCATE( grid_particles(kp,jp,ip)%particles(1:alloc_size) )
2945
2946	IF ( number_of_particles > 0 ) THEN
2947	ALLOCATE( tmp_particles(1:number_of_particles) )
2948	READ ( 90 ) tmp_particles
2949	grid_particles(kp,jp,ip)%particles(1:number_of_particles) = tmp_particles
2950	DEALLOCATE( tmp_particles )
2951	IF ( number_of_particles < alloc_size ) THEN
2952	grid_particles(kp,jp,ip)%particles(number_of_particles+1:alloc_size) &
2953	= zero_particle
2954	ENDIF
2955	ELSE
2956	grid_particles(kp,jp,ip)%particles(1:alloc_size) = zero_particle
2957	ENDIF
2958
2959	ENDDO
2960	ENDDO
2961	ENDDO
2962
2963	CLOSE ( 90 )
2964	!
2965	!-- Must be called to sort particles into blocks, which is needed for a fast
2966	!-- interpolation of the LES fields on the particle position.
2967	CALL lpm_sort_and_delete
2968
2969
2970	END SUBROUTINE lpm_rrd_local_particles
2971
2972
2973	SUBROUTINE lpm_rrd_local( k, nxlf, nxlc, nxl_on_file, nxrf, nxrc, &
2974	nxr_on_file, nynf, nync, nyn_on_file, nysf, &
2975	nysc, nys_on_file, tmp_3d, found )
2976
2977
2978	USE control_parameters, &
2979	ONLY: length, restart_string
2980
2981	INTEGER(iwp) :: k !<
2982	INTEGER(iwp) :: nxlc !<
2983	INTEGER(iwp) :: nxlf !<
2984	INTEGER(iwp) :: nxl_on_file !<
2985	INTEGER(iwp) :: nxrc !<
2986	INTEGER(iwp) :: nxrf !<
2987	INTEGER(iwp) :: nxr_on_file !<
2988	INTEGER(iwp) :: nync !<
2989	INTEGER(iwp) :: nynf !<
2990	INTEGER(iwp) :: nyn_on_file !<
2991	INTEGER(iwp) :: nysc !<
2992	INTEGER(iwp) :: nysf !<
2993	INTEGER(iwp) :: nys_on_file !<
2994
2995	LOGICAL, INTENT(OUT) :: found
2996
2997	REAL(wp), DIMENSION(nzb:nzt+1,nys_on_file-nbgp:nyn_on_file+nbgp,nxl_on_file-nbgp:nxr_on_file+nbgp) :: tmp_3d !<
2998
2999
3000	found = .TRUE.
3001
3002	SELECT CASE ( restart_string(1:length) )
3003
3004	CASE ( 'iran' ) ! matching random numbers is still unresolved issue
3005	IF ( k == 1 ) READ ( 13 ) iran, iran_part
3006
3007	CASE ( 'pc_av' )
3008	IF ( .NOT. ALLOCATED( pc_av ) ) THEN
3009	ALLOCATE( pc_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3010	ENDIF
3011	IF ( k == 1 ) READ ( 13 ) tmp_3d
3012	pc_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3013	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3014
3015	CASE ( 'pr_av' )
3016	IF ( .NOT. ALLOCATED( pr_av ) ) THEN
3017	ALLOCATE( pr_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3018	ENDIF
3019	IF ( k == 1 ) READ ( 13 ) tmp_3d
3020	pr_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3021	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3022
3023	CASE ( 'ql_c_av' )
3024	IF ( .NOT. ALLOCATED( ql_c_av ) ) THEN
3025	ALLOCATE( ql_c_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3026	ENDIF
3027	IF ( k == 1 ) READ ( 13 ) tmp_3d
3028	ql_c_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3029	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3030
3031	CASE ( 'ql_v_av' )
3032	IF ( .NOT. ALLOCATED( ql_v_av ) ) THEN
3033	ALLOCATE( ql_v_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3034	ENDIF
3035	IF ( k == 1 ) READ ( 13 ) tmp_3d
3036	ql_v_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3037	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3038
3039	CASE ( 'ql_vp_av' )
3040	IF ( .NOT. ALLOCATED( ql_vp_av ) ) THEN
3041	ALLOCATE( ql_vp_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3042	ENDIF
3043	IF ( k == 1 ) READ ( 13 ) tmp_3d
3044	ql_vp_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3045	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3046
3047	CASE DEFAULT
3048
3049	found = .FALSE.
3050
3051	END SELECT
3052
3053
3054	END SUBROUTINE lpm_rrd_local
3055
3056	!------------------------------------------------------------------------------!
3057	! Description:
3058	! ------------
3059	!> This routine writes the respective restart data for the lpm.
3060	!------------------------------------------------------------------------------!
3061	SUBROUTINE lpm_wrd_local
3062
3063	CHARACTER (LEN=10) :: particle_binary_version !<
3064
3065	INTEGER(iwp) :: ip !<
3066	INTEGER(iwp) :: jp !<
3067	INTEGER(iwp) :: kp !<
3068	!
3069	!-- First open the output unit.
3070	IF ( myid_char == '' ) THEN
3071	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT'//myid_char, &
3072	FORM='UNFORMATTED')
3073	ELSE
3074	IF ( myid == 0 ) CALL local_system( 'mkdir PARTICLE_RESTART_DATA_OUT' )
3075	#if defined( __parallel )
3076	!
3077	!-- Set a barrier in order to allow that thereafter all other processors
3078	!-- in the directory created by PE0 can open their file
3079	CALL MPI_BARRIER( comm2d, ierr )
3080	#endif
3081	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT/'//myid_char, &
3082	FORM='UNFORMATTED' )
3083	ENDIF
3084
3085	!
3086	!-- Write the version number of the binary format.
3087	!-- Attention: After changes to the following output commands the version
3088	!-- --------- number of the variable particle_binary_version must be
3089	!-- changed! Also, the version number and the list of arrays
3090	!-- to be read in lpm_read_restart_file must be adjusted
3091	!-- accordingly.
3092	particle_binary_version = '4.0'
3093	WRITE ( 90 ) particle_binary_version
3094
3095	!
3096	!-- Write some particle parameters, the size of the particle arrays
3097	WRITE ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
3098	last_particle_release_time, number_of_particle_groups, &
3099	particle_groups, time_write_particle_data
3100
3101	WRITE ( 90 ) prt_count
3102
3103	DO ip = nxl, nxr
3104	DO jp = nys, nyn
3105	DO kp = nzb+1, nzt
3106	number_of_particles = prt_count(kp,jp,ip)
3107	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
3108	IF ( number_of_particles <= 0 ) CYCLE
3109	WRITE ( 90 ) particles
3110	ENDDO
3111	ENDDO
3112	ENDDO
3113
3114	CLOSE ( 90 )
3115
3116	#if defined( __parallel )
3117	CALL MPI_BARRIER( comm2d, ierr )
3118	#endif
3119
3120	CALL wrd_write_string( 'iran' )
3121	WRITE ( 14 ) iran, iran_part
3122
3123
3124	END SUBROUTINE lpm_wrd_local
3125
3126
3127	!------------------------------------------------------------------------------!
3128	! Description:
3129	! ------------
3130	!> This routine writes the respective restart data for the lpm.
3131	!------------------------------------------------------------------------------!
3132	SUBROUTINE lpm_wrd_global
3133
3134	CALL wrd_write_string( 'curvature_solution_effects' )
3135	WRITE ( 14 ) curvature_solution_effects
3136
3137	CALL wrd_write_string( 'interpolation_simple_corrector' )
3138	WRITE ( 14 ) interpolation_simple_corrector
3139
3140	CALL wrd_write_string( 'interpolation_simple_predictor' )
3141	WRITE ( 14 ) interpolation_simple_predictor
3142
3143	CALL wrd_write_string( 'interpolation_trilinear' )
3144	WRITE ( 14 ) interpolation_trilinear
3145
3146	END SUBROUTINE lpm_wrd_global
3147
3148
3149	!------------------------------------------------------------------------------!
3150	! Description:
3151	! ------------
3152	!> This routine writes the respective restart data for the lpm.
3153	!------------------------------------------------------------------------------!
3154	SUBROUTINE lpm_rrd_global( found )
3155
3156	USE control_parameters, &
3157	ONLY: length, restart_string
3158
3159	LOGICAL, INTENT(OUT) :: found
3160
3161	found = .TRUE.
3162
3163	SELECT CASE ( restart_string(1:length) )
3164
3165	CASE ( 'curvature_solution_effects' )
3166	READ ( 13 ) curvature_solution_effects
3167
3168	CASE ( 'interpolation_simple_corrector' )
3169	READ ( 13 ) interpolation_simple_corrector
3170
3171	CASE ( 'interpolation_simple_predictor' )
3172	READ ( 13 ) interpolation_simple_predictor
3173
3174	CASE ( 'interpolation_trilinear' )
3175	READ ( 13 ) interpolation_trilinear
3176
3177	! CASE ( 'global_paramter' )
3178	! READ ( 13 ) global_parameter
3179	! CASE ( 'global_array' )
3180	! IF ( .NOT. ALLOCATED( global_array ) ) ALLOCATE( global_array(1:10) )
3181	! READ ( 13 ) global_array
3182
3183	CASE DEFAULT
3184
3185	found = .FALSE.
3186
3187	END SELECT
3188
3189	END SUBROUTINE lpm_rrd_global
3190
3191
3192	!------------------------------------------------------------------------------!
3193	! Description:
3194	! ------------
3195	!> This is a submodule of the lagrangian particle model. It contains all
3196	!> dynamic processes of the lpm. This includes the advection (resolved and sub-
3197	!> grid scale) as well as the boundary conditions of particles. As a next step
3198	!> this submodule should be excluded as an own file.
3199	!------------------------------------------------------------------------------!
3200	SUBROUTINE lpm_advec (ip,jp,kp)
3201
3202	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
3203
3204	INTEGER(iwp) :: i !< index variable along x
3205	INTEGER(iwp) :: i_next !< index variable along x
3206	INTEGER(iwp) :: ip !< index variable along x
3207	INTEGER(iwp) :: iteration_steps = 1 !< amount of iterations steps for corrector step
3208	INTEGER(iwp) :: j !< index variable along y
3209	INTEGER(iwp) :: j_next !< index variable along y
3210	INTEGER(iwp) :: jp !< index variable along y
3211	INTEGER(iwp) :: k !< index variable along z
3212	INTEGER(iwp) :: k_wall !< vertical index of topography top
3213	INTEGER(iwp) :: kp !< index variable along z
3214	INTEGER(iwp) :: k_next !< index variable along z
3215	INTEGER(iwp) :: kw !< index variable along z
3216	INTEGER(iwp) :: kkw !< index variable along z
3217	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
3218	INTEGER(iwp) :: nb !< block number particles are sorted in
3219	INTEGER(iwp) :: particle_end !< end index for partilce loop
3220	INTEGER(iwp) :: particle_start !< start index for particle loop
3221	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
3222	INTEGER(iwp) :: subbox_end !< end index for loop over subboxes in particle advection
3223	INTEGER(iwp) :: subbox_start !< start index for loop over subboxes in particle advection
3224	INTEGER(iwp) :: nn !< loop variable over iterations steps
3225
3226	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
3227	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
3228
3229	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
3230	REAL(wp) :: alpha !< interpolation facor for x-direction
3231
3232	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
3233	REAL(wp) :: beta !< interpolation facor for y-direction
3234	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
3235	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
3236	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
3237	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
3238	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
3239	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
3240	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
3241	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
3242	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
3243	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
3244	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
3245	REAL(wp) :: diameter !< diamter of droplet
3246	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
3247	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
3248	REAL(wp) :: dt_particle_m !< previous particle time step
3249	REAL(wp) :: dz_temp !< dummy for the vertical grid spacing
3250	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
3251	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
3252	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
3253	REAL(wp) :: exp_arg !< argument in the exponent - particle radius
3254	REAL(wp) :: exp_term !< exponent term
3255	REAL(wp) :: gamma !< interpolation facor for z-direction
3256	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
3257	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
3258	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
3259	REAL(wp) :: random_gauss !< Gaussian-distributed random number used for SGS particle advection
3260	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
3261	REAL(wp) :: rg1 !< Gaussian distributed random number
3262	REAL(wp) :: rg2 !< Gaussian distributed random number
3263	REAL(wp) :: rg3 !< Gaussian distributed random number
3264	REAL(wp) :: sigma !< velocity standard deviation
3265	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
3266	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
3267	REAL(wp) :: unext !< calculated particle u-velocity of corrector step
3268	REAL(wp) :: us_int !< friction velocity at particle grid box
3269	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
3270	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
3271	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
3272	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
3273	REAL(wp) :: vnext !< calculated particle v-velocity of corrector step
3274	REAL(wp) :: vv_int !< dummy to compute interpolated mean SGS TKE, used to scale SGS advection
3275	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
3276	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
3277	REAL(wp) :: wnext !< calculated particle w-velocity of corrector step
3278	REAL(wp) :: w_s !< terminal velocity of droplets
3279	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
3280	REAL(wp) :: xp !< calculated particle position in x of predictor step
3281	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
3282	REAL(wp) :: yp !< calculated particle position in y of predictor step
3283	REAL(wp) :: z_p !< surface layer height (0.5 dz)
3284	REAL(wp) :: zp !< calculated particle position in z of predictor step
3285
3286	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
3287	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
3288	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
3289	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
3290	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
3291	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
3292
3293	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
3294	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !< ratio between the density of the fluid and the density of the particles
3295	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
3296	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
3297	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
3298	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
3299	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
3300	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
3301	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
3302	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
3303	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
3304	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !< SGS particle velocity - u-component
3305	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !< SGS particle velocity - v-component
3306	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !< SGS particle velocity - w-component
3307	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
3308	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
3309	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
3310	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
3311	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
3312	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
3313
3314	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
3315
3316	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
3317	!
3318	!-- Determine height of Prandtl layer and distance between Prandtl-layer
3319	!-- height and horizontal mean roughness height, which are required for
3320	!-- vertical logarithmic interpolation of horizontal particle speeds
3321	!-- (for particles below first vertical grid level).
3322	z_p = zu(nzb+1) - zw(nzb)
3323	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
3324
3325	xv = particles(1:number_of_particles)%x
3326	yv = particles(1:number_of_particles)%y
3327	zv = particles(1:number_of_particles)%z
3328	dt_particle = dt_3d
3329
3330	!
3331	!-- This case uses a simple interpolation method for the particle velocites,
3332	!-- and applying a predictor-corrector method. @note the current time divergence
3333	!-- free time step is denoted with u_t etc.; the velocities of the time level of
3334	!-- t+1 wit u,v, and w, as the model is called after swap timelevel
3335	!-- @attention: for the corrector step the velocities of t(n+1) are required.
3336	!-- Therefore the particle code is executed at the end of the time intermediate
3337	!-- timestep routine. This interpolation method is described in more detail
3338	!-- in Grabowski et al., 2018 (GMD).
3339	IF ( interpolation_simple_corrector ) THEN
3340	!
3341	!-- Predictor step
3342	kkw = kp - 1
3343	DO n = 1, number_of_particles
3344
3345	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3346	u_int(n) = u_t(kp,jp,ip) * ( 1.0_wp - alpha ) + u_t(kp,jp,ip+1) * alpha
3347
3348	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3349	v_int(n) = v_t(kp,jp,ip) * ( 1.0_wp - beta ) + v_t(kp,jp+1,ip) * beta
3350
3351	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3352	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3353	w_int(n) = w_t(kkw,jp,ip) * ( 1.0_wp - gamma ) + w_t(kkw+1,jp,ip) * gamma
3354
3355	ENDDO
3356	!
3357	!-- Corrector step
3358	DO n = 1, number_of_particles
3359
3360	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3361
3362	DO nn = 1, iteration_steps
3363
3364	!
3365	!-- Guess new position
3366	xp = particles(n)%x + u_int(n) * dt_particle(n)
3367	yp = particles(n)%y + v_int(n) * dt_particle(n)
3368	zp = particles(n)%z + w_int(n) * dt_particle(n)
3369	!
3370	!-- x direction
3371	i_next = FLOOR( xp * ddx , KIND=iwp)
3372	alpha = MAX( MIN( ( xp - i_next * dx ) * ddx, 1.0_wp ), 0.0_wp )
3373	!
3374	!-- y direction
3375	j_next = FLOOR( yp * ddy )
3376	beta = MAX( MIN( ( yp - j_next * dy ) * ddy, 1.0_wp ), 0.0_wp )
3377	!
3378	!-- z_direction
3379	k_next = MAX( MIN( FLOOR( zp / (zw(kkw+1)-zw(kkw)) + offset_ocean_nzt ), nzt ), 0)
3380	gamma = MAX( MIN( ( zp - zw(k_next) ) / &
3381	( zw(k_next+1) - zw(k_next) ), 1.0_wp ), 0.0_wp )
3382	!
3383	!-- Calculate part of the corrector step
3384	unext = u(k_next+1, j_next, i_next) * ( 1.0_wp - alpha ) + &
3385	u(k_next+1, j_next, i_next+1) * alpha
3386
3387	vnext = v(k_next+1, j_next, i_next) * ( 1.0_wp - beta ) + &
3388	v(k_next+1, j_next+1, i_next ) * beta
3389
3390	wnext = w(k_next, j_next, i_next) * ( 1.0_wp - gamma ) + &
3391	w(k_next+1, j_next, i_next ) * gamma
3392
3393	!
3394	!-- Calculate interpolated particle velocity with predictor
3395	!-- corrector step. u_int, v_int and w_int describes the part of
3396	!-- the predictor step. unext, vnext and wnext is the part of the
3397	!-- corrector step. The resulting new position is set below. The
3398	!-- implementation is based on Grabowski et al., 2018 (GMD).
3399	u_int(n) = 0.5_wp * ( u_int(n) + unext )
3400	v_int(n) = 0.5_wp * ( v_int(n) + vnext )
3401	w_int(n) = 0.5_wp * ( w_int(n) + wnext )
3402
3403	ENDDO
3404	ENDDO
3405	!
3406	!-- This case uses a simple interpolation method for the particle velocites,
3407	!-- and applying a predictor.
3408	ELSEIF ( interpolation_simple_predictor ) THEN
3409	!
3410	!-- The particle position for the w velociy is based on the value of kp and kp-1
3411	kkw = kp - 1
3412	DO n = 1, number_of_particles
3413	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3414
3415	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3416	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3417
3418	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3419	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3420
3421	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3422	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3423	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3424	ENDDO
3425	!
3426	!-- The trilinear interpolation.
3427	ELSEIF ( interpolation_trilinear ) THEN
3428
3429	start_index = grid_particles(kp,jp,ip)%start_index
3430	end_index = grid_particles(kp,jp,ip)%end_index
3431
3432	DO nb = 0, 7
3433	!
3434	!-- Interpolate u velocity-component
3435	i = ip
3436	j = jp + block_offset(nb)%j_off
3437	k = kp + block_offset(nb)%k_off
3438
3439	DO n = start_index(nb), end_index(nb)
3440	!
3441	!-- Interpolation of the u velocity component onto particle position.
3442	!-- Particles are interpolation bi-linearly in the horizontal and a
3443	!-- linearly in the vertical. An exception is made for particles below
3444	!-- the first vertical grid level in case of a prandtl layer. In this
3445	!-- case the horizontal particle velocity components are determined using
3446	!-- Monin-Obukhov relations (if branch).
3447	!-- First, check if particle is located below first vertical grid level
3448	!-- above topography (Prandtl-layer height)
3449	!-- Determine vertical index of topography top
3450	k_wall = topo_top_ind(jp,ip,0)
3451
3452	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3453	!
3454	!-- Resolved-scale horizontal particle velocity is zero below z0.
3455	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3456	u_int(n) = 0.0_wp
3457	ELSE
3458	!
3459	!-- Determine the sublayer. Further used as index.
3460	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3461	* REAL( number_of_sublayers, KIND=wp ) &
3462	* d_z_p_z0
3463	!
3464	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3465	!-- interpolate linearly between precalculated logarithm.
3466	log_z_z0_int = log_z_z0(INT(height_p)) &
3467	+ ( height_p - INT(height_p) ) &
3468	* ( log_z_z0(INT(height_p)+1) &
3469	- log_z_z0(INT(height_p)) &
3470	)
3471	!
3472	!-- Get friction velocity and momentum flux from new surface data
3473	!-- types.
3474	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3475	surf_def_h(0)%end_index(jp,ip) ) THEN
3476	surf_start = surf_def_h(0)%start_index(jp,ip)
3477	!-- Limit friction velocity. In narrow canyons or holes the
3478	!-- friction velocity can become very small, resulting in a too
3479	!-- large particle speed.
3480	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3481	usws_int = surf_def_h(0)%usws(surf_start)
3482	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3483	surf_lsm_h%end_index(jp,ip) ) THEN
3484	surf_start = surf_lsm_h%start_index(jp,ip)
3485	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3486	usws_int = surf_lsm_h%usws(surf_start)
3487	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3488	surf_usm_h%end_index(jp,ip) ) THEN
3489	surf_start = surf_usm_h%start_index(jp,ip)
3490	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3491	usws_int = surf_usm_h%usws(surf_start)
3492	ENDIF
3493	!
3494	!-- Neutral solution is applied for all situations, e.g. also for
3495	!-- unstable and stable situations. Even though this is not exact
3496	!-- this saves a lot of CPU time since several calls of intrinsic
3497	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3498	!-- as sensitivity studies revealed no significant effect of
3499	!-- using the neutral solution also for un/stable situations.
3500	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
3501	* log_z_z0_int - u_gtrans
3502	ENDIF
3503	!
3504	!-- Particle above the first grid level. Bi-linear interpolation in the
3505	!-- horizontal and linear interpolation in the vertical direction.
3506	ELSE
3507	x = xv(n) - i * dx
3508	y = yv(n) + ( 0.5_wp - j ) * dy
3509	aa = x2 + y2
3510	bb = ( dx - x )2 + y2
3511	cc = x2 + ( dy - y )2
3512	dd = ( dx - x )2 + ( dy - y )2
3513	gg = aa + bb + cc + dd
3514
3515	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
3516	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
3517	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3518
3519	IF ( k == nzt ) THEN
3520	u_int(n) = u_int_l
3521	ELSE
3522	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
3523	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
3524	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3525	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3526	( u_int_u - u_int_l )
3527	ENDIF
3528	ENDIF
3529	ENDDO
3530	!
3531	!-- Same procedure for interpolation of the v velocity-component
3532	i = ip + block_offset(nb)%i_off
3533	j = jp
3534	k = kp + block_offset(nb)%k_off
3535
3536	DO n = start_index(nb), end_index(nb)
3537	!
3538	!-- Determine vertical index of topography top
3539	k_wall = topo_top_ind(jp,ip,0)
3540
3541	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3542	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3543	!
3544	!-- Resolved-scale horizontal particle velocity is zero below z0.
3545	v_int(n) = 0.0_wp
3546	ELSE
3547	!
3548	!-- Determine the sublayer. Further used as index. Please note,
3549	!-- logarithmus can not be reused from above, as in in case of
3550	!-- topography particle on u-grid can be above surface-layer height,
3551	!-- whereas it can be below on v-grid.
3552	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3553	* REAL( number_of_sublayers, KIND=wp ) &
3554	* d_z_p_z0
3555	!
3556	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3557	!-- interpolate linearly between precalculated logarithm.
3558	log_z_z0_int = log_z_z0(INT(height_p)) &
3559	+ ( height_p - INT(height_p) ) &
3560	* ( log_z_z0(INT(height_p)+1) &
3561	- log_z_z0(INT(height_p)) &
3562	)
3563	!
3564	!-- Get friction velocity and momentum flux from new surface data
3565	!-- types.
3566	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3567	surf_def_h(0)%end_index(jp,ip) ) THEN
3568	surf_start = surf_def_h(0)%start_index(jp,ip)
3569	!-- Limit friction velocity. In narrow canyons or holes the
3570	!-- friction velocity can become very small, resulting in a too
3571	!-- large particle speed.
3572	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3573	vsws_int = surf_def_h(0)%vsws(surf_start)
3574	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3575	surf_lsm_h%end_index(jp,ip) ) THEN
3576	surf_start = surf_lsm_h%start_index(jp,ip)
3577	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3578	vsws_int = surf_lsm_h%vsws(surf_start)
3579	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3580	surf_usm_h%end_index(jp,ip) ) THEN
3581	surf_start = surf_usm_h%start_index(jp,ip)
3582	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3583	vsws_int = surf_usm_h%vsws(surf_start)
3584	ENDIF
3585	!
3586	!-- Neutral solution is applied for all situations, e.g. also for
3587	!-- unstable and stable situations. Even though this is not exact
3588	!-- this saves a lot of CPU time since several calls of intrinsic
3589	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3590	!-- as sensitivity studies revealed no significant effect of
3591	!-- using the neutral solution also for un/stable situations.
3592	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
3593	* log_z_z0_int - v_gtrans
3594
3595	ENDIF
3596	ELSE
3597	x = xv(n) + ( 0.5_wp - i ) * dx
3598	y = yv(n) - j * dy
3599	aa = x2 + y2
3600	bb = ( dx - x )2 + y2
3601	cc = x2 + ( dy - y )2
3602	dd = ( dx - x )2 + ( dy - y )2
3603	gg = aa + bb + cc + dd
3604
3605	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
3606	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
3607	) / ( 3.0_wp * gg ) - v_gtrans
3608
3609	IF ( k == nzt ) THEN
3610	v_int(n) = v_int_l
3611	ELSE
3612	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
3613	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
3614	) / ( 3.0_wp * gg ) - v_gtrans
3615	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3616	( v_int_u - v_int_l )
3617	ENDIF
3618	ENDIF
3619	ENDDO
3620	!
3621	!-- Same procedure for interpolation of the w velocity-component
3622	i = ip + block_offset(nb)%i_off
3623	j = jp + block_offset(nb)%j_off
3624	k = kp - 1
3625
3626	DO n = start_index(nb), end_index(nb)
3627	IF ( vertical_particle_advection(particles(n)%group) ) THEN
3628	x = xv(n) + ( 0.5_wp - i ) * dx
3629	y = yv(n) + ( 0.5_wp - j ) * dy
3630	aa = x2 + y2
3631	bb = ( dx - x )2 + y2
3632	cc = x2 + ( dy - y )2
3633	dd = ( dx - x )2 + ( dy - y )2
3634	gg = aa + bb + cc + dd
3635
3636	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
3637	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
3638	) / ( 3.0_wp * gg )
3639
3640	IF ( k == nzt ) THEN
3641	w_int(n) = w_int_l
3642	ELSE
3643	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
3644	( gg-bb ) * w(k+1,j,i+1) + &
3645	( gg-cc ) * w(k+1,j+1,i) + &
3646	( gg-dd ) * w(k+1,j+1,i+1) &
3647	) / ( 3.0_wp * gg )
3648	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
3649	( w_int_u - w_int_l )
3650	ENDIF
3651	ELSE
3652	w_int(n) = 0.0_wp
3653	ENDIF
3654	ENDDO
3655	ENDDO
3656	ENDIF
3657
3658	!-- Interpolate and calculate quantities needed for calculating the SGS
3659	!-- velocities
3660	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
3661
3662	DO nb = 0,7
3663
3664	subbox_at_wall = .FALSE.
3665	!
3666	!-- In case of topography check if subbox is adjacent to a wall
3667	IF ( .NOT. topography == 'flat' ) THEN
3668	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
3669	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
3670	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
3671	IF ( .NOT. BTEST(wall_flags_static_0(k, jp, ip), 0) .OR. &
3672	.NOT. BTEST(wall_flags_static_0(kp, j, ip), 0) .OR. &
3673	.NOT. BTEST(wall_flags_static_0(kp, jp, i ), 0) ) &
3674	THEN
3675	subbox_at_wall = .TRUE.
3676	ENDIF
3677	ENDIF
3678	IF ( subbox_at_wall ) THEN
3679	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
3680	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
3681	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
3682	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
3683	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
3684	!
3685	!-- Set flag for stochastic equation.
3686	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
3687	ELSE
3688	i = ip + block_offset(nb)%i_off
3689	j = jp + block_offset(nb)%j_off
3690	k = kp + block_offset(nb)%k_off
3691
3692	DO n = start_index(nb), end_index(nb)
3693	!
3694	!-- Interpolate TKE
3695	x = xv(n) + ( 0.5_wp - i ) * dx
3696	y = yv(n) + ( 0.5_wp - j ) * dy
3697	aa = x2 + y2
3698	bb = ( dx - x )2 + y2
3699	cc = x2 + ( dy - y )2
3700	dd = ( dx - x )2 + ( dy - y )2
3701	gg = aa + bb + cc + dd
3702
3703	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
3704	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
3705	) / ( 3.0_wp * gg )
3706
3707	IF ( k+1 == nzt+1 ) THEN
3708	e_int(n) = e_int_l
3709	ELSE
3710	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
3711	( gg - bb ) * e(k+1,j,i+1) + &
3712	( gg - cc ) * e(k+1,j+1,i) + &
3713	( gg - dd ) * e(k+1,j+1,i+1) &
3714	) / ( 3.0_wp * gg )
3715	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3716	( e_int_u - e_int_l )
3717	ENDIF
3718	!
3719	!-- Needed to avoid NaN particle velocities (this might not be
3720	!-- required any more)
3721	IF ( e_int(n) <= 0.0_wp ) THEN
3722	e_int(n) = 1.0E-20_wp
3723	ENDIF
3724	!
3725	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
3726	!-- all position variables from above (TKE))
3727	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
3728	( gg - bb ) * de_dx(k,j,i+1) + &
3729	( gg - cc ) * de_dx(k,j+1,i) + &
3730	( gg - dd ) * de_dx(k,j+1,i+1) &
3731	) / ( 3.0_wp * gg )
3732
3733	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3734	de_dx_int(n) = de_dx_int_l
3735	ELSE
3736	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
3737	( gg - bb ) * de_dx(k+1,j,i+1) + &
3738	( gg - cc ) * de_dx(k+1,j+1,i) + &
3739	( gg - dd ) * de_dx(k+1,j+1,i+1) &
3740	) / ( 3.0_wp * gg )
3741	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3742	( de_dx_int_u - de_dx_int_l )
3743	ENDIF
3744	!
3745	!-- Interpolate the TKE gradient along y
3746	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
3747	( gg - bb ) * de_dy(k,j,i+1) + &
3748	( gg - cc ) * de_dy(k,j+1,i) + &
3749	( gg - dd ) * de_dy(k,j+1,i+1) &
3750	) / ( 3.0_wp * gg )
3751	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3752	de_dy_int(n) = de_dy_int_l
3753	ELSE
3754	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
3755	( gg - bb ) * de_dy(k+1,j,i+1) + &
3756	( gg - cc ) * de_dy(k+1,j+1,i) + &
3757	( gg - dd ) * de_dy(k+1,j+1,i+1) &
3758	) / ( 3.0_wp * gg )
3759	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3760	( de_dy_int_u - de_dy_int_l )
3761	ENDIF
3762
3763	!
3764	!-- Interpolate the TKE gradient along z
3765	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
3766	de_dz_int(n) = 0.0_wp
3767	ELSE
3768	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
3769	( gg - bb ) * de_dz(k,j,i+1) + &
3770	( gg - cc ) * de_dz(k,j+1,i) + &
3771	( gg - dd ) * de_dz(k,j+1,i+1) &
3772	) / ( 3.0_wp * gg )
3773
3774	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3775	de_dz_int(n) = de_dz_int_l
3776	ELSE
3777	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
3778	( gg - bb ) * de_dz(k+1,j,i+1) + &
3779	( gg - cc ) * de_dz(k+1,j+1,i) + &
3780	( gg - dd ) * de_dz(k+1,j+1,i+1) &
3781	) / ( 3.0_wp * gg )
3782	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3783	( de_dz_int_u - de_dz_int_l )
3784	ENDIF
3785	ENDIF
3786
3787	!
3788	!-- Interpolate the dissipation of TKE
3789	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
3790	( gg - bb ) * diss(k,j,i+1) + &
3791	( gg - cc ) * diss(k,j+1,i) + &
3792	( gg - dd ) * diss(k,j+1,i+1) &
3793	) / ( 3.0_wp * gg )
3794
3795	IF ( k == nzt ) THEN
3796	diss_int(n) = diss_int_l
3797	ELSE
3798	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
3799	( gg - bb ) * diss(k+1,j,i+1) + &
3800	( gg - cc ) * diss(k+1,j+1,i) + &
3801	( gg - dd ) * diss(k+1,j+1,i+1) &
3802	) / ( 3.0_wp * gg )
3803	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3804	( diss_int_u - diss_int_l )
3805	ENDIF
3806
3807	!
3808	!-- Set flag for stochastic equation.
3809	term_1_2(n) = 1.0_wp
3810	ENDDO
3811	ENDIF
3812	ENDDO
3813
3814	DO nb = 0,7
3815	i = ip + block_offset(nb)%i_off
3816	j = jp + block_offset(nb)%j_off
3817	k = kp + block_offset(nb)%k_off
3818
3819	DO n = start_index(nb), end_index(nb)
3820	!
3821	!-- Vertical interpolation of the horizontally averaged SGS TKE and
3822	!-- resolved-scale velocity variances and use the interpolated values
3823	!-- to calculate the coefficient fs, which is a measure of the ratio
3824	!-- of the subgrid-scale turbulent kinetic energy to the total amount
3825	!-- of turbulent kinetic energy.
3826	IF ( k == 0 ) THEN
3827	e_mean_int = hom(0,1,8,0)
3828	ELSE
3829	e_mean_int = hom(k,1,8,0) + &
3830	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
3831	( zu(k+1) - zu(k) ) * &
3832	( zv(n) - zu(k) )
3833	ENDIF
3834
3835	kw = kp - 1
3836
3837	IF ( k == 0 ) THEN
3838	aa = hom(k+1,1,30,0) * ( zv(n) / &
3839	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3840	bb = hom(k+1,1,31,0) * ( zv(n) / &
3841	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3842	cc = hom(kw+1,1,32,0) * ( zv(n) / &
3843	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
3844	ELSE
3845	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
3846	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3847	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
3848	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3849	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
3850	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
3851	ENDIF
3852
3853	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
3854	!
3855	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
3856	!-- an educated guess for the given case.
3857	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
3858	fs_int(n) = 1.0_wp
3859	ELSE
3860	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
3861	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
3862	ENDIF
3863
3864	ENDDO
3865	ENDDO
3866
3867	DO nb = 0, 7
3868	DO n = start_index(nb), end_index(nb)
3869	rg(n,1) = random_gauss( iran_part, 5.0_wp )
3870	rg(n,2) = random_gauss( iran_part, 5.0_wp )
3871	rg(n,3) = random_gauss( iran_part, 5.0_wp )
3872	ENDDO
3873	ENDDO
3874
3875	DO nb = 0, 7
3876	DO n = start_index(nb), end_index(nb)
3877
3878	!
3879	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
3880	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
3881	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
3882
3883	!
3884	!-- Calculate the next particle timestep. dt_gap is the time needed to
3885	!-- complete the current LES timestep.
3886	dt_gap(n) = dt_3d - particles(n)%dt_sum
3887	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
3888	particles(n)%aux1 = lagr_timescale(n)
3889	particles(n)%aux2 = dt_gap(n)
3890	!
3891	!-- The particle timestep should not be too small in order to prevent
3892	!-- the number of particle timesteps of getting too large
3893	IF ( dt_particle(n) < dt_min_part ) THEN
3894	IF ( dt_min_part < dt_gap(n) ) THEN
3895	dt_particle(n) = dt_min_part
3896	ELSE
3897	dt_particle(n) = dt_gap(n)
3898	ENDIF
3899	ENDIF
3900	rvar1_temp(n) = particles(n)%rvar1
3901	rvar2_temp(n) = particles(n)%rvar2
3902	rvar3_temp(n) = particles(n)%rvar3
3903	!
3904	!-- Calculate the SGS velocity components
3905	IF ( particles(n)%age == 0.0_wp ) THEN
3906	!
3907	!-- For new particles the SGS components are derived from the SGS
3908	!-- TKE. Limit the Gaussian random number to the interval
3909	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
3910	!-- from becoming unrealistically large.
3911	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3912	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
3913	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3914	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
3915	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3916	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
3917
3918	ELSE
3919	!
3920	!-- Restriction of the size of the new timestep: compared to the
3921	!-- previous timestep the increase must not exceed 200%. First,
3922	!-- check if age > age_m, in order to prevent that particles get zero
3923	!-- timestep.
3924	dt_particle_m = MERGE( dt_particle(n), &
3925	particles(n)%age - particles(n)%age_m, &
3926	particles(n)%age - particles(n)%age_m < &
3927	1E-8_wp )
3928	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
3929	dt_particle(n) = 2.0_wp * dt_particle_m
3930	ENDIF
3931
3932	!-- For old particles the SGS components are correlated with the
3933	!-- values from the previous timestep. Random numbers have also to
3934	!-- be limited (see above).
3935	!-- As negative values for the subgrid TKE are not allowed, the
3936	!-- change of the subgrid TKE with time cannot be smaller than
3937	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
3938	!-- value for the change of TKE
3939	de_dt_min = - e_int(n) / dt_particle(n)
3940
3941	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3942
3943	IF ( de_dt < de_dt_min ) THEN
3944	de_dt = de_dt_min
3945	ENDIF
3946
3947	CALL weil_stochastic_eq( rvar1_temp(n), fs_int(n), e_int(n), &
3948	de_dx_int(n), de_dt, diss_int(n), &
3949	dt_particle(n), rg(n,1), term_1_2(n) )
3950
3951	CALL weil_stochastic_eq( rvar2_temp(n), fs_int(n), e_int(n), &
3952	de_dy_int(n), de_dt, diss_int(n), &
3953	dt_particle(n), rg(n,2), term_1_2(n) )
3954
3955	CALL weil_stochastic_eq( rvar3_temp(n), fs_int(n), e_int(n), &
3956	de_dz_int(n), de_dt, diss_int(n), &
3957	dt_particle(n), rg(n,3), term_1_2(n) )
3958
3959	ENDIF
3960
3961	ENDDO
3962	ENDDO
3963	!
3964	!-- Check if the added SGS velocities result in a violation of the CFL-
3965	!-- criterion. If yes choose a smaller timestep based on the new velocities
3966	!-- and calculate SGS velocities again
3967	dz_temp = zw(kp)-zw(kp-1)
3968
3969	DO nb = 0, 7
3970	DO n = start_index(nb), end_index(nb)
3971	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
3972	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
3973	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
3974	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
3975
3976	dt_particle(n) = 0.9_wp * MIN( &
3977	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
3978	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
3979	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
3980
3981	!
3982	!-- Reset temporary SGS velocites to "current" ones
3983	rvar1_temp(n) = particles(n)%rvar1
3984	rvar2_temp(n) = particles(n)%rvar2
3985	rvar3_temp(n) = particles(n)%rvar3
3986
3987	de_dt_min = - e_int(n) / dt_particle(n)
3988
3989	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3990
3991	IF ( de_dt < de_dt_min ) THEN
3992	de_dt = de_dt_min
3993	ENDIF
3994
3995	CALL weil_stochastic_eq( rvar1_temp(n), fs_int(n), e_int(n), &
3996	de_dx_int(n), de_dt, diss_int(n), &
3997	dt_particle(n), rg(n,1), term_1_2(n) )
3998
3999	CALL weil_stochastic_eq( rvar2_temp(n), fs_int(n), e_int(n), &
4000	de_dy_int(n), de_dt, diss_int(n), &
4001	dt_particle(n), rg(n,2), term_1_2(n) )
4002
4003	CALL weil_stochastic_eq( rvar3_temp(n), fs_int(n), e_int(n), &
4004	de_dz_int(n), de_dt, diss_int(n), &
4005	dt_particle(n), rg(n,3), term_1_2(n) )
4006	ENDIF
4007
4008	!
4009	!-- Update particle velocites
4010	particles(n)%rvar1 = rvar1_temp(n)
4011	particles(n)%rvar2 = rvar2_temp(n)
4012	particles(n)%rvar3 = rvar3_temp(n)
4013	u_int(n) = u_int(n) + particles(n)%rvar1
4014	v_int(n) = v_int(n) + particles(n)%rvar2
4015	w_int(n) = w_int(n) + particles(n)%rvar3
4016	!
4017	!-- Store the SGS TKE of the current timelevel which is needed for
4018	!-- for calculating the SGS particle velocities at the next timestep
4019	particles(n)%e_m = e_int(n)
4020	ENDDO
4021	ENDDO
4022
4023	ELSE
4024	!
4025	!-- If no SGS velocities are used, only the particle timestep has to
4026	!-- be set
4027	dt_particle = dt_3d
4028
4029	ENDIF
4030
4031	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
4032	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
4033	!
4034	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4035	!-- number_of_particles. This depends on the selected interpolation method.
4036	!-- If particle interpolation method is not trilinear, then the sorting within
4037	!-- subboxes is not required. However, therefore the index start_index(nb) and
4038	!-- end_index(nb) are not defined and the loops are still over
4039	!-- number_of_particles. @todo find a more generic way to write this loop or
4040	!-- delete trilinear interpolation
4041	IF ( interpolation_trilinear ) THEN
4042	subbox_start = 0
4043	subbox_end = 7
4044	ELSE
4045	subbox_start = 1
4046	subbox_end = 1
4047	ENDIF
4048	!
4049	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4050	!-- are introduced, as they are not required. Accordingly, this loops goes
4051	!-- from 1 to 1.
4052	DO nb = subbox_start, subbox_end
4053	IF ( interpolation_trilinear ) THEN
4054	particle_start = start_index(nb)
4055	particle_end = end_index(nb)
4056	ELSE
4057	particle_start = 1
4058	particle_end = number_of_particles
4059	ENDIF
4060	!
4061	!-- Loop from particle start to particle end
4062	DO n = particle_start, particle_end
4063
4064	!
4065	!-- Particle advection
4066	IF ( dens_ratio(n) == 0.0_wp ) THEN
4067	!
4068	!-- Pure passive transport (without particle inertia)