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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 2271

Last change on this file since 2271 was 2101, checked in by suehring, 8 years ago
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[1873]	1	!> @file lpm_collision_kernels.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[790]	20	! Current revisions:
	21	! -----------------
[1347]	22	!
[2001]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 2101 2017-01-05 16:42:31Z sward $
	27	!
[2001]	28	! 2000 2016-08-20 18:09:15Z knoop
	29	! Forced header and separation lines into 80 columns
	30	!
[1881]	31	! 1880 2016-04-20 09:36:50Z hoffmann
	32	! Bugfix: The index of the larger particle has to be chosen for interpolation.
	33	!
[1874]	34	! 1873 2016-04-18 14:50:06Z maronga
	35	! Module renamed (removed _mod)
	36	!
[1859]	37	! 1858 2016-04-13 13:12:11Z hoffmann
	38	! Interpolation of collision kernels adjusted to more reasonable values.
	39	! Reformatting of the code.
	40	!
[1851]	41	! 1850 2016-04-08 13:29:27Z maronga
	42	! Module renamed
	43	!
[1823]	44	! 1822 2016-04-07 07:49:42Z hoffmann
	45	! PALM kernel has been deleted.
	46	! Bugfix in the calculation of the turbulent enhancement factor of the
	47	! collection efficiency.
	48	!
	49	! Unused variables removed.
	50	!
[1777]	51	! 1776 2016-03-02 17:54:58Z hoffmann
	52	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	53	!
[1683]	54	! 1682 2015-10-07 23:56:08Z knoop
	55	! Code annotations made doxygen readable
	56	!
[1520]	57	! 1519 2015-01-08 10:20:42Z hoffmann
	58	! Bugfix: Using the new particle structure, particles are not sorted by size.
	59	! Hence, computation of collision efficiencies must ensure that the ratio of
	60	! two colliding droplets is < 1.
	61	!
[1360]	62	! 1359 2014-04-11 17:15:14Z hoffmann
	63	! New particle structure integrated.
	64	! Kind definition added to all floating point numbers.
	65	!
[1347]	66	! 1346 2014-03-27 13:18:20Z heinze
	67	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	68	! intrinsic function like MAX, MIN, SIGN
	69	!
[1323]	70	! 1322 2014-03-20 16:38:49Z raasch
	71	! REAL constants defined as wp_kind
	72	!
[1321]	73	! 1320 2014-03-20 08:40:49Z
[1320]	74	! ONLY-attribute added to USE-statements,
	75	! kind-parameters added to all INTEGER and REAL declaration statements,
	76	! kinds are defined in new module kinds,
	77	! revision history before 2012 removed,
	78	! comment fields (!:) to be used for variable explanations added to
	79	! all variable declaration statements
[1008]	80	!
[1093]	81	! 1092 2013-02-02 11:24:22Z raasch
	82	! unused variables removed
	83	!
[1072]	84	! 1071 2012-11-29 16:54:55Z franke
	85	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	86	!
[1037]	87	! 1036 2012-10-22 13:43:42Z raasch
	88	! code put under GPL (PALM 3.9)
	89	!
[1008]	90	! 1007 2012-09-19 14:30:36Z franke
[1007]	91	! converted all units to SI units and replaced some parameters by corresponding
	92	! PALM parameters
	93	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	94	! changed from 10. to 1.0
[829]	95	!
[850]	96	! 849 2012-03-15 10:35:09Z raasch
	97	! routine collision_efficiency_rogers added (moved from former advec_particles
	98	! to here)
	99	!
[836]	100	! 835 2012-02-22 11:21:19Z raasch $
	101	! Bugfix: array diss can be used only in case of Wang kernel
	102	!
[829]	103	! 828 2012-02-21 12:00:36Z raasch
[828]	104	! code has been completely reformatted, routine colker renamed
	105	! recalculate_kernel,
	106	! routine init_kernels added, radius is now communicated to the collision
	107	! routines by array radclass
[790]	108	!
[828]	109	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	110	!
[826]	111	! 825 2012-02-19 03:03:44Z raasch
	112	! routine renamed from wang_kernel to lpm_collision_kernels,
	113	! turbulence_effects on collision replaced by wang_kernel
	114	!
[791]	115	! 790 2011-11-29 03:11:20Z raasch
	116	! initial revision
[790]	117	!
	118	! Description:
	119	! ------------
[1682]	120	!> This module calculates collision efficiencies either due to pure gravitational
	121	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	122	!> including the effects of turbulence (Wang kernel, see Wang and
	123	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	124	!> New J. Phys., 10, 075016). The original code has been
[1682]	125	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	126	!> here.
[790]	127	!------------------------------------------------------------------------------!
[1682]	128	MODULE lpm_collision_kernels_mod
	129
[790]	130
[1320]	131	USE constants, &
	132	ONLY: pi
	133
	134	USE kinds
	135
	136	USE particle_attributes, &
[1822]	137	ONLY: collision_kernel, dissipation_classes, particles, &
	138	radius_classes
[1320]	139
[828]	140	USE pegrid
[790]	141
[828]	142
[790]	143	IMPLICIT NONE
	144
	145	PRIVATE
	146
[1822]	147	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	148	recalculate_kernel
[790]	149
[1682]	150	REAL(wp) :: epsilon !<
	151	REAL(wp) :: rclass_lbound !<
	152	REAL(wp) :: rclass_ubound !<
	153	REAL(wp) :: urms !<
[790]	154
[1822]	155	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	156	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	157	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	158
[1822]	159	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	160	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	161	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	162	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	163	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	164
[1822]	165	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	166
[828]	167	SAVE
[792]	168
[790]	169	!
	170	!-- Public interfaces
[828]	171	INTERFACE init_kernels
	172	MODULE PROCEDURE init_kernels
	173	END INTERFACE init_kernels
[790]	174
[828]	175	INTERFACE recalculate_kernel
	176	MODULE PROCEDURE recalculate_kernel
	177	END INTERFACE recalculate_kernel
[790]	178
	179
[828]	180	CONTAINS
[790]	181
[792]	182
[828]	183	!------------------------------------------------------------------------------!
[1682]	184	! Description:
	185	! ------------
	186	!> Initialization of the collision efficiency matrix with fixed radius and
	187	!> dissipation classes, calculated at simulation start only.
[828]	188	!------------------------------------------------------------------------------!
[1682]	189
	190	SUBROUTINE init_kernels
[792]	191
[828]	192	IMPLICIT NONE
[792]	193
[1682]	194	INTEGER(iwp) :: i !<
	195	INTEGER(iwp) :: j !<
	196	INTEGER(iwp) :: k !<
[790]	197
[828]	198
	199	!
	200	!-- Calculate collision efficiencies for fixed radius- and dissipation
	201	!-- classes
	202	IF ( collision_kernel(6:9) == 'fast' ) THEN
	203
[1822]	204	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	205	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	206	radclass(1:radius_classes) )
	207
	208	!
	209	!-- Calculate the radius class bounds with logarithmic distances
[1858]	210	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	211	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	212	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	213	radclass(1) = EXP( rclass_lbound )
[828]	214	DO i = 2, radius_classes
	215	radclass(i) = EXP( rclass_lbound + &
[1359]	216	( rclass_ubound - rclass_lbound ) * &
	217	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	218	ENDDO
	219
	220	!
[1858]	221	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	222	DO i = 1, dissipation_classes
[1858]	223	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	224	ENDDO
	225	!
	226	!-- Calculate collision efficiencies of the Wang/ayala kernel
	227	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	228	ecf(1:radius_classes,1:radius_classes), &
	229	gck(1:radius_classes,1:radius_classes), &
	230	winf(1:radius_classes) )
	231
	232	DO k = 1, dissipation_classes
	233
	234	epsilon = epsclass(k)
[1359]	235	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	236
	237	CALL turbsd
	238	CALL turb_enhance_eff
	239	CALL effic
	240
	241	DO j = 1, radius_classes
	242	DO i = 1, radius_classes
	243	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	244	ENDDO
	245	ENDDO
	246
	247	ENDDO
	248
	249	!
	250	!-- Calculate collision efficiencies of the Hall kernel
	251	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	252	hwratio(1:radius_classes,1:radius_classes) )
	253
	254	CALL fallg
	255	CALL effic
	256
	257	DO j = 1, radius_classes
	258	DO i = 1, radius_classes
	259	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	260	* ec(i,j) * ABS( winf(j) - winf(i) )
	261	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	262	ENDDO
	263	ENDDO
	264
	265	!
	266	!-- Test output of efficiencies
	267	IF ( j == -1 ) THEN
	268
	269	PRINT, '** Hall kernel'
[1359]	270	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	271	i = 1,radius_classes )
[828]	272	DO j = 1, radius_classes
[1007]	273	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	274	( hkernel(i,j), i = 1,radius_classes )
[828]	275	ENDDO
	276
	277	DO k = 1, dissipation_classes
	278	DO i = 1, radius_classes
	279	DO j = 1, radius_classes
[1359]	280	IF ( hkernel(i,j) == 0.0_wp ) THEN
	281	hwratio(i,j) = 9999999.9_wp
[828]	282	ELSE
	283	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	284	ENDIF
	285	ENDDO
	286	ENDDO
	287
	288	PRINT, '** epsilon = ', epsclass(k)
[1359]	289	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	290	i = 1,radius_classes )
[828]	291	DO j = 1, radius_classes
[1359]	292	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	293	( hwratio(i,j), i = 1,radius_classes )
[828]	294	ENDDO
	295	ENDDO
	296
	297	ENDIF
	298
	299	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	300
	301	ENDIF
	302
	303	END SUBROUTINE init_kernels
	304
	305
[790]	306	!------------------------------------------------------------------------------!
[1682]	307	! Description:
	308	! ------------
	309	!> Calculation of collision kernels during each timestep and for each grid box
[790]	310	!------------------------------------------------------------------------------!
[828]	311	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	312
[1320]	313	USE arrays_3d, &
	314	ONLY: diss
[790]	315
[1320]	316	USE particle_attributes, &
[1858]	317	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	318
[790]	319	IMPLICIT NONE
	320
[1682]	321	INTEGER(iwp) :: i !<
	322	INTEGER(iwp) :: i1 !<
	323	INTEGER(iwp) :: j !<
	324	INTEGER(iwp) :: j1 !<
	325	INTEGER(iwp) :: k1 !<
[790]	326
	327
[1858]	328	number_of_particles = prt_count(k1,j1,i1)
	329	radius_classes = number_of_particles ! necessary to use the same
	330	! subroutines as for
	331	! precalculated kernels
[792]	332
[1858]	333	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	334	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	335
[828]	336	!
[1007]	337	!-- Store particle radii on the radclass array
[1858]	338	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	339
[835]	340	IF ( wang_kernel ) THEN
[1007]	341	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	342	ELSE
[1359]	343	epsilon = 0.0_wp
[835]	344	ENDIF
[1359]	345	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	346
[1359]	347	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	348	!
	349	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	350	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	351	ecf(1:number_of_particles,1:number_of_particles) )
[790]	352
[828]	353	CALL turbsd
	354	CALL turb_enhance_eff
	355	CALL effic
[790]	356
[1858]	357	DO j = 1, number_of_particles
	358	DO i = 1, number_of_particles
	359	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	360	ENDDO
[828]	361	ENDDO
[790]	362
[828]	363	DEALLOCATE( gck, ecf )
[790]	364
	365	ELSE
[828]	366	!
	367	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	368	CALL fallg
	369	CALL effic
	370
[1858]	371	DO j = 1, number_of_particles
	372	DO i = 1, number_of_particles
	373	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	374	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	375	ENDDO
	376	ENDDO
	377
	378	ENDIF
	379
[828]	380	DEALLOCATE( ec, radclass, winf )
[790]	381
[828]	382	END SUBROUTINE recalculate_kernel
[790]	383
[828]	384
[790]	385	!------------------------------------------------------------------------------!
[1682]	386	! Description:
	387	! ------------
[1822]	388	!> Calculation of effects of turbulence on the geometric collision kernel
	389	!> (by including the droplets' average radial relative velocities and their
	390	!> radial distribution function) following the analytic model by Aayala et al.
	391	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	392	!> page 37ff.
	393	!>
	394	!> Input parameters, which need to be replaced by PALM parameters:
	395	!> water density, air density
[790]	396	!------------------------------------------------------------------------------!
[792]	397	SUBROUTINE turbsd
[799]	398
[1320]	399	USE control_parameters, &
	400	ONLY: g, molecular_viscosity
	401
	402	USE particle_attributes, &
	403	ONLY: radius_classes
[790]	404
	405	IMPLICIT NONE
	406
[1682]	407	INTEGER(iwp) :: i !<
	408	INTEGER(iwp) :: j !<
[790]	409
[1682]	410	REAL(wp) :: ao !<
	411	REAL(wp) :: ao_gr !<
	412	REAL(wp) :: bbb !<
	413	REAL(wp) :: be !<
	414	REAL(wp) :: b1 !<
	415	REAL(wp) :: b2 !<
	416	REAL(wp) :: ccc !<
	417	REAL(wp) :: c1 !<
	418	REAL(wp) :: c1_gr !<
	419	REAL(wp) :: c2 !<
	420	REAL(wp) :: d1 !<
	421	REAL(wp) :: d2 !<
	422	REAL(wp) :: eta !<
	423	REAL(wp) :: e1 !<
	424	REAL(wp) :: e2 !<
	425	REAL(wp) :: fao_gr !<
	426	REAL(wp) :: fr !<
	427	REAL(wp) :: grfin !<
	428	REAL(wp) :: lambda !<
	429	REAL(wp) :: lambda_re !<
	430	REAL(wp) :: lf !<
	431	REAL(wp) :: rc !<
	432	REAL(wp) :: rrp !<
	433	REAL(wp) :: sst !<
	434	REAL(wp) :: tauk !<
	435	REAL(wp) :: tl !<
	436	REAL(wp) :: t2 !<
	437	REAL(wp) :: tt !<
	438	REAL(wp) :: t1 !<
	439	REAL(wp) :: vk !<
	440	REAL(wp) :: vrms1xy !<
	441	REAL(wp) :: vrms2xy !<
	442	REAL(wp) :: v1 !<
	443	REAL(wp) :: v1v2xy !<
	444	REAL(wp) :: v1xysq !<
	445	REAL(wp) :: v2 !<
	446	REAL(wp) :: v2xysq !<
	447	REAL(wp) :: wrfin !<
	448	REAL(wp) :: wrgrav2 !<
	449	REAL(wp) :: wrtur2xy !<
	450	REAL(wp) :: xx !<
	451	REAL(wp) :: yy !<
	452	REAL(wp) :: z !<
[790]	453
[1822]	454	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	455	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	456
[1822]	457	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	458	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	459	tl = urms**2 / epsilon
	460	lf = 0.5_wp * urms**3 / epsilon
	461	tauk = SQRT( molecular_viscosity / epsilon )
	462	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	463	vk = eta / tauk
[790]	464
[1359]	465	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	466	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	467
[1822]	468	!
	469	!-- Get terminal velocity of droplets
	470	CALL fallg
[790]	471
[828]	472	DO i = 1, radius_classes
[1822]	473	tau(i) = winf(i) / g ! inertial time scale
	474	st(i) = tau(i) / tauk ! Stokes number
[790]	475	ENDDO
	476
[828]	477	!
[1822]	478	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	479	z = tt / tl
[1322]	480	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	481	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	482	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	483	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	484	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	485	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	486	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	487	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	488	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	489	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	490	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	491
[828]	492	DO i = 1, radius_classes
[790]	493
[1822]	494	v1 = winf(i)
	495	t1 = tau(i)
[790]	496
[828]	497	DO j = 1, i
[1007]	498	rrp = radclass(i) + radclass(j)
[1822]	499	v2 = winf(j)
	500	t2 = tau(j)
[790]	501
[1007]	502	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	503	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	504	v1xysq = v1xysq * urms**2 / t1
	505	vrms1xy = SQRT( v1xysq )
[790]	506
[1007]	507	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	508	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	509	v2xysq = v2xysq * urms**2 / t2
	510	vrms2xy = SQRT( v2xysq )
[790]	511
[828]	512	IF ( winf(i) >= winf(j) ) THEN
[799]	513	v1 = winf(i)
[790]	514	t1 = tau(i)
[799]	515	v2 = winf(j)
[790]	516	t2 = tau(j)
	517	ELSE
[799]	518	v1 = winf(j)
[790]	519	t1 = tau(j)
[799]	520	v2 = winf(i)
[790]	521	t2 = tau(i)
	522	ENDIF
	523
[828]	524	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	525	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	526	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	527	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	528	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	529	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	530	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	531	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	532	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	533	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	534
[828]	535	!
[1822]	536	!-- Calculate radial distribution function (grfin)
[828]	537	IF ( st(j) > st(i) ) THEN
	538	sst = st(j)
[790]	539	ELSE
[828]	540	sst = st(i)
[790]	541	ENDIF
	542
[1359]	543	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	544	sst*2 + 5.3406_wp sst
	545	IF ( xx < 0.0_wp ) xx = 0.0_wp
	546	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	547
[1007]	548	c1_gr = xx / ( g / vk * tauk )**yy
[790]	549
[1322]	550	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	551	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	552	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	553
[1359]	554	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	555	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	556
[1822]	557	!
	558	!-- Calculate general collection kernel (without the consideration of
	559	!-- collection efficiencies)
	560	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	561	gck(j,i) = gck(i,j)
	562
	563	ENDDO
	564	ENDDO
	565
[828]	566	END SUBROUTINE turbsd
[790]	567
[1320]	568	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	569	!
	570	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	571	!-- effects on the collision kernel
[790]	572	IMPLICIT NONE
	573
[1682]	574	REAL(wp) :: a !<
	575	REAL(wp) :: aa1 !<
	576	REAL(wp) :: b !<
	577	REAL(wp) :: tau0 !<
	578	REAL(wp) :: vsett !<
[790]	579
[1359]	580	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	581	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	582
[1007]	583	END FUNCTION phi_w
[792]	584
[1320]	585	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	586	!
	587	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	588	!-- effects on the collision kernel
[790]	589	IMPLICIT NONE
	590
[1682]	591	REAL(wp) :: a !<
	592	REAL(wp) :: aa1 !<
	593	REAL(wp) :: aa2 !<
	594	REAL(wp) :: aa3 !<
	595	REAL(wp) :: aa4 !<
	596	REAL(wp) :: aa5 !<
	597	REAL(wp) :: aa6 !<
	598	REAL(wp) :: b !<
	599	REAL(wp) :: tau1 !<
	600	REAL(wp) :: tau2 !<
	601	REAL(wp) :: vsett1 !<
	602	REAL(wp) :: vsett2 !<
[790]	603
[1359]	604	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	605	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	606	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	607	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	608	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	609	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	610	vsett1 / vsett2
	611	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	612	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	613	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	614	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	615
[828]	616	END FUNCTION zhi
[790]	617
[828]	618
[790]	619	!------------------------------------------------------------------------------!
[1682]	620	! Description:
	621	! ------------
[1822]	622	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	623	!> Meteorol.)
[790]	624	!------------------------------------------------------------------------------!
[828]	625	SUBROUTINE fallg
[790]	626
[1320]	627	USE particle_attributes, &
	628	ONLY: radius_classes
[790]	629
[828]	630	IMPLICIT NONE
[790]	631
[1822]	632	INTEGER(iwp) :: j !<
[790]	633
[1822]	634	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	635	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	636	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	637	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	638	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	639	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	640
[1822]	641	REAL(wp) :: diameter !< droplet diameter in mm
[790]	642
[799]	643
[828]	644	DO j = 1, radius_classes
[790]	645
[1822]	646	diameter = radclass(j) * 2000.0_wp
[799]	647
[1822]	648	IF ( diameter <= d0_rog ) THEN
	649	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	650	EXP( -k_low_rog * diameter ) )
	651	ELSE
	652	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	653	ENDIF
[790]	654
[828]	655	ENDDO
[790]	656
[828]	657	END SUBROUTINE fallg
[790]	658
[828]	659
[790]	660	!------------------------------------------------------------------------------!
[1682]	661	! Description:
	662	! ------------
[1822]	663	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	664	!------------------------------------------------------------------------------!
[828]	665	SUBROUTINE effic
[1320]	666
	667	USE particle_attributes, &
	668	ONLY: radius_classes
[790]	669
[828]	670	IMPLICIT NONE
[790]	671
[1682]	672	INTEGER(iwp) :: i !<
	673	INTEGER(iwp) :: iq !<
	674	INTEGER(iwp) :: ir !<
	675	INTEGER(iwp) :: j !<
	676	INTEGER(iwp) :: k !<
[790]	677
[1682]	678	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	679
[1682]	680	LOGICAL, SAVE :: first = .TRUE. !<
[790]	681
[1682]	682	REAL(wp) :: ek !<
	683	REAL(wp) :: particle_radius !<
	684	REAL(wp) :: pp !<
	685	REAL(wp) :: qq !<
	686	REAL(wp) :: rq !<
[790]	687
[1682]	688	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	689
[1682]	690	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	691
[1682]	692	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	693
[792]	694	!
[828]	695	!-- Initial assignment of constants
	696	IF ( first ) THEN
[790]	697
[792]	698	first = .FALSE.
[1822]	699	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	700	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	701	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	702
[1822]	703	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	704	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	705	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	706	0.90_wp, 0.95_wp, 1.00_wp /)
	707
[1822]	708	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	709	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	710	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	711	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	712	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	713	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	714	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	715	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	716	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	717	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	718	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	719	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	720	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	721	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	722	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	723	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	724	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	725	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	726	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	727	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	728	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	729	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	730	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	731	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	733	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	734	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	735	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	736	0.250_wp, 0.500_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(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	739	0.240_wp, 0.550_wp, 0.800_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(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	742	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	743	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	744	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	745	0.290_wp, 0.590_wp, 0.780_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(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	748	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	749	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	751	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	752	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	753	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	754	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	755	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	756	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	757	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	758	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	759	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	760	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	761	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	762	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	763	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	764	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	765	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	766	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	767	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	768	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	769	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	770	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	771	ENDIF
[790]	772
[792]	773	!
[828]	774	!-- Calculate the radius class index of particles with respect to array r
[1822]	775	!-- Radius has to be in microns
[828]	776	ALLOCATE( ira(1:radius_classes) )
	777	DO j = 1, radius_classes
[1322]	778	particle_radius = radclass(j) * 1.0E6_wp
[828]	779	DO k = 1, 15
	780	IF ( particle_radius < r0(k) ) THEN
	781	ira(j) = k
	782	EXIT
	783	ENDIF
	784	ENDDO
	785	IF ( particle_radius >= r0(15) ) ira(j) = 16
	786	ENDDO
[790]	787
[792]	788	!
[828]	789	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	790	!-- Radius has to be in microns
[828]	791	DO j = 1, radius_classes
	792	DO i = 1, j
[792]	793
[1880]	794	ir = MAX( ira(i), ira(j) )
[1519]	795	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	796	iq = INT( rq * 20 ) + 1
	797	iq = MAX( iq , 2)
[792]	798
[828]	799	IF ( ir < 16 ) THEN
	800	IF ( ir >= 2 ) THEN
[1822]	801	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	802	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	803	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	804	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	805	* ecoll(ir-1,iq-1) &
	806	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	807	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	808	+ pp * qq * ecoll(ir,iq)
	809	ELSE
	810	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	811	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	812	ENDIF
	813	ELSE
	814	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	815	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	816	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	817	ENDIF
[792]	818
[1359]	819	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	820
[828]	821	ec(i,j) = ec(j,i)
[792]	822
[828]	823	ENDDO
	824	ENDDO
[792]	825
[828]	826	DEALLOCATE( ira )
[792]	827
[828]	828	END SUBROUTINE effic
[792]	829
	830
[790]	831	!------------------------------------------------------------------------------!
[1682]	832	! Description:
	833	! ------------
[1822]	834	!> Interpolation of turbulent enhancement factor for collision efficencies
	835	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	836	!------------------------------------------------------------------------------!
[828]	837	SUBROUTINE turb_enhance_eff
[790]	838
[1320]	839	USE particle_attributes, &
	840	ONLY: radius_classes
[790]	841
[828]	842	IMPLICIT NONE
[790]	843
[1682]	844	INTEGER(iwp) :: i !<
	845	INTEGER(iwp) :: iq !<
	846	INTEGER(iwp) :: ir !<
	847	INTEGER(iwp) :: j !<
	848	INTEGER(iwp) :: k !<
	849	INTEGER(iwp) :: kk !<
[790]	850
[1682]	851	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	852
[1682]	853	LOGICAL, SAVE :: first = .TRUE. !<
[790]	854
[1682]	855	REAL(wp) :: particle_radius !<
	856	REAL(wp) :: pp !<
	857	REAL(wp) :: qq !<
	858	REAL(wp) :: rq !<
	859	REAL(wp) :: y1 !<
	860	REAL(wp) :: y2 !<
	861	REAL(wp) :: y3 !<
[790]	862
[1682]	863	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	864	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	865
[1682]	866	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	867	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	868
	869	!
[828]	870	!-- Initial assignment of constants
	871	IF ( first ) THEN
[799]	872
[828]	873	first = .FALSE.
[799]	874
[1359]	875	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	876	100.0_wp /)
	877
	878	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	879	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	880	!
[1822]	881	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	882	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	883	1.207_wp, 1.207_wp, 1.0_wp /)
	884	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	885	1.069_wp, 1.069_wp, 1.0_wp /)
	886	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	887	1.000_wp, 1.000_wp, 1.0_wp /)
	888	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	889	1.025_wp, 1.025_wp, 1.0_wp /)
	890	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	891	1.056_wp, 1.056_wp, 1.0_wp /)
	892	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	893	1.028_wp, 1.028_wp, 1.0_wp /)
	894	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	895	1.046_wp, 1.046_wp, 1.0_wp /)
	896	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	897	1.029_wp, 1.029_wp, 1.0_wp /)
	898	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	899	1.021_wp, 1.021_wp, 1.0_wp /)
	900	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	901	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	902	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	903	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	904	!
[1822]	905	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	906	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	907	1.445_wp, 1.445_wp, 1.0_wp /)
	908	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	909	1.201_wp, 1.201_wp, 1.0_wp /)
	910	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	911	1.150_wp, 1.150_wp, 1.0_wp /)
	912	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	913	1.126_wp, 1.126_wp, 1.0_wp /)
	914	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	915	1.092_wp, 1.092_wp, 1.0_wp /)
	916	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	917	1.051_wp, 1.051_wp, 1.0_wp /)
	918	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	919	1.086_wp, 1.086_wp, 1.0_wp /)
	920	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	921	1.063_wp, 1.063_wp, 1.0_wp /)
	922	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	923	1.100_wp, 1.100_wp, 1.0_wp /)
	924	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	925	1.120_wp, 1.120_wp, 1.0_wp /)
	926	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	927	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	928
[828]	929	ENDIF
[790]	930
[828]	931	!
	932	!-- Calculate the radius class index of particles with respect to array r0
[1822]	933	!-- The droplet radius has to be given in microns.
[828]	934	ALLOCATE( ira(1:radius_classes) )
[790]	935
[828]	936	DO j = 1, radius_classes
[1322]	937	particle_radius = radclass(j) * 1.0E6_wp
[828]	938	DO k = 1, 7
	939	IF ( particle_radius < r0(k) ) THEN
	940	ira(j) = k
	941	EXIT
	942	ENDIF
	943	ENDDO
	944	IF ( particle_radius >= r0(7) ) ira(j) = 8
	945	ENDDO
[799]	946
	947	!
[1822]	948	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	949	!-- The droplet radius has to be given in microns.
[828]	950	DO j = 1, radius_classes
	951	DO i = 1, j
[799]	952
[1880]	953	ir = MAX( ira(i), ira(j) )
[1519]	954	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	955
[828]	956	DO kk = 2, 11
	957	IF ( rq <= rat(kk) ) THEN
	958	iq = kk
	959	EXIT
	960	ENDIF
	961	ENDDO
[790]	962
[1822]	963	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	964
[828]	965	IF ( ir < 8 ) THEN
	966	IF ( ir >= 2 ) THEN
[1822]	967	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	968	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	969	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	970	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	971	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	972	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	973	pp * qq * ecoll_100(ir,iq)
	974	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	975	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	976	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	977	pp * qq * ecoll_400(ir,iq)
[828]	978	ELSE
	979	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	980	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	981	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	982	ENDIF
	983	ELSE
	984	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	985	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	986	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	987	ENDIF
	988	!
[1822]	989	!-- Linear interpolation of turbulent enhancement factor
[1359]	990	IF ( epsilon <= 0.01_wp ) THEN
	991	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	992	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	993	ELSEIF ( epsilon <= 0.06_wp ) THEN
	994	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	995	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	996	ELSE
[1359]	997	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	998	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	999	ENDIF
[790]	1000
[1359]	1001	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1002
[828]	1003	ecf(i,j) = ecf(j,i)
[790]	1004
[828]	1005	ENDDO
	1006	ENDDO
[790]	1007
[828]	1008	END SUBROUTINE turb_enhance_eff
[790]	1009
[825]	1010	END MODULE lpm_collision_kernels_mod

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