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source: palm/trunk/SOURCE/lpm_init.f90 @ 3127

Last change on this file since 3127 was 3065, checked in by Giersch, 6 years ago
New vertical stretching procedure has been introduced
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1	!> @file lpm_init.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_init.f90 3065 2018-06-12 07:03:02Z maronga $
27	! dz was replaced by dzw or dz(1) to allow for right vertical stretching
28	!
29	! 3049 2018-05-29 13:52:36Z Giersch
30	! Error messages revised
31	!
32	! 3045 2018-05-28 07:55:41Z Giersch
33	! Error message revised
34	!
35	! 3039 2018-05-24 13:13:11Z schwenkel
36	! bugfix for lcm with grid stretching
37	!
38	! 2967 2018-04-13 11:22:08Z raasch
39	! nesting routine is only called if nesting is switched on
40	!
41	! 2954 2018-04-09 14:35:46Z schwenkel
42	! Bugfix for particle initialization in case of ocean
43	!
44	! 2801 2018-02-14 16:01:55Z thiele
45	! Introduce particle transfer in nested models.
46	!
47	! 2718 2018-01-02 08:49:38Z maronga
48	! Corrected "Former revisions" section
49	!
50	! 2701 2017-12-15 15:40:50Z suehring
51	! Changes from last commit documented
52	!
53	! 2698 2017-12-14 18:46:24Z suehring
54	! Grid indices passed to lpm_boundary_conds. (responsible Philipp Thiele)
55	!
56	! 2696 2017-12-14 17:12:51Z kanani
57	! Change in file header (GPL part)
58	!
59	! 2628 2017-11-20 12:40:38Z schwenkel
60	! Enabled particle advection with grid stretching.
61	!
62	! 2608 2017-11-13 14:04:26Z schwenkel
63	! Calculation of magnus equation in external module (diagnostic_quantities_mod).
64	!
65	! 2606 2017-11-10 10:36:31Z schwenkel
66	! Changed particle box locations: center of particle box now coincides
67	! with scalar grid point of same index.
68	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
69	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
70	! lpm_sort -> lpm_sort_timeloop_done
71	!
72	! 2375 2017-08-29 14:10:28Z schwenkel
73	! Initialization of chemical aerosol composition
74	!
75	! 2346 2017-08-09 16:39:17Z suehring
76	! Bugfix, correct determination of topography top index
77	!
78	! 2318 2017-07-20 17:27:44Z suehring
79	! Get topography top index via Function call
80	!
81	! 2317 2017-07-20 17:27:19Z suehring
82	! Extended particle data type. Aerosol initialization improved.
83	!
84	! 2305 2017-07-06 11:18:47Z hoffmann
85	! Improved calculation of particle IDs.
86	!
87	! 2274 2017-06-09 13:27:48Z Giersch
88	! Changed error messages
89	!
90	! 2265 2017-06-08 16:58:28Z schwenkel
91	! Unused variables removed.
92	!
93	! 2263 2017-06-08 14:59:01Z schwenkel
94	! Implemented splitting and merging algorithm
95	!
96	! 2233 2017-05-30 18:08:54Z suehring
97	!
98	! 2232 2017-05-30 17:47:52Z suehring
99	! Adjustments according to new topography realization
100	!
101	!
102	! 2223 2017-05-15 16:38:09Z suehring
103	! Add check for particle release at model top
104	!
105	! 2182 2017-03-17 14:27:40Z schwenkel
106	! Added parameters for simplified particle initialization.
107	!
108	! 2122 2017-01-18 12:22:54Z hoffmann
109	! Improved initialization of equilibrium aerosol radii
110	! Calculation of particle ID
111	!
112	! 2000 2016-08-20 18:09:15Z knoop
113	! Forced header and separation lines into 80 columns
114	!
115	! 2016-06-09 16:25:25Z suehring
116	! Bugfix in determining initial particle height and grid index in case of
117	! seed_follows_topography.
118	! Bugfix concerning random positions, ensure that particles do not move more
119	! than one grid length.
120	! Bugfix logarithmic interpolation.
121	! Initial setting of sgs_wf_part.
122	!
123	! 1890 2016-04-22 08:52:11Z hoffmann
124	! Initialization of aerosol equilibrium radius not possible in supersaturated
125	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
126	! initialization.
127	!
128	! 1873 2016-04-18 14:50:06Z maronga
129	! Module renamed (removed _mod
130	!
131	! 1871 2016-04-15 11:46:09Z hoffmann
132	! Initialization of aerosols added.
133	!
134	! 1850 2016-04-08 13:29:27Z maronga
135	! Module renamed
136	!
137	! 1831 2016-04-07 13:15:51Z hoffmann
138	! curvature_solution_effects moved to particle_attributes
139	!
140	! 1822 2016-04-07 07:49:42Z hoffmann
141	! Unused variables removed.
142	!
143	! 1783 2016-03-06 18:36:17Z raasch
144	! netcdf module added
145	!
146	! 1725 2015-11-17 13:01:51Z hoffmann
147	! Bugfix: Processor-dependent seed for random function is generated before it is
148	! used.
149	!
150	! 1691 2015-10-26 16:17:44Z maronga
151	! Renamed prandtl_layer to constant_flux_layer.
152	!
153	! 1685 2015-10-08 07:32:13Z raasch
154	! bugfix concerning vertical index offset in case of ocean
155	!
156	! 1682 2015-10-07 23:56:08Z knoop
157	! Code annotations made doxygen readable
158	!
159	! 1575 2015-03-27 09:56:27Z raasch
160	! initial vertical particle position is allowed to follow the topography
161	!
162	! 1359 2014-04-11 17:15:14Z hoffmann
163	! New particle structure integrated.
164	! Kind definition added to all floating point numbers.
165	! lpm_init changed form a subroutine to a module.
166	!
167	! 1327 2014-03-21 11:00:16Z raasch
168	! -netcdf_output
169	!
170	! 1322 2014-03-20 16:38:49Z raasch
171	! REAL functions provided with KIND-attribute
172	!
173	! 1320 2014-03-20 08:40:49Z raasch
174	! ONLY-attribute added to USE-statements,
175	! kind-parameters added to all INTEGER and REAL declaration statements,
176	! kinds are defined in new module kinds,
177	! revision history before 2012 removed,
178	! comment fields (!:) to be used for variable explanations added to
179	! all variable declaration statements
180	! bugfix: #if defined( __parallel ) added
181	!
182	! 1314 2014-03-14 18:25:17Z suehring
183	! Vertical logarithmic interpolation of horizontal particle speed for particles
184	! between roughness height and first vertical grid level.
185	!
186	! 1092 2013-02-02 11:24:22Z raasch
187	! unused variables removed
188	!
189	! 1036 2012-10-22 13:43:42Z raasch
190	! code put under GPL (PALM 3.9)
191	!
192	! 849 2012-03-15 10:35:09Z raasch
193	! routine renamed: init_particles -> lpm_init
194	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
195	! advec_particles),
196	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
197	!
198	! 828 2012-02-21 12:00:36Z raasch
199	! call of init_kernels, particle feature color renamed class
200	!
201	! 824 2012-02-17 09:09:57Z raasch
202	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
203	! array particles implemented as pointer
204	!
205	! 667 2010-12-23 12:06:00Z suehring/gryschka
206	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
207	! of arrays.
208	!
209	! Revision 1.1 1999/11/25 16:22:38 raasch
210	! Initial revision
211	!
212	!
213	! Description:
214	! ------------
215	!> This routine initializes a set of particles and their attributes (position,
216	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
217	!------------------------------------------------------------------------------!
218	MODULE lpm_init_mod
219
220	USE, INTRINSIC :: ISO_C_BINDING
221
222	USE arrays_3d, &
223	ONLY: de_dx, de_dy, de_dz, dzw, zu, zw
224
225	USE control_parameters, &
226	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
227	dt_3d, dz, initializing_actions, message_string, ocean, &
228	simulated_time
229
230	USE grid_variables, &
231	ONLY: ddx, dx, ddy, dy
232
233	USE indices, &
234	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
235	nzt, wall_flags_0
236
237	USE kinds
238
239	USE lpm_collision_kernels_mod, &
240	ONLY: init_kernels
241
242	USE netcdf_interface, &
243	ONLY: netcdf_data_format
244
245	USE particle_attributes, &
246	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
247	block_offset, block_offset_def, collision_kernel, &
248	curvature_solution_effects, density_ratio, grid_particles, &
249	isf,i_splitting_mode, initial_weighting_factor, ibc_par_b, &
250	ibc_par_lr, ibc_par_ns, ibc_par_t, iran_part, log_z_z0, &
251	max_number_of_particle_groups, min_nr_particle, &
252	number_concentration, &
253	number_particles_per_gridbox, number_of_particles, &
254	number_of_particle_groups, number_of_sublayers, &
255	offset_ocean_nzt, offset_ocean_nzt_m1, &
256	particles, particle_advection_start, particle_groups, &
257	particle_groups_type, particles_per_point, &
258	particle_type, pdx, pdy, pdz, prt_count, psb, psl, psn, psr, &
259	pss, pst, radius, random_start_position, &
260	read_particles_from_restartfile, seed_follows_topography, &
261	sgs_wf_part, sort_count, splitting_function, splitting_mode, &
262	total_number_of_particles, use_sgs_for_particles, &
263	write_particle_statistics, zero_particle, z0_av_global
264
265	USE pegrid
266
267	USE random_function_mod, &
268	ONLY: random_function
269
270	USE surface_mod, &
271	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
272
273	USE pmc_particle_interface, &
274	ONLY: pmcp_g_init
275
276	IMPLICIT NONE
277
278	PRIVATE
279
280	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
281	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
282
283	INTERFACE lpm_init
284	MODULE PROCEDURE lpm_init
285	END INTERFACE lpm_init
286
287	INTERFACE lpm_create_particle
288	MODULE PROCEDURE lpm_create_particle
289	END INTERFACE lpm_create_particle
290
291	PUBLIC lpm_init, lpm_create_particle
292
293	CONTAINS
294
295	!------------------------------------------------------------------------------!
296	! Description:
297	! ------------
298	!> @todo Missing subroutine description.
299	!------------------------------------------------------------------------------!
300	SUBROUTINE lpm_init
301
302	USE lpm_collision_kernels_mod, &
303	ONLY: init_kernels
304
305	USE pmc_interface, &
306	ONLY: nested_run
307
308	IMPLICIT NONE
309
310	INTEGER(iwp) :: i !<
311	INTEGER(iwp) :: j !<
312	INTEGER(iwp) :: k !<
313
314	REAL(wp) :: div !<
315	REAL(wp) :: height_int !<
316	REAL(wp) :: height_p !<
317	REAL(wp) :: z_p !<
318	REAL(wp) :: z0_av_local !<
319
320
321	!
322	!-- In case of oceans runs, the vertical index calculations need an offset,
323	!-- because otherwise the k indices will become negative
324	IF ( ocean ) THEN
325	offset_ocean_nzt = nzt
326	offset_ocean_nzt_m1 = nzt - 1
327	ENDIF
328
329	!
330	!-- Define block offsets for dividing a gridcell in 8 sub cells
331	!-- See documentation for List of subgrid boxes
332	!-- See pack_and_sort in lpm_pack_arrays.f90 for assignment of the subgrid boxes
333	block_offset(0) = block_offset_def ( 0, 0, 0)
334	block_offset(1) = block_offset_def ( 0, 0,-1)
335	block_offset(2) = block_offset_def ( 0,-1, 0)
336	block_offset(3) = block_offset_def ( 0,-1,-1)
337	block_offset(4) = block_offset_def (-1, 0, 0)
338	block_offset(5) = block_offset_def (-1, 0,-1)
339	block_offset(6) = block_offset_def (-1,-1, 0)
340	block_offset(7) = block_offset_def (-1,-1,-1)
341	!
342	!-- Check the number of particle groups.
343	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
344	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
345	max_number_of_particle_groups , &
346	'&number_of_particle_groups reset to ', &
347	max_number_of_particle_groups
348	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
349	number_of_particle_groups = max_number_of_particle_groups
350	ENDIF
351	!
352	!-- Check if downward-facing walls exist. This case, reflection boundary
353	!-- conditions (as well as subgrid-scale velocities) may do not work
354	!-- propably (not realized so far).
355	IF ( surf_def_h(1)%ns >= 1 ) THEN
356	WRITE( message_string, * ) 'Overhanging topography do not work '// &
357	'with particles'
358	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
359
360	ENDIF
361
362	!
363	!-- Set default start positions, if necessary
364	IF ( psl(1) == 9999999.9_wp ) psl(1) = 0.0_wp
365	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx +1 ) * dx
366	IF ( pss(1) == 9999999.9_wp ) pss(1) = 0.0_wp
367	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny +1 ) * dy
368	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
369	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
370
371	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
372	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
373	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
374
375	!
376	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
377	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
378	IF ( number_particles_per_gridbox /= -1 .AND. &
379	number_particles_per_gridbox >= 1 ) THEN
380	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
381	REAL(number_particles_per_gridbox))**0.3333333_wp
382	!
383	!-- Ensure a smooth value (two significant digits) of distance between
384	!-- particles (pdx, pdy, pdz).
385	div = 1000.0_wp
386	DO WHILE ( pdx(1) < div )
387	div = div / 10.0_wp
388	ENDDO
389	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
390	pdy(1) = pdx(1)
391	pdz(1) = pdx(1)
392
393	ENDIF
394
395	DO j = 2, number_of_particle_groups
396	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
397	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
398	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
399	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
400	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
401	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
402	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
403	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
404	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
405	ENDDO
406
407	!
408	!-- Allocate arrays required for calculating particle SGS velocities.
409	!-- Initialize prefactor required for stoachastic Weil equation.
410	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
411	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
412	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
413	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
414
415	sgs_wf_part = 1.0_wp / 3.0_wp
416	ENDIF
417
418	!
419	!-- Allocate array required for logarithmic vertical interpolation of
420	!-- horizontal particle velocities between the surface and the first vertical
421	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
422	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
423	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
424	!-- To obtain exact height levels of particles, linear interpolation is applied
425	!-- (see lpm_advec.f90).
426	IF ( constant_flux_layer ) THEN
427
428	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
429	z_p = zu(nzb+1) - zw(nzb)
430
431	!
432	!-- Calculate horizontal mean value of z0 used for logartihmic
433	!-- interpolation. Note: this is not exact for heterogeneous z0.
434	!-- However, sensitivity studies showed that the effect is
435	!-- negligible.
436	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
437	SUM( surf_usm_h%z0 )
438	z0_av_global = 0.0_wp
439
440	#if defined( __parallel )
441	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
442	comm2d, ierr )
443	#else
444	z0_av_global = z0_av_local
445	#endif
446
447	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
448	!
449	!-- Horizontal wind speed is zero below and at z0
450	log_z_z0(0) = 0.0_wp
451	!
452	!-- Calculate vertical depth of the sublayers
453	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
454	!
455	!-- Precalculate LOG(z/z0)
456	height_p = z0_av_global
457	DO k = 1, number_of_sublayers
458
459	height_p = height_p + height_int
460	log_z_z0(k) = LOG( height_p / z0_av_global )
461
462	ENDDO
463
464	ENDIF
465
466	!
467	!-- Check boundary condition and set internal variables
468	SELECT CASE ( bc_par_b )
469
470	CASE ( 'absorb' )
471	ibc_par_b = 1
472
473	CASE ( 'reflect' )
474	ibc_par_b = 2
475
476	CASE DEFAULT
477	WRITE( message_string, * ) 'unknown boundary condition ', &
478	'bc_par_b = "', TRIM( bc_par_b ), '"'
479	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
480
481	END SELECT
482	SELECT CASE ( bc_par_t )
483
484	CASE ( 'absorb' )
485	ibc_par_t = 1
486
487	CASE ( 'reflect' )
488	ibc_par_t = 2
489
490	CASE ( 'nested' )
491	ibc_par_t = 3
492
493	CASE DEFAULT
494	WRITE( message_string, * ) 'unknown boundary condition ', &
495	'bc_par_t = "', TRIM( bc_par_t ), '"'
496	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
497
498	END SELECT
499	SELECT CASE ( bc_par_lr )
500
501	CASE ( 'cyclic' )
502	ibc_par_lr = 0
503
504	CASE ( 'absorb' )
505	ibc_par_lr = 1
506
507	CASE ( 'reflect' )
508	ibc_par_lr = 2
509
510	CASE ( 'nested' )
511	ibc_par_lr = 3
512
513	CASE DEFAULT
514	WRITE( message_string, * ) 'unknown boundary condition ', &
515	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
516	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
517
518	END SELECT
519	SELECT CASE ( bc_par_ns )
520
521	CASE ( 'cyclic' )
522	ibc_par_ns = 0
523
524	CASE ( 'absorb' )
525	ibc_par_ns = 1
526
527	CASE ( 'reflect' )
528	ibc_par_ns = 2
529
530	CASE ( 'nested' )
531	ibc_par_ns = 3
532
533	CASE DEFAULT
534	WRITE( message_string, * ) 'unknown boundary condition ', &
535	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
536	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
537
538	END SELECT
539	SELECT CASE ( splitting_mode )
540
541	CASE ( 'const' )
542	i_splitting_mode = 1
543
544	CASE ( 'cl_av' )
545	i_splitting_mode = 2
546
547	CASE ( 'gb_av' )
548	i_splitting_mode = 3
549
550	CASE DEFAULT
551	WRITE( message_string, * ) 'unknown splitting_mode = "', &
552	TRIM( splitting_mode ), '"'
553	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
554
555	END SELECT
556	SELECT CASE ( splitting_function )
557
558	CASE ( 'gamma' )
559	isf = 1
560
561	CASE ( 'log' )
562	isf = 2
563
564	CASE ( 'exp' )
565	isf = 3
566
567	CASE DEFAULT
568	WRITE( message_string, * ) 'unknown splitting function = "', &
569	TRIM( splitting_function ), '"'
570	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
571
572	END SELECT
573
574
575	!
576	!-- Initialize collision kernels
577	IF ( collision_kernel /= 'none' ) CALL init_kernels
578
579	!
580	!-- For the first model run of a possible job chain initialize the
581	!-- particles, otherwise read the particle data from restart file.
582	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
583	.AND. read_particles_from_restartfile ) THEN
584
585	CALL lpm_read_restart_file
586
587	ELSE
588
589	!
590	!-- Allocate particle arrays and set attributes of the initial set of
591	!-- particles, which can be also periodically released at later times.
592	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
593	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
594
595	number_of_particles = 0
596
597	sort_count = 0
598	prt_count = 0
599
600	!
601	!-- initialize counter for particle IDs
602	grid_particles%id_counter = 1
603
604	!
605	!-- Initialize all particles with dummy values (otherwise errors may
606	!-- occur within restart runs). The reason for this is still not clear
607	!-- and may be presumably caused by errors in the respective user-interface.
608	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
609	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
610	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
611	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
612	0, 0, 0_idp, .FALSE., -1 )
613
614	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
615
616	!
617	!-- Set values for the density ratio and radius for all particle
618	!-- groups, if necessary
619	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
620	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
621	DO i = 2, number_of_particle_groups
622	IF ( density_ratio(i) == 9999999.9_wp ) THEN
623	density_ratio(i) = density_ratio(i-1)
624	ENDIF
625	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
626	ENDDO
627
628	DO i = 1, number_of_particle_groups
629	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
630	WRITE( message_string, * ) 'particle group #', i, ' has a', &
631	'density ratio /= 0 but radius = 0'
632	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
633	ENDIF
634	particle_groups(i)%density_ratio = density_ratio(i)
635	particle_groups(i)%radius = radius(i)
636	ENDDO
637
638	!
639	!-- Set a seed value for the random number generator to be exclusively
640	!-- used for the particle code. The generated random numbers should be
641	!-- different on the different PEs.
642	iran_part = iran_part + myid
643
644	CALL lpm_create_particle (PHASE_INIT)
645	!
646	!-- User modification of initial particles
647	CALL user_lpm_init
648
649	!
650	!-- Open file for statistical informations about particle conditions
651	IF ( write_particle_statistics ) THEN
652	CALL check_open( 80 )
653	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
654	number_of_particles
655	CALL close_file( 80 )
656	ENDIF
657
658	ENDIF
659
660	IF ( nested_run ) CALL pmcp_g_init
661
662	!
663	!-- To avoid programm abort, assign particles array to the local version of
664	!-- first grid cell
665	number_of_particles = prt_count(nzb+1,nys,nxl)
666	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
667	!
668	!-- Formats
669	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
670
671	END SUBROUTINE lpm_init
672
673	!------------------------------------------------------------------------------!
674	! Description:
675	! ------------
676	!> @todo Missing subroutine description.
677	!------------------------------------------------------------------------------!
678	SUBROUTINE lpm_create_particle (phase)
679
680	USE arrays_3d, &
681	ONLY: zw
682	USE lpm_exchange_horiz_mod, &
683	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
684
685	USE lpm_pack_and_sort_mod, &
686	ONLY: lpm_sort_in_subboxes
687
688	USE particle_attributes, &
689	ONLY: deleted_particles
690
691	IMPLICIT NONE
692
693	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
694	INTEGER(iwp) :: i !< loop variable ( particle groups )
695	INTEGER(iwp) :: ip !< index variable along x
696	INTEGER(iwp) :: j !< loop variable ( particles per point )
697	INTEGER(iwp) :: jp !< index variable along y
698	INTEGER(iwp) :: k !< index variable along z
699	INTEGER(iwp) :: k_surf !< index of surface grid point
700	INTEGER(iwp) :: kp !< index variable along z
701	INTEGER(iwp) :: loop_stride !< loop variable for initialization
702	INTEGER(iwp) :: n !< loop variable ( number of particles )
703	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
704
705	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
706
707	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
708	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
709
710	LOGICAL :: first_stride !< flag for initialization
711
712	REAL(wp) :: pos_x !< increment for particle position in x
713	REAL(wp) :: pos_y !< increment for particle position in y
714	REAL(wp) :: pos_z !< increment for particle position in z
715	REAL(wp) :: rand_contr !< dummy argument for random position
716
717	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
718
719	!
720	!-- Calculate particle positions and store particle attributes, if
721	!-- particle is situated on this PE
722	DO loop_stride = 1, 2
723	first_stride = (loop_stride == 1)
724	IF ( first_stride ) THEN
725	local_count = 0 ! count number of particles
726	ELSE
727	local_count = prt_count ! Start address of new particles
728	ENDIF
729
730	!
731	!-- Calculate initial_weighting_factor diagnostically
732	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
733	initial_weighting_factor = number_concentration * 1.0E6_wp * &
734	pdx(1) * pdy(1) * pdz(1)
735	END IF
736
737	n = 0
738	DO i = 1, number_of_particle_groups
739
740	pos_z = psb(i)
741
742	DO WHILE ( pos_z <= pst(i) )
743
744	IF ( pos_z >= zw(0) .AND. pos_z < zw(nzt) ) THEN
745
746
747	pos_y = pss(i)
748
749	DO WHILE ( pos_y <= psn(i) )
750
751	IF ( pos_y >= nys * dy .AND. &
752	pos_y < ( nyn + 1 ) * dy ) THEN
753
754	pos_x = psl(i)
755
756	xloop: DO WHILE ( pos_x <= psr(i) )
757
758	IF ( pos_x >= nxl * dx .AND. &
759	pos_x < ( nxr + 1) * dx ) THEN
760
761	DO j = 1, particles_per_point
762
763
764	n = n + 1
765	tmp_particle%x = pos_x
766	tmp_particle%y = pos_y
767	tmp_particle%z = pos_z
768	tmp_particle%age = 0.0_wp
769	tmp_particle%age_m = 0.0_wp
770	tmp_particle%dt_sum = 0.0_wp
771	tmp_particle%e_m = 0.0_wp
772	tmp_particle%rvar1 = 0.0_wp
773	tmp_particle%rvar2 = 0.0_wp
774	tmp_particle%rvar3 = 0.0_wp
775	tmp_particle%speed_x = 0.0_wp
776	tmp_particle%speed_y = 0.0_wp
777	tmp_particle%speed_z = 0.0_wp
778	tmp_particle%origin_x = pos_x
779	tmp_particle%origin_y = pos_y
780	tmp_particle%origin_z = pos_z
781	IF ( curvature_solution_effects ) THEN
782	tmp_particle%aux1 = 0.0_wp ! dry aerosol radius
783	tmp_particle%aux2 = dt_3d ! last Rosenbrock timestep
784	ELSE
785	tmp_particle%aux1 = 0.0_wp ! free to use
786	tmp_particle%aux2 = 0.0_wp ! free to use
787	ENDIF
788	tmp_particle%radius = particle_groups(i)%radius
789	tmp_particle%weight_factor = initial_weighting_factor
790	tmp_particle%class = 1
791	tmp_particle%group = i
792	tmp_particle%id = 0_idp
793	tmp_particle%particle_mask = .TRUE.
794	tmp_particle%block_nr = -1
795	!
796	!-- Determine the grid indices of the particle position
797	ip = tmp_particle%x * ddx
798	jp = tmp_particle%y * ddy
799	kp = tmp_particle%z / dz(1) + 1 + offset_ocean_nzt
800	DO WHILE( zw(kp) < tmp_particle%z )
801	kp = kp + 1
802	ENDDO
803	DO WHILE( zw(kp-1) > tmp_particle%z )
804	kp = kp - 1
805	ENDDO
806	!
807	!-- Determine surface level. Therefore, check for
808	!-- upward-facing wall on w-grid.
809	k_surf = get_topography_top_index_ji( jp, ip, 'w' )
810
811	IF ( seed_follows_topography ) THEN
812	!
813	!-- Particle height is given relative to topography
814	kp = kp + k_surf
815	tmp_particle%z = tmp_particle%z + zw(k_surf)
816	!-- Skip particle release if particle position is
817	!-- above model top, or within topography in case
818	!-- of overhanging structures.
819	IF ( kp > nzt .OR. &
820	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
821	pos_x = pos_x + pdx(i)
822	CYCLE xloop
823	ENDIF
824	!
825	!-- Skip particle release if particle position is
826	!-- below surface, or within topography in case
827	!-- of overhanging structures.
828	ELSEIF ( .NOT. seed_follows_topography .AND. &
829	tmp_particle%z <= zw(k_surf) .OR. &
830	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
831	THEN
832	pos_x = pos_x + pdx(i)
833	CYCLE xloop
834	ENDIF
835
836	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
837
838	IF ( .NOT. first_stride ) THEN
839	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
840	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
841	ENDIF
842	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
843	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
844	ENDIF
845	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
846
847	ENDIF
848	ENDDO
849
850	ENDIF
851
852	pos_x = pos_x + pdx(i)
853
854	ENDDO xloop
855
856	ENDIF
857
858	pos_y = pos_y + pdy(i)
859
860	ENDDO
861
862	ENDIF
863
864	pos_z = pos_z + pdz(i)
865
866	ENDDO
867
868	ENDDO
869
870	IF ( first_stride ) THEN
871	DO ip = nxl, nxr
872	DO jp = nys, nyn
873	DO kp = nzb+1, nzt
874	IF ( phase == PHASE_INIT ) THEN
875	IF ( local_count(kp,jp,ip) > 0 ) THEN
876	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
877	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
878	min_nr_particle )
879	ELSE
880	alloc_size = min_nr_particle
881	ENDIF
882	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
883	DO n = 1, alloc_size
884	grid_particles(kp,jp,ip)%particles(n) = zero_particle
885	ENDDO
886	ELSEIF ( phase == PHASE_RELEASE ) THEN
887	IF ( local_count(kp,jp,ip) > 0 ) THEN
888	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
889	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
890	alloc_factor / 100.0_wp ) ), min_nr_particle )
891	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
892	CALL realloc_particles_array(ip,jp,kp,alloc_size)
893	ENDIF
894	ENDIF
895	ENDIF
896	ENDDO
897	ENDDO
898	ENDDO
899	ENDIF
900
901	ENDDO
902
903
904
905	local_start = prt_count+1
906	prt_count = local_count
907
908	!
909	!-- Calculate particle IDs
910	DO ip = nxl, nxr
911	DO jp = nys, nyn
912	DO kp = nzb+1, nzt
913	number_of_particles = prt_count(kp,jp,ip)
914	IF ( number_of_particles <= 0 ) CYCLE
915	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
916
917	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
918
919	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
920	10000_idp*2 kp + 10000_idp * jp + ip
921	!
922	!-- Count the number of particles that have been released before
923	grid_particles(kp,jp,ip)%id_counter = &
924	grid_particles(kp,jp,ip)%id_counter + 1
925
926	ENDDO
927
928	ENDDO
929	ENDDO
930	ENDDO
931
932	!
933	!-- Initialize aerosol background spectrum
934	IF ( curvature_solution_effects ) THEN
935	CALL lpm_init_aerosols(local_start)
936	ENDIF
937
938	!
939	!-- Add random fluctuation to particle positions.
940	IF ( random_start_position ) THEN
941	DO ip = nxl, nxr
942	DO jp = nys, nyn
943	DO kp = nzb+1, nzt
944	number_of_particles = prt_count(kp,jp,ip)
945	IF ( number_of_particles <= 0 ) CYCLE
946	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
947	!
948	!-- Move only new particles. Moreover, limit random fluctuation
949	!-- in order to prevent that particles move more than one grid box,
950	!-- which would lead to problems concerning particle exchange
951	!-- between processors in case pdx/pdy are larger than dx/dy,
952	!-- respectively.
953	DO n = local_start(kp,jp,ip), number_of_particles
954	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
955	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
956	pdx(particles(n)%group)
957	particles(n)%x = particles(n)%x + &
958	MERGE( rand_contr, SIGN( dx, rand_contr ), &
959	ABS( rand_contr ) < dx &
960	)
961	ENDIF
962	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
963	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
964	pdy(particles(n)%group)
965	particles(n)%y = particles(n)%y + &
966	MERGE( rand_contr, SIGN( dy, rand_contr ), &
967	ABS( rand_contr ) < dy &
968	)
969	ENDIF
970	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
971	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
972	pdz(particles(n)%group)
973	particles(n)%z = particles(n)%z + &
974	MERGE( rand_contr, SIGN( dzw(kp), rand_contr ), &
975	ABS( rand_contr ) < dzw(kp) &
976	)
977	ENDIF
978	ENDDO
979	!
980	!-- Identify particles located outside the model domain and reflect
981	!-- or absorb them if necessary.
982	CALL lpm_boundary_conds( 'bottom/top', i, j, k )
983	!
984	!-- Furthermore, remove particles located in topography. Note, as
985	!-- the particle speed is still zero at this point, wall
986	!-- reflection boundary conditions will not work in this case.
987	particles => &
988	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
989	DO n = local_start(kp,jp,ip), number_of_particles
990	i = particles(n)%x * ddx
991	j = particles(n)%y * ddy
992	k = particles(n)%z / dz(1) + 1 + offset_ocean_nzt
993	DO WHILE( zw(k) < particles(n)%z )
994	k = k + 1
995	ENDDO
996	DO WHILE( zw(k-1) > particles(n)%z )
997	k = k - 1
998	ENDDO
999	!
1000	!-- Check if particle is within topography
1001	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
1002	particles(n)%particle_mask = .FALSE.
1003	deleted_particles = deleted_particles + 1
1004	ENDIF
1005
1006	ENDDO
1007	ENDDO
1008	ENDDO
1009	ENDDO
1010	!
1011	!-- Exchange particles between grid cells and processors
1012	CALL lpm_move_particle
1013	CALL lpm_exchange_horiz
1014
1015	ENDIF
1016	!
1017	!-- In case of random_start_position, delete particles identified by
1018	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
1019	!-- which is needed for a fast interpolation of the LES fields on the particle
1020	!-- position.
1021	CALL lpm_sort_in_subboxes
1022
1023	!
1024	!-- Determine the current number of particles
1025	DO ip = nxl, nxr
1026	DO jp = nys, nyn
1027	DO kp = nzb+1, nzt
1028	number_of_particles = number_of_particles &
1029	+ prt_count(kp,jp,ip)
1030	ENDDO
1031	ENDDO
1032	ENDDO
1033	!
1034	!-- Calculate the number of particles of the total domain
1035	#if defined( __parallel )
1036	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1037	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
1038	MPI_INTEGER, MPI_SUM, comm2d, ierr )
1039	#else
1040	total_number_of_particles = number_of_particles
1041	#endif
1042
1043	RETURN
1044
1045	END SUBROUTINE lpm_create_particle
1046
1047	SUBROUTINE lpm_init_aerosols(local_start)
1048
1049	USE arrays_3d, &
1050	ONLY: hyp, pt, q
1051
1052	USE cloud_parameters, &
1053	ONLY: l_d_rv, molecular_weight_of_solute, &
1054	molecular_weight_of_water, rho_l, r_v, rho_s, vanthoff
1055
1056	USE constants, &
1057	ONLY: pi
1058
1059	USE diagnostic_quantities_mod, &
1060	ONLY: magnus
1061
1062
1063	USE kinds
1064
1065	USE particle_attributes, &
1066	ONLY: aero_species, aero_type, aero_weight, log_sigma, na, rm
1067
1068	IMPLICIT NONE
1069
1070	REAL(wp) :: afactor !< curvature effects
1071	REAL(wp) :: bfactor !< solute effects
1072	REAL(wp) :: dlogr !< logarithmic width of radius bin
1073	REAL(wp) :: e_a !< vapor pressure
1074	REAL(wp) :: e_s !< saturation vapor pressure
1075	REAL(wp) :: rmin = 0.005e-6_wp !< minimum aerosol radius
1076	REAL(wp) :: rmax = 10.0e-6_wp !< maximum aerosol radius
1077	REAL(wp) :: r_mid !< mean radius of bin
1078	REAL(wp) :: r_l !< left radius of bin
1079	REAL(wp) :: r_r !< right radius of bin
1080	REAL(wp) :: sigma !< surface tension
1081	REAL(wp) :: t_int !< temperature
1082
1083	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1084
1085	INTEGER(iwp) :: n !<
1086	INTEGER(iwp) :: ip !<
1087	INTEGER(iwp) :: jp !<
1088	INTEGER(iwp) :: kp !<
1089
1090	!
1091	!-- Set constants for different aerosol species
1092	IF ( TRIM(aero_species) .EQ. 'nacl' ) THEN
1093	molecular_weight_of_solute = 0.05844_wp
1094	rho_s = 2165.0_wp
1095	vanthoff = 2.0_wp
1096	ELSEIF ( TRIM(aero_species) .EQ. 'c3h4o4' ) THEN
1097	molecular_weight_of_solute = 0.10406_wp
1098	rho_s = 1600.0_wp
1099	vanthoff = 1.37_wp
1100	ELSEIF ( TRIM(aero_species) .EQ. 'nh4o3' ) THEN
1101	molecular_weight_of_solute = 0.08004_wp
1102	rho_s = 1720.0_wp
1103	vanthoff = 2.31_wp
1104	ELSE
1105	WRITE( message_string, * ) 'unknown aerosol species ', &
1106	'aero_species = "', TRIM( aero_species ), '"'
1107	CALL message( 'lpm_init', 'PA0470', 1, 2, 0, 6, 0 )
1108	ENDIF
1109	!
1110	!-- The following typical aerosol spectra are taken from Jaenicke (1993):
1111	!-- Tropospheric aerosols. Published in Aerosol-Cloud-Climate Interactions.
1112	IF ( TRIM(aero_type) .EQ. 'polar' ) THEN
1113	na = (/ 2.17e1, 1.86e-1, 3.04e-4 /) * 1.0E6
1114	rm = (/ 0.0689, 0.375, 4.29 /) * 1.0E-6
1115	log_sigma = (/ 0.245, 0.300, 0.291 /)
1116	ELSEIF ( TRIM(aero_type) .EQ. 'background' ) THEN
1117	na = (/ 1.29e2, 5.97e1, 6.35e1 /) * 1.0E6
1118	rm = (/ 0.0036, 0.127, 0.259 /) * 1.0E-6
1119	log_sigma = (/ 0.645, 0.253, 0.425 /)
1120	ELSEIF ( TRIM(aero_type) .EQ. 'maritime' ) THEN
1121	na = (/ 1.33e2, 6.66e1, 3.06e0 /) * 1.0E6
1122	rm = (/ 0.0039, 0.133, 0.29 /) * 1.0E-6
1123	log_sigma = (/ 0.657, 0.210, 0.396 /)
1124	ELSEIF ( TRIM(aero_type) .EQ. 'continental' ) THEN
1125	na = (/ 3.20e3, 2.90e3, 3.00e-1 /) * 1.0E6
1126	rm = (/ 0.01, 0.058, 0.9 /) * 1.0E-6
1127	log_sigma = (/ 0.161, 0.217, 0.380 /)
1128	ELSEIF ( TRIM(aero_type) .EQ. 'desert' ) THEN
1129	na = (/ 7.26e2, 1.14e3, 1.78e-1 /) * 1.0E6
1130	rm = (/ 0.001, 0.0188, 10.8 /) * 1.0E-6
1131	log_sigma = (/ 0.247, 0.770, 0.438 /)
1132	ELSEIF ( TRIM(aero_type) .EQ. 'rural' ) THEN
1133	na = (/ 6.65e3, 1.47e2, 1.99e3 /) * 1.0E6
1134	rm = (/ 0.00739, 0.0269, 0.0419 /) * 1.0E-6
1135	log_sigma = (/ 0.225, 0.557, 0.266 /)
1136	ELSEIF ( TRIM(aero_type) .EQ. 'urban' ) THEN
1137	na = (/ 9.93e4, 1.11e3, 3.64e4 /) * 1.0E6
1138	rm = (/ 0.00651, 0.00714, 0.0248 /) * 1.0E-6
1139	log_sigma = (/ 0.245, 0.666, 0.337 /)
1140	ELSEIF ( TRIM(aero_type) .EQ. 'user' ) THEN
1141	CONTINUE
1142	ELSE
1143	WRITE( message_string, * ) 'unknown aerosol type ', &
1144	'aero_type = "', TRIM( aero_type ), '"'
1145	CALL message( 'lpm_init', 'PA0459', 1, 2, 0, 6, 0 )
1146	ENDIF
1147
1148	DO ip = nxl, nxr
1149	DO jp = nys, nyn
1150	DO kp = nzb+1, nzt
1151
1152	number_of_particles = prt_count(kp,jp,ip)
1153	IF ( number_of_particles <= 0 ) CYCLE
1154	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1155
1156	dlogr = ( LOG10(rmax) - LOG10(rmin) ) / ( number_of_particles - local_start(kp,jp,ip) + 1 )
1157	!
1158	!-- Initialize the aerosols with a predefined spectral distribution
1159	!-- of the dry radius (logarithmically increasing bins) and a varying
1160	!-- weighting factor
1161	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1162
1163	r_l = 10.0*( LOG10( rmin ) + (n-1) dlogr )
1164	r_r = 10.0*( LOG10( rmin ) + n dlogr )
1165	r_mid = SQRT( r_l * r_r )
1166
1167	particles(n)%aux1 = r_mid
1168	particles(n)%weight_factor = &
1169	( na(1) / ( SQRT( 2.0 * pi ) * log_sigma(1) ) * &
1170	EXP( - LOG10( r_mid / rm(1) )*2 / ( 2.0 log_sigma(1)**2 ) ) + &
1171	na(2) / ( SQRT( 2.0 * pi ) * log_sigma(2) ) * &
1172	EXP( - LOG10( r_mid / rm(2) )*2 / ( 2.0 log_sigma(2)**2 ) ) + &
1173	na(3) / ( SQRT( 2.0 * pi ) * log_sigma(3) ) * &
1174	EXP( - LOG10( r_mid / rm(3) )*2 / ( 2.0 log_sigma(3)**2 ) ) &
1175	) * ( LOG10(r_r) - LOG10(r_l) ) * ( dx * dy * dzw(kp) )
1176
1177	!
1178	!-- Multiply weight_factor with the namelist parameter aero_weight
1179	!-- to increase or decrease the number of simulated aerosols
1180	particles(n)%weight_factor = particles(n)%weight_factor * aero_weight
1181
1182	IF ( particles(n)%weight_factor - FLOOR(particles(n)%weight_factor,KIND=wp) &
1183	.GT. random_function( iran_part ) ) THEN
1184	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp) + 1.0
1185	ELSE
1186	particles(n)%weight_factor = FLOOR(particles(n)%weight_factor,KIND=wp)
1187	ENDIF
1188	!
1189	!-- Unnecessary particles will be deleted
1190	IF ( particles(n)%weight_factor .LE. 0.0 ) particles(n)%particle_mask = .FALSE.
1191
1192	ENDDO
1193	!
1194	!-- Set particle radius to equilibrium radius based on the environmental
1195	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1196	!-- the sometimes lengthy growth toward their equilibrium radius within
1197	!-- the simulation.
1198	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1199
1200	e_s = magnus( t_int )
1201	e_a = q(kp,jp,ip) * hyp(kp) / ( q(kp,jp,ip) + 0.622_wp )
1202
1203	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1204	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1205
1206	bfactor = vanthoff * molecular_weight_of_water * &
1207	rho_s / ( molecular_weight_of_solute * rho_l )
1208	!
1209	!-- The formula is only valid for subsaturated environments. For
1210	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1211	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1212
1213	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1214	!
1215	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1216	!-- Curry (2007, JGR)
1217	particles(n)%radius = bfactor*0.3333333_wp &
1218	particles(n)%aux1 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1219	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1220	particles(n)%aux1 ) ) / &
1221	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1222	)
1223
1224	ENDDO
1225
1226	ENDDO
1227	ENDDO
1228	ENDDO
1229
1230	END SUBROUTINE lpm_init_aerosols
1231
1232	END MODULE lpm_init_mod

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