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source: palm/trunk/SOURCE/lpm_init.f90 @ 2628

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

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