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source: palm/trunk/SOURCE/lagrangian_particle_model_mod.f90 @ 4329

Last change on this file since 4329 was 4329, checked in by motisi, 5 years ago
Renamed wall_flags_0 to wall_flags_static_0
Property svn:keywords set to `Id`
File size: 353.9 KB

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1	!> @file lagrangian_particle_model_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2019 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lagrangian_particle_model_mod.f90 4329 2019-12-10 15:46:36Z motisi $
27	! Renamed wall_flags_0 to wall_flags_static_0
28	!
29	! 4282 2019-10-29 16:18:46Z schwenkel
30	! Bugfix of particle timeseries in case of more than one particle group
31	!
32	! 4277 2019-10-28 16:53:23Z schwenkel
33	! Bugfix: Added first_call_lpm in use statement
34	!
35	! 4276 2019-10-28 16:03:29Z schwenkel
36	! Modularize lpm: Move conditions in time intergration to module
37	!
38	! 4275 2019-10-28 15:34:55Z schwenkel
39	! Change call of simple predictor corrector method, i.e. two divergence free
40	! velocitiy fields are now used.
41	!
42	! 4232 2019-09-20 09:34:22Z knoop
43	! Removed INCLUDE "mpif.h", as it is not needed because of USE pegrid
44	!
45	! 4195 2019-08-28 13:44:27Z schwenkel
46	! Bugfix for simple_corrector interpolation method in case of ocean runs and
47	! output particle advection interpolation method into header
48	!
49	! 4182 2019-08-22 15:20:23Z scharf
50	! Corrected "Former revisions" section
51	!
52	! 4168 2019-08-16 13:50:17Z suehring
53	! Replace function get_topography_top_index by topo_top_ind
54	!
55	! 4145 2019-08-06 09:55:22Z schwenkel
56	! Some reformatting
57	!
58	! 4144 2019-08-06 09:11:47Z raasch
59	! relational operators .EQ., .NE., etc. replaced by ==, /=, etc.
60	!
61	! 4143 2019-08-05 15:14:53Z schwenkel
62	! Rename variable and change select case to if statement
63	!
64	! 4122 2019-07-26 13:11:56Z schwenkel
65	! Implement reset method as bottom boundary condition
66	!
67	! 4121 2019-07-26 10:01:22Z schwenkel
68	! Implementation of an simple method for interpolating the velocities to
69	! particle position
70	!
71	! 4114 2019-07-23 14:09:27Z schwenkel
72	! Bugfix: Added working precision for if statement
73	!
74	! 4054 2019-06-27 07:42:18Z raasch
75	! bugfix for calculating the minimum particle time step
76	!
77	! 4044 2019-06-19 12:28:27Z schwenkel
78	! Bugfix in case of grid strecting: corrected calculation of k-Index
79	!
80	! 4043 2019-06-18 16:59:00Z schwenkel
81	! Remove min_nr_particle, Add lpm_droplet_interactions_ptq into module
82	!
83	! 4028 2019-06-13 12:21:37Z schwenkel
84	! Further modularization of particle code components
85	!
86	! 4020 2019-06-06 14:57:48Z schwenkel
87	! Removing submodules
88	!
89	! 4018 2019-06-06 13:41:50Z eckhard
90	! Bugfix for former revision
91	!
92	! 4017 2019-06-06 12:16:46Z schwenkel
93	! Modularization of all lagrangian particle model code components
94	!
95	! 3655 2019-01-07 16:51:22Z knoop
96	! bugfix to guarantee correct particle releases in case that the release
97	! interval is smaller than the model timestep
98	!
99	! Revision 1.1 1999/11/25 16:16:06 raasch
100	! Initial revision
101	!
102	!
103	! Description:
104	! ------------
105	!> The embedded LPM allows for studying transport and dispersion processes within
106	!> turbulent flows. This model including passive particles that do not show any
107	!> feedback on the turbulent flow. Further also particles with inertia and
108	!> cloud droplets ca be simulated explicitly.
109	!>
110	!> @todo test lcm
111	!> implement simple interpolation method for subgrid scale velocites
112	!> @note <Enter notes on the module>
113	!> @bug <Enter bug on the module>
114	!------------------------------------------------------------------------------!
115	MODULE lagrangian_particle_model_mod
116
117	USE, INTRINSIC :: ISO_C_BINDING
118
119	USE arrays_3d, &
120	ONLY: de_dx, de_dy, de_dz, dzw, zu, zw, ql_c, ql_v, ql_vp, hyp, &
121	pt, q, exner, ql, diss, e, u, v, w, km, ql_1, ql_2, pt_p, q_p, &
122	d_exner
123
124	USE averaging, &
125	ONLY: ql_c_av, pr_av, pc_av, ql_vp_av, ql_v_av
126
127	USE basic_constants_and_equations_mod, &
128	ONLY: molecular_weight_of_solute, molecular_weight_of_water, magnus, &
129	pi, rd_d_rv, rho_l, r_v, rho_s, vanthoff, l_v, kappa, g, lv_d_cp
130
131	USE control_parameters, &
132	ONLY: bc_dirichlet_l, bc_dirichlet_n, bc_dirichlet_r, bc_dirichlet_s, &
133	cloud_droplets, constant_flux_layer, current_timestep_number, &
134	dt_3d, dt_3d_reached, first_call_lpm, humidity, &
135	dt_3d_reached_l, dt_dopts, dz, initializing_actions, &
136	intermediate_timestep_count, intermediate_timestep_count_max, &
137	message_string, molecular_viscosity, ocean_mode, &
138	particle_maximum_age, iran, &
139	simulated_time, topography, dopts_time_count, &
140	time_since_reference_point, rho_surface, u_gtrans, v_gtrans, &
141	dz_stretch_level, dz_stretch_level_start
142
143	USE cpulog, &
144	ONLY: cpu_log, log_point, log_point_s
145
146	USE indices, &
147	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
148	nzb_max, nzt,nbgp, ngp_2dh_outer, &
149	topo_top_ind, &
150	wall_flags_static_0
151
152	USE kinds
153
154	USE pegrid
155
156	USE particle_attributes
157
158	USE pmc_particle_interface, &
159	ONLY: pmcp_c_get_particle_from_parent, pmcp_p_fill_particle_win, &
160	pmcp_c_send_particle_to_parent, pmcp_p_empty_particle_win, &
161	pmcp_p_delete_particles_in_fine_grid_area, pmcp_g_init, &
162	pmcp_g_print_number_of_particles
163
164	USE pmc_interface, &
165	ONLY: nested_run
166
167	USE grid_variables, &
168	ONLY: ddx, dx, ddy, dy
169
170	USE netcdf_interface, &
171	ONLY: netcdf_data_format, netcdf_deflate, dopts_num, id_set_pts, &
172	id_var_dopts, id_var_time_pts, nc_stat, &
173	netcdf_handle_error
174
175	USE random_function_mod, &
176	ONLY: random_function
177
178	USE statistics, &
179	ONLY: hom
180
181	USE surface_mod, &
182	ONLY: bc_h, &
183	surf_def_h, &
184	surf_lsm_h, &
185	surf_usm_h
186
187	#if defined( __parallel ) && !defined( __mpifh )
188	USE MPI
189	#endif
190
191	#if defined( __netcdf )
192	USE NETCDF
193	#endif
194
195	IMPLICIT NONE
196
197	CHARACTER(LEN=15) :: aero_species = 'nacl' !< aerosol species
198	CHARACTER(LEN=15) :: aero_type = 'maritime' !< aerosol type
199	CHARACTER(LEN=15) :: bc_par_lr = 'cyclic' !< left/right boundary condition
200	CHARACTER(LEN=15) :: bc_par_ns = 'cyclic' !< north/south boundary condition
201	CHARACTER(LEN=15) :: bc_par_b = 'reflect' !< bottom boundary condition
202	CHARACTER(LEN=15) :: bc_par_t = 'absorb' !< top boundary condition
203	CHARACTER(LEN=15) :: collision_kernel = 'none' !< collision kernel
204
205	CHARACTER(LEN=5) :: splitting_function = 'gamma' !< function for calculation critical weighting factor
206	CHARACTER(LEN=5) :: splitting_mode = 'const' !< splitting mode
207
208	CHARACTER(LEN=25) :: particle_advection_interpolation = 'trilinear' !< interpolation method for calculatin the particle
209
210	INTEGER(iwp) :: deleted_particles = 0 !< number of deleted particles per time step
211	INTEGER(iwp) :: i_splitting_mode !< dummy for splitting mode
212	INTEGER(iwp) :: iran_part = -1234567 !< number for random generator
213	INTEGER(iwp) :: max_number_particles_per_gridbox = 100 !< namelist parameter (see documentation)
214	INTEGER(iwp) :: isf !< dummy for splitting function
215	INTEGER(iwp) :: number_particles_per_gridbox = -1 !< namelist parameter (see documentation)
216	INTEGER(iwp) :: number_of_sublayers = 20 !< number of sublayers for particle velocities betwenn surface and first grid level
217	INTEGER(iwp) :: offset_ocean_nzt = 0 !< in case of oceans runs, the vertical index calculations need an offset
218	INTEGER(iwp) :: offset_ocean_nzt_m1 = 0 !< in case of oceans runs, the vertical index calculations need an offset
219	INTEGER(iwp) :: particles_per_point = 1 !< namelist parameter (see documentation)
220	INTEGER(iwp) :: radius_classes = 20 !< namelist parameter (see documentation)
221	INTEGER(iwp) :: splitting_factor = 2 !< namelist parameter (see documentation)
222	INTEGER(iwp) :: splitting_factor_max = 5 !< namelist parameter (see documentation)
223	INTEGER(iwp) :: step_dealloc = 100 !< namelist parameter (see documentation)
224	INTEGER(iwp) :: total_number_of_particles !< total number of particles in the whole model domain
225	INTEGER(iwp) :: trlp_count_sum !< parameter for particle exchange of PEs
226	INTEGER(iwp) :: trlp_count_recv_sum !< parameter for particle exchange of PEs
227	INTEGER(iwp) :: trrp_count_sum !< parameter for particle exchange of PEs
228	INTEGER(iwp) :: trrp_count_recv_sum !< parameter for particle exchange of PEs
229	INTEGER(iwp) :: trsp_count_sum !< parameter for particle exchange of PEs
230	INTEGER(iwp) :: trsp_count_recv_sum !< parameter for particle exchange of PEs
231	INTEGER(iwp) :: trnp_count_sum !< parameter for particle exchange of PEs
232	INTEGER(iwp) :: trnp_count_recv_sum !< parameter for particle exchange of PEs
233
234	LOGICAL :: lagrangian_particle_model = .FALSE. !< namelist parameter (see documentation)
235	LOGICAL :: curvature_solution_effects = .FALSE. !< namelist parameter (see documentation)
236	LOGICAL :: deallocate_memory = .TRUE. !< namelist parameter (see documentation)
237	LOGICAL :: hall_kernel = .FALSE. !< flag for collision kernel
238	LOGICAL :: merging = .FALSE. !< namelist parameter (see documentation)
239	LOGICAL :: random_start_position = .FALSE. !< namelist parameter (see documentation)
240	LOGICAL :: read_particles_from_restartfile = .TRUE. !< namelist parameter (see documentation)
241	LOGICAL :: seed_follows_topography = .FALSE. !< namelist parameter (see documentation)
242	LOGICAL :: splitting = .FALSE. !< namelist parameter (see documentation)
243	LOGICAL :: use_kernel_tables = .FALSE. !< parameter, which turns on the use of precalculated collision kernels
244	LOGICAL :: write_particle_statistics = .FALSE. !< namelist parameter (see documentation)
245	LOGICAL :: interpolation_simple_predictor = .FALSE. !< flag for simple particle advection interpolation with predictor step
246	LOGICAL :: interpolation_simple_corrector = .FALSE. !< flag for simple particle advection interpolation with corrector step
247	LOGICAL :: interpolation_trilinear = .FALSE. !< flag for trilinear particle advection interpolation
248
249	LOGICAL, DIMENSION(max_number_of_particle_groups) :: vertical_particle_advection = .TRUE. !< Switch for vertical particle transport
250
251	REAL(wp) :: aero_weight = 1.0_wp !< namelist parameter (see documentation)
252	REAL(wp) :: dt_min_part = 0.0002_wp !< minimum particle time step when SGS velocities are used (s)
253	REAL(wp) :: dt_prel = 9999999.9_wp !< namelist parameter (see documentation)
254	REAL(wp) :: dt_write_particle_data = 9999999.9_wp !< namelist parameter (see documentation)
255	REAL(wp) :: end_time_prel = 9999999.9_wp !< namelist parameter (see documentation)
256	REAL(wp) :: initial_weighting_factor = 1.0_wp !< namelist parameter (see documentation)
257	REAL(wp) :: last_particle_release_time = 0.0_wp !< last time of particle release
258	REAL(wp) :: log_sigma(3) = 1.0_wp !< namelist parameter (see documentation)
259	REAL(wp) :: na(3) = 0.0_wp !< namelist parameter (see documentation)
260	REAL(wp) :: number_concentration = -1.0_wp !< namelist parameter (see documentation)
261	REAL(wp) :: radius_merge = 1.0E-7_wp !< namelist parameter (see documentation)
262	REAL(wp) :: radius_split = 40.0E-6_wp !< namelist parameter (see documentation)
263	REAL(wp) :: rm(3) = 1.0E-6_wp !< namelist parameter (see documentation)
264	REAL(wp) :: sgs_wf_part !< parameter for sgs
265	REAL(wp) :: time_write_particle_data = 0.0_wp !< write particle data at current time on file
266	REAL(wp) :: weight_factor_merge = -1.0_wp !< namelist parameter (see documentation)
267	REAL(wp) :: weight_factor_split = -1.0_wp !< namelist parameter (see documentation)
268	REAL(wp) :: z0_av_global !< horizontal mean value of z0
269
270	REAL(wp) :: rclass_lbound !<
271	REAL(wp) :: rclass_ubound !<
272
273	REAL(wp), PARAMETER :: c_0 = 3.0_wp !< parameter for lagrangian timescale
274
275	REAL(wp), DIMENSION(max_number_of_particle_groups) :: density_ratio = 9999999.9_wp !< namelist parameter (see documentation)
276	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdx = 9999999.9_wp !< namelist parameter (see documentation)
277	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdy = 9999999.9_wp !< namelist parameter (see documentation)
278	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdz = 9999999.9_wp !< namelist parameter (see documentation)
279	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psb = 9999999.9_wp !< namelist parameter (see documentation)
280	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psl = 9999999.9_wp !< namelist parameter (see documentation)
281	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psn = 9999999.9_wp !< namelist parameter (see documentation)
282	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psr = 9999999.9_wp !< namelist parameter (see documentation)
283	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pss = 9999999.9_wp !< namelist parameter (see documentation)
284	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pst = 9999999.9_wp !< namelist parameter (see documentation).
285	REAL(wp), DIMENSION(max_number_of_particle_groups) :: radius = 9999999.9_wp !< namelist parameter (see documentation)
286
287	REAL(wp), DIMENSION(:), ALLOCATABLE :: log_z_z0 !< Precalculate LOG(z/z0)
288
289	INTEGER(iwp), PARAMETER :: NR_2_direction_move = 10000 !<
290	INTEGER(iwp) :: nr_move_north !<
291	INTEGER(iwp) :: nr_move_south !<
292
293	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_north
294	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_south
295
296	REAL(wp) :: epsilon_collision !<
297	REAL(wp) :: urms !<
298
299	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
300	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
301	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
302
303	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
304	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
305	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
306	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
307	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
308
309	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
310	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: u_t !< u value of old timelevel t
311	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: v_t !< v value of old timelevel t
312	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: w_t !< w value of old timelevel t
313
314
315	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
316	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
317
318	SAVE
319
320	PRIVATE
321
322	PUBLIC lpm_parin, &
323	lpm_header, &
324	lpm_init_arrays,&
325	lpm_init, &
326	lpm_actions, &
327	lpm_data_output_ptseries, &
328	lpm_interaction_droplets_ptq, &
329	lpm_rrd_local_particles, &
330	lpm_wrd_local, &
331	lpm_rrd_global, &
332	lpm_wrd_global, &
333	lpm_rrd_local, &
334	lpm_check_parameters
335
336	PUBLIC lagrangian_particle_model
337
338	INTERFACE lpm_check_parameters
339	MODULE PROCEDURE lpm_check_parameters
340	END INTERFACE lpm_check_parameters
341
342	INTERFACE lpm_parin
343	MODULE PROCEDURE lpm_parin
344	END INTERFACE lpm_parin
345
346	INTERFACE lpm_header
347	MODULE PROCEDURE lpm_header
348	END INTERFACE lpm_header
349
350	INTERFACE lpm_init_arrays
351	MODULE PROCEDURE lpm_init_arrays
352	END INTERFACE lpm_init_arrays
353
354	INTERFACE lpm_init
355	MODULE PROCEDURE lpm_init
356	END INTERFACE lpm_init
357
358	INTERFACE lpm_actions
359	MODULE PROCEDURE lpm_actions
360	END INTERFACE lpm_actions
361
362	INTERFACE lpm_data_output_ptseries
363	MODULE PROCEDURE lpm_data_output_ptseries
364	END INTERFACE
365
366	INTERFACE lpm_rrd_local_particles
367	MODULE PROCEDURE lpm_rrd_local_particles
368	END INTERFACE lpm_rrd_local_particles
369
370	INTERFACE lpm_rrd_global
371	MODULE PROCEDURE lpm_rrd_global
372	END INTERFACE lpm_rrd_global
373
374	INTERFACE lpm_rrd_local
375	MODULE PROCEDURE lpm_rrd_local
376	END INTERFACE lpm_rrd_local
377
378	INTERFACE lpm_wrd_local
379	MODULE PROCEDURE lpm_wrd_local
380	END INTERFACE lpm_wrd_local
381
382	INTERFACE lpm_wrd_global
383	MODULE PROCEDURE lpm_wrd_global
384	END INTERFACE lpm_wrd_global
385
386	INTERFACE lpm_advec
387	MODULE PROCEDURE lpm_advec
388	END INTERFACE lpm_advec
389
390	INTERFACE lpm_calc_liquid_water_content
391	MODULE PROCEDURE lpm_calc_liquid_water_content
392	END INTERFACE
393
394	INTERFACE lpm_interaction_droplets_ptq
395	MODULE PROCEDURE lpm_interaction_droplets_ptq
396	MODULE PROCEDURE lpm_interaction_droplets_ptq_ij
397	END INTERFACE lpm_interaction_droplets_ptq
398
399	INTERFACE lpm_boundary_conds
400	MODULE PROCEDURE lpm_boundary_conds
401	END INTERFACE lpm_boundary_conds
402
403	INTERFACE lpm_droplet_condensation
404	MODULE PROCEDURE lpm_droplet_condensation
405	END INTERFACE
406
407	INTERFACE lpm_droplet_collision
408	MODULE PROCEDURE lpm_droplet_collision
409	END INTERFACE lpm_droplet_collision
410
411	INTERFACE lpm_init_kernels
412	MODULE PROCEDURE lpm_init_kernels
413	END INTERFACE lpm_init_kernels
414
415	INTERFACE lpm_splitting
416	MODULE PROCEDURE lpm_splitting
417	END INTERFACE lpm_splitting
418
419	INTERFACE lpm_merging
420	MODULE PROCEDURE lpm_merging
421	END INTERFACE lpm_merging
422
423	INTERFACE lpm_exchange_horiz
424	MODULE PROCEDURE lpm_exchange_horiz
425	END INTERFACE lpm_exchange_horiz
426
427	INTERFACE lpm_move_particle
428	MODULE PROCEDURE lpm_move_particle
429	END INTERFACE lpm_move_particle
430
431	INTERFACE realloc_particles_array
432	MODULE PROCEDURE realloc_particles_array
433	END INTERFACE realloc_particles_array
434
435	INTERFACE dealloc_particles_array
436	MODULE PROCEDURE dealloc_particles_array
437	END INTERFACE dealloc_particles_array
438
439	INTERFACE lpm_sort_and_delete
440	MODULE PROCEDURE lpm_sort_and_delete
441	END INTERFACE lpm_sort_and_delete
442
443	INTERFACE lpm_sort_timeloop_done
444	MODULE PROCEDURE lpm_sort_timeloop_done
445	END INTERFACE lpm_sort_timeloop_done
446
447	INTERFACE lpm_pack
448	MODULE PROCEDURE lpm_pack
449	END INTERFACE lpm_pack
450
451	CONTAINS
452
453
454	!------------------------------------------------------------------------------!
455	! Description:
456	! ------------
457	!> Parin for &particle_parameters for the Lagrangian particle model
458	!------------------------------------------------------------------------------!
459	SUBROUTINE lpm_parin
460
461	CHARACTER (LEN=80) :: line !<
462
463	NAMELIST /particles_par/ &
464	aero_species, &
465	aero_type, &
466	aero_weight, &
467	alloc_factor, &
468	bc_par_b, &
469	bc_par_lr, &
470	bc_par_ns, &
471	bc_par_t, &
472	collision_kernel, &
473	curvature_solution_effects, &
474	deallocate_memory, &
475	density_ratio, &
476	dissipation_classes, &
477	dt_dopts, &
478	dt_min_part, &
479	dt_prel, &
480	dt_write_particle_data, &
481	end_time_prel, &
482	initial_weighting_factor, &
483	log_sigma, &
484	max_number_particles_per_gridbox, &
485	merging, &
486	na, &
487	number_concentration, &
488	number_of_particle_groups, &
489	number_particles_per_gridbox, &
490	particles_per_point, &
491	particle_advection_start, &
492	particle_advection_interpolation, &
493	particle_maximum_age, &
494	pdx, &
495	pdy, &
496	pdz, &
497	psb, &
498	psl, &
499	psn, &
500	psr, &
501	pss, &
502	pst, &
503	radius, &
504	radius_classes, &
505	radius_merge, &
506	radius_split, &
507	random_start_position, &
508	read_particles_from_restartfile, &
509	rm, &
510	seed_follows_topography, &
511	splitting, &
512	splitting_factor, &
513	splitting_factor_max, &
514	splitting_function, &
515	splitting_mode, &
516	step_dealloc, &
517	use_sgs_for_particles, &
518	vertical_particle_advection, &
519	weight_factor_merge, &
520	weight_factor_split, &
521	write_particle_statistics
522
523	NAMELIST /particle_parameters/ &
524	aero_species, &
525	aero_type, &
526	aero_weight, &
527	alloc_factor, &
528	bc_par_b, &
529	bc_par_lr, &
530	bc_par_ns, &
531	bc_par_t, &
532	collision_kernel, &
533	curvature_solution_effects, &
534	deallocate_memory, &
535	density_ratio, &
536	dissipation_classes, &
537	dt_dopts, &
538	dt_min_part, &
539	dt_prel, &
540	dt_write_particle_data, &
541	end_time_prel, &
542	initial_weighting_factor, &
543	log_sigma, &
544	max_number_particles_per_gridbox, &
545	merging, &
546	na, &
547	number_concentration, &
548	number_of_particle_groups, &
549	number_particles_per_gridbox, &
550	particles_per_point, &
551	particle_advection_start, &
552	particle_advection_interpolation, &
553	particle_maximum_age, &
554	pdx, &
555	pdy, &
556	pdz, &
557	psb, &
558	psl, &
559	psn, &
560	psr, &
561	pss, &
562	pst, &
563	radius, &
564	radius_classes, &
565	radius_merge, &
566	radius_split, &
567	random_start_position, &
568	read_particles_from_restartfile, &
569	rm, &
570	seed_follows_topography, &
571	splitting, &
572	splitting_factor, &
573	splitting_factor_max, &
574	splitting_function, &
575	splitting_mode, &
576	step_dealloc, &
577	use_sgs_for_particles, &
578	vertical_particle_advection, &
579	weight_factor_merge, &
580	weight_factor_split, &
581	write_particle_statistics
582
583	!
584	!-- Position the namelist-file at the beginning (it was already opened in
585	!-- parin), search for the namelist-group of the package and position the
586	!-- file at this line. Do the same for each optionally used package.
587	line = ' '
588
589	!
590	!-- Try to find particles package
591	REWIND ( 11 )
592	line = ' '
593	DO WHILE ( INDEX( line, '&particle_parameters' ) == 0 )
594	READ ( 11, '(A)', END=12 ) line
595	ENDDO
596	BACKSPACE ( 11 )
597	!
598	!-- Read user-defined namelist
599	READ ( 11, particle_parameters, ERR = 10 )
600	!
601	!-- Set flag that indicates that particles are switched on
602	particle_advection = .TRUE.
603
604	GOTO 14
605
606	10 BACKSPACE( 11 )
607	READ( 11 , '(A)') line
608	CALL parin_fail_message( 'particle_parameters', line )
609	!
610	!-- Try to find particles package (old namelist)
611	12 REWIND ( 11 )
612	line = ' '
613	DO WHILE ( INDEX( line, '&particles_par' ) == 0 )
614	READ ( 11, '(A)', END=14 ) line
615	ENDDO
616	BACKSPACE ( 11 )
617	!
618	!-- Read user-defined namelist
619	READ ( 11, particles_par, ERR = 13, END = 14 )
620
621	message_string = 'namelist particles_par is deprecated and will be ' // &
622	'removed in near future. Please use namelist ' // &
623	'particle_parameters instead'
624	CALL message( 'package_parin', 'PA0487', 0, 1, 0, 6, 0 )
625
626	!
627	!-- Set flag that indicates that particles are switched on
628	particle_advection = .TRUE.
629
630	GOTO 14
631
632	13 BACKSPACE( 11 )
633	READ( 11 , '(A)') line
634	CALL parin_fail_message( 'particles_par', line )
635
636	14 CONTINUE
637
638	END SUBROUTINE lpm_parin
639
640	!------------------------------------------------------------------------------!
641	! Description:
642	! ------------
643	!> Writes used particle attributes in header file.
644	!------------------------------------------------------------------------------!
645	SUBROUTINE lpm_header ( io )
646
647	CHARACTER (LEN=40) :: output_format !< netcdf format
648
649	INTEGER(iwp) :: i !<
650	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
651
652
653	IF ( humidity .AND. cloud_droplets ) THEN
654	WRITE ( io, 433 )
655	IF ( curvature_solution_effects ) WRITE ( io, 434 )
656	IF ( collision_kernel /= 'none' ) THEN
657	WRITE ( io, 435 ) TRIM( collision_kernel )
658	IF ( collision_kernel(6:9) == 'fast' ) THEN
659	WRITE ( io, 436 ) radius_classes, dissipation_classes
660	ENDIF
661	ELSE
662	WRITE ( io, 437 )
663	ENDIF
664	ENDIF
665
666	IF ( particle_advection ) THEN
667	!
668	!-- Particle attributes
669	WRITE ( io, 480 ) particle_advection_start, TRIM(particle_advection_interpolation), &
670	dt_prel, bc_par_lr, &
671	bc_par_ns, bc_par_b, bc_par_t, particle_maximum_age, &
672	end_time_prel
673	IF ( use_sgs_for_particles ) WRITE ( io, 488 ) dt_min_part
674	IF ( random_start_position ) WRITE ( io, 481 )
675	IF ( seed_follows_topography ) WRITE ( io, 496 )
676	IF ( particles_per_point > 1 ) WRITE ( io, 489 ) particles_per_point
677	WRITE ( io, 495 ) total_number_of_particles
678	IF ( dt_write_particle_data /= 9999999.9_wp ) THEN
679	WRITE ( io, 485 ) dt_write_particle_data
680	IF ( netcdf_data_format > 1 ) THEN
681	output_format = 'netcdf (64 bit offset) and binary'
682	ELSE
683	output_format = 'netcdf and binary'
684	ENDIF
685	IF ( netcdf_deflate == 0 ) THEN
686	WRITE ( io, 344 ) output_format
687	ELSE
688	WRITE ( io, 354 ) TRIM( output_format ), netcdf_deflate
689	ENDIF
690	ENDIF
691	IF ( dt_dopts /= 9999999.9_wp ) WRITE ( io, 494 ) dt_dopts
692	IF ( write_particle_statistics ) WRITE ( io, 486 )
693
694	WRITE ( io, 487 ) number_of_particle_groups
695
696	DO i = 1, number_of_particle_groups
697	IF ( i == 1 .AND. density_ratio(i) == 9999999.9_wp ) THEN
698	WRITE ( io, 490 ) i, 0.0_wp
699	WRITE ( io, 492 )
700	ELSE
701	WRITE ( io, 490 ) i, radius(i)
702	IF ( density_ratio(i) /= 0.0_wp ) THEN
703	WRITE ( io, 491 ) density_ratio(i)
704	ELSE
705	WRITE ( io, 492 )
706	ENDIF
707	ENDIF
708	WRITE ( io, 493 ) psl(i), psr(i), pss(i), psn(i), psb(i), pst(i), &
709	pdx(i), pdy(i), pdz(i)
710	IF ( .NOT. vertical_particle_advection(i) ) WRITE ( io, 482 )
711	ENDDO
712
713	ENDIF
714
715	344 FORMAT (' Output format: ',A/)
716	354 FORMAT (' Output format: ',A, ' compressed with level: ',I1/)
717
718	433 FORMAT (' Cloud droplets treated explicitly using the Lagrangian part', &
719	'icle model')
720	434 FORMAT (' Curvature and solution effecs are considered for growth of', &
721	' droplets < 1.0E-6 m')
722	435 FORMAT (' Droplet collision is handled by ',A,'-kernel')
723	436 FORMAT (' Fast kernel with fixed radius- and dissipation classes ', &
724	'are used'/ &
725	' number of radius classes: ',I3,' interval ', &
726	'[1.0E-6,2.0E-4] m'/ &
727	' number of dissipation classes: ',I2,' interval ', &
728	'[0,1000] cm2/s3')
729	437 FORMAT (' Droplet collision is switched off')
730
731	480 FORMAT (' Particles:'/ &
732	' ---------'// &
733	' Particle advection is active (switched on at t = ', F7.1, &
734	' s)'/ &
735	' Interpolation of particle velocities is done by using ', A, &
736	' method'/ &
737	' Start of new particle generations every ',F6.1,' s'/ &
738	' Boundary conditions: left/right: ', A, ' north/south: ', A/&
739	' bottom: ', A, ' top: ', A/&
740	' Maximum particle age: ',F9.1,' s'/ &
741	' Advection stopped at t = ',F9.1,' s'/)
742	481 FORMAT (' Particles have random start positions'/)
743	482 FORMAT (' Particles are advected only horizontally'/)
744	485 FORMAT (' Particle data are written on file every ', F9.1, ' s')
745	486 FORMAT (' Particle statistics are written on file'/)
746	487 FORMAT (' Number of particle groups: ',I2/)
747	488 FORMAT (' SGS velocity components are used for particle advection'/ &
748	' minimum timestep for advection:', F8.5/)
749	489 FORMAT (' Number of particles simultaneously released at each ', &
750	'point: ', I5/)
751	490 FORMAT (' Particle group ',I2,':'/ &
752	' Particle radius: ',E10.3, 'm')
753	491 FORMAT (' Particle inertia is activated'/ &
754	' density_ratio (rho_fluid/rho_particle) =',F6.3/)
755	492 FORMAT (' Particles are advected only passively (no inertia)'/)
756	493 FORMAT (' Boundaries of particle source: x:',F8.1,' - ',F8.1,' m'/&
757	' y:',F8.1,' - ',F8.1,' m'/&
758	' z:',F8.1,' - ',F8.1,' m'/&
759	' Particle distances: dx = ',F8.1,' m dy = ',F8.1, &
760	' m dz = ',F8.1,' m'/)
761	494 FORMAT (' Output of particle time series in NetCDF format every ', &
762	F8.2,' s'/)
763	495 FORMAT (' Number of particles in total domain: ',I10/)
764	496 FORMAT (' Initial vertical particle positions are interpreted ', &
765	'as relative to the given topography')
766
767	END SUBROUTINE lpm_header
768
769	!------------------------------------------------------------------------------!
770	! Description:
771	! ------------
772	!> Writes used particle attributes in header file.
773	!------------------------------------------------------------------------------!
774	SUBROUTINE lpm_check_parameters
775
776	!
777	!-- Collision kernels:
778	SELECT CASE ( TRIM( collision_kernel ) )
779
780	CASE ( 'hall', 'hall_fast' )
781	hall_kernel = .TRUE.
782
783	CASE ( 'wang', 'wang_fast' )
784	wang_kernel = .TRUE.
785
786	CASE ( 'none' )
787
788
789	CASE DEFAULT
790	message_string = 'unknown collision kernel: collision_kernel = "' // &
791	TRIM( collision_kernel ) // '"'
792	CALL message( 'lpm_check_parameters', 'PA0350', 1, 2, 0, 6, 0 )
793
794	END SELECT
795	IF ( collision_kernel(6:9) == 'fast' ) use_kernel_tables = .TRUE.
796
797	!
798	!-- Subgrid scale velocites with the simple interpolation method for resolved
799	!-- velocites is not implemented for passive particles. However, for cloud
800	!-- it can be combined as the sgs-velocites for active particles are
801	!-- calculated differently, i.e. no subboxes are needed.
802	IF ( .NOT. TRIM( particle_advection_interpolation ) == 'trilinear' .AND. &
803	use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
804	message_string = 'subrgrid scale velocities in combination with ' // &
805	'simple interpolation method is not ' // &
806	'implemented'
807	CALL message( 'lpm_check_parameters', 'PA0659', 1, 2, 0, 6, 0 )
808	ENDIF
809
810	IF ( nested_run .AND. cloud_droplets ) THEN
811	message_string = 'nested runs in combination with cloud droplets ' // &
812	'is not implemented'
813	CALL message( 'lpm_check_parameters', 'PA0687', 1, 2, 0, 6, 0 )
814	ENDIF
815
816
817	END SUBROUTINE lpm_check_parameters
818
819	!------------------------------------------------------------------------------!
820	! Description:
821	! ------------
822	!> Initialize arrays for lpm
823	!------------------------------------------------------------------------------!
824	SUBROUTINE lpm_init_arrays
825
826	IF ( cloud_droplets ) THEN
827	!
828	!-- Liquid water content, change in liquid water content
829	ALLOCATE ( ql_1(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
830	ql_2(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
831	!
832	!-- Real volume of particles (with weighting), volume of particles
833	ALLOCATE ( ql_v(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
834	ql_vp(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
835	ENDIF
836
837
838	ALLOCATE( u_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
839	v_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
840	w_t(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
841	!
842	!-- Initialize values with current time step
843	u_t = u
844	v_t = v
845	w_t = w
846	!
847	!-- Initial assignment of the pointers
848	IF ( cloud_droplets ) THEN
849	ql => ql_1
850	ql_c => ql_2
851	ENDIF
852
853	END SUBROUTINE lpm_init_arrays
854
855	!------------------------------------------------------------------------------!
856	! Description:
857	! ------------
858	!> Initialize Lagrangian particle model
859	!------------------------------------------------------------------------------!
860	SUBROUTINE lpm_init
861
862	INTEGER(iwp) :: i !<
863	INTEGER(iwp) :: j !<
864	INTEGER(iwp) :: k !<
865
866	REAL(wp) :: div !<
867	REAL(wp) :: height_int !<
868	REAL(wp) :: height_p !<
869	REAL(wp) :: z_p !<
870	REAL(wp) :: z0_av_local !<
871
872	!
873	!-- In case of oceans runs, the vertical index calculations need an offset,
874	!-- because otherwise the k indices will become negative
875	IF ( ocean_mode ) THEN
876	offset_ocean_nzt = nzt
877	offset_ocean_nzt_m1 = nzt - 1
878	ENDIF
879
880	!
881	!-- Define block offsets for dividing a gridcell in 8 sub cells
882	!-- See documentation for List of subgrid boxes
883	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
884	block_offset(0) = block_offset_def ( 0, 0, 0)
885	block_offset(1) = block_offset_def ( 0, 0,-1)
886	block_offset(2) = block_offset_def ( 0,-1, 0)
887	block_offset(3) = block_offset_def ( 0,-1,-1)
888	block_offset(4) = block_offset_def (-1, 0, 0)
889	block_offset(5) = block_offset_def (-1, 0,-1)
890	block_offset(6) = block_offset_def (-1,-1, 0)
891	block_offset(7) = block_offset_def (-1,-1,-1)
892	!
893	!-- Check the number of particle groups.
894	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
895	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
896	max_number_of_particle_groups , &
897	'&number_of_particle_groups reset to ', &
898	max_number_of_particle_groups
899	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
900	number_of_particle_groups = max_number_of_particle_groups
901	ENDIF
902	!
903	!-- Check if downward-facing walls exist. This case, reflection boundary
904	!-- conditions (as well as subgrid-scale velocities) may do not work
905	!-- propably (not realized so far).
906	IF ( surf_def_h(1)%ns >= 1 ) THEN
907	WRITE( message_string, * ) 'Overhanging topography do not work '// &
908	'with particles'
909	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
910
911	ENDIF
912
913	!
914	!-- Set default start positions, if necessary
915	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
916	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
917	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
918	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
919	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
920	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
921
922	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
923	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
924	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
925
926	!
927	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
928	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
929	IF ( number_particles_per_gridbox /= -1 .AND. &
930	number_particles_per_gridbox >= 1 ) THEN
931	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
932	REAL(number_particles_per_gridbox))**0.3333333_wp
933	!
934	!-- Ensure a smooth value (two significant digits) of distance between
935	!-- particles (pdx, pdy, pdz).
936	div = 1000.0_wp
937	DO WHILE ( pdx(1) < div )
938	div = div / 10.0_wp
939	ENDDO
940	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
941	pdy(1) = pdx(1)
942	pdz(1) = pdx(1)
943
944	ENDIF
945
946	DO j = 2, number_of_particle_groups
947	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
948	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
949	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
950	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
951	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
952	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
953	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
954	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
955	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
956	ENDDO
957
958	!
959	!-- Allocate arrays required for calculating particle SGS velocities.
960	!-- Initialize prefactor required for stoachastic Weil equation.
961	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
962	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
963	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
964	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
965
966	de_dx = 0.0_wp
967	de_dy = 0.0_wp
968	de_dz = 0.0_wp
969
970	sgs_wf_part = 1.0_wp / 3.0_wp
971	ENDIF
972
973	!
974	!-- Allocate array required for logarithmic vertical interpolation of
975	!-- horizontal particle velocities between the surface and the first vertical
976	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
977	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
978	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
979	!-- To obtain exact height levels of particles, linear interpolation is applied
980	!-- (see lpm_advec.f90).
981	IF ( constant_flux_layer ) THEN
982
983	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
984	z_p = zu(nzb+1) - zw(nzb)
985
986	!
987	!-- Calculate horizontal mean value of z0 used for logartihmic
988	!-- interpolation. Note: this is not exact for heterogeneous z0.
989	!-- However, sensitivity studies showed that the effect is
990	!-- negligible.
991	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
992	SUM( surf_usm_h%z0 )
993	z0_av_global = 0.0_wp
994
995	#if defined( __parallel )
996	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
997	comm2d, ierr )
998	#else
999	z0_av_global = z0_av_local
1000	#endif
1001
1002	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
1003	!
1004	!-- Horizontal wind speed is zero below and at z0
1005	log_z_z0(0) = 0.0_wp
1006	!
1007	!-- Calculate vertical depth of the sublayers
1008	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
1009	!
1010	!-- Precalculate LOG(z/z0)
1011	height_p = z0_av_global
1012	DO k = 1, number_of_sublayers
1013
1014	height_p = height_p + height_int
1015	log_z_z0(k) = LOG( height_p / z0_av_global )
1016
1017	ENDDO
1018
1019	ENDIF
1020
1021	!
1022	!-- Check which particle interpolation method should be used
1023	IF ( TRIM( particle_advection_interpolation ) == 'trilinear' ) THEN
1024	interpolation_simple_corrector = .FALSE.
1025	interpolation_simple_predictor = .FALSE.
1026	interpolation_trilinear = .TRUE.
1027	ELSEIF ( TRIM( particle_advection_interpolation ) == 'simple_corrector' ) THEN
1028	interpolation_simple_corrector = .TRUE.
1029	interpolation_simple_predictor = .FALSE.
1030	interpolation_trilinear = .FALSE.
1031	ELSEIF ( TRIM( particle_advection_interpolation ) == 'simple_predictor' ) THEN
1032	interpolation_simple_corrector = .FALSE.
1033	interpolation_simple_predictor = .TRUE.
1034	interpolation_trilinear = .FALSE.
1035	ENDIF
1036
1037	!
1038	!-- Check boundary condition and set internal variables
1039	SELECT CASE ( bc_par_b )
1040
1041	CASE ( 'absorb' )
1042	ibc_par_b = 1
1043
1044	CASE ( 'reflect' )
1045	ibc_par_b = 2
1046
1047	CASE ( 'reset' )
1048	ibc_par_b = 3
1049
1050	CASE DEFAULT
1051	WRITE( message_string, * ) 'unknown boundary condition ', &
1052	'bc_par_b = "', TRIM( bc_par_b ), '"'
1053	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
1054
1055	END SELECT
1056	SELECT CASE ( bc_par_t )
1057
1058	CASE ( 'absorb' )
1059	ibc_par_t = 1
1060
1061	CASE ( 'reflect' )
1062	ibc_par_t = 2
1063
1064	CASE ( 'nested' )
1065	ibc_par_t = 3
1066
1067	CASE DEFAULT
1068	WRITE( message_string, * ) 'unknown boundary condition ', &
1069	'bc_par_t = "', TRIM( bc_par_t ), '"'
1070	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
1071
1072	END SELECT
1073	SELECT CASE ( bc_par_lr )
1074
1075	CASE ( 'cyclic' )
1076	ibc_par_lr = 0
1077
1078	CASE ( 'absorb' )
1079	ibc_par_lr = 1
1080
1081	CASE ( 'reflect' )
1082	ibc_par_lr = 2
1083
1084	CASE ( 'nested' )
1085	ibc_par_lr = 3
1086
1087	CASE DEFAULT
1088	WRITE( message_string, * ) 'unknown boundary condition ', &
1089	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
1090	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
1091
1092	END SELECT
1093	SELECT CASE ( bc_par_ns )
1094
1095	CASE ( 'cyclic' )
1096	ibc_par_ns = 0
1097
1098	CASE ( 'absorb' )
1099	ibc_par_ns = 1
1100
1101	CASE ( 'reflect' )
1102	ibc_par_ns = 2
1103
1104	CASE ( 'nested' )
1105	ibc_par_ns = 3
1106
1107	CASE DEFAULT
1108	WRITE( message_string, * ) 'unknown boundary condition ', &
1109	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
1110	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
1111
1112	END SELECT
1113	SELECT CASE ( splitting_mode )
1114
1115	CASE ( 'const' )
1116	i_splitting_mode = 1
1117
1118	CASE ( 'cl_av' )
1119	i_splitting_mode = 2
1120
1121	CASE ( 'gb_av' )
1122	i_splitting_mode = 3
1123
1124	CASE DEFAULT
1125	WRITE( message_string, * ) 'unknown splitting_mode = "', &
1126	TRIM( splitting_mode ), '"'
1127	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
1128
1129	END SELECT
1130	SELECT CASE ( splitting_function )
1131
1132	CASE ( 'gamma' )
1133	isf = 1
1134
1135	CASE ( 'log' )
1136	isf = 2
1137
1138	CASE ( 'exp' )
1139	isf = 3
1140
1141	CASE DEFAULT
1142	WRITE( message_string, * ) 'unknown splitting function = "', &
1143	TRIM( splitting_function ), '"'
1144	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
1145
1146	END SELECT
1147	!
1148	!-- Initialize collision kernels
1149	IF ( collision_kernel /= 'none' ) CALL lpm_init_kernels
1150	!
1151	!-- For the first model run of a possible job chain initialize the
1152	!-- particles, otherwise read the particle data from restart file.
1153	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
1154	.AND. read_particles_from_restartfile ) THEN
1155	CALL lpm_rrd_local_particles
1156	ELSE
1157	!
1158	!-- Allocate particle arrays and set attributes of the initial set of
1159	!-- particles, which can be also periodically released at later times.
1160	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1161	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
1162
1163	number_of_particles = 0
1164	prt_count = 0
1165	!
1166	!-- initialize counter for particle IDs
1167	grid_particles%id_counter = 1
1168	!
1169	!-- Initialize all particles with dummy values (otherwise errors may
1170	!-- occur within restart runs). The reason for this is still not clear
1171	!-- and may be presumably caused by errors in the respective user-interface.
1172	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1173	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1174	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1175	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1176	0, 0, 0_idp, .FALSE., -1 )
1177
1178	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
1179	!
1180	!-- Set values for the density ratio and radius for all particle
1181	!-- groups, if necessary
1182	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
1183	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
1184	DO i = 2, number_of_particle_groups
1185	IF ( density_ratio(i) == 9999999.9_wp ) THEN
1186	density_ratio(i) = density_ratio(i-1)
1187	ENDIF
1188	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
1189	ENDDO
1190
1191	DO i = 1, number_of_particle_groups
1192	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
1193	WRITE( message_string, * ) 'particle group #', i, ' has a', &
1194	'density ratio /= 0 but radius = 0'
1195	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
1196	ENDIF
1197	particle_groups(i)%density_ratio = density_ratio(i)
1198	particle_groups(i)%radius = radius(i)
1199	ENDDO
1200	!
1201	!-- Set a seed value for the random number generator to be exclusively
1202	!-- used for the particle code. The generated random numbers should be
1203	!-- different on the different PEs.
1204	iran_part = iran_part + myid
1205	!
1206	!-- Create the particle set, and set the initial particles
1207	CALL lpm_create_particle( phase_init )
1208	last_particle_release_time = particle_advection_start
1209	!
1210	!-- User modification of initial particles
1211	CALL user_lpm_init
1212	!
1213	!-- Open file for statistical informations about particle conditions
1214	IF ( write_particle_statistics ) THEN
1215	CALL check_open( 80 )
1216	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
1217	number_of_particles
1218	CALL close_file( 80 )
1219	ENDIF
1220
1221	ENDIF
1222
1223	IF ( nested_run ) CALL pmcp_g_init
1224	!
1225	!-- To avoid programm abort, assign particles array to the local version of
1226	!-- first grid cell
1227	number_of_particles = prt_count(nzb+1,nys,nxl)
1228	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
1229	!
1230	!-- Formats
1231	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
1232
1233	END SUBROUTINE lpm_init
1234
1235	!------------------------------------------------------------------------------!
1236	! Description:
1237	! ------------
1238	!> Create Lagrangian particles
1239	!------------------------------------------------------------------------------!
1240	SUBROUTINE lpm_create_particle (phase)
1241
1242	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
1243	INTEGER(iwp) :: i !< loop variable ( particle groups )
1244	INTEGER(iwp) :: ip !< index variable along x
1245	INTEGER(iwp) :: j !< loop variable ( particles per point )
1246	INTEGER(iwp) :: jp !< index variable along y
1247	INTEGER(iwp) :: k !< index variable along z
1248	INTEGER(iwp) :: k_surf !< index of surface grid point
1249	INTEGER(iwp) :: kp !< index variable along z
1250	INTEGER(iwp) :: loop_stride !< loop variable for initialization
1251	INTEGER(iwp) :: n !< loop variable ( number of particles )
1252	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
1253
1254	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
1255
1256	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
1257	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
1258
1259	LOGICAL :: first_stride !< flag for initialization
1260
1261	REAL(wp) :: pos_x !< increment for particle position in x
1262	REAL(wp) :: pos_y !< increment for particle position in y
1263	REAL(wp) :: pos_z !< increment for particle position in z
1264	REAL(wp) :: rand_contr !< dummy argument for random position
1265
1266	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
1267
1268
1269	!
1270	!-- Calculate particle positions and store particle attributes, if
1271	!-- particle is situated on this PE
1272	DO loop_stride = 1, 2
1273	first_stride = (loop_stride == 1)
1274	IF ( first_stride ) THEN
1275	local_count = 0 ! count number of particles
1276	ELSE
1277	local_count = prt_count ! Start address of new particles
1278	ENDIF
1279
1280	!
1281	!-- Calculate initial_weighting_factor diagnostically
1282	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
1283	initial_weighting_factor = number_concentration * &
1284	pdx(1) * pdy(1) * pdz(1)
1285	END IF
1286
1287	n = 0
1288	DO i = 1, number_of_particle_groups
1289	pos_z = psb(i)
1290	DO WHILE ( pos_z <= pst(i) )
1291	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
1292	pos_y = pss(i)
1293	DO WHILE ( pos_y <= psn(i) )
1294	IF ( pos_y >= nys * dy .AND. &
1295	pos_y < ( nyn + 1 ) * dy ) THEN
1296	pos_x = psl(i)
1297	xloop: DO WHILE ( pos_x <= psr(i) )
1298	IF ( pos_x >= nxl * dx .AND. &
1299	pos_x < ( nxr + 1) * dx ) THEN
1300	DO j = 1, particles_per_point
1301	n = n + 1
1302	tmp_particle%x = pos_x
1303	tmp_particle%y = pos_y
1304	tmp_particle%z = pos_z
1305	tmp_particle%age = 0.0_wp
1306	tmp_particle%age_m = 0.0_wp
1307	tmp_particle%dt_sum = 0.0_wp
1308	tmp_particle%e_m = 0.0_wp
1309	tmp_particle%rvar1 = 0.0_wp
1310	tmp_particle%rvar2 = 0.0_wp
1311	tmp_particle%rvar3 = 0.0_wp
1312	tmp_particle%speed_x = 0.0_wp
1313	tmp_particle%speed_y = 0.0_wp
1314	tmp_particle%speed_z = 0.0_wp
1315	tmp_particle%origin_x = pos_x
1316	tmp_particle%origin_y = pos_y
1317	tmp_particle%origin_z = pos_z
1318	IF ( curvature_solution_effects ) THEN
1319	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
1320	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
1321	ELSE
1322	tmp_particle%aux1 = 0.0_wp ! free to use
1323	tmp_particle%aux2 = 0.0_wp ! free to use
1324	ENDIF
1325	tmp_particle%radius = particle_groups(i)%radius
1326	tmp_particle%weight_factor = initial_weighting_factor
1327	tmp_particle%class = 1
1328	tmp_particle%group = i
1329	tmp_particle%id = 0_idp
1330	tmp_particle%particle_mask = .TRUE.
1331	tmp_particle%block_nr = -1
1332	!
1333	!-- Determine the grid indices of the particle position
1334	ip = INT( tmp_particle%x * ddx )
1335	jp = INT( tmp_particle%y * ddy )
1336	!
1337	!-- In case of stretching the actual k index is found iteratively
1338	IF ( dz_stretch_level /= -9999999.9_wp .OR. &
1339	dz_stretch_level_start(1) /= -9999999.9_wp ) THEN
1340	kp = MINLOC( ABS( tmp_particle%z - zu ), DIM = 1 ) - 1
1341	ELSE
1342	kp = INT( tmp_particle%z / dz(1) + 1 + offset_ocean_nzt )
1343	ENDIF
1344	!
1345	!-- Determine surface level. Therefore, check for
1346	!-- upward-facing wall on w-grid.
1347	k_surf = topo_top_ind(jp,ip,3)
1348	IF ( seed_follows_topography ) THEN
1349	!
1350	!-- Particle height is given relative to topography
1351	kp = kp + k_surf
1352	tmp_particle%z = tmp_particle%z + zw(k_surf)
1353	!-- Skip particle release if particle position is
1354	!-- above model top, or within topography in case
1355	!-- of overhanging structures.
1356	IF ( kp > nzt .OR. &
1357	.NOT. BTEST( wall_flags_static_0(kp,jp,ip), 0 ) ) THEN
1358	pos_x = pos_x + pdx(i)
1359	CYCLE xloop
1360	ENDIF
1361	!
1362	!-- Skip particle release if particle position is
1363	!-- below surface, or within topography in case
1364	!-- of overhanging structures.
1365	ELSEIF ( .NOT. seed_follows_topography .AND. &
1366	tmp_particle%z <= zw(k_surf) .OR. &
1367	.NOT. BTEST( wall_flags_static_0(kp,jp,ip), 0 ) )&
1368	THEN
1369	pos_x = pos_x + pdx(i)
1370	CYCLE xloop
1371	ENDIF
1372
1373	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
1374
1375	IF ( .NOT. first_stride ) THEN
1376	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
1377	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
1378	ENDIF
1379	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
1380	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
1381	ENDIF
1382	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
1383	ENDIF
1384	ENDDO
1385	ENDIF
1386	pos_x = pos_x + pdx(i)
1387	ENDDO xloop
1388	ENDIF
1389	pos_y = pos_y + pdy(i)
1390	ENDDO
1391	ENDIF
1392
1393	pos_z = pos_z + pdz(i)
1394	ENDDO
1395	ENDDO
1396
1397	IF ( first_stride ) THEN
1398	DO ip = nxl, nxr
1399	DO jp = nys, nyn
1400	DO kp = nzb+1, nzt
1401	IF ( phase == PHASE_INIT ) THEN
1402	IF ( local_count(kp,jp,ip) > 0 ) THEN
1403	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
1404	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
1405	1 )
1406	ELSE
1407	alloc_size = 1
1408	ENDIF
1409	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
1410	DO n = 1, alloc_size
1411	grid_particles(kp,jp,ip)%particles(n) = zero_particle
1412	ENDDO
1413	ELSEIF ( phase == PHASE_RELEASE ) THEN
1414	IF ( local_count(kp,jp,ip) > 0 ) THEN
1415	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
1416	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
1417	alloc_factor / 100.0_wp ) ), 1 )
1418	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
1419	CALL realloc_particles_array( ip, jp, kp, alloc_size )
1420	ENDIF
1421	ENDIF
1422	ENDIF
1423	ENDDO
1424	ENDDO
1425	ENDDO
1426	ENDIF
1427
1428	ENDDO
1429
1430	local_start = prt_count+1
1431	prt_count = local_count
1432	!
1433	!-- Calculate particle IDs
1434	DO ip = nxl, nxr
1435	DO jp = nys, nyn
1436	DO kp = nzb+1, nzt
1437	number_of_particles = prt_count(kp,jp,ip)
1438	IF ( number_of_particles <= 0 ) CYCLE
1439	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1440
1441	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1442
1443	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
1444	10000_idp*2 kp + 10000_idp * jp + ip
1445	!
1446	!-- Count the number of particles that have been released before
1447	grid_particles(kp,jp,ip)%id_counter = &
1448	grid_particles(kp,jp,ip)%id_counter + 1
1449
1450	ENDDO
1451
1452	ENDDO
1453	ENDDO
1454	ENDDO
1455	!
1456	!-- Initialize aerosol background spectrum
1457	IF ( curvature_solution_effects ) THEN
1458	CALL lpm_init_aerosols( local_start )
1459	ENDIF
1460	!
1461	!-- Add random fluctuation to particle positions.
1462	IF ( random_start_position ) THEN
1463	DO ip = nxl, nxr
1464	DO jp = nys, nyn
1465	DO kp = nzb+1, nzt
1466	number_of_particles = prt_count(kp,jp,ip)
1467	IF ( number_of_particles <= 0 ) CYCLE
1468	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1469	!
1470	!-- Move only new particles. Moreover, limit random fluctuation
1471	!-- in order to prevent that particles move more than one grid box,
1472	!-- which would lead to problems concerning particle exchange
1473	!-- between processors in case pdx/pdy are larger than dx/dy,
1474	!-- respectively.
1475	DO n = local_start(kp,jp,ip), number_of_particles
1476	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
1477	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1478	pdx(particles(n)%group)
1479	particles(n)%x = particles(n)%x + &
1480	MERGE( rand_contr, SIGN( dx, rand_contr ), &
1481	ABS( rand_contr ) < dx &
1482	)
1483	ENDIF
1484	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
1485	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1486	pdy(particles(n)%group)
1487	particles(n)%y = particles(n)%y + &
1488	MERGE( rand_contr, SIGN( dy, rand_contr ), &
1489	ABS( rand_contr ) < dy &
1490	)
1491	ENDIF
1492	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
1493	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1494	pdz(particles(n)%group)
1495	particles(n)%z = particles(n)%z + &
1496	MERGE( rand_contr, SIGN( dzw(kp), rand_contr ), &
1497	ABS( rand_contr ) < dzw(kp) &
1498	)
1499	ENDIF
1500	ENDDO
1501	!
1502	!-- Identify particles located outside the model domain and reflect
1503	!-- or absorb them if necessary.
1504	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
1505	!
1506	!-- Furthermore, remove particles located in topography. Note, as
1507	!-- the particle speed is still zero at this point, wall
1508	!-- reflection boundary conditions will not work in this case.
1509	particles => &
1510	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1511	DO n = local_start(kp,jp,ip), number_of_particles
1512	i = particles(n)%x * ddx
1513	j = particles(n)%y * ddy
1514	k = particles(n)%z / dz(1) + 1 + offset_ocean_nzt
1515	DO WHILE( zw(k) < particles(n)%z )
1516	k = k + 1
1517	ENDDO
1518	DO WHILE( zw(k-1) > particles(n)%z )
1519	k = k - 1
1520	ENDDO
1521	!
1522	!-- Check if particle is within topography
1523	IF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 0 ) ) THEN
1524	particles(n)%particle_mask = .FALSE.
1525	deleted_particles = deleted_particles + 1
1526	ENDIF
1527
1528	ENDDO
1529	ENDDO
1530	ENDDO
1531	ENDDO
1532	!
1533	!-- Exchange particles between grid cells and processors
1534	CALL lpm_move_particle
1535	CALL lpm_exchange_horiz
1536
1537	ENDIF
1538	!
1539	!-- In case of random_start_position, delete particles identified by
1540	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1541	!-- which is needed for a fast interpolation of the LES fields on the particle
1542	!-- position.
1543	CALL lpm_sort_and_delete
1544	!
1545	!-- Determine the current number of particles
1546	DO ip = nxl, nxr
1547	DO jp = nys, nyn
1548	DO kp = nzb+1, nzt
1549	number_of_particles = number_of_particles &
1550	+ prt_count(kp,jp,ip)
1551	ENDDO
1552	ENDDO
1553	ENDDO
1554	!
1555	!-- Calculate the number of particles of the total domain
1556	#if defined( __parallel )
1557	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1558	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1559	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1560	#else
1561	total_number_of_particles = number_of_particles
1562	#endif
1563
1564	RETURN
1565
1566	END SUBROUTINE lpm_create_particle
1567
1568
1569	!------------------------------------------------------------------------------!
1570	! Description:
1571	! ------------
1572	!> This routine initialize the particles as aerosols with physio-chemical
1573	!> properties.
1574	!------------------------------------------------------------------------------!
1575	SUBROUTINE lpm_init_aerosols(local_start)
1576
1577	REAL(wp) :: afactor !< curvature effects
1578	REAL(wp) :: bfactor !< solute effects
1579	REAL(wp) :: dlogr !< logarithmic width of radius bin
1580	REAL(wp) :: e_a !< vapor pressure
1581	REAL(wp) :: e_s !< saturation vapor pressure
1582	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1583	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1584	REAL(wp) :: r_mid !< mean radius of bin
1585	REAL(wp) :: r_l !< left radius of bin
1586	REAL(wp) :: r_r !< right radius of bin
1587	REAL(wp) :: sigma !< surface tension
1588	REAL(wp) :: t_int !< temperature
1589
1590	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1591
1592	INTEGER(iwp) :: n !<
1593	INTEGER(iwp) :: ip !<
1594	INTEGER(iwp) :: jp !<
1595	INTEGER(iwp) :: kp !<
1596
1597	!
1598	!-- Set constants for different aerosol species
1599	IF ( TRIM( aero_species ) == 'nacl' ) THEN
1600	molecular_weight_of_solute = 0.05844_wp
1601	rho_s = 2165.0_wp
1602	vanthoff = 2.0_wp
1603	ELSEIF ( TRIM( aero_species ) == 'c3h4o4' ) THEN
1604	molecular_weight_of_solute = 0.10406_wp
1605	rho_s = 1600.0_wp
1606	vanthoff = 1.37_wp
1607	ELSEIF ( TRIM( aero_species ) == 'nh4o3' ) THEN
1608	molecular_weight_of_solute = 0.08004_wp
1609	rho_s = 1720.0_wp
1610	vanthoff = 2.31_wp
1611	ELSE
1612	WRITE( message_string, * ) 'unknown aerosol species ', &
1613	'aero_species = "', TRIM( aero_species ), '"'
1614	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1615	ENDIF
1616	!
1617	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1618	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1619	IF ( TRIM( aero_type ) == 'polar' ) THEN
1620	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6_wp
1621	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6_wp
1622	log_sigma = (/ 0.245, 0.300, 0.291 /)
1623	ELSEIF ( TRIM( aero_type ) == 'background' ) THEN
1624	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6_wp
1625	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6_wp
1626	log_sigma = (/ 0.645, 0.253, 0.425 /)
1627	ELSEIF ( TRIM( aero_type ) == 'maritime' ) THEN
1628	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6_wp
1629	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6_wp
1630	log_sigma = (/ 0.657, 0.210, 0.396 /)
1631	ELSEIF ( TRIM( aero_type ) == 'continental' ) THEN
1632	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6_wp
1633	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6_wp
1634	log_sigma = (/ 0.161, 0.217, 0.380 /)
1635	ELSEIF ( TRIM( aero_type ) == 'desert' ) THEN
1636	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6_wp
1637	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6_wp
1638	log_sigma = (/ 0.247, 0.770, 0.438 /)
1639	ELSEIF ( TRIM( aero_type ) == 'rural' ) THEN
1640	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6_wp
1641	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6_wp
1642	log_sigma = (/ 0.225, 0.557, 0.266 /)
1643	ELSEIF ( TRIM( aero_type ) == 'urban' ) THEN
1644	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6_wp
1645	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6_wp
1646	log_sigma = (/ 0.245, 0.666, 0.337 /)
1647	ELSEIF ( TRIM( aero_type ) == 'user' ) THEN
1648	CONTINUE
1649	ELSE
1650	WRITE( message_string, * ) 'unknown aerosol type ', &
1651	'aero_type = "', TRIM( aero_type ), '"'
1652	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1653	ENDIF
1654
1655	DO ip = nxl, nxr
1656	DO jp = nys, nyn
1657	DO kp = nzb+1, nzt
1658
1659	number_of_particles = prt_count(kp,jp,ip)
1660	IF ( number_of_particles <= 0 ) CYCLE
1661	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1662
1663	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1664	!
1665	!-- Initialize the aerosols with a predefined spectral distribution
1666	!-- of the dry radius (logarithmically increasing bins) and a varying
1667	!-- weighting factor
1668	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1669
1670	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1671	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1672	r_mid = SQRT( r_l * r_r )
1673
1674	particles(n)%aux1 = r_mid
1675	particles(n)%weight_factor = &
1676	( na(1) / ( SQRT( 2.0_wp * pi ) * log_sigma(1) ) * &
1677	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0_wp log_sigma(1)**2 ) ) + &
1678	na(2) / ( SQRT( 2.0_wp * pi ) * log_sigma(2) ) * &
1679	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0_wp log_sigma(2)**2 ) ) + &
1680	na(3) / ( SQRT( 2.0_wp * pi ) * log_sigma(3) ) * &
1681	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0_wp log_sigma(3)**2 ) ) &
1682	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dzw(kp) )
1683
1684	!
1685	!-- Multiply weight_factor with the namelist parameter aero_weight
1686	!-- to increase or decrease the number of simulated aerosols
1687	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1688
1689	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1690	> random_function( iran_part ) ) THEN
1691	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0_wp
1692	ELSE
1693	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1694	ENDIF
1695	!
1696	!-- Unnecessary particles will be deleted
1697	IF ( particles(n)%weight_factor <= 0.0_wp ) particles(n)%particle_mask = .FALSE.
1698
1699	ENDDO
1700	!
1701	!-- Set particle radius to equilibrium radius based on the environmental
1702	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1703	!-- the sometimes lengthy growth toward their equilibrium radius within
1704	!-- the simulation.
1705	t_int = pt(kp,jp,ip) * exner(kp)
1706
1707	e_s = magnus( t_int )
1708	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + rd_d_rv )
1709
1710	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1711	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1712
1713	bfactor = vanthoff * molecular_weight_of_water * &
1714	rho_s / ( molecular_weight_of_solute * rho_l )
1715	!
1716	!-- The formula is only valid for subsaturated environments. For
1717	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1718	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1719
1720	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1721	!
1722	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1723	!-- Curry (2007, JGR)
1724	particles(n)%radius = bfactor*0.3333333_wp &
1725	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1726	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1727	particles(n)%aux1 ) ) / &
1728	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1729	)
1730
1731	ENDDO
1732
1733	ENDDO
1734	ENDDO
1735	ENDDO
1736
1737	END SUBROUTINE lpm_init_aerosols
1738
1739
1740	!------------------------------------------------------------------------------!
1741	! Description:
1742	! ------------
1743	!> Calculates quantities required for considering the SGS velocity fluctuations
1744	!> in the particle transport by a stochastic approach. The respective
1745	!> quantities are: SGS-TKE gradients and horizontally averaged profiles of the
1746	!> SGS TKE and the resolved-scale velocity variances.
1747	!------------------------------------------------------------------------------!
1748	SUBROUTINE lpm_init_sgs_tke
1749
1750	USE statistics, &
1751	ONLY: flow_statistics_called, hom, sums, sums_l
1752
1753	INTEGER(iwp) :: i !< index variable along x
1754	INTEGER(iwp) :: j !< index variable along y
1755	INTEGER(iwp) :: k !< index variable along z
1756	INTEGER(iwp) :: m !< running index for the surface elements
1757
1758	REAL(wp) :: flag1 !< flag to mask topography
1759
1760	!
1761	!-- TKE gradient along x and y
1762	DO i = nxl, nxr
1763	DO j = nys, nyn
1764	DO k = nzb, nzt+1
1765
1766	IF ( .NOT. BTEST( wall_flags_static_0(k,j,i-1), 0 ) .AND. &
1767	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1768	BTEST( wall_flags_static_0(k,j,i+1), 0 ) ) &
1769	THEN
1770	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1771	( e(k,j,i+1) - e(k,j,i) ) * ddx
1772	ELSEIF ( BTEST( wall_flags_static_0(k,j,i-1), 0 ) .AND. &
1773	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1774	.NOT. BTEST( wall_flags_static_0(k,j,i+1), 0 ) ) &
1775	THEN
1776	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1777	( e(k,j,i) - e(k,j,i-1) ) * ddx
1778	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) .AND. &
1779	.NOT. BTEST( wall_flags_static_0(k,j,i+1), 22 ) ) &
1780	THEN
1781	de_dx(k,j,i) = 0.0_wp
1782	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i-1), 22 ) .AND. &
1783	.NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) ) &
1784	THEN
1785	de_dx(k,j,i) = 0.0_wp
1786	ELSE
1787	de_dx(k,j,i) = sgs_wf_part * ( e(k,j,i+1) - e(k,j,i-1) ) * ddx
1788	ENDIF
1789
1790	IF ( .NOT. BTEST( wall_flags_static_0(k,j-1,i), 0 ) .AND. &
1791	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1792	BTEST( wall_flags_static_0(k,j+1,i), 0 ) ) &
1793	THEN
1794	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1795	( e(k,j+1,i) - e(k,j,i) ) * ddy
1796	ELSEIF ( BTEST( wall_flags_static_0(k,j-1,i), 0 ) .AND. &
1797	BTEST( wall_flags_static_0(k,j,i), 0 ) .AND. &
1798	.NOT. BTEST( wall_flags_static_0(k,j+1,i), 0 ) ) &
1799	THEN
1800	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1801	( e(k,j,i) - e(k,j-1,i) ) * ddy
1802	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) .AND. &
1803	.NOT. BTEST( wall_flags_static_0(k,j+1,i), 22 ) ) &
1804	THEN
1805	de_dy(k,j,i) = 0.0_wp
1806	ELSEIF ( .NOT. BTEST( wall_flags_static_0(k,j-1,i), 22 ) .AND. &
1807	.NOT. BTEST( wall_flags_static_0(k,j,i), 22 ) ) &
1808	THEN
1809	de_dy(k,j,i) = 0.0_wp
1810	ELSE
1811	de_dy(k,j,i) = sgs_wf_part * ( e(k,j+1,i) - e(k,j-1,i) ) * ddy
1812	ENDIF
1813
1814	ENDDO
1815	ENDDO
1816	ENDDO
1817
1818	!
1819	!-- TKE gradient along z at topograhy and including bottom and top boundary conditions
1820	DO i = nxl, nxr
1821	DO j = nys, nyn
1822	DO k = nzb+1, nzt-1
1823	!
1824	!-- Flag to mask topography
1825	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 0 ) )
1826
1827	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1828	( e(k+1,j,i) - e(k-1,j,i) ) / ( zu(k+1) - zu(k-1) ) &
1829	* flag1
1830	ENDDO
1831	!
1832	!-- upward-facing surfaces
1833	DO m = bc_h(0)%start_index(j,i), bc_h(0)%end_index(j,i)
1834	k = bc_h(0)%k(m)
1835	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1836	( e(k+1,j,i) - e(k,j,i) ) / ( zu(k+1) - zu(k) )
1837	ENDDO
1838	!
1839	!-- downward-facing surfaces
1840	DO m = bc_h(1)%start_index(j,i), bc_h(1)%end_index(j,i)
1841	k = bc_h(1)%k(m)
1842	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1843	( e(k,j,i) - e(k-1,j,i) ) / ( zu(k) - zu(k-1) )
1844	ENDDO
1845
1846	de_dz(nzb,j,i) = 0.0_wp
1847	de_dz(nzt,j,i) = 0.0_wp
1848	de_dz(nzt+1,j,i) = 0.0_wp
1849	ENDDO
1850	ENDDO
1851	!
1852	!-- Ghost point exchange
1853	CALL exchange_horiz( de_dx, nbgp )
1854	CALL exchange_horiz( de_dy, nbgp )
1855	CALL exchange_horiz( de_dz, nbgp )
1856	CALL exchange_horiz( diss, nbgp )
1857	!
1858	!-- Set boundary conditions at non-periodic boundaries. Note, at non-period
1859	!-- boundaries zero-gradient boundary conditions are set for the subgrid TKE.
1860	!-- Thus, TKE gradients normal to the respective lateral boundaries are zero,
1861	!-- while tangetial TKE gradients then must be the same as within the prognostic
1862	!-- domain.
1863	IF ( bc_dirichlet_l ) THEN
1864	de_dx(:,:,-1) = 0.0_wp
1865	de_dy(:,:,-1) = de_dy(:,:,0)
1866	de_dz(:,:,-1) = de_dz(:,:,0)
1867	ENDIF
1868	IF ( bc_dirichlet_r ) THEN
1869	de_dx(:,:,nxr+1) = 0.0_wp
1870	de_dy(:,:,nxr+1) = de_dy(:,:,nxr)
1871	de_dz(:,:,nxr+1) = de_dz(:,:,nxr)
1872	ENDIF
1873	IF ( bc_dirichlet_n ) THEN
1874	de_dx(:,nyn+1,:) = de_dx(:,nyn,:)
1875	de_dy(:,nyn+1,:) = 0.0_wp
1876	de_dz(:,nyn+1,:) = de_dz(:,nyn,:)
1877	ENDIF
1878	IF ( bc_dirichlet_s ) THEN
1879	de_dx(:,nys-1,:) = de_dx(:,nys,:)
1880	de_dy(:,nys-1,:) = 0.0_wp
1881	de_dz(:,nys-1,:) = de_dz(:,nys,:)
1882	ENDIF
1883	!
1884	!-- Calculate the horizontally averaged profiles of SGS TKE and resolved
1885	!-- velocity variances (they may have been already calculated in routine
1886	!-- flow_statistics).
1887	IF ( .NOT. flow_statistics_called ) THEN
1888
1889	!
1890	!-- First calculate horizontally averaged profiles of the horizontal
1891	!-- velocities.
1892	sums_l(:,1,0) = 0.0_wp
1893	sums_l(:,2,0) = 0.0_wp
1894
1895	DO i = nxl, nxr
1896	DO j = nys, nyn
1897	DO k = nzb, nzt+1
1898	!
1899	!-- Flag indicating vicinity of wall
1900	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 24 ) )
1901
1902	sums_l(k,1,0) = sums_l(k,1,0) + u(k,j,i) * flag1
1903	sums_l(k,2,0) = sums_l(k,2,0) + v(k,j,i) * flag1
1904	ENDDO
1905	ENDDO
1906	ENDDO
1907
1908	#if defined( __parallel )
1909	!
1910	!-- Compute total sum from local sums
1911	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1912	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, &
1913	MPI_REAL, MPI_SUM, comm2d, ierr )
1914	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1915	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, &
1916	MPI_REAL, MPI_SUM, comm2d, ierr )
1917	#else
1918	sums(:,1) = sums_l(:,1,0)
1919	sums(:,2) = sums_l(:,2,0)
1920	#endif
1921
1922	!
1923	!-- Final values are obtained by division by the total number of grid
1924	!-- points used for the summation.
1925	hom(:,1,1,0) = sums(:,1) / ngp_2dh_outer(:,0) ! u
1926	hom(:,1,2,0) = sums(:,2) / ngp_2dh_outer(:,0) ! v
1927
1928	!
1929	!-- Now calculate the profiles of SGS TKE and the resolved-scale
1930	!-- velocity variances
1931	sums_l(:,8,0) = 0.0_wp
1932	sums_l(:,30,0) = 0.0_wp
1933	sums_l(:,31,0) = 0.0_wp
1934	sums_l(:,32,0) = 0.0_wp
1935	DO i = nxl, nxr
1936	DO j = nys, nyn
1937	DO k = nzb, nzt+1
1938	!
1939	!-- Flag indicating vicinity of wall
1940	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 24 ) )
1941
1942	sums_l(k,8,0) = sums_l(k,8,0) + e(k,j,i) * flag1
1943	sums_l(k,30,0) = sums_l(k,30,0) + ( u(k,j,i) - hom(k,1,1,0) )*2 flag1
1944	sums_l(k,31,0) = sums_l(k,31,0) + ( v(k,j,i) - hom(k,1,2,0) )*2 flag1
1945	sums_l(k,32,0) = sums_l(k,32,0) + w(k,j,i)*2 flag1
1946	ENDDO
1947	ENDDO
1948	ENDDO
1949
1950	#if defined( __parallel )
1951	!
1952	!-- Compute total sum from local sums
1953	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1954	CALL MPI_ALLREDUCE( sums_l(nzb,8,0), sums(nzb,8), nzt+2-nzb, &
1955	MPI_REAL, MPI_SUM, comm2d, ierr )
1956	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1957	CALL MPI_ALLREDUCE( sums_l(nzb,30,0), sums(nzb,30), nzt+2-nzb, &
1958	MPI_REAL, MPI_SUM, comm2d, ierr )
1959	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1960	CALL MPI_ALLREDUCE( sums_l(nzb,31,0), sums(nzb,31), nzt+2-nzb, &
1961	MPI_REAL, MPI_SUM, comm2d, ierr )
1962	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1963	CALL MPI_ALLREDUCE( sums_l(nzb,32,0), sums(nzb,32), nzt+2-nzb, &
1964	MPI_REAL, MPI_SUM, comm2d, ierr )
1965
1966	#else
1967	sums(:,8) = sums_l(:,8,0)
1968	sums(:,30) = sums_l(:,30,0)
1969	sums(:,31) = sums_l(:,31,0)
1970	sums(:,32) = sums_l(:,32,0)
1971	#endif
1972
1973	!
1974	!-- Final values are obtained by division by the total number of grid
1975	!-- points used for the summation.
1976	hom(:,1,8,0) = sums(:,8) / ngp_2dh_outer(:,0) ! e
1977	hom(:,1,30,0) = sums(:,30) / ngp_2dh_outer(:,0) ! u*2
1978	hom(:,1,31,0) = sums(:,31) / ngp_2dh_outer(:,0) ! v*2
1979	hom(:,1,32,0) = sums(:,32) / ngp_2dh_outer(:,0) ! w*2
1980
1981	ENDIF
1982
1983	END SUBROUTINE lpm_init_sgs_tke
1984
1985
1986	!------------------------------------------------------------------------------!
1987	! Description:
1988	! ------------
1989	!> Sobroutine control lpm actions, i.e. all actions during one time step.
1990	!------------------------------------------------------------------------------!
1991	SUBROUTINE lpm_actions( location )
1992
1993	CHARACTER (LEN=*), INTENT(IN) :: location !< call location string
1994
1995	INTEGER(iwp) :: i !<
1996	INTEGER(iwp) :: ie !<
1997	INTEGER(iwp) :: is !<
1998	INTEGER(iwp) :: j !<
1999	INTEGER(iwp) :: je !<
2000	INTEGER(iwp) :: js !<
2001	INTEGER(iwp), SAVE :: lpm_count = 0 !<
2002	INTEGER(iwp) :: k !<
2003	INTEGER(iwp) :: ke !<
2004	INTEGER(iwp) :: ks !<
2005	INTEGER(iwp) :: m !<
2006	INTEGER(iwp), SAVE :: steps = 0 !<
2007
2008	LOGICAL :: first_loop_stride !<
2009
2010
2011	SELECT CASE ( location )
2012
2013	CASE ( 'after_pressure_solver' )
2014	!
2015	!-- The particle model is executed if particle advection start is reached and only at the end
2016	!-- of the intermediate time step loop.
2017	IF ( time_since_reference_point >= particle_advection_start &
2018	.AND. intermediate_timestep_count == intermediate_timestep_count_max ) &
2019	THEN
2020	CALL cpu_log( log_point(25), 'lpm', 'start' )
2021	!
2022	!-- Write particle data at current time on file.
2023	!-- This has to be done here, before particles are further processed,
2024	!-- because they may be deleted within this timestep (in case that
2025	!-- dt_write_particle_data = dt_prel = particle_maximum_age).
2026	time_write_particle_data = time_write_particle_data + dt_3d
2027	IF ( time_write_particle_data >= dt_write_particle_data ) THEN
2028
2029	CALL lpm_data_output_particles
2030	!
2031	!-- The MOD function allows for changes in the output interval with restart
2032	!-- runs.
2033	time_write_particle_data = MOD( time_write_particle_data, &
2034	MAX( dt_write_particle_data, dt_3d ) )
2035	ENDIF
2036
2037	!
2038	!-- Initialize arrays for marking those particles to be deleted after the
2039	!-- (sub-) timestep
2040	deleted_particles = 0
2041
2042	!
2043	!-- Initialize variables used for accumulating the number of particles
2044	!-- xchanged between the subdomains during all sub-timesteps (if sgs
2045	!-- velocities are included). These data are output further below on the
2046	!-- particle statistics file.
2047	trlp_count_sum = 0
2048	trlp_count_recv_sum = 0
2049	trrp_count_sum = 0
2050	trrp_count_recv_sum = 0
2051	trsp_count_sum = 0
2052	trsp_count_recv_sum = 0
2053	trnp_count_sum = 0
2054	trnp_count_recv_sum = 0
2055	!
2056	!-- Calculate exponential term used in case of particle inertia for each
2057	!-- of the particle groups
2058	DO m = 1, number_of_particle_groups
2059	IF ( particle_groups(m)%density_ratio /= 0.0_wp ) THEN
2060	particle_groups(m)%exp_arg = &
2061	4.5_wp * particle_groups(m)%density_ratio * &
2062	molecular_viscosity / ( particle_groups(m)%radius )**2
2063
2064	particle_groups(m)%exp_term = EXP( -particle_groups(m)%exp_arg * &
2065	dt_3d )
2066	ENDIF
2067	ENDDO
2068	!
2069	!-- If necessary, release new set of particles
2070	IF ( ( simulated_time - last_particle_release_time ) >= dt_prel .AND. &
2071	end_time_prel > simulated_time ) THEN
2072	DO WHILE ( ( simulated_time - last_particle_release_time ) >= dt_prel )
2073	CALL lpm_create_particle( PHASE_RELEASE )
2074	last_particle_release_time = last_particle_release_time + dt_prel
2075	ENDDO
2076	ENDIF
2077	!
2078	!-- Reset summation arrays
2079	IF ( cloud_droplets ) THEN
2080	ql_c = 0.0_wp
2081	ql_v = 0.0_wp
2082	ql_vp = 0.0_wp
2083	ENDIF
2084
2085	first_loop_stride = .TRUE.
2086	grid_particles(:,:,:)%time_loop_done = .TRUE.
2087	!
2088	!-- Timestep loop for particle advection.
2089	!-- This loop has to be repeated until the advection time of every particle
2090	!-- (within the total domain!) has reached the LES timestep (dt_3d).
2091	!-- In case of including the SGS velocities, the particle timestep may be
2092	!-- smaller than the LES timestep (because of the Lagrangian timescale
2093	!-- restriction) and particles may require to undergo several particle
2094	!-- timesteps, before the LES timestep is reached. Because the number of these
2095	!-- particle timesteps to be carried out is unknown at first, these steps are
2096	!-- carried out in the following infinite loop with exit condition.
2097	DO
2098	CALL cpu_log( log_point_s(44), 'lpm_advec', 'start' )
2099	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
2100
2101	!
2102	!-- If particle advection includes SGS velocity components, calculate the
2103	!-- required SGS quantities (i.e. gradients of the TKE, as well as
2104	!-- horizontally averaged profiles of the SGS TKE and the resolved-scale
2105	!-- velocity variances)
2106	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
2107	CALL lpm_init_sgs_tke
2108	ENDIF
2109	!
2110	!-- In case SGS-particle speed is considered, particles may carry out
2111	!-- several particle timesteps. In order to prevent unnecessary
2112	!-- treatment of particles that already reached the final time level,
2113	!-- particles are sorted into contiguous blocks of finished and
2114	!-- not-finished particles, in addition to their already sorting
2115	!-- according to their sub-boxes.
2116	IF ( .NOT. first_loop_stride .AND. use_sgs_for_particles ) &
2117	CALL lpm_sort_timeloop_done
2118	DO i = nxl, nxr
2119	DO j = nys, nyn
2120	DO k = nzb+1, nzt
2121
2122	number_of_particles = prt_count(k,j,i)
2123	!
2124	!-- If grid cell gets empty, flag must be true
2125	IF ( number_of_particles <= 0 ) THEN
2126	grid_particles(k,j,i)%time_loop_done = .TRUE.
2127	CYCLE
2128	ENDIF
2129
2130	IF ( .NOT. first_loop_stride .AND. &
2131	grid_particles(k,j,i)%time_loop_done ) CYCLE
2132
2133	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2134
2135	particles(1:number_of_particles)%particle_mask = .TRUE.
2136	!
2137	!-- Initialize the variable storing the total time that a particle
2138	!-- has advanced within the timestep procedure
2139	IF ( first_loop_stride ) THEN
2140	particles(1:number_of_particles)%dt_sum = 0.0_wp
2141	ENDIF
2142	!
2143	!-- Particle (droplet) growth by condensation/evaporation and
2144	!-- collision
2145	IF ( cloud_droplets .AND. first_loop_stride) THEN
2146	!
2147	!-- Droplet growth by condensation / evaporation
2148	CALL lpm_droplet_condensation(i,j,k)
2149	!
2150	!-- Particle growth by collision
2151	IF ( collision_kernel /= 'none' ) THEN
2152	CALL lpm_droplet_collision(i,j,k)
2153	ENDIF
2154
2155	ENDIF
2156	!
2157	!-- Initialize the switch used for the loop exit condition checked
2158	!-- at the end of this loop. If at least one particle has failed to
2159	!-- reach the LES timestep, this switch will be set false in
2160	!-- lpm_advec.
2161	dt_3d_reached_l = .TRUE.
2162
2163	!
2164	!-- Particle advection
2165	CALL lpm_advec( i, j, k )
2166	!
2167	!-- Particle reflection from walls. Only applied if the particles
2168	!-- are in the vertical range of the topography. (Here, some
2169	!-- optimization is still possible.)
2170	IF ( topography /= 'flat' .AND. k < nzb_max + 2 ) THEN
2171	CALL lpm_boundary_conds( 'walls', i, j, k )
2172	ENDIF
2173	!
2174	!-- User-defined actions after the calculation of the new particle
2175	!-- position
2176	CALL user_lpm_advec( i, j, k )
2177	!
2178	!-- Apply boundary conditions to those particles that have crossed
2179	!-- the top or bottom boundary and delete those particles, which are
2180	!-- older than allowed
2181	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
2182	!
2183	!--- If not all particles of the actual grid cell have reached the
2184	!-- LES timestep, this cell has to do another loop iteration. Due to
2185	!-- the fact that particles can move into neighboring grid cells,
2186	!-- these neighbor cells also have to perform another loop iteration.
2187	!-- Please note, this realization does not work properly if
2188	!-- particles move into another subdomain.
2189	IF ( .NOT. dt_3d_reached_l ) THEN
2190	ks = MAX(nzb+1,k-1)
2191	ke = MIN(nzt,k+1)
2192	js = MAX(nys,j-1)
2193	je = MIN(nyn,j+1)
2194	is = MAX(nxl,i-1)
2195	ie = MIN(nxr,i+1)
2196	grid_particles(ks:ke,js:je,is:ie)%time_loop_done = .FALSE.
2197	ELSE
2198	grid_particles(k,j,i)%time_loop_done = .TRUE.
2199	ENDIF
2200
2201	ENDDO
2202	ENDDO
2203	ENDDO
2204	steps = steps + 1
2205	dt_3d_reached_l = ALL(grid_particles(:,:,:)%time_loop_done)
2206	!
2207	!-- Find out, if all particles on every PE have completed the LES timestep
2208	!-- and set the switch corespondingly
2209	#if defined( __parallel )
2210	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2211	CALL MPI_ALLREDUCE( dt_3d_reached_l, dt_3d_reached, 1, MPI_LOGICAL, &
2212	MPI_LAND, comm2d, ierr )
2213	#else
2214	dt_3d_reached = dt_3d_reached_l
2215	#endif
2216	CALL cpu_log( log_point_s(44), 'lpm_advec', 'stop' )
2217
2218	!
2219	!-- Apply splitting and merging algorithm
2220	IF ( cloud_droplets ) THEN
2221	IF ( splitting ) THEN
2222	CALL lpm_splitting
2223	ENDIF
2224	IF ( merging ) THEN
2225	CALL lpm_merging
2226	ENDIF
2227	ENDIF
2228	!
2229	!-- Move Particles local to PE to a different grid cell
2230	CALL lpm_move_particle
2231	!
2232	!-- Horizontal boundary conditions including exchange between subdmains
2233	CALL lpm_exchange_horiz
2234
2235	!
2236	!-- IF .FALSE., lpm_sort_and_delete is done inside pcmp
2237	IF ( .NOT. dt_3d_reached .OR. .NOT. nested_run ) THEN
2238	!
2239	!-- Pack particles (eliminate those marked for deletion),
2240	!-- determine new number of particles
2241	CALL lpm_sort_and_delete
2242
2243	!-- Initialize variables for the next (sub-) timestep, i.e., for marking
2244	!-- those particles to be deleted after the timestep
2245	deleted_particles = 0
2246	ENDIF
2247
2248	IF ( dt_3d_reached ) EXIT
2249
2250	first_loop_stride = .FALSE.
2251	ENDDO ! timestep loop
2252	!
2253	!-- in case of nested runs do the transfer of particles after every full model time step
2254	IF ( nested_run ) THEN
2255	CALL particles_from_parent_to_child
2256	CALL particles_from_child_to_parent
2257	CALL pmcp_p_delete_particles_in_fine_grid_area
2258
2259	CALL lpm_sort_and_delete
2260
2261	deleted_particles = 0
2262	ENDIF
2263
2264	!
2265	!-- Calculate the new liquid water content for each grid box
2266	IF ( cloud_droplets ) CALL lpm_calc_liquid_water_content
2267
2268	!
2269	!-- At the end all arrays are exchanged
2270	IF ( cloud_droplets ) THEN
2271	CALL exchange_horiz( ql, nbgp )
2272	CALL exchange_horiz( ql_c, nbgp )
2273	CALL exchange_horiz( ql_v, nbgp )
2274	CALL exchange_horiz( ql_vp, nbgp )
2275	ENDIF
2276
2277	!
2278	!-- Deallocate unused memory
2279	IF ( deallocate_memory .AND. lpm_count == step_dealloc ) THEN
2280	CALL dealloc_particles_array
2281	lpm_count = 0
2282	ELSEIF ( deallocate_memory ) THEN
2283	lpm_count = lpm_count + 1
2284	ENDIF
2285
2286	!
2287	!-- Write particle statistics (in particular the number of particles
2288	!-- exchanged between the subdomains) on file
2289	IF ( write_particle_statistics ) CALL lpm_write_exchange_statistics
2290	!
2291	!-- Execute Interactions of condnesation and evaporation to humidity and
2292	!-- temperature field
2293	IF ( cloud_droplets ) THEN
2294	CALL lpm_interaction_droplets_ptq
2295	CALL exchange_horiz( pt, nbgp )
2296	CALL exchange_horiz( q, nbgp )
2297	ENDIF
2298
2299	CALL cpu_log( log_point(25), 'lpm', 'stop' )
2300
2301	! !
2302	! !-- Output of particle time series
2303	! IF ( particle_advection ) THEN
2304	! IF ( time_dopts >= dt_dopts .OR. &
2305	! ( time_since_reference_point >= particle_advection_start .AND. &
2306	! first_call_lpm ) ) THEN
2307	! CALL lpm_data_output_ptseries
2308	! time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
2309	! ENDIF
2310	! ENDIF
2311
2312	!
2313	!-- Set this switch to .false. @todo: maybe find better solution.
2314	first_call_lpm = .FALSE.
2315	ENDIF! ENDIF statement of lpm_actions('after_pressure_solver')
2316
2317	CASE ( 'after_integration' )
2318	!
2319	!-- Call at the end of timestep routine to save particle velocities fields
2320	!-- for the next timestep
2321	CALL lpm_swap_timelevel_for_particle_advection
2322
2323	CASE DEFAULT
2324	CONTINUE
2325
2326	END SELECT
2327
2328	END SUBROUTINE lpm_actions
2329
2330
2331	!------------------------------------------------------------------------------!
2332	! Description:
2333	! ------------
2334	!
2335	!------------------------------------------------------------------------------!
2336	SUBROUTINE particles_from_parent_to_child
2337	IMPLICIT NONE
2338
2339	CALL pmcp_c_get_particle_from_parent ! Child actions
2340	CALL pmcp_p_fill_particle_win ! Parent actions
2341
2342	RETURN
2343	END SUBROUTINE particles_from_parent_to_child
2344
2345
2346	!------------------------------------------------------------------------------!
2347	! Description:
2348	! ------------
2349	!
2350	!------------------------------------------------------------------------------!
2351	SUBROUTINE particles_from_child_to_parent
2352	IMPLICIT NONE
2353
2354	CALL pmcp_c_send_particle_to_parent ! Child actions
2355	CALL pmcp_p_empty_particle_win ! Parent actions
2356
2357	RETURN
2358	END SUBROUTINE particles_from_child_to_parent
2359
2360	!------------------------------------------------------------------------------!
2361	! Description:
2362	! ------------
2363	!> This routine write exchange statistics of the lpm in a ascii file.
2364	!------------------------------------------------------------------------------!
2365	SUBROUTINE lpm_write_exchange_statistics
2366
2367	INTEGER(iwp) :: ip !<
2368	INTEGER(iwp) :: jp !<
2369	INTEGER(iwp) :: kp !<
2370	INTEGER(iwp) :: tot_number_of_particles !<
2371
2372	!
2373	!-- Determine the current number of particles
2374	number_of_particles = 0
2375	DO ip = nxl, nxr
2376	DO jp = nys, nyn
2377	DO kp = nzb+1, nzt
2378	number_of_particles = number_of_particles &
2379	+ prt_count(kp,jp,ip)
2380	ENDDO
2381	ENDDO
2382	ENDDO
2383
2384	CALL check_open( 80 )
2385	#if defined( __parallel )
2386	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2387	number_of_particles, pleft, trlp_count_sum, &
2388	trlp_count_recv_sum, pright, trrp_count_sum, &
2389	trrp_count_recv_sum, psouth, trsp_count_sum, &
2390	trsp_count_recv_sum, pnorth, trnp_count_sum, &
2391	trnp_count_recv_sum
2392	#else
2393	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2394	number_of_particles
2395	#endif
2396	CALL close_file( 80 )
2397
2398	IF ( number_of_particles > 0 ) THEN
2399	WRITE(9,*) 'number_of_particles ', number_of_particles, &
2400	current_timestep_number + 1, simulated_time + dt_3d
2401	ENDIF
2402
2403	#if defined( __parallel )
2404	CALL MPI_ALLREDUCE( number_of_particles, tot_number_of_particles, 1, &
2405	MPI_INTEGER, MPI_SUM, comm2d, ierr )
2406	#else
2407	tot_number_of_particles = number_of_particles
2408	#endif
2409
2410	IF ( nested_run ) THEN
2411	CALL pmcp_g_print_number_of_particles( simulated_time+dt_3d, &
2412	tot_number_of_particles)
2413	ENDIF
2414
2415	!
2416	!-- Formats
2417	8000 FORMAT (I6,1X,F7.2,4X,I10,5X,4(I3,1X,I4,'/',I4,2X),6X,I10)
2418
2419
2420	END SUBROUTINE lpm_write_exchange_statistics
2421
2422
2423	!------------------------------------------------------------------------------!
2424	! Description:
2425	! ------------
2426	!> Write particle data in FORTRAN binary and/or netCDF format
2427	!------------------------------------------------------------------------------!
2428	SUBROUTINE lpm_data_output_particles
2429
2430	INTEGER(iwp) :: ip !<
2431	INTEGER(iwp) :: jp !<
2432	INTEGER(iwp) :: kp !<
2433
2434	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'start' )
2435
2436	!
2437	!-- Attention: change version number for unit 85 (in routine check_open)
2438	!-- whenever the output format for this unit is changed!
2439	CALL check_open( 85 )
2440
2441	WRITE ( 85 ) simulated_time
2442	WRITE ( 85 ) prt_count
2443
2444	DO ip = nxl, nxr
2445	DO jp = nys, nyn
2446	DO kp = nzb+1, nzt
2447	number_of_particles = prt_count(kp,jp,ip)
2448	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
2449	IF ( number_of_particles <= 0 ) CYCLE
2450	WRITE ( 85 ) particles
2451	ENDDO
2452	ENDDO
2453	ENDDO
2454
2455	CALL close_file( 85 )
2456
2457
2458	#if defined( __netcdf )
2459	! !
2460	! !-- Output in netCDF format
2461	! CALL check_open( 108 )
2462	!
2463	! !
2464	! !-- Update the NetCDF time axis
2465	! prt_time_count = prt_time_count + 1
2466	!
2467	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_time_prt, &
2468	! (/ simulated_time /), &
2469	! start = (/ prt_time_count /), count = (/ 1 /) )
2470	! CALL netcdf_handle_error( 'lpm_data_output_particles', 1 )
2471	!
2472	! !
2473	! !-- Output the real number of particles used
2474	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_rnop_prt, &
2475	! (/ number_of_particles /), &
2476	! start = (/ prt_time_count /), count = (/ 1 /) )
2477	! CALL netcdf_handle_error( 'lpm_data_output_particles', 2 )
2478	!
2479	! !
2480	! !-- Output all particle attributes
2481	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(1), particles%age, &
2482	! start = (/ 1, prt_time_count /), &
2483	! count = (/ maximum_number_of_particles /) )
2484	! CALL netcdf_handle_error( 'lpm_data_output_particles', 3 )
2485	!
2486	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(2), particles%user, &
2487	! start = (/ 1, prt_time_count /), &
2488	! count = (/ maximum_number_of_particles /) )
2489	! CALL netcdf_handle_error( 'lpm_data_output_particles', 4 )
2490	!
2491	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(3), particles%origin_x, &
2492	! start = (/ 1, prt_time_count /), &
2493	! count = (/ maximum_number_of_particles /) )
2494	! CALL netcdf_handle_error( 'lpm_data_output_particles', 5 )
2495	!
2496	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(4), particles%origin_y, &
2497	! start = (/ 1, prt_time_count /), &
2498	! count = (/ maximum_number_of_particles /) )
2499	! CALL netcdf_handle_error( 'lpm_data_output_particles', 6 )
2500	!
2501	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(5), particles%origin_z, &
2502	! start = (/ 1, prt_time_count /), &
2503	! count = (/ maximum_number_of_particles /) )
2504	! CALL netcdf_handle_error( 'lpm_data_output_particles', 7 )
2505	!
2506	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(6), particles%radius, &
2507	! start = (/ 1, prt_time_count /), &
2508	! count = (/ maximum_number_of_particles /) )
2509	! CALL netcdf_handle_error( 'lpm_data_output_particles', 8 )
2510	!
2511	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(7), particles%speed_x, &
2512	! start = (/ 1, prt_time_count /), &
2513	! count = (/ maximum_number_of_particles /) )
2514	! CALL netcdf_handle_error( 'lpm_data_output_particles', 9 )
2515	!
2516	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(8), particles%speed_y, &
2517	! start = (/ 1, prt_time_count /), &
2518	! count = (/ maximum_number_of_particles /) )
2519	! CALL netcdf_handle_error( 'lpm_data_output_particles', 10 )
2520	!
2521	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(9), particles%speed_z, &
2522	! start = (/ 1, prt_time_count /), &
2523	! count = (/ maximum_number_of_particles /) )
2524	! CALL netcdf_handle_error( 'lpm_data_output_particles', 11 )
2525	!
2526	! nc_stat = NF90_PUT_VAR( id_set_prt,id_var_prt(10), &
2527	! particles%weight_factor, &
2528	! start = (/ 1, prt_time_count /), &
2529	! count = (/ maximum_number_of_particles /) )
2530	! CALL netcdf_handle_error( 'lpm_data_output_particles', 12 )
2531	!
2532	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(11), particles%x, &
2533	! start = (/ 1, prt_time_count /), &
2534	! count = (/ maximum_number_of_particles /) )
2535	! CALL netcdf_handle_error( 'lpm_data_output_particles', 13 )
2536	!
2537	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(12), particles%y, &
2538	! start = (/ 1, prt_time_count /), &
2539	! count = (/ maximum_number_of_particles /) )
2540	! CALL netcdf_handle_error( 'lpm_data_output_particles', 14 )
2541	!
2542	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(13), particles%z, &
2543	! start = (/ 1, prt_time_count /), &
2544	! count = (/ maximum_number_of_particles /) )
2545	! CALL netcdf_handle_error( 'lpm_data_output_particles', 15 )
2546	!
2547	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(14), particles%class, &
2548	! start = (/ 1, prt_time_count /), &
2549	! count = (/ maximum_number_of_particles /) )
2550	! CALL netcdf_handle_error( 'lpm_data_output_particles', 16 )
2551	!
2552	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(15), particles%group, &
2553	! start = (/ 1, prt_time_count /), &
2554	! count = (/ maximum_number_of_particles /) )
2555	! CALL netcdf_handle_error( 'lpm_data_output_particles', 17 )
2556	!
2557	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(16), &
2558	! particles%id2, &
2559	! start = (/ 1, prt_time_count /), &
2560	! count = (/ maximum_number_of_particles /) )
2561	! CALL netcdf_handle_error( 'lpm_data_output_particles', 18 )
2562	!
2563	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(17), particles%id1, &
2564	! start = (/ 1, prt_time_count /), &
2565	! count = (/ maximum_number_of_particles /) )
2566	! CALL netcdf_handle_error( 'lpm_data_output_particles', 19 )
2567	!
2568	#endif
2569
2570	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'stop' )
2571
2572	END SUBROUTINE lpm_data_output_particles
2573
2574	!------------------------------------------------------------------------------!
2575	! Description:
2576	! ------------
2577	!> This routine calculates and provide particle timeseries output.
2578	!------------------------------------------------------------------------------!
2579	SUBROUTINE lpm_data_output_ptseries
2580
2581	INTEGER(iwp) :: i !<
2582	INTEGER(iwp) :: inum !<
2583	INTEGER(iwp) :: j !<
2584	INTEGER(iwp) :: jg !<
2585	INTEGER(iwp) :: k !<
2586	INTEGER(iwp) :: n !<
2587
2588	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value !<
2589	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value_l !<
2590
2591
2592	CALL cpu_log( log_point(36), 'data_output_ptseries', 'start' )
2593
2594	IF ( myid == 0 ) THEN
2595	!
2596	!-- Open file for time series output in NetCDF format
2597	dopts_time_count = dopts_time_count + 1
2598	CALL check_open( 109 )
2599	#if defined( __netcdf )
2600	!
2601	!-- Update the particle time series time axis
2602	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_time_pts, &
2603	(/ time_since_reference_point /), &
2604	start = (/ dopts_time_count /), count = (/ 1 /) )
2605	CALL netcdf_handle_error( 'data_output_ptseries', 391 )
2606	#endif
2607
2608	ENDIF
2609
2610	ALLOCATE( pts_value(0:number_of_particle_groups,dopts_num), &
2611	pts_value_l(0:number_of_particle_groups,dopts_num) )
2612
2613	pts_value_l = 0.0_wp
2614	pts_value_l(:,16) = 9999999.9_wp ! for calculation of minimum radius
2615
2616	!
2617	!-- Calculate or collect the particle time series quantities for all particles
2618	!-- and seperately for each particle group (if there is more than one group)
2619	DO i = nxl, nxr
2620	DO j = nys, nyn
2621	DO k = nzb, nzt
2622	number_of_particles = prt_count(k,j,i)
2623	IF (number_of_particles <= 0) CYCLE
2624	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2625	DO n = 1, number_of_particles
2626
2627	IF ( particles(n)%particle_mask ) THEN ! Restrict analysis to active particles
2628
2629	pts_value_l(0,1) = pts_value_l(0,1) + 1.0_wp ! total # of particles
2630	pts_value_l(0,2) = pts_value_l(0,2) + &
2631	( particles(n)%x - particles(n)%origin_x ) ! mean x
2632	pts_value_l(0,3) = pts_value_l(0,3) + &
2633	( particles(n)%y - particles(n)%origin_y ) ! mean y
2634	pts_value_l(0,4) = pts_value_l(0,4) + &
2635	( particles(n)%z - particles(n)%origin_z ) ! mean z
2636	pts_value_l(0,5) = pts_value_l(0,5) + particles(n)%z ! mean z (absolute)
2637	pts_value_l(0,6) = pts_value_l(0,6) + particles(n)%speed_x ! mean u
2638	pts_value_l(0,7) = pts_value_l(0,7) + particles(n)%speed_y ! mean v
2639	pts_value_l(0,8) = pts_value_l(0,8) + particles(n)%speed_z ! mean w
2640	pts_value_l(0,9) = pts_value_l(0,9) + particles(n)%rvar1 ! mean sgsu
2641	pts_value_l(0,10) = pts_value_l(0,10) + particles(n)%rvar2 ! mean sgsv
2642	pts_value_l(0,11) = pts_value_l(0,11) + particles(n)%rvar3 ! mean sgsw
2643	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2644	pts_value_l(0,12) = pts_value_l(0,12) + 1.0_wp ! # of upward moving prts
2645	pts_value_l(0,13) = pts_value_l(0,13) + &
2646	particles(n)%speed_z ! mean w upw.
2647	ELSE
2648	pts_value_l(0,14) = pts_value_l(0,14) + &
2649	particles(n)%speed_z ! mean w down
2650	ENDIF
2651	pts_value_l(0,15) = pts_value_l(0,15) + particles(n)%radius ! mean rad
2652	pts_value_l(0,16) = MIN( pts_value_l(0,16), particles(n)%radius ) ! minrad
2653	pts_value_l(0,17) = MAX( pts_value_l(0,17), particles(n)%radius ) ! maxrad
2654	pts_value_l(0,18) = pts_value_l(0,18) + 1.0_wp
2655	pts_value_l(0,19) = pts_value_l(0,18) + 1.0_wp
2656	!
2657	!-- Repeat the same for the respective particle group
2658	IF ( number_of_particle_groups > 1 ) THEN
2659	jg = particles(n)%group
2660
2661	pts_value_l(jg,1) = pts_value_l(jg,1) + 1.0_wp
2662	pts_value_l(jg,2) = pts_value_l(jg,2) + &
2663	( particles(n)%x - particles(n)%origin_x )
2664	pts_value_l(jg,3) = pts_value_l(jg,3) + &
2665	( particles(n)%y - particles(n)%origin_y )
2666	pts_value_l(jg,4) = pts_value_l(jg,4) + &
2667	( particles(n)%z - particles(n)%origin_z )
2668	pts_value_l(jg,5) = pts_value_l(jg,5) + particles(n)%z
2669	pts_value_l(jg,6) = pts_value_l(jg,6) + particles(n)%speed_x
2670	pts_value_l(jg,7) = pts_value_l(jg,7) + particles(n)%speed_y
2671	pts_value_l(jg,8) = pts_value_l(jg,8) + particles(n)%speed_z
2672	pts_value_l(jg,9) = pts_value_l(jg,9) + particles(n)%rvar1
2673	pts_value_l(jg,10) = pts_value_l(jg,10) + particles(n)%rvar2
2674	pts_value_l(jg,11) = pts_value_l(jg,11) + particles(n)%rvar3
2675	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2676	pts_value_l(jg,12) = pts_value_l(jg,12) + 1.0_wp
2677	pts_value_l(jg,13) = pts_value_l(jg,13) + particles(n)%speed_z
2678	ELSE
2679	pts_value_l(jg,14) = pts_value_l(jg,14) + particles(n)%speed_z
2680	ENDIF
2681	pts_value_l(jg,15) = pts_value_l(jg,15) + particles(n)%radius
2682	pts_value_l(jg,16) = MIN( pts_value_l(jg,16), particles(n)%radius )
2683	pts_value_l(jg,17) = MAX( pts_value_l(jg,17), particles(n)%radius )
2684	pts_value_l(jg,18) = pts_value_l(jg,18) + 1.0_wp
2685	pts_value_l(jg,19) = pts_value_l(jg,19) + 1.0_wp
2686	ENDIF
2687
2688	ENDIF
2689
2690	ENDDO
2691
2692	ENDDO
2693	ENDDO
2694	ENDDO
2695
2696
2697	#if defined( __parallel )
2698	!
2699	!-- Sum values of the subdomains
2700	inum = number_of_particle_groups + 1
2701
2702	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2703	CALL MPI_ALLREDUCE( pts_value_l(0,1), pts_value(0,1), 15*inum, MPI_REAL, &
2704	MPI_SUM, comm2d, ierr )
2705	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2706	CALL MPI_ALLREDUCE( pts_value_l(0,16), pts_value(0,16), inum, MPI_REAL, &
2707	MPI_MIN, comm2d, ierr )
2708	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2709	CALL MPI_ALLREDUCE( pts_value_l(0,17), pts_value(0,17), inum, MPI_REAL, &
2710	MPI_MAX, comm2d, ierr )
2711	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2712	CALL MPI_ALLREDUCE( pts_value_l(0,18), pts_value(0,18), inum, MPI_REAL, &
2713	MPI_MAX, comm2d, ierr )
2714	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2715	CALL MPI_ALLREDUCE( pts_value_l(0,19), pts_value(0,19), inum, MPI_REAL, &
2716	MPI_MIN, comm2d, ierr )
2717	#else
2718	pts_value(:,1:19) = pts_value_l(:,1:19)
2719	#endif
2720
2721	!
2722	!-- Normalize the above calculated quantities (except min/max values) with the
2723	!-- total number of particles
2724	IF ( number_of_particle_groups > 1 ) THEN
2725	inum = number_of_particle_groups
2726	ELSE
2727	inum = 0
2728	ENDIF
2729
2730	DO j = 0, inum
2731
2732	IF ( pts_value(j,1) > 0.0_wp ) THEN
2733
2734	pts_value(j,2:15) = pts_value(j,2:15) / pts_value(j,1)
2735	IF ( pts_value(j,12) > 0.0_wp .AND. pts_value(j,12) < 1.0_wp ) THEN
2736	pts_value(j,13) = pts_value(j,13) / pts_value(j,12)
2737	pts_value(j,14) = pts_value(j,14) / ( 1.0_wp - pts_value(j,12) )
2738	ELSEIF ( pts_value(j,12) == 0.0_wp ) THEN
2739	pts_value(j,13) = -1.0_wp
2740	ELSE
2741	pts_value(j,14) = -1.0_wp
2742	ENDIF
2743
2744	ENDIF
2745
2746	ENDDO
2747
2748	!
2749	!-- Calculate higher order moments of particle time series quantities,
2750	!-- seperately for each particle group (if there is more than one group)
2751	DO i = nxl, nxr
2752	DO j = nys, nyn
2753	DO k = nzb, nzt
2754	number_of_particles = prt_count(k,j,i)
2755	IF (number_of_particles <= 0) CYCLE
2756	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2757	DO n = 1, number_of_particles
2758
2759	pts_value_l(0,20) = pts_value_l(0,20) + ( particles(n)%x - &
2760	particles(n)%origin_x - pts_value(0,2) )*2 ! x2
2761	pts_value_l(0,21) = pts_value_l(0,21) + ( particles(n)%y - &
2762	particles(n)%origin_y - pts_value(0,3) )*2 ! y2
2763	pts_value_l(0,22) = pts_value_l(0,22) + ( particles(n)%z - &
2764	particles(n)%origin_z - pts_value(0,4) )*2 ! z2
2765	pts_value_l(0,23) = pts_value_l(0,23) + ( particles(n)%speed_x - &
2766	pts_value(0,6) )*2 ! u2
2767	pts_value_l(0,24) = pts_value_l(0,24) + ( particles(n)%speed_y - &
2768	pts_value(0,7) )*2 ! v2
2769	pts_value_l(0,25) = pts_value_l(0,25) + ( particles(n)%speed_z - &
2770	pts_value(0,8) )*2 ! w2
2771	pts_value_l(0,26) = pts_value_l(0,26) + ( particles(n)%rvar1 - &
2772	pts_value(0,9) )**2 ! u"2
2773	pts_value_l(0,27) = pts_value_l(0,27) + ( particles(n)%rvar2 - &
2774	pts_value(0,10) )**2 ! v"2
2775	pts_value_l(0,28) = pts_value_l(0,28) + ( particles(n)%rvar3 - &
2776	pts_value(0,11) )**2 ! w"2
2777	!
2778	!-- Repeat the same for the respective particle group
2779	IF ( number_of_particle_groups > 1 ) THEN
2780	jg = particles(n)%group
2781
2782	pts_value_l(jg,20) = pts_value_l(jg,20) + ( particles(n)%x - &
2783	particles(n)%origin_x - pts_value(jg,2) )**2
2784	pts_value_l(jg,21) = pts_value_l(jg,21) + ( particles(n)%y - &
2785	particles(n)%origin_y - pts_value(jg,3) )**2
2786	pts_value_l(jg,22) = pts_value_l(jg,22) + ( particles(n)%z - &
2787	particles(n)%origin_z - pts_value(jg,4) )**2
2788	pts_value_l(jg,23) = pts_value_l(jg,23) + ( particles(n)%speed_x - &
2789	pts_value(jg,6) )**2
2790	pts_value_l(jg,24) = pts_value_l(jg,24) + ( particles(n)%speed_y - &
2791	pts_value(jg,7) )**2
2792	pts_value_l(jg,25) = pts_value_l(jg,25) + ( particles(n)%speed_z - &
2793	pts_value(jg,8) )**2
2794	pts_value_l(jg,26) = pts_value_l(jg,26) + ( particles(n)%rvar1 - &
2795	pts_value(jg,9) )**2
2796	pts_value_l(jg,27) = pts_value_l(jg,27) + ( particles(n)%rvar2 - &
2797	pts_value(jg,10) )**2
2798	pts_value_l(jg,28) = pts_value_l(jg,28) + ( particles(n)%rvar3 - &
2799	pts_value(jg,11) )**2
2800	ENDIF
2801
2802	ENDDO
2803	ENDDO
2804	ENDDO
2805	ENDDO
2806
2807	pts_value_l(0,29) = ( number_of_particles - pts_value(0,1) / numprocs )**2
2808	! variance of particle numbers
2809	IF ( number_of_particle_groups > 1 ) THEN
2810	DO j = 1, number_of_particle_groups
2811	pts_value_l(j,29) = ( pts_value_l(j,1) - &
2812	pts_value(j,1) / numprocs )**2
2813	ENDDO
2814	ENDIF
2815
2816	#if defined( __parallel )
2817	!
2818	!-- Sum values of the subdomains
2819	inum = number_of_particle_groups + 1
2820
2821	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2822	CALL MPI_ALLREDUCE( pts_value_l(0,20), pts_value(0,20), inum*10, MPI_REAL, &
2823	MPI_SUM, comm2d, ierr )
2824	#else
2825	pts_value(:,20:29) = pts_value_l(:,20:29)
2826	#endif
2827
2828	!
2829	!-- Normalize the above calculated quantities with the total number of
2830	!-- particles
2831	IF ( number_of_particle_groups > 1 ) THEN
2832	inum = number_of_particle_groups
2833	ELSE
2834	inum = 0
2835	ENDIF
2836
2837	DO j = 0, inum
2838
2839	IF ( pts_value(j,1) > 0.0_wp ) THEN
2840	pts_value(j,20:28) = pts_value(j,20:28) / pts_value(j,1)
2841	ENDIF
2842	pts_value(j,29) = pts_value(j,29) / numprocs
2843
2844	ENDDO
2845
2846	#if defined( __netcdf )
2847	!
2848	!-- Output particle time series quantities in NetCDF format
2849	IF ( myid == 0 ) THEN
2850	DO j = 0, inum
2851	DO i = 1, dopts_num
2852	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_dopts(i,j), &
2853	(/ pts_value(j,i) /), &
2854	start = (/ dopts_time_count /), &
2855	count = (/ 1 /) )
2856	CALL netcdf_handle_error( 'data_output_ptseries', 392 )
2857	ENDDO
2858	ENDDO
2859	ENDIF
2860	#endif
2861
2862	DEALLOCATE( pts_value, pts_value_l )
2863
2864	CALL cpu_log( log_point(36), 'data_output_ptseries', 'stop' )
2865
2866	END SUBROUTINE lpm_data_output_ptseries
2867
2868
2869	!------------------------------------------------------------------------------!
2870	! Description:
2871	! ------------
2872	!> This routine reads the respective restart data for the lpm.
2873	!------------------------------------------------------------------------------!
2874	SUBROUTINE lpm_rrd_local_particles
2875
2876	CHARACTER (LEN=10) :: particle_binary_version !<
2877	CHARACTER (LEN=10) :: version_on_file !<
2878
2879	INTEGER(iwp) :: alloc_size !<
2880	INTEGER(iwp) :: ip !<
2881	INTEGER(iwp) :: jp !<
2882	INTEGER(iwp) :: kp !<
2883
2884	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles !<
2885
2886	!
2887	!-- Read particle data from previous model run.
2888	!-- First open the input unit.
2889	IF ( myid_char == '' ) THEN
2890	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN'//myid_char, &
2891	FORM='UNFORMATTED' )
2892	ELSE
2893	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN/'//myid_char, &
2894	FORM='UNFORMATTED' )
2895	ENDIF
2896
2897	!
2898	!-- First compare the version numbers
2899	READ ( 90 ) version_on_file
2900	particle_binary_version = '4.0'
2901	IF ( TRIM( version_on_file ) /= TRIM( particle_binary_version ) ) THEN
2902	message_string = 'version mismatch concerning data from prior ' // &
2903	'run &version on file = "' // &
2904	TRIM( version_on_file ) // &
2905	'&version in program = "' // &
2906	TRIM( particle_binary_version ) // '"'
2907	CALL message( 'lpm_read_restart_file', 'PA0214', 1, 2, 0, 6, 0 )
2908	ENDIF
2909
2910	!
2911	!-- If less particles are stored on the restart file than prescribed by
2912	!-- 1, the remainder is initialized by zero_particle to avoid
2913	!-- errors.
2914	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2915	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2916	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2917	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2918	0, 0, 0_idp, .FALSE., -1 )
2919	!
2920	!-- Read some particle parameters and the size of the particle arrays,
2921	!-- allocate them and read their contents.
2922	READ ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
2923	last_particle_release_time, number_of_particle_groups, &
2924	particle_groups, time_write_particle_data
2925
2926	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
2927	grid_particles(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
2928
2929	READ ( 90 ) prt_count
2930
2931	DO ip = nxl, nxr
2932	DO jp = nys, nyn
2933	DO kp = nzb+1, nzt
2934
2935	number_of_particles = prt_count(kp,jp,ip)
2936	IF ( number_of_particles > 0 ) THEN
2937	alloc_size = MAX( INT( number_of_particles * &
2938	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
2939	1 )
2940	ELSE
2941	alloc_size = 1
2942	ENDIF
2943
2944	ALLOCATE( grid_particles(kp,jp,ip)%particles(1:alloc_size) )
2945
2946	IF ( number_of_particles > 0 ) THEN
2947	ALLOCATE( tmp_particles(1:number_of_particles) )
2948	READ ( 90 ) tmp_particles
2949	grid_particles(kp,jp,ip)%particles(1:number_of_particles) = tmp_particles
2950	DEALLOCATE( tmp_particles )
2951	IF ( number_of_particles < alloc_size ) THEN
2952	grid_particles(kp,jp,ip)%particles(number_of_particles+1:alloc_size) &
2953	= zero_particle
2954	ENDIF
2955	ELSE
2956	grid_particles(kp,jp,ip)%particles(1:alloc_size) = zero_particle
2957	ENDIF
2958
2959	ENDDO
2960	ENDDO
2961	ENDDO
2962
2963	CLOSE ( 90 )
2964	!
2965	!-- Must be called to sort particles into blocks, which is needed for a fast
2966	!-- interpolation of the LES fields on the particle position.
2967	CALL lpm_sort_and_delete
2968
2969
2970	END SUBROUTINE lpm_rrd_local_particles
2971
2972
2973	SUBROUTINE lpm_rrd_local( k, nxlf, nxlc, nxl_on_file, nxrf, nxrc, &
2974	nxr_on_file, nynf, nync, nyn_on_file, nysf, &
2975	nysc, nys_on_file, tmp_3d, found )
2976
2977
2978	USE control_parameters, &
2979	ONLY: length, restart_string
2980
2981	INTEGER(iwp) :: k !<
2982	INTEGER(iwp) :: nxlc !<
2983	INTEGER(iwp) :: nxlf !<
2984	INTEGER(iwp) :: nxl_on_file !<
2985	INTEGER(iwp) :: nxrc !<
2986	INTEGER(iwp) :: nxrf !<
2987	INTEGER(iwp) :: nxr_on_file !<
2988	INTEGER(iwp) :: nync !<
2989	INTEGER(iwp) :: nynf !<
2990	INTEGER(iwp) :: nyn_on_file !<
2991	INTEGER(iwp) :: nysc !<
2992	INTEGER(iwp) :: nysf !<
2993	INTEGER(iwp) :: nys_on_file !<
2994
2995	LOGICAL, INTENT(OUT) :: found
2996
2997	REAL(wp), DIMENSION(nzb:nzt+1,nys_on_file-nbgp:nyn_on_file+nbgp,nxl_on_file-nbgp:nxr_on_file+nbgp) :: tmp_3d !<
2998
2999
3000	found = .TRUE.
3001
3002	SELECT CASE ( restart_string(1:length) )
3003
3004	CASE ( 'iran' ) ! matching random numbers is still unresolved issue
3005	IF ( k == 1 ) READ ( 13 ) iran, iran_part
3006
3007	CASE ( 'pc_av' )
3008	IF ( .NOT. ALLOCATED( pc_av ) ) THEN
3009	ALLOCATE( pc_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3010	ENDIF
3011	IF ( k == 1 ) READ ( 13 ) tmp_3d
3012	pc_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3013	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3014
3015	CASE ( 'pr_av' )
3016	IF ( .NOT. ALLOCATED( pr_av ) ) THEN
3017	ALLOCATE( pr_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3018	ENDIF
3019	IF ( k == 1 ) READ ( 13 ) tmp_3d
3020	pr_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3021	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3022
3023	CASE ( 'ql_c_av' )
3024	IF ( .NOT. ALLOCATED( ql_c_av ) ) THEN
3025	ALLOCATE( ql_c_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3026	ENDIF
3027	IF ( k == 1 ) READ ( 13 ) tmp_3d
3028	ql_c_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3029	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3030
3031	CASE ( 'ql_v_av' )
3032	IF ( .NOT. ALLOCATED( ql_v_av ) ) THEN
3033	ALLOCATE( ql_v_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3034	ENDIF
3035	IF ( k == 1 ) READ ( 13 ) tmp_3d
3036	ql_v_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3037	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3038
3039	CASE ( 'ql_vp_av' )
3040	IF ( .NOT. ALLOCATED( ql_vp_av ) ) THEN
3041	ALLOCATE( ql_vp_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3042	ENDIF
3043	IF ( k == 1 ) READ ( 13 ) tmp_3d
3044	ql_vp_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3045	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3046
3047	CASE DEFAULT
3048
3049	found = .FALSE.
3050
3051	END SELECT
3052
3053
3054	END SUBROUTINE lpm_rrd_local
3055
3056	!------------------------------------------------------------------------------!
3057	! Description:
3058	! ------------
3059	!> This routine writes the respective restart data for the lpm.
3060	!------------------------------------------------------------------------------!
3061	SUBROUTINE lpm_wrd_local
3062
3063	CHARACTER (LEN=10) :: particle_binary_version !<
3064
3065	INTEGER(iwp) :: ip !<
3066	INTEGER(iwp) :: jp !<
3067	INTEGER(iwp) :: kp !<
3068	!
3069	!-- First open the output unit.
3070	IF ( myid_char == '' ) THEN
3071	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT'//myid_char, &
3072	FORM='UNFORMATTED')
3073	ELSE
3074	IF ( myid == 0 ) CALL local_system( 'mkdir PARTICLE_RESTART_DATA_OUT' )
3075	#if defined( __parallel )
3076	!
3077	!-- Set a barrier in order to allow that thereafter all other processors
3078	!-- in the directory created by PE0 can open their file
3079	CALL MPI_BARRIER( comm2d, ierr )
3080	#endif
3081	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT/'//myid_char, &
3082	FORM='UNFORMATTED' )
3083	ENDIF
3084
3085	!
3086	!-- Write the version number of the binary format.
3087	!-- Attention: After changes to the following output commands the version
3088	!-- --------- number of the variable particle_binary_version must be
3089	!-- changed! Also, the version number and the list of arrays
3090	!-- to be read in lpm_read_restart_file must be adjusted
3091	!-- accordingly.
3092	particle_binary_version = '4.0'
3093	WRITE ( 90 ) particle_binary_version
3094
3095	!
3096	!-- Write some particle parameters, the size of the particle arrays
3097	WRITE ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
3098	last_particle_release_time, number_of_particle_groups, &
3099	particle_groups, time_write_particle_data
3100
3101	WRITE ( 90 ) prt_count
3102
3103	DO ip = nxl, nxr
3104	DO jp = nys, nyn
3105	DO kp = nzb+1, nzt
3106	number_of_particles = prt_count(kp,jp,ip)
3107	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
3108	IF ( number_of_particles <= 0 ) CYCLE
3109	WRITE ( 90 ) particles
3110	ENDDO
3111	ENDDO
3112	ENDDO
3113
3114	CLOSE ( 90 )
3115
3116	#if defined( __parallel )
3117	CALL MPI_BARRIER( comm2d, ierr )
3118	#endif
3119
3120	CALL wrd_write_string( 'iran' )
3121	WRITE ( 14 ) iran, iran_part
3122
3123
3124	END SUBROUTINE lpm_wrd_local
3125
3126
3127	!------------------------------------------------------------------------------!
3128	! Description:
3129	! ------------
3130	!> This routine writes the respective restart data for the lpm.
3131	!------------------------------------------------------------------------------!
3132	SUBROUTINE lpm_wrd_global
3133
3134	CALL wrd_write_string( 'curvature_solution_effects' )
3135	WRITE ( 14 ) curvature_solution_effects
3136
3137	CALL wrd_write_string( 'interpolation_simple_corrector' )
3138	WRITE ( 14 ) interpolation_simple_corrector
3139
3140	CALL wrd_write_string( 'interpolation_simple_predictor' )
3141	WRITE ( 14 ) interpolation_simple_predictor
3142
3143	CALL wrd_write_string( 'interpolation_trilinear' )
3144	WRITE ( 14 ) interpolation_trilinear
3145
3146	END SUBROUTINE lpm_wrd_global
3147
3148
3149	!------------------------------------------------------------------------------!
3150	! Description:
3151	! ------------
3152	!> This routine writes the respective restart data for the lpm.
3153	!------------------------------------------------------------------------------!
3154	SUBROUTINE lpm_rrd_global( found )
3155
3156	USE control_parameters, &
3157	ONLY: length, restart_string
3158
3159	LOGICAL, INTENT(OUT) :: found
3160
3161	found = .TRUE.
3162
3163	SELECT CASE ( restart_string(1:length) )
3164
3165	CASE ( 'curvature_solution_effects' )
3166	READ ( 13 ) curvature_solution_effects
3167
3168	CASE ( 'interpolation_simple_corrector' )
3169	READ ( 13 ) interpolation_simple_corrector
3170
3171	CASE ( 'interpolation_simple_predictor' )
3172	READ ( 13 ) interpolation_simple_predictor
3173
3174	CASE ( 'interpolation_trilinear' )
3175	READ ( 13 ) interpolation_trilinear
3176
3177	! CASE ( 'global_paramter' )
3178	! READ ( 13 ) global_parameter
3179	! CASE ( 'global_array' )
3180	! IF ( .NOT. ALLOCATED( global_array ) ) ALLOCATE( global_array(1:10) )
3181	! READ ( 13 ) global_array
3182
3183	CASE DEFAULT
3184
3185	found = .FALSE.
3186
3187	END SELECT
3188
3189	END SUBROUTINE lpm_rrd_global
3190
3191
3192	!------------------------------------------------------------------------------!
3193	! Description:
3194	! ------------
3195	!> This is a submodule of the lagrangian particle model. It contains all
3196	!> dynamic processes of the lpm. This includes the advection (resolved and sub-
3197	!> grid scale) as well as the boundary conditions of particles. As a next step
3198	!> this submodule should be excluded as an own file.
3199	!------------------------------------------------------------------------------!
3200	SUBROUTINE lpm_advec (ip,jp,kp)
3201
3202	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
3203
3204	INTEGER(iwp) :: i !< index variable along x
3205	INTEGER(iwp) :: i_next !< index variable along x
3206	INTEGER(iwp) :: ip !< index variable along x
3207	INTEGER(iwp) :: iteration_steps = 1 !< amount of iterations steps for corrector step
3208	INTEGER(iwp) :: j !< index variable along y
3209	INTEGER(iwp) :: j_next !< index variable along y
3210	INTEGER(iwp) :: jp !< index variable along y
3211	INTEGER(iwp) :: k !< index variable along z
3212	INTEGER(iwp) :: k_wall !< vertical index of topography top
3213	INTEGER(iwp) :: kp !< index variable along z
3214	INTEGER(iwp) :: k_next !< index variable along z
3215	INTEGER(iwp) :: kw !< index variable along z
3216	INTEGER(iwp) :: kkw !< index variable along z
3217	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
3218	INTEGER(iwp) :: nb !< block number particles are sorted in
3219	INTEGER(iwp) :: particle_end !< end index for partilce loop
3220	INTEGER(iwp) :: particle_start !< start index for particle loop
3221	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
3222	INTEGER(iwp) :: subbox_end !< end index for loop over subboxes in particle advection
3223	INTEGER(iwp) :: subbox_start !< start index for loop over subboxes in particle advection
3224	INTEGER(iwp) :: nn !< loop variable over iterations steps
3225
3226	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
3227	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
3228
3229	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
3230	REAL(wp) :: alpha !< interpolation facor for x-direction
3231
3232	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
3233	REAL(wp) :: beta !< interpolation facor for y-direction
3234	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
3235	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
3236	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
3237	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
3238	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
3239	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
3240	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
3241	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
3242	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
3243	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
3244	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
3245	REAL(wp) :: diameter !< diamter of droplet
3246	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
3247	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
3248	REAL(wp) :: dt_particle_m !< previous particle time step
3249	REAL(wp) :: dz_temp !< dummy for the vertical grid spacing
3250	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
3251	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
3252	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
3253	REAL(wp) :: exp_arg !< argument in the exponent - particle radius
3254	REAL(wp) :: exp_term !< exponent term
3255	REAL(wp) :: gamma !< interpolation facor for z-direction
3256	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
3257	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
3258	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
3259	REAL(wp) :: random_gauss !< Gaussian-distributed random number used for SGS particle advection
3260	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
3261	REAL(wp) :: rg1 !< Gaussian distributed random number
3262	REAL(wp) :: rg2 !< Gaussian distributed random number
3263	REAL(wp) :: rg3 !< Gaussian distributed random number
3264	REAL(wp) :: sigma !< velocity standard deviation
3265	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
3266	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
3267	REAL(wp) :: unext !< calculated particle u-velocity of corrector step
3268	REAL(wp) :: us_int !< friction velocity at particle grid box
3269	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
3270	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
3271	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
3272	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
3273	REAL(wp) :: vnext !< calculated particle v-velocity of corrector step
3274	REAL(wp) :: vv_int !< dummy to compute interpolated mean SGS TKE, used to scale SGS advection
3275	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
3276	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
3277	REAL(wp) :: wnext !< calculated particle w-velocity of corrector step
3278	REAL(wp) :: w_s !< terminal velocity of droplets
3279	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
3280	REAL(wp) :: xp !< calculated particle position in x of predictor step
3281	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
3282	REAL(wp) :: yp !< calculated particle position in y of predictor step
3283	REAL(wp) :: z_p !< surface layer height (0.5 dz)
3284	REAL(wp) :: zp !< calculated particle position in z of predictor step
3285
3286	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
3287	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
3288	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
3289	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
3290	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
3291	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
3292
3293	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
3294	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !< ratio between the density of the fluid and the density of the particles
3295	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
3296	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
3297	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
3298	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
3299	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
3300	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
3301	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
3302	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
3303	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
3304	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !< SGS particle velocity - u-component
3305	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !< SGS particle velocity - v-component
3306	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !< SGS particle velocity - w-component
3307	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
3308	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
3309	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
3310	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
3311	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
3312	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
3313
3314	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
3315
3316	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
3317	!
3318	!-- Determine height of Prandtl layer and distance between Prandtl-layer
3319	!-- height and horizontal mean roughness height, which are required for
3320	!-- vertical logarithmic interpolation of horizontal particle speeds
3321	!-- (for particles below first vertical grid level).
3322	z_p = zu(nzb+1) - zw(nzb)
3323	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
3324
3325	xv = particles(1:number_of_particles)%x
3326	yv = particles(1:number_of_particles)%y
3327	zv = particles(1:number_of_particles)%z
3328	dt_particle = dt_3d
3329
3330	!
3331	!-- This case uses a simple interpolation method for the particle velocites,
3332	!-- and applying a predictor-corrector method. @note the current time divergence
3333	!-- free time step is denoted with u_t etc.; the velocities of the time level of
3334	!-- t+1 wit u,v, and w, as the model is called after swap timelevel
3335	!-- @attention: for the corrector step the velocities of t(n+1) are required.
3336	!-- Therefore the particle code is executed at the end of the time intermediate
3337	!-- timestep routine. This interpolation method is described in more detail
3338	!-- in Grabowski et al., 2018 (GMD).
3339	IF ( interpolation_simple_corrector ) THEN
3340	!
3341	!-- Predictor step
3342	kkw = kp - 1
3343	DO n = 1, number_of_particles
3344
3345	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3346	u_int(n) = u_t(kp,jp,ip) * ( 1.0_wp - alpha ) + u_t(kp,jp,ip+1) * alpha
3347
3348	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3349	v_int(n) = v_t(kp,jp,ip) * ( 1.0_wp - beta ) + v_t(kp,jp+1,ip) * beta
3350
3351	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3352	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3353	w_int(n) = w_t(kkw,jp,ip) * ( 1.0_wp - gamma ) + w_t(kkw+1,jp,ip) * gamma
3354
3355	ENDDO
3356	!
3357	!-- Corrector step
3358	DO n = 1, number_of_particles
3359
3360	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3361
3362	DO nn = 1, iteration_steps
3363
3364	!
3365	!-- Guess new position
3366	xp = particles(n)%x + u_int(n) * dt_particle(n)
3367	yp = particles(n)%y + v_int(n) * dt_particle(n)
3368	zp = particles(n)%z + w_int(n) * dt_particle(n)
3369	!
3370	!-- x direction
3371	i_next = FLOOR( xp * ddx , KIND=iwp)
3372	alpha = MAX( MIN( ( xp - i_next * dx ) * ddx, 1.0_wp ), 0.0_wp )
3373	!
3374	!-- y direction
3375	j_next = FLOOR( yp * ddy )
3376	beta = MAX( MIN( ( yp - j_next * dy ) * ddy, 1.0_wp ), 0.0_wp )
3377	!
3378	!-- z_direction
3379	k_next = MAX( MIN( FLOOR( zp / (zw(kkw+1)-zw(kkw)) + offset_ocean_nzt ), nzt ), 0)
3380	gamma = MAX( MIN( ( zp - zw(k_next) ) / &
3381	( zw(k_next+1) - zw(k_next) ), 1.0_wp ), 0.0_wp )
3382	!
3383	!-- Calculate part of the corrector step
3384	unext = u(k_next+1, j_next, i_next) * ( 1.0_wp - alpha ) + &
3385	u(k_next+1, j_next, i_next+1) * alpha
3386
3387	vnext = v(k_next+1, j_next, i_next) * ( 1.0_wp - beta ) + &
3388	v(k_next+1, j_next+1, i_next ) * beta
3389
3390	wnext = w(k_next, j_next, i_next) * ( 1.0_wp - gamma ) + &
3391	w(k_next+1, j_next, i_next ) * gamma
3392
3393	!
3394	!-- Calculate interpolated particle velocity with predictor
3395	!-- corrector step. u_int, v_int and w_int describes the part of
3396	!-- the predictor step. unext, vnext and wnext is the part of the
3397	!-- corrector step. The resulting new position is set below. The
3398	!-- implementation is based on Grabowski et al., 2018 (GMD).
3399	u_int(n) = 0.5_wp * ( u_int(n) + unext )
3400	v_int(n) = 0.5_wp * ( v_int(n) + vnext )
3401	w_int(n) = 0.5_wp * ( w_int(n) + wnext )
3402
3403	ENDDO
3404	ENDDO
3405	!
3406	!-- This case uses a simple interpolation method for the particle velocites,
3407	!-- and applying a predictor.
3408	ELSEIF ( interpolation_simple_predictor ) THEN
3409	!
3410	!-- The particle position for the w velociy is based on the value of kp and kp-1
3411	kkw = kp - 1
3412	DO n = 1, number_of_particles
3413	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3414
3415	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3416	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3417
3418	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3419	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3420
3421	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3422	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3423	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3424	ENDDO
3425	!
3426	!-- The trilinear interpolation.
3427	ELSEIF ( interpolation_trilinear ) THEN
3428
3429	start_index = grid_particles(kp,jp,ip)%start_index
3430	end_index = grid_particles(kp,jp,ip)%end_index
3431
3432	DO nb = 0, 7
3433	!
3434	!-- Interpolate u velocity-component
3435	i = ip
3436	j = jp + block_offset(nb)%j_off
3437	k = kp + block_offset(nb)%k_off
3438
3439	DO n = start_index(nb), end_index(nb)
3440	!
3441	!-- Interpolation of the u velocity component onto particle position.
3442	!-- Particles are interpolation bi-linearly in the horizontal and a
3443	!-- linearly in the vertical. An exception is made for particles below
3444	!-- the first vertical grid level in case of a prandtl layer. In this
3445	!-- case the horizontal particle velocity components are determined using
3446	!-- Monin-Obukhov relations (if branch).
3447	!-- First, check if particle is located below first vertical grid level
3448	!-- above topography (Prandtl-layer height)
3449	!-- Determine vertical index of topography top
3450	k_wall = topo_top_ind(jp,ip,0)
3451
3452	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3453	!
3454	!-- Resolved-scale horizontal particle velocity is zero below z0.
3455	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3456	u_int(n) = 0.0_wp
3457	ELSE
3458	!
3459	!-- Determine the sublayer. Further used as index.
3460	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3461	* REAL( number_of_sublayers, KIND=wp ) &
3462	* d_z_p_z0
3463	!
3464	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3465	!-- interpolate linearly between precalculated logarithm.
3466	log_z_z0_int = log_z_z0(INT(height_p)) &
3467	+ ( height_p - INT(height_p) ) &
3468	* ( log_z_z0(INT(height_p)+1) &
3469	- log_z_z0(INT(height_p)) &
3470	)
3471	!
3472	!-- Get friction velocity and momentum flux from new surface data
3473	!-- types.
3474	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3475	surf_def_h(0)%end_index(jp,ip) ) THEN
3476	surf_start = surf_def_h(0)%start_index(jp,ip)
3477	!-- Limit friction velocity. In narrow canyons or holes the
3478	!-- friction velocity can become very small, resulting in a too
3479	!-- large particle speed.
3480	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3481	usws_int = surf_def_h(0)%usws(surf_start)
3482	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3483	surf_lsm_h%end_index(jp,ip) ) THEN
3484	surf_start = surf_lsm_h%start_index(jp,ip)
3485	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3486	usws_int = surf_lsm_h%usws(surf_start)
3487	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3488	surf_usm_h%end_index(jp,ip) ) THEN
3489	surf_start = surf_usm_h%start_index(jp,ip)
3490	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3491	usws_int = surf_usm_h%usws(surf_start)
3492	ENDIF
3493	!
3494	!-- Neutral solution is applied for all situations, e.g. also for
3495	!-- unstable and stable situations. Even though this is not exact
3496	!-- this saves a lot of CPU time since several calls of intrinsic
3497	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3498	!-- as sensitivity studies revealed no significant effect of
3499	!-- using the neutral solution also for un/stable situations.
3500	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
3501	* log_z_z0_int - u_gtrans
3502	ENDIF
3503	!
3504	!-- Particle above the first grid level. Bi-linear interpolation in the
3505	!-- horizontal and linear interpolation in the vertical direction.
3506	ELSE
3507	x = xv(n) - i * dx
3508	y = yv(n) + ( 0.5_wp - j ) * dy
3509	aa = x2 + y2
3510	bb = ( dx - x )2 + y2
3511	cc = x2 + ( dy - y )2
3512	dd = ( dx - x )2 + ( dy - y )2
3513	gg = aa + bb + cc + dd
3514
3515	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
3516	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
3517	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3518
3519	IF ( k == nzt ) THEN
3520	u_int(n) = u_int_l
3521	ELSE
3522	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
3523	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
3524	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3525	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3526	( u_int_u - u_int_l )
3527	ENDIF
3528	ENDIF
3529	ENDDO
3530	!
3531	!-- Same procedure for interpolation of the v velocity-component
3532	i = ip + block_offset(nb)%i_off
3533	j = jp
3534	k = kp + block_offset(nb)%k_off
3535
3536	DO n = start_index(nb), end_index(nb)
3537	!
3538	!-- Determine vertical index of topography top
3539	k_wall = topo_top_ind(jp,ip,0)
3540
3541	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3542	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3543	!
3544	!-- Resolved-scale horizontal particle velocity is zero below z0.
3545	v_int(n) = 0.0_wp
3546	ELSE
3547	!
3548	!-- Determine the sublayer. Further used as index. Please note,
3549	!-- logarithmus can not be reused from above, as in in case of
3550	!-- topography particle on u-grid can be above surface-layer height,
3551	!-- whereas it can be below on v-grid.
3552	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3553	* REAL( number_of_sublayers, KIND=wp ) &
3554	* d_z_p_z0
3555	!
3556	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3557	!-- interpolate linearly between precalculated logarithm.
3558	log_z_z0_int = log_z_z0(INT(height_p)) &
3559	+ ( height_p - INT(height_p) ) &
3560	* ( log_z_z0(INT(height_p)+1) &
3561	- log_z_z0(INT(height_p)) &
3562	)
3563	!
3564	!-- Get friction velocity and momentum flux from new surface data
3565	!-- types.
3566	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3567	surf_def_h(0)%end_index(jp,ip) ) THEN
3568	surf_start = surf_def_h(0)%start_index(jp,ip)
3569	!-- Limit friction velocity. In narrow canyons or holes the
3570	!-- friction velocity can become very small, resulting in a too
3571	!-- large particle speed.
3572	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3573	vsws_int = surf_def_h(0)%vsws(surf_start)
3574	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3575	surf_lsm_h%end_index(jp,ip) ) THEN
3576	surf_start = surf_lsm_h%start_index(jp,ip)
3577	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3578	vsws_int = surf_lsm_h%vsws(surf_start)
3579	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3580	surf_usm_h%end_index(jp,ip) ) THEN
3581	surf_start = surf_usm_h%start_index(jp,ip)
3582	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3583	vsws_int = surf_usm_h%vsws(surf_start)
3584	ENDIF
3585	!
3586	!-- Neutral solution is applied for all situations, e.g. also for
3587	!-- unstable and stable situations. Even though this is not exact
3588	!-- this saves a lot of CPU time since several calls of intrinsic
3589	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3590	!-- as sensitivity studies revealed no significant effect of
3591	!-- using the neutral solution also for un/stable situations.
3592	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
3593	* log_z_z0_int - v_gtrans
3594
3595	ENDIF
3596	ELSE
3597	x = xv(n) + ( 0.5_wp - i ) * dx
3598	y = yv(n) - j * dy
3599	aa = x2 + y2
3600	bb = ( dx - x )2 + y2
3601	cc = x2 + ( dy - y )2
3602	dd = ( dx - x )2 + ( dy - y )2
3603	gg = aa + bb + cc + dd
3604
3605	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
3606	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
3607	) / ( 3.0_wp * gg ) - v_gtrans
3608
3609	IF ( k == nzt ) THEN
3610	v_int(n) = v_int_l
3611	ELSE
3612	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
3613	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
3614	) / ( 3.0_wp * gg ) - v_gtrans
3615	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3616	( v_int_u - v_int_l )
3617	ENDIF
3618	ENDIF
3619	ENDDO
3620	!
3621	!-- Same procedure for interpolation of the w velocity-component
3622	i = ip + block_offset(nb)%i_off
3623	j = jp + block_offset(nb)%j_off
3624	k = kp - 1
3625
3626	DO n = start_index(nb), end_index(nb)
3627	IF ( vertical_particle_advection(particles(n)%group) ) THEN
3628	x = xv(n) + ( 0.5_wp - i ) * dx
3629	y = yv(n) + ( 0.5_wp - j ) * dy
3630	aa = x2 + y2
3631	bb = ( dx - x )2 + y2
3632	cc = x2 + ( dy - y )2
3633	dd = ( dx - x )2 + ( dy - y )2
3634	gg = aa + bb + cc + dd
3635
3636	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
3637	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
3638	) / ( 3.0_wp * gg )
3639
3640	IF ( k == nzt ) THEN
3641	w_int(n) = w_int_l
3642	ELSE
3643	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
3644	( gg-bb ) * w(k+1,j,i+1) + &
3645	( gg-cc ) * w(k+1,j+1,i) + &
3646	( gg-dd ) * w(k+1,j+1,i+1) &
3647	) / ( 3.0_wp * gg )
3648	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
3649	( w_int_u - w_int_l )
3650	ENDIF
3651	ELSE
3652	w_int(n) = 0.0_wp
3653	ENDIF
3654	ENDDO
3655	ENDDO
3656	ENDIF
3657
3658	!-- Interpolate and calculate quantities needed for calculating the SGS
3659	!-- velocities
3660	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
3661
3662	DO nb = 0,7
3663
3664	subbox_at_wall = .FALSE.
3665	!
3666	!-- In case of topography check if subbox is adjacent to a wall
3667	IF ( .NOT. topography == 'flat' ) THEN
3668	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
3669	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
3670	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
3671	IF ( .NOT. BTEST(wall_flags_static_0(k, jp, ip), 0) .OR. &
3672	.NOT. BTEST(wall_flags_static_0(kp, j, ip), 0) .OR. &
3673	.NOT. BTEST(wall_flags_static_0(kp, jp, i ), 0) ) &
3674	THEN
3675	subbox_at_wall = .TRUE.
3676	ENDIF
3677	ENDIF
3678	IF ( subbox_at_wall ) THEN
3679	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
3680	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
3681	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
3682	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
3683	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
3684	!
3685	!-- Set flag for stochastic equation.
3686	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
3687	ELSE
3688	i = ip + block_offset(nb)%i_off
3689	j = jp + block_offset(nb)%j_off
3690	k = kp + block_offset(nb)%k_off
3691
3692	DO n = start_index(nb), end_index(nb)
3693	!
3694	!-- Interpolate TKE
3695	x = xv(n) + ( 0.5_wp - i ) * dx
3696	y = yv(n) + ( 0.5_wp - j ) * dy
3697	aa = x2 + y2
3698	bb = ( dx - x )2 + y2
3699	cc = x2 + ( dy - y )2
3700	dd = ( dx - x )2 + ( dy - y )2
3701	gg = aa + bb + cc + dd
3702
3703	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
3704	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
3705	) / ( 3.0_wp * gg )
3706
3707	IF ( k+1 == nzt+1 ) THEN
3708	e_int(n) = e_int_l
3709	ELSE
3710	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
3711	( gg - bb ) * e(k+1,j,i+1) + &
3712	( gg - cc ) * e(k+1,j+1,i) + &
3713	( gg - dd ) * e(k+1,j+1,i+1) &
3714	) / ( 3.0_wp * gg )
3715	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3716	( e_int_u - e_int_l )
3717	ENDIF
3718	!
3719	!-- Needed to avoid NaN particle velocities (this might not be
3720	!-- required any more)
3721	IF ( e_int(n) <= 0.0_wp ) THEN
3722	e_int(n) = 1.0E-20_wp
3723	ENDIF
3724	!
3725	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
3726	!-- all position variables from above (TKE))
3727	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
3728	( gg - bb ) * de_dx(k,j,i+1) + &
3729	( gg - cc ) * de_dx(k,j+1,i) + &
3730	( gg - dd ) * de_dx(k,j+1,i+1) &
3731	) / ( 3.0_wp * gg )
3732
3733	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3734	de_dx_int(n) = de_dx_int_l
3735	ELSE
3736	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
3737	( gg - bb ) * de_dx(k+1,j,i+1) + &
3738	( gg - cc ) * de_dx(k+1,j+1,i) + &
3739	( gg - dd ) * de_dx(k+1,j+1,i+1) &
3740	) / ( 3.0_wp * gg )
3741	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3742	( de_dx_int_u - de_dx_int_l )
3743	ENDIF
3744	!
3745	!-- Interpolate the TKE gradient along y
3746	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
3747	( gg - bb ) * de_dy(k,j,i+1) + &
3748	( gg - cc ) * de_dy(k,j+1,i) + &
3749	( gg - dd ) * de_dy(k,j+1,i+1) &
3750	) / ( 3.0_wp * gg )
3751	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3752	de_dy_int(n) = de_dy_int_l
3753	ELSE
3754	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
3755	( gg - bb ) * de_dy(k+1,j,i+1) + &
3756	( gg - cc ) * de_dy(k+1,j+1,i) + &
3757	( gg - dd ) * de_dy(k+1,j+1,i+1) &
3758	) / ( 3.0_wp * gg )
3759	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3760	( de_dy_int_u - de_dy_int_l )
3761	ENDIF
3762
3763	!
3764	!-- Interpolate the TKE gradient along z
3765	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
3766	de_dz_int(n) = 0.0_wp
3767	ELSE
3768	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
3769	( gg - bb ) * de_dz(k,j,i+1) + &
3770	( gg - cc ) * de_dz(k,j+1,i) + &
3771	( gg - dd ) * de_dz(k,j+1,i+1) &
3772	) / ( 3.0_wp * gg )
3773
3774	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3775	de_dz_int(n) = de_dz_int_l
3776	ELSE
3777	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
3778	( gg - bb ) * de_dz(k+1,j,i+1) + &
3779	( gg - cc ) * de_dz(k+1,j+1,i) + &
3780	( gg - dd ) * de_dz(k+1,j+1,i+1) &
3781	) / ( 3.0_wp * gg )
3782	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3783	( de_dz_int_u - de_dz_int_l )
3784	ENDIF
3785	ENDIF
3786
3787	!
3788	!-- Interpolate the dissipation of TKE
3789	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
3790	( gg - bb ) * diss(k,j,i+1) + &
3791	( gg - cc ) * diss(k,j+1,i) + &
3792	( gg - dd ) * diss(k,j+1,i+1) &
3793	) / ( 3.0_wp * gg )
3794
3795	IF ( k == nzt ) THEN
3796	diss_int(n) = diss_int_l
3797	ELSE
3798	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
3799	( gg - bb ) * diss(k+1,j,i+1) + &
3800	( gg - cc ) * diss(k+1,j+1,i) + &
3801	( gg - dd ) * diss(k+1,j+1,i+1) &
3802	) / ( 3.0_wp * gg )
3803	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3804	( diss_int_u - diss_int_l )
3805	ENDIF
3806
3807	!
3808	!-- Set flag for stochastic equation.
3809	term_1_2(n) = 1.0_wp
3810	ENDDO
3811	ENDIF
3812	ENDDO
3813
3814	DO nb = 0,7
3815	i = ip + block_offset(nb)%i_off
3816	j = jp + block_offset(nb)%j_off
3817	k = kp + block_offset(nb)%k_off
3818
3819	DO n = start_index(nb), end_index(nb)
3820	!
3821	!-- Vertical interpolation of the horizontally averaged SGS TKE and
3822	!-- resolved-scale velocity variances and use the interpolated values
3823	!-- to calculate the coefficient fs, which is a measure of the ratio
3824	!-- of the subgrid-scale turbulent kinetic energy to the total amount
3825	!-- of turbulent kinetic energy.
3826	IF ( k == 0 ) THEN
3827	e_mean_int = hom(0,1,8,0)
3828	ELSE
3829	e_mean_int = hom(k,1,8,0) + &
3830	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
3831	( zu(k+1) - zu(k) ) * &
3832	( zv(n) - zu(k) )
3833	ENDIF
3834
3835	kw = kp - 1
3836
3837	IF ( k == 0 ) THEN
3838	aa = hom(k+1,1,30,0) * ( zv(n) / &
3839	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3840	bb = hom(k+1,1,31,0) * ( zv(n) / &
3841	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3842	cc = hom(kw+1,1,32,0) * ( zv(n) / &
3843	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
3844	ELSE
3845	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
3846	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3847	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
3848	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3849	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
3850	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
3851	ENDIF
3852
3853	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
3854	!
3855	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
3856	!-- an educated guess for the given case.
3857	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
3858	fs_int(n) = 1.0_wp
3859	ELSE
3860	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
3861	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
3862	ENDIF
3863
3864	ENDDO
3865	ENDDO
3866
3867	DO nb = 0, 7
3868	DO n = start_index(nb), end_index(nb)
3869	rg(n,1) = random_gauss( iran_part, 5.0_wp )
3870	rg(n,2) = random_gauss( iran_part, 5.0_wp )
3871	rg(n,3) = random_gauss( iran_part, 5.0_wp )
3872	ENDDO
3873	ENDDO
3874
3875	DO nb = 0, 7
3876	DO n = start_index(nb), end_index(nb)
3877
3878	!
3879	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
3880	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
3881	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
3882
3883	!
3884	!-- Calculate the next particle timestep. dt_gap is the time needed to
3885	!-- complete the current LES timestep.
3886	dt_gap(n) = dt_3d - particles(n)%dt_sum
3887	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
3888	particles(n)%aux1 = lagr_timescale(n)
3889	particles(n)%aux2 = dt_gap(n)
3890	!
3891	!-- The particle timestep should not be too small in order to prevent
3892	!-- the number of particle timesteps of getting too large
3893	IF ( dt_particle(n) < dt_min_part ) THEN
3894	IF ( dt_min_part < dt_gap(n) ) THEN
3895	dt_particle(n) = dt_min_part
3896	ELSE
3897	dt_particle(n) = dt_gap(n)
3898	ENDIF
3899	ENDIF
3900	rvar1_temp(n) = particles(n)%rvar1
3901	rvar2_temp(n) = particles(n)%rvar2
3902	rvar3_temp(n) = particles(n)%rvar3
3903	!
3904	!-- Calculate the SGS velocity components
3905	IF ( particles(n)%age == 0.0_wp ) THEN
3906	!
3907	!-- For new particles the SGS components are derived from the SGS
3908	!-- TKE. Limit the Gaussian random number to the interval
3909	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
3910	!-- from becoming unrealistically large.
3911	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3912	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
3913	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3914	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
3915	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3916	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
3917
3918	ELSE
3919	!
3920	!-- Restriction of the size of the new timestep: compared to the
3921	!-- previous timestep the increase must not exceed 200%. First,
3922	!-- check if age > age_m, in order to prevent that particles get zero
3923	!-- timestep.
3924	dt_particle_m = MERGE( dt_particle(n), &
3925	particles(n)%age - particles(n)%age_m, &
3926	particles(n)%age - particles(n)%age_m < &
3927	1E-8_wp )
3928	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
3929	dt_particle(n) = 2.0_wp * dt_particle_m
3930	ENDIF
3931
3932	!-- For old particles the SGS components are correlated with the
3933	!-- values from the previous timestep. Random numbers have also to
3934	!-- be limited (see above).
3935	!-- As negative values for the subgrid TKE are not allowed, the
3936	!-- change of the subgrid TKE with time cannot be smaller than
3937	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
3938	!-- value for the change of TKE
3939	de_dt_min = - e_int(n) / dt_particle(n)
3940
3941	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3942
3943	IF ( de_dt < de_dt_min ) THEN
3944	de_dt = de_dt_min
3945	ENDIF
3946
3947	CALL weil_stochastic_eq( rvar1_temp(n), fs_int(n), e_int(n), &
3948	de_dx_int(n), de_dt, diss_int(n), &
3949	dt_particle(n), rg(n,1), term_1_2(n) )
3950
3951	CALL weil_stochastic_eq( rvar2_temp(n), fs_int(n), e_int(n), &
3952	de_dy_int(n), de_dt, diss_int(n), &
3953	dt_particle(n), rg(n,2), term_1_2(n) )
3954
3955	CALL weil_stochastic_eq( rvar3_temp(n), fs_int(n), e_int(n), &
3956	de_dz_int(n), de_dt, diss_int(n), &
3957	dt_particle(n), rg(n,3), term_1_2(n) )
3958
3959	ENDIF
3960
3961	ENDDO
3962	ENDDO
3963	!
3964	!-- Check if the added SGS velocities result in a violation of the CFL-
3965	!-- criterion. If yes choose a smaller timestep based on the new velocities
3966	!-- and calculate SGS velocities again
3967	dz_temp = zw(kp)-zw(kp-1)
3968
3969	DO nb = 0, 7
3970	DO n = start_index(nb), end_index(nb)
3971	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
3972	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
3973	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
3974	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
3975
3976	dt_particle(n) = 0.9_wp * MIN( &
3977	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
3978	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
3979	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
3980
3981	!
3982	!-- Reset temporary SGS velocites to "current" ones
3983	rvar1_temp(n) = particles(n)%rvar1
3984	rvar2_temp(n) = particles(n)%rvar2
3985	rvar3_temp(n) = particles(n)%rvar3
3986
3987	de_dt_min = - e_int(n) / dt_particle(n)
3988
3989	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3990
3991	IF ( de_dt < de_dt_min ) THEN
3992	de_dt = de_dt_min
3993	ENDIF
3994
3995	CALL weil_stochastic_eq( rvar1_temp(n), fs_int(n), e_int(n), &
3996	de_dx_int(n), de_dt, diss_int(n), &
3997	dt_particle(n), rg(n,1), term_1_2(n) )
3998
3999	CALL weil_stochastic_eq( rvar2_temp(n), fs_int(n), e_int(n), &
4000	de_dy_int(n), de_dt, diss_int(n), &
4001	dt_particle(n), rg(n,2), term_1_2(n) )
4002
4003	CALL weil_stochastic_eq( rvar3_temp(n), fs_int(n), e_int(n), &
4004	de_dz_int(n), de_dt, diss_int(n), &
4005	dt_particle(n), rg(n,3), term_1_2(n) )
4006	ENDIF
4007
4008	!
4009	!-- Update particle velocites
4010	particles(n)%rvar1 = rvar1_temp(n)
4011	particles(n)%rvar2 = rvar2_temp(n)
4012	particles(n)%rvar3 = rvar3_temp(n)
4013	u_int(n) = u_int(n) + particles(n)%rvar1
4014	v_int(n) = v_int(n) + particles(n)%rvar2
4015	w_int(n) = w_int(n) + particles(n)%rvar3
4016	!
4017	!-- Store the SGS TKE of the current timelevel which is needed for
4018	!-- for calculating the SGS particle velocities at the next timestep
4019	particles(n)%e_m = e_int(n)
4020	ENDDO
4021	ENDDO
4022
4023	ELSE
4024	!
4025	!-- If no SGS velocities are used, only the particle timestep has to
4026	!-- be set
4027	dt_particle = dt_3d
4028
4029	ENDIF
4030
4031	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
4032	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
4033	!
4034	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4035	!-- number_of_particles. This depends on the selected interpolation method.
4036	!-- If particle interpolation method is not trilinear, then the sorting within
4037	!-- subboxes is not required. However, therefore the index start_index(nb) and
4038	!-- end_index(nb) are not defined and the loops are still over
4039	!-- number_of_particles. @todo find a more generic way to write this loop or
4040	!-- delete trilinear interpolation
4041	IF ( interpolation_trilinear ) THEN
4042	subbox_start = 0
4043	subbox_end = 7
4044	ELSE
4045	subbox_start = 1
4046	subbox_end = 1
4047	ENDIF
4048	!
4049	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4050	!-- are introduced, as they are not required. Accordingly, this loops goes
4051	!-- from 1 to 1.
4052	DO nb = subbox_start, subbox_end
4053	IF ( interpolation_trilinear ) THEN
4054	particle_start = start_index(nb)
4055	particle_end = end_index(nb)
4056	ELSE
4057	particle_start = 1
4058	particle_end = number_of_particles
4059	ENDIF
4060	!
4061	!-- Loop from particle start to particle end
4062	DO n = particle_start, particle_end
4063
4064	!
4065	!-- Particle advection
4066	IF ( dens_ratio(n) == 0.0_wp ) THEN
4067	!
4068	!-- Pure passive transport (without particle inertia)
4069	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
4070	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
4071	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
4072
4073	particles(n)%speed_x = u_int(n)
4074	particles(n)%speed_y = v_int(n)
4075	particles(n)%speed_z = w_int(n)
4076
4077	ELSE
4078	!
4079	!-- Transport of particles with inertia
4080	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
4081	dt_particle(n)
4082	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
4083	dt_particle(n)
4084	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
4085	dt_particle(n)
4086
4087	!
4088	!-- Update of the particle velocity
4089	IF ( cloud_droplets ) THEN
4090	!
4091	!-- Terminal velocity is computed for vertical direction (Rogers et
4092	!-- al., 1993, J. Appl. Meteorol.)
4093	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4094	IF ( diameter <= d0_rog ) THEN
4095	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4096	ELSE
4097	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4098	ENDIF
4099
4100	!
4101	!-- If selected, add random velocities following Soelch and Kaercher
4102	!-- (2010, Q. J. R. Meteorol. Soc.)
4103	IF ( use_sgs_for_particles ) THEN
4104	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4105	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4106	1.0E-20_wp ) )
4107	sigma = SQRT( e(kp,jp,ip) )
4108
4109	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4110	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4111	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4112
4113	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4114	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4115	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4116	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4117	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4118	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4119
4120	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4121	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4122	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4123	ELSE
4124	particles(n)%speed_x = u_int(n)
4125	particles(n)%speed_y = v_int(n)
4126	particles(n)%speed_z = w_int(n) - w_s
4127	ENDIF
4128
4129	ELSE
4130
4131	IF ( use_sgs_for_particles ) THEN
4132	exp_arg = particle_groups(particles(n)%group)%exp_arg
4133	exp_term = EXP( -exp_arg * dt_particle(n) )
4134	ELSE
4135	exp_arg = particle_groups(particles(n)%group)%exp_arg
4136	exp_term = particle_groups(particles(n)%group)%exp_term
4137	ENDIF
4138	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4139	u_int(n) * ( 1.0_wp - exp_term )
4140	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4141	v_int(n) * ( 1.0_wp - exp_term )
4142	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4143	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
4144	g / exp_arg ) * ( 1.0_wp - exp_term )
4145	ENDIF
4146
4147	ENDIF
4148	ENDDO
4149	ENDDO
4150
4151	ELSE
4152	!
4153	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4154	!-- number_of_particles. This depends on the selected interpolation method.
4155	IF ( interpolation_trilinear ) THEN
4156	subbox_start = 0
4157	subbox_end = 7
4158	ELSE
4159	subbox_start = 1
4160	subbox_end = 1
4161	ENDIF
4162	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4163	!-- are introduced, as they are not required. Accordingly, this loops goes
4164	!-- from 1 to 1.
4165	DO nb = subbox_start, subbox_end
4166	IF ( interpolation_trilinear ) THEN
4167	particle_start = start_index(nb)
4168	particle_end = end_index(nb)
4169	ELSE
4170	particle_start = 1
4171	particle_end = number_of_particles
4172	ENDIF
4173	!
4174	!-- Loop from particle start to particle end
4175	DO n = particle_start, particle_end
4176
4177	!
4178	!-- Transport of particles with inertia
4179	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
4180	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
4181	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
4182	!
4183	!-- Update of the particle velocity
4184	IF ( cloud_droplets ) THEN
4185	!
4186	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
4187	!-- 1993, J. Appl. Meteorol.)
4188	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4189	IF ( diameter <= d0_rog ) THEN
4190	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4191	ELSE
4192	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4193	ENDIF
4194
4195	!
4196	!-- If selected, add random velocities following Soelch and Kaercher
4197	!-- (2010, Q. J. R. Meteorol. Soc.)
4198	IF ( use_sgs_for_particles ) THEN
4199	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4200	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4201	1.0E-20_wp ) )
4202	sigma = SQRT( e(kp,jp,ip) )
4203
4204	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4205	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4206	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4207
4208	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4209	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4210	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4211	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4212	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4213	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4214
4215	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4216	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4217	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4218	ELSE
4219	particles(n)%speed_x = u_int(n)
4220	particles(n)%speed_y = v_int(n)
4221	particles(n)%speed_z = w_int(n) - w_s
4222	ENDIF
4223
4224	ELSE
4225
4226	IF ( use_sgs_for_particles ) THEN
4227	exp_arg = particle_groups(particles(n)%group)%exp_arg
4228	exp_term = EXP( -exp_arg * dt_particle(n) )
4229	ELSE
4230	exp_arg = particle_groups(particles(n)%group)%exp_arg
4231	exp_term = particle_groups(particles(n)%group)%exp_term
4232	ENDIF
4233	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4234	u_int(n) * ( 1.0_wp - exp_term )
4235	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4236	v_int(n) * ( 1.0_wp - exp_term )
4237	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4238	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
4239	exp_arg ) * ( 1.0_wp - exp_term )
4240	ENDIF
4241	ENDDO
4242	ENDDO
4243
4244	ENDIF
4245
4246	!
4247	!-- Store the old age of the particle ( needed to prevent that a
4248	!-- particle crosses several PEs during one timestep, and for the
4249	!-- evaluation of the subgrid particle velocity fluctuations )
4250	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
4251
4252	!
4253	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4254	!-- are introduced, as they are not required. Accordingly, this loops goes
4255	!-- from 1 to 1.
4256	!
4257	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4258	!-- number_of_particles. This depends on the selected interpolation method.
4259	IF ( interpolation_trilinear ) THEN
4260	subbox_start = 0
4261	subbox_end = 7
4262	ELSE
4263	subbox_start = 1
4264	subbox_end = 1
4265	ENDIF
4266	DO nb = subbox_start, subbox_end
4267	IF ( interpolation_trilinear ) THEN
4268	particle_start = start_index(nb)
4269	particle_end = end_index(nb)
4270	ELSE
4271	particle_start = 1
4272	particle_end = number_of_particles
4273	ENDIF
4274	!
4275	!-- Loop from particle start to particle end
4276	DO n = particle_start, particle_end
4277	!
4278	!-- Increment the particle age and the total time that the particle
4279	!-- has advanced within the particle timestep procedure
4280	particles(n)%age = particles(n)%age + dt_particle(n)
4281	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
4282
4283	!
4284	!-- Check whether there is still a particle that has not yet completed
4285	!-- the total LES timestep
4286	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
4287	dt_3d_reached_l = .FALSE.
4288	ENDIF
4289
4290	ENDDO
4291	ENDDO
4292
4293	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
4294
4295
4296	END SUBROUTINE lpm_advec
4297
4298
4299	!------------------------------------------------------------------------------!
4300	! Description:
4301	! ------------
4302	!> Calculation of subgrid-scale particle speed using the stochastic model
4303	!> of Weil et al. (2004, JAS, 61, 2877-2887).
4304	!------------------------------------------------------------------------------!
4305	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
4306	dt_n, rg_n, fac )
4307
4308	REAL(wp) :: a1 !< dummy argument
4309	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
4310	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
4311	REAL(wp) :: diss_n !< dissipation at particle position
4312	REAL(wp) :: dt_n !< particle timestep
4313	REAL(wp) :: e_n !< TKE at particle position
4314	REAL(wp) :: fac !< flag to identify adjacent topography
4315	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
4316	REAL(wp) :: rg_n !< random number
4317	REAL(wp) :: term1 !< memory term
4318	REAL(wp) :: term2 !< drift correction term
4319	REAL(wp) :: term3 !< random term
4320	REAL(wp) :: v_sgs !< subgrid-scale velocity component
4321
4322	!-- At first, limit TKE to a small non-zero number, in order to prevent
4323	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
4324	!-- (could occur at the simulation begin).
4325	e_n = MAX( e_n, 1E-20_wp )
4326	!
4327	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
4328	!-- multiplied by a flag to switch of both terms near topography.
4329	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
4330	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
4331	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
4332	!-- disabled if one of the adjacent grid points belongs to topography.
4333	!-- Moreover, in this case, the previous subgrid-scale component is also set
4334	!-- to zero.
4335
4336	a1 = fs_n * c_0 * diss_n
4337	!
4338	!-- Memory term
4339	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
4340	* fac
4341	!
4342	!-- Drift correction term
4343	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
4344	* fac
4345	!
4346	!-- Random term
4347	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
4348	!
4349	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
4350	!-- subgrid-scale velocity component is set to zero, in order to prevent a
4351	!-- velocity build-up.
4352	!-- This case, set also previous subgrid-scale component to zero.
4353	v_sgs = v_sgs * fac + term1 + term2 + term3
4354
4355	END SUBROUTINE weil_stochastic_eq
4356
4357
4358	!------------------------------------------------------------------------------!
4359	! Description:
4360	! ------------
4361	!> swap timelevel in case of particle advection interpolation 'simple-corrector'
4362	!> This routine is called at the end of one timestep, the velocities are then
4363	!> used for the next timestep
4364	!------------------------------------------------------------------------------!
4365	SUBROUTINE lpm_swap_timelevel_for_particle_advection
4366
4367	!
4368	!-- save the divergence free velocites of t+1 to use them at the end of the
4369	!-- next time step
4370	u_t = u
4371	v_t = v
4372	w_t = w
4373
4374	END SUBROUTINE lpm_swap_timelevel_for_particle_advection
4375
4376
4377	!------------------------------------------------------------------------------!
4378	! Description:
4379	! ------------
4380	!> Boundary conditions for the Lagrangian particles.
4381	!> The routine consists of two different parts. One handles the bottom (flat)
4382	!> and top boundary. In this part, also particles which exceeded their lifetime
4383	!> are deleted.
4384	!> The other part handles the reflection of particles from vertical walls.
4385	!> This part was developed by Jin Zhang during 2006-2007.
4386	!>
4387	!> To do: Code structure for finding the t_index values and for checking the
4388	!> ----- reflection conditions is basically the same for all four cases, so it
4389	!> should be possible to further simplify/shorten it.
4390	!>
4391	!> THE WALLS PART OF THIS ROUTINE HAS NOT BEEN TESTED FOR OCEAN RUNS SO FAR!!!!
4392	!> (see offset_ocean_*)
4393	!------------------------------------------------------------------------------!
4394	SUBROUTINE lpm_boundary_conds( location_bc , i, j, k )
4395
4396	CHARACTER (LEN=*), INTENT(IN) :: location_bc !< general mode: boundary conditions at bottom/top of the model domain
4397	!< or at vertical surfaces (buildings, terrain steps)
4398	INTEGER(iwp), INTENT(IN) :: i !< grid index of particle box along x
4399	INTEGER(iwp), INTENT(IN) :: j !< grid index of particle box along y
4400	INTEGER(iwp), INTENT(IN) :: k !< grid index of particle box along z
4401
4402	INTEGER(iwp) :: inc !< dummy for sorting algorithmus
4403	INTEGER(iwp) :: ir !< dummy for sorting algorithmus
4404	INTEGER(iwp) :: i1 !< grid index (x) of old particle position
4405	INTEGER(iwp) :: i2 !< grid index (x) of current particle position
4406	INTEGER(iwp) :: i3 !< grid index (x) of intermediate particle position
4407	INTEGER(iwp) :: index_reset !< index reset height
4408	INTEGER(iwp) :: jr !< dummy for sorting algorithmus
4409	INTEGER(iwp) :: j1 !< grid index (y) of old particle position
4410	INTEGER(iwp) :: j2 !< grid index (y) of current particle position
4411	INTEGER(iwp) :: j3 !< grid index (y) of intermediate particle position
4412	INTEGER(iwp) :: k1 !< grid index (z) of old particle position
4413	INTEGER(iwp) :: k2 !< grid index (z) of current particle position
4414	INTEGER(iwp) :: k3 !< grid index (z) of intermediate particle position
4415	INTEGER(iwp) :: n !< particle number
4416	INTEGER(iwp) :: particles_top !< maximum reset height
4417	INTEGER(iwp) :: t_index !< running index for intermediate particle timesteps in reflection algorithmus
4418	INTEGER(iwp) :: t_index_number !< number of intermediate particle timesteps in reflection algorithmus
4419	INTEGER(iwp) :: tmp_x !< dummy for sorting algorithm
4420	INTEGER(iwp) :: tmp_y !< dummy for sorting algorithm
4421	INTEGER(iwp) :: tmp_z !< dummy for sorting algorithm
4422
4423	INTEGER(iwp), DIMENSION(0:10) :: x_ind(0:10) = 0 !< index array (x) of intermediate particle positions
4424	INTEGER(iwp), DIMENSION(0:10) :: y_ind(0:10) = 0 !< index array (y) of intermediate particle positions
4425	INTEGER(iwp), DIMENSION(0:10) :: z_ind(0:10) = 0 !< index array (z) of intermediate particle positions
4426
4427	LOGICAL :: cross_wall_x !< flag to check if particle reflection along x is necessary
4428	LOGICAL :: cross_wall_y !< flag to check if particle reflection along y is necessary
4429	LOGICAL :: cross_wall_z !< flag to check if particle reflection along z is necessary
4430	LOGICAL :: reflect_x !< flag to check if particle is already reflected along x
4431	LOGICAL :: reflect_y !< flag to check if particle is already reflected along y
4432	LOGICAL :: reflect_z !< flag to check if particle is already reflected along z
4433	LOGICAL :: tmp_reach_x !< dummy for sorting algorithmus
4434	LOGICAL :: tmp_reach_y !< dummy for sorting algorithmus
4435	LOGICAL :: tmp_reach_z !< dummy for sorting algorithmus
4436	LOGICAL :: x_wall_reached !< flag to check if particle has already reached wall
4437	LOGICAL :: y_wall_reached !< flag to check if particle has already reached wall
4438	LOGICAL :: z_wall_reached !< flag to check if particle has already reached wall
4439
4440	LOGICAL, DIMENSION(0:10) :: reach_x !< flag to check if particle is at a yz-wall
4441	LOGICAL, DIMENSION(0:10) :: reach_y !< flag to check if particle is at a xz-wall
4442	LOGICAL, DIMENSION(0:10) :: reach_z !< flag to check if particle is at a xy-wall
4443
4444	REAL(wp) :: dt_particle !< particle timestep
4445	REAL(wp) :: eps = 1E-10_wp !< security number to check if particle has reached a wall
4446	REAL(wp) :: pos_x !< intermediate particle position (x)
4447	REAL(wp) :: pos_x_old !< particle position (x) at previous particle timestep
4448	REAL(wp) :: pos_y !< intermediate particle position (y)
4449	REAL(wp) :: pos_y_old !< particle position (y) at previous particle timestep
4450	REAL(wp) :: pos_z !< intermediate particle position (z)
4451	REAL(wp) :: pos_z_old !< particle position (z) at previous particle timestep
4452	REAL(wp) :: prt_x !< current particle position (x)
4453	REAL(wp) :: prt_y !< current particle position (y)
4454	REAL(wp) :: prt_z !< current particle position (z)
4455	REAL(wp) :: ran_val !< location of wall in z
4456	REAL(wp) :: reset_top !< location of wall in z
4457	REAL(wp) :: t_old !< previous reflection time
4458	REAL(wp) :: tmp_t !< dummy for sorting algorithmus
4459	REAL(wp) :: xwall !< location of wall in x
4460	REAL(wp) :: ywall !< location of wall in y
4461	REAL(wp) :: zwall !< location of wall in z
4462
4463	REAL(wp), DIMENSION(0:10) :: t !< reflection time
4464
4465	SELECT CASE ( location_bc )
4466
4467	CASE ( 'bottom/top' )
4468
4469	!
4470	!-- Apply boundary conditions to those particles that have crossed the top or
4471	!-- bottom boundary and delete those particles, which are older than allowed
4472	DO n = 1, number_of_particles
4473
4474	!
4475	!-- Stop if particles have moved further than the length of one
4476	!-- PE subdomain (newly released particles have age = age_m!)
4477	IF ( particles(n)%age /= particles(n)%age_m ) THEN
4478	IF ( ABS(particles(n)%speed_x) > &
4479	((nxr-nxl+2)*dx)/(particles(n)%age-particles(n)%age_m) .OR. &
4480	ABS(particles(n)%speed_y) > &
4481	((nyn-nys+2)*dy)/(particles(n)%age-particles(n)%age_m) ) THEN
4482
4483	WRITE( message_string, * ) 'particle too fast. n = ', n
4484	CALL message( 'lpm_boundary_conds', 'PA0148', 2, 2, -1, 6, 1 )
4485	ENDIF
4486	ENDIF
4487
4488	IF ( particles(n)%age > particle_maximum_age .AND. &
4489	particles(n)%particle_mask ) &
4490	THEN
4491	particles(n)%particle_mask = .FALSE.
4492	deleted_particles = deleted_particles + 1
4493	ENDIF
4494
4495	IF ( particles(n)%z >= zw(nz) .AND. particles(n)%particle_mask ) THEN
4496	IF ( ibc_par_t == 1 ) THEN
4497	!
4498	!-- Particle absorption
4499	particles(n)%particle_mask = .FALSE.
4500	deleted_particles = deleted_particles + 1
4501	ELSEIF ( ibc_par_t == 2 ) THEN
4502	!
4503	!-- Particle reflection
4504	particles(n)%z = 2.0_wp * zw(nz) - particles(n)%z
4505	particles(n)%speed_z = -particles(n)%speed_z
4506	IF ( use_sgs_for_particles .AND. &
4507	particles(n)%rvar3 > 0.0_wp ) THEN
4508	particles(n)%rvar3 = -particles(n)%rvar3
4509	ENDIF
4510	ENDIF
4511	ENDIF
4512
4513	IF ( particles(n)%z < zw(0) .AND. particles(n)%particle_mask ) THEN
4514	IF ( ibc_par_b == 1 ) THEN
4515	!
4516	!-- Particle absorption
4517	particles(n)%particle_mask = .FALSE.
4518	deleted_particles = deleted_particles + 1
4519	ELSEIF ( ibc_par_b == 2 ) THEN
4520	!
4521	!-- Particle reflection
4522	particles(n)%z = 2.0_wp * zw(0) - particles(n)%z
4523	particles(n)%speed_z = -particles(n)%speed_z
4524	IF ( use_sgs_for_particles .AND. &
4525	particles(n)%rvar3 < 0.0_wp ) THEN
4526	particles(n)%rvar3 = -particles(n)%rvar3
4527	ENDIF
4528	ELSEIF ( ibc_par_b == 3 ) THEN
4529	!
4530	!-- Find reset height. @note this works only in non-strechted cases
4531	particles_top = INT( pst(1) / dz(1) )
4532	index_reset = MINLOC( prt_count(nzb+1:particles_top,j,i), DIM = 1 )
4533	reset_top = zu(index_reset)
4534	iran_part = iran_part + myid
4535	ran_val = random_function( iran_part )
4536	particles(n)%z = reset_top * ( 1.0 + ( ran_val / 10.0_wp) )
4537	particles(n)%speed_z = 0.0_wp
4538	IF ( curvature_solution_effects ) THEN
4539	particles(n)%radius = particles(n)%aux1
4540	ELSE
4541	particles(n)%radius = 1.0E-8
4542	ENDIF
4543	ENDIF
4544	ENDIF
4545	ENDDO
4546
4547	CASE ( 'walls' )
4548
4549	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'start' )
4550
4551	DO n = 1, number_of_particles
4552	!
4553	!-- Recalculate particle timestep
4554	dt_particle = particles(n)%age - particles(n)%age_m
4555	!
4556	!-- Obtain x/y indices for current particle position
4557	i2 = particles(n)%x * ddx
4558	j2 = particles(n)%y * ddy
4559	IF ( zw(k) < particles(n)%z ) k2 = k + 1
4560	IF ( zw(k) > particles(n)%z .AND. zw(k-1) < particles(n)%z ) k2 = k
4561	IF ( zw(k-1) > particles(n)%z ) k2 = k - 1
4562	!
4563	!-- Save current particle positions
4564	prt_x = particles(n)%x
4565	prt_y = particles(n)%y
4566	prt_z = particles(n)%z
4567	!
4568	!-- Recalculate old particle positions
4569	pos_x_old = particles(n)%x - particles(n)%speed_x * dt_particle
4570	pos_y_old = particles(n)%y - particles(n)%speed_y * dt_particle
4571	pos_z_old = particles(n)%z - particles(n)%speed_z * dt_particle
4572	!
4573	!-- Obtain x/y indices for old particle positions
4574	i1 = i
4575	j1 = j
4576	k1 = k
4577	!
4578	!-- Determine horizontal as well as vertical walls at which particle can
4579	!-- be potentially reflected.
4580	!-- Start with walls aligned in yz layer.
4581	!-- Wall to the right
4582	IF ( prt_x > pos_x_old ) THEN
4583	xwall = ( i1 + 1 ) * dx
4584	!
4585	!-- Wall to the left
4586	ELSE
4587	xwall = i1 * dx
4588	ENDIF
4589	!
4590	!-- Walls aligned in xz layer
4591	!-- Wall to the north
4592	IF ( prt_y > pos_y_old ) THEN
4593	ywall = ( j1 + 1 ) * dy
4594	!-- Wall to the south
4595	ELSE
4596	ywall = j1 * dy
4597	ENDIF
4598
4599	IF ( prt_z > pos_z_old ) THEN
4600	zwall = zw(k)
4601	ELSE
4602	zwall = zw(k-1)
4603	ENDIF
4604	!
4605	!-- Initialize flags to check if particle reflection is necessary
4606	cross_wall_x = .FALSE.
4607	cross_wall_y = .FALSE.
4608	cross_wall_z = .FALSE.
4609	!
4610	!-- Initialize flags to check if a wall is reached
4611	reach_x = .FALSE.
4612	reach_y = .FALSE.
4613	reach_z = .FALSE.
4614	!
4615	!-- Initialize flags to check if a particle was already reflected
4616	reflect_x = .FALSE.
4617	reflect_y = .FALSE.
4618	reflect_z = .FALSE.
4619	!
4620	!-- Initialize flags to check if a wall is already crossed.
4621	!-- ( Required to obtain correct indices. )
4622	x_wall_reached = .FALSE.
4623	y_wall_reached = .FALSE.
4624	z_wall_reached = .FALSE.
4625	!
4626	!-- Initialize time array
4627	t = 0.0_wp
4628	!
4629	!-- Check if particle can reach any wall. This case, calculate the
4630	!-- fractional time needed to reach this wall. Store this fractional
4631	!-- timestep in array t. Moreover, store indices for these grid
4632	!-- boxes where the respective wall belongs to.
4633	!-- Start with x-direction.
4634	t_index = 1
4635	t(t_index) = ( xwall - pos_x_old ) &
4636	/ MERGE( MAX( prt_x - pos_x_old, 1E-30_wp ), &
4637	MIN( prt_x - pos_x_old, -1E-30_wp ), &
4638	prt_x > pos_x_old )
4639	x_ind(t_index) = i2
4640	y_ind(t_index) = j1
4641	z_ind(t_index) = k1
4642	reach_x(t_index) = .TRUE.
4643	reach_y(t_index) = .FALSE.
4644	reach_z(t_index) = .FALSE.
4645	!
4646	!-- Store these values only if particle really reaches any wall. t must
4647	!-- be in a interval between [0:1].
4648	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4649	t_index = t_index + 1
4650	cross_wall_x = .TRUE.
4651	ENDIF
4652	!
4653	!-- y-direction
4654	t(t_index) = ( ywall - pos_y_old ) &
4655	/ MERGE( MAX( prt_y - pos_y_old, 1E-30_wp ), &
4656	MIN( prt_y - pos_y_old, -1E-30_wp ), &
4657	prt_y > pos_y_old )
4658	x_ind(t_index) = i1
4659	y_ind(t_index) = j2
4660	z_ind(t_index) = k1
4661	reach_x(t_index) = .FALSE.
4662	reach_y(t_index) = .TRUE.
4663	reach_z(t_index) = .FALSE.
4664	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4665	t_index = t_index + 1
4666	cross_wall_y = .TRUE.
4667	ENDIF
4668	!
4669	!-- z-direction
4670	t(t_index) = (zwall - pos_z_old ) &
4671	/ MERGE( MAX( prt_z - pos_z_old, 1E-30_wp ), &
4672	MIN( prt_z - pos_z_old, -1E-30_wp ), &
4673	prt_z > pos_z_old )
4674
4675	x_ind(t_index) = i1
4676	y_ind(t_index) = j1
4677	z_ind(t_index) = k2
4678	reach_x(t_index) = .FALSE.
4679	reach_y(t_index) = .FALSE.
4680	reach_z(t_index) = .TRUE.
4681	IF( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp) THEN
4682	t_index = t_index + 1
4683	cross_wall_z = .TRUE.
4684	ENDIF
4685
4686	t_index_number = t_index - 1
4687	!
4688	!-- Carry out reflection only if particle reaches any wall
4689	IF ( cross_wall_x .OR. cross_wall_y .OR. cross_wall_z ) THEN
4690	!
4691	!-- Sort fractional timesteps in ascending order. Also sort the
4692	!-- corresponding indices and flag according to the time interval a
4693	!-- particle reaches the respective wall.
4694	inc = 1
4695	jr = 1
4696	DO WHILE ( inc <= t_index_number )
4697	inc = 3 * inc + 1
4698	ENDDO
4699
4700	DO WHILE ( inc > 1 )
4701	inc = inc / 3
4702	DO ir = inc+1, t_index_number
4703	tmp_t = t(ir)
4704	tmp_x = x_ind(ir)
4705	tmp_y = y_ind(ir)
4706	tmp_z = z_ind(ir)
4707	tmp_reach_x = reach_x(ir)
4708	tmp_reach_y = reach_y(ir)
4709	tmp_reach_z = reach_z(ir)
4710	jr = ir
4711	DO WHILE ( t(jr-inc) > tmp_t )
4712	t(jr) = t(jr-inc)
4713	x_ind(jr) = x_ind(jr-inc)
4714	y_ind(jr) = y_ind(jr-inc)
4715	z_ind(jr) = z_ind(jr-inc)
4716	reach_x(jr) = reach_x(jr-inc)
4717	reach_y(jr) = reach_y(jr-inc)
4718	reach_z(jr) = reach_z(jr-inc)
4719	jr = jr - inc
4720	IF ( jr <= inc ) EXIT
4721	ENDDO
4722	t(jr) = tmp_t
4723	x_ind(jr) = tmp_x
4724	y_ind(jr) = tmp_y
4725	z_ind(jr) = tmp_z
4726	reach_x(jr) = tmp_reach_x
4727	reach_y(jr) = tmp_reach_y
4728	reach_z(jr) = tmp_reach_z
4729	ENDDO
4730	ENDDO
4731	!
4732	!-- Initialize temporary particle positions
4733	pos_x = pos_x_old
4734	pos_y = pos_y_old
4735	pos_z = pos_z_old
4736	!
4737	!-- Loop over all times a particle possibly moves into a new grid box
4738	t_old = 0.0_wp
4739	DO t_index = 1, t_index_number
4740	!
4741	!-- Calculate intermediate particle position according to the
4742	!-- timesteps a particle reaches any wall.
4743	pos_x = pos_x + ( t(t_index) - t_old ) * dt_particle &
4744	* particles(n)%speed_x
4745	pos_y = pos_y + ( t(t_index) - t_old ) * dt_particle &
4746	* particles(n)%speed_y
4747	pos_z = pos_z + ( t(t_index) - t_old ) * dt_particle &
4748	* particles(n)%speed_z
4749	!
4750	!-- Obtain x/y grid indices for intermediate particle position from
4751	!-- sorted index array
4752	i3 = x_ind(t_index)
4753	j3 = y_ind(t_index)
4754	k3 = z_ind(t_index)
4755	!
4756	!-- Check which wall is already reached
4757	IF ( .NOT. x_wall_reached ) x_wall_reached = reach_x(t_index)
4758	IF ( .NOT. y_wall_reached ) y_wall_reached = reach_y(t_index)
4759	IF ( .NOT. z_wall_reached ) z_wall_reached = reach_z(t_index)
4760	!
4761	!-- Check if a particle needs to be reflected at any yz-wall. If
4762	!-- necessary, carry out reflection. Please note, a security
4763	!-- constant is required, as the particle position does not
4764	!-- necessarily exactly match the wall location due to rounding
4765	!-- errors.
4766	IF ( reach_x(t_index) .AND. &
4767	ABS( pos_x - xwall ) < eps .AND. &
4768	.NOT. BTEST(wall_flags_static_0(k3,j3,i3),0) .AND. &
4769	.NOT. reflect_x ) THEN
4770	!
4771	!
4772	!-- Reflection in x-direction.
4773	!-- Ensure correct reflection by MIN/MAX functions, depending on
4774	!-- direction of particle transport.
4775	!-- Due to rounding errors pos_x does not exactly match the wall
4776	!-- location, leading to erroneous reflection.
4777	pos_x = MERGE( MIN( 2.0_wp * xwall - pos_x, xwall ), &
4778	MAX( 2.0_wp * xwall - pos_x, xwall ), &
4779	particles(n)%x > xwall )
4780	!
4781	!-- Change sign of particle speed
4782	particles(n)%speed_x = - particles(n)%speed_x
4783	!
4784	!-- Also change sign of subgrid-scale particle speed
4785	particles(n)%rvar1 = - particles(n)%rvar1
4786	!
4787	!-- Set flag that reflection along x is already done
4788	reflect_x = .TRUE.
4789	!
4790	!-- As the particle does not cross any further yz-wall during
4791	!-- this timestep, set further x-indices to the current one.
4792	x_ind(t_index:t_index_number) = i1
4793	!
4794	!-- If particle already reached the wall but was not reflected,
4795	!-- set further x-indices to the new one.
4796	ELSEIF ( x_wall_reached .AND. .NOT. reflect_x ) THEN
4797	x_ind(t_index:t_index_number) = i2
4798	ENDIF !particle reflection in x direction done
4799
4800	!
4801	!-- Check if a particle needs to be reflected at any xz-wall. If
4802	!-- necessary, carry out reflection. Please note, a security
4803	!-- constant is required, as the particle position does not
4804	!-- necessarily exactly match the wall location due to rounding
4805	!-- errors.
4806	IF ( reach_y(t_index) .AND. &
4807	ABS( pos_y - ywall ) < eps .AND. &
4808	.NOT. BTEST(wall_flags_static_0(k3,j3,i3),0) .AND. &
4809	.NOT. reflect_y ) THEN
4810	!
4811	!
4812	!-- Reflection in y-direction.
4813	!-- Ensure correct reflection by MIN/MAX functions, depending on
4814	!-- direction of particle transport.
4815	!-- Due to rounding errors pos_y does not exactly match the wall
4816	!-- location, leading to erroneous reflection.
4817	pos_y = MERGE( MIN( 2.0_wp * ywall - pos_y, ywall ), &
4818	MAX( 2.0_wp * ywall - pos_y, ywall ), &
4819	particles(n)%y > ywall )
4820	!
4821	!-- Change sign of particle speed
4822	particles(n)%speed_y = - particles(n)%speed_y
4823	!
4824	!-- Also change sign of subgrid-scale particle speed
4825	particles(n)%rvar2 = - particles(n)%rvar2
4826	!
4827	!-- Set flag that reflection along y is already done
4828	reflect_y = .TRUE.
4829	!
4830	!-- As the particle does not cross any further xz-wall during
4831	!-- this timestep, set further y-indices to the current one.
4832	y_ind(t_index:t_index_number) = j1
4833	!
4834	!-- If particle already reached the wall but was not reflected,
4835	!-- set further y-indices to the new one.
4836	ELSEIF ( y_wall_reached .AND. .NOT. reflect_y ) THEN
4837	y_ind(t_index:t_index_number) = j2
4838	ENDIF !particle reflection in y direction done
4839
4840	!
4841	!-- Check if a particle needs to be reflected at any xy-wall. If
4842	!-- necessary, carry out reflection. Please note, a security
4843	!-- constant is required, as the particle position does not
4844	!-- necessarily exactly match the wall location due to rounding
4845	!-- errors.
4846	IF ( reach_z(t_index) .AND. &
4847	ABS( pos_z - zwall ) < eps .AND. &
4848	.NOT. BTEST(wall_flags_static_0(k3,j3,i3),0) .AND. &
4849	.NOT. reflect_z ) THEN
4850	!
4851	!
4852	!-- Reflection in z-direction.
4853	!-- Ensure correct reflection by MIN/MAX functions, depending on
4854	!-- direction of particle transport.
4855	!-- Due to rounding errors pos_z does not exactly match the wall
4856	!-- location, leading to erroneous reflection.
4857	pos_z = MERGE( MIN( 2.0_wp * zwall - pos_z, zwall ), &
4858	MAX( 2.0_wp * zwall - pos_z, zwall ), &
4859	particles(n)%z > zwall )
4860	!
4861	!-- Change sign of particle speed
4862	particles(n)%speed_z = - particles(n)%speed_z
4863	!
4864	!-- Also change sign of subgrid-scale particle speed
4865	particles(n)%rvar3 = - particles(n)%rvar3
4866	!
4867	!-- Set flag that reflection along z is already done
4868	reflect_z = .TRUE.
4869	!
4870	!-- As the particle does not cross any further xy-wall during
4871	!-- this timestep, set further z-indices to the current one.
4872	z_ind(t_index:t_index_number) = k1
4873	!
4874	!-- If particle already reached the wall but was not reflected,
4875	!-- set further z-indices to the new one.
4876	ELSEIF ( z_wall_reached .AND. .NOT. reflect_z ) THEN
4877	z_ind(t_index:t_index_number) = k2
4878	ENDIF !particle reflection in z direction done
4879
4880	!
4881	!-- Swap time
4882	t_old = t(t_index)
4883
4884	ENDDO
4885	!
4886	!-- If a particle was reflected, calculate final position from last
4887	!-- intermediate position.
4888	IF ( reflect_x .OR. reflect_y .OR. reflect_z ) THEN
4889
4890	particles(n)%x = pos_x + ( 1.0_wp - t_old ) * dt_particle &
4891	* particles(n)%speed_x
4892	particles(n)%y = pos_y + ( 1.0_wp - t_old ) * dt_particle &
4893	* particles(n)%speed_y
4894	particles(n)%z = pos_z + ( 1.0_wp - t_old ) * dt_particle &
4895	* particles(n)%speed_z
4896
4897	ENDIF
4898
4899	ENDIF
4900
4901	ENDDO
4902
4903	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'stop' )
4904
4905	CASE DEFAULT
4906	CONTINUE
4907
4908	END SELECT
4909
4910	END SUBROUTINE lpm_boundary_conds
4911
4912
4913	!------------------------------------------------------------------------------!
4914	! Description:
4915	! ------------
4916	!> Calculates change in droplet radius by condensation/evaporation, using
4917	!> either an analytic formula or by numerically integrating the radius growth
4918	!> equation including curvature and solution effects using Rosenbrocks method
4919	!> (see Numerical recipes in FORTRAN, 2nd edition, p. 731).
4920	!> The analytical formula and growth equation follow those given in
4921	!> Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103).
4922	!------------------------------------------------------------------------------!
4923	SUBROUTINE lpm_droplet_condensation (i,j,k)
4924
4925	INTEGER(iwp), INTENT(IN) :: i !<
4926	INTEGER(iwp), INTENT(IN) :: j !<
4927	INTEGER(iwp), INTENT(IN) :: k !<
4928	INTEGER(iwp) :: n !<
4929
4930	REAL(wp) :: afactor !< curvature effects
4931	REAL(wp) :: arg !<
4932	REAL(wp) :: bfactor !< solute effects
4933	REAL(wp) :: ddenom !<
4934	REAL(wp) :: delta_r !<
4935	REAL(wp) :: diameter !< diameter of cloud droplets
4936	REAL(wp) :: diff_coeff !< diffusivity for water vapor
4937	REAL(wp) :: drdt !<
4938	REAL(wp) :: dt_ros !<
4939	REAL(wp) :: dt_ros_sum !<
4940	REAL(wp) :: d2rdtdr !<
4941	REAL(wp) :: e_a !< current vapor pressure
4942	REAL(wp) :: e_s !< current saturation vapor pressure
4943	REAL(wp) :: error !< local truncation error in Rosenbrock
4944	REAL(wp) :: k1 !<
4945	REAL(wp) :: k2 !<
4946	REAL(wp) :: r_err !< First order estimate of Rosenbrock radius
4947	REAL(wp) :: r_ros !< Rosenbrock radius
4948	REAL(wp) :: r_ros_ini !< initial Rosenbrock radius
4949	REAL(wp) :: r0 !< gas-kinetic lengthscale
4950	REAL(wp) :: sigma !< surface tension of water
4951	REAL(wp) :: thermal_conductivity !< thermal conductivity for water
4952	REAL(wp) :: t_int !< temperature
4953	REAL(wp) :: w_s !< terminal velocity of droplets
4954	REAL(wp) :: re_p !< particle Reynolds number
4955	!
4956	!-- Parameters for Rosenbrock method (see Verwer et al., 1999)
4957	REAL(wp), PARAMETER :: prec = 1.0E-3_wp !< precision of Rosenbrock solution
4958	REAL(wp), PARAMETER :: q_increase = 1.5_wp !< increase factor in timestep
4959	REAL(wp), PARAMETER :: q_decrease = 0.9_wp !< decrease factor in timestep
4960	REAL(wp), PARAMETER :: gamma = 0.292893218814_wp !< = 1.0 - 1.0 / SQRT(2.0)
4961	!
4962	!-- Parameters for terminal velocity
4963	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
4964	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
4965	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
4966	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
4967	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
4968	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
4969
4970	REAL(wp), DIMENSION(number_of_particles) :: ventilation_effect !<
4971	REAL(wp), DIMENSION(number_of_particles) :: new_r !<
4972
4973	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' )
4974
4975	!
4976	!-- Absolute temperature
4977	t_int = pt(k,j,i) * exner(k)
4978	!
4979	!-- Saturation vapor pressure (Eq. 10 in Bolton, 1980)
4980	e_s = magnus( t_int )
4981	!
4982	!-- Current vapor pressure
4983	e_a = q(k,j,i) * hyp(k) / ( q(k,j,i) + rd_d_rv )
4984	!
4985	!-- Thermal conductivity for water (from Rogers and Yau, Table 7.1)
4986	thermal_conductivity = 7.94048E-05_wp * t_int + 0.00227011_wp
4987	!
4988	!-- Moldecular diffusivity of water vapor in air (Hall und Pruppacher, 1976)
4989	diff_coeff = 0.211E-4_wp * ( t_int / 273.15_wp )*1.94_wp &
4990	( 101325.0_wp / hyp(k) )
4991	!
4992	!-- Lengthscale for gas-kinetic effects (from Mordy, 1959, p. 23):
4993	r0 = diff_coeff / 0.036_wp * SQRT( 2.0_wp * pi / ( r_v * t_int ) )
4994	!
4995	!-- Calculate effects of heat conductivity and diffusion of water vapor on the
4996	!-- diffusional growth process (usually known as 1.0 / (F_k + F_d) )
4997	ddenom = 1.0_wp / ( rho_l * r_v * t_int / ( e_s * diff_coeff ) + &
4998	( l_v / ( r_v * t_int ) - 1.0_wp ) * rho_l * &
4999	l_v / ( thermal_conductivity * t_int ) &
5000	)
5001	new_r = 0.0_wp
5002	!
5003	!-- Determine ventilation effect on evaporation of large drops
5004	DO n = 1, number_of_particles
5005
5006	IF ( particles(n)%radius >= 4.0E-5_wp .AND. e_a / e_s < 1.0_wp ) THEN
5007	!
5008	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
5009	!-- 1993, J. Appl. Meteorol.)
5010	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
5011	IF ( diameter <= d0_rog ) THEN
5012	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
5013	ELSE
5014	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
5015	ENDIF
5016	!
5017	!-- Calculate droplet's Reynolds number
5018	re_p = 2.0_wp * particles(n)%radius * w_s / molecular_viscosity
5019	!
5020	!-- Ventilation coefficient (Rogers and Yau, 1989):
5021	IF ( re_p > 2.5_wp ) THEN
5022	ventilation_effect(n) = 0.78_wp + 0.28_wp * SQRT( re_p )
5023	ELSE
5024	ventilation_effect(n) = 1.0_wp + 0.09_wp * re_p
5025	ENDIF
5026	ELSE
5027	!
5028	!-- For small droplets or in supersaturated environments, the ventilation
5029	!-- effect does not play a role
5030	ventilation_effect(n) = 1.0_wp
5031	ENDIF
5032	ENDDO
5033
5034	IF( .NOT. curvature_solution_effects ) THEN
5035	!
5036	!-- Use analytic model for diffusional growth including gas-kinetic
5037	!-- effects (Mordy, 1959) but without the impact of aerosols.
5038	DO n = 1, number_of_particles
5039	arg = ( particles(n)%radius + r0 )*2 + 2.0_wp dt_3d * ddenom * &
5040	ventilation_effect(n) * &
5041	( e_a / e_s - 1.0_wp )
5042	arg = MAX( arg, ( 0.01E-6 + r0 )**2 )
5043	new_r(n) = SQRT( arg ) - r0
5044	ENDDO
5045
5046	ELSE
5047	!
5048	!-- Integrate the diffusional growth including gas-kinetic (Mordy, 1959),
5049	!-- as well as curvature and solute effects (e.g., KÃ¶hler, 1936).
5050	!
5051	!-- Curvature effect (afactor) with surface tension (sigma) by Straka (2009)
5052	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
5053	!
5054	!-- Solute effect (afactor)
5055	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
5056
5057	DO n = 1, number_of_particles
5058	!
5059	!-- Solute effect (bfactor)
5060	bfactor = vanthoff * rho_s * particles(n)%aux1*3 &
5061	molecular_weight_of_water / ( rho_l * molecular_weight_of_solute )
5062
5063	dt_ros = particles(n)%aux2 ! use previously stored Rosenbrock timestep
5064	dt_ros_sum = 0.0_wp
5065
5066	r_ros = particles(n)%radius ! initialize Rosenbrock particle radius
5067	r_ros_ini = r_ros
5068	!
5069	!-- Integrate growth equation using a 2nd-order Rosenbrock method
5070	!-- (see Verwer et al., 1999, Eq. (3.2)). The Rosenbrock method adjusts
5071	!-- its with internal timestep to minimize the local truncation error.
5072	DO WHILE ( dt_ros_sum < dt_3d )
5073
5074	dt_ros = MIN( dt_ros, dt_3d - dt_ros_sum )
5075
5076	DO
5077
5078	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5079	afactor / r_ros + &
5080	bfactor / r_ros**3 &
5081	) / ( r_ros + r0 )
5082
5083	d2rdtdr = -ddenom * ventilation_effect(n) * ( &
5084	(e_a / e_s - 1.0_wp ) * r_ros**4 - &
5085	afactor * r0 * r_ros**2 - &
5086	2.0_wp * afactor * r_ros**3 + &
5087	3.0_wp * bfactor * r0 + &
5088	4.0_wp * bfactor * r_ros &
5089	) &
5090	/ ( r_ros*4 ( r_ros + r0 )**2 )
5091
5092	k1 = drdt / ( 1.0_wp - gamma * dt_ros * d2rdtdr )
5093
5094	r_ros = MAX(r_ros_ini + k1 * dt_ros, particles(n)%aux1)
5095	r_err = r_ros
5096
5097	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5098	afactor / r_ros + &
5099	bfactor / r_ros**3 &
5100	) / ( r_ros + r0 )
5101
5102	k2 = ( drdt - dt_ros * 2.0 * gamma * d2rdtdr * k1 ) / &
5103	( 1.0_wp - dt_ros * gamma * d2rdtdr )
5104
5105	r_ros = MAX(r_ros_ini + dt_ros * ( 1.5_wp * k1 + 0.5_wp * k2), particles(n)%aux1)
5106	!
5107	!-- Check error of the solution, and reduce dt_ros if necessary.
5108	error = ABS(r_err - r_ros) / r_ros
5109	IF ( error > prec ) THEN
5110	dt_ros = SQRT( q_decrease * prec / error ) * dt_ros
5111	r_ros = r_ros_ini
5112	ELSE
5113	dt_ros_sum = dt_ros_sum + dt_ros
5114	dt_ros = q_increase * dt_ros
5115	r_ros_ini = r_ros
5116	EXIT
5117	ENDIF
5118
5119	END DO
5120
5121	END DO !Rosenbrock loop
5122	!
5123	!-- Store new particle radius
5124	new_r(n) = r_ros
5125	!
5126	!-- Store internal time step value for next PALM step
5127	particles(n)%aux2 = dt_ros
5128
5129	ENDDO !Particle loop
5130
5131	ENDIF
5132
5133	DO n = 1, number_of_particles
5134	!
5135	!-- Sum up the change in liquid water for the respective grid
5136	!-- box for the computation of the release/depletion of water vapor
5137	!-- and heat.
5138	ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * &
5139	rho_l * 1.33333333_wp * pi * &
5140	( new_r(n)3 - particles(n)%radius3 ) / &
5141	( rho_surface * dx * dy * dzw(k) )
5142	!
5143	!-- Check if the increase in liqid water is not too big. If this is the case,
5144	!-- the model timestep might be too long.
5145	IF ( ql_c(k,j,i) > 100.0_wp ) THEN
5146	WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, &
5147	' ql_c=',ql_c(k,j,i), '&part(',n,')%wf=', &
5148	particles(n)%weight_factor,' delta_r=',delta_r
5149	CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 )
5150	ENDIF
5151	!
5152	!-- Check if the change in the droplet radius is not too big. If this is the
5153	!-- case, the model timestep might be too long.
5154	delta_r = new_r(n) - particles(n)%radius
5155	IF ( delta_r < 0.0_wp .AND. new_r(n) < 0.0_wp ) THEN
5156	WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, &
5157	' e_s=',e_s, ' e_a=',e_a,' t_int=',t_int, &
5158	'&delta_r=',delta_r, &
5159	' particle_radius=',particles(n)%radius
5160	CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 )
5161	ENDIF
5162	!
5163	!-- Sum up the total volume of liquid water (needed below for
5164	!-- re-calculating the weighting factors)
5165	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r(n)**3
5166	!
5167	!-- Determine radius class of the particle needed for collision
5168	IF ( use_kernel_tables ) THEN
5169	particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / &
5170	( rclass_ubound - rclass_lbound ) * &
5171	radius_classes
5172	particles(n)%class = MIN( particles(n)%class, radius_classes )
5173	particles(n)%class = MAX( particles(n)%class, 1 )
5174	ENDIF
5175	!
5176	!-- Store new radius to particle features
5177	particles(n)%radius = new_r(n)
5178
5179	ENDDO
5180
5181	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' )
5182
5183
5184	END SUBROUTINE lpm_droplet_condensation
5185
5186
5187	!------------------------------------------------------------------------------!
5188	! Description:
5189	! ------------
5190	!> Release of latent heat and change of mixing ratio due to condensation /
5191	!> evaporation of droplets.
5192	!------------------------------------------------------------------------------!
5193	SUBROUTINE lpm_interaction_droplets_ptq
5194
5195	INTEGER(iwp) :: i !< running index x direction
5196	INTEGER(iwp) :: j !< running index y direction
5197	INTEGER(iwp) :: k !< running index z direction
5198
5199	REAL(wp) :: flag !< flag to mask topography grid points
5200
5201	DO i = nxl, nxr
5202	DO j = nys, nyn
5203	DO k = nzb+1, nzt
5204	!
5205	!-- Predetermine flag to mask topography
5206	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 0 ) )
5207
5208	q(k,j,i) = q_p(k,j,i) - ql_c(k,j,i) * flag
5209	pt(k,j,i) = pt(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) &
5210	* flag
5211	ENDDO
5212	ENDDO
5213	ENDDO
5214
5215	END SUBROUTINE lpm_interaction_droplets_ptq
5216
5217
5218	!------------------------------------------------------------------------------!
5219	! Description:
5220	! ------------
5221	!> Release of latent heat and change of mixing ratio due to condensation /
5222	!> evaporation of droplets. Call for grid point i,j
5223	!------------------------------------------------------------------------------!
5224	SUBROUTINE lpm_interaction_droplets_ptq_ij( i, j )
5225
5226	INTEGER(iwp) :: i !< running index x direction
5227	INTEGER(iwp) :: j !< running index y direction
5228	INTEGER(iwp) :: k !< running index z direction
5229
5230	REAL(wp) :: flag !< flag to mask topography grid points
5231
5232
5233	DO k = nzb+1, nzt
5234	!
5235	!-- Predetermine flag to mask topography
5236	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_static_0(k,j,i), 0 ) )
5237
5238	q(k,j,i) = q(k,j,i) - ql_c(k,j,i) * flag
5239	pt(k,j,i) = pt(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) * flag
5240	ENDDO
5241
5242	END SUBROUTINE lpm_interaction_droplets_ptq_ij
5243
5244
5245	!------------------------------------------------------------------------------!
5246	! Description:
5247	! ------------
5248	!> Calculate the liquid water content for each grid box.
5249	!------------------------------------------------------------------------------!
5250	SUBROUTINE lpm_calc_liquid_water_content
5251
5252
5253	INTEGER(iwp) :: i !<
5254	INTEGER(iwp) :: j !<
5255	INTEGER(iwp) :: k !<
5256	INTEGER(iwp) :: n !<
5257
5258	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'start' )
5259
5260	!
5261	!-- Set water content initially to zero
5262	ql = 0.0_wp; ql_v = 0.0_wp; ql_vp = 0.0_wp
5263
5264	!
5265	!-- Calculate for each grid box
5266	DO i = nxl, nxr
5267	DO j = nys, nyn
5268	DO k = nzb+1, nzt
5269	number_of_particles = prt_count(k,j,i)
5270	IF ( number_of_particles <= 0 ) CYCLE
5271	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
5272	!
5273	!-- Calculate the total volume in the boxes (ql_v, weighting factor
5274	!-- has to beincluded)
5275	DO n = 1, prt_count(k,j,i)
5276	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * &
5277	particles(n)%radius**3
5278	ENDDO
5279	!
5280	!-- Calculate the liquid water content
5281	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5282	ql(k,j,i) = ql(k,j,i) + rho_l * 1.33333333_wp * pi * &
5283	ql_v(k,j,i) / &
5284	( rho_surface * dx * dy * dzw(k) )
5285	IF ( ql(k,j,i) < 0.0_wp ) THEN
5286	WRITE( message_string, * ) 'LWC out of range: ' , &
5287	ql(k,j,i),i,j,k
5288	CALL message( 'lpm_calc_liquid_water_content', '', 2, 2, &
5289	-1, 6, 1 )
5290	ENDIF
5291	ELSE
5292	ql(k,j,i) = 0.0_wp
5293	ENDIF
5294	ENDDO
5295	ENDDO
5296	ENDDO
5297
5298	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'stop' )
5299
5300	END SUBROUTINE lpm_calc_liquid_water_content
5301
5302
5303	!------------------------------------------------------------------------------!
5304	! Description:
5305	! ------------
5306	!> Calculates change in droplet radius by collision. Droplet collision is
5307	!> calculated for each grid box seperately. Collision is parameterized by
5308	!> using collision kernels. Two different kernels are available:
5309	!> Hall kernel: Kernel from Hall (1980, J. Atmos. Sci., 2486-2507), which
5310	!> considers collision due to pure gravitational effects.
5311	!> Wang kernel: Beside gravitational effects (treated with the Hall-kernel) also
5312	!> the effects of turbulence on the collision are considered using
5313	!> parameterizations of Ayala et al. (2008, New J. Phys., 10,
5314	!> 075015) and Wang and Grabowski (2009, Atmos. Sci. Lett., 10,
5315	!> 1-8). This kernel includes three possible effects of turbulence:
5316	!> the modification of the relative velocity between the droplets,
5317	!> the effect of preferential concentration, and the enhancement of
5318	!> collision efficiencies.
5319	!------------------------------------------------------------------------------!
5320	SUBROUTINE lpm_droplet_collision (i,j,k)
5321
5322	INTEGER(iwp), INTENT(IN) :: i !<
5323	INTEGER(iwp), INTENT(IN) :: j !<
5324	INTEGER(iwp), INTENT(IN) :: k !<
5325
5326	INTEGER(iwp) :: eclass !<
5327	INTEGER(iwp) :: n !<
5328	INTEGER(iwp) :: m !<
5329	INTEGER(iwp) :: rclass_l !<
5330	INTEGER(iwp) :: rclass_s !<
5331
5332	REAL(wp) :: collection_probability !< probability for collection
5333	REAL(wp) :: ddV !< inverse grid box volume
5334	REAL(wp) :: epsilon_collision !< dissipation rate
5335	REAL(wp) :: factor_volume_to_mass !< 4.0 / 3.0 * pi * rho_l
5336	REAL(wp) :: xm !< droplet mass of super-droplet m
5337	REAL(wp) :: xn !< droplet mass of super-droplet n
5338	REAL(wp) :: xsm !< aerosol mass of super-droplet m
5339	REAL(wp) :: xsn !< aerosol mass of super-droplet n
5340
5341	REAL(wp), DIMENSION(:), ALLOCATABLE :: weight !< weighting factor
5342	REAL(wp), DIMENSION(:), ALLOCATABLE :: mass !< total mass of super droplet
5343	REAL(wp), DIMENSION(:), ALLOCATABLE :: aero_mass !< total aerosol mass of super droplet
5344
5345	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'start' )
5346
5347	number_of_particles = prt_count(k,j,i)
5348	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
5349	ddV = 1.0_wp / ( dx * dy * dzw(k) )
5350	!
5351	!-- Collision requires at least one super droplet inside the box
5352	IF ( number_of_particles > 0 ) THEN
5353
5354	IF ( use_kernel_tables ) THEN
5355	!
5356	!-- Fast method with pre-calculated collection kernels for
5357	!-- discrete radius- and dissipation-classes.
5358	IF ( wang_kernel ) THEN
5359	eclass = INT( diss(k,j,i) * 1.0E4_wp / 600.0_wp * &
5360	dissipation_classes ) + 1
5361	epsilon_collision = diss(k,j,i)
5362	ELSE
5363	epsilon_collision = 0.0_wp
5364	ENDIF
5365
5366	IF ( hall_kernel .OR. epsilon_collision * 1.0E4_wp < 0.001_wp ) THEN
5367	eclass = 0 ! Hall kernel is used
5368	ELSE
5369	eclass = MIN( dissipation_classes, eclass )
5370	ENDIF
5371
5372	ELSE
5373	!
5374	!-- Collection kernels are re-calculated for every new
5375	!-- grid box. First, allocate memory for kernel table.
5376	!-- Third dimension is 1, because table is re-calculated for
5377	!-- every new dissipation value.
5378	ALLOCATE( ckernel(1:number_of_particles,1:number_of_particles,1:1) )
5379	!
5380	!-- Now calculate collection kernel for this box. Note that
5381	!-- the kernel is based on the previous time step
5382	CALL recalculate_kernel( i, j, k )
5383
5384	ENDIF
5385	!
5386	!-- Temporary fields for total mass of super-droplet, aerosol mass, and
5387	!-- weighting factor are allocated.
5388	ALLOCATE(mass(1:number_of_particles), weight(1:number_of_particles))
5389	IF ( curvature_solution_effects ) ALLOCATE(aero_mass(1:number_of_particles))
5390
5391	mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5392	particles(1:number_of_particles)%radius*3 &
5393	factor_volume_to_mass
5394
5395	weight(1:number_of_particles) = particles(1:number_of_particles)%weight_factor
5396
5397	IF ( curvature_solution_effects ) THEN
5398	aero_mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5399	particles(1:number_of_particles)%aux1*3 &
5400	4.0_wp / 3.0_wp * pi * rho_s
5401	ENDIF
5402	!
5403	!-- Calculate collision/coalescence
5404	DO n = 1, number_of_particles
5405
5406	DO m = n, number_of_particles
5407	!
5408	!-- For collisions, the weighting factor of at least one super-droplet
5409	!-- needs to be larger or equal to one.
5410	IF ( MIN( weight(n), weight(m) ) < 1.0_wp ) CYCLE
5411	!
5412	!-- Get mass of individual droplets (aerosols)
5413	xn = mass(n) / weight(n)
5414	xm = mass(m) / weight(m)
5415	IF ( curvature_solution_effects ) THEN
5416	xsn = aero_mass(n) / weight(n)
5417	xsm = aero_mass(m) / weight(m)
5418	ENDIF
5419	!
5420	!-- Probability that the necessary collisions take place
5421	IF ( use_kernel_tables ) THEN
5422	rclass_l = particles(n)%class
5423	rclass_s = particles(m)%class
5424
5425	collection_probability = MAX( weight(n), weight(m) ) * &
5426	ckernel(rclass_l,rclass_s,eclass) * ddV * dt_3d
5427	ELSE
5428	collection_probability = MAX( weight(n), weight(m) ) * &
5429	ckernel(n,m,1) * ddV * dt_3d
5430	ENDIF
5431	!
5432	!-- Calculate the number of collections and consider multiple collections.
5433	!-- (Accordingly, p_crit will be 0.0, 1.0, 2.0, ...)
5434	IF ( collection_probability - FLOOR(collection_probability) &
5435	> random_function( iran_part ) ) THEN
5436	collection_probability = FLOOR(collection_probability) + 1.0_wp
5437	ELSE
5438	collection_probability = FLOOR(collection_probability)
5439	ENDIF
5440
5441	IF ( collection_probability > 0.0_wp ) THEN
5442	!
5443	!-- Super-droplet n collects droplets of super-droplet m
5444	IF ( weight(n) < weight(m) ) THEN
5445
5446	mass(n) = mass(n) + weight(n) * xm * collection_probability
5447	weight(m) = weight(m) - weight(n) * collection_probability
5448	mass(m) = mass(m) - weight(n) * xm * collection_probability
5449	IF ( curvature_solution_effects ) THEN
5450	aero_mass(n) = aero_mass(n) + weight(n) * xsm * collection_probability
5451	aero_mass(m) = aero_mass(m) - weight(n) * xsm * collection_probability
5452	ENDIF
5453
5454	ELSEIF ( weight(m) < weight(n) ) THEN
5455
5456	mass(m) = mass(m) + weight(m) * xn * collection_probability
5457	weight(n) = weight(n) - weight(m) * collection_probability
5458	mass(n) = mass(n) - weight(m) * xn * collection_probability
5459	IF ( curvature_solution_effects ) THEN
5460	aero_mass(m) = aero_mass(m) + weight(m) * xsn * collection_probability
5461	aero_mass(n) = aero_mass(n) - weight(m) * xsn * collection_probability
5462	ENDIF
5463
5464	ELSE
5465	!
5466	!-- Collisions of particles of the same weighting factor.
5467	!-- Particle n collects 1/2 weight(n) droplets of particle m,
5468	!-- particle m collects 1/2 weight(m) droplets of particle n.
5469	!-- The total mass mass changes accordingly.
5470	!-- If n = m, the first half of the droplets coalesces with the
5471	!-- second half of the droplets; mass is unchanged because
5472	!-- xm = xn for n = m.
5473	!--
5474	!-- Note: For m = n this equation is an approximation only
5475	!-- valid for weight >> 1 (which is usually the case). The
5476	!-- approximation is weight(n)-1 = weight(n).
5477	mass(n) = mass(n) + 0.5_wp * weight(n) * ( xm - xn )
5478	mass(m) = mass(m) + 0.5_wp * weight(m) * ( xn - xm )
5479	IF ( curvature_solution_effects ) THEN
5480	aero_mass(n) = aero_mass(n) + 0.5_wp * weight(n) * ( xsm - xsn )
5481	aero_mass(m) = aero_mass(m) + 0.5_wp * weight(m) * ( xsn - xsm )
5482	ENDIF
5483	weight(n) = weight(n) - 0.5_wp * weight(m)
5484	weight(m) = weight(n)
5485
5486	ENDIF
5487
5488	ENDIF
5489
5490	ENDDO
5491
5492	ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
5493
5494	ENDDO
5495
5496	IF ( ANY(weight < 0.0_wp) ) THEN
5497	WRITE( message_string, * ) 'negative weighting factor'
5498	CALL message( 'lpm_droplet_collision', 'PA0028', &
5499	2, 2, -1, 6, 1 )
5500	ENDIF
5501
5502	particles(1:number_of_particles)%radius = ( mass(1:number_of_particles) / &
5503	( weight(1:number_of_particles) &
5504	* factor_volume_to_mass &
5505	) &
5506	)**0.33333333333333_wp
5507
5508	IF ( curvature_solution_effects ) THEN
5509	particles(1:number_of_particles)%aux1 = ( aero_mass(1:number_of_particles) / &
5510	( weight(1:number_of_particles) &
5511	* 4.0_wp / 3.0_wp * pi * rho_s &
5512	) &
5513	)**0.33333333333333_wp
5514	ENDIF
5515
5516	particles(1:number_of_particles)%weight_factor = weight(1:number_of_particles)
5517
5518	DEALLOCATE( weight, mass )
5519	IF ( curvature_solution_effects ) DEALLOCATE( aero_mass )
5520	IF ( .NOT. use_kernel_tables ) DEALLOCATE( ckernel )
5521
5522	!
5523	!-- Check if LWC is conserved during collision process
5524	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5525	IF ( ql_vp(k,j,i) / ql_v(k,j,i) >= 1.0001_wp .OR. &
5526	ql_vp(k,j,i) / ql_v(k,j,i) <= 0.9999_wp ) THEN
5527	WRITE( message_string, * ) ' LWC is not conserved during', &
5528	' collision! ', &
5529	' LWC after condensation: ', ql_v(k,j,i), &
5530	' LWC after collision: ', ql_vp(k,j,i)
5531	CALL message( 'lpm_droplet_collision', 'PA0040', 2, 2, -1, 6, 1 )
5532	ENDIF
5533	ENDIF
5534
5535	ENDIF
5536
5537	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'stop' )
5538
5539	END SUBROUTINE lpm_droplet_collision
5540
5541	!------------------------------------------------------------------------------!
5542	! Description:
5543	! ------------
5544	!> Initialization of the collision efficiency matrix with fixed radius and
5545	!> dissipation classes, calculated at simulation start only.
5546	!------------------------------------------------------------------------------!
5547	SUBROUTINE lpm_init_kernels
5548
5549	INTEGER(iwp) :: i !<
5550	INTEGER(iwp) :: j !<
5551	INTEGER(iwp) :: k !<
5552
5553	!
5554	!-- Calculate collision efficiencies for fixed radius- and dissipation
5555	!-- classes
5556	IF ( collision_kernel(6:9) == 'fast' ) THEN
5557
5558	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
5559	0:dissipation_classes), epsclass(1:dissipation_classes), &
5560	radclass(1:radius_classes) )
5561
5562	!
5563	!-- Calculate the radius class bounds with logarithmic distances
5564	!-- in the interval [1.0E-6, 1000.0E-6] m
5565	rclass_lbound = LOG( 1.0E-6_wp )
5566	rclass_ubound = LOG( 1000.0E-6_wp )
5567	radclass(1) = EXP( rclass_lbound )
5568	DO i = 2, radius_classes
5569	radclass(i) = EXP( rclass_lbound + &
5570	( rclass_ubound - rclass_lbound ) * &
5571	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
5572	ENDDO
5573
5574	!
5575	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
5576	DO i = 1, dissipation_classes
5577	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
5578	ENDDO
5579	!
5580	!-- Calculate collision efficiencies of the Wang/ayala kernel
5581	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
5582	ecf(1:radius_classes,1:radius_classes), &
5583	gck(1:radius_classes,1:radius_classes), &
5584	winf(1:radius_classes) )
5585
5586	DO k = 1, dissipation_classes
5587
5588	epsilon_collision = epsclass(k)
5589	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 1.0_wp / 3.0_wp )
5590
5591	CALL turbsd
5592	CALL turb_enhance_eff
5593	CALL effic
5594
5595	DO j = 1, radius_classes
5596	DO i = 1, radius_classes
5597	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
5598	ENDDO
5599	ENDDO
5600
5601	ENDDO
5602
5603	!
5604	!-- Calculate collision efficiencies of the Hall kernel
5605	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
5606	hwratio(1:radius_classes,1:radius_classes) )
5607
5608	CALL fallg
5609	CALL effic
5610
5611	DO j = 1, radius_classes
5612	DO i = 1, radius_classes
5613	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
5614	* ec(i,j) * ABS( winf(j) - winf(i) )
5615	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
5616	ENDDO
5617	ENDDO
5618
5619	!
5620	!-- Test output of efficiencies
5621	IF ( j == -1 ) THEN
5622	PRINT, '** Hall kernel'
5623	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
5624	i = 1,radius_classes )
5625	DO j = 1, radius_classes
5626	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
5627	( hkernel(i,j), i = 1,radius_classes )
5628	ENDDO
5629
5630	DO k = 1, dissipation_classes
5631	DO i = 1, radius_classes
5632	DO j = 1, radius_classes
5633	IF ( hkernel(i,j) == 0.0_wp ) THEN
5634	hwratio(i,j) = 9999999.9_wp
5635	ELSE
5636	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
5637	ENDIF
5638	ENDDO
5639	ENDDO
5640
5641	PRINT, '** epsilon = ', epsclass(k)
5642	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
5643	i = 1,radius_classes )
5644	DO j = 1, radius_classes
5645	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
5646	( hwratio(i,j), i = 1,radius_classes )
5647	ENDDO
5648	ENDDO
5649	ENDIF
5650
5651	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
5652
5653	ENDIF
5654
5655	END SUBROUTINE lpm_init_kernels
5656
5657	!------------------------------------------------------------------------------!
5658	! Description:
5659	! ------------
5660	!> Calculation of collision kernels during each timestep and for each grid box
5661	!------------------------------------------------------------------------------!
5662	SUBROUTINE recalculate_kernel( i1, j1, k1 )
5663
5664
5665	INTEGER(iwp) :: i !<
5666	INTEGER(iwp) :: i1 !<
5667	INTEGER(iwp) :: j !<
5668	INTEGER(iwp) :: j1 !<
5669	INTEGER(iwp) :: k1 !<
5670
5671
5672	number_of_particles = prt_count(k1,j1,i1)
5673	radius_classes = number_of_particles ! necessary to use the same
5674	! subroutines as for
5675	! precalculated kernels
5676
5677	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
5678	radclass(1:number_of_particles), winf(1:number_of_particles) )
5679
5680	!
5681	!-- Store particle radii on the radclass array
5682	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
5683
5684	IF ( wang_kernel ) THEN
5685	epsilon_collision = diss(k1,j1,i1) ! dissipation rate in m2/s3
5686	ELSE
5687	epsilon_collision = 0.0_wp
5688	ENDIF
5689	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 0.33333333333_wp )
5690
5691	IF ( wang_kernel .AND. epsilon_collision > 1.0E-7_wp ) THEN
5692	!
5693	!-- Call routines to calculate efficiencies for the Wang kernel
5694	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
5695	ecf(1:number_of_particles,1:number_of_particles) )
5696
5697	CALL turbsd
5698	CALL turb_enhance_eff
5699	CALL effic
5700
5701	DO j = 1, number_of_particles
5702	DO i = 1, number_of_particles
5703	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
5704	ENDDO
5705	ENDDO
5706
5707	DEALLOCATE( gck, ecf )
5708	ELSE
5709	!
5710	!-- Call routines to calculate efficiencies for the Hall kernel
5711	CALL fallg
5712	CALL effic
5713
5714	DO j = 1, number_of_particles
5715	DO i = 1, number_of_particles
5716	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
5717	* ec(i,j) * ABS( winf(j) - winf(i) )
5718	ENDDO
5719	ENDDO
5720	ENDIF
5721
5722	DEALLOCATE( ec, radclass, winf )
5723
5724	END SUBROUTINE recalculate_kernel
5725
5726	!------------------------------------------------------------------------------!
5727	! Description:
5728	! ------------
5729	!> Calculation of effects of turbulence on the geometric collision kernel
5730	!> (by including the droplets' average radial relative velocities and their
5731	!> radial distribution function) following the analytic model by Aayala et al.
5732	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
5733	!> page 37ff.
5734	!>
5735	!> Input parameters, which need to be replaced by PALM parameters:
5736	!> water density, air density
5737	!------------------------------------------------------------------------------!
5738	SUBROUTINE turbsd
5739
5740	INTEGER(iwp) :: i !<
5741	INTEGER(iwp) :: j !<
5742
5743	REAL(wp) :: ao !<
5744	REAL(wp) :: ao_gr !<
5745	REAL(wp) :: bbb !<
5746	REAL(wp) :: be !<
5747	REAL(wp) :: b1 !<
5748	REAL(wp) :: b2 !<
5749	REAL(wp) :: ccc !<
5750	REAL(wp) :: c1 !<
5751	REAL(wp) :: c1_gr !<
5752	REAL(wp) :: c2 !<
5753	REAL(wp) :: d1 !<
5754	REAL(wp) :: d2 !<
5755	REAL(wp) :: eta !<
5756	REAL(wp) :: e1 !<
5757	REAL(wp) :: e2 !<
5758	REAL(wp) :: fao_gr !<
5759	REAL(wp) :: fr !<
5760	REAL(wp) :: grfin !<
5761	REAL(wp) :: lambda !<
5762	REAL(wp) :: lambda_re !<
5763	REAL(wp) :: lf !<
5764	REAL(wp) :: rc !<
5765	REAL(wp) :: rrp !<
5766	REAL(wp) :: sst !<
5767	REAL(wp) :: tauk !<
5768	REAL(wp) :: tl !<
5769	REAL(wp) :: t2 !<
5770	REAL(wp) :: tt !<
5771	REAL(wp) :: t1 !<
5772	REAL(wp) :: vk !<
5773	REAL(wp) :: vrms1xy !<
5774	REAL(wp) :: vrms2xy !<
5775	REAL(wp) :: v1 !<
5776	REAL(wp) :: v1v2xy !<
5777	REAL(wp) :: v1xysq !<
5778	REAL(wp) :: v2 !<
5779	REAL(wp) :: v2xysq !<
5780	REAL(wp) :: wrfin !<
5781	REAL(wp) :: wrgrav2 !<
5782	REAL(wp) :: wrtur2xy !<
5783	REAL(wp) :: xx !<
5784	REAL(wp) :: yy !<
5785	REAL(wp) :: z !<
5786
5787	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
5788	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
5789
5790	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon_collision )
5791	lambda_re = urms*2 SQRT( 15.0_wp / epsilon_collision / molecular_viscosity )
5792	tl = urms**2 / epsilon_collision
5793	lf = 0.5_wp * urms**3 / epsilon_collision
5794	tauk = SQRT( molecular_viscosity / epsilon_collision )
5795	eta = ( molecular_viscosity3 / epsilon_collision )0.25_wp
5796	vk = eta / tauk
5797
5798	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
5799	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
5800
5801	!
5802	!-- Get terminal velocity of droplets
5803	CALL fallg
5804
5805	DO i = 1, radius_classes
5806	tau(i) = winf(i) / g ! inertial time scale
5807	st(i) = tau(i) / tauk ! Stokes number
5808	ENDDO
5809
5810	!
5811	!-- Calculate average radial relative velocity at contact (wrfin)
5812	z = tt / tl
5813	be = SQRT( 2.0_wp ) * lambda / lf
5814	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
5815	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
5816	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
5817	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
5818	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
5819	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
5820	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
5821	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
5822	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
5823	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
5824
5825	DO i = 1, radius_classes
5826
5827	v1 = winf(i)
5828	t1 = tau(i)
5829
5830	DO j = 1, i
5831	rrp = radclass(i) + radclass(j)
5832	v2 = winf(j)
5833	t2 = tau(j)
5834
5835	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
5836	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
5837	v1xysq = v1xysq * urms**2 / t1
5838	vrms1xy = SQRT( v1xysq )
5839
5840	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
5841	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
5842	v2xysq = v2xysq * urms**2 / t2
5843	vrms2xy = SQRT( v2xysq )
5844
5845	IF ( winf(i) >= winf(j) ) THEN
5846	v1 = winf(i)
5847	t1 = tau(i)
5848	v2 = winf(j)
5849	t2 = tau(j)
5850	ELSE
5851	v1 = winf(j)
5852	t1 = tau(j)
5853	v2 = winf(i)
5854	t2 = tau(i)
5855	ENDIF
5856
5857	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
5858	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
5859	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
5860	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
5861	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
5862	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
5863	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
5864	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
5865	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
5866	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
5867
5868	!
5869	!-- Calculate radial distribution function (grfin)
5870	IF ( st(j) > st(i) ) THEN
5871	sst = st(j)
5872	ELSE
5873	sst = st(i)
5874	ENDIF
5875
5876	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
5877	sst*2 + 5.3406_wp sst
5878	IF ( xx < 0.0_wp ) xx = 0.0_wp
5879	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
5880
5881	c1_gr = xx / ( g / vk * tauk )**yy
5882
5883	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
5884	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
5885	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
5886
5887	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
5888	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
5889
5890	!
5891	!-- Calculate general collection kernel (without the consideration of
5892	!-- collection efficiencies)
5893	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
5894	gck(j,i) = gck(i,j)
5895
5896	ENDDO
5897	ENDDO
5898
5899	END SUBROUTINE turbsd
5900
5901	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
5902	!
5903	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5904	!-- effects on the collision kernel
5905
5906
5907	REAL(wp) :: a !<
5908	REAL(wp) :: aa1 !<
5909	REAL(wp) :: b !<
5910	REAL(wp) :: tau0 !<
5911	REAL(wp) :: vsett !<
5912
5913	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
5914	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
5915
5916	END FUNCTION phi_w
5917
5918	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
5919	!
5920	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5921	!-- effects on the collision kernel
5922
5923	REAL(wp) :: a !<
5924	REAL(wp) :: aa1 !<
5925	REAL(wp) :: aa2 !<
5926	REAL(wp) :: aa3 !<
5927	REAL(wp) :: aa4 !<
5928	REAL(wp) :: aa5 !<
5929	REAL(wp) :: aa6 !<
5930	REAL(wp) :: b !<
5931	REAL(wp) :: tau1 !<
5932	REAL(wp) :: tau2 !<
5933	REAL(wp) :: vsett1 !<
5934	REAL(wp) :: vsett2 !<
5935
5936	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
5937	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
5938	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
5939	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
5940	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
5941	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
5942	vsett1 / vsett2
5943	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
5944	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
5945	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
5946	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
5947
5948	END FUNCTION zhi
5949
5950
5951	!------------------------------------------------------------------------------!
5952	! Description:
5953	! ------------
5954	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
5955	!> Meteorol.)
5956	!------------------------------------------------------------------------------!
5957	SUBROUTINE fallg
5958
5959	INTEGER(iwp) :: j !<
5960
5961	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
5962	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
5963	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
5964	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
5965	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
5966	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
5967
5968	REAL(wp) :: diameter !< droplet diameter in mm
5969
5970
5971	DO j = 1, radius_classes
5972
5973	diameter = radclass(j) * 2000.0_wp
5974
5975	IF ( diameter <= d0_rog ) THEN
5976	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
5977	EXP( -k_low_rog * diameter ) )
5978	ELSE
5979	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
5980	ENDIF
5981
5982	ENDDO
5983
5984	END SUBROUTINE fallg
5985
5986
5987	!------------------------------------------------------------------------------!
5988	! Description:
5989	! ------------
5990	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
5991	!------------------------------------------------------------------------------!
5992	SUBROUTINE effic
5993
5994	INTEGER(iwp) :: i !<
5995	INTEGER(iwp) :: iq !<
5996	INTEGER(iwp) :: ir !<
5997	INTEGER(iwp) :: j !<
5998	INTEGER(iwp) :: k !<
5999
6000	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
6001
6002	LOGICAL, SAVE :: first = .TRUE. !<
6003
6004	REAL(wp) :: ek !<
6005	REAL(wp) :: particle_radius !<
6006	REAL(wp) :: pp !<
6007	REAL(wp) :: qq !<
6008	REAL(wp) :: rq !<
6009
6010	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
6011
6012	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
6013
6014	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
6015
6016	!
6017	!-- Initial assignment of constants
6018	IF ( first ) THEN
6019
6020	first = .FALSE.
6021	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
6022	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
6023	150.0_wp, 200.0_wp, 300.0_wp /)
6024
6025	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
6026	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
6027	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
6028	0.90_wp, 0.95_wp, 1.00_wp /)
6029
6030	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
6031	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
6032	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
6033	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
6034	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
6035	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
6036	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
6037	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
6038	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
6039	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
6040	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
6041	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
6042	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
6043	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
6044	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
6045	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
6046	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
6047	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6048	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
6049	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
6050	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6051	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
6052	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
6053	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6054	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
6055	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
6056	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6057	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
6058	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6059	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6060	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
6061	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6062	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6063	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
6064	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6065	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6066	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
6067	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
6068	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6069	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
6070	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
6071	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6072	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
6073	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
6074	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6075	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
6076	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
6077	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6078	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
6079	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
6080	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6081	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
6082	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
6083	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
6084	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
6085	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
6086	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
6087	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
6088	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
6089	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
6090	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
6091	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
6092	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
6093	ENDIF
6094
6095	!
6096	!-- Calculate the radius class index of particles with respect to array r
6097	!-- Radius has to be in microns
6098	ALLOCATE( ira(1:radius_classes) )
6099	DO j = 1, radius_classes
6100	particle_radius = radclass(j) * 1.0E6_wp
6101	DO k = 1, 15
6102	IF ( particle_radius < r0(k) ) THEN
6103	ira(j) = k
6104	EXIT
6105	ENDIF
6106	ENDDO
6107	IF ( particle_radius >= r0(15) ) ira(j) = 16
6108	ENDDO
6109
6110	!
6111	!-- Two-dimensional linear interpolation of the collision efficiency.
6112	!-- Radius has to be in microns
6113	DO j = 1, radius_classes
6114	DO i = 1, j
6115
6116	ir = MAX( ira(i), ira(j) )
6117	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6118	iq = INT( rq * 20 ) + 1
6119	iq = MAX( iq , 2)
6120
6121	IF ( ir < 16 ) THEN
6122	IF ( ir >= 2 ) THEN
6123	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
6124	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6125	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6126	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
6127	* ecoll(ir-1,iq-1) &
6128	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
6129	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
6130	+ pp * qq * ecoll(ir,iq)
6131	ELSE
6132	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6133	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
6134	ENDIF
6135	ELSE
6136	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6137	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
6138	ec(j,i) = MIN( ek, 1.0_wp )
6139	ENDIF
6140
6141	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
6142
6143	ec(i,j) = ec(j,i)
6144
6145	ENDDO
6146	ENDDO
6147
6148	DEALLOCATE( ira )
6149
6150	END SUBROUTINE effic
6151
6152
6153	!------------------------------------------------------------------------------!
6154	! Description:
6155	! ------------
6156	!> Interpolation of turbulent enhancement factor for collision efficencies
6157	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
6158	!------------------------------------------------------------------------------!
6159	SUBROUTINE turb_enhance_eff
6160
6161	INTEGER(iwp) :: i !<
6162	INTEGER(iwp) :: iq !<
6163	INTEGER(iwp) :: ir !<
6164	INTEGER(iwp) :: j !<
6165	INTEGER(iwp) :: k !<
6166	INTEGER(iwp) :: kk !<
6167
6168	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
6169
6170	LOGICAL, SAVE :: first = .TRUE. !<
6171
6172	REAL(wp) :: particle_radius !<
6173	REAL(wp) :: pp !<
6174	REAL(wp) :: qq !<
6175	REAL(wp) :: rq !<
6176	REAL(wp) :: y1 !<
6177	REAL(wp) :: y2 !<
6178	REAL(wp) :: y3 !<
6179
6180	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
6181	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
6182
6183	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
6184	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
6185
6186	!
6187	!-- Initial assignment of constants
6188	IF ( first ) THEN
6189
6190	first = .FALSE.
6191
6192	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
6193	100.0_wp /)
6194
6195	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
6196	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
6197	!
6198	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
6199	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
6200	1.207_wp, 1.207_wp, 1.0_wp /)
6201	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
6202	1.069_wp, 1.069_wp, 1.0_wp /)
6203	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
6204	1.000_wp, 1.000_wp, 1.0_wp /)
6205	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
6206	1.025_wp, 1.025_wp, 1.0_wp /)
6207	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
6208	1.056_wp, 1.056_wp, 1.0_wp /)
6209	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
6210	1.028_wp, 1.028_wp, 1.0_wp /)
6211	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
6212	1.046_wp, 1.046_wp, 1.0_wp /)
6213	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
6214	1.029_wp, 1.029_wp, 1.0_wp /)
6215	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
6216	1.021_wp, 1.021_wp, 1.0_wp /)
6217	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
6218	1.088_wp, 1.088_wp, 1.0_wp /)
6219	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
6220	2.60_wp, 2.60_wp, 1.0_wp /)
6221	!
6222	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
6223	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
6224	1.445_wp, 1.445_wp, 1.0_wp /)
6225	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
6226	1.201_wp, 1.201_wp, 1.0_wp /)
6227	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
6228	1.150_wp, 1.150_wp, 1.0_wp /)
6229	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
6230	1.126_wp, 1.126_wp, 1.0_wp /)
6231	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
6232	1.092_wp, 1.092_wp, 1.0_wp /)
6233	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
6234	1.051_wp, 1.051_wp, 1.0_wp /)
6235	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
6236	1.086_wp, 1.086_wp, 1.0_wp /)
6237	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
6238	1.063_wp, 1.063_wp, 1.0_wp /)
6239	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
6240	1.100_wp, 1.100_wp, 1.0_wp /)
6241	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
6242	1.120_wp, 1.120_wp, 1.0_wp /)
6243	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
6244	26.0_wp, 26.0_wp, 1.0_wp /)
6245
6246	ENDIF
6247
6248	!
6249	!-- Calculate the radius class index of particles with respect to array r0
6250	!-- The droplet radius has to be given in microns.
6251	ALLOCATE( ira(1:radius_classes) )
6252
6253	DO j = 1, radius_classes
6254	particle_radius = radclass(j) * 1.0E6_wp
6255	DO k = 1, 7
6256	IF ( particle_radius < r0(k) ) THEN
6257	ira(j) = k
6258	EXIT
6259	ENDIF
6260	ENDDO
6261	IF ( particle_radius >= r0(7) ) ira(j) = 8
6262	ENDDO
6263
6264	!
6265	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
6266	!-- The droplet radius has to be given in microns.
6267	DO j = 1, radius_classes
6268	DO i = 1, j
6269
6270	ir = MAX( ira(i), ira(j) )
6271	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6272
6273	DO kk = 2, 11
6274	IF ( rq <= rat(kk) ) THEN
6275	iq = kk
6276	EXIT
6277	ENDIF
6278	ENDDO
6279
6280	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
6281
6282	IF ( ir < 8 ) THEN
6283	IF ( ir >= 2 ) THEN
6284	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
6285	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6286	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6287	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
6288	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
6289	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
6290	pp * qq * ecoll_100(ir,iq)
6291	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
6292	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
6293	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
6294	pp * qq * ecoll_400(ir,iq)
6295	ELSE
6296	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6297	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
6298	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
6299	ENDIF
6300	ELSE
6301	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6302	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
6303	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
6304	ENDIF
6305	!
6306	!-- Linear interpolation of turbulent enhancement factor
6307	IF ( epsilon_collision <= 0.01_wp ) THEN
6308	ecf(j,i) = ( epsilon_collision - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
6309	+ ( epsilon_collision - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
6310	ELSEIF ( epsilon_collision <= 0.06_wp ) THEN
6311	ecf(j,i) = ( epsilon_collision - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6312	+ ( epsilon_collision - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6313	ELSE
6314	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6315	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6316	ENDIF
6317
6318	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
6319
6320	ecf(i,j) = ecf(j,i)
6321
6322	ENDDO
6323	ENDDO
6324
6325	END SUBROUTINE turb_enhance_eff
6326
6327
6328	!------------------------------------------------------------------------------!
6329	! Description:
6330	! ------------
6331	! This routine is a part of the Lagrangian particle model. Super droplets which
6332	! fulfill certain criterion's (e.g. a big weighting factor and a large radius)
6333	! can be split into several super droplets with a reduced number of
6334	! represented particles of every super droplet. This mechanism ensures an
6335	! improved representation of the right tail of the drop size distribution with
6336	! a feasible amount of computational costs. The limits of particle creation
6337	! should be chosen carefully! The idea of this algorithm is based on
6338	! Unterstrasser and Soelch, 2014.
6339	!------------------------------------------------------------------------------!
6340	SUBROUTINE lpm_splitting
6341
6342	INTEGER(iwp) :: i !<
6343	INTEGER(iwp) :: j !<
6344	INTEGER(iwp) :: jpp !<
6345	INTEGER(iwp) :: k !<
6346	INTEGER(iwp) :: n !<
6347	INTEGER(iwp) :: new_particles_gb !< counter of created particles within one grid box
6348	INTEGER(iwp) :: new_size !< new particle array size
6349	INTEGER(iwp) :: np !<
6350	INTEGER(iwp) :: old_size !< old particle array size
6351
6352	INTEGER(iwp), PARAMETER :: n_max = 100 !< number of radii bin for splitting functions
6353
6354	LOGICAL :: first_loop_stride_sp = .TRUE. !< flag to calculate constants only once
6355
6356	REAL(wp) :: diameter !< diameter of droplet
6357	REAL(wp) :: dlog !< factor for DSD calculation
6358	REAL(wp) :: factor_volume_to_mass !< pre calculate factor volume to mass
6359	REAL(wp) :: lambda !< slope parameter of gamma-distribution
6360	REAL(wp) :: lwc !< liquid water content of grid box
6361	REAL(wp) :: lwc_total !< average liquid water content of cloud
6362	REAL(wp) :: m1 !< first moment of DSD
6363	REAL(wp) :: m1_total !< average over all PEs of first moment of DSD
6364	REAL(wp) :: m2 !< second moment of DSD
6365	REAL(wp) :: m2_total !< average average over all PEs second moment of DSD
6366	REAL(wp) :: m3 !< third moment of DSD
6367	REAL(wp) :: m3_total !< average average over all PEs third moment of DSD
6368	REAL(wp) :: mu !< spectral shape parameter of gamma distribution
6369	REAL(wp) :: nrclgb !< number of cloudy grid boxes (ql >= 1.0E-5 kg/kg)
6370	REAL(wp) :: nrclgb_total !< average over all PEs of number of cloudy grid boxes
6371	REAL(wp) :: nr !< number concentration of cloud droplets
6372	REAL(wp) :: nr_total !< average over all PEs of number of cloudy grid boxes
6373	REAL(wp) :: nr0 !< intercept parameter of gamma distribution
6374	REAL(wp) :: pirho_l !< pi * rho_l / 6.0
6375	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6376	!< (Siebesma et al 2003, JAS, 60)
6377	REAL(wp) :: rm !< volume averaged mean radius
6378	REAL(wp) :: rm_total !< average over all PEs of volume averaged mean radius
6379	REAL(wp) :: r_min = 1.0E-6_wp !< minimum radius of approximated spectra
6380	REAL(wp) :: r_max = 1.0E-3_wp !< maximum radius of approximated spectra
6381	REAL(wp) :: sigma_log = 1.5_wp !< standard deviation of the LOG-distribution
6382	REAL(wp) :: zeta !< Parameter for DSD calculation of Seifert
6383
6384	REAL(wp), DIMENSION(0:n_max-1) :: an_spl !< size dependent critical weight factor
6385	REAL(wp), DIMENSION(0:n_max-1) :: r_bin_mid !< mass weighted mean radius of a bin
6386	REAL(wp), DIMENSION(0:n_max) :: r_bin !< boundaries of a radius bin
6387
6388	TYPE(particle_type) :: tmp_particle !< temporary particle TYPE
6389
6390	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'start' )
6391
6392	IF ( first_loop_stride_sp ) THEN
6393	IF ( i_splitting_mode == 2 .OR. i_splitting_mode == 3 ) THEN
6394	dlog = ( LOG10(r_max) - LOG10(r_min) ) / ( n_max - 1 )
6395	DO i = 0, n_max-1
6396	r_bin(i) = 10.0_wp*( LOG10(r_min) + i dlog - 0.5_wp * dlog )
6397	r_bin_mid(i) = 10.0_wp*( LOG10(r_min) + i dlog )
6398	ENDDO
6399	r_bin(n_max) = 10.0_wp*( LOG10(r_min) + n_max dlog - 0.5_wp * dlog )
6400	ENDIF
6401	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
6402	pirho_l = pi * rho_l / 6.0_wp
6403	IF ( weight_factor_split == -1.0_wp ) THEN
6404	weight_factor_split = 0.1_wp * initial_weighting_factor
6405	ENDIF
6406	ENDIF
6407
6408
6409	IF ( i_splitting_mode == 1 ) THEN
6410
6411	DO i = nxl, nxr
6412	DO j = nys, nyn
6413	DO k = nzb+1, nzt
6414
6415	new_particles_gb = 0
6416	number_of_particles = prt_count(k,j,i)
6417	IF ( number_of_particles <= 0 .OR. &
6418	ql(k,j,i) < ql_crit ) CYCLE
6419	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6420	!
6421	!-- Start splitting operations. Each particle is checked if it
6422	!-- fulfilled the splitting criterion's. In splitting mode 'const'
6423	!-- a critical radius (radius_split) a critical weighting factor
6424	!-- (weight_factor_split) and a splitting factor (splitting_factor)
6425	!-- must be prescribed (see particle_parameters). Super droplets
6426	!-- which have a larger radius and larger weighting factor are split
6427	!-- into 'splitting_factor' super droplets. Therefore, the weighting
6428	!-- factor of the super droplet and all created clones is reduced
6429	!-- by the factor of 'splitting_factor'.
6430	DO n = 1, number_of_particles
6431	IF ( particles(n)%particle_mask .AND. &
6432	particles(n)%radius >= radius_split .AND. &
6433	particles(n)%weight_factor >= weight_factor_split ) &
6434	THEN
6435	!
6436	!-- Calculate the new number of particles.
6437	new_size = prt_count(k,j,i) + splitting_factor - 1
6438	!
6439	!-- Cycle if maximum number of particles per grid box
6440	!-- is greater than the allowed maximum number.
6441	IF ( new_size >= max_number_particles_per_gridbox ) CYCLE
6442	!
6443	!-- Reallocate particle array if necessary.
6444	IF ( new_size > SIZE(particles) ) THEN
6445	CALL realloc_particles_array( i, j, k, new_size )
6446	ENDIF
6447	old_size = prt_count(k,j,i)
6448	!
6449	!-- Calculate new weighting factor.
6450	particles(n)%weight_factor = &
6451	particles(n)%weight_factor / splitting_factor
6452	tmp_particle = particles(n)
6453	!
6454	!-- Create splitting_factor-1 new particles.
6455	DO jpp = 1, splitting_factor-1
6456	grid_particles(k,j,i)%particles(jpp+old_size) = &
6457	tmp_particle
6458	ENDDO
6459	new_particles_gb = new_particles_gb + splitting_factor - 1
6460	!
6461	!-- Save the new number of super droplets for every grid box.
6462	prt_count(k,j,i) = prt_count(k,j,i) + &
6463	splitting_factor - 1
6464	ENDIF
6465	ENDDO
6466
6467	ENDDO
6468	ENDDO
6469	ENDDO
6470
6471	ELSEIF ( i_splitting_mode == 2 ) THEN
6472	!
6473	!-- Initialize summing variables.
6474	lwc = 0.0_wp
6475	lwc_total = 0.0_wp
6476	m1 = 0.0_wp
6477	m1_total = 0.0_wp
6478	m2 = 0.0_wp
6479	m2_total = 0.0_wp
6480	m3 = 0.0_wp
6481	m3_total = 0.0_wp
6482	nr = 0.0_wp
6483	nrclgb = 0.0_wp
6484	nrclgb_total = 0.0_wp
6485	nr_total = 0.0_wp
6486	rm = 0.0_wp
6487	rm_total = 0.0_wp
6488
6489	DO i = nxl, nxr
6490	DO j = nys, nyn
6491	DO k = nzb+1, nzt
6492	number_of_particles = prt_count(k,j,i)
6493	IF ( number_of_particles <= 0 .OR. &
6494	ql(k,j,i) < ql_crit ) CYCLE
6495	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6496	nrclgb = nrclgb + 1.0_wp
6497	!
6498	!-- Calculate moments of DSD.
6499	DO n = 1, number_of_particles
6500	IF ( particles(n)%particle_mask .AND. &
6501	particles(n)%radius >= r_min ) &
6502	THEN
6503	nr = nr + particles(n)%weight_factor
6504	rm = rm + factor_volume_to_mass * &
6505	particles(n)%radius*3 &
6506	particles(n)%weight_factor
6507	IF ( isf == 1 ) THEN
6508	diameter = particles(n)%radius * 2.0_wp
6509	lwc = lwc + factor_volume_to_mass * &
6510	particles(n)%radius*3 &
6511	particles(n)%weight_factor
6512	m1 = m1 + particles(n)%weight_factor * diameter
6513	m2 = m2 + particles(n)%weight_factor * diameter**2
6514	m3 = m3 + particles(n)%weight_factor * diameter**3
6515	ENDIF
6516	ENDIF
6517	ENDDO
6518	ENDDO
6519	ENDDO
6520	ENDDO
6521
6522	#if defined( __parallel )
6523	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6524	CALL MPI_ALLREDUCE( nr, nr_total, 1 , &
6525	MPI_REAL, MPI_SUM, comm2d, ierr )
6526	CALL MPI_ALLREDUCE( rm, rm_total, 1 , &
6527	MPI_REAL, MPI_SUM, comm2d, ierr )
6528	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6529	CALL MPI_ALLREDUCE( nrclgb, nrclgb_total, 1 , &
6530	MPI_REAL, MPI_SUM, comm2d, ierr )
6531	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6532	CALL MPI_ALLREDUCE( lwc, lwc_total, 1 , &
6533	MPI_REAL, MPI_SUM, comm2d, ierr )
6534	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6535	CALL MPI_ALLREDUCE( m1, m1_total, 1 , &
6536	MPI_REAL, MPI_SUM, comm2d, ierr )
6537	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6538	CALL MPI_ALLREDUCE( m2, m2_total, 1 , &
6539	MPI_REAL, MPI_SUM, comm2d, ierr )
6540	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6541	CALL MPI_ALLREDUCE( m3, m3_total, 1 , &
6542	MPI_REAL, MPI_SUM, comm2d, ierr )
6543	#endif
6544
6545	!
6546	!-- Calculate number concentration and mean volume averaged radius.
6547	nr_total = MERGE( nr_total / nrclgb_total, &
6548	0.0_wp, nrclgb_total > 0.0_wp &
6549	)
6550	rm_total = MERGE( ( rm_total / &
6551	( nr_total * factor_volume_to_mass ) &
6552	)**0.3333333_wp, 0.0_wp, nrclgb_total > 0.0_wp &
6553	)
6554	!
6555	!-- Check which function should be used to approximate the DSD.
6556	IF ( isf == 1 ) THEN
6557	lwc_total = MERGE( lwc_total / nrclgb_total, &
6558	0.0_wp, nrclgb_total > 0.0_wp &
6559	)
6560	m1_total = MERGE( m1_total / nrclgb_total, &
6561	0.0_wp, nrclgb_total > 0.0_wp &
6562	)
6563	m2_total = MERGE( m2_total / nrclgb_total, &
6564	0.0_wp, nrclgb_total > 0.0_wp &
6565	)
6566	m3_total = MERGE( m3_total / nrclgb_total, &
6567	0.0_wp, nrclgb_total > 0.0_wp &
6568	)
6569	zeta = m1_total * m3_total / m2_total**2
6570	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6571	( zeta - 1.0_wp ), 0.0_wp &
6572	)
6573
6574	lambda = ( pirho_l * nr_total / lwc_total * &
6575	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * ( mu + 1.0_wp ) &
6576	)**0.3333333_wp
6577	nr0 = nr_total / gamma( mu + 1.0_wp ) * lambda**( mu + 1.0_wp )
6578
6579	DO n = 0, n_max-1
6580	diameter = r_bin_mid(n) * 2.0_wp
6581	an_spl(n) = nr0 * diameter*mu EXP( -lambda * diameter ) * &
6582	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6583	ENDDO
6584	ELSEIF ( isf == 2 ) THEN
6585	DO n = 0, n_max-1
6586	an_spl(n) = nr_total / ( SQRT( 2.0_wp * pi ) * &
6587	LOG(sigma_log) * r_bin_mid(n) &
6588	) * &
6589	EXP( -( LOG( r_bin_mid(n) / rm_total )**2 ) / &
6590	( 2.0_wp * LOG(sigma_log)**2 ) &
6591	) * &
6592	( r_bin(n+1) - r_bin(n) )
6593	ENDDO
6594	ELSEIF( isf == 3 ) THEN
6595	DO n = 0, n_max-1
6596	an_spl(n) = 3.0_wp * nr_total * r_bin_mid(n)2 / rm_total3 * &
6597	EXP( - ( r_bin_mid(n)3 / rm_total3 ) ) * &
6598	( r_bin(n+1) - r_bin(n) )
6599	ENDDO
6600	ENDIF
6601	!
6602	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6603	an_spl = MAX(an_spl, 1.0_wp)
6604
6605	DO i = nxl, nxr
6606	DO j = nys, nyn
6607	DO k = nzb+1, nzt
6608	number_of_particles = prt_count(k,j,i)
6609	IF ( number_of_particles <= 0 .OR. &
6610	ql(k,j,i) < ql_crit ) CYCLE
6611	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6612	new_particles_gb = 0
6613	!
6614	!-- Start splitting operations. Each particle is checked if it
6615	!-- fulfilled the splitting criterion's. In splitting mode 'cl_av'
6616	!-- a critical radius (radius_split) and a splitting function must
6617	!-- be prescribed (see particles_par). The critical weighting factor
6618	!-- is calculated while approximating a 'gamma', 'log' or 'exp'-
6619	!-- drop size distribution. In this mode the DSD is calculated as
6620	!-- an average over all cloudy grid boxes. Super droplets which
6621	!-- have a larger radius and larger weighting factor are split into
6622	!-- 'splitting_factor' super droplets. In this case the splitting
6623	!-- factor is calculated of weighting factor of the super droplet
6624	!-- and the approximated number concentration for droplet of such
6625	!-- a size. Due to the splitting, the weighting factor of the
6626	!-- super droplet and all created clones is reduced by the factor
6627	!-- of 'splitting_facor'.
6628	DO n = 1, number_of_particles
6629	DO np = 0, n_max-1
6630	IF ( r_bin(np) >= radius_split .AND. &
6631	particles(n)%particle_mask .AND. &
6632	particles(n)%radius >= r_bin(np) .AND. &
6633	particles(n)%radius < r_bin(np+1) .AND. &
6634	particles(n)%weight_factor >= an_spl(np) ) &
6635	THEN
6636	!
6637	!-- Calculate splitting factor
6638	splitting_factor = &
6639	MIN( INT( particles(n)%weight_factor / &
6640	an_spl(np) &
6641	), splitting_factor_max &
6642	)
6643	IF ( splitting_factor < 2 ) CYCLE
6644	!
6645	!-- Calculate the new number of particles.
6646	new_size = prt_count(k,j,i) + splitting_factor - 1
6647	!
6648	!-- Cycle if maximum number of particles per grid box
6649	!-- is greater than the allowed maximum number.
6650	IF ( new_size >= max_number_particles_per_gridbox ) &
6651	CYCLE
6652	!
6653	!-- Reallocate particle array if necessary.
6654	IF ( new_size > SIZE(particles) ) THEN
6655	CALL realloc_particles_array( i, j, k, new_size )
6656	ENDIF
6657	old_size = prt_count(k,j,i)
6658	new_particles_gb = new_particles_gb + &
6659	splitting_factor - 1
6660	!
6661	!-- Calculate new weighting factor.
6662	particles(n)%weight_factor = &
6663	particles(n)%weight_factor / splitting_factor
6664	tmp_particle = particles(n)
6665	!
6666	!-- Create splitting_factor-1 new particles.
6667	DO jpp = 1, splitting_factor-1
6668	grid_particles(k,j,i)%particles(jpp+old_size) = &
6669	tmp_particle
6670	ENDDO
6671	!
6672	!-- Save the new number of super droplets.
6673	prt_count(k,j,i) = prt_count(k,j,i) + &
6674	splitting_factor - 1
6675	ENDIF
6676	ENDDO
6677	ENDDO
6678
6679	ENDDO
6680	ENDDO
6681	ENDDO
6682
6683	ELSEIF ( i_splitting_mode == 3 ) THEN
6684
6685	DO i = nxl, nxr
6686	DO j = nys, nyn
6687	DO k = nzb+1, nzt
6688
6689	!
6690	!-- Initialize summing variables.
6691	lwc = 0.0_wp
6692	m1 = 0.0_wp
6693	m2 = 0.0_wp
6694	m3 = 0.0_wp
6695	nr = 0.0_wp
6696	rm = 0.0_wp
6697
6698	new_particles_gb = 0
6699	number_of_particles = prt_count(k,j,i)
6700	IF ( number_of_particles <= 0 .OR. &
6701	ql(k,j,i) < ql_crit ) CYCLE
6702	particles => grid_particles(k,j,i)%particles
6703	!
6704	!-- Calculate moments of DSD.
6705	DO n = 1, number_of_particles
6706	IF ( particles(n)%particle_mask .AND. &
6707	particles(n)%radius >= r_min ) &
6708	THEN
6709	nr = nr + particles(n)%weight_factor
6710	rm = rm + factor_volume_to_mass * &
6711	particles(n)%radius*3 &
6712	particles(n)%weight_factor
6713	IF ( isf == 1 ) THEN
6714	diameter = particles(n)%radius * 2.0_wp
6715	lwc = lwc + factor_volume_to_mass * &
6716	particles(n)%radius*3 &
6717	particles(n)%weight_factor
6718	m1 = m1 + particles(n)%weight_factor * diameter
6719	m2 = m2 + particles(n)%weight_factor * diameter**2
6720	m3 = m3 + particles(n)%weight_factor * diameter**3
6721	ENDIF
6722	ENDIF
6723	ENDDO
6724
6725	IF ( nr <= 0.0_wp .OR. rm <= 0.0_wp ) CYCLE
6726	!
6727	!-- Calculate mean volume averaged radius.
6728	rm = ( rm / ( nr * factor_volume_to_mass ) )**0.3333333_wp
6729	!
6730	!-- Check which function should be used to approximate the DSD.
6731	IF ( isf == 1 ) THEN
6732	!
6733	!-- Gamma size distribution to calculate
6734	!-- critical weight_factor (e.g. Marshall + Palmer, 1948).
6735	zeta = m1 * m3 / m2**2
6736	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6737	( zeta - 1.0_wp ), 0.0_wp &
6738	)
6739	lambda = ( pirho_l * nr / lwc * &
6740	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * &
6741	( mu + 1.0_wp ) &
6742	)**0.3333333_wp
6743	nr0 = ( nr / (gamma( mu + 1.0_wp ) ) ) * &
6744	lambda**( mu + 1.0_wp )
6745
6746	DO n = 0, n_max-1
6747	diameter = r_bin_mid(n) * 2.0_wp
6748	an_spl(n) = nr0 * diameter*mu &
6749	EXP( -lambda * diameter ) * &
6750	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6751	ENDDO
6752	ELSEIF ( isf == 2 ) THEN
6753	!
6754	!-- Lognormal size distribution to calculate critical
6755	!-- weight_factor (e.g. Levin, 1971, Bradley + Stow, 1974).
6756	DO n = 0, n_max-1
6757	an_spl(n) = nr / ( SQRT( 2.0_wp * pi ) * &
6758	LOG(sigma_log) * r_bin_mid(n) &
6759	) * &
6760	EXP( -( LOG( r_bin_mid(n) / rm )**2 ) / &
6761	( 2.0_wp * LOG(sigma_log)**2 ) &
6762	) * &
6763	( r_bin(n+1) - r_bin(n) )
6764	ENDDO
6765	ELSEIF ( isf == 3 ) THEN
6766	!
6767	!-- Exponential size distribution to calculate critical
6768	!-- weight_factor (e.g. Berry + Reinhardt, 1974).
6769	DO n = 0, n_max-1
6770	an_spl(n) = 3.0_wp * nr * r_bin_mid(n)2 / rm3 * &
6771	EXP( - ( r_bin_mid(n)3 / rm3 ) ) * &
6772	( r_bin(n+1) - r_bin(n) )
6773	ENDDO
6774	ENDIF
6775
6776	!
6777	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6778	an_spl = MAX(an_spl, 1.0_wp)
6779	!
6780	!-- Start splitting operations. Each particle is checked if it
6781	!-- fulfilled the splitting criterion's. In splitting mode 'gb_av'
6782	!-- a critical radius (radius_split) and a splitting function must
6783	!-- be prescribed (see particles_par). The critical weighting factor
6784	!-- is calculated while appoximating a 'gamma', 'log' or 'exp'-
6785	!-- drop size distribution. In this mode a DSD is calculated for
6786	!-- every cloudy grid box. Super droplets which have a larger
6787	!-- radius and larger weighting factor are split into
6788	!-- 'splitting_factor' super droplets. In this case the splitting
6789	!-- factor is calculated of weighting factor of the super droplet
6790	!-- and theapproximated number concentration for droplet of such
6791	!-- a size. Due to the splitting, the weighting factor of the
6792	!-- super droplet and all created clones is reduced by the factor
6793	!-- of 'splitting_facor'.
6794	DO n = 1, number_of_particles
6795	DO np = 0, n_max-1
6796	IF ( r_bin(np) >= radius_split .AND. &
6797	particles(n)%particle_mask .AND. &
6798	particles(n)%radius >= r_bin(np) .AND. &
6799	particles(n)%radius < r_bin(np+1) .AND. &
6800	particles(n)%weight_factor >= an_spl(np) ) &
6801	THEN
6802	!
6803	!-- Calculate splitting factor.
6804	splitting_factor = &
6805	MIN( INT( particles(n)%weight_factor / &
6806	an_spl(np) &
6807	), splitting_factor_max &
6808	)
6809	IF ( splitting_factor < 2 ) CYCLE
6810
6811	!
6812	!-- Calculate the new number of particles.
6813	new_size = prt_count(k,j,i) + splitting_factor - 1
6814	!
6815	!-- Cycle if maximum number of particles per grid box
6816	!-- is greater than the allowed maximum number.
6817	IF ( new_size >= max_number_particles_per_gridbox ) &
6818	CYCLE
6819	!
6820	!-- Reallocate particle array if necessary.
6821	IF ( new_size > SIZE(particles) ) THEN
6822	CALL realloc_particles_array( i, j, k, new_size )
6823	ENDIF
6824	!
6825	!-- Calculate new weighting factor.
6826	particles(n)%weight_factor = &
6827	particles(n)%weight_factor / splitting_factor
6828	tmp_particle = particles(n)
6829	old_size = prt_count(k,j,i)
6830	!
6831	!-- Create splitting_factor-1 new particles.
6832	DO jpp = 1, splitting_factor-1
6833	grid_particles(k,j,i)%particles( jpp + old_size ) = &
6834	tmp_particle
6835	ENDDO
6836	!
6837	!-- Save the new number of droplets for every grid box.
6838	prt_count(k,j,i) = prt_count(k,j,i) + &
6839	splitting_factor - 1
6840	new_particles_gb = new_particles_gb + &
6841	splitting_factor - 1
6842	ENDIF
6843	ENDDO
6844	ENDDO
6845	ENDDO
6846	ENDDO
6847	ENDDO
6848	ENDIF
6849
6850	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'stop' )
6851
6852	END SUBROUTINE lpm_splitting
6853
6854
6855	!------------------------------------------------------------------------------!
6856	! Description:
6857	! ------------
6858	! This routine is a part of the Lagrangian particle model. Two Super droplets
6859	! which fulfill certain criterion's (e.g. a big weighting factor and a small
6860	! radius) can be merged into one super droplet with a increased number of
6861	! represented particles of the super droplet. This mechanism ensures an
6862	! improved a feasible amount of computational costs. The limits of particle
6863	! creation should be chosen carefully! The idea of this algorithm is based on
6864	! Unterstrasser and Soelch, 2014.
6865	!------------------------------------------------------------------------------!
6866	SUBROUTINE lpm_merging
6867
6868	INTEGER(iwp) :: i !<
6869	INTEGER(iwp) :: j !<
6870	INTEGER(iwp) :: k !<
6871	INTEGER(iwp) :: n !<
6872	INTEGER(iwp) :: merge_drp = 0 !< number of merged droplets
6873
6874
6875	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6876	!< (e.g. Siebesma et al 2003, JAS, 60)
6877
6878	CALL cpu_log( log_point_s(81), 'lpm_merging', 'start' )
6879
6880	merge_drp = 0
6881
6882	IF ( weight_factor_merge == -1.0_wp ) THEN
6883	weight_factor_merge = 0.5_wp * initial_weighting_factor
6884	ENDIF
6885
6886	DO i = nxl, nxr
6887	DO j = nys, nyn
6888	DO k = nzb+1, nzt
6889
6890	number_of_particles = prt_count(k,j,i)
6891	IF ( number_of_particles <= 0 .OR. &
6892	ql(k,j,i) >= ql_crit ) CYCLE
6893	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6894	!
6895	!-- Start merging operations: This routine delete super droplets with
6896	!-- a small radius (radius <= radius_merge) and a low weighting
6897	!-- factor (weight_factor <= weight_factor_merge). The number of
6898	!-- represented particles will be added to the next particle of the
6899	!-- particle array. Tests showed that this simplified method can be
6900	!-- used because it will only take place outside of cloudy grid
6901	!-- boxes where ql <= 1.0E-5 kg/kg. Therefore, especially former cloned
6902	!-- and subsequent evaporated super droplets will be merged.
6903	DO n = 1, number_of_particles-1
6904	IF ( particles(n)%particle_mask .AND. &
6905	particles(n+1)%particle_mask .AND. &
6906	particles(n)%radius <= radius_merge .AND. &
6907	particles(n)%weight_factor <= weight_factor_merge ) &
6908	THEN
6909	particles(n+1)%weight_factor = &
6910	particles(n+1)%weight_factor + &
6911	( particles(n)%radius**3 / &
6912	particles(n+1)%radius*3 &
6913	particles(n)%weight_factor &
6914	)
6915	particles(n)%particle_mask = .FALSE.
6916	deleted_particles = deleted_particles + 1
6917	merge_drp = merge_drp + 1
6918
6919	ENDIF
6920	ENDDO
6921	ENDDO
6922	ENDDO
6923	ENDDO
6924
6925
6926	CALL cpu_log( log_point_s(81), 'lpm_merging', 'stop' )
6927
6928	END SUBROUTINE lpm_merging
6929
6930
6931
6932
6933	!------------------------------------------------------------------------------!
6934	! Description:
6935	! ------------
6936	!> Exchange between subdomains.
6937	!> As soon as one particle has moved beyond the boundary of the domain, it
6938	!> is included in the relevant transfer arrays and marked for subsequent
6939	!> deletion on this PE.
6940	!> First sweep for crossings in x direction. Find out first the number of
6941	!> particles to be transferred and allocate temporary arrays needed to store
6942	!> them.
6943	!> For a one-dimensional decomposition along y, no transfer is necessary,
6944	!> because the particle remains on the PE, but the particle coordinate has to
6945	!> be adjusted.
6946	!------------------------------------------------------------------------------!
6947	SUBROUTINE lpm_exchange_horiz
6948
6949	INTEGER(iwp) :: i !< grid index (x) of particle positition
6950	INTEGER(iwp) :: ip !< index variable along x
6951	INTEGER(iwp) :: j !< grid index (y) of particle positition
6952	INTEGER(iwp) :: jp !< index variable along y
6953	INTEGER(iwp) :: kp !< index variable along z
6954	INTEGER(iwp) :: n !< particle index variable
6955	INTEGER(iwp) :: par_size !< Particle size in bytes
6956	INTEGER(iwp) :: trlp_count !< number of particles send to left PE
6957	INTEGER(iwp) :: trlp_count_recv !< number of particles receive from right PE
6958	INTEGER(iwp) :: trnp_count !< number of particles send to north PE
6959	INTEGER(iwp) :: trnp_count_recv !< number of particles receive from south PE
6960	INTEGER(iwp) :: trrp_count !< number of particles send to right PE
6961	INTEGER(iwp) :: trrp_count_recv !< number of particles receive from left PE
6962	INTEGER(iwp) :: trsp_count !< number of particles send to south PE
6963	INTEGER(iwp) :: trsp_count_recv !< number of particles receive from north PE
6964
6965	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvlp !< particles received from right PE
6966	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvnp !< particles received from south PE
6967	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvrp !< particles received from left PE
6968	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvsp !< particles received from north PE
6969	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trlp !< particles send to left PE
6970	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trnp !< particles send to north PE
6971	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trrp !< particles send to right PE
6972	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trsp !< particles send to south PE
6973
6974	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'start' )
6975
6976	#if defined( __parallel )
6977
6978	!
6979	!-- Exchange between subdomains.
6980	!-- As soon as one particle has moved beyond the boundary of the domain, it
6981	!-- is included in the relevant transfer arrays and marked for subsequent
6982	!-- deletion on this PE.
6983	!-- First sweep for crossings in x direction. Find out first the number of
6984	!-- particles to be transferred and allocate temporary arrays needed to store
6985	!-- them.
6986	!-- For a one-dimensional decomposition along y, no transfer is necessary,
6987	!-- because the particle remains on the PE, but the particle coordinate has to
6988	!-- be adjusted.
6989	trlp_count = 0
6990	trrp_count = 0
6991
6992	trlp_count_recv = 0
6993	trrp_count_recv = 0
6994
6995	IF ( pdims(1) /= 1 ) THEN
6996	!
6997	!-- First calculate the storage necessary for sending and receiving the data.
6998	!-- Compute only first (nxl) and last (nxr) loop iterration.
6999	DO ip = nxl, nxr, nxr - nxl
7000	DO jp = nys, nyn
7001	DO kp = nzb+1, nzt
7002
7003	number_of_particles = prt_count(kp,jp,ip)
7004	IF ( number_of_particles <= 0 ) CYCLE
7005	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7006	DO n = 1, number_of_particles
7007	IF ( particles(n)%particle_mask ) THEN
7008	i = particles(n)%x * ddx
7009	!
7010	!-- Above calculation does not work for indices less than zero
7011	IF ( particles(n)%x < 0.0_wp) i = -1
7012
7013	IF ( i < nxl ) THEN
7014	trlp_count = trlp_count + 1
7015	ELSEIF ( i > nxr ) THEN
7016	trrp_count = trrp_count + 1
7017	ENDIF
7018	ENDIF
7019	ENDDO
7020
7021	ENDDO
7022	ENDDO
7023	ENDDO
7024
7025	IF ( trlp_count == 0 ) trlp_count = 1
7026	IF ( trrp_count == 0 ) trrp_count = 1
7027
7028	ALLOCATE( trlp(trlp_count), trrp(trrp_count) )
7029
7030	trlp = zero_particle
7031	trrp = zero_particle
7032
7033	trlp_count = 0
7034	trrp_count = 0
7035
7036	ENDIF
7037	!
7038	!-- Compute only first (nxl) and last (nxr) loop iterration
7039	DO ip = nxl, nxr, nxr-nxl
7040	DO jp = nys, nyn
7041	DO kp = nzb+1, nzt
7042	number_of_particles = prt_count(kp,jp,ip)
7043	IF ( number_of_particles <= 0 ) CYCLE
7044	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7045	DO n = 1, number_of_particles
7046	!
7047	!-- Only those particles that have not been marked as 'deleted' may
7048	!-- be moved.
7049	IF ( particles(n)%particle_mask ) THEN
7050
7051	i = particles(n)%x * ddx
7052	!
7053	!-- Above calculation does not work for indices less than zero
7054	IF ( particles(n)%x < 0.0_wp ) i = -1
7055
7056	IF ( i < nxl ) THEN
7057	IF ( i < 0 ) THEN
7058	!
7059	!-- Apply boundary condition along x
7060	IF ( ibc_par_lr == 0 ) THEN
7061	!
7062	!-- Cyclic condition
7063	IF ( pdims(1) == 1 ) THEN
7064	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7065	particles(n)%origin_x = ( nx + 1 ) * dx + &
7066	particles(n)%origin_x
7067	ELSE
7068	trlp_count = trlp_count + 1
7069	trlp(trlp_count) = particles(n)
7070	trlp(trlp_count)%x = ( nx + 1 ) * dx + trlp(trlp_count)%x
7071	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x + &
7072	( nx + 1 ) * dx
7073	particles(n)%particle_mask = .FALSE.
7074	deleted_particles = deleted_particles + 1
7075
7076	IF ( trlp(trlp_count)%x >= (nx + 1)* dx - 1.0E-12_wp ) THEN
7077	trlp(trlp_count)%x = trlp(trlp_count)%x - 1.0E-10_wp
7078	!++ why is 1 subtracted in next statement???
7079	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x - 1
7080	ENDIF
7081
7082	ENDIF
7083
7084	ELSEIF ( ibc_par_lr == 1 ) THEN
7085	!
7086	!-- Particle absorption
7087	particles(n)%particle_mask = .FALSE.
7088	deleted_particles = deleted_particles + 1
7089
7090	ELSEIF ( ibc_par_lr == 2 ) THEN
7091	!
7092	!-- Particle reflection
7093	particles(n)%x = -particles(n)%x
7094	particles(n)%speed_x = -particles(n)%speed_x
7095
7096	ENDIF
7097	ELSE
7098	!
7099	!-- Store particle data in the transfer array, which will be
7100	!-- send to the neighbouring PE
7101	trlp_count = trlp_count + 1
7102	trlp(trlp_count) = particles(n)
7103	particles(n)%particle_mask = .FALSE.
7104	deleted_particles = deleted_particles + 1
7105
7106	ENDIF
7107
7108	ELSEIF ( i > nxr ) THEN
7109	IF ( i > nx ) THEN
7110	!
7111	!-- Apply boundary condition along x
7112	IF ( ibc_par_lr == 0 ) THEN
7113	!
7114	!-- Cyclic condition
7115	IF ( pdims(1) == 1 ) THEN
7116	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7117	particles(n)%origin_x = particles(n)%origin_x - &
7118	( nx + 1 ) * dx
7119	ELSE
7120	trrp_count = trrp_count + 1
7121	trrp(trrp_count) = particles(n)
7122	trrp(trrp_count)%x = trrp(trrp_count)%x - ( nx + 1 ) * dx
7123	trrp(trrp_count)%origin_x = trrp(trrp_count)%origin_x - &
7124	( nx + 1 ) * dx
7125	particles(n)%particle_mask = .FALSE.
7126	deleted_particles = deleted_particles + 1
7127
7128	ENDIF
7129
7130	ELSEIF ( ibc_par_lr == 1 ) THEN
7131	!
7132	!-- Particle absorption
7133	particles(n)%particle_mask = .FALSE.
7134	deleted_particles = deleted_particles + 1
7135
7136	ELSEIF ( ibc_par_lr == 2 ) THEN
7137	!
7138	!-- Particle reflection
7139	particles(n)%x = 2 * ( nx * dx ) - particles(n)%x
7140	particles(n)%speed_x = -particles(n)%speed_x
7141
7142	ENDIF
7143	ELSE
7144	!
7145	!-- Store particle data in the transfer array, which will be send
7146	!-- to the neighbouring PE
7147	trrp_count = trrp_count + 1
7148	trrp(trrp_count) = particles(n)
7149	particles(n)%particle_mask = .FALSE.
7150	deleted_particles = deleted_particles + 1
7151
7152	ENDIF
7153
7154	ENDIF
7155	ENDIF
7156
7157	ENDDO
7158	ENDDO
7159	ENDDO
7160	ENDDO
7161
7162	!
7163	!-- STORAGE_SIZE returns the storage size of argument A in bits. However , it
7164	!-- is needed in bytes. The function C_SIZEOF which produces this value directly
7165	!-- causes problems with gfortran. For this reason the use of C_SIZEOF is avoided
7166	par_size = STORAGE_SIZE(trlp(1))/8
7167
7168
7169	!
7170	!-- Allocate arrays required for north-south exchange, as these
7171	!-- are used directly after particles are exchange along x-direction.
7172	ALLOCATE( move_also_north(1:NR_2_direction_move) )
7173	ALLOCATE( move_also_south(1:NR_2_direction_move) )
7174
7175	nr_move_north = 0
7176	nr_move_south = 0
7177	!
7178	!-- Send left boundary, receive right boundary (but first exchange how many
7179	!-- and check, if particle storage must be extended)
7180	IF ( pdims(1) /= 1 ) THEN
7181
7182	CALL MPI_SENDRECV( trlp_count, 1, MPI_INTEGER, pleft, 0, &
7183	trrp_count_recv, 1, MPI_INTEGER, pright, 0, &
7184	comm2d, status, ierr )
7185
7186	ALLOCATE(rvrp(MAX(1,trrp_count_recv)))
7187
7188	CALL MPI_SENDRECV( trlp, max(1,trlp_count)*par_size, MPI_BYTE,&
7189	pleft, 1, rvrp, &
7190	max(1,trrp_count_recv)*par_size, MPI_BYTE, pright, 1,&
7191	comm2d, status, ierr )
7192
7193	IF ( trrp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvrp(1:trrp_count_recv))
7194
7195	DEALLOCATE(rvrp)
7196
7197	!
7198	!-- Send right boundary, receive left boundary
7199	CALL MPI_SENDRECV( trrp_count, 1, MPI_INTEGER, pright, 0, &
7200	trlp_count_recv, 1, MPI_INTEGER, pleft, 0, &
7201	comm2d, status, ierr )
7202
7203	ALLOCATE(rvlp(MAX(1,trlp_count_recv)))
7204	!
7205	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7206	!-- variables in structure particle_type (due to the calculation of par_size)
7207	CALL MPI_SENDRECV( trrp, max(1,trrp_count)*par_size, MPI_BYTE,&
7208	pright, 1, rvlp, &
7209	max(1,trlp_count_recv)*par_size, MPI_BYTE, pleft, 1, &
7210	comm2d, status, ierr )
7211
7212	IF ( trlp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvlp(1:trlp_count_recv))
7213
7214	DEALLOCATE( rvlp )
7215	DEALLOCATE( trlp, trrp )
7216
7217	ENDIF
7218
7219	!
7220	!-- Check whether particles have crossed the boundaries in y direction. Note
7221	!-- that this case can also apply to particles that have just been received
7222	!-- from the adjacent right or left PE.
7223	!-- Find out first the number of particles to be transferred and allocate
7224	!-- temporary arrays needed to store them.
7225	!-- For a one-dimensional decomposition along y, no transfer is necessary,
7226	!-- because the particle remains on the PE.
7227	trsp_count = nr_move_south
7228	trnp_count = nr_move_north
7229
7230	trsp_count_recv = 0
7231	trnp_count_recv = 0
7232
7233	IF ( pdims(2) /= 1 ) THEN
7234	!
7235	!-- First calculate the storage necessary for sending and receiving the
7236	!-- data
7237	DO ip = nxl, nxr
7238	DO jp = nys, nyn, nyn-nys !compute only first (nys) and last (nyn) loop iterration
7239	DO kp = nzb+1, nzt
7240	number_of_particles = prt_count(kp,jp,ip)
7241	IF ( number_of_particles <= 0 ) CYCLE
7242	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7243	DO n = 1, number_of_particles
7244	IF ( particles(n)%particle_mask ) THEN
7245	j = particles(n)%y * ddy
7246	!
7247	!-- Above calculation does not work for indices less than zero
7248	IF ( particles(n)%y < 0.0_wp) j = -1
7249
7250	IF ( j < nys ) THEN
7251	trsp_count = trsp_count + 1
7252	ELSEIF ( j > nyn ) THEN
7253	trnp_count = trnp_count + 1
7254	ENDIF
7255	ENDIF
7256	ENDDO
7257	ENDDO
7258	ENDDO
7259	ENDDO
7260
7261	IF ( trsp_count == 0 ) trsp_count = 1
7262	IF ( trnp_count == 0 ) trnp_count = 1
7263
7264	ALLOCATE( trsp(trsp_count), trnp(trnp_count) )
7265
7266	trsp = zero_particle
7267	trnp = zero_particle
7268
7269	trsp_count = nr_move_south
7270	trnp_count = nr_move_north
7271
7272	trsp(1:nr_move_south) = move_also_south(1:nr_move_south)
7273	trnp(1:nr_move_north) = move_also_north(1:nr_move_north)
7274
7275	ENDIF
7276
7277	DO ip = nxl, nxr
7278	DO jp = nys, nyn, nyn-nys ! compute only first (nys) and last (nyn) loop iterration
7279	DO kp = nzb+1, nzt
7280	number_of_particles = prt_count(kp,jp,ip)
7281	IF ( number_of_particles <= 0 ) CYCLE
7282	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7283	DO n = 1, number_of_particles
7284	!
7285	!-- Only those particles that have not been marked as 'deleted' may
7286	!-- be moved.
7287	IF ( particles(n)%particle_mask ) THEN
7288
7289	j = particles(n)%y * ddy
7290	!
7291	!-- Above calculation does not work for indices less than zero
7292	IF ( particles(n)%y < 0.0_wp ) j = -1
7293
7294	IF ( j < nys ) THEN
7295	IF ( j < 0 ) THEN
7296	!
7297	!-- Apply boundary condition along y
7298	IF ( ibc_par_ns == 0 ) THEN
7299	!
7300	!-- Cyclic condition
7301	IF ( pdims(2) == 1 ) THEN
7302	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7303	particles(n)%origin_y = ( ny + 1 ) * dy + &
7304	particles(n)%origin_y
7305	ELSE
7306	trsp_count = trsp_count + 1
7307	trsp(trsp_count) = particles(n)
7308	trsp(trsp_count)%y = ( ny + 1 ) * dy + &
7309	trsp(trsp_count)%y
7310	trsp(trsp_count)%origin_y = trsp(trsp_count)%origin_y &
7311	+ ( ny + 1 ) * dy
7312	particles(n)%particle_mask = .FALSE.
7313	deleted_particles = deleted_particles + 1
7314
7315	IF ( trsp(trsp_count)%y >= (ny+1)* dy - 1.0E-12_wp ) THEN
7316	trsp(trsp_count)%y = trsp(trsp_count)%y - 1.0E-10_wp
7317	!++ why is 1 subtracted in next statement???
7318	trsp(trsp_count)%origin_y = &
7319	trsp(trsp_count)%origin_y - 1
7320	ENDIF
7321
7322	ENDIF
7323
7324	ELSEIF ( ibc_par_ns == 1 ) THEN
7325	!
7326	!-- Particle absorption
7327	particles(n)%particle_mask = .FALSE.
7328	deleted_particles = deleted_particles + 1
7329
7330	ELSEIF ( ibc_par_ns == 2 ) THEN
7331	!
7332	!-- Particle reflection
7333	particles(n)%y = -particles(n)%y
7334	particles(n)%speed_y = -particles(n)%speed_y
7335
7336	ENDIF
7337	ELSE
7338	!
7339	!-- Store particle data in the transfer array, which will
7340	!-- be send to the neighbouring PE
7341	trsp_count = trsp_count + 1
7342	trsp(trsp_count) = particles(n)
7343	particles(n)%particle_mask = .FALSE.
7344	deleted_particles = deleted_particles + 1
7345
7346	ENDIF
7347
7348	ELSEIF ( j > nyn ) THEN
7349	IF ( j > ny ) THEN
7350	!
7351	!-- Apply boundary condition along y
7352	IF ( ibc_par_ns == 0 ) THEN
7353	!
7354	!-- Cyclic condition
7355	IF ( pdims(2) == 1 ) THEN
7356	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7357	particles(n)%origin_y = &
7358	particles(n)%origin_y - ( ny + 1 ) * dy
7359	ELSE
7360	trnp_count = trnp_count + 1
7361	trnp(trnp_count) = particles(n)
7362	trnp(trnp_count)%y = &
7363	trnp(trnp_count)%y - ( ny + 1 ) * dy
7364	trnp(trnp_count)%origin_y = &
7365	trnp(trnp_count)%origin_y - ( ny + 1 ) * dy
7366	particles(n)%particle_mask = .FALSE.
7367	deleted_particles = deleted_particles + 1
7368	ENDIF
7369
7370	ELSEIF ( ibc_par_ns == 1 ) THEN
7371	!
7372	!-- Particle absorption
7373	particles(n)%particle_mask = .FALSE.
7374	deleted_particles = deleted_particles + 1
7375
7376	ELSEIF ( ibc_par_ns == 2 ) THEN
7377	!
7378	!-- Particle reflection
7379	particles(n)%y = 2 * ( ny * dy ) - particles(n)%y
7380	particles(n)%speed_y = -particles(n)%speed_y
7381
7382	ENDIF
7383	ELSE
7384	!
7385	!-- Store particle data in the transfer array, which will
7386	!-- be send to the neighbouring PE
7387	trnp_count = trnp_count + 1
7388	trnp(trnp_count) = particles(n)
7389	particles(n)%particle_mask = .FALSE.
7390	deleted_particles = deleted_particles + 1
7391
7392	ENDIF
7393
7394	ENDIF
7395	ENDIF
7396	ENDDO
7397	ENDDO
7398	ENDDO
7399	ENDDO
7400
7401	!
7402	!-- Send front boundary, receive back boundary (but first exchange how many
7403	!-- and check, if particle storage must be extended)
7404	IF ( pdims(2) /= 1 ) THEN
7405
7406	CALL MPI_SENDRECV( trsp_count, 1, MPI_INTEGER, psouth, 0, &
7407	trnp_count_recv, 1, MPI_INTEGER, pnorth, 0, &
7408	comm2d, status, ierr )
7409
7410	ALLOCATE(rvnp(MAX(1,trnp_count_recv)))
7411	!
7412	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7413	!-- variables in structure particle_type (due to the calculation of par_size)
7414	CALL MPI_SENDRECV( trsp, trsp_count*par_size, MPI_BYTE, &
7415	psouth, 1, rvnp, &
7416	trnp_count_recv*par_size, MPI_BYTE, pnorth, 1, &
7417	comm2d, status, ierr )
7418
7419	IF ( trnp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvnp(1:trnp_count_recv))
7420
7421	DEALLOCATE(rvnp)
7422
7423	!
7424	!-- Send back boundary, receive front boundary
7425	CALL MPI_SENDRECV( trnp_count, 1, MPI_INTEGER, pnorth, 0, &
7426	trsp_count_recv, 1, MPI_INTEGER, psouth, 0, &
7427	comm2d, status, ierr )
7428
7429	ALLOCATE(rvsp(MAX(1,trsp_count_recv)))
7430	!
7431	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7432	!-- variables in structure particle_type (due to the calculation of par_size)
7433	CALL MPI_SENDRECV( trnp, trnp_count*par_size, MPI_BYTE, &
7434	pnorth, 1, rvsp, &
7435	trsp_count_recv*par_size, MPI_BYTE, psouth, 1, &
7436	comm2d, status, ierr )
7437
7438	IF ( trsp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvsp(1:trsp_count_recv))
7439
7440	DEALLOCATE(rvsp)
7441
7442	number_of_particles = number_of_particles + trsp_count_recv
7443
7444	DEALLOCATE( trsp, trnp )
7445
7446	ENDIF
7447
7448	DEALLOCATE( move_also_north )
7449	DEALLOCATE( move_also_south )
7450
7451	#else
7452
7453	DO ip = nxl, nxr, nxr-nxl
7454	DO jp = nys, nyn
7455	DO kp = nzb+1, nzt
7456	number_of_particles = prt_count(kp,jp,ip)
7457	IF ( number_of_particles <= 0 ) CYCLE
7458	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7459	DO n = 1, number_of_particles
7460	!
7461	!-- Apply boundary conditions
7462
7463	IF ( particles(n)%x < 0.0_wp ) THEN
7464
7465	IF ( ibc_par_lr == 0 ) THEN
7466	!
7467	!-- Cyclic boundary. Relevant coordinate has to be changed.
7468	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7469	particles(n)%origin_x = ( nx + 1 ) * dx + &
7470	particles(n)%origin_x
7471	ELSEIF ( ibc_par_lr == 1 ) THEN
7472	!
7473	!-- Particle absorption
7474	particles(n)%particle_mask = .FALSE.
7475	deleted_particles = deleted_particles + 1
7476
7477	ELSEIF ( ibc_par_lr == 2 ) THEN
7478	!
7479	!-- Particle reflection
7480	particles(n)%x = -dx - particles(n)%x
7481	particles(n)%speed_x = -particles(n)%speed_x
7482	ENDIF
7483
7484	ELSEIF ( particles(n)%x >= ( nx + 1) * dx ) THEN
7485
7486	IF ( ibc_par_lr == 0 ) THEN
7487	!
7488	!-- Cyclic boundary. Relevant coordinate has to be changed.
7489	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7490	particles(n)%origin_x = particles(n)%origin_x - &
7491	( nx + 1 ) * dx
7492
7493	ELSEIF ( ibc_par_lr == 1 ) THEN
7494	!
7495	!-- Particle absorption
7496	particles(n)%particle_mask = .FALSE.
7497	deleted_particles = deleted_particles + 1
7498
7499	ELSEIF ( ibc_par_lr == 2 ) THEN
7500	!
7501	!-- Particle reflection
7502	particles(n)%x = ( nx + 1 ) * dx - particles(n)%x
7503	particles(n)%speed_x = -particles(n)%speed_x
7504	ENDIF
7505
7506	ENDIF
7507	ENDDO
7508	ENDDO
7509	ENDDO
7510	ENDDO
7511
7512	DO ip = nxl, nxr
7513	DO jp = nys, nyn, nyn-nys
7514	DO kp = nzb+1, nzt
7515	number_of_particles = prt_count(kp,jp,ip)
7516	IF ( number_of_particles <= 0 ) CYCLE
7517	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7518	DO n = 1, number_of_particles
7519
7520	IF ( particles(n)%y < 0.0_wp) THEN
7521
7522	IF ( ibc_par_ns == 0 ) THEN
7523	!
7524	!-- Cyclic boundary. Relevant coordinate has to be changed.
7525	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7526	particles(n)%origin_y = ( ny + 1 ) * dy + &
7527	particles(n)%origin_y
7528
7529	ELSEIF ( ibc_par_ns == 1 ) THEN
7530	!
7531	!-- Particle absorption
7532	particles(n)%particle_mask = .FALSE.
7533	deleted_particles = deleted_particles + 1
7534
7535	ELSEIF ( ibc_par_ns == 2 ) THEN
7536	!
7537	!-- Particle reflection
7538	particles(n)%y = -dy - particles(n)%y
7539	particles(n)%speed_y = -particles(n)%speed_y
7540	ENDIF
7541
7542	ELSEIF ( particles(n)%y >= ( ny + 1) * dy ) THEN
7543
7544	IF ( ibc_par_ns == 0 ) THEN
7545	!
7546	!-- Cyclic boundary. Relevant coordinate has to be changed.
7547	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7548	particles(n)%origin_y = particles(n)%origin_y - &
7549	( ny + 1 ) * dy
7550
7551	ELSEIF ( ibc_par_ns == 1 ) THEN
7552	!
7553	!-- Particle absorption
7554	particles(n)%particle_mask = .FALSE.
7555	deleted_particles = deleted_particles + 1
7556
7557	ELSEIF ( ibc_par_ns == 2 ) THEN
7558	!
7559	!-- Particle reflection
7560	particles(n)%y = ( ny + 1 ) * dy - particles(n)%y
7561	particles(n)%speed_y = -particles(n)%speed_y
7562	ENDIF
7563
7564	ENDIF
7565
7566	ENDDO
7567	ENDDO
7568	ENDDO
7569	ENDDO
7570	#endif
7571
7572	!
7573	!-- Accumulate the number of particles transferred between the subdomains
7574	#if defined( __parallel )
7575	trlp_count_sum = trlp_count_sum + trlp_count
7576	trlp_count_recv_sum = trlp_count_recv_sum + trlp_count_recv
7577	trrp_count_sum = trrp_count_sum + trrp_count
7578	trrp_count_recv_sum = trrp_count_recv_sum + trrp_count_recv
7579	trsp_count_sum = trsp_count_sum + trsp_count
7580	trsp_count_recv_sum = trsp_count_recv_sum + trsp_count_recv
7581	trnp_count_sum = trnp_count_sum + trnp_count
7582	trnp_count_recv_sum = trnp_count_recv_sum + trnp_count_recv
7583	#endif
7584
7585	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'stop' )
7586
7587	END SUBROUTINE lpm_exchange_horiz
7588
7589	!------------------------------------------------------------------------------!
7590	! Description:
7591	! ------------
7592	!> If a particle moves from one processor to another, this subroutine moves
7593	!> the corresponding elements from the particle arrays of the old grid cells
7594	!> to the particle arrays of the new grid cells.
7595	!------------------------------------------------------------------------------!
7596	SUBROUTINE lpm_add_particles_to_gridcell (particle_array)
7597
7598	IMPLICIT NONE
7599
7600	INTEGER(iwp) :: ip !< grid index (x) of particle
7601	INTEGER(iwp) :: jp !< grid index (x) of particle
7602	INTEGER(iwp) :: kp !< grid index (x) of particle
7603	INTEGER(iwp) :: n !< index variable of particle
7604	INTEGER(iwp) :: pindex !< dummy argument for new number of particles per grid box
7605
7606	LOGICAL :: pack_done !<
7607
7608	TYPE(particle_type), DIMENSION(:), INTENT(IN) :: particle_array !< new particles in a grid box
7609	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: temp_ns !< temporary particle array for reallocation
7610
7611	pack_done = .FALSE.
7612
7613	DO n = 1, SIZE(particle_array)
7614
7615	IF ( .NOT. particle_array(n)%particle_mask ) CYCLE
7616
7617	ip = particle_array(n)%x * ddx
7618	jp = particle_array(n)%y * ddy
7619	!
7620	!-- In case of stretching the actual k index must be found
7621	IF ( dz_stretch_level /= -9999999.9_wp .OR. &
7622	dz_stretch_level_start(1) /= -9999999.9_wp ) THEN
7623	kp = MINLOC( ABS( particle_array(n)%z - zu ), DIM = 1 ) - 1
7624	ELSE
7625	kp = INT( particle_array(n)%z / dz(1) + 1 + offset_ocean_nzt )
7626	ENDIF
7627
7628	IF ( ip >= nxl .AND. ip <= nxr .AND. jp >= nys .AND. jp <= nyn &
7629	.AND. kp >= nzb+1 .AND. kp <= nzt) THEN ! particle stays on processor
7630	number_of_particles = prt_count(kp,jp,ip)
7631	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7632
7633	pindex = prt_count(kp,jp,ip)+1
7634	IF( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7635	IF ( pack_done ) THEN
7636	CALL realloc_particles_array ( ip, jp, kp )
7637	ELSE
7638	CALL lpm_pack
7639	prt_count(kp,jp,ip) = number_of_particles
7640	pindex = prt_count(kp,jp,ip)+1
7641	IF ( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7642	CALL realloc_particles_array ( ip, jp, kp )
7643	ENDIF
7644	pack_done = .TRUE.
7645	ENDIF
7646	ENDIF
7647	grid_particles(kp,jp,ip)%particles(pindex) = particle_array(n)
7648	prt_count(kp,jp,ip) = pindex
7649	ELSE
7650	IF ( jp <= nys - 1 ) THEN
7651	nr_move_south = nr_move_south+1
7652	!
7653	!-- Before particle information is swapped to exchange-array, check
7654	!-- if enough memory is allocated. If required, reallocate exchange
7655	!-- array.
7656	IF ( nr_move_south > SIZE(move_also_south) ) THEN
7657	!
7658	!-- At first, allocate further temporary array to swap particle
7659	!-- information.
7660	ALLOCATE( temp_ns(SIZE(move_also_south)+NR_2_direction_move) )
7661	temp_ns(1:nr_move_south-1) = move_also_south(1:nr_move_south-1)
7662	DEALLOCATE( move_also_south )
7663	ALLOCATE( move_also_south(SIZE(temp_ns)) )
7664	move_also_south(1:nr_move_south-1) = temp_ns(1:nr_move_south-1)
7665	DEALLOCATE( temp_ns )
7666
7667	ENDIF
7668
7669	move_also_south(nr_move_south) = particle_array(n)
7670
7671	IF ( jp == -1 ) THEN
7672	!
7673	!-- Apply boundary condition along y
7674	IF ( ibc_par_ns == 0 ) THEN
7675	move_also_south(nr_move_south)%y = &
7676	move_also_south(nr_move_south)%y + ( ny + 1 ) * dy
7677	move_also_south(nr_move_south)%origin_y = &
7678	move_also_south(nr_move_south)%origin_y + ( ny + 1 ) * dy
7679	ELSEIF ( ibc_par_ns == 1 ) THEN
7680	!
7681	!-- Particle absorption
7682	move_also_south(nr_move_south)%particle_mask = .FALSE.
7683	deleted_particles = deleted_particles + 1
7684
7685	ELSEIF ( ibc_par_ns == 2 ) THEN
7686	!
7687	!-- Particle reflection
7688	move_also_south(nr_move_south)%y = &
7689	-move_also_south(nr_move_south)%y
7690	move_also_south(nr_move_south)%speed_y = &
7691	-move_also_south(nr_move_south)%speed_y
7692
7693	ENDIF
7694	ENDIF
7695	ELSEIF ( jp >= nyn+1 ) THEN
7696	nr_move_north = nr_move_north+1
7697	!
7698	!-- Before particle information is swapped to exchange-array, check
7699	!-- if enough memory is allocated. If required, reallocate exchange
7700	!-- array.
7701	IF ( nr_move_north > SIZE(move_also_north) ) THEN
7702	!
7703	!-- At first, allocate further temporary array to swap particle
7704	!-- information.
7705	ALLOCATE( temp_ns(SIZE(move_also_north)+NR_2_direction_move) )
7706	temp_ns(1:nr_move_north-1) = move_also_south(1:nr_move_north-1)
7707	DEALLOCATE( move_also_north )
7708	ALLOCATE( move_also_north(SIZE(temp_ns)) )
7709	move_also_north(1:nr_move_north-1) = temp_ns(1:nr_move_north-1)
7710	DEALLOCATE( temp_ns )
7711
7712	ENDIF
7713
7714	move_also_north(nr_move_north) = particle_array(n)
7715	IF ( jp == ny+1 ) THEN
7716	!
7717	!-- Apply boundary condition along y
7718	IF ( ibc_par_ns == 0 ) THEN
7719
7720	move_also_north(nr_move_north)%y = &
7721	move_also_north(nr_move_north)%y - ( ny + 1 ) * dy
7722	move_also_north(nr_move_north)%origin_y = &
7723	move_also_north(nr_move_north)%origin_y - ( ny + 1 ) * dy
7724	ELSEIF ( ibc_par_ns == 1 ) THEN
7725	!
7726	!-- Particle absorption
7727	move_also_north(nr_move_north)%particle_mask = .FALSE.
7728	deleted_particles = deleted_particles + 1
7729
7730	ELSEIF ( ibc_par_ns == 2 ) THEN
7731	!
7732	!-- Particle reflection
7733	move_also_north(nr_move_north)%y = &
7734	-move_also_north(nr_move_north)%y
7735	move_also_north(nr_move_north)%speed_y = &
7736	-move_also_north(nr_move_north)%speed_y
7737
7738	ENDIF
7739	ENDIF
7740	ELSE
7741	WRITE(0,'(a,8i7)') 'particle out of range ',myid,ip,jp,kp,nxl,nxr,nys,nyn
7742	ENDIF
7743	ENDIF
7744	ENDDO
7745
7746	RETURN
7747
7748	END SUBROUTINE lpm_add_particles_to_gridcell
7749
7750
7751	!------------------------------------------------------------------------------!
7752	! Description:
7753	! ------------
7754	!> If a particle moves from one grid cell to another (on the current
7755	!> processor!), this subroutine moves the corresponding element from the
7756	!> particle array of the old grid cell to the particle array of the new grid
7757	!> cell.
7758	!------------------------------------------------------------------------------!
7759	SUBROUTINE lpm_move_particle
7760
7761	INTEGER(iwp) :: i !< grid index (x) of particle position
7762	INTEGER(iwp) :: ip !< index variable along x
7763	INTEGER(iwp) :: j !< grid index (y) of particle position
7764	INTEGER(iwp) :: jp !< index variable along y
7765	INTEGER(iwp) :: k !< grid index (z) of particle position
7766	INTEGER(iwp) :: kp !< index variable along z
7767	INTEGER(iwp) :: n !< index variable for particle array
7768	INTEGER(iwp) :: np_before_move !< number of particles per grid box before moving
7769	INTEGER(iwp) :: pindex !< dummy argument for number of new particle per grid box
7770
7771	TYPE(particle_type), DIMENSION(:), POINTER :: particles_before_move !< particles before moving
7772
7773	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'start' )
7774	CALL lpm_check_cfl
7775	DO ip = nxl, nxr
7776	DO jp = nys, nyn
7777	DO kp = nzb+1, nzt
7778
7779	np_before_move = prt_count(kp,jp,ip)
7780	IF ( np_before_move <= 0 ) CYCLE
7781	particles_before_move => grid_particles(kp,jp,ip)%particles(1:np_before_move)
7782
7783	DO n = 1, np_before_move
7784	i = particles_before_move(n)%x * ddx
7785	j = particles_before_move(n)%y * ddy
7786	k = kp
7787	!
7788	!-- Find correct vertical particle grid box (necessary in case of grid stretching)
7789	!-- Due to the CFL limitations only the neighbouring grid boxes are considered.
7790	IF( zw(k) < particles_before_move(n)%z ) k = k + 1
7791	IF( zw(k-1) > particles_before_move(n)%z ) k = k - 1
7792
7793	!-- For lpm_exchange_horiz to work properly particles need to be moved to the outermost gridboxes
7794	!-- of the respective processor. If the particle index is inside the processor the following lines
7795	!-- will not change the index
7796	i = MIN ( i , nxr )
7797	i = MAX ( i , nxl )
7798	j = MIN ( j , nyn )
7799	j = MAX ( j , nys )
7800
7801	k = MIN ( k , nzt )
7802	k = MAX ( k , nzb+1 )
7803
7804	!
7805	!-- Check, if particle has moved to another grid cell.
7806	IF ( i /= ip .OR. j /= jp .OR. k /= kp ) THEN
7807	!!
7808	!-- If the particle stays on the same processor, the particle
7809	!-- will be added to the particle array of the new processor.
7810	number_of_particles = prt_count(k,j,i)
7811	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7812
7813	pindex = prt_count(k,j,i)+1
7814	IF ( pindex > SIZE(grid_particles(k,j,i)%particles) ) &
7815	THEN
7816	CALL realloc_particles_array( i, j, k )
7817	ENDIF
7818
7819	grid_particles(k,j,i)%particles(pindex) = particles_before_move(n)
7820	prt_count(k,j,i) = pindex
7821
7822	particles_before_move(n)%particle_mask = .FALSE.
7823	ENDIF
7824	ENDDO
7825
7826	ENDDO
7827	ENDDO
7828	ENDDO
7829
7830	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'stop' )
7831
7832	RETURN
7833
7834	END SUBROUTINE lpm_move_particle
7835
7836
7837	!------------------------------------------------------------------------------!
7838	! Description:
7839	! ------------
7840	!> Check CFL-criterion for each particle. If one particle violated the
7841	!> criterion the particle will be deleted and a warning message is given.
7842	!------------------------------------------------------------------------------!
7843	SUBROUTINE lpm_check_cfl
7844
7845	IMPLICIT NONE
7846
7847	INTEGER(iwp) :: i !< running index, x-direction
7848	INTEGER(iwp) :: j !< running index, y-direction
7849	INTEGER(iwp) :: k !< running index, z-direction
7850	INTEGER(iwp) :: n !< running index, number of particles
7851
7852	DO i = nxl, nxr
7853	DO j = nys, nyn
7854	DO k = nzb+1, nzt
7855	number_of_particles = prt_count(k,j,i)
7856	IF ( number_of_particles <= 0 ) CYCLE
7857	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7858	DO n = 1, number_of_particles
7859	!
7860	!-- Note, check for CFL does not work at first particle timestep
7861	!-- when both, age and age_m are zero.
7862	IF ( particles(n)%age - particles(n)%age_m > 0.0_wp ) THEN
7863	IF(ABS(particles(n)%speed_x) > &
7864	(dx/(particles(n)%age-particles(n)%age_m)) .OR. &
7865	ABS(particles(n)%speed_y) > &
7866	(dy/(particles(n)%age-particles(n)%age_m)) .OR. &
7867	ABS(particles(n)%speed_z) > &
7868	((zw(k)-zw(k-1))/(particles(n)%age-particles(n)%age_m))) &
7869	THEN
7870	WRITE( message_string, * ) &
7871	'Particle violated CFL-criterion: &particle with id ', &
7872	particles(n)%id, ' will be deleted!'
7873	CALL message( 'lpm_check_cfl', 'PA0475', 0, 1, -1, 6, 0 )
7874	particles(n)%particle_mask= .FALSE.
7875	ENDIF
7876	ENDIF
7877	ENDDO
7878	ENDDO
7879	ENDDO
7880	ENDDO
7881
7882	END SUBROUTINE lpm_check_cfl
7883
7884
7885	!------------------------------------------------------------------------------!
7886	! Description:
7887	! ------------
7888	!> If the allocated memory for the particle array do not suffice to add arriving
7889	!> particles from neighbour grid cells, this subrouting reallocates the
7890	!> particle array to assure enough memory is available.
7891	!------------------------------------------------------------------------------!
7892	SUBROUTINE realloc_particles_array ( i, j, k, size_in )
7893
7894	INTEGER(iwp), INTENT(IN) :: i !<
7895	INTEGER(iwp), INTENT(IN) :: j !<
7896	INTEGER(iwp), INTENT(IN) :: k !<
7897	INTEGER(iwp), INTENT(IN), OPTIONAL :: size_in !<
7898
7899	INTEGER(iwp) :: old_size !<
7900	INTEGER(iwp) :: new_size !<
7901	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7902	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7903
7904	old_size = SIZE(grid_particles(k,j,i)%particles)
7905
7906	IF ( PRESENT(size_in) ) THEN
7907	new_size = size_in
7908	ELSE
7909	new_size = old_size * ( 1.0_wp + alloc_factor / 100.0_wp )
7910	ENDIF
7911
7912	new_size = MAX( new_size, 1, old_size + 1 )
7913
7914	IF ( old_size <= 500 ) THEN
7915
7916	tmp_particles_s(1:old_size) = grid_particles(k,j,i)%particles(1:old_size)
7917
7918	DEALLOCATE(grid_particles(k,j,i)%particles)
7919	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7920
7921	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_s(1:old_size)
7922	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7923
7924	ELSE
7925
7926	ALLOCATE(tmp_particles_d(new_size))
7927	tmp_particles_d(1:old_size) = grid_particles(k,j,i)%particles
7928
7929	DEALLOCATE(grid_particles(k,j,i)%particles)
7930	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7931
7932	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_d(1:old_size)
7933	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7934
7935	DEALLOCATE(tmp_particles_d)
7936
7937	ENDIF
7938	particles => grid_particles(k,j,i)%particles(1:new_size)
7939
7940	RETURN
7941
7942	END SUBROUTINE realloc_particles_array
7943
7944
7945	!------------------------------------------------------------------------------!
7946	! Description:
7947	! ------------
7948	!> Not needed but allocated space for particles is dealloced.
7949	!------------------------------------------------------------------------------!
7950	SUBROUTINE dealloc_particles_array
7951
7952
7953	INTEGER(iwp) :: i !<
7954	INTEGER(iwp) :: j !<
7955	INTEGER(iwp) :: k !<
7956	INTEGER(iwp) :: old_size !<
7957	INTEGER(iwp) :: new_size !<
7958
7959	LOGICAL :: dealloc
7960
7961	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7962	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7963
7964	DO i = nxl, nxr
7965	DO j = nys, nyn
7966	DO k = nzb+1, nzt
7967	!
7968	!-- Determine number of active particles
7969	number_of_particles = prt_count(k,j,i)
7970	!
7971	!-- Determine allocated memory size
7972	old_size = SIZE( grid_particles(k,j,i)%particles )
7973	!
7974	!-- Check for large unused memory
7975	dealloc = ( ( number_of_particles < 1 .AND. &
7976	old_size > 1 ) .OR. &
7977	( number_of_particles > 1 .AND. &
7978	old_size - number_of_particles * &
7979	( 1.0_wp + 0.01_wp * alloc_factor ) > 0.0_wp ) )
7980
7981	IF ( dealloc ) THEN
7982	IF ( number_of_particles < 1 ) THEN
7983	new_size = 1
7984	ELSE
7985	new_size = INT( number_of_particles * ( 1.0_wp + 0.01_wp * alloc_factor ) )
7986	ENDIF
7987
7988	IF ( number_of_particles <= 500 ) THEN
7989
7990	tmp_particles_s(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
7991
7992	DEALLOCATE(grid_particles(k,j,i)%particles)
7993	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7994
7995	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_s(1:number_of_particles)
7996	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
7997
7998	ELSE
7999
8000	ALLOCATE(tmp_particles_d(number_of_particles))
8001	tmp_particles_d(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
8002
8003	DEALLOCATE(grid_particles(k,j,i)%particles)
8004	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
8005
8006	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_d(1:number_of_particles)
8007	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
8008
8009	DEALLOCATE(tmp_particles_d)
8010
8011	ENDIF
8012
8013	ENDIF
8014	ENDDO
8015	ENDDO
8016	ENDDO
8017
8018	END SUBROUTINE dealloc_particles_array
8019
8020
8021	!------------------------------------------------------------------------------!
8022	! Description:
8023	! -----------
8024	!> Routine for the whole processor
8025	!> Sort all particles into the 8 respective subgrid boxes (in case of trilinear
8026	!> interpolation method) and free space of particles which has been marked for
8027	!> deletion.
8028	!------------------------------------------------------------------------------!
8029	SUBROUTINE lpm_sort_and_delete
8030
8031	INTEGER(iwp) :: i !<
8032	INTEGER(iwp) :: ip !<
8033	INTEGER(iwp) :: is !<
8034	INTEGER(iwp) :: j !<
8035	INTEGER(iwp) :: jp !<
8036	INTEGER(iwp) :: kp !<
8037	INTEGER(iwp) :: m !<
8038	INTEGER(iwp) :: n !<
8039	INTEGER(iwp) :: nn !<
8040	INTEGER(iwp) :: sort_index !<
8041
8042	INTEGER(iwp), DIMENSION(0:7) :: sort_count !<
8043
8044	TYPE(particle_type), DIMENSION(:,:), ALLOCATABLE :: sort_particles !<
8045
8046	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'start' )
8047	IF ( interpolation_trilinear ) THEN
8048	DO ip = nxl, nxr
8049	DO jp = nys, nyn
8050	DO kp = nzb+1, nzt
8051	number_of_particles = prt_count(kp,jp,ip)
8052	IF ( number_of_particles <= 0 ) CYCLE
8053	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8054	nn = 0
8055	sort_count = 0
8056	ALLOCATE( sort_particles(number_of_particles, 0:7) )
8057
8058	DO n = 1, number_of_particles
8059	sort_index = 0
8060
8061	IF ( particles(n)%particle_mask ) THEN
8062	nn = nn + 1
8063	!
8064	!-- Sorting particles with a binary scheme
8065	!-- sort_index=111_2=7_10 -> particle at the left,south,bottom subgridbox
8066	!-- sort_index=000_2=0_10 -> particle at the right,north,top subgridbox
8067	!-- For this the center of the gridbox is calculated
8068	i = (particles(n)%x + 0.5_wp * dx) * ddx
8069	j = (particles(n)%y + 0.5_wp * dy) * ddy
8070
8071	IF ( i == ip ) sort_index = sort_index + 4
8072	IF ( j == jp ) sort_index = sort_index + 2
8073	IF ( zu(kp) > particles(n)%z ) sort_index = sort_index + 1
8074
8075	sort_count(sort_index) = sort_count(sort_index) + 1
8076	m = sort_count(sort_index)
8077	sort_particles(m,sort_index) = particles(n)
8078	sort_particles(m,sort_index)%block_nr = sort_index
8079	ENDIF
8080	ENDDO
8081	!
8082	!-- Delete and resort particles by overwritting and set
8083	!-- the number_of_particles to the actual value.
8084	nn = 0
8085	DO is = 0,7
8086	grid_particles(kp,jp,ip)%start_index(is) = nn + 1
8087	DO n = 1,sort_count(is)
8088	nn = nn + 1
8089	particles(nn) = sort_particles(n,is)
8090	ENDDO
8091	grid_particles(kp,jp,ip)%end_index(is) = nn
8092	ENDDO
8093
8094	number_of_particles = nn
8095	prt_count(kp,jp,ip) = number_of_particles
8096	DEALLOCATE(sort_particles)
8097	ENDDO
8098	ENDDO
8099	ENDDO
8100
8101	!-- In case of the simple interpolation method the particles must not
8102	!-- be sorted in subboxes. Particles marked for deletion however, must be
8103	!-- deleted and number of particles must be recalculated as it is also
8104	!-- done for the trilinear particle advection interpolation method.
8105	ELSE
8106
8107	DO ip = nxl, nxr
8108	DO jp = nys, nyn
8109	DO kp = nzb+1, nzt
8110
8111	number_of_particles = prt_count(kp,jp,ip)
8112	IF ( number_of_particles <= 0 ) CYCLE
8113	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8114	!
8115	!-- Repack particles array, i.e. delete particles and recalculate
8116	!-- number of particles
8117	CALL lpm_pack
8118	prt_count(kp,jp,ip) = number_of_particles
8119	ENDDO
8120	ENDDO
8121	ENDDO
8122	ENDIF
8123	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'stop' )
8124
8125	END SUBROUTINE lpm_sort_and_delete
8126
8127
8128	!------------------------------------------------------------------------------!
8129	! Description:
8130	! ------------
8131	!> Move all particles not marked for deletion to lowest indices (packing)
8132	!------------------------------------------------------------------------------!
8133	SUBROUTINE lpm_pack
8134
8135	INTEGER(iwp) :: n !<
8136	INTEGER(iwp) :: nn !<
8137	!
8138	!-- Find out elements marked for deletion and move data from highest index
8139	!-- values to these free indices
8140	nn = number_of_particles
8141
8142	DO WHILE ( .NOT. particles(nn)%particle_mask )
8143	nn = nn-1
8144	IF ( nn == 0 ) EXIT
8145	ENDDO
8146
8147	IF ( nn > 0 ) THEN
8148	DO n = 1, number_of_particles
8149	IF ( .NOT. particles(n)%particle_mask ) THEN
8150	particles(n) = particles(nn)
8151	nn = nn - 1
8152	DO WHILE ( .NOT. particles(nn)%particle_mask )
8153	nn = nn-1
8154	IF ( n == nn ) EXIT
8155	ENDDO
8156	ENDIF
8157	IF ( n == nn ) EXIT
8158	ENDDO
8159	ENDIF
8160
8161	!
8162	!-- The number of deleted particles has been determined in routines
8163	!-- lpm_boundary_conds, lpm_droplet_collision, and lpm_exchange_horiz
8164	number_of_particles = nn
8165
8166	END SUBROUTINE lpm_pack
8167
8168
8169	!------------------------------------------------------------------------------!
8170	! Description:
8171	! ------------
8172	!> Sort particles in each sub-grid box into two groups: particles that already
8173	!> completed the LES timestep, and particles that need further timestepping to
8174	!> complete the LES timestep.
8175	!------------------------------------------------------------------------------!
8176	SUBROUTINE lpm_sort_timeloop_done
8177
8178	INTEGER(iwp) :: end_index !< particle end index for each sub-box
8179	INTEGER(iwp) :: i !< index of particle grid box in x-direction
8180	INTEGER(iwp) :: j !< index of particle grid box in y-direction
8181	INTEGER(iwp) :: k !< index of particle grid box in z-direction
8182	INTEGER(iwp) :: n !< running index for number of particles
8183	INTEGER(iwp) :: nb !< index of subgrid boux
8184	INTEGER(iwp) :: nf !< indices for particles in each sub-box that already finalized their substeps
8185	INTEGER(iwp) :: nnf !< indices for particles in each sub-box that need further treatment
8186	INTEGER(iwp) :: num_finalized !< number of particles in each sub-box that already finalized their substeps
8187	INTEGER(iwp) :: start_index !< particle start index for each sub-box
8188
8189	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: sort_particles !< temporary particle array
8190
8191	DO i = nxl, nxr
8192	DO j = nys, nyn
8193	DO k = nzb+1, nzt
8194
8195	number_of_particles = prt_count(k,j,i)
8196	IF ( number_of_particles <= 0 ) CYCLE
8197	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
8198
8199	DO nb = 0, 7
8200	!
8201	!-- Obtain start and end index for each subgrid box
8202	start_index = grid_particles(k,j,i)%start_index(nb)
8203	end_index = grid_particles(k,j,i)%end_index(nb)
8204	!
8205	!-- Allocate temporary array used for sorting.
8206	ALLOCATE( sort_particles(start_index:end_index) )
8207	!
8208	!-- Determine number of particles already completed the LES
8209	!-- timestep, and write them into a temporary array.
8210	nf = start_index
8211	num_finalized = 0
8212	DO n = start_index, end_index
8213	IF ( dt_3d - particles(n)%dt_sum < 1E-8_wp ) THEN
8214	sort_particles(nf) = particles(n)
8215	nf = nf + 1
8216	num_finalized = num_finalized + 1
8217	ENDIF
8218	ENDDO
8219	!
8220	!-- Determine number of particles that not completed the LES
8221	!-- timestep, and write them into a temporary array.
8222	nnf = nf
8223	DO n = start_index, end_index
8224	IF ( dt_3d - particles(n)%dt_sum > 1E-8_wp ) THEN
8225	sort_particles(nnf) = particles(n)
8226	nnf = nnf + 1
8227	ENDIF
8228	ENDDO
8229	!
8230	!-- Write back sorted particles
8231	particles(start_index:end_index) = &
8232	sort_particles(start_index:end_index)
8233	!
8234	!-- Determine updated start_index, used to masked already
8235	!-- completed particles.
8236	grid_particles(k,j,i)%start_index(nb) = &
8237	grid_particles(k,j,i)%start_index(nb) &
8238	+ num_finalized
8239	!
8240	!-- Deallocate dummy array
8241	DEALLOCATE ( sort_particles )
8242	!
8243	!-- Finally, if number of non-completed particles is non zero
8244	!-- in any of the sub-boxes, set control flag appropriately.
8245	IF ( nnf > nf ) &
8246	grid_particles(k,j,i)%time_loop_done = .FALSE.
8247
8248	ENDDO
8249	ENDDO
8250	ENDDO
8251	ENDDO
8252
8253	END SUBROUTINE lpm_sort_timeloop_done
8254
8255	END MODULE lagrangian_particle_model_mod

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