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source: palm/trunk/SOURCE/lpm_init.f90 @ 3010

Last change on this file since 3010 was 2967, checked in by raasch, 7 years ago
bugfix: missing parallel cpp-directives added
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File size: 47.2 KB

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1	!> @file lpm_init.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 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_init.f90 2967 2018-04-13 11:22:08Z Giersch $
27	! nesting routine is only called if nesting is switched on
28	!
29	! 2954 2018-04-09 14:35:46Z schwenkel
30	! Bugfix for particle initialization in case of ocean
31	!
32	! 2801 2018-02-14 16:01:55Z thiele
33	! Introduce particle transfer in nested models.
34	!
35	! 2718 2018-01-02 08:49:38Z maronga
36	! Corrected "Former revisions" section
37	!
38	! 2701 2017-12-15 15:40:50Z suehring
39	! Changes from last commit documented
40	!
41	! 2698 2017-12-14 18:46:24Z suehring
42	! Grid indices passed to lpm_boundary_conds. (responsible Philipp Thiele)
43	!
44	! 2696 2017-12-14 17:12:51Z kanani
45	! Change in file header (GPL part)
46	!
47	! 2628 2017-11-20 12:40:38Z schwenkel
48	! Enabled particle advection with grid stretching.
49	!
50	! 2608 2017-11-13 14:04:26Z schwenkel
51	! Calculation of magnus equation in external module (diagnostic_quantities_mod).
52	!
53	! 2606 2017-11-10 10:36:31Z schwenkel
54	! Changed particle box locations: center of particle box now coincides
55	! with scalar grid point of same index.
56	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
57	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
58	! lpm_sort -> lpm_sort_timeloop_done
59	!
60	! 2375 2017-08-29 14:10:28Z schwenkel
61	! Initialization of chemical aerosol composition
62	!
63	! 2346 2017-08-09 16:39:17Z suehring
64	! Bugfix, correct determination of topography top index
65	!
66	! 2318 2017-07-20 17:27:44Z suehring
67	! Get topography top index via Function call
68	!
69	! 2317 2017-07-20 17:27:19Z suehring
70	! Extended particle data type. Aerosol initialization improved.
71	!
72	! 2305 2017-07-06 11:18:47Z hoffmann
73	! Improved calculation of particle IDs.
74	!
75	! 2274 2017-06-09 13:27:48Z Giersch
76	! Changed error messages
77	!
78	! 2265 2017-06-08 16:58:28Z schwenkel
79	! Unused variables removed.
80	!
81	! 2263 2017-06-08 14:59:01Z schwenkel
82	! Implemented splitting and merging algorithm
83	!
84	! 2233 2017-05-30 18:08:54Z suehring
85	!
86	! 2232 2017-05-30 17:47:52Z suehring
87	! Adjustments according to new topography realization
88	!
89	!
90	! 2223 2017-05-15 16:38:09Z suehring
91	! Add check for particle release at model top
92	!
93	! 2182 2017-03-17 14:27:40Z schwenkel
94	! Added parameters for simplified particle initialization.
95	!
96	! 2122 2017-01-18 12:22:54Z hoffmann
97	! Improved initialization of equilibrium aerosol radii
98	! Calculation of particle ID
99	!
100	! 2000 2016-08-20 18:09:15Z knoop
101	! Forced header and separation lines into 80 columns
102	!
103	! 2016-06-09 16:25:25Z suehring
104	! Bugfix in determining initial particle height and grid index in case of
105	! seed_follows_topography.
106	! Bugfix concerning random positions, ensure that particles do not move more
107	! than one grid length.
108	! Bugfix logarithmic interpolation.
109	! Initial setting of sgs_wf_part.
110	!
111	! 1890 2016-04-22 08:52:11Z hoffmann
112	! Initialization of aerosol equilibrium radius not possible in supersaturated
113	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
114	! initialization.
115	!
116	! 1873 2016-04-18 14:50:06Z maronga
117	! Module renamed (removed _mod
118	!
119	! 1871 2016-04-15 11:46:09Z hoffmann
120	! Initialization of aerosols added.
121	!
122	! 1850 2016-04-08 13:29:27Z maronga
123	! Module renamed
124	!
125	! 1831 2016-04-07 13:15:51Z hoffmann
126	! curvature_solution_effects moved to particle_attributes
127	!
128	! 1822 2016-04-07 07:49:42Z hoffmann
129	! Unused variables removed.
130	!
131	! 1783 2016-03-06 18:36:17Z raasch
132	! netcdf module added
133	!
134	! 1725 2015-11-17 13:01:51Z hoffmann
135	! Bugfix: Processor-dependent seed for random function is generated before it is
136	! used.
137	!
138	! 1691 2015-10-26 16:17:44Z maronga
139	! Renamed prandtl_layer to constant_flux_layer.
140	!
141	! 1685 2015-10-08 07:32:13Z raasch
142	! bugfix concerning vertical index offset in case of ocean
143	!
144	! 1682 2015-10-07 23:56:08Z knoop
145	! Code annotations made doxygen readable
146	!
147	! 1575 2015-03-27 09:56:27Z raasch
148	! initial vertical particle position is allowed to follow the topography
149	!
150	! 1359 2014-04-11 17:15:14Z hoffmann
151	! New particle structure integrated.
152	! Kind definition added to all floating point numbers.
153	! lpm_init changed form a subroutine to a module.
154	!
155	! 1327 2014-03-21 11:00:16Z raasch
156	! -netcdf_output
157	!
158	! 1322 2014-03-20 16:38:49Z raasch
159	! REAL functions provided with KIND-attribute
160	!
161	! 1320 2014-03-20 08:40:49Z raasch
162	! ONLY-attribute added to USE-statements,
163	! kind-parameters added to all INTEGER and REAL declaration statements,
164	! kinds are defined in new module kinds,
165	! revision history before 2012 removed,
166	! comment fields (!:) to be used for variable explanations added to
167	! all variable declaration statements
168	! bugfix: #if defined( __parallel ) added
169	!
170	! 1314 2014-03-14 18:25:17Z suehring
171	! Vertical logarithmic interpolation of horizontal particle speed for particles
172	! between roughness height and first vertical grid level.
173	!
174	! 1092 2013-02-02 11:24:22Z raasch
175	! unused variables removed
176	!
177	! 1036 2012-10-22 13:43:42Z raasch
178	! code put under GPL (PALM 3.9)
179	!
180	! 849 2012-03-15 10:35:09Z raasch
181	! routine renamed: init_particles -> lpm_init
182	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
183	! advec_particles),
184	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
185	!
186	! 828 2012-02-21 12:00:36Z raasch
187	! call of init_kernels, particle feature color renamed class
188	!
189	! 824 2012-02-17 09:09:57Z raasch
190	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
191	! array particles implemented as pointer
192	!
193	! 667 2010-12-23 12:06:00Z suehring/gryschka
194	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
195	! of arrays.
196	!
197	! Revision 1.1 1999/11/25 16:22:38 raasch
198	! Initial revision
199	!
200	!
201	! Description:
202	! ------------
203	!> This routine initializes a set of particles and their attributes (position,
204	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
205	!------------------------------------------------------------------------------!
206	MODULE lpm_init_mod
207
208	USE, INTRINSIC :: ISO_C_BINDING
209
210	USE arrays_3d, &
211	ONLY: de_dx, de_dy, de_dz, zu, zw
212
213	USE control_parameters, &
214	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
215	dt_3d, dz, initializing_actions, message_string, ocean, &
216	simulated_time
217
218	USE grid_variables, &
219	ONLY: ddx, dx, ddy, dy
220
221	USE indices, &
222	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
223	nzt, wall_flags_0
224
225	USE kinds
226
227	USE lpm_collision_kernels_mod, &
228	ONLY: init_kernels
229
230	USE netcdf_interface, &
231	ONLY: netcdf_data_format
232
233	USE particle_attributes, &
234	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
235	block_offset, block_offset_def, collision_kernel, &
236	curvature_solution_effects, density_ratio, grid_particles, &
237	isf,i_splitting_mode, initial_weighting_factor, ibc_par_b, &
238	ibc_par_lr, ibc_par_ns, ibc_par_t, iran_part, log_z_z0, &
239	max_number_of_particle_groups, min_nr_particle, &
240	number_concentration, &
241	number_particles_per_gridbox, number_of_particles, &
242	number_of_particle_groups, number_of_sublayers, &
243	offset_ocean_nzt, offset_ocean_nzt_m1, &
244	particles, particle_advection_start, particle_groups, &
245	particle_groups_type, particles_per_point, &
246	particle_type, pdx, pdy, pdz, prt_count, psb, psl, psn, psr, &
247	pss, pst, radius, random_start_position, &
248	read_particles_from_restartfile, seed_follows_topography, &
249	sgs_wf_part, sort_count, splitting_function, splitting_mode, &
250	total_number_of_particles, use_sgs_for_particles, &
251	write_particle_statistics, zero_particle, z0_av_global
252
253	USE pegrid
254
255	USE random_function_mod, &
256	ONLY: random_function
257
258	USE surface_mod, &
259	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
260
261	USE pmc_particle_interface, &
262	ONLY: pmcp_g_init
263
264	IMPLICIT NONE
265
266	PRIVATE
267
268	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
269	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
270
271	INTERFACE lpm_init
272	MODULE PROCEDURE lpm_init
273	END INTERFACE lpm_init
274
275	INTERFACE lpm_create_particle
276	MODULE PROCEDURE lpm_create_particle
277	END INTERFACE lpm_create_particle
278
279	PUBLIC lpm_init, lpm_create_particle
280
281	CONTAINS
282
283	!------------------------------------------------------------------------------!
284	! Description:
285	! ------------
286	!> @todo Missing subroutine description.
287	!------------------------------------------------------------------------------!
288	SUBROUTINE lpm_init
289
290	USE lpm_collision_kernels_mod, &
291	ONLY: init_kernels
292
293	USE pmc_interface, &
294	ONLY: nested_run
295
296	IMPLICIT NONE
297
298	INTEGER(iwp) :: i !<
299	INTEGER(iwp) :: j !<
300	INTEGER(iwp) :: k !<
301
302	REAL(wp) :: div !<
303	REAL(wp) :: height_int !<
304	REAL(wp) :: height_p !<
305	REAL(wp) :: z_p !<
306	REAL(wp) :: z0_av_local !<
307
308
309	!
310	!-- In case of oceans runs, the vertical index calculations need an offset,
311	!-- because otherwise the k indices will become negative
312	IF ( ocean ) THEN
313	offset_ocean_nzt = nzt
314	offset_ocean_nzt_m1 = nzt - 1
315	ENDIF
316
317	!
318	!-- Define block offsets for dividing a gridcell in 8 sub cells
319	!-- See documentation for List of subgrid boxes
320	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
321	block_offset(0) = block_offset_def ( 0, 0, 0)
322	block_offset(1) = block_offset_def ( 0, 0,-1)
323	block_offset(2) = block_offset_def ( 0,-1, 0)
324	block_offset(3) = block_offset_def ( 0,-1,-1)
325	block_offset(4) = block_offset_def (-1, 0, 0)
326	block_offset(5) = block_offset_def (-1, 0,-1)
327	block_offset(6) = block_offset_def (-1,-1, 0)
328	block_offset(7) = block_offset_def (-1,-1,-1)
329	!
330	!-- Check the number of particle groups.
331	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
332	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
333	max_number_of_particle_groups , &
334	'&number_of_particle_groups reset to ', &
335	max_number_of_particle_groups
336	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
337	number_of_particle_groups = max_number_of_particle_groups
338	ENDIF
339	!
340	!-- Check if downward-facing walls exist. This case, reflection boundary
341	!-- conditions (as well as subgrid-scale velocities) may do not work
342	!-- propably (not realized so far).
343	IF ( surf_def_h(1)%ns >= 1 ) THEN
344	WRITE( message_string, * ) 'Overhanging topography do not work '// &
345	'with particles'
346	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
347
348	ENDIF
349
350	!
351	!-- Set default start positions, if necessary
352	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
353	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
354	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
355	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
356	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
357	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
358
359	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
360	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
361	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
362
363	!
364	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
365	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
366	IF ( number_particles_per_gridbox /= -1 .AND. &
367	number_particles_per_gridbox >= 1 ) THEN
368	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
369	REAL(number_particles_per_gridbox))**0.3333333_wp
370	!
371	!-- Ensure a smooth value (two significant digits) of distance between
372	!-- particles (pdx, pdy, pdz).
373	div = 1000.0_wp
374	DO WHILE ( pdx(1) < div )
375	div = div / 10.0_wp
376	ENDDO
377	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
378	pdy(1) = pdx(1)
379	pdz(1) = pdx(1)
380
381	ENDIF
382
383	DO j = 2, number_of_particle_groups
384	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
385	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
386	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
387	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
388	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
389	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
390	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
391	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
392	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
393	ENDDO
394
395	!
396	!-- Allocate arrays required for calculating particle SGS velocities.
397	!-- Initialize prefactor required for stoachastic Weil equation.
398	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
399	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
400	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
401	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
402
403	sgs_wf_part = 1.0_wp / 3.0_wp
404	ENDIF
405
406	!
407	!-- Allocate array required for logarithmic vertical interpolation of
408	!-- horizontal particle velocities between the surface and the first vertical
409	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
410	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
411	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
412	!-- To obtain exact height levels of particles, linear interpolation is applied
413	!-- (see lpm_advec.f90).
414	IF ( constant_flux_layer ) THEN
415
416	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
417	z_p = zu(nzb+1) - zw(nzb)
418
419	!
420	!-- Calculate horizontal mean value of z0 used for logartihmic
421	!-- interpolation. Note: this is not exact for heterogeneous z0.
422	!-- However, sensitivity studies showed that the effect is
423	!-- negligible.
424	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
425	SUM( surf_usm_h%z0 )
426	z0_av_global = 0.0_wp
427
428	#if defined( __parallel )
429	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
430	comm2d, ierr )
431	#else
432	z0_av_global = z0_av_local
433	#endif
434
435	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
436	!
437	!-- Horizontal wind speed is zero below and at z0
438	log_z_z0(0) = 0.0_wp
439	!
440	!-- Calculate vertical depth of the sublayers
441	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
442	!
443	!-- Precalculate LOG(z/z0)
444	height_p = z0_av_global
445	DO k = 1, number_of_sublayers
446
447	height_p = height_p + height_int
448	log_z_z0(k) = LOG( height_p / z0_av_global )
449
450	ENDDO
451
452	ENDIF
453
454	!
455	!-- Check boundary condition and set internal variables
456	SELECT CASE ( bc_par_b )
457
458	CASE ( 'absorb' )
459	ibc_par_b = 1
460
461	CASE ( 'reflect' )
462	ibc_par_b = 2
463
464	CASE DEFAULT
465	WRITE( message_string, * ) 'unknown boundary condition ', &
466	'bc_par_b = "', TRIM( bc_par_b ), '"'
467	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
468
469	END SELECT
470	SELECT CASE ( bc_par_t )
471
472	CASE ( 'absorb' )
473	ibc_par_t = 1
474
475	CASE ( 'reflect' )
476	ibc_par_t = 2
477
478	CASE ( 'nested' )
479	ibc_par_t = 3
480
481	CASE DEFAULT
482	WRITE( message_string, * ) 'unknown boundary condition ', &
483	'bc_par_t = "', TRIM( bc_par_t ), '"'
484	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
485
486	END SELECT
487	SELECT CASE ( bc_par_lr )
488
489	CASE ( 'cyclic' )
490	ibc_par_lr = 0
491
492	CASE ( 'absorb' )
493	ibc_par_lr = 1
494
495	CASE ( 'reflect' )
496	ibc_par_lr = 2
497
498	CASE ( 'nested' )
499	ibc_par_lr = 3
500
501	CASE DEFAULT
502	WRITE( message_string, * ) 'unknown boundary condition ', &
503	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
504	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
505
506	END SELECT
507	SELECT CASE ( bc_par_ns )
508
509	CASE ( 'cyclic' )
510	ibc_par_ns = 0
511
512	CASE ( 'absorb' )
513	ibc_par_ns = 1
514
515	CASE ( 'reflect' )
516	ibc_par_ns = 2
517
518	CASE ( 'nested' )
519	ibc_par_ns = 3
520
521	CASE DEFAULT
522	WRITE( message_string, * ) 'unknown boundary condition ', &
523	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
524	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
525
526	END SELECT
527	SELECT CASE ( splitting_mode )
528
529	CASE ( 'const' )
530	i_splitting_mode = 1
531
532	CASE ( 'cl_av' )
533	i_splitting_mode = 2
534
535	CASE ( 'gb_av' )
536	i_splitting_mode = 3
537
538	CASE DEFAULT
539	WRITE( message_string, * ) 'unknown splitting condition ', &
540	'splitting_mode = "', TRIM( splitting_mode ), '"'
541	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
542
543	END SELECT
544	SELECT CASE ( splitting_function )
545
546	CASE ( 'gamma' )
547	isf = 1
548
549	CASE ( 'log' )
550	isf = 2
551
552	CASE ( 'exp' )
553	isf = 3
554
555	CASE DEFAULT
556	WRITE( message_string, * ) 'unknown splitting function ', &
557	'splitting_function = "', TRIM( splitting_function ), '"'
558	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
559
560	END SELECT
561
562
563	!
564	!-- Initialize collision kernels
565	IF ( collision_kernel /= 'none' ) CALL init_kernels
566
567	!
568	!-- For the first model run of a possible job chain initialize the
569	!-- particles, otherwise read the particle data from restart file.
570	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
571	.AND. read_particles_from_restartfile ) THEN
572
573	CALL lpm_read_restart_file
574
575	ELSE
576
577	!
578	!-- Allocate particle arrays and set attributes of the initial set of
579	!-- particles, which can be also periodically released at later times.
580	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
581	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
582
583	number_of_particles = 0
584
585	sort_count = 0
586	prt_count = 0
587
588	!
589	!-- initialize counter for particle IDs
590	grid_particles%id_counter = 1
591
592	!
593	!-- Initialize all particles with dummy values (otherwise errors may
594	!-- occur within restart runs). The reason for this is still not clear
595	!-- and may be presumably caused by errors in the respective user-interface.
596	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
597	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
598	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
599	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
600	0, 0, 0_idp, .FALSE., -1 )
601
602	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
603
604	!
605	!-- Set values for the density ratio and radius for all particle
606	!-- groups, if necessary
607	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
608	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
609	DO i = 2, number_of_particle_groups
610	IF ( density_ratio(i) == 9999999.9_wp ) THEN
611	density_ratio(i) = density_ratio(i-1)
612	ENDIF
613	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
614	ENDDO
615
616	DO i = 1, number_of_particle_groups
617	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
618	WRITE( message_string, * ) 'particle group #', i, 'has a', &
619	'density ratio /= 0 but radius = 0'
620	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
621	ENDIF
622	particle_groups(i)%density_ratio = density_ratio(i)
623	particle_groups(i)%radius = radius(i)
624	ENDDO
625
626	!
627	!-- Set a seed value for the random number generator to be exclusively
628	!-- used for the particle code. The generated random numbers should be
629	!-- different on the different PEs.
630	iran_part = iran_part + myid
631
632	CALL lpm_create_particle (PHASE_INIT)
633	!
634	!-- User modification of initial particles
635	CALL user_lpm_init
636
637	!
638	!-- Open file for statistical informations about particle conditions
639	IF ( write_particle_statistics ) THEN
640	CALL check_open( 80 )
641	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
642	number_of_particles
643	CALL close_file( 80 )
644	ENDIF
645
646	ENDIF
647
648	IF ( nested_run ) CALL pmcp_g_init
649
650	!
651	!-- To avoid programm abort, assign particles array to the local version of
652	!-- first grid cell
653	number_of_particles = prt_count(nzb+1,nys,nxl)
654	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
655	!
656	!-- Formats
657	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
658
659	END SUBROUTINE lpm_init
660
661	!------------------------------------------------------------------------------!
662	! Description:
663	! ------------
664	!> @todo Missing subroutine description.
665	!------------------------------------------------------------------------------!
666	SUBROUTINE lpm_create_particle (phase)
667
668	USE arrays_3d, &
669	ONLY: zw
670	USE lpm_exchange_horiz_mod, &
671	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
672
673	USE lpm_pack_and_sort_mod, &
674	ONLY: lpm_sort_in_subboxes
675
676	USE particle_attributes, &
677	ONLY: deleted_particles
678
679	IMPLICIT NONE
680
681	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
682	INTEGER(iwp) :: i !< loop variable ( particle groups )
683	INTEGER(iwp) :: ip !< index variable along x
684	INTEGER(iwp) :: j !< loop variable ( particles per point )
685	INTEGER(iwp) :: jp !< index variable along y
686	INTEGER(iwp) :: k !< index variable along z
687	INTEGER(iwp) :: k_surf !< index of surface grid point
688	INTEGER(iwp) :: kp !< index variable along z
689	INTEGER(iwp) :: loop_stride !< loop variable for initialization
690	INTEGER(iwp) :: n !< loop variable ( number of particles )
691	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
692
693	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
694
695	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
696	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
697
698	LOGICAL :: first_stride !< flag for initialization
699
700	REAL(wp) :: pos_x !< increment for particle position in x
701	REAL(wp) :: pos_y !< increment for particle position in y
702	REAL(wp) :: pos_z !< increment for particle position in z
703	REAL(wp) :: rand_contr !< dummy argument for random position
704
705	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
706
707	!
708	!-- Calculate particle positions and store particle attributes, if
709	!-- particle is situated on this PE
710	DO loop_stride = 1, 2
711	first_stride = (loop_stride == 1)
712	IF ( first_stride ) THEN
713	local_count = 0 ! count number of particles
714	ELSE
715	local_count = prt_count ! Start address of new particles
716	ENDIF
717
718	!
719	!-- Calculate initial_weighting_factor diagnostically
720	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
721	initial_weighting_factor = number_concentration * 1.0E6_wp * &
722	pdx(1) * pdy(1) * pdz(1)
723	END IF
724
725	n = 0
726	DO i = 1, number_of_particle_groups
727
728	pos_z = psb(i)
729
730	DO WHILE ( pos_z <= pst(i) )
731
732	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
733
734
735	pos_y = pss(i)
736
737	DO WHILE ( pos_y <= psn(i) )
738
739	IF ( pos_y >= nys * dy .AND. &
740	pos_y < ( nyn + 1 ) * dy ) THEN
741
742	pos_x = psl(i)
743
744	xloop: DO WHILE ( pos_x <= psr(i) )
745
746	IF ( pos_x >= nxl * dx .AND. &
747	pos_x < ( nxr + 1) * dx ) THEN
748
749	DO j = 1, particles_per_point
750
751
752	n = n + 1
753	tmp_particle%x = pos_x
754	tmp_particle%y = pos_y
755	tmp_particle%z = pos_z
756	tmp_particle%age = 0.0_wp
757	tmp_particle%age_m = 0.0_wp
758	tmp_particle%dt_sum = 0.0_wp
759	tmp_particle%e_m = 0.0_wp
760	tmp_particle%rvar1 = 0.0_wp
761	tmp_particle%rvar2 = 0.0_wp
762	tmp_particle%rvar3 = 0.0_wp
763	tmp_particle%speed_x = 0.0_wp
764	tmp_particle%speed_y = 0.0_wp
765	tmp_particle%speed_z = 0.0_wp
766	tmp_particle%origin_x = pos_x
767	tmp_particle%origin_y = pos_y
768	tmp_particle%origin_z = pos_z
769	IF ( curvature_solution_effects ) THEN
770	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
771	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
772	ELSE
773	tmp_particle%aux1 = 0.0_wp ! free to use
774	tmp_particle%aux2 = 0.0_wp ! free to use
775	ENDIF
776	tmp_particle%radius = particle_groups(i)%radius
777	tmp_particle%weight_factor = initial_weighting_factor
778	tmp_particle%class = 1
779	tmp_particle%group = i
780	tmp_particle%id = 0_idp
781	tmp_particle%particle_mask = .TRUE.
782	tmp_particle%block_nr = -1
783	!
784	!-- Determine the grid indices of the particle position
785	ip = tmp_particle%x * ddx
786	jp = tmp_particle%y * ddy
787	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
788	DO WHILE( zw(kp) < tmp_particle%z )
789	kp = kp + 1
790	ENDDO
791	DO WHILE( zw(kp-1) > tmp_particle%z )
792	kp = kp - 1
793	ENDDO
794	!
795	!-- Determine surface level. Therefore, check for
796	!-- upward-facing wall on w-grid.
797	k_surf = get_topography_top_index_ji( jp, ip, 'w' )
798
799	IF ( seed_follows_topography ) THEN
800	!
801	!-- Particle height is given relative to topography
802	kp = kp + k_surf
803	tmp_particle%z = tmp_particle%z + zw(k_surf)
804	!-- Skip particle release if particle position is
805	!-- above model top, or within topography in case
806	!-- of overhanging structures.
807	IF ( kp > nzt .OR. &
808	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
809	pos_x = pos_x + pdx(i)
810	CYCLE xloop
811	ENDIF
812	!
813	!-- Skip particle release if particle position is
814	!-- below surface, or within topography in case
815	!-- of overhanging structures.
816	ELSEIF ( .NOT. seed_follows_topography .AND. &
817	tmp_particle%z <= zw(k_surf) .OR. &
818	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
819	THEN
820	pos_x = pos_x + pdx(i)
821	CYCLE xloop
822	ENDIF
823
824	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
825
826	IF ( .NOT. first_stride ) THEN
827	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
828	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
829	ENDIF
830	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
831	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
832	ENDIF
833	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
834
835	ENDIF
836	ENDDO
837
838	ENDIF
839
840	pos_x = pos_x + pdx(i)
841
842	ENDDO xloop
843
844	ENDIF
845
846	pos_y = pos_y + pdy(i)
847
848	ENDDO
849
850	ENDIF
851
852	pos_z = pos_z + pdz(i)
853
854	ENDDO
855
856	ENDDO
857
858	IF ( first_stride ) THEN
859	DO ip = nxl, nxr
860	DO jp = nys, nyn
861	DO kp = nzb+1, nzt
862	IF ( phase == PHASE_INIT ) THEN
863	IF ( local_count(kp,jp,ip) > 0 ) THEN
864	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
865	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
866	min_nr_particle )
867	ELSE
868	alloc_size = min_nr_particle
869	ENDIF
870	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
871	DO n = 1, alloc_size
872	grid_particles(kp,jp,ip)%particles(n) = zero_particle
873	ENDDO
874	ELSEIF ( phase == PHASE_RELEASE ) THEN
875	IF ( local_count(kp,jp,ip) > 0 ) THEN
876	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
877	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
878	alloc_factor / 100.0_wp ) ), min_nr_particle )
879	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
880	CALL realloc_particles_array(ip,jp,kp,alloc_size)
881	ENDIF
882	ENDIF
883	ENDIF
884	ENDDO
885	ENDDO
886	ENDDO
887	ENDIF
888
889	ENDDO
890
891
892
893	local_start = prt_count+1
894	prt_count = local_count
895
896	!
897	!-- Calculate particle IDs
898	DO ip = nxl, nxr
899	DO jp = nys, nyn
900	DO kp = nzb+1, nzt
901	number_of_particles = prt_count(kp,jp,ip)
902	IF ( number_of_particles <= 0 ) CYCLE
903	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
904
905	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
906
907	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
908	10000_idp*2 kp + 10000_idp * jp + ip
909	!
910	!-- Count the number of particles that have been released before
911	grid_particles(kp,jp,ip)%id_counter = &
912	grid_particles(kp,jp,ip)%id_counter + 1
913
914	ENDDO
915
916	ENDDO
917	ENDDO
918	ENDDO
919
920	!
921	!-- Initialize aerosol background spectrum
922	IF ( curvature_solution_effects ) THEN
923	CALL lpm_init_aerosols(local_start)
924	ENDIF
925
926	!
927	!-- Add random fluctuation to particle positions.
928	IF ( random_start_position ) THEN
929	DO ip = nxl, nxr
930	DO jp = nys, nyn
931	DO kp = nzb+1, nzt
932	number_of_particles = prt_count(kp,jp,ip)
933	IF ( number_of_particles <= 0 ) CYCLE
934	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
935	!
936	!-- Move only new particles. Moreover, limit random fluctuation
937	!-- in order to prevent that particles move more than one grid box,
938	!-- which would lead to problems concerning particle exchange
939	!-- between processors in case pdx/pdy are larger than dx/dy,
940	!-- respectively.
941	DO n = local_start(kp,jp,ip), number_of_particles
942	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
943	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
944	pdx(particles(n)%group)
945	particles(n)%x = particles(n)%x + &
946	MERGE( rand_contr, SIGN( dx, rand_contr ), &
947	ABS( rand_contr ) < dx &
948	)
949	ENDIF
950	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
951	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
952	pdy(particles(n)%group)
953	particles(n)%y = particles(n)%y + &
954	MERGE( rand_contr, SIGN( dy, rand_contr ), &
955	ABS( rand_contr ) < dy &
956	)
957	ENDIF
958	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
959	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
960	pdz(particles(n)%group)
961	particles(n)%z = particles(n)%z + &
962	MERGE( rand_contr, SIGN( dz, rand_contr ), &
963	ABS( rand_contr ) < dz &
964	)
965	ENDIF
966	ENDDO
967	!
968	!-- Identify particles located outside the model domain and reflect
969	!-- or absorb them if necessary.
970	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
971	!
972	!-- Furthermore, remove particles located in topography. Note, as
973	!-- the particle speed is still zero at this point, wall
974	!-- reflection boundary conditions will not work in this case.
975	particles => &
976	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
977	DO n = local_start(kp,jp,ip), number_of_particles
978	i = particles(n)%x * ddx
979	j = particles(n)%y * ddy
980	k = particles(n)%z / dz + 1 + offset_ocean_nzt
981	DO WHILE( zw(k) < particles(n)%z )
982	k = k + 1
983	ENDDO
984	DO WHILE( zw(k-1) > particles(n)%z )
985	k = k - 1
986	ENDDO
987	!
988	!-- Check if particle is within topography
989	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
990	particles(n)%particle_mask = .FALSE.
991	deleted_particles = deleted_particles + 1
992	ENDIF
993
994	ENDDO
995	ENDDO
996	ENDDO
997	ENDDO
998	!
999	!-- Exchange particles between grid cells and processors
1000	CALL lpm_move_particle
1001	CALL lpm_exchange_horiz
1002
1003	ENDIF
1004	!
1005	!-- In case of random_start_position, delete particles identified by
1006	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1007	!-- which is needed for a fast interpolation of the LES fields on the particle
1008	!-- position.
1009	CALL lpm_sort_in_subboxes
1010
1011	!
1012	!-- Determine the current number of particles
1013	DO ip = nxl, nxr
1014	DO jp = nys, nyn
1015	DO kp = nzb+1, nzt
1016	number_of_particles = number_of_particles &
1017	+ prt_count(kp,jp,ip)
1018	ENDDO
1019	ENDDO
1020	ENDDO
1021	!
1022	!-- Calculate the number of particles of the total domain
1023	#if defined( __parallel )
1024	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1025	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1026	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1027	#else
1028	total_number_of_particles = number_of_particles
1029	#endif
1030
1031	RETURN
1032
1033	END SUBROUTINE lpm_create_particle
1034
1035	SUBROUTINE lpm_init_aerosols(local_start)
1036
1037	USE arrays_3d, &
1038	ONLY: hyp, pt, q
1039
1040	USE cloud_parameters, &
1041	ONLY: l_d_rv, molecular_weight_of_solute, &
1042	molecular_weight_of_water, rho_l, r_v, rho_s, vanthoff
1043
1044	USE constants, &
1045	ONLY: pi
1046
1047	USE diagnostic_quantities_mod, &
1048	ONLY: magnus
1049
1050
1051	USE kinds
1052
1053	USE particle_attributes, &
1054	ONLY: aero_species, aero_type, aero_weight, log_sigma, na, rm
1055
1056	IMPLICIT NONE
1057
1058	REAL(wp) :: afactor !< curvature effects
1059	REAL(wp) :: bfactor !< solute effects
1060	REAL(wp) :: dlogr !< logarithmic width of radius bin
1061	REAL(wp) :: e_a !< vapor pressure
1062	REAL(wp) :: e_s !< saturation vapor pressure
1063	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1064	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1065	REAL(wp) :: r_mid !< mean radius of bin
1066	REAL(wp) :: r_l !< left radius of bin
1067	REAL(wp) :: r_r !< right radius of bin
1068	REAL(wp) :: sigma !< surface tension
1069	REAL(wp) :: t_int !< temperature
1070
1071	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1072
1073	INTEGER(iwp) :: n !<
1074	INTEGER(iwp) :: ip !<
1075	INTEGER(iwp) :: jp !<
1076	INTEGER(iwp) :: kp !<
1077
1078	!
1079	!-- Set constants for different aerosol species
1080	IF ( TRIM(aero_species) .EQ. 'nacl' ) THEN
1081	molecular_weight_of_solute = 0.05844_wp
1082	rho_s = 2165.0_wp
1083	vanthoff = 2.0_wp
1084	ELSEIF ( TRIM(aero_species) .EQ. 'c3h4o4' ) THEN
1085	molecular_weight_of_solute = 0.10406_wp
1086	rho_s = 1600.0_wp
1087	vanthoff = 1.37_wp
1088	ELSEIF ( TRIM(aero_species) .EQ. 'nh4o3' ) THEN
1089	molecular_weight_of_solute = 0.08004_wp
1090	rho_s = 1720.0_wp
1091	vanthoff = 2.31_wp
1092	ELSE
1093	WRITE( message_string, * ) 'unknown aerosol species ', &
1094	'aero_species = "', TRIM( aero_species ), '"'
1095	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1096	ENDIF
1097	!
1098	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1099	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1100	IF ( TRIM(aero_type) .EQ. 'polar' ) THEN
1101	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6
1102	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6
1103	log_sigma = (/ 0.245, 0.300, 0.291 /)
1104	ELSEIF ( TRIM(aero_type) .EQ. 'background' ) THEN
1105	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6
1106	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6
1107	log_sigma = (/ 0.645, 0.253, 0.425 /)
1108	ELSEIF ( TRIM(aero_type) .EQ. 'maritime' ) THEN
1109	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6
1110	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6
1111	log_sigma = (/ 0.657, 0.210, 0.396 /)
1112	ELSEIF ( TRIM(aero_type) .EQ. 'continental' ) THEN
1113	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6
1114	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6
1115	log_sigma = (/ 0.161, 0.217, 0.380 /)
1116	ELSEIF ( TRIM(aero_type) .EQ. 'desert' ) THEN
1117	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6
1118	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6
1119	log_sigma = (/ 0.247, 0.770, 0.438 /)
1120	ELSEIF ( TRIM(aero_type) .EQ. 'rural' ) THEN
1121	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6
1122	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6
1123	log_sigma = (/ 0.225, 0.557, 0.266 /)
1124	ELSEIF ( TRIM(aero_type) .EQ. 'urban' ) THEN
1125	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6
1126	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6
1127	log_sigma = (/ 0.245, 0.666, 0.337 /)
1128	ELSEIF ( TRIM(aero_type) .EQ. 'user' ) THEN
1129	CONTINUE
1130	ELSE
1131	WRITE( message_string, * ) 'unknown aerosol type ', &
1132	'aero_type = "', TRIM( aero_type ), '"'
1133	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1134	ENDIF
1135
1136	DO ip = nxl, nxr
1137	DO jp = nys, nyn
1138	DO kp = nzb+1, nzt
1139
1140	number_of_particles = prt_count(kp,jp,ip)
1141	IF ( number_of_particles <= 0 ) CYCLE
1142	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1143
1144	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1145	!
1146	!-- Initialize the aerosols with a predefined spectral distribution
1147	!-- of the dry radius (logarithmically increasing bins) and a varying
1148	!-- weighting factor
1149	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1150
1151	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1152	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1153	r_mid = SQRT( r_l * r_r )
1154
1155	particles(n)%aux1 = r_mid
1156	particles(n)%weight_factor = &
1157	( na(1) / ( SQRT( 2.0 * pi ) * log_sigma(1) ) * &
1158	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0 log_sigma(1)**2 ) ) + &
1159	na(2) / ( SQRT( 2.0 * pi ) * log_sigma(2) ) * &
1160	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0 log_sigma(2)**2 ) ) + &
1161	na(3) / ( SQRT( 2.0 * pi ) * log_sigma(3) ) * &
1162	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0 log_sigma(3)**2 ) ) &
1163	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dz )
1164
1165	!
1166	!-- Multiply weight_factor with the namelist parameter aero_weight
1167	!-- to increase or decrease the number of simulated aerosols
1168	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1169
1170	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1171	.GT. random_function( iran_part ) ) THEN
1172	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0
1173	ELSE
1174	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1175	ENDIF
1176	!
1177	!-- Unnecessary particles will be deleted
1178	IF ( particles(n)%weight_factor .LE. 0.0 ) particles(n)%particle_mask = .FALSE.
1179
1180	ENDDO
1181	!
1182	!-- Set particle radius to equilibrium radius based on the environmental
1183	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1184	!-- the sometimes lengthy growth toward their equilibrium radius within
1185	!-- the simulation.
1186	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1187
1188	e_s = magnus( t_int )
1189	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + 0.622_wp )
1190
1191	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1192	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1193
1194	bfactor = vanthoff * molecular_weight_of_water * &
1195	rho_s / ( molecular_weight_of_solute * rho_l )
1196	!
1197	!-- The formula is only valid for subsaturated environments. For
1198	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1199	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1200
1201	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1202	!
1203	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1204	!-- Curry (2007, JGR)
1205	particles(n)%radius = bfactor*0.3333333_wp &
1206	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1207	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1208	particles(n)%aux1 ) ) / &
1209	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1210	)
1211
1212	ENDDO
1213
1214	ENDDO
1215	ENDDO
1216	ENDDO
1217
1218	END SUBROUTINE lpm_init_aerosols
1219
1220	END MODULE lpm_init_mod

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