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lagrangian_particle_model_mod.f90 @ 4276

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