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source: palm/trunk/SOURCE/lpm_advec.f90 @ 3038

Last change on this file since 3038 was 2969, checked in by thiele, 7 years ago
Bugfix in Interpolation indices
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File size: 55.2 KB

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[1682]	1	!> @file lpm_advec.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	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	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[849]	20	! Current revisions:
	21	! ------------------
[2701]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_advec.f90 2969 2018-04-13 11:55:09Z gronemeier $
[2969]	27	! Bugfix in Interpolation indices.
	28	!
	29	! 2886 2018-03-14 11:51:53Z thiele
[2886]	30	! Bugfix in passive particle SGS Model:
	31	! Sometimes the added SGS velocities would lead to a violation of the CFL
	32	! criterion for single particles. For this a check was added after the
	33	! calculation of SGS velocities.
	34	!
	35	! 2718 2018-01-02 08:49:38Z maronga
[2716]	36	! Corrected "Former revisions" section
	37	!
	38	! 2701 2017-12-15 15:40:50Z suehring
	39	! Changes from last commit documented
	40	!
	41	! 2698 2017-12-14 18:46:24Z suehring
[2698]	42	! Particle interpolations at walls in case of SGS velocities revised and not
	43	! required parts are removed. (responsible Philipp Thiele)
[2716]	44	! Bugfix in get_topography_top_index
[2698]	45	!
[2716]	46	! 2696 2017-12-14 17:12:51Z kanani
	47	! Change in file header (GPL part)
	48	!
	49	! 2630 2017-11-20 12:58:20Z schwenkel
[2629]	50	! Removed indices ilog and jlog which are no longer needed since particle box
	51	! locations are identical to scalar boxes and topography.
	52	!
[2630]	53	! 2628 2017-11-20 12:40:38Z raasch
[2610]	54	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
	55	!
	56	! 2606 2017-11-10 10:36:31Z schwenkel
[2606]	57	! Changed particle box locations: center of particle box now coincides
	58	! with scalar grid point of same index.
	59	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
	60	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
	61	! lpm_sort -> lpm_sort_timeloop_done
	62	!
	63	! 2417 2017-09-06 15:22:27Z suehring
[2417]	64	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
	65	! particle loop runs from start_index up to end_index instead from 1 to
	66	! number_of_particles. This way, it is possible to skip unnecessary
	67	! computations for particles that already completed the LES timestep.
	68	!
	69	! 2318 2017-07-20 17:27:44Z suehring
[2318]	70	! Get topography top index via Function call
	71	!
	72	! 2317 2017-07-20 17:27:19Z suehring
[1930]	73	!
[2233]	74	! 2232 2017-05-30 17:47:52Z suehring
	75	! Adjustments to new topography and surface concept
	76	!
[2101]	77	! 2100 2017-01-05 16:40:16Z suehring
	78	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
	79	! at the begin of simulations and/or in non-turbulent regions.
	80	!
[2001]	81	! 2000 2016-08-20 18:09:15Z knoop
	82	! Forced header and separation lines into 80 columns
	83	!
[1937]	84	! 1936 2016-06-13 13:37:44Z suehring
	85	! Formatting adjustments
	86	!
[1930]	87	! 1929 2016-06-09 16:25:25Z suehring
[1929]	88	! Put stochastic equation in an extra subroutine.
	89	! Set flag for stochastic equation to communicate whether a particle is near
	90	! topography. This case, memory and drift term are disabled in the Weil equation.
[1889]	91	!
[1929]	92	! Enable vertical logarithmic interpolation also above topography. This case,
	93	! set a lower limit for the friction velocity, as it can become very small
[1930]	94	! in narrow street canyons, leading to too large particle speeds.
[1823]	95	!
[1889]	96	! 1888 2016-04-21 12:20:49Z suehring
	97	! Bugfix concerning logarithmic interpolation of particle speed
	98	!
[1823]	99	! 1822 2016-04-07 07:49:42Z hoffmann
[1822]	100	! Random velocity fluctuations for particles added. Terminal fall velocity
	101	! for droplets is calculated from a parameterization (which is better than
	102	! the previous, physically correct calculation, which demands a very short
	103	! time step that is not used in the model).
	104	!
	105	! Unused variables deleted.
[1321]	106	!
[1692]	107	! 1691 2015-10-26 16:17:44Z maronga
	108	! Renamed prandtl_layer to constant_flux_layer.
	109	!
[1686]	110	! 1685 2015-10-08 07:32:13Z raasch
	111	! TKE check for negative values (so far, only zero value was checked)
	112	! offset_ocean_nzt_m1 removed
	113	!
[1683]	114	! 1682 2015-10-07 23:56:08Z knoop
	115	! Code annotations made doxygen readable
	116	!
[1584]	117	! 1583 2015-04-15 12:16:27Z suehring
	118	! Bugfix: particle advection within Prandtl-layer in case of Galilei
	119	! transformation.
	120	!
[1370]	121	! 1369 2014-04-24 05:57:38Z raasch
	122	! usage of module interfaces removed
	123	!
[1360]	124	! 1359 2014-04-11 17:15:14Z hoffmann
	125	! New particle structure integrated.
	126	! Kind definition added to all floating point numbers.
	127	!
[1323]	128	! 1322 2014-03-20 16:38:49Z raasch
	129	! REAL constants defined as wp_kind
	130	!
[1321]	131	! 1320 2014-03-20 08:40:49Z raasch
[1320]	132	! ONLY-attribute added to USE-statements,
	133	! kind-parameters added to all INTEGER and REAL declaration statements,
	134	! kinds are defined in new module kinds,
	135	! revision history before 2012 removed,
	136	! comment fields (!:) to be used for variable explanations added to
	137	! all variable declaration statements
[849]	138	!
[1315]	139	! 1314 2014-03-14 18:25:17Z suehring
	140	! Vertical logarithmic interpolation of horizontal particle speed for particles
	141	! between roughness height and first vertical grid level.
	142	!
[1037]	143	! 1036 2012-10-22 13:43:42Z raasch
	144	! code put under GPL (PALM 3.9)
	145	!
[850]	146	! 849 2012-03-15 10:35:09Z raasch
	147	! initial revision (former part of advec_particles)
[849]	148	!
[850]	149	!
[849]	150	! Description:
	151	! ------------
[1682]	152	!> Calculation of new particle positions due to advection using a simple Euler
	153	!> scheme. Particles may feel inertia effects. SGS transport can be included
	154	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
[849]	155	!------------------------------------------------------------------------------!
[1682]	156	SUBROUTINE lpm_advec (ip,jp,kp)
	157
[849]	158
[1320]	159	USE arrays_3d, &
[2232]	160	ONLY: de_dx, de_dy, de_dz, diss, e, km, u, v, w, zu, zw
[849]	161
[1359]	162	USE cpulog
	163
	164	USE pegrid
	165
[1320]	166	USE control_parameters, &
[1691]	167	ONLY: atmos_ocean_sign, cloud_droplets, constant_flux_layer, dt_3d, &
[1822]	168	dt_3d_reached_l, dz, g, kappa, topography, u_gtrans, v_gtrans
[849]	169
[1320]	170	USE grid_variables, &
	171	ONLY: ddx, dx, ddy, dy
	172
	173	USE indices, &
[2698]	174	ONLY: nzb, nzt, wall_flags_0
[1320]	175
	176	USE kinds
	177
	178	USE particle_attributes, &
[1822]	179	ONLY: block_offset, c_0, dt_min_part, grid_particles, &
[1359]	180	iran_part, log_z_z0, number_of_particles, number_of_sublayers, &
[1929]	181	particles, particle_groups, offset_ocean_nzt, sgs_wf_part, &
	182	use_sgs_for_particles, vertical_particle_advection, z0_av_global
[1320]	183
	184	USE statistics, &
	185	ONLY: hom
[849]	186
[2232]	187	USE surface_mod, &
[2698]	188	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
[2232]	189
[1320]	190	IMPLICIT NONE
[849]	191
[2698]	192	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
	193
[1929]	194	INTEGER(iwp) :: agp !< loop variable
	195	INTEGER(iwp) :: gp_outside_of_building(1:8) !< number of grid points used for particle interpolation in case of topography
	196	INTEGER(iwp) :: i !< index variable along x
	197	INTEGER(iwp) :: ip !< index variable along x
	198	INTEGER(iwp) :: j !< index variable along y
	199	INTEGER(iwp) :: jp !< index variable along y
	200	INTEGER(iwp) :: k !< index variable along z
[2232]	201	INTEGER(iwp) :: k_wall !< vertical index of topography top
[1929]	202	INTEGER(iwp) :: kp !< index variable along z
	203	INTEGER(iwp) :: kw !< index variable along z
	204	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
	205	INTEGER(iwp) :: nb !< block number particles are sorted in
	206	INTEGER(iwp) :: num_gp !< number of adjacent grid points inside topography
[2232]	207	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
[849]	208
[1929]	209	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
	210	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
[1359]	211
[1929]	212	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
	213	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
	214	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
	215	REAL(wp) :: d_sum !< dummy argument for horizontal particle interpolation in case of topography
	216	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
	217	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
	218	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
	219	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
	220	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
	221	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
	222	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
	223	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
	224	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
	225	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
[1822]	226	REAL(wp) :: diameter !< diamter of droplet
[1929]	227	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
	228	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
	229	REAL(wp) :: dt_particle_m !< previous particle time step
[2886]	230	REAL(wp) :: dz_temp !<
[1929]	231	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
	232	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
	233	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
[1682]	234	REAL(wp) :: exp_arg !<
	235	REAL(wp) :: exp_term !<
[1929]	236	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
	237	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
	238	REAL(wp) :: location(1:30,1:3) !< wall locations
	239	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
[1682]	240	REAL(wp) :: random_gauss !<
[1822]	241	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
	242	REAL(wp) :: rg1 !< Gaussian distributed random number
	243	REAL(wp) :: rg2 !< Gaussian distributed random number
	244	REAL(wp) :: rg3 !< Gaussian distributed random number
	245	REAL(wp) :: sigma !< velocity standard deviation
[1929]	246	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
	247	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
	248	REAL(wp) :: us_int !< friction velocity at particle grid box
[2232]	249	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
[1929]	250	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
	251	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
[2232]	252	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
[1682]	253	REAL(wp) :: vv_int !<
[1929]	254	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
	255	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
[1822]	256	REAL(wp) :: w_s !< terminal velocity of droplets
[1929]	257	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
	258	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
	259	REAL(wp) :: z_p !< surface layer height (0.5 dz)
[849]	260
[1822]	261	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
	262	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
	263	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
	264	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
	265	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
	266	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
	267
[1929]	268	REAL(wp), DIMENSION(1:30) :: d_gp_pl !< dummy argument for particle interpolation scheme in case of topography
	269	REAL(wp), DIMENSION(1:30) :: de_dxi !< horizontal TKE gradient along x at adjacent wall
	270	REAL(wp), DIMENSION(1:30) :: de_dyi !< horizontal TKE gradient along y at adjacent wall
	271	REAL(wp), DIMENSION(1:30) :: de_dzi !< horizontal TKE gradient along z at adjacent wall
	272	REAL(wp), DIMENSION(1:30) :: dissi !< dissipation at adjacent wall
	273	REAL(wp), DIMENSION(1:30) :: ei !< TKE at adjacent wall
[849]	274
[2886]	275	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
	276	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !<
	277	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
	278	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
	279	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
	280	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
	281	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
	282	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
	283	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
	284	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
	285	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
	286	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !<
	287	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !<
	288	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !<
	289	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
	290	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
	291	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
	292	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
	293	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
	294	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
[1359]	295
[1929]	296	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
[1359]	297
	298	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
	299
[1314]	300	!
	301	!-- Determine height of Prandtl layer and distance between Prandtl-layer
	302	!-- height and horizontal mean roughness height, which are required for
	303	!-- vertical logarithmic interpolation of horizontal particle speeds
	304	!-- (for particles below first vertical grid level).
	305	z_p = zu(nzb+1) - zw(nzb)
[1359]	306	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
[849]	307
[1359]	308	start_index = grid_particles(kp,jp,ip)%start_index
	309	end_index = grid_particles(kp,jp,ip)%end_index
[849]	310
[1359]	311	xv = particles(1:number_of_particles)%x
	312	yv = particles(1:number_of_particles)%y
	313	zv = particles(1:number_of_particles)%z
[849]	314
[1359]	315	DO nb = 0, 7
[2606]	316	!
	317	!-- Interpolate u velocity-component
[1359]	318	i = ip
	319	j = jp + block_offset(nb)%j_off
	320	k = kp + block_offset(nb)%k_off
[2606]	321
[1359]	322	DO n = start_index(nb), end_index(nb)
[1314]	323	!
[1359]	324	!-- Interpolation of the u velocity component onto particle position.
	325	!-- Particles are interpolation bi-linearly in the horizontal and a
	326	!-- linearly in the vertical. An exception is made for particles below
	327	!-- the first vertical grid level in case of a prandtl layer. In this
	328	!-- case the horizontal particle velocity components are determined using
	329	!-- Monin-Obukhov relations (if branch).
	330	!-- First, check if particle is located below first vertical grid level
[2232]	331	!-- above topography (Prandtl-layer height)
	332	!-- Determine vertical index of topography top
[2698]	333	k_wall = get_topography_top_index_ji( jp, ip, 's' )
[1929]	334
[2232]	335	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
[1314]	336	!
[1359]	337	!-- Resolved-scale horizontal particle velocity is zero below z0.
[2232]	338	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1359]	339	u_int(n) = 0.0_wp
	340	ELSE
[1314]	341	!
[1359]	342	!-- Determine the sublayer. Further used as index.
[2232]	343	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	344	* REAL( number_of_sublayers, KIND=wp ) &
[1359]	345	* d_z_p_z0
[1314]	346	!
[1359]	347	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	348	!-- interpolate linearly between precalculated logarithm.
[1929]	349	log_z_z0_int = log_z_z0(INT(height_p)) &
[1359]	350	+ ( height_p - INT(height_p) ) &
	351	* ( log_z_z0(INT(height_p)+1) &
	352	- log_z_z0(INT(height_p)) &
	353	)
[1314]	354	!
[2232]	355	!-- Get friction velocity and momentum flux from new surface data
	356	!-- types.
[2628]	357	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	358	surf_def_h(0)%end_index(jp,ip) ) THEN
	359	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	360	!-- Limit friction velocity. In narrow canyons or holes the
	361	!-- friction velocity can become very small, resulting in a too
	362	!-- large particle speed.
	363	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
	364	usws_int = surf_def_h(0)%usws(surf_start)
[2628]	365	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	366	surf_lsm_h%end_index(jp,ip) ) THEN
	367	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	368	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
	369	usws_int = surf_lsm_h%usws(surf_start)
[2628]	370	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	371	surf_usm_h%end_index(jp,ip) ) THEN
	372	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	373	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
	374	usws_int = surf_usm_h%usws(surf_start)
	375	ENDIF
	376
[1929]	377	!
[1359]	378	!-- Neutral solution is applied for all situations, e.g. also for
	379	!-- unstable and stable situations. Even though this is not exact
	380	!-- this saves a lot of CPU time since several calls of intrinsic
	381	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	382	!-- as sensitivity studies revealed no significant effect of
	383	!-- using the neutral solution also for un/stable situations.
[2232]	384	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	385	* log_z_z0_int - u_gtrans
	386
[1359]	387	ENDIF
	388	!
	389	!-- Particle above the first grid level. Bi-linear interpolation in the
	390	!-- horizontal and linear interpolation in the vertical direction.
[1314]	391	ELSE
	392
[2969]	393	x = xv(n) - i * dx
	394	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	395	aa = x2 + y2
	396	bb = ( dx - x )2 + y2
	397	cc = x2 + ( dy - y )2
	398	dd = ( dx - x )2 + ( dy - y )2
	399	gg = aa + bb + cc + dd
[1314]	400
[1359]	401	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
	402	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
	403	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[1314]	404
[1359]	405	IF ( k == nzt ) THEN
	406	u_int(n) = u_int_l
	407	ELSE
	408	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
	409	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
	410	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
	411	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dz * &
	412	( u_int_u - u_int_l )
	413	ENDIF
[1929]	414
[1314]	415	ENDIF
	416
[1359]	417	ENDDO
[2606]	418	!
	419	!-- Same procedure for interpolation of the v velocity-component
[1359]	420	i = ip + block_offset(nb)%i_off
	421	j = jp
	422	k = kp + block_offset(nb)%k_off
[2606]	423
[1359]	424	DO n = start_index(nb), end_index(nb)
[1685]	425
[2232]	426	!
	427	!-- Determine vertical index of topography top
[2698]	428	k_wall = get_topography_top_index_ji( jp,ip, 's' )
[849]	429
[2232]	430	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
	431	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1314]	432	!
[1359]	433	!-- Resolved-scale horizontal particle velocity is zero below z0.
	434	v_int(n) = 0.0_wp
	435	ELSE
	436	!
[1929]	437	!-- Determine the sublayer. Further used as index. Please note,
	438	!-- logarithmus can not be reused from above, as in in case of
	439	!-- topography particle on u-grid can be above surface-layer height,
	440	!-- whereas it can be below on v-grid.
[2232]	441	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	442	* REAL( number_of_sublayers, KIND=wp ) &
[1929]	443	* d_z_p_z0
	444	!
	445	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	446	!-- interpolate linearly between precalculated logarithm.
	447	log_z_z0_int = log_z_z0(INT(height_p)) &
	448	+ ( height_p - INT(height_p) ) &
	449	* ( log_z_z0(INT(height_p)+1) &
	450	- log_z_z0(INT(height_p)) &
	451	)
	452	!
[2232]	453	!-- Get friction velocity and momentum flux from new surface data
	454	!-- types.
[2628]	455	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	456	surf_def_h(0)%end_index(jp,ip) ) THEN
	457	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	458	!-- Limit friction velocity. In narrow canyons or holes the
	459	!-- friction velocity can become very small, resulting in a too
	460	!-- large particle speed.
	461	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
[2610]	462	vsws_int = surf_def_h(0)%vsws(surf_start)
[2628]	463	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	464	surf_lsm_h%end_index(jp,ip) ) THEN
	465	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	466	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
[2610]	467	vsws_int = surf_lsm_h%vsws(surf_start)
[2628]	468	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	469	surf_usm_h%end_index(jp,ip) ) THEN
	470	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	471	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
[2610]	472	vsws_int = surf_usm_h%vsws(surf_start)
[2232]	473	ENDIF
[1929]	474	!
[1359]	475	!-- Neutral solution is applied for all situations, e.g. also for
	476	!-- unstable and stable situations. Even though this is not exact
	477	!-- this saves a lot of CPU time since several calls of intrinsic
	478	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	479	!-- as sensitivity studies revealed no significant effect of
	480	!-- using the neutral solution also for un/stable situations.
[2232]	481	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	482	* log_z_z0_int - v_gtrans
[1314]	483
[1359]	484	ENDIF
[1929]	485
[1359]	486	ELSE
[2969]	487	x = xv(n) + ( 0.5_wp - i ) * dx
	488	y = yv(n) - j * dy
[1359]	489	aa = x2 + y2
	490	bb = ( dx - x )2 + y2
	491	cc = x2 + ( dy - y )2
	492	dd = ( dx - x )2 + ( dy - y )2
	493	gg = aa + bb + cc + dd
[1314]	494
[1359]	495	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
	496	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
	497	) / ( 3.0_wp * gg ) - v_gtrans
[1314]	498
[1359]	499	IF ( k == nzt ) THEN
	500	v_int(n) = v_int_l
	501	ELSE
	502	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
	503	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
	504	) / ( 3.0_wp * gg ) - v_gtrans
	505	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dz * &
	506	( v_int_u - v_int_l )
	507	ENDIF
[1929]	508
[1314]	509	ENDIF
	510
[1359]	511	ENDDO
[2606]	512	!
	513	!-- Same procedure for interpolation of the w velocity-component
[1359]	514	i = ip + block_offset(nb)%i_off
	515	j = jp + block_offset(nb)%j_off
[1929]	516	k = kp - 1
[2606]	517
[1359]	518	DO n = start_index(nb), end_index(nb)
[849]	519
[1359]	520	IF ( vertical_particle_advection(particles(n)%group) ) THEN
[849]	521
[2969]	522	x = xv(n) + ( 0.5_wp - i ) * dx
	523	y = yv(n) + ( 0.5_wp - j ) * dy
[849]	524	aa = x2 + y2
	525	bb = ( dx - x )2 + y2
	526	cc = x2 + ( dy - y )2
	527	dd = ( dx - x )2 + ( dy - y )2
	528	gg = aa + bb + cc + dd
	529
[1359]	530	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
	531	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
	532	) / ( 3.0_wp * gg )
[849]	533
[1359]	534	IF ( k == nzt ) THEN
	535	w_int(n) = w_int_l
[849]	536	ELSE
[1359]	537	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
	538	( gg-bb ) * w(k+1,j,i+1) + &
	539	( gg-cc ) * w(k+1,j+1,i) + &
	540	( gg-dd ) * w(k+1,j+1,i+1) &
	541	) / ( 3.0_wp * gg )
	542	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dz * &
	543	( w_int_u - w_int_l )
[849]	544	ENDIF
	545
[1359]	546	ELSE
[849]	547
[1359]	548	w_int(n) = 0.0_wp
[849]	549
[1359]	550	ENDIF
	551
	552	ENDDO
	553
	554	ENDDO
	555
	556	!-- Interpolate and calculate quantities needed for calculating the SGS
	557	!-- velocities
[1822]	558	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[2698]	559
	560	DO nb = 0,7
	561
	562	subbox_at_wall = .FALSE.
	563	!
	564	!-- In case of topography check if subbox is adjacent to a wall
	565	IF ( .NOT. topography == 'flat' ) THEN
	566	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
	567	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
	568	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
	569	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
	570	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
	571	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
	572	THEN
	573	subbox_at_wall = .TRUE.
	574	ENDIF
	575	ENDIF
	576	IF ( subbox_at_wall ) THEN
	577	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
	578	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
	579	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
	580	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
	581	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
	582	!
	583	!-- Set flag for stochastic equation.
	584	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
	585	ELSE
[1359]	586	i = ip + block_offset(nb)%i_off
	587	j = jp + block_offset(nb)%j_off
	588	k = kp + block_offset(nb)%k_off
	589
	590	DO n = start_index(nb), end_index(nb)
[849]	591	!
[1359]	592	!-- Interpolate TKE
[2969]	593	x = xv(n) + ( 0.5_wp - i ) * dx
	594	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	595	aa = x2 + y2
	596	bb = ( dx - x )2 + y2
	597	cc = x2 + ( dy - y )2
	598	dd = ( dx - x )2 + ( dy - y )2
	599	gg = aa + bb + cc + dd
[849]	600
[1359]	601	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
	602	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
	603	) / ( 3.0_wp * gg )
	604
	605	IF ( k+1 == nzt+1 ) THEN
	606	e_int(n) = e_int_l
	607	ELSE
	608	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
	609	( gg - bb ) * e(k+1,j,i+1) + &
	610	( gg - cc ) * e(k+1,j+1,i) + &
	611	( gg - dd ) * e(k+1,j+1,i+1) &
	612	) / ( 3.0_wp * gg )
	613	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dz * &
	614	( e_int_u - e_int_l )
	615	ENDIF
[849]	616	!
[1685]	617	!-- Needed to avoid NaN particle velocities (this might not be
	618	!-- required any more)
	619	IF ( e_int(n) <= 0.0_wp ) THEN
[1359]	620	e_int(n) = 1.0E-20_wp
	621	ENDIF
	622	!
	623	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
	624	!-- all position variables from above (TKE))
	625	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
	626	( gg - bb ) * de_dx(k,j,i+1) + &
	627	( gg - cc ) * de_dx(k,j+1,i) + &
	628	( gg - dd ) * de_dx(k,j+1,i+1) &
	629	) / ( 3.0_wp * gg )
[849]	630
	631	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
[1359]	632	de_dx_int(n) = de_dx_int_l
[849]	633	ELSE
[1359]	634	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
	635	( gg - bb ) * de_dx(k+1,j,i+1) + &
	636	( gg - cc ) * de_dx(k+1,j+1,i) + &
	637	( gg - dd ) * de_dx(k+1,j+1,i+1) &
	638	) / ( 3.0_wp * gg )
	639	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dz * &
	640	( de_dx_int_u - de_dx_int_l )
[849]	641	ENDIF
[1359]	642	!
	643	!-- Interpolate the TKE gradient along y
	644	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
	645	( gg - bb ) * de_dy(k,j,i+1) + &
	646	( gg - cc ) * de_dy(k,j+1,i) + &
	647	( gg - dd ) * de_dy(k,j+1,i+1) &
	648	) / ( 3.0_wp * gg )
	649	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	650	de_dy_int(n) = de_dy_int_l
	651	ELSE
	652	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
[2698]	653	( gg - bb ) * de_dy(k+1,j,i+1) + &
	654	( gg - cc ) * de_dy(k+1,j+1,i) + &
	655	( gg - dd ) * de_dy(k+1,j+1,i+1) &
[1359]	656	) / ( 3.0_wp * gg )
[2698]	657	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dz * &
	658	( de_dy_int_u - de_dy_int_l )
[1359]	659	ENDIF
[849]	660
	661	!
[1359]	662	!-- Interpolate the TKE gradient along z
	663	IF ( zv(n) < 0.5_wp * dz ) THEN
	664	de_dz_int(n) = 0.0_wp
	665	ELSE
	666	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
	667	( gg - bb ) * de_dz(k,j,i+1) + &
	668	( gg - cc ) * de_dz(k,j+1,i) + &
	669	( gg - dd ) * de_dz(k,j+1,i+1) &
	670	) / ( 3.0_wp * gg )
[849]	671
[1359]	672	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	673	de_dz_int(n) = de_dz_int_l
	674	ELSE
	675	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
	676	( gg - bb ) * de_dz(k+1,j,i+1) + &
	677	( gg - cc ) * de_dz(k+1,j+1,i) + &
	678	( gg - dd ) * de_dz(k+1,j+1,i+1) &
	679	) / ( 3.0_wp * gg )
	680	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dz * &
	681	( de_dz_int_u - de_dz_int_l )
	682	ENDIF
	683	ENDIF
[849]	684
[1359]	685	!
	686	!-- Interpolate the dissipation of TKE
	687	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
	688	( gg - bb ) * diss(k,j,i+1) + &
	689	( gg - cc ) * diss(k,j+1,i) + &
	690	( gg - dd ) * diss(k,j+1,i+1) &
[2698]	691	) / ( 3.0_wp * gg )
[849]	692
[1359]	693	IF ( k == nzt ) THEN
	694	diss_int(n) = diss_int_l
	695	ELSE
	696	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
	697	( gg - bb ) * diss(k+1,j,i+1) + &
	698	( gg - cc ) * diss(k+1,j+1,i) + &
	699	( gg - dd ) * diss(k+1,j+1,i+1) &
	700	) / ( 3.0_wp * gg )
	701	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dz * &
[2698]	702	( diss_int_u - diss_int_l )
[1359]	703	ENDIF
	704
[1929]	705	!
	706	!-- Set flag for stochastic equation.
	707	term_1_2(n) = 1.0_wp
[1359]	708	ENDDO
[2698]	709	ENDIF
	710	ENDDO
[1359]	711
	712	DO nb = 0,7
	713	i = ip + block_offset(nb)%i_off
	714	j = jp + block_offset(nb)%j_off
	715	k = kp + block_offset(nb)%k_off
[849]	716
[1359]	717	DO n = start_index(nb), end_index(nb)
[849]	718	!
[1359]	719	!-- Vertical interpolation of the horizontally averaged SGS TKE and
	720	!-- resolved-scale velocity variances and use the interpolated values
	721	!-- to calculate the coefficient fs, which is a measure of the ratio
	722	!-- of the subgrid-scale turbulent kinetic energy to the total amount
	723	!-- of turbulent kinetic energy.
	724	IF ( k == 0 ) THEN
	725	e_mean_int = hom(0,1,8,0)
	726	ELSE
	727	e_mean_int = hom(k,1,8,0) + &
	728	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
	729	( zu(k+1) - zu(k) ) * &
	730	( zv(n) - zu(k) )
	731	ENDIF
[849]	732
[1685]	733	kw = kp - 1
[849]	734
[1359]	735	IF ( k == 0 ) THEN
	736	aa = hom(k+1,1,30,0) * ( zv(n) / &
	737	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	738	bb = hom(k+1,1,31,0) * ( zv(n) / &
	739	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	740	cc = hom(kw+1,1,32,0) * ( zv(n) / &
	741	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
	742	ELSE
	743	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
	744	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	745	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
	746	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	747	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
	748	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
	749	ENDIF
[849]	750
[1359]	751	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
	752	!
	753	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
	754	!-- an educated guess for the given case.
	755	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
	756	fs_int(n) = 1.0_wp
	757	ELSE
	758	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
	759	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
	760	ENDIF
[849]	761
[1359]	762	ENDDO
	763	ENDDO
[849]	764
[2417]	765	DO nb = 0, 7
	766	DO n = start_index(nb), end_index(nb)
	767	rg(n,1) = random_gauss( iran_part, 5.0_wp )
	768	rg(n,2) = random_gauss( iran_part, 5.0_wp )
	769	rg(n,3) = random_gauss( iran_part, 5.0_wp )
	770	ENDDO
	771	ENDDO
[1359]	772
[2417]	773	DO nb = 0, 7
	774	DO n = start_index(nb), end_index(nb)
[1359]	775
[849]	776	!
[2417]	777	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
[2886]	778	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
[2417]	779	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
[849]	780
	781	!
[2417]	782	!-- Calculate the next particle timestep. dt_gap is the time needed to
	783	!-- complete the current LES timestep.
[2886]	784	dt_gap(n) = dt_3d - particles(n)%dt_sum
	785	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
	786	particles(n)%aux1 = lagr_timescale(n)
	787	particles(n)%aux2 = dt_gap(n)
[849]	788	!
[2417]	789	!-- The particle timestep should not be too small in order to prevent
	790	!-- the number of particle timesteps of getting too large
[2886]	791	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap(n) ) THEN
[2417]	792	dt_particle(n) = dt_min_part
	793	ENDIF
[2886]	794	rvar1_temp(n) = particles(n)%rvar1
	795	rvar2_temp(n) = particles(n)%rvar2
	796	rvar3_temp(n) = particles(n)%rvar3
[849]	797	!
[2417]	798	!-- Calculate the SGS velocity components
	799	IF ( particles(n)%age == 0.0_wp ) THEN
[849]	800	!
[2417]	801	!-- For new particles the SGS components are derived from the SGS
	802	!-- TKE. Limit the Gaussian random number to the interval
	803	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
	804	!-- from becoming unrealistically large.
[2886]	805	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	806	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
	807	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	808	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
	809	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	810	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
[849]	811
[2417]	812	ELSE
[849]	813	!
[2417]	814	!-- Restriction of the size of the new timestep: compared to the
	815	!-- previous timestep the increase must not exceed 200%. First,
	816	!-- check if age > age_m, in order to prevent that particles get zero
	817	!-- timestep.
	818	dt_particle_m = MERGE( dt_particle(n), &
	819	particles(n)%age - particles(n)%age_m, &
	820	particles(n)%age - particles(n)%age_m < &
	821	1E-8_wp )
	822	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
	823	dt_particle(n) = 2.0_wp * dt_particle_m
	824	ENDIF
[849]	825
[2417]	826	!-- For old particles the SGS components are correlated with the
	827	!-- values from the previous timestep. Random numbers have also to
	828	!-- be limited (see above).
	829	!-- As negative values for the subgrid TKE are not allowed, the
	830	!-- change of the subgrid TKE with time cannot be smaller than
	831	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
	832	!-- value for the change of TKE
	833	de_dt_min = - e_int(n) / dt_particle(n)
[849]	834
[2417]	835	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
[849]	836
[2417]	837	IF ( de_dt < de_dt_min ) THEN
	838	de_dt = de_dt_min
	839	ENDIF
[849]	840
[2886]	841	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
[2417]	842	de_dx_int(n), de_dt, diss_int(n), &
	843	dt_particle(n), rg(n,1), term_1_2(n) )
[849]	844
[2886]	845	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
[2417]	846	de_dy_int(n), de_dt, diss_int(n), &
	847	dt_particle(n), rg(n,2), term_1_2(n) )
[849]	848
[2886]	849	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
[2417]	850	de_dz_int(n), de_dt, diss_int(n), &
	851	dt_particle(n), rg(n,3), term_1_2(n) )
[849]	852
[2417]	853	ENDIF
[849]	854
[2886]	855	ENDDO
	856	ENDDO
	857	!
	858	!-- Check if the added SGS velocities result in a violation of the CFL-
	859	!-- criterion. If yes choose a smaller timestep based on the new velocities
	860	!-- and calculate SGS velocities again
	861	dz_temp = zw(kp)-zw(kp-1)
	862
	863	DO nb = 0, 7
	864	DO n = start_index(nb), end_index(nb)
	865	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
	866	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
	867	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
	868	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
	869
	870	dt_particle(n) = 0.9_wp * MIN( &
	871	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
	872	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
	873	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
	874
	875	!
	876	!-- Reset temporary SGS velocites to "current" ones
	877	rvar1_temp(n) = particles(n)%rvar1
	878	rvar2_temp(n) = particles(n)%rvar2
	879	rvar3_temp(n) = particles(n)%rvar3
	880
	881	de_dt_min = - e_int(n) / dt_particle(n)
	882
	883	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
	884
	885	IF ( de_dt < de_dt_min ) THEN
	886	de_dt = de_dt_min
	887	ENDIF
	888
	889	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
	890	de_dx_int(n), de_dt, diss_int(n), &
	891	dt_particle(n), rg(n,1), term_1_2(n) )
	892
	893	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
	894	de_dy_int(n), de_dt, diss_int(n), &
	895	dt_particle(n), rg(n,2), term_1_2(n) )
	896
	897	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
	898	de_dz_int(n), de_dt, diss_int(n), &
	899	dt_particle(n), rg(n,3), term_1_2(n) )
	900	ENDIF
	901
	902	!
	903	!-- Update particle velocites
	904	particles(n)%rvar1 = rvar1_temp(n)
	905	particles(n)%rvar2 = rvar2_temp(n)
	906	particles(n)%rvar3 = rvar3_temp(n)
[2417]	907	u_int(n) = u_int(n) + particles(n)%rvar1
	908	v_int(n) = v_int(n) + particles(n)%rvar2
	909	w_int(n) = w_int(n) + particles(n)%rvar3
[849]	910	!
[2417]	911	!-- Store the SGS TKE of the current timelevel which is needed for
	912	!-- for calculating the SGS particle velocities at the next timestep
	913	particles(n)%e_m = e_int(n)
	914	ENDDO
[1359]	915	ENDDO
[2886]	916
[1359]	917	ELSE
[849]	918	!
[1359]	919	!-- If no SGS velocities are used, only the particle timestep has to
	920	!-- be set
	921	dt_particle = dt_3d
[849]	922
[1359]	923	ENDIF
[849]	924
[1359]	925	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
[849]	926
[1359]	927	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
[2417]	928	DO nb = 0, 7
	929	DO n = start_index(nb), end_index(nb)
[1359]	930
[849]	931	!
[2417]	932	!-- Particle advection
	933	IF ( dens_ratio(n) == 0.0_wp ) THEN
[849]	934	!
[2417]	935	!-- Pure passive transport (without particle inertia)
	936	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
	937	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
	938	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
[849]	939
[2417]	940	particles(n)%speed_x = u_int(n)
	941	particles(n)%speed_y = v_int(n)
	942	particles(n)%speed_z = w_int(n)
[849]	943
[2417]	944	ELSE
[849]	945	!
[2417]	946	!-- Transport of particles with inertia
	947	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
	948	dt_particle(n)
	949	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
	950	dt_particle(n)
	951	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
	952	dt_particle(n)
[849]	953
	954	!
[2417]	955	!-- Update of the particle velocity
	956	IF ( cloud_droplets ) THEN
	957	!
	958	!-- Terminal velocity is computed for vertical direction (Rogers et
	959	!-- al., 1993, J. Appl. Meteorol.)
	960	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	961	IF ( diameter <= d0_rog ) THEN
	962	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	963	ELSE
	964	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	965	ENDIF
	966
	967	!
	968	!-- If selected, add random velocities following Soelch and Kaercher
	969	!-- (2010, Q. J. R. Meteorol. Soc.)
	970	IF ( use_sgs_for_particles ) THEN
[2886]	971	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	972	RL = EXP( -1.0_wp * dt_3d / lagr_timescale(n) )
[2417]	973	sigma = SQRT( e(kp,jp,ip) )
	974
	975	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	976	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	977	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	978
	979	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	980	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	981	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	982	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	983	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	984	SQRT( 1.0_wp - RL*2 ) sigma * rg3
	985
	986	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	987	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	988	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
	989	ELSE
	990	particles(n)%speed_x = u_int(n)
	991	particles(n)%speed_y = v_int(n)
	992	particles(n)%speed_z = w_int(n) - w_s
	993	ENDIF
	994
	995	ELSE
	996
	997	IF ( use_sgs_for_particles ) THEN
	998	exp_arg = particle_groups(particles(n)%group)%exp_arg
	999	exp_term = EXP( -exp_arg * dt_particle(n) )
	1000	ELSE
	1001	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1002	exp_term = particle_groups(particles(n)%group)%exp_term
	1003	ENDIF
	1004	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
	1005	u_int(n) * ( 1.0_wp - exp_term )
	1006	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
	1007	v_int(n) * ( 1.0_wp - exp_term )
	1008	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1009	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
	1010	g / exp_arg ) * ( 1.0_wp - exp_term )
	1011	ENDIF
	1012
	1013	ENDIF
	1014	ENDDO
	1015	ENDDO
	1016
	1017	ELSE
	1018
	1019	DO nb = 0, 7
	1020	DO n = start_index(nb), end_index(nb)
	1021	!
	1022	!-- Transport of particles with inertia
	1023	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
	1024	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
	1025	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
	1026	!
[1359]	1027	!-- Update of the particle velocity
	1028	IF ( cloud_droplets ) THEN
[1822]	1029	!
[2417]	1030	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
	1031	!-- 1993, J. Appl. Meteorol.)
[1822]	1032	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	1033	IF ( diameter <= d0_rog ) THEN
	1034	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	1035	ELSE
	1036	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	1037	ENDIF
[1359]	1038
[1822]	1039	!
	1040	!-- If selected, add random velocities following Soelch and Kaercher
	1041	!-- (2010, Q. J. R. Meteorol. Soc.)
	1042	IF ( use_sgs_for_particles ) THEN
[2886]	1043	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	1044	RL = EXP( -1.0_wp * dt_3d / lagr_timescale(n) )
[2417]	1045	sigma = SQRT( e(kp,jp,ip) )
[1822]	1046
[2417]	1047	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1048	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1049	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
[1822]	1050
[2417]	1051	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	1052	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	1053	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	1054	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	1055	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	1056	SQRT( 1.0_wp - RL*2 ) sigma * rg3
[1822]	1057
[2417]	1058	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	1059	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	1060	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
[1822]	1061	ELSE
[2417]	1062	particles(n)%speed_x = u_int(n)
	1063	particles(n)%speed_y = v_int(n)
	1064	particles(n)%speed_z = w_int(n) - w_s
[1822]	1065	ENDIF
	1066
[1359]	1067	ELSE
[1822]	1068
	1069	IF ( use_sgs_for_particles ) THEN
	1070	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1071	exp_term = EXP( -exp_arg * dt_particle(n) )
	1072	ELSE
	1073	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1074	exp_term = particle_groups(particles(n)%group)%exp_term
	1075	ENDIF
[2417]	1076	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
[1822]	1077	u_int(n) * ( 1.0_wp - exp_term )
[2417]	1078	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
[1822]	1079	v_int(n) * ( 1.0_wp - exp_term )
[2417]	1080	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1081	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
	1082	exp_arg ) * ( 1.0_wp - exp_term )
[1359]	1083	ENDIF
[2417]	1084	ENDDO
[1359]	1085	ENDDO
	1086
[2417]	1087	ENDIF
[1359]	1088
	1089	!
[2417]	1090	!-- Store the old age of the particle ( needed to prevent that a
	1091	!-- particle crosses several PEs during one timestep, and for the
	1092	!-- evaluation of the subgrid particle velocity fluctuations )
	1093	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
	1094
	1095	DO nb = 0, 7
	1096	DO n = start_index(nb), end_index(nb)
[1822]	1097	!
[2417]	1098	!-- Increment the particle age and the total time that the particle
	1099	!-- has advanced within the particle timestep procedure
	1100	particles(n)%age = particles(n)%age + dt_particle(n)
	1101	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
[1359]	1102
[1822]	1103	!
[2417]	1104	!-- Check whether there is still a particle that has not yet completed
	1105	!-- the total LES timestep
	1106	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
	1107	dt_3d_reached_l = .FALSE.
[849]	1108	ENDIF
[1822]	1109
[1359]	1110	ENDDO
[849]	1111	ENDDO
	1112
[1359]	1113	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
[849]	1114
[1929]	1115
[849]	1116	END SUBROUTINE lpm_advec
[1929]	1117
	1118	! Description:
	1119	! ------------
	1120	!> Calculation of subgrid-scale particle speed using the stochastic model
	1121	!> of Weil et al. (2004, JAS, 61, 2877-2887).
	1122	!------------------------------------------------------------------------------!
	1123	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
	1124	dt_n, rg_n, fac )
	1125
	1126	USE kinds
	1127
	1128	USE particle_attributes, &
	1129	ONLY: c_0, sgs_wf_part
	1130
	1131	IMPLICIT NONE
	1132
	1133	REAL(wp) :: a1 !< dummy argument
	1134	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
	1135	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
	1136	REAL(wp) :: diss_n !< dissipation at particle position
	1137	REAL(wp) :: dt_n !< particle timestep
	1138	REAL(wp) :: e_n !< TKE at particle position
	1139	REAL(wp) :: fac !< flag to identify adjacent topography
	1140	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
	1141	REAL(wp) :: sgs_w !< constant (1/3)
	1142	REAL(wp) :: rg_n !< random number
	1143	REAL(wp) :: term1 !< memory term
	1144	REAL(wp) :: term2 !< drift correction term
	1145	REAL(wp) :: term3 !< random term
	1146	REAL(wp) :: v_sgs !< subgrid-scale velocity component
	1147
[2100]	1148	!-- At first, limit TKE to a small non-zero number, in order to prevent
	1149	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
	1150	!-- (could occur at the simulation begin).
	1151	e_n = MAX( e_n, 1E-20_wp )
[1929]	1152	!
	1153	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
	1154	!-- multiplied by a flag to switch of both terms near topography.
	1155	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
	1156	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
	1157	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
	1158	!-- disabled if one of the adjacent grid points belongs to topography.
	1159	!-- Moreover, in this case, the previous subgrid-scale component is also set
	1160	!-- to zero.
	1161
	1162	a1 = fs_n * c_0 * diss_n
	1163	!
	1164	!-- Memory term
	1165	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
	1166	* fac
	1167	!
	1168	!-- Drift correction term
	1169	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
	1170	* fac
	1171	!
	1172	!-- Random term
	1173	term3 = SQRT( MAX( a1, 1E-20 ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
	1174	!
	1175	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
	1176	!-- subgrid-scale velocity component is set to zero, in order to prevent a
	1177	!-- velocity build-up.
	1178	!-- This case, set also previous subgrid-scale component to zero.
	1179	v_sgs = v_sgs * fac + term1 + term2 + term3
	1180
	1181	END SUBROUTINE weil_stochastic_eq

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