Home

Context Navigation

source: palm/trunk/SOURCE/lagrangian_particle_model_mod.f90 @ 4143

Last change on this file since 4143 was 4143, checked in by schwenkel, 6 years ago
Rename variable and change select case to if statement
Property svn:keywords set to `Id`
File size: 352.2 KB

Line
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 4143 2019-08-05 15:14:53Z schwenkel $
27	! Rename variable and change select case to if statement
28	!
29	! 4122 2019-07-26 13:11:56Z schwenkel
30	! Implement reset method as bottom boundary condition
31	!
32	! 4121 2019-07-26 10:01:22Z schwenkel
33	! Implementation of an simple method for interpolating the velocities to
34	! particle position
35	!
36	! 4114 2019-07-23 14:09:27Z schwenkel
37	! Bugfix: Added working precision for if statement
38	!
39	! 4054 2019-06-27 07:42:18Z raasch
40	! bugfix for calculating the minimum particle time step
41	!
42	! 4044 2019-06-19 12:28:27Z schwenkel
43	! Bugfix in case of grid strecting: corrected calculation of k-Index
44	!
45	! 4043 2019-06-18 16:59:00Z schwenkel
46	! Remove min_nr_particle, Add lpm_droplet_interactions_ptq into module
47	!
48	! 4028 2019-06-13 12:21:37Z schwenkel
49	! Further modularization of particle code components
50	!
51	! 4020 2019-06-06 14:57:48Z schwenkel
52	! Removing submodules
53	!
54	! 4018 2019-06-06 13:41:50Z eckhard
55	! Bugfix for former revision
56	!
57	! 4017 2019-06-06 12:16:46Z schwenkel
58	! Modularization of all lagrangian particle model code components
59	!
60	! 3655 2019-01-07 16:51:22Z knoop
61	! bugfix to guarantee correct particle releases in case that the release
62	! interval is smaller than the model timestep
63	!
64	! 2801 2018-02-14 16:01:55Z thiele
65	! Changed lpm from subroutine to module.
66	! Introduce particle transfer in nested models.
67	!
68	! 2718 2018-01-02 08:49:38Z maronga
69	! Corrected "Former revisions" section
70	!
71	! 2701 2017-12-15 15:40:50Z suehring
72	! Changes from last commit documented
73	!
74	! 2698 2017-12-14 18:46:24Z suehring
75	! Grid indices passed to lpm_boundary_conds. (responsible Philipp Thiele)
76	!
77	! 2696 2017-12-14 17:12:51Z kanani
78	! Change in file header (GPL part)
79	!
80	! 2606 2017-11-10 10:36:31Z schwenkel
81	! Changed particle box locations: center of particle box now coincides
82	! with scalar grid point of same index.
83	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
84	! lpm_pack_all_arrays -> lpm_sort_and_delete, lpm_pack_arrays -> lpm_pack
85	! lpm_sort -> lpm_sort_timeloop_done
86	!
87	! 2418 2017-09-06 15:24:24Z suehring
88	! Major bugfixes in modeling SGS particle speeds (since revision 1359).
89	! Particle sorting added to distinguish between already completed and
90	! non-completed particles.
91	!
92	! 2263 2017-06-08 14:59:01Z schwenkel
93	! Implemented splitting and merging algorithm
94	!
95	! 2233 2017-05-30 18:08:54Z suehring
96	!
97	! 2232 2017-05-30 17:47:52Z suehring
98	! Adjustments to new topography concept
99	!
100	! 2000 2016-08-20 18:09:15Z knoop
101	! Forced header and separation lines into 80 columns
102	!
103	! 1936 2016-06-13 13:37:44Z suehring
104	! Call routine for deallocation of unused memory.
105	! Formatting adjustments
106	!
107	! 1929 2016-06-09 16:25:25Z suehring
108	! Call wall boundary conditions only if particles are in the vertical range of
109	! topography.
110	!
111	! 1822 2016-04-07 07:49:42Z hoffmann
112	! Tails removed.
113	!
114	! Initialization of sgs model not necessary for the use of cloud_droplets and
115	! use_sgs_for_particles.
116	!
117	! lpm_release_set integrated.
118	!
119	! Unused variabled removed.
120	!
121	! 1682 2015-10-07 23:56:08Z knoop
122	! Code annotations made doxygen readable
123	!
124	! 1416 2014-06-04 16:04:03Z suehring
125	! user_lpm_advec is called for each gridpoint.
126	! Bugfix: in order to prevent an infinite loop, time_loop_done is set .TRUE.
127	! at the head of the do-loop.
128	!
129	! 1359 2014-04-11 17:15:14Z hoffmann
130	! New particle structure integrated.
131	! Kind definition added to all floating point numbers.
132	!
133	! 1320 2014-03-20 08:40:49Z raasch
134	! ONLY-attribute added to USE-statements,
135	! kind-parameters added to all INTEGER and REAL declaration statements,
136	! kinds are defined in new module kinds,
137	! revision history before 2012 removed,
138	! comment fields (!:) to be used for variable explanations added to
139	! all variable declaration statements
140	!
141	! 1318 2014-03-17 13:35:16Z raasch
142	! module interfaces removed
143	!
144	! 1036 2012-10-22 13:43:42Z raasch
145	! code put under GPL (PALM 3.9)
146	!
147	! 851 2012-03-15 14:32:58Z raasch
148	! Bugfix: resetting of particle_mask and tail mask moved from routine
149	! lpm_exchange_horiz to here (end of sub-timestep loop)
150	!
151	! 849 2012-03-15 10:35:09Z raasch
152	! original routine advec_particles split into several subroutines and renamed
153	! lpm
154	!
155	! 831 2012-02-22 00:29:39Z raasch
156	! thermal_conductivity_l and diff_coeff_l now depend on temperature and
157	! pressure
158	!
159	! 828 2012-02-21 12:00:36Z raasch
160	! fast hall/wang kernels with fixed radius/dissipation classes added,
161	! particle feature color renamed class, routine colker renamed
162	! recalculate_kernel,
163	! lower limit for droplet radius changed from 1E-7 to 1E-8
164	!
165	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
166	!
167	! 825 2012-02-19 03:03:44Z raasch
168	! droplet growth by condensation may include curvature and solution effects,
169	! initialisation of temporary particle array for resorting removed,
170	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
171	! module wang_kernel_mod renamed lpm_collision_kernels_mod,
172	! wang_collision_kernel renamed wang_kernel
173	!
174	!
175	! Revision 1.1 1999/11/25 16:16:06 raasch
176	! Initial revision
177	!
178	!
179	! Description:
180	! ------------
181	!> The embedded LPM allows for studying transport and dispersion processes within
182	!> turbulent flows. This model including passive particles that do not show any
183	!> feedback on the turbulent flow. Further also particles with inertia and
184	!> cloud droplets ca be simulated explicitly.
185	!>
186	!> @todo test lcm
187	!> implement simple interpolation method for subgrid scale velocites
188	!> @note <Enter notes on the module>
189	!> @bug <Enter bug on the module>
190	!------------------------------------------------------------------------------!
191	MODULE lagrangian_particle_model_mod
192
193	USE, INTRINSIC :: ISO_C_BINDING
194
195	USE arrays_3d, &
196	ONLY: de_dx, de_dy, de_dz, dzw, zu, zw, ql_c, ql_v, ql_vp, hyp, &
197	pt, q, exner, ql, diss, e, u, v, w, km, ql_1, ql_2, pt_p, q_p, &
198	d_exner, u_p, v_p, w_p
199
200	USE averaging, &
201	ONLY: ql_c_av, pr_av, pc_av, ql_vp_av, ql_v_av
202
203	USE basic_constants_and_equations_mod, &
204	ONLY: molecular_weight_of_solute, molecular_weight_of_water, magnus, &
205	pi, rd_d_rv, rho_l, r_v, rho_s, vanthoff, l_v, kappa, g, lv_d_cp
206
207	USE control_parameters, &
208	ONLY: bc_dirichlet_l, bc_dirichlet_n, bc_dirichlet_r, bc_dirichlet_s, &
209	cloud_droplets, constant_flux_layer, current_timestep_number, &
210	dt_3d, dt_3d_reached, humidity, &
211	dt_3d_reached_l, dt_dopts, dz, initializing_actions, &
212	message_string, molecular_viscosity, ocean_mode, &
213	particle_maximum_age, iran, &
214	simulated_time, topography, dopts_time_count, &
215	time_since_reference_point, rho_surface, u_gtrans, v_gtrans, &
216	dz_stretch_level, dz_stretch_level_start
217
218	USE cpulog, &
219	ONLY: cpu_log, log_point, log_point_s
220
221	USE indices, &
222	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
223	nzb_max, nzt, wall_flags_0,nbgp, ngp_2dh_outer
224
225	USE kinds
226
227	USE pegrid
228
229	USE particle_attributes
230
231	USE pmc_particle_interface, &
232	ONLY: pmcp_c_get_particle_from_parent, pmcp_p_fill_particle_win, &
233	pmcp_c_send_particle_to_parent, pmcp_p_empty_particle_win, &
234	pmcp_p_delete_particles_in_fine_grid_area, pmcp_g_init, &
235	pmcp_g_print_number_of_particles
236
237	USE pmc_interface, &
238	ONLY: nested_run
239
240	USE grid_variables, &
241	ONLY: ddx, dx, ddy, dy
242
243	USE netcdf_interface, &
244	ONLY: netcdf_data_format, netcdf_deflate, dopts_num, id_set_pts, &
245	id_var_dopts, id_var_time_pts, nc_stat, &
246	netcdf_handle_error
247
248	USE random_function_mod, &
249	ONLY: random_function
250
251	USE statistics, &
252	ONLY: hom
253
254	USE surface_mod, &
255	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h,&
256	bc_h
257
258	#if defined( __parallel ) && !defined( __mpifh )
259	USE MPI
260	#endif
261
262	#if defined( __parallel ) && defined( __mpifh )
263	INCLUDE "mpif.h"
264	#endif
265
266	#if defined( __netcdf )
267	USE NETCDF
268	#endif
269
270	IMPLICIT NONE
271
272	CHARACTER(LEN=15) :: aero_species = 'nacl' !< aerosol species
273	CHARACTER(LEN=15) :: aero_type = 'maritime' !< aerosol type
274	CHARACTER(LEN=15) :: bc_par_lr = 'cyclic' !< left/right boundary condition
275	CHARACTER(LEN=15) :: bc_par_ns = 'cyclic' !< north/south boundary condition
276	CHARACTER(LEN=15) :: bc_par_b = 'reflect' !< bottom boundary condition
277	CHARACTER(LEN=15) :: bc_par_t = 'absorb' !< top boundary condition
278	CHARACTER(LEN=15) :: collision_kernel = 'none' !< collision kernel
279
280	CHARACTER(LEN=5) :: splitting_function = 'gamma' !< function for calculation critical weighting factor
281	CHARACTER(LEN=5) :: splitting_mode = 'const' !< splitting mode
282
283	CHARACTER(LEN=25) :: particle_advection_interpolation = 'trilinear' !< interpolation method for calculatin the particle
284
285	INTEGER(iwp) :: deleted_particles = 0 !< number of deleted particles per time step
286	INTEGER(iwp) :: i_splitting_mode !< dummy for splitting mode
287	INTEGER(iwp) :: iran_part = -1234567 !< number for random generator
288	INTEGER(iwp) :: max_number_particles_per_gridbox = 100 !< namelist parameter (see documentation)
289	INTEGER(iwp) :: isf !< dummy for splitting function
290	INTEGER(iwp) :: number_particles_per_gridbox = -1 !< namelist parameter (see documentation)
291	INTEGER(iwp) :: number_of_sublayers = 20 !< number of sublayers for particle velocities betwenn surface and first grid level
292	INTEGER(iwp) :: offset_ocean_nzt = 0 !< in case of oceans runs, the vertical index calculations need an offset
293	INTEGER(iwp) :: offset_ocean_nzt_m1 = 0 !< in case of oceans runs, the vertical index calculations need an offset
294	INTEGER(iwp) :: particles_per_point = 1 !< namelist parameter (see documentation)
295	INTEGER(iwp) :: radius_classes = 20 !< namelist parameter (see documentation)
296	INTEGER(iwp) :: splitting_factor = 2 !< namelist parameter (see documentation)
297	INTEGER(iwp) :: splitting_factor_max = 5 !< namelist parameter (see documentation)
298	INTEGER(iwp) :: step_dealloc = 100 !< namelist parameter (see documentation)
299	INTEGER(iwp) :: total_number_of_particles !< total number of particles in the whole model domain
300	INTEGER(iwp) :: trlp_count_sum !< parameter for particle exchange of PEs
301	INTEGER(iwp) :: trlp_count_recv_sum !< parameter for particle exchange of PEs
302	INTEGER(iwp) :: trrp_count_sum !< parameter for particle exchange of PEs
303	INTEGER(iwp) :: trrp_count_recv_sum !< parameter for particle exchange of PEs
304	INTEGER(iwp) :: trsp_count_sum !< parameter for particle exchange of PEs
305	INTEGER(iwp) :: trsp_count_recv_sum !< parameter for particle exchange of PEs
306	INTEGER(iwp) :: trnp_count_sum !< parameter for particle exchange of PEs
307	INTEGER(iwp) :: trnp_count_recv_sum !< parameter for particle exchange of PEs
308
309	LOGICAL :: lagrangian_particle_model = .FALSE. !< namelist parameter (see documentation)
310	LOGICAL :: curvature_solution_effects = .FALSE. !< namelist parameter (see documentation)
311	LOGICAL :: deallocate_memory = .TRUE. !< namelist parameter (see documentation)
312	LOGICAL :: hall_kernel = .FALSE. !< flag for collision kernel
313	LOGICAL :: merging = .FALSE. !< namelist parameter (see documentation)
314	LOGICAL :: random_start_position = .FALSE. !< namelist parameter (see documentation)
315	LOGICAL :: read_particles_from_restartfile = .TRUE. !< namelist parameter (see documentation)
316	LOGICAL :: seed_follows_topography = .FALSE. !< namelist parameter (see documentation)
317	LOGICAL :: splitting = .FALSE. !< namelist parameter (see documentation)
318	LOGICAL :: use_kernel_tables = .FALSE. !< parameter, which turns on the use of precalculated collision kernels
319	LOGICAL :: write_particle_statistics = .FALSE. !< namelist parameter (see documentation)
320	LOGICAL :: interpolation_simple_predictor = .FALSE. !< flag for simple particle advection interpolation with predictor step
321	LOGICAL :: interpolation_simple_corrector = .FALSE. !< flag for simple particle advection interpolation with corrector step
322	LOGICAL :: interpolation_trilinear = .FALSE. !< flag for trilinear particle advection interpolation
323
324	LOGICAL, DIMENSION(max_number_of_particle_groups) :: vertical_particle_advection = .TRUE. !< Switch for vertical particle transport
325
326	REAL(wp) :: aero_weight = 1.0_wp !< namelist parameter (see documentation)
327	REAL(wp) :: dt_min_part = 0.0002_wp !< minimum particle time step when SGS velocities are used (s)
328	REAL(wp) :: dt_prel = 9999999.9_wp !< namelist parameter (see documentation)
329	REAL(wp) :: dt_write_particle_data = 9999999.9_wp !< namelist parameter (see documentation)
330	REAL(wp) :: end_time_prel = 9999999.9_wp !< namelist parameter (see documentation)
331	REAL(wp) :: initial_weighting_factor = 1.0_wp !< namelist parameter (see documentation)
332	REAL(wp) :: last_particle_release_time = 0.0_wp !< last time of particle release
333	REAL(wp) :: log_sigma(3) = 1.0_wp !< namelist parameter (see documentation)
334	REAL(wp) :: na(3) = 0.0_wp !< namelist parameter (see documentation)
335	REAL(wp) :: number_concentration = -1.0_wp !< namelist parameter (see documentation)
336	REAL(wp) :: radius_merge = 1.0E-7_wp !< namelist parameter (see documentation)
337	REAL(wp) :: radius_split = 40.0E-6_wp !< namelist parameter (see documentation)
338	REAL(wp) :: rm(3) = 1.0E-6_wp !< namelist parameter (see documentation)
339	REAL(wp) :: sgs_wf_part !< parameter for sgs
340	REAL(wp) :: time_write_particle_data = 0.0_wp !< write particle data at current time on file
341	REAL(wp) :: weight_factor_merge = -1.0_wp !< namelist parameter (see documentation)
342	REAL(wp) :: weight_factor_split = -1.0_wp !< namelist parameter (see documentation)
343	REAL(wp) :: z0_av_global !< horizontal mean value of z0
344
345	REAL(wp) :: rclass_lbound !<
346	REAL(wp) :: rclass_ubound !<
347
348	REAL(wp), PARAMETER :: c_0 = 3.0_wp !< parameter for lagrangian timescale
349
350	REAL(wp), DIMENSION(max_number_of_particle_groups) :: density_ratio = 9999999.9_wp !< namelist parameter (see documentation)
351	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdx = 9999999.9_wp !< namelist parameter (see documentation)
352	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdy = 9999999.9_wp !< namelist parameter (see documentation)
353	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pdz = 9999999.9_wp !< namelist parameter (see documentation)
354	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psb = 9999999.9_wp !< namelist parameter (see documentation)
355	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psl = 9999999.9_wp !< namelist parameter (see documentation)
356	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psn = 9999999.9_wp !< namelist parameter (see documentation)
357	REAL(wp), DIMENSION(max_number_of_particle_groups) :: psr = 9999999.9_wp !< namelist parameter (see documentation)
358	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pss = 9999999.9_wp !< namelist parameter (see documentation)
359	REAL(wp), DIMENSION(max_number_of_particle_groups) :: pst = 9999999.9_wp !< namelist parameter (see documentation).
360	REAL(wp), DIMENSION(max_number_of_particle_groups) :: radius = 9999999.9_wp !< namelist parameter (see documentation)
361
362	REAL(wp), DIMENSION(:), ALLOCATABLE :: log_z_z0 !< Precalculate LOG(z/z0)
363
364	INTEGER(iwp), PARAMETER :: NR_2_direction_move = 10000 !<
365	INTEGER(iwp) :: nr_move_north !<
366	INTEGER(iwp) :: nr_move_south !<
367
368	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_north
369	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: move_also_south
370
371	REAL(wp) :: epsilon_collision !<
372	REAL(wp) :: urms !<
373
374	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
375	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
376	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
377
378	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
379	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
380	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
381	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
382	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
383
384	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
385
386	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
387	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
388
389	SAVE
390
391	PRIVATE
392
393	PUBLIC lpm_parin, &
394	lpm_header, &
395	lpm_init_arrays,&
396	lpm_init, &
397	lpm_actions, &
398	lpm_data_output_ptseries, &
399	lpm_interaction_droplets_ptq, &
400	lpm_rrd_local_particles, &
401	lpm_wrd_local, &
402	lpm_rrd_global, &
403	lpm_wrd_global, &
404	lpm_rrd_local, &
405	lpm_check_parameters
406
407	PUBLIC lagrangian_particle_model
408
409	INTERFACE lpm_check_parameters
410	MODULE PROCEDURE lpm_check_parameters
411	END INTERFACE lpm_check_parameters
412
413	INTERFACE lpm_parin
414	MODULE PROCEDURE lpm_parin
415	END INTERFACE lpm_parin
416
417	INTERFACE lpm_header
418	MODULE PROCEDURE lpm_header
419	END INTERFACE lpm_header
420
421	INTERFACE lpm_init_arrays
422	MODULE PROCEDURE lpm_init_arrays
423	END INTERFACE lpm_init_arrays
424
425	INTERFACE lpm_init
426	MODULE PROCEDURE lpm_init
427	END INTERFACE lpm_init
428
429	INTERFACE lpm_actions
430	MODULE PROCEDURE lpm_actions
431	END INTERFACE lpm_actions
432
433	INTERFACE lpm_data_output_ptseries
434	MODULE PROCEDURE lpm_data_output_ptseries
435	END INTERFACE
436
437	INTERFACE lpm_rrd_local_particles
438	MODULE PROCEDURE lpm_rrd_local_particles
439	END INTERFACE lpm_rrd_local_particles
440
441	INTERFACE lpm_rrd_global
442	MODULE PROCEDURE lpm_rrd_global
443	END INTERFACE lpm_rrd_global
444
445	INTERFACE lpm_rrd_local
446	MODULE PROCEDURE lpm_rrd_local
447	END INTERFACE lpm_rrd_local
448
449	INTERFACE lpm_wrd_local
450	MODULE PROCEDURE lpm_wrd_local
451	END INTERFACE lpm_wrd_local
452
453	INTERFACE lpm_wrd_global
454	MODULE PROCEDURE lpm_wrd_global
455	END INTERFACE lpm_wrd_global
456
457	INTERFACE lpm_advec
458	MODULE PROCEDURE lpm_advec
459	END INTERFACE lpm_advec
460
461	INTERFACE lpm_calc_liquid_water_content
462	MODULE PROCEDURE lpm_calc_liquid_water_content
463	END INTERFACE
464
465	INTERFACE lpm_interaction_droplets_ptq
466	MODULE PROCEDURE lpm_interaction_droplets_ptq
467	MODULE PROCEDURE lpm_interaction_droplets_ptq_ij
468	END INTERFACE lpm_interaction_droplets_ptq
469
470	INTERFACE lpm_boundary_conds
471	MODULE PROCEDURE lpm_boundary_conds
472	END INTERFACE lpm_boundary_conds
473
474	INTERFACE lpm_droplet_condensation
475	MODULE PROCEDURE lpm_droplet_condensation
476	END INTERFACE
477
478	INTERFACE lpm_droplet_collision
479	MODULE PROCEDURE lpm_droplet_collision
480	END INTERFACE lpm_droplet_collision
481
482	INTERFACE lpm_init_kernels
483	MODULE PROCEDURE lpm_init_kernels
484	END INTERFACE lpm_init_kernels
485
486	INTERFACE lpm_splitting
487	MODULE PROCEDURE lpm_splitting
488	END INTERFACE lpm_splitting
489
490	INTERFACE lpm_merging
491	MODULE PROCEDURE lpm_merging
492	END INTERFACE lpm_merging
493
494	INTERFACE lpm_exchange_horiz
495	MODULE PROCEDURE lpm_exchange_horiz
496	END INTERFACE lpm_exchange_horiz
497
498	INTERFACE lpm_move_particle
499	MODULE PROCEDURE lpm_move_particle
500	END INTERFACE lpm_move_particle
501
502	INTERFACE realloc_particles_array
503	MODULE PROCEDURE realloc_particles_array
504	END INTERFACE realloc_particles_array
505
506	INTERFACE dealloc_particles_array
507	MODULE PROCEDURE dealloc_particles_array
508	END INTERFACE dealloc_particles_array
509
510	INTERFACE lpm_sort_and_delete
511	MODULE PROCEDURE lpm_sort_and_delete
512	END INTERFACE lpm_sort_and_delete
513
514	INTERFACE lpm_sort_timeloop_done
515	MODULE PROCEDURE lpm_sort_timeloop_done
516	END INTERFACE lpm_sort_timeloop_done
517
518	INTERFACE lpm_pack
519	MODULE PROCEDURE lpm_pack
520	END INTERFACE lpm_pack
521
522	CONTAINS
523
524
525	!------------------------------------------------------------------------------!
526	! Description:
527	! ------------
528	!> Parin for &particle_parameters for the Lagrangian particle model
529	!------------------------------------------------------------------------------!
530	SUBROUTINE lpm_parin
531
532	CHARACTER (LEN=80) :: line !<
533
534	NAMELIST /particles_par/ &
535	aero_species, &
536	aero_type, &
537	aero_weight, &
538	alloc_factor, &
539	bc_par_b, &
540	bc_par_lr, &
541	bc_par_ns, &
542	bc_par_t, &
543	collision_kernel, &
544	curvature_solution_effects, &
545	deallocate_memory, &
546	density_ratio, &
547	dissipation_classes, &
548	dt_dopts, &
549	dt_min_part, &
550	dt_prel, &
551	dt_write_particle_data, &
552	end_time_prel, &
553	initial_weighting_factor, &
554	log_sigma, &
555	max_number_particles_per_gridbox, &
556	merging, &
557	na, &
558	number_concentration, &
559	number_of_particle_groups, &
560	number_particles_per_gridbox, &
561	particles_per_point, &
562	particle_advection_start, &
563	particle_advection_interpolation, &
564	particle_maximum_age, &
565	pdx, &
566	pdy, &
567	pdz, &
568	psb, &
569	psl, &
570	psn, &
571	psr, &
572	pss, &
573	pst, &
574	radius, &
575	radius_classes, &
576	radius_merge, &
577	radius_split, &
578	random_start_position, &
579	read_particles_from_restartfile, &
580	rm, &
581	seed_follows_topography, &
582	splitting, &
583	splitting_factor, &
584	splitting_factor_max, &
585	splitting_function, &
586	splitting_mode, &
587	step_dealloc, &
588	use_sgs_for_particles, &
589	vertical_particle_advection, &
590	weight_factor_merge, &
591	weight_factor_split, &
592	write_particle_statistics
593
594	NAMELIST /particle_parameters/ &
595	aero_species, &
596	aero_type, &
597	aero_weight, &
598	alloc_factor, &
599	bc_par_b, &
600	bc_par_lr, &
601	bc_par_ns, &
602	bc_par_t, &
603	collision_kernel, &
604	curvature_solution_effects, &
605	deallocate_memory, &
606	density_ratio, &
607	dissipation_classes, &
608	dt_dopts, &
609	dt_min_part, &
610	dt_prel, &
611	dt_write_particle_data, &
612	end_time_prel, &
613	initial_weighting_factor, &
614	log_sigma, &
615	max_number_particles_per_gridbox, &
616	merging, &
617	na, &
618	number_concentration, &
619	number_of_particle_groups, &
620	number_particles_per_gridbox, &
621	particles_per_point, &
622	particle_advection_start, &
623	particle_advection_interpolation, &
624	particle_maximum_age, &
625	pdx, &
626	pdy, &
627	pdz, &
628	psb, &
629	psl, &
630	psn, &
631	psr, &
632	pss, &
633	pst, &
634	radius, &
635	radius_classes, &
636	radius_merge, &
637	radius_split, &
638	random_start_position, &
639	read_particles_from_restartfile, &
640	rm, &
641	seed_follows_topography, &
642	splitting, &
643	splitting_factor, &
644	splitting_factor_max, &
645	splitting_function, &
646	splitting_mode, &
647	step_dealloc, &
648	use_sgs_for_particles, &
649	vertical_particle_advection, &
650	weight_factor_merge, &
651	weight_factor_split, &
652	write_particle_statistics
653
654	!
655	!-- Position the namelist-file at the beginning (it was already opened in
656	!-- parin), search for the namelist-group of the package and position the
657	!-- file at this line. Do the same for each optionally used package.
658	line = ' '
659
660	!
661	!-- Try to find particles package
662	REWIND ( 11 )
663	line = ' '
664	DO WHILE ( INDEX( line, '&particle_parameters' ) == 0 )
665	READ ( 11, '(A)', END=12 ) line
666	ENDDO
667	BACKSPACE ( 11 )
668	!
669	!-- Read user-defined namelist
670	READ ( 11, particle_parameters, ERR = 10 )
671	!
672	!-- Set flag that indicates that particles are switched on
673	particle_advection = .TRUE.
674
675	GOTO 14
676
677	10 BACKSPACE( 11 )
678	READ( 11 , '(A)') line
679	CALL parin_fail_message( 'particle_parameters', line )
680	!
681	!-- Try to find particles package (old namelist)
682	12 REWIND ( 11 )
683	line = ' '
684	DO WHILE ( INDEX( line, '&particles_par' ) == 0 )
685	READ ( 11, '(A)', END=14 ) line
686	ENDDO
687	BACKSPACE ( 11 )
688	!
689	!-- Read user-defined namelist
690	READ ( 11, particles_par, ERR = 13, END = 14 )
691
692	message_string = 'namelist particles_par is deprecated and will be ' // &
693	'removed in near future. Please use namelist ' // &
694	'particle_parameters instead'
695	CALL message( 'package_parin', 'PA0487', 0, 1, 0, 6, 0 )
696
697	!
698	!-- Set flag that indicates that particles are switched on
699	particle_advection = .TRUE.
700
701	GOTO 14
702
703	13 BACKSPACE( 11 )
704	READ( 11 , '(A)') line
705	CALL parin_fail_message( 'particles_par', line )
706
707	14 CONTINUE
708
709	END SUBROUTINE lpm_parin
710
711	!------------------------------------------------------------------------------!
712	! Description:
713	! ------------
714	!> Writes used particle attributes in header file.
715	!------------------------------------------------------------------------------!
716	SUBROUTINE lpm_header ( io )
717
718	CHARACTER (LEN=40) :: output_format !< netcdf format
719
720	INTEGER(iwp) :: i !<
721	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
722
723
724	IF ( humidity .AND. cloud_droplets ) THEN
725	WRITE ( io, 433 )
726	IF ( curvature_solution_effects ) WRITE ( io, 434 )
727	IF ( collision_kernel /= 'none' ) THEN
728	WRITE ( io, 435 ) TRIM( collision_kernel )
729	IF ( collision_kernel(6:9) == 'fast' ) THEN
730	WRITE ( io, 436 ) radius_classes, dissipation_classes
731	ENDIF
732	ELSE
733	WRITE ( io, 437 )
734	ENDIF
735	ENDIF
736
737	IF ( particle_advection ) THEN
738	!
739	!-- Particle attributes
740	WRITE ( io, 480 ) particle_advection_start, dt_prel, bc_par_lr, &
741	bc_par_ns, bc_par_b, bc_par_t, particle_maximum_age, &
742	end_time_prel
743	IF ( use_sgs_for_particles ) WRITE ( io, 488 ) dt_min_part
744	IF ( random_start_position ) WRITE ( io, 481 )
745	IF ( seed_follows_topography ) WRITE ( io, 496 )
746	IF ( particles_per_point > 1 ) WRITE ( io, 489 ) particles_per_point
747	WRITE ( io, 495 ) total_number_of_particles
748	IF ( dt_write_particle_data /= 9999999.9_wp ) THEN
749	WRITE ( io, 485 ) dt_write_particle_data
750	IF ( netcdf_data_format > 1 ) THEN
751	output_format = 'netcdf (64 bit offset) and binary'
752	ELSE
753	output_format = 'netcdf and binary'
754	ENDIF
755	IF ( netcdf_deflate == 0 ) THEN
756	WRITE ( io, 344 ) output_format
757	ELSE
758	WRITE ( io, 354 ) TRIM( output_format ), netcdf_deflate
759	ENDIF
760	ENDIF
761	IF ( dt_dopts /= 9999999.9_wp ) WRITE ( io, 494 ) dt_dopts
762	IF ( write_particle_statistics ) WRITE ( io, 486 )
763
764	WRITE ( io, 487 ) number_of_particle_groups
765
766	DO i = 1, number_of_particle_groups
767	IF ( i == 1 .AND. density_ratio(i) == 9999999.9_wp ) THEN
768	WRITE ( io, 490 ) i, 0.0_wp
769	WRITE ( io, 492 )
770	ELSE
771	WRITE ( io, 490 ) i, radius(i)
772	IF ( density_ratio(i) /= 0.0_wp ) THEN
773	WRITE ( io, 491 ) density_ratio(i)
774	ELSE
775	WRITE ( io, 492 )
776	ENDIF
777	ENDIF
778	WRITE ( io, 493 ) psl(i), psr(i), pss(i), psn(i), psb(i), pst(i), &
779	pdx(i), pdy(i), pdz(i)
780	IF ( .NOT. vertical_particle_advection(i) ) WRITE ( io, 482 )
781	ENDDO
782
783	ENDIF
784
785	344 FORMAT (' Output format: ',A/)
786	354 FORMAT (' Output format: ',A, ' compressed with level: ',I1/)
787
788	433 FORMAT (' Cloud droplets treated explicitly using the Lagrangian part', &
789	'icle model')
790	434 FORMAT (' Curvature and solution effecs are considered for growth of', &
791	' droplets < 1.0E-6 m')
792	435 FORMAT (' Droplet collision is handled by ',A,'-kernel')
793	436 FORMAT (' Fast kernel with fixed radius- and dissipation classes ', &
794	'are used'/ &
795	' number of radius classes: ',I3,' interval ', &
796	'[1.0E-6,2.0E-4] m'/ &
797	' number of dissipation classes: ',I2,' interval ', &
798	'[0,1000] cm2/s3')
799	437 FORMAT (' Droplet collision is switched off')
800
801	480 FORMAT (' Particles:'/ &
802	' ---------'// &
803	' Particle advection is active (switched on at t = ', F7.1, &
804	' s)'/ &
805	' Start of new particle generations every ',F6.1,' s'/ &
806	' Boundary conditions: left/right: ', A, ' north/south: ', A/&
807	' bottom: ', A, ' top: ', A/&
808	' Maximum particle age: ',F9.1,' s'/ &
809	' Advection stopped at t = ',F9.1,' s'/)
810	481 FORMAT (' Particles have random start positions'/)
811	482 FORMAT (' Particles are advected only horizontally'/)
812	485 FORMAT (' Particle data are written on file every ', F9.1, ' s')
813	486 FORMAT (' Particle statistics are written on file'/)
814	487 FORMAT (' Number of particle groups: ',I2/)
815	488 FORMAT (' SGS velocity components are used for particle advection'/ &
816	' minimum timestep for advection:', F8.5/)
817	489 FORMAT (' Number of particles simultaneously released at each ', &
818	'point: ', I5/)
819	490 FORMAT (' Particle group ',I2,':'/ &
820	' Particle radius: ',E10.3, 'm')
821	491 FORMAT (' Particle inertia is activated'/ &
822	' density_ratio (rho_fluid/rho_particle) =',F6.3/)
823	492 FORMAT (' Particles are advected only passively (no inertia)'/)
824	493 FORMAT (' Boundaries of particle source: x:',F8.1,' - ',F8.1,' m'/&
825	' y:',F8.1,' - ',F8.1,' m'/&
826	' z:',F8.1,' - ',F8.1,' m'/&
827	' Particle distances: dx = ',F8.1,' m dy = ',F8.1, &
828	' m dz = ',F8.1,' m'/)
829	494 FORMAT (' Output of particle time series in NetCDF format every ', &
830	F8.2,' s'/)
831	495 FORMAT (' Number of particles in total domain: ',I10/)
832	496 FORMAT (' Initial vertical particle positions are interpreted ', &
833	'as relative to the given topography')
834
835	END SUBROUTINE lpm_header
836
837	!------------------------------------------------------------------------------!
838	! Description:
839	! ------------
840	!> Writes used particle attributes in header file.
841	!------------------------------------------------------------------------------!
842	SUBROUTINE lpm_check_parameters
843
844	!
845	!-- Collision kernels:
846	SELECT CASE ( TRIM( collision_kernel ) )
847
848	CASE ( 'hall', 'hall_fast' )
849	hall_kernel = .TRUE.
850
851	CASE ( 'wang', 'wang_fast' )
852	wang_kernel = .TRUE.
853
854	CASE ( 'none' )
855
856
857	CASE DEFAULT
858	message_string = 'unknown collision kernel: collision_kernel = "' // &
859	TRIM( collision_kernel ) // '"'
860	CALL message( 'check_parameters', 'PA0350', 1, 2, 0, 6, 0 )
861
862	END SELECT
863	IF ( collision_kernel(6:9) == 'fast' ) use_kernel_tables = .TRUE.
864
865	!
866	!-- Subgrid scale velocites with the simple interpolation method for resolved
867	!-- velocites is not implemented for passive particles. However, for cloud
868	!-- it can be combined as the sgs-velocites for active particles are
869	!-- calculated differently, i.e. no subboxes are needed.
870	IF ( .NOT. TRIM(particle_advection_interpolation) == 'trilinear' .AND. &
871	use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
872	message_string = 'subrgrid scale velocities in combination with ' // &
873	'simple interpolation method is not ' // &
874	'implemented'
875	CALL message( 'check_parameters', 'PA0659', 1, 2, 0, 6, 0 )
876	ENDIF
877
878	END SUBROUTINE
879
880	!------------------------------------------------------------------------------!
881	! Description:
882	! ------------
883	!> Initialize arrays for lpm
884	!------------------------------------------------------------------------------!
885	SUBROUTINE lpm_init_arrays
886
887	IF ( cloud_droplets ) THEN
888	!
889	!-- Liquid water content, change in liquid water content
890	ALLOCATE ( ql_1(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
891	ql_2(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
892	!
893	!-- Real volume of particles (with weighting), volume of particles
894	ALLOCATE ( ql_v(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
895	ql_vp(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
896	ENDIF
897
898	!
899	!-- Initial assignment of the pointers
900	IF ( cloud_droplets ) THEN
901	ql => ql_1
902	ql_c => ql_2
903	ENDIF
904
905	END SUBROUTINE lpm_init_arrays
906
907	!------------------------------------------------------------------------------!
908	! Description:
909	! ------------
910	!> Initialize Lagrangian particle model
911	!------------------------------------------------------------------------------!
912	SUBROUTINE lpm_init
913
914	INTEGER(iwp) :: i !<
915	INTEGER(iwp) :: j !<
916	INTEGER(iwp) :: k !<
917
918	REAL(wp) :: div !<
919	REAL(wp) :: height_int !<
920	REAL(wp) :: height_p !<
921	REAL(wp) :: z_p !<
922	REAL(wp) :: z0_av_local !<
923
924	!
925	!-- In case of oceans runs, the vertical index calculations need an offset,
926	!-- because otherwise the k indices will become negative
927	IF ( ocean_mode ) THEN
928	offset_ocean_nzt = nzt
929	offset_ocean_nzt_m1 = nzt - 1
930	ENDIF
931
932	!
933	!-- Define block offsets for dividing a gridcell in 8 sub cells
934	!-- See documentation for List of subgrid boxes
935	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
936	block_offset(0) = block_offset_def ( 0, 0, 0)
937	block_offset(1) = block_offset_def ( 0, 0,-1)
938	block_offset(2) = block_offset_def ( 0,-1, 0)
939	block_offset(3) = block_offset_def ( 0,-1,-1)
940	block_offset(4) = block_offset_def (-1, 0, 0)
941	block_offset(5) = block_offset_def (-1, 0,-1)
942	block_offset(6) = block_offset_def (-1,-1, 0)
943	block_offset(7) = block_offset_def (-1,-1,-1)
944	!
945	!-- Check the number of particle groups.
946	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
947	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
948	max_number_of_particle_groups , &
949	'&number_of_particle_groups reset to ', &
950	max_number_of_particle_groups
951	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
952	number_of_particle_groups = max_number_of_particle_groups
953	ENDIF
954	!
955	!-- Check if downward-facing walls exist. This case, reflection boundary
956	!-- conditions (as well as subgrid-scale velocities) may do not work
957	!-- propably (not realized so far).
958	IF ( surf_def_h(1)%ns >= 1 ) THEN
959	WRITE( message_string, * ) 'Overhanging topography do not work '// &
960	'with particles'
961	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
962
963	ENDIF
964
965	!
966	!-- Set default start positions, if necessary
967	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
968	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
969	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
970	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
971	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
972	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
973
974	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
975	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
976	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
977
978	!
979	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
980	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
981	IF ( number_particles_per_gridbox /= -1 .AND. &
982	number_particles_per_gridbox >= 1 ) THEN
983	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
984	REAL(number_particles_per_gridbox))**0.3333333_wp
985	!
986	!-- Ensure a smooth value (two significant digits) of distance between
987	!-- particles (pdx, pdy, pdz).
988	div = 1000.0_wp
989	DO WHILE ( pdx(1) < div )
990	div = div / 10.0_wp
991	ENDDO
992	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
993	pdy(1) = pdx(1)
994	pdz(1) = pdx(1)
995
996	ENDIF
997
998	DO j = 2, number_of_particle_groups
999	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
1000	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
1001	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
1002	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
1003	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
1004	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
1005	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
1006	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
1007	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
1008	ENDDO
1009
1010	!
1011	!-- Allocate arrays required for calculating particle SGS velocities.
1012	!-- Initialize prefactor required for stoachastic Weil equation.
1013	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
1014	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1015	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1016	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
1017
1018	de_dx = 0.0_wp
1019	de_dy = 0.0_wp
1020	de_dz = 0.0_wp
1021
1022	sgs_wf_part = 1.0_wp / 3.0_wp
1023	ENDIF
1024
1025	!
1026	!-- Allocate array required for logarithmic vertical interpolation of
1027	!-- horizontal particle velocities between the surface and the first vertical
1028	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
1029	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
1030	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
1031	!-- To obtain exact height levels of particles, linear interpolation is applied
1032	!-- (see lpm_advec.f90).
1033	IF ( constant_flux_layer ) THEN
1034
1035	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
1036	z_p = zu(nzb+1) - zw(nzb)
1037
1038	!
1039	!-- Calculate horizontal mean value of z0 used for logartihmic
1040	!-- interpolation. Note: this is not exact for heterogeneous z0.
1041	!-- However, sensitivity studies showed that the effect is
1042	!-- negligible.
1043	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
1044	SUM( surf_usm_h%z0 )
1045	z0_av_global = 0.0_wp
1046
1047	#if defined( __parallel )
1048	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
1049	comm2d, ierr )
1050	#else
1051	z0_av_global = z0_av_local
1052	#endif
1053
1054	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
1055	!
1056	!-- Horizontal wind speed is zero below and at z0
1057	log_z_z0(0) = 0.0_wp
1058	!
1059	!-- Calculate vertical depth of the sublayers
1060	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
1061	!
1062	!-- Precalculate LOG(z/z0)
1063	height_p = z0_av_global
1064	DO k = 1, number_of_sublayers
1065
1066	height_p = height_p + height_int
1067	log_z_z0(k) = LOG( height_p / z0_av_global )
1068
1069	ENDDO
1070
1071	ENDIF
1072
1073	!
1074	!-- Check which particle interpolation method should be used
1075	IF ( TRIM(particle_advection_interpolation) == 'trilinear' ) THEN
1076	interpolation_simple_corrector = .FALSE.
1077	interpolation_simple_predictor = .FALSE.
1078	interpolation_trilinear = .TRUE.
1079	ELSEIF ( TRIM(particle_advection_interpolation) == 'simple_corrector' ) THEN
1080	interpolation_simple_corrector = .TRUE.
1081	interpolation_simple_predictor = .FALSE.
1082	interpolation_trilinear = .FALSE.
1083	ELSEIF ( TRIM(particle_advection_interpolation) == 'simple_predictor' ) THEN
1084	interpolation_simple_corrector = .FALSE.
1085	interpolation_simple_predictor = .TRUE.
1086	interpolation_trilinear = .FALSE.
1087	ENDIF
1088
1089	!
1090	!-- Check boundary condition and set internal variables
1091	SELECT CASE ( bc_par_b )
1092
1093	CASE ( 'absorb' )
1094	ibc_par_b = 1
1095
1096	CASE ( 'reflect' )
1097	ibc_par_b = 2
1098
1099	CASE ( 'reset' )
1100	ibc_par_b = 3
1101
1102	CASE DEFAULT
1103	WRITE( message_string, * ) 'unknown boundary condition ', &
1104	'bc_par_b = "', TRIM( bc_par_b ), '"'
1105	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
1106
1107	END SELECT
1108	SELECT CASE ( bc_par_t )
1109
1110	CASE ( 'absorb' )
1111	ibc_par_t = 1
1112
1113	CASE ( 'reflect' )
1114	ibc_par_t = 2
1115
1116	CASE ( 'nested' )
1117	ibc_par_t = 3
1118
1119	CASE DEFAULT
1120	WRITE( message_string, * ) 'unknown boundary condition ', &
1121	'bc_par_t = "', TRIM( bc_par_t ), '"'
1122	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
1123
1124	END SELECT
1125	SELECT CASE ( bc_par_lr )
1126
1127	CASE ( 'cyclic' )
1128	ibc_par_lr = 0
1129
1130	CASE ( 'absorb' )
1131	ibc_par_lr = 1
1132
1133	CASE ( 'reflect' )
1134	ibc_par_lr = 2
1135
1136	CASE ( 'nested' )
1137	ibc_par_lr = 3
1138
1139	CASE DEFAULT
1140	WRITE( message_string, * ) 'unknown boundary condition ', &
1141	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
1142	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
1143
1144	END SELECT
1145	SELECT CASE ( bc_par_ns )
1146
1147	CASE ( 'cyclic' )
1148	ibc_par_ns = 0
1149
1150	CASE ( 'absorb' )
1151	ibc_par_ns = 1
1152
1153	CASE ( 'reflect' )
1154	ibc_par_ns = 2
1155
1156	CASE ( 'nested' )
1157	ibc_par_ns = 3
1158
1159	CASE DEFAULT
1160	WRITE( message_string, * ) 'unknown boundary condition ', &
1161	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
1162	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
1163
1164	END SELECT
1165	SELECT CASE ( splitting_mode )
1166
1167	CASE ( 'const' )
1168	i_splitting_mode = 1
1169
1170	CASE ( 'cl_av' )
1171	i_splitting_mode = 2
1172
1173	CASE ( 'gb_av' )
1174	i_splitting_mode = 3
1175
1176	CASE DEFAULT
1177	WRITE( message_string, * ) 'unknown splitting_mode = "', &
1178	TRIM( splitting_mode ), '"'
1179	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
1180
1181	END SELECT
1182	SELECT CASE ( splitting_function )
1183
1184	CASE ( 'gamma' )
1185	isf = 1
1186
1187	CASE ( 'log' )
1188	isf = 2
1189
1190	CASE ( 'exp' )
1191	isf = 3
1192
1193	CASE DEFAULT
1194	WRITE( message_string, * ) 'unknown splitting function = "', &
1195	TRIM( splitting_function ), '"'
1196	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
1197
1198	END SELECT
1199	!
1200	!-- Initialize collision kernels
1201	IF ( collision_kernel /= 'none' ) CALL lpm_init_kernels
1202	!
1203	!-- For the first model run of a possible job chain initialize the
1204	!-- particles, otherwise read the particle data from restart file.
1205	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
1206	.AND. read_particles_from_restartfile ) THEN
1207	CALL lpm_rrd_local_particles
1208	ELSE
1209	!
1210	!-- Allocate particle arrays and set attributes of the initial set of
1211	!-- particles, which can be also periodically released at later times.
1212	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
1213	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
1214
1215	number_of_particles = 0
1216	prt_count = 0
1217	!
1218	!-- initialize counter for particle IDs
1219	grid_particles%id_counter = 1
1220	!
1221	!-- Initialize all particles with dummy values (otherwise errors may
1222	!-- occur within restart runs). The reason for this is still not clear
1223	!-- and may be presumably caused by errors in the respective user-interface.
1224	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1225	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1226	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1227	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
1228	0, 0, 0_idp, .FALSE., -1 )
1229
1230	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
1231	!
1232	!-- Set values for the density ratio and radius for all particle
1233	!-- groups, if necessary
1234	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
1235	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
1236	DO i = 2, number_of_particle_groups
1237	IF ( density_ratio(i) == 9999999.9_wp ) THEN
1238	density_ratio(i) = density_ratio(i-1)
1239	ENDIF
1240	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
1241	ENDDO
1242
1243	DO i = 1, number_of_particle_groups
1244	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
1245	WRITE( message_string, * ) 'particle group #', i, ' has a', &
1246	'density ratio /= 0 but radius = 0'
1247	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
1248	ENDIF
1249	particle_groups(i)%density_ratio = density_ratio(i)
1250	particle_groups(i)%radius = radius(i)
1251	ENDDO
1252	!
1253	!-- Set a seed value for the random number generator to be exclusively
1254	!-- used for the particle code. The generated random numbers should be
1255	!-- different on the different PEs.
1256	iran_part = iran_part + myid
1257	!
1258	!-- Create the particle set, and set the initial particles
1259	CALL lpm_create_particle( phase_init )
1260	last_particle_release_time = particle_advection_start
1261	!
1262	!-- User modification of initial particles
1263	CALL user_lpm_init
1264	!
1265	!-- Open file for statistical informations about particle conditions
1266	IF ( write_particle_statistics ) THEN
1267	CALL check_open( 80 )
1268	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
1269	number_of_particles
1270	CALL close_file( 80 )
1271	ENDIF
1272
1273	ENDIF
1274
1275	IF ( nested_run ) CALL pmcp_g_init
1276	!
1277	!-- To avoid programm abort, assign particles array to the local version of
1278	!-- first grid cell
1279	number_of_particles = prt_count(nzb+1,nys,nxl)
1280	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
1281	!
1282	!-- Formats
1283	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
1284
1285	END SUBROUTINE lpm_init
1286
1287	!------------------------------------------------------------------------------!
1288	! Description:
1289	! ------------
1290	!> Create Lagrangian particles
1291	!------------------------------------------------------------------------------!
1292	SUBROUTINE lpm_create_particle (phase)
1293
1294	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
1295	INTEGER(iwp) :: i !< loop variable ( particle groups )
1296	INTEGER(iwp) :: ip !< index variable along x
1297	INTEGER(iwp) :: j !< loop variable ( particles per point )
1298	INTEGER(iwp) :: jp !< index variable along y
1299	INTEGER(iwp) :: k !< index variable along z
1300	INTEGER(iwp) :: k_surf !< index of surface grid point
1301	INTEGER(iwp) :: kp !< index variable along z
1302	INTEGER(iwp) :: loop_stride !< loop variable for initialization
1303	INTEGER(iwp) :: n !< loop variable ( number of particles )
1304	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
1305
1306	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
1307
1308	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
1309	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
1310
1311	LOGICAL :: first_stride !< flag for initialization
1312
1313	REAL(wp) :: pos_x !< increment for particle position in x
1314	REAL(wp) :: pos_y !< increment for particle position in y
1315	REAL(wp) :: pos_z !< increment for particle position in z
1316	REAL(wp) :: rand_contr !< dummy argument for random position
1317
1318	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
1319
1320	!
1321	!-- Calculate particle positions and store particle attributes, if
1322	!-- particle is situated on this PE
1323	DO loop_stride = 1, 2
1324	first_stride = (loop_stride == 1)
1325	IF ( first_stride ) THEN
1326	local_count = 0 ! count number of particles
1327	ELSE
1328	local_count = prt_count ! Start address of new particles
1329	ENDIF
1330
1331	!
1332	!-- Calculate initial_weighting_factor diagnostically
1333	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
1334	initial_weighting_factor = number_concentration * &
1335	pdx(1) * pdy(1) * pdz(1)
1336	END IF
1337
1338	n = 0
1339	DO i = 1, number_of_particle_groups
1340	pos_z = psb(i)
1341	DO WHILE ( pos_z <= pst(i) )
1342	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
1343	pos_y = pss(i)
1344	DO WHILE ( pos_y <= psn(i) )
1345	IF ( pos_y >= nys * dy .AND. &
1346	pos_y < ( nyn + 1 ) * dy ) THEN
1347	pos_x = psl(i)
1348	xloop: DO WHILE ( pos_x <= psr(i) )
1349	IF ( pos_x >= nxl * dx .AND. &
1350	pos_x < ( nxr + 1) * dx ) THEN
1351	DO j = 1, particles_per_point
1352	n = n + 1
1353	tmp_particle%x = pos_x
1354	tmp_particle%y = pos_y
1355	tmp_particle%z = pos_z
1356	tmp_particle%age = 0.0_wp
1357	tmp_particle%age_m = 0.0_wp
1358	tmp_particle%dt_sum = 0.0_wp
1359	tmp_particle%e_m = 0.0_wp
1360	tmp_particle%rvar1 = 0.0_wp
1361	tmp_particle%rvar2 = 0.0_wp
1362	tmp_particle%rvar3 = 0.0_wp
1363	tmp_particle%speed_x = 0.0_wp
1364	tmp_particle%speed_y = 0.0_wp
1365	tmp_particle%speed_z = 0.0_wp
1366	tmp_particle%origin_x = pos_x
1367	tmp_particle%origin_y = pos_y
1368	tmp_particle%origin_z = pos_z
1369	IF ( curvature_solution_effects ) THEN
1370	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
1371	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
1372	ELSE
1373	tmp_particle%aux1 = 0.0_wp ! free to use
1374	tmp_particle%aux2 = 0.0_wp ! free to use
1375	ENDIF
1376	tmp_particle%radius = particle_groups(i)%radius
1377	tmp_particle%weight_factor = initial_weighting_factor
1378	tmp_particle%class = 1
1379	tmp_particle%group = i
1380	tmp_particle%id = 0_idp
1381	tmp_particle%particle_mask = .TRUE.
1382	tmp_particle%block_nr = -1
1383	!
1384	!-- Determine the grid indices of the particle position
1385	ip = INT( tmp_particle%x * ddx )
1386	jp = INT( tmp_particle%y * ddy )
1387	!
1388	!-- In case of stretching the actual k index is found iteratively
1389	IF ( dz_stretch_level .NE. -9999999.9_wp .OR. &
1390	dz_stretch_level_start(1) .NE. -9999999.9_wp ) THEN
1391	kp = MINLOC( ABS( tmp_particle%z - zu ), DIM = 1 ) - 1
1392	ELSE
1393	kp = INT( tmp_particle%z / dz(1) + 1 + offset_ocean_nzt )
1394	ENDIF
1395	!
1396	!-- Determine surface level. Therefore, check for
1397	!-- upward-facing wall on w-grid.
1398	k_surf = get_topography_top_index_ji( jp, ip, 'w' )
1399	IF ( seed_follows_topography ) THEN
1400	!
1401	!-- Particle height is given relative to topography
1402	kp = kp + k_surf
1403	tmp_particle%z = tmp_particle%z + zw(k_surf)
1404	!-- Skip particle release if particle position is
1405	!-- above model top, or within topography in case
1406	!-- of overhanging structures.
1407	IF ( kp > nzt .OR. &
1408	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
1409	pos_x = pos_x + pdx(i)
1410	CYCLE xloop
1411	ENDIF
1412	!
1413	!-- Skip particle release if particle position is
1414	!-- below surface, or within topography in case
1415	!-- of overhanging structures.
1416	ELSEIF ( .NOT. seed_follows_topography .AND. &
1417	tmp_particle%z <= zw(k_surf) .OR. &
1418	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
1419	THEN
1420	pos_x = pos_x + pdx(i)
1421	CYCLE xloop
1422	ENDIF
1423
1424	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
1425
1426	IF ( .NOT. first_stride ) THEN
1427	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
1428	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
1429	ENDIF
1430	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
1431	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
1432	ENDIF
1433	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
1434	ENDIF
1435	ENDDO
1436	ENDIF
1437	pos_x = pos_x + pdx(i)
1438	ENDDO xloop
1439	ENDIF
1440	pos_y = pos_y + pdy(i)
1441	ENDDO
1442	ENDIF
1443
1444	pos_z = pos_z + pdz(i)
1445	ENDDO
1446	ENDDO
1447
1448	IF ( first_stride ) THEN
1449	DO ip = nxl, nxr
1450	DO jp = nys, nyn
1451	DO kp = nzb+1, nzt
1452	IF ( phase == PHASE_INIT ) THEN
1453	IF ( local_count(kp,jp,ip) > 0 ) THEN
1454	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
1455	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
1456	1 )
1457	ELSE
1458	alloc_size = 1
1459	ENDIF
1460	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
1461	DO n = 1, alloc_size
1462	grid_particles(kp,jp,ip)%particles(n) = zero_particle
1463	ENDDO
1464	ELSEIF ( phase == PHASE_RELEASE ) THEN
1465	IF ( local_count(kp,jp,ip) > 0 ) THEN
1466	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
1467	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
1468	alloc_factor / 100.0_wp ) ), 1 )
1469	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
1470	CALL realloc_particles_array(ip,jp,kp,alloc_size)
1471	ENDIF
1472	ENDIF
1473	ENDIF
1474	ENDDO
1475	ENDDO
1476	ENDDO
1477	ENDIF
1478
1479	ENDDO
1480
1481	local_start = prt_count+1
1482	prt_count = local_count
1483	!
1484	!-- Calculate particle IDs
1485	DO ip = nxl, nxr
1486	DO jp = nys, nyn
1487	DO kp = nzb+1, nzt
1488	number_of_particles = prt_count(kp,jp,ip)
1489	IF ( number_of_particles <= 0 ) CYCLE
1490	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1491
1492	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1493
1494	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
1495	10000_idp*2 kp + 10000_idp * jp + ip
1496	!
1497	!-- Count the number of particles that have been released before
1498	grid_particles(kp,jp,ip)%id_counter = &
1499	grid_particles(kp,jp,ip)%id_counter + 1
1500
1501	ENDDO
1502
1503	ENDDO
1504	ENDDO
1505	ENDDO
1506	!
1507	!-- Initialize aerosol background spectrum
1508	IF ( curvature_solution_effects ) THEN
1509	CALL lpm_init_aerosols(local_start)
1510	ENDIF
1511	!
1512	!-- Add random fluctuation to particle positions.
1513	IF ( random_start_position ) THEN
1514	DO ip = nxl, nxr
1515	DO jp = nys, nyn
1516	DO kp = nzb+1, nzt
1517	number_of_particles = prt_count(kp,jp,ip)
1518	IF ( number_of_particles <= 0 ) CYCLE
1519	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1520	!
1521	!-- Move only new particles. Moreover, limit random fluctuation
1522	!-- in order to prevent that particles move more than one grid box,
1523	!-- which would lead to problems concerning particle exchange
1524	!-- between processors in case pdx/pdy are larger than dx/dy,
1525	!-- respectively.
1526	DO n = local_start(kp,jp,ip), number_of_particles
1527	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
1528	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1529	pdx(particles(n)%group)
1530	particles(n)%x = particles(n)%x + &
1531	MERGE( rand_contr, SIGN( dx, rand_contr ), &
1532	ABS( rand_contr ) < dx &
1533	)
1534	ENDIF
1535	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
1536	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1537	pdy(particles(n)%group)
1538	particles(n)%y = particles(n)%y + &
1539	MERGE( rand_contr, SIGN( dy, rand_contr ), &
1540	ABS( rand_contr ) < dy &
1541	)
1542	ENDIF
1543	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
1544	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
1545	pdz(particles(n)%group)
1546	particles(n)%z = particles(n)%z + &
1547	MERGE( rand_contr, SIGN( dzw(kp), rand_contr ), &
1548	ABS( rand_contr ) < dzw(kp) &
1549	)
1550	ENDIF
1551	ENDDO
1552	!
1553	!-- Identify particles located outside the model domain and reflect
1554	!-- or absorb them if necessary.
1555	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
1556	!
1557	!-- Furthermore, remove particles located in topography. Note, as
1558	!-- the particle speed is still zero at this point, wall
1559	!-- reflection boundary conditions will not work in this case.
1560	particles => &
1561	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1562	DO n = local_start(kp,jp,ip), number_of_particles
1563	i = particles(n)%x * ddx
1564	j = particles(n)%y * ddy
1565	k = particles(n)%z / dz(1) + 1 + offset_ocean_nzt
1566	DO WHILE( zw(k) < particles(n)%z )
1567	k = k + 1
1568	ENDDO
1569	DO WHILE( zw(k-1) > particles(n)%z )
1570	k = k - 1
1571	ENDDO
1572	!
1573	!-- Check if particle is within topography
1574	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
1575	particles(n)%particle_mask = .FALSE.
1576	deleted_particles = deleted_particles + 1
1577	ENDIF
1578
1579	ENDDO
1580	ENDDO
1581	ENDDO
1582	ENDDO
1583	!
1584	!-- Exchange particles between grid cells and processors
1585	CALL lpm_move_particle
1586	CALL lpm_exchange_horiz
1587
1588	ENDIF
1589	!
1590	!-- In case of random_start_position, delete particles identified by
1591	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1592	!-- which is needed for a fast interpolation of the LES fields on the particle
1593	!-- position.
1594	CALL lpm_sort_and_delete
1595	!
1596	!-- Determine the current number of particles
1597	DO ip = nxl, nxr
1598	DO jp = nys, nyn
1599	DO kp = nzb+1, nzt
1600	number_of_particles = number_of_particles &
1601	+ prt_count(kp,jp,ip)
1602	ENDDO
1603	ENDDO
1604	ENDDO
1605	!
1606	!-- Calculate the number of particles of the total domain
1607	#if defined( __parallel )
1608	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1609	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1610	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1611	#else
1612	total_number_of_particles = number_of_particles
1613	#endif
1614
1615	RETURN
1616
1617	END SUBROUTINE lpm_create_particle
1618
1619
1620	!------------------------------------------------------------------------------!
1621	! Description:
1622	! ------------
1623	!> This routine initialize the particles as aerosols with physio-chemical
1624	!> properties.
1625	!------------------------------------------------------------------------------!
1626	SUBROUTINE lpm_init_aerosols(local_start)
1627
1628	REAL(wp) :: afactor !< curvature effects
1629	REAL(wp) :: bfactor !< solute effects
1630	REAL(wp) :: dlogr !< logarithmic width of radius bin
1631	REAL(wp) :: e_a !< vapor pressure
1632	REAL(wp) :: e_s !< saturation vapor pressure
1633	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1634	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1635	REAL(wp) :: r_mid !< mean radius of bin
1636	REAL(wp) :: r_l !< left radius of bin
1637	REAL(wp) :: r_r !< right radius of bin
1638	REAL(wp) :: sigma !< surface tension
1639	REAL(wp) :: t_int !< temperature
1640
1641	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1642
1643	INTEGER(iwp) :: n !<
1644	INTEGER(iwp) :: ip !<
1645	INTEGER(iwp) :: jp !<
1646	INTEGER(iwp) :: kp !<
1647
1648	!
1649	!-- Set constants for different aerosol species
1650	IF ( TRIM(aero_species) .EQ. 'nacl' ) THEN
1651	molecular_weight_of_solute = 0.05844_wp
1652	rho_s = 2165.0_wp
1653	vanthoff = 2.0_wp
1654	ELSEIF ( TRIM(aero_species) .EQ. 'c3h4o4' ) THEN
1655	molecular_weight_of_solute = 0.10406_wp
1656	rho_s = 1600.0_wp
1657	vanthoff = 1.37_wp
1658	ELSEIF ( TRIM(aero_species) .EQ. 'nh4o3' ) THEN
1659	molecular_weight_of_solute = 0.08004_wp
1660	rho_s = 1720.0_wp
1661	vanthoff = 2.31_wp
1662	ELSE
1663	WRITE( message_string, * ) 'unknown aerosol species ', &
1664	'aero_species = "', TRIM( aero_species ), '"'
1665	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1666	ENDIF
1667	!
1668	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1669	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1670	IF ( TRIM(aero_type) .EQ. 'polar' ) THEN
1671	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6_wp
1672	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6_wp
1673	log_sigma = (/ 0.245, 0.300, 0.291 /)
1674	ELSEIF ( TRIM(aero_type) .EQ. 'background' ) THEN
1675	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6_wp
1676	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6_wp
1677	log_sigma = (/ 0.645, 0.253, 0.425 /)
1678	ELSEIF ( TRIM(aero_type) .EQ. 'maritime' ) THEN
1679	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6_wp
1680	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6_wp
1681	log_sigma = (/ 0.657, 0.210, 0.396 /)
1682	ELSEIF ( TRIM(aero_type) .EQ. 'continental' ) THEN
1683	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6_wp
1684	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6_wp
1685	log_sigma = (/ 0.161, 0.217, 0.380 /)
1686	ELSEIF ( TRIM(aero_type) .EQ. 'desert' ) THEN
1687	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6_wp
1688	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6_wp
1689	log_sigma = (/ 0.247, 0.770, 0.438 /)
1690	ELSEIF ( TRIM(aero_type) .EQ. 'rural' ) THEN
1691	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6_wp
1692	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6_wp
1693	log_sigma = (/ 0.225, 0.557, 0.266 /)
1694	ELSEIF ( TRIM(aero_type) .EQ. 'urban' ) THEN
1695	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6_wp
1696	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6_wp
1697	log_sigma = (/ 0.245, 0.666, 0.337 /)
1698	ELSEIF ( TRIM(aero_type) .EQ. 'user' ) THEN
1699	CONTINUE
1700	ELSE
1701	WRITE( message_string, * ) 'unknown aerosol type ', &
1702	'aero_type = "', TRIM( aero_type ), '"'
1703	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1704	ENDIF
1705
1706	DO ip = nxl, nxr
1707	DO jp = nys, nyn
1708	DO kp = nzb+1, nzt
1709
1710	number_of_particles = prt_count(kp,jp,ip)
1711	IF ( number_of_particles <= 0 ) CYCLE
1712	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1713
1714	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1715	!
1716	!-- Initialize the aerosols with a predefined spectral distribution
1717	!-- of the dry radius (logarithmically increasing bins) and a varying
1718	!-- weighting factor
1719	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1720
1721	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1722	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1723	r_mid = SQRT( r_l * r_r )
1724
1725	particles(n)%aux1 = r_mid
1726	particles(n)%weight_factor = &
1727	( na(1) / ( SQRT( 2.0_wp * pi ) * log_sigma(1) ) * &
1728	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0_wp log_sigma(1)**2 ) ) + &
1729	na(2) / ( SQRT( 2.0_wp * pi ) * log_sigma(2) ) * &
1730	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0_wp log_sigma(2)**2 ) ) + &
1731	na(3) / ( SQRT( 2.0_wp * pi ) * log_sigma(3) ) * &
1732	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0_wp log_sigma(3)**2 ) ) &
1733	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dzw(kp) )
1734
1735	!
1736	!-- Multiply weight_factor with the namelist parameter aero_weight
1737	!-- to increase or decrease the number of simulated aerosols
1738	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1739
1740	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1741	.GT. random_function( iran_part ) ) THEN
1742	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0_wp
1743	ELSE
1744	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1745	ENDIF
1746	!
1747	!-- Unnecessary particles will be deleted
1748	IF ( particles(n)%weight_factor .LE. 0.0_wp ) particles(n)%particle_mask = .FALSE.
1749
1750	ENDDO
1751	!
1752	!-- Set particle radius to equilibrium radius based on the environmental
1753	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1754	!-- the sometimes lengthy growth toward their equilibrium radius within
1755	!-- the simulation.
1756	t_int = pt(kp,jp,ip) * exner(kp)
1757
1758	e_s = magnus( t_int )
1759	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + rd_d_rv )
1760
1761	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1762	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1763
1764	bfactor = vanthoff * molecular_weight_of_water * &
1765	rho_s / ( molecular_weight_of_solute * rho_l )
1766	!
1767	!-- The formula is only valid for subsaturated environments. For
1768	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1769	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1770
1771	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1772	!
1773	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1774	!-- Curry (2007, JGR)
1775	particles(n)%radius = bfactor*0.3333333_wp &
1776	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1777	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1778	particles(n)%aux1 ) ) / &
1779	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1780	)
1781
1782	ENDDO
1783
1784	ENDDO
1785	ENDDO
1786	ENDDO
1787
1788	END SUBROUTINE lpm_init_aerosols
1789
1790
1791	!------------------------------------------------------------------------------!
1792	! Description:
1793	! ------------
1794	!> Calculates quantities required for considering the SGS velocity fluctuations
1795	!> in the particle transport by a stochastic approach. The respective
1796	!> quantities are: SGS-TKE gradients and horizontally averaged profiles of the
1797	!> SGS TKE and the resolved-scale velocity variances.
1798	!------------------------------------------------------------------------------!
1799	SUBROUTINE lpm_init_sgs_tke
1800
1801	USE statistics, &
1802	ONLY: flow_statistics_called, hom, sums, sums_l
1803
1804	INTEGER(iwp) :: i !< index variable along x
1805	INTEGER(iwp) :: j !< index variable along y
1806	INTEGER(iwp) :: k !< index variable along z
1807	INTEGER(iwp) :: m !< running index for the surface elements
1808
1809	REAL(wp) :: flag1 !< flag to mask topography
1810
1811	!
1812	!-- TKE gradient along x and y
1813	DO i = nxl, nxr
1814	DO j = nys, nyn
1815	DO k = nzb, nzt+1
1816
1817	IF ( .NOT. BTEST( wall_flags_0(k,j,i-1), 0 ) .AND. &
1818	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1819	BTEST( wall_flags_0(k,j,i+1), 0 ) ) &
1820	THEN
1821	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1822	( e(k,j,i+1) - e(k,j,i) ) * ddx
1823	ELSEIF ( BTEST( wall_flags_0(k,j,i-1), 0 ) .AND. &
1824	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1825	.NOT. BTEST( wall_flags_0(k,j,i+1), 0 ) ) &
1826	THEN
1827	de_dx(k,j,i) = 2.0_wp * sgs_wf_part * &
1828	( e(k,j,i) - e(k,j,i-1) ) * ddx
1829	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i), 22 ) .AND. &
1830	.NOT. BTEST( wall_flags_0(k,j,i+1), 22 ) ) &
1831	THEN
1832	de_dx(k,j,i) = 0.0_wp
1833	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i-1), 22 ) .AND. &
1834	.NOT. BTEST( wall_flags_0(k,j,i), 22 ) ) &
1835	THEN
1836	de_dx(k,j,i) = 0.0_wp
1837	ELSE
1838	de_dx(k,j,i) = sgs_wf_part * ( e(k,j,i+1) - e(k,j,i-1) ) * ddx
1839	ENDIF
1840
1841	IF ( .NOT. BTEST( wall_flags_0(k,j-1,i), 0 ) .AND. &
1842	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1843	BTEST( wall_flags_0(k,j+1,i), 0 ) ) &
1844	THEN
1845	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1846	( e(k,j+1,i) - e(k,j,i) ) * ddy
1847	ELSEIF ( BTEST( wall_flags_0(k,j-1,i), 0 ) .AND. &
1848	BTEST( wall_flags_0(k,j,i), 0 ) .AND. &
1849	.NOT. BTEST( wall_flags_0(k,j+1,i), 0 ) ) &
1850	THEN
1851	de_dy(k,j,i) = 2.0_wp * sgs_wf_part * &
1852	( e(k,j,i) - e(k,j-1,i) ) * ddy
1853	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j,i), 22 ) .AND. &
1854	.NOT. BTEST( wall_flags_0(k,j+1,i), 22 ) ) &
1855	THEN
1856	de_dy(k,j,i) = 0.0_wp
1857	ELSEIF ( .NOT. BTEST( wall_flags_0(k,j-1,i), 22 ) .AND. &
1858	.NOT. BTEST( wall_flags_0(k,j,i), 22 ) ) &
1859	THEN
1860	de_dy(k,j,i) = 0.0_wp
1861	ELSE
1862	de_dy(k,j,i) = sgs_wf_part * ( e(k,j+1,i) - e(k,j-1,i) ) * ddy
1863	ENDIF
1864
1865	ENDDO
1866	ENDDO
1867	ENDDO
1868
1869	!
1870	!-- TKE gradient along z at topograhy and including bottom and top boundary conditions
1871	DO i = nxl, nxr
1872	DO j = nys, nyn
1873	DO k = nzb+1, nzt-1
1874	!
1875	!-- Flag to mask topography
1876	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
1877
1878	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1879	( e(k+1,j,i) - e(k-1,j,i) ) / ( zu(k+1) - zu(k-1) ) &
1880	* flag1
1881	ENDDO
1882	!
1883	!-- upward-facing surfaces
1884	DO m = bc_h(0)%start_index(j,i), bc_h(0)%end_index(j,i)
1885	k = bc_h(0)%k(m)
1886	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1887	( e(k+1,j,i) - e(k,j,i) ) / ( zu(k+1) - zu(k) )
1888	ENDDO
1889	!
1890	!-- downward-facing surfaces
1891	DO m = bc_h(1)%start_index(j,i), bc_h(1)%end_index(j,i)
1892	k = bc_h(1)%k(m)
1893	de_dz(k,j,i) = 2.0_wp * sgs_wf_part * &
1894	( e(k,j,i) - e(k-1,j,i) ) / ( zu(k) - zu(k-1) )
1895	ENDDO
1896
1897	de_dz(nzb,j,i) = 0.0_wp
1898	de_dz(nzt,j,i) = 0.0_wp
1899	de_dz(nzt+1,j,i) = 0.0_wp
1900	ENDDO
1901	ENDDO
1902	!
1903	!-- Ghost point exchange
1904	CALL exchange_horiz( de_dx, nbgp )
1905	CALL exchange_horiz( de_dy, nbgp )
1906	CALL exchange_horiz( de_dz, nbgp )
1907	CALL exchange_horiz( diss, nbgp )
1908	!
1909	!-- Set boundary conditions at non-periodic boundaries. Note, at non-period
1910	!-- boundaries zero-gradient boundary conditions are set for the subgrid TKE.
1911	!-- Thus, TKE gradients normal to the respective lateral boundaries are zero,
1912	!-- while tangetial TKE gradients then must be the same as within the prognostic
1913	!-- domain.
1914	IF ( bc_dirichlet_l ) THEN
1915	de_dx(:,:,-1) = 0.0_wp
1916	de_dy(:,:,-1) = de_dy(:,:,0)
1917	de_dz(:,:,-1) = de_dz(:,:,0)
1918	ENDIF
1919	IF ( bc_dirichlet_r ) THEN
1920	de_dx(:,:,nxr+1) = 0.0_wp
1921	de_dy(:,:,nxr+1) = de_dy(:,:,nxr)
1922	de_dz(:,:,nxr+1) = de_dz(:,:,nxr)
1923	ENDIF
1924	IF ( bc_dirichlet_n ) THEN
1925	de_dx(:,nyn+1,:) = de_dx(:,nyn,:)
1926	de_dy(:,nyn+1,:) = 0.0_wp
1927	de_dz(:,nyn+1,:) = de_dz(:,nyn,:)
1928	ENDIF
1929	IF ( bc_dirichlet_s ) THEN
1930	de_dx(:,nys-1,:) = de_dx(:,nys,:)
1931	de_dy(:,nys-1,:) = 0.0_wp
1932	de_dz(:,nys-1,:) = de_dz(:,nys,:)
1933	ENDIF
1934	!
1935	!-- Calculate the horizontally averaged profiles of SGS TKE and resolved
1936	!-- velocity variances (they may have been already calculated in routine
1937	!-- flow_statistics).
1938	IF ( .NOT. flow_statistics_called ) THEN
1939
1940	!
1941	!-- First calculate horizontally averaged profiles of the horizontal
1942	!-- velocities.
1943	sums_l(:,1,0) = 0.0_wp
1944	sums_l(:,2,0) = 0.0_wp
1945
1946	DO i = nxl, nxr
1947	DO j = nys, nyn
1948	DO k = nzb, nzt+1
1949	!
1950	!-- Flag indicating vicinity of wall
1951	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 24 ) )
1952
1953	sums_l(k,1,0) = sums_l(k,1,0) + u(k,j,i) * flag1
1954	sums_l(k,2,0) = sums_l(k,2,0) + v(k,j,i) * flag1
1955	ENDDO
1956	ENDDO
1957	ENDDO
1958
1959	#if defined( __parallel )
1960	!
1961	!-- Compute total sum from local sums
1962	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1963	CALL MPI_ALLREDUCE( sums_l(nzb,1,0), sums(nzb,1), nzt+2-nzb, &
1964	MPI_REAL, MPI_SUM, comm2d, ierr )
1965	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1966	CALL MPI_ALLREDUCE( sums_l(nzb,2,0), sums(nzb,2), nzt+2-nzb, &
1967	MPI_REAL, MPI_SUM, comm2d, ierr )
1968	#else
1969	sums(:,1) = sums_l(:,1,0)
1970	sums(:,2) = sums_l(:,2,0)
1971	#endif
1972
1973	!
1974	!-- Final values are obtained by division by the total number of grid
1975	!-- points used for the summation.
1976	hom(:,1,1,0) = sums(:,1) / ngp_2dh_outer(:,0) ! u
1977	hom(:,1,2,0) = sums(:,2) / ngp_2dh_outer(:,0) ! v
1978
1979	!
1980	!-- Now calculate the profiles of SGS TKE and the resolved-scale
1981	!-- velocity variances
1982	sums_l(:,8,0) = 0.0_wp
1983	sums_l(:,30,0) = 0.0_wp
1984	sums_l(:,31,0) = 0.0_wp
1985	sums_l(:,32,0) = 0.0_wp
1986	DO i = nxl, nxr
1987	DO j = nys, nyn
1988	DO k = nzb, nzt+1
1989	!
1990	!-- Flag indicating vicinity of wall
1991	flag1 = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 24 ) )
1992
1993	sums_l(k,8,0) = sums_l(k,8,0) + e(k,j,i) * flag1
1994	sums_l(k,30,0) = sums_l(k,30,0) + ( u(k,j,i) - hom(k,1,1,0) )*2 flag1
1995	sums_l(k,31,0) = sums_l(k,31,0) + ( v(k,j,i) - hom(k,1,2,0) )*2 flag1
1996	sums_l(k,32,0) = sums_l(k,32,0) + w(k,j,i)*2 flag1
1997	ENDDO
1998	ENDDO
1999	ENDDO
2000
2001	#if defined( __parallel )
2002	!
2003	!-- Compute total sum from local sums
2004	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2005	CALL MPI_ALLREDUCE( sums_l(nzb,8,0), sums(nzb,8), nzt+2-nzb, &
2006	MPI_REAL, MPI_SUM, comm2d, ierr )
2007	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2008	CALL MPI_ALLREDUCE( sums_l(nzb,30,0), sums(nzb,30), nzt+2-nzb, &
2009	MPI_REAL, MPI_SUM, comm2d, ierr )
2010	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2011	CALL MPI_ALLREDUCE( sums_l(nzb,31,0), sums(nzb,31), nzt+2-nzb, &
2012	MPI_REAL, MPI_SUM, comm2d, ierr )
2013	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2014	CALL MPI_ALLREDUCE( sums_l(nzb,32,0), sums(nzb,32), nzt+2-nzb, &
2015	MPI_REAL, MPI_SUM, comm2d, ierr )
2016
2017	#else
2018	sums(:,8) = sums_l(:,8,0)
2019	sums(:,30) = sums_l(:,30,0)
2020	sums(:,31) = sums_l(:,31,0)
2021	sums(:,32) = sums_l(:,32,0)
2022	#endif
2023
2024	!
2025	!-- Final values are obtained by division by the total number of grid
2026	!-- points used for the summation.
2027	hom(:,1,8,0) = sums(:,8) / ngp_2dh_outer(:,0) ! e
2028	hom(:,1,30,0) = sums(:,30) / ngp_2dh_outer(:,0) ! u*2
2029	hom(:,1,31,0) = sums(:,31) / ngp_2dh_outer(:,0) ! v*2
2030	hom(:,1,32,0) = sums(:,32) / ngp_2dh_outer(:,0) ! w*2
2031
2032	ENDIF
2033
2034	END SUBROUTINE lpm_init_sgs_tke
2035
2036
2037	!------------------------------------------------------------------------------!
2038	! Description:
2039	! ------------
2040	!> Sobroutine control lpm actions, i.e. all actions during one time step.
2041	!------------------------------------------------------------------------------!
2042	SUBROUTINE lpm_actions( location )
2043
2044	CHARACTER (LEN=*), INTENT(IN) :: location !< call location string
2045
2046	INTEGER(iwp) :: i !<
2047	INTEGER(iwp) :: ie !<
2048	INTEGER(iwp) :: is !<
2049	INTEGER(iwp) :: j !<
2050	INTEGER(iwp) :: je !<
2051	INTEGER(iwp) :: js !<
2052	INTEGER(iwp), SAVE :: lpm_count = 0 !<
2053	INTEGER(iwp) :: k !<
2054	INTEGER(iwp) :: ke !<
2055	INTEGER(iwp) :: ks !<
2056	INTEGER(iwp) :: m !<
2057	INTEGER(iwp), SAVE :: steps = 0 !<
2058
2059	LOGICAL :: first_loop_stride !<
2060
2061
2062	SELECT CASE ( location )
2063
2064	CASE ( 'after_prognostic_equations' )
2065
2066	CALL cpu_log( log_point(25), 'lpm', 'start' )
2067	!
2068	!-- Write particle data at current time on file.
2069	!-- This has to be done here, before particles are further processed,
2070	!-- because they may be deleted within this timestep (in case that
2071	!-- dt_write_particle_data = dt_prel = particle_maximum_age).
2072	time_write_particle_data = time_write_particle_data + dt_3d
2073	IF ( time_write_particle_data >= dt_write_particle_data ) THEN
2074
2075	CALL lpm_data_output_particles
2076	!
2077	!-- The MOD function allows for changes in the output interval with restart
2078	!-- runs.
2079	time_write_particle_data = MOD( time_write_particle_data, &
2080	MAX( dt_write_particle_data, dt_3d ) )
2081	ENDIF
2082
2083	!
2084	!-- Initialize arrays for marking those particles to be deleted after the
2085	!-- (sub-) timestep
2086	deleted_particles = 0
2087
2088	!
2089	!-- Initialize variables used for accumulating the number of particles
2090	!-- xchanged between the subdomains during all sub-timesteps (if sgs
2091	!-- velocities are included). These data are output further below on the
2092	!-- particle statistics file.
2093	trlp_count_sum = 0
2094	trlp_count_recv_sum = 0
2095	trrp_count_sum = 0
2096	trrp_count_recv_sum = 0
2097	trsp_count_sum = 0
2098	trsp_count_recv_sum = 0
2099	trnp_count_sum = 0
2100	trnp_count_recv_sum = 0
2101	!
2102	!-- Calculate exponential term used in case of particle inertia for each
2103	!-- of the particle groups
2104	DO m = 1, number_of_particle_groups
2105	IF ( particle_groups(m)%density_ratio /= 0.0_wp ) THEN
2106	particle_groups(m)%exp_arg = &
2107	4.5_wp * particle_groups(m)%density_ratio * &
2108	molecular_viscosity / ( particle_groups(m)%radius )**2
2109
2110	particle_groups(m)%exp_term = EXP( -particle_groups(m)%exp_arg * &
2111	dt_3d )
2112	ENDIF
2113	ENDDO
2114	!
2115	!-- If necessary, release new set of particles
2116	IF ( ( simulated_time - last_particle_release_time ) >= dt_prel .AND. end_time_prel > simulated_time ) &
2117	THEN
2118	DO WHILE ( ( simulated_time - last_particle_release_time ) >= dt_prel )
2119	CALL lpm_create_particle( PHASE_RELEASE )
2120	last_particle_release_time = last_particle_release_time + dt_prel
2121	ENDDO
2122	ENDIF
2123	!
2124	!-- Reset summation arrays
2125	IF ( cloud_droplets ) THEN
2126	ql_c = 0.0_wp
2127	ql_v = 0.0_wp
2128	ql_vp = 0.0_wp
2129	ENDIF
2130
2131	first_loop_stride = .TRUE.
2132	grid_particles(:,:,:)%time_loop_done = .TRUE.
2133	!
2134	!-- Timestep loop for particle advection.
2135	!-- This loop has to be repeated until the advection time of every particle
2136	!-- (within the total domain!) has reached the LES timestep (dt_3d).
2137	!-- In case of including the SGS velocities, the particle timestep may be
2138	!-- smaller than the LES timestep (because of the Lagrangian timescale
2139	!-- restriction) and particles may require to undergo several particle
2140	!-- timesteps, before the LES timestep is reached. Because the number of these
2141	!-- particle timesteps to be carried out is unknown at first, these steps are
2142	!-- carried out in the following infinite loop with exit condition.
2143	DO
2144	CALL cpu_log( log_point_s(44), 'lpm_advec', 'start' )
2145	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
2146
2147	!
2148	!-- If particle advection includes SGS velocity components, calculate the
2149	!-- required SGS quantities (i.e. gradients of the TKE, as well as
2150	!-- horizontally averaged profiles of the SGS TKE and the resolved-scale
2151	!-- velocity variances)
2152	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
2153	CALL lpm_init_sgs_tke
2154	ENDIF
2155	!
2156	!-- In case SGS-particle speed is considered, particles may carry out
2157	!-- several particle timesteps. In order to prevent unnecessary
2158	!-- treatment of particles that already reached the final time level,
2159	!-- particles are sorted into contiguous blocks of finished and
2160	!-- not-finished particles, in addition to their already sorting
2161	!-- according to their sub-boxes.
2162	IF ( .NOT. first_loop_stride .AND. use_sgs_for_particles ) &
2163	CALL lpm_sort_timeloop_done
2164	DO i = nxl, nxr
2165	DO j = nys, nyn
2166	DO k = nzb+1, nzt
2167
2168	number_of_particles = prt_count(k,j,i)
2169	!
2170	!-- If grid cell gets empty, flag must be true
2171	IF ( number_of_particles <= 0 ) THEN
2172	grid_particles(k,j,i)%time_loop_done = .TRUE.
2173	CYCLE
2174	ENDIF
2175
2176	IF ( .NOT. first_loop_stride .AND. &
2177	grid_particles(k,j,i)%time_loop_done ) CYCLE
2178
2179	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2180
2181	particles(1:number_of_particles)%particle_mask = .TRUE.
2182	!
2183	!-- Initialize the variable storing the total time that a particle
2184	!-- has advanced within the timestep procedure
2185	IF ( first_loop_stride ) THEN
2186	particles(1:number_of_particles)%dt_sum = 0.0_wp
2187	ENDIF
2188	!
2189	!-- Particle (droplet) growth by condensation/evaporation and
2190	!-- collision
2191	IF ( cloud_droplets .AND. first_loop_stride) THEN
2192	!
2193	!-- Droplet growth by condensation / evaporation
2194	CALL lpm_droplet_condensation(i,j,k)
2195	!
2196	!-- Particle growth by collision
2197	IF ( collision_kernel /= 'none' ) THEN
2198	CALL lpm_droplet_collision(i,j,k)
2199	ENDIF
2200
2201	ENDIF
2202	!
2203	!-- Initialize the switch used for the loop exit condition checked
2204	!-- at the end of this loop. If at least one particle has failed to
2205	!-- reach the LES timestep, this switch will be set false in
2206	!-- lpm_advec.
2207	dt_3d_reached_l = .TRUE.
2208
2209	!
2210	!-- Particle advection
2211	CALL lpm_advec(i,j,k)
2212	!
2213	!-- Particle reflection from walls. Only applied if the particles
2214	!-- are in the vertical range of the topography. (Here, some
2215	!-- optimization is still possible.)
2216	IF ( topography /= 'flat' .AND. k < nzb_max + 2 ) THEN
2217	CALL lpm_boundary_conds( 'walls', i, j, k )
2218	ENDIF
2219	!
2220	!-- User-defined actions after the calculation of the new particle
2221	!-- position
2222	CALL user_lpm_advec(i,j,k)
2223	!
2224	!-- Apply boundary conditions to those particles that have crossed
2225	!-- the top or bottom boundary and delete those particles, which are
2226	!-- older than allowed
2227	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
2228	!
2229	!--- If not all particles of the actual grid cell have reached the
2230	!-- LES timestep, this cell has to do another loop iteration. Due to
2231	!-- the fact that particles can move into neighboring grid cells,
2232	!-- these neighbor cells also have to perform another loop iteration.
2233	!-- Please note, this realization does not work properly if
2234	!-- particles move into another subdomain.
2235	IF ( .NOT. dt_3d_reached_l ) THEN
2236	ks = MAX(nzb+1,k-1)
2237	ke = MIN(nzt,k+1)
2238	js = MAX(nys,j-1)
2239	je = MIN(nyn,j+1)
2240	is = MAX(nxl,i-1)
2241	ie = MIN(nxr,i+1)
2242	grid_particles(ks:ke,js:je,is:ie)%time_loop_done = .FALSE.
2243	ELSE
2244	grid_particles(k,j,i)%time_loop_done = .TRUE.
2245	ENDIF
2246
2247	ENDDO
2248	ENDDO
2249	ENDDO
2250	steps = steps + 1
2251	dt_3d_reached_l = ALL(grid_particles(:,:,:)%time_loop_done)
2252	!
2253	!-- Find out, if all particles on every PE have completed the LES timestep
2254	!-- and set the switch corespondingly
2255	#if defined( __parallel )
2256	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2257	CALL MPI_ALLREDUCE( dt_3d_reached_l, dt_3d_reached, 1, MPI_LOGICAL, &
2258	MPI_LAND, comm2d, ierr )
2259	#else
2260	dt_3d_reached = dt_3d_reached_l
2261	#endif
2262	CALL cpu_log( log_point_s(44), 'lpm_advec', 'stop' )
2263
2264	!
2265	!-- Apply splitting and merging algorithm
2266	IF ( cloud_droplets ) THEN
2267	IF ( splitting ) THEN
2268	CALL lpm_splitting
2269	ENDIF
2270	IF ( merging ) THEN
2271	CALL lpm_merging
2272	ENDIF
2273	ENDIF
2274	!
2275	!-- Move Particles local to PE to a different grid cell
2276	CALL lpm_move_particle
2277	!
2278	!-- Horizontal boundary conditions including exchange between subdmains
2279	CALL lpm_exchange_horiz
2280
2281	!
2282	!-- IF .FALSE., lpm_sort_and_delete is done inside pcmp
2283	IF ( .NOT. dt_3d_reached .OR. .NOT. nested_run ) THEN
2284	!
2285	!-- Pack particles (eliminate those marked for deletion),
2286	!-- determine new number of particles
2287	CALL lpm_sort_and_delete
2288
2289	!-- Initialize variables for the next (sub-) timestep, i.e., for marking
2290	!-- those particles to be deleted after the timestep
2291	deleted_particles = 0
2292	ENDIF
2293
2294	IF ( dt_3d_reached ) EXIT
2295
2296	first_loop_stride = .FALSE.
2297	ENDDO ! timestep loop
2298	!
2299	!-- in case of nested runs do the transfer of particles after every full model time step
2300	IF ( nested_run ) THEN
2301	CALL particles_from_parent_to_child
2302	CALL particles_from_child_to_parent
2303	CALL pmcp_p_delete_particles_in_fine_grid_area
2304
2305	CALL lpm_sort_and_delete
2306
2307	deleted_particles = 0
2308	ENDIF
2309
2310	!
2311	!-- Calculate the new liquid water content for each grid box
2312	IF ( cloud_droplets ) CALL lpm_calc_liquid_water_content
2313
2314	!
2315	!-- Deallocate unused memory
2316	IF ( deallocate_memory .AND. lpm_count == step_dealloc ) THEN
2317	CALL dealloc_particles_array
2318	lpm_count = 0
2319	ELSEIF ( deallocate_memory ) THEN
2320	lpm_count = lpm_count + 1
2321	ENDIF
2322
2323	!
2324	!-- Write particle statistics (in particular the number of particles
2325	!-- exchanged between the subdomains) on file
2326	IF ( write_particle_statistics ) CALL lpm_write_exchange_statistics
2327
2328	CALL cpu_log( log_point(25), 'lpm', 'stop' )
2329
2330	! !
2331	! !-- Output of particle time series
2332	! IF ( particle_advection ) THEN
2333	! IF ( time_dopts >= dt_dopts .OR. &
2334	! ( time_since_reference_point >= particle_advection_start .AND. &
2335	! first_call_lpm ) ) THEN
2336	! CALL lpm_data_output_ptseries
2337	! time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
2338	! ENDIF
2339	! ENDIF
2340
2341	CASE DEFAULT
2342	CONTINUE
2343
2344	END SELECT
2345
2346	END SUBROUTINE lpm_actions
2347
2348
2349	!------------------------------------------------------------------------------!
2350	! Description:
2351	! ------------
2352	!
2353	!------------------------------------------------------------------------------!
2354	SUBROUTINE particles_from_parent_to_child
2355	IMPLICIT NONE
2356
2357	CALL pmcp_c_get_particle_from_parent ! Child actions
2358	CALL pmcp_p_fill_particle_win ! Parent actions
2359
2360	RETURN
2361	END SUBROUTINE particles_from_parent_to_child
2362
2363
2364	!------------------------------------------------------------------------------!
2365	! Description:
2366	! ------------
2367	!
2368	!------------------------------------------------------------------------------!
2369	SUBROUTINE particles_from_child_to_parent
2370	IMPLICIT NONE
2371
2372	CALL pmcp_c_send_particle_to_parent ! Child actions
2373	CALL pmcp_p_empty_particle_win ! Parent actions
2374
2375	RETURN
2376	END SUBROUTINE particles_from_child_to_parent
2377
2378	!------------------------------------------------------------------------------!
2379	! Description:
2380	! ------------
2381	!> This routine write exchange statistics of the lpm in a ascii file.
2382	!------------------------------------------------------------------------------!
2383	SUBROUTINE lpm_write_exchange_statistics
2384
2385	INTEGER(iwp) :: ip !<
2386	INTEGER(iwp) :: jp !<
2387	INTEGER(iwp) :: kp !<
2388	INTEGER(iwp) :: tot_number_of_particles
2389
2390	!
2391	!-- Determine the current number of particles
2392	number_of_particles = 0
2393	DO ip = nxl, nxr
2394	DO jp = nys, nyn
2395	DO kp = nzb+1, nzt
2396	number_of_particles = number_of_particles &
2397	+ prt_count(kp,jp,ip)
2398	ENDDO
2399	ENDDO
2400	ENDDO
2401
2402	CALL check_open( 80 )
2403	#if defined( __parallel )
2404	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2405	number_of_particles, pleft, trlp_count_sum, &
2406	trlp_count_recv_sum, pright, trrp_count_sum, &
2407	trrp_count_recv_sum, psouth, trsp_count_sum, &
2408	trsp_count_recv_sum, pnorth, trnp_count_sum, &
2409	trnp_count_recv_sum
2410	#else
2411	WRITE ( 80, 8000 ) current_timestep_number+1, simulated_time+dt_3d, &
2412	number_of_particles
2413	#endif
2414	CALL close_file( 80 )
2415
2416	IF ( number_of_particles > 0 ) THEN
2417	WRITE(9,*) 'number_of_particles ', number_of_particles, &
2418	current_timestep_number + 1, simulated_time + dt_3d
2419	ENDIF
2420
2421	#if defined( __parallel )
2422	CALL MPI_ALLREDUCE( number_of_particles, tot_number_of_particles, 1, &
2423	MPI_INTEGER, MPI_SUM, comm2d, ierr )
2424	#else
2425	tot_number_of_particles = number_of_particles
2426	#endif
2427
2428	IF ( nested_run ) THEN
2429	CALL pmcp_g_print_number_of_particles( simulated_time+dt_3d, &
2430	tot_number_of_particles)
2431	ENDIF
2432
2433	!
2434	!-- Formats
2435	8000 FORMAT (I6,1X,F7.2,4X,I10,5X,4(I3,1X,I4,'/',I4,2X),6X,I10)
2436
2437
2438	END SUBROUTINE lpm_write_exchange_statistics
2439
2440
2441	!------------------------------------------------------------------------------!
2442	! Description:
2443	! ------------
2444	!> Write particle data in FORTRAN binary and/or netCDF format
2445	!------------------------------------------------------------------------------!
2446	SUBROUTINE lpm_data_output_particles
2447
2448	INTEGER(iwp) :: ip !<
2449	INTEGER(iwp) :: jp !<
2450	INTEGER(iwp) :: kp !<
2451
2452	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'start' )
2453
2454	!
2455	!-- Attention: change version number for unit 85 (in routine check_open)
2456	!-- whenever the output format for this unit is changed!
2457	CALL check_open( 85 )
2458
2459	WRITE ( 85 ) simulated_time
2460	WRITE ( 85 ) prt_count
2461
2462	DO ip = nxl, nxr
2463	DO jp = nys, nyn
2464	DO kp = nzb+1, nzt
2465	number_of_particles = prt_count(kp,jp,ip)
2466	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
2467	IF ( number_of_particles <= 0 ) CYCLE
2468	WRITE ( 85 ) particles
2469	ENDDO
2470	ENDDO
2471	ENDDO
2472
2473	CALL close_file( 85 )
2474
2475
2476	#if defined( __netcdf )
2477	! !
2478	! !-- Output in netCDF format
2479	! CALL check_open( 108 )
2480	!
2481	! !
2482	! !-- Update the NetCDF time axis
2483	! prt_time_count = prt_time_count + 1
2484	!
2485	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_time_prt, &
2486	! (/ simulated_time /), &
2487	! start = (/ prt_time_count /), count = (/ 1 /) )
2488	! CALL netcdf_handle_error( 'lpm_data_output_particles', 1 )
2489	!
2490	! !
2491	! !-- Output the real number of particles used
2492	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_rnop_prt, &
2493	! (/ number_of_particles /), &
2494	! start = (/ prt_time_count /), count = (/ 1 /) )
2495	! CALL netcdf_handle_error( 'lpm_data_output_particles', 2 )
2496	!
2497	! !
2498	! !-- Output all particle attributes
2499	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(1), particles%age, &
2500	! start = (/ 1, prt_time_count /), &
2501	! count = (/ maximum_number_of_particles /) )
2502	! CALL netcdf_handle_error( 'lpm_data_output_particles', 3 )
2503	!
2504	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(2), particles%user, &
2505	! start = (/ 1, prt_time_count /), &
2506	! count = (/ maximum_number_of_particles /) )
2507	! CALL netcdf_handle_error( 'lpm_data_output_particles', 4 )
2508	!
2509	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(3), particles%origin_x, &
2510	! start = (/ 1, prt_time_count /), &
2511	! count = (/ maximum_number_of_particles /) )
2512	! CALL netcdf_handle_error( 'lpm_data_output_particles', 5 )
2513	!
2514	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(4), particles%origin_y, &
2515	! start = (/ 1, prt_time_count /), &
2516	! count = (/ maximum_number_of_particles /) )
2517	! CALL netcdf_handle_error( 'lpm_data_output_particles', 6 )
2518	!
2519	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(5), particles%origin_z, &
2520	! start = (/ 1, prt_time_count /), &
2521	! count = (/ maximum_number_of_particles /) )
2522	! CALL netcdf_handle_error( 'lpm_data_output_particles', 7 )
2523	!
2524	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(6), particles%radius, &
2525	! start = (/ 1, prt_time_count /), &
2526	! count = (/ maximum_number_of_particles /) )
2527	! CALL netcdf_handle_error( 'lpm_data_output_particles', 8 )
2528	!
2529	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(7), particles%speed_x, &
2530	! start = (/ 1, prt_time_count /), &
2531	! count = (/ maximum_number_of_particles /) )
2532	! CALL netcdf_handle_error( 'lpm_data_output_particles', 9 )
2533	!
2534	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(8), particles%speed_y, &
2535	! start = (/ 1, prt_time_count /), &
2536	! count = (/ maximum_number_of_particles /) )
2537	! CALL netcdf_handle_error( 'lpm_data_output_particles', 10 )
2538	!
2539	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(9), particles%speed_z, &
2540	! start = (/ 1, prt_time_count /), &
2541	! count = (/ maximum_number_of_particles /) )
2542	! CALL netcdf_handle_error( 'lpm_data_output_particles', 11 )
2543	!
2544	! nc_stat = NF90_PUT_VAR( id_set_prt,id_var_prt(10), &
2545	! particles%weight_factor, &
2546	! start = (/ 1, prt_time_count /), &
2547	! count = (/ maximum_number_of_particles /) )
2548	! CALL netcdf_handle_error( 'lpm_data_output_particles', 12 )
2549	!
2550	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(11), particles%x, &
2551	! start = (/ 1, prt_time_count /), &
2552	! count = (/ maximum_number_of_particles /) )
2553	! CALL netcdf_handle_error( 'lpm_data_output_particles', 13 )
2554	!
2555	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(12), particles%y, &
2556	! start = (/ 1, prt_time_count /), &
2557	! count = (/ maximum_number_of_particles /) )
2558	! CALL netcdf_handle_error( 'lpm_data_output_particles', 14 )
2559	!
2560	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(13), particles%z, &
2561	! start = (/ 1, prt_time_count /), &
2562	! count = (/ maximum_number_of_particles /) )
2563	! CALL netcdf_handle_error( 'lpm_data_output_particles', 15 )
2564	!
2565	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(14), particles%class, &
2566	! start = (/ 1, prt_time_count /), &
2567	! count = (/ maximum_number_of_particles /) )
2568	! CALL netcdf_handle_error( 'lpm_data_output_particles', 16 )
2569	!
2570	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(15), particles%group, &
2571	! start = (/ 1, prt_time_count /), &
2572	! count = (/ maximum_number_of_particles /) )
2573	! CALL netcdf_handle_error( 'lpm_data_output_particles', 17 )
2574	!
2575	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(16), &
2576	! particles%id2, &
2577	! start = (/ 1, prt_time_count /), &
2578	! count = (/ maximum_number_of_particles /) )
2579	! CALL netcdf_handle_error( 'lpm_data_output_particles', 18 )
2580	!
2581	! nc_stat = NF90_PUT_VAR( id_set_prt, id_var_prt(17), particles%id1, &
2582	! start = (/ 1, prt_time_count /), &
2583	! count = (/ maximum_number_of_particles /) )
2584	! CALL netcdf_handle_error( 'lpm_data_output_particles', 19 )
2585	!
2586	#endif
2587
2588	CALL cpu_log( log_point_s(40), 'lpm_data_output', 'stop' )
2589
2590	END SUBROUTINE lpm_data_output_particles
2591
2592	!------------------------------------------------------------------------------!
2593	! Description:
2594	! ------------
2595	!> This routine calculates and provide particle timeseries output.
2596	!------------------------------------------------------------------------------!
2597	SUBROUTINE lpm_data_output_ptseries
2598
2599	INTEGER(iwp) :: i !<
2600	INTEGER(iwp) :: inum !<
2601	INTEGER(iwp) :: j !<
2602	INTEGER(iwp) :: jg !<
2603	INTEGER(iwp) :: k !<
2604	INTEGER(iwp) :: n !<
2605
2606	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value !<
2607	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pts_value_l !<
2608
2609
2610	CALL cpu_log( log_point(36), 'data_output_ptseries', 'start' )
2611
2612	IF ( myid == 0 ) THEN
2613	!
2614	!-- Open file for time series output in NetCDF format
2615	dopts_time_count = dopts_time_count + 1
2616	CALL check_open( 109 )
2617	#if defined( __netcdf )
2618	!
2619	!-- Update the particle time series time axis
2620	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_time_pts, &
2621	(/ time_since_reference_point /), &
2622	start = (/ dopts_time_count /), count = (/ 1 /) )
2623	CALL netcdf_handle_error( 'data_output_ptseries', 391 )
2624	#endif
2625
2626	ENDIF
2627
2628	ALLOCATE( pts_value(0:number_of_particle_groups,dopts_num), &
2629	pts_value_l(0:number_of_particle_groups,dopts_num) )
2630
2631	pts_value_l = 0.0_wp
2632	pts_value_l(:,16) = 9999999.9_wp ! for calculation of minimum radius
2633
2634	!
2635	!-- Calculate or collect the particle time series quantities for all particles
2636	!-- and seperately for each particle group (if there is more than one group)
2637	DO i = nxl, nxr
2638	DO j = nys, nyn
2639	DO k = nzb, nzt
2640	number_of_particles = prt_count(k,j,i)
2641	IF (number_of_particles <= 0) CYCLE
2642	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2643	DO n = 1, number_of_particles
2644
2645	IF ( particles(n)%particle_mask ) THEN ! Restrict analysis to active particles
2646
2647	pts_value_l(0,1) = pts_value_l(0,1) + 1.0_wp ! total # of particles
2648	pts_value_l(0,2) = pts_value_l(0,2) + &
2649	( particles(n)%x - particles(n)%origin_x ) ! mean x
2650	pts_value_l(0,3) = pts_value_l(0,3) + &
2651	( particles(n)%y - particles(n)%origin_y ) ! mean y
2652	pts_value_l(0,4) = pts_value_l(0,4) + &
2653	( particles(n)%z - particles(n)%origin_z ) ! mean z
2654	pts_value_l(0,5) = pts_value_l(0,5) + particles(n)%z ! mean z (absolute)
2655	pts_value_l(0,6) = pts_value_l(0,6) + particles(n)%speed_x ! mean u
2656	pts_value_l(0,7) = pts_value_l(0,7) + particles(n)%speed_y ! mean v
2657	pts_value_l(0,8) = pts_value_l(0,8) + particles(n)%speed_z ! mean w
2658	pts_value_l(0,9) = pts_value_l(0,9) + particles(n)%rvar1 ! mean sgsu
2659	pts_value_l(0,10) = pts_value_l(0,10) + particles(n)%rvar2 ! mean sgsv
2660	pts_value_l(0,11) = pts_value_l(0,11) + particles(n)%rvar3 ! mean sgsw
2661	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2662	pts_value_l(0,12) = pts_value_l(0,12) + 1.0_wp ! # of upward moving prts
2663	pts_value_l(0,13) = pts_value_l(0,13) + &
2664	particles(n)%speed_z ! mean w upw.
2665	ELSE
2666	pts_value_l(0,14) = pts_value_l(0,14) + &
2667	particles(n)%speed_z ! mean w down
2668	ENDIF
2669	pts_value_l(0,15) = pts_value_l(0,15) + particles(n)%radius ! mean rad
2670	pts_value_l(0,16) = MIN( pts_value_l(0,16), particles(n)%radius ) ! minrad
2671	pts_value_l(0,17) = MAX( pts_value_l(0,17), particles(n)%radius ) ! maxrad
2672	pts_value_l(0,18) = pts_value_l(0,18) + 1.0_wp
2673	pts_value_l(0,19) = pts_value_l(0,18) + 1.0_wp
2674	!
2675	!-- Repeat the same for the respective particle group
2676	IF ( number_of_particle_groups > 1 ) THEN
2677	jg = particles(n)%group
2678
2679	pts_value_l(jg,1) = pts_value_l(jg,1) + 1.0_wp
2680	pts_value_l(jg,2) = pts_value_l(jg,2) + &
2681	( particles(n)%x - particles(n)%origin_x )
2682	pts_value_l(jg,3) = pts_value_l(jg,3) + &
2683	( particles(n)%y - particles(n)%origin_y )
2684	pts_value_l(jg,4) = pts_value_l(jg,4) + &
2685	( particles(n)%z - particles(n)%origin_z )
2686	pts_value_l(jg,5) = pts_value_l(jg,5) + particles(n)%z
2687	pts_value_l(jg,6) = pts_value_l(jg,6) + particles(n)%speed_x
2688	pts_value_l(jg,7) = pts_value_l(jg,7) + particles(n)%speed_y
2689	pts_value_l(jg,8) = pts_value_l(jg,8) + particles(n)%speed_z
2690	pts_value_l(jg,9) = pts_value_l(jg,9) + particles(n)%rvar1
2691	pts_value_l(jg,10) = pts_value_l(jg,10) + particles(n)%rvar2
2692	pts_value_l(jg,11) = pts_value_l(jg,11) + particles(n)%rvar3
2693	IF ( particles(n)%speed_z > 0.0_wp ) THEN
2694	pts_value_l(jg,12) = pts_value_l(jg,12) + 1.0_wp
2695	pts_value_l(jg,13) = pts_value_l(jg,13) + particles(n)%speed_z
2696	ELSE
2697	pts_value_l(jg,14) = pts_value_l(jg,14) + particles(n)%speed_z
2698	ENDIF
2699	pts_value_l(jg,15) = pts_value_l(jg,15) + particles(n)%radius
2700	pts_value_l(jg,16) = MIN( pts_value(jg,16), particles(n)%radius )
2701	pts_value_l(jg,17) = MAX( pts_value(jg,17), particles(n)%radius )
2702	pts_value_l(jg,18) = pts_value_l(jg,18) + 1.0_wp
2703	pts_value_l(jg,19) = pts_value_l(jg,19) + 1.0_wp
2704	ENDIF
2705
2706	ENDIF
2707
2708	ENDDO
2709
2710	ENDDO
2711	ENDDO
2712	ENDDO
2713
2714
2715	#if defined( __parallel )
2716	!
2717	!-- Sum values of the subdomains
2718	inum = number_of_particle_groups + 1
2719
2720	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2721	CALL MPI_ALLREDUCE( pts_value_l(0,1), pts_value(0,1), 15*inum, MPI_REAL, &
2722	MPI_SUM, comm2d, ierr )
2723	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2724	CALL MPI_ALLREDUCE( pts_value_l(0,16), pts_value(0,16), inum, MPI_REAL, &
2725	MPI_MIN, comm2d, ierr )
2726	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2727	CALL MPI_ALLREDUCE( pts_value_l(0,17), pts_value(0,17), inum, MPI_REAL, &
2728	MPI_MAX, comm2d, ierr )
2729	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2730	CALL MPI_ALLREDUCE( pts_value_l(0,18), pts_value(0,18), inum, MPI_REAL, &
2731	MPI_MAX, comm2d, ierr )
2732	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2733	CALL MPI_ALLREDUCE( pts_value_l(0,19), pts_value(0,19), inum, MPI_REAL, &
2734	MPI_MIN, comm2d, ierr )
2735	#else
2736	pts_value(:,1:19) = pts_value_l(:,1:19)
2737	#endif
2738
2739	!
2740	!-- Normalize the above calculated quantities (except min/max values) with the
2741	!-- total number of particles
2742	IF ( number_of_particle_groups > 1 ) THEN
2743	inum = number_of_particle_groups
2744	ELSE
2745	inum = 0
2746	ENDIF
2747
2748	DO j = 0, inum
2749
2750	IF ( pts_value(j,1) > 0.0_wp ) THEN
2751
2752	pts_value(j,2:15) = pts_value(j,2:15) / pts_value(j,1)
2753	IF ( pts_value(j,12) > 0.0_wp .AND. pts_value(j,12) < 1.0_wp ) THEN
2754	pts_value(j,13) = pts_value(j,13) / pts_value(j,12)
2755	pts_value(j,14) = pts_value(j,14) / ( 1.0_wp - pts_value(j,12) )
2756	ELSEIF ( pts_value(j,12) == 0.0_wp ) THEN
2757	pts_value(j,13) = -1.0_wp
2758	ELSE
2759	pts_value(j,14) = -1.0_wp
2760	ENDIF
2761
2762	ENDIF
2763
2764	ENDDO
2765
2766	!
2767	!-- Calculate higher order moments of particle time series quantities,
2768	!-- seperately for each particle group (if there is more than one group)
2769	DO i = nxl, nxr
2770	DO j = nys, nyn
2771	DO k = nzb, nzt
2772	number_of_particles = prt_count(k,j,i)
2773	IF (number_of_particles <= 0) CYCLE
2774	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
2775	DO n = 1, number_of_particles
2776
2777	pts_value_l(0,20) = pts_value_l(0,20) + ( particles(n)%x - &
2778	particles(n)%origin_x - pts_value(0,2) )*2 ! x2
2779	pts_value_l(0,21) = pts_value_l(0,21) + ( particles(n)%y - &
2780	particles(n)%origin_y - pts_value(0,3) )*2 ! y2
2781	pts_value_l(0,22) = pts_value_l(0,22) + ( particles(n)%z - &
2782	particles(n)%origin_z - pts_value(0,4) )*2 ! z2
2783	pts_value_l(0,23) = pts_value_l(0,23) + ( particles(n)%speed_x - &
2784	pts_value(0,6) )*2 ! u2
2785	pts_value_l(0,24) = pts_value_l(0,24) + ( particles(n)%speed_y - &
2786	pts_value(0,7) )*2 ! v2
2787	pts_value_l(0,25) = pts_value_l(0,25) + ( particles(n)%speed_z - &
2788	pts_value(0,8) )*2 ! w2
2789	pts_value_l(0,26) = pts_value_l(0,26) + ( particles(n)%rvar1 - &
2790	pts_value(0,9) )**2 ! u"2
2791	pts_value_l(0,27) = pts_value_l(0,27) + ( particles(n)%rvar2 - &
2792	pts_value(0,10) )**2 ! v"2
2793	pts_value_l(0,28) = pts_value_l(0,28) + ( particles(n)%rvar3 - &
2794	pts_value(0,11) )**2 ! w"2
2795	!
2796	!-- Repeat the same for the respective particle group
2797	IF ( number_of_particle_groups > 1 ) THEN
2798	jg = particles(n)%group
2799
2800	pts_value_l(jg,20) = pts_value_l(jg,20) + ( particles(n)%x - &
2801	particles(n)%origin_x - pts_value(jg,2) )**2
2802	pts_value_l(jg,21) = pts_value_l(jg,21) + ( particles(n)%y - &
2803	particles(n)%origin_y - pts_value(jg,3) )**2
2804	pts_value_l(jg,22) = pts_value_l(jg,22) + ( particles(n)%z - &
2805	particles(n)%origin_z - pts_value(jg,4) )**2
2806	pts_value_l(jg,23) = pts_value_l(jg,23) + ( particles(n)%speed_x - &
2807	pts_value(jg,6) )**2
2808	pts_value_l(jg,24) = pts_value_l(jg,24) + ( particles(n)%speed_y - &
2809	pts_value(jg,7) )**2
2810	pts_value_l(jg,25) = pts_value_l(jg,25) + ( particles(n)%speed_z - &
2811	pts_value(jg,8) )**2
2812	pts_value_l(jg,26) = pts_value_l(jg,26) + ( particles(n)%rvar1 - &
2813	pts_value(jg,9) )**2
2814	pts_value_l(jg,27) = pts_value_l(jg,27) + ( particles(n)%rvar2 - &
2815	pts_value(jg,10) )**2
2816	pts_value_l(jg,28) = pts_value_l(jg,28) + ( particles(n)%rvar3 - &
2817	pts_value(jg,11) )**2
2818	ENDIF
2819
2820	ENDDO
2821	ENDDO
2822	ENDDO
2823	ENDDO
2824
2825	pts_value_l(0,29) = ( number_of_particles - pts_value(0,1) / numprocs )**2
2826	! variance of particle numbers
2827	IF ( number_of_particle_groups > 1 ) THEN
2828	DO j = 1, number_of_particle_groups
2829	pts_value_l(j,29) = ( pts_value_l(j,1) - &
2830	pts_value(j,1) / numprocs )**2
2831	ENDDO
2832	ENDIF
2833
2834	#if defined( __parallel )
2835	!
2836	!-- Sum values of the subdomains
2837	inum = number_of_particle_groups + 1
2838
2839	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
2840	CALL MPI_ALLREDUCE( pts_value_l(0,20), pts_value(0,20), inum*10, MPI_REAL, &
2841	MPI_SUM, comm2d, ierr )
2842	#else
2843	pts_value(:,20:29) = pts_value_l(:,20:29)
2844	#endif
2845
2846	!
2847	!-- Normalize the above calculated quantities with the total number of
2848	!-- particles
2849	IF ( number_of_particle_groups > 1 ) THEN
2850	inum = number_of_particle_groups
2851	ELSE
2852	inum = 0
2853	ENDIF
2854
2855	DO j = 0, inum
2856
2857	IF ( pts_value(j,1) > 0.0_wp ) THEN
2858	pts_value(j,20:28) = pts_value(j,20:28) / pts_value(j,1)
2859	ENDIF
2860	pts_value(j,29) = pts_value(j,29) / numprocs
2861
2862	ENDDO
2863
2864	#if defined( __netcdf )
2865	!
2866	!-- Output particle time series quantities in NetCDF format
2867	IF ( myid == 0 ) THEN
2868	DO j = 0, inum
2869	DO i = 1, dopts_num
2870	nc_stat = NF90_PUT_VAR( id_set_pts, id_var_dopts(i,j), &
2871	(/ pts_value(j,i) /), &
2872	start = (/ dopts_time_count /), &
2873	count = (/ 1 /) )
2874	CALL netcdf_handle_error( 'data_output_ptseries', 392 )
2875	ENDDO
2876	ENDDO
2877	ENDIF
2878	#endif
2879
2880	DEALLOCATE( pts_value, pts_value_l )
2881
2882	CALL cpu_log( log_point(36), 'data_output_ptseries', 'stop' )
2883
2884	END SUBROUTINE lpm_data_output_ptseries
2885
2886
2887	!------------------------------------------------------------------------------!
2888	! Description:
2889	! ------------
2890	!> This routine reads the respective restart data for the lpm.
2891	!------------------------------------------------------------------------------!
2892	SUBROUTINE lpm_rrd_local_particles
2893
2894	CHARACTER (LEN=10) :: particle_binary_version !<
2895	CHARACTER (LEN=10) :: version_on_file !<
2896
2897	INTEGER(iwp) :: alloc_size !<
2898	INTEGER(iwp) :: ip !<
2899	INTEGER(iwp) :: jp !<
2900	INTEGER(iwp) :: kp !<
2901
2902	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles !<
2903
2904	!
2905	!-- Read particle data from previous model run.
2906	!-- First open the input unit.
2907	IF ( myid_char == '' ) THEN
2908	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN'//myid_char, &
2909	FORM='UNFORMATTED' )
2910	ELSE
2911	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_IN/'//myid_char, &
2912	FORM='UNFORMATTED' )
2913	ENDIF
2914
2915	!
2916	!-- First compare the version numbers
2917	READ ( 90 ) version_on_file
2918	particle_binary_version = '4.0'
2919	IF ( TRIM( version_on_file ) /= TRIM( particle_binary_version ) ) THEN
2920	message_string = 'version mismatch concerning data from prior ' // &
2921	'run &version on file = "' // &
2922	TRIM( version_on_file ) // &
2923	'&version in program = "' // &
2924	TRIM( particle_binary_version ) // '"'
2925	CALL message( 'lpm_read_restart_file', 'PA0214', 1, 2, 0, 6, 0 )
2926	ENDIF
2927
2928	!
2929	!-- If less particles are stored on the restart file than prescribed by
2930	!-- 1, the remainder is initialized by zero_particle to avoid
2931	!-- errors.
2932	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2933	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2934	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2935	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
2936	0, 0, 0_idp, .FALSE., -1 )
2937	!
2938	!-- Read some particle parameters and the size of the particle arrays,
2939	!-- allocate them and read their contents.
2940	READ ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
2941	last_particle_release_time, number_of_particle_groups, &
2942	particle_groups, time_write_particle_data
2943
2944	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
2945	grid_particles(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
2946
2947	READ ( 90 ) prt_count
2948
2949	DO ip = nxl, nxr
2950	DO jp = nys, nyn
2951	DO kp = nzb+1, nzt
2952
2953	number_of_particles = prt_count(kp,jp,ip)
2954	IF ( number_of_particles > 0 ) THEN
2955	alloc_size = MAX( INT( number_of_particles * &
2956	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
2957	1 )
2958	ELSE
2959	alloc_size = 1
2960	ENDIF
2961
2962	ALLOCATE( grid_particles(kp,jp,ip)%particles(1:alloc_size) )
2963
2964	IF ( number_of_particles > 0 ) THEN
2965	ALLOCATE( tmp_particles(1:number_of_particles) )
2966	READ ( 90 ) tmp_particles
2967	grid_particles(kp,jp,ip)%particles(1:number_of_particles) = tmp_particles
2968	DEALLOCATE( tmp_particles )
2969	IF ( number_of_particles < alloc_size ) THEN
2970	grid_particles(kp,jp,ip)%particles(number_of_particles+1:alloc_size) &
2971	= zero_particle
2972	ENDIF
2973	ELSE
2974	grid_particles(kp,jp,ip)%particles(1:alloc_size) = zero_particle
2975	ENDIF
2976
2977	ENDDO
2978	ENDDO
2979	ENDDO
2980
2981	CLOSE ( 90 )
2982	!
2983	!-- Must be called to sort particles into blocks, which is needed for a fast
2984	!-- interpolation of the LES fields on the particle position.
2985	CALL lpm_sort_and_delete
2986
2987
2988	END SUBROUTINE lpm_rrd_local_particles
2989
2990
2991	SUBROUTINE lpm_rrd_local( k, nxlf, nxlc, nxl_on_file, nxrf, nxrc, &
2992	nxr_on_file, nynf, nync, nyn_on_file, nysf, &
2993	nysc, nys_on_file, tmp_3d, found )
2994
2995
2996	USE control_parameters, &
2997	ONLY: length, restart_string
2998
2999	INTEGER(iwp) :: k !<
3000	INTEGER(iwp) :: nxlc !<
3001	INTEGER(iwp) :: nxlf !<
3002	INTEGER(iwp) :: nxl_on_file !<
3003	INTEGER(iwp) :: nxrc !<
3004	INTEGER(iwp) :: nxrf !<
3005	INTEGER(iwp) :: nxr_on_file !<
3006	INTEGER(iwp) :: nync !<
3007	INTEGER(iwp) :: nynf !<
3008	INTEGER(iwp) :: nyn_on_file !<
3009	INTEGER(iwp) :: nysc !<
3010	INTEGER(iwp) :: nysf !<
3011	INTEGER(iwp) :: nys_on_file !<
3012
3013	LOGICAL, INTENT(OUT) :: found
3014
3015	REAL(wp), DIMENSION(nzb:nzt+1,nys_on_file-nbgp:nyn_on_file+nbgp,nxl_on_file-nbgp:nxr_on_file+nbgp) :: tmp_3d !<
3016
3017
3018	found = .TRUE.
3019
3020	SELECT CASE ( restart_string(1:length) )
3021
3022	CASE ( 'iran' ) ! matching random numbers is still unresolved issue
3023	IF ( k == 1 ) READ ( 13 ) iran, iran_part
3024
3025	CASE ( 'pc_av' )
3026	IF ( .NOT. ALLOCATED( pc_av ) ) THEN
3027	ALLOCATE( pc_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3028	ENDIF
3029	IF ( k == 1 ) READ ( 13 ) tmp_3d
3030	pc_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3031	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3032
3033	CASE ( 'pr_av' )
3034	IF ( .NOT. ALLOCATED( pr_av ) ) THEN
3035	ALLOCATE( pr_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3036	ENDIF
3037	IF ( k == 1 ) READ ( 13 ) tmp_3d
3038	pr_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3039	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3040
3041	CASE ( 'ql_c_av' )
3042	IF ( .NOT. ALLOCATED( ql_c_av ) ) THEN
3043	ALLOCATE( ql_c_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3044	ENDIF
3045	IF ( k == 1 ) READ ( 13 ) tmp_3d
3046	ql_c_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3047	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3048
3049	CASE ( 'ql_v_av' )
3050	IF ( .NOT. ALLOCATED( ql_v_av ) ) THEN
3051	ALLOCATE( ql_v_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3052	ENDIF
3053	IF ( k == 1 ) READ ( 13 ) tmp_3d
3054	ql_v_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3055	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3056
3057	CASE ( 'ql_vp_av' )
3058	IF ( .NOT. ALLOCATED( ql_vp_av ) ) THEN
3059	ALLOCATE( ql_vp_av(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
3060	ENDIF
3061	IF ( k == 1 ) READ ( 13 ) tmp_3d
3062	ql_vp_av(:,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
3063	tmp_3d(:,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)
3064
3065	CASE DEFAULT
3066
3067	found = .FALSE.
3068
3069	END SELECT
3070
3071
3072	END SUBROUTINE lpm_rrd_local
3073
3074	!------------------------------------------------------------------------------!
3075	! Description:
3076	! ------------
3077	!> This routine writes the respective restart data for the lpm.
3078	!------------------------------------------------------------------------------!
3079	SUBROUTINE lpm_wrd_local
3080
3081	CHARACTER (LEN=10) :: particle_binary_version !<
3082
3083	INTEGER(iwp) :: ip !<
3084	INTEGER(iwp) :: jp !<
3085	INTEGER(iwp) :: kp !<
3086	!
3087	!-- First open the output unit.
3088	IF ( myid_char == '' ) THEN
3089	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT'//myid_char, &
3090	FORM='UNFORMATTED')
3091	ELSE
3092	IF ( myid == 0 ) CALL local_system( 'mkdir PARTICLE_RESTART_DATA_OUT' )
3093	#if defined( __parallel )
3094	!
3095	!-- Set a barrier in order to allow that thereafter all other processors
3096	!-- in the directory created by PE0 can open their file
3097	CALL MPI_BARRIER( comm2d, ierr )
3098	#endif
3099	OPEN ( 90, FILE='PARTICLE_RESTART_DATA_OUT/'//myid_char, &
3100	FORM='UNFORMATTED' )
3101	ENDIF
3102
3103	!
3104	!-- Write the version number of the binary format.
3105	!-- Attention: After changes to the following output commands the version
3106	!-- --------- number of the variable particle_binary_version must be
3107	!-- changed! Also, the version number and the list of arrays
3108	!-- to be read in lpm_read_restart_file must be adjusted
3109	!-- accordingly.
3110	particle_binary_version = '4.0'
3111	WRITE ( 90 ) particle_binary_version
3112
3113	!
3114	!-- Write some particle parameters, the size of the particle arrays
3115	WRITE ( 90 ) bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
3116	last_particle_release_time, number_of_particle_groups, &
3117	particle_groups, time_write_particle_data
3118
3119	WRITE ( 90 ) prt_count
3120
3121	DO ip = nxl, nxr
3122	DO jp = nys, nyn
3123	DO kp = nzb+1, nzt
3124	number_of_particles = prt_count(kp,jp,ip)
3125	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
3126	IF ( number_of_particles <= 0 ) CYCLE
3127	WRITE ( 90 ) particles
3128	ENDDO
3129	ENDDO
3130	ENDDO
3131
3132	CLOSE ( 90 )
3133
3134	#if defined( __parallel )
3135	CALL MPI_BARRIER( comm2d, ierr )
3136	#endif
3137
3138	CALL wrd_write_string( 'iran' )
3139	WRITE ( 14 ) iran, iran_part
3140
3141
3142	END SUBROUTINE lpm_wrd_local
3143
3144
3145	!------------------------------------------------------------------------------!
3146	! Description:
3147	! ------------
3148	!> This routine writes the respective restart data for the lpm.
3149	!------------------------------------------------------------------------------!
3150	SUBROUTINE lpm_wrd_global
3151
3152	CALL wrd_write_string( 'curvature_solution_effects' )
3153	WRITE ( 14 ) curvature_solution_effects
3154
3155	CALL wrd_write_string( 'interpolation_simple_corrector' )
3156	WRITE ( 14 ) interpolation_simple_corrector
3157
3158	CALL wrd_write_string( 'interpolation_simple_predictor' )
3159	WRITE ( 14 ) interpolation_simple_predictor
3160
3161	CALL wrd_write_string( 'interpolation_trilinear' )
3162	WRITE ( 14 ) interpolation_trilinear
3163
3164	END SUBROUTINE lpm_wrd_global
3165
3166
3167	!------------------------------------------------------------------------------!
3168	! Description:
3169	! ------------
3170	!> This routine writes the respective restart data for the lpm.
3171	!------------------------------------------------------------------------------!
3172	SUBROUTINE lpm_rrd_global( found )
3173
3174	USE control_parameters, &
3175	ONLY: length, restart_string
3176
3177	LOGICAL, INTENT(OUT) :: found
3178
3179	found = .TRUE.
3180
3181	SELECT CASE ( restart_string(1:length) )
3182
3183	CASE ( 'curvature_solution_effects' )
3184	READ ( 13 ) curvature_solution_effects
3185
3186	CASE ( 'interpolation_simple_corrector' )
3187	READ ( 13 ) interpolation_simple_corrector
3188
3189	CASE ( 'interpolation_simple_predictor' )
3190	READ ( 13 ) interpolation_simple_predictor
3191
3192	CASE ( 'interpolation_trilinear' )
3193	READ ( 13 ) interpolation_trilinear
3194
3195	! CASE ( 'global_paramter' )
3196	! READ ( 13 ) global_parameter
3197	! CASE ( 'global_array' )
3198	! IF ( .NOT. ALLOCATED( global_array ) ) ALLOCATE( global_array(1:10) )
3199	! READ ( 13 ) global_array
3200
3201	CASE DEFAULT
3202
3203	found = .FALSE.
3204
3205	END SELECT
3206
3207	END SUBROUTINE lpm_rrd_global
3208
3209
3210	!------------------------------------------------------------------------------!
3211	! Description:
3212	! ------------
3213	!> This is a submodule of the lagrangian particle model. It contains all
3214	!> dynamic processes of the lpm. This includes the advection (resolved and sub-
3215	!> grid scale) as well as the boundary conditions of particles. As a next step
3216	!> this submodule should be excluded as an own file.
3217	!------------------------------------------------------------------------------!
3218	SUBROUTINE lpm_advec (ip,jp,kp)
3219
3220	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
3221
3222	INTEGER(iwp) :: i !< index variable along x
3223	INTEGER(iwp) :: i_next !< index variable along x
3224	INTEGER(iwp) :: ip !< index variable along x
3225	INTEGER(iwp) :: iteration_steps = 1 !< amount of iterations steps for corrector step
3226	INTEGER(iwp) :: j !< index variable along y
3227	INTEGER(iwp) :: j_next !< index variable along y
3228	INTEGER(iwp) :: jp !< index variable along y
3229	INTEGER(iwp) :: k !< index variable along z
3230	INTEGER(iwp) :: k_wall !< vertical index of topography top
3231	INTEGER(iwp) :: kp !< index variable along z
3232	INTEGER(iwp) :: k_next !< index variable along z
3233	INTEGER(iwp) :: kw !< index variable along z
3234	INTEGER(iwp) :: kkw !< index variable along z
3235	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
3236	INTEGER(iwp) :: nb !< block number particles are sorted in
3237	INTEGER(iwp) :: particle_end !< end index for partilce loop
3238	INTEGER(iwp) :: particle_start !< start index for particle loop
3239	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
3240	INTEGER(iwp) :: subbox_end !< end index for loop over subboxes in particle advection
3241	INTEGER(iwp) :: subbox_start !< start index for loop over subboxes in particle advection
3242	INTEGER(iwp) :: nn !< loop variable over iterations steps
3243
3244	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
3245	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
3246
3247	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
3248	REAL(wp) :: alpha !< interpolation facor for x-direction
3249
3250	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
3251	REAL(wp) :: beta !< interpolation facor for y-direction
3252	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
3253	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
3254	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
3255	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
3256	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
3257	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
3258	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
3259	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
3260	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
3261	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
3262	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
3263	REAL(wp) :: diameter !< diamter of droplet
3264	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
3265	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
3266	REAL(wp) :: dt_particle_m !< previous particle time step
3267	REAL(wp) :: dz_temp !< dummy for the vertical grid spacing
3268	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
3269	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
3270	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
3271	REAL(wp) :: exp_arg !< argument in the exponent - particle radius
3272	REAL(wp) :: exp_term !< exponent term
3273	REAL(wp) :: gamma !< interpolation facor for z-direction
3274	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
3275	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
3276	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
3277	REAL(wp) :: random_gauss !< Gaussian-distributed random number used for SGS particle advection
3278	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
3279	REAL(wp) :: rg1 !< Gaussian distributed random number
3280	REAL(wp) :: rg2 !< Gaussian distributed random number
3281	REAL(wp) :: rg3 !< Gaussian distributed random number
3282	REAL(wp) :: sigma !< velocity standard deviation
3283	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
3284	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
3285	REAL(wp) :: unext !< calculated particle u-velocity of corrector step
3286	REAL(wp) :: us_int !< friction velocity at particle grid box
3287	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
3288	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
3289	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
3290	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
3291	REAL(wp) :: vnext !< calculated particle v-velocity of corrector step
3292	REAL(wp) :: vv_int !< dummy to compute interpolated mean SGS TKE, used to scale SGS advection
3293	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
3294	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
3295	REAL(wp) :: wnext !< calculated particle w-velocity of corrector step
3296	REAL(wp) :: w_s !< terminal velocity of droplets
3297	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
3298	REAL(wp) :: xp !< calculated particle position in x of predictor step
3299	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
3300	REAL(wp) :: yp !< calculated particle position in y of predictor step
3301	REAL(wp) :: z_p !< surface layer height (0.5 dz)
3302	REAL(wp) :: zp !< calculated particle position in z of predictor step
3303
3304	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
3305	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
3306	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
3307	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
3308	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
3309	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
3310
3311	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
3312	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !< ratio between the density of the fluid and the density of the particles
3313	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
3314	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
3315	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
3316	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
3317	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
3318	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
3319	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
3320	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
3321	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
3322	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !< SGS particle velocity - u-component
3323	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !< SGS particle velocity - v-component
3324	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !< SGS particle velocity - w-component
3325	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
3326	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
3327	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
3328	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
3329	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
3330	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
3331
3332	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
3333
3334	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
3335	!
3336	!-- Determine height of Prandtl layer and distance between Prandtl-layer
3337	!-- height and horizontal mean roughness height, which are required for
3338	!-- vertical logarithmic interpolation of horizontal particle speeds
3339	!-- (for particles below first vertical grid level).
3340	z_p = zu(nzb+1) - zw(nzb)
3341	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
3342
3343	xv = particles(1:number_of_particles)%x
3344	yv = particles(1:number_of_particles)%y
3345	zv = particles(1:number_of_particles)%z
3346	dt_particle = dt_3d
3347
3348	!
3349	!-- This case uses a simple interpolation method for the particle velocites,
3350	!-- and applying a predictor-corrector method. @attention: for the corrector
3351	!-- step the velocities of t(n+1) are required. However, at this moment of
3352	!-- the time integration they are not free of divergence. This interpolation
3353	!-- method is described in more detail in Grabowski et al., 2018 (GMD).
3354	IF ( interpolation_simple_corrector ) THEN
3355	!
3356	!-- Predictor step
3357	kkw = kp - 1
3358	DO n = 1, number_of_particles
3359
3360	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3361	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3362
3363	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3364	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3365
3366	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3367	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3368	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3369
3370	ENDDO
3371	!
3372	!-- Corrector step
3373	DO n = 1, number_of_particles
3374
3375	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3376
3377	DO nn = 1, iteration_steps
3378
3379	!
3380	!-- Guess new position
3381	xp = particles(n)%x + u_int(n) * dt_particle(n)
3382	yp = particles(n)%y + v_int(n) * dt_particle(n)
3383	zp = particles(n)%z + w_int(n) * dt_particle(n)
3384	!
3385	!-- x direction
3386	i_next = FLOOR( xp * ddx , KIND=iwp)
3387	alpha = MAX( MIN( ( xp - i_next * dx ) * ddx, 1.0_wp ), 0.0_wp )
3388	!
3389	!-- y direction
3390	j_next = FLOOR( yp * ddy )
3391	beta = MAX( MIN( ( yp - j_next * dy ) * ddy, 1.0_wp ), 0.0_wp )
3392	!
3393	!-- z_direction
3394	k_next = MAX( MIN( FLOOR( zp / (zw(kkw+1)-zw(kkw)) ), nzt ), 0)
3395	gamma = MAX( MIN( ( zp - zw(k_next) ) / &
3396	( zw(k_next+1) - zw(k_next) ), 1.0_wp ), 0.0_wp )
3397	!
3398	!-- Calculate part of the corrector step
3399	unext = u_p(k_next+1, j_next, i_next) * ( 1.0_wp - alpha ) + &
3400	u_p(k_next+1, j_next, i_next+1) * alpha
3401
3402	vnext = v_p(k_next+1, j_next, i_next) * ( 1.0_wp - beta ) + &
3403	v_p(k_next+1, j_next+1, i_next ) * beta
3404
3405	wnext = w_p(k_next, j_next, i_next) * ( 1.0_wp - gamma ) + &
3406	w_p(k_next+1, j_next, i_next ) * gamma
3407
3408	!
3409	!-- Calculate interpolated particle velocity with predictor
3410	!-- corrector step. u_int, v_int and w_int describes the part of
3411	!-- the predictor step. unext, vnext and wnext is the part of the
3412	!-- corrector step. The resulting new position is set below. The
3413	!-- implementation is based on Grabowski et al., 2018 (GMD).
3414	u_int(n) = 0.5_wp * ( u_int(n) + unext )
3415	v_int(n) = 0.5_wp * ( v_int(n) + vnext )
3416	w_int(n) = 0.5_wp * ( w_int(n) + wnext )
3417
3418	ENDDO
3419	ENDDO
3420	!
3421	!-- This case uses a simple interpolation method for the particle velocites,
3422	!-- and applying a predictor.
3423	ELSEIF ( interpolation_simple_predictor ) THEN
3424	!
3425	!-- The particle position for the w velociy is based on the value of kp and kp-1
3426	kkw = kp - 1
3427	DO n = 1, number_of_particles
3428	IF ( .NOT. particles(n)%particle_mask ) CYCLE
3429
3430	alpha = MAX( MIN( ( particles(n)%x - ip * dx ) * ddx, 1.0_wp ), 0.0_wp )
3431	u_int(n) = u(kp,jp,ip) * ( 1.0_wp - alpha ) + u(kp,jp,ip+1) * alpha
3432
3433	beta = MAX( MIN( ( particles(n)%y - jp * dy ) * ddy, 1.0_wp ), 0.0_wp )
3434	v_int(n) = v(kp,jp,ip) * ( 1.0_wp - beta ) + v(kp,jp+1,ip) * beta
3435
3436	gamma = MAX( MIN( ( particles(n)%z - zw(kkw) ) / &
3437	( zw(kkw+1) - zw(kkw) ), 1.0_wp ), 0.0_wp )
3438	w_int(n) = w(kkw,jp,ip) * ( 1.0_wp - gamma ) + w(kkw+1,jp,ip) * gamma
3439	ENDDO
3440	!
3441	!-- The trilinear interpolation.
3442	ELSEIF ( interpolation_trilinear ) THEN
3443
3444	start_index = grid_particles(kp,jp,ip)%start_index
3445	end_index = grid_particles(kp,jp,ip)%end_index
3446
3447	DO nb = 0, 7
3448	!
3449	!-- Interpolate u velocity-component
3450	i = ip
3451	j = jp + block_offset(nb)%j_off
3452	k = kp + block_offset(nb)%k_off
3453
3454	DO n = start_index(nb), end_index(nb)
3455	!
3456	!-- Interpolation of the u velocity component onto particle position.
3457	!-- Particles are interpolation bi-linearly in the horizontal and a
3458	!-- linearly in the vertical. An exception is made for particles below
3459	!-- the first vertical grid level in case of a prandtl layer. In this
3460	!-- case the horizontal particle velocity components are determined using
3461	!-- Monin-Obukhov relations (if branch).
3462	!-- First, check if particle is located below first vertical grid level
3463	!-- above topography (Prandtl-layer height)
3464	!-- Determine vertical index of topography top
3465	k_wall = get_topography_top_index_ji( jp, ip, 's' )
3466
3467	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3468	!
3469	!-- Resolved-scale horizontal particle velocity is zero below z0.
3470	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3471	u_int(n) = 0.0_wp
3472	ELSE
3473	!
3474	!-- Determine the sublayer. Further used as index.
3475	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3476	* REAL( number_of_sublayers, KIND=wp ) &
3477	* d_z_p_z0
3478	!
3479	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3480	!-- interpolate linearly between precalculated logarithm.
3481	log_z_z0_int = log_z_z0(INT(height_p)) &
3482	+ ( height_p - INT(height_p) ) &
3483	* ( log_z_z0(INT(height_p)+1) &
3484	- log_z_z0(INT(height_p)) &
3485	)
3486	!
3487	!-- Get friction velocity and momentum flux from new surface data
3488	!-- types.
3489	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3490	surf_def_h(0)%end_index(jp,ip) ) THEN
3491	surf_start = surf_def_h(0)%start_index(jp,ip)
3492	!-- Limit friction velocity. In narrow canyons or holes the
3493	!-- friction velocity can become very small, resulting in a too
3494	!-- large particle speed.
3495	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3496	usws_int = surf_def_h(0)%usws(surf_start)
3497	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3498	surf_lsm_h%end_index(jp,ip) ) THEN
3499	surf_start = surf_lsm_h%start_index(jp,ip)
3500	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3501	usws_int = surf_lsm_h%usws(surf_start)
3502	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3503	surf_usm_h%end_index(jp,ip) ) THEN
3504	surf_start = surf_usm_h%start_index(jp,ip)
3505	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3506	usws_int = surf_usm_h%usws(surf_start)
3507	ENDIF
3508	!
3509	!-- Neutral solution is applied for all situations, e.g. also for
3510	!-- unstable and stable situations. Even though this is not exact
3511	!-- this saves a lot of CPU time since several calls of intrinsic
3512	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3513	!-- as sensitivity studies revealed no significant effect of
3514	!-- using the neutral solution also for un/stable situations.
3515	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
3516	* log_z_z0_int - u_gtrans
3517	ENDIF
3518	!
3519	!-- Particle above the first grid level. Bi-linear interpolation in the
3520	!-- horizontal and linear interpolation in the vertical direction.
3521	ELSE
3522	x = xv(n) - i * dx
3523	y = yv(n) + ( 0.5_wp - j ) * dy
3524	aa = x2 + y2
3525	bb = ( dx - x )2 + y2
3526	cc = x2 + ( dy - y )2
3527	dd = ( dx - x )2 + ( dy - y )2
3528	gg = aa + bb + cc + dd
3529
3530	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
3531	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
3532	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3533
3534	IF ( k == nzt ) THEN
3535	u_int(n) = u_int_l
3536	ELSE
3537	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
3538	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
3539	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
3540	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3541	( u_int_u - u_int_l )
3542	ENDIF
3543	ENDIF
3544	ENDDO
3545	!
3546	!-- Same procedure for interpolation of the v velocity-component
3547	i = ip + block_offset(nb)%i_off
3548	j = jp
3549	k = kp + block_offset(nb)%k_off
3550
3551	DO n = start_index(nb), end_index(nb)
3552	!
3553	!-- Determine vertical index of topography top
3554	k_wall = get_topography_top_index_ji( jp,ip, 's' )
3555
3556	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
3557	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
3558	!
3559	!-- Resolved-scale horizontal particle velocity is zero below z0.
3560	v_int(n) = 0.0_wp
3561	ELSE
3562	!
3563	!-- Determine the sublayer. Further used as index. Please note,
3564	!-- logarithmus can not be reused from above, as in in case of
3565	!-- topography particle on u-grid can be above surface-layer height,
3566	!-- whereas it can be below on v-grid.
3567	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
3568	* REAL( number_of_sublayers, KIND=wp ) &
3569	* d_z_p_z0
3570	!
3571	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
3572	!-- interpolate linearly between precalculated logarithm.
3573	log_z_z0_int = log_z_z0(INT(height_p)) &
3574	+ ( height_p - INT(height_p) ) &
3575	* ( log_z_z0(INT(height_p)+1) &
3576	- log_z_z0(INT(height_p)) &
3577	)
3578	!
3579	!-- Get friction velocity and momentum flux from new surface data
3580	!-- types.
3581	IF ( surf_def_h(0)%start_index(jp,ip) <= &
3582	surf_def_h(0)%end_index(jp,ip) ) THEN
3583	surf_start = surf_def_h(0)%start_index(jp,ip)
3584	!-- Limit friction velocity. In narrow canyons or holes the
3585	!-- friction velocity can become very small, resulting in a too
3586	!-- large particle speed.
3587	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
3588	vsws_int = surf_def_h(0)%vsws(surf_start)
3589	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
3590	surf_lsm_h%end_index(jp,ip) ) THEN
3591	surf_start = surf_lsm_h%start_index(jp,ip)
3592	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
3593	vsws_int = surf_lsm_h%vsws(surf_start)
3594	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
3595	surf_usm_h%end_index(jp,ip) ) THEN
3596	surf_start = surf_usm_h%start_index(jp,ip)
3597	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
3598	vsws_int = surf_usm_h%vsws(surf_start)
3599	ENDIF
3600	!
3601	!-- Neutral solution is applied for all situations, e.g. also for
3602	!-- unstable and stable situations. Even though this is not exact
3603	!-- this saves a lot of CPU time since several calls of intrinsic
3604	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
3605	!-- as sensitivity studies revealed no significant effect of
3606	!-- using the neutral solution also for un/stable situations.
3607	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
3608	* log_z_z0_int - v_gtrans
3609
3610	ENDIF
3611	ELSE
3612	x = xv(n) + ( 0.5_wp - i ) * dx
3613	y = yv(n) - j * dy
3614	aa = x2 + y2
3615	bb = ( dx - x )2 + y2
3616	cc = x2 + ( dy - y )2
3617	dd = ( dx - x )2 + ( dy - y )2
3618	gg = aa + bb + cc + dd
3619
3620	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
3621	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
3622	) / ( 3.0_wp * gg ) - v_gtrans
3623
3624	IF ( k == nzt ) THEN
3625	v_int(n) = v_int_l
3626	ELSE
3627	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
3628	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
3629	) / ( 3.0_wp * gg ) - v_gtrans
3630	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3631	( v_int_u - v_int_l )
3632	ENDIF
3633	ENDIF
3634	ENDDO
3635	!
3636	!-- Same procedure for interpolation of the w velocity-component
3637	i = ip + block_offset(nb)%i_off
3638	j = jp + block_offset(nb)%j_off
3639	k = kp - 1
3640
3641	DO n = start_index(nb), end_index(nb)
3642	IF ( vertical_particle_advection(particles(n)%group) ) THEN
3643	x = xv(n) + ( 0.5_wp - i ) * dx
3644	y = yv(n) + ( 0.5_wp - j ) * dy
3645	aa = x2 + y2
3646	bb = ( dx - x )2 + y2
3647	cc = x2 + ( dy - y )2
3648	dd = ( dx - x )2 + ( dy - y )2
3649	gg = aa + bb + cc + dd
3650
3651	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
3652	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
3653	) / ( 3.0_wp * gg )
3654
3655	IF ( k == nzt ) THEN
3656	w_int(n) = w_int_l
3657	ELSE
3658	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
3659	( gg-bb ) * w(k+1,j,i+1) + &
3660	( gg-cc ) * w(k+1,j+1,i) + &
3661	( gg-dd ) * w(k+1,j+1,i+1) &
3662	) / ( 3.0_wp * gg )
3663	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
3664	( w_int_u - w_int_l )
3665	ENDIF
3666	ELSE
3667	w_int(n) = 0.0_wp
3668	ENDIF
3669	ENDDO
3670	ENDDO
3671	ENDIF
3672
3673	!-- Interpolate and calculate quantities needed for calculating the SGS
3674	!-- velocities
3675	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
3676
3677	DO nb = 0,7
3678
3679	subbox_at_wall = .FALSE.
3680	!
3681	!-- In case of topography check if subbox is adjacent to a wall
3682	IF ( .NOT. topography == 'flat' ) THEN
3683	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
3684	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
3685	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
3686	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
3687	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
3688	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
3689	THEN
3690	subbox_at_wall = .TRUE.
3691	ENDIF
3692	ENDIF
3693	IF ( subbox_at_wall ) THEN
3694	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
3695	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
3696	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
3697	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
3698	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
3699	!
3700	!-- Set flag for stochastic equation.
3701	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
3702	ELSE
3703	i = ip + block_offset(nb)%i_off
3704	j = jp + block_offset(nb)%j_off
3705	k = kp + block_offset(nb)%k_off
3706
3707	DO n = start_index(nb), end_index(nb)
3708	!
3709	!-- Interpolate TKE
3710	x = xv(n) + ( 0.5_wp - i ) * dx
3711	y = yv(n) + ( 0.5_wp - j ) * dy
3712	aa = x2 + y2
3713	bb = ( dx - x )2 + y2
3714	cc = x2 + ( dy - y )2
3715	dd = ( dx - x )2 + ( dy - y )2
3716	gg = aa + bb + cc + dd
3717
3718	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
3719	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
3720	) / ( 3.0_wp * gg )
3721
3722	IF ( k+1 == nzt+1 ) THEN
3723	e_int(n) = e_int_l
3724	ELSE
3725	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
3726	( gg - bb ) * e(k+1,j,i+1) + &
3727	( gg - cc ) * e(k+1,j+1,i) + &
3728	( gg - dd ) * e(k+1,j+1,i+1) &
3729	) / ( 3.0_wp * gg )
3730	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3731	( e_int_u - e_int_l )
3732	ENDIF
3733	!
3734	!-- Needed to avoid NaN particle velocities (this might not be
3735	!-- required any more)
3736	IF ( e_int(n) <= 0.0_wp ) THEN
3737	e_int(n) = 1.0E-20_wp
3738	ENDIF
3739	!
3740	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
3741	!-- all position variables from above (TKE))
3742	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
3743	( gg - bb ) * de_dx(k,j,i+1) + &
3744	( gg - cc ) * de_dx(k,j+1,i) + &
3745	( gg - dd ) * de_dx(k,j+1,i+1) &
3746	) / ( 3.0_wp * gg )
3747
3748	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3749	de_dx_int(n) = de_dx_int_l
3750	ELSE
3751	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
3752	( gg - bb ) * de_dx(k+1,j,i+1) + &
3753	( gg - cc ) * de_dx(k+1,j+1,i) + &
3754	( gg - dd ) * de_dx(k+1,j+1,i+1) &
3755	) / ( 3.0_wp * gg )
3756	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3757	( de_dx_int_u - de_dx_int_l )
3758	ENDIF
3759	!
3760	!-- Interpolate the TKE gradient along y
3761	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
3762	( gg - bb ) * de_dy(k,j,i+1) + &
3763	( gg - cc ) * de_dy(k,j+1,i) + &
3764	( gg - dd ) * de_dy(k,j+1,i+1) &
3765	) / ( 3.0_wp * gg )
3766	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3767	de_dy_int(n) = de_dy_int_l
3768	ELSE
3769	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
3770	( gg - bb ) * de_dy(k+1,j,i+1) + &
3771	( gg - cc ) * de_dy(k+1,j+1,i) + &
3772	( gg - dd ) * de_dy(k+1,j+1,i+1) &
3773	) / ( 3.0_wp * gg )
3774	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3775	( de_dy_int_u - de_dy_int_l )
3776	ENDIF
3777
3778	!
3779	!-- Interpolate the TKE gradient along z
3780	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
3781	de_dz_int(n) = 0.0_wp
3782	ELSE
3783	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
3784	( gg - bb ) * de_dz(k,j,i+1) + &
3785	( gg - cc ) * de_dz(k,j+1,i) + &
3786	( gg - dd ) * de_dz(k,j+1,i+1) &
3787	) / ( 3.0_wp * gg )
3788
3789	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
3790	de_dz_int(n) = de_dz_int_l
3791	ELSE
3792	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
3793	( gg - bb ) * de_dz(k+1,j,i+1) + &
3794	( gg - cc ) * de_dz(k+1,j+1,i) + &
3795	( gg - dd ) * de_dz(k+1,j+1,i+1) &
3796	) / ( 3.0_wp * gg )
3797	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3798	( de_dz_int_u - de_dz_int_l )
3799	ENDIF
3800	ENDIF
3801
3802	!
3803	!-- Interpolate the dissipation of TKE
3804	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
3805	( gg - bb ) * diss(k,j,i+1) + &
3806	( gg - cc ) * diss(k,j+1,i) + &
3807	( gg - dd ) * diss(k,j+1,i+1) &
3808	) / ( 3.0_wp * gg )
3809
3810	IF ( k == nzt ) THEN
3811	diss_int(n) = diss_int_l
3812	ELSE
3813	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
3814	( gg - bb ) * diss(k+1,j,i+1) + &
3815	( gg - cc ) * diss(k+1,j+1,i) + &
3816	( gg - dd ) * diss(k+1,j+1,i+1) &
3817	) / ( 3.0_wp * gg )
3818	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
3819	( diss_int_u - diss_int_l )
3820	ENDIF
3821
3822	!
3823	!-- Set flag for stochastic equation.
3824	term_1_2(n) = 1.0_wp
3825	ENDDO
3826	ENDIF
3827	ENDDO
3828
3829	DO nb = 0,7
3830	i = ip + block_offset(nb)%i_off
3831	j = jp + block_offset(nb)%j_off
3832	k = kp + block_offset(nb)%k_off
3833
3834	DO n = start_index(nb), end_index(nb)
3835	!
3836	!-- Vertical interpolation of the horizontally averaged SGS TKE and
3837	!-- resolved-scale velocity variances and use the interpolated values
3838	!-- to calculate the coefficient fs, which is a measure of the ratio
3839	!-- of the subgrid-scale turbulent kinetic energy to the total amount
3840	!-- of turbulent kinetic energy.
3841	IF ( k == 0 ) THEN
3842	e_mean_int = hom(0,1,8,0)
3843	ELSE
3844	e_mean_int = hom(k,1,8,0) + &
3845	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
3846	( zu(k+1) - zu(k) ) * &
3847	( zv(n) - zu(k) )
3848	ENDIF
3849
3850	kw = kp - 1
3851
3852	IF ( k == 0 ) THEN
3853	aa = hom(k+1,1,30,0) * ( zv(n) / &
3854	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3855	bb = hom(k+1,1,31,0) * ( zv(n) / &
3856	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
3857	cc = hom(kw+1,1,32,0) * ( zv(n) / &
3858	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
3859	ELSE
3860	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
3861	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3862	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
3863	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
3864	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
3865	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
3866	ENDIF
3867
3868	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
3869	!
3870	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
3871	!-- an educated guess for the given case.
3872	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
3873	fs_int(n) = 1.0_wp
3874	ELSE
3875	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
3876	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
3877	ENDIF
3878
3879	ENDDO
3880	ENDDO
3881
3882	DO nb = 0, 7
3883	DO n = start_index(nb), end_index(nb)
3884	rg(n,1) = random_gauss( iran_part, 5.0_wp )
3885	rg(n,2) = random_gauss( iran_part, 5.0_wp )
3886	rg(n,3) = random_gauss( iran_part, 5.0_wp )
3887	ENDDO
3888	ENDDO
3889
3890	DO nb = 0, 7
3891	DO n = start_index(nb), end_index(nb)
3892
3893	!
3894	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
3895	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
3896	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
3897
3898	!
3899	!-- Calculate the next particle timestep. dt_gap is the time needed to
3900	!-- complete the current LES timestep.
3901	dt_gap(n) = dt_3d - particles(n)%dt_sum
3902	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
3903	particles(n)%aux1 = lagr_timescale(n)
3904	particles(n)%aux2 = dt_gap(n)
3905	!
3906	!-- The particle timestep should not be too small in order to prevent
3907	!-- the number of particle timesteps of getting too large
3908	IF ( dt_particle(n) < dt_min_part ) THEN
3909	IF ( dt_min_part < dt_gap(n) ) THEN
3910	dt_particle(n) = dt_min_part
3911	ELSE
3912	dt_particle(n) = dt_gap(n)
3913	ENDIF
3914	ENDIF
3915	rvar1_temp(n) = particles(n)%rvar1
3916	rvar2_temp(n) = particles(n)%rvar2
3917	rvar3_temp(n) = particles(n)%rvar3
3918	!
3919	!-- Calculate the SGS velocity components
3920	IF ( particles(n)%age == 0.0_wp ) THEN
3921	!
3922	!-- For new particles the SGS components are derived from the SGS
3923	!-- TKE. Limit the Gaussian random number to the interval
3924	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
3925	!-- from becoming unrealistically large.
3926	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3927	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
3928	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3929	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
3930	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
3931	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
3932
3933	ELSE
3934	!
3935	!-- Restriction of the size of the new timestep: compared to the
3936	!-- previous timestep the increase must not exceed 200%. First,
3937	!-- check if age > age_m, in order to prevent that particles get zero
3938	!-- timestep.
3939	dt_particle_m = MERGE( dt_particle(n), &
3940	particles(n)%age - particles(n)%age_m, &
3941	particles(n)%age - particles(n)%age_m < &
3942	1E-8_wp )
3943	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
3944	dt_particle(n) = 2.0_wp * dt_particle_m
3945	ENDIF
3946
3947	!-- For old particles the SGS components are correlated with the
3948	!-- values from the previous timestep. Random numbers have also to
3949	!-- be limited (see above).
3950	!-- As negative values for the subgrid TKE are not allowed, the
3951	!-- change of the subgrid TKE with time cannot be smaller than
3952	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
3953	!-- value for the change of TKE
3954	de_dt_min = - e_int(n) / dt_particle(n)
3955
3956	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
3957
3958	IF ( de_dt < de_dt_min ) THEN
3959	de_dt = de_dt_min
3960	ENDIF
3961
3962	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
3963	de_dx_int(n), de_dt, diss_int(n), &
3964	dt_particle(n), rg(n,1), term_1_2(n) )
3965
3966	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
3967	de_dy_int(n), de_dt, diss_int(n), &
3968	dt_particle(n), rg(n,2), term_1_2(n) )
3969
3970	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
3971	de_dz_int(n), de_dt, diss_int(n), &
3972	dt_particle(n), rg(n,3), term_1_2(n) )
3973
3974	ENDIF
3975
3976	ENDDO
3977	ENDDO
3978	!
3979	!-- Check if the added SGS velocities result in a violation of the CFL-
3980	!-- criterion. If yes choose a smaller timestep based on the new velocities
3981	!-- and calculate SGS velocities again
3982	dz_temp = zw(kp)-zw(kp-1)
3983
3984	DO nb = 0, 7
3985	DO n = start_index(nb), end_index(nb)
3986	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
3987	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
3988	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
3989	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
3990
3991	dt_particle(n) = 0.9_wp * MIN( &
3992	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
3993	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
3994	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
3995
3996	!
3997	!-- Reset temporary SGS velocites to "current" ones
3998	rvar1_temp(n) = particles(n)%rvar1
3999	rvar2_temp(n) = particles(n)%rvar2
4000	rvar3_temp(n) = particles(n)%rvar3
4001
4002	de_dt_min = - e_int(n) / dt_particle(n)
4003
4004	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
4005
4006	IF ( de_dt < de_dt_min ) THEN
4007	de_dt = de_dt_min
4008	ENDIF
4009
4010	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
4011	de_dx_int(n), de_dt, diss_int(n), &
4012	dt_particle(n), rg(n,1), term_1_2(n) )
4013
4014	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
4015	de_dy_int(n), de_dt, diss_int(n), &
4016	dt_particle(n), rg(n,2), term_1_2(n) )
4017
4018	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
4019	de_dz_int(n), de_dt, diss_int(n), &
4020	dt_particle(n), rg(n,3), term_1_2(n) )
4021	ENDIF
4022
4023	!
4024	!-- Update particle velocites
4025	particles(n)%rvar1 = rvar1_temp(n)
4026	particles(n)%rvar2 = rvar2_temp(n)
4027	particles(n)%rvar3 = rvar3_temp(n)
4028	u_int(n) = u_int(n) + particles(n)%rvar1
4029	v_int(n) = v_int(n) + particles(n)%rvar2
4030	w_int(n) = w_int(n) + particles(n)%rvar3
4031	!
4032	!-- Store the SGS TKE of the current timelevel which is needed for
4033	!-- for calculating the SGS particle velocities at the next timestep
4034	particles(n)%e_m = e_int(n)
4035	ENDDO
4036	ENDDO
4037
4038	ELSE
4039	!
4040	!-- If no SGS velocities are used, only the particle timestep has to
4041	!-- be set
4042	dt_particle = dt_3d
4043
4044	ENDIF
4045
4046	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
4047	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
4048	!
4049	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4050	!-- number_of_particles. This depends on the selected interpolation method.
4051	!-- If particle interpolation method is not trilinear, then the sorting within
4052	!-- subboxes is not required. However, therefore the index start_index(nb) and
4053	!-- end_index(nb) are not defined and the loops are still over
4054	!-- number_of_particles. @todo find a more generic way to write this loop or
4055	!-- delete trilinear interpolation
4056	IF ( interpolation_trilinear ) THEN
4057	subbox_start = 0
4058	subbox_end = 7
4059	ELSE
4060	subbox_start = 1
4061	subbox_end = 1
4062	ENDIF
4063	!
4064	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4065	!-- are introduced, as they are not required. Accordingly, this loops goes
4066	!-- from 1 to 1.
4067	DO nb = subbox_start, subbox_end
4068	IF ( interpolation_trilinear ) THEN
4069	particle_start = start_index(nb)
4070	particle_end = end_index(nb)
4071	ELSE
4072	particle_start = 1
4073	particle_end = number_of_particles
4074	ENDIF
4075	!
4076	!-- Loop from particle start to particle end
4077	DO n = particle_start, particle_end
4078
4079	!
4080	!-- Particle advection
4081	IF ( dens_ratio(n) == 0.0_wp ) THEN
4082	!
4083	!-- Pure passive transport (without particle inertia)
4084	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
4085	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
4086	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
4087
4088	particles(n)%speed_x = u_int(n)
4089	particles(n)%speed_y = v_int(n)
4090	particles(n)%speed_z = w_int(n)
4091
4092	ELSE
4093	!
4094	!-- Transport of particles with inertia
4095	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
4096	dt_particle(n)
4097	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
4098	dt_particle(n)
4099	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
4100	dt_particle(n)
4101
4102	!
4103	!-- Update of the particle velocity
4104	IF ( cloud_droplets ) THEN
4105	!
4106	!-- Terminal velocity is computed for vertical direction (Rogers et
4107	!-- al., 1993, J. Appl. Meteorol.)
4108	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4109	IF ( diameter <= d0_rog ) THEN
4110	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4111	ELSE
4112	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4113	ENDIF
4114
4115	!
4116	!-- If selected, add random velocities following Soelch and Kaercher
4117	!-- (2010, Q. J. R. Meteorol. Soc.)
4118	IF ( use_sgs_for_particles ) THEN
4119	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4120	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4121	1.0E-20_wp ) )
4122	sigma = SQRT( e(kp,jp,ip) )
4123
4124	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4125	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4126	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4127
4128	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4129	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4130	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4131	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4132	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4133	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4134
4135	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4136	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4137	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4138	ELSE
4139	particles(n)%speed_x = u_int(n)
4140	particles(n)%speed_y = v_int(n)
4141	particles(n)%speed_z = w_int(n) - w_s
4142	ENDIF
4143
4144	ELSE
4145
4146	IF ( use_sgs_for_particles ) THEN
4147	exp_arg = particle_groups(particles(n)%group)%exp_arg
4148	exp_term = EXP( -exp_arg * dt_particle(n) )
4149	ELSE
4150	exp_arg = particle_groups(particles(n)%group)%exp_arg
4151	exp_term = particle_groups(particles(n)%group)%exp_term
4152	ENDIF
4153	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4154	u_int(n) * ( 1.0_wp - exp_term )
4155	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4156	v_int(n) * ( 1.0_wp - exp_term )
4157	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4158	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
4159	g / exp_arg ) * ( 1.0_wp - exp_term )
4160	ENDIF
4161
4162	ENDIF
4163	ENDDO
4164	ENDDO
4165
4166	ELSE
4167	!
4168	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4169	!-- number_of_particles. This depends on the selected interpolation method.
4170	IF ( interpolation_trilinear ) THEN
4171	subbox_start = 0
4172	subbox_end = 7
4173	ELSE
4174	subbox_start = 1
4175	subbox_end = 1
4176	ENDIF
4177	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4178	!-- are introduced, as they are not required. Accordingly, this loops goes
4179	!-- from 1 to 1.
4180	DO nb = subbox_start, subbox_end
4181	IF ( interpolation_trilinear ) THEN
4182	particle_start = start_index(nb)
4183	particle_end = end_index(nb)
4184	ELSE
4185	particle_start = 1
4186	particle_end = number_of_particles
4187	ENDIF
4188	!
4189	!-- Loop from particle start to particle end
4190	DO n = particle_start, particle_end
4191
4192	!
4193	!-- Transport of particles with inertia
4194	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
4195	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
4196	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
4197	!
4198	!-- Update of the particle velocity
4199	IF ( cloud_droplets ) THEN
4200	!
4201	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
4202	!-- 1993, J. Appl. Meteorol.)
4203	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
4204	IF ( diameter <= d0_rog ) THEN
4205	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
4206	ELSE
4207	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
4208	ENDIF
4209
4210	!
4211	!-- If selected, add random velocities following Soelch and Kaercher
4212	!-- (2010, Q. J. R. Meteorol. Soc.)
4213	IF ( use_sgs_for_particles ) THEN
4214	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
4215	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
4216	1.0E-20_wp ) )
4217	sigma = SQRT( e(kp,jp,ip) )
4218
4219	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4220	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4221	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
4222
4223	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
4224	SQRT( 1.0_wp - RL*2 ) sigma * rg1
4225	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
4226	SQRT( 1.0_wp - RL*2 ) sigma * rg2
4227	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
4228	SQRT( 1.0_wp - RL*2 ) sigma * rg3
4229
4230	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
4231	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
4232	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
4233	ELSE
4234	particles(n)%speed_x = u_int(n)
4235	particles(n)%speed_y = v_int(n)
4236	particles(n)%speed_z = w_int(n) - w_s
4237	ENDIF
4238
4239	ELSE
4240
4241	IF ( use_sgs_for_particles ) THEN
4242	exp_arg = particle_groups(particles(n)%group)%exp_arg
4243	exp_term = EXP( -exp_arg * dt_particle(n) )
4244	ELSE
4245	exp_arg = particle_groups(particles(n)%group)%exp_arg
4246	exp_term = particle_groups(particles(n)%group)%exp_term
4247	ENDIF
4248	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
4249	u_int(n) * ( 1.0_wp - exp_term )
4250	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
4251	v_int(n) * ( 1.0_wp - exp_term )
4252	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
4253	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
4254	exp_arg ) * ( 1.0_wp - exp_term )
4255	ENDIF
4256	ENDDO
4257	ENDDO
4258
4259	ENDIF
4260
4261	!
4262	!-- Store the old age of the particle ( needed to prevent that a
4263	!-- particle crosses several PEs during one timestep, and for the
4264	!-- evaluation of the subgrid particle velocity fluctuations )
4265	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
4266
4267	!
4268	!-- loop over subboxes. In case of simple interpolation scheme no subboxes
4269	!-- are introduced, as they are not required. Accordingly, this loops goes
4270	!-- from 1 to 1.
4271	!
4272	!-- Decide whether the particle loop runs over the subboxes or only over 1,
4273	!-- number_of_particles. This depends on the selected interpolation method.
4274	IF ( interpolation_trilinear ) THEN
4275	subbox_start = 0
4276	subbox_end = 7
4277	ELSE
4278	subbox_start = 1
4279	subbox_end = 1
4280	ENDIF
4281	DO nb = subbox_start, subbox_end
4282	IF ( interpolation_trilinear ) THEN
4283	particle_start = start_index(nb)
4284	particle_end = end_index(nb)
4285	ELSE
4286	particle_start = 1
4287	particle_end = number_of_particles
4288	ENDIF
4289	!
4290	!-- Loop from particle start to particle end
4291	DO n = particle_start, particle_end
4292	!
4293	!-- Increment the particle age and the total time that the particle
4294	!-- has advanced within the particle timestep procedure
4295	particles(n)%age = particles(n)%age + dt_particle(n)
4296	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
4297
4298	!
4299	!-- Check whether there is still a particle that has not yet completed
4300	!-- the total LES timestep
4301	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
4302	dt_3d_reached_l = .FALSE.
4303	ENDIF
4304
4305	ENDDO
4306	ENDDO
4307
4308	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
4309
4310
4311	END SUBROUTINE lpm_advec
4312
4313
4314	!------------------------------------------------------------------------------!
4315	! Description:
4316	! ------------
4317	!> Calculation of subgrid-scale particle speed using the stochastic model
4318	!> of Weil et al. (2004, JAS, 61, 2877-2887).
4319	!------------------------------------------------------------------------------!
4320	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
4321	dt_n, rg_n, fac )
4322
4323	REAL(wp) :: a1 !< dummy argument
4324	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
4325	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
4326	REAL(wp) :: diss_n !< dissipation at particle position
4327	REAL(wp) :: dt_n !< particle timestep
4328	REAL(wp) :: e_n !< TKE at particle position
4329	REAL(wp) :: fac !< flag to identify adjacent topography
4330	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
4331	REAL(wp) :: rg_n !< random number
4332	REAL(wp) :: term1 !< memory term
4333	REAL(wp) :: term2 !< drift correction term
4334	REAL(wp) :: term3 !< random term
4335	REAL(wp) :: v_sgs !< subgrid-scale velocity component
4336
4337	!-- At first, limit TKE to a small non-zero number, in order to prevent
4338	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
4339	!-- (could occur at the simulation begin).
4340	e_n = MAX( e_n, 1E-20_wp )
4341	!
4342	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
4343	!-- multiplied by a flag to switch of both terms near topography.
4344	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
4345	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
4346	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
4347	!-- disabled if one of the adjacent grid points belongs to topography.
4348	!-- Moreover, in this case, the previous subgrid-scale component is also set
4349	!-- to zero.
4350
4351	a1 = fs_n * c_0 * diss_n
4352	!
4353	!-- Memory term
4354	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
4355	* fac
4356	!
4357	!-- Drift correction term
4358	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
4359	* fac
4360	!
4361	!-- Random term
4362	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
4363	!
4364	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
4365	!-- subgrid-scale velocity component is set to zero, in order to prevent a
4366	!-- velocity build-up.
4367	!-- This case, set also previous subgrid-scale component to zero.
4368	v_sgs = v_sgs * fac + term1 + term2 + term3
4369
4370	END SUBROUTINE weil_stochastic_eq
4371
4372
4373	!------------------------------------------------------------------------------!
4374	! Description:
4375	! ------------
4376	!> Boundary conditions for the Lagrangian particles.
4377	!> The routine consists of two different parts. One handles the bottom (flat)
4378	!> and top boundary. In this part, also particles which exceeded their lifetime
4379	!> are deleted.
4380	!> The other part handles the reflection of particles from vertical walls.
4381	!> This part was developed by Jin Zhang during 2006-2007.
4382	!>
4383	!> To do: Code structure for finding the t_index values and for checking the
4384	!> ----- reflection conditions is basically the same for all four cases, so it
4385	!> should be possible to further simplify/shorten it.
4386	!>
4387	!> THE WALLS PART OF THIS ROUTINE HAS NOT BEEN TESTED FOR OCEAN RUNS SO FAR!!!!
4388	!> (see offset_ocean_*)
4389	!------------------------------------------------------------------------------!
4390	SUBROUTINE lpm_boundary_conds( location_bc , i, j, k )
4391
4392	CHARACTER (LEN=*), INTENT(IN) :: location_bc !< general mode: boundary conditions at bottom/top of the model domain
4393	!< or at vertical surfaces (buildings, terrain steps)
4394	INTEGER(iwp), INTENT(IN) :: i !< grid index of particle box along x
4395	INTEGER(iwp), INTENT(IN) :: j !< grid index of particle box along y
4396	INTEGER(iwp), INTENT(IN) :: k !< grid index of particle box along z
4397
4398	INTEGER(iwp) :: inc !< dummy for sorting algorithmus
4399	INTEGER(iwp) :: ir !< dummy for sorting algorithmus
4400	INTEGER(iwp) :: i1 !< grid index (x) of old particle position
4401	INTEGER(iwp) :: i2 !< grid index (x) of current particle position
4402	INTEGER(iwp) :: i3 !< grid index (x) of intermediate particle position
4403	INTEGER(iwp) :: index_reset !< index reset height
4404	INTEGER(iwp) :: jr !< dummy for sorting algorithmus
4405	INTEGER(iwp) :: j1 !< grid index (y) of old particle position
4406	INTEGER(iwp) :: j2 !< grid index (y) of current particle position
4407	INTEGER(iwp) :: j3 !< grid index (y) of intermediate particle position
4408	INTEGER(iwp) :: k1 !< grid index (z) of old particle position
4409	INTEGER(iwp) :: k2 !< grid index (z) of current particle position
4410	INTEGER(iwp) :: k3 !< grid index (z) of intermediate particle position
4411	INTEGER(iwp) :: n !< particle number
4412	INTEGER(iwp) :: particles_top !< maximum reset height
4413	INTEGER(iwp) :: t_index !< running index for intermediate particle timesteps in reflection algorithmus
4414	INTEGER(iwp) :: t_index_number !< number of intermediate particle timesteps in reflection algorithmus
4415	INTEGER(iwp) :: tmp_x !< dummy for sorting algorithm
4416	INTEGER(iwp) :: tmp_y !< dummy for sorting algorithm
4417	INTEGER(iwp) :: tmp_z !< dummy for sorting algorithm
4418
4419	INTEGER(iwp), DIMENSION(0:10) :: x_ind(0:10) = 0 !< index array (x) of intermediate particle positions
4420	INTEGER(iwp), DIMENSION(0:10) :: y_ind(0:10) = 0 !< index array (y) of intermediate particle positions
4421	INTEGER(iwp), DIMENSION(0:10) :: z_ind(0:10) = 0 !< index array (z) of intermediate particle positions
4422
4423	LOGICAL :: cross_wall_x !< flag to check if particle reflection along x is necessary
4424	LOGICAL :: cross_wall_y !< flag to check if particle reflection along y is necessary
4425	LOGICAL :: cross_wall_z !< flag to check if particle reflection along z is necessary
4426	LOGICAL :: reflect_x !< flag to check if particle is already reflected along x
4427	LOGICAL :: reflect_y !< flag to check if particle is already reflected along y
4428	LOGICAL :: reflect_z !< flag to check if particle is already reflected along z
4429	LOGICAL :: tmp_reach_x !< dummy for sorting algorithmus
4430	LOGICAL :: tmp_reach_y !< dummy for sorting algorithmus
4431	LOGICAL :: tmp_reach_z !< dummy for sorting algorithmus
4432	LOGICAL :: x_wall_reached !< flag to check if particle has already reached wall
4433	LOGICAL :: y_wall_reached !< flag to check if particle has already reached wall
4434	LOGICAL :: z_wall_reached !< flag to check if particle has already reached wall
4435
4436	LOGICAL, DIMENSION(0:10) :: reach_x !< flag to check if particle is at a yz-wall
4437	LOGICAL, DIMENSION(0:10) :: reach_y !< flag to check if particle is at a xz-wall
4438	LOGICAL, DIMENSION(0:10) :: reach_z !< flag to check if particle is at a xy-wall
4439
4440	REAL(wp) :: dt_particle !< particle timestep
4441	REAL(wp) :: eps = 1E-10_wp !< security number to check if particle has reached a wall
4442	REAL(wp) :: pos_x !< intermediate particle position (x)
4443	REAL(wp) :: pos_x_old !< particle position (x) at previous particle timestep
4444	REAL(wp) :: pos_y !< intermediate particle position (y)
4445	REAL(wp) :: pos_y_old !< particle position (y) at previous particle timestep
4446	REAL(wp) :: pos_z !< intermediate particle position (z)
4447	REAL(wp) :: pos_z_old !< particle position (z) at previous particle timestep
4448	REAL(wp) :: prt_x !< current particle position (x)
4449	REAL(wp) :: prt_y !< current particle position (y)
4450	REAL(wp) :: prt_z !< current particle position (z)
4451	REAL(wp) :: ran_val !< location of wall in z
4452	REAL(wp) :: reset_top !< location of wall in z
4453	REAL(wp) :: t_old !< previous reflection time
4454	REAL(wp) :: tmp_t !< dummy for sorting algorithmus
4455	REAL(wp) :: xwall !< location of wall in x
4456	REAL(wp) :: ywall !< location of wall in y
4457	REAL(wp) :: zwall !< location of wall in z
4458
4459	REAL(wp), DIMENSION(0:10) :: t !< reflection time
4460
4461	SELECT CASE ( location_bc )
4462
4463	CASE ( 'bottom/top' )
4464
4465	!
4466	!-- Apply boundary conditions to those particles that have crossed the top or
4467	!-- bottom boundary and delete those particles, which are older than allowed
4468	DO n = 1, number_of_particles
4469
4470	!
4471	!-- Stop if particles have moved further than the length of one
4472	!-- PE subdomain (newly released particles have age = age_m!)
4473	IF ( particles(n)%age /= particles(n)%age_m ) THEN
4474	IF ( ABS(particles(n)%speed_x) > &
4475	((nxr-nxl+2)*dx)/(particles(n)%age-particles(n)%age_m) .OR. &
4476	ABS(particles(n)%speed_y) > &
4477	((nyn-nys+2)*dy)/(particles(n)%age-particles(n)%age_m) ) THEN
4478
4479	WRITE( message_string, * ) 'particle too fast. n = ', n
4480	CALL message( 'lpm_boundary_conds', 'PA0148', 2, 2, -1, 6, 1 )
4481	ENDIF
4482	ENDIF
4483
4484	IF ( particles(n)%age > particle_maximum_age .AND. &
4485	particles(n)%particle_mask ) &
4486	THEN
4487	particles(n)%particle_mask = .FALSE.
4488	deleted_particles = deleted_particles + 1
4489	ENDIF
4490
4491	IF ( particles(n)%z >= zw(nz) .AND. particles(n)%particle_mask ) THEN
4492	IF ( ibc_par_t == 1 ) THEN
4493	!
4494	!-- Particle absorption
4495	particles(n)%particle_mask = .FALSE.
4496	deleted_particles = deleted_particles + 1
4497	ELSEIF ( ibc_par_t == 2 ) THEN
4498	!
4499	!-- Particle reflection
4500	particles(n)%z = 2.0_wp * zw(nz) - particles(n)%z
4501	particles(n)%speed_z = -particles(n)%speed_z
4502	IF ( use_sgs_for_particles .AND. &
4503	particles(n)%rvar3 > 0.0_wp ) THEN
4504	particles(n)%rvar3 = -particles(n)%rvar3
4505	ENDIF
4506	ENDIF
4507	ENDIF
4508
4509	IF ( particles(n)%z < zw(0) .AND. particles(n)%particle_mask ) THEN
4510	IF ( ibc_par_b == 1 ) THEN
4511	!
4512	!-- Particle absorption
4513	particles(n)%particle_mask = .FALSE.
4514	deleted_particles = deleted_particles + 1
4515	ELSEIF ( ibc_par_b == 2 ) THEN
4516	!
4517	!-- Particle reflection
4518	particles(n)%z = 2.0_wp * zw(0) - particles(n)%z
4519	particles(n)%speed_z = -particles(n)%speed_z
4520	IF ( use_sgs_for_particles .AND. &
4521	particles(n)%rvar3 < 0.0_wp ) THEN
4522	particles(n)%rvar3 = -particles(n)%rvar3
4523	ENDIF
4524	ELSEIF ( ibc_par_b == 3 ) THEN
4525	!
4526	!-- Find reset height. @note this works only in non-strechted cases
4527	particles_top = INT( pst(1) / dz(1) )
4528	index_reset = MINLOC( prt_count(nzb+1:particles_top,j,i), DIM = 1 )
4529	reset_top = zu(index_reset)
4530	iran_part = iran_part + myid
4531	ran_val = random_function( iran_part )
4532	particles(n)%z = reset_top * ( 1.0 + ( ran_val / 10.0_wp) )
4533	particles(n)%speed_z = 0.0_wp
4534	IF ( curvature_solution_effects ) THEN
4535	particles(n)%radius = particles(n)%aux1
4536	ELSE
4537	particles(n)%radius = 1.0E-8
4538	ENDIF
4539	ENDIF
4540	ENDIF
4541	ENDDO
4542
4543	CASE ( 'walls' )
4544
4545	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'start' )
4546
4547	DO n = 1, number_of_particles
4548	!
4549	!-- Recalculate particle timestep
4550	dt_particle = particles(n)%age - particles(n)%age_m
4551	!
4552	!-- Obtain x/y indices for current particle position
4553	i2 = particles(n)%x * ddx
4554	j2 = particles(n)%y * ddy
4555	IF (zw(k) < particles(n)%z ) k2 = k + 1
4556	IF (zw(k) > particles(n)%z .AND. zw(k-1) < particles(n)%z ) k2 = k
4557	IF (zw(k-1) > particles(n)%z ) k2 = k - 1
4558	!
4559	!-- Save current particle positions
4560	prt_x = particles(n)%x
4561	prt_y = particles(n)%y
4562	prt_z = particles(n)%z
4563	!
4564	!-- Recalculate old particle positions
4565	pos_x_old = particles(n)%x - particles(n)%speed_x * dt_particle
4566	pos_y_old = particles(n)%y - particles(n)%speed_y * dt_particle
4567	pos_z_old = particles(n)%z - particles(n)%speed_z * dt_particle
4568	!
4569	!-- Obtain x/y indices for old particle positions
4570	i1 = i
4571	j1 = j
4572	k1 = k
4573	!
4574	!-- Determine horizontal as well as vertical walls at which particle can
4575	!-- be potentially reflected.
4576	!-- Start with walls aligned in yz layer.
4577	!-- Wall to the right
4578	IF ( prt_x > pos_x_old ) THEN
4579	xwall = ( i1 + 1 ) * dx
4580	!
4581	!-- Wall to the left
4582	ELSE
4583	xwall = i1 * dx
4584	ENDIF
4585	!
4586	!-- Walls aligned in xz layer
4587	!-- Wall to the north
4588	IF ( prt_y > pos_y_old ) THEN
4589	ywall = ( j1 +1 ) * dy
4590	!-- Wall to the south
4591	ELSE
4592	ywall = j1 * dy
4593	ENDIF
4594
4595	IF ( prt_z > pos_z_old ) THEN
4596	zwall = zw(k)
4597	ELSE
4598	zwall = zw(k-1)
4599	ENDIF
4600	!
4601	!-- Initialize flags to check if particle reflection is necessary
4602	cross_wall_x = .FALSE.
4603	cross_wall_y = .FALSE.
4604	cross_wall_z = .FALSE.
4605	!
4606	!-- Initialize flags to check if a wall is reached
4607	reach_x = .FALSE.
4608	reach_y = .FALSE.
4609	reach_z = .FALSE.
4610	!
4611	!-- Initialize flags to check if a particle was already reflected
4612	reflect_x = .FALSE.
4613	reflect_y = .FALSE.
4614	reflect_z = .FALSE.
4615	!
4616	!-- Initialize flags to check if a wall is already crossed.
4617	!-- ( Required to obtain correct indices. )
4618	x_wall_reached = .FALSE.
4619	y_wall_reached = .FALSE.
4620	z_wall_reached = .FALSE.
4621	!
4622	!-- Initialize time array
4623	t = 0.0_wp
4624	!
4625	!-- Check if particle can reach any wall. This case, calculate the
4626	!-- fractional time needed to reach this wall. Store this fractional
4627	!-- timestep in array t. Moreover, store indices for these grid
4628	!-- boxes where the respective wall belongs to.
4629	!-- Start with x-direction.
4630	t_index = 1
4631	t(t_index) = ( xwall - pos_x_old ) &
4632	/ MERGE( MAX( prt_x - pos_x_old, 1E-30_wp ), &
4633	MIN( prt_x - pos_x_old, -1E-30_wp ), &
4634	prt_x > pos_x_old )
4635	x_ind(t_index) = i2
4636	y_ind(t_index) = j1
4637	z_ind(t_index) = k1
4638	reach_x(t_index) = .TRUE.
4639	reach_y(t_index) = .FALSE.
4640	reach_z(t_index) = .FALSE.
4641	!
4642	!-- Store these values only if particle really reaches any wall. t must
4643	!-- be in a interval between [0:1].
4644	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4645	t_index = t_index + 1
4646	cross_wall_x = .TRUE.
4647	ENDIF
4648	!
4649	!-- y-direction
4650	t(t_index) = ( ywall - pos_y_old ) &
4651	/ MERGE( MAX( prt_y - pos_y_old, 1E-30_wp ), &
4652	MIN( prt_y - pos_y_old, -1E-30_wp ), &
4653	prt_y > pos_y_old )
4654	x_ind(t_index) = i1
4655	y_ind(t_index) = j2
4656	z_ind(t_index) = k1
4657	reach_x(t_index) = .FALSE.
4658	reach_y(t_index) = .TRUE.
4659	reach_z(t_index) = .FALSE.
4660	IF ( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp ) THEN
4661	t_index = t_index + 1
4662	cross_wall_y = .TRUE.
4663	ENDIF
4664	!
4665	!-- z-direction
4666	t(t_index) = (zwall - pos_z_old ) &
4667	/ MERGE( MAX( prt_z - pos_z_old, 1E-30_wp ), &
4668	MIN( prt_z - pos_z_old, -1E-30_wp ), &
4669	prt_z > pos_z_old )
4670
4671	x_ind(t_index) = i1
4672	y_ind(t_index) = j1
4673	z_ind(t_index) = k2
4674	reach_x(t_index) = .FALSE.
4675	reach_y(t_index) = .FALSE.
4676	reach_z(t_index) = .TRUE.
4677	IF( t(t_index) <= 1.0_wp .AND. t(t_index) >= 0.0_wp) THEN
4678	t_index = t_index + 1
4679	cross_wall_z = .TRUE.
4680	ENDIF
4681
4682	t_index_number = t_index - 1
4683	!
4684	!-- Carry out reflection only if particle reaches any wall
4685	IF ( cross_wall_x .OR. cross_wall_y .OR. cross_wall_z ) THEN
4686	!
4687	!-- Sort fractional timesteps in ascending order. Also sort the
4688	!-- corresponding indices and flag according to the time interval a
4689	!-- particle reaches the respective wall.
4690	inc = 1
4691	jr = 1
4692	DO WHILE ( inc <= t_index_number )
4693	inc = 3 * inc + 1
4694	ENDDO
4695
4696	DO WHILE ( inc > 1 )
4697	inc = inc / 3
4698	DO ir = inc+1, t_index_number
4699	tmp_t = t(ir)
4700	tmp_x = x_ind(ir)
4701	tmp_y = y_ind(ir)
4702	tmp_z = z_ind(ir)
4703	tmp_reach_x = reach_x(ir)
4704	tmp_reach_y = reach_y(ir)
4705	tmp_reach_z = reach_z(ir)
4706	jr = ir
4707	DO WHILE ( t(jr-inc) > tmp_t )
4708	t(jr) = t(jr-inc)
4709	x_ind(jr) = x_ind(jr-inc)
4710	y_ind(jr) = y_ind(jr-inc)
4711	z_ind(jr) = z_ind(jr-inc)
4712	reach_x(jr) = reach_x(jr-inc)
4713	reach_y(jr) = reach_y(jr-inc)
4714	reach_z(jr) = reach_z(jr-inc)
4715	jr = jr - inc
4716	IF ( jr <= inc ) EXIT
4717	ENDDO
4718	t(jr) = tmp_t
4719	x_ind(jr) = tmp_x
4720	y_ind(jr) = tmp_y
4721	z_ind(jr) = tmp_z
4722	reach_x(jr) = tmp_reach_x
4723	reach_y(jr) = tmp_reach_y
4724	reach_z(jr) = tmp_reach_z
4725	ENDDO
4726	ENDDO
4727	!
4728	!-- Initialize temporary particle positions
4729	pos_x = pos_x_old
4730	pos_y = pos_y_old
4731	pos_z = pos_z_old
4732	!
4733	!-- Loop over all times a particle possibly moves into a new grid box
4734	t_old = 0.0_wp
4735	DO t_index = 1, t_index_number
4736	!
4737	!-- Calculate intermediate particle position according to the
4738	!-- timesteps a particle reaches any wall.
4739	pos_x = pos_x + ( t(t_index) - t_old ) * dt_particle &
4740	* particles(n)%speed_x
4741	pos_y = pos_y + ( t(t_index) - t_old ) * dt_particle &
4742	* particles(n)%speed_y
4743	pos_z = pos_z + ( t(t_index) - t_old ) * dt_particle &
4744	* particles(n)%speed_z
4745	!
4746	!-- Obtain x/y grid indices for intermediate particle position from
4747	!-- sorted index array
4748	i3 = x_ind(t_index)
4749	j3 = y_ind(t_index)
4750	k3 = z_ind(t_index)
4751	!
4752	!-- Check which wall is already reached
4753	IF ( .NOT. x_wall_reached ) x_wall_reached = reach_x(t_index)
4754	IF ( .NOT. y_wall_reached ) y_wall_reached = reach_y(t_index)
4755	IF ( .NOT. z_wall_reached ) z_wall_reached = reach_z(t_index)
4756	!
4757	!-- Check if a particle needs to be reflected at any yz-wall. If
4758	!-- necessary, carry out reflection. Please note, a security
4759	!-- constant is required, as the particle position does not
4760	!-- necessarily exactly match the wall location due to rounding
4761	!-- errors.
4762	IF ( reach_x(t_index) .AND. &
4763	ABS( pos_x - xwall ) < eps .AND. &
4764	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4765	.NOT. reflect_x ) THEN
4766	!
4767	!
4768	!-- Reflection in x-direction.
4769	!-- Ensure correct reflection by MIN/MAX functions, depending on
4770	!-- direction of particle transport.
4771	!-- Due to rounding errors pos_x does not exactly match the wall
4772	!-- location, leading to erroneous reflection.
4773	pos_x = MERGE( MIN( 2.0_wp * xwall - pos_x, xwall ), &
4774	MAX( 2.0_wp * xwall - pos_x, xwall ), &
4775	particles(n)%x > xwall )
4776	!
4777	!-- Change sign of particle speed
4778	particles(n)%speed_x = - particles(n)%speed_x
4779	!
4780	!-- Also change sign of subgrid-scale particle speed
4781	particles(n)%rvar1 = - particles(n)%rvar1
4782	!
4783	!-- Set flag that reflection along x is already done
4784	reflect_x = .TRUE.
4785	!
4786	!-- As the particle does not cross any further yz-wall during
4787	!-- this timestep, set further x-indices to the current one.
4788	x_ind(t_index:t_index_number) = i1
4789	!
4790	!-- If particle already reached the wall but was not reflected,
4791	!-- set further x-indices to the new one.
4792	ELSEIF ( x_wall_reached .AND. .NOT. reflect_x ) THEN
4793	x_ind(t_index:t_index_number) = i2
4794	ENDIF !particle reflection in x direction done
4795
4796	!
4797	!-- Check if a particle needs to be reflected at any xz-wall. If
4798	!-- necessary, carry out reflection. Please note, a security
4799	!-- constant is required, as the particle position does not
4800	!-- necessarily exactly match the wall location due to rounding
4801	!-- errors.
4802	IF ( reach_y(t_index) .AND. &
4803	ABS( pos_y - ywall ) < eps .AND. &
4804	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4805	.NOT. reflect_y ) THEN
4806	!
4807	!
4808	!-- Reflection in y-direction.
4809	!-- Ensure correct reflection by MIN/MAX functions, depending on
4810	!-- direction of particle transport.
4811	!-- Due to rounding errors pos_y does not exactly match the wall
4812	!-- location, leading to erroneous reflection.
4813	pos_y = MERGE( MIN( 2.0_wp * ywall - pos_y, ywall ), &
4814	MAX( 2.0_wp * ywall - pos_y, ywall ), &
4815	particles(n)%y > ywall )
4816	!
4817	!-- Change sign of particle speed
4818	particles(n)%speed_y = - particles(n)%speed_y
4819	!
4820	!-- Also change sign of subgrid-scale particle speed
4821	particles(n)%rvar2 = - particles(n)%rvar2
4822	!
4823	!-- Set flag that reflection along y is already done
4824	reflect_y = .TRUE.
4825	!
4826	!-- As the particle does not cross any further xz-wall during
4827	!-- this timestep, set further y-indices to the current one.
4828	y_ind(t_index:t_index_number) = j1
4829	!
4830	!-- If particle already reached the wall but was not reflected,
4831	!-- set further y-indices to the new one.
4832	ELSEIF ( y_wall_reached .AND. .NOT. reflect_y ) THEN
4833	y_ind(t_index:t_index_number) = j2
4834	ENDIF !particle reflection in y direction done
4835
4836	!
4837	!-- Check if a particle needs to be reflected at any xy-wall. If
4838	!-- necessary, carry out reflection. Please note, a security
4839	!-- constant is required, as the particle position does not
4840	!-- necessarily exactly match the wall location due to rounding
4841	!-- errors.
4842	IF ( reach_z(t_index) .AND. &
4843	ABS( pos_z - zwall ) < eps .AND. &
4844	.NOT. BTEST(wall_flags_0(k3,j3,i3),0) .AND. &
4845	.NOT. reflect_z ) THEN
4846	!
4847	!
4848	!-- Reflection in z-direction.
4849	!-- Ensure correct reflection by MIN/MAX functions, depending on
4850	!-- direction of particle transport.
4851	!-- Due to rounding errors pos_z does not exactly match the wall
4852	!-- location, leading to erroneous reflection.
4853	pos_z = MERGE( MIN( 2.0_wp * zwall - pos_z, zwall ), &
4854	MAX( 2.0_wp * zwall - pos_z, zwall ), &
4855	particles(n)%z > zwall )
4856	!
4857	!-- Change sign of particle speed
4858	particles(n)%speed_z = - particles(n)%speed_z
4859	!
4860	!-- Also change sign of subgrid-scale particle speed
4861	particles(n)%rvar3 = - particles(n)%rvar3
4862	!
4863	!-- Set flag that reflection along z is already done
4864	reflect_z = .TRUE.
4865	!
4866	!-- As the particle does not cross any further xy-wall during
4867	!-- this timestep, set further z-indices to the current one.
4868	z_ind(t_index:t_index_number) = k1
4869	!
4870	!-- If particle already reached the wall but was not reflected,
4871	!-- set further z-indices to the new one.
4872	ELSEIF ( z_wall_reached .AND. .NOT. reflect_z ) THEN
4873	z_ind(t_index:t_index_number) = k2
4874	ENDIF !particle reflection in z direction done
4875
4876	!
4877	!-- Swap time
4878	t_old = t(t_index)
4879
4880	ENDDO
4881	!
4882	!-- If a particle was reflected, calculate final position from last
4883	!-- intermediate position.
4884	IF ( reflect_x .OR. reflect_y .OR. reflect_z ) THEN
4885
4886	particles(n)%x = pos_x + ( 1.0_wp - t_old ) * dt_particle &
4887	* particles(n)%speed_x
4888	particles(n)%y = pos_y + ( 1.0_wp - t_old ) * dt_particle &
4889	* particles(n)%speed_y
4890	particles(n)%z = pos_z + ( 1.0_wp - t_old ) * dt_particle &
4891	* particles(n)%speed_z
4892
4893	ENDIF
4894
4895	ENDIF
4896
4897	ENDDO
4898
4899	CALL cpu_log( log_point_s(48), 'lpm_wall_reflect', 'stop' )
4900
4901	CASE DEFAULT
4902	CONTINUE
4903
4904	END SELECT
4905
4906	END SUBROUTINE lpm_boundary_conds
4907
4908
4909	!------------------------------------------------------------------------------!
4910	! Description:
4911	! ------------
4912	!> Calculates change in droplet radius by condensation/evaporation, using
4913	!> either an analytic formula or by numerically integrating the radius growth
4914	!> equation including curvature and solution effects using Rosenbrocks method
4915	!> (see Numerical recipes in FORTRAN, 2nd edition, p. 731).
4916	!> The analytical formula and growth equation follow those given in
4917	!> Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103).
4918	!------------------------------------------------------------------------------!
4919	SUBROUTINE lpm_droplet_condensation (i,j,k)
4920
4921	INTEGER(iwp), INTENT(IN) :: i !<
4922	INTEGER(iwp), INTENT(IN) :: j !<
4923	INTEGER(iwp), INTENT(IN) :: k !<
4924	INTEGER(iwp) :: n !<
4925
4926	REAL(wp) :: afactor !< curvature effects
4927	REAL(wp) :: arg !<
4928	REAL(wp) :: bfactor !< solute effects
4929	REAL(wp) :: ddenom !<
4930	REAL(wp) :: delta_r !<
4931	REAL(wp) :: diameter !< diameter of cloud droplets
4932	REAL(wp) :: diff_coeff !< diffusivity for water vapor
4933	REAL(wp) :: drdt !<
4934	REAL(wp) :: dt_ros !<
4935	REAL(wp) :: dt_ros_sum !<
4936	REAL(wp) :: d2rdtdr !<
4937	REAL(wp) :: e_a !< current vapor pressure
4938	REAL(wp) :: e_s !< current saturation vapor pressure
4939	REAL(wp) :: error !< local truncation error in Rosenbrock
4940	REAL(wp) :: k1 !<
4941	REAL(wp) :: k2 !<
4942	REAL(wp) :: r_err !< First order estimate of Rosenbrock radius
4943	REAL(wp) :: r_ros !< Rosenbrock radius
4944	REAL(wp) :: r_ros_ini !< initial Rosenbrock radius
4945	REAL(wp) :: r0 !< gas-kinetic lengthscale
4946	REAL(wp) :: sigma !< surface tension of water
4947	REAL(wp) :: thermal_conductivity !< thermal conductivity for water
4948	REAL(wp) :: t_int !< temperature
4949	REAL(wp) :: w_s !< terminal velocity of droplets
4950	REAL(wp) :: re_p !< particle Reynolds number
4951	!
4952	!-- Parameters for Rosenbrock method (see Verwer et al., 1999)
4953	REAL(wp), PARAMETER :: prec = 1.0E-3_wp !< precision of Rosenbrock solution
4954	REAL(wp), PARAMETER :: q_increase = 1.5_wp !< increase factor in timestep
4955	REAL(wp), PARAMETER :: q_decrease = 0.9_wp !< decrease factor in timestep
4956	REAL(wp), PARAMETER :: gamma = 0.292893218814_wp !< = 1.0 - 1.0 / SQRT(2.0)
4957	!
4958	!-- Parameters for terminal velocity
4959	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
4960	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
4961	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
4962	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
4963	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
4964	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
4965
4966	REAL(wp), DIMENSION(number_of_particles) :: ventilation_effect !<
4967	REAL(wp), DIMENSION(number_of_particles) :: new_r !<
4968
4969	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' )
4970
4971	!
4972	!-- Absolute temperature
4973	t_int = pt(k,j,i) * exner(k)
4974	!
4975	!-- Saturation vapor pressure (Eq. 10 in Bolton, 1980)
4976	e_s = magnus( t_int )
4977	!
4978	!-- Current vapor pressure
4979	e_a = q(k,j,i) * hyp(k) / ( q(k,j,i) + rd_d_rv )
4980	!
4981	!-- Thermal conductivity for water (from Rogers and Yau, Table 7.1)
4982	thermal_conductivity = 7.94048E-05_wp * t_int + 0.00227011_wp
4983	!
4984	!-- Moldecular diffusivity of water vapor in air (Hall und Pruppacher, 1976)
4985	diff_coeff = 0.211E-4_wp * ( t_int / 273.15_wp )*1.94_wp &
4986	( 101325.0_wp / hyp(k) )
4987	!
4988	!-- Lengthscale for gas-kinetic effects (from Mordy, 1959, p. 23):
4989	r0 = diff_coeff / 0.036_wp * SQRT( 2.0_wp * pi / ( r_v * t_int ) )
4990	!
4991	!-- Calculate effects of heat conductivity and diffusion of water vapor on the
4992	!-- diffusional growth process (usually known as 1.0 / (F_k + F_d) )
4993	ddenom = 1.0_wp / ( rho_l * r_v * t_int / ( e_s * diff_coeff ) + &
4994	( l_v / ( r_v * t_int ) - 1.0_wp ) * rho_l * &
4995	l_v / ( thermal_conductivity * t_int ) &
4996	)
4997	new_r = 0.0_wp
4998	!
4999	!-- Determine ventilation effect on evaporation of large drops
5000	DO n = 1, number_of_particles
5001
5002	IF ( particles(n)%radius >= 4.0E-5_wp .AND. e_a / e_s < 1.0_wp ) THEN
5003	!
5004	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
5005	!-- 1993, J. Appl. Meteorol.)
5006	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
5007	IF ( diameter <= d0_rog ) THEN
5008	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
5009	ELSE
5010	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
5011	ENDIF
5012	!
5013	!-- Calculate droplet's Reynolds number
5014	re_p = 2.0_wp * particles(n)%radius * w_s / molecular_viscosity
5015	!
5016	!-- Ventilation coefficient (Rogers and Yau, 1989):
5017	IF ( re_p > 2.5_wp ) THEN
5018	ventilation_effect(n) = 0.78_wp + 0.28_wp * SQRT( re_p )
5019	ELSE
5020	ventilation_effect(n) = 1.0_wp + 0.09_wp * re_p
5021	ENDIF
5022	ELSE
5023	!
5024	!-- For small droplets or in supersaturated environments, the ventilation
5025	!-- effect does not play a role
5026	ventilation_effect(n) = 1.0_wp
5027	ENDIF
5028	ENDDO
5029
5030	IF( .NOT. curvature_solution_effects ) THEN
5031	!
5032	!-- Use analytic model for diffusional growth including gas-kinetic
5033	!-- effects (Mordy, 1959) but without the impact of aerosols.
5034	DO n = 1, number_of_particles
5035	arg = ( particles(n)%radius + r0 )*2 + 2.0_wp dt_3d * ddenom * &
5036	ventilation_effect(n) * &
5037	( e_a / e_s - 1.0_wp )
5038	arg = MAX( arg, ( 0.01E-6 + r0 )**2 )
5039	new_r(n) = SQRT( arg ) - r0
5040	ENDDO
5041
5042	ELSE
5043	!
5044	!-- Integrate the diffusional growth including gas-kinetic (Mordy, 1959),
5045	!-- as well as curvature and solute effects (e.g., KÃ¶hler, 1936).
5046	!
5047	!-- Curvature effect (afactor) with surface tension (sigma) by Straka (2009)
5048	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
5049	!
5050	!-- Solute effect (afactor)
5051	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
5052
5053	DO n = 1, number_of_particles
5054	!
5055	!-- Solute effect (bfactor)
5056	bfactor = vanthoff * rho_s * particles(n)%aux1*3 &
5057	molecular_weight_of_water / ( rho_l * molecular_weight_of_solute )
5058
5059	dt_ros = particles(n)%aux2 ! use previously stored Rosenbrock timestep
5060	dt_ros_sum = 0.0_wp
5061
5062	r_ros = particles(n)%radius ! initialize Rosenbrock particle radius
5063	r_ros_ini = r_ros
5064	!
5065	!-- Integrate growth equation using a 2nd-order Rosenbrock method
5066	!-- (see Verwer et al., 1999, Eq. (3.2)). The Rosenbrock method adjusts
5067	!-- its with internal timestep to minimize the local truncation error.
5068	DO WHILE ( dt_ros_sum < dt_3d )
5069
5070	dt_ros = MIN( dt_ros, dt_3d - dt_ros_sum )
5071
5072	DO
5073
5074	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5075	afactor / r_ros + &
5076	bfactor / r_ros**3 &
5077	) / ( r_ros + r0 )
5078
5079	d2rdtdr = -ddenom * ventilation_effect(n) * ( &
5080	(e_a / e_s - 1.0_wp ) * r_ros**4 - &
5081	afactor * r0 * r_ros**2 - &
5082	2.0_wp * afactor * r_ros**3 + &
5083	3.0_wp * bfactor * r0 + &
5084	4.0_wp * bfactor * r_ros &
5085	) &
5086	/ ( r_ros*4 ( r_ros + r0 )**2 )
5087
5088	k1 = drdt / ( 1.0_wp - gamma * dt_ros * d2rdtdr )
5089
5090	r_ros = MAX(r_ros_ini + k1 * dt_ros, particles(n)%aux1)
5091	r_err = r_ros
5092
5093	drdt = ddenom * ventilation_effect(n) * ( e_a / e_s - 1.0_wp - &
5094	afactor / r_ros + &
5095	bfactor / r_ros**3 &
5096	) / ( r_ros + r0 )
5097
5098	k2 = ( drdt - dt_ros * 2.0 * gamma * d2rdtdr * k1 ) / &
5099	( 1.0_wp - dt_ros * gamma * d2rdtdr )
5100
5101	r_ros = MAX(r_ros_ini + dt_ros * ( 1.5_wp * k1 + 0.5_wp * k2), particles(n)%aux1)
5102	!
5103	!-- Check error of the solution, and reduce dt_ros if necessary.
5104	error = ABS(r_err - r_ros) / r_ros
5105	IF ( error .GT. prec ) THEN
5106	dt_ros = SQRT( q_decrease * prec / error ) * dt_ros
5107	r_ros = r_ros_ini
5108	ELSE
5109	dt_ros_sum = dt_ros_sum + dt_ros
5110	dt_ros = q_increase * dt_ros
5111	r_ros_ini = r_ros
5112	EXIT
5113	ENDIF
5114
5115	END DO
5116
5117	END DO !Rosenbrock loop
5118	!
5119	!-- Store new particle radius
5120	new_r(n) = r_ros
5121	!
5122	!-- Store internal time step value for next PALM step
5123	particles(n)%aux2 = dt_ros
5124
5125	ENDDO !Particle loop
5126
5127	ENDIF
5128
5129	DO n = 1, number_of_particles
5130	!
5131	!-- Sum up the change in liquid water for the respective grid
5132	!-- box for the computation of the release/depletion of water vapor
5133	!-- and heat.
5134	ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * &
5135	rho_l * 1.33333333_wp * pi * &
5136	( new_r(n)3 - particles(n)%radius3 ) / &
5137	( rho_surface * dx * dy * dzw(k) )
5138	!
5139	!-- Check if the increase in liqid water is not too big. If this is the case,
5140	!-- the model timestep might be too long.
5141	IF ( ql_c(k,j,i) > 100.0_wp ) THEN
5142	WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, &
5143	' ql_c=',ql_c(k,j,i), '&part(',n,')%wf=', &
5144	particles(n)%weight_factor,' delta_r=',delta_r
5145	CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 )
5146	ENDIF
5147	!
5148	!-- Check if the change in the droplet radius is not too big. If this is the
5149	!-- case, the model timestep might be too long.
5150	delta_r = new_r(n) - particles(n)%radius
5151	IF ( delta_r < 0.0_wp .AND. new_r(n) < 0.0_wp ) THEN
5152	WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, &
5153	' e_s=',e_s, ' e_a=',e_a,' t_int=',t_int, &
5154	'&delta_r=',delta_r, &
5155	' particle_radius=',particles(n)%radius
5156	CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 )
5157	ENDIF
5158	!
5159	!-- Sum up the total volume of liquid water (needed below for
5160	!-- re-calculating the weighting factors)
5161	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r(n)**3
5162	!
5163	!-- Determine radius class of the particle needed for collision
5164	IF ( use_kernel_tables ) THEN
5165	particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / &
5166	( rclass_ubound - rclass_lbound ) * &
5167	radius_classes
5168	particles(n)%class = MIN( particles(n)%class, radius_classes )
5169	particles(n)%class = MAX( particles(n)%class, 1 )
5170	ENDIF
5171	!
5172	!-- Store new radius to particle features
5173	particles(n)%radius = new_r(n)
5174
5175	ENDDO
5176
5177	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' )
5178
5179
5180	END SUBROUTINE lpm_droplet_condensation
5181
5182
5183	!------------------------------------------------------------------------------!
5184	! Description:
5185	! ------------
5186	!> Release of latent heat and change of mixing ratio due to condensation /
5187	!> evaporation of droplets.
5188	!------------------------------------------------------------------------------!
5189	SUBROUTINE lpm_interaction_droplets_ptq
5190
5191	INTEGER(iwp) :: i !< running index x direction
5192	INTEGER(iwp) :: j !< running index y direction
5193	INTEGER(iwp) :: k !< running index z direction
5194
5195	REAL(wp) :: flag !< flag to mask topography grid points
5196
5197	DO i = nxl, nxr
5198	DO j = nys, nyn
5199	DO k = nzb+1, nzt
5200	!
5201	!-- Predetermine flag to mask topography
5202	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
5203
5204	q_p(k,j,i) = q_p(k,j,i) - ql_c(k,j,i) * flag
5205	pt_p(k,j,i) = pt_p(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) &
5206	* flag
5207	ENDDO
5208	ENDDO
5209	ENDDO
5210
5211	END SUBROUTINE lpm_interaction_droplets_ptq
5212
5213
5214	!------------------------------------------------------------------------------!
5215	! Description:
5216	! ------------
5217	!> Release of latent heat and change of mixing ratio due to condensation /
5218	!> evaporation of droplets. Call for grid point i,j
5219	!------------------------------------------------------------------------------!
5220	SUBROUTINE lpm_interaction_droplets_ptq_ij( i, j )
5221
5222	INTEGER(iwp) :: i !< running index x direction
5223	INTEGER(iwp) :: j !< running index y direction
5224	INTEGER(iwp) :: k !< running index z direction
5225
5226	REAL(wp) :: flag !< flag to mask topography grid points
5227
5228
5229	DO k = nzb+1, nzt
5230	!
5231	!-- Predetermine flag to mask topography
5232	flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) )
5233
5234	q_p(k,j,i) = q_p(k,j,i) - ql_c(k,j,i) * flag
5235	pt_p(k,j,i) = pt_p(k,j,i) + lv_d_cp * ql_c(k,j,i) * d_exner(k) * flag
5236	ENDDO
5237
5238	END SUBROUTINE lpm_interaction_droplets_ptq_ij
5239
5240
5241	!------------------------------------------------------------------------------!
5242	! Description:
5243	! ------------
5244	!> Calculate the liquid water content for each grid box.
5245	!------------------------------------------------------------------------------!
5246	SUBROUTINE lpm_calc_liquid_water_content
5247
5248
5249	INTEGER(iwp) :: i !<
5250	INTEGER(iwp) :: j !<
5251	INTEGER(iwp) :: k !<
5252	INTEGER(iwp) :: n !<
5253
5254	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'start' )
5255
5256	!
5257	!-- Set water content initially to zero
5258	ql = 0.0_wp; ql_v = 0.0_wp; ql_vp = 0.0_wp
5259
5260	!
5261	!-- Calculate for each grid box
5262	DO i = nxl, nxr
5263	DO j = nys, nyn
5264	DO k = nzb+1, nzt
5265	number_of_particles = prt_count(k,j,i)
5266	IF ( number_of_particles <= 0 ) CYCLE
5267	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
5268	!
5269	!-- Calculate the total volume in the boxes (ql_v, weighting factor
5270	!-- has to beincluded)
5271	DO n = 1, prt_count(k,j,i)
5272	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * &
5273	particles(n)%radius**3
5274	ENDDO
5275	!
5276	!-- Calculate the liquid water content
5277	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5278	ql(k,j,i) = ql(k,j,i) + rho_l * 1.33333333_wp * pi * &
5279	ql_v(k,j,i) / &
5280	( rho_surface * dx * dy * dzw(k) )
5281	IF ( ql(k,j,i) < 0.0_wp ) THEN
5282	WRITE( message_string, * ) 'LWC out of range: ' , &
5283	ql(k,j,i),i,j,k
5284	CALL message( 'lpm_calc_liquid_water_content', '', 2, 2, &
5285	-1, 6, 1 )
5286	ENDIF
5287	ELSE
5288	ql(k,j,i) = 0.0_wp
5289	ENDIF
5290	ENDDO
5291	ENDDO
5292	ENDDO
5293
5294	CALL cpu_log( log_point_s(45), 'lpm_calc_ql', 'stop' )
5295
5296	END SUBROUTINE lpm_calc_liquid_water_content
5297
5298
5299	!------------------------------------------------------------------------------!
5300	! Description:
5301	! ------------
5302	!> Calculates change in droplet radius by collision. Droplet collision is
5303	!> calculated for each grid box seperately. Collision is parameterized by
5304	!> using collision kernels. Two different kernels are available:
5305	!> Hall kernel: Kernel from Hall (1980, J. Atmos. Sci., 2486-2507), which
5306	!> considers collision due to pure gravitational effects.
5307	!> Wang kernel: Beside gravitational effects (treated with the Hall-kernel) also
5308	!> the effects of turbulence on the collision are considered using
5309	!> parameterizations of Ayala et al. (2008, New J. Phys., 10,
5310	!> 075015) and Wang and Grabowski (2009, Atmos. Sci. Lett., 10,
5311	!> 1-8). This kernel includes three possible effects of turbulence:
5312	!> the modification of the relative velocity between the droplets,
5313	!> the effect of preferential concentration, and the enhancement of
5314	!> collision efficiencies.
5315	!------------------------------------------------------------------------------!
5316	SUBROUTINE lpm_droplet_collision (i,j,k)
5317
5318	INTEGER(iwp), INTENT(IN) :: i !<
5319	INTEGER(iwp), INTENT(IN) :: j !<
5320	INTEGER(iwp), INTENT(IN) :: k !<
5321
5322	INTEGER(iwp) :: eclass !<
5323	INTEGER(iwp) :: n !<
5324	INTEGER(iwp) :: m !<
5325	INTEGER(iwp) :: rclass_l !<
5326	INTEGER(iwp) :: rclass_s !<
5327
5328	REAL(wp) :: collection_probability !< probability for collection
5329	REAL(wp) :: ddV !< inverse grid box volume
5330	REAL(wp) :: epsilon_collision !< dissipation rate
5331	REAL(wp) :: factor_volume_to_mass !< 4.0 / 3.0 * pi * rho_l
5332	REAL(wp) :: xm !< droplet mass of super-droplet m
5333	REAL(wp) :: xn !< droplet mass of super-droplet n
5334	REAL(wp) :: xsm !< aerosol mass of super-droplet m
5335	REAL(wp) :: xsn !< aerosol mass of super-droplet n
5336
5337	REAL(wp), DIMENSION(:), ALLOCATABLE :: weight !< weighting factor
5338	REAL(wp), DIMENSION(:), ALLOCATABLE :: mass !< total mass of super droplet
5339	REAL(wp), DIMENSION(:), ALLOCATABLE :: aero_mass !< total aerosol mass of super droplet
5340
5341	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'start' )
5342
5343	number_of_particles = prt_count(k,j,i)
5344	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
5345	ddV = 1.0_wp / ( dx * dy * dzw(k) )
5346	!
5347	!-- Collision requires at least one super droplet inside the box
5348	IF ( number_of_particles > 0 ) THEN
5349
5350	IF ( use_kernel_tables ) THEN
5351	!
5352	!-- Fast method with pre-calculated collection kernels for
5353	!-- discrete radius- and dissipation-classes.
5354	IF ( wang_kernel ) THEN
5355	eclass = INT( diss(k,j,i) * 1.0E4_wp / 600.0_wp * &
5356	dissipation_classes ) + 1
5357	epsilon_collision = diss(k,j,i)
5358	ELSE
5359	epsilon_collision = 0.0_wp
5360	ENDIF
5361
5362	IF ( hall_kernel .OR. epsilon_collision * 1.0E4_wp < 0.001_wp ) THEN
5363	eclass = 0 ! Hall kernel is used
5364	ELSE
5365	eclass = MIN( dissipation_classes, eclass )
5366	ENDIF
5367
5368	ELSE
5369	!
5370	!-- Collection kernels are re-calculated for every new
5371	!-- grid box. First, allocate memory for kernel table.
5372	!-- Third dimension is 1, because table is re-calculated for
5373	!-- every new dissipation value.
5374	ALLOCATE( ckernel(1:number_of_particles,1:number_of_particles,1:1) )
5375	!
5376	!-- Now calculate collection kernel for this box. Note that
5377	!-- the kernel is based on the previous time step
5378	CALL recalculate_kernel( i, j, k )
5379
5380	ENDIF
5381	!
5382	!-- Temporary fields for total mass of super-droplet, aerosol mass, and
5383	!-- weighting factor are allocated.
5384	ALLOCATE(mass(1:number_of_particles), weight(1:number_of_particles))
5385	IF ( curvature_solution_effects ) ALLOCATE(aero_mass(1:number_of_particles))
5386
5387	mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5388	particles(1:number_of_particles)%radius*3 &
5389	factor_volume_to_mass
5390
5391	weight(1:number_of_particles) = particles(1:number_of_particles)%weight_factor
5392
5393	IF ( curvature_solution_effects ) THEN
5394	aero_mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
5395	particles(1:number_of_particles)%aux1*3 &
5396	4.0_wp / 3.0_wp * pi * rho_s
5397	ENDIF
5398	!
5399	!-- Calculate collision/coalescence
5400	DO n = 1, number_of_particles
5401
5402	DO m = n, number_of_particles
5403	!
5404	!-- For collisions, the weighting factor of at least one super-droplet
5405	!-- needs to be larger or equal to one.
5406	IF ( MIN( weight(n), weight(m) ) .LT. 1.0_wp ) CYCLE
5407	!
5408	!-- Get mass of individual droplets (aerosols)
5409	xn = mass(n) / weight(n)
5410	xm = mass(m) / weight(m)
5411	IF ( curvature_solution_effects ) THEN
5412	xsn = aero_mass(n) / weight(n)
5413	xsm = aero_mass(m) / weight(m)
5414	ENDIF
5415	!
5416	!-- Probability that the necessary collisions take place
5417	IF ( use_kernel_tables ) THEN
5418	rclass_l = particles(n)%class
5419	rclass_s = particles(m)%class
5420
5421	collection_probability = MAX( weight(n), weight(m) ) * &
5422	ckernel(rclass_l,rclass_s,eclass) * ddV * dt_3d
5423	ELSE
5424	collection_probability = MAX( weight(n), weight(m) ) * &
5425	ckernel(n,m,1) * ddV * dt_3d
5426	ENDIF
5427	!
5428	!-- Calculate the number of collections and consider multiple collections.
5429	!-- (Accordingly, p_crit will be 0.0, 1.0, 2.0, ...)
5430	IF ( collection_probability - FLOOR(collection_probability) &
5431	.GT. random_function( iran_part ) ) THEN
5432	collection_probability = FLOOR(collection_probability) + 1.0_wp
5433	ELSE
5434	collection_probability = FLOOR(collection_probability)
5435	ENDIF
5436
5437	IF ( collection_probability .GT. 0.0_wp ) THEN
5438	!
5439	!-- Super-droplet n collects droplets of super-droplet m
5440	IF ( weight(n) .LT. weight(m) ) THEN
5441
5442	mass(n) = mass(n) + weight(n) * xm * collection_probability
5443	weight(m) = weight(m) - weight(n) * collection_probability
5444	mass(m) = mass(m) - weight(n) * xm * collection_probability
5445	IF ( curvature_solution_effects ) THEN
5446	aero_mass(n) = aero_mass(n) + weight(n) * xsm * collection_probability
5447	aero_mass(m) = aero_mass(m) - weight(n) * xsm * collection_probability
5448	ENDIF
5449
5450	ELSEIF ( weight(m) .LT. weight(n) ) THEN
5451
5452	mass(m) = mass(m) + weight(m) * xn * collection_probability
5453	weight(n) = weight(n) - weight(m) * collection_probability
5454	mass(n) = mass(n) - weight(m) * xn * collection_probability
5455	IF ( curvature_solution_effects ) THEN
5456	aero_mass(m) = aero_mass(m) + weight(m) * xsn * collection_probability
5457	aero_mass(n) = aero_mass(n) - weight(m) * xsn * collection_probability
5458	ENDIF
5459
5460	ELSE
5461	!
5462	!-- Collisions of particles of the same weighting factor.
5463	!-- Particle n collects 1/2 weight(n) droplets of particle m,
5464	!-- particle m collects 1/2 weight(m) droplets of particle n.
5465	!-- The total mass mass changes accordingly.
5466	!-- If n = m, the first half of the droplets coalesces with the
5467	!-- second half of the droplets; mass is unchanged because
5468	!-- xm = xn for n = m.
5469	!--
5470	!-- Note: For m = n this equation is an approximation only
5471	!-- valid for weight >> 1 (which is usually the case). The
5472	!-- approximation is weight(n)-1 = weight(n).
5473	mass(n) = mass(n) + 0.5_wp * weight(n) * ( xm - xn )
5474	mass(m) = mass(m) + 0.5_wp * weight(m) * ( xn - xm )
5475	IF ( curvature_solution_effects ) THEN
5476	aero_mass(n) = aero_mass(n) + 0.5_wp * weight(n) * ( xsm - xsn )
5477	aero_mass(m) = aero_mass(m) + 0.5_wp * weight(m) * ( xsn - xsm )
5478	ENDIF
5479	weight(n) = weight(n) - 0.5_wp * weight(m)
5480	weight(m) = weight(n)
5481
5482	ENDIF
5483
5484	ENDIF
5485
5486	ENDDO
5487
5488	ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
5489
5490	ENDDO
5491
5492	IF ( ANY(weight < 0.0_wp) ) THEN
5493	WRITE( message_string, * ) 'negative weighting factor'
5494	CALL message( 'lpm_droplet_collision', 'PA0028', &
5495	2, 2, -1, 6, 1 )
5496	ENDIF
5497
5498	particles(1:number_of_particles)%radius = ( mass(1:number_of_particles) / &
5499	( weight(1:number_of_particles) &
5500	* factor_volume_to_mass &
5501	) &
5502	)**0.33333333333333_wp
5503
5504	IF ( curvature_solution_effects ) THEN
5505	particles(1:number_of_particles)%aux1 = ( aero_mass(1:number_of_particles) / &
5506	( weight(1:number_of_particles) &
5507	* 4.0_wp / 3.0_wp * pi * rho_s &
5508	) &
5509	)**0.33333333333333_wp
5510	ENDIF
5511
5512	particles(1:number_of_particles)%weight_factor = weight(1:number_of_particles)
5513
5514	DEALLOCATE( weight, mass )
5515	IF ( curvature_solution_effects ) DEALLOCATE( aero_mass )
5516	IF ( .NOT. use_kernel_tables ) DEALLOCATE( ckernel )
5517
5518	!
5519	!-- Check if LWC is conserved during collision process
5520	IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
5521	IF ( ql_vp(k,j,i) / ql_v(k,j,i) >= 1.0001_wp .OR. &
5522	ql_vp(k,j,i) / ql_v(k,j,i) <= 0.9999_wp ) THEN
5523	WRITE( message_string, * ) ' LWC is not conserved during', &
5524	' collision! ', &
5525	' LWC after condensation: ', ql_v(k,j,i), &
5526	' LWC after collision: ', ql_vp(k,j,i)
5527	CALL message( 'lpm_droplet_collision', 'PA0040', 2, 2, -1, 6, 1 )
5528	ENDIF
5529	ENDIF
5530
5531	ENDIF
5532
5533	CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'stop' )
5534
5535	END SUBROUTINE lpm_droplet_collision
5536
5537	!------------------------------------------------------------------------------!
5538	! Description:
5539	! ------------
5540	!> Initialization of the collision efficiency matrix with fixed radius and
5541	!> dissipation classes, calculated at simulation start only.
5542	!------------------------------------------------------------------------------!
5543	SUBROUTINE lpm_init_kernels
5544
5545	INTEGER(iwp) :: i !<
5546	INTEGER(iwp) :: j !<
5547	INTEGER(iwp) :: k !<
5548
5549	!
5550	!-- Calculate collision efficiencies for fixed radius- and dissipation
5551	!-- classes
5552	IF ( collision_kernel(6:9) == 'fast' ) THEN
5553
5554	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
5555	0:dissipation_classes), epsclass(1:dissipation_classes), &
5556	radclass(1:radius_classes) )
5557
5558	!
5559	!-- Calculate the radius class bounds with logarithmic distances
5560	!-- in the interval [1.0E-6, 1000.0E-6] m
5561	rclass_lbound = LOG( 1.0E-6_wp )
5562	rclass_ubound = LOG( 1000.0E-6_wp )
5563	radclass(1) = EXP( rclass_lbound )
5564	DO i = 2, radius_classes
5565	radclass(i) = EXP( rclass_lbound + &
5566	( rclass_ubound - rclass_lbound ) * &
5567	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
5568	ENDDO
5569
5570	!
5571	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
5572	DO i = 1, dissipation_classes
5573	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
5574	ENDDO
5575	!
5576	!-- Calculate collision efficiencies of the Wang/ayala kernel
5577	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
5578	ecf(1:radius_classes,1:radius_classes), &
5579	gck(1:radius_classes,1:radius_classes), &
5580	winf(1:radius_classes) )
5581
5582	DO k = 1, dissipation_classes
5583
5584	epsilon_collision = epsclass(k)
5585	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 1.0_wp / 3.0_wp )
5586
5587	CALL turbsd
5588	CALL turb_enhance_eff
5589	CALL effic
5590
5591	DO j = 1, radius_classes
5592	DO i = 1, radius_classes
5593	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
5594	ENDDO
5595	ENDDO
5596
5597	ENDDO
5598
5599	!
5600	!-- Calculate collision efficiencies of the Hall kernel
5601	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
5602	hwratio(1:radius_classes,1:radius_classes) )
5603
5604	CALL fallg
5605	CALL effic
5606
5607	DO j = 1, radius_classes
5608	DO i = 1, radius_classes
5609	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
5610	* ec(i,j) * ABS( winf(j) - winf(i) )
5611	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
5612	ENDDO
5613	ENDDO
5614
5615	!
5616	!-- Test output of efficiencies
5617	IF ( j == -1 ) THEN
5618	PRINT, '** Hall kernel'
5619	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
5620	i = 1,radius_classes )
5621	DO j = 1, radius_classes
5622	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
5623	( hkernel(i,j), i = 1,radius_classes )
5624	ENDDO
5625
5626	DO k = 1, dissipation_classes
5627	DO i = 1, radius_classes
5628	DO j = 1, radius_classes
5629	IF ( hkernel(i,j) == 0.0_wp ) THEN
5630	hwratio(i,j) = 9999999.9_wp
5631	ELSE
5632	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
5633	ENDIF
5634	ENDDO
5635	ENDDO
5636
5637	PRINT, '** epsilon = ', epsclass(k)
5638	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
5639	i = 1,radius_classes )
5640	DO j = 1, radius_classes
5641	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
5642	( hwratio(i,j), i = 1,radius_classes )
5643	ENDDO
5644	ENDDO
5645	ENDIF
5646
5647	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
5648
5649	ENDIF
5650
5651	END SUBROUTINE lpm_init_kernels
5652
5653	!------------------------------------------------------------------------------!
5654	! Description:
5655	! ------------
5656	!> Calculation of collision kernels during each timestep and for each grid box
5657	!------------------------------------------------------------------------------!
5658	SUBROUTINE recalculate_kernel( i1, j1, k1 )
5659
5660
5661	INTEGER(iwp) :: i !<
5662	INTEGER(iwp) :: i1 !<
5663	INTEGER(iwp) :: j !<
5664	INTEGER(iwp) :: j1 !<
5665	INTEGER(iwp) :: k1 !<
5666
5667
5668	number_of_particles = prt_count(k1,j1,i1)
5669	radius_classes = number_of_particles ! necessary to use the same
5670	! subroutines as for
5671	! precalculated kernels
5672
5673	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
5674	radclass(1:number_of_particles), winf(1:number_of_particles) )
5675
5676	!
5677	!-- Store particle radii on the radclass array
5678	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
5679
5680	IF ( wang_kernel ) THEN
5681	epsilon_collision = diss(k1,j1,i1) ! dissipation rate in m2/s3
5682	ELSE
5683	epsilon_collision = 0.0_wp
5684	ENDIF
5685	urms = 2.02_wp * ( epsilon_collision / 0.04_wp )**( 0.33333333333_wp )
5686
5687	IF ( wang_kernel .AND. epsilon_collision > 1.0E-7_wp ) THEN
5688	!
5689	!-- Call routines to calculate efficiencies for the Wang kernel
5690	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
5691	ecf(1:number_of_particles,1:number_of_particles) )
5692
5693	CALL turbsd
5694	CALL turb_enhance_eff
5695	CALL effic
5696
5697	DO j = 1, number_of_particles
5698	DO i = 1, number_of_particles
5699	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
5700	ENDDO
5701	ENDDO
5702
5703	DEALLOCATE( gck, ecf )
5704	ELSE
5705	!
5706	!-- Call routines to calculate efficiencies for the Hall kernel
5707	CALL fallg
5708	CALL effic
5709
5710	DO j = 1, number_of_particles
5711	DO i = 1, number_of_particles
5712	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
5713	* ec(i,j) * ABS( winf(j) - winf(i) )
5714	ENDDO
5715	ENDDO
5716	ENDIF
5717
5718	DEALLOCATE( ec, radclass, winf )
5719
5720	END SUBROUTINE recalculate_kernel
5721
5722	!------------------------------------------------------------------------------!
5723	! Description:
5724	! ------------
5725	!> Calculation of effects of turbulence on the geometric collision kernel
5726	!> (by including the droplets' average radial relative velocities and their
5727	!> radial distribution function) following the analytic model by Aayala et al.
5728	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
5729	!> page 37ff.
5730	!>
5731	!> Input parameters, which need to be replaced by PALM parameters:
5732	!> water density, air density
5733	!------------------------------------------------------------------------------!
5734	SUBROUTINE turbsd
5735
5736	INTEGER(iwp) :: i !<
5737	INTEGER(iwp) :: j !<
5738
5739	REAL(wp) :: ao !<
5740	REAL(wp) :: ao_gr !<
5741	REAL(wp) :: bbb !<
5742	REAL(wp) :: be !<
5743	REAL(wp) :: b1 !<
5744	REAL(wp) :: b2 !<
5745	REAL(wp) :: ccc !<
5746	REAL(wp) :: c1 !<
5747	REAL(wp) :: c1_gr !<
5748	REAL(wp) :: c2 !<
5749	REAL(wp) :: d1 !<
5750	REAL(wp) :: d2 !<
5751	REAL(wp) :: eta !<
5752	REAL(wp) :: e1 !<
5753	REAL(wp) :: e2 !<
5754	REAL(wp) :: fao_gr !<
5755	REAL(wp) :: fr !<
5756	REAL(wp) :: grfin !<
5757	REAL(wp) :: lambda !<
5758	REAL(wp) :: lambda_re !<
5759	REAL(wp) :: lf !<
5760	REAL(wp) :: rc !<
5761	REAL(wp) :: rrp !<
5762	REAL(wp) :: sst !<
5763	REAL(wp) :: tauk !<
5764	REAL(wp) :: tl !<
5765	REAL(wp) :: t2 !<
5766	REAL(wp) :: tt !<
5767	REAL(wp) :: t1 !<
5768	REAL(wp) :: vk !<
5769	REAL(wp) :: vrms1xy !<
5770	REAL(wp) :: vrms2xy !<
5771	REAL(wp) :: v1 !<
5772	REAL(wp) :: v1v2xy !<
5773	REAL(wp) :: v1xysq !<
5774	REAL(wp) :: v2 !<
5775	REAL(wp) :: v2xysq !<
5776	REAL(wp) :: wrfin !<
5777	REAL(wp) :: wrgrav2 !<
5778	REAL(wp) :: wrtur2xy !<
5779	REAL(wp) :: xx !<
5780	REAL(wp) :: yy !<
5781	REAL(wp) :: z !<
5782
5783	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
5784	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
5785
5786	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon_collision )
5787	lambda_re = urms*2 SQRT( 15.0_wp / epsilon_collision / molecular_viscosity )
5788	tl = urms**2 / epsilon_collision
5789	lf = 0.5_wp * urms**3 / epsilon_collision
5790	tauk = SQRT( molecular_viscosity / epsilon_collision )
5791	eta = ( molecular_viscosity3 / epsilon_collision )0.25_wp
5792	vk = eta / tauk
5793
5794	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
5795	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
5796
5797	!
5798	!-- Get terminal velocity of droplets
5799	CALL fallg
5800
5801	DO i = 1, radius_classes
5802	tau(i) = winf(i) / g ! inertial time scale
5803	st(i) = tau(i) / tauk ! Stokes number
5804	ENDDO
5805
5806	!
5807	!-- Calculate average radial relative velocity at contact (wrfin)
5808	z = tt / tl
5809	be = SQRT( 2.0_wp ) * lambda / lf
5810	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
5811	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
5812	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
5813	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
5814	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
5815	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
5816	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
5817	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
5818	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
5819	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
5820
5821	DO i = 1, radius_classes
5822
5823	v1 = winf(i)
5824	t1 = tau(i)
5825
5826	DO j = 1, i
5827	rrp = radclass(i) + radclass(j)
5828	v2 = winf(j)
5829	t2 = tau(j)
5830
5831	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
5832	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
5833	v1xysq = v1xysq * urms**2 / t1
5834	vrms1xy = SQRT( v1xysq )
5835
5836	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
5837	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
5838	v2xysq = v2xysq * urms**2 / t2
5839	vrms2xy = SQRT( v2xysq )
5840
5841	IF ( winf(i) >= winf(j) ) THEN
5842	v1 = winf(i)
5843	t1 = tau(i)
5844	v2 = winf(j)
5845	t2 = tau(j)
5846	ELSE
5847	v1 = winf(j)
5848	t1 = tau(j)
5849	v2 = winf(i)
5850	t2 = tau(i)
5851	ENDIF
5852
5853	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
5854	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
5855	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
5856	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
5857	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
5858	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
5859	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
5860	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
5861	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
5862	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
5863
5864	!
5865	!-- Calculate radial distribution function (grfin)
5866	IF ( st(j) > st(i) ) THEN
5867	sst = st(j)
5868	ELSE
5869	sst = st(i)
5870	ENDIF
5871
5872	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
5873	sst*2 + 5.3406_wp sst
5874	IF ( xx < 0.0_wp ) xx = 0.0_wp
5875	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
5876
5877	c1_gr = xx / ( g / vk * tauk )**yy
5878
5879	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
5880	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
5881	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
5882
5883	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
5884	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
5885
5886	!
5887	!-- Calculate general collection kernel (without the consideration of
5888	!-- collection efficiencies)
5889	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
5890	gck(j,i) = gck(i,j)
5891
5892	ENDDO
5893	ENDDO
5894
5895	END SUBROUTINE turbsd
5896
5897	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
5898	!
5899	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5900	!-- effects on the collision kernel
5901
5902
5903	REAL(wp) :: a !<
5904	REAL(wp) :: aa1 !<
5905	REAL(wp) :: b !<
5906	REAL(wp) :: tau0 !<
5907	REAL(wp) :: vsett !<
5908
5909	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
5910	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
5911
5912	END FUNCTION phi_w
5913
5914	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
5915	!
5916	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
5917	!-- effects on the collision kernel
5918
5919	REAL(wp) :: a !<
5920	REAL(wp) :: aa1 !<
5921	REAL(wp) :: aa2 !<
5922	REAL(wp) :: aa3 !<
5923	REAL(wp) :: aa4 !<
5924	REAL(wp) :: aa5 !<
5925	REAL(wp) :: aa6 !<
5926	REAL(wp) :: b !<
5927	REAL(wp) :: tau1 !<
5928	REAL(wp) :: tau2 !<
5929	REAL(wp) :: vsett1 !<
5930	REAL(wp) :: vsett2 !<
5931
5932	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
5933	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
5934	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
5935	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
5936	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
5937	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
5938	vsett1 / vsett2
5939	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
5940	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
5941	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
5942	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
5943
5944	END FUNCTION zhi
5945
5946
5947	!------------------------------------------------------------------------------!
5948	! Description:
5949	! ------------
5950	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
5951	!> Meteorol.)
5952	!------------------------------------------------------------------------------!
5953	SUBROUTINE fallg
5954
5955	INTEGER(iwp) :: j !<
5956
5957	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
5958	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
5959	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
5960	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
5961	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
5962	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
5963
5964	REAL(wp) :: diameter !< droplet diameter in mm
5965
5966
5967	DO j = 1, radius_classes
5968
5969	diameter = radclass(j) * 2000.0_wp
5970
5971	IF ( diameter <= d0_rog ) THEN
5972	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
5973	EXP( -k_low_rog * diameter ) )
5974	ELSE
5975	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
5976	ENDIF
5977
5978	ENDDO
5979
5980	END SUBROUTINE fallg
5981
5982
5983	!------------------------------------------------------------------------------!
5984	! Description:
5985	! ------------
5986	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
5987	!------------------------------------------------------------------------------!
5988	SUBROUTINE effic
5989
5990	INTEGER(iwp) :: i !<
5991	INTEGER(iwp) :: iq !<
5992	INTEGER(iwp) :: ir !<
5993	INTEGER(iwp) :: j !<
5994	INTEGER(iwp) :: k !<
5995
5996	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
5997
5998	LOGICAL, SAVE :: first = .TRUE. !<
5999
6000	REAL(wp) :: ek !<
6001	REAL(wp) :: particle_radius !<
6002	REAL(wp) :: pp !<
6003	REAL(wp) :: qq !<
6004	REAL(wp) :: rq !<
6005
6006	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
6007
6008	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
6009
6010	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
6011
6012	!
6013	!-- Initial assignment of constants
6014	IF ( first ) THEN
6015
6016	first = .FALSE.
6017	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
6018	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
6019	150.0_wp, 200.0_wp, 300.0_wp /)
6020
6021	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
6022	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
6023	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
6024	0.90_wp, 0.95_wp, 1.00_wp /)
6025
6026	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
6027	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
6028	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
6029	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
6030	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
6031	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
6032	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
6033	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
6034	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
6035	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
6036	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
6037	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
6038	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
6039	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
6040	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
6041	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
6042	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
6043	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6044	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
6045	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
6046	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6047	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
6048	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
6049	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6050	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
6051	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
6052	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6053	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
6054	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6055	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6056	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
6057	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6058	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6059	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
6060	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
6061	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6062	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
6063	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
6064	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6065	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
6066	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
6067	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6068	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
6069	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
6070	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6071	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
6072	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
6073	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6074	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
6075	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
6076	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
6077	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
6078	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
6079	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
6080	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
6081	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
6082	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
6083	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
6084	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
6085	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
6086	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
6087	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
6088	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
6089	ENDIF
6090
6091	!
6092	!-- Calculate the radius class index of particles with respect to array r
6093	!-- Radius has to be in microns
6094	ALLOCATE( ira(1:radius_classes) )
6095	DO j = 1, radius_classes
6096	particle_radius = radclass(j) * 1.0E6_wp
6097	DO k = 1, 15
6098	IF ( particle_radius < r0(k) ) THEN
6099	ira(j) = k
6100	EXIT
6101	ENDIF
6102	ENDDO
6103	IF ( particle_radius >= r0(15) ) ira(j) = 16
6104	ENDDO
6105
6106	!
6107	!-- Two-dimensional linear interpolation of the collision efficiency.
6108	!-- Radius has to be in microns
6109	DO j = 1, radius_classes
6110	DO i = 1, j
6111
6112	ir = MAX( ira(i), ira(j) )
6113	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6114	iq = INT( rq * 20 ) + 1
6115	iq = MAX( iq , 2)
6116
6117	IF ( ir < 16 ) THEN
6118	IF ( ir >= 2 ) THEN
6119	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
6120	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6121	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6122	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
6123	* ecoll(ir-1,iq-1) &
6124	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
6125	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
6126	+ pp * qq * ecoll(ir,iq)
6127	ELSE
6128	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6129	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
6130	ENDIF
6131	ELSE
6132	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6133	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
6134	ec(j,i) = MIN( ek, 1.0_wp )
6135	ENDIF
6136
6137	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
6138
6139	ec(i,j) = ec(j,i)
6140
6141	ENDDO
6142	ENDDO
6143
6144	DEALLOCATE( ira )
6145
6146	END SUBROUTINE effic
6147
6148
6149	!------------------------------------------------------------------------------!
6150	! Description:
6151	! ------------
6152	!> Interpolation of turbulent enhancement factor for collision efficencies
6153	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
6154	!------------------------------------------------------------------------------!
6155	SUBROUTINE turb_enhance_eff
6156
6157	INTEGER(iwp) :: i !<
6158	INTEGER(iwp) :: iq !<
6159	INTEGER(iwp) :: ir !<
6160	INTEGER(iwp) :: j !<
6161	INTEGER(iwp) :: k !<
6162	INTEGER(iwp) :: kk !<
6163
6164	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
6165
6166	LOGICAL, SAVE :: first = .TRUE. !<
6167
6168	REAL(wp) :: particle_radius !<
6169	REAL(wp) :: pp !<
6170	REAL(wp) :: qq !<
6171	REAL(wp) :: rq !<
6172	REAL(wp) :: y1 !<
6173	REAL(wp) :: y2 !<
6174	REAL(wp) :: y3 !<
6175
6176	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
6177	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
6178
6179	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
6180	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
6181
6182	!
6183	!-- Initial assignment of constants
6184	IF ( first ) THEN
6185
6186	first = .FALSE.
6187
6188	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
6189	100.0_wp /)
6190
6191	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
6192	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
6193	!
6194	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
6195	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
6196	1.207_wp, 1.207_wp, 1.0_wp /)
6197	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
6198	1.069_wp, 1.069_wp, 1.0_wp /)
6199	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
6200	1.000_wp, 1.000_wp, 1.0_wp /)
6201	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
6202	1.025_wp, 1.025_wp, 1.0_wp /)
6203	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
6204	1.056_wp, 1.056_wp, 1.0_wp /)
6205	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
6206	1.028_wp, 1.028_wp, 1.0_wp /)
6207	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
6208	1.046_wp, 1.046_wp, 1.0_wp /)
6209	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
6210	1.029_wp, 1.029_wp, 1.0_wp /)
6211	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
6212	1.021_wp, 1.021_wp, 1.0_wp /)
6213	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
6214	1.088_wp, 1.088_wp, 1.0_wp /)
6215	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
6216	2.60_wp, 2.60_wp, 1.0_wp /)
6217	!
6218	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
6219	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
6220	1.445_wp, 1.445_wp, 1.0_wp /)
6221	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
6222	1.201_wp, 1.201_wp, 1.0_wp /)
6223	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
6224	1.150_wp, 1.150_wp, 1.0_wp /)
6225	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
6226	1.126_wp, 1.126_wp, 1.0_wp /)
6227	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
6228	1.092_wp, 1.092_wp, 1.0_wp /)
6229	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
6230	1.051_wp, 1.051_wp, 1.0_wp /)
6231	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
6232	1.086_wp, 1.086_wp, 1.0_wp /)
6233	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
6234	1.063_wp, 1.063_wp, 1.0_wp /)
6235	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
6236	1.100_wp, 1.100_wp, 1.0_wp /)
6237	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
6238	1.120_wp, 1.120_wp, 1.0_wp /)
6239	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
6240	26.0_wp, 26.0_wp, 1.0_wp /)
6241
6242	ENDIF
6243
6244	!
6245	!-- Calculate the radius class index of particles with respect to array r0
6246	!-- The droplet radius has to be given in microns.
6247	ALLOCATE( ira(1:radius_classes) )
6248
6249	DO j = 1, radius_classes
6250	particle_radius = radclass(j) * 1.0E6_wp
6251	DO k = 1, 7
6252	IF ( particle_radius < r0(k) ) THEN
6253	ira(j) = k
6254	EXIT
6255	ENDIF
6256	ENDDO
6257	IF ( particle_radius >= r0(7) ) ira(j) = 8
6258	ENDDO
6259
6260	!
6261	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
6262	!-- The droplet radius has to be given in microns.
6263	DO j = 1, radius_classes
6264	DO i = 1, j
6265
6266	ir = MAX( ira(i), ira(j) )
6267	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
6268
6269	DO kk = 2, 11
6270	IF ( rq <= rat(kk) ) THEN
6271	iq = kk
6272	EXIT
6273	ENDIF
6274	ENDDO
6275
6276	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
6277
6278	IF ( ir < 8 ) THEN
6279	IF ( ir >= 2 ) THEN
6280	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
6281	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
6282	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6283	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
6284	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
6285	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
6286	pp * qq * ecoll_100(ir,iq)
6287	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
6288	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
6289	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
6290	pp * qq * ecoll_400(ir,iq)
6291	ELSE
6292	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6293	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
6294	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
6295	ENDIF
6296	ELSE
6297	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
6298	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
6299	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
6300	ENDIF
6301	!
6302	!-- Linear interpolation of turbulent enhancement factor
6303	IF ( epsilon_collision <= 0.01_wp ) THEN
6304	ecf(j,i) = ( epsilon_collision - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
6305	+ ( epsilon_collision - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
6306	ELSEIF ( epsilon_collision <= 0.06_wp ) THEN
6307	ecf(j,i) = ( epsilon_collision - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6308	+ ( epsilon_collision - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6309	ELSE
6310	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
6311	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
6312	ENDIF
6313
6314	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
6315
6316	ecf(i,j) = ecf(j,i)
6317
6318	ENDDO
6319	ENDDO
6320
6321	END SUBROUTINE turb_enhance_eff
6322
6323
6324	!------------------------------------------------------------------------------!
6325	! Description:
6326	! ------------
6327	! This routine is a part of the Lagrangian particle model. Super droplets which
6328	! fulfill certain criterion's (e.g. a big weighting factor and a large radius)
6329	! can be split into several super droplets with a reduced number of
6330	! represented particles of every super droplet. This mechanism ensures an
6331	! improved representation of the right tail of the drop size distribution with
6332	! a feasible amount of computational costs. The limits of particle creation
6333	! should be chosen carefully! The idea of this algorithm is based on
6334	! Unterstrasser and Soelch, 2014.
6335	!------------------------------------------------------------------------------!
6336	SUBROUTINE lpm_splitting
6337
6338	INTEGER(iwp) :: i !<
6339	INTEGER(iwp) :: j !<
6340	INTEGER(iwp) :: jpp !<
6341	INTEGER(iwp) :: k !<
6342	INTEGER(iwp) :: n !<
6343	INTEGER(iwp) :: new_particles_gb !< counter of created particles within one grid box
6344	INTEGER(iwp) :: new_size !< new particle array size
6345	INTEGER(iwp) :: np !<
6346	INTEGER(iwp) :: old_size !< old particle array size
6347
6348	INTEGER(iwp), PARAMETER :: n_max = 100 !< number of radii bin for splitting functions
6349
6350	LOGICAL :: first_loop_stride_sp = .TRUE. !< flag to calculate constants only once
6351
6352	REAL(wp) :: diameter !< diameter of droplet
6353	REAL(wp) :: dlog !< factor for DSD calculation
6354	REAL(wp) :: factor_volume_to_mass !< pre calculate factor volume to mass
6355	REAL(wp) :: lambda !< slope parameter of gamma-distribution
6356	REAL(wp) :: lwc !< liquid water content of grid box
6357	REAL(wp) :: lwc_total !< average liquid water content of cloud
6358	REAL(wp) :: m1 !< first moment of DSD
6359	REAL(wp) :: m1_total !< average over all PEs of first moment of DSD
6360	REAL(wp) :: m2 !< second moment of DSD
6361	REAL(wp) :: m2_total !< average average over all PEs second moment of DSD
6362	REAL(wp) :: m3 !< third moment of DSD
6363	REAL(wp) :: m3_total !< average average over all PEs third moment of DSD
6364	REAL(wp) :: mu !< spectral shape parameter of gamma distribution
6365	REAL(wp) :: nrclgb !< number of cloudy grid boxes (ql >= 1.0E-5 kg/kg)
6366	REAL(wp) :: nrclgb_total !< average over all PEs of number of cloudy grid boxes
6367	REAL(wp) :: nr !< number concentration of cloud droplets
6368	REAL(wp) :: nr_total !< average over all PEs of number of cloudy grid boxes
6369	REAL(wp) :: nr0 !< intercept parameter of gamma distribution
6370	REAL(wp) :: pirho_l !< pi * rho_l / 6.0
6371	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6372	!< (Siebesma et al 2003, JAS, 60)
6373	REAL(wp) :: rm !< volume averaged mean radius
6374	REAL(wp) :: rm_total !< average over all PEs of volume averaged mean radius
6375	REAL(wp) :: r_min = 1.0E-6_wp !< minimum radius of approximated spectra
6376	REAL(wp) :: r_max = 1.0E-3_wp !< maximum radius of approximated spectra
6377	REAL(wp) :: sigma_log = 1.5_wp !< standard deviation of the LOG-distribution
6378	REAL(wp) :: zeta !< Parameter for DSD calculation of Seifert
6379
6380	REAL(wp), DIMENSION(0:n_max-1) :: an_spl !< size dependent critical weight factor
6381	REAL(wp), DIMENSION(0:n_max-1) :: r_bin_mid !< mass weighted mean radius of a bin
6382	REAL(wp), DIMENSION(0:n_max) :: r_bin !< boundaries of a radius bin
6383
6384	TYPE(particle_type) :: tmp_particle !< temporary particle TYPE
6385
6386	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'start' )
6387
6388	IF ( first_loop_stride_sp ) THEN
6389	IF ( i_splitting_mode == 2 .OR. i_splitting_mode == 3 ) THEN
6390	dlog = ( LOG10(r_max) - LOG10(r_min) ) / ( n_max - 1 )
6391	DO i = 0, n_max-1
6392	r_bin(i) = 10.0_wp*( LOG10(r_min) + i dlog - 0.5_wp * dlog )
6393	r_bin_mid(i) = 10.0_wp*( LOG10(r_min) + i dlog )
6394	ENDDO
6395	r_bin(n_max) = 10.0_wp*( LOG10(r_min) + n_max dlog - 0.5_wp * dlog )
6396	ENDIF
6397	factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
6398	pirho_l = pi * rho_l / 6.0_wp
6399	IF ( weight_factor_split == -1.0_wp ) THEN
6400	weight_factor_split = 0.1_wp * initial_weighting_factor
6401	ENDIF
6402	ENDIF
6403
6404
6405	IF ( i_splitting_mode == 1 ) THEN
6406
6407	DO i = nxl, nxr
6408	DO j = nys, nyn
6409	DO k = nzb+1, nzt
6410
6411	new_particles_gb = 0
6412	number_of_particles = prt_count(k,j,i)
6413	IF ( number_of_particles <= 0 .OR. &
6414	ql(k,j,i) < ql_crit ) CYCLE
6415	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6416	!
6417	!-- Start splitting operations. Each particle is checked if it
6418	!-- fulfilled the splitting criterion's. In splitting mode 'const'
6419	!-- a critical radius (radius_split) a critical weighting factor
6420	!-- (weight_factor_split) and a splitting factor (splitting_factor)
6421	!-- must be prescribed (see particle_parameters). Super droplets
6422	!-- which have a larger radius and larger weighting factor are split
6423	!-- into 'splitting_factor' super droplets. Therefore, the weighting
6424	!-- factor of the super droplet and all created clones is reduced
6425	!-- by the factor of 'splitting_factor'.
6426	DO n = 1, number_of_particles
6427	IF ( particles(n)%particle_mask .AND. &
6428	particles(n)%radius >= radius_split .AND. &
6429	particles(n)%weight_factor >= weight_factor_split ) &
6430	THEN
6431	!
6432	!-- Calculate the new number of particles.
6433	new_size = prt_count(k,j,i) + splitting_factor - 1
6434	!
6435	!-- Cycle if maximum number of particles per grid box
6436	!-- is greater than the allowed maximum number.
6437	IF ( new_size >= max_number_particles_per_gridbox ) CYCLE
6438	!
6439	!-- Reallocate particle array if necessary.
6440	IF ( new_size > SIZE(particles) ) THEN
6441	CALL realloc_particles_array(i,j,k,new_size)
6442	ENDIF
6443	old_size = prt_count(k,j,i)
6444	!
6445	!-- Calculate new weighting factor.
6446	particles(n)%weight_factor = &
6447	particles(n)%weight_factor / splitting_factor
6448	tmp_particle = particles(n)
6449	!
6450	!-- Create splitting_factor-1 new particles.
6451	DO jpp = 1, splitting_factor-1
6452	grid_particles(k,j,i)%particles(jpp+old_size) = &
6453	tmp_particle
6454	ENDDO
6455	new_particles_gb = new_particles_gb + splitting_factor - 1
6456	!
6457	!-- Save the new number of super droplets for every grid box.
6458	prt_count(k,j,i) = prt_count(k,j,i) + &
6459	splitting_factor - 1
6460	ENDIF
6461	ENDDO
6462
6463	ENDDO
6464	ENDDO
6465	ENDDO
6466
6467	ELSEIF ( i_splitting_mode == 2 ) THEN
6468	!
6469	!-- Initialize summing variables.
6470	lwc = 0.0_wp
6471	lwc_total = 0.0_wp
6472	m1 = 0.0_wp
6473	m1_total = 0.0_wp
6474	m2 = 0.0_wp
6475	m2_total = 0.0_wp
6476	m3 = 0.0_wp
6477	m3_total = 0.0_wp
6478	nr = 0.0_wp
6479	nrclgb = 0.0_wp
6480	nrclgb_total = 0.0_wp
6481	nr_total = 0.0_wp
6482	rm = 0.0_wp
6483	rm_total = 0.0_wp
6484
6485	DO i = nxl, nxr
6486	DO j = nys, nyn
6487	DO k = nzb+1, nzt
6488	number_of_particles = prt_count(k,j,i)
6489	IF ( number_of_particles <= 0 .OR. &
6490	ql(k,j,i) < ql_crit ) CYCLE
6491	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6492	nrclgb = nrclgb + 1.0_wp
6493	!
6494	!-- Calculate moments of DSD.
6495	DO n = 1, number_of_particles
6496	IF ( particles(n)%particle_mask .AND. &
6497	particles(n)%radius >= r_min ) &
6498	THEN
6499	nr = nr + particles(n)%weight_factor
6500	rm = rm + factor_volume_to_mass * &
6501	particles(n)%radius*3 &
6502	particles(n)%weight_factor
6503	IF ( isf == 1 ) THEN
6504	diameter = particles(n)%radius * 2.0_wp
6505	lwc = lwc + factor_volume_to_mass * &
6506	particles(n)%radius*3 &
6507	particles(n)%weight_factor
6508	m1 = m1 + particles(n)%weight_factor * diameter
6509	m2 = m2 + particles(n)%weight_factor * diameter**2
6510	m3 = m3 + particles(n)%weight_factor * diameter**3
6511	ENDIF
6512	ENDIF
6513	ENDDO
6514	ENDDO
6515	ENDDO
6516	ENDDO
6517
6518	#if defined( __parallel )
6519	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6520	CALL MPI_ALLREDUCE( nr, nr_total, 1 , &
6521	MPI_REAL, MPI_SUM, comm2d, ierr )
6522	CALL MPI_ALLREDUCE( rm, rm_total, 1 , &
6523	MPI_REAL, MPI_SUM, comm2d, ierr )
6524	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6525	CALL MPI_ALLREDUCE( nrclgb, nrclgb_total, 1 , &
6526	MPI_REAL, MPI_SUM, comm2d, ierr )
6527	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6528	CALL MPI_ALLREDUCE( lwc, lwc_total, 1 , &
6529	MPI_REAL, MPI_SUM, comm2d, ierr )
6530	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6531	CALL MPI_ALLREDUCE( m1, m1_total, 1 , &
6532	MPI_REAL, MPI_SUM, comm2d, ierr )
6533	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6534	CALL MPI_ALLREDUCE( m2, m2_total, 1 , &
6535	MPI_REAL, MPI_SUM, comm2d, ierr )
6536	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
6537	CALL MPI_ALLREDUCE( m3, m3_total, 1 , &
6538	MPI_REAL, MPI_SUM, comm2d, ierr )
6539	#endif
6540
6541	!
6542	!-- Calculate number concentration and mean volume averaged radius.
6543	nr_total = MERGE( nr_total / nrclgb_total, &
6544	0.0_wp, nrclgb_total > 0.0_wp &
6545	)
6546	rm_total = MERGE( ( rm_total / &
6547	( nr_total * factor_volume_to_mass ) &
6548	)**0.3333333_wp, 0.0_wp, nrclgb_total > 0.0_wp &
6549	)
6550	!
6551	!-- Check which function should be used to approximate the DSD.
6552	IF ( isf == 1 ) THEN
6553	lwc_total = MERGE( lwc_total / nrclgb_total, &
6554	0.0_wp, nrclgb_total > 0.0_wp &
6555	)
6556	m1_total = MERGE( m1_total / nrclgb_total, &
6557	0.0_wp, nrclgb_total > 0.0_wp &
6558	)
6559	m2_total = MERGE( m2_total / nrclgb_total, &
6560	0.0_wp, nrclgb_total > 0.0_wp &
6561	)
6562	m3_total = MERGE( m3_total / nrclgb_total, &
6563	0.0_wp, nrclgb_total > 0.0_wp &
6564	)
6565	zeta = m1_total * m3_total / m2_total**2
6566	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6567	( zeta - 1.0_wp ), 0.0_wp &
6568	)
6569
6570	lambda = ( pirho_l * nr_total / lwc_total * &
6571	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * ( mu + 1.0_wp ) &
6572	)**0.3333333_wp
6573	nr0 = nr_total / gamma( mu + 1.0_wp ) * lambda**( mu + 1.0_wp )
6574
6575	DO n = 0, n_max-1
6576	diameter = r_bin_mid(n) * 2.0_wp
6577	an_spl(n) = nr0 * diameter*mu EXP( -lambda * diameter ) * &
6578	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6579	ENDDO
6580	ELSEIF ( isf == 2 ) THEN
6581	DO n = 0, n_max-1
6582	an_spl(n) = nr_total / ( SQRT( 2.0_wp * pi ) * &
6583	LOG(sigma_log) * r_bin_mid(n) &
6584	) * &
6585	EXP( -( LOG( r_bin_mid(n) / rm_total )**2 ) / &
6586	( 2.0_wp * LOG(sigma_log)**2 ) &
6587	) * &
6588	( r_bin(n+1) - r_bin(n) )
6589	ENDDO
6590	ELSEIF( isf == 3 ) THEN
6591	DO n = 0, n_max-1
6592	an_spl(n) = 3.0_wp * nr_total * r_bin_mid(n)2 / rm_total3 * &
6593	EXP( - ( r_bin_mid(n)3 / rm_total3 ) ) * &
6594	( r_bin(n+1) - r_bin(n) )
6595	ENDDO
6596	ENDIF
6597	!
6598	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6599	an_spl = MAX(an_spl, 1.0_wp)
6600
6601	DO i = nxl, nxr
6602	DO j = nys, nyn
6603	DO k = nzb+1, nzt
6604	number_of_particles = prt_count(k,j,i)
6605	IF ( number_of_particles <= 0 .OR. &
6606	ql(k,j,i) < ql_crit ) CYCLE
6607	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6608	new_particles_gb = 0
6609	!
6610	!-- Start splitting operations. Each particle is checked if it
6611	!-- fulfilled the splitting criterion's. In splitting mode 'cl_av'
6612	!-- a critical radius (radius_split) and a splitting function must
6613	!-- be prescribed (see particles_par). The critical weighting factor
6614	!-- is calculated while approximating a 'gamma', 'log' or 'exp'-
6615	!-- drop size distribution. In this mode the DSD is calculated as
6616	!-- an average over all cloudy grid boxes. Super droplets which
6617	!-- have a larger radius and larger weighting factor are split into
6618	!-- 'splitting_factor' super droplets. In this case the splitting
6619	!-- factor is calculated of weighting factor of the super droplet
6620	!-- and the approximated number concentration for droplet of such
6621	!-- a size. Due to the splitting, the weighting factor of the
6622	!-- super droplet and all created clones is reduced by the factor
6623	!-- of 'splitting_facor'.
6624	DO n = 1, number_of_particles
6625	DO np = 0, n_max-1
6626	IF ( r_bin(np) >= radius_split .AND. &
6627	particles(n)%particle_mask .AND. &
6628	particles(n)%radius >= r_bin(np) .AND. &
6629	particles(n)%radius < r_bin(np+1) .AND. &
6630	particles(n)%weight_factor >= an_spl(np) ) &
6631	THEN
6632	!
6633	!-- Calculate splitting factor
6634	splitting_factor = &
6635	MIN( INT( particles(n)%weight_factor / &
6636	an_spl(np) &
6637	), splitting_factor_max &
6638	)
6639	IF ( splitting_factor < 2 ) CYCLE
6640	!
6641	!-- Calculate the new number of particles.
6642	new_size = prt_count(k,j,i) + splitting_factor - 1
6643	!
6644	!-- Cycle if maximum number of particles per grid box
6645	!-- is greater than the allowed maximum number.
6646	IF ( new_size >= max_number_particles_per_gridbox ) &
6647	CYCLE
6648	!
6649	!-- Reallocate particle array if necessary.
6650	IF ( new_size > SIZE(particles) ) THEN
6651	CALL realloc_particles_array(i,j,k,new_size)
6652	ENDIF
6653	old_size = prt_count(k,j,i)
6654	new_particles_gb = new_particles_gb + &
6655	splitting_factor - 1
6656	!
6657	!-- Calculate new weighting factor.
6658	particles(n)%weight_factor = &
6659	particles(n)%weight_factor / splitting_factor
6660	tmp_particle = particles(n)
6661	!
6662	!-- Create splitting_factor-1 new particles.
6663	DO jpp = 1, splitting_factor-1
6664	grid_particles(k,j,i)%particles(jpp+old_size) = &
6665	tmp_particle
6666	ENDDO
6667	!
6668	!-- Save the new number of super droplets.
6669	prt_count(k,j,i) = prt_count(k,j,i) + &
6670	splitting_factor - 1
6671	ENDIF
6672	ENDDO
6673	ENDDO
6674
6675	ENDDO
6676	ENDDO
6677	ENDDO
6678
6679	ELSEIF ( i_splitting_mode == 3 ) THEN
6680
6681	DO i = nxl, nxr
6682	DO j = nys, nyn
6683	DO k = nzb+1, nzt
6684
6685	!
6686	!-- Initialize summing variables.
6687	lwc = 0.0_wp
6688	m1 = 0.0_wp
6689	m2 = 0.0_wp
6690	m3 = 0.0_wp
6691	nr = 0.0_wp
6692	rm = 0.0_wp
6693
6694	new_particles_gb = 0
6695	number_of_particles = prt_count(k,j,i)
6696	IF ( number_of_particles <= 0 .OR. &
6697	ql(k,j,i) < ql_crit ) CYCLE
6698	particles => grid_particles(k,j,i)%particles
6699	!
6700	!-- Calculate moments of DSD.
6701	DO n = 1, number_of_particles
6702	IF ( particles(n)%particle_mask .AND. &
6703	particles(n)%radius >= r_min ) &
6704	THEN
6705	nr = nr + particles(n)%weight_factor
6706	rm = rm + factor_volume_to_mass * &
6707	particles(n)%radius*3 &
6708	particles(n)%weight_factor
6709	IF ( isf == 1 ) THEN
6710	diameter = particles(n)%radius * 2.0_wp
6711	lwc = lwc + factor_volume_to_mass * &
6712	particles(n)%radius*3 &
6713	particles(n)%weight_factor
6714	m1 = m1 + particles(n)%weight_factor * diameter
6715	m2 = m2 + particles(n)%weight_factor * diameter**2
6716	m3 = m3 + particles(n)%weight_factor * diameter**3
6717	ENDIF
6718	ENDIF
6719	ENDDO
6720
6721	IF ( nr <= 0.0_wp .OR. rm <= 0.0_wp ) CYCLE
6722	!
6723	!-- Calculate mean volume averaged radius.
6724	rm = ( rm / ( nr * factor_volume_to_mass ) )**0.3333333_wp
6725	!
6726	!-- Check which function should be used to approximate the DSD.
6727	IF ( isf == 1 ) THEN
6728	!
6729	!-- Gamma size distribution to calculate
6730	!-- critical weight_factor (e.g. Marshall + Palmer, 1948).
6731	zeta = m1 * m3 / m2**2
6732	mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / &
6733	( zeta - 1.0_wp ), 0.0_wp &
6734	)
6735	lambda = ( pirho_l * nr / lwc * &
6736	( mu + 3.0_wp ) * ( mu + 2.0_wp ) * &
6737	( mu + 1.0_wp ) &
6738	)**0.3333333_wp
6739	nr0 = ( nr / (gamma( mu + 1.0_wp ) ) ) * &
6740	lambda**( mu + 1.0_wp )
6741
6742	DO n = 0, n_max-1
6743	diameter = r_bin_mid(n) * 2.0_wp
6744	an_spl(n) = nr0 * diameter*mu &
6745	EXP( -lambda * diameter ) * &
6746	( r_bin(n+1) - r_bin(n) ) * 2.0_wp
6747	ENDDO
6748	ELSEIF ( isf == 2 ) THEN
6749	!
6750	!-- Lognormal size distribution to calculate critical
6751	!-- weight_factor (e.g. Levin, 1971, Bradley + Stow, 1974).
6752	DO n = 0, n_max-1
6753	an_spl(n) = nr / ( SQRT( 2.0_wp * pi ) * &
6754	LOG(sigma_log) * r_bin_mid(n) &
6755	) * &
6756	EXP( -( LOG( r_bin_mid(n) / rm )**2 ) / &
6757	( 2.0_wp * LOG(sigma_log)**2 ) &
6758	) * &
6759	( r_bin(n+1) - r_bin(n) )
6760	ENDDO
6761	ELSEIF ( isf == 3 ) THEN
6762	!
6763	!-- Exponential size distribution to calculate critical
6764	!-- weight_factor (e.g. Berry + Reinhardt, 1974).
6765	DO n = 0, n_max-1
6766	an_spl(n) = 3.0_wp * nr * r_bin_mid(n)2 / rm3 * &
6767	EXP( - ( r_bin_mid(n)3 / rm3 ) ) * &
6768	( r_bin(n+1) - r_bin(n) )
6769	ENDDO
6770	ENDIF
6771
6772	!
6773	!-- Criterion to avoid super droplets with a weighting factor < 1.0.
6774	an_spl = MAX(an_spl, 1.0_wp)
6775	!
6776	!-- Start splitting operations. Each particle is checked if it
6777	!-- fulfilled the splitting criterion's. In splitting mode 'gb_av'
6778	!-- a critical radius (radius_split) and a splitting function must
6779	!-- be prescribed (see particles_par). The critical weighting factor
6780	!-- is calculated while appoximating a 'gamma', 'log' or 'exp'-
6781	!-- drop size distribution. In this mode a DSD is calculated for
6782	!-- every cloudy grid box. Super droplets which have a larger
6783	!-- radius and larger weighting factor are split into
6784	!-- 'splitting_factor' super droplets. In this case the splitting
6785	!-- factor is calculated of weighting factor of the super droplet
6786	!-- and theapproximated number concentration for droplet of such
6787	!-- a size. Due to the splitting, the weighting factor of the
6788	!-- super droplet and all created clones is reduced by the factor
6789	!-- of 'splitting_facor'.
6790	DO n = 1, number_of_particles
6791	DO np = 0, n_max-1
6792	IF ( r_bin(np) >= radius_split .AND. &
6793	particles(n)%particle_mask .AND. &
6794	particles(n)%radius >= r_bin(np) .AND. &
6795	particles(n)%radius < r_bin(np+1) .AND. &
6796	particles(n)%weight_factor >= an_spl(np) ) &
6797	THEN
6798	!
6799	!-- Calculate splitting factor.
6800	splitting_factor = &
6801	MIN( INT( particles(n)%weight_factor / &
6802	an_spl(np) &
6803	), splitting_factor_max &
6804	)
6805	IF ( splitting_factor < 2 ) CYCLE
6806
6807	!
6808	!-- Calculate the new number of particles.
6809	new_size = prt_count(k,j,i) + splitting_factor - 1
6810	!
6811	!-- Cycle if maximum number of particles per grid box
6812	!-- is greater than the allowed maximum number.
6813	IF ( new_size >= max_number_particles_per_gridbox ) &
6814	CYCLE
6815	!
6816	!-- Reallocate particle array if necessary.
6817	IF ( new_size > SIZE(particles) ) THEN
6818	CALL realloc_particles_array(i,j,k,new_size)
6819	ENDIF
6820	!
6821	!-- Calculate new weighting factor.
6822	particles(n)%weight_factor = &
6823	particles(n)%weight_factor / splitting_factor
6824	tmp_particle = particles(n)
6825	old_size = prt_count(k,j,i)
6826	!
6827	!-- Create splitting_factor-1 new particles.
6828	DO jpp = 1, splitting_factor-1
6829	grid_particles(k,j,i)%particles(jpp+old_size) = &
6830	tmp_particle
6831	ENDDO
6832	!
6833	!-- Save the new number of droplets for every grid box.
6834	prt_count(k,j,i) = prt_count(k,j,i) + &
6835	splitting_factor - 1
6836	new_particles_gb = new_particles_gb + &
6837	splitting_factor - 1
6838	ENDIF
6839	ENDDO
6840	ENDDO
6841	ENDDO
6842	ENDDO
6843	ENDDO
6844	ENDIF
6845
6846	CALL cpu_log( log_point_s(80), 'lpm_splitting', 'stop' )
6847
6848	END SUBROUTINE lpm_splitting
6849
6850
6851	!------------------------------------------------------------------------------!
6852	! Description:
6853	! ------------
6854	! This routine is a part of the Lagrangian particle model. Two Super droplets
6855	! which fulfill certain criterion's (e.g. a big weighting factor and a small
6856	! radius) can be merged into one super droplet with a increased number of
6857	! represented particles of the super droplet. This mechanism ensures an
6858	! improved a feasible amount of computational costs. The limits of particle
6859	! creation should be chosen carefully! The idea of this algorithm is based on
6860	! Unterstrasser and Soelch, 2014.
6861	!------------------------------------------------------------------------------!
6862	SUBROUTINE lpm_merging
6863
6864	INTEGER(iwp) :: i !<
6865	INTEGER(iwp) :: j !<
6866	INTEGER(iwp) :: k !<
6867	INTEGER(iwp) :: n !<
6868	INTEGER(iwp) :: merge_drp = 0 !< number of merged droplets
6869
6870
6871	REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells
6872	!< (e.g. Siebesma et al 2003, JAS, 60)
6873
6874	CALL cpu_log( log_point_s(81), 'lpm_merging', 'start' )
6875
6876	merge_drp = 0
6877
6878	IF ( weight_factor_merge == -1.0_wp ) THEN
6879	weight_factor_merge = 0.5_wp * initial_weighting_factor
6880	ENDIF
6881
6882	DO i = nxl, nxr
6883	DO j = nys, nyn
6884	DO k = nzb+1, nzt
6885
6886	number_of_particles = prt_count(k,j,i)
6887	IF ( number_of_particles <= 0 .OR. &
6888	ql(k,j,i) >= ql_crit ) CYCLE
6889	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
6890	!
6891	!-- Start merging operations: This routine delete super droplets with
6892	!-- a small radius (radius <= radius_merge) and a low weighting
6893	!-- factor (weight_factor <= weight_factor_merge). The number of
6894	!-- represented particles will be added to the next particle of the
6895	!-- particle array. Tests showed that this simplified method can be
6896	!-- used because it will only take place outside of cloudy grid
6897	!-- boxes where ql <= 1.0E-5 kg/kg. Therefore, especially former cloned
6898	!-- and subsequent evaporated super droplets will be merged.
6899	DO n = 1, number_of_particles-1
6900	IF ( particles(n)%particle_mask .AND. &
6901	particles(n+1)%particle_mask .AND. &
6902	particles(n)%radius <= radius_merge .AND. &
6903	particles(n)%weight_factor <= weight_factor_merge ) &
6904	THEN
6905	particles(n+1)%weight_factor = &
6906	particles(n+1)%weight_factor + &
6907	( particles(n)%radius**3 / &
6908	particles(n+1)%radius*3 &
6909	particles(n)%weight_factor &
6910	)
6911	particles(n)%particle_mask = .FALSE.
6912	deleted_particles = deleted_particles + 1
6913	merge_drp = merge_drp + 1
6914
6915	ENDIF
6916	ENDDO
6917	ENDDO
6918	ENDDO
6919	ENDDO
6920
6921
6922	CALL cpu_log( log_point_s(81), 'lpm_merging', 'stop' )
6923
6924	END SUBROUTINE lpm_merging
6925
6926
6927
6928
6929	!------------------------------------------------------------------------------!
6930	! Description:
6931	! ------------
6932	!> Exchange between subdomains.
6933	!> As soon as one particle has moved beyond the boundary of the domain, it
6934	!> is included in the relevant transfer arrays and marked for subsequent
6935	!> deletion on this PE.
6936	!> First sweep for crossings in x direction. Find out first the number of
6937	!> particles to be transferred and allocate temporary arrays needed to store
6938	!> them.
6939	!> For a one-dimensional decomposition along y, no transfer is necessary,
6940	!> because the particle remains on the PE, but the particle coordinate has to
6941	!> be adjusted.
6942	!------------------------------------------------------------------------------!
6943	SUBROUTINE lpm_exchange_horiz
6944
6945	INTEGER(iwp) :: i !< grid index (x) of particle positition
6946	INTEGER(iwp) :: ip !< index variable along x
6947	INTEGER(iwp) :: j !< grid index (y) of particle positition
6948	INTEGER(iwp) :: jp !< index variable along y
6949	INTEGER(iwp) :: kp !< index variable along z
6950	INTEGER(iwp) :: n !< particle index variable
6951	INTEGER(iwp) :: par_size !< Particle size in bytes
6952	INTEGER(iwp) :: trlp_count !< number of particles send to left PE
6953	INTEGER(iwp) :: trlp_count_recv !< number of particles receive from right PE
6954	INTEGER(iwp) :: trnp_count !< number of particles send to north PE
6955	INTEGER(iwp) :: trnp_count_recv !< number of particles receive from south PE
6956	INTEGER(iwp) :: trrp_count !< number of particles send to right PE
6957	INTEGER(iwp) :: trrp_count_recv !< number of particles receive from left PE
6958	INTEGER(iwp) :: trsp_count !< number of particles send to south PE
6959	INTEGER(iwp) :: trsp_count_recv !< number of particles receive from north PE
6960
6961	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvlp !< particles received from right PE
6962	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvnp !< particles received from south PE
6963	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvrp !< particles received from left PE
6964	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: rvsp !< particles received from north PE
6965	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trlp !< particles send to left PE
6966	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trnp !< particles send to north PE
6967	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trrp !< particles send to right PE
6968	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: trsp !< particles send to south PE
6969
6970	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'start' )
6971
6972	#if defined( __parallel )
6973
6974	!
6975	!-- Exchange between subdomains.
6976	!-- As soon as one particle has moved beyond the boundary of the domain, it
6977	!-- is included in the relevant transfer arrays and marked for subsequent
6978	!-- deletion on this PE.
6979	!-- First sweep for crossings in x direction. Find out first the number of
6980	!-- particles to be transferred and allocate temporary arrays needed to store
6981	!-- them.
6982	!-- For a one-dimensional decomposition along y, no transfer is necessary,
6983	!-- because the particle remains on the PE, but the particle coordinate has to
6984	!-- be adjusted.
6985	trlp_count = 0
6986	trrp_count = 0
6987
6988	trlp_count_recv = 0
6989	trrp_count_recv = 0
6990
6991	IF ( pdims(1) /= 1 ) THEN
6992	!
6993	!-- First calculate the storage necessary for sending and receiving the data.
6994	!-- Compute only first (nxl) and last (nxr) loop iterration.
6995	DO ip = nxl, nxr, nxr - nxl
6996	DO jp = nys, nyn
6997	DO kp = nzb+1, nzt
6998
6999	number_of_particles = prt_count(kp,jp,ip)
7000	IF ( number_of_particles <= 0 ) CYCLE
7001	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7002	DO n = 1, number_of_particles
7003	IF ( particles(n)%particle_mask ) THEN
7004	i = particles(n)%x * ddx
7005	!
7006	!-- Above calculation does not work for indices less than zero
7007	IF ( particles(n)%x < 0.0_wp) i = -1
7008
7009	IF ( i < nxl ) THEN
7010	trlp_count = trlp_count + 1
7011	ELSEIF ( i > nxr ) THEN
7012	trrp_count = trrp_count + 1
7013	ENDIF
7014	ENDIF
7015	ENDDO
7016
7017	ENDDO
7018	ENDDO
7019	ENDDO
7020
7021	IF ( trlp_count == 0 ) trlp_count = 1
7022	IF ( trrp_count == 0 ) trrp_count = 1
7023
7024	ALLOCATE( trlp(trlp_count), trrp(trrp_count) )
7025
7026	trlp = zero_particle
7027	trrp = zero_particle
7028
7029	trlp_count = 0
7030	trrp_count = 0
7031
7032	ENDIF
7033	!
7034	!-- Compute only first (nxl) and last (nxr) loop iterration
7035	DO ip = nxl, nxr, nxr-nxl
7036	DO jp = nys, nyn
7037	DO kp = nzb+1, nzt
7038	number_of_particles = prt_count(kp,jp,ip)
7039	IF ( number_of_particles <= 0 ) CYCLE
7040	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7041	DO n = 1, number_of_particles
7042	!
7043	!-- Only those particles that have not been marked as 'deleted' may
7044	!-- be moved.
7045	IF ( particles(n)%particle_mask ) THEN
7046
7047	i = particles(n)%x * ddx
7048	!
7049	!-- Above calculation does not work for indices less than zero
7050	IF ( particles(n)%x < 0.0_wp ) i = -1
7051
7052	IF ( i < nxl ) THEN
7053	IF ( i < 0 ) THEN
7054	!
7055	!-- Apply boundary condition along x
7056	IF ( ibc_par_lr == 0 ) THEN
7057	!
7058	!-- Cyclic condition
7059	IF ( pdims(1) == 1 ) THEN
7060	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7061	particles(n)%origin_x = ( nx + 1 ) * dx + &
7062	particles(n)%origin_x
7063	ELSE
7064	trlp_count = trlp_count + 1
7065	trlp(trlp_count) = particles(n)
7066	trlp(trlp_count)%x = ( nx + 1 ) * dx + trlp(trlp_count)%x
7067	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x + &
7068	( nx + 1 ) * dx
7069	particles(n)%particle_mask = .FALSE.
7070	deleted_particles = deleted_particles + 1
7071
7072	IF ( trlp(trlp_count)%x >= (nx + 1)* dx - 1.0E-12_wp ) THEN
7073	trlp(trlp_count)%x = trlp(trlp_count)%x - 1.0E-10_wp
7074	!++ why is 1 subtracted in next statement???
7075	trlp(trlp_count)%origin_x = trlp(trlp_count)%origin_x - 1
7076	ENDIF
7077
7078	ENDIF
7079
7080	ELSEIF ( ibc_par_lr == 1 ) THEN
7081	!
7082	!-- Particle absorption
7083	particles(n)%particle_mask = .FALSE.
7084	deleted_particles = deleted_particles + 1
7085
7086	ELSEIF ( ibc_par_lr == 2 ) THEN
7087	!
7088	!-- Particle reflection
7089	particles(n)%x = -particles(n)%x
7090	particles(n)%speed_x = -particles(n)%speed_x
7091
7092	ENDIF
7093	ELSE
7094	!
7095	!-- Store particle data in the transfer array, which will be
7096	!-- send to the neighbouring PE
7097	trlp_count = trlp_count + 1
7098	trlp(trlp_count) = particles(n)
7099	particles(n)%particle_mask = .FALSE.
7100	deleted_particles = deleted_particles + 1
7101
7102	ENDIF
7103
7104	ELSEIF ( i > nxr ) THEN
7105	IF ( i > nx ) THEN
7106	!
7107	!-- Apply boundary condition along x
7108	IF ( ibc_par_lr == 0 ) THEN
7109	!
7110	!-- Cyclic condition
7111	IF ( pdims(1) == 1 ) THEN
7112	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7113	particles(n)%origin_x = particles(n)%origin_x - &
7114	( nx + 1 ) * dx
7115	ELSE
7116	trrp_count = trrp_count + 1
7117	trrp(trrp_count) = particles(n)
7118	trrp(trrp_count)%x = trrp(trrp_count)%x - ( nx + 1 ) * dx
7119	trrp(trrp_count)%origin_x = trrp(trrp_count)%origin_x - &
7120	( nx + 1 ) * dx
7121	particles(n)%particle_mask = .FALSE.
7122	deleted_particles = deleted_particles + 1
7123
7124	ENDIF
7125
7126	ELSEIF ( ibc_par_lr == 1 ) THEN
7127	!
7128	!-- Particle absorption
7129	particles(n)%particle_mask = .FALSE.
7130	deleted_particles = deleted_particles + 1
7131
7132	ELSEIF ( ibc_par_lr == 2 ) THEN
7133	!
7134	!-- Particle reflection
7135	particles(n)%x = 2 * ( nx * dx ) - particles(n)%x
7136	particles(n)%speed_x = -particles(n)%speed_x
7137
7138	ENDIF
7139	ELSE
7140	!
7141	!-- Store particle data in the transfer array, which will be send
7142	!-- to the neighbouring PE
7143	trrp_count = trrp_count + 1
7144	trrp(trrp_count) = particles(n)
7145	particles(n)%particle_mask = .FALSE.
7146	deleted_particles = deleted_particles + 1
7147
7148	ENDIF
7149
7150	ENDIF
7151	ENDIF
7152
7153	ENDDO
7154	ENDDO
7155	ENDDO
7156	ENDDO
7157
7158	!
7159	!-- STORAGE_SIZE returns the storage size of argument A in bits. However , it
7160	!-- is needed in bytes. The function C_SIZEOF which produces this value directly
7161	!-- causes problems with gfortran. For this reason the use of C_SIZEOF is avoided
7162	par_size = STORAGE_SIZE(trlp(1))/8
7163
7164
7165	!
7166	!-- Allocate arrays required for north-south exchange, as these
7167	!-- are used directly after particles are exchange along x-direction.
7168	ALLOCATE( move_also_north(1:NR_2_direction_move) )
7169	ALLOCATE( move_also_south(1:NR_2_direction_move) )
7170
7171	nr_move_north = 0
7172	nr_move_south = 0
7173	!
7174	!-- Send left boundary, receive right boundary (but first exchange how many
7175	!-- and check, if particle storage must be extended)
7176	IF ( pdims(1) /= 1 ) THEN
7177
7178	CALL MPI_SENDRECV( trlp_count, 1, MPI_INTEGER, pleft, 0, &
7179	trrp_count_recv, 1, MPI_INTEGER, pright, 0, &
7180	comm2d, status, ierr )
7181
7182	ALLOCATE(rvrp(MAX(1,trrp_count_recv)))
7183
7184	CALL MPI_SENDRECV( trlp, max(1,trlp_count)*par_size, MPI_BYTE,&
7185	pleft, 1, rvrp, &
7186	max(1,trrp_count_recv)*par_size, MPI_BYTE, pright, 1,&
7187	comm2d, status, ierr )
7188
7189	IF ( trrp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvrp(1:trrp_count_recv))
7190
7191	DEALLOCATE(rvrp)
7192
7193	!
7194	!-- Send right boundary, receive left boundary
7195	CALL MPI_SENDRECV( trrp_count, 1, MPI_INTEGER, pright, 0, &
7196	trlp_count_recv, 1, MPI_INTEGER, pleft, 0, &
7197	comm2d, status, ierr )
7198
7199	ALLOCATE(rvlp(MAX(1,trlp_count_recv)))
7200	!
7201	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7202	!-- variables in structure particle_type (due to the calculation of par_size)
7203	CALL MPI_SENDRECV( trrp, max(1,trrp_count)*par_size, MPI_BYTE,&
7204	pright, 1, rvlp, &
7205	max(1,trlp_count_recv)*par_size, MPI_BYTE, pleft, 1, &
7206	comm2d, status, ierr )
7207
7208	IF ( trlp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvlp(1:trlp_count_recv))
7209
7210	DEALLOCATE( rvlp )
7211	DEALLOCATE( trlp, trrp )
7212
7213	ENDIF
7214
7215	!
7216	!-- Check whether particles have crossed the boundaries in y direction. Note
7217	!-- that this case can also apply to particles that have just been received
7218	!-- from the adjacent right or left PE.
7219	!-- Find out first the number of particles to be transferred and allocate
7220	!-- temporary arrays needed to store them.
7221	!-- For a one-dimensional decomposition along y, no transfer is necessary,
7222	!-- because the particle remains on the PE.
7223	trsp_count = nr_move_south
7224	trnp_count = nr_move_north
7225
7226	trsp_count_recv = 0
7227	trnp_count_recv = 0
7228
7229	IF ( pdims(2) /= 1 ) THEN
7230	!
7231	!-- First calculate the storage necessary for sending and receiving the
7232	!-- data
7233	DO ip = nxl, nxr
7234	DO jp = nys, nyn, nyn-nys !compute only first (nys) and last (nyn) loop iterration
7235	DO kp = nzb+1, nzt
7236	number_of_particles = prt_count(kp,jp,ip)
7237	IF ( number_of_particles <= 0 ) CYCLE
7238	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7239	DO n = 1, number_of_particles
7240	IF ( particles(n)%particle_mask ) THEN
7241	j = particles(n)%y * ddy
7242	!
7243	!-- Above calculation does not work for indices less than zero
7244	IF ( particles(n)%y < 0.0_wp) j = -1
7245
7246	IF ( j < nys ) THEN
7247	trsp_count = trsp_count + 1
7248	ELSEIF ( j > nyn ) THEN
7249	trnp_count = trnp_count + 1
7250	ENDIF
7251	ENDIF
7252	ENDDO
7253	ENDDO
7254	ENDDO
7255	ENDDO
7256
7257	IF ( trsp_count == 0 ) trsp_count = 1
7258	IF ( trnp_count == 0 ) trnp_count = 1
7259
7260	ALLOCATE( trsp(trsp_count), trnp(trnp_count) )
7261
7262	trsp = zero_particle
7263	trnp = zero_particle
7264
7265	trsp_count = nr_move_south
7266	trnp_count = nr_move_north
7267
7268	trsp(1:nr_move_south) = move_also_south(1:nr_move_south)
7269	trnp(1:nr_move_north) = move_also_north(1:nr_move_north)
7270
7271	ENDIF
7272
7273	DO ip = nxl, nxr
7274	DO jp = nys, nyn, nyn-nys ! compute only first (nys) and last (nyn) loop iterration
7275	DO kp = nzb+1, nzt
7276	number_of_particles = prt_count(kp,jp,ip)
7277	IF ( number_of_particles <= 0 ) CYCLE
7278	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7279	DO n = 1, number_of_particles
7280	!
7281	!-- Only those particles that have not been marked as 'deleted' may
7282	!-- be moved.
7283	IF ( particles(n)%particle_mask ) THEN
7284
7285	j = particles(n)%y * ddy
7286	!
7287	!-- Above calculation does not work for indices less than zero
7288	IF ( particles(n)%y < 0.0_wp ) j = -1
7289
7290	IF ( j < nys ) THEN
7291	IF ( j < 0 ) THEN
7292	!
7293	!-- Apply boundary condition along y
7294	IF ( ibc_par_ns == 0 ) THEN
7295	!
7296	!-- Cyclic condition
7297	IF ( pdims(2) == 1 ) THEN
7298	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7299	particles(n)%origin_y = ( ny + 1 ) * dy + &
7300	particles(n)%origin_y
7301	ELSE
7302	trsp_count = trsp_count + 1
7303	trsp(trsp_count) = particles(n)
7304	trsp(trsp_count)%y = ( ny + 1 ) * dy + &
7305	trsp(trsp_count)%y
7306	trsp(trsp_count)%origin_y = trsp(trsp_count)%origin_y &
7307	+ ( ny + 1 ) * dy
7308	particles(n)%particle_mask = .FALSE.
7309	deleted_particles = deleted_particles + 1
7310
7311	IF ( trsp(trsp_count)%y >= (ny+1)* dy - 1.0E-12_wp ) THEN
7312	trsp(trsp_count)%y = trsp(trsp_count)%y - 1.0E-10_wp
7313	!++ why is 1 subtracted in next statement???
7314	trsp(trsp_count)%origin_y = &
7315	trsp(trsp_count)%origin_y - 1
7316	ENDIF
7317
7318	ENDIF
7319
7320	ELSEIF ( ibc_par_ns == 1 ) THEN
7321	!
7322	!-- Particle absorption
7323	particles(n)%particle_mask = .FALSE.
7324	deleted_particles = deleted_particles + 1
7325
7326	ELSEIF ( ibc_par_ns == 2 ) THEN
7327	!
7328	!-- Particle reflection
7329	particles(n)%y = -particles(n)%y
7330	particles(n)%speed_y = -particles(n)%speed_y
7331
7332	ENDIF
7333	ELSE
7334	!
7335	!-- Store particle data in the transfer array, which will
7336	!-- be send to the neighbouring PE
7337	trsp_count = trsp_count + 1
7338	trsp(trsp_count) = particles(n)
7339	particles(n)%particle_mask = .FALSE.
7340	deleted_particles = deleted_particles + 1
7341
7342	ENDIF
7343
7344	ELSEIF ( j > nyn ) THEN
7345	IF ( j > ny ) THEN
7346	!
7347	!-- Apply boundary condition along y
7348	IF ( ibc_par_ns == 0 ) THEN
7349	!
7350	!-- Cyclic condition
7351	IF ( pdims(2) == 1 ) THEN
7352	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7353	particles(n)%origin_y = &
7354	particles(n)%origin_y - ( ny + 1 ) * dy
7355	ELSE
7356	trnp_count = trnp_count + 1
7357	trnp(trnp_count) = particles(n)
7358	trnp(trnp_count)%y = &
7359	trnp(trnp_count)%y - ( ny + 1 ) * dy
7360	trnp(trnp_count)%origin_y = &
7361	trnp(trnp_count)%origin_y - ( ny + 1 ) * dy
7362	particles(n)%particle_mask = .FALSE.
7363	deleted_particles = deleted_particles + 1
7364	ENDIF
7365
7366	ELSEIF ( ibc_par_ns == 1 ) THEN
7367	!
7368	!-- Particle absorption
7369	particles(n)%particle_mask = .FALSE.
7370	deleted_particles = deleted_particles + 1
7371
7372	ELSEIF ( ibc_par_ns == 2 ) THEN
7373	!
7374	!-- Particle reflection
7375	particles(n)%y = 2 * ( ny * dy ) - particles(n)%y
7376	particles(n)%speed_y = -particles(n)%speed_y
7377
7378	ENDIF
7379	ELSE
7380	!
7381	!-- Store particle data in the transfer array, which will
7382	!-- be send to the neighbouring PE
7383	trnp_count = trnp_count + 1
7384	trnp(trnp_count) = particles(n)
7385	particles(n)%particle_mask = .FALSE.
7386	deleted_particles = deleted_particles + 1
7387
7388	ENDIF
7389
7390	ENDIF
7391	ENDIF
7392	ENDDO
7393	ENDDO
7394	ENDDO
7395	ENDDO
7396
7397	!
7398	!-- Send front boundary, receive back boundary (but first exchange how many
7399	!-- and check, if particle storage must be extended)
7400	IF ( pdims(2) /= 1 ) THEN
7401
7402	CALL MPI_SENDRECV( trsp_count, 1, MPI_INTEGER, psouth, 0, &
7403	trnp_count_recv, 1, MPI_INTEGER, pnorth, 0, &
7404	comm2d, status, ierr )
7405
7406	ALLOCATE(rvnp(MAX(1,trnp_count_recv)))
7407	!
7408	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7409	!-- variables in structure particle_type (due to the calculation of par_size)
7410	CALL MPI_SENDRECV( trsp, trsp_count*par_size, MPI_BYTE, &
7411	psouth, 1, rvnp, &
7412	trnp_count_recv*par_size, MPI_BYTE, pnorth, 1, &
7413	comm2d, status, ierr )
7414
7415	IF ( trnp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvnp(1:trnp_count_recv))
7416
7417	DEALLOCATE(rvnp)
7418
7419	!
7420	!-- Send back boundary, receive front boundary
7421	CALL MPI_SENDRECV( trnp_count, 1, MPI_INTEGER, pnorth, 0, &
7422	trsp_count_recv, 1, MPI_INTEGER, psouth, 0, &
7423	comm2d, status, ierr )
7424
7425	ALLOCATE(rvsp(MAX(1,trsp_count_recv)))
7426	!
7427	!-- This MPI_SENDRECV should work even with odd mixture on 32 and 64 Bit
7428	!-- variables in structure particle_type (due to the calculation of par_size)
7429	CALL MPI_SENDRECV( trnp, trnp_count*par_size, MPI_BYTE, &
7430	pnorth, 1, rvsp, &
7431	trsp_count_recv*par_size, MPI_BYTE, psouth, 1, &
7432	comm2d, status, ierr )
7433
7434	IF ( trsp_count_recv > 0 ) CALL lpm_add_particles_to_gridcell(rvsp(1:trsp_count_recv))
7435
7436	DEALLOCATE(rvsp)
7437
7438	number_of_particles = number_of_particles + trsp_count_recv
7439
7440	DEALLOCATE( trsp, trnp )
7441
7442	ENDIF
7443
7444	DEALLOCATE( move_also_north )
7445	DEALLOCATE( move_also_south )
7446
7447	#else
7448
7449	DO ip = nxl, nxr, nxr-nxl
7450	DO jp = nys, nyn
7451	DO kp = nzb+1, nzt
7452	number_of_particles = prt_count(kp,jp,ip)
7453	IF ( number_of_particles <= 0 ) CYCLE
7454	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7455	DO n = 1, number_of_particles
7456	!
7457	!-- Apply boundary conditions
7458
7459	IF ( particles(n)%x < 0.0_wp ) THEN
7460
7461	IF ( ibc_par_lr == 0 ) THEN
7462	!
7463	!-- Cyclic boundary. Relevant coordinate has to be changed.
7464	particles(n)%x = ( nx + 1 ) * dx + particles(n)%x
7465	particles(n)%origin_x = ( nx + 1 ) * dx + &
7466	particles(n)%origin_x
7467	ELSEIF ( ibc_par_lr == 1 ) THEN
7468	!
7469	!-- Particle absorption
7470	particles(n)%particle_mask = .FALSE.
7471	deleted_particles = deleted_particles + 1
7472
7473	ELSEIF ( ibc_par_lr == 2 ) THEN
7474	!
7475	!-- Particle reflection
7476	particles(n)%x = -dx - particles(n)%x
7477	particles(n)%speed_x = -particles(n)%speed_x
7478	ENDIF
7479
7480	ELSEIF ( particles(n)%x >= ( nx + 1) * dx ) THEN
7481
7482	IF ( ibc_par_lr == 0 ) THEN
7483	!
7484	!-- Cyclic boundary. Relevant coordinate has to be changed.
7485	particles(n)%x = particles(n)%x - ( nx + 1 ) * dx
7486	particles(n)%origin_x = particles(n)%origin_x - &
7487	( nx + 1 ) * dx
7488
7489	ELSEIF ( ibc_par_lr == 1 ) THEN
7490	!
7491	!-- Particle absorption
7492	particles(n)%particle_mask = .FALSE.
7493	deleted_particles = deleted_particles + 1
7494
7495	ELSEIF ( ibc_par_lr == 2 ) THEN
7496	!
7497	!-- Particle reflection
7498	particles(n)%x = ( nx + 1 ) * dx - particles(n)%x
7499	particles(n)%speed_x = -particles(n)%speed_x
7500	ENDIF
7501
7502	ENDIF
7503	ENDDO
7504	ENDDO
7505	ENDDO
7506	ENDDO
7507
7508	DO ip = nxl, nxr
7509	DO jp = nys, nyn, nyn-nys
7510	DO kp = nzb+1, nzt
7511	number_of_particles = prt_count(kp,jp,ip)
7512	IF ( number_of_particles <= 0 ) CYCLE
7513	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7514	DO n = 1, number_of_particles
7515
7516	IF ( particles(n)%y < 0.0_wp) THEN
7517
7518	IF ( ibc_par_ns == 0 ) THEN
7519	!
7520	!-- Cyclic boundary. Relevant coordinate has to be changed.
7521	particles(n)%y = ( ny + 1 ) * dy + particles(n)%y
7522	particles(n)%origin_y = ( ny + 1 ) * dy + &
7523	particles(n)%origin_y
7524
7525	ELSEIF ( ibc_par_ns == 1 ) THEN
7526	!
7527	!-- Particle absorption
7528	particles(n)%particle_mask = .FALSE.
7529	deleted_particles = deleted_particles + 1
7530
7531	ELSEIF ( ibc_par_ns == 2 ) THEN
7532	!
7533	!-- Particle reflection
7534	particles(n)%y = -dy - particles(n)%y
7535	particles(n)%speed_y = -particles(n)%speed_y
7536	ENDIF
7537
7538	ELSEIF ( particles(n)%y >= ( ny + 1) * dy ) THEN
7539
7540	IF ( ibc_par_ns == 0 ) THEN
7541	!
7542	!-- Cyclic boundary. Relevant coordinate has to be changed.
7543	particles(n)%y = particles(n)%y - ( ny + 1 ) * dy
7544	particles(n)%origin_y = particles(n)%origin_y - &
7545	( ny + 1 ) * dy
7546
7547	ELSEIF ( ibc_par_ns == 1 ) THEN
7548	!
7549	!-- Particle absorption
7550	particles(n)%particle_mask = .FALSE.
7551	deleted_particles = deleted_particles + 1
7552
7553	ELSEIF ( ibc_par_ns == 2 ) THEN
7554	!
7555	!-- Particle reflection
7556	particles(n)%y = ( ny + 1 ) * dy - particles(n)%y
7557	particles(n)%speed_y = -particles(n)%speed_y
7558	ENDIF
7559
7560	ENDIF
7561
7562	ENDDO
7563	ENDDO
7564	ENDDO
7565	ENDDO
7566	#endif
7567
7568	!
7569	!-- Accumulate the number of particles transferred between the subdomains
7570	#if defined( __parallel )
7571	trlp_count_sum = trlp_count_sum + trlp_count
7572	trlp_count_recv_sum = trlp_count_recv_sum + trlp_count_recv
7573	trrp_count_sum = trrp_count_sum + trrp_count
7574	trrp_count_recv_sum = trrp_count_recv_sum + trrp_count_recv
7575	trsp_count_sum = trsp_count_sum + trsp_count
7576	trsp_count_recv_sum = trsp_count_recv_sum + trsp_count_recv
7577	trnp_count_sum = trnp_count_sum + trnp_count
7578	trnp_count_recv_sum = trnp_count_recv_sum + trnp_count_recv
7579	#endif
7580
7581	CALL cpu_log( log_point_s(23), 'lpm_exchange_horiz', 'stop' )
7582
7583	END SUBROUTINE lpm_exchange_horiz
7584
7585	!------------------------------------------------------------------------------!
7586	! Description:
7587	! ------------
7588	!> If a particle moves from one processor to another, this subroutine moves
7589	!> the corresponding elements from the particle arrays of the old grid cells
7590	!> to the particle arrays of the new grid cells.
7591	!------------------------------------------------------------------------------!
7592	SUBROUTINE lpm_add_particles_to_gridcell (particle_array)
7593
7594	IMPLICIT NONE
7595
7596	INTEGER(iwp) :: ip !< grid index (x) of particle
7597	INTEGER(iwp) :: jp !< grid index (x) of particle
7598	INTEGER(iwp) :: kp !< grid index (x) of particle
7599	INTEGER(iwp) :: n !< index variable of particle
7600	INTEGER(iwp) :: pindex !< dummy argument for new number of particles per grid box
7601
7602	LOGICAL :: pack_done !<
7603
7604	TYPE(particle_type), DIMENSION(:), INTENT(IN) :: particle_array !< new particles in a grid box
7605	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: temp_ns !< temporary particle array for reallocation
7606
7607	pack_done = .FALSE.
7608
7609	DO n = 1, SIZE(particle_array)
7610
7611	IF ( .NOT. particle_array(n)%particle_mask ) CYCLE
7612
7613	ip = particle_array(n)%x * ddx
7614	jp = particle_array(n)%y * ddy
7615	!
7616	!-- In case of stretching the actual k index must be found
7617	IF ( dz_stretch_level .NE. -9999999.9_wp .OR. &
7618	dz_stretch_level_start(1) .NE. -9999999.9_wp ) THEN
7619	kp = MINLOC( ABS( particle_array(n)%z - zu ), DIM = 1 ) - 1
7620	ELSE
7621	kp = INT( particle_array(n)%z / dz(1) + 1 + offset_ocean_nzt )
7622	ENDIF
7623
7624	IF ( ip >= nxl .AND. ip <= nxr .AND. jp >= nys .AND. jp <= nyn &
7625	.AND. kp >= nzb+1 .AND. kp <= nzt) THEN ! particle stays on processor
7626	number_of_particles = prt_count(kp,jp,ip)
7627	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
7628
7629	pindex = prt_count(kp,jp,ip)+1
7630	IF( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7631	IF ( pack_done ) THEN
7632	CALL realloc_particles_array (ip,jp,kp)
7633	ELSE
7634	CALL lpm_pack
7635	prt_count(kp,jp,ip) = number_of_particles
7636	pindex = prt_count(kp,jp,ip)+1
7637	IF ( pindex > SIZE(grid_particles(kp,jp,ip)%particles) ) THEN
7638	CALL realloc_particles_array (ip,jp,kp)
7639	ENDIF
7640	pack_done = .TRUE.
7641	ENDIF
7642	ENDIF
7643	grid_particles(kp,jp,ip)%particles(pindex) = particle_array(n)
7644	prt_count(kp,jp,ip) = pindex
7645	ELSE
7646	IF ( jp <= nys - 1 ) THEN
7647	nr_move_south = nr_move_south+1
7648	!
7649	!-- Before particle information is swapped to exchange-array, check
7650	!-- if enough memory is allocated. If required, reallocate exchange
7651	!-- array.
7652	IF ( nr_move_south > SIZE(move_also_south) ) THEN
7653	!
7654	!-- At first, allocate further temporary array to swap particle
7655	!-- information.
7656	ALLOCATE( temp_ns(SIZE(move_also_south)+NR_2_direction_move) )
7657	temp_ns(1:nr_move_south-1) = move_also_south(1:nr_move_south-1)
7658	DEALLOCATE( move_also_south )
7659	ALLOCATE( move_also_south(SIZE(temp_ns)) )
7660	move_also_south(1:nr_move_south-1) = temp_ns(1:nr_move_south-1)
7661	DEALLOCATE( temp_ns )
7662
7663	ENDIF
7664
7665	move_also_south(nr_move_south) = particle_array(n)
7666
7667	IF ( jp == -1 ) THEN
7668	!
7669	!-- Apply boundary condition along y
7670	IF ( ibc_par_ns == 0 ) THEN
7671	move_also_south(nr_move_south)%y = &
7672	move_also_south(nr_move_south)%y + ( ny + 1 ) * dy
7673	move_also_south(nr_move_south)%origin_y = &
7674	move_also_south(nr_move_south)%origin_y + ( ny + 1 ) * dy
7675	ELSEIF ( ibc_par_ns == 1 ) THEN
7676	!
7677	!-- Particle absorption
7678	move_also_south(nr_move_south)%particle_mask = .FALSE.
7679	deleted_particles = deleted_particles + 1
7680
7681	ELSEIF ( ibc_par_ns == 2 ) THEN
7682	!
7683	!-- Particle reflection
7684	move_also_south(nr_move_south)%y = &
7685	-move_also_south(nr_move_south)%y
7686	move_also_south(nr_move_south)%speed_y = &
7687	-move_also_south(nr_move_south)%speed_y
7688
7689	ENDIF
7690	ENDIF
7691	ELSEIF ( jp >= nyn+1 ) THEN
7692	nr_move_north = nr_move_north+1
7693	!
7694	!-- Before particle information is swapped to exchange-array, check
7695	!-- if enough memory is allocated. If required, reallocate exchange
7696	!-- array.
7697	IF ( nr_move_north > SIZE(move_also_north) ) THEN
7698	!
7699	!-- At first, allocate further temporary array to swap particle
7700	!-- information.
7701	ALLOCATE( temp_ns(SIZE(move_also_north)+NR_2_direction_move) )
7702	temp_ns(1:nr_move_north-1) = move_also_south(1:nr_move_north-1)
7703	DEALLOCATE( move_also_north )
7704	ALLOCATE( move_also_north(SIZE(temp_ns)) )
7705	move_also_north(1:nr_move_north-1) = temp_ns(1:nr_move_north-1)
7706	DEALLOCATE( temp_ns )
7707
7708	ENDIF
7709
7710	move_also_north(nr_move_north) = particle_array(n)
7711	IF ( jp == ny+1 ) THEN
7712	!
7713	!-- Apply boundary condition along y
7714	IF ( ibc_par_ns == 0 ) THEN
7715
7716	move_also_north(nr_move_north)%y = &
7717	move_also_north(nr_move_north)%y - ( ny + 1 ) * dy
7718	move_also_north(nr_move_north)%origin_y = &
7719	move_also_north(nr_move_north)%origin_y - ( ny + 1 ) * dy
7720	ELSEIF ( ibc_par_ns == 1 ) THEN
7721	!
7722	!-- Particle absorption
7723	move_also_north(nr_move_north)%particle_mask = .FALSE.
7724	deleted_particles = deleted_particles + 1
7725
7726	ELSEIF ( ibc_par_ns == 2 ) THEN
7727	!
7728	!-- Particle reflection
7729	move_also_north(nr_move_north)%y = &
7730	-move_also_north(nr_move_north)%y
7731	move_also_north(nr_move_north)%speed_y = &
7732	-move_also_north(nr_move_north)%speed_y
7733
7734	ENDIF
7735	ENDIF
7736	ELSE
7737	WRITE(0,'(a,8i7)') 'particle out of range ',myid,ip,jp,kp,nxl,nxr,nys,nyn
7738	ENDIF
7739	ENDIF
7740	ENDDO
7741
7742	RETURN
7743
7744	END SUBROUTINE lpm_add_particles_to_gridcell
7745
7746
7747	!------------------------------------------------------------------------------!
7748	! Description:
7749	! ------------
7750	!> If a particle moves from one grid cell to another (on the current
7751	!> processor!), this subroutine moves the corresponding element from the
7752	!> particle array of the old grid cell to the particle array of the new grid
7753	!> cell.
7754	!------------------------------------------------------------------------------!
7755	SUBROUTINE lpm_move_particle
7756
7757	INTEGER(iwp) :: i !< grid index (x) of particle position
7758	INTEGER(iwp) :: ip !< index variable along x
7759	INTEGER(iwp) :: j !< grid index (y) of particle position
7760	INTEGER(iwp) :: jp !< index variable along y
7761	INTEGER(iwp) :: k !< grid index (z) of particle position
7762	INTEGER(iwp) :: kp !< index variable along z
7763	INTEGER(iwp) :: n !< index variable for particle array
7764	INTEGER(iwp) :: np_before_move !< number of particles per grid box before moving
7765	INTEGER(iwp) :: pindex !< dummy argument for number of new particle per grid box
7766
7767	TYPE(particle_type), DIMENSION(:), POINTER :: particles_before_move !< particles before moving
7768
7769	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'start' )
7770	CALL lpm_check_cfl
7771	DO ip = nxl, nxr
7772	DO jp = nys, nyn
7773	DO kp = nzb+1, nzt
7774
7775	np_before_move = prt_count(kp,jp,ip)
7776	IF ( np_before_move <= 0 ) CYCLE
7777	particles_before_move => grid_particles(kp,jp,ip)%particles(1:np_before_move)
7778
7779	DO n = 1, np_before_move
7780	i = particles_before_move(n)%x * ddx
7781	j = particles_before_move(n)%y * ddy
7782	k = kp
7783	!
7784	!-- Find correct vertical particle grid box (necessary in case of grid stretching)
7785	!-- Due to the CFL limitations only the neighbouring grid boxes are considered.
7786	IF( zw(k) < particles_before_move(n)%z ) k = k + 1
7787	IF( zw(k-1) > particles_before_move(n)%z ) k = k - 1
7788
7789	!-- For lpm_exchange_horiz to work properly particles need to be moved to the outermost gridboxes
7790	!-- of the respective processor. If the particle index is inside the processor the following lines
7791	!-- will not change the index
7792	i = MIN ( i , nxr )
7793	i = MAX ( i , nxl )
7794	j = MIN ( j , nyn )
7795	j = MAX ( j , nys )
7796
7797	k = MIN ( k , nzt )
7798	k = MAX ( k , nzb+1 )
7799
7800	!
7801	!-- Check, if particle has moved to another grid cell.
7802	IF ( i /= ip .OR. j /= jp .OR. k /= kp ) THEN
7803	!!
7804	!-- If the particle stays on the same processor, the particle
7805	!-- will be added to the particle array of the new processor.
7806	number_of_particles = prt_count(k,j,i)
7807	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7808
7809	pindex = prt_count(k,j,i)+1
7810	IF ( pindex > SIZE(grid_particles(k,j,i)%particles) ) &
7811	THEN
7812	CALL realloc_particles_array(i,j,k)
7813	ENDIF
7814
7815	grid_particles(k,j,i)%particles(pindex) = particles_before_move(n)
7816	prt_count(k,j,i) = pindex
7817
7818	particles_before_move(n)%particle_mask = .FALSE.
7819	ENDIF
7820	ENDDO
7821
7822	ENDDO
7823	ENDDO
7824	ENDDO
7825
7826	CALL cpu_log( log_point_s(41), 'lpm_move_particle', 'stop' )
7827
7828	RETURN
7829
7830	END SUBROUTINE lpm_move_particle
7831
7832
7833	!------------------------------------------------------------------------------!
7834	! Description:
7835	! ------------
7836	!> Check CFL-criterion for each particle. If one particle violated the
7837	!> criterion the particle will be deleted and a warning message is given.
7838	!------------------------------------------------------------------------------!
7839	SUBROUTINE lpm_check_cfl
7840
7841	IMPLICIT NONE
7842
7843	INTEGER(iwp) :: i !< running index, x-direction
7844	INTEGER(iwp) :: j !< running index, y-direction
7845	INTEGER(iwp) :: k !< running index, z-direction
7846	INTEGER(iwp) :: n !< running index, number of particles
7847
7848	DO i = nxl, nxr
7849	DO j = nys, nyn
7850	DO k = nzb+1, nzt
7851	number_of_particles = prt_count(k,j,i)
7852	IF ( number_of_particles <= 0 ) CYCLE
7853	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
7854	DO n = 1, number_of_particles
7855	!
7856	!-- Note, check for CFL does not work at first particle timestep
7857	!-- when both, age and age_m are zero.
7858	IF ( particles(n)%age - particles(n)%age_m > 0.0_wp ) THEN
7859	IF(ABS(particles(n)%speed_x) > &
7860	(dx/(particles(n)%age-particles(n)%age_m)) .OR. &
7861	ABS(particles(n)%speed_y) > &
7862	(dy/(particles(n)%age-particles(n)%age_m)) .OR. &
7863	ABS(particles(n)%speed_z) > &
7864	((zw(k)-zw(k-1))/(particles(n)%age-particles(n)%age_m))) &
7865	THEN
7866	WRITE( message_string, * ) &
7867	'Particle violated CFL-criterion: &particle with id ', &
7868	particles(n)%id, ' will be deleted!'
7869	CALL message( 'lpm_check_cfl', 'PA0475', 0, 1, -1, 6, 0 )
7870	particles(n)%particle_mask= .FALSE.
7871	ENDIF
7872	ENDIF
7873	ENDDO
7874	ENDDO
7875	ENDDO
7876	ENDDO
7877
7878	END SUBROUTINE lpm_check_cfl
7879
7880
7881	!------------------------------------------------------------------------------!
7882	! Description:
7883	! ------------
7884	!> If the allocated memory for the particle array do not suffice to add arriving
7885	!> particles from neighbour grid cells, this subrouting reallocates the
7886	!> particle array to assure enough memory is available.
7887	!------------------------------------------------------------------------------!
7888	SUBROUTINE realloc_particles_array ( i, j, k, size_in )
7889
7890	INTEGER(iwp), INTENT(IN) :: i !<
7891	INTEGER(iwp), INTENT(IN) :: j !<
7892	INTEGER(iwp), INTENT(IN) :: k !<
7893	INTEGER(iwp), INTENT(IN), OPTIONAL :: size_in !<
7894
7895	INTEGER(iwp) :: old_size !<
7896	INTEGER(iwp) :: new_size !<
7897	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7898	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7899
7900	old_size = SIZE(grid_particles(k,j,i)%particles)
7901
7902	IF ( PRESENT(size_in) ) THEN
7903	new_size = size_in
7904	ELSE
7905	new_size = old_size * ( 1.0_wp + alloc_factor / 100.0_wp )
7906	ENDIF
7907
7908	new_size = MAX( new_size, 1, old_size + 1 )
7909
7910	IF ( old_size <= 500 ) THEN
7911
7912	tmp_particles_s(1:old_size) = grid_particles(k,j,i)%particles(1:old_size)
7913
7914	DEALLOCATE(grid_particles(k,j,i)%particles)
7915	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7916
7917	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_s(1:old_size)
7918	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7919
7920	ELSE
7921
7922	ALLOCATE(tmp_particles_d(new_size))
7923	tmp_particles_d(1:old_size) = grid_particles(k,j,i)%particles
7924
7925	DEALLOCATE(grid_particles(k,j,i)%particles)
7926	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7927
7928	grid_particles(k,j,i)%particles(1:old_size) = tmp_particles_d(1:old_size)
7929	grid_particles(k,j,i)%particles(old_size+1:new_size) = zero_particle
7930
7931	DEALLOCATE(tmp_particles_d)
7932
7933	ENDIF
7934	particles => grid_particles(k,j,i)%particles(1:new_size)
7935
7936	RETURN
7937
7938	END SUBROUTINE realloc_particles_array
7939
7940
7941	!------------------------------------------------------------------------------!
7942	! Description:
7943	! ------------
7944	!> Not needed but allocated space for particles is dealloced.
7945	!------------------------------------------------------------------------------!
7946	SUBROUTINE dealloc_particles_array
7947
7948
7949	INTEGER(iwp) :: i
7950	INTEGER(iwp) :: j
7951	INTEGER(iwp) :: k
7952	INTEGER(iwp) :: old_size !<
7953	INTEGER(iwp) :: new_size !<
7954
7955	LOGICAL :: dealloc
7956
7957	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: tmp_particles_d !<
7958	TYPE(particle_type), DIMENSION(500) :: tmp_particles_s !<
7959
7960	DO i = nxl, nxr
7961	DO j = nys, nyn
7962	DO k = nzb+1, nzt
7963	!
7964	!-- Determine number of active particles
7965	number_of_particles = prt_count(k,j,i)
7966	!
7967	!-- Determine allocated memory size
7968	old_size = SIZE( grid_particles(k,j,i)%particles )
7969	!
7970	!-- Check for large unused memory
7971	dealloc = ( ( number_of_particles < 1 .AND. &
7972	old_size > 1 ) .OR. &
7973	( number_of_particles > 1 .AND. &
7974	old_size - number_of_particles * &
7975	( 1.0_wp + 0.01_wp * alloc_factor ) > 0.0_wp ) )
7976
7977	IF ( dealloc ) THEN
7978	IF ( number_of_particles < 1 ) THEN
7979	new_size = 1
7980	ELSE
7981	new_size = INT( number_of_particles * ( 1.0_wp + 0.01_wp * alloc_factor ) )
7982	ENDIF
7983
7984	IF ( number_of_particles <= 500 ) THEN
7985
7986	tmp_particles_s(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
7987
7988	DEALLOCATE(grid_particles(k,j,i)%particles)
7989	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
7990
7991	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_s(1:number_of_particles)
7992	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
7993
7994	ELSE
7995
7996	ALLOCATE(tmp_particles_d(number_of_particles))
7997	tmp_particles_d(1:number_of_particles) = grid_particles(k,j,i)%particles(1:number_of_particles)
7998
7999	DEALLOCATE(grid_particles(k,j,i)%particles)
8000	ALLOCATE(grid_particles(k,j,i)%particles(new_size))
8001
8002	grid_particles(k,j,i)%particles(1:number_of_particles) = tmp_particles_d(1:number_of_particles)
8003	grid_particles(k,j,i)%particles(number_of_particles+1:new_size) = zero_particle
8004
8005	DEALLOCATE(tmp_particles_d)
8006
8007	ENDIF
8008
8009	ENDIF
8010	ENDDO
8011	ENDDO
8012	ENDDO
8013
8014	END SUBROUTINE dealloc_particles_array
8015
8016
8017	!------------------------------------------------------------------------------!
8018	! Description:
8019	! -----------
8020	!> Routine for the whole processor
8021	!> Sort all particles into the 8 respective subgrid boxes (in case of trilinear
8022	!> interpolation method) and free space of particles which has been marked for
8023	!> deletion.
8024	!------------------------------------------------------------------------------!
8025	SUBROUTINE lpm_sort_and_delete
8026
8027	INTEGER(iwp) :: i !<
8028	INTEGER(iwp) :: ip !<
8029	INTEGER(iwp) :: is !<
8030	INTEGER(iwp) :: j !<
8031	INTEGER(iwp) :: jp !<
8032	INTEGER(iwp) :: kp !<
8033	INTEGER(iwp) :: m !<
8034	INTEGER(iwp) :: n !<
8035	INTEGER(iwp) :: nn !<
8036	INTEGER(iwp) :: sort_index !<
8037
8038	INTEGER(iwp), DIMENSION(0:7) :: sort_count !<
8039
8040	TYPE(particle_type), DIMENSION(:,:), ALLOCATABLE :: sort_particles !<
8041
8042	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'start' )
8043	IF ( interpolation_trilinear ) THEN
8044	DO ip = nxl, nxr
8045	DO jp = nys, nyn
8046	DO kp = nzb+1, nzt
8047	number_of_particles = prt_count(kp,jp,ip)
8048	IF ( number_of_particles <= 0 ) CYCLE
8049	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8050	nn = 0
8051	sort_count = 0
8052	ALLOCATE( sort_particles(number_of_particles, 0:7) )
8053
8054	DO n = 1, number_of_particles
8055	sort_index = 0
8056
8057	IF ( particles(n)%particle_mask ) THEN
8058	nn = nn + 1
8059	!
8060	!-- Sorting particles with a binary scheme
8061	!-- sort_index=111_2=7_10 -> particle at the left,south,bottom subgridbox
8062	!-- sort_index=000_2=0_10 -> particle at the right,north,top subgridbox
8063	!-- For this the center of the gridbox is calculated
8064	i = (particles(n)%x + 0.5_wp * dx) * ddx
8065	j = (particles(n)%y + 0.5_wp * dy) * ddy
8066
8067	IF ( i == ip ) sort_index = sort_index + 4
8068	IF ( j == jp ) sort_index = sort_index + 2
8069	IF ( zu(kp) > particles(n)%z ) sort_index = sort_index + 1
8070
8071	sort_count(sort_index) = sort_count(sort_index) + 1
8072	m = sort_count(sort_index)
8073	sort_particles(m,sort_index) = particles(n)
8074	sort_particles(m,sort_index)%block_nr = sort_index
8075	ENDIF
8076	ENDDO
8077	!
8078	!-- Delete and resort particles by overwritting and set
8079	!-- the number_of_particles to the actual value.
8080	nn = 0
8081	DO is = 0,7
8082	grid_particles(kp,jp,ip)%start_index(is) = nn + 1
8083	DO n = 1,sort_count(is)
8084	nn = nn + 1
8085	particles(nn) = sort_particles(n,is)
8086	ENDDO
8087	grid_particles(kp,jp,ip)%end_index(is) = nn
8088	ENDDO
8089
8090	number_of_particles = nn
8091	prt_count(kp,jp,ip) = number_of_particles
8092	DEALLOCATE(sort_particles)
8093	ENDDO
8094	ENDDO
8095	ENDDO
8096
8097	!-- In case of the simple interpolation method the particles must not
8098	!-- be sorted in subboxes. Particles marked for deletion however, must be
8099	!-- deleted and number of particles must be recalculated as it is also
8100	!-- done for the trilinear particle advection interpolation method.
8101	ELSE
8102
8103	DO ip = nxl, nxr
8104	DO jp = nys, nyn
8105	DO kp = nzb+1, nzt
8106
8107	number_of_particles = prt_count(kp,jp,ip)
8108	IF ( number_of_particles <= 0 ) CYCLE
8109	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
8110	!
8111	!-- Repack particles array, i.e. delete particles and recalculate
8112	!-- number of particles
8113	CALL lpm_pack
8114	prt_count(kp,jp,ip) = number_of_particles
8115	ENDDO
8116	ENDDO
8117	ENDDO
8118	ENDIF
8119	CALL cpu_log( log_point_s(51), 'lpm_sort_and_delete', 'stop' )
8120
8121	END SUBROUTINE lpm_sort_and_delete
8122
8123
8124	!------------------------------------------------------------------------------!
8125	! Description:
8126	! ------------
8127	!> Move all particles not marked for deletion to lowest indices (packing)
8128	!------------------------------------------------------------------------------!
8129	SUBROUTINE lpm_pack
8130
8131	INTEGER(iwp) :: n !<
8132	INTEGER(iwp) :: nn !<
8133	!
8134	!-- Find out elements marked for deletion and move data from highest index
8135	!-- values to these free indices
8136	nn = number_of_particles
8137
8138	DO WHILE ( .NOT. particles(nn)%particle_mask )
8139	nn = nn-1
8140	IF ( nn == 0 ) EXIT
8141	ENDDO
8142
8143	IF ( nn > 0 ) THEN
8144	DO n = 1, number_of_particles
8145	IF ( .NOT. particles(n)%particle_mask ) THEN
8146	particles(n) = particles(nn)
8147	nn = nn - 1
8148	DO WHILE ( .NOT. particles(nn)%particle_mask )
8149	nn = nn-1
8150	IF ( n == nn ) EXIT
8151	ENDDO
8152	ENDIF
8153	IF ( n == nn ) EXIT
8154	ENDDO
8155	ENDIF
8156
8157	!
8158	!-- The number of deleted particles has been determined in routines
8159	!-- lpm_boundary_conds, lpm_droplet_collision, and lpm_exchange_horiz
8160	number_of_particles = nn
8161
8162	END SUBROUTINE lpm_pack
8163
8164
8165	!------------------------------------------------------------------------------!
8166	! Description:
8167	! ------------
8168	!> Sort particles in each sub-grid box into two groups: particles that already
8169	!> completed the LES timestep, and particles that need further timestepping to
8170	!> complete the LES timestep.
8171	!------------------------------------------------------------------------------!
8172	SUBROUTINE lpm_sort_timeloop_done
8173
8174	INTEGER(iwp) :: end_index !< particle end index for each sub-box
8175	INTEGER(iwp) :: i !< index of particle grid box in x-direction
8176	INTEGER(iwp) :: j !< index of particle grid box in y-direction
8177	INTEGER(iwp) :: k !< index of particle grid box in z-direction
8178	INTEGER(iwp) :: n !< running index for number of particles
8179	INTEGER(iwp) :: nb !< index of subgrid boux
8180	INTEGER(iwp) :: nf !< indices for particles in each sub-box that already finalized their substeps
8181	INTEGER(iwp) :: nnf !< indices for particles in each sub-box that need further treatment
8182	INTEGER(iwp) :: num_finalized !< number of particles in each sub-box that already finalized their substeps
8183	INTEGER(iwp) :: start_index !< particle start index for each sub-box
8184
8185	TYPE(particle_type), DIMENSION(:), ALLOCATABLE :: sort_particles !< temporary particle array
8186
8187	DO i = nxl, nxr
8188	DO j = nys, nyn
8189	DO k = nzb+1, nzt
8190
8191	number_of_particles = prt_count(k,j,i)
8192	IF ( number_of_particles <= 0 ) CYCLE
8193	particles => grid_particles(k,j,i)%particles(1:number_of_particles)
8194
8195	DO nb = 0, 7
8196	!
8197	!-- Obtain start and end index for each subgrid box
8198	start_index = grid_particles(k,j,i)%start_index(nb)
8199	end_index = grid_particles(k,j,i)%end_index(nb)
8200	!
8201	!-- Allocate temporary array used for sorting.
8202	ALLOCATE( sort_particles(start_index:end_index) )
8203	!
8204	!-- Determine number of particles already completed the LES
8205	!-- timestep, and write them into a temporary array.
8206	nf = start_index
8207	num_finalized = 0
8208	DO n = start_index, end_index
8209	IF ( dt_3d - particles(n)%dt_sum < 1E-8_wp ) THEN
8210	sort_particles(nf) = particles(n)
8211	nf = nf + 1
8212	num_finalized = num_finalized + 1
8213	ENDIF
8214	ENDDO
8215	!
8216	!-- Determine number of particles that not completed the LES
8217	!-- timestep, and write them into a temporary array.
8218	nnf = nf
8219	DO n = start_index, end_index
8220	IF ( dt_3d - particles(n)%dt_sum > 1E-8_wp ) THEN
8221	sort_particles(nnf) = particles(n)
8222	nnf = nnf + 1
8223	ENDIF
8224	ENDDO
8225	!
8226	!-- Write back sorted particles
8227	particles(start_index:end_index) = &
8228	sort_particles(start_index:end_index)
8229	!
8230	!-- Determine updated start_index, used to masked already
8231	!-- completed particles.
8232	grid_particles(k,j,i)%start_index(nb) = &
8233	grid_particles(k,j,i)%start_index(nb) &
8234	+ num_finalized
8235	!
8236	!-- Deallocate dummy array
8237	DEALLOCATE ( sort_particles )
8238	!
8239	!-- Finally, if number of non-completed particles is non zero
8240	!-- in any of the sub-boxes, set control flag appropriately.
8241	IF ( nnf > nf ) &
8242	grid_particles(k,j,i)%time_loop_done = .FALSE.
8243
8244	ENDDO
8245	ENDDO
8246	ENDDO
8247	ENDDO
8248
8249	END SUBROUTINE lpm_sort_timeloop_done
8250
8251	END MODULE lagrangian_particle_model_mod

Note: See TracBrowser for help on using the repository browser.

Download in other formats:

| Impressum | ©Leibniz Universität Hannover |