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source: palm/trunk/SOURCE/lpm_init.f90 @ 2305

Last change on this file since 2305 was 2305, checked in by hoffmann, 7 years ago
Improved calculation of particle IDs.
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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 2305 2017-07-06 11:18:47Z hoffmann $
27	! Improved calculation of particle IDs.
28	!
29	! 2274 2017-06-09 13:27:48Z Giersch
30	! Changed error messages
31	!
32	! 2265 2017-06-08 16:58:28Z schwenkel
33	! Unused variables removed.
34	!
35	! 2263 2017-06-08 14:59:01Z schwenkel
36	! Implemented splitting and merging algorithm
37	!
38	! 2233 2017-05-30 18:08:54Z suehring
39	!
40	! 2232 2017-05-30 17:47:52Z suehring
41	! Adjustments according to new topography realization
42	!
43	!
44	! 2223 2017-05-15 16:38:09Z suehring
45	! Add check for particle release at model top
46	!
47	! 2182 2017-03-17 14:27:40Z schwenkel
48	! Added parameters for simplified particle initialization.
49	!
50	! 2122 2017-01-18 12:22:54Z hoffmann
51	! Improved initialization of equilibrium aerosol radii
52	! Calculation of particle ID
53	!
54	! 2000 2016-08-20 18:09:15Z knoop
55	! Forced header and separation lines into 80 columns
56	!
57	! 2016-06-09 16:25:25Z suehring
58	! Bugfix in determining initial particle height and grid index in case of
59	! seed_follows_topography.
60	! Bugfix concerning random positions, ensure that particles do not move more
61	! than one grid length.
62	! Bugfix logarithmic interpolation.
63	! Initial setting of sgs_wf_part.
64	!
65	! 1890 2016-04-22 08:52:11Z hoffmann
66	! Initialization of aerosol equilibrium radius not possible in supersaturated
67	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
68	! initialization.
69	!
70	! 1873 2016-04-18 14:50:06Z maronga
71	! Module renamed (removed _mod
72	!
73	! 1871 2016-04-15 11:46:09Z hoffmann
74	! Initialization of aerosols added.
75	!
76	! 1850 2016-04-08 13:29:27Z maronga
77	! Module renamed
78	!
79	! 1831 2016-04-07 13:15:51Z hoffmann
80	! curvature_solution_effects moved to particle_attributes
81	!
82	! 1822 2016-04-07 07:49:42Z hoffmann
83	! Unused variables removed.
84	!
85	! 1783 2016-03-06 18:36:17Z raasch
86	! netcdf module added
87	!
88	! 1725 2015-11-17 13:01:51Z hoffmann
89	! Bugfix: Processor-dependent seed for random function is generated before it is
90	! used.
91	!
92	! 1691 2015-10-26 16:17:44Z maronga
93	! Renamed prandtl_layer to constant_flux_layer.
94	!
95	! 1685 2015-10-08 07:32:13Z raasch
96	! bugfix concerning vertical index offset in case of ocean
97	!
98	! 1682 2015-10-07 23:56:08Z knoop
99	! Code annotations made doxygen readable
100	!
101	! 1575 2015-03-27 09:56:27Z raasch
102	! initial vertical particle position is allowed to follow the topography
103	!
104	! 1359 2014-04-11 17:15:14Z hoffmann
105	! New particle structure integrated.
106	! Kind definition added to all floating point numbers.
107	! lpm_init changed form a subroutine to a module.
108	!
109	! 1327 2014-03-21 11:00:16Z raasch
110	! -netcdf_output
111	!
112	! 1322 2014-03-20 16:38:49Z raasch
113	! REAL functions provided with KIND-attribute
114	!
115	! 1320 2014-03-20 08:40:49Z raasch
116	! ONLY-attribute added to USE-statements,
117	! kind-parameters added to all INTEGER and REAL declaration statements,
118	! kinds are defined in new module kinds,
119	! revision history before 2012 removed,
120	! comment fields (!:) to be used for variable explanations added to
121	! all variable declaration statements
122	! bugfix: #if defined( __parallel ) added
123	!
124	! 1314 2014-03-14 18:25:17Z suehring
125	! Vertical logarithmic interpolation of horizontal particle speed for particles
126	! between roughness height and first vertical grid level.
127	!
128	! 1092 2013-02-02 11:24:22Z raasch
129	! unused variables removed
130	!
131	! 1036 2012-10-22 13:43:42Z raasch
132	! code put under GPL (PALM 3.9)
133	!
134	! 849 2012-03-15 10:35:09Z raasch
135	! routine renamed: init_particles -> lpm_init
136	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
137	! advec_particles),
138	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
139	!
140	! 828 2012-02-21 12:00:36Z raasch
141	! call of init_kernels, particle feature color renamed class
142	!
143	! 824 2012-02-17 09:09:57Z raasch
144	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
145	! array particles implemented as pointer
146	!
147	! 667 2010-12-23 12:06:00Z suehring/gryschka
148	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
149	! of arrays.
150	!
151	! Revision 1.1 1999/11/25 16:22:38 raasch
152	! Initial revision
153	!
154	!
155	! Description:
156	! ------------
157	!> This routine initializes a set of particles and their attributes (position,
158	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
159	!------------------------------------------------------------------------------!
160	MODULE lpm_init_mod
161
162	USE, INTRINSIC :: ISO_C_BINDING
163
164	USE arrays_3d, &
165	ONLY: de_dx, de_dy, de_dz, zu, zw
166
167	USE control_parameters, &
168	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
169	dz, initializing_actions, message_string, ocean, simulated_time
170
171	USE grid_variables, &
172	ONLY: ddx, dx, ddy, dy
173
174	USE indices, &
175	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
176	nzb_max, nzt, wall_flags_0
177
178	USE kinds
179
180	USE lpm_collision_kernels_mod, &
181	ONLY: init_kernels
182
183	USE netcdf_interface, &
184	ONLY: netcdf_data_format
185
186	USE particle_attributes, &
187	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
188	block_offset, block_offset_def, collision_kernel, &
189	curvature_solution_effects, density_ratio, grid_particles, &
190	isf,i_splitting_mode, initial_weighting_factor, ibc_par_b, &
191	ibc_par_lr, ibc_par_ns, ibc_par_t, iran_part, log_z_z0, &
192	max_number_of_particle_groups, min_nr_particle, &
193	number_concentration, &
194	number_particles_per_gridbox, number_of_particles, &
195	number_of_particle_groups, number_of_sublayers, &
196	offset_ocean_nzt, offset_ocean_nzt_m1, &
197	particles, particle_advection_start, particle_groups, &
198	particle_groups_type, particles_per_point, &
199	particle_type, pdx, pdy, pdz, prt_count, psb, psl, psn, psr, &
200	pss, pst, radius, random_start_position, &
201	read_particles_from_restartfile, seed_follows_topography, &
202	sgs_wf_part, sort_count, splitting_function, splitting_mode, &
203	total_number_of_particles, use_sgs_for_particles, &
204	write_particle_statistics, zero_particle, z0_av_global
205
206	USE pegrid
207
208	USE random_function_mod, &
209	ONLY: random_function
210
211	USE surface_mod, &
212	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
213
214	IMPLICIT NONE
215
216	PRIVATE
217
218	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
219	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
220
221	INTERFACE lpm_init
222	MODULE PROCEDURE lpm_init
223	END INTERFACE lpm_init
224
225	INTERFACE lpm_create_particle
226	MODULE PROCEDURE lpm_create_particle
227	END INTERFACE lpm_create_particle
228
229	PUBLIC lpm_init, lpm_create_particle
230
231	CONTAINS
232
233	!------------------------------------------------------------------------------!
234	! Description:
235	! ------------
236	!> @todo Missing subroutine description.
237	!------------------------------------------------------------------------------!
238	SUBROUTINE lpm_init
239
240	USE lpm_collision_kernels_mod, &
241	ONLY: init_kernels
242
243	IMPLICIT NONE
244
245	INTEGER(iwp) :: i !<
246	INTEGER(iwp) :: j !<
247	INTEGER(iwp) :: k !<
248
249	REAL(wp) :: div !<
250	REAL(wp) :: height_int !<
251	REAL(wp) :: height_p !<
252	REAL(wp) :: z_p !<
253	REAL(wp) :: z0_av_local !<
254
255
256	!
257	!-- In case of oceans runs, the vertical index calculations need an offset,
258	!-- because otherwise the k indices will become negative
259	IF ( ocean ) THEN
260	offset_ocean_nzt = nzt
261	offset_ocean_nzt_m1 = nzt - 1
262	ENDIF
263
264	!
265	!-- Define block offsets for dividing a gridcell in 8 sub cells
266
267	block_offset(0) = block_offset_def (-1,-1,-1)
268	block_offset(1) = block_offset_def (-1,-1, 0)
269	block_offset(2) = block_offset_def (-1, 0,-1)
270	block_offset(3) = block_offset_def (-1, 0, 0)
271	block_offset(4) = block_offset_def ( 0,-1,-1)
272	block_offset(5) = block_offset_def ( 0,-1, 0)
273	block_offset(6) = block_offset_def ( 0, 0,-1)
274	block_offset(7) = block_offset_def ( 0, 0, 0)
275	!
276	!-- Check the number of particle groups.
277	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
278	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
279	max_number_of_particle_groups , &
280	'&number_of_particle_groups reset to ', &
281	max_number_of_particle_groups
282	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
283	number_of_particle_groups = max_number_of_particle_groups
284	ENDIF
285	!
286	!-- Check if downward-facing walls exist. This case, reflection boundary
287	!-- conditions (as well as subgrid-scale velocities) may do not work
288	!-- propably (not realized so far).
289	IF ( surf_def_h(1)%ns >= 1 ) THEN
290	WRITE( message_string, * ) 'Overhanging topography do not work '// &
291	'with particles'
292	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
293
294	ENDIF
295
296	!
297	!-- Set default start positions, if necessary
298	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
299	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
300	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
301	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
302	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
303	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
304
305	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
306	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
307	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
308
309	!
310	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
311	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
312	IF ( number_particles_per_gridbox /= -1 .AND. &
313	number_particles_per_gridbox >= 1 ) THEN
314	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
315	REAL(number_particles_per_gridbox))**0.3333333_wp
316	!
317	!-- Ensure a smooth value (two significant digits) of distance between
318	!-- particles (pdx, pdy, pdz).
319	div = 1000.0_wp
320	DO WHILE ( pdx(1) < div )
321	div = div / 10.0_wp
322	ENDDO
323	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
324	pdy(1) = pdx(1)
325	pdz(1) = pdx(1)
326
327	ENDIF
328
329	DO j = 2, number_of_particle_groups
330	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
331	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
332	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
333	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
334	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
335	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
336	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
337	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
338	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
339	ENDDO
340
341	!
342	!-- Allocate arrays required for calculating particle SGS velocities.
343	!-- Initialize prefactor required for stoachastic Weil equation.
344	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
345	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
346	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
347	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
348
349	sgs_wf_part = 1.0_wp / 3.0_wp
350	ENDIF
351
352	!
353	!-- Allocate array required for logarithmic vertical interpolation of
354	!-- horizontal particle velocities between the surface and the first vertical
355	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
356	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
357	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
358	!-- To obtain exact height levels of particles, linear interpolation is applied
359	!-- (see lpm_advec.f90).
360	IF ( constant_flux_layer ) THEN
361
362	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
363	z_p = zu(nzb+1) - zw(nzb)
364
365	!
366	!-- Calculate horizontal mean value of z0 used for logartihmic
367	!-- interpolation. Note: this is not exact for heterogeneous z0.
368	!-- However, sensitivity studies showed that the effect is
369	!-- negligible.
370	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
371	SUM( surf_usm_h%z0 )
372	z0_av_global = 0.0_wp
373
374	#if defined( __parallel )
375	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
376	comm2d, ierr )
377	#else
378	z0_av_global = z0_av_local
379	#endif
380
381	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
382	!
383	!-- Horizontal wind speed is zero below and at z0
384	log_z_z0(0) = 0.0_wp
385	!
386	!-- Calculate vertical depth of the sublayers
387	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
388	!
389	!-- Precalculate LOG(z/z0)
390	height_p = z0_av_global
391	DO k = 1, number_of_sublayers
392
393	height_p = height_p + height_int
394	log_z_z0(k) = LOG( height_p / z0_av_global )
395
396	ENDDO
397
398	ENDIF
399
400	!
401	!-- Check boundary condition and set internal variables
402	SELECT CASE ( bc_par_b )
403
404	CASE ( 'absorb' )
405	ibc_par_b = 1
406
407	CASE ( 'reflect' )
408	ibc_par_b = 2
409
410	CASE DEFAULT
411	WRITE( message_string, * ) 'unknown boundary condition ', &
412	'bc_par_b = "', TRIM( bc_par_b ), '"'
413	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
414
415	END SELECT
416	SELECT CASE ( bc_par_t )
417
418	CASE ( 'absorb' )
419	ibc_par_t = 1
420
421	CASE ( 'reflect' )
422	ibc_par_t = 2
423
424	CASE DEFAULT
425	WRITE( message_string, * ) 'unknown boundary condition ', &
426	'bc_par_t = "', TRIM( bc_par_t ), '"'
427	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
428
429	END SELECT
430	SELECT CASE ( bc_par_lr )
431
432	CASE ( 'cyclic' )
433	ibc_par_lr = 0
434
435	CASE ( 'absorb' )
436	ibc_par_lr = 1
437
438	CASE ( 'reflect' )
439	ibc_par_lr = 2
440
441	CASE DEFAULT
442	WRITE( message_string, * ) 'unknown boundary condition ', &
443	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
444	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
445
446	END SELECT
447	SELECT CASE ( bc_par_ns )
448
449	CASE ( 'cyclic' )
450	ibc_par_ns = 0
451
452	CASE ( 'absorb' )
453	ibc_par_ns = 1
454
455	CASE ( 'reflect' )
456	ibc_par_ns = 2
457
458	CASE DEFAULT
459	WRITE( message_string, * ) 'unknown boundary condition ', &
460	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
461	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
462
463	END SELECT
464	SELECT CASE ( splitting_mode )
465
466	CASE ( 'const' )
467	i_splitting_mode = 1
468
469	CASE ( 'cl_av' )
470	i_splitting_mode = 2
471
472	CASE ( 'gb_av' )
473	i_splitting_mode = 3
474
475	CASE DEFAULT
476	WRITE( message_string, * ) 'unknown splitting condition ', &
477	'splitting_mode = "', TRIM( splitting_mode ), '"'
478	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
479
480	END SELECT
481	SELECT CASE ( splitting_function )
482
483	CASE ( 'gamma' )
484	isf = 1
485
486	CASE ( 'log' )
487	isf = 2
488
489	CASE ( 'exp' )
490	isf = 3
491
492	CASE DEFAULT
493	WRITE( message_string, * ) 'unknown splitting function ', &
494	'splitting_function = "', TRIM( splitting_function ), '"'
495	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
496
497	END SELECT
498
499
500	!
501	!-- Initialize collision kernels
502	IF ( collision_kernel /= 'none' ) CALL init_kernels
503
504	!
505	!-- For the first model run of a possible job chain initialize the
506	!-- particles, otherwise read the particle data from restart file.
507	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
508	.AND. read_particles_from_restartfile ) THEN
509
510	CALL lpm_read_restart_file
511
512	ELSE
513
514	!
515	!-- Allocate particle arrays and set attributes of the initial set of
516	!-- particles, which can be also periodically released at later times.
517	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
518	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
519
520	number_of_particles = 0
521
522	sort_count = 0
523	prt_count = 0
524
525	!
526	!-- initialize counter for particle IDs
527	grid_particles%id_counter = 1
528
529	!
530	!-- Initialize all particles with dummy values (otherwise errors may
531	!-- occur within restart runs). The reason for this is still not clear
532	!-- and may be presumably caused by errors in the respective user-interface.
533	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
534	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
535	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
536	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
537	0, 0, 0_idp, .FALSE., -1 )
538
539	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
540
541	!
542	!-- Set values for the density ratio and radius for all particle
543	!-- groups, if necessary
544	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
545	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
546	DO i = 2, number_of_particle_groups
547	IF ( density_ratio(i) == 9999999.9_wp ) THEN
548	density_ratio(i) = density_ratio(i-1)
549	ENDIF
550	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
551	ENDDO
552
553	DO i = 1, number_of_particle_groups
554	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
555	WRITE( message_string, * ) 'particle group #', i, 'has a', &
556	'density ratio /= 0 but radius = 0'
557	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
558	ENDIF
559	particle_groups(i)%density_ratio = density_ratio(i)
560	particle_groups(i)%radius = radius(i)
561	ENDDO
562
563	!
564	!-- Set a seed value for the random number generator to be exclusively
565	!-- used for the particle code. The generated random numbers should be
566	!-- different on the different PEs.
567	iran_part = iran_part + myid
568
569	CALL lpm_create_particle (PHASE_INIT)
570	!
571	!-- User modification of initial particles
572	CALL user_lpm_init
573
574	!
575	!-- Open file for statistical informations about particle conditions
576	IF ( write_particle_statistics ) THEN
577	CALL check_open( 80 )
578	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
579	number_of_particles
580	CALL close_file( 80 )
581	ENDIF
582
583	ENDIF
584
585	!
586	!-- To avoid programm abort, assign particles array to the local version of
587	!-- first grid cell
588	number_of_particles = prt_count(nzb+1,nys,nxl)
589	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
590	!
591	!-- Formats
592	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
593
594	END SUBROUTINE lpm_init
595
596	!------------------------------------------------------------------------------!
597	! Description:
598	! ------------
599	!> @todo Missing subroutine description.
600	!------------------------------------------------------------------------------!
601	SUBROUTINE lpm_create_particle (phase)
602
603	USE lpm_exchange_horiz_mod, &
604	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
605
606	USE lpm_pack_arrays_mod, &
607	ONLY: lpm_pack_all_arrays
608
609	USE particle_attributes, &
610	ONLY: deleted_particles, monodisperse_aerosols
611
612	IMPLICIT NONE
613
614	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
615	INTEGER(iwp) :: i !< loop variable ( particle groups )
616	INTEGER(iwp) :: ip !< index variable along x
617	INTEGER(iwp) :: j !< loop variable ( particles per point )
618	INTEGER(iwp) :: jp !< index variable along y
619	INTEGER(iwp) :: k !< index variable along z
620	INTEGER(iwp) :: k_surf !< index of surface grid point
621	INTEGER(iwp) :: kp !< index variable along z
622	INTEGER(iwp) :: loop_stride !< loop variable for initialization
623	INTEGER(iwp) :: n !< loop variable ( number of particles )
624	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
625
626	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
627
628	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
629	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
630
631	LOGICAL :: first_stride !< flag for initialization
632
633	REAL(wp) :: pos_x !< increment for particle position in x
634	REAL(wp) :: pos_y !< increment for particle position in y
635	REAL(wp) :: pos_z !< increment for particle position in z
636	REAL(wp) :: rand_contr !< dummy argument for random position
637
638	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
639
640	!
641	!-- Calculate particle positions and store particle attributes, if
642	!-- particle is situated on this PE
643	DO loop_stride = 1, 2
644	first_stride = (loop_stride == 1)
645	IF ( first_stride ) THEN
646	local_count = 0 ! count number of particles
647	ELSE
648	local_count = prt_count ! Start address of new particles
649	ENDIF
650
651	!
652	!-- Calculate initial_weighting_factor diagnostically
653	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
654	initial_weighting_factor = number_concentration * 1.0E6_wp * &
655	pdx(1) * pdy(1) * pdz(1)
656	END IF
657
658	n = 0
659	DO i = 1, number_of_particle_groups
660
661	pos_z = psb(i)
662
663	DO WHILE ( pos_z <= pst(i) )
664
665	IF ( pos_z >= 0.0_wp .AND. pos_z < zw(nzt) ) THEN
666
667
668	pos_y = pss(i)
669
670	DO WHILE ( pos_y <= psn(i) )
671
672	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
673	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
674
675	pos_x = psl(i)
676
677	xloop: DO WHILE ( pos_x <= psr(i) )
678
679	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
680	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
681
682	DO j = 1, particles_per_point
683
684
685	n = n + 1
686	tmp_particle%x = pos_x
687	tmp_particle%y = pos_y
688	tmp_particle%z = pos_z
689	tmp_particle%age = 0.0_wp
690	tmp_particle%age_m = 0.0_wp
691	tmp_particle%dt_sum = 0.0_wp
692	tmp_particle%user = 0.0_wp !unused, free for the user
693	tmp_particle%e_m = 0.0_wp
694	IF ( curvature_solution_effects ) THEN
695	!
696	!-- Initial values (internal timesteps, derivative)
697	!-- for Rosenbrock method
698	tmp_particle%rvar1 = 1.0E-6_wp !last Rosenbrock timestep
699	tmp_particle%rvar2 = 0.1E-6_wp !dry aerosol radius
700	tmp_particle%rvar3 = -9999999.9_wp !unused in this configuration
701	ELSE
702	!
703	!-- Initial values for SGS velocities
704	tmp_particle%rvar1 = 0.0_wp
705	tmp_particle%rvar2 = 0.0_wp
706	tmp_particle%rvar3 = 0.0_wp
707	ENDIF
708	tmp_particle%speed_x = 0.0_wp
709	tmp_particle%speed_y = 0.0_wp
710	tmp_particle%speed_z = 0.0_wp
711	tmp_particle%origin_x = pos_x
712	tmp_particle%origin_y = pos_y
713	tmp_particle%origin_z = pos_z
714	tmp_particle%radius = particle_groups(i)%radius
715	tmp_particle%weight_factor = initial_weighting_factor
716	tmp_particle%class = 1
717	tmp_particle%group = i
718	tmp_particle%id = 0_idp
719	tmp_particle%particle_mask = .TRUE.
720	tmp_particle%block_nr = -1
721	!
722	!-- Determine the grid indices of the particle position
723	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
724	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
725	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
726	!
727	!-- Determine surface level. Therefore, check for
728	!-- upward-facing wall on w-grid. MAXLOC will return
729	!-- the index of the lowest upward-facing wall.
730	k_surf = MAXLOC( &
731	MERGE( 1, 0, &
732	BTEST( wall_flags_0(nzb:nzb_max,jp,ip), 18 )&
733	), DIM = 1 &
734	) - 1
735
736	IF ( seed_follows_topography ) THEN
737	!
738	!-- Particle height is given relative to topography
739	kp = kp + k_surf
740	tmp_particle%z = tmp_particle%z + zw(k_surf)
741	!-- Skip particle release if particle position is
742	!-- above model top, or within topography in case
743	!-- of overhanging structures.
744	IF ( kp > nzt .OR. &
745	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
746	pos_x = pos_x + pdx(i)
747	CYCLE xloop
748	ENDIF
749	!
750	!-- Skip particle release if particle position is
751	!-- below surface, or within topography in case
752	!-- of overhanging structures.
753	ELSEIF ( .NOT. seed_follows_topography .AND. &
754	tmp_particle%z <= zw(k_surf) .OR. &
755	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
756	THEN
757	pos_x = pos_x + pdx(i)
758	CYCLE xloop
759	ENDIF
760
761	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
762
763	IF ( .NOT. first_stride ) THEN
764	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
765	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
766	ENDIF
767	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
768	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
769	ENDIF
770	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
771
772	ENDIF
773	ENDDO
774
775	ENDIF
776
777	pos_x = pos_x + pdx(i)
778
779	ENDDO xloop
780
781	ENDIF
782
783	pos_y = pos_y + pdy(i)
784
785	ENDDO
786
787	ENDIF
788
789	pos_z = pos_z + pdz(i)
790
791	ENDDO
792
793	ENDDO
794
795	IF ( first_stride ) THEN
796	DO ip = nxl, nxr
797	DO jp = nys, nyn
798	DO kp = nzb+1, nzt
799	IF ( phase == PHASE_INIT ) THEN
800	IF ( local_count(kp,jp,ip) > 0 ) THEN
801	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
802	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
803	min_nr_particle )
804	ELSE
805	alloc_size = min_nr_particle
806	ENDIF
807	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
808	DO n = 1, alloc_size
809	grid_particles(kp,jp,ip)%particles(n) = zero_particle
810	ENDDO
811	ELSEIF ( phase == PHASE_RELEASE ) THEN
812	IF ( local_count(kp,jp,ip) > 0 ) THEN
813	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
814	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
815	alloc_factor / 100.0_wp ) ), min_nr_particle )
816	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
817	CALL realloc_particles_array(ip,jp,kp,alloc_size)
818	ENDIF
819	ENDIF
820	ENDIF
821	ENDDO
822	ENDDO
823	ENDDO
824	ENDIF
825
826	ENDDO
827
828
829
830	local_start = prt_count+1
831	prt_count = local_count
832
833	!
834	!-- Calculate particle IDs
835	DO ip = nxl, nxr
836	DO jp = nys, nyn
837	DO kp = nzb+1, nzt
838	number_of_particles = prt_count(kp,jp,ip)
839	IF ( number_of_particles <= 0 ) CYCLE
840	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
841
842	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
843
844	particles(n)%id = 10000_idp*3 grid_particles(kp,jp,ip)%id_counter + &
845	10000_idp*2 kp + 10000_idp * jp + ip
846	!
847	!-- Count the number of particles that have been released before
848	grid_particles(kp,jp,ip)%id_counter = &
849	grid_particles(kp,jp,ip)%id_counter + 1
850
851	ENDDO
852
853	ENDDO
854	ENDDO
855	ENDDO
856
857	!
858	!-- Initialize aerosol background spectrum
859	IF ( curvature_solution_effects .AND. .NOT. monodisperse_aerosols ) THEN
860	CALL lpm_init_aerosols(local_start)
861	ENDIF
862
863	!
864	!-- Add random fluctuation to particle positions.
865	IF ( random_start_position ) THEN
866	DO ip = nxl, nxr
867	DO jp = nys, nyn
868	DO kp = nzb+1, nzt
869	number_of_particles = prt_count(kp,jp,ip)
870	IF ( number_of_particles <= 0 ) CYCLE
871	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
872	!
873	!-- Move only new particles. Moreover, limit random fluctuation
874	!-- in order to prevent that particles move more than one grid box,
875	!-- which would lead to problems concerning particle exchange
876	!-- between processors in case pdx/pdy are larger than dx/dy,
877	!-- respectively.
878	DO n = local_start(kp,jp,ip), number_of_particles
879	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
880	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
881	pdx(particles(n)%group)
882	particles(n)%x = particles(n)%x + &
883	MERGE( rand_contr, SIGN( dx, rand_contr ), &
884	ABS( rand_contr ) < dx &
885	)
886	ENDIF
887	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
888	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
889	pdy(particles(n)%group)
890	particles(n)%y = particles(n)%y + &
891	MERGE( rand_contr, SIGN( dy, rand_contr ), &
892	ABS( rand_contr ) < dy &
893	)
894	ENDIF
895	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
896	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
897	pdz(particles(n)%group)
898	particles(n)%z = particles(n)%z + &
899	MERGE( rand_contr, SIGN( dz, rand_contr ), &
900	ABS( rand_contr ) < dz &
901	)
902	ENDIF
903	ENDDO
904	!
905	!-- Identify particles located outside the model domain and reflect
906	!-- or absorb them if necessary.
907	CALL lpm_boundary_conds( 'bottom/top' )
908	!
909	!-- Furthermore, remove particles located in topography. Note, as
910	!-- the particle speed is still zero at this point, wall
911	!-- reflection boundary conditions will not work in this case.
912	particles => &
913	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
914	DO n = local_start(kp,jp,ip), number_of_particles
915	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
916	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
917	k = particles(n)%z / dz + 1 + offset_ocean_nzt
918	!
919	!-- Check if particle is within topography
920	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
921	particles(n)%particle_mask = .FALSE.
922	deleted_particles = deleted_particles + 1
923	ENDIF
924
925	ENDDO
926	ENDDO
927	ENDDO
928	ENDDO
929	!
930	!-- Exchange particles between grid cells and processors
931	CALL lpm_move_particle
932	CALL lpm_exchange_horiz
933
934	ENDIF
935	!
936	!-- In case of random_start_position, delete particles identified by
937	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
938	!-- which is needed for a fast interpolation of the LES fields on the particle
939	!-- position.
940	CALL lpm_pack_all_arrays
941
942	!
943	!-- Determine the current number of particles
944	DO ip = nxl, nxr
945	DO jp = nys, nyn
946	DO kp = nzb+1, nzt
947	number_of_particles = number_of_particles &
948	+ prt_count(kp,jp,ip)
949	ENDDO
950	ENDDO
951	ENDDO
952	!
953	!-- Calculate the number of particles of the total domain
954	#if defined( __parallel )
955	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
956	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
957	MPI_INTEGER, MPI_SUM, comm2d, ierr )
958	#else
959	total_number_of_particles = number_of_particles
960	#endif
961
962	RETURN
963
964	END SUBROUTINE lpm_create_particle
965
966	SUBROUTINE lpm_init_aerosols(local_start)
967
968	USE arrays_3d, &
969	ONLY: hyp, pt, q
970
971	USE cloud_parameters, &
972	ONLY: l_d_rv, rho_l, r_v
973
974	USE constants, &
975	ONLY: pi
976
977	USE kinds
978
979	USE particle_attributes, &
980	ONLY: init_aerosol_probabilistic, molecular_weight_of_solute, &
981	molecular_weight_of_water, n1, n2, n3, rho_s, rm1, rm2, rm3, &
982	s1, s2, s3, vanthoff
983
984	IMPLICIT NONE
985
986	REAL(wp), DIMENSION(:), ALLOCATABLE :: cdf !< CDF of aerosol spectrum
987	REAL(wp), DIMENSION(:), ALLOCATABLE :: r_temp !< dry aerosol radius spectrum
988
989	REAL(wp) :: afactor !< curvature effects
990	REAL(wp) :: bfactor !< solute effects
991	REAL(wp) :: dr !< width of radius bin
992	REAL(wp) :: e_a !< vapor pressure
993	REAL(wp) :: e_s !< saturation vapor pressure
994	REAL(wp) :: n_init !< sum of all aerosol concentrations
995	REAL(wp) :: pdf !< PDF of aerosol spectrum
996	REAL(wp) :: rmin = 1.0e-8_wp !< minimum aerosol radius
997	REAL(wp) :: rmax = 1.0e-6_wp !< maximum aerosol radius
998	REAL(wp) :: rs_rand !< random number
999	REAL(wp) :: r_mid !< mean radius
1000	REAL(wp) :: sigma !< surface tension
1001	REAL(wp) :: t_int !< temperature
1002	REAL(wp) :: weight_sum !< sum of all weighting factors
1003
1004	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1005
1006	INTEGER(iwp) :: n !<
1007	INTEGER(iwp) :: nn !<
1008	INTEGER(iwp) :: no_bins = 999 !< number of bins
1009	INTEGER(iwp) :: ip !<
1010	INTEGER(iwp) :: jp !<
1011	INTEGER(iwp) :: kp !<
1012
1013	LOGICAL :: new_pdf = .FALSE. !< check if aerosol PDF has to be recalculated
1014
1015	!
1016	!-- Compute aerosol background distribution
1017	IF ( init_aerosol_probabilistic ) THEN
1018	ALLOCATE( cdf(0:no_bins), r_temp(0:no_bins) )
1019	DO n = 0, no_bins
1020	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1021	REAL(no_bins, KIND=wp) * REAL(n, KIND=wp) )
1022
1023	cdf(n) = 0.0_wp
1024	n_init = n1 + n2 + n3
1025	IF ( n1 > 0.0_wp ) THEN
1026	cdf(n) = cdf(n) + n1 / n_init * ( 0.5_wp + 0.5_wp * &
1027	ERF( LOG( r_temp(n) / rm1 ) / &
1028	( SQRT(2.0_wp) * LOG(s1) ) &
1029	) )
1030	ENDIF
1031	IF ( n2 > 0.0_wp ) THEN
1032	cdf(n) = cdf(n) + n2 / n_init * ( 0.5_wp + 0.5_wp * &
1033	ERF( LOG( r_temp(n) / rm2 ) / &
1034	( SQRT(2.0_wp) * LOG(s2) ) &
1035	) )
1036	ENDIF
1037	IF ( n3 > 0.0_wp ) THEN
1038	cdf(n) = cdf(n) + n3 / n_init * ( 0.5_wp + 0.5_wp * &
1039	ERF( LOG( r_temp(n) / rm3 ) / &
1040	( SQRT(2.0_wp) * LOG(s3) ) &
1041	) )
1042	ENDIF
1043
1044	ENDDO
1045	ENDIF
1046
1047	DO ip = nxl, nxr
1048	DO jp = nys, nyn
1049	DO kp = nzb+1, nzt
1050
1051	number_of_particles = prt_count(kp,jp,ip)
1052	IF ( number_of_particles <= 0 ) CYCLE
1053	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1054	!
1055	!-- Initialize the aerosols with a predefined spectral distribution
1056	!-- of the dry radius (logarithmically increasing bins) and a varying
1057	!-- weighting factor
1058	IF ( .NOT. init_aerosol_probabilistic ) THEN
1059
1060	new_pdf = .FALSE.
1061	IF ( .NOT. ALLOCATED( r_temp ) ) THEN
1062	new_pdf = .TRUE.
1063	ELSE
1064	IF ( SIZE( r_temp ) .NE. &
1065	number_of_particles - local_start(kp,jp,ip) + 2 ) THEN
1066	new_pdf = .TRUE.
1067	DEALLOCATE( r_temp )
1068	ENDIF
1069	ENDIF
1070
1071	IF ( new_pdf ) THEN
1072
1073	no_bins = number_of_particles + 1 - local_start(kp,jp,ip)
1074	ALLOCATE( r_temp(0:no_bins) )
1075
1076	DO n = 0, no_bins
1077	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1078	REAL(no_bins, KIND=wp) * &
1079	REAL(n, KIND=wp) )
1080	ENDDO
1081
1082	ENDIF
1083
1084	!
1085	!-- Calculate radius and concentration of each aerosol
1086	DO n = local_start(kp,jp,ip), number_of_particles
1087
1088	nn = n - local_start(kp,jp,ip)
1089
1090	r_mid = SQRT( r_temp(nn) * r_temp(nn+1) )
1091	dr = r_temp(nn+1) - r_temp(nn)
1092
1093	pdf = 0.0_wp
1094	n_init = n1 + n2 + n3
1095	IF ( n1 > 0.0_wp ) THEN
1096	pdf = pdf + n1 / n_init * ( 1.0_wp / ( r_mid * LOG(s1) * &
1097	SQRT( 2.0_wp * pi ) &
1098	) * &
1099	EXP( -( LOG( r_mid / rm1 ) )**2 / &
1100	( 2.0_wp * LOG(s1)**2 ) &
1101	) &
1102	)
1103	ENDIF
1104	IF ( n2 > 0.0_wp ) THEN
1105	pdf = pdf + n2 / n_init * ( 1.0_wp / ( r_mid * LOG(s2) * &
1106	SQRT( 2.0_wp * pi ) &
1107	) * &
1108	EXP( -( LOG( r_mid / rm2 ) )**2 / &
1109	( 2.0_wp * LOG(s2)**2 ) &
1110	) &
1111	)
1112	ENDIF
1113	IF ( n3 > 0.0_wp ) THEN
1114	pdf = pdf + n3 / n_init * ( 1.0_wp / ( r_mid * LOG(s3) * &
1115	SQRT( 2.0_wp * pi ) &
1116	) * &
1117	EXP( -( LOG( r_mid / rm3 ) )**2 / &
1118	( 2.0_wp * LOG(s3)**2 ) &
1119	) &
1120	)
1121	ENDIF
1122
1123	particles(n)%rvar2 = r_mid
1124	particles(n)%weight_factor = pdf * dr
1125
1126	END DO
1127	!
1128	!-- Adjust weighting factors to initialize the same number of aerosols
1129	!-- in every grid box
1130	weight_sum = SUM(particles(local_start(kp,jp,ip):number_of_particles)%weight_factor)
1131
1132	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor = &
1133	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor / &
1134	weight_sum * initial_weighting_factor * ( no_bins + 1 )
1135
1136	ENDIF
1137	!
1138	!-- Initialize the aerosols with a predefined weighting factor but
1139	!-- a randomly choosen dry radius
1140	IF ( init_aerosol_probabilistic ) THEN
1141
1142	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1143
1144	rs_rand = -1.0_wp
1145	DO WHILE ( rs_rand .LT. cdf(0) .OR. rs_rand .GE. cdf(no_bins) )
1146	rs_rand = random_function( iran_part )
1147	ENDDO
1148	!
1149	!-- Determine aerosol dry radius by a random number generator
1150	DO nn = 0, no_bins-1
1151	IF ( cdf(nn) .LE. rs_rand .AND. cdf(nn+1) .GT. rs_rand ) THEN
1152	particles(n)%rvar2 = r_temp(nn) + ( r_temp(nn+1) - r_temp(nn) ) / &
1153	( cdf(nn+1) - cdf(nn) ) * ( rs_rand - cdf(nn) )
1154	EXIT
1155	ENDIF
1156	ENDDO
1157
1158	ENDDO
1159
1160	ENDIF
1161
1162	!
1163	!-- Set particle radius to equilibrium radius based on the environmental
1164	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1165	!-- the sometimes lengthy growth toward their equilibrium radius within
1166	!-- the simulation.
1167	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1168
1169	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
1170	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
1171
1172	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1173	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1174
1175	bfactor = vanthoff * molecular_weight_of_water * &
1176	rho_s / ( molecular_weight_of_solute * rho_l )
1177	!
1178	!-- The formula is only valid for subsaturated environments. For
1179	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1180	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1181
1182	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1183	!
1184	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1185	!-- Curry (2007, JGR)
1186	particles(n)%radius = bfactor*0.3333333_wp &
1187	particles(n)%rvar2 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1188	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1189	particles(n)%rvar2 ) ) / &
1190	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1191	)
1192
1193	ENDDO
1194
1195	ENDDO
1196	ENDDO
1197	ENDDO
1198	!
1199	!-- Deallocate used arrays
1200	IF ( ALLOCATED(r_temp) ) DEALLOCATE( r_temp )
1201	IF ( ALLOCATED(cdf) ) DEALLOCATE( cdf )
1202
1203	END SUBROUTINE lpm_init_aerosols
1204
1205	END MODULE lpm_init_mod

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