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source: palm/trunk/SOURCE/lpm_init.f90 @ 2414

Last change on this file since 2414 was 2375, checked in by schwenkel, 7 years ago
improved aerosol initialization for bulk microphysics
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1	!> @file lpm_init.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
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 2375 2017-08-29 14:10:28Z Giersch $
27	! Initialization of chemical aerosol composition
28	!
29	! 2346 2017-08-09 16:39:17Z suehring
30	! Bugfix, correct determination of topography top index
31	!
32	! 2318 2017-07-20 17:27:44Z suehring
33	! Get topography top index via Function call
34	!
35	! 2317 2017-07-20 17:27:19Z suehring
36	! Extended particle data type. Aerosol initialization improved.
37	!
38	! 2305 2017-07-06 11:18:47Z hoffmann
39	! Improved calculation of particle IDs.
40	!
41	! 2274 2017-06-09 13:27:48Z Giersch
42	! Changed error messages
43	!
44	! 2265 2017-06-08 16:58:28Z schwenkel
45	! Unused variables removed.
46	!
47	! 2263 2017-06-08 14:59:01Z schwenkel
48	! Implemented splitting and merging algorithm
49	!
50	! 2233 2017-05-30 18:08:54Z suehring
51	!
52	! 2232 2017-05-30 17:47:52Z suehring
53	! Adjustments according to new topography realization
54	!
55	!
56	! 2223 2017-05-15 16:38:09Z suehring
57	! Add check for particle release at model top
58	!
59	! 2182 2017-03-17 14:27:40Z schwenkel
60	! Added parameters for simplified particle initialization.
61	!
62	! 2122 2017-01-18 12:22:54Z hoffmann
63	! Improved initialization of equilibrium aerosol radii
64	! Calculation of particle ID
65	!
66	! 2000 2016-08-20 18:09:15Z knoop
67	! Forced header and separation lines into 80 columns
68	!
69	! 2016-06-09 16:25:25Z suehring
70	! Bugfix in determining initial particle height and grid index in case of
71	! seed_follows_topography.
72	! Bugfix concerning random positions, ensure that particles do not move more
73	! than one grid length.
74	! Bugfix logarithmic interpolation.
75	! Initial setting of sgs_wf_part.
76	!
77	! 1890 2016-04-22 08:52:11Z hoffmann
78	! Initialization of aerosol equilibrium radius not possible in supersaturated
79	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
80	! initialization.
81	!
82	! 1873 2016-04-18 14:50:06Z maronga
83	! Module renamed (removed _mod
84	!
85	! 1871 2016-04-15 11:46:09Z hoffmann
86	! Initialization of aerosols added.
87	!
88	! 1850 2016-04-08 13:29:27Z maronga
89	! Module renamed
90	!
91	! 1831 2016-04-07 13:15:51Z hoffmann
92	! curvature_solution_effects moved to particle_attributes
93	!
94	! 1822 2016-04-07 07:49:42Z hoffmann
95	! Unused variables removed.
96	!
97	! 1783 2016-03-06 18:36:17Z raasch
98	! netcdf module added
99	!
100	! 1725 2015-11-17 13:01:51Z hoffmann
101	! Bugfix: Processor-dependent seed for random function is generated before it is
102	! used.
103	!
104	! 1691 2015-10-26 16:17:44Z maronga
105	! Renamed prandtl_layer to constant_flux_layer.
106	!
107	! 1685 2015-10-08 07:32:13Z raasch
108	! bugfix concerning vertical index offset in case of ocean
109	!
110	! 1682 2015-10-07 23:56:08Z knoop
111	! Code annotations made doxygen readable
112	!
113	! 1575 2015-03-27 09:56:27Z raasch
114	! initial vertical particle position is allowed to follow the topography
115	!
116	! 1359 2014-04-11 17:15:14Z hoffmann
117	! New particle structure integrated.
118	! Kind definition added to all floating point numbers.
119	! lpm_init changed form a subroutine to a module.
120	!
121	! 1327 2014-03-21 11:00:16Z raasch
122	! -netcdf_output
123	!
124	! 1322 2014-03-20 16:38:49Z raasch
125	! REAL functions provided with KIND-attribute
126	!
127	! 1320 2014-03-20 08:40:49Z raasch
128	! ONLY-attribute added to USE-statements,
129	! kind-parameters added to all INTEGER and REAL declaration statements,
130	! kinds are defined in new module kinds,
131	! revision history before 2012 removed,
132	! comment fields (!:) to be used for variable explanations added to
133	! all variable declaration statements
134	! bugfix: #if defined( __parallel ) added
135	!
136	! 1314 2014-03-14 18:25:17Z suehring
137	! Vertical logarithmic interpolation of horizontal particle speed for particles
138	! between roughness height and first vertical grid level.
139	!
140	! 1092 2013-02-02 11:24:22Z raasch
141	! unused variables removed
142	!
143	! 1036 2012-10-22 13:43:42Z raasch
144	! code put under GPL (PALM 3.9)
145	!
146	! 849 2012-03-15 10:35:09Z raasch
147	! routine renamed: init_particles -> lpm_init
148	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
149	! advec_particles),
150	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
151	!
152	! 828 2012-02-21 12:00:36Z raasch
153	! call of init_kernels, particle feature color renamed class
154	!
155	! 824 2012-02-17 09:09:57Z raasch
156	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
157	! array particles implemented as pointer
158	!
159	! 667 2010-12-23 12:06:00Z suehring/gryschka
160	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
161	! of arrays.
162	!
163	! Revision 1.1 1999/11/25 16:22:38 raasch
164	! Initial revision
165	!
166	!
167	! Description:
168	! ------------
169	!> This routine initializes a set of particles and their attributes (position,
170	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
171	!------------------------------------------------------------------------------!
172	MODULE lpm_init_mod
173
174	USE, INTRINSIC :: ISO_C_BINDING
175
176	USE arrays_3d, &
177	ONLY: de_dx, de_dy, de_dz, zu, zw
178
179	USE control_parameters, &
180	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
181	dt_3d, dz, initializing_actions, message_string, ocean, &
182	simulated_time
183
184	USE grid_variables, &
185	ONLY: ddx, dx, ddy, dy
186
187	USE indices, &
188	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
189	nzt, wall_flags_0
190
191	USE kinds
192
193	USE lpm_collision_kernels_mod, &
194	ONLY: init_kernels
195
196	USE netcdf_interface, &
197	ONLY: netcdf_data_format
198
199	USE particle_attributes, &
200	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
201	block_offset, block_offset_def, collision_kernel, &
202	curvature_solution_effects, density_ratio, grid_particles, &
203	isf,i_splitting_mode, initial_weighting_factor, ibc_par_b, &
204	ibc_par_lr, ibc_par_ns, ibc_par_t, iran_part, log_z_z0, &
205	max_number_of_particle_groups, min_nr_particle, &
206	number_concentration, &
207	number_particles_per_gridbox, number_of_particles, &
208	number_of_particle_groups, number_of_sublayers, &
209	offset_ocean_nzt, offset_ocean_nzt_m1, &
210	particles, particle_advection_start, particle_groups, &
211	particle_groups_type, particles_per_point, &
212	particle_type, pdx, pdy, pdz, prt_count, psb, psl, psn, psr, &
213	pss, pst, radius, random_start_position, &
214	read_particles_from_restartfile, seed_follows_topography, &
215	sgs_wf_part, sort_count, splitting_function, splitting_mode, &
216	total_number_of_particles, use_sgs_for_particles, &
217	write_particle_statistics, zero_particle, z0_av_global
218
219	USE pegrid
220
221	USE random_function_mod, &
222	ONLY: random_function
223
224	USE surface_mod, &
225	ONLY: get_topography_top_index, surf_def_h, surf_lsm_h, surf_usm_h
226
227	IMPLICIT NONE
228
229	PRIVATE
230
231	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
232	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
233
234	INTERFACE lpm_init
235	MODULE PROCEDURE lpm_init
236	END INTERFACE lpm_init
237
238	INTERFACE lpm_create_particle
239	MODULE PROCEDURE lpm_create_particle
240	END INTERFACE lpm_create_particle
241
242	PUBLIC lpm_init, lpm_create_particle
243
244	CONTAINS
245
246	!------------------------------------------------------------------------------!
247	! Description:
248	! ------------
249	!> @todo Missing subroutine description.
250	!------------------------------------------------------------------------------!
251	SUBROUTINE lpm_init
252
253	USE lpm_collision_kernels_mod, &
254	ONLY: init_kernels
255
256	IMPLICIT NONE
257
258	INTEGER(iwp) :: i !<
259	INTEGER(iwp) :: j !<
260	INTEGER(iwp) :: k !<
261
262	REAL(wp) :: div !<
263	REAL(wp) :: height_int !<
264	REAL(wp) :: height_p !<
265	REAL(wp) :: z_p !<
266	REAL(wp) :: z0_av_local !<
267
268
269	!
270	!-- In case of oceans runs, the vertical index calculations need an offset,
271	!-- because otherwise the k indices will become negative
272	IF ( ocean ) THEN
273	offset_ocean_nzt = nzt
274	offset_ocean_nzt_m1 = nzt - 1
275	ENDIF
276
277	!
278	!-- Define block offsets for dividing a gridcell in 8 sub cells
279
280	block_offset(0) = block_offset_def (-1,-1,-1)
281	block_offset(1) = block_offset_def (-1,-1, 0)
282	block_offset(2) = block_offset_def (-1, 0,-1)
283	block_offset(3) = block_offset_def (-1, 0, 0)
284	block_offset(4) = block_offset_def ( 0,-1,-1)
285	block_offset(5) = block_offset_def ( 0,-1, 0)
286	block_offset(6) = block_offset_def ( 0, 0,-1)
287	block_offset(7) = block_offset_def ( 0, 0, 0)
288	!
289	!-- Check the number of particle groups.
290	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
291	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
292	max_number_of_particle_groups , &
293	'&number_of_particle_groups reset to ', &
294	max_number_of_particle_groups
295	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
296	number_of_particle_groups = max_number_of_particle_groups
297	ENDIF
298	!
299	!-- Check if downward-facing walls exist. This case, reflection boundary
300	!-- conditions (as well as subgrid-scale velocities) may do not work
301	!-- propably (not realized so far).
302	IF ( surf_def_h(1)%ns >= 1 ) THEN
303	WRITE( message_string, * ) 'Overhanging topography do not work '// &
304	'with particles'
305	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
306
307	ENDIF
308
309	!
310	!-- Set default start positions, if necessary
311	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
312	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
313	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
314	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
315	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
316	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
317
318	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
319	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
320	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
321
322	!
323	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
324	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
325	IF ( number_particles_per_gridbox /= -1 .AND. &
326	number_particles_per_gridbox >= 1 ) THEN
327	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
328	REAL(number_particles_per_gridbox))**0.3333333_wp
329	!
330	!-- Ensure a smooth value (two significant digits) of distance between
331	!-- particles (pdx, pdy, pdz).
332	div = 1000.0_wp
333	DO WHILE ( pdx(1) < div )
334	div = div / 10.0_wp
335	ENDDO
336	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
337	pdy(1) = pdx(1)
338	pdz(1) = pdx(1)
339
340	ENDIF
341
342	DO j = 2, number_of_particle_groups
343	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
344	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
345	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
346	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
347	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
348	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
349	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
350	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
351	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
352	ENDDO
353
354	!
355	!-- Allocate arrays required for calculating particle SGS velocities.
356	!-- Initialize prefactor required for stoachastic Weil equation.
357	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
358	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
359	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
360	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
361
362	sgs_wf_part = 1.0_wp / 3.0_wp
363	ENDIF
364
365	!
366	!-- Allocate array required for logarithmic vertical interpolation of
367	!-- horizontal particle velocities between the surface and the first vertical
368	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
369	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
370	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
371	!-- To obtain exact height levels of particles, linear interpolation is applied
372	!-- (see lpm_advec.f90).
373	IF ( constant_flux_layer ) THEN
374
375	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
376	z_p = zu(nzb+1) - zw(nzb)
377
378	!
379	!-- Calculate horizontal mean value of z0 used for logartihmic
380	!-- interpolation. Note: this is not exact for heterogeneous z0.
381	!-- However, sensitivity studies showed that the effect is
382	!-- negligible.
383	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
384	SUM( surf_usm_h%z0 )
385	z0_av_global = 0.0_wp
386
387	#if defined( __parallel )
388	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
389	comm2d, ierr )
390	#else
391	z0_av_global = z0_av_local
392	#endif
393
394	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
395	!
396	!-- Horizontal wind speed is zero below and at z0
397	log_z_z0(0) = 0.0_wp
398	!
399	!-- Calculate vertical depth of the sublayers
400	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
401	!
402	!-- Precalculate LOG(z/z0)
403	height_p = z0_av_global
404	DO k = 1, number_of_sublayers
405
406	height_p = height_p + height_int
407	log_z_z0(k) = LOG( height_p / z0_av_global )
408
409	ENDDO
410
411	ENDIF
412
413	!
414	!-- Check boundary condition and set internal variables
415	SELECT CASE ( bc_par_b )
416
417	CASE ( 'absorb' )
418	ibc_par_b = 1
419
420	CASE ( 'reflect' )
421	ibc_par_b = 2
422
423	CASE DEFAULT
424	WRITE( message_string, * ) 'unknown boundary condition ', &
425	'bc_par_b = "', TRIM( bc_par_b ), '"'
426	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
427
428	END SELECT
429	SELECT CASE ( bc_par_t )
430
431	CASE ( 'absorb' )
432	ibc_par_t = 1
433
434	CASE ( 'reflect' )
435	ibc_par_t = 2
436
437	CASE DEFAULT
438	WRITE( message_string, * ) 'unknown boundary condition ', &
439	'bc_par_t = "', TRIM( bc_par_t ), '"'
440	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
441
442	END SELECT
443	SELECT CASE ( bc_par_lr )
444
445	CASE ( 'cyclic' )
446	ibc_par_lr = 0
447
448	CASE ( 'absorb' )
449	ibc_par_lr = 1
450
451	CASE ( 'reflect' )
452	ibc_par_lr = 2
453
454	CASE DEFAULT
455	WRITE( message_string, * ) 'unknown boundary condition ', &
456	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
457	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
458
459	END SELECT
460	SELECT CASE ( bc_par_ns )
461
462	CASE ( 'cyclic' )
463	ibc_par_ns = 0
464
465	CASE ( 'absorb' )
466	ibc_par_ns = 1
467
468	CASE ( 'reflect' )
469	ibc_par_ns = 2
470
471	CASE DEFAULT
472	WRITE( message_string, * ) 'unknown boundary condition ', &
473	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
474	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
475
476	END SELECT
477	SELECT CASE ( splitting_mode )
478
479	CASE ( 'const' )
480	i_splitting_mode = 1
481
482	CASE ( 'cl_av' )
483	i_splitting_mode = 2
484
485	CASE ( 'gb_av' )
486	i_splitting_mode = 3
487
488	CASE DEFAULT
489	WRITE( message_string, * ) 'unknown splitting condition ', &
490	'splitting_mode = "', TRIM( splitting_mode ), '"'
491	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
492
493	END SELECT
494	SELECT CASE ( splitting_function )
495
496	CASE ( 'gamma' )
497	isf = 1
498
499	CASE ( 'log' )
500	isf = 2
501
502	CASE ( 'exp' )
503	isf = 3
504
505	CASE DEFAULT
506	WRITE( message_string, * ) 'unknown splitting function ', &
507	'splitting_function = "', TRIM( splitting_function ), '"'
508	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
509
510	END SELECT
511
512
513	!
514	!-- Initialize collision kernels
515	IF ( collision_kernel /= 'none' ) CALL init_kernels
516
517	!
518	!-- For the first model run of a possible job chain initialize the
519	!-- particles, otherwise read the particle data from restart file.
520	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
521	.AND. read_particles_from_restartfile ) THEN
522
523	CALL lpm_read_restart_file
524
525	ELSE
526
527	!
528	!-- Allocate particle arrays and set attributes of the initial set of
529	!-- particles, which can be also periodically released at later times.
530	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
531	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
532
533	number_of_particles = 0
534
535	sort_count = 0
536	prt_count = 0
537
538	!
539	!-- initialize counter for particle IDs
540	grid_particles%id_counter = 1
541
542	!
543	!-- Initialize all particles with dummy values (otherwise errors may
544	!-- occur within restart runs). The reason for this is still not clear
545	!-- and may be presumably caused by errors in the respective user-interface.
546	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
547	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
548	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
549	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
550	0, 0, 0_idp, .FALSE., -1 )
551
552	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
553
554	!
555	!-- Set values for the density ratio and radius for all particle
556	!-- groups, if necessary
557	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
558	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
559	DO i = 2, number_of_particle_groups
560	IF ( density_ratio(i) == 9999999.9_wp ) THEN
561	density_ratio(i) = density_ratio(i-1)
562	ENDIF
563	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
564	ENDDO
565
566	DO i = 1, number_of_particle_groups
567	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
568	WRITE( message_string, * ) 'particle group #', i, 'has a', &
569	'density ratio /= 0 but radius = 0'
570	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
571	ENDIF
572	particle_groups(i)%density_ratio = density_ratio(i)
573	particle_groups(i)%radius = radius(i)
574	ENDDO
575
576	!
577	!-- Set a seed value for the random number generator to be exclusively
578	!-- used for the particle code. The generated random numbers should be
579	!-- different on the different PEs.
580	iran_part = iran_part + myid
581
582	CALL lpm_create_particle (PHASE_INIT)
583	!
584	!-- User modification of initial particles
585	CALL user_lpm_init
586
587	!
588	!-- Open file for statistical informations about particle conditions
589	IF ( write_particle_statistics ) THEN
590	CALL check_open( 80 )
591	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
592	number_of_particles
593	CALL close_file( 80 )
594	ENDIF
595
596	ENDIF
597
598	!
599	!-- To avoid programm abort, assign particles array to the local version of
600	!-- first grid cell
601	number_of_particles = prt_count(nzb+1,nys,nxl)
602	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
603	!
604	!-- Formats
605	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
606
607	END SUBROUTINE lpm_init
608
609	!------------------------------------------------------------------------------!
610	! Description:
611	! ------------
612	!> @todo Missing subroutine description.
613	!------------------------------------------------------------------------------!
614	SUBROUTINE lpm_create_particle (phase)
615
616	USE lpm_exchange_horiz_mod, &
617	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
618
619	USE lpm_pack_arrays_mod, &
620	ONLY: lpm_pack_all_arrays
621
622	USE particle_attributes, &
623	ONLY: deleted_particles
624
625	IMPLICIT NONE
626
627	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
628	INTEGER(iwp) :: i !< loop variable ( particle groups )
629	INTEGER(iwp) :: ip !< index variable along x
630	INTEGER(iwp) :: j !< loop variable ( particles per point )
631	INTEGER(iwp) :: jp !< index variable along y
632	INTEGER(iwp) :: k !< index variable along z
633	INTEGER(iwp) :: k_surf !< index of surface grid point
634	INTEGER(iwp) :: kp !< index variable along z
635	INTEGER(iwp) :: loop_stride !< loop variable for initialization
636	INTEGER(iwp) :: n !< loop variable ( number of particles )
637	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
638
639	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
640
641	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
642	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
643
644	LOGICAL :: first_stride !< flag for initialization
645
646	REAL(wp) :: pos_x !< increment for particle position in x
647	REAL(wp) :: pos_y !< increment for particle position in y
648	REAL(wp) :: pos_z !< increment for particle position in z
649	REAL(wp) :: rand_contr !< dummy argument for random position
650
651	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
652
653	!
654	!-- Calculate particle positions and store particle attributes, if
655	!-- particle is situated on this PE
656	DO loop_stride = 1, 2
657	first_stride = (loop_stride == 1)
658	IF ( first_stride ) THEN
659	local_count = 0 ! count number of particles
660	ELSE
661	local_count = prt_count ! Start address of new particles
662	ENDIF
663
664	!
665	!-- Calculate initial_weighting_factor diagnostically
666	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
667	initial_weighting_factor = number_concentration * 1.0E6_wp * &
668	pdx(1) * pdy(1) * pdz(1)
669	END IF
670
671	n = 0
672	DO i = 1, number_of_particle_groups
673
674	pos_z = psb(i)
675
676	DO WHILE ( pos_z <= pst(i) )
677
678	IF ( pos_z >= 0.0_wp .AND. pos_z < zw(nzt) ) THEN
679
680
681	pos_y = pss(i)
682
683	DO WHILE ( pos_y <= psn(i) )
684
685	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
686	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
687
688	pos_x = psl(i)
689
690	xloop: DO WHILE ( pos_x <= psr(i) )
691
692	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
693	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
694
695	DO j = 1, particles_per_point
696
697
698	n = n + 1
699	tmp_particle%x = pos_x
700	tmp_particle%y = pos_y
701	tmp_particle%z = pos_z
702	tmp_particle%age = 0.0_wp
703	tmp_particle%age_m = 0.0_wp
704	tmp_particle%dt_sum = 0.0_wp
705	tmp_particle%e_m = 0.0_wp
706	tmp_particle%rvar1 = 0.0_wp
707	tmp_particle%rvar2 = 0.0_wp
708	tmp_particle%rvar3 = 0.0_wp
709	tmp_particle%speed_x = 0.0_wp
710	tmp_particle%speed_y = 0.0_wp
711	tmp_particle%speed_z = 0.0_wp
712	tmp_particle%origin_x = pos_x
713	tmp_particle%origin_y = pos_y
714	tmp_particle%origin_z = pos_z
715	IF ( curvature_solution_effects ) THEN
716	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
717	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
718	ELSE
719	tmp_particle%aux1 = 0.0_wp ! free to use
720	tmp_particle%aux2 = 0.0_wp ! free to use
721	ENDIF
722	tmp_particle%radius = particle_groups(i)%radius
723	tmp_particle%weight_factor = initial_weighting_factor
724	tmp_particle%class = 1
725	tmp_particle%group = i
726	tmp_particle%id = 0_idp
727	tmp_particle%particle_mask = .TRUE.
728	tmp_particle%block_nr = -1
729	!
730	!-- Determine the grid indices of the particle position
731	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
732	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
733	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
734	!
735	!-- Determine surface level. Therefore, check for
736	!-- upward-facing wall on w-grid.
737	k_surf = get_topography_top_index( jp, ip, 'w' )
738
739	IF ( seed_follows_topography ) THEN
740	!
741	!-- Particle height is given relative to topography
742	kp = kp + k_surf
743	tmp_particle%z = tmp_particle%z + zw(k_surf)
744	!-- Skip particle release if particle position is
745	!-- above model top, or within topography in case
746	!-- of overhanging structures.
747	IF ( kp > nzt .OR. &
748	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
749	pos_x = pos_x + pdx(i)
750	CYCLE xloop
751	ENDIF
752	!
753	!-- Skip particle release if particle position is
754	!-- below surface, or within topography in case
755	!-- of overhanging structures.
756	ELSEIF ( .NOT. seed_follows_topography .AND. &
757	tmp_particle%z <= zw(k_surf) .OR. &
758	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
759	THEN
760	pos_x = pos_x + pdx(i)
761	CYCLE xloop
762	ENDIF
763
764	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
765
766	IF ( .NOT. first_stride ) THEN
767	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
768	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
769	ENDIF
770	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
771	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
772	ENDIF
773	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
774
775	ENDIF
776	ENDDO
777
778	ENDIF
779
780	pos_x = pos_x + pdx(i)
781
782	ENDDO xloop
783
784	ENDIF
785
786	pos_y = pos_y + pdy(i)
787
788	ENDDO
789
790	ENDIF
791
792	pos_z = pos_z + pdz(i)
793
794	ENDDO
795
796	ENDDO
797
798	IF ( first_stride ) THEN
799	DO ip = nxl, nxr
800	DO jp = nys, nyn
801	DO kp = nzb+1, nzt
802	IF ( phase == PHASE_INIT ) THEN
803	IF ( local_count(kp,jp,ip) > 0 ) THEN
804	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
805	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
806	min_nr_particle )
807	ELSE
808	alloc_size = min_nr_particle
809	ENDIF
810	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
811	DO n = 1, alloc_size
812	grid_particles(kp,jp,ip)%particles(n) = zero_particle
813	ENDDO
814	ELSEIF ( phase == PHASE_RELEASE ) THEN
815	IF ( local_count(kp,jp,ip) > 0 ) THEN
816	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
817	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
818	alloc_factor / 100.0_wp ) ), min_nr_particle )
819	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
820	CALL realloc_particles_array(ip,jp,kp,alloc_size)
821	ENDIF
822	ENDIF
823	ENDIF
824	ENDDO
825	ENDDO
826	ENDDO
827	ENDIF
828
829	ENDDO
830
831
832
833	local_start = prt_count+1
834	prt_count = local_count
835
836	!
837	!-- Calculate particle IDs
838	DO ip = nxl, nxr
839	DO jp = nys, nyn
840	DO kp = nzb+1, nzt
841	number_of_particles = prt_count(kp,jp,ip)
842	IF ( number_of_particles <= 0 ) CYCLE
843	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
844
845	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
846
847	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
848	10000_idp*2 kp + 10000_idp * jp + ip
849	!
850	!-- Count the number of particles that have been released before
851	grid_particles(kp,jp,ip)%id_counter = &
852	grid_particles(kp,jp,ip)%id_counter + 1
853
854	ENDDO
855
856	ENDDO
857	ENDDO
858	ENDDO
859
860	!
861	!-- Initialize aerosol background spectrum
862	IF ( curvature_solution_effects ) THEN
863	CALL lpm_init_aerosols(local_start)
864	ENDIF
865
866	!
867	!-- Add random fluctuation to particle positions.
868	IF ( random_start_position ) THEN
869	DO ip = nxl, nxr
870	DO jp = nys, nyn
871	DO kp = nzb+1, nzt
872	number_of_particles = prt_count(kp,jp,ip)
873	IF ( number_of_particles <= 0 ) CYCLE
874	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
875	!
876	!-- Move only new particles. Moreover, limit random fluctuation
877	!-- in order to prevent that particles move more than one grid box,
878	!-- which would lead to problems concerning particle exchange
879	!-- between processors in case pdx/pdy are larger than dx/dy,
880	!-- respectively.
881	DO n = local_start(kp,jp,ip), number_of_particles
882	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
883	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
884	pdx(particles(n)%group)
885	particles(n)%x = particles(n)%x + &
886	MERGE( rand_contr, SIGN( dx, rand_contr ), &
887	ABS( rand_contr ) < dx &
888	)
889	ENDIF
890	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
891	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
892	pdy(particles(n)%group)
893	particles(n)%y = particles(n)%y + &
894	MERGE( rand_contr, SIGN( dy, rand_contr ), &
895	ABS( rand_contr ) < dy &
896	)
897	ENDIF
898	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
899	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
900	pdz(particles(n)%group)
901	particles(n)%z = particles(n)%z + &
902	MERGE( rand_contr, SIGN( dz, rand_contr ), &
903	ABS( rand_contr ) < dz &
904	)
905	ENDIF
906	ENDDO
907	!
908	!-- Identify particles located outside the model domain and reflect
909	!-- or absorb them if necessary.
910	CALL lpm_boundary_conds( 'bottom/top' )
911	!
912	!-- Furthermore, remove particles located in topography. Note, as
913	!-- the particle speed is still zero at this point, wall
914	!-- reflection boundary conditions will not work in this case.
915	particles => &
916	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
917	DO n = local_start(kp,jp,ip), number_of_particles
918	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
919	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
920	k = particles(n)%z / dz + 1 + offset_ocean_nzt
921	!
922	!-- Check if particle is within topography
923	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
924	particles(n)%particle_mask = .FALSE.
925	deleted_particles = deleted_particles + 1
926	ENDIF
927
928	ENDDO
929	ENDDO
930	ENDDO
931	ENDDO
932	!
933	!-- Exchange particles between grid cells and processors
934	CALL lpm_move_particle
935	CALL lpm_exchange_horiz
936
937	ENDIF
938	!
939	!-- In case of random_start_position, delete particles identified by
940	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
941	!-- which is needed for a fast interpolation of the LES fields on the particle
942	!-- position.
943	CALL lpm_pack_all_arrays
944
945	!
946	!-- Determine the current number of particles
947	DO ip = nxl, nxr
948	DO jp = nys, nyn
949	DO kp = nzb+1, nzt
950	number_of_particles = number_of_particles &
951	+ prt_count(kp,jp,ip)
952	ENDDO
953	ENDDO
954	ENDDO
955	!
956	!-- Calculate the number of particles of the total domain
957	#if defined( __parallel )
958	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
959	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
960	MPI_INTEGER, MPI_SUM, comm2d, ierr )
961	#else
962	total_number_of_particles = number_of_particles
963	#endif
964
965	RETURN
966
967	END SUBROUTINE lpm_create_particle
968
969	SUBROUTINE lpm_init_aerosols(local_start)
970
971	USE arrays_3d, &
972	ONLY: hyp, pt, q
973
974	USE cloud_parameters, &
975	ONLY: l_d_rv, molecular_weight_of_solute, &
976	molecular_weight_of_water, rho_l, r_v, rho_s, vanthoff
977
978	USE constants, &
979	ONLY: pi
980
981	USE kinds
982
983	USE particle_attributes, &
984	ONLY: aero_species, aero_type, aero_weight, log_sigma, na, rm
985
986	IMPLICIT NONE
987
988	REAL(wp) :: afactor !< curvature effects
989	REAL(wp) :: bfactor !< solute effects
990	REAL(wp) :: dlogr !< logarithmic width of radius bin
991	REAL(wp) :: e_a !< vapor pressure
992	REAL(wp) :: e_s !< saturation vapor pressure
993	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
994	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
995	REAL(wp) :: r_mid !< mean radius of bin
996	REAL(wp) :: r_l !< left radius of bin
997	REAL(wp) :: r_r !< right radius of bin
998	REAL(wp) :: sigma !< surface tension
999	REAL(wp) :: t_int !< temperature
1000
1001	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1002
1003	INTEGER(iwp) :: n !<
1004	INTEGER(iwp) :: ip !<
1005	INTEGER(iwp) :: jp !<
1006	INTEGER(iwp) :: kp !<
1007
1008	!
1009	!-- Set constants for different aerosol species
1010	IF ( TRIM(aero_species) .EQ. 'nacl' ) THEN
1011	molecular_weight_of_solute = 0.05844_wp
1012	rho_s = 2165.0_wp
1013	vanthoff = 2.0_wp
1014	ELSEIF ( TRIM(aero_species) .EQ. 'c3h4o4' ) THEN
1015	molecular_weight_of_solute = 0.10406_wp
1016	rho_s = 1600.0_wp
1017	vanthoff = 1.37_wp
1018	ELSEIF ( TRIM(aero_species) .EQ. 'nh4o3' ) THEN
1019	molecular_weight_of_solute = 0.08004_wp
1020	rho_s = 1720.0_wp
1021	vanthoff = 2.31_wp
1022	ELSE
1023	WRITE( message_string, * ) 'unknown aerosol species ', &
1024	'aero_species = "', TRIM( aero_species ), '"'
1025	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1026	ENDIF
1027	!
1028	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1029	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1030	IF ( TRIM(aero_type) .EQ. 'polar' ) THEN
1031	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6
1032	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6
1033	log_sigma = (/ 0.245, 0.300, 0.291 /)
1034	ELSEIF ( TRIM(aero_type) .EQ. 'background' ) THEN
1035	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6
1036	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6
1037	log_sigma = (/ 0.645, 0.253, 0.425 /)
1038	ELSEIF ( TRIM(aero_type) .EQ. 'maritime' ) THEN
1039	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6
1040	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6
1041	log_sigma = (/ 0.657, 0.210, 0.396 /)
1042	ELSEIF ( TRIM(aero_type) .EQ. 'continental' ) THEN
1043	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6
1044	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6
1045	log_sigma = (/ 0.161, 0.217, 0.380 /)
1046	ELSEIF ( TRIM(aero_type) .EQ. 'desert' ) THEN
1047	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6
1048	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6
1049	log_sigma = (/ 0.247, 0.770, 0.438 /)
1050	ELSEIF ( TRIM(aero_type) .EQ. 'rural' ) THEN
1051	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6
1052	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6
1053	log_sigma = (/ 0.225, 0.557, 0.266 /)
1054	ELSEIF ( TRIM(aero_type) .EQ. 'urban' ) THEN
1055	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6
1056	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6
1057	log_sigma = (/ 0.245, 0.666, 0.337 /)
1058	ELSEIF ( TRIM(aero_type) .EQ. 'user' ) THEN
1059	CONTINUE
1060	ELSE
1061	WRITE( message_string, * ) 'unknown aerosol type ', &
1062	'aero_type = "', TRIM( aero_type ), '"'
1063	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1064	ENDIF
1065
1066	DO ip = nxl, nxr
1067	DO jp = nys, nyn
1068	DO kp = nzb+1, nzt
1069
1070	number_of_particles = prt_count(kp,jp,ip)
1071	IF ( number_of_particles <= 0 ) CYCLE
1072	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1073
1074	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1075	!
1076	!-- Initialize the aerosols with a predefined spectral distribution
1077	!-- of the dry radius (logarithmically increasing bins) and a varying
1078	!-- weighting factor
1079	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1080
1081	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1082	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1083	r_mid = SQRT( r_l * r_r )
1084
1085	particles(n)%aux1 = r_mid
1086	particles(n)%weight_factor = &
1087	( na(1) / ( SQRT( 2.0 * pi ) * log_sigma(1) ) * &
1088	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0 log_sigma(1)**2 ) ) + &
1089	na(2) / ( SQRT( 2.0 * pi ) * log_sigma(2) ) * &
1090	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0 log_sigma(2)**2 ) ) + &
1091	na(3) / ( SQRT( 2.0 * pi ) * log_sigma(3) ) * &
1092	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0 log_sigma(3)**2 ) ) &
1093	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dz )
1094
1095	!
1096	!-- Multiply weight_factor with the namelist parameter aero_weight
1097	!-- to increase or decrease the number of simulated aerosols
1098	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1099
1100	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1101	.GT. random_function( iran_part ) ) THEN
1102	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0
1103	ELSE
1104	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1105	ENDIF
1106	!
1107	!-- Unnecessary particles will be deleted
1108	IF ( particles(n)%weight_factor .LE. 0.0 ) particles(n)%particle_mask = .FALSE.
1109
1110	ENDDO
1111	!
1112	!-- Set particle radius to equilibrium radius based on the environmental
1113	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1114	!-- the sometimes lengthy growth toward their equilibrium radius within
1115	!-- the simulation.
1116	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1117
1118	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
1119	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
1120
1121	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1122	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1123
1124	bfactor = vanthoff * molecular_weight_of_water * &
1125	rho_s / ( molecular_weight_of_solute * rho_l )
1126	!
1127	!-- The formula is only valid for subsaturated environments. For
1128	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1129	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1130
1131	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1132	!
1133	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1134	!-- Curry (2007, JGR)
1135	particles(n)%radius = bfactor*0.3333333_wp &
1136	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1137	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1138	particles(n)%aux1 ) ) / &
1139	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1140	)
1141
1142	ENDDO
1143
1144	ENDDO
1145	ENDDO
1146	ENDDO
1147
1148	END SUBROUTINE lpm_init_aerosols
1149
1150	END MODULE lpm_init_mod

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