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source: palm/trunk/SOURCE/lagrangian_particle_model_mod.f90 @ 4121

Last change on this file since 4121 was 4121, checked in by schwenkel, 6 years ago
Implementation of an simple method for interpolating the velocities to particle position
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File size: 350.1 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 4121 2019-07-26 10:01:22Z schwenkel $
27	! Implementation of an simple method for interpolating the velocities to
28	! particle position
29	!
30	! 4114 2019-07-23 14:09:27Z schwenkel
31	! Bugfix: Added working precision for if statement
32	!
33	! 4054 2019-06-27 07:42:18Z raasch
34	! bugfix for calculating the minimum particle time step
35	!
36	! 4044 2019-06-19 12:28:27Z schwenkel
37	! Bugfix in case of grid strecting: corrected calculation of k-Index
38	!
39	! 4043 2019-06-18 16:59:00Z schwenkel
40	! Remove min_nr_particle, Add lpm_droplet_interactions_ptq into module
41	!
42	! 4028 2019-06-13 12:21:37Z schwenkel
43	! Further modularization of particle code components
44	!
45	! 4020 2019-06-06 14:57:48Z schwenkel
46	! Removing submodules
47	!
48	! 4018 2019-06-06 13:41:50Z eckhard
49	! Bugfix for former revision
50	!
51	! 4017 2019-06-06 12:16:46Z schwenkel
52	! Modularization of all lagrangian particle model code components
53	!
54	! 3655 2019-01-07 16:51:22Z knoop
55	! bugfix to guarantee correct particle releases in case that the release
56	! interval is smaller than the model timestep
57	!
58	! 2801 2018-02-14 16:01:55Z thiele
59	! Changed lpm from subroutine to module.
60	! Introduce particle transfer in nested models.
61	!
62	! 2718 2018-01-02 08:49:38Z maronga
63	! Corrected "Former revisions" section
64	!
65	! 2701 2017-12-15 15:40:50Z suehring
66	! Changes from last commit documented
67	!
68	! 2698 2017-12-14 18:46:24Z suehring
69	! Grid indices passed to lpm_boundary_conds. (responsible Philipp Thiele)
70	!
71	! 2696 2017-12-14 17:12:51Z kanani
72	! Change in file header (GPL part)
73	!
74	! 2606 2017-11-10 10:36:31Z schwenkel
75	! Changed particle box locations: center of particle box now coincides
76	! with scalar grid point of same index.
77	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
78	! lpm_pack_all_arrays -> lpm_sort_and_delete, lpm_pack_arrays -> lpm_pack
79	! lpm_sort -> lpm_sort_timeloop_done
80	!
81	! 2418 2017-09-06 15:24:24Z suehring
82	! Major bugfixes in modeling SGS particle speeds (since revision 1359).
83	! Particle sorting added to distinguish between already completed and
84	! non-completed particles.
85	!
86	! 2263 2017-06-08 14:59:01Z schwenkel
87	! Implemented splitting and merging algorithm
88	!
89	! 2233 2017-05-30 18:08:54Z suehring
90	!
91	! 2232 2017-05-30 17:47:52Z suehring
92	! Adjustments to new topography concept
93	!
94	! 2000 2016-08-20 18:09:15Z knoop
95	! Forced header and separation lines into 80 columns
96	!
97	! 1936 2016-06-13 13:37:44Z suehring
98	! Call routine for deallocation of unused memory.
99	! Formatting adjustments
100	!
101	! 1929 2016-06-09 16:25:25Z suehring
102	! Call wall boundary conditions only if particles are in the vertical range of
103	! topography.
104	!
105	! 1822 2016-04-07 07:49:42Z hoffmann
106	! Tails removed.
107	!
108	! Initialization of sgs model not necessary for the use of cloud_droplets and
109	! use_sgs_for_particles.
110	!
111	! lpm_release_set integrated.
112	!
113	! Unused variabled removed.
114	!
115	! 1682 2015-10-07 23:56:08Z knoop
116	! Code annotations made doxygen readable
117	!
118	! 1416 2014-06-04 16:04:03Z suehring
119	! user_lpm_advec is called for each gridpoint.
120	! Bugfix: in order to prevent an infinite loop, time_loop_done is set .TRUE.
121	! at the head of the do-loop.
122	!
123	! 1359 2014-04-11 17:15:14Z hoffmann
124	! New particle structure integrated.
125	! Kind definition added to all floating point numbers.
126	!
127	! 1320 2014-03-20 08:40:49Z raasch
128	! ONLY-attribute added to USE-statements,
129	! kind-parameters added to all INTEGER and REAL declaration statements,
130	! kinds are defined in new module kinds,
131	! revision history before 2012 removed,
132	! comment fields (!:) to be used for variable explanations added to
133	! all variable declaration statements
134	!
135	! 1318 2014-03-17 13:35:16Z raasch
136	! module interfaces removed
137	!
138	! 1036 2012-10-22 13:43:42Z raasch
139	! code put under GPL (PALM 3.9)
140	!
141	! 851 2012-03-15 14:32:58Z raasch
142	! Bugfix: resetting of particle_mask and tail mask moved from routine
143	! lpm_exchange_horiz to here (end of sub-timestep loop)
144	!
145	! 849 2012-03-15 10:35:09Z raasch
146	! original routine advec_particles split into several subroutines and renamed
147	! lpm
148	!
149	! 831 2012-02-22 00:29:39Z raasch
150	! thermal_conductivity_l and diff_coeff_l now depend on temperature and
151	! pressure
152	!
153	! 828 2012-02-21 12:00:36Z raasch
154	! fast hall/wang kernels with fixed radius/dissipation classes added,
155	! particle feature color renamed class, routine colker renamed
156	! recalculate_kernel,
157	! lower limit for droplet radius changed from 1E-7 to 1E-8
158	!
159	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
160	!
161	! 825 2012-02-19 03:03:44Z raasch
162	! droplet growth by condensation may include curvature and solution effects,
163	! initialisation of temporary particle array for resorting removed,
164	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
165	! module wang_kernel_mod renamed lpm_collision_kernels_mod,
166	! wang_collision_kernel renamed wang_kernel
167	!
168	!
169	! Revision 1.1 1999/11/25 16:16:06 raasch
170	! Initial revision
171	!
172	!
173	! Description:
174	! ------------
175	!>
176	!------------------------------------------------------------------------------!
177	MODULE lagrangian_particle_model_mod
178
179	USE, INTRINSIC :: ISO_C_BINDING
180
181	USE arrays_3d, &
182	ONLY: de_dx, de_dy, de_dz, dzw, zu, zw, ql_c, ql_v, ql_vp, hyp, &
183	pt, q, exner, ql, diss, e, u, v, w, km, ql_1, ql_2, pt_p, q_p, &
184	d_exner, u_p, v_p, w_p
185
186	USE averaging, &
187	ONLY: ql_c_av, pr_av, pc_av, ql_vp_av, ql_v_av
188
189	USE basic_constants_and_equations_mod, &
190	ONLY: molecular_weight_of_solute, molecular_weight_of_water, magnus, &
191	pi, rd_d_rv, rho_l, r_v, rho_s, vanthoff, l_v, kappa, g, lv_d_cp
192
193	USE control_parameters, &
194	ONLY: bc_dirichlet_l, bc_dirichlet_n, bc_dirichlet_r, bc_dirichlet_s, &
195	cloud_droplets, constant_flux_layer, current_timestep_number, &
196	dt_3d, dt_3d_reached, humidity, &
197	dt_3d_reached_l, dt_dopts, dz, initializing_actions, &
198	message_string, molecular_viscosity, ocean_mode, &
199	particle_maximum_age, iran, &
200	simulated_time, topography, dopts_time_count, &
201	time_since_reference_point, rho_surface, u_gtrans, v_gtrans, &
202	dz_stretch_level, dz_stretch_level_start
203
204	USE cpulog, &
205	ONLY: cpu_log, log_point, log_point_s
206
207	USE indices, &
208	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
209	nzb_max, nzt, wall_flags_0,nbgp, ngp_2dh_outer
210
211	USE kinds
212
213	USE pegrid
214
215	USE particle_attributes
216
217	USE pmc_particle_interface, &
218	ONLY: pmcp_c_get_particle_from_parent, pmcp_p_fill_particle_win, &
219	pmcp_c_send_particle_to_parent, pmcp_p_empty_particle_win, &
220	pmcp_p_delete_particles_in_fine_grid_area, pmcp_g_init, &
221	pmcp_g_print_number_of_particles
222
223	USE pmc_interface, &
224	ONLY: nested_run
225
226	USE grid_variables, &
227	ONLY: ddx, dx, ddy, dy
228
229	USE netcdf_interface, &
230	ONLY: netcdf_data_format, netcdf_deflate, dopts_num, id_set_pts, &
231	id_var_dopts, id_var_time_pts, nc_stat, &
232	netcdf_handle_error
233
234	USE random_function_mod, &
235	ONLY: random_function
236
237	USE statistics, &
238	ONLY: hom
239
240	USE surface_mod, &
241	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h,&
242	bc_h
243
244	#if defined( __parallel ) && !defined( __mpifh )
245	USE MPI
246	#endif
247
248	#if defined( __parallel ) && defined( __mpifh )
249	INCLUDE "mpif.h"
250	#endif
251
252	#if defined( __netcdf )
253	USE NETCDF
254	#endif
255
256
257	USE arrays_3d, &
258	ONLY:
259
260	USE indices, &
261	ONLY: nxl, nxr, nyn, nys, nzb, nzt, wall_flags_0
262
263	USE kinds
264
265	USE pegrid
266
267	IMPLICIT NONE
268
269	CHARACTER(LEN=15) :: aero_species = 'nacl' !< aerosol species
270	CHARACTER(LEN=15) :: aero_type = 'maritime' !< aerosol type
271	CHARACTER(LEN=15) :: bc_par_lr = 'cyclic' !< left/right boundary condition
272	CHARACTER(LEN=15) :: bc_par_ns = 'cyclic' !< north/south boundary condition
273	CHARACTER(LEN=15) :: bc_par_b = 'reflect' !< bottom boundary condition
274	CHARACTER(LEN=15) :: bc_par_t = 'absorb' !< top boundary condition
275	CHARACTER(LEN=15) :: collision_kernel = 'none' !< collision kernel
276
277	CHARACTER(LEN=5) :: splitting_function = 'gamma' !< function for calculation critical weighting factor
278	CHARACTER(LEN=5) :: splitting_mode = 'const' !< splitting mode
279
280	CHARACTER(LEN=25) :: particle_interpolation = 'trilinear' !< interpolation method for calculatin the particle
281
282	INTEGER(iwp) :: deleted_particles = 0 !< number of deleted particles per time step
283	INTEGER(iwp) :: i_splitting_mode !< dummy for splitting mode
284	INTEGER(iwp) :: iran_part = -1234567 !< number for random generator
285	INTEGER(iwp) :: max_number_particles_per_gridbox = 100 !< namelist parameter (see documentation)
286	INTEGER(iwp) :: isf !< dummy for splitting function
287	INTEGER(iwp) :: number_particles_per_gridbox = -1 !< namelist parameter (see documentation)
288	INTEGER(iwp) :: number_of_sublayers = 20 !< number of sublayers for particle velocities betwenn surface and first grid level
289	INTEGER(iwp) :: offset_ocean_nzt = 0 !< in case of oceans runs, the vertical index calculations need an offset
290	INTEGER(iwp) :: offset_ocean_nzt_m1 = 0 !< in case of oceans runs, the vertical index calculations need an offset
291	INTEGER(iwp) :: particles_per_point = 1 !< namelist parameter (see documentation)
292	INTEGER(iwp) :: radius_classes = 20 !< namelist parameter (see documentation)
293	INTEGER(iwp) :: splitting_factor = 2 !< namelist parameter (see documentation)
294	INTEGER(iwp) :: splitting_factor_max = 5 !< namelist parameter (see documentation)
295	INTEGER(iwp) :: step_dealloc = 100 !< namelist parameter (see documentation)
296	INTEGER(iwp) :: total_number_of_particles !< total number of particles in the whole model domain
297	INTEGER(iwp) :: trlp_count_sum !< parameter for particle exchange of PEs
298	INTEGER(iwp) :: trlp_count_recv_sum !< parameter for particle exchange of PEs
299	INTEGER(iwp) :: trrp_count_sum !< parameter for particle exchange of PEs
300	INTEGER(iwp) :: trrp_count_recv_sum !< parameter for particle exchange of PEs
301	INTEGER(iwp) :: trsp_count_sum !< parameter for particle exchange of PEs
302	INTEGER(iwp) :: trsp_count_recv_sum !< parameter for particle exchange of PEs
303	INTEGER(iwp) :: trnp_count_sum !< parameter for particle exchange of PEs
304	INTEGER(iwp) :: trnp_count_recv_sum !< parameter for particle exchange of PEs
305
306	LOGICAL :: lagrangian_particle_model = .FALSE. !< namelist parameter (see documentation)
307	LOGICAL :: curvature_solution_effects = .FALSE. !< namelist parameter (see documentation)
308	LOGICAL :: deallocate_memory = .TRUE. !< namelist parameter (see documentation)
309	LOGICAL :: hall_kernel = .FALSE. !< flag for collision kernel
310	LOGICAL :: merging = .FALSE. !< namelist parameter (see documentation)
311	LOGICAL :: random_start_position = .FALSE. !< namelist parameter (see documentation)
312	LOGICAL :: read_particles_from_restartfile = .TRUE. !< namelist parameter (see documentation)
313	LOGICAL :: seed_follows_topography = .FALSE. !< namelist parameter (see documentation)
314	LOGICAL :: splitting = .FALSE. !< namelist parameter (see documentation)
315	LOGICAL :: use_kernel_tables = .FALSE. !< parameter, which turns on the use of precalculated collision kernels
316	LOGICAL :: write_particle_statistics = .FALSE. !< namelist parameter (see documentation)
317
318	LOGICAL, DIMENSION(max_number_of_particle_groups) :: vertical_particle_advection = .TRUE. !< Switch for vertical particle transport
319
320	REAL(wp) :: aero_weight = 1.0_wp !< namelist parameter (see documentation)
321	REAL(wp) :: dt_min_part = 0.0002_wp !< minimum particle time step when SGS velocities are used (s)
322	REAL(wp) :: dt_prel = 9999999.9_wp !< namelist parameter (see documentation)
323	REAL(wp) :: dt_write_particle_data = 9999999.9_wp !< namelist parameter (see documentation)
324	REAL(wp) :: end_time_prel = 9999999.9_wp !< namelist parameter (see documentation)
325	REAL(wp) :: initial_weighting_factor = 1.0_wp !< namelist parameter (see documentation)
326	REAL(wp) :: last_particle_release_time = 0.0_wp !< last time of particle release
327	REAL(wp) :: log_sigma(3) = 1.0_wp !< namelist parameter (see documentation)
328	REAL(wp) :: na(3) = 0.0_wp !< namelist parameter (see documentation)
329	REAL(wp) :: number_concentration = -1.0_wp !< namelist parameter (see documentation)
330	REAL(wp) :: radius_merge = 1.0E-7_wp !< namelist parameter (see documentation)
331	REAL(wp) :: radius_split = 40.0E-6_wp !< namelist parameter (see documentation)
332	REAL(wp) :: rm(3) = 1.0E-6_wp !< namelist parameter (see documentation)
333	REAL(wp) :: sgs_wf_part !< parameter for sgs
334	REAL(wp) :: time_write_particle_data = 0.0_wp !< write particle data at current time on file
335	REAL(wp) :: weight_factor_merge = -1.0_wp !< namelist parameter (see documentation)
336	REAL(wp) :: weight_factor_split = -1.0_wp !< namelist parameter (see documentation)
337	REAL(wp) :: z0_av_global !< horizontal mean value of z0
338
339	REAL(wp) :: rclass_lbound !<
340	REAL(wp) :: rclass_ubound !<
341
342	REAL(wp), PARAMETER :: c_0 = 3.0_wp !< parameter for lagrangian timescale
343
344	REAL(wp), DIMENSION(max_number_of_particle_groups) :: density_ratio = 9999999.9_wp !< namelist parameter (see documentation)
345	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdx = 9999999.9_wp !< namelist parameter (see documentation)
346	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdy = 9999999.9_wp !< namelist parameter (see documentation)
347	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdz = 9999999.9_wp !< namelist parameter (see documentation)
348	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psb = 9999999.9_wp !< namelist parameter (see documentation)
349	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psl = 9999999.9_wp !< namelist parameter (see documentation)
350	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psn = 9999999.9_wp !< namelist parameter (see documentation)
351	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psr = 9999999.9_wp !< namelist parameter (see documentation)
352	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pss = 9999999.9_wp !< namelist parameter (see documentation)
353	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pst = 9999999.9_wp !< namelist parameter (see documentation).
354	REAL(wp), DIMENSION(max_number_of_particle_groups) :: radius = 9999999.9_wp !< namelist parameter (see documentation)
355
356	REAL(wp), DIMENSION(:), ALLOCATABLE :: log_z_z0 !< Precalculate LOG(z/z0)
357
358	INTEGER(iwp), PARAMETER :: NR_2_direction_move = 10000 !<
359	INTEGER(iwp) :: nr_move_north !<
360	INTEGER(iwp) :: nr_move_south !<
361
362	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_north
363	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_south
364
365	REAL(wp) :: epsilon_collision !<
366	REAL(wp) :: urms !<
367
368	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
369	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
370	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
371
372	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
373	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
374	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
375	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
376	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
377
378	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
379
380	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
381	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
382
383	SAVE
384
385	PRIVATE
386
387	PUBLIC lpm_parin, &
388	lpm_header, &
389	lpm_init_arrays,&
390	lpm_init, &
391	lpm_actions, &
392	lpm_data_output_ptseries, &
393	lpm_interaction_droplets_ptq, &
394	lpm_rrd_local_particles, &
395	lpm_wrd_local, &
396	lpm_rrd_global, &
397	lpm_wrd_global, &
398	lpm_rrd_local, &
399	lpm_check_parameters
400
401	PUBLIC lagrangian_particle_model
402
403	INTERFACE lpm_check_parameters
404	MODULE PROCEDURE lpm_check_parameters
405	END INTERFACE lpm_check_parameters
406
407	INTERFACE lpm_parin
408	MODULE PROCEDURE lpm_parin
409	END INTERFACE lpm_parin
410
411	INTERFACE lpm_header
412	MODULE PROCEDURE lpm_header
413	END INTERFACE lpm_header
414
415	INTERFACE lpm_init_arrays
416	MODULE PROCEDURE lpm_init_arrays
417	END INTERFACE lpm_init_arrays
418
419	INTERFACE lpm_init
420	MODULE PROCEDURE lpm_init
421	END INTERFACE lpm_init
422
423	INTERFACE lpm_actions
424	MODULE PROCEDURE lpm_actions
425	END INTERFACE lpm_actions
426
427	INTERFACE lpm_data_output_ptseries
428	MODULE PROCEDURE lpm_data_output_ptseries
429	END INTERFACE
430
431	INTERFACE lpm_rrd_local_particles
432	MODULE PROCEDURE lpm_rrd_local_particles
433	END INTERFACE lpm_rrd_local_particles
434
435	INTERFACE lpm_rrd_global
436	MODULE PROCEDURE lpm_rrd_global
437	END INTERFACE lpm_rrd_global
438
439	INTERFACE lpm_rrd_local
440	MODULE PROCEDURE lpm_rrd_local
441	END INTERFACE lpm_rrd_local
442
443	INTERFACE lpm_wrd_local
444	MODULE PROCEDURE lpm_wrd_local
445	END INTERFACE lpm_wrd_local
446
447	INTERFACE lpm_wrd_global
448	MODULE PROCEDURE lpm_wrd_global
449	END INTERFACE lpm_wrd_global
450
451	INTERFACE lpm_advec
452	MODULE PROCEDURE lpm_advec
453	END INTERFACE lpm_advec
454
455	INTERFACE lpm_calc_liquid_water_content
456	MODULE PROCEDURE lpm_calc_liquid_water_content
457	END INTERFACE
458
459	INTERFACE lpm_interaction_droplets_ptq
460	MODULE PROCEDURE lpm_interaction_droplets_ptq
461	MODULE PROCEDURE lpm_interaction_droplets_ptq_ij
462	END INTERFACE lpm_interaction_droplets_ptq
463
464	INTERFACE lpm_boundary_conds
465	MODULE PROCEDURE lpm_boundary_conds
466	END INTERFACE lpm_boundary_conds
467
468	INTERFACE lpm_droplet_condensation
469	MODULE PROCEDURE lpm_droplet_condensation
470	END INTERFACE
471
472	INTERFACE lpm_droplet_collision
473	MODULE PROCEDURE lpm_droplet_collision
474	END INTERFACE lpm_droplet_collision
475
476	INTERFACE lpm_init_kernels
477	MODULE PROCEDURE lpm_init_kernels
478	END INTERFACE lpm_init_kernels
479
480	INTERFACE lpm_splitting
481	MODULE PROCEDURE lpm_splitting
482	END INTERFACE lpm_splitting
483
484	INTERFACE lpm_merging
485	MODULE PROCEDURE lpm_merging
486	END INTERFACE lpm_merging
487
488	INTERFACE lpm_exchange_horiz
489	MODULE PROCEDURE lpm_exchange_horiz
490	END INTERFACE lpm_exchange_horiz
491
492	INTERFACE lpm_move_particle
493	MODULE PROCEDURE lpm_move_particle
494	END INTERFACE lpm_move_particle
495
496	INTERFACE realloc_particles_array
497	MODULE PROCEDURE realloc_particles_array
498	END INTERFACE realloc_particles_array
499
500	INTERFACE dealloc_particles_array
501	MODULE PROCEDURE dealloc_particles_array
502	END INTERFACE dealloc_particles_array
503
504	INTERFACE lpm_sort_and_delete
505	MODULE PROCEDURE lpm_sort_and_delete
506	END INTERFACE lpm_sort_and_delete
507
508	INTERFACE lpm_sort_timeloop_done
509	MODULE PROCEDURE lpm_sort_timeloop_done
510	END INTERFACE lpm_sort_timeloop_done
511
512	INTERFACE lpm_pack
513	MODULE PROCEDURE lpm_pack
514	END INTERFACE lpm_pack
515
516	CONTAINS
517
518
519	!------------------------------------------------------------------------------!
520	! Description:
521	! ------------
522	!> Parin for &particle_parameters for the Lagrangian particle model
523	!------------------------------------------------------------------------------!
524	SUBROUTINE lpm_parin
525
526	CHARACTER (LEN=80) :: line !<
527
528	NAMELIST /particles_par/ &
529	aero_species, &
530	aero_type, &
531	aero_weight, &
532	alloc_factor, &
533	bc_par_b, &
534	bc_par_lr, &
535	bc_par_ns, &
536	bc_par_t, &
537	collision_kernel, &
538	curvature_solution_effects, &
539	deallocate_memory, &
540	density_ratio, &
541	dissipation_classes, &
542	dt_dopts, &
543	dt_min_part, &
544	dt_prel, &
545	dt_write_particle_data, &
546	end_time_prel, &
547	initial_weighting_factor, &
548	log_sigma, &
549	max_number_particles_per_gridbox, &
550	merging, &
551	na, &
552	number_concentration, &
553	number_of_particle_groups, &
554	number_particles_per_gridbox, &
555	particles_per_point, &
556	particle_advection_start, &
557	particle_interpolation, &
558	particle_maximum_age, &
559	pdx, &
560	pdy, &
561	pdz, &
562	psb, &
563	psl, &
564	psn, &
565	psr, &
566	pss, &
567	pst, &
568	radius, &
569	radius_classes, &
570	radius_merge, &
571	radius_split, &
572	random_start_position, &
573	read_particles_from_restartfile, &
574	rm, &
575	seed_follows_topography, &
576	splitting, &
577	splitting_factor, &
578	splitting_factor_max, &
579	splitting_function, &
580	splitting_mode, &
581	step_dealloc, &
582	use_sgs_for_particles, &
583	vertical_particle_advection, &
584	weight_factor_merge, &
585	weight_factor_split, &
586	write_particle_statistics
587
588	NAMELIST /particle_parameters/ &
589	aero_species, &
590	aero_type, &
591	aero_weight, &
592	alloc_factor, &
593	bc_par_b, &
594	bc_par_lr, &
595	bc_par_ns, &
596	bc_par_t, &
597	collision_kernel, &
598	curvature_solution_effects, &
599	deallocate_memory, &
600	density_ratio, &
601	dissipation_classes, &
602	dt_dopts, &
603	dt_min_part, &
604	dt_prel, &
605	dt_write_particle_data, &
606	end_time_prel, &
607	initial_weighting_factor, &
608	log_sigma, &
609	max_number_particles_per_gridbox, &
610	merging, &
611	na, &
612	number_concentration, &
613	number_of_particle_groups, &
614	number_particles_per_gridbox, &
615	particles_per_point, &
616	particle_advection_start, &
617	particle_interpolation, &
618	particle_maximum_age, &
619	pdx, &
620	pdy, &
621	pdz, &
622	psb, &
623	psl, &
624	psn, &
625	psr, &
626	pss, &
627	pst, &
628	radius, &
629	radius_classes, &
630	radius_merge, &
631	radius_split, &
632	random_start_position, &
633	read_particles_from_restartfile, &
634	rm, &
635	seed_follows_topography, &
636	splitting, &
637	splitting_factor, &
638	splitting_factor_max, &
639	splitting_function, &
640	splitting_mode, &
641	step_dealloc, &
642	use_sgs_for_particles, &
643	vertical_particle_advection, &
644	weight_factor_merge, &
645	weight_factor_split, &
646	write_particle_statistics
647
648	!
649	!-- Position the namelist-file at the beginning (it was already opened in
650	!-- parin), search for the namelist-group of the package and position the
651	!-- file at this line. Do the same for each optionally used package.
652	line = ' '
653
654	!
655	!-- Try to find particles package
656	REWIND ( 11 )
657	line = ' '
658	DO WHILE ( INDEX( line, '&particle_parameters' ) == 0 )
659	READ ( 11, '(A)', END=12 ) line
660	ENDDO
661	BACKSPACE ( 11 )
662	!
663	!-- Read user-defined namelist
664	READ ( 11, particle_parameters, ERR = 10 )
665	!
666	!-- Set flag that indicates that particles are switched on
667	particle_advection = .TRUE.
668
669	GOTO 14
670
671	10 BACKSPACE( 11 )
672	READ( 11 , '(A)') line
673	CALL parin_fail_message( 'particle_parameters', line )
674	!
675	!-- Try to find particles package (old namelist)
676	12 REWIND ( 11 )
677	line = ' '
678	DO WHILE ( INDEX( line, '&particles_par' ) == 0 )
679	READ ( 11, '(A)', END=14 ) line
680	ENDDO
681	BACKSPACE ( 11 )
682	!
683	!-- Read user-defined namelist
684	READ ( 11, particles_par, ERR = 13, END = 14 )
685
686	message_string = 'namelist particles_par is deprecated and will be ' // &
687	'removed in near future. Please use namelist ' // &
688	'particle_parameters instead'
689	CALL message( 'package_parin', 'PA0487', 0, 1, 0, 6, 0 )
690
691	!
692	!-- Set flag that indicates that particles are switched on
693	particle_advection = .TRUE.
694
695	GOTO 14
696
697	13 BACKSPACE( 11 )
698	READ( 11 , '(A)') line
699	CALL parin_fail_message( 'particles_par', line )
700
701	14 CONTINUE
702
703	END SUBROUTINE lpm_parin
704
705	!------------------------------------------------------------------------------!
706	! Description:
707	! ------------
708	!> Writes used particle attributes in header file.
709	!------------------------------------------------------------------------------!
710	SUBROUTINE lpm_header ( io )
711
712	CHARACTER (LEN=40) :: output_format !< netcdf format
713
714	INTEGER(iwp) :: i !<
715	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
716
717
718	IF ( humidity .AND. cloud_droplets ) THEN
719	WRITE ( io, 433 )
720	IF ( curvature_solution_effects ) WRITE ( io, 434 )
721	IF ( collision_kernel /= 'none' ) THEN
722	WRITE ( io, 435 ) TRIM( collision_kernel )
723	IF ( collision_kernel(6:9) == 'fast' ) THEN
724	WRITE ( io, 436 ) radius_classes, dissipation_classes
725	ENDIF
726	ELSE
727	WRITE ( io, 437 )
728	ENDIF
729	ENDIF
730
731	IF ( particle_advection ) THEN
732	!
733	!-- Particle attributes
734	WRITE ( io, 480 ) particle_advection_start, dt_prel, bc_par_lr, &
735	bc_par_ns, bc_par_b, bc_par_t, particle_maximum_age, &
736	end_time_prel
737	IF ( use_sgs_for_particles ) WRITE ( io, 488 ) dt_min_part
738	IF ( random_start_position ) WRITE ( io, 481 )
739	IF ( seed_follows_topography ) WRITE ( io, 496 )
740	IF ( particles_per_point > 1 ) WRITE ( io, 489 ) particles_per_point
741	WRITE ( io, 495 ) total_number_of_particles
742	IF ( dt_write_particle_data /= 9999999.9_wp ) THEN
743	WRITE ( io, 485 ) dt_write_particle_data
744	IF ( netcdf_data_format > 1 ) THEN
745	output_format = 'netcdf (64 bit offset) and binary'
746	ELSE
747	output_format = 'netcdf and binary'
748	ENDIF
749	IF ( netcdf_deflate == 0 ) THEN
750	WRITE ( io, 344 ) output_format
751	ELSE
752	WRITE ( io, 354 ) TRIM( output_format ), netcdf_deflate
753	ENDIF
754	ENDIF
755	IF ( dt_dopts /= 9999999.9_wp ) WRITE ( io, 494 ) dt_dopts
756	IF ( write_particle_statistics ) WRITE ( io, 486 )
757
758	WRITE ( io, 487 ) number_of_particle_groups
759
760	DO i = 1, number_of_particle_groups
761	IF ( i == 1 .AND. density_ratio(i) == 9999999.9_wp ) THEN
762	WRITE ( io, 490 ) i, 0.0_wp
763	WRITE ( io, 492 )
764	ELSE
765	WRITE ( io, 490 ) i, radius(i)
766	IF ( density_ratio(i) /= 0.0_wp ) THEN
767	WRITE ( io, 491 ) density_ratio(i)
768	ELSE
769	WRITE ( io, 492 )
770	ENDIF
771	ENDIF
772	WRITE ( io, 493 ) psl(i), psr(i), pss(i), psn(i), psb(i), pst(i), &
773	pdx(i), pdy(i), pdz(i)
774	IF ( .NOT. vertical_particle_advection(i) ) WRITE ( io, 482 )
775	ENDDO
776
777	ENDIF
778
779	344 FORMAT (' Output format: ',A/)
780	354 FORMAT (' Output format: ',A, ' compressed with level: ',I1/)
781
782	433 FORMAT (' Cloud droplets treated explicitly using the Lagrangian part', &
783	'icle model')
784	434 FORMAT (' Curvature and solution effecs are considered for growth of', &
785	' droplets < 1.0E-6 m')
786	435 FORMAT (' Droplet collision is handled by ',A,'-kernel')
787	436 FORMAT (' Fast kernel with fixed radius- and dissipation classes ', &
788	'are used'/ &
789	' number of radius classes: ',I3,' interval ', &
790	'[1.0E-6,2.0E-4] m'/ &
791	' number of dissipation classes: ',I2,' interval ', &
792	'[0,1000] cm2/s3')
793	437 FORMAT (' Droplet collision is switched off')
794
795	480 FORMAT (' Particles:'/ &
796	' ---------'// &
797	' Particle advection is active (switched on at t = ', F7.1, &
798	' s)'/ &
799	' Start of new particle generations every ',F6.1,' s'/ &
800	' Boundary conditions: left/right: ', A, ' north/south: ', A/&
801	' bottom: ', A, ' top: ', A/&
802	' Maximum particle age: ',F9.1,' s'/ &
803	' Advection stopped at t = ',F9.1,' s'/)
804	481 FORMAT (' Particles have random start positions'/)
805	482 FORMAT (' Particles are advected only horizontally'/)
806	485 FORMAT (' Particle data are written on file every ', F9.1, ' s')
807	486 FORMAT (' Particle statistics are written on file'/)
808	487 FORMAT (' Number of particle groups: ',I2/)
809	488 FORMAT (' SGS velocity components are used for particle advection'/ &
810	' minimum timestep for advection:', F8.5/)
811	489 FORMAT (' Number of particles simultaneously released at each ', &
812	'point: ', I5/)
813	490 FORMAT (' Particle group ',I2,':'/ &
814	' Particle radius: ',E10.3, 'm')
815	491 FORMAT (' Particle inertia is activated'/ &
816	' density_ratio (rho_fluid/rho_particle) =',F6.3/)
817	492 FORMAT (' Particles are advected only passively (no inertia)'/)
818	493 FORMAT (' Boundaries of particle source: x:',F8.1,' - ',F8.1,' m'/&
819	' y:',F8.1,' - ',F8.1,' m'/&
820	' z:',F8.1,' - ',F8.1,' m'/&
821	' Particle distances: dx = ',F8.1,' m dy = ',F8.1, &
822	' m dz = ',F8.1,' m'/)
823	494 FORMAT (' Output of particle time series in NetCDF format every ', &
824	F8.2,' s'/)
825	495 FORMAT (' Number of particles in total domain: ',I10/)
826	496 FORMAT (' Initial vertical particle positions are interpreted ', &
827	'as relative to the given topography')
828
829	END SUBROUTINE lpm_header
830
831	!------------------------------------------------------------------------------!
832	! Description:
833	! ------------
834	!> Writes used particle attributes in header file.
835	!------------------------------------------------------------------------------!
836	SUBROUTINE lpm_check_parameters
837
838	!
839	!-- Collision kernels:
840	SELECT CASE ( TRIM( collision_kernel ) )
841
842	CASE ( 'hall', 'hall_fast' )
843	hall_kernel = .TRUE.
844
845	CASE ( 'wang', 'wang_fast' )
846	wang_kernel = .TRUE.
847
848	CASE ( 'none' )
849
850
851	CASE DEFAULT
852	message_string = 'unknown collision kernel: collision_kernel = "' // &
853	TRIM( collision_kernel ) // '"'
854	CALL message( 'check_parameters', 'PA0350', 1, 2, 0, 6, 0 )
855
856	END SELECT
857	IF ( collision_kernel(6:9) == 'fast' ) use_kernel_tables = .TRUE.
858
859	!
860	!-- Subgrid scale velocites with the simple interpolation method for resolved
861	!-- velocites is not implemented for passive particles. However, for cloud
862	!-- it can be combined as the sgs-velocites for active particles are
863	!-- calculated differently, i.e. no subboxes are needed.
864	IF ( .NOT. TRIM(particle_interpolation) == 'trilinear' .AND. &
865	use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
866	message_string = 'subrgrid scale velocities in combination with ' // &
867	'simple interpolation method is not ' // &
868	'implemented'
869	CALL message( 'check_parameters', 'PA0659', 1, 2, 0, 6, 0 )
870	ENDIF
871
872	END SUBROUTINE
873
874	!------------------------------------------------------------------------------!
875	! Description:
876	! ------------
877	!> Initialize arrays for lpm
878	!------------------------------------------------------------------------------!
879	SUBROUTINE lpm_init_arrays
880
881	IF ( cloud_droplets ) THEN
882	!
883	!-- Liquid water content, change in liquid water content
884	ALLOCATE ( ql_1(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
885	ql_2(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
886	!
887	!-- Real volume of particles (with weighting), volume of particles
888	ALLOCATE ( ql_v(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
889	ql_vp(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
890	ENDIF
891
892	!
893	!-- Initial assignment of the pointers
894	IF ( cloud_droplets ) THEN
895	ql => ql_1
896	ql_c => ql_2
897	ENDIF
898
899	END SUBROUTINE lpm_init_arrays
900
901	!------------------------------------------------------------------------------!
902	! Description:
903	! ------------
904	!> Initialize Lagrangian particle model
905	!------------------------------------------------------------------------------!
906	SUBROUTINE lpm_init
907
908	INTEGER(iwp) :: i !<
909	INTEGER(iwp) :: j !<
910	INTEGER(iwp) :: k !<
911
912	REAL(wp) :: div !<
913	REAL(wp) :: height_int !<
914	REAL(wp) :: height_p !<
915	REAL(wp) :: z_p !<
916	REAL(wp) :: z0_av_local !<
917
918	!
919	!-- In case of oceans runs, the vertical index calculations need an offset,
920	!-- because otherwise the k indices will become negative
921	IF ( ocean_mode ) THEN
922	offset_ocean_nzt = nzt
923	offset_ocean_nzt_m1 = nzt - 1
924	ENDIF
925
926	!
927	!-- Define block offsets for dividing a gridcell in 8 sub cells
928	!-- See documentation for List of subgrid boxes
929	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
930	block_offset(0) = block_offset_def ( 0, 0, 0)
931	block_offset(1) = block_offset_def ( 0, 0,-1)
932	block_offset(2) = block_offset_def ( 0,-1, 0)
933	block_offset(3) = block_offset_def ( 0,-1,-1)
934	block_offset(4) = block_offset_def (-1, 0, 0)
935	block_offset(5) = block_offset_def (-1, 0,-1)
936	block_offset(6) = block_offset_def (-1,-1, 0)
937	block_offset(7) = block_offset_def (-1,-1,-1)
938	!
939	!-- Check the number of particle groups.
940	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
941	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
942	max_number_of_particle_groups , &
943	'&number_of_particle_groups reset to ', &
944	max_number_of_particle_groups
945	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
946	number_of_particle_groups = max_number_of_particle_groups
947	ENDIF
948	!
949	!-- Check if downward-facing walls exist. This case, reflection boundary
950	!-- conditions (as well as subgrid-scale velocities) may do not work
951	!-- propably (not realized so far).
952	IF ( surf_def_h(1)%ns >= 1 ) THEN
953	WRITE( message_string, * ) 'Overhanging topography do not work '// &
954	'with particles'
955	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
956
957	ENDIF
958
959	!
960	!-- Set default start positions, if necessary
961	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
962	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
963	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
964	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
965	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
966	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
967
968	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
969	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
970	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
971
972	!
973	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
974	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
975	IF ( number_particles_per_gridbox /= -1 .AND. &
976	number_particles_per_gridbox >= 1 ) THEN
977	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
978	REAL(number_particles_per_gridbox))**0.3333333_wp
979	!
980	!-- Ensure a smooth value (two significant digits) of distance between
981	!-- particles (pdx, pdy, pdz).
982	div = 1000.0_wp
983	DO WHILE ( pdx(1) < div )
984	div = div / 10.0_wp
985	ENDDO
986	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
987	pdy(1) = pdx(1)
988	pdz(1) = pdx(1)
989
990	ENDIF
991
992	DO j = 2, number_of_particle_groups
993	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
994	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
995	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
996	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
997	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
998	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
999	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
1000	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
1001	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
1002	ENDDO
1003
1004	!
1005	!-- Allocate arrays required for calculating particle SGS velocities.
1006	!-- Initialize prefactor required for stoachastic Weil equation.
1007	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
1008	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1009	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1010	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
1011
1012	de_dx = 0.0_wp
1013	de_dy = 0.0_wp
1014	de_dz = 0.0_wp
1015
1016	sgs_wf_part = 1.0_wp / 3.0_wp
1017	ENDIF
1018
1019	!
1020	!-- Allocate array required for logarithmic vertical interpolation of
1021	!-- horizontal particle velocities between the surface and the first vertical
1022	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
1023	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
1024	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
1025	!-- To obtain exact height levels of particles, linear interpolation is applied
1026	!-- (see lpm_advec.f90).
1027	IF ( constant_flux_layer ) THEN
1028
1029	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
1030	z_p = zu(nzb+1) - zw(nzb)
1031
1032	!
1033	!-- Calculate horizontal mean value of z0 used for logartihmic
1034	!-- interpolation. Note: this is not exact for heterogeneous z0.
1035	!-- However, sensitivity studies showed that the effect is
1036	!-- negligible.
1037	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
1038	SUM( surf_usm_h%z0 )
1039	z0_av_global = 0.0_wp
1040
1041	#if defined( __parallel )
1042	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
1043	comm2d, ierr )
1044	#else
1045	z0_av_global = z0_av_local
1046	#endif
1047
1048	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
1049	!
1050	!-- Horizontal wind speed is zero below and at z0
1051	log_z_z0(0) = 0.0_wp
1052	!
1053	!-- Calculate vertical depth of the sublayers
1054	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
1055	!
1056	!-- Precalculate LOG(z/z0)
1057	height_p = z0_av_global
1058	DO k = 1, number_of_sublayers
1059
1060	height_p = height_p + height_int
1061	log_z_z0(k) = LOG( height_p / z0_av_global )
1062
1063	ENDDO
1064
1065	ENDIF
1066
1067	!
1068	!-- Check boundary condition and set internal variables
1069	SELECT CASE ( bc_par_b )
1070
1071	CASE ( 'absorb' )
1072	ibc_par_b = 1
1073
1074	CASE ( 'reflect' )
1075	ibc_par_b = 2
1076
1077	CASE DEFAULT
1078	WRITE( message_string, * ) 'unknown boundary condition ', &
1079	'bc_par_b = "', TRIM( bc_par_b ), '"'
1080	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
1081
1082	END SELECT
1083	SELECT CASE ( bc_par_t )
1084
1085	CASE ( 'absorb' )
1086	ibc_par_t = 1
1087
1088	CASE ( 'reflect' )
1089	ibc_par_t = 2
1090
1091	CASE ( 'nested' )
1092	ibc_par_t = 3
1093
1094	CASE DEFAULT
1095	WRITE( message_string, * ) 'unknown boundary condition ', &
1096	'bc_par_t = "', TRIM( bc_par_t ), '"'
1097	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
1098
1099	END SELECT
1100	SELECT CASE ( bc_par_lr )
1101
1102	CASE ( 'cyclic' )
1103	ibc_par_lr = 0
1104
1105	CASE ( 'absorb' )
1106	ibc_par_lr = 1
1107
1108	CASE ( 'reflect' )
1109	ibc_par_lr = 2
1110
1111	CASE ( 'nested' )
1112	ibc_par_lr = 3
1113
1114	CASE DEFAULT
1115	WRITE( message_string, * ) 'unknown boundary condition ', &
1116	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
1117	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
1118
1119	END SELECT
1120	SELECT CASE ( bc_par_ns )
1121
1122	CASE ( 'cyclic' )
1123	ibc_par_ns = 0
1124
1125	CASE ( 'absorb' )
1126	ibc_par_ns = 1
1127
1128	CASE ( 'reflect' )
1129	ibc_par_ns = 2
1130
1131	CASE ( 'nested' )
1132	ibc_par_ns = 3
1133
1134	CASE DEFAULT
1135	WRITE( message_string, * ) 'unknown boundary condition ', &
1136	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
1137	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
1138
1139	END SELECT
1140	SELECT CASE ( splitting_mode )
1141
1142	CASE ( 'const' )
1143	i_splitting_mode = 1
1144
1145	CASE ( 'cl_av' )
1146	i_splitting_mode = 2
1147
1148	CASE ( 'gb_av' )
1149	i_splitting_mode = 3
1150
1151	CASE DEFAULT
1152	WRITE( message_string, * ) 'unknown splitting_mode = "', &
1153	TRIM( splitting_mode ), '"'
1154	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
1155
1156	END SELECT
1157	SELECT CASE ( splitting_function )
1158
1159	CASE ( 'gamma' )
1160	isf = 1
1161
1162	CASE ( 'log' )
1163	isf = 2
1164
1165	CASE ( 'exp' )
1166	isf = 3
1167
1168	CASE DEFAULT
1169	WRITE( message_string, * ) 'unknown splitting function = "', &
1170	TRIM( splitting_function ), '"'
1171	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
1172
1173	END SELECT
1174	!
1175	!-- Initialize collision kernels
1176	IF ( collision_kernel /= 'none' ) CALL lpm_init_kernels
1177	!
1178	!-- For the first model run of a possible job chain initialize the
1179	!-- particles, otherwise read the particle data from restart file.
1180	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
1181	.AND. read_particles_from_restartfile ) THEN
1182	CALL lpm_rrd_local_particles
1183	ELSE
1184	!
1185	!-- Allocate particle arrays and set attributes of the initial set of
1186	!-- particles, which can be also periodically released at later times.
1187	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1188	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
1189
1190	number_of_particles = 0
1191	prt_count = 0
1192	!
1193	!-- initialize counter for particle IDs
1194	grid_particles%id_counter = 1
1195	!
1196	!-- Initialize all particles with dummy values (otherwise errors may
1197	!-- occur within restart runs). The reason for this is still not clear
1198	!-- and may be presumably caused by errors in the respective user-interface.
1199	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1200	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1201	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1202	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1203	0, 0, 0_idp, .FALSE., -1 )
1204
1205	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
1206	!
1207	!-- Set values for the density ratio and radius for all particle
1208	!-- groups, if necessary
1209	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
1210	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
1211	DO i = 2, number_of_particle_groups
1212	IF ( density_ratio(i) == 9999999.9_wp ) THEN
1213	density_ratio(i) = density_ratio(i-1)
1214	ENDIF
1215	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
1216	ENDDO
1217
1218	DO i = 1, number_of_particle_groups
1219	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
1220	WRITE( message_string, * ) 'particle group #', i, ' has a', &
1221	'density ratio /= 0 but radius = 0'
1222	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
1223	ENDIF
1224	particle_groups(i)%density_ratio = density_ratio(i)
1225	particle_groups(i)%radius = radius(i)
1226	ENDDO
1227	!
1228	!-- Set a seed value for the random number generator to be exclusively
1229	!-- used for the particle code. The generated random numbers should be
1230	!-- different on the different PEs.
1231	iran_part = iran_part + myid
1232	!
1233	!-- Create the particle set, and set the initial particles
1234	CALL lpm_create_particle( phase_init )
1235	last_particle_release_time = particle_advection_start
1236	!
1237	!-- User modification of initial particles
1238	CALL user_lpm_init
1239	!
1240	!-- Open file for statistical informations about particle conditions
1241	IF ( write_particle_statistics ) THEN
1242	CALL check_open( 80 )
1243	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
1244	number_of_particles
1245	CALL close_file( 80 )
1246	ENDIF
1247
1248	ENDIF
1249
1250	IF ( nested_run ) CALL pmcp_g_init
1251	!
1252	!-- To avoid programm abort, assign particles array to the local version of
1253	!-- first grid cell
1254	number_of_particles = prt_count(nzb+1,nys,nxl)
1255	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
1256	!
1257	!-- Formats
1258	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
1259
1260	END SUBROUTINE lpm_init
1261
1262	!------------------------------------------------------------------------------!
1263	! Description:
1264	! ------------
1265	!> Create Lagrangian particles
1266	!------------------------------------------------------------------------------!
1267	SUBROUTINE lpm_create_particle (phase)
1268
1269	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
1270	INTEGER(iwp) :: i !< loop variable ( particle groups )
1271	INTEGER(iwp) :: ip !< index variable along x
1272	INTEGER(iwp) :: j !< loop variable ( particles per point )
1273	INTEGER(iwp) :: jp !< index variable along y
1274	INTEGER(iwp) :: k !< index variable along z
1275	INTEGER(iwp) :: k_surf !< index of surface grid point
1276	INTEGER(iwp) :: kp !< index variable along z
1277	INTEGER(iwp) :: loop_stride !< loop variable for initialization
1278	INTEGER(iwp) :: n !< loop variable ( number of particles )
1279	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
1280
1281	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
1282
1283	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
1284	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
1285
1286	LOGICAL :: first_stride !< flag for initialization
1287
1288	REAL(wp) :: pos_x !< increment for particle position in x
1289	REAL(wp) :: pos_y !< increment for particle position in y
1290	REAL(wp) :: pos_z !< increment for particle position in z
1291	REAL(wp) :: rand_contr !< dummy argument for random position
1292
1293	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
1294
1295	!
1296	!-- Calculate particle positions and store particle attributes, if
1297	!-- particle is situated on this PE
1298	DO loop_stride = 1, 2
1299	first_stride = (loop_stride == 1)
1300	IF ( first_stride ) THEN
1301	local_count = 0 ! count number of particles
1302	ELSE
1303	local_count = prt_count ! Start address of new particles
1304	ENDIF
1305
1306	!
1307	!-- Calculate initial_weighting_factor diagnostically
1308	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
1309	initial_weighting_factor = number_concentration * &
1310	pdx(1) * pdy(1) * pdz(1)
1311	END IF
1312
1313	n = 0
1314	DO i = 1, number_of_particle_groups
1315	pos_z = psb(i)
1316	DO WHILE ( pos_z <= pst(i) )
1317	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
1318	pos_y = pss(i)
1319	DO WHILE ( pos_y <= psn(i) )
1320	IF ( pos_y >= nys * dy .AND. &
1321	pos_y < ( nyn + 1 ) * dy ) THEN
1322	pos_x = psl(i)
1323	xloop: DO WHILE ( pos_x <= psr(i) )
1324	IF ( pos_x >= nxl * dx .AND. &
1325	pos_x < ( nxr + 1) * dx ) THEN
1326	DO j = 1, particles_per_point
1327	n = n + 1
1328	tmp_particle%x = pos_x
1329	tmp_particle%y = pos_y
1330	tmp_particle%z = pos_z
1331	tmp_particle%age = 0.0_wp
1332	tmp_particle%age_m = 0.0_wp
1333	tmp_particle%dt_sum = 0.0_wp
1334	tmp_particle%e_m = 0.0_wp
1335	tmp_particle%rvar1 = 0.0_wp
1336	tmp_particle%rvar2 = 0.0_wp
1337	tmp_particle%rvar3 = 0.0_wp
1338	tmp_particle%speed_x = 0.0_wp
1339	tmp_particle%speed_y = 0.0_wp
1340	tmp_particle%speed_z = 0.0_wp
1341	tmp_particle%origin_x = pos_x
1342	tmp_particle%origin_y = pos_y
1343	tmp_particle%origin_z = pos_z
1344	IF ( curvature_solution_effects ) THEN
1345	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
1346	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
1347	ELSE
1348	tmp_particle%aux1 = 0.0_wp ! free to use
1349	tmp_particle%aux2 = 0.0_wp ! free to use
1350	ENDIF
1351	tmp_particle%radius = particle_groups(i)%radius
1352	tmp_particle%weight_factor = initial_weighting_factor
1353	tmp_particle%class = 1
1354	tmp_particle%group = i
1355	tmp_particle%id = 0_idp
1356	tmp_particle%particle_mask = .TRUE.
1357	tmp_particle%block_nr = -1
1358	!
1359	!-- Determine the grid indices of the particle position
1360	ip = INT( tmp_particle%x * ddx )
1361	jp = INT( tmp_particle%y * ddy )
1362	!
1363	!-- In case of stretching the actual k index is found iteratively
1364	IF ( dz_stretch_level .NE. -9999999.9_wp .OR. &
1365	dz_stretch_level_start(1) .NE. -9999999.9_wp ) THEN
1366	kp = MINLOC( ABS( tmp_particle%z - zu ), DIM = 1 ) - 1
1367	ELSE
1368	kp = INT( tmp_particle%z / dz(1) + 1 + offset_ocean_nzt )
1369	ENDIF
1370	!
1371	!-- Determine surface level. Therefore, check for
1372	!-- upward-facing wall on w-grid.
1373	k_surf = get_topography_top_index_ji( jp, ip, 'w' )
1374	IF ( seed_follows_topography ) THEN
1375	!
1376	!-- Particle height is given relative to topography
1377	kp = kp + k_surf
1378	tmp_particle%z = tmp_particle%z + zw(k_surf)
1379	!-- Skip particle release if particle position is
1380	!-- above model top, or within topography in case
1381	!-- of overhanging structures.
1382	IF ( kp > nzt .OR. &
1383	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
1384	pos_x = pos_x + pdx(i)
1385	CYCLE xloop
1386	ENDIF
1387	!
1388	!-- Skip particle release if particle position is
1389	!-- below surface, or within topography in case
1390	!-- of overhanging structures.
1391	ELSEIF ( .NOT. seed_follows_topography .AND. &
1392	tmp_particle%z <= zw(k_surf) .OR. &
1393	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
1394	THEN
1395	pos_x = pos_x + pdx(i)
1396	CYCLE xloop
1397	ENDIF
1398
1399	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
1400
1401	IF ( .NOT. first_stride ) THEN
1402	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
1403	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
1404	ENDIF
1405	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
1406	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
1407	ENDIF
1408	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
1409	ENDIF
1410	ENDDO
1411	ENDIF
1412	pos_x = pos_x + pdx(i)
1413	ENDDO xloop
1414	ENDIF
1415	pos_y = pos_y + pdy(i)
1416	ENDDO
1417	ENDIF
1418
1419	pos_z = pos_z + pdz(i)
1420	ENDDO
1421	ENDDO
1422
1423	IF ( first_stride ) THEN
1424	DO ip = nxl, nxr
1425	DO jp = nys, nyn
1426	DO kp = nzb+1, nzt
1427	IF ( phase == PHASE_INIT ) THEN
1428	IF ( local_count(kp,jp,ip) > 0 ) THEN
1429	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
1430	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
1431	1 )
1432	ELSE
1433	alloc_size = 1
1434	ENDIF
1435	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
1436	DO n = 1, alloc_size
1437	grid_particles(kp,jp,ip)%particles(n) = zero_particle
1438	ENDDO
1439	ELSEIF ( phase == PHASE_RELEASE ) THEN
1440	IF ( local_count(kp,jp,ip) > 0 ) THEN
1441	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
1442	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
1443	alloc_factor / 100.0_wp ) ), 1 )
1444	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
1445	CALL realloc_particles_array(ip,jp,kp,alloc_size)
1446	ENDIF
1447	ENDIF
1448	ENDIF
1449	ENDDO
1450	ENDDO
1451	ENDDO
1452	ENDIF
1453
1454	ENDDO
1455
1456	local_start = prt_count+1
1457	prt_count = local_count
1458	!
1459	!-- Calculate particle IDs
1460	DO ip = nxl, nxr
1461	DO jp = nys, nyn
1462	DO kp = nzb+1, nzt
1463	number_of_particles = prt_count(kp,jp,ip)
1464	IF ( number_of_particles <= 0 ) CYCLE
1465	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1466
1467	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1468
1469	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
1470	10000_idp*2 kp + 10000_idp * jp + ip
1471	!
1472	!-- Count the number of particles that have been released before
1473	grid_particles(kp,jp,ip)%id_counter = &
1474	grid_particles(kp,jp,ip)%id_counter + 1
1475
1476	ENDDO
1477
1478	ENDDO
1479	ENDDO
1480	ENDDO
1481	!
1482	!-- Initialize aerosol background spectrum
1483	IF ( curvature_solution_effects ) THEN
1484	CALL lpm_init_aerosols(local_start)
1485	ENDIF
1486	!
1487	!-- Add random fluctuation to particle positions.
1488	IF ( random_start_position ) THEN
1489	DO ip = nxl, nxr
1490	DO jp = nys, nyn
1491	DO kp = nzb+1, nzt
1492	number_of_particles = prt_count(kp,jp,ip)
1493	IF ( number_of_particles <= 0 ) CYCLE
1494	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1495	!
1496	!-- Move only new particles. Moreover, limit random fluctuation
1497	!-- in order to prevent that particles move more than one grid box,
1498	!-- which would lead to problems concerning particle exchange
1499	!-- between processors in case pdx/pdy are larger than dx/dy,
1500	!-- respectively.
1501	DO n = local_start(kp,jp,ip), number_of_particles
1502	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
1503	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1504	pdx(particles(n)%group)
1505	particles(n)%x = particles(n)%x + &
1506	MERGE( rand_contr, SIGN( dx, rand_contr ), &
1507	ABS( rand_contr ) < dx &
1508	)
1509	ENDIF
1510	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
1511	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1512	pdy(particles(n)%group)
1513	particles(n)%y = particles(n)%y + &
1514	MERGE( rand_contr, SIGN( dy, rand_contr ), &
1515	ABS( rand_contr ) < dy &
1516	)
1517	ENDIF
1518	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
1519	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1520	pdz(particles(n)%group)
1521	particles(n)%z = particles(n)%z + &
1522	MERGE( rand_contr, SIGN( dzw(kp), rand_contr ), &
1523	ABS( rand_contr ) < dzw(kp) &
1524	)
1525	ENDIF
1526	ENDDO
1527	!
1528	!-- Identify particles located outside the model domain and reflect
1529	!-- or absorb them if necessary.
1530	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
1531	!
1532	!-- Furthermore, remove particles located in topography. Note, as
1533	!-- the particle speed is still zero at this point, wall
1534	!-- reflection boundary conditions will not work in this case.
1535	particles => &
1536	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1537	DO n = local_start(kp,jp,ip), number_of_particles
1538	i = particles(n)%x * ddx
1539	j = particles(n)%y * ddy
1540	k = particles(n)%z / dz(1) + 1 + offset_ocean_nzt
1541	DO WHILE( zw(k) < particles(n)%z )
1542	k = k + 1
1543	ENDDO
1544	DO WHILE( zw(k-1) > particles(n)%z )
1545	k = k - 1
1546	ENDDO
1547	!
1548	!-- Check if particle is within topography
1549	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
1550	particles(n)%particle_mask = .FALSE.
1551	deleted_particles = deleted_particles + 1
1552	ENDIF
1553
1554	ENDDO
1555	ENDDO
1556	ENDDO
1557	ENDDO
1558	!
1559	!-- Exchange particles between grid cells and processors
1560	CALL lpm_move_particle
1561	CALL lpm_exchange_horiz
1562
1563	ENDIF
1564	!
1565	!-- In case of random_start_position, delete particles identified by
1566	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1567	!-- which is needed for a fast interpolation of the LES fields on the particle
1568	!-- position.
1569	CALL lpm_sort_and_delete
1570	!
1571	!-- Determine the current number of particles
1572	DO ip = nxl, nxr
1573	DO jp = nys, nyn
1574	DO kp = nzb+1, nzt
1575	number_of_particles = number_of_particles &
1576	+ prt_count(kp,jp,ip)
1577	ENDDO
1578	ENDDO
1579	ENDDO
1580	!
1581	!-- Calculate the number of particles of the total domain
1582	#if defined( __parallel )
1583	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1584	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1585	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1586	#else
1587	total_number_of_particles = number_of_particles
1588	#endif
1589
1590	RETURN
1591
1592	END SUBROUTINE lpm_create_particle
1593
1594
1595	!------------------------------------------------------------------------------!
1596	! Description:
1597	! ------------
1598	!> This routine initialize the particles as aerosols with physio-chemical
1599	!> properties.
1600	!------------------------------------------------------------------------------!
1601	SUBROUTINE lpm_init_aerosols(local_start)
1602
1603	REAL(wp) :: afactor !< curvature effects
1604	REAL(wp) :: bfactor !< solute effects
1605	REAL(wp) :: dlogr !< logarithmic width of radius bin
1606	REAL(wp) :: e_a !< vapor pressure
1607	REAL(wp) :: e_s !< saturation vapor pressure
1608	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1609	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1610	REAL(wp) :: r_mid !< mean radius of bin
1611	REAL(wp) :: r_l !< left radius of bin
1612	REAL(wp) :: r_r !< right radius of bin
1613	REAL(wp) :: sigma !< surface tension
1614	REAL(wp) :: t_int !< temperature
1615
1616	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1617
1618	INTEGER(iwp) :: n !<
1619	INTEGER(iwp) :: ip !<
1620	INTEGER(iwp) :: jp !<
1621	INTEGER(iwp) :: kp !<
1622
1623	!
1624	!-- Set constants for different aerosol species
1625	IF ( TRIM(aero_species) .EQ. 'nacl' ) THEN
1626	molecular_weight_of_solute = 0.05844_wp
1627	rho_s = 2165.0_wp
1628	vanthoff = 2.0_wp
1629	ELSEIF ( TRIM(aero_species) .EQ. 'c3h4o4' ) THEN
1630	molecular_weight_of_solute = 0.10406_wp
1631	rho_s = 1600.0_wp
1632	vanthoff = 1.37_wp
1633	ELSEIF ( TRIM(aero_species) .EQ. 'nh4o3' ) THEN
1634	molecular_weight_of_solute = 0.08004_wp
1635	rho_s = 1720.0_wp
1636	vanthoff = 2.31_wp
1637	ELSE
1638	WRITE( message_string, * ) 'unknown aerosol species ', &
1639	'aero_species = "', TRIM( aero_species ), '"'
1640	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1641	ENDIF
1642	!
1643	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1644	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1645	IF ( TRIM(aero_type) .EQ. 'polar' ) THEN
1646	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6_wp
1647	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6_wp
1648	log_sigma = (/ 0.245, 0.300, 0.291 /)
1649	ELSEIF ( TRIM(aero_type) .EQ. 'background' ) THEN
1650	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6_wp
1651	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6_wp
1652	log_sigma = (/ 0.645, 0.253, 0.425 /)
1653	ELSEIF ( TRIM(aero_type) .EQ. 'maritime' ) THEN
1654	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6_wp
1655	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6_wp
1656	log_sigma = (/ 0.657, 0.210, 0.396 /)
1657	ELSEIF ( TRIM(aero_type) .EQ. 'continental' ) THEN
1658	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6_wp
1659	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6_wp
1660	log_sigma = (/ 0.161, 0.217, 0.380 /)
1661	ELSEIF ( TRIM(aero_type) .EQ. 'desert' ) THEN
1662	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6_wp
1663	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6_wp
1664	log_sigma = (/ 0.247, 0.770, 0.438 /)
1665	ELSEIF ( TRIM(aero_type) .EQ. 'rural' ) THEN
1666	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6_wp
1667	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6_wp
1668	log_sigma = (/ 0.225, 0.557, 0.266 /)
1669	ELSEIF ( TRIM(aero_type) .EQ. 'urban' ) THEN
1670	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6_wp
1671	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6_wp
1672	log_sigma = (/ 0.245, 0.666, 0.337 /)
1673	ELSEIF ( TRIM(aero_type) .EQ. 'user' ) THEN
1674	CONTINUE
1675	ELSE
1676	WRITE( message_string, * ) 'unknown aerosol type ', &
1677	'aero_type = "', TRIM( aero_type ), '"'
1678	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1679	ENDIF
1680
1681	DO ip = nxl, nxr
1682	DO jp = nys, nyn
1683	DO kp = nzb+1, nzt
1684
1685	number_of_particles = prt_count(kp,jp,ip)
1686	IF ( number_of_particles <= 0 ) CYCLE
1687	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1688
1689	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1690	!
1691	!-- Initialize the aerosols with a predefined spectral distribution
1692	!-- of the dry radius (logarithmically increasing bins) and a varying
1693	!-- weighting factor
1694	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1695
1696	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1697	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1698	r_mid = SQRT( r_l * r_r )
1699
1700	particles(n)%aux1 = r_mid
1701	particles(n)%weight_factor = &
1702	( na(1) / ( SQRT( 2.0_wp * pi ) * log_sigma(1) ) * &
1703	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0_wp log_sigma(1)**2 ) ) + &
1704	na(2) / ( SQRT( 2.0_wp * pi ) * log_sigma(2) ) * &
1705	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0_wp log_sigma(2)**2 ) ) + &
1706	na(3) / ( SQRT( 2.0_wp * pi ) * log_sigma(3) ) * &
1707	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0_wp log_sigma(3)**2 ) ) &
1708	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dzw(kp) )
1709
1710	!
1711	!-- Multiply weight_factor with the namelist parameter aero_weight
1712	!-- to increase or decrease the number of simulated aerosols
1713	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1714
1715	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1716	.GT. random_function( iran_part ) ) THEN
1717	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0_wp
1718	ELSE
1719	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1720	ENDIF
1721	!
1722	!-- Unnecessary particles will be deleted
1723	IF ( particles(n)%weight_factor .LE. 0.0_wp ) particles(n)%particle_mask = .FALSE.
1724
1725	ENDDO
1726	!
1727	!-- Set particle radius to equilibrium radius based on the environmental
1728	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1729	!-- the sometimes lengthy growth toward their equilibrium radius within
1730	!-- the simulation.
1731	t_int = pt(kp,jp,ip) * exner(kp)
1732
1733	e_s = magnus( t_int )
1734	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + rd_d_rv )
1735
1736	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1737	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1738
1739	bfactor = vanthoff * molecular_weight_of_water * &
1740	rho_s / ( molecular_weight_of_solute * rho_l )
1741	!
1742	!-- The formula is only valid for subsaturated environments. For
1743	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1744	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1745
1746	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1747	!
1748	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1749	!-- Curry (2007, JGR)
1750	particles(n)%radius = bfactor*0.3333333_wp &
1751	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1752	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1753	particles(n)%aux1 ) ) / &
1754	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1755	)
1756
1757	ENDDO
1758
1759	ENDDO
1760	ENDDO
1761	ENDDO
1762
1763	END SUBROUTINE lpm_init_aerosols
1764
1765
1766	!------------------------------------------------------------------------------!
1767	! Description:
1768	! ------------
1769	!> Calculates quantities required for considering the SGS velocity fluctuations
1770	!> in the particle transport by a stochastic approach. The respective
1771	!> quantities are: SGS-TKE gradients and horizontally averaged profiles of the
1772	!> SGS TKE and the resolved-scale velocity variances.
1773	!------------------------------------------------------------------------------!
1774	SUBROUTINE lpm_init_sgs_tke
1775
1776	USE statistics, &
1777	ONLY: flow_statistics_called, hom, sums, sums_l
1778
1779	INTEGER(iwp) :: i !< index variable along x
1780	INTEGER(iwp) :: j !< index variable along y
1781	INTEGER(iwp) :: k !< index variable along z
1782	INTEGER(iwp) :: m !< running index for the surface elements
1783
1784	REAL(wp) :: flag1 !< flag to mask topography
1785
1786	!
1787	!-- TKE gradient along x and y
1788	DO i = nxl, nxr
1789	DO j = nys, nyn
1790	DO k = nzb, nzt+1
1791
1792	IF ( .NOT. BTEST( wall_flags_0(k,j,i-1), 0 ) .AND. &
1793	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1794	BTEST( wall_flags_0(k,j,i+1), 0 ) ) &
1795	THEN
1796	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1797	( e(k,j,i+1) - e(k,j,i) ) * ddx
1798	ELSEIF ( BTEST( wall_flags_0(k,j,i-1), 0 ) .AND. &
1799	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1800	.NOT. BTEST( wall_flags_0(k,j,i+1), 0 ) ) &
1801	THEN
1802	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1803	( e(k,j,i) - e(k,j,i-1) ) * ddx
1804	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i), 22 ) .AND. &
1805	.NOT. BTEST( wall_flags_0(k,j,i+1), 22 ) ) &
1806	THEN
1807	de_dx(k,j,i) = 0.0_wp
1808	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i-1), 22 ) .AND. &
1809	.NOT. BTEST( wall_flags_0(k,j,i), 22 ) ) &
1810	THEN
1811	de_dx(k,j,i) = 0.0_wp
1812	ELSE
1813	de_dx(k,j,i) = sgs_wf_part * ( e(k,j,i+1) - e(k,j,i-1) ) * ddx
1814	ENDIF
1815
1816	IF ( .NOT. BTEST( wall_flags_0(k,j-1,i), 0 ) .AND. &
1817	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1818	BTEST( wall_flags_0(k,j+1,i), 0 ) ) &
1819	THEN
1820	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1821	( e(k,j+1,i) - e(k,j,i) ) * ddy
1822	ELSEIF ( BTEST( wall_flags_0(k,j-1,i), 0 ) .AND. &
1823	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1824	.NOT. BTEST( wall_flags_0(k,j+1,i), 0 ) ) &
1825	THEN
1826	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1827	( e(k,j,i) - e(k,j-1,i) ) * ddy
1828	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i), 22 ) .AND. &
1829	.NOT. BTEST( wall_flags_0(k,j+1,i), 22 ) ) &
1830	THEN
1831	de_dy(k,j,i) = 0.0_wp
1832	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j-1,i), 22 ) .AND. &
1833	.NOT. BTEST( wall_flags_0(k,j,i), 22 ) ) &
1834	THEN
1835	de_dy(k,j,i) = 0.0_wp
1836	ELSE
1837	de_dy(k,j,i) = sgs_wf_part * ( e(k,j+1,i) - e(k,j-1,i) ) * ddy
1838	ENDIF
1839
1840	ENDDO
1841	ENDDO
1842	ENDDO
1843
1844	!
1845	!-- TKE gradient along z at topograhy and including bottom and top boundary conditions
1846	DO i = nxl, nxr
1847	DO j = nys, nyn
1848	DO k = nzb+1, nzt-1
1849	!
1850	!-- Flag to mask topography
1851	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
1852
1853	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1854	( e(k+1,j,i) - e(k-1,j,i) ) / ( zu(k+1) - zu(k-1) ) &
1855	* flag1
1856	ENDDO
1857	!
1858	!-- upward-facing surfaces
1859	DO m = bc_h(0)%start_index(j,i), bc_h(0)%end_index(j,i)
1860	k = bc_h(0)%k(m)
1861	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1862	( e(k+1,j,i) - e(k,j,i) ) / ( zu(k+1) - zu(k) )
1863	ENDDO
1864	!
1865	!-- downward-facing surfaces
1866	DO m = bc_h(1)%start_index(j,i), bc_h(1)%end_index(j,i)
1867	k = bc_h(1)%k(m)
1868	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1869	( e(k,j,i) - e(k-1,j,i) ) / ( zu(k) - zu(k-1) )
1870	ENDDO
1871
1872	de_dz(nzb,j,i) = 0.0_wp
1873	de_dz(nzt,j,i) = 0.0_wp
1874	de_dz(nzt+1,j,i) = 0.0_wp
1875	ENDDO
1876	ENDDO
1877	!
1878	!-- Ghost point exchange
1879	CALL exchange_horiz( de_dx, nbgp )
1880	CALL exchange_horiz( de_dy, nbgp )
1881	CALL exchange_horiz( de_dz, nbgp )
1882	CALL exchange_horiz( diss, nbgp )
1883	!
1884	!-- Set boundary conditions at non-periodic boundaries. Note, at non-period
1885	!-- boundaries zero-gradient boundary conditions are set for the subgrid TKE.
1886	!-- Thus, TKE gradients normal to the respective lateral boundaries are zero,
1887	!-- while tangetial TKE gradients then must be the same as within the prognostic
1888	!-- domain.
1889	IF ( bc_dirichlet_l ) THEN
1890	de_dx(:,:,-1) = 0.0_wp
1891	de_dy(:,:,-1) = de_dy(:,:,0)
1892	de_dz(:,:,-1) = de_dz(:,:,0)
1893	ENDIF
1894	IF ( bc_dirichlet_r ) THEN
1895	de_dx(:,:,nxr+1) = 0.0_wp
1896	de_dy(:,:,nxr+1) = de_dy(:,:,nxr)
1897	de_dz(:,:,nxr+1) = de_dz(:,:,nxr)
1898	ENDIF
1899	IF ( bc_dirichlet_n ) THEN
1900	de_dx(:,nyn+1,:) = de_dx(:,nyn,:)
1901	de_dy(:,nyn+1,:) = 0.0_wp
1902	de_dz(:,nyn+1,:) = de_dz(:,nyn,:)
1903	ENDIF
1904	IF ( bc_dirichlet_s ) THEN
1905	de_dx(:,nys-1,:) = de_dx(:,nys,:)
1906	de_dy(:,nys-1,:) = 0.0_wp
1907	de_dz(:,nys-1,:) = de_dz(:,nys,:)
1908	ENDIF
1909	!
1910	!-- Calculate the horizontally averaged profiles of SGS TKE and resolved
1911	!-- velocity variances (they may have been already calculated in routine
1912	!-- flow_statistics).
1913	IF ( .NOT. flow_statistics_called ) THEN
1914
1915	!
1916	!-- First calculate horizontally averaged profiles of the horizontal
1917	!-- velocities.
1918	sums_l(:,1,0) = 0.0_wp
1919	sums_l(:,2,0) = 0.0_wp
1920
1921	DO i = nxl, nxr
1922	DO j = nys, nyn
1923	DO k = nzb, nzt+1
1924	!
1925	!-- Flag indicating vicinity of wall
1926	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 24 ) )
1927
1928	sums_l(k,1,0) = sums_l(k,1,0) + u(k,j,i) * flag1
1929	sums_l(k,2,0) = sums_l(k,2,0) + v(k,j,i) * flag1
1930	ENDDO
1931	ENDDO
1932	ENDDO
1933
1934	#if defined( __parallel )
1935	!
1936	!-- Compute total sum from local sums
1937	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1938	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, &
1939	MPI_REAL, MPI_SUM, comm2d, ierr )
1940	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1941	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, &
1942	MPI_REAL, MPI_SUM, comm2d, ierr )
1943	#else
1944	sums(:,1) = sums_l(:,1,0)
1945	sums(:,2) = sums_l(:,2,0)
1946	#endif
1947
1948	!
1949	!-- Final values are obtained by division by the total number of grid
1950	!-- points used for the summation.
1951	hom(:,1,1,0) = sums(:,1) / ngp_2dh_outer(:,0) ! u
1952	hom(:,1,2,0) = sums(:,2) / ngp_2dh_outer(:,0) ! v
1953
1954	!
1955	!-- Now calculate the profiles of SGS TKE and the resolved-scale
1956	!-- velocity variances
1957	sums_l(:,8,0) = 0.0_wp
1958	sums_l(:,30,0) = 0.0_wp
1959	sums_l(:,31,0) = 0.0_wp
1960	sums_l(:,32,0) = 0.0_wp
1961	DO i = nxl, nxr
1962	DO j = nys, nyn
1963	DO k = nzb, nzt+1
1964	!
1965	!-- Flag indicating vicinity of wall
1966	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 24 ) )
1967
1968	sums_l(k,8,0) = sums_l(k,8,0) + e(k,j,i) * flag1
1969	sums_l(k,30,0) = sums_l(k,30,0) + ( u(k,j,i) - hom(k,1,1,0) )*2 flag1
1970	sums_l(k,31,0) = sums_l(k,31,0) + ( v(k,j,i) - hom(k,1,2,0) )*2 flag1
1971	sums_l(k,32,0) = sums_l(k,32,0) + w(k,j,i)*2 flag1
1972	ENDDO
1973	ENDDO
1974	ENDDO
1975
1976	#if defined( __parallel )
1977	!
1978	!-- Compute total sum from local sums
1979	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1980	CALL MPI_ALLREDUCE( sums_l(nzb,8,0), sums(nzb,8), nzt+2-nzb, &
1981	MPI_REAL, MPI_SUM, comm2d, ierr )
1982	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1983	CALL MPI_ALLREDUCE( sums_l(nzb,30,0), sums(nzb,30), nzt+2-nzb, &
1984	MPI_REAL, MPI_SUM, comm2d, ierr )
1985	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1986	CALL MPI_ALLREDUCE( sums_l(nzb,31,0), sums(nzb,31), nzt+2-nzb, &
1987	MPI_REAL, MPI_SUM, comm2d, ierr )
1988	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1989	CALL MPI_ALLREDUCE( sums_l(nzb,32,0), sums(nzb,32), nzt+2-nzb, &
1990	MPI_REAL, MPI_SUM, comm2d, ierr )
1991
1992	#else
1993	sums(:,8) = sums_l(:,8,0)
1994	sums(:,30) = sums_l(:,30,0)
1995	sums(:,31) = sums_l(:,31,0)
1996	sums(:,32) = sums_l(:,32,0)
1997	#endif
1998
1999	!
2000	!-- Final values are obtained by division by the total number of grid
2001	!-- points used for the summation.
2002	hom(:,1,8,0) = sums(:,8) / ngp_2dh_outer(:,0) ! e
2003	hom(:,1,30,0) = sums(:,30) / ngp_2dh_outer(:,0) ! u*2
2004	hom(:,1,31,0) = sums(:,31) / ngp_2dh_outer(:,0) ! v*2
2005	hom(:,1,32,0) = sums(:,32) / ngp_2dh_outer(:,0) ! w*2
2006
2007	ENDIF
2008
2009	END SUBROUTINE lpm_init_sgs_tke
2010
2011
2012	!------------------------------------------------------------------------------!
2013	! Description:
2014	! ------------
2015	!> Sobroutine control lpm actions, i.e. all actions during one time step.
2016	!------------------------------------------------------------------------------!
2017	SUBROUTINE lpm_actions( location )
2018
2019	CHARACTER (LEN=*), INTENT(IN) :: location !< call location string
2020
2021	INTEGER(iwp) :: i !<
2022	INTEGER(iwp) :: ie !<
2023	INTEGER(iwp) :: is !<
2024	INTEGER(iwp) :: j !<
2025	INTEGER(iwp) :: je !<
2026	INTEGER(iwp) :: js !<
2027	INTEGER(iwp), SAVE :: lpm_count = 0 !<
2028	INTEGER(iwp) :: k !<
2029	INTEGER(iwp) :: ke !<
2030	INTEGER(iwp) :: ks !<
2031	INTEGER(iwp) :: m !<
2032	INTEGER(iwp), SAVE :: steps = 0 !<
2033
2034	LOGICAL :: first_loop_stride !<
2035
2036
2037	SELECT CASE ( location )
2038
2039	CASE ( 'after_prognostic_equations' )
2040
2041	CALL cpu_log( log_point(25), 'lpm', 'start' )
2042	!
2043	!-- Write particle data at current time on file.
2044	!-- This has to be done here, before particles are further processed,
2045	!-- because they may be deleted within this timestep (in case that
2046	!-- dt_write_particle_data = dt_prel = particle_maximum_age).
2047	time_write_particle_data = time_write_particle_data + dt_3d
2048	IF ( time_write_particle_data >= dt_write_particle_data ) THEN
2049
2050	CALL lpm_data_output_particles
2051	!
2052	!-- The MOD function allows for changes in the output interval with restart
2053	!-- runs.
2054	time_write_particle_data = MOD( time_write_particle_data, &
2055	MAX( dt_write_particle_data, dt_3d ) )
2056	ENDIF
2057
2058	!
2059	!-- Initialize arrays for marking those particles to be deleted after the
2060	!-- (sub-) timestep
2061	deleted_particles = 0
2062
2063	!
2064	!-- Initialize variables used for accumulating the number of particles
2065	!-- xchanged between the subdomains during all sub-timesteps (if sgs
2066	!-- velocities are included). These data are output further below on the
2067	!-- particle statistics file.
2068	trlp_count_sum = 0
2069	trlp_count_recv_sum = 0
2070	trrp_count_sum = 0
2071	trrp_count_recv_sum = 0
2072	trsp_count_sum = 0
2073	trsp_count_recv_sum = 0
2074	trnp_count_sum = 0
2075	trnp_count_recv_sum = 0
2076	!
2077	!-- Calculate exponential term used in case of particle inertia for each
2078	!-- of the particle groups
2079	DO m = 1, number_of_particle_groups
2080	IF ( particle_groups(m)%density_ratio /= 0.0_wp ) THEN
2081	particle_groups(m)%exp_arg = &
2082	4.5_wp * particle_groups(m)%density_ratio * &
2083	molecular_viscosity / ( particle_groups(m)%radius )**2
2084
2085	particle_groups(m)%exp_term = EXP( -particle_groups(m)%exp_arg * &
2086	dt_3d )
2087	ENDIF
2088	ENDDO
2089	!
2090	!-- If necessary, release new set of particles
2091	IF ( ( simulated_time - last_particle_release_time ) >= dt_prel .AND. end_time_prel > simulated_time ) &
2092	THEN
2093	DO WHILE ( ( simulated_time - last_particle_release_time ) >= dt_prel )
2094	CALL lpm_create_particle( PHASE_RELEASE )
2095	last_particle_release_time = last_particle_release_time + dt_prel
2096	ENDDO
2097	ENDIF
2098	!
2099	!-- Reset summation arrays
2100	IF ( cloud_droplets ) THEN
2101	ql_c = 0.0_wp
2102	ql_v = 0.0_wp
2103	ql_vp = 0.0_wp
2104	ENDIF
2105
2106	first_loop_stride = .TRUE.
2107	grid_particles(:,:,:)%time_loop_done = .TRUE.
2108	!
2109	!-- Timestep loop for particle advection.
2110	!-- This loop has to be repeated until the advection time of every particle
2111	!-- (within the total domain!) has reached the LES timestep (dt_3d).
2112	!-- In case of including the SGS velocities, the particle timestep may be
2113	!-- smaller than the LES timestep (because of the Lagrangian timescale
2114	!-- restriction) and particles may require to undergo several particle
2115	!-- timesteps, before the LES timestep is reached. Because the number of these
2116	!-- particle timesteps to be carried out is unknown at first, these steps are
2117	!-- carried out in the following infinite loop with exit condition.
2118	DO
2119	CALL cpu_log( log_point_s(44), 'lpm_advec', 'start' )
2120	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
2121
2122	!
2123	!-- If particle advection includes SGS velocity components, calculate the
2124	!-- required SGS quantities (i.e. gradients of the TKE, as well as
2125	!-- horizontally averaged profiles of the SGS TKE and the resolved-scale
2126	!-- velocity variances)
2127	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
2128	CALL lpm_init_sgs_tke
2129	ENDIF
2130	!
2131	!-- In case SGS-particle speed is considered, particles may carry out
2132	!-- several particle timesteps. In order to prevent unnecessary
2133	!-- treatment of particles that already reached the final time level,
2134	!-- particles are sorted into contiguous blocks of finished and
2135	!-- not-finished particles, in addition to their already sorting
2136	!-- according to their sub-boxes.
2137	IF ( .NOT. first_loop_stride .AND. use_sgs_for_particles ) &
2138	CALL lpm_sort_timeloop_done
2139	DO i = nxl, nxr
2140	DO j = nys, nyn
2141	DO k = nzb+1, nzt
2142
2143	number_of_particles = prt_count(k,j,i)
2144	!
2145	!-- If grid cell gets empty, flag must be true
2146	IF ( number_of_particles <= 0 ) THEN
2147	grid_particles(k,j,i)%time_loop_done = .TRUE.
2148	CYCLE
2149	ENDIF
2150
2151	IF ( .NOT. first_loop_stride .AND. &
2152	grid_particles(k,j,i)%time_loop_done ) CYCLE
2153
2154	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2155
2156	particles(1:number_of_particles)%particle_mask = .TRUE.
2157	!
2158	!-- Initialize the variable storing the total time that a particle
2159	!-- has advanced within the timestep procedure
2160	IF ( first_loop_stride ) THEN
2161	particles(1:number_of_particles)%dt_sum = 0.0_wp
2162	ENDIF
2163	!
2164	!-- Particle (droplet) growth by condensation/evaporation and
2165	!-- collision
2166	IF ( cloud_droplets .AND. first_loop_stride) THEN
2167	!
2168	!-- Droplet growth by condensation / evaporation
2169	CALL lpm_droplet_condensation(i,j,k)
2170	!
2171	!-- Particle growth by collision
2172	IF ( collision_kernel /= 'none' ) THEN
2173	CALL lpm_droplet_collision(i,j,k)
2174	ENDIF
2175
2176	ENDIF
2177	!
2178	!-- Initialize the switch used for the loop exit condition checked
2179	!-- at the end of this loop. If at least one particle has failed to
2180	!-- reach the LES timestep, this switch will be set false in
2181	!-- lpm_advec.
2182	dt_3d_reached_l = .TRUE.
2183
2184	!
2185	!-- Particle advection
2186	CALL lpm_advec(TRIM(particle_interpolation),i,j,k)
2187	!
2188	!-- Particle reflection from walls. Only applied if the particles
2189	!-- are in the vertical range of the topography. (Here, some
2190	!-- optimization is still possible.)
2191	IF ( topography /= 'flat' .AND. k < nzb_max + 2 ) THEN
2192	CALL lpm_boundary_conds( 'walls', i, j, k )
2193	ENDIF
2194	!
2195	!-- User-defined actions after the calculation of the new particle
2196	!-- position
2197	CALL user_lpm_advec(i,j,k)
2198	!
2199	!-- Apply boundary conditions to those particles that have crossed
2200	!-- the top or bottom boundary and delete those particles, which are
2201	!-- older than allowed
2202	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
2203	!
2204	!--- If not all particles of the actual grid cell have reached the
2205	!-- LES timestep, this cell has to do another loop iteration. Due to
2206	!-- the fact that particles can move into neighboring grid cells,
2207	!-- these neighbor cells also have to perform another loop iteration.
2208	!-- Please note, this realization does not work properly if
2209	!-- particles move into another subdomain.
2210	IF ( .NOT. dt_3d_reached_l ) THEN
2211	ks = MAX(nzb+1,k-1)
2212	ke = MIN(nzt,k+1)
2213	js = MAX(nys,j-1)
2214	je = MIN(nyn,j+1)
2215	is = MAX(nxl,i-1)
2216	ie = MIN(nxr,i+1)
2217	grid_particles(ks:ke,js:je,is:ie)%time_loop_done = .FALSE.
2218	ELSE
2219	grid_particles(k,j,i)%time_loop_done = .TRUE.
2220	ENDIF
2221
2222	ENDDO
2223	ENDDO
2224	ENDDO
2225	steps = steps + 1
2226	dt_3d_reached_l = ALL(grid_particles(:,:,:)%time_loop_done)
2227	!
2228	!-- Find out, if all particles on every PE have completed the LES timestep
2229	!-- and set the switch corespondingly
2230	#if defined( __parallel )
2231	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2232	CALL MPI_ALLREDUCE( dt_3d_reached_l, dt_3d_reached, 1, MPI_LOGICAL, &
2233	MPI_LAND, comm2d, ierr )
2234	#else
2235	dt_3d_reached = dt_3d_reached_l
2236	#endif
2237	CALL cpu_log( log_point_s(44), 'lpm_advec', 'stop' )
2238
2239	!
2240	!-- Apply splitting and merging algorithm
2241	IF ( cloud_droplets ) THEN
2242	IF ( splitting ) THEN
2243	CALL lpm_splitting
2244	ENDIF
2245	IF ( merging ) THEN
2246	CALL lpm_merging
2247	ENDIF
2248	ENDIF
2249	!
2250	!-- Move Particles local to PE to a different grid cell
2251	CALL lpm_move_particle
2252	!
2253	!-- Horizontal boundary conditions including exchange between subdmains
2254	CALL lpm_exchange_horiz
2255
2256	!
2257	!-- IF .FALSE., lpm_sort_and_delete is done inside pcmp
2258	IF ( .NOT. dt_3d_reached .OR. .NOT. nested_run ) THEN
2259	!
2260	!-- Pack particles (eliminate those marked for deletion),
2261	!-- determine new number of particles
2262	CALL lpm_sort_and_delete
2263
2264	!-- Initialize variables for the next (sub-) timestep, i.e., for marking
2265	!-- those particles to be deleted after the timestep
2266	deleted_particles = 0
2267	ENDIF
2268
2269	IF ( dt_3d_reached ) EXIT
2270
2271	first_loop_stride = .FALSE.
2272	ENDDO ! timestep loop
2273	!
2274	!-- in case of nested runs do the transfer of particles after every full model time step
2275	IF ( nested_run ) THEN
2276	CALL particles_from_parent_to_child
2277	CALL particles_from_child_to_parent
2278	CALL pmcp_p_delete_particles_in_fine_grid_area
2279
2280	CALL lpm_sort_and_delete
2281
2282	deleted_particles = 0
2283	ENDIF
2284
2285	!
2286	!-- Calculate the new liquid water content for each grid box
2287	IF ( cloud_droplets ) CALL lpm_calc_liquid_water_content
2288
2289	!
2290	!-- Deallocate unused memory
2291	IF ( deallocate_memory .AND. lpm_count == step_dealloc ) THEN
2292	CALL dealloc_particles_array
2293	lpm_count = 0
2294	ELSEIF ( deallocate_memory ) THEN
2295	lpm_count = lpm_count + 1
2296	ENDIF
2297
2298	!
2299	!-- Write particle statistics (in particular the number of particles
2300	!-- exchanged between the subdomains) on file
2301	IF ( write_particle_statistics ) CALL lpm_write_exchange_statistics
2302
2303	CALL cpu_log( log_point(25), 'lpm', 'stop' )
2304
2305	! !
2306	! !-- Output of particle time series
2307	! IF ( particle_advection ) THEN
2308	! IF ( time_dopts >= dt_dopts .OR. &
2309	! ( time_since_reference_point >= particle_advection_start .AND. &
2310	! first_call_lpm ) ) THEN
2311	! CALL lpm_data_output_ptseries
2312	! time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
2313	! ENDIF
2314	! ENDIF
2315
2316	CASE DEFAULT
2317	CONTINUE
2318
2319	END SELECT
2320
2321	END SUBROUTINE lpm_actions
2322
2323
2324	!------------------------------------------------------------------------------!
2325	! Description:
2326	! ------------
2327	!
2328	!------------------------------------------------------------------------------!
2329	SUBROUTINE particles_from_parent_to_child
2330	IMPLICIT NONE
2331
2332	CALL pmcp_c_get_particle_from_parent ! Child actions
2333	CALL pmcp_p_fill_particle_win ! Parent actions
2334
2335	RETURN
2336	END SUBROUTINE particles_from_parent_to_child
2337
2338
2339	!------------------------------------------------------------------------------!
2340	! Description:
2341	! ------------
2342	!
2343	!------------------------------------------------------------------------------!
2344	SUBROUTINE particles_from_child_to_parent
2345	IMPLICIT NONE
2346
2347	CALL pmcp_c_send_particle_to_parent ! Child actions
2348	CALL pmcp_p_empty_particle_win ! Parent actions
2349
2350	RETURN
2351	END SUBROUTINE particles_from_child_to_parent
2352
2353	!------------------------------------------------------------------------------!
2354	! Description:
2355	! ------------
2356	!> This routine write exchange statistics of the lpm in a ascii file.
2357	!------------------------------------------------------------------------------!
2358	SUBROUTINE lpm_write_exchange_statistics
2359
2360	INTEGER(iwp) :: ip !<
2361	INTEGER(iwp) :: jp !<
2362	INTEGER(iwp) :: kp !<
2363	INTEGER(iwp) :: tot_number_of_particles
2364
2365	!
2366	!-- Determine the current number of particles
2367	number_of_particles = 0
2368	DO ip = nxl, nxr
2369	DO jp = nys, nyn
2370	DO kp = nzb+1, nzt
2371	number_of_particles = number_of_particles &
2372	+ prt_count(kp,jp,ip)
2373	ENDDO
2374	ENDDO
2375	ENDDO
2376
2377	CALL check_open( 80 )
2378	#if defined( __parallel )
2379	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2380	number_of_particles, pleft, trlp_count_sum, &
2381	trlp_count_recv_sum, pright, trrp_count_sum, &
2382	trrp_count_recv_sum, psouth, trsp_count_sum, &
2383	trsp_count_recv_sum, pnorth, trnp_count_sum, &
2384	trnp_count_recv_sum
2385	#else
2386	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2387	number_of_particles
2388	#endif
2389	CALL close_file( 80 )
2390
2391	IF ( number_of_particles > 0 ) THEN
2392	WRITE(9,*) 'number_of_particles ', number_of_particles, &
2393	current_timestep_number + 1, simulated_time + dt_3d
2394	ENDIF
2395
2396	#if defined( __parallel )
2397	CALL MPI_ALLREDUCE( number_of_particles, tot_number_of_particles, 1, &
2398	MPI_INTEGER, MPI_SUM, comm2d, ierr )
2399	#else
2400	tot_number_of_particles = number_of_particles
2401	#endif
2402
2403	IF ( nested_run ) THEN
2404	CALL pmcp_g_print_number_of_particles( simulated_time+dt_3d, &
2405	tot_number_of_particles)
2406	ENDIF
2407
2408	!
2409	!-- Formats
2410	8000 FORMAT (I6,1X,F7.2,4X,I10,5X,4(I3,1X,I4,'/',I4,2X),6X,I10)
2411
2412
2413	END SUBROUTINE lpm_write_exchange_statistics
2414
2415
2416	!------------------------------------------------------------------------------!
2417	! Description:
2418	! ------------
2419	!> Write particle data in FORTRAN binary and/or netCDF format
2420	!------------------------------------------------------------------------------!
2421	SUBROUTINE lpm_data_output_particles
2422
2423	INTEGER(iwp) :: ip !<
2424	INTEGER(iwp) :: jp !<
2425	INTEGER(iwp) :: kp !<
2426
2427	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'start' )
2428
2429	!
2430	!-- Attention: change version number for unit 85 (in routine check_open)
2431	!-- whenever the output format for this unit is changed!
2432	CALL check_open( 85 )
2433
2434	WRITE ( 85 ) simulated_time
2435	WRITE ( 85 ) prt_count
2436
2437	DO ip = nxl, nxr
2438	DO jp = nys, nyn
2439	DO kp = nzb+1, nzt
2440	number_of_particles = prt_count(kp,jp,ip)
2441	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
2442	IF ( number_of_particles <= 0 ) CYCLE
2443	WRITE ( 85 ) particles
2444	ENDDO
2445	ENDDO
2446	ENDDO
2447
2448	CALL close_file( 85 )
2449
2450
2451	#if defined( __netcdf )
2452	! !
2453	! !-- Output in netCDF format
2454	! CALL check_open( 108 )
2455	!
2456	! !
2457	! !-- Update the NetCDF time axis
2458	! prt_time_count = prt_time_count + 1
2459	!
2460	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_time_prt, &
2461	! (/ simulated_time /), &
2462	! start = (/ prt_time_count /), count = (/ 1 /) )
2463	! CALL netcdf_handle_error( 'lpm_data_output_particles', 1 )
2464	!
2465	! !
2466	! !-- Output the real number of particles used
2467	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_rnop_prt, &
2468	! (/ number_of_particles /), &
2469	! start = (/ prt_time_count /), count = (/ 1 /) )
2470	! CALL netcdf_handle_error( 'lpm_data_output_particles', 2 )
2471	!
2472	! !
2473	! !-- Output all particle attributes
2474	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(1), particles%age, &
2475	! start = (/ 1, prt_time_count /), &
2476	! count = (/ maximum_number_of_particles /) )
2477	! CALL netcdf_handle_error( 'lpm_data_output_particles', 3 )
2478	!
2479	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(2), particles%user, &
2480	! start = (/ 1, prt_time_count /), &
2481	! count = (/ maximum_number_of_particles /) )
2482	! CALL netcdf_handle_error( 'lpm_data_output_particles', 4 )
2483	!
2484	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(3), particles%origin_x, &
2485	! start = (/ 1, prt_time_count /), &
2486	! count = (/ maximum_number_of_particles /) )
2487	! CALL netcdf_handle_error( 'lpm_data_output_particles', 5 )
2488	!
2489	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(4), particles%origin_y, &
2490	! start = (/ 1, prt_time_count /), &
2491	! count = (/ maximum_number_of_particles /) )
2492	! CALL netcdf_handle_error( 'lpm_data_output_particles', 6 )
2493	!
2494	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(5), particles%origin_z, &
2495	! start = (/ 1, prt_time_count /), &
2496	! count = (/ maximum_number_of_particles /) )
2497	! CALL netcdf_handle_error( 'lpm_data_output_particles', 7 )
2498	!
2499	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(6), particles%radius, &
2500	! start = (/ 1, prt_time_count /), &
2501	! count = (/ maximum_number_of_particles /) )
2502	! CALL netcdf_handle_error( 'lpm_data_output_particles', 8 )
2503	!
2504	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(7), particles%speed_x, &
2505	! start = (/ 1, prt_time_count /), &
2506	! count = (/ maximum_number_of_particles /) )
2507	! CALL netcdf_handle_error( 'lpm_data_output_particles', 9 )
2508	!
2509	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(8), particles%speed_y, &
2510	! start = (/ 1, prt_time_count /), &
2511	! count = (/ maximum_number_of_particles /) )
2512	! CALL netcdf_handle_error( 'lpm_data_output_particles', 10 )
2513	!
2514	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(9), particles%speed_z, &
2515	! start = (/ 1, prt_time_count /), &
2516	! count = (/ maximum_number_of_particles /) )
2517	! CALL netcdf_handle_error( 'lpm_data_output_particles', 11 )
2518	!
2519	! nc_stat = NF90_PUT_VAR( id_set_prt,id_var_prt(10), &
2520	! particles%weight_factor, &
2521	! start = (/ 1, prt_time_count /), &
2522	! count = (/ maximum_number_of_particles /) )
2523	! CALL netcdf_handle_error( 'lpm_data_output_particles', 12 )
2524	!
2525	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(11), particles%x, &
2526	! start = (/ 1, prt_time_count /), &
2527	! count = (/ maximum_number_of_particles /) )
2528	! CALL netcdf_handle_error( 'lpm_data_output_particles', 13 )
2529	!
2530	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(12), particles%y, &
2531	! start = (/ 1, prt_time_count /), &
2532	! count = (/ maximum_number_of_particles /) )
2533	! CALL netcdf_handle_error( 'lpm_data_output_particles', 14 )
2534	!
2535	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(13), particles%z, &
2536	! start = (/ 1, prt_time_count /), &
2537	! count = (/ maximum_number_of_particles /) )
2538	! CALL netcdf_handle_error( 'lpm_data_output_particles', 15 )
2539	!
2540	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(14), particles%class, &
2541	! start = (/ 1, prt_time_count /), &
2542	! count = (/ maximum_number_of_particles /) )
2543	! CALL netcdf_handle_error( 'lpm_data_output_particles', 16 )
2544	!
2545	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(15), particles%group, &
2546	! start = (/ 1, prt_time_count /), &
2547	! count = (/ maximum_number_of_particles /) )
2548	! CALL netcdf_handle_error( 'lpm_data_output_particles', 17 )
2549	!
2550	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(16), &
2551	! particles%id2, &
2552	! start = (/ 1, prt_time_count /), &
2553	! count = (/ maximum_number_of_particles /) )
2554	! CALL netcdf_handle_error( 'lpm_data_output_particles', 18 )
2555	!
2556	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(17), particles%id1, &
2557	! start = (/ 1, prt_time_count /), &
2558	! count = (/ maximum_number_of_particles /) )
2559	! CALL netcdf_handle_error( 'lpm_data_output_particles', 19 )
2560	!
2561	#endif
2562
2563	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'stop' )
2564
2565	END SUBROUTINE lpm_data_output_particles
2566
2567	!------------------------------------------------------------------------------!
2568	! Description:
2569	! ------------
2570	!> This routine calculates and provide particle timeseries output.
2571	!------------------------------------------------------------------------------!
2572	SUBROUTINE lpm_data_output_ptseries
2573
2574	INTEGER(iwp) :: i !<
2575	INTEGER(iwp) :: inum !<
2576	INTEGER(iwp) :: j !<
2577	INTEGER(iwp) :: jg !<
2578	INTEGER(iwp) :: k !<
2579	INTEGER(iwp) :: n !<
2580
2581	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value !<
2582	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value_l !<
2583
2584
2585	CALL cpu_log( log_point(36), 'data_output_ptseries', 'start' )
2586
2587	IF ( myid == 0 ) THEN
2588	!
2589	!-- Open file for time series output in NetCDF format
2590	dopts_time_count = dopts_time_count + 1
2591	CALL check_open( 109 )
2592	#if defined( __netcdf )
2593	!
2594	!-- Update the particle time series time axis
2595	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_time_pts, &
2596	(/ time_since_reference_point /), &
2597	start = (/ dopts_time_count /), count = (/ 1 /) )
2598	CALL netcdf_handle_error( 'data_output_ptseries', 391 )
2599	#endif
2600
2601	ENDIF
2602
2603	ALLOCATE( pts_value(0:number_of_particle_groups,dopts_num), &
2604	pts_value_l(0:number_of_particle_groups,dopts_num) )
2605
2606	pts_value_l = 0.0_wp
2607	pts_value_l(:,16) = 9999999.9_wp ! for calculation of minimum radius
2608
2609	!
2610	!-- Calculate or collect the particle time series quantities for all particles
2611	!-- and seperately for each particle group (if there is more than one group)
2612	DO i = nxl, nxr
2613	DO j = nys, nyn
2614	DO k = nzb, nzt
2615	number_of_particles = prt_count(k,j,i)
2616	IF (number_of_particles <= 0) CYCLE
2617	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2618	DO n = 1, number_of_particles
2619
2620	IF ( particles(n)%particle_mask ) THEN ! Restrict analysis to active particles
2621
2622	pts_value_l(0,1) = pts_value_l(0,1) + 1.0_wp ! total # of particles
2623	pts_value_l(0,2) = pts_value_l(0,2) + &
2624	( particles(n)%x - particles(n)%origin_x ) ! mean x
2625	pts_value_l(0,3) = pts_value_l(0,3) + &
2626	( particles(n)%y - particles(n)%origin_y ) ! mean y
2627	pts_value_l(0,4) = pts_value_l(0,4) + &
2628	( particles(n)%z - particles(n)%origin_z ) ! mean z
2629	pts_value_l(0,5) = pts_value_l(0,5) + particles(n)%z ! mean z (absolute)
2630	pts_value_l(0,6) = pts_value_l(0,6) + particles(n)%speed_x ! mean u
2631	pts_value_l(0,7) = pts_value_l(0,7) + particles(n)%speed_y ! mean v
2632	pts_value_l(0,8) = pts_value_l(0,8) + particles(n)%speed_z ! mean w
2633	pts_value_l(0,9) = pts_value_l(0,9) + particles(n)%rvar1 ! mean sgsu
2634	pts_value_l(0,10) = pts_value_l(0,10) + particles(n)%rvar2 ! mean sgsv
2635	pts_value_l(0,11) = pts_value_l(0,11) + particles(n)%rvar3 ! mean sgsw
2636	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2637	pts_value_l(0,12) = pts_value_l(0,12) + 1.0_wp ! # of upward moving prts
2638	pts_value_l(0,13) = pts_value_l(0,13) + &
2639	particles(n)%speed_z ! mean w upw.
2640	ELSE
2641	pts_value_l(0,14) = pts_value_l(0,14) + &
2642	particles(n)%speed_z ! mean w down
2643	ENDIF
2644	pts_value_l(0,15) = pts_value_l(0,15) + particles(n)%radius ! mean rad
2645	pts_value_l(0,16) = MIN( pts_value_l(0,16), particles(n)%radius ) ! minrad
2646	pts_value_l(0,17) = MAX( pts_value_l(0,17), particles(n)%radius ) ! maxrad
2647	pts_value_l(0,18) = pts_value_l(0,18) + 1.0_wp
2648	pts_value_l(0,19) = pts_value_l(0,18) + 1.0_wp
2649	!
2650	!-- Repeat the same for the respective particle group
2651	IF ( number_of_particle_groups > 1 ) THEN
2652	jg = particles(n)%group
2653
2654	pts_value_l(jg,1) = pts_value_l(jg,1) + 1.0_wp
2655	pts_value_l(jg,2) = pts_value_l(jg,2) + &
2656	( particles(n)%x - particles(n)%origin_x )
2657	pts_value_l(jg,3) = pts_value_l(jg,3) + &
2658	( particles(n)%y - particles(n)%origin_y )
2659	pts_value_l(jg,4) = pts_value_l(jg,4) + &
2660	( particles(n)%z - particles(n)%origin_z )
2661	pts_value_l(jg,5) = pts_value_l(jg,5) + particles(n)%z
2662	pts_value_l(jg,6) = pts_value_l(jg,6) + particles(n)%speed_x
2663	pts_value_l(jg,7) = pts_value_l(jg,7) + particles(n)%speed_y
2664	pts_value_l(jg,8) = pts_value_l(jg,8) + particles(n)%speed_z
2665	pts_value_l(jg,9) = pts_value_l(jg,9) + particles(n)%rvar1
2666	pts_value_l(jg,10) = pts_value_l(jg,10) + particles(n)%rvar2
2667	pts_value_l(jg,11) = pts_value_l(jg,11) + particles(n)%rvar3
2668	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2669	pts_value_l(jg,12) = pts_value_l(jg,12) + 1.0_wp
2670	pts_value_l(jg,13) = pts_value_l(jg,13) + particles(n)%speed_z
2671	ELSE
2672	pts_value_l(jg,14) = pts_value_l(jg,14) + particles(n)%speed_z
2673	ENDIF
2674	pts_value_l(jg,15) = pts_value_l(jg,15) + particles(n)%radius
2675	pts_value_l(jg,16) = MIN( pts_value(jg,16), particles(n)%radius )
2676	pts_value_l(jg,17) = MAX( pts_value(jg,17), particles(n)%radius )
2677	pts_value_l(jg,18) = pts_value_l(jg,18) + 1.0_wp
2678	pts_value_l(jg,19) = pts_value_l(jg,19) + 1.0_wp
2679	ENDIF
2680
2681	ENDIF
2682
2683	ENDDO
2684
2685	ENDDO
2686	ENDDO
2687	ENDDO
2688
2689
2690	#if defined( __parallel )
2691	!
2692	!-- Sum values of the subdomains
2693	inum = number_of_particle_groups + 1
2694
2695	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2696	CALL MPI_ALLREDUCE( pts_value_l(0,1), pts_value(0,1), 15*inum, MPI_REAL, &
2697	MPI_SUM, comm2d, ierr )
2698	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2699	CALL MPI_ALLREDUCE( pts_value_l(0,16), pts_value(0,16), inum, MPI_REAL, &
2700	MPI_MIN, comm2d, ierr )
2701	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2702	CALL MPI_ALLREDUCE( pts_value_l(0,17), pts_value(0,17), inum, MPI_REAL, &
2703	MPI_MAX, comm2d, ierr )
2704	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2705	CALL MPI_ALLREDUCE( pts_value_l(0,18), pts_value(0,18), inum, MPI_REAL, &
2706	MPI_MAX, comm2d, ierr )
2707	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2708	CALL MPI_ALLREDUCE( pts_value_l(0,19), pts_value(0,19), inum, MPI_REAL, &
2709	MPI_MIN, comm2d, ierr )
2710	#else
2711	pts_value(:,1:19) = pts_value_l(:,1:19)
2712	#endif
2713
2714	!
2715	!-- Normalize the above calculated quantities (except min/max values) with the
2716	!-- total number of particles
2717	IF ( number_of_particle_groups > 1 ) THEN
2718	inum = number_of_particle_groups
2719	ELSE
2720	inum = 0
2721	ENDIF
2722
2723	DO j = 0, inum
2724
2725	IF ( pts_value(j,1) > 0.0_wp ) THEN
2726
2727	pts_value(j,2:15) = pts_value(j,2:15) / pts_value(j,1)
2728	IF ( pts_value(j,12) > 0.0_wp .AND. pts_value(j,12) < 1.0_wp ) THEN
2729	pts_value(j,13) = pts_value(j,13) / pts_value(j,12)
2730	pts_value(j,14) = pts_value(j,14) / ( 1.0_wp - pts_value(j,12) )
2731	ELSEIF ( pts_value(j,12) == 0.0_wp ) THEN
2732	pts_value(j,13) = -1.0_wp
2733	ELSE
2734	pts_value(j,14) = -1.0_wp
2735	ENDIF
2736
2737	ENDIF
2738
2739	ENDDO
2740
2741	!
2742	!-- Calculate higher order moments of particle time series quantities,
2743	!-- seperately for each particle group (if there is more than one group)
2744	DO i = nxl, nxr
2745	DO j = nys, nyn
2746	DO k = nzb, nzt
2747	number_of_particles = prt_count(k,j,i)
2748	IF (number_of_particles <= 0) CYCLE
2749	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2750	DO n = 1, number_of_particles
2751
2752	pts_value_l(0,20) = pts_value_l(0,20) + ( particles(n)%x - &
2753	particles(n)%origin_x - pts_value(0,2) )*2 ! x2
2754	pts_value_l(0,21) = pts_value_l(0,21) + ( particles(n)%y - &
2755	particles(n)%origin_y - pts_value(0,3) )*2 ! y2
2756	pts_value_l(0,22) = pts_value_l(0,22) + ( particles(n)%z - &
2757	particles(n)%origin_z - pts_value(0,4) )*2 ! z2
2758	pts_value_l(0,23) = pts_value_l(0,23) + ( particles(n)%speed_x - &
2759	pts_value(0,6) )*2 ! u2
2760	pts_value_l(0,24) = pts_value_l(0,24) + ( particles(n)%speed_y - &
2761	pts_value(0,7) )*2 ! v2
2762	pts_value_l(0,25) = pts_value_l(0,25) + ( particles(n)%speed_z - &
2763	pts_value(0,8) )*2 ! w2
2764	pts_value_l(0,26) = pts_value_l(0,26) + ( particles(n)%rvar1 - &
2765	pts_value(0,9) )**2 ! u"2
2766	pts_value_l(0,27) = pts_value_l(0,27) + ( particles(n)%rvar2 - &
2767	pts_value(0,10) )**2 ! v"2
2768	pts_value_l(0,28) = pts_value_l(0,28) + ( particles(n)%rvar3 - &
2769	pts_value(0,11) )**2 ! w"2
2770	!
2771	!-- Repeat the same for the respective particle group
2772	IF ( number_of_particle_groups > 1 ) THEN
2773	jg = particles(n)%group
2774
2775	pts_value_l(jg,20) = pts_value_l(jg,20) + ( particles(n)%x - &
2776	particles(n)%origin_x - pts_value(jg,2) )**2
2777	pts_value_l(jg,21) = pts_value_l(jg,21) + ( particles(n)%y - &
2778	particles(n)%origin_y - pts_value(jg,3) )**2
2779	pts_value_l(jg,22) = pts_value_l(jg,22) + ( particles(n)%z - &
2780	particles(n)%origin_z - pts_value(jg,4) )**2
2781	pts_value_l(jg,23) = pts_value_l(jg,23) + ( particles(n)%speed_x - &
2782	pts_value(jg,6) )**2
2783	pts_value_l(jg,24) = pts_value_l(jg,24) + ( particles(n)%speed_y - &
2784	pts_value(jg,7) )**2
2785	pts_value_l(jg,25) = pts_value_l(jg,25) + ( particles(n)%speed_z - &
2786	pts_value(jg,8) )**2
2787	pts_value_l(jg,26) = pts_value_l(jg,26) + ( particles(n)%rvar1 - &
2788	pts_value(jg,9) )**2
2789	pts_value_l(jg,27) = pts_value_l(jg,27) + ( particles(n)%rvar2 - &
2790	pts_value(jg,10) )**2
2791	pts_value_l(jg,28) = pts_value_l(jg,28) + ( particles(n)%rvar3 - &
2792	pts_value(jg,11) )**2
2793	ENDIF
2794
2795	ENDDO
2796	ENDDO
2797	ENDDO
2798	ENDDO
2799
2800	pts_value_l(0,29) = ( number_of_particles - pts_value(0,1) / numprocs )**2
2801	! variance of particle numbers
2802	IF ( number_of_particle_groups > 1 ) THEN
2803	DO j = 1, number_of_particle_groups
2804	pts_value_l(j,29) = ( pts_value_l(j,1) - &
2805	pts_value(j,1) / numprocs )**2
2806	ENDDO
2807	ENDIF
2808
2809	#if defined( __parallel )
2810	!
2811	!-- Sum values of the subdomains
2812	inum = number_of_particle_groups + 1
2813
2814	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2815	CALL MPI_ALLREDUCE( pts_value_l(0,20), pts_value(0,20), inum*10, MPI_REAL, &
2816	MPI_SUM, comm2d, ierr )
2817	#else
2818	pts_value(:,20:29) = pts_value_l(:,20:29)
2819	#endif
2820
2821	!
2822	!-- Normalize the above calculated quantities with the total number of
2823	!-- particles
2824	IF ( number_of_particle_groups > 1 ) THEN
2825	inum = number_of_particle_groups
2826	ELSE
2827	inum = 0
2828	ENDIF
2829
2830	DO j = 0, inum
2831
2832	IF ( pts_value(j,1) > 0.0_wp ) THEN
2833	pts_value(j,20:28) = pts_value(j,20:28) / pts_value(j,1)
2834	ENDIF
2835	pts_value(j,29) = pts_value(j,29) / numprocs
2836
2837	ENDDO
2838
2839	#if defined( __netcdf )
2840	!
2841	!-- Output particle time series quantities in NetCDF format
2842	IF ( myid == 0 ) THEN
2843	DO j = 0, inum
2844	DO i = 1, dopts_num
2845	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_dopts(i,j), &
2846	(/ pts_value(j,i) /), &
2847	start = (/ dopts_time_count /), &
2848	count = (/ 1 /) )
2849	CALL netcdf_handle_error( 'data_output_ptseries', 392 )
2850	ENDDO
2851	ENDDO
2852	ENDIF
2853	#endif
2854
2855	DEALLOCATE( pts_value, pts_value_l )
2856
2857	CALL cpu_log( log_point(36), 'data_output_ptseries', 'stop' )
2858
2859	END SUBROUTINE lpm_data_output_ptseries
2860
2861
2862	!------------------------------------------------------------------------------!
2863	! Description:
2864	! ------------
2865	!> This routine reads the respective restart data for the lpm.
2866	!------------------------------------------------------------------------------!
2867	SUBROUTINE lpm_rrd_local_particles
2868
2869	CHARACTER (LEN=10) :: particle_binary_version !<
2870	CHARACTER (LEN=10) :: version_on_file !<
2871
2872	INTEGER(iwp) :: alloc_size !<
2873	INTEGER(iwp) :: ip !<
2874	INTEGER(iwp) :: jp !<
2875	INTEGER(iwp) :: kp !<
2876
2877	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles !<
2878
2879	!
2880	!-- Read particle data from previous model run.
2881	!-- First open the input unit.
2882	IF ( myid_char == '' ) THEN
2883	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN'//myid_char, &
2884	FORM='UNFORMATTED' )
2885	ELSE
2886	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN/'//myid_char, &
2887	FORM='UNFORMATTED' )
2888	ENDIF
2889
2890	!
2891	!-- First compare the version numbers
2892	READ ( 90 ) version_on_file
2893	particle_binary_version = '4.0'
2894	IF ( TRIM( version_on_file ) /= TRIM( particle_binary_version ) ) THEN
2895	message_string = 'version mismatch concerning data from prior ' // &
2896	'run &version on file = "' // &
2897	TRIM( version_on_file ) // &
2898	'&version in program = "' // &
2899	TRIM( particle_binary_version ) // '"'
2900	CALL message( 'lpm_read_restart_file', 'PA0214', 1, 2, 0, 6, 0 )
2901	ENDIF
2902
2903	!
2904	!-- If less particles are stored on the restart file than prescribed by
2905	!-- 1, the remainder is initialized by zero_particle to avoid
2906	!-- errors.
2907	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2908	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2909	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2910	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2911	0, 0, 0_idp, .FALSE., -1 )
2912	!
2913	!-- Read some particle parameters and the size of the particle arrays,
2914	!-- allocate them and read their contents.
2915	READ ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
2916	last_particle_release_time, number_of_particle_groups, &
2917	particle_groups, time_write_particle_data
2918
2919	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
2920	grid_particles(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
2921
2922	READ ( 90 ) prt_count
2923
2924	DO ip = nxl, nxr
2925	DO jp = nys, nyn
2926	DO kp = nzb+1, nzt
2927
2928	number_of_particles = prt_count(kp,jp,ip)
2929	IF ( number_of_particles > 0 ) THEN
2930	alloc_size = MAX( INT( number_of_particles * &
2931	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
2932	1 )
2933	ELSE
2934	alloc_size = 1
2935	ENDIF
2936
2937	ALLOCATE( grid_particles(kp,jp,ip)%particles(1:alloc_size) )
2938
2939	IF ( number_of_particles > 0 ) THEN
2940	ALLOCATE( tmp_particles(1:number_of_particles) )
2941	READ ( 90 ) tmp_particles
2942	grid_particles(kp,jp,ip)%particles(1:number_of_particles) = tmp_particles
2943	DEALLOCATE( tmp_particles )
2944	IF ( number_of_particles < alloc_size ) THEN
2945	grid_particles(kp,jp,ip)%particles(number_of_particles+1:alloc_size) &
2946	= zero_particle
2947	ENDIF
2948	ELSE
2949	grid_particles(kp,jp,ip)%particles(1:alloc_size) = zero_particle
2950	ENDIF
2951
2952	ENDDO
2953	ENDDO
2954	ENDDO
2955
2956	CLOSE ( 90 )
2957	!
2958	!-- Must be called to sort particles into blocks, which is needed for a fast
2959	!-- interpolation of the LES fields on the particle position.
2960	CALL lpm_sort_and_delete
2961
2962
2963	END SUBROUTINE lpm_rrd_local_particles
2964
2965
2966	SUBROUTINE lpm_rrd_local( k, nxlf, nxlc, nxl_on_file, nxrf, nxrc, &
2967	nxr_on_file, nynf, nync, nyn_on_file, nysf, &
2968	nysc, nys_on_file, tmp_3d, found )
2969
2970
2971	USE control_parameters, &
2972	ONLY: length, restart_string
2973
2974	INTEGER(iwp) :: k !<
2975	INTEGER(iwp) :: nxlc !<
2976	INTEGER(iwp) :: nxlf !<
2977	INTEGER(iwp) :: nxl_on_file !<
2978	INTEGER(iwp) :: nxrc !<
2979	INTEGER(iwp) :: nxrf !<
2980	INTEGER(iwp) :: nxr_on_file !<
2981	INTEGER(iwp) :: nync !<
2982	INTEGER(iwp) :: nynf !<
2983	INTEGER(iwp) :: nyn_on_file !<
2984	INTEGER(iwp) :: nysc !<
2985	INTEGER(iwp) :: nysf !<
2986	INTEGER(iwp) :: nys_on_file !<
2987
2988	LOGICAL, INTENT(OUT) :: found
2989
2990	REAL(wp), DIMENSION(nzb:nzt+1,nys_on_file-nbgp:nyn_on_file+nbgp,nxl_on_file-nbgp:nxr_on_file+nbgp) :: tmp_3d !<
2991
2992
2993	found = .TRUE.
2994
2995	SELECT CASE ( restart_string(1:length) )
2996
2997	CASE ( 'iran' ) ! matching random numbers is still unresolved issue
2998	IF ( k == 1 ) READ ( 13 ) iran, iran_part
2999
3000	CASE ( 'pc_av' )
3001	IF ( .NOT. ALLOCATED( pc_av ) ) THEN
3002	ALLOCATE( pc_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3003	ENDIF
3004	IF ( k == 1 ) READ ( 13 ) tmp_3d
3005	pc_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3006	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3007
3008	CASE ( 'pr_av' )
3009	IF ( .NOT. ALLOCATED( pr_av ) ) THEN
3010	ALLOCATE( pr_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3011	ENDIF
3012	IF ( k == 1 ) READ ( 13 ) tmp_3d
3013	pr_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3014	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3015
3016	CASE ( 'ql_c_av' )
3017	IF ( .NOT. ALLOCATED( ql_c_av ) ) THEN
3018	ALLOCATE( ql_c_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3019	ENDIF
3020	IF ( k == 1 ) READ ( 13 ) tmp_3d
3021	ql_c_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3022	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3023
3024	CASE ( 'ql_v_av' )
3025	IF ( .NOT. ALLOCATED( ql_v_av ) ) THEN
3026	ALLOCATE( ql_v_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3027	ENDIF
3028	IF ( k == 1 ) READ ( 13 ) tmp_3d
3029	ql_v_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3030	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3031
3032	CASE ( 'ql_vp_av' )
3033	IF ( .NOT. ALLOCATED( ql_vp_av ) ) THEN
3034	ALLOCATE( ql_vp_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3035	ENDIF
3036	IF ( k == 1 ) READ ( 13 ) tmp_3d
3037	ql_vp_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3038	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3039
3040	CASE DEFAULT
3041
3042	found = .FALSE.
3043
3044	END SELECT
3045
3046
3047	END SUBROUTINE lpm_rrd_local
3048
3049	!------------------------------------------------------------------------------!
3050	! Description:
3051	! ------------
3052	!> This routine writes the respective restart data for the lpm.
3053	!------------------------------------------------------------------------------!
3054	SUBROUTINE lpm_wrd_local
3055
3056	CHARACTER (LEN=10) :: particle_binary_version !<
3057
3058	INTEGER(iwp) :: ip !<
3059	INTEGER(iwp) :: jp !<
3060	INTEGER(iwp) :: kp !<
3061	!
3062	!-- First open the output unit.
3063	IF ( myid_char == '' ) THEN
3064	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT'//myid_char, &
3065	FORM='UNFORMATTED')
3066	ELSE
3067	IF ( myid == 0 ) CALL local_system( 'mkdir PARTICLE_RESTART_DATA_OUT' )
3068	#if defined( __parallel )
3069	!
3070	!-- Set a barrier in order to allow that thereafter all other processors
3071	!-- in the directory created by PE0 can open their file
3072	CALL MPI_BARRIER( comm2d, ierr )
3073	#endif
3074	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT/'//myid_char, &
3075	FORM='UNFORMATTED' )
3076	ENDIF
3077
3078	!
3079	!-- Write the version number of the binary format.
3080	!-- Attention: After changes to the following output commands the version
3081	!-- --------- number of the variable particle_binary_version must be
3082	!-- changed! Also, the version number and the list of arrays
3083	!-- to be read in lpm_read_restart_file must be adjusted
3084	!-- accordingly.
3085	particle_binary_version = '4.0'
3086	WRITE ( 90 ) particle_binary_version
3087
3088	!
3089	!-- Write some particle parameters, the size of the particle arrays
3090	WRITE ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
3091	last_particle_release_time, number_of_particle_groups, &
3092	particle_groups, time_write_particle_data
3093
3094	WRITE ( 90 ) prt_count
3095
3096	DO ip = nxl, nxr
3097	DO jp = nys, nyn
3098	DO kp = nzb+1, nzt
3099	number_of_particles = prt_count(kp,jp,ip)
3100	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
3101	IF ( number_of_particles <= 0 ) CYCLE
3102	WRITE ( 90 ) particles
3103	ENDDO
3104	ENDDO
3105	ENDDO
3106
3107	CLOSE ( 90 )
3108
3109	#if defined( __parallel )
3110	CALL MPI_BARRIER( comm2d, ierr )
3111	#endif
3112
3113	CALL wrd_write_string( 'iran' )
3114	WRITE ( 14 ) iran, iran_part
3115
3116
3117	END SUBROUTINE lpm_wrd_local
3118
3119
3120	!------------------------------------------------------------------------------!
3121	! Description:
3122	! ------------
3123	!> This routine writes the respective restart data for the lpm.
3124	!------------------------------------------------------------------------------!
3125	SUBROUTINE lpm_wrd_global
3126
3127	CALL wrd_write_string( 'curvature_solution_effects' )
3128	WRITE ( 14 ) curvature_solution_effects
3129
3130	END SUBROUTINE lpm_wrd_global
3131
3132
3133	!------------------------------------------------------------------------------!
3134	! Description:
3135	! ------------
3136	!> This routine writes the respective restart data for the lpm.
3137	!------------------------------------------------------------------------------!
3138	SUBROUTINE lpm_rrd_global( found )
3139
3140	USE control_parameters, &
3141	ONLY: length, restart_string
3142
3143	LOGICAL, INTENT(OUT) :: found
3144
3145	found = .TRUE.
3146
3147	SELECT CASE ( restart_string(1:length) )
3148
3149	CASE ( 'curvature_solution_effects' )
3150	READ ( 13 ) curvature_solution_effects
3151
3152	! CASE ( 'global_paramter' )
3153	! READ ( 13 ) global_parameter
3154	! CASE ( 'global_array' )
3155	! IF ( .NOT. ALLOCATED( global_array ) ) ALLOCATE( global_array(1:10) )
3156	! READ ( 13 ) global_array
3157
3158	CASE DEFAULT
3159
3160	found = .FALSE.
3161
3162	END SELECT
3163
3164	END SUBROUTINE lpm_rrd_global
3165
3166
3167	!------------------------------------------------------------------------------!
3168	! Description:
3169	! ------------
3170	!> This is a submodule of the lagrangian particle model. It contains all
3171	!> dynamic processes of the lpm. This includes the advection (resolved and sub-
3172	!> grid scale) as well as the boundary conditions of particles. As a next step
3173	!> this submodule should be excluded as an own file.
3174	!------------------------------------------------------------------------------!
3175	SUBROUTINE lpm_advec (interpolation_method,ip,jp,kp)
3176
3177	CHARACTER (LEN=*), INTENT(IN) :: interpolation_method !<
3178	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
3179
3180	INTEGER(iwp) :: i !< index variable along x
3181	INTEGER(iwp) :: i_next !< index variable along x
3182	INTEGER(iwp) :: ip !< index variable along x
3183	INTEGER(iwp) :: iteration_steps = 1 !< amount of iterations steps for corrector step
3184	INTEGER(iwp) :: j !< index variable along y
3185	INTEGER(iwp) :: j_next !< index variable along y
3186	INTEGER(iwp) :: jp !< index variable along y
3187	INTEGER(iwp) :: k !< index variable along z
3188	INTEGER(iwp) :: k_wall !< vertical index of topography top
3189	INTEGER(iwp) :: kp !< index variable along z
3190	INTEGER(iwp) :: k_next !< index variable along z
3191	INTEGER(iwp) :: kw !< index variable along z
3192	INTEGER(iwp) :: kkw !< index variable along z
3193	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
3194	INTEGER(iwp) :: nb !< block number particles are sorted in
3195	INTEGER(iwp) :: particle_end !< end index for partilce loop
3196	INTEGER(iwp) :: particle_start !< start index for particle loop
3197	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
3198	INTEGER(iwp) :: subbox_end !< end index for loop over subboxes in particle advection
3199	INTEGER(iwp) :: subbox_start !< start index for loop over subboxes in particle advection
3200	INTEGER(iwp) :: nn !< loop variable over iterations steps
3201
3202	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
3203	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
3204
3205	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
3206	REAL(wp) :: alpha !< interpolation facor for x-direction
3207
3208	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
3209	REAL(wp) :: beta !< interpolation facor for y-direction
3210	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
3211	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
3212	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
3213	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
3214	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
3215	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
3216	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
3217	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
3218	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
3219	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
3220	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
3221	REAL(wp) :: diameter !< diamter of droplet
3222	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
3223	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
3224	REAL(wp) :: dt_particle_m !< previous particle time step
3225	REAL(wp) :: dz_temp !< dummy for the vertical grid spacing
3226	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
3227	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
3228	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
3229	REAL(wp) :: exp_arg !< argument in the exponent - particle radius
3230	REAL(wp) :: exp_term !< exponent term
3231	REAL(wp) :: gamma !< interpolation facor for z-direction
3232	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
3233	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
3234	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
3235	REAL(wp) :: random_gauss !< Gaussian-distributed random number used for SGS particle advection
3236	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
3237	REAL(wp) :: rg1 !< Gaussian distributed random number
3238	REAL(wp) :: rg2 !< Gaussian distributed random number
3239	REAL(wp) :: rg3 !< Gaussian distributed random number
3240	REAL(wp) :: sigma !< velocity standard deviation
3241	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
3242	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
3243	REAL(wp) :: unext !< calculated particle u-velocity of corrector step
3244	REAL(wp) :: us_int !< friction velocity at particle grid box
3245	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
3246	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
3247	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
3248	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
3249	REAL(wp) :: vnext !< calculated particle v-velocity of corrector step
3250	REAL(wp) :: vv_int !< dummy to compute interpolated mean SGS TKE, used to scale SGS advection
3251	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
3252	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
3253	REAL(wp) :: wnext !< calculated particle w-velocity of corrector step
3254	REAL(wp) :: w_s !< terminal velocity of droplets
3255	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
3256	REAL(wp) :: xp !< calculated particle position in x of predictor step
3257	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
3258	REAL(wp) :: yp !< calculated particle position in y of predictor step
3259	REAL(wp) :: z_p !< surface layer height (0.5 dz)
3260	REAL(wp) :: zp !< calculated particle position in z of predictor step
3261
3262	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
3263	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
3264	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
3265	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
3266	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
3267	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
3268
3269	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
3270	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !< ratio between the density of the fluid and the density of the particles
3271	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
3272	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
3273	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
3274	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
3275	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
3276	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
3277	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
3278	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
3279	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
3280	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !< SGS particle velocity - u-component
3281	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !< SGS particle velocity - v-component
3282	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !< SGS particle velocity - w-component
3283	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
3284	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
3285	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
3286	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
3287	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
3288	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
3289
3290	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
3291
3292	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
3293	!
3294	!-- Determine height of Prandtl layer and distance between Prandtl-layer
3295	!-- height and horizontal mean roughness height, which are required for
3296	!-- vertical logarithmic interpolation of horizontal particle speeds
3297	!-- (for particles below first vertical grid level).
3298	z_p = zu(nzb+1) - zw(nzb)
3299	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
3300
3301	xv = particles(1:number_of_particles)%x
3302	yv = particles(1:number_of_particles)%y
3303	zv = particles(1:number_of_particles)%z
3304	dt_particle = dt_3d
3305
3306
3307	SELECT CASE ( interpolation_method )
3308
3309	!
3310	!-- This case uses a simple interpolation method for the particle velocites,
3311	!-- and applying a predictor-corrector method. @attention: for the corrector
3312	!-- step the velocities of t(n+1) are required. However, at this moment of
3313	!-- the time integration they are not free of divergence. This interpolation
3314	!-- method is described in more detail in Grabowski et al., 2018 (GMD).
3315	CASE ( 'simple_corrector' )
3316	!
3317	!-- Predictor step
3318	kkw = kp - 1
3319	DO n = 1, number_of_particles
3320
3321	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3322	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3323
3324	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3325	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3326
3327	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3328	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3329	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3330
3331	ENDDO
3332
3333	!
3334	!-- Corrector step
3335	DO n = 1, number_of_particles
3336
3337	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3338
3339	DO nn = 1, iteration_steps
3340
3341	!
3342	!-- Guess new position
3343	xp = particles(n)%x + u_int(n) * dt_particle(n)
3344	yp = particles(n)%y + v_int(n) * dt_particle(n)
3345	zp = particles(n)%z + w_int(n) * dt_particle(n)
3346	!
3347	!-- x direction
3348	i_next = FLOOR( xp * ddx , KIND=iwp)
3349	alpha = MAX( MIN( ( xp - i_next * dx ) * ddx, 1.0_wp ), 0.0_wp )
3350	!
3351	!-- y direction
3352	j_next = FLOOR( yp * ddy )
3353	beta = MAX( MIN( ( yp - j_next * dy ) * ddy, 1.0_wp ), 0.0_wp )
3354	!
3355	!-- z_direction
3356	k_next = MAX( MIN( FLOOR( zp / (zw(kkw+1)-zw(kkw)) ), nzt ), 0)
3357	gamma = MAX( MIN( ( zp - zw(k_next) ) / &
3358	( zw(k_next+1) - zw(k_next) ), 1.0_wp ), 0.0_wp )
3359	!
3360	!-- Calculate part of the corrector step
3361	unext = u_p(k_next+1, j_next, i_next) * ( 1.0_wp - alpha ) + &
3362	u_p(k_next+1, j_next, i_next+1) * alpha
3363
3364	vnext = v_p(k_next+1, j_next, i_next) * ( 1.0_wp - beta ) + &
3365	v_p(k_next+1, j_next+1, i_next ) * beta
3366
3367	wnext = w_p(k_next, j_next, i_next) * ( 1.0_wp - gamma ) + &
3368	w_p(k_next+1, j_next, i_next ) * gamma
3369
3370	!
3371	!-- Calculate interpolated particle velocity with predictor
3372	!-- corrector step. u_int, v_int and w_int describes the part of
3373	!-- the predictor step. unext, vnext and wnext is the part of the
3374	!-- corrector step. The resulting new position is set below. The
3375	!-- implementation is based on Grabowski et al., 2018 (GMD).
3376	u_int(n) = 0.5_wp * ( u_int(n) + unext )
3377	v_int(n) = 0.5_wp * ( v_int(n) + vnext )
3378	w_int(n) = 0.5_wp * ( w_int(n) + wnext )
3379
3380	ENDDO
3381	ENDDO
3382
3383
3384	!
3385	!-- This case uses a simple interpolation method for the particle velocites,
3386	!-- and applying a predictor.
3387	CASE ( 'simple_predictor' )
3388	!
3389	!-- The particle position for the w velociy is based on the value of kp and kp-1
3390	kkw = kp - 1
3391	DO n = 1, number_of_particles
3392	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3393
3394	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3395	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3396
3397	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3398	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3399
3400	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3401	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3402	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3403	ENDDO
3404	!
3405	!-- The trilinear interpolation.
3406	CASE ( 'trilinear' )
3407
3408	start_index = grid_particles(kp,jp,ip)%start_index
3409	end_index = grid_particles(kp,jp,ip)%end_index
3410
3411	DO nb = 0, 7
3412	!
3413	!-- Interpolate u velocity-component
3414	i = ip
3415	j = jp + block_offset(nb)%j_off
3416	k = kp + block_offset(nb)%k_off
3417
3418	DO n = start_index(nb), end_index(nb)
3419	!
3420	!-- Interpolation of the u velocity component onto particle position.
3421	!-- Particles are interpolation bi-linearly in the horizontal and a
3422	!-- linearly in the vertical. An exception is made for particles below
3423	!-- the first vertical grid level in case of a prandtl layer. In this
3424	!-- case the horizontal particle velocity components are determined using
3425	!-- Monin-Obukhov relations (if branch).
3426	!-- First, check if particle is located below first vertical grid level
3427	!-- above topography (Prandtl-layer height)
3428	!-- Determine vertical index of topography top
3429	k_wall = get_topography_top_index_ji( jp, ip, 's' )
3430
3431	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3432	!
3433	!-- Resolved-scale horizontal particle velocity is zero below z0.
3434	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3435	u_int(n) = 0.0_wp
3436	ELSE
3437	!
3438	!-- Determine the sublayer. Further used as index.
3439	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3440	* REAL( number_of_sublayers, KIND=wp ) &
3441	* d_z_p_z0
3442	!
3443	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3444	!-- interpolate linearly between precalculated logarithm.
3445	log_z_z0_int = log_z_z0(INT(height_p)) &
3446	+ ( height_p - INT(height_p) ) &
3447	* ( log_z_z0(INT(height_p)+1) &
3448	- log_z_z0(INT(height_p)) &
3449	)
3450	!
3451	!-- Get friction velocity and momentum flux from new surface data
3452	!-- types.
3453	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3454	surf_def_h(0)%end_index(jp,ip) ) THEN
3455	surf_start = surf_def_h(0)%start_index(jp,ip)
3456	!-- Limit friction velocity. In narrow canyons or holes the
3457	!-- friction velocity can become very small, resulting in a too
3458	!-- large particle speed.
3459	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3460	usws_int = surf_def_h(0)%usws(surf_start)
3461	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3462	surf_lsm_h%end_index(jp,ip) ) THEN
3463	surf_start = surf_lsm_h%start_index(jp,ip)
3464	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3465	usws_int = surf_lsm_h%usws(surf_start)
3466	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3467	surf_usm_h%end_index(jp,ip) ) THEN
3468	surf_start = surf_usm_h%start_index(jp,ip)
3469	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3470	usws_int = surf_usm_h%usws(surf_start)
3471	ENDIF
3472	!
3473	!-- Neutral solution is applied for all situations, e.g. also for
3474	!-- unstable and stable situations. Even though this is not exact
3475	!-- this saves a lot of CPU time since several calls of intrinsic
3476	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3477	!-- as sensitivity studies revealed no significant effect of
3478	!-- using the neutral solution also for un/stable situations.
3479	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
3480	* log_z_z0_int - u_gtrans
3481	ENDIF
3482	!
3483	!-- Particle above the first grid level. Bi-linear interpolation in the
3484	!-- horizontal and linear interpolation in the vertical direction.
3485	ELSE
3486	x = xv(n) - i * dx
3487	y = yv(n) + ( 0.5_wp - j ) * dy
3488	aa = x2 + y2
3489	bb = ( dx - x )2 + y2
3490	cc = x2 + ( dy - y )2
3491	dd = ( dx - x )2 + ( dy - y )2
3492	gg = aa + bb + cc + dd
3493
3494	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
3495	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
3496	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3497
3498	IF ( k == nzt ) THEN
3499	u_int(n) = u_int_l
3500	ELSE
3501	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
3502	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
3503	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3504	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3505	( u_int_u - u_int_l )
3506	ENDIF
3507	ENDIF
3508	ENDDO
3509	!
3510	!-- Same procedure for interpolation of the v velocity-component
3511	i = ip + block_offset(nb)%i_off
3512	j = jp
3513	k = kp + block_offset(nb)%k_off
3514
3515	DO n = start_index(nb), end_index(nb)
3516	!
3517	!-- Determine vertical index of topography top
3518	k_wall = get_topography_top_index_ji( jp,ip, 's' )
3519
3520	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3521	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3522	!
3523	!-- Resolved-scale horizontal particle velocity is zero below z0.
3524	v_int(n) = 0.0_wp
3525	ELSE
3526	!
3527	!-- Determine the sublayer. Further used as index. Please note,
3528	!-- logarithmus can not be reused from above, as in in case of
3529	!-- topography particle on u-grid can be above surface-layer height,
3530	!-- whereas it can be below on v-grid.
3531	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3532	* REAL( number_of_sublayers, KIND=wp ) &
3533	* d_z_p_z0
3534	!
3535	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3536	!-- interpolate linearly between precalculated logarithm.
3537	log_z_z0_int = log_z_z0(INT(height_p)) &
3538	+ ( height_p - INT(height_p) ) &
3539	* ( log_z_z0(INT(height_p)+1) &
3540	- log_z_z0(INT(height_p)) &
3541	)
3542	!
3543	!-- Get friction velocity and momentum flux from new surface data
3544	!-- types.
3545	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3546	surf_def_h(0)%end_index(jp,ip) ) THEN
3547	surf_start = surf_def_h(0)%start_index(jp,ip)
3548	!-- Limit friction velocity. In narrow canyons or holes the
3549	!-- friction velocity can become very small, resulting in a too
3550	!-- large particle speed.
3551	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3552	vsws_int = surf_def_h(0)%vsws(surf_start)
3553	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3554	surf_lsm_h%end_index(jp,ip) ) THEN
3555	surf_start = surf_lsm_h%start_index(jp,ip)
3556	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3557	vsws_int = surf_lsm_h%vsws(surf_start)
3558	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3559	surf_usm_h%end_index(jp,ip) ) THEN
3560	surf_start = surf_usm_h%start_index(jp,ip)
3561	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3562	vsws_int = surf_usm_h%vsws(surf_start)
3563	ENDIF
3564	!
3565	!-- Neutral solution is applied for all situations, e.g. also for
3566	!-- unstable and stable situations. Even though this is not exact
3567	!-- this saves a lot of CPU time since several calls of intrinsic
3568	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3569	!-- as sensitivity studies revealed no significant effect of
3570	!-- using the neutral solution also for un/stable situations.
3571	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
3572	* log_z_z0_int - v_gtrans
3573
3574	ENDIF
3575	ELSE
3576	x = xv(n) + ( 0.5_wp - i ) * dx
3577	y = yv(n) - j * dy
3578	aa = x2 + y2
3579	bb = ( dx - x )2 + y2
3580	cc = x2 + ( dy - y )2
3581	dd = ( dx - x )2 + ( dy - y )2
3582	gg = aa + bb + cc + dd
3583
3584	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
3585	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
3586	) / ( 3.0_wp * gg ) - v_gtrans
3587
3588	IF ( k == nzt ) THEN
3589	v_int(n) = v_int_l
3590	ELSE
3591	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
3592	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
3593	) / ( 3.0_wp * gg ) - v_gtrans
3594	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3595	( v_int_u - v_int_l )
3596	ENDIF
3597	ENDIF
3598	ENDDO
3599	!
3600	!-- Same procedure for interpolation of the w velocity-component
3601	i = ip + block_offset(nb)%i_off
3602	j = jp + block_offset(nb)%j_off
3603	k = kp - 1
3604
3605	DO n = start_index(nb), end_index(nb)
3606	IF ( vertical_particle_advection(particles(n)%group) ) THEN
3607	x = xv(n) + ( 0.5_wp - i ) * dx
3608	y = yv(n) + ( 0.5_wp - j ) * dy
3609	aa = x2 + y2
3610	bb = ( dx - x )2 + y2
3611	cc = x2 + ( dy - y )2
3612	dd = ( dx - x )2 + ( dy - y )2
3613	gg = aa + bb + cc + dd
3614
3615	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
3616	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
3617	) / ( 3.0_wp * gg )
3618
3619	IF ( k == nzt ) THEN
3620	w_int(n) = w_int_l
3621	ELSE
3622	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
3623	( gg-bb ) * w(k+1,j,i+1) + &
3624	( gg-cc ) * w(k+1,j+1,i) + &
3625	( gg-dd ) * w(k+1,j+1,i+1) &
3626	) / ( 3.0_wp * gg )
3627	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
3628	( w_int_u - w_int_l )
3629	ENDIF
3630	ELSE
3631	w_int(n) = 0.0_wp
3632	ENDIF
3633	ENDDO
3634	ENDDO
3635
3636	CASE DEFAULT
3637	WRITE( message_string, * ) 'unknown particle velocity interpolation method = "', &
3638	TRIM( interpolation_method ), '"'
3639	CALL message( 'lpm_advec', 'PA0660', 1, 2, 0, 6, 0 )
3640
3641	END SELECT
3642
3643	!-- Interpolate and calculate quantities needed for calculating the SGS
3644	!-- velocities
3645	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
3646
3647	DO nb = 0,7
3648
3649	subbox_at_wall = .FALSE.
3650	!
3651	!-- In case of topography check if subbox is adjacent to a wall
3652	IF ( .NOT. topography == 'flat' ) THEN
3653	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
3654	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
3655	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
3656	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
3657	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
3658	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
3659	THEN
3660	subbox_at_wall = .TRUE.
3661	ENDIF
3662	ENDIF
3663	IF ( subbox_at_wall ) THEN
3664	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
3665	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
3666	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
3667	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
3668	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
3669	!
3670	!-- Set flag for stochastic equation.
3671	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
3672	ELSE
3673	i = ip + block_offset(nb)%i_off
3674	j = jp + block_offset(nb)%j_off
3675	k = kp + block_offset(nb)%k_off
3676
3677	DO n = start_index(nb), end_index(nb)
3678	!
3679	!-- Interpolate TKE
3680	x = xv(n) + ( 0.5_wp - i ) * dx
3681	y = yv(n) + ( 0.5_wp - j ) * dy
3682	aa = x2 + y2
3683	bb = ( dx - x )2 + y2
3684	cc = x2 + ( dy - y )2
3685	dd = ( dx - x )2 + ( dy - y )2
3686	gg = aa + bb + cc + dd
3687
3688	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
3689	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
3690	) / ( 3.0_wp * gg )
3691
3692	IF ( k+1 == nzt+1 ) THEN
3693	e_int(n) = e_int_l
3694	ELSE
3695	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
3696	( gg - bb ) * e(k+1,j,i+1) + &
3697	( gg - cc ) * e(k+1,j+1,i) + &
3698	( gg - dd ) * e(k+1,j+1,i+1) &
3699	) / ( 3.0_wp * gg )
3700	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3701	( e_int_u - e_int_l )
3702	ENDIF
3703	!
3704	!-- Needed to avoid NaN particle velocities (this might not be
3705	!-- required any more)
3706	IF ( e_int(n) <= 0.0_wp ) THEN
3707	e_int(n) = 1.0E-20_wp
3708	ENDIF
3709	!
3710	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
3711	!-- all position variables from above (TKE))
3712	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
3713	( gg - bb ) * de_dx(k,j,i+1) + &
3714	( gg - cc ) * de_dx(k,j+1,i) + &
3715	( gg - dd ) * de_dx(k,j+1,i+1) &
3716	) / ( 3.0_wp * gg )
3717
3718	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3719	de_dx_int(n) = de_dx_int_l
3720	ELSE
3721	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
3722	( gg - bb ) * de_dx(k+1,j,i+1) + &
3723	( gg - cc ) * de_dx(k+1,j+1,i) + &
3724	( gg - dd ) * de_dx(k+1,j+1,i+1) &
3725	) / ( 3.0_wp * gg )
3726	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3727	( de_dx_int_u - de_dx_int_l )
3728	ENDIF
3729	!
3730	!-- Interpolate the TKE gradient along y
3731	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
3732	( gg - bb ) * de_dy(k,j,i+1) + &
3733	( gg - cc ) * de_dy(k,j+1,i) + &
3734	( gg - dd ) * de_dy(k,j+1,i+1) &
3735	) / ( 3.0_wp * gg )
3736	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3737	de_dy_int(n) = de_dy_int_l
3738	ELSE
3739	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
3740	( gg - bb ) * de_dy(k+1,j,i+1) + &
3741	( gg - cc ) * de_dy(k+1,j+1,i) + &
3742	( gg - dd ) * de_dy(k+1,j+1,i+1) &
3743	) / ( 3.0_wp * gg )
3744	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3745	( de_dy_int_u - de_dy_int_l )
3746	ENDIF
3747
3748	!
3749	!-- Interpolate the TKE gradient along z
3750	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
3751	de_dz_int(n) = 0.0_wp
3752	ELSE
3753	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
3754	( gg - bb ) * de_dz(k,j,i+1) + &
3755	( gg - cc ) * de_dz(k,j+1,i) + &
3756	( gg - dd ) * de_dz(k,j+1,i+1) &
3757	) / ( 3.0_wp * gg )
3758
3759	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3760	de_dz_int(n) = de_dz_int_l
3761	ELSE
3762	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
3763	( gg - bb ) * de_dz(k+1,j,i+1) + &
3764	( gg - cc ) * de_dz(k+1,j+1,i) + &
3765	( gg - dd ) * de_dz(k+1,j+1,i+1) &
3766	) / ( 3.0_wp * gg )
3767	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3768	( de_dz_int_u - de_dz_int_l )
3769	ENDIF
3770	ENDIF
3771
3772	!
3773	!-- Interpolate the dissipation of TKE
3774	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
3775	( gg - bb ) * diss(k,j,i+1) + &
3776	( gg - cc ) * diss(k,j+1,i) + &
3777	( gg - dd ) * diss(k,j+1,i+1) &
3778	) / ( 3.0_wp * gg )
3779
3780	IF ( k == nzt ) THEN
3781	diss_int(n) = diss_int_l
3782	ELSE
3783	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
3784	( gg - bb ) * diss(k+1,j,i+1) + &
3785	( gg - cc ) * diss(k+1,j+1,i) + &
3786	( gg - dd ) * diss(k+1,j+1,i+1) &
3787	) / ( 3.0_wp * gg )
3788	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3789	( diss_int_u - diss_int_l )
3790	ENDIF
3791
3792	!
3793	!-- Set flag for stochastic equation.
3794	term_1_2(n) = 1.0_wp
3795	ENDDO
3796	ENDIF
3797	ENDDO
3798
3799	DO nb = 0,7
3800	i = ip + block_offset(nb)%i_off
3801	j = jp + block_offset(nb)%j_off
3802	k = kp + block_offset(nb)%k_off
3803
3804	DO n = start_index(nb), end_index(nb)
3805	!
3806	!-- Vertical interpolation of the horizontally averaged SGS TKE and
3807	!-- resolved-scale velocity variances and use the interpolated values
3808	!-- to calculate the coefficient fs, which is a measure of the ratio
3809	!-- of the subgrid-scale turbulent kinetic energy to the total amount
3810	!-- of turbulent kinetic energy.
3811	IF ( k == 0 ) THEN
3812	e_mean_int = hom(0,1,8,0)
3813	ELSE
3814	e_mean_int = hom(k,1,8,0) + &
3815	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
3816	( zu(k+1) - zu(k) ) * &
3817	( zv(n) - zu(k) )
3818	ENDIF
3819
3820	kw = kp - 1
3821
3822	IF ( k == 0 ) THEN
3823	aa = hom(k+1,1,30,0) * ( zv(n) / &
3824	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3825	bb = hom(k+1,1,31,0) * ( zv(n) / &
3826	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3827	cc = hom(kw+1,1,32,0) * ( zv(n) / &
3828	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
3829	ELSE
3830	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
3831	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3832	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
3833	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3834	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
3835	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
3836	ENDIF
3837
3838	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
3839	!
3840	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
3841	!-- an educated guess for the given case.
3842	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
3843	fs_int(n) = 1.0_wp
3844	ELSE
3845	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
3846	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
3847	ENDIF
3848
3849	ENDDO
3850	ENDDO
3851
3852	DO nb = 0, 7
3853	DO n = start_index(nb), end_index(nb)
3854	rg(n,1) = random_gauss( iran_part, 5.0_wp )
3855	rg(n,2) = random_gauss( iran_part, 5.0_wp )
3856	rg(n,3) = random_gauss( iran_part, 5.0_wp )
3857	ENDDO
3858	ENDDO
3859
3860	DO nb = 0, 7
3861	DO n = start_index(nb), end_index(nb)
3862
3863	!
3864	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
3865	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
3866	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
3867
3868	!
3869	!-- Calculate the next particle timestep. dt_gap is the time needed to
3870	!-- complete the current LES timestep.
3871	dt_gap(n) = dt_3d - particles(n)%dt_sum
3872	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
3873	particles(n)%aux1 = lagr_timescale(n)
3874	particles(n)%aux2 = dt_gap(n)
3875	!
3876	!-- The particle timestep should not be too small in order to prevent
3877	!-- the number of particle timesteps of getting too large
3878	IF ( dt_particle(n) < dt_min_part ) THEN
3879	IF ( dt_min_part < dt_gap(n) ) THEN
3880	dt_particle(n) = dt_min_part
3881	ELSE
3882	dt_particle(n) = dt_gap(n)
3883	ENDIF
3884	ENDIF
3885	rvar1_temp(n) = particles(n)%rvar1
3886	rvar2_temp(n) = particles(n)%rvar2
3887	rvar3_temp(n) = particles(n)%rvar3
3888	!
3889	!-- Calculate the SGS velocity components
3890	IF ( particles(n)%age == 0.0_wp ) THEN
3891	!
3892	!-- For new particles the SGS components are derived from the SGS
3893	!-- TKE. Limit the Gaussian random number to the interval
3894	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
3895	!-- from becoming unrealistically large.
3896	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3897	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
3898	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3899	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
3900	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3901	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
3902
3903	ELSE
3904	!
3905	!-- Restriction of the size of the new timestep: compared to the
3906	!-- previous timestep the increase must not exceed 200%. First,
3907	!-- check if age > age_m, in order to prevent that particles get zero
3908	!-- timestep.
3909	dt_particle_m = MERGE( dt_particle(n), &
3910	particles(n)%age - particles(n)%age_m, &
3911	particles(n)%age - particles(n)%age_m < &
3912	1E-8_wp )
3913	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
3914	dt_particle(n) = 2.0_wp * dt_particle_m
3915	ENDIF
3916
3917	!-- For old particles the SGS components are correlated with the
3918	!-- values from the previous timestep. Random numbers have also to
3919	!-- be limited (see above).
3920	!-- As negative values for the subgrid TKE are not allowed, the
3921	!-- change of the subgrid TKE with time cannot be smaller than
3922	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
3923	!-- value for the change of TKE
3924	de_dt_min = - e_int(n) / dt_particle(n)
3925
3926	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3927
3928	IF ( de_dt < de_dt_min ) THEN
3929	de_dt = de_dt_min
3930	ENDIF
3931
3932	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
3933	de_dx_int(n), de_dt, diss_int(n), &
3934	dt_particle(n), rg(n,1), term_1_2(n) )
3935
3936	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
3937	de_dy_int(n), de_dt, diss_int(n), &
3938	dt_particle(n), rg(n,2), term_1_2(n) )
3939
3940	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
3941	de_dz_int(n), de_dt, diss_int(n), &
3942	dt_particle(n), rg(n,3), term_1_2(n) )
3943
3944	ENDIF
3945
3946	ENDDO
3947	ENDDO
3948	!
3949	!-- Check if the added SGS velocities result in a violation of the CFL-
3950	!-- criterion. If yes choose a smaller timestep based on the new velocities
3951	!-- and calculate SGS velocities again
3952	dz_temp = zw(kp)-zw(kp-1)
3953
3954	DO nb = 0, 7
3955	DO n = start_index(nb), end_index(nb)
3956	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
3957	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
3958	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
3959	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
3960
3961	dt_particle(n) = 0.9_wp * MIN( &
3962	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
3963	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
3964	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
3965
3966	!
3967	!-- Reset temporary SGS velocites to "current" ones
3968	rvar1_temp(n) = particles(n)%rvar1
3969	rvar2_temp(n) = particles(n)%rvar2
3970	rvar3_temp(n) = particles(n)%rvar3
3971
3972	de_dt_min = - e_int(n) / dt_particle(n)
3973
3974	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3975
3976	IF ( de_dt < de_dt_min ) THEN
3977	de_dt = de_dt_min
3978	ENDIF
3979
3980	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
3981	de_dx_int(n), de_dt, diss_int(n), &
3982	dt_particle(n), rg(n,1), term_1_2(n) )
3983
3984	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
3985	de_dy_int(n), de_dt, diss_int(n), &
3986	dt_particle(n), rg(n,2), term_1_2(n) )
3987
3988	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
3989	de_dz_int(n), de_dt, diss_int(n), &
3990	dt_particle(n), rg(n,3), term_1_2(n) )
3991	ENDIF
3992
3993	!
3994	!-- Update particle velocites
3995	particles(n)%rvar1 = rvar1_temp(n)
3996	particles(n)%rvar2 = rvar2_temp(n)
3997	particles(n)%rvar3 = rvar3_temp(n)
3998	u_int(n) = u_int(n) + particles(n)%rvar1
3999	v_int(n) = v_int(n) + particles(n)%rvar2
4000	w_int(n) = w_int(n) + particles(n)%rvar3
4001	!
4002	!-- Store the SGS TKE of the current timelevel which is needed for
4003	!-- for calculating the SGS particle velocities at the next timestep
4004	particles(n)%e_m = e_int(n)
4005	ENDDO
4006	ENDDO
4007
4008	ELSE
4009	!
4010	!-- If no SGS velocities are used, only the particle timestep has to
4011	!-- be set
4012	dt_particle = dt_3d
4013
4014	ENDIF
4015
4016	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
4017	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
4018	!
4019	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4020	!-- number_of_particles. This depends on the selected interpolation method.
4021	!-- If particle interpolation method is not trilinear, then the sorting within
4022	!-- subboxes is not required. However, therefore the index start_index(nb) and
4023	!-- end_index(nb) are not defined and the loops are still over
4024	!-- number_of_particles. @todo find a more generic way to write this loop or
4025	!-- delete trilinear interpolation
4026	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4027	subbox_start = 0
4028	subbox_end = 7
4029	ELSE
4030	subbox_start = 1
4031	subbox_end = 1
4032	ENDIF
4033	!
4034	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4035	!-- are introduced, as they are not required. Accordingly, this loops goes
4036	!-- from 1 to 1.
4037	DO nb = subbox_start, subbox_end
4038	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4039	particle_start = start_index(nb)
4040	particle_end = end_index(nb)
4041	ELSE
4042	particle_start = 1
4043	particle_end = number_of_particles
4044	ENDIF
4045	!
4046	!-- Loop from particle start to particle end
4047	DO n = particle_start, particle_end
4048
4049	!
4050	!-- Particle advection
4051	IF ( dens_ratio(n) == 0.0_wp ) THEN
4052	!
4053	!-- Pure passive transport (without particle inertia)
4054	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
4055	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
4056	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
4057
4058	particles(n)%speed_x = u_int(n)
4059	particles(n)%speed_y = v_int(n)
4060	particles(n)%speed_z = w_int(n)
4061
4062	ELSE
4063	!
4064	!-- Transport of particles with inertia
4065	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
4066	dt_particle(n)
4067	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
4068	dt_particle(n)
4069	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
4070	dt_particle(n)
4071
4072	!
4073	!-- Update of the particle velocity
4074	IF ( cloud_droplets ) THEN
4075	!
4076	!-- Terminal velocity is computed for vertical direction (Rogers et
4077	!-- al., 1993, J. Appl. Meteorol.)
4078	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4079	IF ( diameter <= d0_rog ) THEN
4080	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4081	ELSE
4082	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4083	ENDIF
4084
4085	!
4086	!-- If selected, add random velocities following Soelch and Kaercher
4087	!-- (2010, Q. J. R. Meteorol. Soc.)
4088	IF ( use_sgs_for_particles ) THEN
4089	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4090	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4091	1.0E-20_wp ) )
4092	sigma = SQRT( e(kp,jp,ip) )
4093
4094	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4095	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4096	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4097
4098	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4099	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4100	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4101	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4102	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4103	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4104
4105	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4106	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4107	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4108	ELSE
4109	particles(n)%speed_x = u_int(n)
4110	particles(n)%speed_y = v_int(n)
4111	particles(n)%speed_z = w_int(n) - w_s
4112	ENDIF
4113
4114	ELSE
4115
4116	IF ( use_sgs_for_particles ) THEN
4117	exp_arg = particle_groups(particles(n)%group)%exp_arg
4118	exp_term = EXP( -exp_arg * dt_particle(n) )
4119	ELSE
4120	exp_arg = particle_groups(particles(n)%group)%exp_arg
4121	exp_term = particle_groups(particles(n)%group)%exp_term
4122	ENDIF
4123	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4124	u_int(n) * ( 1.0_wp - exp_term )
4125	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4126	v_int(n) * ( 1.0_wp - exp_term )
4127	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4128	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
4129	g / exp_arg ) * ( 1.0_wp - exp_term )
4130	ENDIF
4131
4132	ENDIF
4133	ENDDO
4134	ENDDO
4135
4136	ELSE
4137	!
4138	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4139	!-- number_of_particles. This depends on the selected interpolation method.
4140	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4141	subbox_start = 0
4142	subbox_end = 7
4143	ELSE
4144	subbox_start = 1
4145	subbox_end = 1
4146	ENDIF
4147	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4148	!-- are introduced, as they are not required. Accordingly, this loops goes
4149	!-- from 1 to 1.
4150	DO nb = subbox_start, subbox_end
4151	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4152	particle_start = start_index(nb)
4153	particle_end = end_index(nb)
4154	ELSE
4155	particle_start = 1
4156	particle_end = number_of_particles
4157	ENDIF
4158	!
4159	!-- Loop from particle start to particle end
4160	DO n = particle_start, particle_end
4161
4162	!
4163	!-- Transport of particles with inertia
4164	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
4165	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
4166	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
4167	!
4168	!-- Update of the particle velocity
4169	IF ( cloud_droplets ) THEN
4170	!
4171	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
4172	!-- 1993, J. Appl. Meteorol.)
4173	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4174	IF ( diameter <= d0_rog ) THEN
4175	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4176	ELSE
4177	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4178	ENDIF
4179
4180	!
4181	!-- If selected, add random velocities following Soelch and Kaercher
4182	!-- (2010, Q. J. R. Meteorol. Soc.)
4183	IF ( use_sgs_for_particles ) THEN
4184	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4185	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4186	1.0E-20_wp ) )
4187	sigma = SQRT( e(kp,jp,ip) )
4188
4189	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4190	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4191	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4192
4193	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4194	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4195	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4196	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4197	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4198	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4199
4200	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4201	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4202	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4203	ELSE
4204	particles(n)%speed_x = u_int(n)
4205	particles(n)%speed_y = v_int(n)
4206	particles(n)%speed_z = w_int(n) - w_s
4207	ENDIF
4208
4209	ELSE
4210
4211	IF ( use_sgs_for_particles ) THEN
4212	exp_arg = particle_groups(particles(n)%group)%exp_arg
4213	exp_term = EXP( -exp_arg * dt_particle(n) )
4214	ELSE
4215	exp_arg = particle_groups(particles(n)%group)%exp_arg
4216	exp_term = particle_groups(particles(n)%group)%exp_term
4217	ENDIF
4218	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4219	u_int(n) * ( 1.0_wp - exp_term )
4220	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4221	v_int(n) * ( 1.0_wp - exp_term )
4222	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4223	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
4224	exp_arg ) * ( 1.0_wp - exp_term )
4225	ENDIF
4226	ENDDO
4227	ENDDO
4228
4229	ENDIF
4230
4231	!
4232	!-- Store the old age of the particle ( needed to prevent that a
4233	!-- particle crosses several PEs during one timestep, and for the
4234	!-- evaluation of the subgrid particle velocity fluctuations )
4235	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
4236
4237	!
4238	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4239	!-- are introduced, as they are not required. Accordingly, this loops goes
4240	!-- from 1 to 1.
4241	!
4242	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4243	!-- number_of_particles. This depends on the selected interpolation method.
4244	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4245	subbox_start = 0
4246	subbox_end = 7
4247	ELSE
4248	subbox_start = 1
4249	subbox_end = 1
4250	ENDIF
4251	DO nb = subbox_start, subbox_end
4252	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
4253	particle_start = start_index(nb)
4254	particle_end = end_index(nb)
4255	ELSE
4256	particle_start = 1
4257	particle_end = number_of_particles
4258	ENDIF
4259	!
4260	!-- Loop from particle start to particle end
4261	DO n = particle_start, particle_end
4262	!
4263	!-- Increment the particle age and the total time that the particle
4264	!-- has advanced within the particle timestep procedure
4265	particles(n)%age = particles(n)%age + dt_particle(n)
4266	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
4267
4268	!
4269	!-- Check whether there is still a particle that has not yet completed
4270	!-- the total LES timestep
4271	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
4272	dt_3d_reached_l = .FALSE.
4273	ENDIF
4274
4275	ENDDO
4276	ENDDO
4277
4278	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
4279
4280
4281	END SUBROUTINE lpm_advec
4282
4283
4284	!------------------------------------------------------------------------------!
4285	! Description:
4286	! ------------
4287	!> Calculation of subgrid-scale particle speed using the stochastic model
4288	!> of Weil et al. (2004, JAS, 61, 2877-2887).
4289	!------------------------------------------------------------------------------!
4290	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
4291	dt_n, rg_n, fac )
4292
4293	REAL(wp) :: a1 !< dummy argument
4294	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
4295	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
4296	REAL(wp) :: diss_n !< dissipation at particle position
4297	REAL(wp) :: dt_n !< particle timestep
4298	REAL(wp) :: e_n !< TKE at particle position
4299	REAL(wp) :: fac !< flag to identify adjacent topography
4300	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
4301	REAL(wp) :: rg_n !< random number
4302	REAL(wp) :: term1 !< memory term
4303	REAL(wp) :: term2 !< drift correction term
4304	REAL(wp) :: term3 !< random term
4305	REAL(wp) :: v_sgs !< subgrid-scale velocity component
4306
4307	!-- At first, limit TKE to a small non-zero number, in order to prevent
4308	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
4309	!-- (could occur at the simulation begin).
4310	e_n = MAX( e_n, 1E-20_wp )
4311	!
4312	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
4313	!-- multiplied by a flag to switch of both terms near topography.
4314	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
4315	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
4316	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
4317	!-- disabled if one of the adjacent grid points belongs to topography.
4318	!-- Moreover, in this case, the previous subgrid-scale component is also set
4319	!-- to zero.
4320
4321	a1 = fs_n * c_0 * diss_n
4322	!
4323	!-- Memory term
4324	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
4325	* fac
4326	!
4327	!-- Drift correction term
4328	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
4329	* fac
4330	!
4331	!-- Random term
4332	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
4333	!
4334	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
4335	!-- subgrid-scale velocity component is set to zero, in order to prevent a
4336	!-- velocity build-up.
4337	!-- This case, set also previous subgrid-scale component to zero.
4338	v_sgs = v_sgs * fac + term1 + term2 + term3
4339
4340	END SUBROUTINE weil_stochastic_eq
4341
4342
4343	!------------------------------------------------------------------------------!
4344	! Description:
4345	! ------------
4346	!> Boundary conditions for the Lagrangian particles.
4347	!> The routine consists of two different parts. One handles the bottom (flat)
4348	!> and top boundary. In this part, also particles which exceeded their lifetime
4349	!> are deleted.
4350	!> The other part handles the reflection of particles from vertical walls.
4351	!> This part was developed by Jin Zhang during 2006-2007.
4352	!>
4353	!> To do: Code structure for finding the t_index values and for checking the
4354	!> ----- reflection conditions is basically the same for all four cases, so it
4355	!> should be possible to further simplify/shorten it.
4356	!>
4357	!> THE WALLS PART OF THIS ROUTINE HAS NOT BEEN TESTED FOR OCEAN RUNS SO FAR!!!!
4358	!> (see offset_ocean_*)
4359	!------------------------------------------------------------------------------!
4360	SUBROUTINE lpm_boundary_conds( location_bc , i, j, k )
4361
4362	CHARACTER (LEN=*), INTENT(IN) :: location_bc !< general mode: boundary conditions at bottom/top of the model domain
4363	!< or at vertical surfaces (buildings, terrain steps)
4364	INTEGER(iwp), INTENT(IN) :: i !< grid index of particle box along x
4365	INTEGER(iwp), INTENT(IN) :: j !< grid index of particle box along y
4366	INTEGER(iwp), INTENT(IN) :: k !< grid index of particle box along z
4367
4368	INTEGER(iwp) :: inc !< dummy for sorting algorithmus
4369	INTEGER(iwp) :: ir !< dummy for sorting algorithmus
4370	INTEGER(iwp) :: i1 !< grid index (x) of old particle position
4371	INTEGER(iwp) :: i2 !< grid index (x) of current particle position
4372	INTEGER(iwp) :: i3 !< grid index (x) of intermediate particle position
4373	INTEGER(iwp) :: jr !< dummy for sorting algorithmus
4374	INTEGER(iwp) :: j1 !< grid index (y) of old particle position
4375	INTEGER(iwp) :: j2 !< grid index (y) of current particle position
4376	INTEGER(iwp) :: j3 !< grid index (y) of intermediate particle position
4377	INTEGER(iwp) :: k1 !< grid index (z) of old particle position
4378	INTEGER(iwp) :: k2 !< grid index (z) of current particle position
4379	INTEGER(iwp) :: k3 !< grid index (z) of intermediate particle position
4380	INTEGER(iwp) :: n !< particle number
4381	INTEGER(iwp) :: t_index !< running index for intermediate particle timesteps in reflection algorithmus
4382	INTEGER(iwp) :: t_index_number !< number of intermediate particle timesteps in reflection algorithmus
4383	INTEGER(iwp) :: tmp_x !< dummy for sorting algorithm
4384	INTEGER(iwp) :: tmp_y !< dummy for sorting algorithm
4385	INTEGER(iwp) :: tmp_z !< dummy for sorting algorithm
4386
4387	INTEGER(iwp), DIMENSION(0:10) :: x_ind(0:10) = 0 !< index array (x) of intermediate particle positions
4388	INTEGER(iwp), DIMENSION(0:10) :: y_ind(0:10) = 0 !< index array (y) of intermediate particle positions
4389	INTEGER(iwp), DIMENSION(0:10) :: z_ind(0:10) = 0 !< index array (z) of intermediate particle positions
4390
4391	LOGICAL :: cross_wall_x !< flag to check if particle reflection along x is necessary
4392	LOGICAL :: cross_wall_y !< flag to check if particle reflection along y is necessary
4393	LOGICAL :: cross_wall_z !< flag to check if particle reflection along z is necessary
4394	LOGICAL :: reflect_x !< flag to check if particle is already reflected along x
4395	LOGICAL :: reflect_y !< flag to check if particle is already reflected along y
4396	LOGICAL :: reflect_z !< flag to check if particle is already reflected along z
4397	LOGICAL :: tmp_reach_x !< dummy for sorting algorithmus
4398	LOGICAL :: tmp_reach_y !< dummy for sorting algorithmus
4399	LOGICAL :: tmp_reach_z !< dummy for sorting algorithmus
4400	LOGICAL :: x_wall_reached !< flag to check if particle has already reached wall
4401	LOGICAL :: y_wall_reached !< flag to check if particle has already reached wall
4402	LOGICAL :: z_wall_reached !< flag to check if particle has already reached wall
4403
4404	LOGICAL, DIMENSION(0:10) :: reach_x !< flag to check if particle is at a yz-wall
4405	LOGICAL, DIMENSION(0:10) :: reach_y !< flag to check if particle is at a xz-wall
4406	LOGICAL, DIMENSION(0:10) :: reach_z !< flag to check if particle is at a xy-wall
4407
4408	REAL(wp) :: dt_particle !< particle timestep
4409	REAL(wp) :: eps = 1E-10_wp !< security number to check if particle has reached a wall
4410	REAL(wp) :: pos_x !< intermediate particle position (x)
4411	REAL(wp) :: pos_x_old !< particle position (x) at previous particle timestep
4412	REAL(wp) :: pos_y !< intermediate particle position (y)
4413	REAL(wp) :: pos_y_old !< particle position (y) at previous particle timestep
4414	REAL(wp) :: pos_z !< intermediate particle position (z)
4415	REAL(wp) :: pos_z_old !< particle position (z) at previous particle timestep
4416	REAL(wp) :: prt_x !< current particle position (x)
4417	REAL(wp) :: prt_y !< current particle position (y)
4418	REAL(wp) :: prt_z !< current particle position (z)
4419	REAL(wp) :: t_old !< previous reflection time
4420	REAL(wp) :: tmp_t !< dummy for sorting algorithmus
4421	REAL(wp) :: xwall !< location of wall in x
4422	REAL(wp) :: ywall !< location of wall in y
4423	REAL(wp) :: zwall !< location of wall in z
4424
4425	REAL(wp), DIMENSION(0:10) :: t !< reflection time
4426
4427	SELECT CASE ( location_bc )
4428
4429	CASE ( 'bottom/top' )
4430
4431	!
4432	!-- Apply boundary conditions to those particles that have crossed the top or
4433	!-- bottom boundary and delete those particles, which are older than allowed
4434	DO n = 1, number_of_particles
4435
4436	!
4437	!-- Stop if particles have moved further than the length of one
4438	!-- PE subdomain (newly released particles have age = age_m!)
4439	IF ( particles(n)%age /= particles(n)%age_m ) THEN
4440	IF ( ABS(particles(n)%speed_x) > &
4441	((nxr-nxl+2)*dx)/(particles(n)%age-particles(n)%age_m) .OR. &
4442	ABS(particles(n)%speed_y) > &
4443	((nyn-nys+2)*dy)/(particles(n)%age-particles(n)%age_m) ) THEN
4444
4445	WRITE( message_string, * ) 'particle too fast. n = ', n
4446	CALL message( 'lpm_boundary_conds', 'PA0148', 2, 2, -1, 6, 1 )
4447	ENDIF
4448	ENDIF
4449
4450	IF ( particles(n)%age > particle_maximum_age .AND. &
4451	particles(n)%particle_mask ) &
4452	THEN
4453	particles(n)%particle_mask = .FALSE.
4454	deleted_particles = deleted_particles + 1
4455	ENDIF
4456
4457	IF ( particles(n)%z >= zw(nz) .AND. particles(n)%particle_mask ) THEN
4458	IF ( ibc_par_t == 1 ) THEN
4459	!
4460	!-- Particle absorption
4461	particles(n)%particle_mask = .FALSE.
4462	deleted_particles = deleted_particles + 1
4463	ELSEIF ( ibc_par_t == 2 ) THEN
4464	!
4465	!-- Particle reflection
4466	particles(n)%z = 2.0_wp * zw(nz) - particles(n)%z
4467	particles(n)%speed_z = -particles(n)%speed_z
4468	IF ( use_sgs_for_particles .AND. &
4469	particles(n)%rvar3 > 0.0_wp ) THEN
4470	particles(n)%rvar3 = -particles(n)%rvar3
4471	ENDIF
4472	ENDIF
4473	ENDIF
4474
4475	IF ( particles(n)%z < zw(0) .AND. particles(n)%particle_mask ) THEN
4476	IF ( ibc_par_b == 1 ) THEN
4477	!
4478	!-- Particle absorption
4479	particles(n)%particle_mask = .FALSE.
4480	deleted_particles = deleted_particles + 1
4481	ELSEIF ( ibc_par_b == 2 ) THEN
4482	!
4483	!-- Particle reflection
4484	particles(n)%z = 2.0_wp * zw(0) - particles(n)%z
4485	particles(n)%speed_z = -particles(n)%speed_z
4486	IF ( use_sgs_for_particles .AND. &
4487	particles(n)%rvar3 < 0.0_wp ) THEN
4488	particles(n)%rvar3 = -particles(n)%rvar3
4489	ENDIF
4490	ENDIF
4491	ENDIF
4492	ENDDO
4493
4494	CASE ( 'walls' )
4495
4496	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'start' )
4497
4498	DO n = 1, number_of_particles
4499	!
4500	!-- Recalculate particle timestep
4501	dt_particle = particles(n)%age - particles(n)%age_m
4502	!
4503	!-- Obtain x/y indices for current particle position
4504	i2 = particles(n)%x * ddx
4505	j2 = particles(n)%y * ddy
4506	IF (zw(k) < particles(n)%z ) k2 = k + 1
4507	IF (zw(k) > particles(n)%z .AND. zw(k-1) < particles(n)%z ) k2 = k
4508	IF (zw(k-1) > particles(n)%z ) k2 = k - 1
4509	!
4510	!-- Save current particle positions
4511	prt_x = particles(n)%x
4512	prt_y = particles(n)%y
4513	prt_z = particles(n)%z
4514	!
4515	!-- Recalculate old particle positions
4516	pos_x_old = particles(n)%x - particles(n)%speed_x * dt_particle
4517	pos_y_old = particles(n)%y - particles(n)%speed_y * dt_particle
4518	pos_z_old = particles(n)%z - particles(n)%speed_z * dt_particle
4519	!
4520	!-- Obtain x/y indices for old particle positions
4521	i1 = i
4522	j1 = j
4523	k1 = k
4524	!
4525	!-- Determine horizontal as well as vertical walls at which particle can
4526	!-- be potentially reflected.
4527	!-- Start with walls aligned in yz layer.
4528	!-- Wall to the right
4529	IF ( prt_x > pos_x_old ) THEN
4530	xwall = ( i1 + 1 ) * dx
4531	!
4532	!-- Wall to the left
4533	ELSE
4534	xwall = i1 * dx
4535	ENDIF
4536	!
4537	!-- Walls aligned in xz layer
4538	!-- Wall to the north
4539	IF ( prt_y > pos_y_old ) THEN
4540	ywall = ( j1 +1 ) * dy
4541	!-- Wall to the south
4542	ELSE
4543	ywall = j1 * dy
4544	ENDIF
4545
4546	IF ( prt_z > pos_z_old ) THEN
4547	zwall = zw(k)
4548	ELSE
4549	zwall = zw(k-1)
4550	ENDIF
4551	!
4552	!-- Initialize flags to check if particle reflection is necessary
4553	cross_wall_x = .FALSE.
4554	cross_wall_y = .FALSE.
4555	cross_wall_z = .FALSE.
4556	!
4557	!-- Initialize flags to check if a wall is reached
4558	reach_x = .FALSE.
4559	reach_y = .FALSE.
4560	reach_z = .FALSE.
4561	!
4562	!-- Initialize flags to check if a particle was already reflected
4563	reflect_x = .FALSE.
4564	reflect_y = .FALSE.
4565	reflect_z = .FALSE.
4566	!
4567	!-- Initialize flags to check if a wall is already crossed.
4568	!-- ( Required to obtain correct indices. )
4569	x_wall_reached = .FALSE.
4570	y_wall_reached = .FALSE.
4571	z_wall_reached = .FALSE.
4572	!
4573	!-- Initialize time array
4574	t = 0.0_wp
4575	!
4576	!-- Check if particle can reach any wall. This case, calculate the
4577	!-- fractional time needed to reach this wall. Store this fractional
4578	!-- timestep in array t. Moreover, store indices for these grid
4579	!-- boxes where the respective wall belongs to.
4580	!-- Start with x-direction.
4581	t_index = 1
4582	t(t_index) = ( xwall - pos_x_old ) &
4583	/ MERGE( MAX( prt_x - pos_x_old, 1E-30_wp ), &
4584	MIN( prt_x - pos_x_old, -1E-30_wp ), &
4585	prt_x > pos_x_old )
4586	x_ind(t_index) = i2
4587	y_ind(t_index) = j1
4588	z_ind(t_index) = k1
4589	reach_x(t_index) = .TRUE.
4590	reach_y(t_index) = .FALSE.
4591	reach_z(t_index) = .FALSE.
4592	!
4593	!-- Store these values only if particle really reaches any wall. t must
4594	!-- be in a interval between [0:1].
4595	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4596	t_index = t_index + 1
4597	cross_wall_x = .TRUE.
4598	ENDIF
4599	!
4600	!-- y-direction
4601	t(t_index) = ( ywall - pos_y_old ) &
4602	/ MERGE( MAX( prt_y - pos_y_old, 1E-30_wp ), &
4603	MIN( prt_y - pos_y_old, -1E-30_wp ), &
4604	prt_y > pos_y_old )
4605	x_ind(t_index) = i1
4606	y_ind(t_index) = j2
4607	z_ind(t_index) = k1
4608	reach_x(t_index) = .FALSE.
4609	reach_y(t_index) = .TRUE.
4610	reach_z(t_index) = .FALSE.
4611	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4612	t_index = t_index + 1
4613	cross_wall_y = .TRUE.
4614	ENDIF
4615	!
4616	!-- z-direction
4617	t(t_index) = (zwall - pos_z_old ) &
4618	/ MERGE( MAX( prt_z - pos_z_old, 1E-30_wp ), &
4619	MIN( prt_z - pos_z_old, -1E-30_wp ), &
4620	prt_z > pos_z_old )
4621
4622	x_ind(t_index) = i1
4623	y_ind(t_index) = j1
4624	z_ind(t_index) = k2
4625	reach_x(t_index) = .FALSE.
4626	reach_y(t_index) = .FALSE.
4627	reach_z(t_index) = .TRUE.
4628	IF( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp) THEN
4629	t_index = t_index + 1
4630	cross_wall_z = .TRUE.
4631	ENDIF
4632
4633	t_index_number = t_index - 1
4634	!
4635	!-- Carry out reflection only if particle reaches any wall
4636	IF ( cross_wall_x .OR. cross_wall_y .OR. cross_wall_z ) THEN
4637	!
4638	!-- Sort fractional timesteps in ascending order. Also sort the
4639	!-- corresponding indices and flag according to the time interval a
4640	!-- particle reaches the respective wall.
4641	inc = 1
4642	jr = 1
4643	DO WHILE ( inc <= t_index_number )
4644	inc = 3 * inc + 1
4645	ENDDO
4646
4647	DO WHILE ( inc > 1 )
4648	inc = inc / 3
4649	DO ir = inc+1, t_index_number
4650	tmp_t = t(ir)
4651	tmp_x = x_ind(ir)
4652	tmp_y = y_ind(ir)
4653	tmp_z = z_ind(ir)
4654	tmp_reach_x = reach_x(ir)
4655	tmp_reach_y = reach_y(ir)
4656	tmp_reach_z = reach_z(ir)
4657	jr = ir
4658	DO WHILE ( t(jr-inc) > tmp_t )
4659	t(jr) = t(jr-inc)
4660	x_ind(jr) = x_ind(jr-inc)
4661	y_ind(jr) = y_ind(jr-inc)
4662	z_ind(jr) = z_ind(jr-inc)
4663	reach_x(jr) = reach_x(jr-inc)
4664	reach_y(jr) = reach_y(jr-inc)
4665	reach_z(jr) = reach_z(jr-inc)
4666	jr = jr - inc
4667	IF ( jr <= inc ) EXIT
4668	ENDDO
4669	t(jr) = tmp_t
4670	x_ind(jr) = tmp_x
4671	y_ind(jr) = tmp_y
4672	z_ind(jr) = tmp_z
4673	reach_x(jr) = tmp_reach_x
4674	reach_y(jr) = tmp_reach_y
4675	reach_z(jr) = tmp_reach_z
4676	ENDDO
4677	ENDDO
4678	!
4679	!-- Initialize temporary particle positions
4680	pos_x = pos_x_old
4681	pos_y = pos_y_old
4682	pos_z = pos_z_old
4683	!
4684	!-- Loop over all times a particle possibly moves into a new grid box
4685	t_old = 0.0_wp
4686	DO t_index = 1, t_index_number
4687	!
4688	!-- Calculate intermediate particle position according to the
4689	!-- timesteps a particle reaches any wall.
4690	pos_x = pos_x + ( t(t_index) - t_old ) * dt_particle &
4691	* particles(n)%speed_x
4692	pos_y = pos_y + ( t(t_index) - t_old ) * dt_particle &
4693	* particles(n)%speed_y
4694	pos_z = pos_z + ( t(t_index) - t_old ) * dt_particle &
4695	* particles(n)%speed_z
4696	!
4697	!-- Obtain x/y grid indices for intermediate particle position from
4698	!-- sorted index array
4699	i3 = x_ind(t_index)
4700	j3 = y_ind(t_index)
4701	k3 = z_ind(t_index)
4702	!
4703	!-- Check which wall is already reached
4704	IF ( .NOT. x_wall_reached ) x_wall_reached = reach_x(t_index)
4705	IF ( .NOT. y_wall_reached ) y_wall_reached = reach_y(t_index)
4706	IF ( .NOT. z_wall_reached ) z_wall_reached = reach_z(t_index)
4707	!
4708	!-- Check if a particle needs to be reflected at any yz-wall. If
4709	!-- necessary, carry out reflection. Please note, a security
4710	!-- constant is required, as the particle position does not
4711	!-- necessarily exactly match the wall location due to rounding
4712	!-- errors.
4713	IF ( reach_x(t_index) .AND. &
4714	ABS( pos_x - xwall ) < eps .AND. &
4715	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4716	.NOT. reflect_x ) THEN
4717	!
4718	!
4719	!-- Reflection in x-direction.
4720	!-- Ensure correct reflection by MIN/MAX functions, depending on
4721	!-- direction of particle transport.
4722	!-- Due to rounding errors pos_x does not exactly match the wall
4723	!-- location, leading to erroneous reflection.
4724	pos_x = MERGE( MIN( 2.0_wp * xwall - pos_x, xwall ), &
4725	MAX( 2.0_wp * xwall - pos_x, xwall ), &
4726	particles(n)%x > xwall )
4727	!
4728	!-- Change sign of particle speed
4729	particles(n)%speed_x = - particles(n)%speed_x
4730	!
4731	!-- Also change sign of subgrid-scale particle speed
4732	particles(n)%rvar1 = - particles(n)%rvar1
4733	!
4734	!-- Set flag that reflection along x is already done
4735	reflect_x = .TRUE.
4736	!
4737	!-- As the particle does not cross any further yz-wall during
4738	!-- this timestep, set further x-indices to the current one.
4739	x_ind(t_index:t_index_number) = i1
4740	!
4741	!-- If particle already reached the wall but was not reflected,
4742	!-- set further x-indices to the new one.
4743	ELSEIF ( x_wall_reached .AND. .NOT. reflect_x ) THEN
4744	x_ind(t_index:t_index_number) = i2
4745	ENDIF !particle reflection in x direction done
4746
4747	!
4748	!-- Check if a particle needs to be reflected at any xz-wall. If
4749	!-- necessary, carry out reflection. Please note, a security
4750	!-- constant is required, as the particle position does not
4751	!-- necessarily exactly match the wall location due to rounding
4752	!-- errors.
4753	IF ( reach_y(t_index) .AND. &
4754	ABS( pos_y - ywall ) < eps .AND. &
4755	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4756	.NOT. reflect_y ) THEN
4757	!
4758	!
4759	!-- Reflection in y-direction.
4760	!-- Ensure correct reflection by MIN/MAX functions, depending on
4761	!-- direction of particle transport.
4762	!-- Due to rounding errors pos_y does not exactly match the wall
4763	!-- location, leading to erroneous reflection.
4764	pos_y = MERGE( MIN( 2.0_wp * ywall - pos_y, ywall ), &
4765	MAX( 2.0_wp * ywall - pos_y, ywall ), &
4766	particles(n)%y > ywall )
4767	!
4768	!-- Change sign of particle speed
4769	particles(n)%speed_y = - particles(n)%speed_y
4770	!
4771	!-- Also change sign of subgrid-scale particle speed
4772	particles(n)%rvar2 = - particles(n)%rvar2
4773	!
4774	!-- Set flag that reflection along y is already done
4775	reflect_y = .TRUE.
4776	!
4777	!-- As the particle does not cross any further xz-wall during
4778	!-- this timestep, set further y-indices to the current one.
4779	y_ind(t_index:t_index_number) = j1
4780	!
4781	!-- If particle already reached the wall but was not reflected,
4782	!-- set further y-indices to the new one.
4783	ELSEIF ( y_wall_reached .AND. .NOT. reflect_y ) THEN
4784	y_ind(t_index:t_index_number) = j2
4785	ENDIF !particle reflection in y direction done
4786
4787	!
4788	!-- Check if a particle needs to be reflected at any xy-wall. If
4789	!-- necessary, carry out reflection. Please note, a security
4790	!-- constant is required, as the particle position does not
4791	!-- necessarily exactly match the wall location due to rounding
4792	!-- errors.
4793	IF ( reach_z(t_index) .AND. &
4794	ABS( pos_z - zwall ) < eps .AND. &
4795	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4796	.NOT. reflect_z ) THEN
4797	!
4798	!
4799	!-- Reflection in z-direction.
4800	!-- Ensure correct reflection by MIN/MAX functions, depending on
4801	!-- direction of particle transport.
4802	!-- Due to rounding errors pos_z does not exactly match the wall
4803	!-- location, leading to erroneous reflection.
4804	pos_z = MERGE( MIN( 2.0_wp * zwall - pos_z, zwall ), &
4805	MAX( 2.0_wp * zwall - pos_z, zwall ), &
4806	particles(n)%z > zwall )
4807	!
4808	!-- Change sign of particle speed
4809	particles(n)%speed_z = - particles(n)%speed_z
4810	!
4811	!-- Also change sign of subgrid-scale particle speed
4812	particles(n)%rvar3 = - particles(n)%rvar3
4813	!
4814	!-- Set flag that reflection along z is already done
4815	reflect_z = .TRUE.
4816	!
4817	!-- As the particle does not cross any further xy-wall during
4818	!-- this timestep, set further z-indices to the current one.
4819	z_ind(t_index:t_index_number) = k1
4820	!
4821	!-- If particle already reached the wall but was not reflected,
4822	!-- set further z-indices to the new one.
4823	ELSEIF ( z_wall_reached .AND. .NOT. reflect_z ) THEN
4824	z_ind(t_index:t_index_number) = k2
4825	ENDIF !particle reflection in z direction done
4826
4827	!
4828	!-- Swap time
4829	t_old = t(t_index)
4830
4831	ENDDO
4832	!
4833	!-- If a particle was reflected, calculate final position from last
4834	!-- intermediate position.
4835	IF ( reflect_x .OR. reflect_y .OR. reflect_z ) THEN
4836
4837	particles(n)%x = pos_x + ( 1.0_wp - t_old ) * dt_particle &
4838	* particles(n)%speed_x
4839	particles(n)%y = pos_y + ( 1.0_wp - t_old ) * dt_particle &
4840	* particles(n)%speed_y
4841	particles(n)%z = pos_z + ( 1.0_wp - t_old ) * dt_particle &
4842	* particles(n)%speed_z
4843
4844	ENDIF
4845
4846	ENDIF
4847
4848	ENDDO
4849
4850	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'stop' )
4851
4852	CASE DEFAULT
4853	CONTINUE
4854
4855	END SELECT
4856
4857	END SUBROUTINE lpm_boundary_conds
4858
4859
4860	!------------------------------------------------------------------------------!
4861	! Description:
4862	! ------------
4863	!> Calculates change in droplet radius by condensation/evaporation, using
4864	!> either an analytic formula or by numerically integrating the radius growth
4865	!> equation including curvature and solution effects using Rosenbrocks method
4866	!> (see Numerical recipes in FORTRAN, 2nd edition, p. 731).
4867	!> The analytical formula and growth equation follow those given in
4868	!> Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103).
4869	!------------------------------------------------------------------------------!
4870	SUBROUTINE lpm_droplet_condensation (i,j,k)
4871
4872	INTEGER(iwp), INTENT(IN) :: i !<
4873	INTEGER(iwp), INTENT(IN) :: j !<
4874	INTEGER(iwp), INTENT(IN) :: k !<
4875	INTEGER(iwp) :: n !<
4876
4877	REAL(wp) :: afactor !< curvature effects
4878	REAL(wp) :: arg !<
4879	REAL(wp) :: bfactor !< solute effects
4880	REAL(wp) :: ddenom !<
4881	REAL(wp) :: delta_r !<
4882	REAL(wp) :: diameter !< diameter of cloud droplets
4883	REAL(wp) :: diff_coeff !< diffusivity for water vapor
4884	REAL(wp) :: drdt !<
4885	REAL(wp) :: dt_ros !<
4886	REAL(wp) :: dt_ros_sum !<
4887	REAL(wp) :: d2rdtdr !<
4888	REAL(wp) :: e_a !< current vapor pressure
4889	REAL(wp) :: e_s !< current saturation vapor pressure
4890	REAL(wp) :: error !< local truncation error in Rosenbrock
4891	REAL(wp) :: k1 !<
4892	REAL(wp) :: k2 !<
4893	REAL(wp) :: r_err !< First order estimate of Rosenbrock radius
4894	REAL(wp) :: r_ros !< Rosenbrock radius
4895	REAL(wp) :: r_ros_ini !< initial Rosenbrock radius
4896	REAL(wp) :: r0 !< gas-kinetic lengthscale
4897	REAL(wp) :: sigma !< surface tension of water
4898	REAL(wp) :: thermal_conductivity !< thermal conductivity for water
4899	REAL(wp) :: t_int !< temperature
4900	REAL(wp) :: w_s !< terminal velocity of droplets
4901	REAL(wp) :: re_p !< particle Reynolds number
4902	!
4903	!-- Parameters for Rosenbrock method (see Verwer et al., 1999)
4904	REAL(wp), PARAMETER :: prec = 1.0E-3_wp !< precision of Rosenbrock solution
4905	REAL(wp), PARAMETER :: q_increase = 1.5_wp !< increase factor in timestep
4906	REAL(wp), PARAMETER :: q_decrease = 0.9_wp !< decrease factor in timestep
4907	REAL(wp), PARAMETER :: gamma = 0.292893218814_wp !< = 1.0 - 1.0 / SQRT(2.0)
4908	!
4909	!-- Parameters for terminal velocity
4910	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
4911	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
4912	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
4913	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
4914	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
4915	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
4916
4917	REAL(wp), DIMENSION(number_of_particles) :: ventilation_effect !<
4918	REAL(wp), DIMENSION(number_of_particles) :: new_r !<
4919
4920	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' )
4921
4922	!
4923	!-- Absolute temperature
4924	t_int = pt(k,j,i) * exner(k)
4925	!
4926	!-- Saturation vapor pressure (Eq. 10 in Bolton, 1980)
4927	e_s = magnus( t_int )
4928	!
4929	!-- Current vapor pressure
4930	e_a = q(k,j,i) * hyp(k) / ( q(k,j,i) + rd_d_rv )
4931	!
4932	!-- Thermal conductivity for water (from Rogers and Yau, Table 7.1)
4933	thermal_conductivity = 7.94048E-05_wp * t_int + 0.00227011_wp
4934	!
4935	!-- Moldecular diffusivity of water vapor in air (Hall und Pruppacher, 1976)
4936	diff_coeff = 0.211E-4_wp * ( t_int / 273.15_wp )*1.94_wp &
4937	( 101325.0_wp / hyp(k) )
4938	!
4939	!-- Lengthscale for gas-kinetic effects (from Mordy, 1959, p. 23):
4940	r0 = diff_coeff / 0.036_wp * SQRT( 2.0_wp * pi / ( r_v * t_int ) )
4941	!
4942	!-- Calculate effects of heat conductivity and diffusion of water vapor on the
4943	!-- diffusional growth process (usually known as 1.0 / (F_k + F_d) )
4944	ddenom = 1.0_wp / ( rho_l * r_v * t_int / ( e_s * diff_coeff ) + &
4945	( l_v / ( r_v * t_int ) - 1.0_wp ) * rho_l * &
4946	l_v / ( thermal_conductivity * t_int ) &
4947	)
4948	new_r = 0.0_wp
4949	!
4950	!-- Determine ventilation effect on evaporation of large drops
4951	DO n = 1, number_of_particles
4952
4953	IF ( particles(n)%radius >= 4.0E-5_wp .AND. e_a / e_s < 1.0_wp ) THEN
4954	!
4955	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
4956	!-- 1993, J. Appl. Meteorol.)
4957	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4958	IF ( diameter <= d0_rog ) THEN
4959	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4960	ELSE
4961	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4962	ENDIF
4963	!
4964	!-- Calculate droplet's Reynolds number
4965	re_p = 2.0_wp * particles(n)%radius * w_s / molecular_viscosity
4966	!
4967	!-- Ventilation coefficient (Rogers and Yau, 1989):
4968	IF ( re_p > 2.5_wp ) THEN
4969	ventilation_effect(n) = 0.78_wp + 0.28_wp * SQRT( re_p )
4970	ELSE
4971	ventilation_effect(n) = 1.0_wp + 0.09_wp * re_p
4972	ENDIF
4973	ELSE
4974	!
4975	!-- For small droplets or in supersaturated environments, the ventilation
4976	!-- effect does not play a role
4977	ventilation_effect(n) = 1.0_wp
4978	ENDIF
4979	ENDDO
4980
4981	IF( .NOT. curvature_solution_effects ) then
4982	!
4983	!-- Use analytic model for diffusional growth including gas-kinetic
4984	!-- effects (Mordy, 1959) but without the impact of aerosols.
4985	DO n = 1, number_of_particles
4986	arg = ( particles(n)%radius + r0 )*2 + 2.0_wp dt_3d * ddenom * &
4987	ventilation_effect(n) * &
4988	( e_a / e_s - 1.0_wp )
4989	arg = MAX( arg, ( 0.01E-6 + r0 )**2 )
4990	new_r(n) = SQRT( arg ) - r0
4991	ENDDO
4992
4993	ELSE
4994	!
4995	!-- Integrate the diffusional growth including gas-kinetic (Mordy, 1959),
4996	!-- as well as curvature and solute effects (e.g., KÃ¶hler, 1936).
4997	!
4998	!-- Curvature effect (afactor) with surface tension (sigma) by Straka (2009)
4999	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
5000	!
5001	!-- Solute effect (afactor)
5002	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
5003
5004	DO n = 1, number_of_particles
5005	!
5006	!-- Solute effect (bfactor)
5007	bfactor = vanthoff * rho_s * particles(n)%aux1*3 &
5008	molecular_weight_of_water / ( rho_l * molecular_weight_of_solute )
5009
5010	dt_ros = particles(n)%aux2 ! use previously stored Rosenbrock timestep
5011	dt_ros_sum = 0.0_wp
5012
5013	r_ros = particles(n)%radius ! initialize Rosenbrock particle radius
5014	r_ros_ini = r_ros
5015	!
5016	!-- Integrate growth equation using a 2nd-order Rosenbrock method
5017	!-- (see Verwer et al., 1999, Eq. (3.2)). The Rosenbrock method adjusts
5018	!-- its with internal timestep to minimize the local truncation error.
5019	DO WHILE ( dt_ros_sum < dt_3d )
5020
5021	dt_ros = MIN( dt_ros, dt_3d - dt_ros_sum )
5022
5023	DO
5024
5025	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5026	afactor / r_ros + &
5027	bfactor / r_ros**3 &
5028	) / ( r_ros + r0 )
5029
5030	d2rdtdr = -ddenom * ventilation_effect(n) * ( &
5031	(e_a / e_s - 1.0_wp ) * r_ros**4 - &
5032	afactor * r0 * r_ros**2 - &
5033	2.0_wp * afactor * r_ros**3 + &
5034	3.0_wp * bfactor * r0 + &
5035	4.0_wp * bfactor * r_ros &
5036	) &
5037	/ ( r_ros*4 ( r_ros + r0 )**2 )
5038
5039	k1 = drdt / ( 1.0_wp - gamma * dt_ros * d2rdtdr )
5040
5041	r_ros = MAX(r_ros_ini + k1 * dt_ros, particles(n)%aux1)
5042	r_err = r_ros
5043
5044	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5045	afactor / r_ros + &
5046	bfactor / r_ros**3 &
5047	) / ( r_ros + r0 )
5048
5049	k2 = ( drdt - dt_ros * 2.0 * gamma * d2rdtdr * k1 ) / &
5050	( 1.0_wp - dt_ros * gamma * d2rdtdr )
5051
5052	r_ros = MAX(r_ros_ini + dt_ros * ( 1.5_wp * k1 + 0.5_wp * k2), particles(n)%aux1)
5053	!
5054	!-- Check error of the solution, and reduce dt_ros if necessary.
5055	error = ABS(r_err - r_ros) / r_ros
5056	IF ( error .GT. prec ) THEN
5057	dt_ros = SQRT( q_decrease * prec / error ) * dt_ros
5058	r_ros = r_ros_ini
5059	ELSE
5060	dt_ros_sum = dt_ros_sum + dt_ros
5061	dt_ros = q_increase * dt_ros
5062	r_ros_ini = r_ros
5063	EXIT
5064	ENDIF
5065
5066	END DO
5067
5068	END DO !Rosenbrock loop
5069	!
5070	!-- Store new particle radius
5071	new_r(n) = r_ros
5072	!
5073	!-- Store internal time step value for next PALM step
5074	particles(n)%aux2 = dt_ros
5075
5076	ENDDO !Particle loop
5077
5078	ENDIF
5079
5080	DO n = 1, number_of_particles
5081	!
5082	!-- Sum up the change in liquid water for the respective grid
5083	!-- box for the computation of the release/depletion of water vapor
5084	!-- and heat.
5085	ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * &
5086	rho_l * 1.33333333_wp * pi * &
5087	( new_r(n)3 - particles(n)%radius3 ) / &
5088	( rho_surface * dx * dy * dzw(k) )
5089	!
5090	!-- Check if the increase in liqid water is not too big. If this is the case,
5091	!-- the model timestep might be too long.
5092	IF ( ql_c(k,j,i) > 100.0_wp ) THEN
5093	WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, &
5094	' ql_c=',ql_c(k,j,i), '&part(',n,')%wf=', &
5095	particles(n)%weight_factor,' delta_r=',delta_r
5096	CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 )
5097	ENDIF
5098	!
5099	!-- Check if the change in the droplet radius is not too big. If this is the
5100	!-- case, the model timestep might be too long.
5101	delta_r = new_r(n) - particles(n)%radius
5102	IF ( delta_r < 0.0_wp .AND. new_r(n) < 0.0_wp ) THEN
5103	WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, &
5104	' e_s=',e_s, ' e_a=',e_a,' t_int=',t_int, &
5105	'&delta_r=',delta_r, &
5106	' particle_radius=',particles(n)%radius
5107	CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 )
5108	ENDIF
5109	!
5110	!-- Sum up the total volume of liquid water (needed below for
5111	!-- re-calculating the weighting factors)
5112	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r(n)**3
5113	!
5114	!-- Determine radius class of the particle needed for collision
5115	IF ( use_kernel_tables ) THEN
5116	particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / &
5117	( rclass_ubound - rclass_lbound ) * &
5118	radius_classes
5119	particles(n)%class = MIN( particles(n)%class, radius_classes )
5120	particles(n)%class = MAX( particles(n)%class, 1 )
5121	ENDIF
5122	!
5123	!-- Store new radius to particle features
5124	particles(n)%radius = new_r(n)
5125
5126	ENDDO
5127
5128	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' )
5129
5130
5131	END SUBROUTINE lpm_droplet_condensation
5132
5133
5134	!------------------------------------------------------------------------------!
5135	! Description:
5136	! ------------
5137	!> Release of latent heat and change of mixing ratio due to condensation /
5138	!> evaporation of droplets.
5139	!------------------------------------------------------------------------------!
5140	SUBROUTINE lpm_interaction_droplets_ptq
5141
5142	INTEGER(iwp) :: i !< running index x direction
5143	INTEGER(iwp) :: j !< running index y direction
5144	INTEGER(iwp) :: k !< running index z direction
5145
5146	REAL(wp) :: flag !< flag to mask topography grid points
5147
5148	DO i = nxl, nxr
5149	DO j = nys, nyn
5150	DO k = nzb+1, nzt
5151	!
5152	!-- Predetermine flag to mask topography
5153	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
5154
5155	q_p(k,j,i) = q_p(k,j,i) - ql_c(k,j,i) * flag
5156	pt_p(k,j,i) = pt_p(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) &
5157	* flag
5158	ENDDO
5159	ENDDO
5160	ENDDO
5161
5162	END SUBROUTINE lpm_interaction_droplets_ptq
5163
5164
5165	!------------------------------------------------------------------------------!
5166	! Description:
5167	! ------------
5168	!> Release of latent heat and change of mixing ratio due to condensation /
5169	!> evaporation of droplets. Call for grid point i,j
5170	!------------------------------------------------------------------------------!
5171	SUBROUTINE lpm_interaction_droplets_ptq_ij( i, j )
5172
5173	INTEGER(iwp) :: i !< running index x direction
5174	INTEGER(iwp) :: j !< running index y direction
5175	INTEGER(iwp) :: k !< running index z direction
5176
5177	REAL(wp) :: flag !< flag to mask topography grid points
5178
5179
5180	DO k = nzb+1, nzt
5181	!
5182	!-- Predetermine flag to mask topography
5183	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
5184
5185	q_p(k,j,i) = q_p(k,j,i) - ql_c(k,j,i) * flag
5186	pt_p(k,j,i) = pt_p(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) * flag
5187	ENDDO
5188
5189	END SUBROUTINE lpm_interaction_droplets_ptq_ij
5190
5191
5192	!------------------------------------------------------------------------------!
5193	! Description:
5194	! ------------
5195	!> Calculate the liquid water content for each grid box.
5196	!------------------------------------------------------------------------------!
5197	SUBROUTINE lpm_calc_liquid_water_content
5198
5199
5200	INTEGER(iwp) :: i !<
5201	INTEGER(iwp) :: j !<
5202	INTEGER(iwp) :: k !<
5203	INTEGER(iwp) :: n !<
5204
5205	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'start' )
5206
5207	!
5208	!-- Set water content initially to zero
5209	ql = 0.0_wp; ql_v = 0.0_wp; ql_vp = 0.0_wp
5210
5211	!
5212	!-- Calculate for each grid box
5213	DO i = nxl, nxr
5214	DO j = nys, nyn
5215	DO k = nzb+1, nzt
5216	number_of_particles = prt_count(k,j,i)
5217	IF ( number_of_particles <= 0 ) CYCLE
5218	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
5219	!
5220	!-- Calculate the total volume in the boxes (ql_v, weighting factor
5221	!-- has to beincluded)
5222	DO n = 1, prt_count(k,j,i)
5223	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * &
5224	particles(n)%radius**3
5225	ENDDO
5226	!
5227	!-- Calculate the liquid water content
5228	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5229	ql(k,j,i) = ql(k,j,i) + rho_l * 1.33333333_wp * pi * &
5230	ql_v(k,j,i) / &
5231	( rho_surface * dx * dy * dzw(k) )
5232	IF ( ql(k,j,i) < 0.0_wp ) THEN
5233	WRITE( message_string, * ) 'LWC out of range: ' , &
5234	ql(k,j,i),i,j,k
5235	CALL message( 'lpm_calc_liquid_water_content', '', 2, 2, &
5236	-1, 6, 1 )
5237	ENDIF
5238	ELSE
5239	ql(k,j,i) = 0.0_wp
5240	ENDIF
5241	ENDDO
5242	ENDDO
5243	ENDDO
5244
5245	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'stop' )
5246
5247	END SUBROUTINE lpm_calc_liquid_water_content
5248
5249
5250	!------------------------------------------------------------------------------!
5251	! Description:
5252	! ------------
5253	!> Calculates change in droplet radius by collision. Droplet collision is
5254	!> calculated for each grid box seperately. Collision is parameterized by
5255	!> using collision kernels. Two different kernels are available:
5256	!> Hall kernel: Kernel from Hall (1980, J. Atmos. Sci., 2486-2507), which
5257	!> considers collision due to pure gravitational effects.
5258	!> Wang kernel: Beside gravitational effects (treated with the Hall-kernel) also
5259	!> the effects of turbulence on the collision are considered using
5260	!> parameterizations of Ayala et al. (2008, New J. Phys., 10,
5261	!> 075015) and Wang and Grabowski (2009, Atmos. Sci. Lett., 10,
5262	!> 1-8). This kernel includes three possible effects of turbulence:
5263	!> the modification of the relative velocity between the droplets,
5264	!> the effect of preferential concentration, and the enhancement of
5265	!> collision efficiencies.
5266	!------------------------------------------------------------------------------!
5267	SUBROUTINE lpm_droplet_collision (i,j,k)
5268
5269	INTEGER(iwp), INTENT(IN) :: i !<
5270	INTEGER(iwp), INTENT(IN) :: j !<
5271	INTEGER(iwp), INTENT(IN) :: k !<
5272
5273	INTEGER(iwp) :: eclass !<
5274	INTEGER(iwp) :: n !<
5275	INTEGER(iwp) :: m !<
5276	INTEGER(iwp) :: rclass_l !<
5277	INTEGER(iwp) :: rclass_s !<
5278
5279	REAL(wp) :: collection_probability !< probability for collection
5280	REAL(wp) :: ddV !< inverse grid box volume
5281	REAL(wp) :: epsilon_collision !< dissipation rate
5282	REAL(wp) :: factor_volume_to_mass !< 4.0 / 3.0 * pi * rho_l
5283	REAL(wp) :: xm !< droplet mass of super-droplet m
5284	REAL(wp) :: xn !< droplet mass of super-droplet n
5285	REAL(wp) :: xsm !< aerosol mass of super-droplet m
5286	REAL(wp) :: xsn !< aerosol mass of super-droplet n
5287
5288	REAL(wp), DIMENSION(:), ALLOCATABLE :: weight !< weighting factor
5289	REAL(wp), DIMENSION(:), ALLOCATABLE :: mass !< total mass of super droplet
5290	REAL(wp), DIMENSION(:), ALLOCATABLE :: aero_mass !< total aerosol mass of super droplet
5291
5292	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'start' )
5293
5294	number_of_particles = prt_count(k,j,i)
5295	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
5296	ddV = 1.0_wp / ( dx * dy * dzw(k) )
5297	!
5298	!-- Collision requires at least one super droplet inside the box
5299	IF ( number_of_particles > 0 ) THEN
5300
5301	IF ( use_kernel_tables ) THEN
5302	!
5303	!-- Fast method with pre-calculated collection kernels for
5304	!-- discrete radius- and dissipation-classes.
5305	IF ( wang_kernel ) THEN
5306	eclass = INT( diss(k,j,i) * 1.0E4_wp / 600.0_wp * &
5307	dissipation_classes ) + 1
5308	epsilon_collision = diss(k,j,i)
5309	ELSE
5310	epsilon_collision = 0.0_wp
5311	ENDIF
5312
5313	IF ( hall_kernel .OR. epsilon_collision * 1.0E4_wp < 0.001_wp ) THEN
5314	eclass = 0 ! Hall kernel is used
5315	ELSE
5316	eclass = MIN( dissipation_classes, eclass )
5317	ENDIF
5318
5319	ELSE
5320	!
5321	!-- Collection kernels are re-calculated for every new
5322	!-- grid box. First, allocate memory for kernel table.
5323	!-- Third dimension is 1, because table is re-calculated for
5324	!-- every new dissipation value.
5325	ALLOCATE( ckernel(1:number_of_particles,1:number_of_particles,1:1) )
5326	!
5327	!-- Now calculate collection kernel for this box. Note that
5328	!-- the kernel is based on the previous time step
5329	CALL recalculate_kernel( i, j, k )
5330
5331	ENDIF
5332	!
5333	!-- Temporary fields for total mass of super-droplet, aerosol mass, and
5334	!-- weighting factor are allocated.
5335	ALLOCATE(mass(1:number_of_particles), weight(1:number_of_particles))
5336	IF ( curvature_solution_effects ) ALLOCATE(aero_mass(1:number_of_particles))
5337
5338	mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5339	particles(1:number_of_particles)%radius*3 &
5340	factor_volume_to_mass
5341
5342	weight(1:number_of_particles) = particles(1:number_of_particles)%weight_factor
5343
5344	IF ( curvature_solution_effects ) THEN
5345	aero_mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5346	particles(1:number_of_particles)%aux1*3 &
5347	4.0_wp / 3.0_wp * pi * rho_s
5348	ENDIF
5349	!
5350	!-- Calculate collision/coalescence
5351	DO n = 1, number_of_particles
5352
5353	DO m = n, number_of_particles
5354	!
5355	!-- For collisions, the weighting factor of at least one super-droplet
5356	!-- needs to be larger or equal to one.
5357	IF ( MIN( weight(n), weight(m) ) .LT. 1.0_wp ) CYCLE
5358	!
5359	!-- Get mass of individual droplets (aerosols)
5360	xn = mass(n) / weight(n)
5361	xm = mass(m) / weight(m)
5362	IF ( curvature_solution_effects ) THEN
5363	xsn = aero_mass(n) / weight(n)
5364	xsm = aero_mass(m) / weight(m)
5365	ENDIF
5366	!
5367	!-- Probability that the necessary collisions take place
5368	IF ( use_kernel_tables ) THEN
5369	rclass_l = particles(n)%class
5370	rclass_s = particles(m)%class
5371
5372	collection_probability = MAX( weight(n), weight(m) ) * &
5373	ckernel(rclass_l,rclass_s,eclass) * ddV * dt_3d
5374	ELSE
5375	collection_probability = MAX( weight(n), weight(m) ) * &
5376	ckernel(n,m,1) * ddV * dt_3d
5377	ENDIF
5378	!
5379	!-- Calculate the number of collections and consider multiple collections.
5380	!-- (Accordingly, p_crit will be 0.0, 1.0, 2.0, ...)
5381	IF ( collection_probability - FLOOR(collection_probability) &
5382	.GT. random_function( iran_part ) ) THEN
5383	collection_probability = FLOOR(collection_probability) + 1.0_wp
5384	ELSE
5385	collection_probability = FLOOR(collection_probability)
5386	ENDIF
5387
5388	IF ( collection_probability .GT. 0.0_wp ) THEN
5389	!
5390	!-- Super-droplet n collects droplets of super-droplet m
5391	IF ( weight(n) .LT. weight(m) ) THEN
5392
5393	mass(n) = mass(n) + weight(n) * xm * collection_probability
5394	weight(m) = weight(m) - weight(n) * collection_probability
5395	mass(m) = mass(m) - weight(n) * xm * collection_probability
5396	IF ( curvature_solution_effects ) THEN
5397	aero_mass(n) = aero_mass(n) + weight(n) * xsm * collection_probability
5398	aero_mass(m) = aero_mass(m) - weight(n) * xsm * collection_probability
5399	ENDIF
5400
5401	ELSEIF ( weight(m) .LT. weight(n) ) THEN
5402
5403	mass(m) = mass(m) + weight(m) * xn * collection_probability
5404	weight(n) = weight(n) - weight(m) * collection_probability
5405	mass(n) = mass(n) - weight(m) * xn * collection_probability
5406	IF ( curvature_solution_effects ) THEN
5407	aero_mass(m) = aero_mass(m) + weight(m) * xsn * collection_probability
5408	aero_mass(n) = aero_mass(n) - weight(m) * xsn * collection_probability
5409	ENDIF
5410
5411	ELSE
5412	!
5413	!-- Collisions of particles of the same weighting factor.
5414	!-- Particle n collects 1/2 weight(n) droplets of particle m,
5415	!-- particle m collects 1/2 weight(m) droplets of particle n.
5416	!-- The total mass mass changes accordingly.
5417	!-- If n = m, the first half of the droplets coalesces with the
5418	!-- second half of the droplets; mass is unchanged because
5419	!-- xm = xn for n = m.
5420	!--
5421	!-- Note: For m = n this equation is an approximation only
5422	!-- valid for weight >> 1 (which is usually the case). The
5423	!-- approximation is weight(n)-1 = weight(n).
5424	mass(n) = mass(n) + 0.5_wp * weight(n) * ( xm - xn )
5425	mass(m) = mass(m) + 0.5_wp * weight(m) * ( xn - xm )
5426	IF ( curvature_solution_effects ) THEN
5427	aero_mass(n) = aero_mass(n) + 0.5_wp * weight(n) * ( xsm - xsn )
5428	aero_mass(m) = aero_mass(m) + 0.5_wp * weight(m) * ( xsn - xsm )
5429	ENDIF
5430	weight(n) = weight(n) - 0.5_wp * weight(m)
5431	weight(m) = weight(n)
5432
5433	ENDIF
5434
5435	ENDIF
5436
5437	ENDDO
5438
5439	ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
5440
5441	ENDDO
5442
5443	IF ( ANY(weight < 0.0_wp) ) THEN
5444	WRITE( message_string, * ) 'negative weighting factor'
5445	CALL message( 'lpm_droplet_collision', 'PA0028', &
5446	2, 2, -1, 6, 1 )
5447	ENDIF
5448
5449	particles(1:number_of_particles)%radius = ( mass(1:number_of_particles) / &
5450	( weight(1:number_of_particles) &
5451	* factor_volume_to_mass &
5452	) &
5453	)**0.33333333333333_wp
5454
5455	IF ( curvature_solution_effects ) THEN
5456	particles(1:number_of_particles)%aux1 = ( aero_mass(1:number_of_particles) / &
5457	( weight(1:number_of_particles) &
5458	* 4.0_wp / 3.0_wp * pi * rho_s &
5459	) &
5460	)**0.33333333333333_wp
5461	ENDIF
5462
5463	particles(1:number_of_particles)%weight_factor = weight(1:number_of_particles)
5464
5465	DEALLOCATE( weight, mass )
5466	IF ( curvature_solution_effects ) DEALLOCATE( aero_mass )
5467	IF ( .NOT. use_kernel_tables ) DEALLOCATE( ckernel )
5468
5469	!
5470	!-- Check if LWC is conserved during collision process
5471	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5472	IF ( ql_vp(k,j,i) / ql_v(k,j,i) >= 1.0001_wp .OR. &
5473	ql_vp(k,j,i) / ql_v(k,j,i) <= 0.9999_wp ) THEN
5474	WRITE( message_string, * ) ' LWC is not conserved during', &
5475	' collision! ', &
5476	' LWC after condensation: ', ql_v(k,j,i), &
5477	' LWC after collision: ', ql_vp(k,j,i)
5478	CALL message( 'lpm_droplet_collision', 'PA0040', 2, 2, -1, 6, 1 )
5479	ENDIF
5480	ENDIF
5481
5482	ENDIF
5483
5484	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'stop' )
5485
5486	END SUBROUTINE lpm_droplet_collision
5487
5488	!------------------------------------------------------------------------------!
5489	! Description:
5490	! ------------
5491	!> Initialization of the collision efficiency matrix with fixed radius and
5492	!> dissipation classes, calculated at simulation start only.
5493	!------------------------------------------------------------------------------!
5494	SUBROUTINE lpm_init_kernels
5495
5496	INTEGER(iwp) :: i !<
5497	INTEGER(iwp) :: j !<
5498	INTEGER(iwp) :: k !<
5499
5500	!
5501	!-- Calculate collision efficiencies for fixed radius- and dissipation
5502	!-- classes
5503	IF ( collision_kernel(6:9) == 'fast' ) THEN
5504
5505	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
5506	0:dissipation_classes), epsclass(1:dissipation_classes), &
5507	radclass(1:radius_classes) )
5508
5509	!
5510	!-- Calculate the radius class bounds with logarithmic distances
5511	!-- in the interval [1.0E-6, 1000.0E-6] m
5512	rclass_lbound = LOG( 1.0E-6_wp )
5513	rclass_ubound = LOG( 1000.0E-6_wp )
5514	radclass(1) = EXP( rclass_lbound )
5515	DO i = 2, radius_classes
5516	radclass(i) = EXP( rclass_lbound + &
5517	( rclass_ubound - rclass_lbound ) * &
5518	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
5519	ENDDO
5520
5521	!
5522	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
5523	DO i = 1, dissipation_classes
5524	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
5525	ENDDO
5526	!
5527	!-- Calculate collision efficiencies of the Wang/ayala kernel
5528	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
5529	ecf(1:radius_classes,1:radius_classes), &
5530	gck(1:radius_classes,1:radius_classes), &
5531	winf(1:radius_classes) )
5532
5533	DO k = 1, dissipation_classes
5534
5535	epsilon_collision = epsclass(k)
5536	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 1.0_wp / 3.0_wp )
5537
5538	CALL turbsd
5539	CALL turb_enhance_eff
5540	CALL effic
5541
5542	DO j = 1, radius_classes
5543	DO i = 1, radius_classes
5544	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
5545	ENDDO
5546	ENDDO
5547
5548	ENDDO
5549
5550	!
5551	!-- Calculate collision efficiencies of the Hall kernel
5552	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
5553	hwratio(1:radius_classes,1:radius_classes) )
5554
5555	CALL fallg
5556	CALL effic
5557
5558	DO j = 1, radius_classes
5559	DO i = 1, radius_classes
5560	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
5561	* ec(i,j) * ABS( winf(j) - winf(i) )
5562	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
5563	ENDDO
5564	ENDDO
5565
5566	!
5567	!-- Test output of efficiencies
5568	IF ( j == -1 ) THEN
5569	PRINT, '** Hall kernel'
5570	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
5571	i = 1,radius_classes )
5572	DO j = 1, radius_classes
5573	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
5574	( hkernel(i,j), i = 1,radius_classes )
5575	ENDDO
5576
5577	DO k = 1, dissipation_classes
5578	DO i = 1, radius_classes
5579	DO j = 1, radius_classes
5580	IF ( hkernel(i,j) == 0.0_wp ) THEN
5581	hwratio(i,j) = 9999999.9_wp
5582	ELSE
5583	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
5584	ENDIF
5585	ENDDO
5586	ENDDO
5587
5588	PRINT, '** epsilon = ', epsclass(k)
5589	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
5590	i = 1,radius_classes )
5591	DO j = 1, radius_classes
5592	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
5593	( hwratio(i,j), i = 1,radius_classes )
5594	ENDDO
5595	ENDDO
5596	ENDIF
5597
5598	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
5599
5600	ENDIF
5601
5602	END SUBROUTINE lpm_init_kernels
5603
5604	!------------------------------------------------------------------------------!
5605	! Description:
5606	! ------------
5607	!> Calculation of collision kernels during each timestep and for each grid box
5608	!------------------------------------------------------------------------------!
5609	SUBROUTINE recalculate_kernel( i1, j1, k1 )
5610
5611
5612	INTEGER(iwp) :: i !<
5613	INTEGER(iwp) :: i1 !<
5614	INTEGER(iwp) :: j !<
5615	INTEGER(iwp) :: j1 !<
5616	INTEGER(iwp) :: k1 !<
5617
5618
5619	number_of_particles = prt_count(k1,j1,i1)
5620	radius_classes = number_of_particles ! necessary to use the same
5621	! subroutines as for
5622	! precalculated kernels
5623
5624	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
5625	radclass(1:number_of_particles), winf(1:number_of_particles) )
5626
5627	!
5628	!-- Store particle radii on the radclass array
5629	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
5630
5631	IF ( wang_kernel ) THEN
5632	epsilon_collision = diss(k1,j1,i1) ! dissipation rate in m2/s3
5633	ELSE
5634	epsilon_collision = 0.0_wp
5635	ENDIF
5636	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 0.33333333333_wp )
5637
5638	IF ( wang_kernel .AND. epsilon_collision > 1.0E-7_wp ) THEN
5639	!
5640	!-- Call routines to calculate efficiencies for the Wang kernel
5641	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
5642	ecf(1:number_of_particles,1:number_of_particles) )
5643
5644	CALL turbsd
5645	CALL turb_enhance_eff
5646	CALL effic
5647
5648	DO j = 1, number_of_particles
5649	DO i = 1, number_of_particles
5650	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
5651	ENDDO
5652	ENDDO
5653
5654	DEALLOCATE( gck, ecf )
5655	ELSE
5656	!
5657	!-- Call routines to calculate efficiencies for the Hall kernel
5658	CALL fallg
5659	CALL effic
5660
5661	DO j = 1, number_of_particles
5662	DO i = 1, number_of_particles
5663	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
5664	* ec(i,j) * ABS( winf(j) - winf(i) )
5665	ENDDO
5666	ENDDO
5667	ENDIF
5668
5669	DEALLOCATE( ec, radclass, winf )
5670
5671	END SUBROUTINE recalculate_kernel
5672
5673	!------------------------------------------------------------------------------!
5674	! Description:
5675	! ------------
5676	!> Calculation of effects of turbulence on the geometric collision kernel
5677	!> (by including the droplets' average radial relative velocities and their
5678	!> radial distribution function) following the analytic model by Aayala et al.
5679	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
5680	!> page 37ff.
5681	!>
5682	!> Input parameters, which need to be replaced by PALM parameters:
5683	!> water density, air density
5684	!------------------------------------------------------------------------------!
5685	SUBROUTINE turbsd
5686
5687	INTEGER(iwp) :: i !<
5688	INTEGER(iwp) :: j !<
5689
5690	REAL(wp) :: ao !<
5691	REAL(wp) :: ao_gr !<
5692	REAL(wp) :: bbb !<
5693	REAL(wp) :: be !<
5694	REAL(wp) :: b1 !<
5695	REAL(wp) :: b2 !<
5696	REAL(wp) :: ccc !<
5697	REAL(wp) :: c1 !<
5698	REAL(wp) :: c1_gr !<
5699	REAL(wp) :: c2 !<
5700	REAL(wp) :: d1 !<
5701	REAL(wp) :: d2 !<
5702	REAL(wp) :: eta !<
5703	REAL(wp) :: e1 !<
5704	REAL(wp) :: e2 !<
5705	REAL(wp) :: fao_gr !<
5706	REAL(wp) :: fr !<
5707	REAL(wp) :: grfin !<
5708	REAL(wp) :: lambda !<
5709	REAL(wp) :: lambda_re !<
5710	REAL(wp) :: lf !<
5711	REAL(wp) :: rc !<
5712	REAL(wp) :: rrp !<
5713	REAL(wp) :: sst !<
5714	REAL(wp) :: tauk !<
5715	REAL(wp) :: tl !<
5716	REAL(wp) :: t2 !<
5717	REAL(wp) :: tt !<
5718	REAL(wp) :: t1 !<
5719	REAL(wp) :: vk !<
5720	REAL(wp) :: vrms1xy !<
5721	REAL(wp) :: vrms2xy !<
5722	REAL(wp) :: v1 !<
5723	REAL(wp) :: v1v2xy !<
5724	REAL(wp) :: v1xysq !<
5725	REAL(wp) :: v2 !<
5726	REAL(wp) :: v2xysq !<
5727	REAL(wp) :: wrfin !<
5728	REAL(wp) :: wrgrav2 !<
5729	REAL(wp) :: wrtur2xy !<
5730	REAL(wp) :: xx !<
5731	REAL(wp) :: yy !<
5732	REAL(wp) :: z !<
5733
5734	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
5735	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
5736
5737	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon_collision )
5738	lambda_re = urms*2 SQRT( 15.0_wp / epsilon_collision / molecular_viscosity )
5739	tl = urms**2 / epsilon_collision
5740	lf = 0.5_wp * urms**3 / epsilon_collision
5741	tauk = SQRT( molecular_viscosity / epsilon_collision )
5742	eta = ( molecular_viscosity3 / epsilon_collision )0.25_wp
5743	vk = eta / tauk
5744
5745	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
5746	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
5747
5748	!
5749	!-- Get terminal velocity of droplets
5750	CALL fallg
5751
5752	DO i = 1, radius_classes
5753	tau(i) = winf(i) / g ! inertial time scale
5754	st(i) = tau(i) / tauk ! Stokes number
5755	ENDDO
5756
5757	!
5758	!-- Calculate average radial relative velocity at contact (wrfin)
5759	z = tt / tl
5760	be = SQRT( 2.0_wp ) * lambda / lf
5761	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
5762	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
5763	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
5764	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
5765	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
5766	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
5767	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
5768	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
5769	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
5770	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
5771
5772	DO i = 1, radius_classes
5773
5774	v1 = winf(i)
5775	t1 = tau(i)
5776
5777	DO j = 1, i
5778	rrp = radclass(i) + radclass(j)
5779	v2 = winf(j)
5780	t2 = tau(j)
5781
5782	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
5783	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
5784	v1xysq = v1xysq * urms**2 / t1
5785	vrms1xy = SQRT( v1xysq )
5786
5787	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
5788	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
5789	v2xysq = v2xysq * urms**2 / t2
5790	vrms2xy = SQRT( v2xysq )
5791
5792	IF ( winf(i) >= winf(j) ) THEN
5793	v1 = winf(i)
5794	t1 = tau(i)
5795	v2 = winf(j)
5796	t2 = tau(j)
5797	ELSE
5798	v1 = winf(j)
5799	t1 = tau(j)
5800	v2 = winf(i)
5801	t2 = tau(i)
5802	ENDIF
5803
5804	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
5805	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
5806	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
5807	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
5808	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
5809	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
5810	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
5811	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
5812	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
5813	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
5814
5815	!
5816	!-- Calculate radial distribution function (grfin)
5817	IF ( st(j) > st(i) ) THEN
5818	sst = st(j)
5819	ELSE
5820	sst = st(i)
5821	ENDIF
5822
5823	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
5824	sst*2 + 5.3406_wp sst
5825	IF ( xx < 0.0_wp ) xx = 0.0_wp
5826	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
5827
5828	c1_gr = xx / ( g / vk * tauk )**yy
5829
5830	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
5831	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
5832	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
5833
5834	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
5835	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
5836
5837	!
5838	!-- Calculate general collection kernel (without the consideration of
5839	!-- collection efficiencies)
5840	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
5841	gck(j,i) = gck(i,j)
5842
5843	ENDDO
5844	ENDDO
5845
5846	END SUBROUTINE turbsd
5847
5848	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
5849	!
5850	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5851	!-- effects on the collision kernel
5852
5853
5854	REAL(wp) :: a !<
5855	REAL(wp) :: aa1 !<
5856	REAL(wp) :: b !<
5857	REAL(wp) :: tau0 !<
5858	REAL(wp) :: vsett !<
5859
5860	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
5861	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
5862
5863	END FUNCTION phi_w
5864
5865	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
5866	!
5867	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5868	!-- effects on the collision kernel
5869
5870	REAL(wp) :: a !<
5871	REAL(wp) :: aa1 !<
5872	REAL(wp) :: aa2 !<
5873	REAL(wp) :: aa3 !<
5874	REAL(wp) :: aa4 !<
5875	REAL(wp) :: aa5 !<
5876	REAL(wp) :: aa6 !<
5877	REAL(wp) :: b !<
5878	REAL(wp) :: tau1 !<
5879	REAL(wp) :: tau2 !<
5880	REAL(wp) :: vsett1 !<
5881	REAL(wp) :: vsett2 !<
5882
5883	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
5884	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
5885	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
5886	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
5887	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
5888	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
5889	vsett1 / vsett2
5890	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
5891	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
5892	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
5893	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
5894
5895	END FUNCTION zhi
5896
5897
5898	!------------------------------------------------------------------------------!
5899	! Description:
5900	! ------------
5901	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
5902	!> Meteorol.)
5903	!------------------------------------------------------------------------------!
5904	SUBROUTINE fallg
5905
5906	INTEGER(iwp) :: j !<
5907
5908	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
5909	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
5910	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
5911	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
5912	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
5913	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
5914
5915	REAL(wp) :: diameter !< droplet diameter in mm
5916
5917
5918	DO j = 1, radius_classes
5919
5920	diameter = radclass(j) * 2000.0_wp
5921
5922	IF ( diameter <= d0_rog ) THEN
5923	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
5924	EXP( -k_low_rog * diameter ) )
5925	ELSE
5926	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
5927	ENDIF
5928
5929	ENDDO
5930
5931	END SUBROUTINE fallg
5932
5933
5934	!------------------------------------------------------------------------------!
5935	! Description:
5936	! ------------
5937	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
5938	!------------------------------------------------------------------------------!
5939	SUBROUTINE effic
5940
5941	INTEGER(iwp) :: i !<
5942	INTEGER(iwp) :: iq !<
5943	INTEGER(iwp) :: ir !<
5944	INTEGER(iwp) :: j !<
5945	INTEGER(iwp) :: k !<
5946
5947	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
5948
5949	LOGICAL, SAVE :: first = .TRUE. !<
5950
5951	REAL(wp) :: ek !<
5952	REAL(wp) :: particle_radius !<
5953	REAL(wp) :: pp !<
5954	REAL(wp) :: qq !<
5955	REAL(wp) :: rq !<
5956
5957	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
5958
5959	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
5960
5961	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
5962
5963	!
5964	!-- Initial assignment of constants
5965	IF ( first ) THEN
5966
5967	first = .FALSE.
5968	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
5969	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
5970	150.0_wp, 200.0_wp, 300.0_wp /)
5971
5972	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
5973	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
5974	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
5975	0.90_wp, 0.95_wp, 1.00_wp /)
5976
5977	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
5978	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
5979	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
5980	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
5981	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
5982	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
5983	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
5984	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
5985	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
5986	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
5987	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
5988	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
5989	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
5990	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
5991	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
5992	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
5993	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
5994	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
5995	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
5996	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
5997	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
5998	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
5999	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
6000	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6001	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
6002	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
6003	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6004	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
6005	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6006	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6007	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
6008	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6009	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6010	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
6011	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6012	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6013	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
6014	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
6015	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6016	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
6017	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
6018	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6019	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
6020	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
6021	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6022	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
6023	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
6024	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6025	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
6026	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
6027	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6028	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
6029	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
6030	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
6031	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
6032	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
6033	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
6034	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
6035	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
6036	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
6037	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
6038	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
6039	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
6040	ENDIF
6041
6042	!
6043	!-- Calculate the radius class index of particles with respect to array r
6044	!-- Radius has to be in microns
6045	ALLOCATE( ira(1:radius_classes) )
6046	DO j = 1, radius_classes
6047	particle_radius = radclass(j) * 1.0E6_wp
6048	DO k = 1, 15
6049	IF ( particle_radius < r0(k) ) THEN
6050	ira(j) = k
6051	EXIT
6052	ENDIF
6053	ENDDO
6054	IF ( particle_radius >= r0(15) ) ira(j) = 16
6055	ENDDO
6056
6057	!
6058	!-- Two-dimensional linear interpolation of the collision efficiency.
6059	!-- Radius has to be in microns
6060	DO j = 1, radius_classes
6061	DO i = 1, j
6062
6063	ir = MAX( ira(i), ira(j) )
6064	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6065	iq = INT( rq * 20 ) + 1
6066	iq = MAX( iq , 2)
6067
6068	IF ( ir < 16 ) THEN
6069	IF ( ir >= 2 ) THEN
6070	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
6071	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6072	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6073	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
6074	* ecoll(ir-1,iq-1) &
6075	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
6076	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
6077	+ pp * qq * ecoll(ir,iq)
6078	ELSE
6079	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6080	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
6081	ENDIF
6082	ELSE
6083	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6084	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
6085	ec(j,i) = MIN( ek, 1.0_wp )
6086	ENDIF
6087
6088	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
6089
6090	ec(i,j) = ec(j,i)
6091
6092	ENDDO
6093	ENDDO
6094
6095	DEALLOCATE( ira )
6096
6097	END SUBROUTINE effic
6098
6099
6100	!------------------------------------------------------------------------------!
6101	! Description:
6102	! ------------
6103	!> Interpolation of turbulent enhancement factor for collision efficencies
6104	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
6105	!------------------------------------------------------------------------------!
6106	SUBROUTINE turb_enhance_eff
6107
6108	INTEGER(iwp) :: i !<
6109	INTEGER(iwp) :: iq !<
6110	INTEGER(iwp) :: ir !<
6111	INTEGER(iwp) :: j !<
6112	INTEGER(iwp) :: k !<
6113	INTEGER(iwp) :: kk !<
6114
6115	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
6116
6117	LOGICAL, SAVE :: first = .TRUE. !<
6118
6119	REAL(wp) :: particle_radius !<
6120	REAL(wp) :: pp !<
6121	REAL(wp) :: qq !<
6122	REAL(wp) :: rq !<
6123	REAL(wp) :: y1 !<
6124	REAL(wp) :: y2 !<
6125	REAL(wp) :: y3 !<
6126
6127	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
6128	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
6129
6130	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
6131	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
6132
6133	!
6134	!-- Initial assignment of constants
6135	IF ( first ) THEN
6136
6137	first = .FALSE.
6138
6139	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
6140	100.0_wp /)
6141
6142	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
6143	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
6144	!
6145	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
6146	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
6147	1.207_wp, 1.207_wp, 1.0_wp /)
6148	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
6149	1.069_wp, 1.069_wp, 1.0_wp /)
6150	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
6151	1.000_wp, 1.000_wp, 1.0_wp /)
6152	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
6153	1.025_wp, 1.025_wp, 1.0_wp /)
6154	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
6155	1.056_wp, 1.056_wp, 1.0_wp /)
6156	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
6157	1.028_wp, 1.028_wp, 1.0_wp /)
6158	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
6159	1.046_wp, 1.046_wp, 1.0_wp /)
6160	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
6161	1.029_wp, 1.029_wp, 1.0_wp /)
6162	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
6163	1.021_wp, 1.021_wp, 1.0_wp /)
6164	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
6165	1.088_wp, 1.088_wp, 1.0_wp /)
6166	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
6167	2.60_wp, 2.60_wp, 1.0_wp /)
6168	!
6169	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
6170	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
6171	1.445_wp, 1.445_wp, 1.0_wp /)
6172	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
6173	1.201_wp, 1.201_wp, 1.0_wp /)
6174	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
6175	1.150_wp, 1.150_wp, 1.0_wp /)
6176	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
6177	1.126_wp, 1.126_wp, 1.0_wp /)
6178	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
6179	1.092_wp, 1.092_wp, 1.0_wp /)
6180	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
6181	1.051_wp, 1.051_wp, 1.0_wp /)
6182	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
6183	1.086_wp, 1.086_wp, 1.0_wp /)
6184	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
6185	1.063_wp, 1.063_wp, 1.0_wp /)
6186	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
6187	1.100_wp, 1.100_wp, 1.0_wp /)
6188	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
6189	1.120_wp, 1.120_wp, 1.0_wp /)
6190	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
6191	26.0_wp, 26.0_wp, 1.0_wp /)
6192
6193	ENDIF
6194
6195	!
6196	!-- Calculate the radius class index of particles with respect to array r0
6197	!-- The droplet radius has to be given in microns.
6198	ALLOCATE( ira(1:radius_classes) )
6199
6200	DO j = 1, radius_classes
6201	particle_radius = radclass(j) * 1.0E6_wp
6202	DO k = 1, 7
6203	IF ( particle_radius < r0(k) ) THEN
6204	ira(j) = k
6205	EXIT
6206	ENDIF
6207	ENDDO
6208	IF ( particle_radius >= r0(7) ) ira(j) = 8
6209	ENDDO
6210
6211	!
6212	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
6213	!-- The droplet radius has to be given in microns.
6214	DO j = 1, radius_classes
6215	DO i = 1, j
6216
6217	ir = MAX( ira(i), ira(j) )
6218	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6219
6220	DO kk = 2, 11
6221	IF ( rq <= rat(kk) ) THEN
6222	iq = kk
6223	EXIT
6224	ENDIF
6225	ENDDO
6226
6227	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
6228
6229	IF ( ir < 8 ) THEN
6230	IF ( ir >= 2 ) THEN
6231	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
6232	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6233	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6234	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
6235	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
6236	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
6237	pp * qq * ecoll_100(ir,iq)
6238	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
6239	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
6240	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
6241	pp * qq * ecoll_400(ir,iq)
6242	ELSE
6243	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6244	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
6245	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
6246	ENDIF
6247	ELSE
6248	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6249	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
6250	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
6251	ENDIF
6252	!
6253	!-- Linear interpolation of turbulent enhancement factor
6254	IF ( epsilon_collision <= 0.01_wp ) THEN
6255	ecf(j,i) = ( epsilon_collision - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
6256	+ ( epsilon_collision - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
6257	ELSEIF ( epsilon_collision <= 0.06_wp ) THEN
6258	ecf(j,i) = ( epsilon_collision - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6259	+ ( epsilon_collision - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6260	ELSE
6261	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6262	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6263	ENDIF
6264
6265	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
6266
6267	ecf(i,j) = ecf(j,i)
6268
6269	ENDDO
6270	ENDDO
6271
6272	END SUBROUTINE turb_enhance_eff
6273
6274
6275	!------------------------------------------------------------------------------!
6276	! Description:
6277	! ------------
6278	! This routine is a part of the Lagrangian particle model. Super droplets which
6279	! fulfill certain criterion's (e.g. a big weighting factor and a large radius)
6280	! can be split into several super droplets with a reduced number of
6281	! represented particles of every super droplet. This mechanism ensures an
6282	! improved representation of the right tail of the drop size distribution with
6283	! a feasible amount of computational costs. The limits of particle creation
6284	! should be chosen carefully! The idea of this algorithm is based on
6285	! Unterstrasser and Soelch, 2014.
6286	!------------------------------------------------------------------------------!
6287	SUBROUTINE lpm_splitting
6288
6289	INTEGER(iwp) :: i !<
6290	INTEGER(iwp) :: j !<
6291	INTEGER(iwp) :: jpp !<
6292	INTEGER(iwp) :: k !<
6293	INTEGER(iwp) :: n !<
6294	INTEGER(iwp) :: new_particles_gb !< counter of created particles within one grid box
6295	INTEGER(iwp) :: new_size !< new particle array size
6296	INTEGER(iwp) :: np !<
6297	INTEGER(iwp) :: old_size !< old particle array size
6298
6299	INTEGER(iwp), PARAMETER :: n_max = 100 !< number of radii bin for splitting functions
6300
6301	LOGICAL :: first_loop_stride_sp = .TRUE. !< flag to calculate constants only once
6302
6303	REAL(wp) :: diameter !< diameter of droplet
6304	REAL(wp) :: dlog !< factor for DSD calculation
6305	REAL(wp) :: factor_volume_to_mass !< pre calculate factor volume to mass
6306	REAL(wp) :: lambda !< slope parameter of gamma-distribution
6307	REAL(wp) :: lwc !< liquid water content of grid box
6308	REAL(wp) :: lwc_total !< average liquid water content of cloud
6309	REAL(wp) :: m1 !< first moment of DSD
6310	REAL(wp) :: m1_total !< average over all PEs of first moment of DSD
6311	REAL(wp) :: m2 !< second moment of DSD
6312	REAL(wp) :: m2_total !< average average over all PEs second moment of DSD
6313	REAL(wp) :: m3 !< third moment of DSD
6314	REAL(wp) :: m3_total !< average average over all PEs third moment of DSD
6315	REAL(wp) :: mu !< spectral shape parameter of gamma distribution
6316	REAL(wp) :: nrclgb !< number of cloudy grid boxes (ql >= 1.0E-5 kg/kg)
6317	REAL(wp) :: nrclgb_total !< average over all PEs of number of cloudy grid boxes
6318	REAL(wp) :: nr !< number concentration of cloud droplets
6319	REAL(wp) :: nr_total !< average over all PEs of number of cloudy grid boxes
6320	REAL(wp) :: nr0 !< intercept parameter of gamma distribution
6321	REAL(wp) :: pirho_l !< pi * rho_l / 6.0
6322	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6323	!< (Siebesma et al 2003, JAS, 60)
6324	REAL(wp) :: rm !< volume averaged mean radius
6325	REAL(wp) :: rm_total !< average over all PEs of volume averaged mean radius
6326	REAL(wp) :: r_min = 1.0E-6_wp !< minimum radius of approximated spectra
6327	REAL(wp) :: r_max = 1.0E-3_wp !< maximum radius of approximated spectra
6328	REAL(wp) :: sigma_log = 1.5_wp !< standard deviation of the LOG-distribution
6329	REAL(wp) :: zeta !< Parameter for DSD calculation of Seifert
6330
6331	REAL(wp), DIMENSION(0:n_max-1) :: an_spl !< size dependent critical weight factor
6332	REAL(wp), DIMENSION(0:n_max-1) :: r_bin_mid !< mass weighted mean radius of a bin
6333	REAL(wp), DIMENSION(0:n_max) :: r_bin !< boundaries of a radius bin
6334
6335	TYPE(particle_type) :: tmp_particle !< temporary particle TYPE
6336
6337	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'start' )
6338
6339	IF ( first_loop_stride_sp ) THEN
6340	IF ( i_splitting_mode == 2 .OR. i_splitting_mode == 3 ) THEN
6341	dlog = ( LOG10(r_max) - LOG10(r_min) ) / ( n_max - 1 )
6342	DO i = 0, n_max-1
6343	r_bin(i) = 10.0_wp*( LOG10(r_min) + i dlog - 0.5_wp * dlog )
6344	r_bin_mid(i) = 10.0_wp*( LOG10(r_min) + i dlog )
6345	ENDDO
6346	r_bin(n_max) = 10.0_wp*( LOG10(r_min) + n_max dlog - 0.5_wp * dlog )
6347	ENDIF
6348	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
6349	pirho_l = pi * rho_l / 6.0_wp
6350	IF ( weight_factor_split == -1.0_wp ) THEN
6351	weight_factor_split = 0.1_wp * initial_weighting_factor
6352	ENDIF
6353	ENDIF
6354
6355
6356	IF ( i_splitting_mode == 1 ) THEN
6357
6358	DO i = nxl, nxr
6359	DO j = nys, nyn
6360	DO k = nzb+1, nzt
6361
6362	new_particles_gb = 0
6363	number_of_particles = prt_count(k,j,i)
6364	IF ( number_of_particles <= 0 .OR. &
6365	ql(k,j,i) < ql_crit ) CYCLE
6366	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6367	!
6368	!-- Start splitting operations. Each particle is checked if it
6369	!-- fulfilled the splitting criterion's. In splitting mode 'const'
6370	!-- a critical radius (radius_split) a critical weighting factor
6371	!-- (weight_factor_split) and a splitting factor (splitting_factor)
6372	!-- must be prescribed (see particle_parameters). Super droplets
6373	!-- which have a larger radius and larger weighting factor are split
6374	!-- into 'splitting_factor' super droplets. Therefore, the weighting
6375	!-- factor of the super droplet and all created clones is reduced
6376	!-- by the factor of 'splitting_factor'.
6377	DO n = 1, number_of_particles
6378	IF ( particles(n)%particle_mask .AND. &
6379	particles(n)%radius >= radius_split .AND. &
6380	particles(n)%weight_factor >= weight_factor_split ) &
6381	THEN
6382	!
6383	!-- Calculate the new number of particles.
6384	new_size = prt_count(k,j,i) + splitting_factor - 1
6385	!
6386	!-- Cycle if maximum number of particles per grid box
6387	!-- is greater than the allowed maximum number.
6388	IF ( new_size >= max_number_particles_per_gridbox ) CYCLE
6389	!
6390	!-- Reallocate particle array if necessary.
6391	IF ( new_size > SIZE(particles) ) THEN
6392	CALL realloc_particles_array(i,j,k,new_size)
6393	ENDIF
6394	old_size = prt_count(k,j,i)
6395	!
6396	!-- Calculate new weighting factor.
6397	particles(n)%weight_factor = &
6398	particles(n)%weight_factor / splitting_factor
6399	tmp_particle = particles(n)
6400	!
6401	!-- Create splitting_factor-1 new particles.
6402	DO jpp = 1, splitting_factor-1
6403	grid_particles(k,j,i)%particles(jpp+old_size) = &
6404	tmp_particle
6405	ENDDO
6406	new_particles_gb = new_particles_gb + splitting_factor - 1
6407	!
6408	!-- Save the new number of super droplets for every grid box.
6409	prt_count(k,j,i) = prt_count(k,j,i) + &
6410	splitting_factor - 1
6411	ENDIF
6412	ENDDO
6413
6414	ENDDO
6415	ENDDO
6416	ENDDO
6417
6418	ELSEIF ( i_splitting_mode == 2 ) THEN
6419	!
6420	!-- Initialize summing variables.
6421	lwc = 0.0_wp
6422	lwc_total = 0.0_wp
6423	m1 = 0.0_wp
6424	m1_total = 0.0_wp
6425	m2 = 0.0_wp
6426	m2_total = 0.0_wp
6427	m3 = 0.0_wp
6428	m3_total = 0.0_wp
6429	nr = 0.0_wp
6430	nrclgb = 0.0_wp
6431	nrclgb_total = 0.0_wp
6432	nr_total = 0.0_wp
6433	rm = 0.0_wp
6434	rm_total = 0.0_wp
6435
6436	DO i = nxl, nxr
6437	DO j = nys, nyn
6438	DO k = nzb+1, nzt
6439	number_of_particles = prt_count(k,j,i)
6440	IF ( number_of_particles <= 0 .OR. &
6441	ql(k,j,i) < ql_crit ) CYCLE
6442	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6443	nrclgb = nrclgb + 1.0_wp
6444	!
6445	!-- Calculate moments of DSD.
6446	DO n = 1, number_of_particles
6447	IF ( particles(n)%particle_mask .AND. &
6448	particles(n)%radius >= r_min ) &
6449	THEN
6450	nr = nr + particles(n)%weight_factor
6451	rm = rm + factor_volume_to_mass * &
6452	particles(n)%radius*3 &
6453	particles(n)%weight_factor
6454	IF ( isf == 1 ) THEN
6455	diameter = particles(n)%radius * 2.0_wp
6456	lwc = lwc + factor_volume_to_mass * &
6457	particles(n)%radius*3 &
6458	particles(n)%weight_factor
6459	m1 = m1 + particles(n)%weight_factor * diameter
6460	m2 = m2 + particles(n)%weight_factor * diameter**2
6461	m3 = m3 + particles(n)%weight_factor * diameter**3
6462	ENDIF
6463	ENDIF
6464	ENDDO
6465	ENDDO
6466	ENDDO
6467	ENDDO
6468
6469	#if defined( __parallel )
6470	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6471	CALL MPI_ALLREDUCE( nr, nr_total, 1 , &
6472	MPI_REAL, MPI_SUM, comm2d, ierr )
6473	CALL MPI_ALLREDUCE( rm, rm_total, 1 , &
6474	MPI_REAL, MPI_SUM, comm2d, ierr )
6475	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6476	CALL MPI_ALLREDUCE( nrclgb, nrclgb_total, 1 , &
6477	MPI_REAL, MPI_SUM, comm2d, ierr )
6478	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6479	CALL MPI_ALLREDUCE( lwc, lwc_total, 1 , &
6480	MPI_REAL, MPI_SUM, comm2d, ierr )
6481	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6482	CALL MPI_ALLREDUCE( m1, m1_total, 1 , &
6483	MPI_REAL, MPI_SUM, comm2d, ierr )
6484	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6485	CALL MPI_ALLREDUCE( m2, m2_total, 1 , &
6486	MPI_REAL, MPI_SUM, comm2d, ierr )
6487	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6488	CALL MPI_ALLREDUCE( m3, m3_total, 1 , &
6489	MPI_REAL, MPI_SUM, comm2d, ierr )
6490	#endif
6491
6492	!
6493	!-- Calculate number concentration and mean volume averaged radius.
6494	nr_total = MERGE( nr_total / nrclgb_total, &
6495	0.0_wp, nrclgb_total > 0.0_wp &
6496	)
6497	rm_total = MERGE( ( rm_total / &
6498	( nr_total * factor_volume_to_mass ) &
6499	)**0.3333333_wp, 0.0_wp, nrclgb_total > 0.0_wp &
6500	)
6501	!
6502	!-- Check which function should be used to approximate the DSD.
6503	IF ( isf == 1 ) THEN
6504	lwc_total = MERGE( lwc_total / nrclgb_total, &
6505	0.0_wp, nrclgb_total > 0.0_wp &
6506	)
6507	m1_total = MERGE( m1_total / nrclgb_total, &
6508	0.0_wp, nrclgb_total > 0.0_wp &
6509	)
6510	m2_total = MERGE( m2_total / nrclgb_total, &
6511	0.0_wp, nrclgb_total > 0.0_wp &
6512	)
6513	m3_total = MERGE( m3_total / nrclgb_total, &
6514	0.0_wp, nrclgb_total > 0.0_wp &
6515	)
6516	zeta = m1_total * m3_total / m2_total**2
6517	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6518	( zeta - 1.0_wp ), 0.0_wp &
6519	)
6520
6521	lambda = ( pirho_l * nr_total / lwc_total * &
6522	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * ( mu + 1.0_wp ) &
6523	)**0.3333333_wp
6524	nr0 = nr_total / gamma( mu + 1.0_wp ) * lambda**( mu + 1.0_wp )
6525
6526	DO n = 0, n_max-1
6527	diameter = r_bin_mid(n) * 2.0_wp
6528	an_spl(n) = nr0 * diameter*mu EXP( -lambda * diameter ) * &
6529	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6530	ENDDO
6531	ELSEIF ( isf == 2 ) THEN
6532	DO n = 0, n_max-1
6533	an_spl(n) = nr_total / ( SQRT( 2.0_wp * pi ) * &
6534	LOG(sigma_log) * r_bin_mid(n) &
6535	) * &
6536	EXP( -( LOG( r_bin_mid(n) / rm_total )**2 ) / &
6537	( 2.0_wp * LOG(sigma_log)**2 ) &
6538	) * &
6539	( r_bin(n+1) - r_bin(n) )
6540	ENDDO
6541	ELSEIF( isf == 3 ) THEN
6542	DO n = 0, n_max-1
6543	an_spl(n) = 3.0_wp * nr_total * r_bin_mid(n)2 / rm_total3 * &
6544	EXP( - ( r_bin_mid(n)3 / rm_total3 ) ) * &
6545	( r_bin(n+1) - r_bin(n) )
6546	ENDDO
6547	ENDIF
6548	!
6549	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6550	an_spl = MAX(an_spl, 1.0_wp)
6551
6552	DO i = nxl, nxr
6553	DO j = nys, nyn
6554	DO k = nzb+1, nzt
6555	number_of_particles = prt_count(k,j,i)
6556	IF ( number_of_particles <= 0 .OR. &
6557	ql(k,j,i) < ql_crit ) CYCLE
6558	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6559	new_particles_gb = 0
6560	!
6561	!-- Start splitting operations. Each particle is checked if it
6562	!-- fulfilled the splitting criterion's. In splitting mode 'cl_av'
6563	!-- a critical radius (radius_split) and a splitting function must
6564	!-- be prescribed (see particles_par). The critical weighting factor
6565	!-- is calculated while approximating a 'gamma', 'log' or 'exp'-
6566	!-- drop size distribution. In this mode the DSD is calculated as
6567	!-- an average over all cloudy grid boxes. Super droplets which
6568	!-- have a larger radius and larger weighting factor are split into
6569	!-- 'splitting_factor' super droplets. In this case the splitting
6570	!-- factor is calculated of weighting factor of the super droplet
6571	!-- and the approximated number concentration for droplet of such
6572	!-- a size. Due to the splitting, the weighting factor of the
6573	!-- super droplet and all created clones is reduced by the factor
6574	!-- of 'splitting_facor'.
6575	DO n = 1, number_of_particles
6576	DO np = 0, n_max-1
6577	IF ( r_bin(np) >= radius_split .AND. &
6578	particles(n)%particle_mask .AND. &
6579	particles(n)%radius >= r_bin(np) .AND. &
6580	particles(n)%radius < r_bin(np+1) .AND. &
6581	particles(n)%weight_factor >= an_spl(np) ) &
6582	THEN
6583	!
6584	!-- Calculate splitting factor
6585	splitting_factor = &
6586	MIN( INT( particles(n)%weight_factor / &
6587	an_spl(np) &
6588	), splitting_factor_max &
6589	)
6590	IF ( splitting_factor < 2 ) CYCLE
6591	!
6592	!-- Calculate the new number of particles.
6593	new_size = prt_count(k,j,i) + splitting_factor - 1
6594	!
6595	!-- Cycle if maximum number of particles per grid box
6596	!-- is greater than the allowed maximum number.
6597	IF ( new_size >= max_number_particles_per_gridbox ) &
6598	CYCLE
6599	!
6600	!-- Reallocate particle array if necessary.
6601	IF ( new_size > SIZE(particles) ) THEN
6602	CALL realloc_particles_array(i,j,k,new_size)
6603	ENDIF
6604	old_size = prt_count(k,j,i)
6605	new_particles_gb = new_particles_gb + &
6606	splitting_factor - 1
6607	!
6608	!-- Calculate new weighting factor.
6609	particles(n)%weight_factor = &
6610	particles(n)%weight_factor / splitting_factor
6611	tmp_particle = particles(n)
6612	!
6613	!-- Create splitting_factor-1 new particles.
6614	DO jpp = 1, splitting_factor-1
6615	grid_particles(k,j,i)%particles(jpp+old_size) = &
6616	tmp_particle
6617	ENDDO
6618	!
6619	!-- Save the new number of super droplets.
6620	prt_count(k,j,i) = prt_count(k,j,i) + &
6621	splitting_factor - 1
6622	ENDIF
6623	ENDDO
6624	ENDDO
6625
6626	ENDDO
6627	ENDDO
6628	ENDDO
6629
6630	ELSEIF ( i_splitting_mode == 3 ) THEN
6631
6632	DO i = nxl, nxr
6633	DO j = nys, nyn
6634	DO k = nzb+1, nzt
6635
6636	!
6637	!-- Initialize summing variables.
6638	lwc = 0.0_wp
6639	m1 = 0.0_wp
6640	m2 = 0.0_wp
6641	m3 = 0.0_wp
6642	nr = 0.0_wp
6643	rm = 0.0_wp
6644
6645	new_particles_gb = 0
6646	number_of_particles = prt_count(k,j,i)
6647	IF ( number_of_particles <= 0 .OR. &
6648	ql(k,j,i) < ql_crit ) CYCLE
6649	particles => grid_particles(k,j,i)%particles
6650	!
6651	!-- Calculate moments of DSD.
6652	DO n = 1, number_of_particles
6653	IF ( particles(n)%particle_mask .AND. &
6654	particles(n)%radius >= r_min ) &
6655	THEN
6656	nr = nr + particles(n)%weight_factor
6657	rm = rm + factor_volume_to_mass * &
6658	particles(n)%radius*3 &
6659	particles(n)%weight_factor
6660	IF ( isf == 1 ) THEN
6661	diameter = particles(n)%radius * 2.0_wp
6662	lwc = lwc + factor_volume_to_mass * &
6663	particles(n)%radius*3 &
6664	particles(n)%weight_factor
6665	m1 = m1 + particles(n)%weight_factor * diameter
6666	m2 = m2 + particles(n)%weight_factor * diameter**2
6667	m3 = m3 + particles(n)%weight_factor * diameter**3
6668	ENDIF
6669	ENDIF
6670	ENDDO
6671
6672	IF ( nr <= 0.0_wp .OR. rm <= 0.0_wp ) CYCLE
6673	!
6674	!-- Calculate mean volume averaged radius.
6675	rm = ( rm / ( nr * factor_volume_to_mass ) )**0.3333333_wp
6676	!
6677	!-- Check which function should be used to approximate the DSD.
6678	IF ( isf == 1 ) THEN
6679	!
6680	!-- Gamma size distribution to calculate
6681	!-- critical weight_factor (e.g. Marshall + Palmer, 1948).
6682	zeta = m1 * m3 / m2**2
6683	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6684	( zeta - 1.0_wp ), 0.0_wp &
6685	)
6686	lambda = ( pirho_l * nr / lwc * &
6687	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * &
6688	( mu + 1.0_wp ) &
6689	)**0.3333333_wp
6690	nr0 = ( nr / (gamma( mu + 1.0_wp ) ) ) * &
6691	lambda**( mu + 1.0_wp )
6692
6693	DO n = 0, n_max-1
6694	diameter = r_bin_mid(n) * 2.0_wp
6695	an_spl(n) = nr0 * diameter*mu &
6696	EXP( -lambda * diameter ) * &
6697	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6698	ENDDO
6699	ELSEIF ( isf == 2 ) THEN
6700	!
6701	!-- Lognormal size distribution to calculate critical
6702	!-- weight_factor (e.g. Levin, 1971, Bradley + Stow, 1974).
6703	DO n = 0, n_max-1
6704	an_spl(n) = nr / ( SQRT( 2.0_wp * pi ) * &
6705	LOG(sigma_log) * r_bin_mid(n) &
6706	) * &
6707	EXP( -( LOG( r_bin_mid(n) / rm )**2 ) / &
6708	( 2.0_wp * LOG(sigma_log)**2 ) &
6709	) * &
6710	( r_bin(n+1) - r_bin(n) )
6711	ENDDO
6712	ELSEIF ( isf == 3 ) THEN
6713	!
6714	!-- Exponential size distribution to calculate critical
6715	!-- weight_factor (e.g. Berry + Reinhardt, 1974).
6716	DO n = 0, n_max-1
6717	an_spl(n) = 3.0_wp * nr * r_bin_mid(n)2 / rm3 * &
6718	EXP( - ( r_bin_mid(n)3 / rm3 ) ) * &
6719	( r_bin(n+1) - r_bin(n) )
6720	ENDDO
6721	ENDIF
6722
6723	!
6724	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6725	an_spl = MAX(an_spl, 1.0_wp)
6726	!
6727	!-- Start splitting operations. Each particle is checked if it
6728	!-- fulfilled the splitting criterion's. In splitting mode 'gb_av'
6729	!-- a critical radius (radius_split) and a splitting function must
6730	!-- be prescribed (see particles_par). The critical weighting factor
6731	!-- is calculated while appoximating a 'gamma', 'log' or 'exp'-
6732	!-- drop size distribution. In this mode a DSD is calculated for
6733	!-- every cloudy grid box. Super droplets which have a larger
6734	!-- radius and larger weighting factor are split into
6735	!-- 'splitting_factor' super droplets. In this case the splitting
6736	!-- factor is calculated of weighting factor of the super droplet
6737	!-- and theapproximated number concentration for droplet of such
6738	!-- a size. Due to the splitting, the weighting factor of the
6739	!-- super droplet and all created clones is reduced by the factor
6740	!-- of 'splitting_facor'.
6741	DO n = 1, number_of_particles
6742	DO np = 0, n_max-1
6743	IF ( r_bin(np) >= radius_split .AND. &
6744	particles(n)%particle_mask .AND. &
6745	particles(n)%radius >= r_bin(np) .AND. &
6746	particles(n)%radius < r_bin(np+1) .AND. &
6747	particles(n)%weight_factor >= an_spl(np) ) &
6748	THEN
6749	!
6750	!-- Calculate splitting factor.
6751	splitting_factor = &
6752	MIN( INT( particles(n)%weight_factor / &
6753	an_spl(np) &
6754	), splitting_factor_max &
6755	)
6756	IF ( splitting_factor < 2 ) CYCLE
6757
6758	!
6759	!-- Calculate the new number of particles.
6760	new_size = prt_count(k,j,i) + splitting_factor - 1
6761	!
6762	!-- Cycle if maximum number of particles per grid box
6763	!-- is greater than the allowed maximum number.
6764	IF ( new_size >= max_number_particles_per_gridbox ) &
6765	CYCLE
6766	!
6767	!-- Reallocate particle array if necessary.
6768	IF ( new_size > SIZE(particles) ) THEN
6769	CALL realloc_particles_array(i,j,k,new_size)
6770	ENDIF
6771	!
6772	!-- Calculate new weighting factor.
6773	particles(n)%weight_factor = &
6774	particles(n)%weight_factor / splitting_factor
6775	tmp_particle = particles(n)
6776	old_size = prt_count(k,j,i)
6777	!
6778	!-- Create splitting_factor-1 new particles.
6779	DO jpp = 1, splitting_factor-1
6780	grid_particles(k,j,i)%particles(jpp+old_size) = &
6781	tmp_particle
6782	ENDDO
6783	!
6784	!-- Save the new number of droplets for every grid box.
6785	prt_count(k,j,i) = prt_count(k,j,i) + &
6786	splitting_factor - 1
6787	new_particles_gb = new_particles_gb + &
6788	splitting_factor - 1
6789	ENDIF
6790	ENDDO
6791	ENDDO
6792	ENDDO
6793	ENDDO
6794	ENDDO
6795	ENDIF
6796
6797	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'stop' )
6798
6799	END SUBROUTINE lpm_splitting
6800
6801
6802	!------------------------------------------------------------------------------!
6803	! Description:
6804	! ------------
6805	! This routine is a part of the Lagrangian particle model. Two Super droplets
6806	! which fulfill certain criterion's (e.g. a big weighting factor and a small
6807	! radius) can be merged into one super droplet with a increased number of
6808	! represented particles of the super droplet. This mechanism ensures an
6809	! improved a feasible amount of computational costs. The limits of particle
6810	! creation should be chosen carefully! The idea of this algorithm is based on
6811	! Unterstrasser and Soelch, 2014.
6812	!------------------------------------------------------------------------------!
6813	SUBROUTINE lpm_merging
6814
6815	INTEGER(iwp) :: i !<
6816	INTEGER(iwp) :: j !<
6817	INTEGER(iwp) :: k !<
6818	INTEGER(iwp) :: n !<
6819	INTEGER(iwp) :: merge_drp = 0 !< number of merged droplets
6820
6821
6822	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6823	!< (e.g. Siebesma et al 2003, JAS, 60)
6824
6825	CALL cpu_log( log_point_s(81), 'lpm_merging', 'start' )
6826
6827	merge_drp = 0
6828
6829	IF ( weight_factor_merge == -1.0_wp ) THEN
6830	weight_factor_merge = 0.5_wp * initial_weighting_factor
6831	ENDIF
6832
6833	DO i = nxl, nxr
6834	DO j = nys, nyn
6835	DO k = nzb+1, nzt
6836
6837	number_of_particles = prt_count(k,j,i)
6838	IF ( number_of_particles <= 0 .OR. &
6839	ql(k,j,i) >= ql_crit ) CYCLE
6840	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6841	!
6842	!-- Start merging operations: This routine delete super droplets with
6843	!-- a small radius (radius <= radius_merge) and a low weighting
6844	!-- factor (weight_factor <= weight_factor_merge). The number of
6845	!-- represented particles will be added to the next particle of the
6846	!-- particle array. Tests showed that this simplified method can be
6847	!-- used because it will only take place outside of cloudy grid
6848	!-- boxes where ql <= 1.0E-5 kg/kg. Therefore, especially former cloned
6849	!-- and subsequent evaporated super droplets will be merged.
6850	DO n = 1, number_of_particles-1
6851	IF ( particles(n)%particle_mask .AND. &
6852	particles(n+1)%particle_mask .AND. &
6853	particles(n)%radius <= radius_merge .AND. &
6854	particles(n)%weight_factor <= weight_factor_merge ) &
6855	THEN
6856	particles(n+1)%weight_factor = &
6857	particles(n+1)%weight_factor + &
6858	( particles(n)%radius**3 / &
6859	particles(n+1)%radius*3 &
6860	particles(n)%weight_factor &
6861	)
6862	particles(n)%particle_mask = .FALSE.
6863	deleted_particles = deleted_particles + 1
6864	merge_drp = merge_drp + 1
6865
6866	ENDIF
6867	ENDDO
6868	ENDDO
6869	ENDDO
6870	ENDDO
6871
6872
6873	CALL cpu_log( log_point_s(81), 'lpm_merging', 'stop' )
6874
6875	END SUBROUTINE lpm_merging
6876
6877
6878
6879
6880	!------------------------------------------------------------------------------!
6881	! Description:
6882	! ------------
6883	!> Exchange between subdomains.
6884	!> As soon as one particle has moved beyond the boundary of the domain, it
6885	!> is included in the relevant transfer arrays and marked for subsequent
6886	!> deletion on this PE.
6887	!> First sweep for crossings in x direction. Find out first the number of
6888	!> particles to be transferred and allocate temporary arrays needed to store
6889	!> them.
6890	!> For a one-dimensional decomposition along y, no transfer is necessary,
6891	!> because the particle remains on the PE, but the particle coordinate has to
6892	!> be adjusted.
6893	!------------------------------------------------------------------------------!
6894	SUBROUTINE lpm_exchange_horiz
6895
6896	INTEGER(iwp) :: i !< grid index (x) of particle positition
6897	INTEGER(iwp) :: ip !< index variable along x
6898	INTEGER(iwp) :: j !< grid index (y) of particle positition
6899	INTEGER(iwp) :: jp !< index variable along y
6900	INTEGER(iwp) :: kp !< index variable along z
6901	INTEGER(iwp) :: n !< particle index variable
6902	INTEGER(iwp) :: par_size !< Particle size in bytes
6903	INTEGER(iwp) :: trlp_count !< number of particles send to left PE
6904	INTEGER(iwp) :: trlp_count_recv !< number of particles receive from right PE
6905	INTEGER(iwp) :: trnp_count !< number of particles send to north PE
6906	INTEGER(iwp) :: trnp_count_recv !< number of particles receive from south PE
6907	INTEGER(iwp) :: trrp_count !< number of particles send to right PE
6908	INTEGER(iwp) :: trrp_count_recv !< number of particles receive from left PE
6909	INTEGER(iwp) :: trsp_count !< number of particles send to south PE
6910	INTEGER(iwp) :: trsp_count_recv !< number of particles receive from north PE
6911
6912	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvlp !< particles received from right PE
6913	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvnp !< particles received from south PE
6914	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvrp !< particles received from left PE
6915	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvsp !< particles received from north PE
6916	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trlp !< particles send to left PE
6917	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trnp !< particles send to north PE
6918	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trrp !< particles send to right PE
6919	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trsp !< particles send to south PE
6920
6921	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'start' )
6922
6923	#if defined( __parallel )
6924
6925	!
6926	!-- Exchange between subdomains.
6927	!-- As soon as one particle has moved beyond the boundary of the domain, it
6928	!-- is included in the relevant transfer arrays and marked for subsequent
6929	!-- deletion on this PE.
6930	!-- First sweep for crossings in x direction. Find out first the number of
6931	!-- particles to be transferred and allocate temporary arrays needed to store
6932	!-- them.
6933	!-- For a one-dimensional decomposition along y, no transfer is necessary,
6934	!-- because the particle remains on the PE, but the particle coordinate has to
6935	!-- be adjusted.
6936	trlp_count = 0
6937	trrp_count = 0
6938
6939	trlp_count_recv = 0
6940	trrp_count_recv = 0
6941
6942	IF ( pdims(1) /= 1 ) THEN
6943	!
6944	!-- First calculate the storage necessary for sending and receiving the data.
6945	!-- Compute only first (nxl) and last (nxr) loop iterration.
6946	DO ip = nxl, nxr, nxr - nxl
6947	DO jp = nys, nyn
6948	DO kp = nzb+1, nzt
6949
6950	number_of_particles = prt_count(kp,jp,ip)
6951	IF ( number_of_particles <= 0 ) CYCLE
6952	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
6953	DO n = 1, number_of_particles
6954	IF ( particles(n)%particle_mask ) THEN
6955	i = particles(n)%x * ddx
6956	!
6957	!-- Above calculation does not work for indices less than zero
6958	IF ( particles(n)%x < 0.0_wp) i = -1
6959
6960	IF ( i < nxl ) THEN
6961	trlp_count = trlp_count + 1
6962	ELSEIF ( i > nxr ) THEN
6963	trrp_count = trrp_count + 1
6964	ENDIF
6965	ENDIF
6966	ENDDO
6967
6968	ENDDO
6969	ENDDO
6970	ENDDO
6971
6972	IF ( trlp_count == 0 ) trlp_count = 1
6973	IF ( trrp_count == 0 ) trrp_count = 1
6974
6975	ALLOCATE( trlp(trlp_count), trrp(trrp_count) )
6976
6977	trlp = zero_particle
6978	trrp = zero_particle
6979
6980	trlp_count = 0
6981	trrp_count = 0
6982
6983	ENDIF
6984	!
6985	!-- Compute only first (nxl) and last (nxr) loop iterration
6986	DO ip = nxl, nxr, nxr-nxl
6987	DO jp = nys, nyn
6988	DO kp = nzb+1, nzt
6989	number_of_particles = prt_count(kp,jp,ip)
6990	IF ( number_of_particles <= 0 ) CYCLE
6991	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
6992	DO n = 1, number_of_particles
6993	!
6994	!-- Only those particles that have not been marked as 'deleted' may
6995	!-- be moved.
6996	IF ( particles(n)%particle_mask ) THEN
6997
6998	i = particles(n)%x * ddx
6999	!
7000	!-- Above calculation does not work for indices less than zero
7001	IF ( particles(n)%x < 0.0_wp ) i = -1
7002
7003	IF ( i < nxl ) THEN
7004	IF ( i < 0 ) THEN
7005	!
7006	!-- Apply boundary condition along x
7007	IF ( ibc_par_lr == 0 ) THEN
7008	!
7009	!-- Cyclic condition
7010	IF ( pdims(1) == 1 ) THEN
7011	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7012	particles(n)%origin_x = ( nx + 1 ) * dx + &
7013	particles(n)%origin_x
7014	ELSE
7015	trlp_count = trlp_count + 1
7016	trlp(trlp_count) = particles(n)
7017	trlp(trlp_count)%x = ( nx + 1 ) * dx + trlp(trlp_count)%x
7018	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x + &
7019	( nx + 1 ) * dx
7020	particles(n)%particle_mask = .FALSE.
7021	deleted_particles = deleted_particles + 1
7022
7023	IF ( trlp(trlp_count)%x >= (nx + 1)* dx - 1.0E-12_wp ) THEN
7024	trlp(trlp_count)%x = trlp(trlp_count)%x - 1.0E-10_wp
7025	!++ why is 1 subtracted in next statement???
7026	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x - 1
7027	ENDIF
7028
7029	ENDIF
7030
7031	ELSEIF ( ibc_par_lr == 1 ) THEN
7032	!
7033	!-- Particle absorption
7034	particles(n)%particle_mask = .FALSE.
7035	deleted_particles = deleted_particles + 1
7036
7037	ELSEIF ( ibc_par_lr == 2 ) THEN
7038	!
7039	!-- Particle reflection
7040	particles(n)%x = -particles(n)%x
7041	particles(n)%speed_x = -particles(n)%speed_x
7042
7043	ENDIF
7044	ELSE
7045	!
7046	!-- Store particle data in the transfer array, which will be
7047	!-- send to the neighbouring PE
7048	trlp_count = trlp_count + 1
7049	trlp(trlp_count) = particles(n)
7050	particles(n)%particle_mask = .FALSE.
7051	deleted_particles = deleted_particles + 1
7052
7053	ENDIF
7054
7055	ELSEIF ( i > nxr ) THEN
7056	IF ( i > nx ) THEN
7057	!
7058	!-- Apply boundary condition along x
7059	IF ( ibc_par_lr == 0 ) THEN
7060	!
7061	!-- Cyclic condition
7062	IF ( pdims(1) == 1 ) THEN
7063	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7064	particles(n)%origin_x = particles(n)%origin_x - &
7065	( nx + 1 ) * dx
7066	ELSE
7067	trrp_count = trrp_count + 1
7068	trrp(trrp_count) = particles(n)
7069	trrp(trrp_count)%x = trrp(trrp_count)%x - ( nx + 1 ) * dx
7070	trrp(trrp_count)%origin_x = trrp(trrp_count)%origin_x - &
7071	( nx + 1 ) * dx
7072	particles(n)%particle_mask = .FALSE.
7073	deleted_particles = deleted_particles + 1
7074
7075	ENDIF
7076
7077	ELSEIF ( ibc_par_lr == 1 ) THEN
7078	!
7079	!-- Particle absorption
7080	particles(n)%particle_mask = .FALSE.
7081	deleted_particles = deleted_particles + 1
7082
7083	ELSEIF ( ibc_par_lr == 2 ) THEN
7084	!
7085	!-- Particle reflection
7086	particles(n)%x = 2 * ( nx * dx ) - particles(n)%x
7087	particles(n)%speed_x = -particles(n)%speed_x
7088
7089	ENDIF
7090	ELSE
7091	!
7092	!-- Store particle data in the transfer array, which will be send
7093	!-- to the neighbouring PE
7094	trrp_count = trrp_count + 1
7095	trrp(trrp_count) = particles(n)
7096	particles(n)%particle_mask = .FALSE.
7097	deleted_particles = deleted_particles + 1
7098
7099	ENDIF
7100
7101	ENDIF
7102	ENDIF
7103
7104	ENDDO
7105	ENDDO
7106	ENDDO
7107	ENDDO
7108
7109	!
7110	!-- STORAGE_SIZE returns the storage size of argument A in bits. However , it
7111	!-- is needed in bytes. The function C_SIZEOF which produces this value directly
7112	!-- causes problems with gfortran. For this reason the use of C_SIZEOF is avoided
7113	par_size = STORAGE_SIZE(trlp(1))/8
7114
7115
7116	!
7117	!-- Allocate arrays required for north-south exchange, as these
7118	!-- are used directly after particles are exchange along x-direction.
7119	ALLOCATE( move_also_north(1:NR_2_direction_move) )
7120	ALLOCATE( move_also_south(1:NR_2_direction_move) )
7121
7122	nr_move_north = 0
7123	nr_move_south = 0
7124	!
7125	!-- Send left boundary, receive right boundary (but first exchange how many
7126	!-- and check, if particle storage must be extended)
7127	IF ( pdims(1) /= 1 ) THEN
7128
7129	CALL MPI_SENDRECV( trlp_count, 1, MPI_INTEGER, pleft, 0, &
7130	trrp_count_recv, 1, MPI_INTEGER, pright, 0, &
7131	comm2d, status, ierr )
7132
7133	ALLOCATE(rvrp(MAX(1,trrp_count_recv)))
7134
7135	CALL MPI_SENDRECV( trlp, max(1,trlp_count)*par_size, MPI_BYTE,&
7136	pleft, 1, rvrp, &
7137	max(1,trrp_count_recv)*par_size, MPI_BYTE, pright, 1,&
7138	comm2d, status, ierr )
7139
7140	IF ( trrp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvrp(1:trrp_count_recv))
7141
7142	DEALLOCATE(rvrp)
7143
7144	!
7145	!-- Send right boundary, receive left boundary
7146	CALL MPI_SENDRECV( trrp_count, 1, MPI_INTEGER, pright, 0, &
7147	trlp_count_recv, 1, MPI_INTEGER, pleft, 0, &
7148	comm2d, status, ierr )
7149
7150	ALLOCATE(rvlp(MAX(1,trlp_count_recv)))
7151	!
7152	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7153	!-- variables in structure particle_type (due to the calculation of par_size)
7154	CALL MPI_SENDRECV( trrp, max(1,trrp_count)*par_size, MPI_BYTE,&
7155	pright, 1, rvlp, &
7156	max(1,trlp_count_recv)*par_size, MPI_BYTE, pleft, 1, &
7157	comm2d, status, ierr )
7158
7159	IF ( trlp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvlp(1:trlp_count_recv))
7160
7161	DEALLOCATE( rvlp )
7162	DEALLOCATE( trlp, trrp )
7163
7164	ENDIF
7165
7166	!
7167	!-- Check whether particles have crossed the boundaries in y direction. Note
7168	!-- that this case can also apply to particles that have just been received
7169	!-- from the adjacent right or left PE.
7170	!-- Find out first the number of particles to be transferred and allocate
7171	!-- temporary arrays needed to store them.
7172	!-- For a one-dimensional decomposition along y, no transfer is necessary,
7173	!-- because the particle remains on the PE.
7174	trsp_count = nr_move_south
7175	trnp_count = nr_move_north
7176
7177	trsp_count_recv = 0
7178	trnp_count_recv = 0
7179
7180	IF ( pdims(2) /= 1 ) THEN
7181	!
7182	!-- First calculate the storage necessary for sending and receiving the
7183	!-- data
7184	DO ip = nxl, nxr
7185	DO jp = nys, nyn, nyn-nys !compute only first (nys) and last (nyn) loop iterration
7186	DO kp = nzb+1, nzt
7187	number_of_particles = prt_count(kp,jp,ip)
7188	IF ( number_of_particles <= 0 ) CYCLE
7189	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7190	DO n = 1, number_of_particles
7191	IF ( particles(n)%particle_mask ) THEN
7192	j = particles(n)%y * ddy
7193	!
7194	!-- Above calculation does not work for indices less than zero
7195	IF ( particles(n)%y < 0.0_wp) j = -1
7196
7197	IF ( j < nys ) THEN
7198	trsp_count = trsp_count + 1
7199	ELSEIF ( j > nyn ) THEN
7200	trnp_count = trnp_count + 1
7201	ENDIF
7202	ENDIF
7203	ENDDO
7204	ENDDO
7205	ENDDO
7206	ENDDO
7207
7208	IF ( trsp_count == 0 ) trsp_count = 1
7209	IF ( trnp_count == 0 ) trnp_count = 1
7210
7211	ALLOCATE( trsp(trsp_count), trnp(trnp_count) )
7212
7213	trsp = zero_particle
7214	trnp = zero_particle
7215
7216	trsp_count = nr_move_south
7217	trnp_count = nr_move_north
7218
7219	trsp(1:nr_move_south) = move_also_south(1:nr_move_south)
7220	trnp(1:nr_move_north) = move_also_north(1:nr_move_north)
7221
7222	ENDIF
7223
7224	DO ip = nxl, nxr
7225	DO jp = nys, nyn, nyn-nys ! compute only first (nys) and last (nyn) loop iterration
7226	DO kp = nzb+1, nzt
7227	number_of_particles = prt_count(kp,jp,ip)
7228	IF ( number_of_particles <= 0 ) CYCLE
7229	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7230	DO n = 1, number_of_particles
7231	!
7232	!-- Only those particles that have not been marked as 'deleted' may
7233	!-- be moved.
7234	IF ( particles(n)%particle_mask ) THEN
7235
7236	j = particles(n)%y * ddy
7237	!
7238	!-- Above calculation does not work for indices less than zero
7239	IF ( particles(n)%y < 0.0_wp ) j = -1
7240
7241	IF ( j < nys ) THEN
7242	IF ( j < 0 ) THEN
7243	!
7244	!-- Apply boundary condition along y
7245	IF ( ibc_par_ns == 0 ) THEN
7246	!
7247	!-- Cyclic condition
7248	IF ( pdims(2) == 1 ) THEN
7249	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7250	particles(n)%origin_y = ( ny + 1 ) * dy + &
7251	particles(n)%origin_y
7252	ELSE
7253	trsp_count = trsp_count + 1
7254	trsp(trsp_count) = particles(n)
7255	trsp(trsp_count)%y = ( ny + 1 ) * dy + &
7256	trsp(trsp_count)%y
7257	trsp(trsp_count)%origin_y = trsp(trsp_count)%origin_y &
7258	+ ( ny + 1 ) * dy
7259	particles(n)%particle_mask = .FALSE.
7260	deleted_particles = deleted_particles + 1
7261
7262	IF ( trsp(trsp_count)%y >= (ny+1)* dy - 1.0E-12_wp ) THEN
7263	trsp(trsp_count)%y = trsp(trsp_count)%y - 1.0E-10_wp
7264	!++ why is 1 subtracted in next statement???
7265	trsp(trsp_count)%origin_y = &
7266	trsp(trsp_count)%origin_y - 1
7267	ENDIF
7268
7269	ENDIF
7270
7271	ELSEIF ( ibc_par_ns == 1 ) THEN
7272	!
7273	!-- Particle absorption
7274	particles(n)%particle_mask = .FALSE.
7275	deleted_particles = deleted_particles + 1
7276
7277	ELSEIF ( ibc_par_ns == 2 ) THEN
7278	!
7279	!-- Particle reflection
7280	particles(n)%y = -particles(n)%y
7281	particles(n)%speed_y = -particles(n)%speed_y
7282
7283	ENDIF
7284	ELSE
7285	!
7286	!-- Store particle data in the transfer array, which will
7287	!-- be send to the neighbouring PE
7288	trsp_count = trsp_count + 1
7289	trsp(trsp_count) = particles(n)
7290	particles(n)%particle_mask = .FALSE.
7291	deleted_particles = deleted_particles + 1
7292
7293	ENDIF
7294
7295	ELSEIF ( j > nyn ) THEN
7296	IF ( j > ny ) THEN
7297	!
7298	!-- Apply boundary condition along y
7299	IF ( ibc_par_ns == 0 ) THEN
7300	!
7301	!-- Cyclic condition
7302	IF ( pdims(2) == 1 ) THEN
7303	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7304	particles(n)%origin_y = &
7305	particles(n)%origin_y - ( ny + 1 ) * dy
7306	ELSE
7307	trnp_count = trnp_count + 1
7308	trnp(trnp_count) = particles(n)
7309	trnp(trnp_count)%y = &
7310	trnp(trnp_count)%y - ( ny + 1 ) * dy
7311	trnp(trnp_count)%origin_y = &
7312	trnp(trnp_count)%origin_y - ( ny + 1 ) * dy
7313	particles(n)%particle_mask = .FALSE.
7314	deleted_particles = deleted_particles + 1
7315	ENDIF
7316
7317	ELSEIF ( ibc_par_ns == 1 ) THEN
7318	!
7319	!-- Particle absorption
7320	particles(n)%particle_mask = .FALSE.
7321	deleted_particles = deleted_particles + 1
7322
7323	ELSEIF ( ibc_par_ns == 2 ) THEN
7324	!
7325	!-- Particle reflection
7326	particles(n)%y = 2 * ( ny * dy ) - particles(n)%y
7327	particles(n)%speed_y = -particles(n)%speed_y
7328
7329	ENDIF
7330	ELSE
7331	!
7332	!-- Store particle data in the transfer array, which will
7333	!-- be send to the neighbouring PE
7334	trnp_count = trnp_count + 1
7335	trnp(trnp_count) = particles(n)
7336	particles(n)%particle_mask = .FALSE.
7337	deleted_particles = deleted_particles + 1
7338
7339	ENDIF
7340
7341	ENDIF
7342	ENDIF
7343	ENDDO
7344	ENDDO
7345	ENDDO
7346	ENDDO
7347
7348	!
7349	!-- Send front boundary, receive back boundary (but first exchange how many
7350	!-- and check, if particle storage must be extended)
7351	IF ( pdims(2) /= 1 ) THEN
7352
7353	CALL MPI_SENDRECV( trsp_count, 1, MPI_INTEGER, psouth, 0, &
7354	trnp_count_recv, 1, MPI_INTEGER, pnorth, 0, &
7355	comm2d, status, ierr )
7356
7357	ALLOCATE(rvnp(MAX(1,trnp_count_recv)))
7358	!
7359	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7360	!-- variables in structure particle_type (due to the calculation of par_size)
7361	CALL MPI_SENDRECV( trsp, trsp_count*par_size, MPI_BYTE, &
7362	psouth, 1, rvnp, &
7363	trnp_count_recv*par_size, MPI_BYTE, pnorth, 1, &
7364	comm2d, status, ierr )
7365
7366	IF ( trnp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvnp(1:trnp_count_recv))
7367
7368	DEALLOCATE(rvnp)
7369
7370	!
7371	!-- Send back boundary, receive front boundary
7372	CALL MPI_SENDRECV( trnp_count, 1, MPI_INTEGER, pnorth, 0, &
7373	trsp_count_recv, 1, MPI_INTEGER, psouth, 0, &
7374	comm2d, status, ierr )
7375
7376	ALLOCATE(rvsp(MAX(1,trsp_count_recv)))
7377	!
7378	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7379	!-- variables in structure particle_type (due to the calculation of par_size)
7380	CALL MPI_SENDRECV( trnp, trnp_count*par_size, MPI_BYTE, &
7381	pnorth, 1, rvsp, &
7382	trsp_count_recv*par_size, MPI_BYTE, psouth, 1, &
7383	comm2d, status, ierr )
7384
7385	IF ( trsp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvsp(1:trsp_count_recv))
7386
7387	DEALLOCATE(rvsp)
7388
7389	number_of_particles = number_of_particles + trsp_count_recv
7390
7391	DEALLOCATE( trsp, trnp )
7392
7393	ENDIF
7394
7395	DEALLOCATE( move_also_north )
7396	DEALLOCATE( move_also_south )
7397
7398	#else
7399
7400	DO ip = nxl, nxr, nxr-nxl
7401	DO jp = nys, nyn
7402	DO kp = nzb+1, nzt
7403	number_of_particles = prt_count(kp,jp,ip)
7404	IF ( number_of_particles <= 0 ) CYCLE
7405	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7406	DO n = 1, number_of_particles
7407	!
7408	!-- Apply boundary conditions
7409
7410	IF ( particles(n)%x < 0.0_wp ) THEN
7411
7412	IF ( ibc_par_lr == 0 ) THEN
7413	!
7414	!-- Cyclic boundary. Relevant coordinate has to be changed.
7415	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7416	particles(n)%origin_x = ( nx + 1 ) * dx + &
7417	particles(n)%origin_x
7418	ELSEIF ( ibc_par_lr == 1 ) THEN
7419	!
7420	!-- Particle absorption
7421	particles(n)%particle_mask = .FALSE.
7422	deleted_particles = deleted_particles + 1
7423
7424	ELSEIF ( ibc_par_lr == 2 ) THEN
7425	!
7426	!-- Particle reflection
7427	particles(n)%x = -dx - particles(n)%x
7428	particles(n)%speed_x = -particles(n)%speed_x
7429	ENDIF
7430
7431	ELSEIF ( particles(n)%x >= ( nx + 1) * dx ) THEN
7432
7433	IF ( ibc_par_lr == 0 ) THEN
7434	!
7435	!-- Cyclic boundary. Relevant coordinate has to be changed.
7436	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7437	particles(n)%origin_x = particles(n)%origin_x - &
7438	( nx + 1 ) * dx
7439
7440	ELSEIF ( ibc_par_lr == 1 ) THEN
7441	!
7442	!-- Particle absorption
7443	particles(n)%particle_mask = .FALSE.
7444	deleted_particles = deleted_particles + 1
7445
7446	ELSEIF ( ibc_par_lr == 2 ) THEN
7447	!
7448	!-- Particle reflection
7449	particles(n)%x = ( nx + 1 ) * dx - particles(n)%x
7450	particles(n)%speed_x = -particles(n)%speed_x
7451	ENDIF
7452
7453	ENDIF
7454	ENDDO
7455	ENDDO
7456	ENDDO
7457	ENDDO
7458
7459	DO ip = nxl, nxr
7460	DO jp = nys, nyn, nyn-nys
7461	DO kp = nzb+1, nzt
7462	number_of_particles = prt_count(kp,jp,ip)
7463	IF ( number_of_particles <= 0 ) CYCLE
7464	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7465	DO n = 1, number_of_particles
7466
7467	IF ( particles(n)%y < 0.0_wp) THEN
7468
7469	IF ( ibc_par_ns == 0 ) THEN
7470	!
7471	!-- Cyclic boundary. Relevant coordinate has to be changed.
7472	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7473	particles(n)%origin_y = ( ny + 1 ) * dy + &
7474	particles(n)%origin_y
7475
7476	ELSEIF ( ibc_par_ns == 1 ) THEN
7477	!
7478	!-- Particle absorption
7479	particles(n)%particle_mask = .FALSE.
7480	deleted_particles = deleted_particles + 1
7481
7482	ELSEIF ( ibc_par_ns == 2 ) THEN
7483	!
7484	!-- Particle reflection
7485	particles(n)%y = -dy - particles(n)%y
7486	particles(n)%speed_y = -particles(n)%speed_y
7487	ENDIF
7488
7489	ELSEIF ( particles(n)%y >= ( ny + 1) * dy ) THEN
7490
7491	IF ( ibc_par_ns == 0 ) THEN
7492	!
7493	!-- Cyclic boundary. Relevant coordinate has to be changed.
7494	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7495	particles(n)%origin_y = particles(n)%origin_y - &
7496	( ny + 1 ) * dy
7497
7498	ELSEIF ( ibc_par_ns == 1 ) THEN
7499	!
7500	!-- Particle absorption
7501	particles(n)%particle_mask = .FALSE.
7502	deleted_particles = deleted_particles + 1
7503
7504	ELSEIF ( ibc_par_ns == 2 ) THEN
7505	!
7506	!-- Particle reflection
7507	particles(n)%y = ( ny + 1 ) * dy - particles(n)%y
7508	particles(n)%speed_y = -particles(n)%speed_y
7509	ENDIF
7510
7511	ENDIF
7512
7513	ENDDO
7514	ENDDO
7515	ENDDO
7516	ENDDO
7517	#endif
7518
7519	!
7520	!-- Accumulate the number of particles transferred between the subdomains
7521	#if defined( __parallel )
7522	trlp_count_sum = trlp_count_sum + trlp_count
7523	trlp_count_recv_sum = trlp_count_recv_sum + trlp_count_recv
7524	trrp_count_sum = trrp_count_sum + trrp_count
7525	trrp_count_recv_sum = trrp_count_recv_sum + trrp_count_recv
7526	trsp_count_sum = trsp_count_sum + trsp_count
7527	trsp_count_recv_sum = trsp_count_recv_sum + trsp_count_recv
7528	trnp_count_sum = trnp_count_sum + trnp_count
7529	trnp_count_recv_sum = trnp_count_recv_sum + trnp_count_recv
7530	#endif
7531
7532	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'stop' )
7533
7534	END SUBROUTINE lpm_exchange_horiz
7535
7536	!------------------------------------------------------------------------------!
7537	! Description:
7538	! ------------
7539	!> If a particle moves from one processor to another, this subroutine moves
7540	!> the corresponding elements from the particle arrays of the old grid cells
7541	!> to the particle arrays of the new grid cells.
7542	!------------------------------------------------------------------------------!
7543	SUBROUTINE lpm_add_particles_to_gridcell (particle_array)
7544
7545	IMPLICIT NONE
7546
7547	INTEGER(iwp) :: ip !< grid index (x) of particle
7548	INTEGER(iwp) :: jp !< grid index (x) of particle
7549	INTEGER(iwp) :: kp !< grid index (x) of particle
7550	INTEGER(iwp) :: n !< index variable of particle
7551	INTEGER(iwp) :: pindex !< dummy argument for new number of particles per grid box
7552
7553	LOGICAL :: pack_done !<
7554
7555	TYPE(particle_type), DIMENSION(:), INTENT(IN) :: particle_array !< new particles in a grid box
7556	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: temp_ns !< temporary particle array for reallocation
7557
7558	pack_done = .FALSE.
7559
7560	DO n = 1, SIZE(particle_array)
7561
7562	IF ( .NOT. particle_array(n)%particle_mask ) CYCLE
7563
7564	ip = particle_array(n)%x * ddx
7565	jp = particle_array(n)%y * ddy
7566	!
7567	!-- In case of stretching the actual k index must be found
7568	IF ( dz_stretch_level .NE. -9999999.9_wp .OR. &
7569	dz_stretch_level_start(1) .NE. -9999999.9_wp ) THEN
7570	kp = MINLOC( ABS( particle_array(n)%z - zu ), DIM = 1 ) - 1
7571	ELSE
7572	kp = INT( particle_array(n)%z / dz(1) + 1 + offset_ocean_nzt )
7573	ENDIF
7574
7575	IF ( ip >= nxl .AND. ip <= nxr .AND. jp >= nys .AND. jp <= nyn &
7576	.AND. kp >= nzb+1 .AND. kp <= nzt) THEN ! particle stays on processor
7577	number_of_particles = prt_count(kp,jp,ip)
7578	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7579
7580	pindex = prt_count(kp,jp,ip)+1
7581	IF( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7582	IF ( pack_done ) THEN
7583	CALL realloc_particles_array (ip,jp,kp)
7584	ELSE
7585	CALL lpm_pack
7586	prt_count(kp,jp,ip) = number_of_particles
7587	pindex = prt_count(kp,jp,ip)+1
7588	IF ( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7589	CALL realloc_particles_array (ip,jp,kp)
7590	ENDIF
7591	pack_done = .TRUE.
7592	ENDIF
7593	ENDIF
7594	grid_particles(kp,jp,ip)%particles(pindex) = particle_array(n)
7595	prt_count(kp,jp,ip) = pindex
7596	ELSE
7597	IF ( jp <= nys - 1 ) THEN
7598	nr_move_south = nr_move_south+1
7599	!
7600	!-- Before particle information is swapped to exchange-array, check
7601	!-- if enough memory is allocated. If required, reallocate exchange
7602	!-- array.
7603	IF ( nr_move_south > SIZE(move_also_south) ) THEN
7604	!
7605	!-- At first, allocate further temporary array to swap particle
7606	!-- information.
7607	ALLOCATE( temp_ns(SIZE(move_also_south)+NR_2_direction_move) )
7608	temp_ns(1:nr_move_south-1) = move_also_south(1:nr_move_south-1)
7609	DEALLOCATE( move_also_south )
7610	ALLOCATE( move_also_south(SIZE(temp_ns)) )
7611	move_also_south(1:nr_move_south-1) = temp_ns(1:nr_move_south-1)
7612	DEALLOCATE( temp_ns )
7613
7614	ENDIF
7615
7616	move_also_south(nr_move_south) = particle_array(n)
7617
7618	IF ( jp == -1 ) THEN
7619	!
7620	!-- Apply boundary condition along y
7621	IF ( ibc_par_ns == 0 ) THEN
7622	move_also_south(nr_move_south)%y = &
7623	move_also_south(nr_move_south)%y + ( ny + 1 ) * dy
7624	move_also_south(nr_move_south)%origin_y = &
7625	move_also_south(nr_move_south)%origin_y + ( ny + 1 ) * dy
7626	ELSEIF ( ibc_par_ns == 1 ) THEN
7627	!
7628	!-- Particle absorption
7629	move_also_south(nr_move_south)%particle_mask = .FALSE.
7630	deleted_particles = deleted_particles + 1
7631
7632	ELSEIF ( ibc_par_ns == 2 ) THEN
7633	!
7634	!-- Particle reflection
7635	move_also_south(nr_move_south)%y = &
7636	-move_also_south(nr_move_south)%y
7637	move_also_south(nr_move_south)%speed_y = &
7638	-move_also_south(nr_move_south)%speed_y
7639
7640	ENDIF
7641	ENDIF
7642	ELSEIF ( jp >= nyn+1 ) THEN
7643	nr_move_north = nr_move_north+1
7644	!
7645	!-- Before particle information is swapped to exchange-array, check
7646	!-- if enough memory is allocated. If required, reallocate exchange
7647	!-- array.
7648	IF ( nr_move_north > SIZE(move_also_north) ) THEN
7649	!
7650	!-- At first, allocate further temporary array to swap particle
7651	!-- information.
7652	ALLOCATE( temp_ns(SIZE(move_also_north)+NR_2_direction_move) )
7653	temp_ns(1:nr_move_north-1) = move_also_south(1:nr_move_north-1)
7654	DEALLOCATE( move_also_north )
7655	ALLOCATE( move_also_north(SIZE(temp_ns)) )
7656	move_also_north(1:nr_move_north-1) = temp_ns(1:nr_move_north-1)
7657	DEALLOCATE( temp_ns )
7658
7659	ENDIF
7660
7661	move_also_north(nr_move_north) = particle_array(n)
7662	IF ( jp == ny+1 ) THEN
7663	!
7664	!-- Apply boundary condition along y
7665	IF ( ibc_par_ns == 0 ) THEN
7666
7667	move_also_north(nr_move_north)%y = &
7668	move_also_north(nr_move_north)%y - ( ny + 1 ) * dy
7669	move_also_north(nr_move_north)%origin_y = &
7670	move_also_north(nr_move_north)%origin_y - ( ny + 1 ) * dy
7671	ELSEIF ( ibc_par_ns == 1 ) THEN
7672	!
7673	!-- Particle absorption
7674	move_also_north(nr_move_north)%particle_mask = .FALSE.
7675	deleted_particles = deleted_particles + 1
7676
7677	ELSEIF ( ibc_par_ns == 2 ) THEN
7678	!
7679	!-- Particle reflection
7680	move_also_north(nr_move_north)%y = &
7681	-move_also_north(nr_move_north)%y
7682	move_also_north(nr_move_north)%speed_y = &
7683	-move_also_north(nr_move_north)%speed_y
7684
7685	ENDIF
7686	ENDIF
7687	ELSE
7688	WRITE(0,'(a,8i7)') 'particle out of range ',myid,ip,jp,kp,nxl,nxr,nys,nyn
7689	ENDIF
7690	ENDIF
7691	ENDDO
7692
7693	RETURN
7694
7695	END SUBROUTINE lpm_add_particles_to_gridcell
7696
7697
7698	!------------------------------------------------------------------------------!
7699	! Description:
7700	! ------------
7701	!> If a particle moves from one grid cell to another (on the current
7702	!> processor!), this subroutine moves the corresponding element from the
7703	!> particle array of the old grid cell to the particle array of the new grid
7704	!> cell.
7705	!------------------------------------------------------------------------------!
7706	SUBROUTINE lpm_move_particle
7707
7708	INTEGER(iwp) :: i !< grid index (x) of particle position
7709	INTEGER(iwp) :: ip !< index variable along x
7710	INTEGER(iwp) :: j !< grid index (y) of particle position
7711	INTEGER(iwp) :: jp !< index variable along y
7712	INTEGER(iwp) :: k !< grid index (z) of particle position
7713	INTEGER(iwp) :: kp !< index variable along z
7714	INTEGER(iwp) :: n !< index variable for particle array
7715	INTEGER(iwp) :: np_before_move !< number of particles per grid box before moving
7716	INTEGER(iwp) :: pindex !< dummy argument for number of new particle per grid box
7717
7718	TYPE(particle_type), DIMENSION(:), POINTER :: particles_before_move !< particles before moving
7719
7720	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'start' )
7721	CALL lpm_check_cfl
7722	DO ip = nxl, nxr
7723	DO jp = nys, nyn
7724	DO kp = nzb+1, nzt
7725
7726	np_before_move = prt_count(kp,jp,ip)
7727	IF ( np_before_move <= 0 ) CYCLE
7728	particles_before_move => grid_particles(kp,jp,ip)%particles(1:np_before_move)
7729
7730	DO n = 1, np_before_move
7731	i = particles_before_move(n)%x * ddx
7732	j = particles_before_move(n)%y * ddy
7733	k = kp
7734	!
7735	!-- Find correct vertical particle grid box (necessary in case of grid stretching)
7736	!-- Due to the CFL limitations only the neighbouring grid boxes are considered.
7737	IF( zw(k) < particles_before_move(n)%z ) k = k + 1
7738	IF( zw(k-1) > particles_before_move(n)%z ) k = k - 1
7739
7740	!-- For lpm_exchange_horiz to work properly particles need to be moved to the outermost gridboxes
7741	!-- of the respective processor. If the particle index is inside the processor the following lines
7742	!-- will not change the index
7743	i = MIN ( i , nxr )
7744	i = MAX ( i , nxl )
7745	j = MIN ( j , nyn )
7746	j = MAX ( j , nys )
7747
7748	k = MIN ( k , nzt )
7749	k = MAX ( k , nzb+1 )
7750
7751	!
7752	!-- Check, if particle has moved to another grid cell.
7753	IF ( i /= ip .OR. j /= jp .OR. k /= kp ) THEN
7754	!!
7755	!-- If the particle stays on the same processor, the particle
7756	!-- will be added to the particle array of the new processor.
7757	number_of_particles = prt_count(k,j,i)
7758	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7759
7760	pindex = prt_count(k,j,i)+1
7761	IF ( pindex > SIZE(grid_particles(k,j,i)%particles) ) &
7762	THEN
7763	CALL realloc_particles_array(i,j,k)
7764	ENDIF
7765
7766	grid_particles(k,j,i)%particles(pindex) = particles_before_move(n)
7767	prt_count(k,j,i) = pindex
7768
7769	particles_before_move(n)%particle_mask = .FALSE.
7770	ENDIF
7771	ENDDO
7772
7773	ENDDO
7774	ENDDO
7775	ENDDO
7776
7777	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'stop' )
7778
7779	RETURN
7780
7781	END SUBROUTINE lpm_move_particle
7782
7783
7784	!------------------------------------------------------------------------------!
7785	! Description:
7786	! ------------
7787	!> Check CFL-criterion for each particle. If one particle violated the
7788	!> criterion the particle will be deleted and a warning message is given.
7789	!------------------------------------------------------------------------------!
7790	SUBROUTINE lpm_check_cfl
7791
7792	IMPLICIT NONE
7793
7794	INTEGER(iwp) :: i !< running index, x-direction
7795	INTEGER(iwp) :: j !< running index, y-direction
7796	INTEGER(iwp) :: k !< running index, z-direction
7797	INTEGER(iwp) :: n !< running index, number of particles
7798
7799	DO i = nxl, nxr
7800	DO j = nys, nyn
7801	DO k = nzb+1, nzt
7802	number_of_particles = prt_count(k,j,i)
7803	IF ( number_of_particles <= 0 ) CYCLE
7804	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7805	DO n = 1, number_of_particles
7806	!
7807	!-- Note, check for CFL does not work at first particle timestep
7808	!-- when both, age and age_m are zero.
7809	IF ( particles(n)%age - particles(n)%age_m > 0.0_wp ) THEN
7810	IF(ABS(particles(n)%speed_x) > &
7811	(dx/(particles(n)%age-particles(n)%age_m)) .OR. &
7812	ABS(particles(n)%speed_y) > &
7813	(dy/(particles(n)%age-particles(n)%age_m)) .OR. &
7814	ABS(particles(n)%speed_z) > &
7815	((zw(k)-zw(k-1))/(particles(n)%age-particles(n)%age_m))) &
7816	THEN
7817	WRITE( message_string, * ) &
7818	'Particle violated CFL-criterion: &particle with id ', &
7819	particles(n)%id, ' will be deleted!'
7820	CALL message( 'lpm_check_cfl', 'PA0475', 0, 1, -1, 6, 0 )
7821	particles(n)%particle_mask= .FALSE.
7822	ENDIF
7823	ENDIF
7824	ENDDO
7825	ENDDO
7826	ENDDO
7827	ENDDO
7828
7829	END SUBROUTINE lpm_check_cfl
7830
7831
7832	!------------------------------------------------------------------------------!
7833	! Description:
7834	! ------------
7835	!> If the allocated memory for the particle array do not suffice to add arriving
7836	!> particles from neighbour grid cells, this subrouting reallocates the
7837	!> particle array to assure enough memory is available.
7838	!------------------------------------------------------------------------------!
7839	SUBROUTINE realloc_particles_array ( i, j, k, size_in )
7840
7841	INTEGER(iwp), INTENT(IN) :: i !<
7842	INTEGER(iwp), INTENT(IN) :: j !<
7843	INTEGER(iwp), INTENT(IN) :: k !<
7844	INTEGER(iwp), INTENT(IN), OPTIONAL :: size_in !<
7845
7846	INTEGER(iwp) :: old_size !<
7847	INTEGER(iwp) :: new_size !<
7848	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7849	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7850
7851	old_size = SIZE(grid_particles(k,j,i)%particles)
7852
7853	IF ( PRESENT(size_in) ) THEN
7854	new_size = size_in
7855	ELSE
7856	new_size = old_size * ( 1.0_wp + alloc_factor / 100.0_wp )
7857	ENDIF
7858
7859	new_size = MAX( new_size, 1, old_size + 1 )
7860
7861	IF ( old_size <= 500 ) THEN
7862
7863	tmp_particles_s(1:old_size) = grid_particles(k,j,i)%particles(1:old_size)
7864
7865	DEALLOCATE(grid_particles(k,j,i)%particles)
7866	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7867
7868	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_s(1:old_size)
7869	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7870
7871	ELSE
7872
7873	ALLOCATE(tmp_particles_d(new_size))
7874	tmp_particles_d(1:old_size) = grid_particles(k,j,i)%particles
7875
7876	DEALLOCATE(grid_particles(k,j,i)%particles)
7877	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7878
7879	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_d(1:old_size)
7880	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7881
7882	DEALLOCATE(tmp_particles_d)
7883
7884	ENDIF
7885	particles => grid_particles(k,j,i)%particles(1:new_size)
7886
7887	RETURN
7888
7889	END SUBROUTINE realloc_particles_array
7890
7891
7892	!------------------------------------------------------------------------------!
7893	! Description:
7894	! ------------
7895	!> Not needed but allocated space for particles is dealloced.
7896	!------------------------------------------------------------------------------!
7897	SUBROUTINE dealloc_particles_array
7898
7899
7900	INTEGER(iwp) :: i
7901	INTEGER(iwp) :: j
7902	INTEGER(iwp) :: k
7903	INTEGER(iwp) :: old_size !<
7904	INTEGER(iwp) :: new_size !<
7905
7906	LOGICAL :: dealloc
7907
7908	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7909	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7910
7911	DO i = nxl, nxr
7912	DO j = nys, nyn
7913	DO k = nzb+1, nzt
7914	!
7915	!-- Determine number of active particles
7916	number_of_particles = prt_count(k,j,i)
7917	!
7918	!-- Determine allocated memory size
7919	old_size = SIZE( grid_particles(k,j,i)%particles )
7920	!
7921	!-- Check for large unused memory
7922	dealloc = ( ( number_of_particles < 1 .AND. &
7923	old_size > 1 ) .OR. &
7924	( number_of_particles > 1 .AND. &
7925	old_size - number_of_particles * &
7926	( 1.0_wp + 0.01_wp * alloc_factor ) > 0.0_wp ) )
7927
7928	IF ( dealloc ) THEN
7929	IF ( number_of_particles < 1 ) THEN
7930	new_size = 1
7931	ELSE
7932	new_size = INT( number_of_particles * ( 1.0_wp + 0.01_wp * alloc_factor ) )
7933	ENDIF
7934
7935	IF ( number_of_particles <= 500 ) THEN
7936
7937	tmp_particles_s(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
7938
7939	DEALLOCATE(grid_particles(k,j,i)%particles)
7940	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7941
7942	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_s(1:number_of_particles)
7943	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
7944
7945	ELSE
7946
7947	ALLOCATE(tmp_particles_d(number_of_particles))
7948	tmp_particles_d(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
7949
7950	DEALLOCATE(grid_particles(k,j,i)%particles)
7951	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7952
7953	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_d(1:number_of_particles)
7954	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
7955
7956	DEALLOCATE(tmp_particles_d)
7957
7958	ENDIF
7959
7960	ENDIF
7961	ENDDO
7962	ENDDO
7963	ENDDO
7964
7965	END SUBROUTINE dealloc_particles_array
7966
7967
7968	!------------------------------------------------------------------------------!
7969	! Description:
7970	! -----------
7971	!> Routine for the whole processor
7972	!> Sort all particles into the 8 respective subgrid boxes and free space of
7973	!> particles which has been marked for deletion
7974	!------------------------------------------------------------------------------!
7975	SUBROUTINE lpm_sort_and_delete
7976
7977	INTEGER(iwp) :: i !<
7978	INTEGER(iwp) :: ip !<
7979	INTEGER(iwp) :: is !<
7980	INTEGER(iwp) :: j !<
7981	INTEGER(iwp) :: jp !<
7982	INTEGER(iwp) :: kp !<
7983	INTEGER(iwp) :: m !<
7984	INTEGER(iwp) :: n !<
7985	INTEGER(iwp) :: nn !<
7986	INTEGER(iwp) :: sort_index !<
7987
7988	INTEGER(iwp), DIMENSION(0:7) :: sort_count !<
7989
7990	TYPE(particle_type), DIMENSION(:,:), ALLOCATABLE :: sort_particles !<
7991
7992	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'start' )
7993	IF ( TRIM(particle_interpolation) == 'trilinear' ) THEN
7994	DO ip = nxl, nxr
7995	DO jp = nys, nyn
7996	DO kp = nzb+1, nzt
7997	number_of_particles = prt_count(kp,jp,ip)
7998	IF ( number_of_particles <= 0 ) CYCLE
7999	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8000	nn = 0
8001	sort_count = 0
8002	ALLOCATE( sort_particles(number_of_particles, 0:7) )
8003
8004	DO n = 1, number_of_particles
8005	sort_index = 0
8006
8007	IF ( particles(n)%particle_mask ) THEN
8008	nn = nn + 1
8009	!
8010	!-- Sorting particles with a binary scheme
8011	!-- sort_index=111_2=7_10 -> particle at the left,south,bottom subgridbox
8012	!-- sort_index=000_2=0_10 -> particle at the right,north,top subgridbox
8013	!-- For this the center of the gridbox is calculated
8014	i = (particles(n)%x + 0.5_wp * dx) * ddx
8015	j = (particles(n)%y + 0.5_wp * dy) * ddy
8016
8017	IF ( i == ip ) sort_index = sort_index + 4
8018	IF ( j == jp ) sort_index = sort_index + 2
8019	IF ( zu(kp) > particles(n)%z ) sort_index = sort_index + 1
8020
8021	sort_count(sort_index) = sort_count(sort_index) + 1
8022	m = sort_count(sort_index)
8023	sort_particles(m,sort_index) = particles(n)
8024	sort_particles(m,sort_index)%block_nr = sort_index
8025	ENDIF
8026	ENDDO
8027
8028	nn = 0
8029	DO is = 0,7
8030	grid_particles(kp,jp,ip)%start_index(is) = nn + 1
8031	DO n = 1,sort_count(is)
8032	nn = nn + 1
8033	particles(nn) = sort_particles(n,is)
8034	ENDDO
8035	grid_particles(kp,jp,ip)%end_index(is) = nn
8036	ENDDO
8037
8038	number_of_particles = nn
8039	prt_count(kp,jp,ip) = number_of_particles
8040	DEALLOCATE(sort_particles)
8041	ENDDO
8042	ENDDO
8043	ENDDO
8044
8045	!-- In case of the simple interpolation method the particles must not
8046	!-- be sorted in subboxes but particles marked for deletion must be
8047	!-- deleted and number of particles must be recalculated
8048	ELSE
8049
8050	DO ip = nxl, nxr
8051	DO jp = nys, nyn
8052	DO kp = nzb+1, nzt
8053
8054	number_of_particles = prt_count(kp,jp,ip)
8055	IF ( number_of_particles <= 0 ) CYCLE
8056	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8057	!
8058	!-- repack particles array, i.e. delete particles and recalculate
8059	!-- number of particles
8060	CALL lpm_pack
8061	prt_count(kp,jp,ip) = number_of_particles
8062	ENDDO
8063	ENDDO
8064	ENDDO
8065	ENDIF
8066	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'stop' )
8067
8068	END SUBROUTINE lpm_sort_and_delete
8069
8070
8071	!------------------------------------------------------------------------------!
8072	! Description:
8073	! ------------
8074	!> Move all particles not marked for deletion to lowest indices (packing)
8075	!------------------------------------------------------------------------------!
8076	SUBROUTINE lpm_pack
8077
8078	INTEGER(iwp) :: n !<
8079	INTEGER(iwp) :: nn !<
8080	!
8081	!-- Find out elements marked for deletion and move data from highest index
8082	!-- values to these free indices
8083	nn = number_of_particles
8084
8085	DO WHILE ( .NOT. particles(nn)%particle_mask )
8086	nn = nn-1
8087	IF ( nn == 0 ) EXIT
8088	ENDDO
8089
8090	IF ( nn > 0 ) THEN
8091	DO n = 1, number_of_particles
8092	IF ( .NOT. particles(n)%particle_mask ) THEN
8093	particles(n) = particles(nn)
8094	nn = nn - 1
8095	DO WHILE ( .NOT. particles(nn)%particle_mask )
8096	nn = nn-1
8097	IF ( n == nn ) EXIT
8098	ENDDO
8099	ENDIF
8100	IF ( n == nn ) EXIT
8101	ENDDO
8102	ENDIF
8103
8104	!
8105	!-- The number of deleted particles has been determined in routines
8106	!-- lpm_boundary_conds, lpm_droplet_collision, and lpm_exchange_horiz
8107	number_of_particles = nn
8108
8109	END SUBROUTINE lpm_pack
8110
8111
8112	!------------------------------------------------------------------------------!
8113	! Description:
8114	! ------------
8115	!> Sort particles in each sub-grid box into two groups: particles that already
8116	!> completed the LES timestep, and particles that need further timestepping to
8117	!> complete the LES timestep.
8118	!------------------------------------------------------------------------------!
8119	SUBROUTINE lpm_sort_timeloop_done
8120
8121	INTEGER(iwp) :: end_index !< particle end index for each sub-box
8122	INTEGER(iwp) :: i !< index of particle grid box in x-direction
8123	INTEGER(iwp) :: j !< index of particle grid box in y-direction
8124	INTEGER(iwp) :: k !< index of particle grid box in z-direction
8125	INTEGER(iwp) :: n !< running index for number of particles
8126	INTEGER(iwp) :: nb !< index of subgrid boux
8127	INTEGER(iwp) :: nf !< indices for particles in each sub-box that already finalized their substeps
8128	INTEGER(iwp) :: nnf !< indices for particles in each sub-box that need further treatment
8129	INTEGER(iwp) :: num_finalized !< number of particles in each sub-box that already finalized their substeps
8130	INTEGER(iwp) :: start_index !< particle start index for each sub-box
8131
8132	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: sort_particles !< temporary particle array
8133
8134	DO i = nxl, nxr
8135	DO j = nys, nyn
8136	DO k = nzb+1, nzt
8137
8138	number_of_particles = prt_count(k,j,i)
8139	IF ( number_of_particles <= 0 ) CYCLE
8140	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
8141
8142	DO nb = 0, 7
8143	!
8144	!-- Obtain start and end index for each subgrid box
8145	start_index = grid_particles(k,j,i)%start_index(nb)
8146	end_index = grid_particles(k,j,i)%end_index(nb)
8147	!
8148	!-- Allocate temporary array used for sorting.
8149	ALLOCATE( sort_particles(start_index:end_index) )
8150	!
8151	!-- Determine number of particles already completed the LES
8152	!-- timestep, and write them into a temporary array.
8153	nf = start_index
8154	num_finalized = 0
8155	DO n = start_index, end_index
8156	IF ( dt_3d - particles(n)%dt_sum < 1E-8_wp ) THEN
8157	sort_particles(nf) = particles(n)
8158	nf = nf + 1
8159	num_finalized = num_finalized + 1
8160	ENDIF
8161	ENDDO
8162	!
8163	!-- Determine number of particles that not completed the LES
8164	!-- timestep, and write them into a temporary array.
8165	nnf = nf
8166	DO n = start_index, end_index
8167	IF ( dt_3d - particles(n)%dt_sum > 1E-8_wp ) THEN
8168	sort_particles(nnf) = particles(n)
8169	nnf = nnf + 1
8170	ENDIF
8171	ENDDO
8172	!
8173	!-- Write back sorted particles
8174	particles(start_index:end_index) = &
8175	sort_particles(start_index:end_index)
8176	!
8177	!-- Determine updated start_index, used to masked already
8178	!-- completed particles.
8179	grid_particles(k,j,i)%start_index(nb) = &
8180	grid_particles(k,j,i)%start_index(nb) &
8181	+ num_finalized
8182	!
8183	!-- Deallocate dummy array
8184	DEALLOCATE ( sort_particles )
8185	!
8186	!-- Finally, if number of non-completed particles is non zero
8187	!-- in any of the sub-boxes, set control flag appropriately.
8188	IF ( nnf > nf ) &
8189	grid_particles(k,j,i)%time_loop_done = .FALSE.
8190
8191	ENDDO
8192	ENDDO
8193	ENDDO
8194	ENDDO
8195
8196	END SUBROUTINE lpm_sort_timeloop_done
8197
8198	END MODULE lagrangian_particle_model_mod

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