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source: palm/trunk/SOURCE/lpm_init.f90 @ 2195

Last change on this file since 2195 was 2183, checked in by schwenkel, 8 years ago
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[1873]	1	!> @file lpm_init.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	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.
[1036]	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[254]	20	! Current revisions:
[1]	21	! -----------------
[1930]	22	!
[2183]	23	!
[1930]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_init.f90 2183 2017-03-17 14:29:15Z raasch $
	27	!
[2183]	28	! 2182 2017-03-17 14:27:40Z schwenkel
	29	! Added parameters for simplified particle initialization.
	30	!
[2123]	31	! 2122 2017-01-18 12:22:54Z hoffmann
	32	! Improved initialization of equilibrium aerosol radii
	33	! Calculation of particle ID
	34	!
[2001]	35	! 2000 2016-08-20 18:09:15Z knoop
	36	! Forced header and separation lines into 80 columns
	37	!
[1930]	38	! 2016-06-09 16:25:25Z suehring
[1929]	39	! Bugfix in determining initial particle height and grid index in case of
	40	! seed_follows_topography.
	41	! Bugfix concerning random positions, ensure that particles do not move more
	42	! than one grid length.
	43	! Bugfix logarithmic interpolation.
	44	! Initial setting of sgs_wf_part.
[1321]	45	!
[1891]	46	! 1890 2016-04-22 08:52:11Z hoffmann
	47	! Initialization of aerosol equilibrium radius not possible in supersaturated
	48	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
	49	! initialization.
	50	!
[1874]	51	! 1873 2016-04-18 14:50:06Z maronga
[1929]	52	! Module renamed (removed _mod
[1874]	53	!
[1872]	54	! 1871 2016-04-15 11:46:09Z hoffmann
	55	! Initialization of aerosols added.
	56	!
[1851]	57	! 1850 2016-04-08 13:29:27Z maronga
	58	! Module renamed
	59	!
[1832]	60	! 1831 2016-04-07 13:15:51Z hoffmann
	61	! curvature_solution_effects moved to particle_attributes
	62	!
[1823]	63	! 1822 2016-04-07 07:49:42Z hoffmann
	64	! Unused variables removed.
	65	!
[1784]	66	! 1783 2016-03-06 18:36:17Z raasch
	67	! netcdf module added
	68	!
[1726]	69	! 1725 2015-11-17 13:01:51Z hoffmann
	70	! Bugfix: Processor-dependent seed for random function is generated before it is
	71	! used.
	72	!
[1692]	73	! 1691 2015-10-26 16:17:44Z maronga
	74	! Renamed prandtl_layer to constant_flux_layer.
	75	!
[1686]	76	! 1685 2015-10-08 07:32:13Z raasch
	77	! bugfix concerning vertical index offset in case of ocean
	78	!
[1683]	79	! 1682 2015-10-07 23:56:08Z knoop
	80	! Code annotations made doxygen readable
	81	!
[1576]	82	! 1575 2015-03-27 09:56:27Z raasch
	83	! initial vertical particle position is allowed to follow the topography
	84	!
[1360]	85	! 1359 2014-04-11 17:15:14Z hoffmann
	86	! New particle structure integrated.
	87	! Kind definition added to all floating point numbers.
	88	! lpm_init changed form a subroutine to a module.
	89	!
[1329]	90	! 1327 2014-03-21 11:00:16Z raasch
	91	! -netcdf_output
	92	!
[1323]	93	! 1322 2014-03-20 16:38:49Z raasch
	94	! REAL functions provided with KIND-attribute
	95	!
[1321]	96	! 1320 2014-03-20 08:40:49Z raasch
[1320]	97	! ONLY-attribute added to USE-statements,
	98	! kind-parameters added to all INTEGER and REAL declaration statements,
	99	! kinds are defined in new module kinds,
	100	! revision history before 2012 removed,
	101	! comment fields (!:) to be used for variable explanations added to
	102	! all variable declaration statements
	103	! bugfix: #if defined( __parallel ) added
[850]	104	!
[1315]	105	! 1314 2014-03-14 18:25:17Z suehring
	106	! Vertical logarithmic interpolation of horizontal particle speed for particles
	107	! between roughness height and first vertical grid level.
	108	!
[1093]	109	! 1092 2013-02-02 11:24:22Z raasch
	110	! unused variables removed
	111	!
[1037]	112	! 1036 2012-10-22 13:43:42Z raasch
	113	! code put under GPL (PALM 3.9)
	114	!
[850]	115	! 849 2012-03-15 10:35:09Z raasch
[849]	116	! routine renamed: init_particles -> lpm_init
	117	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
	118	! advec_particles),
	119	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
[392]	120	!
[829]	121	! 828 2012-02-21 12:00:36Z raasch
	122	! call of init_kernels, particle feature color renamed class
	123	!
[826]	124	! 824 2012-02-17 09:09:57Z raasch
	125	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
	126	! array particles implemented as pointer
	127	!
[668]	128	! 667 2010-12-23 12:06:00Z suehring/gryschka
	129	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
	130	! of arrays.
	131	!
[1]	132	! Revision 1.1 1999/11/25 16:22:38 raasch
	133	! Initial revision
	134	!
	135	!
	136	! Description:
	137	! ------------
[1682]	138	!> This routine initializes a set of particles and their attributes (position,
	139	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
[1]	140	!------------------------------------------------------------------------------!
[1682]	141	MODULE lpm_init_mod
	142
[1]	143
[1320]	144	USE arrays_3d, &
	145	ONLY: de_dx, de_dy, de_dz, zu, zw, z0
	146
	147	USE control_parameters, &
[1691]	148	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
[1783]	149	dz, initializing_actions, message_string, ocean, simulated_time
[1320]	150
	151	USE grid_variables, &
[1359]	152	ONLY: ddx, dx, ddy, dy
[1320]	153
	154	USE indices, &
[1575]	155	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
	156	nzb_w_inner, nzt
[1320]	157
	158	USE kinds
	159
	160	USE lpm_collision_kernels_mod, &
	161	ONLY: init_kernels
	162
[1783]	163	USE netcdf_interface, &
	164	ONLY: netcdf_data_format
	165
[1320]	166	USE particle_attributes, &
[1359]	167	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
	168	block_offset, block_offset_def, collision_kernel, &
[1831]	169	curvature_solution_effects, &
[1822]	170	density_ratio, grid_particles, &
[1359]	171	initial_weighting_factor, ibc_par_b, ibc_par_lr, ibc_par_ns, &
	172	ibc_par_t, iran_part, log_z_z0, &
	173	max_number_of_particle_groups, maximum_number_of_particles, &
[1822]	174	min_nr_particle, mpi_particle_type, &
[2182]	175	number_concentration, number_particles_per_gridbox, &
[1822]	176	number_of_particles, &
[1320]	177	number_of_particle_groups, number_of_sublayers, &
[1822]	178	offset_ocean_nzt, offset_ocean_nzt_m1, &
[1359]	179	particles, particle_advection_start, particle_groups, &
	180	particle_groups_type, particles_per_point, &
[1822]	181	particle_type, pdx, pdy, pdz, &
[1359]	182	prt_count, psb, psl, psn, psr, pss, pst, &
[1320]	183	radius, random_start_position, read_particles_from_restartfile,&
[1929]	184	seed_follows_topography, sgs_wf_part, sort_count, &
[1822]	185	total_number_of_particles, &
	186	use_sgs_for_particles, &
[1359]	187	write_particle_statistics, uniform_particles, zero_particle, &
	188	z0_av_global
[1320]	189
[1]	190	USE pegrid
	191
[1320]	192	USE random_function_mod, &
	193	ONLY: random_function
[1]	194
[1359]	195	IMPLICIT NONE
[1320]	196
[1359]	197	PRIVATE
	198
[1682]	199	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
	200	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
[1359]	201
	202	INTERFACE lpm_init
	203	MODULE PROCEDURE lpm_init
	204	END INTERFACE lpm_init
	205
	206	INTERFACE lpm_create_particle
	207	MODULE PROCEDURE lpm_create_particle
	208	END INTERFACE lpm_create_particle
	209
	210	PUBLIC lpm_init, lpm_create_particle
	211
[1929]	212	CONTAINS
[1359]	213
[1682]	214	!------------------------------------------------------------------------------!
	215	! Description:
	216	! ------------
	217	!> @todo Missing subroutine description.
	218	!------------------------------------------------------------------------------!
[1359]	219	SUBROUTINE lpm_init
	220
	221	USE lpm_collision_kernels_mod, &
	222	ONLY: init_kernels
	223
[1]	224	IMPLICIT NONE
	225
[1682]	226	INTEGER(iwp) :: i !<
	227	INTEGER(iwp) :: j !<
	228	INTEGER(iwp) :: k !<
[1320]	229
[1]	230	#if defined( __parallel )
[1682]	231	INTEGER(iwp), DIMENSION(3) :: blocklengths !<
	232	INTEGER(iwp), DIMENSION(3) :: displacements !<
	233	INTEGER(iwp), DIMENSION(3) :: types !<
[1]	234	#endif
	235
[2182]	236	REAL(wp) :: div !<
[1682]	237	REAL(wp) :: height_int !<
	238	REAL(wp) :: height_p !<
	239	REAL(wp) :: z_p !<
	240	REAL(wp) :: z0_av_local !<
[1]	241
	242	#if defined( __parallel )
	243	!
	244	!-- Define MPI derived datatype for FORTRAN datatype particle_type (see module
[82]	245	!-- particle_attributes). Integer length is 4 byte, Real is 8 byte
[1359]	246	blocklengths(1) = 19; blocklengths(2) = 6; blocklengths(3) = 1
	247	displacements(1) = 0; displacements(2) = 152; displacements(3) = 176
	248
[1]	249	types(1) = MPI_REAL
	250	types(2) = MPI_INTEGER
	251	types(3) = MPI_UB
	252	CALL MPI_TYPE_STRUCT( 3, blocklengths, displacements, types, &
	253	mpi_particle_type, ierr )
	254	CALL MPI_TYPE_COMMIT( mpi_particle_type, ierr )
	255	#endif
	256
	257	!
[150]	258	!-- In case of oceans runs, the vertical index calculations need an offset,
	259	!-- because otherwise the k indices will become negative
	260	IF ( ocean ) THEN
	261	offset_ocean_nzt = nzt
	262	offset_ocean_nzt_m1 = nzt - 1
	263	ENDIF
	264
[1359]	265	!
	266	!-- Define block offsets for dividing a gridcell in 8 sub cells
[150]	267
[1359]	268	block_offset(0) = block_offset_def (-1,-1,-1)
	269	block_offset(1) = block_offset_def (-1,-1, 0)
	270	block_offset(2) = block_offset_def (-1, 0,-1)
	271	block_offset(3) = block_offset_def (-1, 0, 0)
	272	block_offset(4) = block_offset_def ( 0,-1,-1)
	273	block_offset(5) = block_offset_def ( 0,-1, 0)
	274	block_offset(6) = block_offset_def ( 0, 0,-1)
	275	block_offset(7) = block_offset_def ( 0, 0, 0)
[150]	276	!
[1]	277	!-- Check the number of particle groups.
	278	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
[274]	279	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
	280	max_number_of_particle_groups , &
[254]	281	'&number_of_particle_groups reset to ', &
	282	max_number_of_particle_groups
[849]	283	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
[1]	284	number_of_particle_groups = max_number_of_particle_groups
	285	ENDIF
	286
	287	!
	288	!-- Set default start positions, if necessary
[1359]	289	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
	290	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
	291	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
	292	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
	293	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
	294	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
[1]	295
[1359]	296	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
	297	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
	298	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
[1]	299
[2182]	300	!
	301	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
	302	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
	303	IF ( number_particles_per_gridbox /= -1 .AND. &
	304	number_particles_per_gridbox >= 1 ) THEN
	305	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
	306	REAL(number_particles_per_gridbox))**0.3333333_wp
	307	!
	308	!-- Ensure a smooth value (two significant digits) of distance between
	309	!-- particles (pdx, pdy, pdz).
	310	div = 1000.0_wp
	311	DO WHILE ( pdx(1) < div )
	312	div = div / 10.0_wp
	313	ENDDO
	314	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
	315	pdy(1) = pdx(1)
	316	pdz(1) = pdx(1)
	317
	318	ENDIF
	319
[1]	320	DO j = 2, number_of_particle_groups
[1359]	321	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
	322	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
	323	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
	324	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
	325	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
	326	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
	327	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
	328	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
	329	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
[1]	330	ENDDO
	331
	332	!
[1929]	333	!-- Allocate arrays required for calculating particle SGS velocities.
	334	!-- Initialize prefactor required for stoachastic Weil equation.
[1822]	335	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[849]	336	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	337	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	338	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
[1929]	339
	340	sgs_wf_part = 1.0_wp / 3.0_wp
[849]	341	ENDIF
	342
	343	!
[1314]	344	!-- Allocate array required for logarithmic vertical interpolation of
	345	!-- horizontal particle velocities between the surface and the first vertical
	346	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
	347	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
	348	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
	349	!-- To obtain exact height levels of particles, linear interpolation is applied
	350	!-- (see lpm_advec.f90).
[1691]	351	IF ( constant_flux_layer ) THEN
[1314]	352
	353	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
	354	z_p = zu(nzb+1) - zw(nzb)
	355
	356	!
	357	!-- Calculate horizontal mean value of z0 used for logartihmic
	358	!-- interpolation. Note: this is not exact for heterogeneous z0.
	359	!-- However, sensitivity studies showed that the effect is
	360	!-- negligible.
	361	z0_av_local = SUM( z0(nys:nyn,nxl:nxr) )
[1359]	362	z0_av_global = 0.0_wp
[1314]	363
[1320]	364	#if defined( __parallel )
[1314]	365	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
	366	comm2d, ierr )
[1320]	367	#else
	368	z0_av_global = z0_av_local
	369	#endif
[1314]	370
	371	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
	372	!
	373	!-- Horizontal wind speed is zero below and at z0
[1359]	374	log_z_z0(0) = 0.0_wp
[1314]	375	!
	376	!-- Calculate vertical depth of the sublayers
[1322]	377	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
[1314]	378	!
	379	!-- Precalculate LOG(z/z0)
[1929]	380	height_p = z0_av_global
[1314]	381	DO k = 1, number_of_sublayers
	382
	383	height_p = height_p + height_int
	384	log_z_z0(k) = LOG( height_p / z0_av_global )
	385
	386	ENDDO
	387
	388	ENDIF
	389
	390	!
[1359]	391	!-- Check boundary condition and set internal variables
	392	SELECT CASE ( bc_par_b )
	393
	394	CASE ( 'absorb' )
	395	ibc_par_b = 1
	396
	397	CASE ( 'reflect' )
	398	ibc_par_b = 2
	399
	400	CASE DEFAULT
	401	WRITE( message_string, * ) 'unknown boundary condition ', &
	402	'bc_par_b = "', TRIM( bc_par_b ), '"'
	403	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
	404
	405	END SELECT
	406	SELECT CASE ( bc_par_t )
	407
	408	CASE ( 'absorb' )
	409	ibc_par_t = 1
	410
	411	CASE ( 'reflect' )
	412	ibc_par_t = 2
	413
	414	CASE DEFAULT
	415	WRITE( message_string, * ) 'unknown boundary condition ', &
	416	'bc_par_t = "', TRIM( bc_par_t ), '"'
	417	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
	418
	419	END SELECT
	420	SELECT CASE ( bc_par_lr )
	421
	422	CASE ( 'cyclic' )
	423	ibc_par_lr = 0
	424
	425	CASE ( 'absorb' )
	426	ibc_par_lr = 1
	427
	428	CASE ( 'reflect' )
	429	ibc_par_lr = 2
	430
	431	CASE DEFAULT
	432	WRITE( message_string, * ) 'unknown boundary condition ', &
	433	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
	434	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
	435
	436	END SELECT
	437	SELECT CASE ( bc_par_ns )
	438
	439	CASE ( 'cyclic' )
	440	ibc_par_ns = 0
	441
	442	CASE ( 'absorb' )
	443	ibc_par_ns = 1
	444
	445	CASE ( 'reflect' )
	446	ibc_par_ns = 2
	447
	448	CASE DEFAULT
	449	WRITE( message_string, * ) 'unknown boundary condition ', &
	450	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
	451	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
	452
	453	END SELECT
	454
	455	!
[828]	456	!-- Initialize collision kernels
	457	IF ( collision_kernel /= 'none' ) CALL init_kernels
	458
	459	!
[1]	460	!-- For the first model run of a possible job chain initialize the
[849]	461	!-- particles, otherwise read the particle data from restart file.
[1]	462	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
	463	.AND. read_particles_from_restartfile ) THEN
	464
[849]	465	CALL lpm_read_restart_file
[1]	466
	467	ELSE
	468
	469	!
	470	!-- Allocate particle arrays and set attributes of the initial set of
	471	!-- particles, which can be also periodically released at later times.
[1359]	472	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	473	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
[1]	474
[1359]	475	maximum_number_of_particles = 0
	476	number_of_particles = 0
[792]	477
	478	sort_count = 0
[1359]	479	prt_count = 0
[792]	480
[1]	481	!
[2122]	482	!-- initialize counter for particle IDs
	483	grid_particles%id_counter = 0
	484
	485	!
[1]	486	!-- Initialize all particles with dummy values (otherwise errors may
	487	!-- occur within restart runs). The reason for this is still not clear
	488	!-- and may be presumably caused by errors in the respective user-interface.
[1359]	489	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	490	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	491	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
[2122]	492	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	493	0, 0, 0, 0, .FALSE., -1 )
[1822]	494
[1359]	495	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[1]	496
	497	!
	498	!-- Set values for the density ratio and radius for all particle
	499	!-- groups, if necessary
[1359]	500	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
	501	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
[1]	502	DO i = 2, number_of_particle_groups
[1359]	503	IF ( density_ratio(i) == 9999999.9_wp ) THEN
[1]	504	density_ratio(i) = density_ratio(i-1)
	505	ENDIF
[1359]	506	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
[1]	507	ENDDO
	508
	509	DO i = 1, number_of_particle_groups
[1359]	510	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
[254]	511	WRITE( message_string, * ) 'particle group #', i, 'has a', &
	512	'density ratio /= 0 but radius = 0'
[849]	513	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
[1]	514	ENDIF
	515	particle_groups(i)%density_ratio = density_ratio(i)
	516	particle_groups(i)%radius = radius(i)
	517	ENDDO
	518
	519	!
[1359]	520	!-- Set a seed value for the random number generator to be exclusively
	521	!-- used for the particle code. The generated random numbers should be
	522	!-- different on the different PEs.
	523	iran_part = iran_part + myid
	524
[1725]	525	CALL lpm_create_particle (PHASE_INIT)
[1359]	526	!
	527	!-- User modification of initial particles
	528	CALL user_lpm_init
	529
	530	!
	531	!-- Open file for statistical informations about particle conditions
	532	IF ( write_particle_statistics ) THEN
	533	CALL check_open( 80 )
	534	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
	535	number_of_particles, &
	536	maximum_number_of_particles
	537	CALL close_file( 80 )
	538	ENDIF
	539
	540	ENDIF
	541
	542	!
	543	!-- To avoid programm abort, assign particles array to the local version of
	544	!-- first grid cell
	545	number_of_particles = prt_count(nzb+1,nys,nxl)
	546	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
	547	!
	548	!-- Formats
	549	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
	550
	551	END SUBROUTINE lpm_init
	552
[1682]	553	!------------------------------------------------------------------------------!
	554	! Description:
	555	! ------------
	556	!> @todo Missing subroutine description.
	557	!------------------------------------------------------------------------------!
[1359]	558	SUBROUTINE lpm_create_particle (phase)
	559
	560	USE lpm_exchange_horiz_mod, &
	561	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
	562
	563	USE lpm_pack_arrays_mod, &
	564	ONLY: lpm_pack_all_arrays
	565
[1871]	566	USE particle_attributes, &
[1929]	567	ONLY: deleted_particles, monodisperse_aerosols
[1871]	568
[1359]	569	IMPLICIT NONE
	570
[1929]	571	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
	572	INTEGER(iwp) :: i !< loop variable ( particle groups )
	573	INTEGER(iwp) :: ip !< index variable along x
	574	INTEGER(iwp) :: j !< loop variable ( particles per point )
	575	INTEGER(iwp) :: jp !< index variable along y
	576	INTEGER(iwp) :: kp !< index variable along z
	577	INTEGER(iwp) :: loop_stride !< loop variable for initialization
	578	INTEGER(iwp) :: n !< loop variable ( number of particles )
	579	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
[1359]	580
[1929]	581	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
[1359]	582
[1929]	583	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
	584	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
[1359]	585
[1929]	586	LOGICAL :: first_stride !< flag for initialization
[1359]	587
[1929]	588	REAL(wp) :: pos_x !< increment for particle position in x
	589	REAL(wp) :: pos_y !< increment for particle position in y
	590	REAL(wp) :: pos_z !< increment for particle position in z
	591	REAL(wp) :: rand_contr !< dummy argument for random position
[1359]	592
[1929]	593	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
[1359]	594
	595	!
	596	!-- Calculate particle positions and store particle attributes, if
	597	!-- particle is situated on this PE
	598	DO loop_stride = 1, 2
	599	first_stride = (loop_stride == 1)
	600	IF ( first_stride ) THEN
	601	local_count = 0 ! count number of particles
	602	ELSE
	603	local_count = prt_count ! Start address of new particles
	604	ENDIF
	605
[2182]	606	!
	607	!-- Calculate initial_weighting_factor diagnostically
	608	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
	609	initial_weighting_factor = number_concentration * 1.0E6_wp * &
	610	pdx(1) * pdy(1) * pdz(1)
	611	END IF
	612
[1]	613	n = 0
	614	DO i = 1, number_of_particle_groups
	615
	616	pos_z = psb(i)
	617
	618	DO WHILE ( pos_z <= pst(i) )
	619
	620	pos_y = pss(i)
	621
	622	DO WHILE ( pos_y <= psn(i) )
	623
[1359]	624	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
	625	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
[1]	626
	627	pos_x = psl(i)
	628
[1575]	629	xloop: DO WHILE ( pos_x <= psr(i) )
[1]	630
[1359]	631	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
	632	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
[1]	633
	634	DO j = 1, particles_per_point
	635
	636	n = n + 1
[1359]	637	tmp_particle%x = pos_x
	638	tmp_particle%y = pos_y
	639	tmp_particle%z = pos_z
	640	tmp_particle%age = 0.0_wp
	641	tmp_particle%age_m = 0.0_wp
	642	tmp_particle%dt_sum = 0.0_wp
[2122]	643	tmp_particle%user = 0.0_wp !unused, free for the user
[1359]	644	tmp_particle%e_m = 0.0_wp
[824]	645	IF ( curvature_solution_effects ) THEN
	646	!
	647	!-- Initial values (internal timesteps, derivative)
	648	!-- for Rosenbrock method
[1871]	649	tmp_particle%rvar1 = 1.0E-6_wp !last Rosenbrock timestep
	650	tmp_particle%rvar2 = 0.1E-6_wp !dry aerosol radius
[2122]	651	tmp_particle%rvar3 = -9999999.9_wp !unused in this configuration
[824]	652	ELSE
	653	!
	654	!-- Initial values for SGS velocities
[1359]	655	tmp_particle%rvar1 = 0.0_wp
	656	tmp_particle%rvar2 = 0.0_wp
	657	tmp_particle%rvar3 = 0.0_wp
[824]	658	ENDIF
[1359]	659	tmp_particle%speed_x = 0.0_wp
	660	tmp_particle%speed_y = 0.0_wp
	661	tmp_particle%speed_z = 0.0_wp
	662	tmp_particle%origin_x = pos_x
	663	tmp_particle%origin_y = pos_y
	664	tmp_particle%origin_z = pos_z
	665	tmp_particle%radius = particle_groups(i)%radius
	666	tmp_particle%weight_factor = initial_weighting_factor
	667	tmp_particle%class = 1
	668	tmp_particle%group = i
[2122]	669	tmp_particle%id1 = 0
	670	tmp_particle%id2 = 0
[1359]	671	tmp_particle%particle_mask = .TRUE.
[2122]	672	tmp_particle%block_nr = -1
[1]	673	!
[1575]	674	!-- Determine the grid indices of the particle position
[1359]	675	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
	676	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
[1685]	677	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
[1]	678
[1575]	679	IF ( seed_follows_topography ) THEN
	680	!
	681	!-- Particle height is given relative to topography
	682	kp = kp + nzb_w_inner(jp,ip)
[1929]	683	tmp_particle%z = tmp_particle%z + &
	684	zw(nzb_w_inner(jp,ip))
[1575]	685	IF ( kp > nzt ) THEN
	686	pos_x = pos_x + pdx(i)
	687	CYCLE xloop
	688	ENDIF
[1929]	689	ELSEIF ( .NOT. seed_follows_topography .AND. &
	690	tmp_particle%z <= zw(nzb_w_inner(jp,ip)) ) THEN
	691	pos_x = pos_x + pdx(i)
	692	CYCLE xloop
[1575]	693	ENDIF
	694
[1359]	695	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
[2182]	696
[1359]	697	IF ( .NOT. first_stride ) THEN
	698	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
	699	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
	700	ENDIF
	701	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
	702	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
	703	ENDIF
	704	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
[1929]	705
[1359]	706	ENDIF
[1]	707	ENDDO
	708
	709	ENDIF
	710
	711	pos_x = pos_x + pdx(i)
	712
[1575]	713	ENDDO xloop
[1]	714
	715	ENDIF
	716
	717	pos_y = pos_y + pdy(i)
	718
	719	ENDDO
	720
	721	pos_z = pos_z + pdz(i)
	722
	723	ENDDO
	724
	725	ENDDO
	726
[1359]	727	IF ( first_stride ) THEN
	728	DO ip = nxl, nxr
	729	DO jp = nys, nyn
	730	DO kp = nzb+1, nzt
	731	IF ( phase == PHASE_INIT ) THEN
	732	IF ( local_count(kp,jp,ip) > 0 ) THEN
	733	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
	734	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
	735	min_nr_particle )
	736	ELSE
	737	alloc_size = min_nr_particle
	738	ENDIF
	739	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
	740	DO n = 1, alloc_size
	741	grid_particles(kp,jp,ip)%particles(n) = zero_particle
	742	ENDDO
	743	ELSEIF ( phase == PHASE_RELEASE ) THEN
	744	IF ( local_count(kp,jp,ip) > 0 ) THEN
	745	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
	746	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
	747	alloc_factor / 100.0_wp ) ), min_nr_particle )
	748	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
[2182]	749	CALL realloc_particles_array(ip,jp,kp,alloc_size)
[1359]	750	ENDIF
	751	ENDIF
	752	ENDIF
	753	ENDDO
	754	ENDDO
	755	ENDDO
	756	ENDIF
[1929]	757
[1359]	758	ENDDO
[1]	759
[2182]	760
	761
[1359]	762	local_start = prt_count+1
	763	prt_count = local_count
[1871]	764
[1]	765	!
[2122]	766	!-- Calculate particle IDs
	767	DO ip = nxl, nxr
	768	DO jp = nys, nyn
	769	DO kp = nzb+1, nzt
	770	number_of_particles = prt_count(kp,jp,ip)
	771	IF ( number_of_particles <= 0 ) CYCLE
	772	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	773
	774	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	775
[2182]	776	particles(n)%id1 = 10000_iwp * grid_particles(kp,jp,ip)%id_counter + kp
	777	particles(n)%id2 = 10000_iwp * jp + ip
[2122]	778
	779	grid_particles(kp,jp,ip)%id_counter = &
	780	grid_particles(kp,jp,ip)%id_counter + 1
	781
	782	ENDDO
	783
	784	ENDDO
	785	ENDDO
	786	ENDDO
	787
	788	!
[1871]	789	!-- Initialize aerosol background spectrum
	790	IF ( curvature_solution_effects .AND. .NOT. monodisperse_aerosols ) THEN
	791	CALL lpm_init_aerosols(local_start)
	792	ENDIF
	793
	794	!
[1929]	795	!-- Add random fluctuation to particle positions.
[1359]	796	IF ( random_start_position ) THEN
	797	DO ip = nxl, nxr
	798	DO jp = nys, nyn
	799	DO kp = nzb+1, nzt
	800	number_of_particles = prt_count(kp,jp,ip)
	801	IF ( number_of_particles <= 0 ) CYCLE
	802	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
[1929]	803	!
	804	!-- Move only new particles. Moreover, limit random fluctuation
	805	!-- in order to prevent that particles move more than one grid box,
	806	!-- which would lead to problems concerning particle exchange
	807	!-- between processors in case pdx/pdy are larger than dx/dy,
	808	!-- respectively.
	809	DO n = local_start(kp,jp,ip), number_of_particles
[1359]	810	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
[1929]	811	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	812	pdx(particles(n)%group)
[1359]	813	particles(n)%x = particles(n)%x + &
[1929]	814	MERGE( rand_contr, SIGN( dx, rand_contr ), &
	815	ABS( rand_contr ) < dx &
	816	)
[1359]	817	ENDIF
	818	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
[1929]	819	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	820	pdy(particles(n)%group)
[1359]	821	particles(n)%y = particles(n)%y + &
[1929]	822	MERGE( rand_contr, SIGN( dy, rand_contr ), &
	823	ABS( rand_contr ) < dy &
	824	)
[1359]	825	ENDIF
	826	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
[1929]	827	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	828	pdz(particles(n)%group)
[1359]	829	particles(n)%z = particles(n)%z + &
[1929]	830	MERGE( rand_contr, SIGN( dz, rand_contr ), &
	831	ABS( rand_contr ) < dz &
	832	)
[1359]	833	ENDIF
	834	ENDDO
[1]	835	!
[1929]	836	!-- Identify particles located outside the model domain and reflect
	837	!-- or absorb them if necessary.
[1359]	838	CALL lpm_boundary_conds( 'bottom/top' )
[1929]	839	!
	840	!-- Furthermore, remove particles located in topography. Note, as
	841	!-- the particle speed is still zero at this point, wall
	842	!-- reflection boundary conditions will not work in this case.
	843	particles => &
	844	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	845	DO n = local_start(kp,jp,ip), number_of_particles
	846	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
	847	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
	848	IF ( particles(n)%z <= zw(nzb_w_inner(j,i)) ) THEN
	849	particles(n)%particle_mask = .FALSE.
	850	deleted_particles = deleted_particles + 1
	851	ENDIF
	852	ENDDO
[1359]	853	ENDDO
	854	ENDDO
	855	ENDDO
[1]	856	!
[1359]	857	!-- Exchange particles between grid cells and processors
	858	CALL lpm_move_particle
	859	CALL lpm_exchange_horiz
[1]	860
[1359]	861	ENDIF
[1]	862	!
[1359]	863	!-- In case of random_start_position, delete particles identified by
	864	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
	865	!-- which is needed for a fast interpolation of the LES fields on the particle
	866	!-- position.
	867	CALL lpm_pack_all_arrays
[1]	868
	869	!
[1359]	870	!-- Determine maximum number of particles (i.e., all possible particles that
	871	!-- have been allocated) and the current number of particles
	872	DO ip = nxl, nxr
	873	DO jp = nys, nyn
	874	DO kp = nzb+1, nzt
	875	maximum_number_of_particles = maximum_number_of_particles &
	876	+ SIZE(grid_particles(kp,jp,ip)%particles)
	877	number_of_particles = number_of_particles &
	878	+ prt_count(kp,jp,ip)
[1]	879	ENDDO
[1359]	880	ENDDO
	881	ENDDO
[1]	882	!
[1822]	883	!-- Calculate the number of particles of the total domain
[1]	884	#if defined( __parallel )
[1359]	885	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	886	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
	887	MPI_INTEGER, MPI_SUM, comm2d, ierr )
[1]	888	#else
[1359]	889	total_number_of_particles = number_of_particles
[1]	890	#endif
	891
[1359]	892	RETURN
[1]	893
[1359]	894	END SUBROUTINE lpm_create_particle
[336]	895
[1871]	896	SUBROUTINE lpm_init_aerosols(local_start)
	897
	898	USE arrays_3d, &
	899	ONLY: hyp, pt, q
	900
	901	USE cloud_parameters, &
[2122]	902	ONLY: l_d_rv, rho_l, r_v
[1871]	903
	904	USE constants, &
	905	ONLY: pi
	906
	907	USE kinds
	908
	909	USE particle_attributes, &
	910	ONLY: init_aerosol_probabilistic, molecular_weight_of_solute, &
	911	molecular_weight_of_water, n1, n2, n3, rho_s, rm1, rm2, rm3, &
	912	s1, s2, s3, vanthoff
	913
	914	IMPLICIT NONE
	915
	916	REAL(wp), DIMENSION(:), ALLOCATABLE :: cdf !< CDF of aerosol spectrum
	917	REAL(wp), DIMENSION(:), ALLOCATABLE :: r_temp !< dry aerosol radius spectrum
	918
[2122]	919	REAL(wp) :: afactor !< curvature effects
[1871]	920	REAL(wp) :: bfactor !< solute effects
	921	REAL(wp) :: dr !< width of radius bin
	922	REAL(wp) :: e_a !< vapor pressure
	923	REAL(wp) :: e_s !< saturation vapor pressure
	924	REAL(wp) :: n_init !< sum of all aerosol concentrations
	925	REAL(wp) :: pdf !< PDF of aerosol spectrum
	926	REAL(wp) :: rmin = 1.0e-8_wp !< minimum aerosol radius
	927	REAL(wp) :: rmax = 1.0e-6_wp !< maximum aerosol radius
	928	REAL(wp) :: rs_rand !< random number
	929	REAL(wp) :: r_mid !< mean radius
[2122]	930	REAL(wp) :: sigma !< surface tension
[1871]	931	REAL(wp) :: t_int !< temperature
	932	REAL(wp) :: weight_sum !< sum of all weighting factors
	933
[1890]	934	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
[1871]	935
	936	INTEGER(iwp) :: n !<
	937	INTEGER(iwp) :: nn !<
	938	INTEGER(iwp) :: no_bins = 999 !< number of bins
	939	INTEGER(iwp) :: ip !<
	940	INTEGER(iwp) :: jp !<
	941	INTEGER(iwp) :: kp !<
	942
	943	LOGICAL :: new_pdf = .FALSE. !< check if aerosol PDF has to be recalculated
	944
	945	!
	946	!-- Compute aerosol background distribution
	947	IF ( init_aerosol_probabilistic ) THEN
	948	ALLOCATE( cdf(0:no_bins), r_temp(0:no_bins) )
	949	DO n = 0, no_bins
	950	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
	951	REAL(no_bins, KIND=wp) * REAL(n, KIND=wp) )
	952
	953	cdf(n) = 0.0_wp
	954	n_init = n1 + n2 + n3
	955	IF ( n1 > 0.0_wp ) THEN
	956	cdf(n) = cdf(n) + n1 / n_init * ( 0.5_wp + 0.5_wp * &
	957	ERF( LOG( r_temp(n) / rm1 ) / &
	958	( SQRT(2.0_wp) * LOG(s1) ) &
	959	) )
	960	ENDIF
	961	IF ( n2 > 0.0_wp ) THEN
	962	cdf(n) = cdf(n) + n2 / n_init * ( 0.5_wp + 0.5_wp * &
	963	ERF( LOG( r_temp(n) / rm2 ) / &
	964	( SQRT(2.0_wp) * LOG(s2) ) &
	965	) )
	966	ENDIF
	967	IF ( n3 > 0.0_wp ) THEN
	968	cdf(n) = cdf(n) + n3 / n_init * ( 0.5_wp + 0.5_wp * &
	969	ERF( LOG( r_temp(n) / rm3 ) / &
	970	( SQRT(2.0_wp) * LOG(s3) ) &
	971	) )
	972	ENDIF
	973
	974	ENDDO
	975	ENDIF
	976
	977	DO ip = nxl, nxr
	978	DO jp = nys, nyn
	979	DO kp = nzb+1, nzt
	980
	981	number_of_particles = prt_count(kp,jp,ip)
	982	IF ( number_of_particles <= 0 ) CYCLE
	983	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	984	!
	985	!-- Initialize the aerosols with a predefined spectral distribution
	986	!-- of the dry radius (logarithmically increasing bins) and a varying
	987	!-- weighting factor
	988	IF ( .NOT. init_aerosol_probabilistic ) THEN
	989
	990	new_pdf = .FALSE.
	991	IF ( .NOT. ALLOCATED( r_temp ) ) THEN
	992	new_pdf = .TRUE.
	993	ELSE
	994	IF ( SIZE( r_temp ) .NE. &
	995	number_of_particles - local_start(kp,jp,ip) + 2 ) THEN
	996	new_pdf = .TRUE.
	997	DEALLOCATE( r_temp )
	998	ENDIF
	999	ENDIF
	1000
	1001	IF ( new_pdf ) THEN
	1002
	1003	no_bins = number_of_particles + 1 - local_start(kp,jp,ip)
	1004	ALLOCATE( r_temp(0:no_bins) )
	1005
	1006	DO n = 0, no_bins
	1007	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
	1008	REAL(no_bins, KIND=wp) * &
	1009	REAL(n, KIND=wp) )
	1010	ENDDO
	1011
	1012	ENDIF
	1013
	1014	!
	1015	!-- Calculate radius and concentration of each aerosol
	1016	DO n = local_start(kp,jp,ip), number_of_particles
	1017
	1018	nn = n - local_start(kp,jp,ip)
	1019
	1020	r_mid = SQRT( r_temp(nn) * r_temp(nn+1) )
	1021	dr = r_temp(nn+1) - r_temp(nn)
	1022
	1023	pdf = 0.0_wp
	1024	n_init = n1 + n2 + n3
	1025	IF ( n1 > 0.0_wp ) THEN
	1026	pdf = pdf + n1 / n_init * ( 1.0_wp / ( r_mid * LOG(s1) * &
	1027	SQRT( 2.0_wp * pi ) &
	1028	) * &
	1029	EXP( -( LOG( r_mid / rm1 ) )**2 / &
	1030	( 2.0_wp * LOG(s1)**2 ) &
	1031	) &
	1032	)
	1033	ENDIF
	1034	IF ( n2 > 0.0_wp ) THEN
	1035	pdf = pdf + n2 / n_init * ( 1.0_wp / ( r_mid * LOG(s2) * &
	1036	SQRT( 2.0_wp * pi ) &
	1037	) * &
	1038	EXP( -( LOG( r_mid / rm2 ) )**2 / &
	1039	( 2.0_wp * LOG(s2)**2 ) &
	1040	) &
	1041	)
	1042	ENDIF
	1043	IF ( n3 > 0.0_wp ) THEN
	1044	pdf = pdf + n3 / n_init * ( 1.0_wp / ( r_mid * LOG(s3) * &
	1045	SQRT( 2.0_wp * pi ) &
	1046	) * &
	1047	EXP( -( LOG( r_mid / rm3 ) )**2 / &
	1048	( 2.0_wp * LOG(s3)**2 ) &
	1049	) &
	1050	)
	1051	ENDIF
	1052
	1053	particles(n)%rvar2 = r_mid
	1054	particles(n)%weight_factor = pdf * dr
	1055
	1056	END DO
	1057	!
	1058	!-- Adjust weighting factors to initialize the same number of aerosols
	1059	!-- in every grid box
	1060	weight_sum = SUM(particles(local_start(kp,jp,ip):number_of_particles)%weight_factor)
	1061
	1062	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor = &
	1063	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor / &
	1064	weight_sum * initial_weighting_factor * ( no_bins + 1 )
	1065
	1066	ENDIF
	1067	!
	1068	!-- Initialize the aerosols with a predefined weighting factor but
	1069	!-- a randomly choosen dry radius
	1070	IF ( init_aerosol_probabilistic ) THEN
	1071
	1072	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	1073
	1074	rs_rand = -1.0_wp
	1075	DO WHILE ( rs_rand .LT. cdf(0) .OR. rs_rand .GE. cdf(no_bins) )
	1076	rs_rand = random_function( iran_part )
	1077	ENDDO
	1078	!
	1079	!-- Determine aerosol dry radius by a random number generator
	1080	DO nn = 0, no_bins-1
	1081	IF ( cdf(nn) .LE. rs_rand .AND. cdf(nn+1) .GT. rs_rand ) THEN
	1082	particles(n)%rvar2 = r_temp(nn) + ( r_temp(nn+1) - r_temp(nn) ) / &
	1083	( cdf(nn+1) - cdf(nn) ) * ( rs_rand - cdf(nn) )
	1084	EXIT
	1085	ENDIF
	1086	ENDDO
	1087
	1088	ENDDO
	1089
	1090	ENDIF
	1091
	1092	!
	1093	!-- Set particle radius to equilibrium radius based on the environmental
	1094	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
	1095	!-- the sometimes lengthy growth toward their equilibrium radius within
	1096	!-- the simulation.
	1097	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
	1098
	1099	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
	1100	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
	1101
[2122]	1102	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
	1103	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
	1104
	1105	bfactor = vanthoff * molecular_weight_of_water * &
	1106	rho_s / ( molecular_weight_of_solute * rho_l )
[1871]	1107	!
[1890]	1108	!-- The formula is only valid for subsaturated environments. For
[2122]	1109	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
	1110	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
[1871]	1111
[2122]	1112	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	1113	!
	1114	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
	1115	!-- Curry (2007, JGR)
	1116	particles(n)%radius = bfactor*0.3333333_wp &
	1117	particles(n)%rvar2 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
	1118	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
	1119	particles(n)%rvar2 ) ) / &
	1120	( 1.0_wp - e_a / e_s )**0.6666666_wp &
	1121	)
[1871]	1122
[2122]	1123	ENDDO
[1871]	1124
	1125	ENDDO
	1126	ENDDO
	1127	ENDDO
	1128	!
	1129	!-- Deallocate used arrays
	1130	IF ( ALLOCATED(r_temp) ) DEALLOCATE( r_temp )
	1131	IF ( ALLOCATED(cdf) ) DEALLOCATE( cdf )
	1132
	1133	END SUBROUTINE lpm_init_aerosols
	1134
[1359]	1135	END MODULE lpm_init_mod

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