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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1836

Last change on this file since 1836 was 1823, checked in by hoffmann, 9 years ago
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[1682]	1	!> @file lpm_collision_kernels.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[790]	19	! Current revisions:
	20	! -----------------
[1777]	21	!
[1347]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels.f90 1823 2016-04-07 08:57:52Z raasch $
	26	!
[1823]	27	! 1822 2016-04-07 07:49:42Z hoffmann
	28	! PALM kernel has been deleted.
	29	! Bugfix in the calculation of the turbulent enhancement factor of the
	30	! collection efficiency.
	31	!
	32	! Unused variables removed.
	33	!
[1777]	34	! 1776 2016-03-02 17:54:58Z hoffmann
	35	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	36	!
[1683]	37	! 1682 2015-10-07 23:56:08Z knoop
	38	! Code annotations made doxygen readable
	39	!
[1520]	40	! 1519 2015-01-08 10:20:42Z hoffmann
	41	! Bugfix: Using the new particle structure, particles are not sorted by size.
	42	! Hence, computation of collision efficiencies must ensure that the ratio of
	43	! two colliding droplets is < 1.
	44	!
[1360]	45	! 1359 2014-04-11 17:15:14Z hoffmann
	46	! New particle structure integrated.
	47	! Kind definition added to all floating point numbers.
	48	!
[1347]	49	! 1346 2014-03-27 13:18:20Z heinze
	50	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	51	! intrinsic function like MAX, MIN, SIGN
	52	!
[1323]	53	! 1322 2014-03-20 16:38:49Z raasch
	54	! REAL constants defined as wp_kind
	55	!
[1321]	56	! 1320 2014-03-20 08:40:49Z
[1320]	57	! ONLY-attribute added to USE-statements,
	58	! kind-parameters added to all INTEGER and REAL declaration statements,
	59	! kinds are defined in new module kinds,
	60	! revision history before 2012 removed,
	61	! comment fields (!:) to be used for variable explanations added to
	62	! all variable declaration statements
[1008]	63	!
[1093]	64	! 1092 2013-02-02 11:24:22Z raasch
	65	! unused variables removed
	66	!
[1072]	67	! 1071 2012-11-29 16:54:55Z franke
	68	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	69	!
[1037]	70	! 1036 2012-10-22 13:43:42Z raasch
	71	! code put under GPL (PALM 3.9)
	72	!
[1008]	73	! 1007 2012-09-19 14:30:36Z franke
[1007]	74	! converted all units to SI units and replaced some parameters by corresponding
	75	! PALM parameters
	76	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	77	! changed from 10. to 1.0
[829]	78	!
[850]	79	! 849 2012-03-15 10:35:09Z raasch
	80	! routine collision_efficiency_rogers added (moved from former advec_particles
	81	! to here)
	82	!
[836]	83	! 835 2012-02-22 11:21:19Z raasch $
	84	! Bugfix: array diss can be used only in case of Wang kernel
	85	!
[829]	86	! 828 2012-02-21 12:00:36Z raasch
[828]	87	! code has been completely reformatted, routine colker renamed
	88	! recalculate_kernel,
	89	! routine init_kernels added, radius is now communicated to the collision
	90	! routines by array radclass
[790]	91	!
[828]	92	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	93	!
[826]	94	! 825 2012-02-19 03:03:44Z raasch
	95	! routine renamed from wang_kernel to lpm_collision_kernels,
	96	! turbulence_effects on collision replaced by wang_kernel
	97	!
[791]	98	! 790 2011-11-29 03:11:20Z raasch
	99	! initial revision
[790]	100	!
	101	! Description:
	102	! ------------
[1682]	103	!> This module calculates collision efficiencies either due to pure gravitational
	104	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	105	!> including the effects of turbulence (Wang kernel, see Wang and
	106	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	107	!> New J. Phys., 10, 075016). The original code has been
[1682]	108	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	109	!> here.
[790]	110	!------------------------------------------------------------------------------!
[1682]	111	MODULE lpm_collision_kernels_mod
	112
[790]	113
[1320]	114	USE constants, &
	115	ONLY: pi
	116
	117	USE kinds
	118
	119	USE particle_attributes, &
[1822]	120	ONLY: collision_kernel, dissipation_classes, particles, &
	121	radius_classes
[1320]	122
[828]	123	USE pegrid
[790]	124
[828]	125
[790]	126	IMPLICIT NONE
	127
	128	PRIVATE
	129
[1822]	130	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	131	recalculate_kernel
[790]	132
[1682]	133	REAL(wp) :: epsilon !<
	134	REAL(wp) :: rclass_lbound !<
	135	REAL(wp) :: rclass_ubound !<
	136	REAL(wp) :: urms !<
[790]	137
[1822]	138	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	139	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	140	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	141
[1822]	142	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	143	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	144	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	145	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	146	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	147
[1822]	148	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	149
[828]	150	SAVE
[792]	151
[790]	152	!
	153	!-- Public interfaces
[828]	154	INTERFACE init_kernels
	155	MODULE PROCEDURE init_kernels
	156	END INTERFACE init_kernels
[790]	157
[828]	158	INTERFACE recalculate_kernel
	159	MODULE PROCEDURE recalculate_kernel
	160	END INTERFACE recalculate_kernel
[790]	161
	162
[828]	163	CONTAINS
[790]	164
[792]	165
[828]	166	!------------------------------------------------------------------------------!
[1682]	167	! Description:
	168	! ------------
	169	!> Initialization of the collision efficiency matrix with fixed radius and
	170	!> dissipation classes, calculated at simulation start only.
[828]	171	!------------------------------------------------------------------------------!
[1682]	172
	173	SUBROUTINE init_kernels
[792]	174
[828]	175	IMPLICIT NONE
[792]	176
[1682]	177	INTEGER(iwp) :: i !<
	178	INTEGER(iwp) :: j !<
	179	INTEGER(iwp) :: k !<
[790]	180
[828]	181
	182	!
	183	!-- Calculate collision efficiencies for fixed radius- and dissipation
	184	!-- classes
	185	IF ( collision_kernel(6:9) == 'fast' ) THEN
	186
[1822]	187	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	188	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	189	radclass(1:radius_classes) )
	190
	191	!
	192	!-- Calculate the radius class bounds with logarithmic distances
	193	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	194	rclass_lbound = LOG( 1.0E-6_wp )
	195	rclass_ubound = LOG( 2.0E-4_wp )
[1822]	196	radclass(1) = EXP( rclass_lbound )
[828]	197	DO i = 2, radius_classes
	198	radclass(i) = EXP( rclass_lbound + &
[1359]	199	( rclass_ubound - rclass_lbound ) * &
	200	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	201	ENDDO
	202
	203	!
[1007]	204	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	205	DO i = 1, dissipation_classes
[1359]	206	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	207	ENDDO
	208	!
	209	!-- Calculate collision efficiencies of the Wang/ayala kernel
	210	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	211	ecf(1:radius_classes,1:radius_classes), &
	212	gck(1:radius_classes,1:radius_classes), &
	213	winf(1:radius_classes) )
	214
	215	DO k = 1, dissipation_classes
	216
	217	epsilon = epsclass(k)
[1359]	218	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	219
	220	CALL turbsd
	221	CALL turb_enhance_eff
	222	CALL effic
	223
	224	DO j = 1, radius_classes
	225	DO i = 1, radius_classes
	226	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	227	ENDDO
	228	ENDDO
	229
	230	ENDDO
	231
	232	!
	233	!-- Calculate collision efficiencies of the Hall kernel
	234	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	235	hwratio(1:radius_classes,1:radius_classes) )
	236
	237	CALL fallg
	238	CALL effic
	239
	240	DO j = 1, radius_classes
	241	DO i = 1, radius_classes
	242	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	243	* ec(i,j) * ABS( winf(j) - winf(i) )
	244	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	245	ENDDO
	246	ENDDO
	247
	248	!
	249	!-- Test output of efficiencies
	250	IF ( j == -1 ) THEN
	251
	252	PRINT, '** Hall kernel'
[1359]	253	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	254	i = 1,radius_classes )
[828]	255	DO j = 1, radius_classes
[1007]	256	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	257	( hkernel(i,j), i = 1,radius_classes )
[828]	258	ENDDO
	259
	260	DO k = 1, dissipation_classes
	261	DO i = 1, radius_classes
	262	DO j = 1, radius_classes
[1359]	263	IF ( hkernel(i,j) == 0.0_wp ) THEN
	264	hwratio(i,j) = 9999999.9_wp
[828]	265	ELSE
	266	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	267	ENDIF
	268	ENDDO
	269	ENDDO
	270
	271	PRINT, '** epsilon = ', epsclass(k)
[1359]	272	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	273	i = 1,radius_classes )
[828]	274	DO j = 1, radius_classes
[1359]	275	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	276	( hwratio(i,j), i = 1,radius_classes )
[828]	277	ENDDO
	278	ENDDO
	279
	280	ENDIF
	281
	282	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	283
	284	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	285	THEN
	286	!
	287	!-- Initial settings for Hall- and Wang-Kernel
	288	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	289	ENDIF
	290
	291	END SUBROUTINE init_kernels
	292
	293
[790]	294	!------------------------------------------------------------------------------!
[1682]	295	! Description:
	296	! ------------
	297	!> Calculation of collision kernels during each timestep and for each grid box
[790]	298	!------------------------------------------------------------------------------!
[828]	299	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	300
[1320]	301	USE arrays_3d, &
	302	ONLY: diss
[790]	303
[1320]	304	USE particle_attributes, &
[1359]	305	ONLY: prt_count, radius_classes, wang_kernel
[1320]	306
[790]	307	IMPLICIT NONE
	308
[1682]	309	INTEGER(iwp) :: i !<
	310	INTEGER(iwp) :: i1 !<
	311	INTEGER(iwp) :: j !<
	312	INTEGER(iwp) :: j1 !<
	313	INTEGER(iwp) :: k1 !<
	314	INTEGER(iwp) :: pend !<
	315	INTEGER(iwp) :: pstart !<
[790]	316
	317
[1359]	318	pstart = 1
	319	pend = prt_count(k1,j1,i1)
[828]	320	radius_classes = prt_count(k1,j1,i1)
[792]	321
[828]	322	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	323	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	324
[828]	325	!
[1007]	326	!-- Store particle radii on the radclass array
	327	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	328
[835]	329	IF ( wang_kernel ) THEN
[1007]	330	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	331	ELSE
[1359]	332	epsilon = 0.0_wp
[835]	333	ENDIF
[1359]	334	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	335
[1359]	336	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	337	!
	338	!-- Call routines to calculate efficiencies for the Wang kernel
	339	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	340	ecf(1:radius_classes,1:radius_classes) )
[790]	341
[828]	342	CALL turbsd
	343	CALL turb_enhance_eff
	344	CALL effic
[790]	345
[828]	346	DO j = 1, radius_classes
	347	DO i = 1, radius_classes
	348	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	349	ENDDO
[828]	350	ENDDO
[790]	351
[828]	352	DEALLOCATE( gck, ecf )
[790]	353
	354	ELSE
[828]	355	!
	356	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	357	CALL fallg
	358	CALL effic
	359
[828]	360	DO j = 1, radius_classes
	361	DO i = 1, radius_classes
	362	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	363	( radclass(j) + radclass(i) )**2 &
	364	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	365	ENDDO
	366	ENDDO
	367
	368	ENDIF
	369
[828]	370	DEALLOCATE( ec, radclass, winf )
[790]	371
[828]	372	END SUBROUTINE recalculate_kernel
[790]	373
[828]	374
[790]	375	!------------------------------------------------------------------------------!
[1682]	376	! Description:
	377	! ------------
[1822]	378	!> Calculation of effects of turbulence on the geometric collision kernel
	379	!> (by including the droplets' average radial relative velocities and their
	380	!> radial distribution function) following the analytic model by Aayala et al.
	381	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	382	!> page 37ff.
	383	!>
	384	!> Input parameters, which need to be replaced by PALM parameters:
	385	!> water density, air density
[790]	386	!------------------------------------------------------------------------------!
[792]	387	SUBROUTINE turbsd
[799]	388
[1320]	389	USE control_parameters, &
	390	ONLY: g, molecular_viscosity
	391
	392	USE particle_attributes, &
	393	ONLY: radius_classes
[790]	394
	395	IMPLICIT NONE
	396
[1682]	397	INTEGER(iwp) :: i !<
	398	INTEGER(iwp) :: j !<
[790]	399
[1682]	400	REAL(wp) :: ao !<
	401	REAL(wp) :: ao_gr !<
	402	REAL(wp) :: bbb !<
	403	REAL(wp) :: be !<
	404	REAL(wp) :: b1 !<
	405	REAL(wp) :: b2 !<
	406	REAL(wp) :: ccc !<
	407	REAL(wp) :: c1 !<
	408	REAL(wp) :: c1_gr !<
	409	REAL(wp) :: c2 !<
	410	REAL(wp) :: d1 !<
	411	REAL(wp) :: d2 !<
	412	REAL(wp) :: eta !<
	413	REAL(wp) :: e1 !<
	414	REAL(wp) :: e2 !<
	415	REAL(wp) :: fao_gr !<
	416	REAL(wp) :: fr !<
	417	REAL(wp) :: grfin !<
	418	REAL(wp) :: lambda !<
	419	REAL(wp) :: lambda_re !<
	420	REAL(wp) :: lf !<
	421	REAL(wp) :: rc !<
	422	REAL(wp) :: rrp !<
	423	REAL(wp) :: sst !<
	424	REAL(wp) :: tauk !<
	425	REAL(wp) :: tl !<
	426	REAL(wp) :: t2 !<
	427	REAL(wp) :: tt !<
	428	REAL(wp) :: t1 !<
	429	REAL(wp) :: vk !<
	430	REAL(wp) :: vrms1xy !<
	431	REAL(wp) :: vrms2xy !<
	432	REAL(wp) :: v1 !<
	433	REAL(wp) :: v1v2xy !<
	434	REAL(wp) :: v1xysq !<
	435	REAL(wp) :: v2 !<
	436	REAL(wp) :: v2xysq !<
	437	REAL(wp) :: wrfin !<
	438	REAL(wp) :: wrgrav2 !<
	439	REAL(wp) :: wrtur2xy !<
	440	REAL(wp) :: xx !<
	441	REAL(wp) :: yy !<
	442	REAL(wp) :: z !<
[790]	443
[1822]	444	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	445	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	446
[1822]	447	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	448	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	449	tl = urms**2 / epsilon
	450	lf = 0.5_wp * urms**3 / epsilon
	451	tauk = SQRT( molecular_viscosity / epsilon )
	452	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	453	vk = eta / tauk
[790]	454
[1359]	455	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	456	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	457
[1822]	458	!
	459	!-- Get terminal velocity of droplets
	460	CALL fallg
[790]	461
[828]	462	DO i = 1, radius_classes
[1822]	463	tau(i) = winf(i) / g ! inertial time scale
	464	st(i) = tau(i) / tauk ! Stokes number
[790]	465	ENDDO
	466
[828]	467	!
[1822]	468	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	469	z = tt / tl
[1322]	470	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	471	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	472	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	473	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	474	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	475	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	476	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	477	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	478	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	479	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	480	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	481
[828]	482	DO i = 1, radius_classes
[790]	483
[1822]	484	v1 = winf(i)
	485	t1 = tau(i)
[790]	486
[828]	487	DO j = 1, i
[1007]	488	rrp = radclass(i) + radclass(j)
[1822]	489	v2 = winf(j)
	490	t2 = tau(j)
[790]	491
[1007]	492	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	493	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	494	v1xysq = v1xysq * urms**2 / t1
	495	vrms1xy = SQRT( v1xysq )
[790]	496
[1007]	497	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	498	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	499	v2xysq = v2xysq * urms**2 / t2
	500	vrms2xy = SQRT( v2xysq )
[790]	501
[828]	502	IF ( winf(i) >= winf(j) ) THEN
[799]	503	v1 = winf(i)
[790]	504	t1 = tau(i)
[799]	505	v2 = winf(j)
[790]	506	t2 = tau(j)
	507	ELSE
[799]	508	v1 = winf(j)
[790]	509	t1 = tau(j)
[799]	510	v2 = winf(i)
[790]	511	t2 = tau(i)
	512	ENDIF
	513
[828]	514	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	515	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	516	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	517	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	518	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	519	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	520	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	521	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	522	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	523	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	524
[828]	525	!
[1822]	526	!-- Calculate radial distribution function (grfin)
[828]	527	IF ( st(j) > st(i) ) THEN
	528	sst = st(j)
[790]	529	ELSE
[828]	530	sst = st(i)
[790]	531	ENDIF
	532
[1359]	533	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	534	sst*2 + 5.3406_wp sst
	535	IF ( xx < 0.0_wp ) xx = 0.0_wp
	536	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	537
[1007]	538	c1_gr = xx / ( g / vk * tauk )**yy
[790]	539
[1322]	540	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	541	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	542	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	543
[1359]	544	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	545	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	546
[1822]	547	!
	548	!-- Calculate general collection kernel (without the consideration of
	549	!-- collection efficiencies)
	550	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	551	gck(j,i) = gck(i,j)
	552
	553	ENDDO
	554	ENDDO
	555
[828]	556	END SUBROUTINE turbsd
[790]	557
[1320]	558	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	559	!
	560	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	561	!-- effects on the collision kernel
[790]	562	IMPLICIT NONE
	563
[1682]	564	REAL(wp) :: a !<
	565	REAL(wp) :: aa1 !<
	566	REAL(wp) :: b !<
	567	REAL(wp) :: tau0 !<
	568	REAL(wp) :: vsett !<
[790]	569
[1359]	570	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	571	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	572
[1007]	573	END FUNCTION phi_w
[792]	574
[1320]	575	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	576	!
	577	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	578	!-- effects on the collision kernel
[790]	579	IMPLICIT NONE
	580
[1682]	581	REAL(wp) :: a !<
	582	REAL(wp) :: aa1 !<
	583	REAL(wp) :: aa2 !<
	584	REAL(wp) :: aa3 !<
	585	REAL(wp) :: aa4 !<
	586	REAL(wp) :: aa5 !<
	587	REAL(wp) :: aa6 !<
	588	REAL(wp) :: b !<
	589	REAL(wp) :: tau1 !<
	590	REAL(wp) :: tau2 !<
	591	REAL(wp) :: vsett1 !<
	592	REAL(wp) :: vsett2 !<
[790]	593
[1359]	594	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	595	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	596	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	597	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	598	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	599	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	600	vsett1 / vsett2
	601	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	602	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	603	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	604	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	605
[828]	606	END FUNCTION zhi
[790]	607
[828]	608
[790]	609	!------------------------------------------------------------------------------!
[1682]	610	! Description:
	611	! ------------
[1822]	612	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	613	!> Meteorol.)
[790]	614	!------------------------------------------------------------------------------!
[828]	615	SUBROUTINE fallg
[790]	616
[1320]	617	USE particle_attributes, &
	618	ONLY: radius_classes
[790]	619
[828]	620	IMPLICIT NONE
[790]	621
[1822]	622	INTEGER(iwp) :: j !<
[790]	623
[1822]	624	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	625	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	626	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	627	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	628	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	629	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	630
[1822]	631	REAL(wp) :: diameter !< droplet diameter in mm
[790]	632
[799]	633
[828]	634	DO j = 1, radius_classes
[790]	635
[1822]	636	diameter = radclass(j) * 2000.0_wp
[799]	637
[1822]	638	IF ( diameter <= d0_rog ) THEN
	639	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	640	EXP( -k_low_rog * diameter ) )
	641	ELSE
	642	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	643	ENDIF
[790]	644
[828]	645	ENDDO
[790]	646
[828]	647	END SUBROUTINE fallg
[790]	648
[828]	649
[790]	650	!------------------------------------------------------------------------------!
[1682]	651	! Description:
	652	! ------------
[1822]	653	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	654	!------------------------------------------------------------------------------!
[828]	655	SUBROUTINE effic
[1320]	656
	657	USE particle_attributes, &
	658	ONLY: radius_classes
[790]	659
[828]	660	IMPLICIT NONE
[790]	661
[1682]	662	INTEGER(iwp) :: i !<
	663	INTEGER(iwp) :: iq !<
	664	INTEGER(iwp) :: ir !<
	665	INTEGER(iwp) :: j !<
	666	INTEGER(iwp) :: k !<
[790]	667
[1682]	668	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	669
[1682]	670	LOGICAL, SAVE :: first = .TRUE. !<
[790]	671
[1682]	672	REAL(wp) :: ek !<
	673	REAL(wp) :: particle_radius !<
	674	REAL(wp) :: pp !<
	675	REAL(wp) :: qq !<
	676	REAL(wp) :: rq !<
[790]	677
[1682]	678	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	679
[1682]	680	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	681
[1682]	682	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	683
[792]	684	!
[828]	685	!-- Initial assignment of constants
	686	IF ( first ) THEN
[790]	687
[792]	688	first = .FALSE.
[1822]	689	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	690	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	691	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	692
[1822]	693	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	694	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	695	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	696	0.90_wp, 0.95_wp, 1.00_wp /)
	697
[1822]	698	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	699	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	700	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	701	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	702	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	703	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	704	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	705	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	706	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	707	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	708	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	709	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	710	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	711	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	712	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	713	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	714	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	715	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	716	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	717	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	718	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	719	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	720	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	721	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	722	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	723	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	724	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	725	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	726	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	727	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	728	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	729	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	730	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	731	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	732	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	733	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	734	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	735	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	736	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	737	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	738	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	739	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	740	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	741	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	742	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	743	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	744	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	745	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	746	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	747	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	748	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	749	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	750	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	751	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	752	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	753	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	754	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	755	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	756	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	757	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	758	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	759	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	760	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	761	ENDIF
[790]	762
[792]	763	!
[828]	764	!-- Calculate the radius class index of particles with respect to array r
[1822]	765	!-- Radius has to be in microns
[828]	766	ALLOCATE( ira(1:radius_classes) )
	767	DO j = 1, radius_classes
[1322]	768	particle_radius = radclass(j) * 1.0E6_wp
[828]	769	DO k = 1, 15
	770	IF ( particle_radius < r0(k) ) THEN
	771	ira(j) = k
	772	EXIT
	773	ENDIF
	774	ENDDO
	775	IF ( particle_radius >= r0(15) ) ira(j) = 16
	776	ENDDO
[790]	777
[792]	778	!
[828]	779	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	780	!-- Radius has to be in microns
[828]	781	DO j = 1, radius_classes
	782	DO i = 1, j
[792]	783
[828]	784	ir = ira(j)
[1519]	785	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	786	iq = INT( rq * 20 ) + 1
	787	iq = MAX( iq , 2)
[792]	788
[828]	789	IF ( ir < 16 ) THEN
	790	IF ( ir >= 2 ) THEN
[1822]	791	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	792	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	793	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	794	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	795	* ecoll(ir-1,iq-1) &
	796	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	797	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	798	+ pp * qq * ecoll(ir,iq)
	799	ELSE
	800	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	801	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	802	ENDIF
	803	ELSE
	804	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	805	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	806	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	807	ENDIF
[792]	808
[1359]	809	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	810
[828]	811	ec(i,j) = ec(j,i)
[792]	812
[828]	813	ENDDO
	814	ENDDO
[792]	815
[828]	816	DEALLOCATE( ira )
[792]	817
[828]	818	END SUBROUTINE effic
[792]	819
	820
[790]	821	!------------------------------------------------------------------------------!
[1682]	822	! Description:
	823	! ------------
[1822]	824	!> Interpolation of turbulent enhancement factor for collision efficencies
	825	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	826	!------------------------------------------------------------------------------!
[828]	827	SUBROUTINE turb_enhance_eff
[790]	828
[1320]	829	USE particle_attributes, &
	830	ONLY: radius_classes
[790]	831
[828]	832	IMPLICIT NONE
[790]	833
[1682]	834	INTEGER(iwp) :: i !<
	835	INTEGER(iwp) :: iq !<
	836	INTEGER(iwp) :: ir !<
	837	INTEGER(iwp) :: j !<
	838	INTEGER(iwp) :: k !<
	839	INTEGER(iwp) :: kk !<
[790]	840
[1682]	841	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	842
[1682]	843	LOGICAL, SAVE :: first = .TRUE. !<
[790]	844
[1682]	845	REAL(wp) :: particle_radius !<
	846	REAL(wp) :: pp !<
	847	REAL(wp) :: qq !<
	848	REAL(wp) :: rq !<
	849	REAL(wp) :: y1 !<
	850	REAL(wp) :: y2 !<
	851	REAL(wp) :: y3 !<
[790]	852
[1682]	853	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	854	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	855
[1682]	856	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	857	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	858
	859	!
[828]	860	!-- Initial assignment of constants
	861	IF ( first ) THEN
[799]	862
[828]	863	first = .FALSE.
[799]	864
[1359]	865	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	866	100.0_wp /)
	867
	868	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	869	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	870	!
[1822]	871	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	872	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	873	1.207_wp, 1.207_wp, 1.0_wp /)
	874	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	875	1.069_wp, 1.069_wp, 1.0_wp /)
	876	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	877	1.000_wp, 1.000_wp, 1.0_wp /)
	878	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	879	1.025_wp, 1.025_wp, 1.0_wp /)
	880	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	881	1.056_wp, 1.056_wp, 1.0_wp /)
	882	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	883	1.028_wp, 1.028_wp, 1.0_wp /)
	884	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	885	1.046_wp, 1.046_wp, 1.0_wp /)
	886	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	887	1.029_wp, 1.029_wp, 1.0_wp /)
	888	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	889	1.021_wp, 1.021_wp, 1.0_wp /)
	890	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	891	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	892	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	893	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	894	!
[1822]	895	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	896	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	897	1.445_wp, 1.445_wp, 1.0_wp /)
	898	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	899	1.201_wp, 1.201_wp, 1.0_wp /)
	900	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	901	1.150_wp, 1.150_wp, 1.0_wp /)
	902	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	903	1.126_wp, 1.126_wp, 1.0_wp /)
	904	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	905	1.092_wp, 1.092_wp, 1.0_wp /)
	906	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	907	1.051_wp, 1.051_wp, 1.0_wp /)
	908	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	909	1.086_wp, 1.086_wp, 1.0_wp /)
	910	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	911	1.063_wp, 1.063_wp, 1.0_wp /)
	912	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	913	1.100_wp, 1.100_wp, 1.0_wp /)
	914	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	915	1.120_wp, 1.120_wp, 1.0_wp /)
	916	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	917	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	918
[828]	919	ENDIF
[790]	920
[828]	921	!
	922	!-- Calculate the radius class index of particles with respect to array r0
[1822]	923	!-- The droplet radius has to be given in microns.
[828]	924	ALLOCATE( ira(1:radius_classes) )
[790]	925
[828]	926	DO j = 1, radius_classes
[1322]	927	particle_radius = radclass(j) * 1.0E6_wp
[828]	928	DO k = 1, 7
	929	IF ( particle_radius < r0(k) ) THEN
	930	ira(j) = k
	931	EXIT
	932	ENDIF
	933	ENDDO
	934	IF ( particle_radius >= r0(7) ) ira(j) = 8
	935	ENDDO
[799]	936
	937	!
[1822]	938	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	939	!-- The droplet radius has to be given in microns.
[828]	940	DO j = 1, radius_classes
	941	DO i = 1, j
[799]	942
[828]	943	ir = ira(j)
[1519]	944	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	945
[828]	946	DO kk = 2, 11
	947	IF ( rq <= rat(kk) ) THEN
	948	iq = kk
	949	EXIT
	950	ENDIF
	951	ENDDO
[790]	952
[1822]	953	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	954
[828]	955	IF ( ir < 8 ) THEN
	956	IF ( ir >= 2 ) THEN
[1822]	957	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	958	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	959	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	960	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	961	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	962	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	963	pp * qq * ecoll_100(ir,iq)
	964	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	965	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	966	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	967	pp * qq * ecoll_400(ir,iq)
[828]	968	ELSE
	969	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	970	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	971	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	972	ENDIF
	973	ELSE
	974	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	975	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	976	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	977	ENDIF
	978	!
[1822]	979	!-- Linear interpolation of turbulent enhancement factor
[1359]	980	IF ( epsilon <= 0.01_wp ) THEN
	981	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	982	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	983	ELSEIF ( epsilon <= 0.06_wp ) THEN
	984	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	985	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	986	ELSE
[1359]	987	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	988	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	989	ENDIF
[790]	990
[1359]	991	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	992
[828]	993	ecf(i,j) = ecf(j,i)
[790]	994
[828]	995	ENDDO
	996	ENDDO
[790]	997
[828]	998	END SUBROUTINE turb_enhance_eff
[790]	999
[825]	1000	END MODULE lpm_collision_kernels_mod

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