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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 3552

Last change on this file since 3552 was 3274, checked in by knoop, 6 years ago
Modularization of all bulk cloud physics code components
Property svn:keywords set to `Id`
File size: 39.2 KB

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[1873]	1	!> @file lpm_collision_kernels.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	!
[790]	20	! Current revisions:
	21	! -----------------
[1347]	22	!
[2001]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 3274 2018-09-24 15:42:55Z suehring $
[3274]	27	! Modularization of all bulk cloud physics code components
	28	!
	29	! 2718 2018-01-02 08:49:38Z maronga
[2716]	30	! Corrected "Former revisions" section
	31	!
	32	! 2696 2017-12-14 17:12:51Z kanani
	33	! Change in file header (GPL part)
[1321]	34	!
[2716]	35	! 2101 2017-01-05 16:42:31Z suehring
	36	!
[2001]	37	! 2000 2016-08-20 18:09:15Z knoop
	38	! Forced header and separation lines into 80 columns
	39	!
[1881]	40	! 1880 2016-04-20 09:36:50Z hoffmann
	41	! Bugfix: The index of the larger particle has to be chosen for interpolation.
	42	!
[1874]	43	! 1873 2016-04-18 14:50:06Z maronga
	44	! Module renamed (removed _mod)
	45	!
[1859]	46	! 1858 2016-04-13 13:12:11Z hoffmann
	47	! Interpolation of collision kernels adjusted to more reasonable values.
	48	! Reformatting of the code.
	49	!
[1851]	50	! 1850 2016-04-08 13:29:27Z maronga
	51	! Module renamed
	52	!
[1823]	53	! 1822 2016-04-07 07:49:42Z hoffmann
	54	! PALM kernel has been deleted.
	55	! Bugfix in the calculation of the turbulent enhancement factor of the
	56	! collection efficiency.
	57	!
	58	! Unused variables removed.
	59	!
[1777]	60	! 1776 2016-03-02 17:54:58Z hoffmann
	61	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	62	!
[1683]	63	! 1682 2015-10-07 23:56:08Z knoop
	64	! Code annotations made doxygen readable
	65	!
[1520]	66	! 1519 2015-01-08 10:20:42Z hoffmann
	67	! Bugfix: Using the new particle structure, particles are not sorted by size.
	68	! Hence, computation of collision efficiencies must ensure that the ratio of
	69	! two colliding droplets is < 1.
	70	!
[1360]	71	! 1359 2014-04-11 17:15:14Z hoffmann
	72	! New particle structure integrated.
	73	! Kind definition added to all floating point numbers.
	74	!
[1347]	75	! 1346 2014-03-27 13:18:20Z heinze
	76	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	77	! intrinsic function like MAX, MIN, SIGN
	78	!
[1323]	79	! 1322 2014-03-20 16:38:49Z raasch
	80	! REAL constants defined as wp_kind
	81	!
[1321]	82	! 1320 2014-03-20 08:40:49Z
[1320]	83	! ONLY-attribute added to USE-statements,
	84	! kind-parameters added to all INTEGER and REAL declaration statements,
	85	! kinds are defined in new module kinds,
	86	! revision history before 2012 removed,
	87	! comment fields (!:) to be used for variable explanations added to
	88	! all variable declaration statements
[1008]	89	!
[1093]	90	! 1092 2013-02-02 11:24:22Z raasch
	91	! unused variables removed
	92	!
[1072]	93	! 1071 2012-11-29 16:54:55Z franke
	94	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	95	!
[1037]	96	! 1036 2012-10-22 13:43:42Z raasch
	97	! code put under GPL (PALM 3.9)
	98	!
[1008]	99	! 1007 2012-09-19 14:30:36Z franke
[1007]	100	! converted all units to SI units and replaced some parameters by corresponding
	101	! PALM parameters
	102	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	103	! changed from 10. to 1.0
[829]	104	!
[850]	105	! 849 2012-03-15 10:35:09Z raasch
	106	! routine collision_efficiency_rogers added (moved from former advec_particles
	107	! to here)
	108	!
[836]	109	! 835 2012-02-22 11:21:19Z raasch $
	110	! Bugfix: array diss can be used only in case of Wang kernel
	111	!
[829]	112	! 828 2012-02-21 12:00:36Z raasch
[828]	113	! code has been completely reformatted, routine colker renamed
	114	! recalculate_kernel,
	115	! routine init_kernels added, radius is now communicated to the collision
	116	! routines by array radclass
[790]	117	!
[828]	118	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	119	!
[826]	120	! 825 2012-02-19 03:03:44Z raasch
	121	! routine renamed from wang_kernel to lpm_collision_kernels,
	122	! turbulence_effects on collision replaced by wang_kernel
	123	!
[791]	124	! 790 2011-11-29 03:11:20Z raasch
	125	! initial revision
[790]	126	!
	127	! Description:
	128	! ------------
[1682]	129	!> This module calculates collision efficiencies either due to pure gravitational
	130	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	131	!> including the effects of turbulence (Wang kernel, see Wang and
	132	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	133	!> New J. Phys., 10, 075016). The original code has been
[1682]	134	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	135	!> here.
[790]	136	!------------------------------------------------------------------------------!
[1682]	137	MODULE lpm_collision_kernels_mod
	138
[790]	139
[3274]	140	USE basic_constants_and_equations_mod, &
	141	ONLY: g, pi
[1320]	142
	143	USE kinds
	144
	145	USE particle_attributes, &
[1822]	146	ONLY: collision_kernel, dissipation_classes, particles, &
	147	radius_classes
[1320]	148
[828]	149	USE pegrid
[790]	150
[828]	151
[790]	152	IMPLICIT NONE
	153
	154	PRIVATE
	155
[1822]	156	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	157	recalculate_kernel
[790]	158
[1682]	159	REAL(wp) :: epsilon !<
	160	REAL(wp) :: rclass_lbound !<
	161	REAL(wp) :: rclass_ubound !<
	162	REAL(wp) :: urms !<
[790]	163
[1822]	164	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	165	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	166	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	167
[1822]	168	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	169	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	170	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	171	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	172	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	173
[1822]	174	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	175
[828]	176	SAVE
[792]	177
[790]	178	!
	179	!-- Public interfaces
[828]	180	INTERFACE init_kernels
	181	MODULE PROCEDURE init_kernels
	182	END INTERFACE init_kernels
[790]	183
[828]	184	INTERFACE recalculate_kernel
	185	MODULE PROCEDURE recalculate_kernel
	186	END INTERFACE recalculate_kernel
[790]	187
	188
[828]	189	CONTAINS
[790]	190
[792]	191
[828]	192	!------------------------------------------------------------------------------!
[1682]	193	! Description:
	194	! ------------
	195	!> Initialization of the collision efficiency matrix with fixed radius and
	196	!> dissipation classes, calculated at simulation start only.
[828]	197	!------------------------------------------------------------------------------!
[1682]	198
	199	SUBROUTINE init_kernels
[792]	200
[828]	201	IMPLICIT NONE
[792]	202
[1682]	203	INTEGER(iwp) :: i !<
	204	INTEGER(iwp) :: j !<
	205	INTEGER(iwp) :: k !<
[790]	206
[828]	207
	208	!
	209	!-- Calculate collision efficiencies for fixed radius- and dissipation
	210	!-- classes
	211	IF ( collision_kernel(6:9) == 'fast' ) THEN
	212
[1822]	213	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	214	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	215	radclass(1:radius_classes) )
	216
	217	!
	218	!-- Calculate the radius class bounds with logarithmic distances
[1858]	219	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	220	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	221	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	222	radclass(1) = EXP( rclass_lbound )
[828]	223	DO i = 2, radius_classes
	224	radclass(i) = EXP( rclass_lbound + &
[1359]	225	( rclass_ubound - rclass_lbound ) * &
	226	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	227	ENDDO
	228
	229	!
[1858]	230	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	231	DO i = 1, dissipation_classes
[1858]	232	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	233	ENDDO
	234	!
	235	!-- Calculate collision efficiencies of the Wang/ayala kernel
	236	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	237	ecf(1:radius_classes,1:radius_classes), &
	238	gck(1:radius_classes,1:radius_classes), &
	239	winf(1:radius_classes) )
	240
	241	DO k = 1, dissipation_classes
	242
	243	epsilon = epsclass(k)
[1359]	244	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	245
	246	CALL turbsd
	247	CALL turb_enhance_eff
	248	CALL effic
	249
	250	DO j = 1, radius_classes
	251	DO i = 1, radius_classes
	252	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	253	ENDDO
	254	ENDDO
	255
	256	ENDDO
	257
	258	!
	259	!-- Calculate collision efficiencies of the Hall kernel
	260	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	261	hwratio(1:radius_classes,1:radius_classes) )
	262
	263	CALL fallg
	264	CALL effic
	265
	266	DO j = 1, radius_classes
	267	DO i = 1, radius_classes
	268	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	269	* ec(i,j) * ABS( winf(j) - winf(i) )
	270	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	271	ENDDO
	272	ENDDO
	273
	274	!
	275	!-- Test output of efficiencies
	276	IF ( j == -1 ) THEN
	277
	278	PRINT, '** Hall kernel'
[1359]	279	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	280	i = 1,radius_classes )
[828]	281	DO j = 1, radius_classes
[1007]	282	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	283	( hkernel(i,j), i = 1,radius_classes )
[828]	284	ENDDO
	285
	286	DO k = 1, dissipation_classes
	287	DO i = 1, radius_classes
	288	DO j = 1, radius_classes
[1359]	289	IF ( hkernel(i,j) == 0.0_wp ) THEN
	290	hwratio(i,j) = 9999999.9_wp
[828]	291	ELSE
	292	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	293	ENDIF
	294	ENDDO
	295	ENDDO
	296
	297	PRINT, '** epsilon = ', epsclass(k)
[1359]	298	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	299	i = 1,radius_classes )
[828]	300	DO j = 1, radius_classes
[1359]	301	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	302	( hwratio(i,j), i = 1,radius_classes )
[828]	303	ENDDO
	304	ENDDO
	305
	306	ENDIF
	307
	308	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	309
	310	ENDIF
	311
	312	END SUBROUTINE init_kernels
	313
	314
[790]	315	!------------------------------------------------------------------------------!
[1682]	316	! Description:
	317	! ------------
	318	!> Calculation of collision kernels during each timestep and for each grid box
[790]	319	!------------------------------------------------------------------------------!
[828]	320	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	321
[1320]	322	USE arrays_3d, &
	323	ONLY: diss
[790]	324
[1320]	325	USE particle_attributes, &
[1858]	326	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	327
[790]	328	IMPLICIT NONE
	329
[1682]	330	INTEGER(iwp) :: i !<
	331	INTEGER(iwp) :: i1 !<
	332	INTEGER(iwp) :: j !<
	333	INTEGER(iwp) :: j1 !<
	334	INTEGER(iwp) :: k1 !<
[790]	335
	336
[1858]	337	number_of_particles = prt_count(k1,j1,i1)
	338	radius_classes = number_of_particles ! necessary to use the same
	339	! subroutines as for
	340	! precalculated kernels
[792]	341
[1858]	342	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	343	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	344
[828]	345	!
[1007]	346	!-- Store particle radii on the radclass array
[1858]	347	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	348
[835]	349	IF ( wang_kernel ) THEN
[1007]	350	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	351	ELSE
[1359]	352	epsilon = 0.0_wp
[835]	353	ENDIF
[1359]	354	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	355
[1359]	356	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	357	!
	358	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	359	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	360	ecf(1:number_of_particles,1:number_of_particles) )
[790]	361
[828]	362	CALL turbsd
	363	CALL turb_enhance_eff
	364	CALL effic
[790]	365
[1858]	366	DO j = 1, number_of_particles
	367	DO i = 1, number_of_particles
	368	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	369	ENDDO
[828]	370	ENDDO
[790]	371
[828]	372	DEALLOCATE( gck, ecf )
[790]	373
	374	ELSE
[828]	375	!
	376	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	377	CALL fallg
	378	CALL effic
	379
[1858]	380	DO j = 1, number_of_particles
	381	DO i = 1, number_of_particles
	382	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	383	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	384	ENDDO
	385	ENDDO
	386
	387	ENDIF
	388
[828]	389	DEALLOCATE( ec, radclass, winf )
[790]	390
[828]	391	END SUBROUTINE recalculate_kernel
[790]	392
[828]	393
[790]	394	!------------------------------------------------------------------------------!
[1682]	395	! Description:
	396	! ------------
[1822]	397	!> Calculation of effects of turbulence on the geometric collision kernel
	398	!> (by including the droplets' average radial relative velocities and their
	399	!> radial distribution function) following the analytic model by Aayala et al.
	400	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	401	!> page 37ff.
	402	!>
	403	!> Input parameters, which need to be replaced by PALM parameters:
	404	!> water density, air density
[790]	405	!------------------------------------------------------------------------------!
[792]	406	SUBROUTINE turbsd
[799]	407
[1320]	408	USE control_parameters, &
[3274]	409	ONLY: molecular_viscosity
[1320]	410
	411	USE particle_attributes, &
	412	ONLY: radius_classes
[790]	413
	414	IMPLICIT NONE
	415
[1682]	416	INTEGER(iwp) :: i !<
	417	INTEGER(iwp) :: j !<
[790]	418
[1682]	419	REAL(wp) :: ao !<
	420	REAL(wp) :: ao_gr !<
	421	REAL(wp) :: bbb !<
	422	REAL(wp) :: be !<
	423	REAL(wp) :: b1 !<
	424	REAL(wp) :: b2 !<
	425	REAL(wp) :: ccc !<
	426	REAL(wp) :: c1 !<
	427	REAL(wp) :: c1_gr !<
	428	REAL(wp) :: c2 !<
	429	REAL(wp) :: d1 !<
	430	REAL(wp) :: d2 !<
	431	REAL(wp) :: eta !<
	432	REAL(wp) :: e1 !<
	433	REAL(wp) :: e2 !<
	434	REAL(wp) :: fao_gr !<
	435	REAL(wp) :: fr !<
	436	REAL(wp) :: grfin !<
	437	REAL(wp) :: lambda !<
	438	REAL(wp) :: lambda_re !<
	439	REAL(wp) :: lf !<
	440	REAL(wp) :: rc !<
	441	REAL(wp) :: rrp !<
	442	REAL(wp) :: sst !<
	443	REAL(wp) :: tauk !<
	444	REAL(wp) :: tl !<
	445	REAL(wp) :: t2 !<
	446	REAL(wp) :: tt !<
	447	REAL(wp) :: t1 !<
	448	REAL(wp) :: vk !<
	449	REAL(wp) :: vrms1xy !<
	450	REAL(wp) :: vrms2xy !<
	451	REAL(wp) :: v1 !<
	452	REAL(wp) :: v1v2xy !<
	453	REAL(wp) :: v1xysq !<
	454	REAL(wp) :: v2 !<
	455	REAL(wp) :: v2xysq !<
	456	REAL(wp) :: wrfin !<
	457	REAL(wp) :: wrgrav2 !<
	458	REAL(wp) :: wrtur2xy !<
	459	REAL(wp) :: xx !<
	460	REAL(wp) :: yy !<
	461	REAL(wp) :: z !<
[790]	462
[1822]	463	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	464	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	465
[1822]	466	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	467	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	468	tl = urms**2 / epsilon
	469	lf = 0.5_wp * urms**3 / epsilon
	470	tauk = SQRT( molecular_viscosity / epsilon )
	471	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	472	vk = eta / tauk
[790]	473
[1359]	474	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	475	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	476
[1822]	477	!
	478	!-- Get terminal velocity of droplets
	479	CALL fallg
[790]	480
[828]	481	DO i = 1, radius_classes
[1822]	482	tau(i) = winf(i) / g ! inertial time scale
	483	st(i) = tau(i) / tauk ! Stokes number
[790]	484	ENDDO
	485
[828]	486	!
[1822]	487	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	488	z = tt / tl
[1322]	489	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	490	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	491	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	492	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	493	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	494	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	495	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	496	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	497	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	498	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	499	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	500
[828]	501	DO i = 1, radius_classes
[790]	502
[1822]	503	v1 = winf(i)
	504	t1 = tau(i)
[790]	505
[828]	506	DO j = 1, i
[1007]	507	rrp = radclass(i) + radclass(j)
[1822]	508	v2 = winf(j)
	509	t2 = tau(j)
[790]	510
[1007]	511	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	512	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	513	v1xysq = v1xysq * urms**2 / t1
	514	vrms1xy = SQRT( v1xysq )
[790]	515
[1007]	516	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	517	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	518	v2xysq = v2xysq * urms**2 / t2
	519	vrms2xy = SQRT( v2xysq )
[790]	520
[828]	521	IF ( winf(i) >= winf(j) ) THEN
[799]	522	v1 = winf(i)
[790]	523	t1 = tau(i)
[799]	524	v2 = winf(j)
[790]	525	t2 = tau(j)
	526	ELSE
[799]	527	v1 = winf(j)
[790]	528	t1 = tau(j)
[799]	529	v2 = winf(i)
[790]	530	t2 = tau(i)
	531	ENDIF
	532
[828]	533	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	534	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	535	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	536	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	537	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	538	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	539	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	540	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	541	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	542	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	543
[828]	544	!
[1822]	545	!-- Calculate radial distribution function (grfin)
[828]	546	IF ( st(j) > st(i) ) THEN
	547	sst = st(j)
[790]	548	ELSE
[828]	549	sst = st(i)
[790]	550	ENDIF
	551
[1359]	552	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	553	sst*2 + 5.3406_wp sst
	554	IF ( xx < 0.0_wp ) xx = 0.0_wp
	555	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	556
[1007]	557	c1_gr = xx / ( g / vk * tauk )**yy
[790]	558
[1322]	559	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	560	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	561	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	562
[1359]	563	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	564	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	565
[1822]	566	!
	567	!-- Calculate general collection kernel (without the consideration of
	568	!-- collection efficiencies)
	569	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	570	gck(j,i) = gck(i,j)
	571
	572	ENDDO
	573	ENDDO
	574
[828]	575	END SUBROUTINE turbsd
[790]	576
[1320]	577	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	578	!
	579	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	580	!-- effects on the collision kernel
[790]	581	IMPLICIT NONE
	582
[1682]	583	REAL(wp) :: a !<
	584	REAL(wp) :: aa1 !<
	585	REAL(wp) :: b !<
	586	REAL(wp) :: tau0 !<
	587	REAL(wp) :: vsett !<
[790]	588
[1359]	589	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	590	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	591
[1007]	592	END FUNCTION phi_w
[792]	593
[1320]	594	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	595	!
	596	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	597	!-- effects on the collision kernel
[790]	598	IMPLICIT NONE
	599
[1682]	600	REAL(wp) :: a !<
	601	REAL(wp) :: aa1 !<
	602	REAL(wp) :: aa2 !<
	603	REAL(wp) :: aa3 !<
	604	REAL(wp) :: aa4 !<
	605	REAL(wp) :: aa5 !<
	606	REAL(wp) :: aa6 !<
	607	REAL(wp) :: b !<
	608	REAL(wp) :: tau1 !<
	609	REAL(wp) :: tau2 !<
	610	REAL(wp) :: vsett1 !<
	611	REAL(wp) :: vsett2 !<
[790]	612
[1359]	613	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	614	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	615	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	616	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	617	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	618	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	619	vsett1 / vsett2
	620	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	621	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	622	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	623	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	624
[828]	625	END FUNCTION zhi
[790]	626
[828]	627
[790]	628	!------------------------------------------------------------------------------!
[1682]	629	! Description:
	630	! ------------
[1822]	631	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	632	!> Meteorol.)
[790]	633	!------------------------------------------------------------------------------!
[828]	634	SUBROUTINE fallg
[790]	635
[1320]	636	USE particle_attributes, &
	637	ONLY: radius_classes
[790]	638
[828]	639	IMPLICIT NONE
[790]	640
[1822]	641	INTEGER(iwp) :: j !<
[790]	642
[1822]	643	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	644	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	645	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	646	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	647	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	648	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	649
[1822]	650	REAL(wp) :: diameter !< droplet diameter in mm
[790]	651
[799]	652
[828]	653	DO j = 1, radius_classes
[790]	654
[1822]	655	diameter = radclass(j) * 2000.0_wp
[799]	656
[1822]	657	IF ( diameter <= d0_rog ) THEN
	658	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	659	EXP( -k_low_rog * diameter ) )
	660	ELSE
	661	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	662	ENDIF
[790]	663
[828]	664	ENDDO
[790]	665
[828]	666	END SUBROUTINE fallg
[790]	667
[828]	668
[790]	669	!------------------------------------------------------------------------------!
[1682]	670	! Description:
	671	! ------------
[1822]	672	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	673	!------------------------------------------------------------------------------!
[828]	674	SUBROUTINE effic
[1320]	675
	676	USE particle_attributes, &
	677	ONLY: radius_classes
[790]	678
[828]	679	IMPLICIT NONE
[790]	680
[1682]	681	INTEGER(iwp) :: i !<
	682	INTEGER(iwp) :: iq !<
	683	INTEGER(iwp) :: ir !<
	684	INTEGER(iwp) :: j !<
	685	INTEGER(iwp) :: k !<
[790]	686
[1682]	687	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	688
[1682]	689	LOGICAL, SAVE :: first = .TRUE. !<
[790]	690
[1682]	691	REAL(wp) :: ek !<
	692	REAL(wp) :: particle_radius !<
	693	REAL(wp) :: pp !<
	694	REAL(wp) :: qq !<
	695	REAL(wp) :: rq !<
[790]	696
[1682]	697	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	698
[1682]	699	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	700
[1682]	701	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	702
[792]	703	!
[828]	704	!-- Initial assignment of constants
	705	IF ( first ) THEN
[790]	706
[792]	707	first = .FALSE.
[1822]	708	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	709	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	710	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	711
[1822]	712	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	713	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	714	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	715	0.90_wp, 0.95_wp, 1.00_wp /)
	716
[1822]	717	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	718	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	719	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	720	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	721	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	722	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	723	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	724	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	725	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	726	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	727	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	728	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	729	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	730	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	731	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	733	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	734	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	735	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	736	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	737	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	738	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	739	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	740	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	741	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	742	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	743	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	744	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	745	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	746	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	747	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	748	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	749	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	751	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	752	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	753	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	754	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	755	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	756	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	757	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	758	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	759	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	760	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	761	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	762	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	763	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	764	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	765	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	766	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	767	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	768	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	769	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	770	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	771	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	772	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	773	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	774	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	775	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	776	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	777	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	778	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	779	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	780	ENDIF
[790]	781
[792]	782	!
[828]	783	!-- Calculate the radius class index of particles with respect to array r
[1822]	784	!-- Radius has to be in microns
[828]	785	ALLOCATE( ira(1:radius_classes) )
	786	DO j = 1, radius_classes
[1322]	787	particle_radius = radclass(j) * 1.0E6_wp
[828]	788	DO k = 1, 15
	789	IF ( particle_radius < r0(k) ) THEN
	790	ira(j) = k
	791	EXIT
	792	ENDIF
	793	ENDDO
	794	IF ( particle_radius >= r0(15) ) ira(j) = 16
	795	ENDDO
[790]	796
[792]	797	!
[828]	798	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	799	!-- Radius has to be in microns
[828]	800	DO j = 1, radius_classes
	801	DO i = 1, j
[792]	802
[1880]	803	ir = MAX( ira(i), ira(j) )
[1519]	804	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	805	iq = INT( rq * 20 ) + 1
	806	iq = MAX( iq , 2)
[792]	807
[828]	808	IF ( ir < 16 ) THEN
	809	IF ( ir >= 2 ) THEN
[1822]	810	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	811	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	812	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	813	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	814	* ecoll(ir-1,iq-1) &
	815	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	816	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	817	+ pp * qq * ecoll(ir,iq)
	818	ELSE
	819	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	820	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	821	ENDIF
	822	ELSE
	823	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	824	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	825	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	826	ENDIF
[792]	827
[1359]	828	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	829
[828]	830	ec(i,j) = ec(j,i)
[792]	831
[828]	832	ENDDO
	833	ENDDO
[792]	834
[828]	835	DEALLOCATE( ira )
[792]	836
[828]	837	END SUBROUTINE effic
[792]	838
	839
[790]	840	!------------------------------------------------------------------------------!
[1682]	841	! Description:
	842	! ------------
[1822]	843	!> Interpolation of turbulent enhancement factor for collision efficencies
	844	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	845	!------------------------------------------------------------------------------!
[828]	846	SUBROUTINE turb_enhance_eff
[790]	847
[1320]	848	USE particle_attributes, &
	849	ONLY: radius_classes
[790]	850
[828]	851	IMPLICIT NONE
[790]	852
[1682]	853	INTEGER(iwp) :: i !<
	854	INTEGER(iwp) :: iq !<
	855	INTEGER(iwp) :: ir !<
	856	INTEGER(iwp) :: j !<
	857	INTEGER(iwp) :: k !<
	858	INTEGER(iwp) :: kk !<
[790]	859
[1682]	860	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	861
[1682]	862	LOGICAL, SAVE :: first = .TRUE. !<
[790]	863
[1682]	864	REAL(wp) :: particle_radius !<
	865	REAL(wp) :: pp !<
	866	REAL(wp) :: qq !<
	867	REAL(wp) :: rq !<
	868	REAL(wp) :: y1 !<
	869	REAL(wp) :: y2 !<
	870	REAL(wp) :: y3 !<
[790]	871
[1682]	872	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	873	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	874
[1682]	875	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	876	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	877
	878	!
[828]	879	!-- Initial assignment of constants
	880	IF ( first ) THEN
[799]	881
[828]	882	first = .FALSE.
[799]	883
[1359]	884	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	885	100.0_wp /)
	886
	887	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	888	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	889	!
[1822]	890	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	891	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	892	1.207_wp, 1.207_wp, 1.0_wp /)
	893	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	894	1.069_wp, 1.069_wp, 1.0_wp /)
	895	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	896	1.000_wp, 1.000_wp, 1.0_wp /)
	897	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	898	1.025_wp, 1.025_wp, 1.0_wp /)
	899	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	900	1.056_wp, 1.056_wp, 1.0_wp /)
	901	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	902	1.028_wp, 1.028_wp, 1.0_wp /)
	903	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	904	1.046_wp, 1.046_wp, 1.0_wp /)
	905	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	906	1.029_wp, 1.029_wp, 1.0_wp /)
	907	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	908	1.021_wp, 1.021_wp, 1.0_wp /)
	909	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	910	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	911	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	912	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	913	!
[1822]	914	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	915	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	916	1.445_wp, 1.445_wp, 1.0_wp /)
	917	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	918	1.201_wp, 1.201_wp, 1.0_wp /)
	919	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	920	1.150_wp, 1.150_wp, 1.0_wp /)
	921	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	922	1.126_wp, 1.126_wp, 1.0_wp /)
	923	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	924	1.092_wp, 1.092_wp, 1.0_wp /)
	925	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	926	1.051_wp, 1.051_wp, 1.0_wp /)
	927	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	928	1.086_wp, 1.086_wp, 1.0_wp /)
	929	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	930	1.063_wp, 1.063_wp, 1.0_wp /)
	931	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	932	1.100_wp, 1.100_wp, 1.0_wp /)
	933	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	934	1.120_wp, 1.120_wp, 1.0_wp /)
	935	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	936	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	937
[828]	938	ENDIF
[790]	939
[828]	940	!
	941	!-- Calculate the radius class index of particles with respect to array r0
[1822]	942	!-- The droplet radius has to be given in microns.
[828]	943	ALLOCATE( ira(1:radius_classes) )
[790]	944
[828]	945	DO j = 1, radius_classes
[1322]	946	particle_radius = radclass(j) * 1.0E6_wp
[828]	947	DO k = 1, 7
	948	IF ( particle_radius < r0(k) ) THEN
	949	ira(j) = k
	950	EXIT
	951	ENDIF
	952	ENDDO
	953	IF ( particle_radius >= r0(7) ) ira(j) = 8
	954	ENDDO
[799]	955
	956	!
[1822]	957	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	958	!-- The droplet radius has to be given in microns.
[828]	959	DO j = 1, radius_classes
	960	DO i = 1, j
[799]	961
[1880]	962	ir = MAX( ira(i), ira(j) )
[1519]	963	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	964
[828]	965	DO kk = 2, 11
	966	IF ( rq <= rat(kk) ) THEN
	967	iq = kk
	968	EXIT
	969	ENDIF
	970	ENDDO
[790]	971
[1822]	972	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	973
[828]	974	IF ( ir < 8 ) THEN
	975	IF ( ir >= 2 ) THEN
[1822]	976	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	977	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	978	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	979	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	980	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	981	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	982	pp * qq * ecoll_100(ir,iq)
	983	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	984	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	985	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	986	pp * qq * ecoll_400(ir,iq)
[828]	987	ELSE
	988	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	989	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	990	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	991	ENDIF
	992	ELSE
	993	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	994	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	995	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	996	ENDIF
	997	!
[1822]	998	!-- Linear interpolation of turbulent enhancement factor
[1359]	999	IF ( epsilon <= 0.01_wp ) THEN
	1000	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	1001	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	1002	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1003	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1004	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1005	ELSE
[1359]	1006	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1007	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1008	ENDIF
[790]	1009
[1359]	1010	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1011
[828]	1012	ecf(i,j) = ecf(j,i)
[790]	1013
[828]	1014	ENDDO
	1015	ENDDO
[790]	1016
[828]	1017	END SUBROUTINE turb_enhance_eff
[790]	1018
[825]	1019	END MODULE lpm_collision_kernels_mod

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