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source: palm/trunk/SOURCE/lpm_collision_kernels_mod.f90 @ 1854

Last change on this file since 1854 was 1851, checked in by maronga, 8 years ago
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[1850]	1	!> @file lpm_collision_kernels_mod.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	! -----------------
[1347]	21	!
[1851]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels_mod.f90 1851 2016-04-08 13:32:50Z maronga $
	26	!
[1851]	27	! 1850 2016-04-08 13:29:27Z maronga
	28	! Module renamed
	29	!
	30	!
[1823]	31	! 1822 2016-04-07 07:49:42Z hoffmann
	32	! PALM kernel has been deleted.
	33	! Bugfix in the calculation of the turbulent enhancement factor of the
	34	! collection efficiency.
	35	!
	36	! Unused variables removed.
	37	!
[1777]	38	! 1776 2016-03-02 17:54:58Z hoffmann
	39	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	40	!
[1683]	41	! 1682 2015-10-07 23:56:08Z knoop
	42	! Code annotations made doxygen readable
	43	!
[1520]	44	! 1519 2015-01-08 10:20:42Z hoffmann
	45	! Bugfix: Using the new particle structure, particles are not sorted by size.
	46	! Hence, computation of collision efficiencies must ensure that the ratio of
	47	! two colliding droplets is < 1.
	48	!
[1360]	49	! 1359 2014-04-11 17:15:14Z hoffmann
	50	! New particle structure integrated.
	51	! Kind definition added to all floating point numbers.
	52	!
[1347]	53	! 1346 2014-03-27 13:18:20Z heinze
	54	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	55	! intrinsic function like MAX, MIN, SIGN
	56	!
[1323]	57	! 1322 2014-03-20 16:38:49Z raasch
	58	! REAL constants defined as wp_kind
	59	!
[1321]	60	! 1320 2014-03-20 08:40:49Z
[1320]	61	! ONLY-attribute added to USE-statements,
	62	! kind-parameters added to all INTEGER and REAL declaration statements,
	63	! kinds are defined in new module kinds,
	64	! revision history before 2012 removed,
	65	! comment fields (!:) to be used for variable explanations added to
	66	! all variable declaration statements
[1008]	67	!
[1093]	68	! 1092 2013-02-02 11:24:22Z raasch
	69	! unused variables removed
	70	!
[1072]	71	! 1071 2012-11-29 16:54:55Z franke
	72	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	73	!
[1037]	74	! 1036 2012-10-22 13:43:42Z raasch
	75	! code put under GPL (PALM 3.9)
	76	!
[1008]	77	! 1007 2012-09-19 14:30:36Z franke
[1007]	78	! converted all units to SI units and replaced some parameters by corresponding
	79	! PALM parameters
	80	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	81	! changed from 10. to 1.0
[829]	82	!
[850]	83	! 849 2012-03-15 10:35:09Z raasch
	84	! routine collision_efficiency_rogers added (moved from former advec_particles
	85	! to here)
	86	!
[836]	87	! 835 2012-02-22 11:21:19Z raasch $
	88	! Bugfix: array diss can be used only in case of Wang kernel
	89	!
[829]	90	! 828 2012-02-21 12:00:36Z raasch
[828]	91	! code has been completely reformatted, routine colker renamed
	92	! recalculate_kernel,
	93	! routine init_kernels added, radius is now communicated to the collision
	94	! routines by array radclass
[790]	95	!
[828]	96	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	97	!
[826]	98	! 825 2012-02-19 03:03:44Z raasch
	99	! routine renamed from wang_kernel to lpm_collision_kernels,
	100	! turbulence_effects on collision replaced by wang_kernel
	101	!
[791]	102	! 790 2011-11-29 03:11:20Z raasch
	103	! initial revision
[790]	104	!
	105	! Description:
	106	! ------------
[1682]	107	!> This module calculates collision efficiencies either due to pure gravitational
	108	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	109	!> including the effects of turbulence (Wang kernel, see Wang and
	110	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	111	!> New J. Phys., 10, 075016). The original code has been
[1682]	112	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	113	!> here.
[790]	114	!------------------------------------------------------------------------------!
[1682]	115	MODULE lpm_collision_kernels_mod
	116
[790]	117
[1320]	118	USE constants, &
	119	ONLY: pi
	120
	121	USE kinds
	122
	123	USE particle_attributes, &
[1822]	124	ONLY: collision_kernel, dissipation_classes, particles, &
	125	radius_classes
[1320]	126
[828]	127	USE pegrid
[790]	128
[828]	129
[790]	130	IMPLICIT NONE
	131
	132	PRIVATE
	133
[1822]	134	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	135	recalculate_kernel
[790]	136
[1682]	137	REAL(wp) :: epsilon !<
	138	REAL(wp) :: rclass_lbound !<
	139	REAL(wp) :: rclass_ubound !<
	140	REAL(wp) :: urms !<
[790]	141
[1822]	142	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	143	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	144	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	145
[1822]	146	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	147	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	148	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	149	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	150	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	151
[1822]	152	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	153
[828]	154	SAVE
[792]	155
[790]	156	!
	157	!-- Public interfaces
[828]	158	INTERFACE init_kernels
	159	MODULE PROCEDURE init_kernels
	160	END INTERFACE init_kernels
[790]	161
[828]	162	INTERFACE recalculate_kernel
	163	MODULE PROCEDURE recalculate_kernel
	164	END INTERFACE recalculate_kernel
[790]	165
	166
[828]	167	CONTAINS
[790]	168
[792]	169
[828]	170	!------------------------------------------------------------------------------!
[1682]	171	! Description:
	172	! ------------
	173	!> Initialization of the collision efficiency matrix with fixed radius and
	174	!> dissipation classes, calculated at simulation start only.
[828]	175	!------------------------------------------------------------------------------!
[1682]	176
	177	SUBROUTINE init_kernels
[792]	178
[828]	179	IMPLICIT NONE
[792]	180
[1682]	181	INTEGER(iwp) :: i !<
	182	INTEGER(iwp) :: j !<
	183	INTEGER(iwp) :: k !<
[790]	184
[828]	185
	186	!
	187	!-- Calculate collision efficiencies for fixed radius- and dissipation
	188	!-- classes
	189	IF ( collision_kernel(6:9) == 'fast' ) THEN
	190
[1822]	191	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	192	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	193	radclass(1:radius_classes) )
	194
	195	!
	196	!-- Calculate the radius class bounds with logarithmic distances
	197	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	198	rclass_lbound = LOG( 1.0E-6_wp )
	199	rclass_ubound = LOG( 2.0E-4_wp )
[1822]	200	radclass(1) = EXP( rclass_lbound )
[828]	201	DO i = 2, radius_classes
	202	radclass(i) = EXP( rclass_lbound + &
[1359]	203	( rclass_ubound - rclass_lbound ) * &
	204	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	205	ENDDO
	206
	207	!
[1007]	208	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	209	DO i = 1, dissipation_classes
[1359]	210	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	211	ENDDO
	212	!
	213	!-- Calculate collision efficiencies of the Wang/ayala kernel
	214	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	215	ecf(1:radius_classes,1:radius_classes), &
	216	gck(1:radius_classes,1:radius_classes), &
	217	winf(1:radius_classes) )
	218
	219	DO k = 1, dissipation_classes
	220
	221	epsilon = epsclass(k)
[1359]	222	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	223
	224	CALL turbsd
	225	CALL turb_enhance_eff
	226	CALL effic
	227
	228	DO j = 1, radius_classes
	229	DO i = 1, radius_classes
	230	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	231	ENDDO
	232	ENDDO
	233
	234	ENDDO
	235
	236	!
	237	!-- Calculate collision efficiencies of the Hall kernel
	238	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	239	hwratio(1:radius_classes,1:radius_classes) )
	240
	241	CALL fallg
	242	CALL effic
	243
	244	DO j = 1, radius_classes
	245	DO i = 1, radius_classes
	246	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	247	* ec(i,j) * ABS( winf(j) - winf(i) )
	248	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	249	ENDDO
	250	ENDDO
	251
	252	!
	253	!-- Test output of efficiencies
	254	IF ( j == -1 ) THEN
	255
	256	PRINT, '** Hall kernel'
[1359]	257	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	258	i = 1,radius_classes )
[828]	259	DO j = 1, radius_classes
[1007]	260	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	261	( hkernel(i,j), i = 1,radius_classes )
[828]	262	ENDDO
	263
	264	DO k = 1, dissipation_classes
	265	DO i = 1, radius_classes
	266	DO j = 1, radius_classes
[1359]	267	IF ( hkernel(i,j) == 0.0_wp ) THEN
	268	hwratio(i,j) = 9999999.9_wp
[828]	269	ELSE
	270	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	271	ENDIF
	272	ENDDO
	273	ENDDO
	274
	275	PRINT, '** epsilon = ', epsclass(k)
[1359]	276	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	277	i = 1,radius_classes )
[828]	278	DO j = 1, radius_classes
[1359]	279	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	280	( hwratio(i,j), i = 1,radius_classes )
[828]	281	ENDDO
	282	ENDDO
	283
	284	ENDIF
	285
	286	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	287
	288	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	289	THEN
	290	!
	291	!-- Initial settings for Hall- and Wang-Kernel
	292	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	293	ENDIF
	294
	295	END SUBROUTINE init_kernels
	296
	297
[790]	298	!------------------------------------------------------------------------------!
[1682]	299	! Description:
	300	! ------------
	301	!> Calculation of collision kernels during each timestep and for each grid box
[790]	302	!------------------------------------------------------------------------------!
[828]	303	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	304
[1320]	305	USE arrays_3d, &
	306	ONLY: diss
[790]	307
[1320]	308	USE particle_attributes, &
[1359]	309	ONLY: prt_count, radius_classes, wang_kernel
[1320]	310
[790]	311	IMPLICIT NONE
	312
[1682]	313	INTEGER(iwp) :: i !<
	314	INTEGER(iwp) :: i1 !<
	315	INTEGER(iwp) :: j !<
	316	INTEGER(iwp) :: j1 !<
	317	INTEGER(iwp) :: k1 !<
	318	INTEGER(iwp) :: pend !<
	319	INTEGER(iwp) :: pstart !<
[790]	320
	321
[1359]	322	pstart = 1
	323	pend = prt_count(k1,j1,i1)
[828]	324	radius_classes = prt_count(k1,j1,i1)
[792]	325
[828]	326	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	327	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	328
[828]	329	!
[1007]	330	!-- Store particle radii on the radclass array
	331	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	332
[835]	333	IF ( wang_kernel ) THEN
[1007]	334	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	335	ELSE
[1359]	336	epsilon = 0.0_wp
[835]	337	ENDIF
[1359]	338	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	339
[1359]	340	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	341	!
	342	!-- Call routines to calculate efficiencies for the Wang kernel
	343	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	344	ecf(1:radius_classes,1:radius_classes) )
[790]	345
[828]	346	CALL turbsd
	347	CALL turb_enhance_eff
	348	CALL effic
[790]	349
[828]	350	DO j = 1, radius_classes
	351	DO i = 1, radius_classes
	352	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	353	ENDDO
[828]	354	ENDDO
[790]	355
[828]	356	DEALLOCATE( gck, ecf )
[790]	357
	358	ELSE
[828]	359	!
	360	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	361	CALL fallg
	362	CALL effic
	363
[828]	364	DO j = 1, radius_classes
	365	DO i = 1, radius_classes
	366	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	367	( radclass(j) + radclass(i) )**2 &
	368	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	369	ENDDO
	370	ENDDO
	371
	372	ENDIF
	373
[828]	374	DEALLOCATE( ec, radclass, winf )
[790]	375
[828]	376	END SUBROUTINE recalculate_kernel
[790]	377
[828]	378
[790]	379	!------------------------------------------------------------------------------!
[1682]	380	! Description:
	381	! ------------
[1822]	382	!> Calculation of effects of turbulence on the geometric collision kernel
	383	!> (by including the droplets' average radial relative velocities and their
	384	!> radial distribution function) following the analytic model by Aayala et al.
	385	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	386	!> page 37ff.
	387	!>
	388	!> Input parameters, which need to be replaced by PALM parameters:
	389	!> water density, air density
[790]	390	!------------------------------------------------------------------------------!
[792]	391	SUBROUTINE turbsd
[799]	392
[1320]	393	USE control_parameters, &
	394	ONLY: g, molecular_viscosity
	395
	396	USE particle_attributes, &
	397	ONLY: radius_classes
[790]	398
	399	IMPLICIT NONE
	400
[1682]	401	INTEGER(iwp) :: i !<
	402	INTEGER(iwp) :: j !<
[790]	403
[1682]	404	REAL(wp) :: ao !<
	405	REAL(wp) :: ao_gr !<
	406	REAL(wp) :: bbb !<
	407	REAL(wp) :: be !<
	408	REAL(wp) :: b1 !<
	409	REAL(wp) :: b2 !<
	410	REAL(wp) :: ccc !<
	411	REAL(wp) :: c1 !<
	412	REAL(wp) :: c1_gr !<
	413	REAL(wp) :: c2 !<
	414	REAL(wp) :: d1 !<
	415	REAL(wp) :: d2 !<
	416	REAL(wp) :: eta !<
	417	REAL(wp) :: e1 !<
	418	REAL(wp) :: e2 !<
	419	REAL(wp) :: fao_gr !<
	420	REAL(wp) :: fr !<
	421	REAL(wp) :: grfin !<
	422	REAL(wp) :: lambda !<
	423	REAL(wp) :: lambda_re !<
	424	REAL(wp) :: lf !<
	425	REAL(wp) :: rc !<
	426	REAL(wp) :: rrp !<
	427	REAL(wp) :: sst !<
	428	REAL(wp) :: tauk !<
	429	REAL(wp) :: tl !<
	430	REAL(wp) :: t2 !<
	431	REAL(wp) :: tt !<
	432	REAL(wp) :: t1 !<
	433	REAL(wp) :: vk !<
	434	REAL(wp) :: vrms1xy !<
	435	REAL(wp) :: vrms2xy !<
	436	REAL(wp) :: v1 !<
	437	REAL(wp) :: v1v2xy !<
	438	REAL(wp) :: v1xysq !<
	439	REAL(wp) :: v2 !<
	440	REAL(wp) :: v2xysq !<
	441	REAL(wp) :: wrfin !<
	442	REAL(wp) :: wrgrav2 !<
	443	REAL(wp) :: wrtur2xy !<
	444	REAL(wp) :: xx !<
	445	REAL(wp) :: yy !<
	446	REAL(wp) :: z !<
[790]	447
[1822]	448	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	449	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	450
[1822]	451	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	452	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	453	tl = urms**2 / epsilon
	454	lf = 0.5_wp * urms**3 / epsilon
	455	tauk = SQRT( molecular_viscosity / epsilon )
	456	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	457	vk = eta / tauk
[790]	458
[1359]	459	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	460	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	461
[1822]	462	!
	463	!-- Get terminal velocity of droplets
	464	CALL fallg
[790]	465
[828]	466	DO i = 1, radius_classes
[1822]	467	tau(i) = winf(i) / g ! inertial time scale
	468	st(i) = tau(i) / tauk ! Stokes number
[790]	469	ENDDO
	470
[828]	471	!
[1822]	472	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	473	z = tt / tl
[1322]	474	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	475	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	476	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	477	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	478	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	479	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	480	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	481	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	482	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	483	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	484	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	485
[828]	486	DO i = 1, radius_classes
[790]	487
[1822]	488	v1 = winf(i)
	489	t1 = tau(i)
[790]	490
[828]	491	DO j = 1, i
[1007]	492	rrp = radclass(i) + radclass(j)
[1822]	493	v2 = winf(j)
	494	t2 = tau(j)
[790]	495
[1007]	496	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	497	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	498	v1xysq = v1xysq * urms**2 / t1
	499	vrms1xy = SQRT( v1xysq )
[790]	500
[1007]	501	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	502	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	503	v2xysq = v2xysq * urms**2 / t2
	504	vrms2xy = SQRT( v2xysq )
[790]	505
[828]	506	IF ( winf(i) >= winf(j) ) THEN
[799]	507	v1 = winf(i)
[790]	508	t1 = tau(i)
[799]	509	v2 = winf(j)
[790]	510	t2 = tau(j)
	511	ELSE
[799]	512	v1 = winf(j)
[790]	513	t1 = tau(j)
[799]	514	v2 = winf(i)
[790]	515	t2 = tau(i)
	516	ENDIF
	517
[828]	518	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	519	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	520	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	521	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	522	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	523	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	524	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	525	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	526	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	527	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	528
[828]	529	!
[1822]	530	!-- Calculate radial distribution function (grfin)
[828]	531	IF ( st(j) > st(i) ) THEN
	532	sst = st(j)
[790]	533	ELSE
[828]	534	sst = st(i)
[790]	535	ENDIF
	536
[1359]	537	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	538	sst*2 + 5.3406_wp sst
	539	IF ( xx < 0.0_wp ) xx = 0.0_wp
	540	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	541
[1007]	542	c1_gr = xx / ( g / vk * tauk )**yy
[790]	543
[1322]	544	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	545	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	546	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	547
[1359]	548	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	549	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	550
[1822]	551	!
	552	!-- Calculate general collection kernel (without the consideration of
	553	!-- collection efficiencies)
	554	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	555	gck(j,i) = gck(i,j)
	556
	557	ENDDO
	558	ENDDO
	559
[828]	560	END SUBROUTINE turbsd
[790]	561
[1320]	562	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	563	!
	564	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	565	!-- effects on the collision kernel
[790]	566	IMPLICIT NONE
	567
[1682]	568	REAL(wp) :: a !<
	569	REAL(wp) :: aa1 !<
	570	REAL(wp) :: b !<
	571	REAL(wp) :: tau0 !<
	572	REAL(wp) :: vsett !<
[790]	573
[1359]	574	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	575	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	576
[1007]	577	END FUNCTION phi_w
[792]	578
[1320]	579	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	580	!
	581	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	582	!-- effects on the collision kernel
[790]	583	IMPLICIT NONE
	584
[1682]	585	REAL(wp) :: a !<
	586	REAL(wp) :: aa1 !<
	587	REAL(wp) :: aa2 !<
	588	REAL(wp) :: aa3 !<
	589	REAL(wp) :: aa4 !<
	590	REAL(wp) :: aa5 !<
	591	REAL(wp) :: aa6 !<
	592	REAL(wp) :: b !<
	593	REAL(wp) :: tau1 !<
	594	REAL(wp) :: tau2 !<
	595	REAL(wp) :: vsett1 !<
	596	REAL(wp) :: vsett2 !<
[790]	597
[1359]	598	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	599	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	600	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	601	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	602	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	603	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	604	vsett1 / vsett2
	605	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	606	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	607	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	608	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	609
[828]	610	END FUNCTION zhi
[790]	611
[828]	612
[790]	613	!------------------------------------------------------------------------------!
[1682]	614	! Description:
	615	! ------------
[1822]	616	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	617	!> Meteorol.)
[790]	618	!------------------------------------------------------------------------------!
[828]	619	SUBROUTINE fallg
[790]	620
[1320]	621	USE particle_attributes, &
	622	ONLY: radius_classes
[790]	623
[828]	624	IMPLICIT NONE
[790]	625
[1822]	626	INTEGER(iwp) :: j !<
[790]	627
[1822]	628	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	629	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	630	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	631	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	632	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	633	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	634
[1822]	635	REAL(wp) :: diameter !< droplet diameter in mm
[790]	636
[799]	637
[828]	638	DO j = 1, radius_classes
[790]	639
[1822]	640	diameter = radclass(j) * 2000.0_wp
[799]	641
[1822]	642	IF ( diameter <= d0_rog ) THEN
	643	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	644	EXP( -k_low_rog * diameter ) )
	645	ELSE
	646	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	647	ENDIF
[790]	648
[828]	649	ENDDO
[790]	650
[828]	651	END SUBROUTINE fallg
[790]	652
[828]	653
[790]	654	!------------------------------------------------------------------------------!
[1682]	655	! Description:
	656	! ------------
[1822]	657	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	658	!------------------------------------------------------------------------------!
[828]	659	SUBROUTINE effic
[1320]	660
	661	USE particle_attributes, &
	662	ONLY: radius_classes
[790]	663
[828]	664	IMPLICIT NONE
[790]	665
[1682]	666	INTEGER(iwp) :: i !<
	667	INTEGER(iwp) :: iq !<
	668	INTEGER(iwp) :: ir !<
	669	INTEGER(iwp) :: j !<
	670	INTEGER(iwp) :: k !<
[790]	671
[1682]	672	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	673
[1682]	674	LOGICAL, SAVE :: first = .TRUE. !<
[790]	675
[1682]	676	REAL(wp) :: ek !<
	677	REAL(wp) :: particle_radius !<
	678	REAL(wp) :: pp !<
	679	REAL(wp) :: qq !<
	680	REAL(wp) :: rq !<
[790]	681
[1682]	682	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	683
[1682]	684	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	685
[1682]	686	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	687
[792]	688	!
[828]	689	!-- Initial assignment of constants
	690	IF ( first ) THEN
[790]	691
[792]	692	first = .FALSE.
[1822]	693	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	694	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	695	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	696
[1822]	697	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	698	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	699	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	700	0.90_wp, 0.95_wp, 1.00_wp /)
	701
[1822]	702	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	703	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	704	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	705	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	706	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	707	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	708	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	709	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	710	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	711	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	712	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	713	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	714	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	715	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	716	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	717	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	718	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	719	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	720	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	721	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	722	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	723	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	724	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	725	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	726	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	727	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	728	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	729	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	730	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	731	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	733	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	734	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	735	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	736	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	737	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	738	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	739	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	740	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	741	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	742	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	743	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	744	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	745	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	746	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	747	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	748	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	749	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	751	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	752	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	753	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	754	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	755	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	756	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	757	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	758	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	759	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	760	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	761	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	762	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	763	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	764	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	765	ENDIF
[790]	766
[792]	767	!
[828]	768	!-- Calculate the radius class index of particles with respect to array r
[1822]	769	!-- Radius has to be in microns
[828]	770	ALLOCATE( ira(1:radius_classes) )
	771	DO j = 1, radius_classes
[1322]	772	particle_radius = radclass(j) * 1.0E6_wp
[828]	773	DO k = 1, 15
	774	IF ( particle_radius < r0(k) ) THEN
	775	ira(j) = k
	776	EXIT
	777	ENDIF
	778	ENDDO
	779	IF ( particle_radius >= r0(15) ) ira(j) = 16
	780	ENDDO
[790]	781
[792]	782	!
[828]	783	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	784	!-- Radius has to be in microns
[828]	785	DO j = 1, radius_classes
	786	DO i = 1, j
[792]	787
[828]	788	ir = ira(j)
[1519]	789	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	790	iq = INT( rq * 20 ) + 1
	791	iq = MAX( iq , 2)
[792]	792
[828]	793	IF ( ir < 16 ) THEN
	794	IF ( ir >= 2 ) THEN
[1822]	795	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	796	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	797	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	798	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	799	* ecoll(ir-1,iq-1) &
	800	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	801	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	802	+ pp * qq * ecoll(ir,iq)
	803	ELSE
	804	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	805	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	806	ENDIF
	807	ELSE
	808	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	809	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	810	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	811	ENDIF
[792]	812
[1359]	813	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	814
[828]	815	ec(i,j) = ec(j,i)
[792]	816
[828]	817	ENDDO
	818	ENDDO
[792]	819
[828]	820	DEALLOCATE( ira )
[792]	821
[828]	822	END SUBROUTINE effic
[792]	823
	824
[790]	825	!------------------------------------------------------------------------------!
[1682]	826	! Description:
	827	! ------------
[1822]	828	!> Interpolation of turbulent enhancement factor for collision efficencies
	829	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	830	!------------------------------------------------------------------------------!
[828]	831	SUBROUTINE turb_enhance_eff
[790]	832
[1320]	833	USE particle_attributes, &
	834	ONLY: radius_classes
[790]	835
[828]	836	IMPLICIT NONE
[790]	837
[1682]	838	INTEGER(iwp) :: i !<
	839	INTEGER(iwp) :: iq !<
	840	INTEGER(iwp) :: ir !<
	841	INTEGER(iwp) :: j !<
	842	INTEGER(iwp) :: k !<
	843	INTEGER(iwp) :: kk !<
[790]	844
[1682]	845	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	846
[1682]	847	LOGICAL, SAVE :: first = .TRUE. !<
[790]	848
[1682]	849	REAL(wp) :: particle_radius !<
	850	REAL(wp) :: pp !<
	851	REAL(wp) :: qq !<
	852	REAL(wp) :: rq !<
	853	REAL(wp) :: y1 !<
	854	REAL(wp) :: y2 !<
	855	REAL(wp) :: y3 !<
[790]	856
[1682]	857	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	858	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	859
[1682]	860	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	861	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	862
	863	!
[828]	864	!-- Initial assignment of constants
	865	IF ( first ) THEN
[799]	866
[828]	867	first = .FALSE.
[799]	868
[1359]	869	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	870	100.0_wp /)
	871
	872	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	873	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	874	!
[1822]	875	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	876	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	877	1.207_wp, 1.207_wp, 1.0_wp /)
	878	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	879	1.069_wp, 1.069_wp, 1.0_wp /)
	880	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	881	1.000_wp, 1.000_wp, 1.0_wp /)
	882	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	883	1.025_wp, 1.025_wp, 1.0_wp /)
	884	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	885	1.056_wp, 1.056_wp, 1.0_wp /)
	886	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	887	1.028_wp, 1.028_wp, 1.0_wp /)
	888	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	889	1.046_wp, 1.046_wp, 1.0_wp /)
	890	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	891	1.029_wp, 1.029_wp, 1.0_wp /)
	892	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	893	1.021_wp, 1.021_wp, 1.0_wp /)
	894	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	895	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	896	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	897	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	898	!
[1822]	899	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	900	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	901	1.445_wp, 1.445_wp, 1.0_wp /)
	902	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	903	1.201_wp, 1.201_wp, 1.0_wp /)
	904	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	905	1.150_wp, 1.150_wp, 1.0_wp /)
	906	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	907	1.126_wp, 1.126_wp, 1.0_wp /)
	908	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	909	1.092_wp, 1.092_wp, 1.0_wp /)
	910	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	911	1.051_wp, 1.051_wp, 1.0_wp /)
	912	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	913	1.086_wp, 1.086_wp, 1.0_wp /)
	914	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	915	1.063_wp, 1.063_wp, 1.0_wp /)
	916	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	917	1.100_wp, 1.100_wp, 1.0_wp /)
	918	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	919	1.120_wp, 1.120_wp, 1.0_wp /)
	920	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	921	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	922
[828]	923	ENDIF
[790]	924
[828]	925	!
	926	!-- Calculate the radius class index of particles with respect to array r0
[1822]	927	!-- The droplet radius has to be given in microns.
[828]	928	ALLOCATE( ira(1:radius_classes) )
[790]	929
[828]	930	DO j = 1, radius_classes
[1322]	931	particle_radius = radclass(j) * 1.0E6_wp
[828]	932	DO k = 1, 7
	933	IF ( particle_radius < r0(k) ) THEN
	934	ira(j) = k
	935	EXIT
	936	ENDIF
	937	ENDDO
	938	IF ( particle_radius >= r0(7) ) ira(j) = 8
	939	ENDDO
[799]	940
	941	!
[1822]	942	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	943	!-- The droplet radius has to be given in microns.
[828]	944	DO j = 1, radius_classes
	945	DO i = 1, j
[799]	946
[828]	947	ir = ira(j)
[1519]	948	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	949
[828]	950	DO kk = 2, 11
	951	IF ( rq <= rat(kk) ) THEN
	952	iq = kk
	953	EXIT
	954	ENDIF
	955	ENDDO
[790]	956
[1822]	957	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	958
[828]	959	IF ( ir < 8 ) THEN
	960	IF ( ir >= 2 ) THEN
[1822]	961	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	962	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	963	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	964	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	965	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	966	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	967	pp * qq * ecoll_100(ir,iq)
	968	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	969	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	970	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	971	pp * qq * ecoll_400(ir,iq)
[828]	972	ELSE
	973	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	974	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	975	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	976	ENDIF
	977	ELSE
	978	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	979	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	980	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	981	ENDIF
	982	!
[1822]	983	!-- Linear interpolation of turbulent enhancement factor
[1359]	984	IF ( epsilon <= 0.01_wp ) THEN
	985	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	986	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	987	ELSEIF ( epsilon <= 0.06_wp ) THEN
	988	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	989	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	990	ELSE
[1359]	991	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	992	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	993	ENDIF
[790]	994
[1359]	995	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	996
[828]	997	ecf(i,j) = ecf(j,i)
[790]	998
[828]	999	ENDDO
	1000	ENDDO
[790]	1001
[828]	1002	END SUBROUTINE turb_enhance_eff
[790]	1003
[825]	1004	END MODULE lpm_collision_kernels_mod

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