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

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