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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 2233 2017-05-30 18:08:54Z knoop $
27	!
28	! 2232 2017-05-30 17:47:52Z suehring
29	! Adjustments according to new topography realization
30	!
31	!
32	! 2223 2017-05-15 16:38:09Z suehring
33	! Add check for particle release at model top
34	!
35	! 2182 2017-03-17 14:27:40Z schwenkel
36	! Added parameters for simplified particle initialization.
37	!
38	! 2122 2017-01-18 12:22:54Z hoffmann
39	! Improved initialization of equilibrium aerosol radii
40	! Calculation of particle ID
41	!
42	! 2000 2016-08-20 18:09:15Z knoop
43	! Forced header and separation lines into 80 columns
44	!
45	! 2016-06-09 16:25:25Z suehring
46	! Bugfix in determining initial particle height and grid index in case of
47	! seed_follows_topography.
48	! Bugfix concerning random positions, ensure that particles do not move more
49	! than one grid length.
50	! Bugfix logarithmic interpolation.
51	! Initial setting of sgs_wf_part.
52	!
53	! 1890 2016-04-22 08:52:11Z hoffmann
54	! Initialization of aerosol equilibrium radius not possible in supersaturated
55	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
56	! initialization.
57	!
58	! 1873 2016-04-18 14:50:06Z maronga
59	! Module renamed (removed _mod
60	!
61	! 1871 2016-04-15 11:46:09Z hoffmann
62	! Initialization of aerosols added.
63	!
64	! 1850 2016-04-08 13:29:27Z maronga
65	! Module renamed
66	!
67	! 1831 2016-04-07 13:15:51Z hoffmann
68	! curvature_solution_effects moved to particle_attributes
69	!
70	! 1822 2016-04-07 07:49:42Z hoffmann
71	! Unused variables removed.
72	!
73	! 1783 2016-03-06 18:36:17Z raasch
74	! netcdf module added
75	!
76	! 1725 2015-11-17 13:01:51Z hoffmann
77	! Bugfix: Processor-dependent seed for random function is generated before it is
78	! used.
79	!
80	! 1691 2015-10-26 16:17:44Z maronga
81	! Renamed prandtl_layer to constant_flux_layer.
82	!
83	! 1685 2015-10-08 07:32:13Z raasch
84	! bugfix concerning vertical index offset in case of ocean
85	!
86	! 1682 2015-10-07 23:56:08Z knoop
87	! Code annotations made doxygen readable
88	!
89	! 1575 2015-03-27 09:56:27Z raasch
90	! initial vertical particle position is allowed to follow the topography
91	!
92	! 1359 2014-04-11 17:15:14Z hoffmann
93	! New particle structure integrated.
94	! Kind definition added to all floating point numbers.
95	! lpm_init changed form a subroutine to a module.
96	!
97	! 1327 2014-03-21 11:00:16Z raasch
98	! -netcdf_output
99	!
100	! 1322 2014-03-20 16:38:49Z raasch
101	! REAL functions provided with KIND-attribute
102	!
103	! 1320 2014-03-20 08:40:49Z raasch
104	! ONLY-attribute added to USE-statements,
105	! kind-parameters added to all INTEGER and REAL declaration statements,
106	! kinds are defined in new module kinds,
107	! revision history before 2012 removed,
108	! comment fields (!:) to be used for variable explanations added to
109	! all variable declaration statements
110	! bugfix: #if defined( __parallel ) added
111	!
112	! 1314 2014-03-14 18:25:17Z suehring
113	! Vertical logarithmic interpolation of horizontal particle speed for particles
114	! between roughness height and first vertical grid level.
115	!
116	! 1092 2013-02-02 11:24:22Z raasch
117	! unused variables removed
118	!
119	! 1036 2012-10-22 13:43:42Z raasch
120	! code put under GPL (PALM 3.9)
121	!
122	! 849 2012-03-15 10:35:09Z raasch
123	! routine renamed: init_particles -> lpm_init
124	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
125	! advec_particles),
126	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
127	!
128	! 828 2012-02-21 12:00:36Z raasch
129	! call of init_kernels, particle feature color renamed class
130	!
131	! 824 2012-02-17 09:09:57Z raasch
132	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
133	! array particles implemented as pointer
134	!
135	! 667 2010-12-23 12:06:00Z suehring/gryschka
136	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
137	! of arrays.
138	!
139	! Revision 1.1 1999/11/25 16:22:38 raasch
140	! Initial revision
141	!
142	!
143	! Description:
144	! ------------
145	!> This routine initializes a set of particles and their attributes (position,
146	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
147	!------------------------------------------------------------------------------!
148	MODULE lpm_init_mod
149
150
151	USE arrays_3d, &
152	ONLY: de_dx, de_dy, de_dz, zu, zw
153
154	USE control_parameters, &
155	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
156	dz, initializing_actions, message_string, ocean, simulated_time
157
158	USE grid_variables, &
159	ONLY: ddx, dx, ddy, dy
160
161	USE indices, &
162	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
163	nzb_max, nzt, wall_flags_0
164
165	USE kinds
166
167	USE lpm_collision_kernels_mod, &
168	ONLY: init_kernels
169
170	USE netcdf_interface, &
171	ONLY: netcdf_data_format
172
173	USE particle_attributes, &
174	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
175	block_offset, block_offset_def, collision_kernel, &
176	curvature_solution_effects, &
177	density_ratio, grid_particles, &
178	initial_weighting_factor, ibc_par_b, ibc_par_lr, ibc_par_ns, &
179	ibc_par_t, iran_part, log_z_z0, &
180	max_number_of_particle_groups, maximum_number_of_particles, &
181	min_nr_particle, mpi_particle_type, &
182	number_concentration, number_particles_per_gridbox, &
183	number_of_particles, &
184	number_of_particle_groups, number_of_sublayers, &
185	offset_ocean_nzt, offset_ocean_nzt_m1, &
186	particles, particle_advection_start, particle_groups, &
187	particle_groups_type, particles_per_point, &
188	particle_type, pdx, pdy, pdz, &
189	prt_count, psb, psl, psn, psr, pss, pst, &
190	radius, random_start_position, read_particles_from_restartfile,&
191	seed_follows_topography, sgs_wf_part, sort_count, &
192	total_number_of_particles, &
193	use_sgs_for_particles, &
194	write_particle_statistics, uniform_particles, zero_particle, &
195	z0_av_global
196
197	USE pegrid
198
199	USE random_function_mod, &
200	ONLY: random_function
201
202	USE surface_mod, &
203	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
204
205	IMPLICIT NONE
206
207	PRIVATE
208
209	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
210	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
211
212	INTERFACE lpm_init
213	MODULE PROCEDURE lpm_init
214	END INTERFACE lpm_init
215
216	INTERFACE lpm_create_particle
217	MODULE PROCEDURE lpm_create_particle
218	END INTERFACE lpm_create_particle
219
220	PUBLIC lpm_init, lpm_create_particle
221
222	CONTAINS
223
224	!------------------------------------------------------------------------------!
225	! Description:
226	! ------------
227	!> @todo Missing subroutine description.
228	!------------------------------------------------------------------------------!
229	SUBROUTINE lpm_init
230
231	USE lpm_collision_kernels_mod, &
232	ONLY: init_kernels
233
234	IMPLICIT NONE
235
236	INTEGER(iwp) :: i !<
237	INTEGER(iwp) :: j !<
238	INTEGER(iwp) :: k !<
239
240	#if defined( __parallel )
241	INTEGER(iwp), DIMENSION(3) :: blocklengths !<
242	INTEGER(iwp), DIMENSION(3) :: displacements !<
243	INTEGER(iwp), DIMENSION(3) :: types !<
244	#endif
245
246	REAL(wp) :: div !<
247	REAL(wp) :: height_int !<
248	REAL(wp) :: height_p !<
249	REAL(wp) :: z_p !<
250	REAL(wp) :: z0_av_local !<
251
252	#if defined( __parallel )
253	!
254	!-- Define MPI derived datatype for FORTRAN datatype particle_type (see module
255	!-- particle_attributes). Integer length is 4 byte, Real is 8 byte
256	blocklengths(1) = 19; blocklengths(2) = 6; blocklengths(3) = 1
257	displacements(1) = 0; displacements(2) = 152; displacements(3) = 176
258
259	types(1) = MPI_REAL
260	types(2) = MPI_INTEGER
261	types(3) = MPI_UB
262	CALL MPI_TYPE_STRUCT( 3, blocklengths, displacements, types, &
263	mpi_particle_type, ierr )
264	CALL MPI_TYPE_COMMIT( mpi_particle_type, ierr )
265	#endif
266
267	!
268	!-- In case of oceans runs, the vertical index calculations need an offset,
269	!-- because otherwise the k indices will become negative
270	IF ( ocean ) THEN
271	offset_ocean_nzt = nzt
272	offset_ocean_nzt_m1 = nzt - 1
273	ENDIF
274
275	!
276	!-- Define block offsets for dividing a gridcell in 8 sub cells
277
278	block_offset(0) = block_offset_def (-1,-1,-1)
279	block_offset(1) = block_offset_def (-1,-1, 0)
280	block_offset(2) = block_offset_def (-1, 0,-1)
281	block_offset(3) = block_offset_def (-1, 0, 0)
282	block_offset(4) = block_offset_def ( 0,-1,-1)
283	block_offset(5) = block_offset_def ( 0,-1, 0)
284	block_offset(6) = block_offset_def ( 0, 0,-1)
285	block_offset(7) = block_offset_def ( 0, 0, 0)
286	!
287	!-- Check the number of particle groups.
288	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
289	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
290	max_number_of_particle_groups , &
291	'&number_of_particle_groups reset to ', &
292	max_number_of_particle_groups
293	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
294	number_of_particle_groups = max_number_of_particle_groups
295	ENDIF
296	!
297	!-- Check if downward-facing walls exist. This case, reflection boundary
298	!-- conditions (as well as subgrid-scale velocities) may do not work
299	!-- propably (not realized so far).
300	IF ( surf_def_h(1)%ns >= 1 ) THEN
301	WRITE( message_string, * ) 'Overhanging topograpyh do not work '// &
302	'with particles'
303	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
304
305	ENDIF
306
307	!
308	!-- Set default start positions, if necessary
309	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
310	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
311	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
312	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
313	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
314	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
315
316	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
317	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
318	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
319
320	!
321	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
322	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
323	IF ( number_particles_per_gridbox /= -1 .AND. &
324	number_particles_per_gridbox >= 1 ) THEN
325	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
326	REAL(number_particles_per_gridbox))**0.3333333_wp
327	!
328	!-- Ensure a smooth value (two significant digits) of distance between
329	!-- particles (pdx, pdy, pdz).
330	div = 1000.0_wp
331	DO WHILE ( pdx(1) < div )
332	div = div / 10.0_wp
333	ENDDO
334	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
335	pdy(1) = pdx(1)
336	pdz(1) = pdx(1)
337
338	ENDIF
339
340	DO j = 2, number_of_particle_groups
341	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
342	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
343	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
344	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
345	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
346	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
347	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
348	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
349	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
350	ENDDO
351
352	!
353	!-- Allocate arrays required for calculating particle SGS velocities.
354	!-- Initialize prefactor required for stoachastic Weil equation.
355	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
356	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
357	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
358	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
359
360	sgs_wf_part = 1.0_wp / 3.0_wp
361	ENDIF
362
363	!
364	!-- Allocate array required for logarithmic vertical interpolation of
365	!-- horizontal particle velocities between the surface and the first vertical
366	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
367	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
368	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
369	!-- To obtain exact height levels of particles, linear interpolation is applied
370	!-- (see lpm_advec.f90).
371	IF ( constant_flux_layer ) THEN
372
373	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
374	z_p = zu(nzb+1) - zw(nzb)
375
376	!
377	!-- Calculate horizontal mean value of z0 used for logartihmic
378	!-- interpolation. Note: this is not exact for heterogeneous z0.
379	!-- However, sensitivity studies showed that the effect is
380	!-- negligible.
381	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
382	SUM( surf_usm_h%z0 )
383	z0_av_global = 0.0_wp
384
385	#if defined( __parallel )
386	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
387	comm2d, ierr )
388	#else
389	z0_av_global = z0_av_local
390	#endif
391
392	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
393	!
394	!-- Horizontal wind speed is zero below and at z0
395	log_z_z0(0) = 0.0_wp
396	!
397	!-- Calculate vertical depth of the sublayers
398	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
399	!
400	!-- Precalculate LOG(z/z0)
401	height_p = z0_av_global
402	DO k = 1, number_of_sublayers
403
404	height_p = height_p + height_int
405	log_z_z0(k) = LOG( height_p / z0_av_global )
406
407	ENDDO
408
409	ENDIF
410
411	!
412	!-- Check boundary condition and set internal variables
413	SELECT CASE ( bc_par_b )
414
415	CASE ( 'absorb' )
416	ibc_par_b = 1
417
418	CASE ( 'reflect' )
419	ibc_par_b = 2
420
421	CASE DEFAULT
422	WRITE( message_string, * ) 'unknown boundary condition ', &
423	'bc_par_b = "', TRIM( bc_par_b ), '"'
424	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
425
426	END SELECT
427	SELECT CASE ( bc_par_t )
428
429	CASE ( 'absorb' )
430	ibc_par_t = 1
431
432	CASE ( 'reflect' )
433	ibc_par_t = 2
434
435	CASE DEFAULT
436	WRITE( message_string, * ) 'unknown boundary condition ', &
437	'bc_par_t = "', TRIM( bc_par_t ), '"'
438	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
439
440	END SELECT
441	SELECT CASE ( bc_par_lr )
442
443	CASE ( 'cyclic' )
444	ibc_par_lr = 0
445
446	CASE ( 'absorb' )
447	ibc_par_lr = 1
448
449	CASE ( 'reflect' )
450	ibc_par_lr = 2
451
452	CASE DEFAULT
453	WRITE( message_string, * ) 'unknown boundary condition ', &
454	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
455	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
456
457	END SELECT
458	SELECT CASE ( bc_par_ns )
459
460	CASE ( 'cyclic' )
461	ibc_par_ns = 0
462
463	CASE ( 'absorb' )
464	ibc_par_ns = 1
465
466	CASE ( 'reflect' )
467	ibc_par_ns = 2
468
469	CASE DEFAULT
470	WRITE( message_string, * ) 'unknown boundary condition ', &
471	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
472	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
473
474	END SELECT
475
476	!
477	!-- Initialize collision kernels
478	IF ( collision_kernel /= 'none' ) CALL init_kernels
479
480	!
481	!-- For the first model run of a possible job chain initialize the
482	!-- particles, otherwise read the particle data from restart file.
483	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
484	.AND. read_particles_from_restartfile ) THEN
485
486	CALL lpm_read_restart_file
487
488	ELSE
489
490	!
491	!-- Allocate particle arrays and set attributes of the initial set of
492	!-- particles, which can be also periodically released at later times.
493	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
494	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
495
496	maximum_number_of_particles = 0
497	number_of_particles = 0
498
499	sort_count = 0
500	prt_count = 0
501
502	!
503	!-- initialize counter for particle IDs
504	grid_particles%id_counter = 0
505
506	!
507	!-- Initialize all particles with dummy values (otherwise errors may
508	!-- occur within restart runs). The reason for this is still not clear
509	!-- and may be presumably caused by errors in the respective user-interface.
510	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
511	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
512	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
513	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
514	0, 0, 0, 0, .FALSE., -1 )
515
516	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
517
518	!
519	!-- Set values for the density ratio and radius for all particle
520	!-- groups, if necessary
521	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
522	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
523	DO i = 2, number_of_particle_groups
524	IF ( density_ratio(i) == 9999999.9_wp ) THEN
525	density_ratio(i) = density_ratio(i-1)
526	ENDIF
527	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
528	ENDDO
529
530	DO i = 1, number_of_particle_groups
531	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
532	WRITE( message_string, * ) 'particle group #', i, 'has a', &
533	'density ratio /= 0 but radius = 0'
534	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
535	ENDIF
536	particle_groups(i)%density_ratio = density_ratio(i)
537	particle_groups(i)%radius = radius(i)
538	ENDDO
539
540	!
541	!-- Set a seed value for the random number generator to be exclusively
542	!-- used for the particle code. The generated random numbers should be
543	!-- different on the different PEs.
544	iran_part = iran_part + myid
545
546	CALL lpm_create_particle (PHASE_INIT)
547	!
548	!-- User modification of initial particles
549	CALL user_lpm_init
550
551	!
552	!-- Open file for statistical informations about particle conditions
553	IF ( write_particle_statistics ) THEN
554	CALL check_open( 80 )
555	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
556	number_of_particles, &
557	maximum_number_of_particles
558	CALL close_file( 80 )
559	ENDIF
560
561	ENDIF
562
563	!
564	!-- To avoid programm abort, assign particles array to the local version of
565	!-- first grid cell
566	number_of_particles = prt_count(nzb+1,nys,nxl)
567	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
568	!
569	!-- Formats
570	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
571
572	END SUBROUTINE lpm_init
573
574	!------------------------------------------------------------------------------!
575	! Description:
576	! ------------
577	!> @todo Missing subroutine description.
578	!------------------------------------------------------------------------------!
579	SUBROUTINE lpm_create_particle (phase)
580
581	USE lpm_exchange_horiz_mod, &
582	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
583
584	USE lpm_pack_arrays_mod, &
585	ONLY: lpm_pack_all_arrays
586
587	USE particle_attributes, &
588	ONLY: deleted_particles, monodisperse_aerosols
589
590	IMPLICIT NONE
591
592	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
593	INTEGER(iwp) :: i !< loop variable ( particle groups )
594	INTEGER(iwp) :: ip !< index variable along x
595	INTEGER(iwp) :: j !< loop variable ( particles per point )
596	INTEGER(iwp) :: jp !< index variable along y
597	INTEGER(iwp) :: k !< index variable along z
598	INTEGER(iwp) :: k_surf !< index of surface grid point
599	INTEGER(iwp) :: kp !< index variable along z
600	INTEGER(iwp) :: loop_stride !< loop variable for initialization
601	INTEGER(iwp) :: n !< loop variable ( number of particles )
602	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
603
604	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
605
606	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
607	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
608
609	LOGICAL :: first_stride !< flag for initialization
610
611	REAL(wp) :: pos_x !< increment for particle position in x
612	REAL(wp) :: pos_y !< increment for particle position in y
613	REAL(wp) :: pos_z !< increment for particle position in z
614	REAL(wp) :: rand_contr !< dummy argument for random position
615
616	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
617
618	!
619	!-- Calculate particle positions and store particle attributes, if
620	!-- particle is situated on this PE
621	DO loop_stride = 1, 2
622	first_stride = (loop_stride == 1)
623	IF ( first_stride ) THEN
624	local_count = 0 ! count number of particles
625	ELSE
626	local_count = prt_count ! Start address of new particles
627	ENDIF
628
629	!
630	!-- Calculate initial_weighting_factor diagnostically
631	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
632	initial_weighting_factor = number_concentration * 1.0E6_wp * &
633	pdx(1) * pdy(1) * pdz(1)
634	END IF
635
636	n = 0
637	DO i = 1, number_of_particle_groups
638
639	pos_z = psb(i)
640
641	DO WHILE ( pos_z <= pst(i) )
642
643	IF ( pos_z >= 0.0_wp .AND. pos_z < zw(nzt) ) THEN
644
645
646	pos_y = pss(i)
647
648	DO WHILE ( pos_y <= psn(i) )
649
650	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
651	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
652
653	pos_x = psl(i)
654
655	xloop: DO WHILE ( pos_x <= psr(i) )
656
657	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
658	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
659
660	DO j = 1, particles_per_point
661
662	n = n + 1
663	tmp_particle%x = pos_x
664	tmp_particle%y = pos_y
665	tmp_particle%z = pos_z
666	tmp_particle%age = 0.0_wp
667	tmp_particle%age_m = 0.0_wp
668	tmp_particle%dt_sum = 0.0_wp
669	tmp_particle%user = 0.0_wp !unused, free for the user
670	tmp_particle%e_m = 0.0_wp
671	IF ( curvature_solution_effects ) THEN
672	!
673	!-- Initial values (internal timesteps, derivative)
674	!-- for Rosenbrock method
675	tmp_particle%rvar1 = 1.0E-6_wp !last Rosenbrock timestep
676	tmp_particle%rvar2 = 0.1E-6_wp !dry aerosol radius
677	tmp_particle%rvar3 = -9999999.9_wp !unused in this configuration
678	ELSE
679	!
680	!-- Initial values for SGS velocities
681	tmp_particle%rvar1 = 0.0_wp
682	tmp_particle%rvar2 = 0.0_wp
683	tmp_particle%rvar3 = 0.0_wp
684	ENDIF
685	tmp_particle%speed_x = 0.0_wp
686	tmp_particle%speed_y = 0.0_wp
687	tmp_particle%speed_z = 0.0_wp
688	tmp_particle%origin_x = pos_x
689	tmp_particle%origin_y = pos_y
690	tmp_particle%origin_z = pos_z
691	tmp_particle%radius = particle_groups(i)%radius
692	tmp_particle%weight_factor = initial_weighting_factor
693	tmp_particle%class = 1
694	tmp_particle%group = i
695	tmp_particle%id1 = 0
696	tmp_particle%id2 = 0
697	tmp_particle%particle_mask = .TRUE.
698	tmp_particle%block_nr = -1
699	!
700	!-- Determine the grid indices of the particle position
701	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
702	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
703	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
704	!
705	!-- Determine surface level. Therefore, check for
706	!-- upward-facing wall on w-grid. MAXLOC will return
707	!-- the index of the lowest upward-facing wall.
708	k_surf = MAXLOC( &
709	MERGE( 1, 0, &
710	BTEST( wall_flags_0(nzb:nzb_max,jp,ip), 18 )&
711	), DIM = 1 &
712	) - 1
713
714	IF ( seed_follows_topography ) THEN
715	!
716	!-- Particle height is given relative to topography
717	kp = kp + k_surf
718	tmp_particle%z = tmp_particle%z + zw(k_surf)
719	!-- Skip particle release if particle position is
720	!-- above model top, or within topography in case
721	!-- of overhanging structures.
722	IF ( kp > nzt .OR. &
723	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
724	pos_x = pos_x + pdx(i)
725	CYCLE xloop
726	ENDIF
727	!
728	!-- Skip particle release if particle position is
729	!-- below surface, or within topography in case
730	!-- of overhanging structures.
731	ELSEIF ( .NOT. seed_follows_topography .AND. &
732	tmp_particle%z <= zw(k_surf) .OR. &
733	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
734	THEN
735	pos_x = pos_x + pdx(i)
736	CYCLE xloop
737	ENDIF
738
739	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
740
741	IF ( .NOT. first_stride ) THEN
742	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
743	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
744	ENDIF
745	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
746	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
747	ENDIF
748	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
749
750	ENDIF
751	ENDDO
752
753	ENDIF
754
755	pos_x = pos_x + pdx(i)
756
757	ENDDO xloop
758
759	ENDIF
760
761	pos_y = pos_y + pdy(i)
762
763	ENDDO
764
765	ENDIF
766
767	pos_z = pos_z + pdz(i)
768
769	ENDDO
770
771	ENDDO
772
773	IF ( first_stride ) THEN
774	DO ip = nxl, nxr
775	DO jp = nys, nyn
776	DO kp = nzb+1, nzt
777	IF ( phase == PHASE_INIT ) THEN
778	IF ( local_count(kp,jp,ip) > 0 ) THEN
779	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
780	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
781	min_nr_particle )
782	ELSE
783	alloc_size = min_nr_particle
784	ENDIF
785	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
786	DO n = 1, alloc_size
787	grid_particles(kp,jp,ip)%particles(n) = zero_particle
788	ENDDO
789	ELSEIF ( phase == PHASE_RELEASE ) THEN
790	IF ( local_count(kp,jp,ip) > 0 ) THEN
791	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
792	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
793	alloc_factor / 100.0_wp ) ), min_nr_particle )
794	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
795	CALL realloc_particles_array(ip,jp,kp,alloc_size)
796	ENDIF
797	ENDIF
798	ENDIF
799	ENDDO
800	ENDDO
801	ENDDO
802	ENDIF
803
804	ENDDO
805
806
807
808	local_start = prt_count+1
809	prt_count = local_count
810
811	!
812	!-- Calculate particle IDs
813	DO ip = nxl, nxr
814	DO jp = nys, nyn
815	DO kp = nzb+1, nzt
816	number_of_particles = prt_count(kp,jp,ip)
817	IF ( number_of_particles <= 0 ) CYCLE
818	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
819
820	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
821
822	particles(n)%id1 = 10000_iwp * grid_particles(kp,jp,ip)%id_counter + kp
823	particles(n)%id2 = 10000_iwp * jp + ip
824
825	grid_particles(kp,jp,ip)%id_counter = &
826	grid_particles(kp,jp,ip)%id_counter + 1
827
828	ENDDO
829
830	ENDDO
831	ENDDO
832	ENDDO
833
834	!
835	!-- Initialize aerosol background spectrum
836	IF ( curvature_solution_effects .AND. .NOT. monodisperse_aerosols ) THEN
837	CALL lpm_init_aerosols(local_start)
838	ENDIF
839
840	!
841	!-- Add random fluctuation to particle positions.
842	IF ( random_start_position ) THEN
843	DO ip = nxl, nxr
844	DO jp = nys, nyn
845	DO kp = nzb+1, nzt
846	number_of_particles = prt_count(kp,jp,ip)
847	IF ( number_of_particles <= 0 ) CYCLE
848	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
849	!
850	!-- Move only new particles. Moreover, limit random fluctuation
851	!-- in order to prevent that particles move more than one grid box,
852	!-- which would lead to problems concerning particle exchange
853	!-- between processors in case pdx/pdy are larger than dx/dy,
854	!-- respectively.
855	DO n = local_start(kp,jp,ip), number_of_particles
856	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
857	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
858	pdx(particles(n)%group)
859	particles(n)%x = particles(n)%x + &
860	MERGE( rand_contr, SIGN( dx, rand_contr ), &
861	ABS( rand_contr ) < dx &
862	)
863	ENDIF
864	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
865	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
866	pdy(particles(n)%group)
867	particles(n)%y = particles(n)%y + &
868	MERGE( rand_contr, SIGN( dy, rand_contr ), &
869	ABS( rand_contr ) < dy &
870	)
871	ENDIF
872	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
873	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
874	pdz(particles(n)%group)
875	particles(n)%z = particles(n)%z + &
876	MERGE( rand_contr, SIGN( dz, rand_contr ), &
877	ABS( rand_contr ) < dz &
878	)
879	ENDIF
880	ENDDO
881	!
882	!-- Identify particles located outside the model domain and reflect
883	!-- or absorb them if necessary.
884	CALL lpm_boundary_conds( 'bottom/top' )
885	!
886	!-- Furthermore, remove particles located in topography. Note, as
887	!-- the particle speed is still zero at this point, wall
888	!-- reflection boundary conditions will not work in this case.
889	particles => &
890	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
891	DO n = local_start(kp,jp,ip), number_of_particles
892	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
893	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
894	k = particles(n)%z / dz + 1 + offset_ocean_nzt
895	!
896	!-- Check if particle is within topography
897	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
898	particles(n)%particle_mask = .FALSE.
899	deleted_particles = deleted_particles + 1
900	ENDIF
901
902	ENDDO
903	ENDDO
904	ENDDO
905	ENDDO
906	!
907	!-- Exchange particles between grid cells and processors
908	CALL lpm_move_particle
909	CALL lpm_exchange_horiz
910
911	ENDIF
912	!
913	!-- In case of random_start_position, delete particles identified by
914	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
915	!-- which is needed for a fast interpolation of the LES fields on the particle
916	!-- position.
917	CALL lpm_pack_all_arrays
918
919	!
920	!-- Determine maximum number of particles (i.e., all possible particles that
921	!-- have been allocated) and the current number of particles
922	DO ip = nxl, nxr
923	DO jp = nys, nyn
924	DO kp = nzb+1, nzt
925	maximum_number_of_particles = maximum_number_of_particles &
926	+ SIZE(grid_particles(kp,jp,ip)%particles)
927	number_of_particles = number_of_particles &
928	+ prt_count(kp,jp,ip)
929	ENDDO
930	ENDDO
931	ENDDO
932	!
933	!-- Calculate the number of particles of the total domain
934	#if defined( __parallel )
935	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
936	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
937	MPI_INTEGER, MPI_SUM, comm2d, ierr )
938	#else
939	total_number_of_particles = number_of_particles
940	#endif
941
942	RETURN
943
944	END SUBROUTINE lpm_create_particle
945
946	SUBROUTINE lpm_init_aerosols(local_start)
947
948	USE arrays_3d, &
949	ONLY: hyp, pt, q
950
951	USE cloud_parameters, &
952	ONLY: l_d_rv, rho_l, r_v
953
954	USE constants, &
955	ONLY: pi
956
957	USE kinds
958
959	USE particle_attributes, &
960	ONLY: init_aerosol_probabilistic, molecular_weight_of_solute, &
961	molecular_weight_of_water, n1, n2, n3, rho_s, rm1, rm2, rm3, &
962	s1, s2, s3, vanthoff
963
964	IMPLICIT NONE
965
966	REAL(wp), DIMENSION(:), ALLOCATABLE :: cdf !< CDF of aerosol spectrum
967	REAL(wp), DIMENSION(:), ALLOCATABLE :: r_temp !< dry aerosol radius spectrum
968
969	REAL(wp) :: afactor !< curvature effects
970	REAL(wp) :: bfactor !< solute effects
971	REAL(wp) :: dr !< width of radius bin
972	REAL(wp) :: e_a !< vapor pressure
973	REAL(wp) :: e_s !< saturation vapor pressure
974	REAL(wp) :: n_init !< sum of all aerosol concentrations
975	REAL(wp) :: pdf !< PDF of aerosol spectrum
976	REAL(wp) :: rmin = 1.0e-8_wp !< minimum aerosol radius
977	REAL(wp) :: rmax = 1.0e-6_wp !< maximum aerosol radius
978	REAL(wp) :: rs_rand !< random number
979	REAL(wp) :: r_mid !< mean radius
980	REAL(wp) :: sigma !< surface tension
981	REAL(wp) :: t_int !< temperature
982	REAL(wp) :: weight_sum !< sum of all weighting factors
983
984	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
985
986	INTEGER(iwp) :: n !<
987	INTEGER(iwp) :: nn !<
988	INTEGER(iwp) :: no_bins = 999 !< number of bins
989	INTEGER(iwp) :: ip !<
990	INTEGER(iwp) :: jp !<
991	INTEGER(iwp) :: kp !<
992
993	LOGICAL :: new_pdf = .FALSE. !< check if aerosol PDF has to be recalculated
994
995	!
996	!-- Compute aerosol background distribution
997	IF ( init_aerosol_probabilistic ) THEN
998	ALLOCATE( cdf(0:no_bins), r_temp(0:no_bins) )
999	DO n = 0, no_bins
1000	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1001	REAL(no_bins, KIND=wp) * REAL(n, KIND=wp) )
1002
1003	cdf(n) = 0.0_wp
1004	n_init = n1 + n2 + n3
1005	IF ( n1 > 0.0_wp ) THEN
1006	cdf(n) = cdf(n) + n1 / n_init * ( 0.5_wp + 0.5_wp * &
1007	ERF( LOG( r_temp(n) / rm1 ) / &
1008	( SQRT(2.0_wp) * LOG(s1) ) &
1009	) )
1010	ENDIF
1011	IF ( n2 > 0.0_wp ) THEN
1012	cdf(n) = cdf(n) + n2 / n_init * ( 0.5_wp + 0.5_wp * &
1013	ERF( LOG( r_temp(n) / rm2 ) / &
1014	( SQRT(2.0_wp) * LOG(s2) ) &
1015	) )
1016	ENDIF
1017	IF ( n3 > 0.0_wp ) THEN
1018	cdf(n) = cdf(n) + n3 / n_init * ( 0.5_wp + 0.5_wp * &
1019	ERF( LOG( r_temp(n) / rm3 ) / &
1020	( SQRT(2.0_wp) * LOG(s3) ) &
1021	) )
1022	ENDIF
1023
1024	ENDDO
1025	ENDIF
1026
1027	DO ip = nxl, nxr
1028	DO jp = nys, nyn
1029	DO kp = nzb+1, nzt
1030
1031	number_of_particles = prt_count(kp,jp,ip)
1032	IF ( number_of_particles <= 0 ) CYCLE
1033	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1034	!
1035	!-- Initialize the aerosols with a predefined spectral distribution
1036	!-- of the dry radius (logarithmically increasing bins) and a varying
1037	!-- weighting factor
1038	IF ( .NOT. init_aerosol_probabilistic ) THEN
1039
1040	new_pdf = .FALSE.
1041	IF ( .NOT. ALLOCATED( r_temp ) ) THEN
1042	new_pdf = .TRUE.
1043	ELSE
1044	IF ( SIZE( r_temp ) .NE. &
1045	number_of_particles - local_start(kp,jp,ip) + 2 ) THEN
1046	new_pdf = .TRUE.
1047	DEALLOCATE( r_temp )
1048	ENDIF
1049	ENDIF
1050
1051	IF ( new_pdf ) THEN
1052
1053	no_bins = number_of_particles + 1 - local_start(kp,jp,ip)
1054	ALLOCATE( r_temp(0:no_bins) )
1055
1056	DO n = 0, no_bins
1057	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1058	REAL(no_bins, KIND=wp) * &
1059	REAL(n, KIND=wp) )
1060	ENDDO
1061
1062	ENDIF
1063
1064	!
1065	!-- Calculate radius and concentration of each aerosol
1066	DO n = local_start(kp,jp,ip), number_of_particles
1067
1068	nn = n - local_start(kp,jp,ip)
1069
1070	r_mid = SQRT( r_temp(nn) * r_temp(nn+1) )
1071	dr = r_temp(nn+1) - r_temp(nn)
1072
1073	pdf = 0.0_wp
1074	n_init = n1 + n2 + n3
1075	IF ( n1 > 0.0_wp ) THEN
1076	pdf = pdf + n1 / n_init * ( 1.0_wp / ( r_mid * LOG(s1) * &
1077	SQRT( 2.0_wp * pi ) &
1078	) * &
1079	EXP( -( LOG( r_mid / rm1 ) )**2 / &
1080	( 2.0_wp * LOG(s1)**2 ) &
1081	) &
1082	)
1083	ENDIF
1084	IF ( n2 > 0.0_wp ) THEN
1085	pdf = pdf + n2 / n_init * ( 1.0_wp / ( r_mid * LOG(s2) * &
1086	SQRT( 2.0_wp * pi ) &
1087	) * &
1088	EXP( -( LOG( r_mid / rm2 ) )**2 / &
1089	( 2.0_wp * LOG(s2)**2 ) &
1090	) &
1091	)
1092	ENDIF
1093	IF ( n3 > 0.0_wp ) THEN
1094	pdf = pdf + n3 / n_init * ( 1.0_wp / ( r_mid * LOG(s3) * &
1095	SQRT( 2.0_wp * pi ) &
1096	) * &
1097	EXP( -( LOG( r_mid / rm3 ) )**2 / &
1098	( 2.0_wp * LOG(s3)**2 ) &
1099	) &
1100	)
1101	ENDIF
1102
1103	particles(n)%rvar2 = r_mid
1104	particles(n)%weight_factor = pdf * dr
1105
1106	END DO
1107	!
1108	!-- Adjust weighting factors to initialize the same number of aerosols
1109	!-- in every grid box
1110	weight_sum = SUM(particles(local_start(kp,jp,ip):number_of_particles)%weight_factor)
1111
1112	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor = &
1113	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor / &
1114	weight_sum * initial_weighting_factor * ( no_bins + 1 )
1115
1116	ENDIF
1117	!
1118	!-- Initialize the aerosols with a predefined weighting factor but
1119	!-- a randomly choosen dry radius
1120	IF ( init_aerosol_probabilistic ) THEN
1121
1122	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1123
1124	rs_rand = -1.0_wp
1125	DO WHILE ( rs_rand .LT. cdf(0) .OR. rs_rand .GE. cdf(no_bins) )
1126	rs_rand = random_function( iran_part )
1127	ENDDO
1128	!
1129	!-- Determine aerosol dry radius by a random number generator
1130	DO nn = 0, no_bins-1
1131	IF ( cdf(nn) .LE. rs_rand .AND. cdf(nn+1) .GT. rs_rand ) THEN
1132	particles(n)%rvar2 = r_temp(nn) + ( r_temp(nn+1) - r_temp(nn) ) / &
1133	( cdf(nn+1) - cdf(nn) ) * ( rs_rand - cdf(nn) )
1134	EXIT
1135	ENDIF
1136	ENDDO
1137
1138	ENDDO
1139
1140	ENDIF
1141
1142	!
1143	!-- Set particle radius to equilibrium radius based on the environmental
1144	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1145	!-- the sometimes lengthy growth toward their equilibrium radius within
1146	!-- the simulation.
1147	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1148
1149	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
1150	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
1151
1152	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1153	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1154
1155	bfactor = vanthoff * molecular_weight_of_water * &
1156	rho_s / ( molecular_weight_of_solute * rho_l )
1157	!
1158	!-- The formula is only valid for subsaturated environments. For
1159	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1160	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1161
1162	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1163	!
1164	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1165	!-- Curry (2007, JGR)
1166	particles(n)%radius = bfactor*0.3333333_wp &
1167	particles(n)%rvar2 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1168	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1169	particles(n)%rvar2 ) ) / &
1170	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1171	)
1172
1173	ENDDO
1174
1175	ENDDO
1176	ENDDO
1177	ENDDO
1178	!
1179	!-- Deallocate used arrays
1180	IF ( ALLOCATED(r_temp) ) DEALLOCATE( r_temp )
1181	IF ( ALLOCATED(cdf) ) DEALLOCATE( cdf )
1182
1183	END SUBROUTINE lpm_init_aerosols
1184
1185	END MODULE lpm_init_mod

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