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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 2000

Last change on this file since 2000 was 2000, checked in by knoop, 8 years ago
Forced header and separation lines into 80 columns
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File size: 38.9 KB

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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	!
[1818]	17	! Copyright 1997-2016 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[790]	20	! Current revisions:
	21	! -----------------
[2000]	22	! Forced header and separation lines into 80 columns
[1347]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 2000 2016-08-20 18:09:15Z knoop $
	27	!
[1881]	28	! 1880 2016-04-20 09:36:50Z hoffmann
	29	! Bugfix: The index of the larger particle has to be chosen for interpolation.
	30	!
[1874]	31	! 1873 2016-04-18 14:50:06Z maronga
	32	! Module renamed (removed _mod)
	33	!
[1859]	34	! 1858 2016-04-13 13:12:11Z hoffmann
	35	! Interpolation of collision kernels adjusted to more reasonable values.
	36	! Reformatting of the code.
	37	!
[1851]	38	! 1850 2016-04-08 13:29:27Z maronga
	39	! Module renamed
	40	!
[1823]	41	! 1822 2016-04-07 07:49:42Z hoffmann
	42	! PALM kernel has been deleted.
	43	! Bugfix in the calculation of the turbulent enhancement factor of the
	44	! collection efficiency.
	45	!
	46	! Unused variables removed.
	47	!
[1777]	48	! 1776 2016-03-02 17:54:58Z hoffmann
	49	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	50	!
[1683]	51	! 1682 2015-10-07 23:56:08Z knoop
	52	! Code annotations made doxygen readable
	53	!
[1520]	54	! 1519 2015-01-08 10:20:42Z hoffmann
	55	! Bugfix: Using the new particle structure, particles are not sorted by size.
	56	! Hence, computation of collision efficiencies must ensure that the ratio of
	57	! two colliding droplets is < 1.
	58	!
[1360]	59	! 1359 2014-04-11 17:15:14Z hoffmann
	60	! New particle structure integrated.
	61	! Kind definition added to all floating point numbers.
	62	!
[1347]	63	! 1346 2014-03-27 13:18:20Z heinze
	64	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	65	! intrinsic function like MAX, MIN, SIGN
	66	!
[1323]	67	! 1322 2014-03-20 16:38:49Z raasch
	68	! REAL constants defined as wp_kind
	69	!
[1321]	70	! 1320 2014-03-20 08:40:49Z
[1320]	71	! ONLY-attribute added to USE-statements,
	72	! kind-parameters added to all INTEGER and REAL declaration statements,
	73	! kinds are defined in new module kinds,
	74	! revision history before 2012 removed,
	75	! comment fields (!:) to be used for variable explanations added to
	76	! all variable declaration statements
[1008]	77	!
[1093]	78	! 1092 2013-02-02 11:24:22Z raasch
	79	! unused variables removed
	80	!
[1072]	81	! 1071 2012-11-29 16:54:55Z franke
	82	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	83	!
[1037]	84	! 1036 2012-10-22 13:43:42Z raasch
	85	! code put under GPL (PALM 3.9)
	86	!
[1008]	87	! 1007 2012-09-19 14:30:36Z franke
[1007]	88	! converted all units to SI units and replaced some parameters by corresponding
	89	! PALM parameters
	90	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	91	! changed from 10. to 1.0
[829]	92	!
[850]	93	! 849 2012-03-15 10:35:09Z raasch
	94	! routine collision_efficiency_rogers added (moved from former advec_particles
	95	! to here)
	96	!
[836]	97	! 835 2012-02-22 11:21:19Z raasch $
	98	! Bugfix: array diss can be used only in case of Wang kernel
	99	!
[829]	100	! 828 2012-02-21 12:00:36Z raasch
[828]	101	! code has been completely reformatted, routine colker renamed
	102	! recalculate_kernel,
	103	! routine init_kernels added, radius is now communicated to the collision
	104	! routines by array radclass
[790]	105	!
[828]	106	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	107	!
[826]	108	! 825 2012-02-19 03:03:44Z raasch
	109	! routine renamed from wang_kernel to lpm_collision_kernels,
	110	! turbulence_effects on collision replaced by wang_kernel
	111	!
[791]	112	! 790 2011-11-29 03:11:20Z raasch
	113	! initial revision
[790]	114	!
	115	! Description:
	116	! ------------
[1682]	117	!> This module calculates collision efficiencies either due to pure gravitational
	118	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	119	!> including the effects of turbulence (Wang kernel, see Wang and
	120	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	121	!> New J. Phys., 10, 075016). The original code has been
[1682]	122	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	123	!> here.
[790]	124	!------------------------------------------------------------------------------!
[1682]	125	MODULE lpm_collision_kernels_mod
	126
[790]	127
[1320]	128	USE constants, &
	129	ONLY: pi
	130
	131	USE kinds
	132
	133	USE particle_attributes, &
[1822]	134	ONLY: collision_kernel, dissipation_classes, particles, &
	135	radius_classes
[1320]	136
[828]	137	USE pegrid
[790]	138
[828]	139
[790]	140	IMPLICIT NONE
	141
	142	PRIVATE
	143
[1822]	144	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	145	recalculate_kernel
[790]	146
[1682]	147	REAL(wp) :: epsilon !<
	148	REAL(wp) :: rclass_lbound !<
	149	REAL(wp) :: rclass_ubound !<
	150	REAL(wp) :: urms !<
[790]	151
[1822]	152	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	153	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	154	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	155
[1822]	156	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	157	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	158	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	159	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	160	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	161
[1822]	162	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	163
[828]	164	SAVE
[792]	165
[790]	166	!
	167	!-- Public interfaces
[828]	168	INTERFACE init_kernels
	169	MODULE PROCEDURE init_kernels
	170	END INTERFACE init_kernels
[790]	171
[828]	172	INTERFACE recalculate_kernel
	173	MODULE PROCEDURE recalculate_kernel
	174	END INTERFACE recalculate_kernel
[790]	175
	176
[828]	177	CONTAINS
[790]	178
[792]	179
[828]	180	!------------------------------------------------------------------------------!
[1682]	181	! Description:
	182	! ------------
	183	!> Initialization of the collision efficiency matrix with fixed radius and
	184	!> dissipation classes, calculated at simulation start only.
[828]	185	!------------------------------------------------------------------------------!
[1682]	186
	187	SUBROUTINE init_kernels
[792]	188
[828]	189	IMPLICIT NONE
[792]	190
[1682]	191	INTEGER(iwp) :: i !<
	192	INTEGER(iwp) :: j !<
	193	INTEGER(iwp) :: k !<
[790]	194
[828]	195
	196	!
	197	!-- Calculate collision efficiencies for fixed radius- and dissipation
	198	!-- classes
	199	IF ( collision_kernel(6:9) == 'fast' ) THEN
	200
[1822]	201	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	202	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	203	radclass(1:radius_classes) )
	204
	205	!
	206	!-- Calculate the radius class bounds with logarithmic distances
[1858]	207	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	208	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	209	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	210	radclass(1) = EXP( rclass_lbound )
[828]	211	DO i = 2, radius_classes
	212	radclass(i) = EXP( rclass_lbound + &
[1359]	213	( rclass_ubound - rclass_lbound ) * &
	214	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	215	ENDDO
	216
	217	!
[1858]	218	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	219	DO i = 1, dissipation_classes
[1858]	220	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	221	ENDDO
	222	!
	223	!-- Calculate collision efficiencies of the Wang/ayala kernel
	224	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	225	ecf(1:radius_classes,1:radius_classes), &
	226	gck(1:radius_classes,1:radius_classes), &
	227	winf(1:radius_classes) )
	228
	229	DO k = 1, dissipation_classes
	230
	231	epsilon = epsclass(k)
[1359]	232	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	233
	234	CALL turbsd
	235	CALL turb_enhance_eff
	236	CALL effic
	237
	238	DO j = 1, radius_classes
	239	DO i = 1, radius_classes
	240	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	241	ENDDO
	242	ENDDO
	243
	244	ENDDO
	245
	246	!
	247	!-- Calculate collision efficiencies of the Hall kernel
	248	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	249	hwratio(1:radius_classes,1:radius_classes) )
	250
	251	CALL fallg
	252	CALL effic
	253
	254	DO j = 1, radius_classes
	255	DO i = 1, radius_classes
	256	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	257	* ec(i,j) * ABS( winf(j) - winf(i) )
	258	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	259	ENDDO
	260	ENDDO
	261
	262	!
	263	!-- Test output of efficiencies
	264	IF ( j == -1 ) THEN
	265
	266	PRINT, '** Hall kernel'
[1359]	267	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	268	i = 1,radius_classes )
[828]	269	DO j = 1, radius_classes
[1007]	270	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	271	( hkernel(i,j), i = 1,radius_classes )
[828]	272	ENDDO
	273
	274	DO k = 1, dissipation_classes
	275	DO i = 1, radius_classes
	276	DO j = 1, radius_classes
[1359]	277	IF ( hkernel(i,j) == 0.0_wp ) THEN
	278	hwratio(i,j) = 9999999.9_wp
[828]	279	ELSE
	280	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	281	ENDIF
	282	ENDDO
	283	ENDDO
	284
	285	PRINT, '** epsilon = ', epsclass(k)
[1359]	286	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	287	i = 1,radius_classes )
[828]	288	DO j = 1, radius_classes
[1359]	289	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	290	( hwratio(i,j), i = 1,radius_classes )
[828]	291	ENDDO
	292	ENDDO
	293
	294	ENDIF
	295
	296	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	297
	298	ENDIF
	299
	300	END SUBROUTINE init_kernels
	301
	302
[790]	303	!------------------------------------------------------------------------------!
[1682]	304	! Description:
	305	! ------------
	306	!> Calculation of collision kernels during each timestep and for each grid box
[790]	307	!------------------------------------------------------------------------------!
[828]	308	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	309
[1320]	310	USE arrays_3d, &
	311	ONLY: diss
[790]	312
[1320]	313	USE particle_attributes, &
[1858]	314	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	315
[790]	316	IMPLICIT NONE
	317
[1682]	318	INTEGER(iwp) :: i !<
	319	INTEGER(iwp) :: i1 !<
	320	INTEGER(iwp) :: j !<
	321	INTEGER(iwp) :: j1 !<
	322	INTEGER(iwp) :: k1 !<
[790]	323
	324
[1858]	325	number_of_particles = prt_count(k1,j1,i1)
	326	radius_classes = number_of_particles ! necessary to use the same
	327	! subroutines as for
	328	! precalculated kernels
[792]	329
[1858]	330	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	331	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	332
[828]	333	!
[1007]	334	!-- Store particle radii on the radclass array
[1858]	335	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	336
[835]	337	IF ( wang_kernel ) THEN
[1007]	338	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	339	ELSE
[1359]	340	epsilon = 0.0_wp
[835]	341	ENDIF
[1359]	342	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	343
[1359]	344	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	345	!
	346	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	347	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	348	ecf(1:number_of_particles,1:number_of_particles) )
[790]	349
[828]	350	CALL turbsd
	351	CALL turb_enhance_eff
	352	CALL effic
[790]	353
[1858]	354	DO j = 1, number_of_particles
	355	DO i = 1, number_of_particles
	356	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	357	ENDDO
[828]	358	ENDDO
[790]	359
[828]	360	DEALLOCATE( gck, ecf )
[790]	361
	362	ELSE
[828]	363	!
	364	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	365	CALL fallg
	366	CALL effic
	367
[1858]	368	DO j = 1, number_of_particles
	369	DO i = 1, number_of_particles
	370	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	371	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	372	ENDDO
	373	ENDDO
	374
	375	ENDIF
	376
[828]	377	DEALLOCATE( ec, radclass, winf )
[790]	378
[828]	379	END SUBROUTINE recalculate_kernel
[790]	380
[828]	381
[790]	382	!------------------------------------------------------------------------------!
[1682]	383	! Description:
	384	! ------------
[1822]	385	!> Calculation of effects of turbulence on the geometric collision kernel
	386	!> (by including the droplets' average radial relative velocities and their
	387	!> radial distribution function) following the analytic model by Aayala et al.
	388	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	389	!> page 37ff.
	390	!>
	391	!> Input parameters, which need to be replaced by PALM parameters:
	392	!> water density, air density
[790]	393	!------------------------------------------------------------------------------!
[792]	394	SUBROUTINE turbsd
[799]	395
[1320]	396	USE control_parameters, &
	397	ONLY: g, molecular_viscosity
	398
	399	USE particle_attributes, &
	400	ONLY: radius_classes
[790]	401
	402	IMPLICIT NONE
	403
[1682]	404	INTEGER(iwp) :: i !<
	405	INTEGER(iwp) :: j !<
[790]	406
[1682]	407	REAL(wp) :: ao !<
	408	REAL(wp) :: ao_gr !<
	409	REAL(wp) :: bbb !<
	410	REAL(wp) :: be !<
	411	REAL(wp) :: b1 !<
	412	REAL(wp) :: b2 !<
	413	REAL(wp) :: ccc !<
	414	REAL(wp) :: c1 !<
	415	REAL(wp) :: c1_gr !<
	416	REAL(wp) :: c2 !<
	417	REAL(wp) :: d1 !<
	418	REAL(wp) :: d2 !<
	419	REAL(wp) :: eta !<
	420	REAL(wp) :: e1 !<
	421	REAL(wp) :: e2 !<
	422	REAL(wp) :: fao_gr !<
	423	REAL(wp) :: fr !<
	424	REAL(wp) :: grfin !<
	425	REAL(wp) :: lambda !<
	426	REAL(wp) :: lambda_re !<
	427	REAL(wp) :: lf !<
	428	REAL(wp) :: rc !<
	429	REAL(wp) :: rrp !<
	430	REAL(wp) :: sst !<
	431	REAL(wp) :: tauk !<
	432	REAL(wp) :: tl !<
	433	REAL(wp) :: t2 !<
	434	REAL(wp) :: tt !<
	435	REAL(wp) :: t1 !<
	436	REAL(wp) :: vk !<
	437	REAL(wp) :: vrms1xy !<
	438	REAL(wp) :: vrms2xy !<
	439	REAL(wp) :: v1 !<
	440	REAL(wp) :: v1v2xy !<
	441	REAL(wp) :: v1xysq !<
	442	REAL(wp) :: v2 !<
	443	REAL(wp) :: v2xysq !<
	444	REAL(wp) :: wrfin !<
	445	REAL(wp) :: wrgrav2 !<
	446	REAL(wp) :: wrtur2xy !<
	447	REAL(wp) :: xx !<
	448	REAL(wp) :: yy !<
	449	REAL(wp) :: z !<
[790]	450
[1822]	451	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	452	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	453
[1822]	454	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	455	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	456	tl = urms**2 / epsilon
	457	lf = 0.5_wp * urms**3 / epsilon
	458	tauk = SQRT( molecular_viscosity / epsilon )
	459	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	460	vk = eta / tauk
[790]	461
[1359]	462	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	463	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	464
[1822]	465	!
	466	!-- Get terminal velocity of droplets
	467	CALL fallg
[790]	468
[828]	469	DO i = 1, radius_classes
[1822]	470	tau(i) = winf(i) / g ! inertial time scale
	471	st(i) = tau(i) / tauk ! Stokes number
[790]	472	ENDDO
	473
[828]	474	!
[1822]	475	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	476	z = tt / tl
[1322]	477	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	478	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	479	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	480	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	481	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	482	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	483	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	484	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	485	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	486	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	487	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	488
[828]	489	DO i = 1, radius_classes
[790]	490
[1822]	491	v1 = winf(i)
	492	t1 = tau(i)
[790]	493
[828]	494	DO j = 1, i
[1007]	495	rrp = radclass(i) + radclass(j)
[1822]	496	v2 = winf(j)
	497	t2 = tau(j)
[790]	498
[1007]	499	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	500	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	501	v1xysq = v1xysq * urms**2 / t1
	502	vrms1xy = SQRT( v1xysq )
[790]	503
[1007]	504	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	505	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	506	v2xysq = v2xysq * urms**2 / t2
	507	vrms2xy = SQRT( v2xysq )
[790]	508
[828]	509	IF ( winf(i) >= winf(j) ) THEN
[799]	510	v1 = winf(i)
[790]	511	t1 = tau(i)
[799]	512	v2 = winf(j)
[790]	513	t2 = tau(j)
	514	ELSE
[799]	515	v1 = winf(j)
[790]	516	t1 = tau(j)
[799]	517	v2 = winf(i)
[790]	518	t2 = tau(i)
	519	ENDIF
	520
[828]	521	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	522	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	523	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	524	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	525	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	526	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	527	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	528	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	529	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	530	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	531
[828]	532	!
[1822]	533	!-- Calculate radial distribution function (grfin)
[828]	534	IF ( st(j) > st(i) ) THEN
	535	sst = st(j)
[790]	536	ELSE
[828]	537	sst = st(i)
[790]	538	ENDIF
	539
[1359]	540	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	541	sst*2 + 5.3406_wp sst
	542	IF ( xx < 0.0_wp ) xx = 0.0_wp
	543	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	544
[1007]	545	c1_gr = xx / ( g / vk * tauk )**yy
[790]	546
[1322]	547	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	548	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	549	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	550
[1359]	551	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	552	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	553
[1822]	554	!
	555	!-- Calculate general collection kernel (without the consideration of
	556	!-- collection efficiencies)
	557	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	558	gck(j,i) = gck(i,j)
	559
	560	ENDDO
	561	ENDDO
	562
[828]	563	END SUBROUTINE turbsd
[790]	564
[1320]	565	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	566	!
	567	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	568	!-- effects on the collision kernel
[790]	569	IMPLICIT NONE
	570
[1682]	571	REAL(wp) :: a !<
	572	REAL(wp) :: aa1 !<
	573	REAL(wp) :: b !<
	574	REAL(wp) :: tau0 !<
	575	REAL(wp) :: vsett !<
[790]	576
[1359]	577	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	578	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	579
[1007]	580	END FUNCTION phi_w
[792]	581
[1320]	582	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	583	!
	584	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	585	!-- effects on the collision kernel
[790]	586	IMPLICIT NONE
	587
[1682]	588	REAL(wp) :: a !<
	589	REAL(wp) :: aa1 !<
	590	REAL(wp) :: aa2 !<
	591	REAL(wp) :: aa3 !<
	592	REAL(wp) :: aa4 !<
	593	REAL(wp) :: aa5 !<
	594	REAL(wp) :: aa6 !<
	595	REAL(wp) :: b !<
	596	REAL(wp) :: tau1 !<
	597	REAL(wp) :: tau2 !<
	598	REAL(wp) :: vsett1 !<
	599	REAL(wp) :: vsett2 !<
[790]	600
[1359]	601	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	602	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	603	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	604	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	605	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	606	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	607	vsett1 / vsett2
	608	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	609	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	610	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	611	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	612
[828]	613	END FUNCTION zhi
[790]	614
[828]	615
[790]	616	!------------------------------------------------------------------------------!
[1682]	617	! Description:
	618	! ------------
[1822]	619	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	620	!> Meteorol.)
[790]	621	!------------------------------------------------------------------------------!
[828]	622	SUBROUTINE fallg
[790]	623
[1320]	624	USE particle_attributes, &
	625	ONLY: radius_classes
[790]	626
[828]	627	IMPLICIT NONE
[790]	628
[1822]	629	INTEGER(iwp) :: j !<
[790]	630
[1822]	631	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	632	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	633	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	634	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	635	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	636	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	637
[1822]	638	REAL(wp) :: diameter !< droplet diameter in mm
[790]	639
[799]	640
[828]	641	DO j = 1, radius_classes
[790]	642
[1822]	643	diameter = radclass(j) * 2000.0_wp
[799]	644
[1822]	645	IF ( diameter <= d0_rog ) THEN
	646	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	647	EXP( -k_low_rog * diameter ) )
	648	ELSE
	649	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	650	ENDIF
[790]	651
[828]	652	ENDDO
[790]	653
[828]	654	END SUBROUTINE fallg
[790]	655
[828]	656
[790]	657	!------------------------------------------------------------------------------!
[1682]	658	! Description:
	659	! ------------
[1822]	660	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	661	!------------------------------------------------------------------------------!
[828]	662	SUBROUTINE effic
[1320]	663
	664	USE particle_attributes, &
	665	ONLY: radius_classes
[790]	666
[828]	667	IMPLICIT NONE
[790]	668
[1682]	669	INTEGER(iwp) :: i !<
	670	INTEGER(iwp) :: iq !<
	671	INTEGER(iwp) :: ir !<
	672	INTEGER(iwp) :: j !<
	673	INTEGER(iwp) :: k !<
[790]	674
[1682]	675	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	676
[1682]	677	LOGICAL, SAVE :: first = .TRUE. !<
[790]	678
[1682]	679	REAL(wp) :: ek !<
	680	REAL(wp) :: particle_radius !<
	681	REAL(wp) :: pp !<
	682	REAL(wp) :: qq !<
	683	REAL(wp) :: rq !<
[790]	684
[1682]	685	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	686
[1682]	687	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	688
[1682]	689	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	690
[792]	691	!
[828]	692	!-- Initial assignment of constants
	693	IF ( first ) THEN
[790]	694
[792]	695	first = .FALSE.
[1822]	696	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	697	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	698	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	699
[1822]	700	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	701	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	702	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	703	0.90_wp, 0.95_wp, 1.00_wp /)
	704
[1822]	705	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	706	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	707	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	708	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	709	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	710	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	711	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	712	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	713	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	714	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	715	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	716	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	717	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	718	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	719	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	720	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	721	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	722	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	723	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	724	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	725	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	726	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	727	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	728	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	729	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	730	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	731	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	733	0.250_wp, 0.500_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(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	736	0.240_wp, 0.550_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(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	739	0.290_wp, 0.580_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(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	742	0.290_wp, 0.590_wp, 0.780_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(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	745	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	746	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	747	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	748	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	749	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	751	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	752	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	753	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	754	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	755	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	756	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	757	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	758	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	759	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	760	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	761	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	762	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	763	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	764	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	765	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	766	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	767	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	768	ENDIF
[790]	769
[792]	770	!
[828]	771	!-- Calculate the radius class index of particles with respect to array r
[1822]	772	!-- Radius has to be in microns
[828]	773	ALLOCATE( ira(1:radius_classes) )
	774	DO j = 1, radius_classes
[1322]	775	particle_radius = radclass(j) * 1.0E6_wp
[828]	776	DO k = 1, 15
	777	IF ( particle_radius < r0(k) ) THEN
	778	ira(j) = k
	779	EXIT
	780	ENDIF
	781	ENDDO
	782	IF ( particle_radius >= r0(15) ) ira(j) = 16
	783	ENDDO
[790]	784
[792]	785	!
[828]	786	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	787	!-- Radius has to be in microns
[828]	788	DO j = 1, radius_classes
	789	DO i = 1, j
[792]	790
[1880]	791	ir = MAX( ira(i), ira(j) )
[1519]	792	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	793	iq = INT( rq * 20 ) + 1
	794	iq = MAX( iq , 2)
[792]	795
[828]	796	IF ( ir < 16 ) THEN
	797	IF ( ir >= 2 ) THEN
[1822]	798	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	799	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	800	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	801	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	802	* ecoll(ir-1,iq-1) &
	803	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	804	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	805	+ pp * qq * ecoll(ir,iq)
	806	ELSE
	807	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	808	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	809	ENDIF
	810	ELSE
	811	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	812	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	813	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	814	ENDIF
[792]	815
[1359]	816	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	817
[828]	818	ec(i,j) = ec(j,i)
[792]	819
[828]	820	ENDDO
	821	ENDDO
[792]	822
[828]	823	DEALLOCATE( ira )
[792]	824
[828]	825	END SUBROUTINE effic
[792]	826
	827
[790]	828	!------------------------------------------------------------------------------!
[1682]	829	! Description:
	830	! ------------
[1822]	831	!> Interpolation of turbulent enhancement factor for collision efficencies
	832	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	833	!------------------------------------------------------------------------------!
[828]	834	SUBROUTINE turb_enhance_eff
[790]	835
[1320]	836	USE particle_attributes, &
	837	ONLY: radius_classes
[790]	838
[828]	839	IMPLICIT NONE
[790]	840
[1682]	841	INTEGER(iwp) :: i !<
	842	INTEGER(iwp) :: iq !<
	843	INTEGER(iwp) :: ir !<
	844	INTEGER(iwp) :: j !<
	845	INTEGER(iwp) :: k !<
	846	INTEGER(iwp) :: kk !<
[790]	847
[1682]	848	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	849
[1682]	850	LOGICAL, SAVE :: first = .TRUE. !<
[790]	851
[1682]	852	REAL(wp) :: particle_radius !<
	853	REAL(wp) :: pp !<
	854	REAL(wp) :: qq !<
	855	REAL(wp) :: rq !<
	856	REAL(wp) :: y1 !<
	857	REAL(wp) :: y2 !<
	858	REAL(wp) :: y3 !<
[790]	859
[1682]	860	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	861	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	862
[1682]	863	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	864	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	865
	866	!
[828]	867	!-- Initial assignment of constants
	868	IF ( first ) THEN
[799]	869
[828]	870	first = .FALSE.
[799]	871
[1359]	872	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	873	100.0_wp /)
	874
	875	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	876	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	877	!
[1822]	878	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	879	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	880	1.207_wp, 1.207_wp, 1.0_wp /)
	881	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	882	1.069_wp, 1.069_wp, 1.0_wp /)
	883	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	884	1.000_wp, 1.000_wp, 1.0_wp /)
	885	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	886	1.025_wp, 1.025_wp, 1.0_wp /)
	887	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	888	1.056_wp, 1.056_wp, 1.0_wp /)
	889	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	890	1.028_wp, 1.028_wp, 1.0_wp /)
	891	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	892	1.046_wp, 1.046_wp, 1.0_wp /)
	893	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	894	1.029_wp, 1.029_wp, 1.0_wp /)
	895	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	896	1.021_wp, 1.021_wp, 1.0_wp /)
	897	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	898	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	899	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	900	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	901	!
[1822]	902	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	903	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	904	1.445_wp, 1.445_wp, 1.0_wp /)
	905	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	906	1.201_wp, 1.201_wp, 1.0_wp /)
	907	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	908	1.150_wp, 1.150_wp, 1.0_wp /)
	909	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	910	1.126_wp, 1.126_wp, 1.0_wp /)
	911	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	912	1.092_wp, 1.092_wp, 1.0_wp /)
	913	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	914	1.051_wp, 1.051_wp, 1.0_wp /)
	915	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	916	1.086_wp, 1.086_wp, 1.0_wp /)
	917	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	918	1.063_wp, 1.063_wp, 1.0_wp /)
	919	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	920	1.100_wp, 1.100_wp, 1.0_wp /)
	921	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	922	1.120_wp, 1.120_wp, 1.0_wp /)
	923	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	924	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	925
[828]	926	ENDIF
[790]	927
[828]	928	!
	929	!-- Calculate the radius class index of particles with respect to array r0
[1822]	930	!-- The droplet radius has to be given in microns.
[828]	931	ALLOCATE( ira(1:radius_classes) )
[790]	932
[828]	933	DO j = 1, radius_classes
[1322]	934	particle_radius = radclass(j) * 1.0E6_wp
[828]	935	DO k = 1, 7
	936	IF ( particle_radius < r0(k) ) THEN
	937	ira(j) = k
	938	EXIT
	939	ENDIF
	940	ENDDO
	941	IF ( particle_radius >= r0(7) ) ira(j) = 8
	942	ENDDO
[799]	943
	944	!
[1822]	945	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	946	!-- The droplet radius has to be given in microns.
[828]	947	DO j = 1, radius_classes
	948	DO i = 1, j
[799]	949
[1880]	950	ir = MAX( ira(i), ira(j) )
[1519]	951	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	952
[828]	953	DO kk = 2, 11
	954	IF ( rq <= rat(kk) ) THEN
	955	iq = kk
	956	EXIT
	957	ENDIF
	958	ENDDO
[790]	959
[1822]	960	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	961
[828]	962	IF ( ir < 8 ) THEN
	963	IF ( ir >= 2 ) THEN
[1822]	964	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	965	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	966	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	967	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	968	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	969	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	970	pp * qq * ecoll_100(ir,iq)
	971	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	972	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	973	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	974	pp * qq * ecoll_400(ir,iq)
[828]	975	ELSE
	976	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	977	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	978	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	979	ENDIF
	980	ELSE
	981	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	982	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	983	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	984	ENDIF
	985	!
[1822]	986	!-- Linear interpolation of turbulent enhancement factor
[1359]	987	IF ( epsilon <= 0.01_wp ) THEN
	988	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	989	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	990	ELSEIF ( epsilon <= 0.06_wp ) THEN
	991	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	992	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	993	ELSE
[1359]	994	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	995	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	996	ENDIF
[790]	997
[1359]	998	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	999
[828]	1000	ecf(i,j) = ecf(j,i)
[790]	1001
[828]	1002	ENDDO
	1003	ENDDO
[790]	1004
[828]	1005	END SUBROUTINE turb_enhance_eff
[790]	1006
[825]	1007	END MODULE lpm_collision_kernels_mod

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